Properties

Label 1386.2.k.p.991.1
Level $1386$
Weight $2$
Character 1386.991
Analytic conductor $11.067$
Analytic rank $0$
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: \(0\)
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 991.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1386.991
Dual form 1386.2.k.p.793.1

$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

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

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
\(5\) 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 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 −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) −3.00000 −0.670820
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 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 −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) 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 −0.981236 0.192809i \(-0.938240\pi\)
0.323640 0.946180i \(-0.395093\pi\)
\(38\) 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 0.954441 0.298401i \(-0.0964533\pi\)
−0.735643 + 0.677369i \(0.763120\pi\)
\(48\) 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 −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 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 −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0 0
\(61\) −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i \(-0.270381\pi\)
−0.980507 + 0.196485i \(0.937047\pi\)
\(62\) −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 0.305424 + 0.952217i \(0.401202\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) −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 −0.918594 0.395203i \(-0.870674\pi\)
0.801553 + 0.597924i \(0.204008\pi\)
\(74\) 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 0.956325 + 0.292306i \(0.0944227\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 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 0.986303 + 0.164946i \(0.0527450\pi\)
−0.350304 + 0.936636i \(0.613922\pi\)
\(90\) 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 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 0 0
\(103\) −10.0000 17.3205i −0.985329 1.70664i −0.640464 0.767988i \(-0.721258\pi\)
−0.344865 0.938652i \(-0.612075\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) 0 0
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) −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 0.999602 + 0.0281993i \(0.00897729\pi\)
−0.475380 + 0.879781i \(0.657689\pi\)
\(132\) 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 −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 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 0.999953 0.00974235i \(-0.00310113\pi\)
−0.508413 + 0.861113i \(0.669768\pi\)
\(150\) 0 0
\(151\) −2.50000 + 4.33013i −0.203447 + 0.352381i −0.949637 0.313353i \(-0.898548\pi\)
0.746190 + 0.665733i \(0.231881\pi\)
\(152\) 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 −0.775113 0.631822i \(-0.782307\pi\)
0.934731 + 0.355357i \(0.115641\pi\)
\(158\) −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 0.950615 + 0.310372i \(0.100454\pi\)
−0.206518 + 0.978443i \(0.566213\pi\)
\(164\) −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 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 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 −0.731858 0.681457i \(-0.761346\pi\)
0.956088 + 0.293079i \(0.0946798\pi\)
\(180\) 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 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 0 0
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) 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 −0.632581 0.774494i \(-0.718005\pi\)
0.987022 + 0.160585i \(0.0513380\pi\)
\(200\) 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 −0.502204 0.864749i \(-0.667477\pi\)
0.999997 + 0.00254715i \(0.000810783\pi\)
\(228\) 0 0
\(229\) −10.0000 17.3205i −0.660819 1.14457i −0.980401 0.197013i \(-0.936876\pi\)
0.319582 0.947559i \(-0.396457\pi\)
\(230\) −9.00000 −0.593442
\(231\) 0 0
\(232\) 0 0
\(233\) 10.5000 + 18.1865i 0.687878 + 1.19144i 0.972523 + 0.232806i \(0.0747909\pi\)
−0.284645 + 0.958633i \(0.591876\pi\)
\(234\) 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 −0.794393 0.607404i \(-0.792211\pi\)
0.923224 + 0.384262i \(0.125544\pi\)
\(242\) 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 −0.948523 0.316709i \(-0.897422\pi\)
0.199983 0.979799i \(-0.435911\pi\)
\(258\) 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 −0.133281 + 0.991078i \(0.542551\pi\)
−0.791658 + 0.610964i \(0.790782\pi\)
\(264\) 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 −0.541533 0.840679i \(-0.682156\pi\)
0.998816 + 0.0486418i \(0.0154893\pi\)
\(270\) 0 0
\(271\) −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) 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 −0.995997 0.0893846i \(-0.971510\pi\)
0.575408 + 0.817867i \(0.304843\pi\)
\(278\) 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 −0.524057 0.851683i \(-0.675582\pi\)
0.999608 + 0.0280052i \(0.00891551\pi\)
\(284\) 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 −0.905416 0.424526i \(-0.860441\pi\)
0.820358 + 0.571850i \(0.193774\pi\)
\(312\) 0 0
\(313\) 5.00000 + 8.66025i 0.282617 + 0.489506i 0.972028 0.234863i \(-0.0754642\pi\)
−0.689412 + 0.724370i \(0.742131\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −13.0000 −0.731307
\(317\) −7.50000 12.9904i −0.421242 0.729612i 0.574819 0.818280i \(-0.305072\pi\)
−0.996061 + 0.0886679i \(0.971739\pi\)
\(318\) 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 0.999667 + 0.0257885i \(0.00820965\pi\)
−0.477500 + 0.878632i \(0.658457\pi\)
\(332\) 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 0.433503 + 0.901152i \(0.357278\pi\)
−0.997172 + 0.0751519i \(0.976056\pi\)
\(348\) 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 0.122308 + 0.992492i \(0.460970\pi\)
−0.920677 + 0.390324i \(0.872363\pi\)
\(354\) 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 0.979791 0.200026i \(-0.0641026\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(360\) 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 −0.705509 0.708700i \(-0.749282\pi\)
0.966507 + 0.256639i \(0.0826151\pi\)
\(368\) 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 −0.993484 0.113975i \(-0.963641\pi\)
0.398036 0.917370i \(-0.369692\pi\)
\(374\) 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 −0.990702 0.136047i \(-0.956560\pi\)
0.377531 0.925997i \(-0.376773\pi\)
\(384\) 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 0.466915 + 0.884302i \(0.345366\pi\)
−0.999286 + 0.0377914i \(0.987968\pi\)
\(390\) 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 0.967537 + 0.252731i \(0.0813288\pi\)
−0.264897 + 0.964277i \(0.585338\pi\)
\(398\) 10.0000 0.501255
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i \(-0.0698049\pi\)
−0.676425 + 0.736512i \(0.736472\pi\)
\(402\) 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 −0.889689 0.456566i \(-0.849079\pi\)
0.840243 + 0.542211i \(0.182412\pi\)
\(410\) −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 0.237460 + 0.971397i \(0.423685\pi\)
−0.959985 + 0.280052i \(0.909648\pi\)
\(432\) 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 −0.893843 0.448379i \(-0.852001\pi\)
0.0586141 0.998281i \(-0.481332\pi\)
\(440\) 3.00000 0.143019
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i \(-0.973557\pi\)
0.426414 0.904528i \(-0.359777\pi\)
\(444\) 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 0.773631 + 0.633636i \(0.218438\pi\)
0.161929 + 0.986802i \(0.448228\pi\)
\(458\) 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 −0.690225 0.723595i \(-0.742488\pi\)
−0.281539 0.959550i \(-0.590845\pi\)
\(468\) 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 −0.969920 0.243426i \(-0.921729\pi\)
0.695773 + 0.718262i \(0.255062\pi\)
\(480\) 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 0.0100195 + 0.999950i \(0.496811\pi\)
−0.870992 + 0.491298i \(0.836523\pi\)
\(488\) 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 0.550572 0.834788i \(-0.314410\pi\)
−0.998233 + 0.0594153i \(0.981076\pi\)
\(500\) −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 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 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 0.120656 0.992694i \(-0.461500\pi\)
0.799370 0.600839i \(-0.205167\pi\)
\(522\) 0 0
\(523\) 5.00000 + 8.66025i 0.218635 + 0.378686i 0.954391 0.298560i \(-0.0965063\pi\)
−0.735756 + 0.677247i \(0.763173\pi\)
\(524\) −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 0.723234 0.690604i \(-0.242655\pi\)
−0.959697 + 0.281037i \(0.909322\pi\)
\(542\) 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 −0.491496 0.870880i \(-0.663550\pi\)
0.999952 0.00979220i \(-0.00311700\pi\)
\(558\) 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 −0.964315 0.264758i \(-0.914708\pi\)
0.711445 + 0.702742i \(0.248041\pi\)
\(564\) 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 −0.850935 0.525271i \(-0.823964\pi\)
−0.0294311 0.999567i \(-0.509370\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) −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 −0.986922 0.161198i \(-0.948464\pi\)
0.633062 + 0.774101i \(0.281798\pi\)
\(578\) −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 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) 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 −0.671140 0.741331i \(-0.734195\pi\)
0.977581 + 0.210558i \(0.0675282\pi\)
\(600\) 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 −0.896394 0.443257i \(-0.853823\pi\)
0.0643251 0.997929i \(-0.479511\pi\)
\(608\) −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 −0.985046 0.172294i \(-0.944882\pi\)
0.641734 + 0.766927i \(0.278215\pi\)
\(614\) 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 −0.365927 0.930644i \(-0.619248\pi\)
0.988924 0.148420i \(-0.0474187\pi\)
\(620\) 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 −0.959848 0.280521i \(-0.909493\pi\)
0.722862 + 0.690992i \(0.242826\pi\)
\(642\) 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 −0.680096 0.733123i \(-0.738062\pi\)
0.974951 + 0.222419i \(0.0713952\pi\)
\(648\) 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 0.681137 0.732156i \(-0.261486\pi\)
−0.974634 + 0.223803i \(0.928153\pi\)
\(654\) 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 −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) −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 0.802600 0.596518i \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) 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 −0.539750 0.841825i \(-0.681481\pi\)
0.998917 + 0.0465244i \(0.0148145\pi\)
\(684\) 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 0.560014 0.828483i \(-0.310796\pi\)
−0.997494 + 0.0707446i \(0.977462\pi\)
\(692\) 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 0.704118 0.710083i \(-0.251342\pi\)
−0.967009 + 0.254743i \(0.918009\pi\)
\(710\) 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 0.958051 + 0.286599i \(0.0925247\pi\)
−0.230823 + 0.972996i \(0.574142\pi\)
\(720\) 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 −0.864045 0.503415i \(-0.832077\pi\)
−0.00394730 0.999992i \(-0.501256\pi\)
\(734\) 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 −0.759287 0.650756i \(-0.774452\pi\)
0.943215 + 0.332184i \(0.107785\pi\)
\(740\) 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 −0.810860 0.585240i \(-0.801000\pi\)
−0.101403 0.994845i \(-0.532333\pi\)
\(752\) 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 0.697467 0.716617i \(-0.254310\pi\)
−0.969342 + 0.245716i \(0.920977\pi\)
\(762\) 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 −0.990721 0.135910i \(-0.956604\pi\)
0.613062 + 0.790034i \(0.289937\pi\)
\(774\) 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 0.298521 + 0.954403i \(0.403507\pi\)
−0.975798 + 0.218675i \(0.929827\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −39.0000 −1.38756
\(791\) −9.00000 + 46.7654i −0.320003 + 1.66279i