Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,2,Mod(127,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.f (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.01834519640\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 253.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.253 |
Dual form | 378.2.f.a.127.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −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 | \(0.400725\pi\) |
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.00000 | 0.948683 | ||||||||
\(11\) | −3.00000 | − | 5.19615i | −0.904534 | − | 1.56670i | −0.821541 | − | 0.570149i | \(-0.806886\pi\) |
−0.0829925 | − | 0.996550i | \(-0.526448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.73205i | −0.277350 | + | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | −0.500000 | + | 0.866025i | −0.133631 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.00000 | −1.60591 | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | −1.50000 | − | 2.59808i | −0.335410 | − | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | + | 5.19615i | −0.639602 | + | 1.10782i | ||||
\(23\) | 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 | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 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 | + | 5.19615i | 0.514496 | + | 0.891133i | ||||
\(35\) | 3.00000 | 0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 3.50000 | + | 6.06218i | 0.567775 | + | 0.983415i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.50000 | + | 2.59808i | −0.237171 | + | 0.410792i | ||||
\(41\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | − | 1.73205i | −0.152499 | − | 0.264135i | 0.779647 | − | 0.626219i | \(-0.215399\pi\) |
−0.932145 | + | 0.362084i | \(0.882065\pi\) | |||||||
\(44\) | 6.00000 | 0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | −0.442326 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −2.00000 | + | 3.46410i | −0.282843 | + | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.0000 | 2.42712 | ||||||||
\(56\) | −0.500000 | − | 0.866025i | −0.0668153 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | − | 5.19615i | 0.393919 | − | 0.682288i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 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 | ||||||||
\(67\) | −4.00000 | + | 6.92820i | −0.488678 | + | 0.846415i | −0.999915 | − | 0.0130248i | \(-0.995854\pi\) |
0.511237 | + | 0.859440i | \(0.329187\pi\) | |||||||
\(68\) | 3.00000 | − | 5.19615i | 0.363803 | − | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.50000 | − | 2.59808i | −0.179284 | − | 0.310530i | ||||
\(71\) | −3.00000 | −0.356034 | −0.178017 | − | 0.984027i | \(-0.556968\pi\) | ||||
−0.178017 | + | 0.984027i | \(0.556968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | −1.00000 | − | 1.73205i | −0.116248 | − | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.50000 | − | 6.06218i | 0.401478 | − | 0.695379i | ||||
\(77\) | −3.00000 | + | 5.19615i | −0.341882 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.50000 | − | 4.33013i | −0.281272 | − | 0.487177i | 0.690426 | − | 0.723403i | \(-0.257423\pi\) |
−0.971698 | + | 0.236225i | \(0.924090\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | + | 10.3923i | 0.658586 | + | 1.14070i | 0.980982 | + | 0.194099i | \(0.0621783\pi\) |
−0.322396 | + | 0.946605i | \(0.604488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | − | 15.5885i | 0.976187 | − | 1.69081i | ||||
\(86\) | −1.00000 | + | 1.73205i | −0.107833 | + | 0.186772i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.00000 | − | 5.19615i | −0.319801 | − | 0.553912i | ||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 1.50000 | + | 2.59808i | 0.156386 | + | 0.270868i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.5000 | − | 18.1865i | 1.07728 | − | 1.86590i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | − | 1.73205i | −0.101535 | − | 0.175863i | 0.810782 | − | 0.585348i | \(-0.199042\pi\) |
−0.912317 | + | 0.409484i | \(0.865709\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | 4.50000 | + | 7.79423i | 0.447767 | + | 0.775555i | 0.998240 | − | 0.0592978i | \(-0.0188862\pi\) |
−0.550474 | + | 0.834853i | \(0.685553\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.00000 | − | 8.66025i | 0.492665 | − | 0.853320i | −0.507300 | − | 0.861770i | \(-0.669356\pi\) |
0.999964 | + | 0.00844953i | \(0.00268960\pi\) | |||||||
\(104\) | −1.00000 | + | 1.73205i | −0.0980581 | + | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | + | 5.19615i | 0.291386 | + | 0.504695i | ||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | −9.00000 | − | 15.5885i | −0.858116 | − | 1.48630i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.500000 | + | 0.866025i | −0.0472456 | + | 0.0818317i | ||||
\(113\) | 7.50000 | − | 12.9904i | 0.705541 | − | 1.22203i | −0.260955 | − | 0.965351i | \(-0.584038\pi\) |
0.966496 | − | 0.256681i | \(-0.0826291\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.50000 | + | 7.79423i | 0.419627 | + | 0.726816i | ||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | + | 5.19615i | 0.275010 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | −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 | ||||||||
\(127\) | 17.0000 | 1.50851 | 0.754253 | − | 0.656584i | \(-0.227999\pi\) | ||||
0.754253 | + | 0.656584i | \(0.227999\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | + | 5.19615i | −0.263117 | + | 0.455733i | ||||
\(131\) | −4.50000 | + | 7.79423i | −0.393167 | + | 0.680985i | −0.992865 | − | 0.119241i | \(-0.961954\pi\) |
0.599699 | + | 0.800226i | \(0.295287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.50000 | + | 6.06218i | 0.303488 | + | 0.525657i | ||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | 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 | ||||||||
\(139\) | −2.50000 | + | 4.33013i | −0.212047 | + | 0.367277i | −0.952355 | − | 0.304991i | \(-0.901346\pi\) |
0.740308 | + | 0.672268i | \(0.234680\pi\) | |||||||
\(140\) | −1.50000 | + | 2.59808i | −0.126773 | + | 0.219578i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.50000 | + | 2.59808i | 0.125877 | + | 0.218026i | ||||
\(143\) | 12.0000 | 1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.0000 | −1.49482 | ||||||||
\(146\) | −1.00000 | − | 1.73205i | −0.0827606 | − | 0.143346i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | + | 1.73205i | −0.0821995 | + | 0.142374i | ||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.5000 | − | 19.9186i | −0.935857 | − | 1.62095i | −0.773099 | − | 0.634285i | \(-0.781294\pi\) |
−0.162758 | − | 0.986666i | \(-0.552039\pi\) | |||||||
\(152\) | −7.00000 | −0.567775 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | −3.00000 | − | 5.19615i | −0.240966 | − | 0.417365i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.50000 | − | 11.2583i | 0.518756 | − | 0.898513i | −0.481006 | − | 0.876717i | \(-0.659728\pi\) |
0.999762 | − | 0.0217953i | \(-0.00693820\pi\) | |||||||
\(158\) | −2.50000 | + | 4.33013i | −0.198889 | + | 0.344486i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.50000 | − | 2.59808i | −0.118585 | − | 0.205396i | ||||
\(161\) | −3.00000 | −0.236433 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | − | 10.3923i | 0.465690 | − | 0.806599i | ||||
\(167\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | −18.0000 | −1.38054 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | −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 | ||||||||
\(175\) | −2.00000 | + | 3.46410i | −0.151186 | + | 0.261861i | ||||
\(176\) | −3.00000 | + | 5.19615i | −0.226134 | + | 0.391675i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.0000 | −1.34538 | −0.672692 | − | 0.739923i | \(-0.734862\pi\) | ||||
−0.672692 | + | 0.739923i | \(0.734862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.0000 | −1.85824 | −0.929118 | − | 0.369784i | \(-0.879432\pi\) | ||||
−0.929118 | + | 0.369784i | \(0.879432\pi\) | |||||||
\(182\) | −1.00000 | − | 1.73205i | −0.0741249 | − | 0.128388i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.50000 | − | 2.59808i | 0.110581 | − | 0.191533i | ||||
\(185\) | −3.00000 | + | 5.19615i | −0.220564 | + | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.0000 | + | 31.1769i | 1.31629 | + | 2.27988i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −21.0000 | −1.52350 | ||||||||
\(191\) | −4.50000 | − | 7.79423i | −0.325609 | − | 0.563971i | 0.656027 | − | 0.754738i | \(-0.272236\pi\) |
−0.981635 | + | 0.190767i | \(0.938902\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.50000 | + | 14.7224i | −0.611843 | + | 1.05974i | 0.379086 | + | 0.925361i | \(0.376238\pi\) |
−0.990930 | + | 0.134382i | \(0.957095\pi\) | |||||||
\(194\) | −1.00000 | + | 1.73205i | −0.0717958 | + | 0.124354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.500000 | − | 0.866025i | −0.0357143 | − | 0.0618590i | ||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | −2.00000 | − | 3.46410i | −0.141421 | − | 0.244949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.50000 | − | 7.79423i | 0.316619 | − | 0.548400i | ||||
\(203\) | 3.00000 | − | 5.19615i | 0.210559 | − | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.0000 | −0.696733 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 21.0000 | + | 36.3731i | 1.45260 | + | 2.51598i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | + | 6.92820i | −0.275371 | + | 0.476957i | −0.970229 | − | 0.242190i | \(-0.922134\pi\) |
0.694857 | + | 0.719148i | \(0.255467\pi\) | |||||||
\(212\) | 3.00000 | − | 5.19615i | 0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | 6.00000 | 0.409197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 5.00000 | + | 8.66025i | 0.338643 | + | 0.586546i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.00000 | + | 15.5885i | −0.606780 | + | 1.05097i | ||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0000 | + | 24.2487i | 0.937509 | + | 1.62381i | 0.770097 | + | 0.637927i | \(0.220208\pi\) |
0.167412 | + | 0.985887i | \(0.446459\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.0000 | −0.997785 | ||||||||
\(227\) | −7.50000 | − | 12.9904i | −0.497792 | − | 0.862202i | 0.502204 | − | 0.864749i | \(-0.332523\pi\) |
−0.999997 | + | 0.00254715i | \(0.999189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.500000 | − | 0.866025i | 0.0330409 | − | 0.0572286i | −0.849032 | − | 0.528341i | \(-0.822814\pi\) |
0.882073 | + | 0.471113i | \(0.156147\pi\) | |||||||
\(230\) | 4.50000 | − | 7.79423i | 0.296721 | − | 0.513936i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | + | 5.19615i | 0.196960 | + | 0.341144i | ||||
\(233\) | −9.00000 | −0.589610 | −0.294805 | − | 0.955557i | \(-0.595255\pi\) | ||||
−0.294805 | + | 0.955557i | \(0.595255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.00000 | − | 5.19615i | 0.194461 | − | 0.336817i | ||||
\(239\) | −7.50000 | + | 12.9904i | −0.485135 | + | 0.840278i | −0.999854 | − | 0.0170808i | \(-0.994563\pi\) |
0.514719 | + | 0.857359i | \(0.327896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.00000 | − | 6.92820i | −0.257663 | − | 0.446285i | 0.707953 | − | 0.706260i | \(-0.249619\pi\) |
−0.965615 | + | 0.259975i | \(0.916286\pi\) | |||||||
\(242\) | 25.0000 | 1.60706 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.00000 | 0.320092 | ||||||||
\(245\) | −1.50000 | − | 2.59808i | −0.0958315 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.00000 | − | 12.1244i | 0.445399 | − | 0.771454i | ||||
\(248\) | −1.00000 | + | 1.73205i | −0.0635001 | + | 0.109985i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.50000 | + | 2.59808i | 0.0948683 | + | 0.164317i | ||||
\(251\) | −3.00000 | −0.189358 | −0.0946792 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946792 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | −8.50000 | − | 14.7224i | −0.533337 | − | 0.923768i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 9.00000 | − | 15.5885i | 0.561405 | − | 0.972381i | −0.435970 | − | 0.899961i | \(-0.643595\pi\) |
0.997374 | − | 0.0724199i | \(-0.0230722\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | − | 1.73205i | −0.0621370 | − | 0.107624i | ||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.00000 | 0.556022 | ||||||||
\(263\) | −10.5000 | − | 18.1865i | −0.647458 | − | 1.12143i | −0.983728 | − | 0.179664i | \(-0.942499\pi\) |
0.336270 | − | 0.941766i | \(-0.390834\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | − | 15.5885i | 0.552866 | − | 0.957591i | ||||
\(266\) | 3.50000 | − | 6.06218i | 0.214599 | − | 0.371696i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.00000 | − | 6.92820i | −0.244339 | − | 0.423207i | ||||
\(269\) | 9.00000 | 0.548740 | 0.274370 | − | 0.961624i | \(-0.411531\pi\) | ||||
0.274370 | + | 0.961624i | \(0.411531\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.0000 | −1.70088 | −0.850439 | − | 0.526073i | \(-0.823664\pi\) | ||||
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | 3.00000 | + | 5.19615i | 0.181902 | + | 0.315063i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.00000 | − | 5.19615i | 0.181237 | − | 0.313911i | ||||
\(275\) | −12.0000 | + | 20.7846i | −0.723627 | + | 1.25336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.00000 | + | 13.8564i | 0.480673 | + | 0.832551i | 0.999754 | − | 0.0221745i | \(-0.00705893\pi\) |
−0.519081 | + | 0.854725i | \(0.673726\pi\) | |||||||
\(278\) | 5.00000 | 0.299880 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.00000 | 0.179284 | ||||||||
\(281\) | −13.5000 | − | 23.3827i | −0.805342 | − | 1.39489i | −0.916060 | − | 0.401042i | \(-0.868648\pi\) |
0.110717 | − | 0.993852i | \(-0.464685\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.50000 | − | 16.4545i | 0.564716 | − | 0.978117i | −0.432360 | − | 0.901701i | \(-0.642319\pi\) |
0.997076 | − | 0.0764162i | \(-0.0243478\pi\) | |||||||
\(284\) | 1.50000 | − | 2.59808i | 0.0890086 | − | 0.154167i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | − | 10.3923i | −0.354787 | − | 0.614510i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 9.00000 | + | 15.5885i | 0.528498 | + | 0.915386i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.00000 | + | 1.73205i | −0.0585206 | + | 0.101361i | ||||
\(293\) | −1.50000 | + | 2.59808i | −0.0876309 | + | 0.151781i | −0.906509 | − | 0.422186i | \(-0.861263\pi\) |
0.818878 | + | 0.573967i | \(0.194596\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.00000 | 0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 3.00000 | + | 5.19615i | 0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | + | 1.73205i | −0.0576390 | + | 0.0998337i | ||||
\(302\) | −11.5000 | + | 19.9186i | −0.661751 | + | 1.14619i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.50000 | + | 6.06218i | 0.200739 | + | 0.347690i | ||||
\(305\) | 15.0000 | 0.858898 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.0000 | −1.42683 | −0.713413 | − | 0.700744i | \(-0.752851\pi\) | ||||
−0.713413 | + | 0.700744i | \(0.752851\pi\) | |||||||
\(308\) | −3.00000 | − | 5.19615i | −0.170941 | − | 0.296078i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.00000 | + | 5.19615i | −0.170389 | + | 0.295122i | ||||
\(311\) | 6.00000 | − | 10.3923i | 0.340229 | − | 0.589294i | −0.644246 | − | 0.764818i | \(-0.722829\pi\) |
0.984475 | + | 0.175525i | \(0.0561621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | + | 8.66025i | 0.282617 | + | 0.489506i | 0.972028 | − | 0.234863i | \(-0.0754642\pi\) |
−0.689412 | + | 0.724370i | \(0.742131\pi\) | |||||||
\(314\) | −13.0000 | −0.733632 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.00000 | 0.281272 | ||||||||
\(317\) | 9.00000 | + | 15.5885i | 0.505490 | + | 0.875535i | 0.999980 | + | 0.00635137i | \(0.00202172\pi\) |
−0.494489 | + | 0.869184i | \(0.664645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0000 | − | 31.1769i | 1.00781 | − | 1.74557i | ||||
\(320\) | −1.50000 | + | 2.59808i | −0.0838525 | + | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.50000 | + | 2.59808i | 0.0835917 | + | 0.144785i | ||||
\(323\) | 42.0000 | 2.33694 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.00000 | 0.443760 | ||||||||
\(326\) | −1.00000 | − | 1.73205i | −0.0553849 | − | 0.0959294i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0000 | − | 22.5167i | −0.714545 | − | 1.23763i | −0.963135 | − | 0.269019i | \(-0.913301\pi\) |
0.248590 | − | 0.968609i | \(-0.420033\pi\) | |||||||
\(332\) | −12.0000 | −0.658586 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0000 | − | 20.7846i | −0.655630 | − | 1.13558i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | − | 19.0526i | 0.599208 | − | 1.03786i | −0.393730 | − | 0.919226i | \(-0.628816\pi\) |
0.992938 | − | 0.118633i | \(-0.0378512\pi\) | |||||||
\(338\) | 4.50000 | − | 7.79423i | 0.244768 | − | 0.423950i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.00000 | + | 15.5885i | 0.488094 | + | 0.845403i | ||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −1.00000 | − | 1.73205i | −0.0539164 | − | 0.0933859i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.00000 | + | 5.19615i | −0.161281 | + | 0.279347i | ||||
\(347\) | −12.0000 | + | 20.7846i | −0.644194 | + | 1.11578i | 0.340293 | + | 0.940319i | \(0.389474\pi\) |
−0.984487 | + | 0.175457i | \(0.943860\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.0000 | − | 22.5167i | −0.695874 | − | 1.20529i | −0.969885 | − | 0.243563i | \(-0.921684\pi\) |
0.274011 | − | 0.961727i | \(-0.411649\pi\) | |||||||
\(350\) | 4.00000 | 0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.00000 | 0.319801 | ||||||||
\(353\) | −9.00000 | − | 15.5885i | −0.479022 | − | 0.829690i | 0.520689 | − | 0.853746i | \(-0.325675\pi\) |
−0.999711 | + | 0.0240566i | \(0.992342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.50000 | − | 7.79423i | 0.238835 | − | 0.413675i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.00000 | + | 15.5885i | 0.475665 | + | 0.823876i | ||||
\(359\) | 3.00000 | 0.158334 | 0.0791670 | − | 0.996861i | \(-0.474774\pi\) | ||||
0.0791670 | + | 0.996861i | \(0.474774\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | 12.5000 | + | 21.6506i | 0.656985 | + | 1.13793i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.00000 | + | 1.73205i | −0.0524142 | + | 0.0907841i | ||||
\(365\) | −3.00000 | + | 5.19615i | −0.157027 | + | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.00000 | − | 6.92820i | −0.208798 | − | 0.361649i | 0.742538 | − | 0.669804i | \(-0.233622\pi\) |
−0.951336 | + | 0.308155i | \(0.900289\pi\) | |||||||
\(368\) | −3.00000 | −0.156386 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | 3.00000 | + | 5.19615i | 0.155752 | + | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.00000 | + | 12.1244i | −0.362446 | + | 0.627775i | −0.988363 | − | 0.152115i | \(-0.951392\pi\) |
0.625917 | + | 0.779890i | \(0.284725\pi\) | |||||||
\(374\) | 18.0000 | − | 31.1769i | 0.930758 | − | 1.61212i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | 10.5000 | + | 18.1865i | 0.538639 | + | 0.932949i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.50000 | + | 7.79423i | −0.230240 | + | 0.398787i | ||||
\(383\) | −9.00000 | + | 15.5885i | −0.459879 | + | 0.796533i | −0.998954 | − | 0.0457244i | \(-0.985440\pi\) |
0.539076 | + | 0.842257i | \(0.318774\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.00000 | − | 15.5885i | −0.458682 | − | 0.794461i | ||||
\(386\) | 17.0000 | 0.865277 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.00000 | 0.101535 | ||||||||
\(389\) | 12.0000 | + | 20.7846i | 0.608424 | + | 1.05382i | 0.991500 | + | 0.130105i | \(0.0415314\pi\) |
−0.383076 | + | 0.923717i | \(0.625135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | + | 15.5885i | −0.455150 | + | 0.788342i | ||||
\(392\) | −0.500000 | + | 0.866025i | −0.0252538 | + | 0.0437409i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.00000 | + | 15.5885i | 0.453413 | + | 0.785335i | ||||
\(395\) | 15.0000 | 0.754732 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.0000 | 1.30490 | 0.652451 | − | 0.757831i | \(-0.273741\pi\) | ||||
0.652451 | + | 0.757831i | \(0.273741\pi\) | |||||||
\(398\) | −7.00000 | − | 12.1244i | −0.350878 | − | 0.607739i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | 1.50000 | − | 2.59808i | 0.0749064 | − | 0.129742i | −0.826139 | − | 0.563466i | \(-0.809468\pi\) |
0.901046 | + | 0.433724i | \(0.142801\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | − | 3.46410i | −0.0996271 | − | 0.172559i | ||||
\(404\) | −9.00000 | −0.447767 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | −6.00000 | − | 10.3923i | −0.297409 | − | 0.515127i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0000 | + | 27.7128i | −0.791149 | + | 1.37031i | 0.134107 | + | 0.990967i | \(0.457183\pi\) |
−0.925256 | + | 0.379344i | \(0.876150\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.00000 | + | 8.66025i | 0.246332 | + | 0.426660i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −36.0000 | −1.76717 | ||||||||
\(416\) | −1.00000 | − | 1.73205i | −0.0490290 | − | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 21.0000 | − | 36.3731i | 1.02714 | − | 1.77906i | ||||
\(419\) | 7.50000 | − | 12.9904i | 0.366399 | − | 0.634622i | −0.622601 | − | 0.782540i | \(-0.713924\pi\) |
0.989000 | + | 0.147918i | \(0.0472572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | + | 8.66025i | 0.243685 | + | 0.422075i | 0.961761 | − | 0.273890i | \(-0.0883103\pi\) |
−0.718076 | + | 0.695965i | \(0.754977\pi\) | |||||||
\(422\) | 8.00000 | 0.389434 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 12.0000 | + | 20.7846i | 0.582086 | + | 1.00820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.50000 | + | 4.33013i | −0.120983 | + | 0.209550i | ||||
\(428\) | −6.00000 | + | 10.3923i | −0.290021 | + | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.00000 | − | 5.19615i | −0.144673 | − | 0.250581i | ||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | −1.00000 | − | 1.73205i | −0.0480015 | − | 0.0831411i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.00000 | − | 8.66025i | 0.239457 | − | 0.414751i | ||||
\(437\) | −10.5000 | + | 18.1865i | −0.502283 | + | 0.869980i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | − | 6.92820i | −0.190910 | − | 0.330665i | 0.754642 | − | 0.656136i | \(-0.227810\pi\) |
−0.945552 | + | 0.325471i | \(0.894477\pi\) | |||||||
\(440\) | 18.0000 | 0.858116 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | 9.00000 | + | 15.5885i | 0.427603 | + | 0.740630i | 0.996660 | − | 0.0816684i | \(-0.0260248\pi\) |
−0.569057 | + | 0.822298i | \(0.692691\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.0000 | − | 24.2487i | 0.662919 | − | 1.14821i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.500000 | − | 0.866025i | −0.0236228 | − | 0.0409159i | ||||
\(449\) | −33.0000 | −1.55737 | −0.778683 | − | 0.627417i | \(-0.784112\pi\) | ||||
−0.778683 | + | 0.627417i | \(0.784112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 7.50000 | + | 12.9904i | 0.352770 | + | 0.611016i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.50000 | + | 12.9904i | −0.351992 | + | 0.609669i | ||||
\(455\) | −3.00000 | + | 5.19615i | −0.140642 | + | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5000 | − | 25.1147i | −0.678281 | − | 1.17482i | −0.975498 | − | 0.220008i | \(-0.929392\pi\) |
0.297217 | − | 0.954810i | \(-0.403942\pi\) | |||||||
\(458\) | −1.00000 | −0.0467269 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.00000 | −0.419627 | ||||||||
\(461\) | −16.5000 | − | 28.5788i | −0.768482 | − | 1.33105i | −0.938386 | − | 0.345589i | \(-0.887679\pi\) |
0.169904 | − | 0.985461i | \(-0.445654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.50000 | − | 11.2583i | 0.302081 | − | 0.523219i | −0.674526 | − | 0.738251i | \(-0.735652\pi\) |
0.976607 | + | 0.215032i | \(0.0689855\pi\) | |||||||
\(464\) | 3.00000 | − | 5.19615i | 0.139272 | − | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.50000 | + | 7.79423i | 0.208458 | + | 0.361061i | ||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.00000 | + | 10.3923i | −0.275880 | + | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.0000 | + | 24.2487i | 0.642364 | + | 1.11261i | ||||
\(476\) | −6.00000 | −0.275010 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.0000 | 0.686084 | ||||||||
\(479\) | −3.00000 | − | 5.19615i | −0.137073 | − | 0.237418i | 0.789314 | − | 0.613990i | \(-0.210436\pi\) |
−0.926388 | + | 0.376571i | \(0.877103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | + | 3.46410i | −0.0911922 | + | 0.157949i | ||||
\(482\) | −4.00000 | + | 6.92820i | −0.182195 | + | 0.315571i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.5000 | − | 21.6506i | −0.568182 | − | 0.984120i | ||||
\(485\) | 6.00000 | 0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.0000 | 1.31412 | 0.657058 | − | 0.753840i | \(-0.271801\pi\) | ||||
0.657058 | + | 0.753840i | \(0.271801\pi\) | |||||||
\(488\) | −2.50000 | − | 4.33013i | −0.113170 | − | 0.196016i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.50000 | + | 2.59808i | −0.0677631 | + | 0.117369i | ||||
\(491\) | 9.00000 | − | 15.5885i | 0.406164 | − | 0.703497i | −0.588292 | − | 0.808649i | \(-0.700199\pi\) |
0.994456 | + | 0.105151i | \(0.0335327\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0000 | − | 31.1769i | −0.810679 | − | 1.40414i | ||||
\(494\) | −14.0000 | −0.629890 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 1.50000 | + | 2.59808i | 0.0672842 | + | 0.116540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0000 | + | 27.7128i | −0.716258 | + | 1.24060i | 0.246214 | + | 0.969216i | \(0.420813\pi\) |
−0.962472 | + | 0.271380i | \(0.912520\pi\) | |||||||
\(500\) | 1.50000 | − | 2.59808i | 0.0670820 | − | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.50000 | + | 2.59808i | 0.0669483 | + | 0.115958i | ||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.0000 | −1.20148 | ||||||||
\(506\) | 9.00000 | + | 15.5885i | 0.400099 | + | 0.692991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.50000 | + | 14.7224i | −0.377127 | + | 0.653202i | ||||
\(509\) | 15.0000 | − | 25.9808i | 0.664863 | − | 1.15158i | −0.314459 | − | 0.949271i | \(-0.601823\pi\) |
0.979322 | − | 0.202306i | \(-0.0648436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.00000 | − | 1.73205i | −0.0442374 | − | 0.0766214i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | 15.0000 | + | 25.9808i | 0.660979 | + | 1.14485i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.00000 | + | 1.73205i | −0.0439375 | + | 0.0761019i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.00000 | − | 5.19615i | −0.131559 | − | 0.227866i | ||||
\(521\) | −24.0000 | −1.05146 | −0.525730 | − | 0.850652i | \(-0.676208\pi\) | ||||
−0.525730 | + | 0.850652i | \(0.676208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.0000 | −0.568450 | −0.284225 | − | 0.958758i | \(-0.591736\pi\) | ||||
−0.284225 | + | 0.958758i | \(0.591736\pi\) | |||||||
\(524\) | −4.50000 | − | 7.79423i | −0.196583 | − | 0.340492i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.5000 | + | 18.1865i | −0.457822 | + | 0.792971i | ||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | −18.0000 | −0.781870 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.00000 | −0.303488 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0000 | + | 31.1769i | −0.778208 | + | 1.34790i | ||||
\(536\) | −4.00000 | + | 6.92820i | −0.172774 | + | 0.299253i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.50000 | − | 7.79423i | −0.194009 | − | 0.336033i | ||||
\(539\) | 6.00000 | 0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.0000 | 1.63375 | 0.816874 | − | 0.576816i | \(-0.195705\pi\) | ||||
0.816874 | + | 0.576816i | \(0.195705\pi\) | |||||||
\(542\) | 14.0000 | + | 24.2487i | 0.601351 | + | 1.04157i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.00000 | − | 5.19615i | 0.128624 | − | 0.222783i | ||||
\(545\) | 15.0000 | − | 25.9808i | 0.642529 | − | 1.11289i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0000 | − | 27.7128i | −0.684111 | − | 1.18491i | −0.973715 | − | 0.227768i | \(-0.926857\pi\) |
0.289605 | − | 0.957146i | \(-0.406476\pi\) | |||||||
\(548\) | −6.00000 | −0.256307 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 24.0000 | 1.02336 | ||||||||
\(551\) | −21.0000 | − | 36.3731i | −0.894630 | − | 1.54954i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.50000 | + | 4.33013i | −0.106311 | + | 0.184136i | ||||
\(554\) | 8.00000 | − | 13.8564i | 0.339887 | − | 0.588702i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.50000 | − | 4.33013i | −0.106024 | − | 0.183638i | ||||
\(557\) | 24.0000 | 1.01691 | 0.508456 | − | 0.861088i | \(-0.330216\pi\) | ||||
0.508456 | + | 0.861088i | \(0.330216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | −1.50000 | − | 2.59808i | −0.0633866 | − | 0.109789i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.5000 | + | 23.3827i | −0.569463 | + | 0.986339i | ||||
\(563\) | −16.5000 | + | 28.5788i | −0.695392 | + | 1.20445i | 0.274656 | + | 0.961542i | \(0.411436\pi\) |
−0.970048 | + | 0.242912i | \(0.921897\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.5000 | + | 38.9711i | 0.946582 | + | 1.63953i | ||||
\(566\) | −19.0000 | −0.798630 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.00000 | −0.125877 | ||||||||
\(569\) | −9.00000 | − | 15.5885i | −0.377300 | − | 0.653502i | 0.613369 | − | 0.789797i | \(-0.289814\pi\) |
−0.990668 | + | 0.136295i | \(0.956481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | + | 27.7128i | −0.669579 | + | 1.15975i | 0.308443 | + | 0.951243i | \(0.400192\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | −6.00000 | + | 10.3923i | −0.250873 | + | 0.434524i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | −0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.00000 | −0.166522 | −0.0832611 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832611 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(578\) | −9.50000 | − | 16.4545i | −0.395148 | − | 0.684416i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.00000 | − | 15.5885i | 0.373705 | − | 0.647275i | ||||
\(581\) | 6.00000 | − | 10.3923i | 0.248922 | − | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | + | 31.1769i | 0.745484 | + | 1.29122i | ||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.00000 | 0.123929 | ||||||||
\(587\) | −1.50000 | − | 2.59808i | −0.0619116 | − | 0.107234i | 0.833408 | − | 0.552658i | \(-0.186386\pi\) |
−0.895320 | + | 0.445424i | \(0.853053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.00000 | − | 12.1244i | 0.288430 | − | 0.499575i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00000 | − | 1.73205i | −0.0410997 | − | 0.0711868i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.0000 | −0.737928 | ||||||||
\(596\) | −3.00000 | − | 5.19615i | −0.122885 | − | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.00000 | − | 5.19615i | 0.122679 | − | 0.212486i | ||||
\(599\) | −12.0000 | + | 20.7846i | −0.490307 | + | 0.849236i | −0.999938 | − | 0.0111569i | \(-0.996449\pi\) |
0.509631 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.00000 | − | 12.1244i | −0.285536 | − | 0.494563i | 0.687203 | − | 0.726465i | \(-0.258838\pi\) |
−0.972739 | + | 0.231903i | \(0.925505\pi\) | |||||||
\(602\) | 2.00000 | 0.0815139 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.0000 | 0.935857 | ||||||||
\(605\) | −37.5000 | − | 64.9519i | −1.52459 | − | 2.64067i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.0000 | − | 19.0526i | 0.446476 | − | 0.773320i | −0.551678 | − | 0.834058i | \(-0.686012\pi\) |
0.998154 | + | 0.0607380i | \(0.0193454\pi\) | |||||||
\(608\) | 3.50000 | − | 6.06218i | 0.141944 | − | 0.245854i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.50000 | − | 12.9904i | −0.303666 | − | 0.525965i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.00000 | 0.323117 | 0.161558 | − | 0.986863i | \(-0.448348\pi\) | ||||
0.161558 | + | 0.986863i | \(0.448348\pi\) | |||||||
\(614\) | 12.5000 | + | 21.6506i | 0.504459 | + | 0.873749i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.00000 | + | 5.19615i | −0.120873 | + | 0.209359i | ||||
\(617\) | 21.0000 | − | 36.3731i | 0.845428 | − | 1.46432i | −0.0398207 | − | 0.999207i | \(-0.512679\pi\) |
0.885249 | − | 0.465118i | \(-0.153988\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.50000 | + | 6.06218i | 0.140677 | + | 0.243659i | 0.927752 | − | 0.373198i | \(-0.121739\pi\) |
−0.787075 | + | 0.616858i | \(0.788405\pi\) | |||||||
\(620\) | 6.00000 | 0.240966 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.0000 | −0.481156 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 5.00000 | − | 8.66025i | 0.199840 | − | 0.346133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.50000 | + | 11.2583i | 0.259378 | + | 0.449256i | ||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.00000 | −0.278666 | −0.139333 | − | 0.990246i | \(-0.544496\pi\) | ||||
−0.139333 | + | 0.990246i | \(0.544496\pi\) | |||||||
\(632\) | −2.50000 | − | 4.33013i | −0.0994447 | − | 0.172243i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.00000 | − | 15.5885i | 0.357436 | − | 0.619097i | ||||
\(635\) | −25.5000 | + | 44.1673i | −1.01194 | + | 1.75273i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | − | 1.73205i | −0.0396214 | − | 0.0686264i | ||||
\(638\) | −36.0000 | −1.42525 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.00000 | 0.118585 | ||||||||
\(641\) | 13.5000 | + | 23.3827i | 0.533218 | + | 0.923561i | 0.999247 | + | 0.0387913i | \(0.0123508\pi\) |
−0.466029 | + | 0.884769i | \(0.654316\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.00000 | − | 3.46410i | 0.0788723 | − | 0.136611i | −0.823891 | − | 0.566748i | \(-0.808201\pi\) |
0.902764 | + | 0.430137i | \(0.141535\pi\) | |||||||
\(644\) | 1.50000 | − | 2.59808i | 0.0591083 | − | 0.102379i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.0000 | − | 36.3731i | −0.826234 | − | 1.43108i | ||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.00000 | − | 6.92820i | −0.156893 | − | 0.271746i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.00000 | + | 1.73205i | −0.0391630 | + | 0.0678323i | ||||
\(653\) | −18.0000 | + | 31.1769i | −0.704394 | + | 1.22005i | 0.262515 | + | 0.964928i | \(0.415448\pi\) |
−0.966910 | + | 0.255119i | \(0.917885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.5000 | − | 23.3827i | −0.527489 | − | 0.913637i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.0000 | + | 36.3731i | 0.818044 | + | 1.41689i | 0.907122 | + | 0.420869i | \(0.138275\pi\) |
−0.0890776 | + | 0.996025i | \(0.528392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.50000 | + | 4.33013i | −0.0972387 | + | 0.168422i | −0.910541 | − | 0.413419i | \(-0.864334\pi\) |
0.813302 | + | 0.581842i | \(0.197668\pi\) | |||||||
\(662\) | −13.0000 | + | 22.5167i | −0.505259 | + | 0.875135i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | + | 10.3923i | 0.232845 | + | 0.403300i | ||||
\(665\) | −21.0000 | −0.814345 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0000 | 0.696963 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.0000 | + | 20.7846i | −0.463600 | + | 0.802980i | ||||
\(671\) | −15.0000 | + | 25.9808i | −0.579069 | + | 1.00298i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.5000 | + | 32.0429i | 0.713123 | + | 1.23516i | 0.963679 | + | 0.267063i | \(0.0860531\pi\) |
−0.250557 | + | 0.968102i | \(0.580614\pi\) | |||||||
\(674\) | −22.0000 | −0.847408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 21.0000 | + | 36.3731i | 0.807096 | + | 1.39793i | 0.914867 | + | 0.403755i | \(0.132295\pi\) |
−0.107772 | + | 0.994176i | \(0.534372\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.00000 | + | 1.73205i | −0.0383765 | + | 0.0664700i | ||||
\(680\) | 9.00000 | − | 15.5885i | 0.345134 | − | 0.597790i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.00000 | − | 10.3923i | −0.229752 | − | 0.397942i | ||||
\(683\) | 6.00000 | 0.229584 | 0.114792 | − | 0.993390i | \(-0.463380\pi\) | ||||
0.114792 | + | 0.993390i | \(0.463380\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | −0.687745 | ||||||||
\(686\) | −0.500000 | − | 0.866025i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | + | 1.73205i | −0.0381246 | + | 0.0660338i | ||||
\(689\) | 6.00000 | − | 10.3923i | 0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.5000 | − | 40.7032i | −0.893982 | − | 1.54842i | −0.835059 | − | 0.550160i | \(-0.814567\pi\) |
−0.0589228 | − | 0.998263i | \(-0.518767\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | −7.50000 | − | 12.9904i | −0.284491 | − | 0.492753i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −13.0000 | + | 22.5167i | −0.492057 | + | 0.852268i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.00000 | − | 3.46410i | −0.0755929 | − | 0.130931i | ||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0000 | −0.528020 | ||||||||
\(704\) | −3.00000 | − | 5.19615i | −0.113067 | − | 0.195837i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00000 | + | 15.5885i | −0.338719 | + | 0.586679i | ||||
\(707\) | 4.50000 | − | 7.79423i | 0.169240 | − | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.0000 | + | 45.0333i | 0.976450 | + | 1.69126i | 0.675063 | + | 0.737760i | \(0.264116\pi\) |
0.301388 | + | 0.953502i | \(0.402550\pi\) | |||||||
\(710\) | −9.00000 | −0.337764 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.00000 | + | 5.19615i | 0.112351 | + | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | + | 31.1769i | −0.673162 | + | 1.16595i | ||||
\(716\) | 9.00000 | − | 15.5885i | 0.336346 | − | 0.582568i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.50000 | − | 2.59808i | −0.0559795 | − | 0.0969593i | ||||
\(719\) | 36.0000 | 1.34257 | 0.671287 | − | 0.741198i | \(-0.265742\pi\) | ||||
0.671287 | + | 0.741198i | \(0.265742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | −0.372419 | ||||||||
\(722\) | −15.0000 | − | 25.9808i | −0.558242 | − | 0.966904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.5000 | − | 21.6506i | 0.464559 | − | 0.804640i | ||||
\(725\) | 12.0000 | − | 20.7846i | 0.445669 | − | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.00000 | − | 6.92820i | −0.148352 | − | 0.256953i | 0.782267 | − | 0.622944i | \(-0.214063\pi\) |
−0.930618 | + | 0.365991i | \(0.880730\pi\) | |||||||
\(728\) | 2.00000 | 0.0741249 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.00000 | 0.222070 | ||||||||
\(731\) | 6.00000 | + | 10.3923i | 0.221918 | + | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.5000 | + | 25.1147i | −0.535570 | + | 0.927634i | 0.463566 | + | 0.886062i | \(0.346570\pi\) |
−0.999136 | + | 0.0415715i | \(0.986764\pi\) | |||||||
\(734\) | −4.00000 | + | 6.92820i | −0.147643 | + | 0.255725i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.50000 | + | 2.59808i | 0.0552907 | + | 0.0957664i | ||||
\(737\) | 48.0000 | 1.76810 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.0000 | 0.956425 | 0.478213 | − | 0.878244i | \(-0.341285\pi\) | ||||
0.478213 | + | 0.878244i | \(0.341285\pi\) | |||||||
\(740\) | −3.00000 | − | 5.19615i | −0.110282 | − | 0.191014i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.00000 | − | 5.19615i | 0.110133 | − | 0.190757i | ||||
\(743\) | 18.0000 | − | 31.1769i | 0.660356 | − | 1.14377i | −0.320166 | − | 0.947361i | \(-0.603739\pi\) |
0.980522 | − | 0.196409i | \(-0.0629279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.00000 | − | 15.5885i | −0.329734 | − | 0.571117i | ||||
\(746\) | 14.0000 | 0.512576 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −36.0000 | −1.31629 | ||||||||
\(749\) | −6.00000 | − | 10.3923i | −0.219235 | − | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5000 | − | 26.8468i | 0.565603 | − | 0.979653i | −0.431390 | − | 0.902165i | \(-0.641977\pi\) |
0.996993 | − | 0.0774878i | \(-0.0246899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00000 | + | 10.3923i | 0.218507 | + | 0.378465i | ||||
\(755\) | 69.0000 | 2.51117 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | −1.00000 | − | 1.73205i | −0.0363216 | − | 0.0629109i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.5000 | − | 18.1865i | 0.380875 | − | 0.659695i | ||||
\(761\) | −21.0000 | + | 36.3731i | −0.761249 | + | 1.31852i | 0.180957 | + | 0.983491i | \(0.442080\pi\) |
−0.942207 | + | 0.335032i | \(0.891253\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.00000 | + | 8.66025i | 0.181012 | + | 0.313522i | ||||
\(764\) | 9.00000 | 0.325609 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.0000 | 0.650366 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.00000 | + | 12.1244i | −0.252426 | + | 0.437215i | −0.964193 | − | 0.265200i | \(-0.914562\pi\) |
0.711767 | + | 0.702416i | \(0.247895\pi\) | |||||||
\(770\) | −9.00000 | + | 15.5885i | −0.324337 | + | 0.561769i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.50000 | − | 14.7224i | −0.305922 | − | 0.529872i | ||||
\(773\) | 51.0000 | 1.83434 | 0.917171 | − | 0.398493i | \(-0.130467\pi\) | ||||
0.917171 | + | 0.398493i | \(0.130467\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.00000 | 0.287368 | ||||||||
\(776\) | −1.00000 | − | 1.73205i | −0.0358979 | − | 0.0621770i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.0000 | − | 20.7846i | 0.430221 | − | 0.745164i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | + | 15.5885i | 0.322045 | + | 0.557799i | ||||
\(782\) | 18.0000 | 0.643679 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 19.5000 | + | 33.7750i | 0.695985 | + | 1.20548i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.0000 | + | 17.3205i | −0.356462 |