Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1699,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1699");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.z (of order \(6\), 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.3317760000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 25x^{4} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1699.2 | ||
Root | \(-2.15988 + 0.578737i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1699 |
Dual form | 1950.2.z.o.1849.2 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | 2.73861 | − | 1.58114i | 1.03510 | − | 0.597614i | 0.116657 | − | 0.993172i | \(-0.462782\pi\) |
0.918441 | + | 0.395558i | \(0.129449\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 3.60464 | − | 0.0811388i | 0.999747 | − | 0.0225039i | ||||
\(14\) | −3.16228 | −0.845154 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.725489 | − | 0.418861i | 0.175957 | − | 0.101589i | −0.409435 | − | 0.912339i | \(-0.634274\pi\) |
0.585392 | + | 0.810751i | \(0.300941\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −1.58114 | − | 2.73861i | −0.362738 | − | 0.628281i | 0.625672 | − | 0.780086i | \(-0.284825\pi\) |
−0.988410 | + | 0.151805i | \(0.951491\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.16228 | −0.690066 | ||||||||
\(22\) | 2.59808 | − | 1.50000i | 0.553912 | − | 0.319801i | ||||
\(23\) | 1.87259 | + | 1.08114i | 0.390461 | + | 0.225433i | 0.682360 | − | 0.731016i | \(-0.260954\pi\) |
−0.291899 | + | 0.956449i | \(0.594287\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.16228 | − | 1.73205i | −0.620174 | − | 0.339683i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.73861 | + | 1.58114i | 0.517549 | + | 0.298807i | ||||
\(29\) | 2.16228 | − | 3.74517i | 0.401525 | − | 0.695461i | −0.592385 | − | 0.805655i | \(-0.701814\pi\) |
0.993910 | + | 0.110193i | \(0.0351470\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.83772 | 0.509670 | 0.254835 | − | 0.966985i | \(-0.417979\pi\) | ||||
0.254835 | + | 0.966985i | \(0.417979\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 2.59808 | − | 1.50000i | 0.452267 | − | 0.261116i | ||||
\(34\) | −0.837722 | −0.143668 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 7.34981 | + | 4.24342i | 1.20830 | + | 0.697613i | 0.962388 | − | 0.271678i | \(-0.0875787\pi\) |
0.245914 | + | 0.969292i | \(0.420912\pi\) | |||||||
\(38\) | 3.16228i | 0.512989i | ||||||||
\(39\) | −3.16228 | − | 1.73205i | −0.506370 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.74342 | + | 8.21584i | −0.740797 | + | 1.28310i | 0.211336 | + | 0.977414i | \(0.432219\pi\) |
−0.952133 | + | 0.305685i | \(0.901115\pi\) | |||||||
\(42\) | 2.73861 | + | 1.58114i | 0.422577 | + | 0.243975i | ||||
\(43\) | 1.00656 | − | 0.581139i | 0.153499 | − | 0.0886228i | −0.421283 | − | 0.906929i | \(-0.638420\pi\) |
0.574782 | + | 0.818306i | \(0.305087\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.08114 | − | 1.87259i | −0.159405 | − | 0.276098i | ||||
\(47\) | 6.00000i | 0.875190i | 0.899172 | + | 0.437595i | \(0.144170\pi\) | ||||
−0.899172 | + | 0.437595i | \(0.855830\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.837722 | −0.117305 | ||||||||
\(52\) | 1.87259 | + | 3.08114i | 0.259681 | + | 0.427277i | ||||
\(53\) | − | 0.837722i | − | 0.115070i | −0.998343 | − | 0.0575350i | \(-0.981676\pi\) | ||
0.998343 | − | 0.0575350i | \(-0.0183241\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.58114 | − | 2.73861i | −0.211289 | − | 0.365963i | ||||
\(57\) | 3.16228i | 0.418854i | ||||||||
\(58\) | −3.74517 | + | 2.16228i | −0.491766 | + | 0.283921i | ||||
\(59\) | −3.00000 | − | 5.19615i | −0.390567 | − | 0.676481i | 0.601958 | − | 0.798528i | \(-0.294388\pi\) |
−0.992524 | + | 0.122047i | \(0.961054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.24342 | + | 3.88571i | 0.287240 | + | 0.497514i | 0.973150 | − | 0.230172i | \(-0.0739289\pi\) |
−0.685910 | + | 0.727686i | \(0.740596\pi\) | |||||||
\(62\) | −2.45754 | − | 1.41886i | −0.312108 | − | 0.180196i | ||||
\(63\) | 2.73861 | + | 1.58114i | 0.345033 | + | 0.199205i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | −0.369274 | ||||||||
\(67\) | −3.46410 | − | 2.00000i | −0.423207 | − | 0.244339i | 0.273241 | − | 0.961946i | \(-0.411904\pi\) |
−0.696449 | + | 0.717607i | \(0.745238\pi\) | |||||||
\(68\) | 0.725489 | + | 0.418861i | 0.0879784 | + | 0.0507944i | ||||
\(69\) | −1.08114 | − | 1.87259i | −0.130154 | − | 0.225433i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.08114 | + | 12.2649i | 0.840377 | + | 1.45557i | 0.889577 | + | 0.456786i | \(0.150999\pi\) |
−0.0492001 | + | 0.998789i | \(0.515667\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | − | 11.3246i | − | 1.32544i | −0.748868 | − | 0.662719i | \(-0.769402\pi\) | ||
0.748868 | − | 0.662719i | \(-0.230598\pi\) | |||||||
\(74\) | −4.24342 | − | 7.34981i | −0.493287 | − | 0.854398i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.58114 | − | 2.73861i | 0.181369 | − | 0.314140i | ||||
\(77\) | 9.48683i | 1.08112i | ||||||||
\(78\) | 1.87259 | + | 3.08114i | 0.212029 | + | 0.348870i | ||||
\(79\) | −2.83772 | −0.319269 | −0.159634 | − | 0.987176i | \(-0.551032\pi\) | ||||
−0.159634 | + | 0.987176i | \(0.551032\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 8.21584 | − | 4.74342i | 0.907288 | − | 0.523823i | ||||
\(83\) | − | 11.6491i | − | 1.27866i | −0.768934 | − | 0.639328i | \(-0.779213\pi\) | ||
0.768934 | − | 0.639328i | \(-0.220787\pi\) | |||||||
\(84\) | −1.58114 | − | 2.73861i | −0.172516 | − | 0.298807i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.16228 | −0.125332 | ||||||||
\(87\) | −3.74517 | + | 2.16228i | −0.401525 | + | 0.231820i | ||||
\(88\) | 2.59808 | + | 1.50000i | 0.276956 | + | 0.159901i | ||||
\(89\) | −0.418861 | + | 0.725489i | −0.0443992 | + | 0.0769017i | −0.887371 | − | 0.461056i | \(-0.847471\pi\) |
0.842972 | + | 0.537958i | \(0.180804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.74342 | − | 5.92164i | 1.02139 | − | 0.620757i | ||||
\(92\) | 2.16228i | 0.225433i | ||||||||
\(93\) | −2.45754 | − | 1.41886i | −0.254835 | − | 0.147129i | ||||
\(94\) | 3.00000 | − | 5.19615i | 0.309426 | − | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 15.0035 | − | 8.66228i | 1.52338 | − | 0.879521i | 0.523758 | − | 0.851867i | \(-0.324530\pi\) |
0.999618 | − | 0.0276537i | \(-0.00880356\pi\) | |||||||
\(98\) | −2.59808 | + | 1.50000i | −0.262445 | + | 0.151523i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.32456 | + | 7.49035i | −0.430309 | + | 0.745318i | −0.996900 | − | 0.0786819i | \(-0.974929\pi\) |
0.566590 | + | 0.824000i | \(0.308262\pi\) | |||||||
\(102\) | 0.725489 | + | 0.418861i | 0.0718341 | + | 0.0414734i | ||||
\(103\) | 5.48683i | 0.540634i | 0.962771 | + | 0.270317i | \(0.0871285\pi\) | ||||
−0.962771 | + | 0.270317i | \(0.912872\pi\) | |||||||
\(104\) | −0.0811388 | − | 3.60464i | −0.00795632 | − | 0.353464i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.418861 | + | 0.725489i | −0.0406834 | + | 0.0704657i | ||||
\(107\) | 5.19615 | + | 3.00000i | 0.502331 | + | 0.290021i | 0.729676 | − | 0.683793i | \(-0.239671\pi\) |
−0.227345 | + | 0.973814i | \(0.573004\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 10.4868 | 1.00446 | 0.502228 | − | 0.864735i | \(-0.332514\pi\) | ||||
0.502228 | + | 0.864735i | \(0.332514\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.24342 | − | 7.34981i | −0.402767 | − | 0.697613i | ||||
\(112\) | 3.16228i | 0.298807i | ||||||||
\(113\) | 8.94133 | − | 5.16228i | 0.841129 | − | 0.485626i | −0.0165186 | − | 0.999864i | \(-0.505258\pi\) |
0.857648 | + | 0.514237i | \(0.171925\pi\) | |||||||
\(114\) | 1.58114 | − | 2.73861i | 0.148087 | − | 0.256495i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.32456 | 0.401525 | ||||||||
\(117\) | 1.87259 | + | 3.08114i | 0.173121 | + | 0.284851i | ||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | 1.32456 | − | 2.29420i | 0.121422 | − | 0.210309i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | − | 4.48683i | − | 0.406219i | ||||||
\(123\) | 8.21584 | − | 4.74342i | 0.740797 | − | 0.427699i | ||||
\(124\) | 1.41886 | + | 2.45754i | 0.127417 | + | 0.220694i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.58114 | − | 2.73861i | −0.140859 | − | 0.243975i | ||||
\(127\) | −17.6016 | − | 10.1623i | −1.56189 | − | 0.901756i | −0.997066 | − | 0.0765432i | \(-0.975612\pi\) |
−0.564822 | − | 0.825213i | \(-0.691055\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −1.16228 | −0.102333 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.3246 | 1.42628 | 0.713142 | − | 0.701020i | \(-0.247272\pi\) | ||||
0.713142 | + | 0.701020i | \(0.247272\pi\) | |||||||
\(132\) | 2.59808 | + | 1.50000i | 0.226134 | + | 0.130558i | ||||
\(133\) | −8.66025 | − | 5.00000i | −0.750939 | − | 0.433555i | ||||
\(134\) | 2.00000 | + | 3.46410i | 0.172774 | + | 0.299253i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.418861 | − | 0.725489i | −0.0359170 | − | 0.0622102i | ||||
\(137\) | 10.3923 | − | 6.00000i | 0.887875 | − | 0.512615i | 0.0146279 | − | 0.999893i | \(-0.495344\pi\) |
0.873247 | + | 0.487278i | \(0.162010\pi\) | |||||||
\(138\) | 2.16228i | 0.184065i | ||||||||
\(139\) | −2.83772 | − | 4.91508i | −0.240692 | − | 0.416892i | 0.720219 | − | 0.693747i | \(-0.244041\pi\) |
−0.960912 | + | 0.276855i | \(0.910708\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | − | 5.19615i | 0.252646 | − | 0.437595i | ||||
\(142\) | − | 14.1623i | − | 1.18847i | ||||||
\(143\) | −5.19615 | + | 9.48683i | −0.434524 | + | 0.793329i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.66228 | + | 9.80735i | −0.468613 | + | 0.811662i | ||||
\(147\) | −2.59808 | + | 1.50000i | −0.214286 | + | 0.123718i | ||||
\(148\) | 8.48683i | 0.697613i | ||||||||
\(149\) | −3.41886 | − | 5.92164i | −0.280084 | − | 0.485120i | 0.691321 | − | 0.722548i | \(-0.257029\pi\) |
−0.971405 | + | 0.237428i | \(0.923696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.81139 | 0.798439 | 0.399220 | − | 0.916855i | \(-0.369281\pi\) | ||||
0.399220 | + | 0.916855i | \(0.369281\pi\) | |||||||
\(152\) | −2.73861 | + | 1.58114i | −0.222131 | + | 0.128247i | ||||
\(153\) | 0.725489 | + | 0.418861i | 0.0586523 | + | 0.0338629i | ||||
\(154\) | 4.74342 | − | 8.21584i | 0.382235 | − | 0.662051i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0811388 | − | 3.60464i | −0.00649631 | − | 0.288602i | ||||
\(157\) | − | 16.1623i | − | 1.28989i | −0.764229 | − | 0.644945i | \(-0.776880\pi\) | ||
0.764229 | − | 0.644945i | \(-0.223120\pi\) | |||||||
\(158\) | 2.45754 | + | 1.41886i | 0.195511 | + | 0.112879i | ||||
\(159\) | −0.418861 | + | 0.725489i | −0.0332179 | + | 0.0575350i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.83772 | 0.538888 | ||||||||
\(162\) | 0.866025 | − | 0.500000i | 0.0680414 | − | 0.0392837i | ||||
\(163\) | 13.6931 | − | 7.90569i | 1.07252 | − | 0.619222i | 0.143654 | − | 0.989628i | \(-0.454115\pi\) |
0.928870 | + | 0.370406i | \(0.120782\pi\) | |||||||
\(164\) | −9.48683 | −0.740797 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.82456 | + | 10.0884i | −0.452073 | + | 0.783014i | ||||
\(167\) | 7.06874 | + | 4.08114i | 0.546996 | + | 0.315808i | 0.747909 | − | 0.663801i | \(-0.231058\pi\) |
−0.200914 | + | 0.979609i | \(0.564391\pi\) | |||||||
\(168\) | 3.16228i | 0.243975i | ||||||||
\(169\) | 12.9868 | − | 0.584952i | 0.998987 | − | 0.0449963i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.58114 | − | 2.73861i | 0.120913 | − | 0.209427i | ||||
\(172\) | 1.00656 | + | 0.581139i | 0.0767496 | + | 0.0443114i | ||||
\(173\) | −1.45098 | + | 0.837722i | −0.110316 | + | 0.0636909i | −0.554143 | − | 0.832422i | \(-0.686954\pi\) |
0.443827 | + | 0.896113i | \(0.353620\pi\) | |||||||
\(174\) | 4.32456 | 0.327844 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | − | 2.59808i | −0.113067 | − | 0.195837i | ||||
\(177\) | 6.00000i | 0.450988i | ||||||||
\(178\) | 0.725489 | − | 0.418861i | 0.0543777 | − | 0.0313950i | ||||
\(179\) | 11.8246 | − | 20.4807i | 0.883809 | − | 1.53080i | 0.0367358 | − | 0.999325i | \(-0.488304\pi\) |
0.847073 | − | 0.531477i | \(-0.178363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8114 | 0.952263 | 0.476131 | − | 0.879374i | \(-0.342039\pi\) | ||||
0.476131 | + | 0.879374i | \(0.342039\pi\) | |||||||
\(182\) | −11.3989 | + | 0.256584i | −0.844940 | + | 0.0190192i | ||||
\(183\) | − | 4.48683i | − | 0.331676i | ||||||
\(184\) | 1.08114 | − | 1.87259i | 0.0797026 | − | 0.138049i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.41886 | + | 2.45754i | 0.104036 | + | 0.180196i | ||||
\(187\) | 2.51317i | 0.183781i | ||||||||
\(188\) | −5.19615 | + | 3.00000i | −0.378968 | + | 0.218797i | ||||
\(189\) | −1.58114 | − | 2.73861i | −0.115011 | − | 0.199205i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.91886 | − | 13.7159i | −0.572989 | − | 0.992446i | −0.996257 | − | 0.0864411i | \(-0.972451\pi\) |
0.423268 | − | 0.906004i | \(-0.360883\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 15.0035 | + | 8.66228i | 1.07998 | + | 0.623524i | 0.930890 | − | 0.365300i | \(-0.119034\pi\) |
0.149086 | + | 0.988824i | \(0.452367\pi\) | |||||||
\(194\) | −17.3246 | −1.24383 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | −5.19615 | − | 3.00000i | −0.370211 | − | 0.213741i | 0.303340 | − | 0.952882i | \(-0.401898\pi\) |
−0.673550 | + | 0.739141i | \(0.735232\pi\) | |||||||
\(198\) | 2.59808 | + | 1.50000i | 0.184637 | + | 0.106600i | ||||
\(199\) | 4.41886 | + | 7.65369i | 0.313245 | + | 0.542556i | 0.979063 | − | 0.203558i | \(-0.0652506\pi\) |
−0.665818 | + | 0.746114i | \(0.731917\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | + | 3.46410i | 0.141069 | + | 0.244339i | ||||
\(202\) | 7.49035 | − | 4.32456i | 0.527019 | − | 0.304275i | ||||
\(203\) | − | 13.6754i | − | 0.959828i | ||||||
\(204\) | −0.418861 | − | 0.725489i | −0.0293261 | − | 0.0507944i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.74342 | − | 4.75174i | 0.191143 | − | 0.331069i | ||||
\(207\) | 2.16228i | 0.150289i | ||||||||
\(208\) | −1.73205 | + | 3.16228i | −0.120096 | + | 0.219265i | ||||
\(209\) | 9.48683 | 0.656218 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.58114 | + | 11.3989i | −0.453064 | + | 0.784730i | −0.998575 | − | 0.0533737i | \(-0.983003\pi\) |
0.545510 | + | 0.838104i | \(0.316336\pi\) | |||||||
\(212\) | 0.725489 | − | 0.418861i | 0.0498268 | − | 0.0287675i | ||||
\(213\) | − | 14.1623i | − | 0.970383i | ||||||
\(214\) | −3.00000 | − | 5.19615i | −0.205076 | − | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 7.77142 | − | 4.48683i | 0.527559 | − | 0.304586i | ||||
\(218\) | −9.08186 | − | 5.24342i | −0.615101 | − | 0.355129i | ||||
\(219\) | −5.66228 | + | 9.80735i | −0.382621 | + | 0.662719i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.58114 | − | 1.56871i | 0.173626 | − | 0.105523i | ||||
\(222\) | 8.48683i | 0.569599i | ||||||||
\(223\) | −22.6344 | − | 13.0680i | −1.51571 | − | 0.875096i | −0.999830 | − | 0.0184358i | \(-0.994131\pi\) |
−0.515881 | − | 0.856660i | \(-0.672535\pi\) | |||||||
\(224\) | 1.58114 | − | 2.73861i | 0.105644 | − | 0.182981i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.3246 | −0.686779 | ||||||||
\(227\) | −19.0298 | + | 10.9868i | −1.26305 | + | 0.729222i | −0.973663 | − | 0.227991i | \(-0.926784\pi\) |
−0.289386 | + | 0.957213i | \(0.593451\pi\) | |||||||
\(228\) | −2.73861 | + | 1.58114i | −0.181369 | + | 0.104713i | ||||
\(229\) | 16.4868 | 1.08948 | 0.544740 | − | 0.838605i | \(-0.316628\pi\) | ||||
0.544740 | + | 0.838605i | \(0.316628\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.74342 | − | 8.21584i | 0.312094 | − | 0.540562i | ||||
\(232\) | −3.74517 | − | 2.16228i | −0.245883 | − | 0.141960i | ||||
\(233\) | 13.6754i | 0.895908i | 0.894057 | + | 0.447954i | \(0.147847\pi\) | ||||
−0.894057 | + | 0.447954i | \(0.852153\pi\) | |||||||
\(234\) | −0.0811388 | − | 3.60464i | −0.00530421 | − | 0.235643i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.00000 | − | 5.19615i | 0.195283 | − | 0.338241i | ||||
\(237\) | 2.45754 | + | 1.41886i | 0.159634 | + | 0.0921649i | ||||
\(238\) | −2.29420 | + | 1.32456i | −0.148711 | + | 0.0858582i | ||||
\(239\) | −18.4868 | −1.19581 | −0.597907 | − | 0.801566i | \(-0.704001\pi\) | ||||
−0.597907 | + | 0.801566i | \(0.704001\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.00000 | − | 6.92820i | −0.257663 | − | 0.446285i | 0.707953 | − | 0.706260i | \(-0.249619\pi\) |
−0.965615 | + | 0.259975i | \(0.916286\pi\) | |||||||
\(242\) | − | 2.00000i | − | 0.128565i | ||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −2.24342 | + | 3.88571i | −0.143620 | + | 0.248757i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.48683 | −0.604858 | ||||||||
\(247\) | −5.92164 | − | 9.74342i | −0.376785 | − | 0.619959i | ||||
\(248\) | − | 2.83772i | − | 0.180196i | ||||||
\(249\) | −5.82456 | + | 10.0884i | −0.369116 | + | 0.639328i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.50000 | − | 12.9904i | −0.473396 | − | 0.819946i | 0.526140 | − | 0.850398i | \(-0.323639\pi\) |
−0.999536 | + | 0.0304521i | \(0.990305\pi\) | |||||||
\(252\) | 3.16228i | 0.199205i | ||||||||
\(253\) | −5.61776 | + | 3.24342i | −0.353186 | + | 0.203912i | ||||
\(254\) | 10.1623 | + | 17.6016i | 0.637638 | + | 1.10442i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −22.3533 | − | 12.9057i | −1.39436 | − | 0.805035i | −0.400567 | − | 0.916267i | \(-0.631187\pi\) |
−0.993794 | + | 0.111232i | \(0.964520\pi\) | |||||||
\(258\) | 1.00656 | + | 0.581139i | 0.0626658 | + | 0.0361801i | ||||
\(259\) | 26.8377 | 1.66761 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.32456 | 0.267683 | ||||||||
\(262\) | −14.1375 | − | 8.16228i | −0.873416 | − | 0.504267i | ||||
\(263\) | 0.421610 | + | 0.243416i | 0.0259976 | + | 0.0150097i | 0.512942 | − | 0.858423i | \(-0.328555\pi\) |
−0.486945 | + | 0.873433i | \(0.661889\pi\) | |||||||
\(264\) | −1.50000 | − | 2.59808i | −0.0923186 | − | 0.159901i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.00000 | + | 8.66025i | 0.306570 | + | 0.530994i | ||||
\(267\) | 0.725489 | − | 0.418861i | 0.0443992 | − | 0.0256339i | ||||
\(268\) | − | 4.00000i | − | 0.244339i | ||||||
\(269\) | −6.41886 | − | 11.1178i | −0.391365 | − | 0.677864i | 0.601265 | − | 0.799050i | \(-0.294664\pi\) |
−0.992630 | + | 0.121186i | \(0.961330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.162278 | + | 0.281073i | −0.00985767 | + | 0.0170740i | −0.870912 | − | 0.491439i | \(-0.836471\pi\) |
0.861054 | + | 0.508513i | \(0.169805\pi\) | |||||||
\(272\) | 0.837722i | 0.0507944i | ||||||||
\(273\) | −11.3989 | + | 0.256584i | −0.689891 | + | 0.0155291i | ||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.08114 | − | 1.87259i | 0.0650769 | − | 0.112717i | ||||
\(277\) | 7.63089 | − | 4.40569i | 0.458496 | − | 0.264713i | −0.252916 | − | 0.967488i | \(-0.581390\pi\) |
0.711411 | + | 0.702776i | \(0.248056\pi\) | |||||||
\(278\) | 5.67544i | 0.340391i | ||||||||
\(279\) | 1.41886 | + | 2.45754i | 0.0849450 | + | 0.147129i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.4868 | −1.28180 | −0.640898 | − | 0.767626i | \(-0.721438\pi\) | ||||
−0.640898 | + | 0.767626i | \(0.721438\pi\) | |||||||
\(282\) | −5.19615 | + | 3.00000i | −0.309426 | + | 0.178647i | ||||
\(283\) | 16.8761 | + | 9.74342i | 1.00318 | + | 0.579186i | 0.909187 | − | 0.416387i | \(-0.136704\pi\) |
0.0939921 | + | 0.995573i | \(0.470037\pi\) | |||||||
\(284\) | −7.08114 | + | 12.2649i | −0.420188 | + | 0.727787i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.24342 | − | 5.61776i | 0.546575 | − | 0.332185i | ||||
\(287\) | 30.0000i | 1.77084i | ||||||||
\(288\) | 0.866025 | + | 0.500000i | 0.0510310 | + | 0.0294628i | ||||
\(289\) | −8.14911 | + | 14.1147i | −0.479359 | + | 0.830275i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.3246 | −1.01558 | ||||||||
\(292\) | 9.80735 | − | 5.66228i | 0.573932 | − | 0.331360i | ||||
\(293\) | 18.6081 | − | 10.7434i | 1.08710 | − | 0.627637i | 0.154297 | − | 0.988025i | \(-0.450689\pi\) |
0.932803 | + | 0.360387i | \(0.117356\pi\) | |||||||
\(294\) | 3.00000 | 0.174964 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.24342 | − | 7.34981i | 0.246644 | − | 0.427199i | ||||
\(297\) | 2.59808 | + | 1.50000i | 0.150756 | + | 0.0870388i | ||||
\(298\) | 6.83772i | 0.396099i | ||||||||
\(299\) | 6.83772 | + | 3.74517i | 0.395436 | + | 0.216589i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.83772 | − | 3.18303i | 0.105925 | − | 0.183467i | ||||
\(302\) | −8.49691 | − | 4.90569i | −0.488942 | − | 0.282291i | ||||
\(303\) | 7.49035 | − | 4.32456i | 0.430309 | − | 0.248439i | ||||
\(304\) | 3.16228 | 0.181369 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.418861 | − | 0.725489i | −0.0239447 | − | 0.0414734i | ||||
\(307\) | − | 16.6491i | − | 0.950215i | −0.879928 | − | 0.475107i | \(-0.842409\pi\) | ||
0.879928 | − | 0.475107i | \(-0.157591\pi\) | |||||||
\(308\) | −8.21584 | + | 4.74342i | −0.468141 | + | 0.270281i | ||||
\(309\) | 2.74342 | − | 4.75174i | 0.156068 | − | 0.270317i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.48683 | −0.367835 | −0.183917 | − | 0.982942i | \(-0.558878\pi\) | ||||
−0.183917 | + | 0.982942i | \(0.558878\pi\) | |||||||
\(312\) | −1.73205 | + | 3.16228i | −0.0980581 | + | 0.179029i | ||||
\(313\) | 7.64911i | 0.432353i | 0.976354 | + | 0.216177i | \(0.0693587\pi\) | ||||
−0.976354 | + | 0.216177i | \(0.930641\pi\) | |||||||
\(314\) | −8.08114 | + | 13.9969i | −0.456045 | + | 0.789893i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.41886 | − | 2.45754i | −0.0798172 | − | 0.138247i | ||||
\(317\) | 31.8114i | 1.78671i | 0.449356 | + | 0.893353i | \(0.351653\pi\) | ||||
−0.449356 | + | 0.893353i | \(0.648347\pi\) | |||||||
\(318\) | 0.725489 | − | 0.418861i | 0.0406834 | − | 0.0234886i | ||||
\(319\) | 6.48683 | + | 11.2355i | 0.363193 | + | 0.629069i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.00000 | − | 5.19615i | −0.167444 | − | 0.290021i | ||||
\(322\) | −5.92164 | − | 3.41886i | −0.330000 | − | 0.190526i | ||||
\(323\) | −2.29420 | − | 1.32456i | −0.127653 | − | 0.0737002i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.8114 | −0.875712 | ||||||||
\(327\) | −9.08186 | − | 5.24342i | −0.502228 | − | 0.289962i | ||||
\(328\) | 8.21584 | + | 4.74342i | 0.453644 | + | 0.261911i | ||||
\(329\) | 9.48683 | + | 16.4317i | 0.523026 | + | 0.905908i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.58114 | + | 13.1309i | 0.416697 | + | 0.721741i | 0.995605 | − | 0.0936524i | \(-0.0298543\pi\) |
−0.578908 | + | 0.815393i | \(0.696521\pi\) | |||||||
\(332\) | 10.0884 | − | 5.82456i | 0.553674 | − | 0.319664i | ||||
\(333\) | 8.48683i | 0.465076i | ||||||||
\(334\) | −4.08114 | − | 7.06874i | −0.223310 | − | 0.386784i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.58114 | − | 2.73861i | 0.0862582 | − | 0.149404i | ||||
\(337\) | 4.00000i | 0.217894i | 0.994048 | + | 0.108947i | \(0.0347479\pi\) | ||||
−0.994048 | + | 0.108947i | \(0.965252\pi\) | |||||||
\(338\) | −11.5394 | − | 5.98683i | −0.627661 | − | 0.325641i | ||||
\(339\) | −10.3246 | −0.560753 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.25658 | + | 7.37262i | −0.230507 | + | 0.399250i | ||||
\(342\) | −2.73861 | + | 1.58114i | −0.148087 | + | 0.0854982i | ||||
\(343\) | 12.6491i | 0.682988i | ||||||||
\(344\) | −0.581139 | − | 1.00656i | −0.0313329 | − | 0.0542702i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.67544 | 0.0900725 | ||||||||
\(347\) | −1.14710 | + | 0.662278i | −0.0615795 | + | 0.0355529i | −0.530474 | − | 0.847701i | \(-0.677986\pi\) |
0.468894 | + | 0.883254i | \(0.344653\pi\) | |||||||
\(348\) | −3.74517 | − | 2.16228i | −0.200762 | − | 0.115910i | ||||
\(349\) | −17.7302 | + | 30.7097i | −0.949078 | + | 1.64385i | −0.201707 | + | 0.979446i | \(0.564649\pi\) |
−0.747372 | + | 0.664406i | \(0.768685\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.0811388 | − | 3.60464i | −0.00433087 | − | 0.192401i | ||||
\(352\) | 3.00000i | 0.159901i | ||||||||
\(353\) | 17.1572 | + | 9.90569i | 0.913184 | + | 0.527227i | 0.881454 | − | 0.472270i | \(-0.156565\pi\) |
0.0317296 | + | 0.999496i | \(0.489898\pi\) | |||||||
\(354\) | 3.00000 | − | 5.19615i | 0.159448 | − | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.837722 | −0.0443992 | ||||||||
\(357\) | −2.29420 | + | 1.32456i | −0.121422 | + | 0.0701029i | ||||
\(358\) | −20.4807 | + | 11.8246i | −1.08244 | + | 0.624947i | ||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.50000 | − | 7.79423i | 0.236842 | − | 0.410223i | ||||
\(362\) | −11.0950 | − | 6.40569i | −0.583140 | − | 0.336676i | ||||
\(363\) | − | 2.00000i | − | 0.104973i | ||||||
\(364\) | 10.0000 | + | 5.47723i | 0.524142 | + | 0.287085i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.24342 | + | 3.88571i | −0.117265 | + | 0.203109i | ||||
\(367\) | −16.1506 | − | 9.32456i | −0.843055 | − | 0.486738i | 0.0152467 | − | 0.999884i | \(-0.495147\pi\) |
−0.858301 | + | 0.513146i | \(0.828480\pi\) | |||||||
\(368\) | −1.87259 | + | 1.08114i | −0.0976154 | + | 0.0563583i | ||||
\(369\) | −9.48683 | −0.493865 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.32456 | − | 2.29420i | −0.0687675 | − | 0.119109i | ||||
\(372\) | − | 2.83772i | − | 0.147129i | ||||||
\(373\) | −9.08186 | + | 5.24342i | −0.470241 | + | 0.271494i | −0.716341 | − | 0.697751i | \(-0.754184\pi\) |
0.246100 | + | 0.969245i | \(0.420851\pi\) | |||||||
\(374\) | 1.25658 | − | 2.17647i | 0.0649764 | − | 0.112542i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | 7.49035 | − | 13.6754i | 0.385773 | − | 0.704321i | ||||
\(378\) | 3.16228i | 0.162650i | ||||||||
\(379\) | 1.00000 | − | 1.73205i | 0.0513665 | − | 0.0889695i | −0.839199 | − | 0.543825i | \(-0.816976\pi\) |
0.890565 | + | 0.454855i | \(0.150309\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.1623 | + | 17.6016i | 0.520629 | + | 0.901756i | ||||
\(382\) | 15.8377i | 0.810328i | ||||||||
\(383\) | −1.87259 | + | 1.08114i | −0.0956847 | + | 0.0552436i | −0.547079 | − | 0.837081i | \(-0.684260\pi\) |
0.451394 | + | 0.892325i | \(0.350927\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.66228 | − | 15.0035i | −0.440898 | − | 0.763658i | ||||
\(387\) | 1.00656 | + | 0.581139i | 0.0511664 | + | 0.0295409i | ||||
\(388\) | 15.0035 | + | 8.66228i | 0.761688 | + | 0.439761i | ||||
\(389\) | 28.3246 | 1.43611 | 0.718056 | − | 0.695985i | \(-0.245032\pi\) | ||||
0.718056 | + | 0.695985i | \(0.245032\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.81139 | 0.0916058 | ||||||||
\(392\) | −2.59808 | − | 1.50000i | −0.131223 | − | 0.0757614i | ||||
\(393\) | −14.1375 | − | 8.16228i | −0.713142 | − | 0.411732i | ||||
\(394\) | 3.00000 | + | 5.19615i | 0.151138 | + | 0.261778i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.50000 | − | 2.59808i | −0.0753778 | − | 0.130558i | ||||
\(397\) | 10.1112 | − | 5.83772i | 0.507468 | − | 0.292987i | −0.224324 | − | 0.974515i | \(-0.572017\pi\) |
0.731792 | + | 0.681528i | \(0.238684\pi\) | |||||||
\(398\) | − | 8.83772i | − | 0.442995i | ||||||
\(399\) | 5.00000 | + | 8.66025i | 0.250313 | + | 0.433555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.16228 | + | 14.1375i | −0.407605 | + | 0.705992i | −0.994621 | − | 0.103583i | \(-0.966969\pi\) |
0.587016 | + | 0.809575i | \(0.300303\pi\) | |||||||
\(402\) | − | 4.00000i | − | 0.199502i | ||||||
\(403\) | 10.2290 | − | 0.230249i | 0.509541 | − | 0.0114695i | ||||
\(404\) | −8.64911 | −0.430309 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.83772 | + | 11.8433i | −0.339350 | + | 0.587772i | ||||
\(407\) | −22.0494 | + | 12.7302i | −1.09295 | + | 0.631015i | ||||
\(408\) | 0.837722i | 0.0414734i | ||||||||
\(409\) | 15.1623 | + | 26.2618i | 0.749726 | + | 1.29856i | 0.947954 | + | 0.318408i | \(0.103148\pi\) |
−0.198227 | + | 0.980156i | \(0.563518\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.0000 | −0.591916 | ||||||||
\(412\) | −4.75174 | + | 2.74342i | −0.234101 | + | 0.135158i | ||||
\(413\) | −16.4317 | − | 9.48683i | −0.808550 | − | 0.466817i | ||||
\(414\) | 1.08114 | − | 1.87259i | 0.0531351 | − | 0.0920326i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.08114 | − | 1.87259i | 0.151065 | − | 0.0918112i | ||||
\(417\) | 5.67544i | 0.277928i | ||||||||
\(418\) | −8.21584 | − | 4.74342i | −0.401850 | − | 0.232008i | ||||
\(419\) | 4.50000 | − | 7.79423i | 0.219839 | − | 0.380773i | −0.734919 | − | 0.678155i | \(-0.762780\pi\) |
0.954759 | + | 0.297382i | \(0.0961133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.1623 | 1.37255 | 0.686273 | − | 0.727344i | \(-0.259246\pi\) | ||||
0.686273 | + | 0.727344i | \(0.259246\pi\) | |||||||
\(422\) | 11.3989 | − | 6.58114i | 0.554888 | − | 0.320365i | ||||
\(423\) | −5.19615 | + | 3.00000i | −0.252646 | + | 0.145865i | ||||
\(424\) | −0.837722 | −0.0406834 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.08114 | + | 12.2649i | −0.343082 | + | 0.594236i | ||||
\(427\) | 12.2877 | + | 7.09431i | 0.594643 | + | 0.343318i | ||||
\(428\) | 6.00000i | 0.290021i | ||||||||
\(429\) | 9.24342 | − | 5.61776i | 0.446276 | − | 0.271228i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.2434 | − | 21.2062i | 0.589745 | − | 1.02147i | −0.404521 | − | 0.914529i | \(-0.632562\pi\) |
0.994266 | − | 0.106939i | \(-0.0341049\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | −29.9842 | + | 17.3114i | −1.44095 | + | 0.831932i | −0.997913 | − | 0.0645717i | \(-0.979432\pi\) |
−0.443036 | + | 0.896504i | \(0.646099\pi\) | |||||||
\(434\) | −8.97367 | −0.430750 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.24342 | + | 9.08186i | 0.251114 | + | 0.434942i | ||||
\(437\) | − | 6.83772i | − | 0.327093i | ||||||
\(438\) | 9.80735 | − | 5.66228i | 0.468613 | − | 0.270554i | ||||
\(439\) | −18.3246 | + | 31.7391i | −0.874583 | + | 1.51482i | −0.0173773 | + | 0.999849i | \(0.505532\pi\) |
−0.857206 | + | 0.514974i | \(0.827802\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | −3.01969 | + | 0.0679718i | −0.143632 | + | 0.00323309i | ||||
\(443\) | − | 9.00000i | − | 0.427603i | −0.976877 | − | 0.213801i | \(-0.931415\pi\) | ||
0.976877 | − | 0.213801i | \(-0.0685846\pi\) | |||||||
\(444\) | 4.24342 | − | 7.34981i | 0.201384 | − | 0.348807i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.0680 | + | 22.6344i | 0.618786 | + | 1.07177i | ||||
\(447\) | 6.83772i | 0.323413i | ||||||||
\(448\) | −2.73861 | + | 1.58114i | −0.129387 | + | 0.0747018i | ||||
\(449\) | 1.25658 | + | 2.17647i | 0.0593018 | + | 0.102714i | 0.894152 | − | 0.447763i | \(-0.147779\pi\) |
−0.834850 | + | 0.550477i | \(0.814446\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.2302 | − | 24.6475i | −0.670076 | − | 1.16061i | ||||
\(452\) | 8.94133 | + | 5.16228i | 0.420565 | + | 0.242813i | ||||
\(453\) | −8.49691 | − | 4.90569i | −0.399220 | − | 0.230490i | ||||
\(454\) | 21.9737 | 1.03128 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.16228 | 0.148087 | ||||||||
\(457\) | −8.96413 | − | 5.17544i | −0.419324 | − | 0.242097i | 0.275464 | − | 0.961311i | \(-0.411169\pi\) |
−0.694788 | + | 0.719214i | \(0.744502\pi\) | |||||||
\(458\) | −14.2780 | − | 8.24342i | −0.667168 | − | 0.385190i | ||||
\(459\) | −0.418861 | − | 0.725489i | −0.0195508 | − | 0.0338629i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.58114 | + | 14.8630i | 0.399663 | + | 0.692237i | 0.993684 | − | 0.112212i | \(-0.0357937\pi\) |
−0.594021 | + | 0.804450i | \(0.702460\pi\) | |||||||
\(462\) | −8.21584 | + | 4.74342i | −0.382235 | + | 0.220684i | ||||
\(463\) | 4.51317i | 0.209745i | 0.994486 | + | 0.104872i | \(0.0334434\pi\) | ||||
−0.994486 | + | 0.104872i | \(0.966557\pi\) | |||||||
\(464\) | 2.16228 | + | 3.74517i | 0.100381 | + | 0.173865i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.83772 | − | 11.8433i | 0.316751 | − | 0.548629i | ||||
\(467\) | 3.00000i | 0.138823i | 0.997588 | + | 0.0694117i | \(0.0221122\pi\) | ||||
−0.997588 | + | 0.0694117i | \(0.977888\pi\) | |||||||
\(468\) | −1.73205 | + | 3.16228i | −0.0800641 | + | 0.146176i | ||||
\(469\) | −12.6491 | −0.584082 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.08114 | + | 13.9969i | −0.372359 | + | 0.644945i | ||||
\(472\) | −5.19615 | + | 3.00000i | −0.239172 | + | 0.138086i | ||||
\(473\) | 3.48683i | 0.160325i | ||||||||
\(474\) | −1.41886 | − | 2.45754i | −0.0651705 | − | 0.112879i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.64911 | 0.121422 | ||||||||
\(477\) | 0.725489 | − | 0.418861i | 0.0332179 | − | 0.0191783i | ||||
\(478\) | 16.0101 | + | 9.24342i | 0.732283 | + | 0.422784i | ||||
\(479\) | −6.83772 | + | 11.8433i | −0.312424 | + | 0.541133i | −0.978886 | − | 0.204405i | \(-0.934474\pi\) |
0.666463 | + | 0.745538i | \(0.267807\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.8377 | + | 14.6996i | 1.22369 | + | 0.670245i | ||||
\(482\) | 8.00000i | 0.364390i | ||||||||
\(483\) | −5.92164 | − | 3.41886i | −0.269444 | − | 0.155564i | ||||
\(484\) | −1.00000 | + | 1.73205i | −0.0454545 | + | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 2.73861 | − | 1.58114i | 0.124098 | − | 0.0716482i | −0.436666 | − | 0.899624i | \(-0.643841\pi\) |
0.560764 | + | 0.827976i | \(0.310507\pi\) | |||||||
\(488\) | 3.88571 | − | 2.24342i | 0.175898 | − | 0.101555i | ||||
\(489\) | −15.8114 | −0.715016 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.9868 | − | 19.0298i | 0.495829 | − | 0.858801i | −0.504160 | − | 0.863611i | \(-0.668198\pi\) |
0.999988 | + | 0.00480977i | \(0.00153100\pi\) | |||||||
\(492\) | 8.21584 | + | 4.74342i | 0.370399 | + | 0.213850i | ||||
\(493\) | − | 3.62278i | − | 0.163162i | ||||||
\(494\) | 0.256584 | + | 11.3989i | 0.0115442 | + | 0.512859i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.41886 | + | 2.45754i | −0.0637087 | + | 0.110347i | ||||
\(497\) | 38.7850 | + | 22.3925i | 1.73974 | + | 1.00444i | ||||
\(498\) | 10.0884 | − | 5.82456i | 0.452073 | − | 0.261005i | ||||
\(499\) | −39.8114 | −1.78220 | −0.891101 | − | 0.453805i | \(-0.850066\pi\) | ||||
−0.891101 | + | 0.453805i | \(0.850066\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.08114 | − | 7.06874i | −0.182332 | − | 0.315808i | ||||
\(502\) | 15.0000i | 0.669483i | ||||||||
\(503\) | −14.5591 | + | 8.40569i | −0.649158 | + | 0.374791i | −0.788133 | − | 0.615504i | \(-0.788952\pi\) |
0.138976 | + | 0.990296i | \(0.455619\pi\) | |||||||
\(504\) | 1.58114 | − | 2.73861i | 0.0704295 | − | 0.121988i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.48683 | 0.288375 | ||||||||
\(507\) | −11.5394 | − | 5.98683i | −0.512483 | − | 0.265885i | ||||
\(508\) | − | 20.3246i | − | 0.901756i | ||||||
\(509\) | −13.3925 | + | 23.1965i | −0.593613 | + | 1.02817i | 0.400128 | + | 0.916459i | \(0.368966\pi\) |
−0.993741 | + | 0.111709i | \(0.964368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.9057 | − | 31.0136i | −0.792101 | − | 1.37196i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −2.73861 | + | 1.58114i | −0.120913 | + | 0.0698090i | ||||
\(514\) | 12.9057 | + | 22.3533i | 0.569246 | + | 0.985963i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.581139 | − | 1.00656i | −0.0255832 | − | 0.0443114i | ||||
\(517\) | −15.5885 | − | 9.00000i | −0.685580 | − | 0.395820i | ||||
\(518\) | −23.2421 | − | 13.4189i | −1.02120 | − | 0.589591i | ||||
\(519\) | 1.67544 | 0.0735439 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.6491 | −0.904654 | −0.452327 | − | 0.891852i | \(-0.649406\pi\) | ||||
−0.452327 | + | 0.891852i | \(0.649406\pi\) | |||||||
\(522\) | −3.74517 | − | 2.16228i | −0.163922 | − | 0.0946403i | ||||
\(523\) | −28.5560 | − | 16.4868i | −1.24867 | − | 0.720919i | −0.277824 | − | 0.960632i | \(-0.589613\pi\) |
−0.970844 | + | 0.239713i | \(0.922947\pi\) | |||||||
\(524\) | 8.16228 | + | 14.1375i | 0.356571 | + | 0.617599i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.243416 | − | 0.421610i | −0.0106135 | − | 0.0183831i | ||||
\(527\) | 2.05874 | − | 1.18861i | 0.0896799 | − | 0.0517767i | ||||
\(528\) | 3.00000i | 0.130558i | ||||||||
\(529\) | −9.16228 | − | 15.8695i | −0.398360 | − | 0.689980i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.00000 | − | 5.19615i | 0.130189 | − | 0.225494i | ||||
\(532\) | − | 10.0000i | − | 0.433555i | ||||||
\(533\) | −16.4317 | + | 30.0000i | −0.711735 | + | 1.29944i | ||||
\(534\) | −0.837722 | −0.0362518 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.00000 | + | 3.46410i | −0.0863868 | + | 0.149626i | ||||
\(537\) | −20.4807 | + | 11.8246i | −0.883809 | + | 0.510267i | ||||
\(538\) | 12.8377i | 0.553474i | ||||||||
\(539\) | 4.50000 | + | 7.79423i | 0.193829 | + | 0.335721i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.8114 | 1.32469 | 0.662343 | − | 0.749201i | \(-0.269562\pi\) | ||||
0.662343 | + | 0.749201i | \(0.269562\pi\) | |||||||
\(542\) | 0.281073 | − | 0.162278i | 0.0120731 | − | 0.00697042i | ||||
\(543\) | −11.0950 | − | 6.40569i | −0.476131 | − | 0.274895i | ||||
\(544\) | 0.418861 | − | 0.725489i | 0.0179585 | − | 0.0311051i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.0000 | + | 5.47723i | 0.427960 | + | 0.234404i | ||||
\(547\) | − | 14.1359i | − | 0.604409i | −0.953243 | − | 0.302205i | \(-0.902277\pi\) | ||
0.953243 | − | 0.302205i | \(-0.0977226\pi\) | |||||||
\(548\) | 10.3923 | + | 6.00000i | 0.443937 | + | 0.256307i | ||||
\(549\) | −2.24342 | + | 3.88571i | −0.0957467 | + | 0.165838i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.6754 | −0.582594 | ||||||||
\(552\) | −1.87259 | + | 1.08114i | −0.0797026 | + | 0.0460163i | ||||
\(553\) | −7.77142 | + | 4.48683i | −0.330475 | + | 0.190800i | ||||
\(554\) | −8.81139 | −0.374360 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.83772 | − | 4.91508i | 0.120346 | − | 0.208446i | ||||
\(557\) | 16.4317 | + | 9.48683i | 0.696232 | + | 0.401970i | 0.805943 | − | 0.591994i | \(-0.201659\pi\) |
−0.109710 | + | 0.993964i | \(0.534992\pi\) | |||||||
\(558\) | − | 2.83772i | − | 0.120130i | ||||||
\(559\) | 3.58114 | − | 2.17647i | 0.151466 | − | 0.0920547i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.25658 | − | 2.17647i | 0.0530530 | − | 0.0918905i | ||||
\(562\) | 18.6081 | + | 10.7434i | 0.784937 | + | 0.453184i | ||||
\(563\) | 29.4221 | − | 16.9868i | 1.23999 | − | 0.715910i | 0.270899 | − | 0.962608i | \(-0.412679\pi\) |
0.969092 | + | 0.246698i | \(0.0793456\pi\) | |||||||
\(564\) | 6.00000 | 0.252646 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.74342 | − | 16.8761i | −0.409546 | − | 0.709355i | ||||
\(567\) | 3.16228i | 0.132803i | ||||||||
\(568\) | 12.2649 | − | 7.08114i | 0.514623 | − | 0.297118i | ||||
\(569\) | −3.48683 | + | 6.03937i | −0.146176 | + | 0.253184i | −0.929811 | − | 0.368038i | \(-0.880030\pi\) |
0.783635 | + | 0.621221i | \(0.213363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.3246 | −1.35274 | −0.676370 | − | 0.736562i | \(-0.736448\pi\) | ||||
−0.676370 | + | 0.736562i | \(0.736448\pi\) | |||||||
\(572\) | −10.8139 | + | 0.243416i | −0.452152 | + | 0.0101778i | ||||
\(573\) | 15.8377i | 0.661630i | ||||||||
\(574\) | 15.0000 | − | 25.9808i | 0.626088 | − | 1.08442i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 43.0000i | 1.79011i | 0.445952 | + | 0.895057i | \(0.352865\pi\) | ||||
−0.445952 | + | 0.895057i | \(0.647135\pi\) | |||||||
\(578\) | 14.1147 | − | 8.14911i | 0.587093 | − | 0.338958i | ||||
\(579\) | −8.66228 | − | 15.0035i | −0.359992 | − | 0.623524i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.4189 | − | 31.9024i | −0.764143 | − | 1.32353i | ||||
\(582\) | 15.0035 | + | 8.66228i | 0.621915 | + | 0.359063i | ||||
\(583\) | 2.17647 | + | 1.25658i | 0.0901400 | + | 0.0520424i | ||||
\(584\) | −11.3246 | −0.468613 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.4868 | −0.887613 | ||||||||
\(587\) | −18.1865 | − | 10.5000i | −0.750639 | − | 0.433381i | 0.0752860 | − | 0.997162i | \(-0.476013\pi\) |
−0.825925 | + | 0.563781i | \(0.809346\pi\) | |||||||
\(588\) | −2.59808 | − | 1.50000i | −0.107143 | − | 0.0618590i | ||||
\(589\) | −4.48683 | − | 7.77142i | −0.184877 | − | 0.320216i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | + | 5.19615i | 0.123404 | + | 0.213741i | ||||
\(592\) | −7.34981 | + | 4.24342i | −0.302075 | + | 0.174403i | ||||
\(593\) | − | 5.16228i | − | 0.211989i | −0.994367 | − | 0.105995i | \(-0.966197\pi\) | ||
0.994367 | − | 0.105995i | \(-0.0338026\pi\) | |||||||
\(594\) | −1.50000 | − | 2.59808i | −0.0615457 | − | 0.106600i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.41886 | − | 5.92164i | 0.140042 | − | 0.242560i | ||||
\(597\) | − | 8.83772i | − | 0.361704i | ||||||
\(598\) | −4.04905 | − | 6.66228i | −0.165578 | − | 0.272441i | ||||
\(599\) | −1.18861 | −0.0485654 | −0.0242827 | − | 0.999705i | \(-0.507730\pi\) | ||||
−0.0242827 | + | 0.999705i | \(0.507730\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.6491 | + | 37.4974i | −0.883086 | + | 1.52955i | −0.0351935 | + | 0.999381i | \(0.511205\pi\) |
−0.847892 | + | 0.530169i | \(0.822129\pi\) | |||||||
\(602\) | −3.18303 | + | 1.83772i | −0.129731 | + | 0.0749000i | ||||
\(603\) | − | 4.00000i | − | 0.162893i | ||||||
\(604\) | 4.90569 | + | 8.49691i | 0.199610 | + | 0.345734i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.64911 | −0.351346 | ||||||||
\(607\) | −31.4580 | + | 18.1623i | −1.27684 | + | 0.737184i | −0.976266 | − | 0.216574i | \(-0.930512\pi\) |
−0.300574 | + | 0.953758i | \(0.597178\pi\) | |||||||
\(608\) | −2.73861 | − | 1.58114i | −0.111065 | − | 0.0641236i | ||||
\(609\) | −6.83772 | + | 11.8433i | −0.277078 | + | 0.479914i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.486833 | + | 21.6278i | 0.0196952 | + | 0.874968i | ||||
\(612\) | 0.837722i | 0.0338629i | ||||||||
\(613\) | −36.6541 | − | 21.1623i | −1.48045 | − | 0.854736i | −0.480692 | − | 0.876889i | \(-0.659615\pi\) |
−0.999755 | + | 0.0221531i | \(0.992948\pi\) | |||||||
\(614\) | −8.32456 | + | 14.4186i | −0.335952 | + | 0.581885i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.48683 | 0.382235 | ||||||||
\(617\) | 40.9615 | − | 23.6491i | 1.64905 | − | 0.952077i | 0.671594 | − | 0.740919i | \(-0.265610\pi\) |
0.977452 | − | 0.211158i | \(-0.0677236\pi\) | |||||||
\(618\) | −4.75174 | + | 2.74342i | −0.191143 | + | 0.110356i | ||||
\(619\) | −8.00000 | −0.321547 | −0.160774 | − | 0.986991i | \(-0.551399\pi\) | ||||
−0.160774 | + | 0.986991i | \(0.551399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.08114 | − | 1.87259i | 0.0433846 | − | 0.0751443i | ||||
\(622\) | 5.61776 | + | 3.24342i | 0.225252 | + | 0.130049i | ||||
\(623\) | 2.64911i | 0.106134i | ||||||||
\(624\) | 3.08114 | − | 1.87259i | 0.123344 | − | 0.0749635i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.82456 | − | 6.62432i | 0.152860 | − | 0.264761i | ||||
\(627\) | −8.21584 | − | 4.74342i | −0.328109 | − | 0.189434i | ||||
\(628\) | 13.9969 | − | 8.08114i | 0.558539 | − | 0.322473i | ||||
\(629\) | 7.10961 | 0.283479 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.64911 | + | 13.2486i | 0.304506 | + | 0.527420i | 0.977151 | − | 0.212545i | \(-0.0681752\pi\) |
−0.672645 | + | 0.739965i | \(0.734842\pi\) | |||||||
\(632\) | 2.83772i | 0.112879i | ||||||||
\(633\) | 11.3989 | − | 6.58114i | 0.453064 | − | 0.261577i | ||||
\(634\) | 15.9057 | − | 27.5495i | 0.631696 | − | 1.09413i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.837722 | −0.0332179 | ||||||||
\(637\) | 5.19615 | − | 9.48683i | 0.205879 | − | 0.375882i | ||||
\(638\) | − | 12.9737i | − | 0.513632i | ||||||
\(639\) | −7.08114 | + | 12.2649i | −0.280126 | + | 0.485192i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.9737 | − | 22.4710i | −0.512429 | − | 0.887553i | −0.999896 | − | 0.0144117i | \(-0.995412\pi\) |
0.487467 | − | 0.873141i | \(-0.337921\pi\) | |||||||
\(642\) | 6.00000i | 0.236801i | ||||||||
\(643\) | −10.1112 | + | 5.83772i | −0.398748 | + | 0.230217i | −0.685944 | − | 0.727655i | \(-0.740610\pi\) |
0.287196 | + | 0.957872i | \(0.407277\pi\) | |||||||
\(644\) | 3.41886 | + | 5.92164i | 0.134722 | + | 0.233345i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.32456 | + | 2.29420i | 0.0521139 | + | 0.0902640i | ||||
\(647\) | −20.3630 | − | 11.7566i | −0.800552 | − | 0.462199i | 0.0431121 | − | 0.999070i | \(-0.486273\pi\) |
−0.843664 | + | 0.536871i | \(0.819606\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | 18.0000 | 0.706562 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.97367 | −0.351706 | ||||||||
\(652\) | 13.6931 | + | 7.90569i | 0.536262 | + | 0.309611i | ||||
\(653\) | 8.21584 | + | 4.74342i | 0.321511 | + | 0.185624i | 0.652066 | − | 0.758162i | \(-0.273903\pi\) |
−0.330555 | + | 0.943787i | \(0.607236\pi\) | |||||||
\(654\) | 5.24342 | + | 9.08186i | 0.205034 | + | 0.355129i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.74342 | − | 8.21584i | −0.185199 | − | 0.320775i | ||||
\(657\) | 9.80735 | − | 5.66228i | 0.382621 | − | 0.220906i | ||||
\(658\) | − | 18.9737i | − | 0.739671i | ||||||
\(659\) | −7.50000 | − | 12.9904i | −0.292159 | − | 0.506033i | 0.682161 | − | 0.731202i | \(-0.261040\pi\) |
−0.974320 | + | 0.225168i | \(0.927707\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.0000 | + | 22.5167i | −0.505641 | + | 0.875797i | 0.494337 | + | 0.869270i | \(0.335411\pi\) |
−0.999979 | + | 0.00652642i | \(0.997923\pi\) | |||||||
\(662\) | − | 15.1623i | − | 0.589299i | ||||||
\(663\) | −3.01969 | + | 0.0679718i | −0.117275 | + | 0.00263981i | ||||
\(664\) | −11.6491 | −0.452073 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.24342 | − | 7.34981i | 0.164429 | − | 0.284799i | ||||
\(667\) | 8.09811 | − | 4.67544i | 0.313560 | − | 0.181034i | ||||
\(668\) | 8.16228i | 0.315808i | ||||||||
\(669\) | 13.0680 | + | 22.6344i | 0.505237 | + | 0.875096i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.4605 | −0.519637 | ||||||||
\(672\) | −2.73861 | + | 1.58114i | −0.105644 | + | 0.0609938i | ||||
\(673\) | 3.16022 | + | 1.82456i | 0.121818 | + | 0.0703314i | 0.559671 | − | 0.828715i | \(-0.310928\pi\) |
−0.437853 | + | 0.899047i | \(0.644261\pi\) | |||||||
\(674\) | 2.00000 | − | 3.46410i | 0.0770371 | − | 0.133432i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.00000 | + | 10.9545i | 0.269231 | + | 0.421325i | ||||
\(677\) | 32.6491i | 1.25481i | 0.778694 | + | 0.627404i | \(0.215882\pi\) | ||||
−0.778694 | + | 0.627404i | \(0.784118\pi\) | |||||||
\(678\) | 8.94133 | + | 5.16228i | 0.343390 | + | 0.198256i | ||||
\(679\) | 27.3925 | − | 47.4452i | 1.05123 | − | 1.82078i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.9737 | 0.842033 | ||||||||
\(682\) | 7.37262 | − | 4.25658i | 0.282312 | − | 0.162993i | ||||
\(683\) | −25.0691 | + | 14.4737i | −0.959243 | + | 0.553819i | −0.895940 | − | 0.444175i | \(-0.853497\pi\) |
−0.0633033 | + | 0.997994i | \(0.520164\pi\) | |||||||
\(684\) | 3.16228 | 0.120913 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.32456 | − | 10.9545i | 0.241473 | − | 0.418243i | ||||
\(687\) | −14.2780 | − | 8.24342i | −0.544740 | − | 0.314506i | ||||
\(688\) | 1.16228i | 0.0443114i | ||||||||
\(689\) | −0.0679718 | − | 3.01969i | −0.00258952 | − | 0.115041i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.9737 | − | 20.7390i | 0.455500 | − | 0.788949i | −0.543217 | − | 0.839592i | \(-0.682794\pi\) |
0.998717 | + | 0.0506436i | \(0.0161273\pi\) | |||||||
\(692\) | −1.45098 | − | 0.837722i | −0.0551579 | − | 0.0318454i | ||||
\(693\) | −8.21584 | + | 4.74342i | −0.312094 | + | 0.180187i | ||||
\(694\) | 1.32456 | 0.0502794 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.16228 | + | 3.74517i | 0.0819609 | + | 0.141960i | ||||
\(697\) | 7.94733i | 0.301027i | ||||||||
\(698\) | 30.7097 | − | 17.7302i | 1.16238 | − | 0.671100i | ||||
\(699\) | 6.83772 | − | 11.8433i | 0.258626 | − | 0.447954i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.4605 | −0.848321 | −0.424161 | − | 0.905587i | \(-0.639431\pi\) | ||||
−0.424161 | + | 0.905587i | \(0.639431\pi\) | |||||||
\(702\) | −1.73205 | + | 3.16228i | −0.0653720 | + | 0.119352i | ||||
\(703\) | − | 26.8377i | − | 1.01220i | ||||||
\(704\) | 1.50000 | − | 2.59808i | 0.0565334 | − | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.90569 | − | 17.1572i | −0.372806 | − | 0.645718i | ||||
\(707\) | 27.3509i | 1.02864i | ||||||||
\(708\) | −5.19615 | + | 3.00000i | −0.195283 | + | 0.112747i | ||||
\(709\) | 0.756584 | + | 1.31044i | 0.0284141 | + | 0.0492146i | 0.879883 | − | 0.475191i | \(-0.157621\pi\) |
−0.851469 | + | 0.524405i | \(0.824288\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.41886 | − | 2.45754i | −0.0532115 | − | 0.0921649i | ||||
\(712\) | 0.725489 | + | 0.418861i | 0.0271888 | + | 0.0156975i | ||||
\(713\) | 5.31388 | + | 3.06797i | 0.199006 | + | 0.114896i | ||||
\(714\) | 2.64911 | 0.0991405 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 23.6491 | 0.883809 | ||||||||
\(717\) | 16.0101 | + | 9.24342i | 0.597907 | + | 0.345202i | ||||
\(718\) | −10.3923 | − | 6.00000i | −0.387837 | − | 0.223918i | ||||
\(719\) | −23.4057 | − | 40.5399i | −0.872885 | − | 1.51188i | −0.858999 | − | 0.511978i | \(-0.828913\pi\) |
−0.0138864 | − | 0.999904i | \(-0.504420\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.67544 | + | 15.0263i | 0.323090 | + | 0.559609i | ||||
\(722\) | −7.79423 | + | 4.50000i | −0.290071 | + | 0.167473i | ||||
\(723\) | 8.00000i | 0.297523i | ||||||||
\(724\) | 6.40569 | + | 11.0950i | 0.238066 | + | 0.412342i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.00000 | + | 1.73205i | −0.0371135 | + | 0.0642824i | ||||
\(727\) | − | 12.3246i | − | 0.457092i | −0.973533 | − | 0.228546i | \(-0.926603\pi\) | ||
0.973533 | − | 0.228546i | \(-0.0733972\pi\) | |||||||
\(728\) | −5.92164 | − | 9.74342i | −0.219471 | − | 0.361115i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.486833 | − | 0.843219i | 0.0180062 | − | 0.0311876i | ||||
\(732\) | 3.88571 | − | 2.24342i | 0.143620 | − | 0.0829191i | ||||
\(733\) | 19.5132i | 0.720735i | 0.932810 | + | 0.360368i | \(0.117349\pi\) | ||||
−0.932810 | + | 0.360368i | \(0.882651\pi\) | |||||||
\(734\) | 9.32456 | + | 16.1506i | 0.344176 | + | 0.596130i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.16228 | 0.0797026 | ||||||||
\(737\) | 10.3923 | − | 6.00000i | 0.382805 | − | 0.221013i | ||||
\(738\) | 8.21584 | + | 4.74342i | 0.302429 | + | 0.174608i | ||||
\(739\) | 9.64911 | − | 16.7127i | 0.354948 | − | 0.614788i | −0.632161 | − | 0.774837i | \(-0.717832\pi\) |
0.987109 | + | 0.160049i | \(0.0511651\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.256584 | + | 11.3989i | 0.00942583 | + | 0.418748i | ||||
\(742\) | 2.64911i | 0.0972519i | ||||||||
\(743\) | 38.6673 | + | 22.3246i | 1.41856 | + | 0.819009i | 0.996173 | − | 0.0874050i | \(-0.0278574\pi\) |
0.422391 | + | 0.906414i | \(0.361191\pi\) | |||||||
\(744\) | −1.41886 | + | 2.45754i | −0.0520180 | + | 0.0900978i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.4868 | 0.383950 | ||||||||
\(747\) | 10.0884 | − | 5.82456i | 0.369116 | − | 0.213109i | ||||
\(748\) | −2.17647 | + | 1.25658i | −0.0795795 | + | 0.0459452i | ||||
\(749\) | 18.9737 | 0.693283 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.83772 | − | 15.3074i | 0.322493 | − | 0.558574i | −0.658509 | − | 0.752573i | \(-0.728812\pi\) |
0.981002 | + | 0.193999i | \(0.0621458\pi\) | |||||||
\(752\) | −5.19615 | − | 3.00000i | −0.189484 | − | 0.109399i | ||||
\(753\) | 15.0000i | 0.546630i | ||||||||
\(754\) | −13.3246 | + | 8.09811i | −0.485252 | + | 0.294916i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.58114 | − | 2.73861i | 0.0575055 | − | 0.0996024i | ||||
\(757\) | −9.50347 | − | 5.48683i | −0.345410 | − | 0.199422i | 0.317252 | − | 0.948341i | \(-0.397240\pi\) |
−0.662662 | + | 0.748919i | \(0.730573\pi\) | |||||||
\(758\) | −1.73205 | + | 1.00000i | −0.0629109 | + | 0.0363216i | ||||
\(759\) | 6.48683 | 0.235457 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.2302 | + | 40.2360i | 0.842096 | + | 1.45855i | 0.888120 | + | 0.459613i | \(0.152012\pi\) |
−0.0460237 | + | 0.998940i | \(0.514655\pi\) | |||||||
\(762\) | − | 20.3246i | − | 0.736281i | ||||||
\(763\) | 28.7194 | − | 16.5811i | 1.03971 | − | 0.600278i | ||||
\(764\) | 7.91886 | − | 13.7159i | 0.286494 | − | 0.496223i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.16228 | 0.0781263 | ||||||||
\(767\) | −11.2355 | − | 18.4868i | −0.405691 | − | 0.667521i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 7.48683 | − | 12.9676i | 0.269982 | − | 0.467623i | −0.698875 | − | 0.715244i | \(-0.746316\pi\) |
0.968857 | + | 0.247621i | \(0.0796489\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.9057 | + | 22.3533i | 0.464787 | + | 0.805035i | ||||
\(772\) | 17.3246i | 0.623524i | ||||||||
\(773\) | −8.09811 | + | 4.67544i | −0.291269 | + | 0.168164i | −0.638514 | − | 0.769610i | \(-0.720451\pi\) |
0.347245 | + | 0.937774i | \(0.387117\pi\) | |||||||
\(774\) | −0.581139 | − | 1.00656i | −0.0208886 | − | 0.0361801i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.66228 | − | 15.0035i | −0.310958 | − | 0.538594i | ||||
\(777\) | −23.2421 | − | 13.4189i | −0.833807 | − | 0.481399i | ||||
\(778\) | −24.5298 | − | 14.1623i | −0.879435 | − | 0.507742i | ||||
\(779\) | 30.0000 | 1.07486 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.4868 | −1.52030 | ||||||||
\(782\) | −1.56871 | − | 0.905694i | −0.0560969 | − | 0.0323876i | ||||
\(783\) | −3.74517 | − | 2.16228i | −0.133842 | − | 0.0772735i | ||||
\(784\) | 1.50000 | + | 2.59808i | 0.0535714 | + | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.16228 | + | 14.1375i | 0.291139 | + | 0.504267i | ||||
\(787\) | −4.75174 | + | 2.74342i | −0.169381 | + | 0.0977922i | −0.582294 | − | 0.812978i | \(-0.697845\pi\) |
0.412913 | + | 0.910771i | \(0.364511\pi\) | |||||||
\(788\) | − | 6.00000i | − | 0.213741i | ||||||
\(789\) | −0.243416 | − | 0.421610i | −0.00866586 | − | 0.0150097i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.3246 | − | 28.2750i | 0.580434 | − | 1.00534i | ||||
\(792\) | 3.00000i | 0.106600i | ||||||||
\(793\) | 8.40199 | + | 13.8246i | 0.298363 | + | 0.490924i | ||||
\(794\) | −11.6754 | −0.414346 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.41886 | + | 7.65369i | −0.156622 | + | 0.271278i | ||||
\(797\) | 40.3537 | − | 23.2982i | 1.42940 | − | 0.825265i | 0.432328 | − | 0.901716i | \(-0.357692\pi\) |
0.997073 | + | 0.0764510i | \(0.0243589\pi\) | |||||||
\(798\) | − | 10.0000i | − | 0.353996i | ||||||
\(799\) | 2.51317 | + | 4.35293i | 0.0889095 | + | 0.153996i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.837722 | −0.0295995 | ||||||||
\(802\) | 14.1375 | − | 8.16228i | 0.499212 | − | 0.288220i | ||||
\(803\) | 29.4221 | + | 16.9868i | 1.03828 | + | 0.599452i | ||||
\(804\) | −2.00000 | + | 3.46410i | −0.0705346 | + | 0.122169i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.97367 | − | 4.91508i | −0.316084 | − | 0.173126i | ||||
\(807\) | 12.8377i | 0.451909i | ||||||||
\(808\) | 7.49035 | + | 4.32456i | 0.263510 | + | 0.152137i | ||||
\(809\) | −6.41886 | + | 11.1178i | −0.225675 | + | 0.390881i | −0.956522 | − | 0.291661i | \(-0.905792\pi\) |
0.730847 | + | 0.682542i | \(0.239125\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.64911 | −0.233482 | −0.116741 | − | 0.993162i | \(-0.537245\pi\) | ||||
−0.116741 | + | 0.993162i | \(0.537245\pi\) | |||||||
\(812\) | 11.8433 | − | 6.83772i | 0.415618 | − | 0.239957i | ||||
\(813\) | 0.281073 | − | 0.162278i | 0.00985767 | − | 0.00569133i | ||||
\(814\) | 25.4605 | 0.892390 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.418861 | − | 0.725489i | 0.0146631 | − | 0.0253972i | ||||
\(817\) | −3.18303 | − | 1.83772i | −0.111360 | − | 0.0642938i | ||||
\(818\) | − | 30.3246i | − | 1.06027i | ||||||
\(819\) | 10.0000 | + | 5.47723i | 0.349428 | + | 0.191390i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.16228 | + | 3.74517i | −0.0754640 | + | 0.130708i | −0.901288 | − | 0.433221i | \(-0.857377\pi\) |
0.825824 | + | 0.563928i | \(0.190710\pi\) | |||||||
\(822\) | 10.3923 | + | 6.00000i | 0.362473 | + | 0.209274i | ||||
\(823\) | 7.65369 | − | 4.41886i | 0.266791 | − | 0.154032i | −0.360637 | − | 0.932706i | \(-0.617441\pi\) |
0.627428 | + | 0.778674i | \(0.284108\pi\) | |||||||
\(824\) | 5.48683 | 0.191143 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.48683 | + | 16.4317i | 0.330089 | + | 0.571731i | ||||
\(827\) | − | 27.9737i | − | 0.972740i | −0.873753 | − | 0.486370i | \(-0.838321\pi\) | ||
0.873753 | − | 0.486370i | \(-0.161679\pi\) | |||||||
\(828\) | −1.87259 | + | 1.08114i | −0.0650769 | + | 0.0375722i | ||||
\(829\) | −2.48683 | + | 4.30732i | −0.0863713 | + | 0.149599i | −0.905975 | − | 0.423332i | \(-0.860860\pi\) |
0.819603 | + | 0.572931i | \(0.194194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.81139 | −0.305664 | ||||||||
\(832\) | −3.60464 | + | 0.0811388i | −0.124968 | + | 0.00281298i | ||||
\(833\) | − | 2.51317i | − | 0.0870761i | ||||||
\(834\) | 2.83772 | − | 4.91508i | 0.0982623 | − | 0.170195i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.74342 | + | 8.21584i | 0.164054 | + | 0.284151i | ||||
\(837\) | − | 2.83772i | − | 0.0980860i | ||||||
\(838\) | −7.79423 | + | 4.50000i | −0.269247 | + | 0.155450i | ||||
\(839\) | −17.8925 | − | 30.9908i | −0.617719 | − | 1.06992i | −0.989901 | − | 0.141760i | \(-0.954724\pi\) |
0.372182 | − | 0.928160i | \(-0.378610\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.14911 | + | 8.91852i | 0.177556 | + | 0.307535i | ||||
\(842\) | −24.3892 | − | 14.0811i | −0.840509 | − | 0.485268i | ||||
\(843\) | 18.6081 | + | 10.7434i | 0.640898 | + | 0.370023i | ||||
\(844\) | −13.1623 | −0.453064 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | 5.47723 | + | 3.16228i | 0.188200 | + | 0.108657i | ||||
\(848\) | 0.725489 | + | 0.418861i | 0.0249134 | + | 0.0143838i | ||||
\(849\) | −9.74342 | − | 16.8761i | −0.334393 | − | 0.579186i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.17544 | + | 15.8923i | 0.314530 | + | 0.544782i | ||||
\(852\) | 12.2649 | − | 7.08114i | 0.420188 | − | 0.242596i | ||||
\(853\) | − | 18.6491i | − | 0.638533i | −0.947665 | − | 0.319267i | \(-0.896563\pi\) | ||
0.947665 | − | 0.319267i | \(-0.103437\pi\) | |||||||
\(854\) | −7.09431 | − | 12.2877i | −0.242762 | − | 0.420476i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | − | 5.19615i | 0.102538 | − | 0.177601i | ||||
\(857\) | − | 42.2719i | − | 1.44398i | −0.691903 | − | 0.721990i | \(-0.743228\pi\) | ||
0.691903 | − | 0.721990i | \(-0.256772\pi\) | |||||||
\(858\) | −10.8139 | + | 0.243416i | −0.369181 | + | 0.00831010i | ||||
\(859\) | −12.1886 | −0.415870 | −0.207935 | − | 0.978143i | \(-0.566674\pi\) | ||||
−0.207935 | + | 0.978143i | \(0.566674\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.0000 | − | 25.9808i | 0.511199 | − | 0.885422i | ||||
\(862\) | −21.2062 | + | 12.2434i | −0.722287 | + | 0.417012i | ||||
\(863\) | 19.4605i | 0.662443i | 0.943553 | + | 0.331222i | \(0.107461\pi\) | ||||
−0.943553 | + | 0.331222i | \(0.892539\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 34.6228 | 1.17653 | ||||||||
\(867\) | 14.1147 | − | 8.14911i | 0.479359 | − | 0.276758i | ||||
\(868\) | 7.77142 | + | 4.48683i | 0.263779 | + | 0.152293i | ||||
\(869\) | 4.25658 | − | 7.37262i | 0.144395 | − | 0.250099i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.6491 | − | 6.92820i | −0.428599 | − | 0.234753i | ||||
\(872\) | − | 10.4868i | − | 0.355129i | ||||||
\(873\) | 15.0035 | + | 8.66228i | 0.507792 | + | 0.293174i | ||||
\(874\) | −3.41886 | + | 5.92164i | −0.115645 | + | 0.200303i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.3246 | −0.382621 | ||||||||
\(877\) | 49.2001 | − | 28.4057i | 1.66137 | − | 0.959192i | 0.689307 | − | 0.724469i | \(-0.257915\pi\) |
0.972062 | − | 0.234723i | \(-0.0754183\pi\) | |||||||
\(878\) | 31.7391 | − | 18.3246i | 1.07114 | − | 0.618424i | ||||
\(879\) | −21.4868 | −0.724733 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.2302 | − | 19.4514i | 0.378357 | − | 0.655333i | −0.612467 | − | 0.790496i | \(-0.709823\pi\) |
0.990823 | + | 0.135163i | \(0.0431559\pi\) | |||||||
\(882\) | −2.59808 | − | 1.50000i | −0.0874818 | − | 0.0505076i | ||||
\(883\) | 16.6491i | 0.560287i | 0.959958 | + | 0.280144i | \(0.0903821\pi\) | ||||
−0.959958 | + | 0.280144i | \(0.909618\pi\) | |||||||
\(884\) | 2.64911 | + | 1.45098i | 0.0890992 | + | 0.0488017i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.50000 | + | 7.79423i | −0.151180 | + | 0.261852i | ||||
\(887\) | −7.49035 | − | 4.32456i | −0.251501 | − | 0.145204i | 0.368950 | − | 0.929449i | \(-0.379717\pi\) |
−0.620452 | + | 0.784245i | \(0.713051\pi\) | |||||||
\(888\) | −7.34981 | + | 4.24342i | −0.246644 | + | 0.142400i | ||||
\(889\) | −64.2719 | −2.15561 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | − | 2.59808i | −0.0502519 | − | 0.0870388i | ||||
\(892\) | − | 26.1359i | − | 0.875096i | ||||||
\(893\) | 16.4317 | − | 9.48683i | 0.549865 | − | 0.317465i | ||||
\(894\) | 3.41886 | − | 5.92164i | 0.114344 | − | 0.198049i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.16228 | 0.105644 | ||||||||
\(897\) | −4.04905 | − | 6.66228i | −0.135194 | − | 0.222447i | ||||
\(898\) | − | 2.51317i | − | 0.0838655i | ||||||
\(899\) | 6.13594 | − | 10.6278i | 0.204645 | − | 0.354456i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.350889 | − | 0.607758i | −0.0116898 | − | 0.0202474i | ||||
\(902\) | 28.4605i | 0.947631i | ||||||||
\(903\) | −3.18303 | + | 1.83772i | −0.105925 | + | 0.0611556i | ||||
\(904\) | −5.16228 | − | 8.94133i | −0.171695 | − | 0.297384i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.90569 | + | 8.49691i | 0.162981 | + | 0.282291i | ||||
\(907\) | −49.5040 | − | 28.5811i | −1.64375 | − | 0.949021i | −0.979483 | − | 0.201529i | \(-0.935409\pi\) |
−0.664270 | − | 0.747493i | \(-0.731258\pi\) | |||||||
\(908\) | −19.0298 | − | 10.9868i | −0.631525 | − | 0.364611i | ||||
\(909\) | −8.64911 | −0.286873 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.1359 | 1.09784 | 0.548921 | − | 0.835874i | \(-0.315039\pi\) | ||||
0.548921 | + | 0.835874i | \(0.315039\pi\) | |||||||
\(912\) | −2.73861 | − | 1.58114i | −0.0906845 | − | 0.0523567i | ||||
\(913\) | 30.2653 | + | 17.4737i | 1.00163 | + | 0.578294i | ||||
\(914\) | 5.17544 | + | 8.96413i | 0.171188 | + | 0.296507i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.24342 | + | 14.2780i | 0.272370 | + | 0.471759i | ||||
\(917\) | 44.7066 | − | 25.8114i | 1.47634 | − | 0.852367i | ||||
\(918\) | 0.837722i | 0.0276490i | ||||||||
\(919\) | −8.06797 | − | 13.9741i | −0.266138 | − | 0.460964i | 0.701723 | − | 0.712450i | \(-0.252414\pi\) |
−0.967861 | + | 0.251485i | \(0.919081\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.32456 | + | 14.4186i | −0.274303 | + | 0.475107i | ||||
\(922\) | − | 17.1623i | − | 0.565210i | ||||||
\(923\) | 26.5201 | + | 43.6359i | 0.872920 | + | 1.43629i | ||||
\(924\) | 9.48683 | 0.312094 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.25658 | − | 3.90852i | 0.0741559 | − | 0.128442i | ||||
\(927\) | −4.75174 | + | 2.74342i | −0.156068 | + | 0.0901056i | ||||
\(928\) | − | 4.32456i | − | 0.141960i | ||||||
\(929\) | 7.67544 | + | 13.2943i | 0.251823 | + | 0.436171i | 0.964028 | − | 0.265801i | \(-0.0856365\pi\) |
−0.712205 | + | 0.701972i | \(0.752303\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.48683 | −0.310918 | ||||||||
\(932\) | −11.8433 | + | 6.83772i | −0.387940 | + | 0.223977i | ||||
\(933\) | 5.61776 | + | 3.24342i | 0.183917 | + | 0.106185i | ||||
\(934\) | 1.50000 | − | 2.59808i | 0.0490815 | − | 0.0850117i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.08114 | − | 1.87259i | 0.100710 | − | 0.0612074i | ||||
\(937\) | 4.35089i | 0.142137i | 0.997471 | + | 0.0710687i | \(0.0226409\pi\) | ||||
−0.997471 | + | 0.0710687i | \(0.977359\pi\) | |||||||
\(938\) | 10.9545 | + | 6.32456i | 0.357676 | + | 0.206504i | ||||
\(939\) | 3.82456 | − | 6.62432i | 0.124810 | − | 0.216177i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | −0.391189 | −0.195594 | − | 0.980685i | \(-0.562664\pi\) | ||||
−0.195594 | + | 0.980685i | \(0.562664\pi\) | |||||||
\(942\) | 13.9969 | − | 8.08114i | 0.456045 | − | 0.263298i | ||||
\(943\) | −17.7649 | + | 10.2566i | −0.578506 | + | 0.334000i | ||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.74342 | − | 3.01969i | 0.0566834 | − | 0.0981785i | ||||
\(947\) | 41.2653 | + | 23.8246i | 1.34094 | + | 0.774194i | 0.986946 | − | 0.161052i | \(-0.0514888\pi\) |
0.353998 | + | 0.935246i | \(0.384822\pi\) | |||||||
\(948\) | 2.83772i | 0.0921649i | ||||||||
\(949\) | −0.918861 | − | 40.8209i | −0.0298275 | − | 1.32510i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.9057 | − | 27.5495i | 0.515777 | − | 0.893353i | ||||
\(952\) | −2.29420 | − | 1.32456i | −0.0743554 | − | 0.0429291i | ||||
\(953\) | −29.8437 | + | 17.2302i | −0.966731 | + | 0.558143i | −0.898238 | − | 0.439509i | \(-0.855152\pi\) |
−0.0684931 | + | 0.997652i | \(0.521819\pi\) | |||||||
\(954\) | −0.837722 | −0.0271223 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.24342 | − | 16.0101i | −0.298953 | − | 0.517803i | ||||
\(957\) | − | 12.9737i | − | 0.419379i | ||||||
\(958\) | 11.8433 | − | 6.83772i | 0.382639 | − | 0.220917i | ||||
\(959\) | 18.9737 | − | 32.8634i | 0.612692 | − | 1.06121i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.9473 | −0.740237 | ||||||||
\(962\) | −15.8923 | − | 26.1491i | −0.512389 | − | 0.843081i | ||||
\(963\) | 6.00000i | 0.193347i | ||||||||
\(964\) | 4.00000 | − | 6.92820i | 0.128831 | − | 0.223142i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.41886 | + | 5.92164i | 0.110000 | + | 0.190526i | ||||
\(967\) | 52.9737i | 1.70352i | 0.523934 | + | 0.851759i | \(0.324464\pi\) | ||||
−0.523934 | + | 0.851759i | \(0.675536\pi\) | |||||||
\(968\) | 1.73205 | − | 1.00000i | 0.0556702 | − | 0.0321412i | ||||
\(969\) | 1.32456 | + | 2.29420i | 0.0425508 | + | 0.0737002i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.0000 | − | 36.3731i | −0.673922 | − | 1.16727i | −0.976783 | − | 0.214232i | \(-0.931275\pi\) |
0.302861 | − | 0.953035i | \(-0.402058\pi\) | |||||||
\(972\) | 0.866025 | + | 0.500000i | 0.0277778 | + | 0.0160375i | ||||
\(973\) | −15.5428 | − | 8.97367i | −0.498281 | − | 0.287683i | ||||
\(974\) | −3.16228 | −0.101326 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.48683 | −0.143620 | ||||||||
\(977\) | −22.2356 | − | 12.8377i | −0.711379 | − | 0.410715i | 0.100192 | − | 0.994968i | \(-0.468054\pi\) |
−0.811572 | + | 0.584253i | \(0.801388\pi\) | |||||||
\(978\) | 13.6931 | + | 7.90569i | 0.437856 | + | 0.252796i | ||||
\(979\) | −1.25658 | − | 2.17647i | −0.0401606 | − | 0.0695602i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.24342 | + | 9.08186i | 0.167409 | + | 0.289962i | ||||
\(982\) | −19.0298 | + | 10.9868i | −0.607264 | + | 0.350604i | ||||
\(983\) | 29.2982i | 0.934468i | 0.884134 | + | 0.467234i | \(0.154749\pi\) | ||||
−0.884134 | + | 0.467234i | \(0.845251\pi\) | |||||||
\(984\) | −4.74342 | − | 8.21584i | −0.151215 | − | 0.261911i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.81139 | + | 3.13742i | −0.0576864 | + | 0.0999157i | ||||
\(987\) | − | 18.9737i | − | 0.603938i | ||||||
\(988\) | 5.47723 | − | 10.0000i | 0.174254 | − | 0.318142i | ||||
\(989\) | 2.51317 | 0.0799141 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.93203 | + | 12.0066i | −0.220203 | + | 0.381403i | −0.954870 | − | 0.297026i | \(-0.904005\pi\) |
0.734666 | + | 0.678429i | \(0.237339\pi\) | |||||||
\(992\) | 2.45754 | − | 1.41886i | 0.0780270 | − | 0.0450489i | ||||
\(993\) | − | 15.1623i | − | 0.481160i | ||||||
\(994\) | −22.3925 | − | 38.7850i | −0.710248 | − | 1.23019i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.6491 | −0.369116 | ||||||||
\(997\) | −38.9483 | + | 22.4868i | −1.23351 | + | 0.712165i | −0.967759 | − | 0.251878i | \(-0.918952\pi\) |
−0.265747 | + | 0.964043i | \(0.585619\pi\) | |||||||
\(998\) | 34.4777 | + | 19.9057i | 1.09137 | + | 0.630104i | ||||
\(999\) | 4.24342 | − | 7.34981i | 0.134256 | − | 0.232538i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1950.2.z.o.1699.2 | 8 | ||
5.2 | odd | 4 | 1950.2.i.bf.451.2 | yes | 4 | ||
5.3 | odd | 4 | 1950.2.i.ba.451.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 1950.2.z.o.1699.3 | 8 | ||
13.3 | even | 3 | inner | 1950.2.z.o.1849.3 | 8 | ||
65.3 | odd | 12 | 1950.2.i.ba.601.1 | yes | 4 | ||
65.29 | even | 6 | inner | 1950.2.z.o.1849.2 | 8 | ||
65.42 | odd | 12 | 1950.2.i.bf.601.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.i.ba.451.1 | ✓ | 4 | 5.3 | odd | 4 | ||
1950.2.i.ba.601.1 | yes | 4 | 65.3 | odd | 12 | ||
1950.2.i.bf.451.2 | yes | 4 | 5.2 | odd | 4 | ||
1950.2.i.bf.601.2 | yes | 4 | 65.42 | odd | 12 | ||
1950.2.z.o.1699.2 | 8 | 1.1 | even | 1 | trivial | ||
1950.2.z.o.1699.3 | 8 | 5.4 | even | 2 | inner | ||
1950.2.z.o.1849.2 | 8 | 65.29 | even | 6 | inner | ||
1950.2.z.o.1849.3 | 8 | 13.3 | even | 3 | inner |