Properties

Label 1386.2.k.p.793.1
Level $1386$
Weight $2$
Character 1386.793
Analytic conductor $11.067$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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: \(0\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 793.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1386.793
Dual form 1386.2.k.p.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} +(-0.500000 - 0.866025i) q^{11} +2.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-1.00000 + 1.73205i) q^{19} -3.00000 q^{20} -1.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(1.00000 - 1.73205i) q^{26} +(-2.00000 + 1.73205i) q^{28} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +(-7.50000 - 2.59808i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-1.50000 + 2.59808i) q^{40} +9.00000 q^{41} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(1.50000 - 2.59808i) q^{47} +(-6.50000 + 2.59808i) q^{49} -4.00000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} -3.00000 q^{55} +(0.500000 + 2.59808i) q^{56} +(3.00000 + 5.19615i) q^{59} +(-2.50000 + 4.33013i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(-5.50000 - 9.52628i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(-6.00000 + 5.19615i) q^{70} +(-1.00000 - 1.73205i) q^{73} +(4.00000 + 6.92820i) q^{74} +2.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} +(6.50000 - 11.2583i) q^{79} +(1.50000 + 2.59808i) q^{80} +(4.50000 - 7.79423i) q^{82} -9.00000 q^{83} -9.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(0.500000 + 0.866025i) q^{88} +(6.00000 - 10.3923i) q^{89} +(-1.00000 - 5.19615i) q^{91} -3.00000 q^{92} +(-1.50000 - 2.59808i) q^{94} +(3.00000 + 5.19615i) q^{95} +5.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} + 3q^{5} - q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} + 3q^{5} - q^{7} - 2q^{8} - 3q^{10} - q^{11} + 4q^{13} - 5q^{14} - q^{16} - 3q^{17} - 2q^{19} - 6q^{20} - 2q^{22} + 3q^{23} - 4q^{25} + 2q^{26} - 4q^{28} - 2q^{31} + q^{32} - 6q^{34} - 15q^{35} - 8q^{37} + 2q^{38} - 3q^{40} + 18q^{41} - 8q^{43} - q^{44} - 3q^{46} + 3q^{47} - 13q^{49} - 8q^{50} - 2q^{52} + 6q^{53} - 6q^{55} + q^{56} + 6q^{59} - 5q^{61} - 4q^{62} + 2q^{64} + 6q^{65} - 11q^{67} - 3q^{68} - 12q^{70} - 2q^{73} + 8q^{74} + 4q^{76} - 4q^{77} + 13q^{79} + 3q^{80} + 9q^{82} - 18q^{83} - 18q^{85} - 4q^{86} + q^{88} + 12q^{89} - 2q^{91} - 6q^{92} - 3q^{94} + 6q^{95} + 10q^{97} - 2q^{98} + O(q^{100}) \)

Character values

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

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

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
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.50000 2.59808i 0.670820 1.16190i −0.306851 0.951757i \(-0.599275\pi\)
0.977672 0.210138i \(-0.0673912\pi\)
\(6\) 0 0
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −2.50000 0.866025i −0.668153 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) −3.00000 −0.670820
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) 0 0
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) −7.50000 2.59808i −1.26773 0.439155i
\(36\) 0 0
\(37\) −4.00000 + 6.92820i −0.657596 + 1.13899i 0.323640 + 0.946180i \(0.395093\pi\)
−0.981236 + 0.192809i \(0.938240\pi\)
\(38\) 1.00000 + 1.73205i 0.162221 + 0.280976i
\(39\) 0 0
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −1.50000 2.59808i −0.221163 0.383065i
\(47\) 1.50000 2.59808i 0.218797 0.378968i −0.735643 0.677369i \(-0.763120\pi\)
0.954441 + 0.298401i \(0.0964533\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) −4.00000 −0.565685
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 0.500000 + 2.59808i 0.0668153 + 0.347183i
\(57\) 0 0
\(58\) 0 0
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) 0 0
\(61\) −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i \(-0.937047\pi\)
0.660415 + 0.750901i \(0.270381\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.00000 5.19615i 0.372104 0.644503i
\(66\) 0 0
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) −1.50000 + 2.59808i −0.181902 + 0.315063i
\(69\) 0 0
\(70\) −6.00000 + 5.19615i −0.717137 + 0.621059i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) 4.00000 + 6.92820i 0.464991 + 0.805387i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) −2.00000 + 1.73205i −0.227921 + 0.197386i
\(78\) 0 0
\(79\) 6.50000 11.2583i 0.731307 1.26666i −0.225018 0.974355i \(-0.572244\pi\)
0.956325 0.292306i \(-0.0944227\pi\)
\(80\) 1.50000 + 2.59808i 0.167705 + 0.290474i
\(81\) 0 0
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) −9.00000 −0.987878 −0.493939 0.869496i \(-0.664443\pi\)
−0.493939 + 0.869496i \(0.664443\pi\)
\(84\) 0 0
\(85\) −9.00000 −0.976187
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 6.00000 10.3923i 0.635999 1.10158i −0.350304 0.936636i \(-0.613922\pi\)
0.986303 0.164946i \(-0.0527450\pi\)
\(90\) 0 0
\(91\) −1.00000 5.19615i −0.104828 0.544705i
\(92\) −3.00000 −0.312772
\(93\) 0 0
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) 3.00000 + 5.19615i 0.307794 + 0.533114i
\(96\) 0 0
\(97\) 5.00000 0.507673 0.253837 0.967247i \(-0.418307\pi\)
0.253837 + 0.967247i \(0.418307\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) 0 0
\(103\) −10.0000 + 17.3205i −0.985329 + 1.70664i −0.344865 + 0.938652i \(0.612075\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 1.50000 2.59808i 0.145010 0.251166i −0.784366 0.620298i \(-0.787012\pi\)
0.929377 + 0.369132i \(0.120345\pi\)
\(108\) 0 0
\(109\) 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i \(-0.151417\pi\)
−0.841086 + 0.540901i \(0.818083\pi\)
\(110\) −1.50000 + 2.59808i −0.143019 + 0.247717i
\(111\) 0 0
\(112\) 2.50000 + 0.866025i 0.236228 + 0.0818317i
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 0 0
\(115\) −4.50000 7.79423i −0.419627 0.726816i
\(116\) 0 0
\(117\) 0 0
\(118\) 6.00000 0.552345
\(119\) −6.00000 + 5.19615i −0.550019 + 0.476331i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 2.50000 + 4.33013i 0.226339 + 0.392031i
\(123\) 0 0
\(124\) −1.00000 + 1.73205i −0.0898027 + 0.155543i
\(125\) 3.00000 0.268328
\(126\) 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
\(130\) −3.00000 5.19615i −0.263117 0.455733i
\(131\) 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) 0 0
\(133\) 5.00000 + 1.73205i 0.433555 + 0.150188i
\(134\) −11.0000 −0.950255
\(135\) 0 0
\(136\) 1.50000 + 2.59808i 0.128624 + 0.222783i
\(137\) 3.00000 + 5.19615i 0.256307 + 0.443937i 0.965250 0.261329i \(-0.0841608\pi\)
−0.708942 + 0.705266i \(0.750827\pi\)
\(138\) 0 0
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 1.50000 + 7.79423i 0.126773 + 0.658733i
\(141\) 0 0
\(142\) 0 0
\(143\) −1.00000 1.73205i −0.0836242 0.144841i
\(144\) 0 0
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) 6.00000 10.3923i 0.491539 0.851371i −0.508413 0.861113i \(-0.669768\pi\)
0.999953 + 0.00974235i \(0.00310113\pi\)
\(150\) 0 0
\(151\) −2.50000 4.33013i −0.203447 0.352381i 0.746190 0.665733i \(-0.231881\pi\)
−0.949637 + 0.313353i \(0.898548\pi\)
\(152\) 1.00000 1.73205i 0.0811107 0.140488i
\(153\) 0 0
\(154\) 0.500000 + 2.59808i 0.0402911 + 0.209359i
\(155\) −6.00000 −0.481932
\(156\) 0 0
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) −6.50000 11.2583i −0.517112 0.895665i
\(159\) 0 0
\(160\) 3.00000 0.237171
\(161\) −7.50000 2.59808i −0.591083 0.204757i
\(162\) 0 0
\(163\) 9.50000 16.4545i 0.744097 1.28881i −0.206518 0.978443i \(-0.566213\pi\)
0.950615 0.310372i \(-0.100454\pi\)
\(164\) −4.50000 7.79423i −0.351391 0.608627i
\(165\) 0 0
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −4.50000 + 7.79423i −0.345134 + 0.597790i
\(171\) 0 0
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 0 0
\(175\) −8.00000 + 6.92820i −0.604743 + 0.523723i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −6.00000 10.3923i −0.449719 0.778936i
\(179\) 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i \(-0.0946798\pi\)
−0.731858 + 0.681457i \(0.761346\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) −5.00000 1.73205i −0.370625 0.128388i
\(183\) 0 0
\(184\) −1.50000 + 2.59808i −0.110581 + 0.191533i
\(185\) 12.0000 + 20.7846i 0.882258 + 1.52811i
\(186\) 0 0
\(187\) −1.50000 + 2.59808i −0.109691 + 0.189990i
\(188\) −3.00000 −0.218797
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 0 0
\(193\) 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i \(0.0286631\pi\)
−0.420096 + 0.907480i \(0.638004\pi\)
\(194\) 2.50000 4.33013i 0.179490 0.310885i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) 2.00000 + 3.46410i 0.141421 + 0.244949i
\(201\) 0 0
\(202\) −12.0000 −0.844317
\(203\) 0 0
\(204\) 0 0
\(205\) 13.5000 23.3827i 0.942881 1.63312i
\(206\) 10.0000 + 17.3205i 0.696733 + 1.20678i
\(207\) 0 0
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) 0 0
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) −6.00000 + 10.3923i −0.409197 + 0.708749i
\(216\) 0 0
\(217\) −4.00000 + 3.46410i −0.271538 + 0.235159i
\(218\) 1.00000 0.0677285
\(219\) 0 0
\(220\) 1.50000 + 2.59808i 0.101130 + 0.175162i
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 0 0
\(223\) 26.0000 1.74109 0.870544 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) 2.00000 1.73205i 0.133631 0.115728i
\(225\) 0 0
\(226\) 9.00000 15.5885i 0.598671 1.03693i
\(227\) 7.50000 + 12.9904i 0.497792 + 0.862202i 0.999997 0.00254715i \(-0.000810783\pi\)
−0.502204 + 0.864749i \(0.667477\pi\)
\(228\) 0 0
\(229\) −10.0000 + 17.3205i −0.660819 + 1.14457i 0.319582 + 0.947559i \(0.396457\pi\)
−0.980401 + 0.197013i \(0.936876\pi\)
\(230\) −9.00000 −0.593442
\(231\) 0 0
\(232\) 0 0
\(233\) 10.5000 18.1865i 0.687878 1.19144i −0.284645 0.958633i \(-0.591876\pi\)
0.972523 0.232806i \(-0.0747909\pi\)
\(234\) 0 0
\(235\) −4.50000 7.79423i −0.293548 0.508439i
\(236\) 3.00000 5.19615i 0.195283 0.338241i
\(237\) 0 0
\(238\) 1.50000 + 7.79423i 0.0972306 + 0.505225i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 2.00000 + 3.46410i 0.128831 + 0.223142i 0.923224 0.384262i \(-0.125544\pi\)
−0.794393 + 0.607404i \(0.792211\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) 5.00000 0.320092
\(245\) −3.00000 + 20.7846i −0.191663 + 1.32788i
\(246\) 0 0
\(247\) −2.00000 + 3.46410i −0.127257 + 0.220416i
\(248\) 1.00000 + 1.73205i 0.0635001 + 0.109985i
\(249\) 0 0
\(250\) 1.50000 2.59808i 0.0948683 0.164317i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −3.00000 −0.188608
\(254\) −9.50000 + 16.4545i −0.596083 + 1.03245i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −12.0000 + 20.7846i −0.748539 + 1.29651i 0.199983 + 0.979799i \(0.435911\pi\)
−0.948523 + 0.316709i \(0.897422\pi\)
\(258\) 0 0
\(259\) 20.0000 + 6.92820i 1.24274 + 0.430498i
\(260\) −6.00000 −0.372104
\(261\) 0 0
\(262\) −6.00000 10.3923i −0.370681 0.642039i
\(263\) −15.0000 25.9808i −0.924940 1.60204i −0.791658 0.610964i \(-0.790782\pi\)
−0.133281 0.991078i \(-0.542551\pi\)
\(264\) 0 0
\(265\) 18.0000 1.10573
\(266\) 4.00000 3.46410i 0.245256 0.212398i
\(267\) 0 0
\(268\) −5.50000 + 9.52628i −0.335966 + 0.581910i
\(269\) 7.50000 + 12.9904i 0.457283 + 0.792038i 0.998816 0.0486418i \(-0.0154893\pi\)
−0.541533 + 0.840679i \(0.682156\pi\)
\(270\) 0 0
\(271\) −4.00000 + 6.92820i −0.242983 + 0.420858i −0.961563 0.274586i \(-0.911459\pi\)
0.718580 + 0.695444i \(0.244792\pi\)
\(272\) 3.00000 0.181902
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) −2.00000 + 3.46410i −0.120605 + 0.208893i
\(276\) 0 0
\(277\) −7.00000 12.1244i −0.420589 0.728482i 0.575408 0.817867i \(-0.304843\pi\)
−0.995997 + 0.0893846i \(0.971510\pi\)
\(278\) 1.00000 1.73205i 0.0599760 0.103882i
\(279\) 0 0
\(280\) 7.50000 + 2.59808i 0.448211 + 0.155265i
\(281\) 27.0000 1.61068 0.805342 0.592810i \(-0.201981\pi\)
0.805342 + 0.592810i \(0.201981\pi\)
\(282\) 0 0
\(283\) 8.00000 + 13.8564i 0.475551 + 0.823678i 0.999608 0.0280052i \(-0.00891551\pi\)
−0.524057 + 0.851683i \(0.675582\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −2.00000 −0.118262
\(287\) −4.50000 23.3827i −0.265627 1.38024i
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 0 0
\(292\) −1.00000 + 1.73205i −0.0585206 + 0.101361i
\(293\) 18.0000 1.05157 0.525786 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 0 0
\(295\) 18.0000 1.04800
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) 0 0
\(298\) −6.00000 10.3923i −0.347571 0.602010i
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0 0
\(301\) 2.00000 + 10.3923i 0.115278 + 0.599002i
\(302\) −5.00000 −0.287718
\(303\) 0 0
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) 7.50000 + 12.9904i 0.429449 + 0.743827i
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 2.50000 + 0.866025i 0.142451 + 0.0493464i
\(309\) 0 0
\(310\) −3.00000 + 5.19615i −0.170389 + 0.295122i
\(311\) −1.50000 2.59808i −0.0850572 0.147323i 0.820358 0.571850i \(-0.193774\pi\)
−0.905416 + 0.424526i \(0.860441\pi\)
\(312\) 0 0
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −13.0000 −0.731307
\(317\) −7.50000 + 12.9904i −0.421242 + 0.729612i −0.996061 0.0886679i \(-0.971739\pi\)
0.574819 + 0.818280i \(0.305072\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.50000 2.59808i 0.0838525 0.145237i
\(321\) 0 0
\(322\) −6.00000 + 5.19615i −0.334367 + 0.289570i
\(323\) 6.00000 0.333849
\(324\) 0 0
\(325\) −4.00000 6.92820i −0.221880 0.384308i
\(326\) −9.50000 16.4545i −0.526156 0.911330i
\(327\) 0 0
\(328\) −9.00000 −0.496942
\(329\) −7.50000 2.59808i −0.413488 0.143237i
\(330\) 0 0
\(331\) 9.50000 16.4545i 0.522167 0.904420i −0.477500 0.878632i \(-0.658457\pi\)
0.999667 0.0257885i \(-0.00820965\pi\)
\(332\) 4.50000 + 7.79423i 0.246970 + 0.427764i
\(333\) 0 0
\(334\) 0 0
\(335\) −33.0000 −1.80298
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −4.50000 + 7.79423i −0.244768 + 0.423950i
\(339\) 0 0
\(340\) 4.50000 + 7.79423i 0.244047 + 0.422701i
\(341\) −1.00000 + 1.73205i −0.0541530 + 0.0937958i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 3.00000 + 5.19615i 0.161281 + 0.279347i
\(347\) −10.5000 18.1865i −0.563670 0.976304i −0.997172 0.0751519i \(-0.976056\pi\)
0.433503 0.901152i \(-0.357278\pi\)
\(348\) 0 0
\(349\) 23.0000 1.23116 0.615581 0.788074i \(-0.288921\pi\)
0.615581 + 0.788074i \(0.288921\pi\)
\(350\) 2.00000 + 10.3923i 0.106904 + 0.555492i
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) −15.0000 25.9808i −0.798369 1.38282i −0.920677 0.390324i \(-0.872363\pi\)
0.122308 0.992492i \(-0.460970\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −12.0000 −0.635999
\(357\) 0 0
\(358\) 6.00000 0.317110
\(359\) 6.00000 10.3923i 0.316668 0.548485i −0.663123 0.748511i \(-0.730769\pi\)
0.979791 + 0.200026i \(0.0641026\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 10.0000 17.3205i 0.525588 0.910346i
\(363\) 0 0
\(364\) −4.00000 + 3.46410i −0.209657 + 0.181568i
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) 5.00000 + 8.66025i 0.260998 + 0.452062i 0.966507 0.256639i \(-0.0826151\pi\)
−0.705509 + 0.708700i \(0.749282\pi\)
\(368\) 1.50000 + 2.59808i 0.0781929 + 0.135434i
\(369\) 0 0
\(370\) 24.0000 1.24770
\(371\) 12.0000 10.3923i 0.623009 0.539542i
\(372\) 0 0
\(373\) −11.5000 + 19.9186i −0.595447 + 1.03135i 0.398036 + 0.917370i \(0.369692\pi\)
−0.993484 + 0.113975i \(0.963641\pi\)
\(374\) 1.50000 + 2.59808i 0.0775632 + 0.134343i
\(375\) 0 0
\(376\) −1.50000 + 2.59808i −0.0773566 + 0.133986i
\(377\) 0 0
\(378\) 0 0
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 3.00000 5.19615i 0.153897 0.266557i
\(381\) 0 0
\(382\) −6.00000 10.3923i −0.306987 0.531717i
\(383\) −12.0000 + 20.7846i −0.613171 + 1.06204i 0.377531 + 0.925997i \(0.376773\pi\)
−0.990702 + 0.136047i \(0.956560\pi\)
\(384\) 0 0
\(385\) 1.50000 + 7.79423i 0.0764471 + 0.397231i
\(386\) 16.0000 0.814379
\(387\) 0 0
\(388\) −2.50000 4.33013i −0.126918 0.219829i
\(389\) −10.5000 18.1865i −0.532371 0.922094i −0.999286 0.0377914i \(-0.987968\pi\)
0.466915 0.884302i \(-0.345366\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 6.50000 2.59808i 0.328300 0.131223i
\(393\) 0 0
\(394\) 0 0
\(395\) −19.5000 33.7750i −0.981151 1.69940i
\(396\) 0 0
\(397\) 14.0000 24.2487i 0.702640 1.21701i −0.264897 0.964277i \(-0.585338\pi\)
0.967537 0.252731i \(-0.0813288\pi\)
\(398\) 10.0000 0.501255
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i \(-0.736472\pi\)
0.976050 + 0.217545i \(0.0698049\pi\)
\(402\) 0 0
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) −6.00000 + 10.3923i −0.298511 + 0.517036i
\(405\) 0 0
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) −1.00000 1.73205i −0.0494468 0.0856444i 0.840243 0.542211i \(-0.182412\pi\)
−0.889689 + 0.456566i \(0.849079\pi\)
\(410\) −13.5000 23.3827i −0.666717 1.15479i
\(411\) 0 0
\(412\) 20.0000 0.985329
\(413\) 12.0000 10.3923i 0.590481 0.511372i
\(414\) 0 0
\(415\) −13.5000 + 23.3827i −0.662689 + 1.14781i
\(416\) 1.00000 + 1.73205i 0.0490290 + 0.0849208i
\(417\) 0 0
\(418\) 1.00000 1.73205i 0.0489116 0.0847174i
\(419\) −18.0000 −0.879358 −0.439679 0.898155i \(-0.644908\pi\)
−0.439679 + 0.898155i \(0.644908\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) 10.0000 17.3205i 0.486792 0.843149i
\(423\) 0 0
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) −6.00000 + 10.3923i −0.291043 + 0.504101i
\(426\) 0 0
\(427\) 12.5000 + 4.33013i 0.604917 + 0.209550i
\(428\) −3.00000 −0.145010
\(429\) 0 0
\(430\) 6.00000 + 10.3923i 0.289346 + 0.501161i
\(431\) −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i \(-0.909648\pi\)
0.237460 0.971397i \(-0.423685\pi\)
\(432\) 0 0
\(433\) 35.0000 1.68199 0.840996 0.541041i \(-0.181970\pi\)
0.840996 + 0.541041i \(0.181970\pi\)
\(434\) 1.00000 + 5.19615i 0.0480015 + 0.249423i
\(435\) 0 0
\(436\) 0.500000 0.866025i 0.0239457 0.0414751i
\(437\) 3.00000 + 5.19615i 0.143509 + 0.248566i
\(438\) 0 0
\(439\) −17.5000 + 30.3109i −0.835229 + 1.44666i 0.0586141 + 0.998281i \(0.481332\pi\)
−0.893843 + 0.448379i \(0.852001\pi\)
\(440\) 3.00000 0.143019
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) −12.0000 + 20.7846i −0.570137 + 0.987507i 0.426414 + 0.904528i \(0.359777\pi\)
−0.996551 + 0.0829786i \(0.973557\pi\)
\(444\) 0 0
\(445\) −18.0000 31.1769i −0.853282 1.47793i
\(446\) 13.0000 22.5167i 0.615568 1.06619i
\(447\) 0 0
\(448\) −0.500000 2.59808i −0.0236228 0.122748i
\(449\) 36.0000 1.69895 0.849473 0.527633i \(-0.176920\pi\)
0.849473 + 0.527633i \(0.176920\pi\)
\(450\) 0 0
\(451\) −4.50000 7.79423i −0.211897 0.367016i
\(452\) −9.00000 15.5885i −0.423324 0.733219i
\(453\) 0 0
\(454\) 15.0000 0.703985
\(455\) −15.0000 5.19615i −0.703211 0.243599i
\(456\) 0 0
\(457\) 20.0000 34.6410i 0.935561 1.62044i 0.161929 0.986802i \(-0.448228\pi\)
0.773631 0.633636i \(-0.218438\pi\)
\(458\) 10.0000 + 17.3205i 0.467269 + 0.809334i
\(459\) 0 0
\(460\) −4.50000 + 7.79423i −0.209814 + 0.363408i
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −10.5000 18.1865i −0.486403 0.842475i
\(467\) −21.0000 + 36.3731i −0.971764 + 1.68314i −0.281539 + 0.959550i \(0.590845\pi\)
−0.690225 + 0.723595i \(0.742488\pi\)
\(468\) 0 0
\(469\) −22.0000 + 19.0526i −1.01587 + 0.879765i
\(470\) −9.00000 −0.415139
\(471\) 0 0
\(472\) −3.00000 5.19615i −0.138086 0.239172i
\(473\) 2.00000 + 3.46410i 0.0919601 + 0.159280i
\(474\) 0 0
\(475\) 8.00000 0.367065
\(476\) 7.50000 + 2.59808i 0.343762 + 0.119083i
\(477\) 0 0
\(478\) 0 0
\(479\) −6.00000 10.3923i −0.274147 0.474837i 0.695773 0.718262i \(-0.255062\pi\)
−0.969920 + 0.243426i \(0.921729\pi\)
\(480\) 0 0
\(481\) −8.00000 + 13.8564i −0.364769 + 0.631798i
\(482\) 4.00000 0.182195
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 7.50000 12.9904i 0.340557 0.589863i
\(486\) 0 0
\(487\) −19.0000 32.9090i −0.860972 1.49125i −0.870992 0.491298i \(-0.836523\pi\)
0.0100195 0.999950i \(-0.496811\pi\)
\(488\) 2.50000 4.33013i 0.113170 0.196016i
\(489\) 0 0
\(490\) 16.5000 + 12.9904i 0.745394 + 0.586846i
\(491\) −9.00000 −0.406164 −0.203082 0.979162i \(-0.565096\pi\)
−0.203082 + 0.979162i \(0.565096\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 2.00000 + 3.46410i 0.0899843 + 0.155857i
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) 0 0
\(499\) −10.0000 + 17.3205i −0.447661 + 0.775372i −0.998233 0.0594153i \(-0.981076\pi\)
0.550572 + 0.834788i \(0.314410\pi\)
\(500\) −1.50000 2.59808i −0.0670820 0.116190i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) −36.0000 −1.60198
\(506\) −1.50000 + 2.59808i −0.0666831 + 0.115499i
\(507\) 0 0
\(508\) 9.50000 + 16.4545i 0.421494 + 0.730050i
\(509\) −3.00000 + 5.19615i −0.132973 + 0.230315i −0.924821 0.380402i \(-0.875786\pi\)
0.791849 + 0.610718i \(0.209119\pi\)
\(510\) 0 0
\(511\) −4.00000 + 3.46410i −0.176950 + 0.153243i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 12.0000 + 20.7846i 0.529297 + 0.916770i
\(515\) 30.0000 + 51.9615i 1.32196 + 2.28970i
\(516\) 0 0
\(517\) −3.00000 −0.131940
\(518\) 16.0000 13.8564i 0.703000 0.608816i
\(519\) 0 0
\(520\) −3.00000 + 5.19615i −0.131559 + 0.227866i
\(521\) 21.0000 + 36.3731i 0.920027 + 1.59353i 0.799370 + 0.600839i \(0.205167\pi\)
0.120656 + 0.992694i \(0.461500\pi\)
\(522\) 0 0
\(523\) 5.00000 8.66025i 0.218635 0.378686i −0.735756 0.677247i \(-0.763173\pi\)
0.954391 + 0.298560i \(0.0965063\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) −30.0000 −1.30806
\(527\) −3.00000 + 5.19615i −0.130682 + 0.226348i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 9.00000 15.5885i 0.390935 0.677119i
\(531\) 0 0
\(532\) −1.00000 5.19615i −0.0433555 0.225282i
\(533\) 18.0000 0.779667
\(534\) 0 0
\(535\) −4.50000 7.79423i −0.194552 0.336974i
\(536\) 5.50000 + 9.52628i 0.237564 + 0.411473i
\(537\) 0 0
\(538\) 15.0000 0.646696
\(539\) 5.50000 + 4.33013i 0.236902 + 0.186512i
\(540\) 0 0
\(541\) −5.50000 + 9.52628i −0.236463 + 0.409567i −0.959697 0.281037i \(-0.909322\pi\)
0.723234 + 0.690604i \(0.242655\pi\)
\(542\) 4.00000 + 6.92820i 0.171815 + 0.297592i
\(543\) 0 0
\(544\) 1.50000 2.59808i 0.0643120 0.111392i
\(545\) 3.00000 0.128506
\(546\) 0 0
\(547\) 14.0000 0.598597 0.299298 0.954160i \(-0.403247\pi\)
0.299298 + 0.954160i \(0.403247\pi\)
\(548\) 3.00000 5.19615i 0.128154 0.221969i
\(549\) 0 0
\(550\) 2.00000 + 3.46410i 0.0852803 + 0.147710i
\(551\) 0 0
\(552\) 0 0
\(553\) −32.5000 11.2583i −1.38204 0.478753i
\(554\) −14.0000 −0.594803
\(555\) 0 0
\(556\) −1.00000 1.73205i −0.0424094 0.0734553i
\(557\) 12.0000 + 20.7846i 0.508456 + 0.880672i 0.999952 + 0.00979220i \(0.00311700\pi\)
−0.491496 + 0.870880i \(0.663550\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 6.00000 5.19615i 0.253546 0.219578i
\(561\) 0 0
\(562\) 13.5000 23.3827i 0.569463 0.986339i
\(563\) −6.00000 10.3923i −0.252870 0.437983i 0.711445 0.702742i \(-0.248041\pi\)
−0.964315 + 0.264758i \(0.914708\pi\)
\(564\) 0 0
\(565\) 27.0000 46.7654i 1.13590 1.96743i
\(566\) 16.0000 0.672530
\(567\) 0 0
\(568\) 0 0
\(569\) −21.0000 + 36.3731i −0.880366 + 1.52484i −0.0294311 + 0.999567i \(0.509370\pi\)
−0.850935 + 0.525271i \(0.823964\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) −1.00000 + 1.73205i −0.0418121 + 0.0724207i
\(573\) 0 0
\(574\) −22.5000 7.79423i −0.939132 0.325325i
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) −8.50000 14.7224i −0.353860 0.612903i 0.633062 0.774101i \(-0.281798\pi\)
−0.986922 + 0.161198i \(0.948464\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) 0 0
\(580\) 0 0
\(581\) 4.50000 + 23.3827i 0.186691 + 0.970077i
\(582\) 0 0
\(583\) 3.00000 5.19615i 0.124247 0.215203i
\(584\) 1.00000 + 1.73205i 0.0413803 + 0.0716728i
\(585\) 0 0
\(586\) 9.00000 15.5885i 0.371787 0.643953i
\(587\) −18.0000 −0.742940 −0.371470 0.928445i \(-0.621146\pi\)
−0.371470 + 0.928445i \(0.621146\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) 9.00000 15.5885i 0.370524 0.641767i
\(591\) 0 0
\(592\) −4.00000 6.92820i −0.164399 0.284747i
\(593\) −3.00000 + 5.19615i −0.123195 + 0.213380i −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) 0 0
\(595\) 4.50000 + 23.3827i 0.184482 + 0.958597i
\(596\) −12.0000 −0.491539
\(597\) 0 0
\(598\) −3.00000 5.19615i −0.122679 0.212486i
\(599\) 7.50000 + 12.9904i 0.306442 + 0.530773i 0.977581 0.210558i \(-0.0675282\pi\)
−0.671140 + 0.741331i \(0.734195\pi\)
\(600\) 0 0
\(601\) −40.0000 −1.63163 −0.815817 0.578310i \(-0.803712\pi\)
−0.815817 + 0.578310i \(0.803712\pi\)
\(602\) 10.0000 + 3.46410i 0.407570 + 0.141186i
\(603\) 0 0
\(604\) −2.50000 + 4.33013i −0.101724 + 0.176190i
\(605\) 1.50000 + 2.59808i 0.0609837 + 0.105627i
\(606\) 0 0
\(607\) −20.5000 + 35.5070i −0.832069 + 1.44119i 0.0643251 + 0.997929i \(0.479511\pi\)
−0.896394 + 0.443257i \(0.853823\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 0 0
\(610\) 15.0000 0.607332
\(611\) 3.00000 5.19615i 0.121367 0.210214i
\(612\) 0 0
\(613\) −8.50000 14.7224i −0.343312 0.594633i 0.641734 0.766927i \(-0.278215\pi\)
−0.985046 + 0.172294i \(0.944882\pi\)
\(614\) 4.00000 6.92820i 0.161427 0.279600i
\(615\) 0 0
\(616\) 2.00000 1.73205i 0.0805823 0.0697863i
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 15.5000 + 26.8468i 0.622998 + 1.07906i 0.988924 + 0.148420i \(0.0474187\pi\)
−0.365927 + 0.930644i \(0.619248\pi\)
\(620\) 3.00000 + 5.19615i 0.120483 + 0.208683i
\(621\) 0 0
\(622\) −3.00000 −0.120289
\(623\) −30.0000 10.3923i −1.20192 0.416359i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) −5.00000 8.66025i −0.199840 0.346133i
\(627\) 0 0
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) 24.0000 0.956943
\(630\) 0 0
\(631\) −10.0000 −0.398094 −0.199047 0.979990i \(-0.563785\pi\)
−0.199047 + 0.979990i \(0.563785\pi\)
\(632\) −6.50000 + 11.2583i −0.258556 + 0.447832i
\(633\) 0 0
\(634\) 7.50000 + 12.9904i 0.297863 + 0.515914i
\(635\) −28.5000 + 49.3634i −1.13099 + 1.95893i
\(636\) 0 0
\(637\) −13.0000 + 5.19615i −0.515079 + 0.205879i
\(638\) 0 0
\(639\) 0 0
\(640\) −1.50000 2.59808i −0.0592927 0.102698i
\(641\) −6.00000 10.3923i −0.236986 0.410471i 0.722862 0.690992i \(-0.242826\pi\)
−0.959848 + 0.280521i \(0.909493\pi\)
\(642\) 0 0
\(643\) 20.0000 0.788723 0.394362 0.918955i \(-0.370966\pi\)
0.394362 + 0.918955i \(0.370966\pi\)
\(644\) 1.50000 + 7.79423i 0.0591083 + 0.307136i
\(645\) 0 0
\(646\) 3.00000 5.19615i 0.118033 0.204440i
\(647\) 7.50000 + 12.9904i 0.294855 + 0.510705i 0.974951 0.222419i \(-0.0713952\pi\)
−0.680096 + 0.733123i \(0.738062\pi\)
\(648\) 0 0
\(649\) 3.00000 5.19615i 0.117760 0.203967i
\(650\) −8.00000 −0.313786
\(651\) 0 0
\(652\) −19.0000 −0.744097
\(653\) −7.50000 + 12.9904i −0.293498 + 0.508353i −0.974634 0.223803i \(-0.928153\pi\)
0.681137 + 0.732156i \(0.261486\pi\)
\(654\) 0 0
\(655\) −18.0000 31.1769i −0.703318 1.21818i
\(656\) −4.50000 + 7.79423i −0.175695 + 0.304314i
\(657\) 0 0
\(658\) −6.00000 + 5.19615i −0.233904 + 0.202567i
\(659\) 45.0000 1.75295 0.876476 0.481446i \(-0.159888\pi\)
0.876476 + 0.481446i \(0.159888\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) −9.50000 16.4545i −0.369228 0.639522i
\(663\) 0 0
\(664\) 9.00000 0.349268
\(665\) 12.0000 10.3923i 0.465340 0.402996i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) −16.5000 + 28.5788i −0.637451 + 1.10410i
\(671\) 5.00000 0.193023
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) −11.0000 + 19.0526i −0.423704 + 0.733877i
\(675\) 0 0
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −3.00000 + 5.19615i −0.115299 + 0.199704i −0.917899 0.396813i \(-0.870116\pi\)
0.802600 + 0.596518i \(0.203449\pi\)
\(678\) 0 0
\(679\) −2.50000 12.9904i −0.0959412 0.498525i
\(680\) 9.00000 0.345134
\(681\) 0 0
\(682\) 1.00000 + 1.73205i 0.0382920 + 0.0663237i
\(683\) 12.0000 + 20.7846i 0.459167 + 0.795301i 0.998917 0.0465244i \(-0.0148145\pi\)
−0.539750 + 0.841825i \(0.681481\pi\)
\(684\) 0 0
\(685\) 18.0000 0.687745
\(686\) 18.5000 0.866025i 0.706333 0.0330650i
\(687\) 0 0
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) −11.5000 + 19.9186i −0.437481 + 0.757739i −0.997494 0.0707446i \(-0.977462\pi\)
0.560014 + 0.828483i \(0.310796\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −21.0000 −0.797149
\(695\) 3.00000 5.19615i 0.113796 0.197101i
\(696\) 0 0
\(697\) −13.5000 23.3827i −0.511349 0.885682i
\(698\) 11.5000 19.9186i 0.435281 0.753930i
\(699\) 0 0
\(700\) 10.0000 + 3.46410i 0.377964 + 0.130931i
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) −8.00000 13.8564i −0.301726 0.522604i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) −30.0000 −1.12906
\(707\) −24.0000 + 20.7846i −0.902613 + 0.781686i
\(708\) 0 0
\(709\) −7.00000 + 12.1244i −0.262891 + 0.455340i −0.967009 0.254743i \(-0.918009\pi\)
0.704118 + 0.710083i \(0.251342\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −6.00000 + 10.3923i −0.224860 + 0.389468i
\(713\) −6.00000 −0.224702
\(714\) 0 0
\(715\) −6.00000 −0.224387
\(716\) 3.00000 5.19615i 0.112115 0.194189i
\(717\) 0 0
\(718\) −6.00000 10.3923i −0.223918 0.387837i
\(719\) 19.5000 33.7750i 0.727227 1.25959i −0.230823 0.972996i \(-0.574142\pi\)
0.958051 0.286599i \(-0.0925247\pi\)
\(720\) 0 0
\(721\) 50.0000 + 17.3205i 1.86210 + 0.645049i
\(722\) 15.0000 0.558242
\(723\) 0 0
\(724\) −10.0000 17.3205i −0.371647 0.643712i
\(725\) 0 0
\(726\) 0 0
\(727\) −4.00000 −0.148352 −0.0741759 0.997245i \(-0.523633\pi\)
−0.0741759 + 0.997245i \(0.523633\pi\)
\(728\) 1.00000 + 5.19615i 0.0370625 + 0.192582i
\(729\) 0 0
\(730\) −3.00000 + 5.19615i −0.111035 + 0.192318i
\(731\) 6.00000 + 10.3923i 0.221918 + 0.384373i
\(732\) 0 0
\(733\) −23.5000 + 40.7032i −0.867992 + 1.50341i −0.00394730 + 0.999992i \(0.501256\pi\)
−0.864045 + 0.503415i \(0.832077\pi\)
\(734\) 10.0000 0.369107
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) −5.50000 + 9.52628i −0.202595 + 0.350905i
\(738\) 0 0
\(739\) 5.00000 + 8.66025i 0.183928 + 0.318573i 0.943215 0.332184i \(-0.107785\pi\)
−0.759287 + 0.650756i \(0.774452\pi\)
\(740\) 12.0000 20.7846i 0.441129 0.764057i
\(741\) 0 0
\(742\) −3.00000 15.5885i −0.110133 0.572270i
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 0 0
\(745\) −18.0000 31.1769i −0.659469 1.14223i
\(746\) 11.5000 + 19.9186i 0.421045 + 0.729271i
\(747\) 0 0
\(748\) 3.00000 0.109691
\(749\) −7.50000 2.59808i −0.274044 0.0949316i
\(750\) 0 0
\(751\) −25.0000 + 43.3013i −0.912263 + 1.58009i −0.101403 + 0.994845i \(0.532333\pi\)
−0.810860 + 0.585240i \(0.801000\pi\)
\(752\) 1.50000 + 2.59808i 0.0546994 + 0.0947421i
\(753\) 0 0
\(754\) 0 0
\(755\) −15.0000 −0.545906
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) −0.500000 + 0.866025i −0.0181608 + 0.0314555i
\(759\) 0 0
\(760\) −3.00000 5.19615i −0.108821 0.188484i
\(761\) −7.50000 + 12.9904i −0.271875 + 0.470901i −0.969342 0.245716i \(-0.920977\pi\)
0.697467 + 0.716617i \(0.254310\pi\)
\(762\) 0 0
\(763\) 2.00000 1.73205i 0.0724049 0.0627044i
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) 12.0000 + 20.7846i 0.433578 + 0.750978i
\(767\) 6.00000 + 10.3923i 0.216647 + 0.375244i
\(768\) 0 0
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 7.50000 + 2.59808i 0.270281 + 0.0936282i
\(771\) 0 0
\(772\) 8.00000 13.8564i 0.287926 0.498703i
\(773\) −10.5000 18.1865i −0.377659 0.654124i 0.613062 0.790034i \(-0.289937\pi\)
−0.990721 + 0.135910i \(0.956604\pi\)
\(774\) 0 0
\(775\) −4.00000 + 6.92820i −0.143684 + 0.248868i
\(776\) −5.00000 −0.179490
\(777\) 0 0
\(778\) −21.0000 −0.752886
\(779\) −9.00000 + 15.5885i −0.322458 + 0.558514i
\(780\) 0 0
\(781\) 0 0
\(782\) −4.50000 + 7.79423i −0.160920 + 0.278721i
\(783\) 0 0
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) 12.0000 0.428298
\(786\) 0 0
\(787\) −19.0000 32.9090i −0.677277 1.17308i −0.975798 0.218675i \(-0.929827\pi\)
0.298521 0.954403i \(-0.403507\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −39.0000 −1.38756
\(791\) −9.00000 46.7654i −0.320003 1.66279i