Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(49,1950)]
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, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.49");
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.y (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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + \cdots + 14089 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(0.500000 - 4.71596i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.49 |
Dual form | 1950.2.y.m.199.4 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.866025 | − | 0.500000i | −0.353553 | − | 0.204124i | ||||
\(7\) | −2.29099 | + | 3.96812i | −0.865914 | + | 1.49981i | 0.000222235 | 1.00000i | \(0.499929\pi\) | |
−0.866137 | + | 0.499808i | \(0.833404\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.563824 | + | 0.325524i | −0.169999 | + | 0.0981491i | −0.582585 | − | 0.812769i | \(-0.697959\pi\) |
0.412586 | + | 0.910919i | \(0.364626\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −3.35747 | − | 1.31432i | −0.931193 | − | 0.364526i | ||||
\(14\) | 4.58199 | 1.22459 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.03194 | + | 1.75049i | 0.735354 | + | 0.424557i | 0.820378 | − | 0.571822i | \(-0.193763\pi\) |
−0.0850238 | + | 0.996379i | \(0.527097\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.50851 | − | 1.44829i | −0.575492 | − | 0.332261i | 0.183848 | − | 0.982955i | \(-0.441145\pi\) |
−0.759340 | + | 0.650694i | \(0.774478\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.58199i | 0.999872i | ||||||||
\(22\) | 0.563824 | + | 0.325524i | 0.120208 | + | 0.0694019i | ||||
\(23\) | 2.46812 | − | 1.42497i | 0.514638 | − | 0.297126i | −0.220100 | − | 0.975477i | \(-0.570638\pi\) |
0.734738 | + | 0.678351i | \(0.237305\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.540502 | + | 3.56481i | 0.106001 | + | 0.699116i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −2.29099 | − | 3.96812i | −0.432957 | − | 0.749904i | ||||
\(29\) | −4.78243 | − | 8.28342i | −0.888076 | − | 1.53819i | −0.842147 | − | 0.539247i | \(-0.818709\pi\) |
−0.0459282 | − | 0.998945i | \(-0.514625\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.58728i | − | 1.00351i | −0.865011 | − | 0.501753i | \(-0.832689\pi\) | ||
0.865011 | − | 0.501753i | \(-0.167311\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −0.325524 | + | 0.563824i | −0.0566664 | + | 0.0981491i | ||||
\(34\) | − | 3.50098i | − | 0.600414i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 2.31432 | + | 4.00851i | 0.380471 | + | 0.658995i | 0.991130 | − | 0.132899i | \(-0.0424285\pi\) |
−0.610658 | + | 0.791894i | \(0.709095\pi\) | |||||||
\(38\) | 2.89658i | 0.469888i | ||||||||
\(39\) | −3.56481 | + | 0.540502i | −0.570826 | + | 0.0865495i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.03194 | + | 1.75049i | −0.473510 | + | 0.273381i | −0.717708 | − | 0.696344i | \(-0.754809\pi\) |
0.244198 | + | 0.969725i | \(0.421475\pi\) | |||||||
\(42\) | 3.96812 | − | 2.29099i | 0.612294 | − | 0.353508i | ||||
\(43\) | −6.68133 | − | 3.85747i | −1.01889 | − | 0.588258i | −0.105110 | − | 0.994461i | \(-0.533519\pi\) |
−0.913783 | + | 0.406203i | \(0.866853\pi\) | |||||||
\(44\) | − | 0.651048i | − | 0.0981491i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.46812 | − | 1.42497i | −0.363904 | − | 0.210100i | ||||
\(47\) | 2.08630 | 0.304318 | 0.152159 | − | 0.988356i | \(-0.451377\pi\) | ||||
0.152159 | + | 0.988356i | \(0.451377\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | −6.99731 | − | 12.1197i | −0.999615 | − | 1.73138i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.50098 | 0.490236 | ||||||||
\(52\) | 2.81696 | − | 2.25049i | 0.390643 | − | 0.312087i | ||||
\(53\) | 5.58728i | 0.767472i | 0.923443 | + | 0.383736i | \(0.125363\pi\) | ||||
−0.923443 | + | 0.383736i | \(0.874637\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.29099 | + | 3.96812i | −0.306147 | + | 0.530262i | ||||
\(57\) | −2.89658 | −0.383662 | ||||||||
\(58\) | −4.78243 | + | 8.28342i | −0.627964 | + | 1.08767i | ||||
\(59\) | −6.47663 | − | 3.73928i | −0.843185 | − | 0.486813i | 0.0151603 | − | 0.999885i | \(-0.495174\pi\) |
−0.858346 | + | 0.513072i | \(0.828507\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.31432 | − | 5.74056i | 0.424355 | − | 0.735004i | −0.572005 | − | 0.820250i | \(-0.693834\pi\) |
0.996360 | + | 0.0852461i | \(0.0271676\pi\) | |||||||
\(62\) | −4.83873 | + | 2.79364i | −0.614519 | + | 0.354793i | ||||
\(63\) | 2.29099 | + | 3.96812i | 0.288638 | + | 0.499936i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.651048 | 0.0801384 | ||||||||
\(67\) | −4.58365 | − | 7.93912i | −0.559982 | − | 0.969917i | −0.997497 | − | 0.0707063i | \(-0.977475\pi\) |
0.437515 | − | 0.899211i | \(-0.355859\pi\) | |||||||
\(68\) | −3.03194 | + | 1.75049i | −0.367677 | + | 0.212278i | ||||
\(69\) | 1.42497 | − | 2.46812i | 0.171546 | − | 0.297126i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.2778 | − | 6.51127i | −1.33843 | − | 0.772745i | −0.351859 | − | 0.936053i | \(-0.614450\pi\) |
−0.986575 | + | 0.163308i | \(0.947784\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −1.04861 | −0.122731 | −0.0613655 | − | 0.998115i | \(-0.519546\pi\) | ||||
−0.0613655 | + | 0.998115i | \(0.519546\pi\) | |||||||
\(74\) | 2.31432 | − | 4.00851i | 0.269034 | − | 0.465980i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.50851 | − | 1.44829i | 0.287746 | − | 0.166130i | ||||
\(77\) | − | 2.98309i | − | 0.339955i | ||||||
\(78\) | 2.25049 | + | 2.81696i | 0.254818 | + | 0.318958i | ||||
\(79\) | 3.46158 | 0.389458 | 0.194729 | − | 0.980857i | \(-0.437617\pi\) | ||||
0.194729 | + | 0.980857i | \(0.437617\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.03194 | + | 1.75049i | 0.334822 | + | 0.193310i | ||||
\(83\) | −10.5722 | −1.16045 | −0.580226 | − | 0.814455i | \(-0.697036\pi\) | ||||
−0.580226 | + | 0.814455i | \(0.697036\pi\) | |||||||
\(84\) | −3.96812 | − | 2.29099i | −0.432957 | − | 0.249968i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.71493i | 0.831922i | ||||||||
\(87\) | −8.28342 | − | 4.78243i | −0.888076 | − | 0.512731i | ||||
\(88\) | −0.563824 | + | 0.325524i | −0.0601038 | + | 0.0347010i | ||||
\(89\) | 7.10045 | − | 4.09944i | 0.752646 | − | 0.434540i | −0.0740033 | − | 0.997258i | \(-0.523578\pi\) |
0.826649 | + | 0.562718i | \(0.190244\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.9073 | − | 10.3117i | 1.35305 | − | 1.08096i | ||||
\(92\) | 2.84994i | 0.297126i | ||||||||
\(93\) | −2.79364 | − | 4.83873i | −0.289687 | − | 0.501753i | ||||
\(94\) | −1.04315 | − | 1.80679i | −0.107593 | − | 0.186356i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −7.21861 | + | 12.5030i | −0.732939 | + | 1.26949i | 0.222683 | + | 0.974891i | \(0.428519\pi\) |
−0.955622 | + | 0.294596i | \(0.904815\pi\) | |||||||
\(98\) | −6.99731 | + | 12.1197i | −0.706835 | + | 1.22427i | ||||
\(99\) | 0.651048i | 0.0654328i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.13139 | + | 7.15577i | 0.411088 | + | 0.712026i | 0.995009 | − | 0.0997849i | \(-0.0318155\pi\) |
−0.583921 | + | 0.811811i | \(0.698482\pi\) | |||||||
\(102\) | −1.75049 | − | 3.03194i | −0.173325 | − | 0.300207i | ||||
\(103\) | − | 19.7208i | − | 1.94315i | −0.236734 | − | 0.971575i | \(-0.576077\pi\) | ||
0.236734 | − | 0.971575i | \(-0.423923\pi\) | |||||||
\(104\) | −3.35747 | − | 1.31432i | −0.329227 | − | 0.128879i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.83873 | − | 2.79364i | 0.469979 | − | 0.271342i | ||||
\(107\) | −2.21785 | + | 1.28048i | −0.214408 | + | 0.123789i | −0.603358 | − | 0.797470i | \(-0.706171\pi\) |
0.388950 | + | 0.921259i | \(0.372838\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | − | 13.7169i | − | 1.31384i | −0.753960 | − | 0.656920i | \(-0.771859\pi\) | ||
0.753960 | − | 0.656920i | \(-0.228141\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00851 | + | 2.31432i | 0.380471 | + | 0.219665i | ||||
\(112\) | 4.58199 | 0.432957 | ||||||||
\(113\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | 1.44829 | + | 2.50851i | 0.135645 | + | 0.234944i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.56487 | 0.888076 | ||||||||
\(117\) | −2.81696 | + | 2.25049i | −0.260428 | + | 0.208058i | ||||
\(118\) | 7.47857i | 0.688458i | ||||||||
\(119\) | −13.8923 | + | 8.02073i | −1.27351 | + | 0.735259i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.28807 | + | 9.15920i | −0.480733 | + | 0.832655i | ||||
\(122\) | −6.62863 | −0.600128 | ||||||||
\(123\) | −1.75049 | + | 3.03194i | −0.157837 | + | 0.273381i | ||||
\(124\) | 4.83873 | + | 2.79364i | 0.434531 | + | 0.250876i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.29099 | − | 3.96812i | 0.204098 | − | 0.353508i | ||||
\(127\) | 7.76012 | − | 4.48031i | 0.688600 | − | 0.397563i | −0.114488 | − | 0.993425i | \(-0.536523\pi\) |
0.803087 | + | 0.595861i | \(0.203189\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −7.71493 | −0.679262 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.48054 | −0.740948 | −0.370474 | − | 0.928843i | \(-0.620805\pi\) | ||||
−0.370474 | + | 0.928843i | \(0.620805\pi\) | |||||||
\(132\) | −0.325524 | − | 0.563824i | −0.0283332 | − | 0.0490746i | ||||
\(133\) | 11.4940 | − | 6.63605i | 0.996654 | − | 0.575418i | ||||
\(134\) | −4.58365 | + | 7.93912i | −0.395967 | + | 0.685835i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.03194 | + | 1.75049i | 0.259987 | + | 0.150103i | ||||
\(137\) | −6.97859 | + | 12.0873i | −0.596221 | + | 1.03268i | 0.397152 | + | 0.917753i | \(0.369998\pi\) |
−0.993373 | + | 0.114932i | \(0.963335\pi\) | |||||||
\(138\) | −2.84994 | −0.242603 | ||||||||
\(139\) | 4.91182 | − | 8.50753i | 0.416615 | − | 0.721599i | −0.578981 | − | 0.815341i | \(-0.696550\pi\) |
0.995597 | + | 0.0937420i | \(0.0298829\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.80679 | − | 1.04315i | 0.152159 | − | 0.0878490i | ||||
\(142\) | 13.0225i | 1.09283i | ||||||||
\(143\) | 2.32086 | − | 0.351892i | 0.194080 | − | 0.0294267i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.524307 | + | 0.908126i | 0.0433919 | + | 0.0751570i | ||||
\(147\) | −12.1197 | − | 6.99731i | −0.999615 | − | 0.577128i | ||||
\(148\) | −4.62863 | −0.380471 | ||||||||
\(149\) | 17.6473 | + | 10.1887i | 1.44572 | + | 0.834689i | 0.998223 | − | 0.0595936i | \(-0.0189805\pi\) |
0.447502 | + | 0.894283i | \(0.352314\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.5840i | 1.83786i | 0.394422 | + | 0.918930i | \(0.370945\pi\) | ||||
−0.394422 | + | 0.918930i | \(0.629055\pi\) | |||||||
\(152\) | −2.50851 | − | 1.44829i | −0.203467 | − | 0.117472i | ||||
\(153\) | 3.03194 | − | 1.75049i | 0.245118 | − | 0.141519i | ||||
\(154\) | −2.58343 | + | 1.49155i | −0.208179 | + | 0.120192i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.31432 | − | 3.35747i | 0.105230 | − | 0.268812i | ||||
\(157\) | 6.54245i | 0.522145i | 0.965319 | + | 0.261072i | \(0.0840761\pi\) | ||||
−0.965319 | + | 0.261072i | \(0.915924\pi\) | |||||||
\(158\) | −1.73079 | − | 2.99781i | −0.137694 | − | 0.238493i | ||||
\(159\) | 2.79364 | + | 4.83873i | 0.221550 | + | 0.383736i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.0584i | 1.02914i | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −7.09944 | + | 12.2966i | −0.556071 | + | 0.963144i | 0.441748 | + | 0.897139i | \(0.354359\pi\) |
−0.997819 | + | 0.0660047i | \(0.978975\pi\) | |||||||
\(164\) | − | 3.50098i | − | 0.273381i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.28611 | + | 9.15582i | 0.410282 | + | 0.710629i | ||||
\(167\) | −1.42497 | − | 2.46812i | −0.110267 | − | 0.190989i | 0.805611 | − | 0.592445i | \(-0.201837\pi\) |
−0.915878 | + | 0.401457i | \(0.868504\pi\) | |||||||
\(168\) | 4.58199i | 0.353508i | ||||||||
\(169\) | 9.54515 | + | 8.82554i | 0.734242 | + | 0.678888i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.50851 | + | 1.44829i | −0.191831 | + | 0.110754i | ||||
\(172\) | 6.68133 | − | 3.85747i | 0.509446 | − | 0.294129i | ||||
\(173\) | 5.80397 | + | 3.35092i | 0.441267 | + | 0.254766i | 0.704135 | − | 0.710066i | \(-0.251335\pi\) |
−0.262868 | + | 0.964832i | \(0.584668\pi\) | |||||||
\(174\) | 9.56487i | 0.725111i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.563824 | + | 0.325524i | 0.0424998 | + | 0.0245373i | ||||
\(177\) | −7.47857 | −0.562124 | ||||||||
\(178\) | −7.10045 | − | 4.09944i | −0.532201 | − | 0.307266i | ||||
\(179\) | −9.98128 | − | 17.2881i | −0.746036 | − | 1.29217i | −0.949709 | − | 0.313133i | \(-0.898621\pi\) |
0.203673 | − | 0.979039i | \(-0.434712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.19889 | −0.237772 | −0.118886 | − | 0.992908i | \(-0.537932\pi\) | ||||
−0.118886 | + | 0.992908i | \(0.537932\pi\) | |||||||
\(182\) | −15.3839 | − | 6.02218i | −1.14033 | − | 0.446394i | ||||
\(183\) | − | 6.62863i | − | 0.490003i | ||||||
\(184\) | 2.46812 | − | 1.42497i | 0.181952 | − | 0.105050i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.79364 | + | 4.83873i | −0.204840 | + | 0.354793i | ||||
\(187\) | −2.27931 | −0.166679 | ||||||||
\(188\) | −1.04315 | + | 1.80679i | −0.0760795 | + | 0.131774i | ||||
\(189\) | 3.96812 | + | 2.29099i | 0.288638 | + | 0.166645i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.5366 | − | 21.7141i | 0.907118 | − | 1.57117i | 0.0890697 | − | 0.996025i | \(-0.471611\pi\) |
0.818048 | − | 0.575149i | \(-0.195056\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | −4.49546 | − | 7.78636i | −0.323590 | − | 0.560474i | 0.657636 | − | 0.753336i | \(-0.271557\pi\) |
−0.981226 | + | 0.192862i | \(0.938223\pi\) | |||||||
\(194\) | 14.4372 | 1.03653 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.9946 | 0.999615 | ||||||||
\(197\) | −10.8923 | − | 18.8660i | −0.776043 | − | 1.34415i | −0.934206 | − | 0.356733i | \(-0.883890\pi\) |
0.158163 | − | 0.987413i | \(-0.449443\pi\) | |||||||
\(198\) | 0.563824 | − | 0.325524i | 0.0400692 | − | 0.0231340i | ||||
\(199\) | −0.295538 | + | 0.511887i | −0.0209501 | + | 0.0362867i | −0.876310 | − | 0.481747i | \(-0.840002\pi\) |
0.855360 | + | 0.518034i | \(0.173336\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.93912 | − | 4.58365i | −0.559982 | − | 0.323306i | ||||
\(202\) | 4.13139 | − | 7.15577i | 0.290683 | − | 0.503478i | ||||
\(203\) | 43.8261 | 3.07599 | ||||||||
\(204\) | −1.75049 | + | 3.03194i | −0.122559 | + | 0.212278i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −17.0787 | + | 9.86041i | −1.18993 | + | 0.687007i | ||||
\(207\) | − | 2.84994i | − | 0.198084i | ||||||
\(208\) | 0.540502 | + | 3.56481i | 0.0374770 | + | 0.247175i | ||||
\(209\) | 1.88581 | 0.130444 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.09671 | − | 10.5598i | −0.419715 | − | 0.726967i | 0.576196 | − | 0.817312i | \(-0.304537\pi\) |
−0.995911 | + | 0.0903445i | \(0.971203\pi\) | |||||||
\(212\) | −4.83873 | − | 2.79364i | −0.332325 | − | 0.191868i | ||||
\(213\) | −13.0225 | −0.892289 | ||||||||
\(214\) | 2.21785 | + | 1.28048i | 0.151609 | + | 0.0875317i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 22.1710 | + | 12.8004i | 1.50507 | + | 0.868950i | ||||
\(218\) | −11.8792 | + | 6.85845i | −0.804560 | + | 0.464513i | ||||
\(219\) | −0.908126 | + | 0.524307i | −0.0613655 | + | 0.0354294i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.87894 | − | 9.86215i | −0.529995 | − | 0.663400i | ||||
\(222\) | − | 4.62863i | − | 0.310653i | ||||||
\(223\) | 6.57244 | + | 11.3838i | 0.440123 | + | 0.762316i | 0.997698 | − | 0.0678107i | \(-0.0216014\pi\) |
−0.557575 | + | 0.830127i | \(0.688268\pi\) | |||||||
\(224\) | −2.29099 | − | 3.96812i | −0.153073 | − | 0.265131i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.2618 | + | 19.5059i | −0.747469 | + | 1.29465i | 0.201563 | + | 0.979476i | \(0.435398\pi\) |
−0.949032 | + | 0.315179i | \(0.897935\pi\) | |||||||
\(228\) | 1.44829 | − | 2.50851i | 0.0959154 | − | 0.166130i | ||||
\(229\) | − | 22.5279i | − | 1.48868i | −0.667798 | − | 0.744342i | \(-0.732763\pi\) | ||
0.667798 | − | 0.744342i | \(-0.267237\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.49155 | − | 2.58343i | −0.0981365 | − | 0.169977i | ||||
\(232\) | −4.78243 | − | 8.28342i | −0.313982 | − | 0.543833i | ||||
\(233\) | 15.8725i | 1.03984i | 0.854215 | + | 0.519920i | \(0.174038\pi\) | ||||
−0.854215 | + | 0.519920i | \(0.825962\pi\) | |||||||
\(234\) | 3.35747 | + | 1.31432i | 0.219484 | + | 0.0859195i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.47663 | − | 3.73928i | 0.421593 | − | 0.243407i | ||||
\(237\) | 2.99781 | − | 1.73079i | 0.194729 | − | 0.112427i | ||||
\(238\) | 13.8923 | + | 8.02073i | 0.900505 | + | 0.519907i | ||||
\(239\) | 20.9703i | 1.35646i | 0.734852 | + | 0.678228i | \(0.237252\pi\) | ||||
−0.734852 | + | 0.678228i | \(0.762748\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.41101 | − | 3.12405i | −0.348554 | − | 0.201238i | 0.315494 | − | 0.948927i | \(-0.397830\pi\) |
−0.664048 | + | 0.747690i | \(0.731163\pi\) | |||||||
\(242\) | 10.5761 | 0.679860 | ||||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 3.31432 | + | 5.74056i | 0.212177 | + | 0.367502i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.50098 | 0.223215 | ||||||||
\(247\) | 6.51873 | + | 8.15956i | 0.414777 | + | 0.519181i | ||||
\(248\) | − | 5.58728i | − | 0.354793i | ||||||
\(249\) | −9.15582 | + | 5.28611i | −0.580226 | + | 0.334994i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.9759 | + | 22.4749i | −0.819031 | + | 1.41860i | 0.0873659 | + | 0.996176i | \(0.472155\pi\) |
−0.906397 | + | 0.422427i | \(0.861178\pi\) | |||||||
\(252\) | −4.58199 | −0.288638 | ||||||||
\(253\) | −0.927722 | + | 1.60686i | −0.0583254 | + | 0.101023i | ||||
\(254\) | −7.76012 | − | 4.48031i | −0.486914 | − | 0.281120i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 5.97280 | − | 3.44840i | 0.372573 | − | 0.215105i | −0.302009 | − | 0.953305i | \(-0.597657\pi\) |
0.674582 | + | 0.738200i | \(0.264324\pi\) | |||||||
\(258\) | 3.85747 | + | 6.68133i | 0.240155 | + | 0.415961i | ||||
\(259\) | −21.2083 | −1.31782 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.56487 | −0.592050 | ||||||||
\(262\) | 4.24027 | + | 7.34436i | 0.261965 | + | 0.453736i | ||||
\(263\) | −7.10511 | + | 4.10214i | −0.438120 | + | 0.252949i | −0.702800 | − | 0.711388i | \(-0.748067\pi\) |
0.264680 | + | 0.964336i | \(0.414734\pi\) | |||||||
\(264\) | −0.325524 | + | 0.563824i | −0.0200346 | + | 0.0347010i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −11.4940 | − | 6.63605i | −0.704741 | − | 0.406882i | ||||
\(267\) | 4.09944 | − | 7.10045i | 0.250882 | − | 0.434540i | ||||
\(268\) | 9.16730 | 0.559982 | ||||||||
\(269\) | −12.5086 | + | 21.6655i | −0.762661 | + | 1.32097i | 0.178813 | + | 0.983883i | \(0.442774\pi\) |
−0.941474 | + | 0.337085i | \(0.890559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.233654 | − | 0.134900i | 0.0141934 | − | 0.00819459i | −0.492886 | − | 0.870094i | \(-0.664058\pi\) |
0.507080 | + | 0.861899i | \(0.330725\pi\) | |||||||
\(272\) | − | 3.50098i | − | 0.212278i | ||||||
\(273\) | 6.02218 | − | 15.3839i | 0.364479 | − | 0.931074i | ||||
\(274\) | 13.9572 | 0.843184 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.42497 | + | 2.46812i | 0.0857730 | + | 0.148563i | ||||
\(277\) | 13.8324 | + | 7.98616i | 0.831110 | + | 0.479842i | 0.854233 | − | 0.519891i | \(-0.174027\pi\) |
−0.0231225 | + | 0.999733i | \(0.507361\pi\) | |||||||
\(278\) | −9.82364 | −0.589183 | ||||||||
\(279\) | −4.83873 | − | 2.79364i | −0.289687 | − | 0.167251i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.58923i | 0.333425i | 0.986006 | + | 0.166713i | \(0.0533152\pi\) | ||||
−0.986006 | + | 0.166713i | \(0.946685\pi\) | |||||||
\(282\) | −1.80679 | − | 1.04315i | −0.107593 | − | 0.0621186i | ||||
\(283\) | −8.45566 | + | 4.88188i | −0.502637 | + | 0.290198i | −0.729802 | − | 0.683659i | \(-0.760388\pi\) |
0.227165 | + | 0.973856i | \(0.427054\pi\) | |||||||
\(284\) | 11.2778 | − | 6.51127i | 0.669217 | − | 0.386373i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.46518 | − | 1.83398i | −0.0866378 | − | 0.108445i | ||||
\(287\) | − | 16.0415i | − | 0.946898i | ||||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | −2.37155 | − | 4.10765i | −0.139503 | − | 0.241627i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.4372i | 0.846325i | ||||||||
\(292\) | 0.524307 | − | 0.908126i | 0.0306827 | − | 0.0531440i | ||||
\(293\) | 7.50680 | − | 13.0022i | 0.438552 | − | 0.759595i | −0.559026 | − | 0.829150i | \(-0.688825\pi\) |
0.997578 | + | 0.0695556i | \(0.0221581\pi\) | |||||||
\(294\) | 13.9946i | 0.816182i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.31432 | + | 4.00851i | 0.134517 | + | 0.232990i | ||||
\(297\) | 0.325524 | + | 0.563824i | 0.0188888 | + | 0.0327164i | ||||
\(298\) | − | 20.3774i | − | 1.18043i | ||||||
\(299\) | −10.1595 | + | 1.54040i | −0.587538 | + | 0.0890834i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.6138 | − | 17.6749i | 1.76455 | − | 1.01876i | ||||
\(302\) | 19.5583 | − | 11.2920i | 1.12545 | − | 0.649781i | ||||
\(303\) | 7.15577 | + | 4.13139i | 0.411088 | + | 0.237342i | ||||
\(304\) | 2.89658i | 0.166130i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.03194 | − | 1.75049i | −0.173325 | − | 0.100069i | ||||
\(307\) | −6.30760 | −0.359994 | −0.179997 | − | 0.983667i | \(-0.557609\pi\) | ||||
−0.179997 | + | 0.983667i | \(0.557609\pi\) | |||||||
\(308\) | 2.58343 | + | 1.49155i | 0.147205 | + | 0.0849887i | ||||
\(309\) | −9.86041 | − | 17.0787i | −0.560939 | − | 0.971575i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.9703 | −1.52934 | −0.764672 | − | 0.644419i | \(-0.777099\pi\) | ||||
−0.764672 | + | 0.644419i | \(0.777099\pi\) | |||||||
\(312\) | −3.56481 | + | 0.540502i | −0.201818 | + | 0.0305999i | ||||
\(313\) | − | 18.4747i | − | 1.04425i | −0.852869 | − | 0.522126i | \(-0.825139\pi\) | ||
0.852869 | − | 0.522126i | \(-0.174861\pi\) | |||||||
\(314\) | 5.66593 | − | 3.27123i | 0.319747 | − | 0.184606i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.73079 | + | 2.99781i | −0.0973645 | + | 0.168640i | ||||
\(317\) | −2.85533 | −0.160371 | −0.0801856 | − | 0.996780i | \(-0.525551\pi\) | ||||
−0.0801856 | + | 0.996780i | \(0.525551\pi\) | |||||||
\(318\) | 2.79364 | − | 4.83873i | 0.156660 | − | 0.271342i | ||||
\(319\) | 5.39290 | + | 3.11359i | 0.301944 | + | 0.174328i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.28048 | + | 2.21785i | −0.0714693 | + | 0.123789i | ||||
\(322\) | 11.3089 | − | 6.52919i | 0.630219 | − | 0.363857i | ||||
\(323\) | −5.07044 | − | 8.78226i | −0.282127 | − | 0.488658i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.1989 | 0.786404 | ||||||||
\(327\) | −6.85845 | − | 11.8792i | −0.379273 | − | 0.656920i | ||||
\(328\) | −3.03194 | + | 1.75049i | −0.167411 | + | 0.0966548i | ||||
\(329\) | −4.77970 | + | 8.27868i | −0.263513 | + | 0.456418i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.20347 | − | 2.42688i | −0.231044 | − | 0.133393i | 0.380010 | − | 0.924983i | \(-0.375921\pi\) |
−0.611054 | + | 0.791589i | \(0.709254\pi\) | |||||||
\(332\) | 5.28611 | − | 9.15582i | 0.290113 | − | 0.502491i | ||||
\(333\) | 4.62863 | 0.253647 | ||||||||
\(334\) | −1.42497 | + | 2.46812i | −0.0779708 | + | 0.135049i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.96812 | − | 2.29099i | 0.216479 | − | 0.124984i | ||||
\(337\) | 6.21782i | 0.338706i | 0.985555 | + | 0.169353i | \(0.0541679\pi\) | ||||
−0.985555 | + | 0.169353i | \(0.945832\pi\) | |||||||
\(338\) | 2.87057 | − | 12.6791i | 0.156138 | − | 0.689653i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.81879 | + | 3.15024i | 0.0984932 | + | 0.170595i | ||||
\(342\) | 2.50851 | + | 1.44829i | 0.135645 | + | 0.0783146i | ||||
\(343\) | 32.0492 | 1.73050 | ||||||||
\(344\) | −6.68133 | − | 3.85747i | −0.360233 | − | 0.207981i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 6.70184i | − | 0.360293i | ||||||
\(347\) | 7.30853 | + | 4.21958i | 0.392342 | + | 0.226519i | 0.683175 | − | 0.730255i | \(-0.260599\pi\) |
−0.290832 | + | 0.956774i | \(0.593932\pi\) | |||||||
\(348\) | 8.28342 | − | 4.78243i | 0.444038 | − | 0.256365i | ||||
\(349\) | 18.9617 | − | 10.9476i | 1.01500 | − | 0.586009i | 0.102346 | − | 0.994749i | \(-0.467365\pi\) |
0.912651 | + | 0.408740i | \(0.134032\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.31432 | + | 3.35747i | −0.0701530 | + | 0.179208i | ||||
\(352\) | − | 0.651048i | − | 0.0347010i | ||||||
\(353\) | 4.45302 | + | 7.71285i | 0.237010 | + | 0.410514i | 0.959855 | − | 0.280497i | \(-0.0904992\pi\) |
−0.722845 | + | 0.691010i | \(0.757166\pi\) | |||||||
\(354\) | 3.73928 | + | 6.47663i | 0.198741 | + | 0.344229i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.19889i | 0.434540i | ||||||||
\(357\) | −8.02073 | + | 13.8923i | −0.424502 | + | 0.735259i | ||||
\(358\) | −9.98128 | + | 17.2881i | −0.527527 | + | 0.913704i | ||||
\(359\) | 36.9967i | 1.95261i | 0.216401 | + | 0.976305i | \(0.430568\pi\) | ||||
−0.216401 | + | 0.976305i | \(0.569432\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.30491 | − | 9.18837i | −0.279206 | − | 0.483598i | ||||
\(362\) | 1.59944 | + | 2.77032i | 0.0840649 | + | 0.145605i | ||||
\(363\) | 10.5761i | 0.555103i | ||||||||
\(364\) | 2.47657 | + | 16.3339i | 0.129808 | + | 0.856129i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.74056 | + | 3.31432i | −0.300064 | + | 0.173242i | ||||
\(367\) | 17.3875 | − | 10.0387i | 0.907622 | − | 0.524016i | 0.0279569 | − | 0.999609i | \(-0.491100\pi\) |
0.879665 | + | 0.475593i | \(0.157767\pi\) | |||||||
\(368\) | −2.46812 | − | 1.42497i | −0.128660 | − | 0.0742816i | ||||
\(369\) | 3.50098i | 0.182254i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.1710 | − | 12.8004i | −1.15106 | − | 0.664565i | ||||
\(372\) | 5.58728 | 0.289687 | ||||||||
\(373\) | −28.8651 | − | 16.6653i | −1.49458 | − | 0.862896i | −0.494600 | − | 0.869121i | \(-0.664685\pi\) |
−0.999981 | + | 0.00622457i | \(0.998019\pi\) | |||||||
\(374\) | 1.13965 | + | 1.97394i | 0.0589301 | + | 0.102070i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.08630 | 0.107593 | ||||||||
\(377\) | 5.16983 | + | 34.0969i | 0.266260 | + | 1.75608i | ||||
\(378\) | − | 4.58199i | − | 0.235672i | ||||||
\(379\) | 1.43619 | − | 0.829184i | 0.0737721 | − | 0.0425923i | −0.462660 | − | 0.886536i | \(-0.653105\pi\) |
0.536432 | + | 0.843943i | \(0.319772\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.48031 | − | 7.76012i | 0.229533 | − | 0.397563i | ||||
\(382\) | −25.0732 | −1.28286 | ||||||||
\(383\) | 12.7966 | − | 22.1644i | 0.653877 | − | 1.13255i | −0.328297 | − | 0.944574i | \(-0.606475\pi\) |
0.982174 | − | 0.187974i | \(-0.0601919\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.49546 | + | 7.78636i | −0.228813 | + | 0.396315i | ||||
\(387\) | −6.68133 | + | 3.85747i | −0.339631 | + | 0.196086i | ||||
\(388\) | −7.21861 | − | 12.5030i | −0.366469 | − | 0.634744i | ||||
\(389\) | 9.56487 | 0.484958 | 0.242479 | − | 0.970157i | \(-0.422039\pi\) | ||||
0.242479 | + | 0.970157i | \(0.422039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.97758 | 0.504588 | ||||||||
\(392\) | −6.99731 | − | 12.1197i | −0.353417 | − | 0.612137i | ||||
\(393\) | −7.34436 | + | 4.24027i | −0.370474 | + | 0.213893i | ||||
\(394\) | −10.8923 | + | 18.8660i | −0.548746 | + | 0.950455i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.563824 | − | 0.325524i | −0.0283332 | − | 0.0163582i | ||||
\(397\) | 0.231927 | − | 0.401710i | 0.0116401 | − | 0.0201612i | −0.860147 | − | 0.510047i | \(-0.829628\pi\) |
0.871787 | + | 0.489886i | \(0.162961\pi\) | |||||||
\(398\) | 0.591076 | 0.0296279 | ||||||||
\(399\) | 6.63605 | − | 11.4940i | 0.332218 | − | 0.575418i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.6992 | − | 10.2187i | 0.883857 | − | 0.510295i | 0.0119289 | − | 0.999929i | \(-0.496203\pi\) |
0.871928 | + | 0.489634i | \(0.162870\pi\) | |||||||
\(402\) | 9.16730i | 0.457223i | ||||||||
\(403\) | −7.34346 | + | 18.7591i | −0.365804 | + | 0.934458i | ||||
\(404\) | −8.26277 | −0.411088 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.9131 | − | 37.9545i | −1.08753 | − | 1.88365i | ||||
\(407\) | −2.60973 | − | 1.50673i | −0.129360 | − | 0.0746858i | ||||
\(408\) | 3.50098 | 0.173325 | ||||||||
\(409\) | 9.15283 | + | 5.28439i | 0.452578 | + | 0.261296i | 0.708919 | − | 0.705290i | \(-0.249183\pi\) |
−0.256340 | + | 0.966587i | \(0.582517\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.9572i | 0.688457i | ||||||||
\(412\) | 17.0787 | + | 9.86041i | 0.841408 | + | 0.485787i | ||||
\(413\) | 29.6758 | − | 17.1334i | 1.46025 | − | 0.843077i | ||||
\(414\) | −2.46812 | + | 1.42497i | −0.121301 | + | 0.0700334i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.81696 | − | 2.25049i | 0.138113 | − | 0.110339i | ||||
\(417\) | − | 9.82364i | − | 0.481066i | ||||||
\(418\) | −0.942906 | − | 1.63316i | −0.0461191 | − | 0.0798805i | ||||
\(419\) | 14.2835 | + | 24.7397i | 0.697793 | + | 1.20861i | 0.969230 | + | 0.246156i | \(0.0791677\pi\) |
−0.271437 | + | 0.962456i | \(0.587499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 38.4187i | − | 1.87241i | −0.351450 | − | 0.936207i | \(-0.614311\pi\) | ||
0.351450 | − | 0.936207i | \(-0.385689\pi\) | |||||||
\(422\) | −6.09671 | + | 10.5598i | −0.296783 | + | 0.514043i | ||||
\(423\) | 1.04315 | − | 1.80679i | 0.0507197 | − | 0.0878490i | ||||
\(424\) | 5.58728i | 0.271342i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.51127 | + | 11.2778i | 0.315472 | + | 0.546413i | ||||
\(427\) | 15.1862 | + | 26.3032i | 0.734910 | + | 1.27290i | ||||
\(428\) | − | 2.56096i | − | 0.123789i | ||||||
\(429\) | 1.83398 | − | 1.46518i | 0.0885453 | − | 0.0707394i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.84351 | + | 3.95111i | −0.329641 | + | 0.190318i | −0.655681 | − | 0.755038i | \(-0.727619\pi\) |
0.326041 | + | 0.945356i | \(0.394285\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | −14.4301 | − | 8.33120i | −0.693465 | − | 0.400372i | 0.111444 | − | 0.993771i | \(-0.464452\pi\) |
−0.804909 | + | 0.593399i | \(0.797786\pi\) | |||||||
\(434\) | − | 25.6009i | − | 1.22888i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.8792 | + | 6.85845i | 0.568910 | + | 0.328460i | ||||
\(437\) | −8.25507 | −0.394894 | ||||||||
\(438\) | 0.908126 | + | 0.524307i | 0.0433919 | + | 0.0250523i | ||||
\(439\) | 11.1728 | + | 19.3519i | 0.533250 | + | 0.923616i | 0.999246 | + | 0.0388290i | \(0.0123628\pi\) |
−0.465996 | + | 0.884787i | \(0.654304\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.9946 | −0.666410 | ||||||||
\(442\) | −4.60140 | + | 11.7544i | −0.218866 | + | 0.559101i | ||||
\(443\) | − | 17.5200i | − | 0.832398i | −0.909274 | − | 0.416199i | \(-0.863362\pi\) | ||
0.909274 | − | 0.416199i | \(-0.136638\pi\) | |||||||
\(444\) | −4.00851 | + | 2.31432i | −0.190236 | + | 0.109833i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.57244 | − | 11.3838i | 0.311214 | − | 0.539039i | ||||
\(447\) | 20.3774 | 0.963816 | ||||||||
\(448\) | −2.29099 | + | 3.96812i | −0.108239 | + | 0.187476i | ||||
\(449\) | 16.9571 | + | 9.79019i | 0.800255 | + | 0.462028i | 0.843560 | − | 0.537034i | \(-0.180455\pi\) |
−0.0433051 | + | 0.999062i | \(0.513789\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.13965 | − | 1.97394i | 0.0536642 | − | 0.0929491i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.2920 | + | 19.5583i | 0.530544 | + | 0.918930i | ||||
\(454\) | 22.5235 | 1.05708 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.89658 | −0.135645 | ||||||||
\(457\) | −11.3375 | − | 19.6371i | −0.530345 | − | 0.918585i | −0.999373 | − | 0.0354015i | \(-0.988729\pi\) |
0.469028 | − | 0.883183i | \(-0.344604\pi\) | |||||||
\(458\) | −19.5097 | + | 11.2639i | −0.911630 | + | 0.526330i | ||||
\(459\) | 1.75049 | − | 3.03194i | 0.0817060 | − | 0.141519i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.4102 | + | 16.4026i | 1.32319 | + | 0.763947i | 0.984237 | − | 0.176855i | \(-0.0565924\pi\) |
0.338957 | + | 0.940802i | \(0.389926\pi\) | |||||||
\(462\) | −1.49155 | + | 2.58343i | −0.0693930 | + | 0.120192i | ||||
\(463\) | 20.6472 | 0.959555 | 0.479778 | − | 0.877390i | \(-0.340717\pi\) | ||||
0.479778 | + | 0.877390i | \(0.340717\pi\) | |||||||
\(464\) | −4.78243 | + | 8.28342i | −0.222019 | + | 0.384548i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.7460 | − | 7.93624i | 0.636769 | − | 0.367639i | ||||
\(467\) | − | 7.77136i | − | 0.359616i | −0.983702 | − | 0.179808i | \(-0.942452\pi\) | ||
0.983702 | − | 0.179808i | \(-0.0575476\pi\) | |||||||
\(468\) | −0.540502 | − | 3.56481i | −0.0249847 | − | 0.164783i | ||||
\(469\) | 42.0045 | 1.93959 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.27123 | + | 5.66593i | 0.150730 | + | 0.261072i | ||||
\(472\) | −6.47663 | − | 3.73928i | −0.298111 | − | 0.172115i | ||||
\(473\) | 5.02279 | 0.230948 | ||||||||
\(474\) | −2.99781 | − | 1.73079i | −0.137694 | − | 0.0794978i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 16.0415i | − | 0.735259i | ||||||
\(477\) | 4.83873 | + | 2.79364i | 0.221550 | + | 0.127912i | ||||
\(478\) | 18.1608 | − | 10.4851i | 0.830656 | − | 0.479579i | ||||
\(479\) | −15.1745 | + | 8.76102i | −0.693342 | + | 0.400301i | −0.804863 | − | 0.593461i | \(-0.797761\pi\) |
0.111521 | + | 0.993762i | \(0.464428\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.50178 | − | 16.5002i | −0.114071 | − | 0.752344i | ||||
\(482\) | 6.24809i | 0.284593i | ||||||||
\(483\) | 6.52919 | + | 11.3089i | 0.297088 | + | 0.514572i | ||||
\(484\) | −5.28807 | − | 9.15920i | −0.240367 | − | 0.416327i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 10.4412 | − | 18.0846i | 0.473135 | − | 0.819494i | −0.526392 | − | 0.850242i | \(-0.676456\pi\) |
0.999527 | + | 0.0307482i | \(0.00978901\pi\) | |||||||
\(488\) | 3.31432 | − | 5.74056i | 0.150032 | − | 0.259863i | ||||
\(489\) | 14.1989i | 0.642096i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.97312 | − | 13.8098i | −0.359822 | − | 0.623230i | 0.628109 | − | 0.778125i | \(-0.283829\pi\) |
−0.987931 | + | 0.154896i | \(0.950496\pi\) | |||||||
\(492\) | −1.75049 | − | 3.03194i | −0.0789183 | − | 0.136690i | ||||
\(493\) | − | 33.4865i | − | 1.50815i | ||||||
\(494\) | 3.80702 | − | 9.72517i | 0.171286 | − | 0.437556i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.83873 | + | 2.79364i | −0.217265 | + | 0.125438i | ||||
\(497\) | 51.6749 | − | 29.8345i | 2.31794 | − | 1.33826i | ||||
\(498\) | 9.15582 | + | 5.28611i | 0.410282 | + | 0.236876i | ||||
\(499\) | − | 19.1969i | − | 0.859373i | −0.902978 | − | 0.429687i | \(-0.858624\pi\) | ||
0.902978 | − | 0.429687i | \(-0.141376\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.46812 | − | 1.42497i | −0.110267 | − | 0.0636629i | ||||
\(502\) | 25.9518 | 1.15828 | ||||||||
\(503\) | 16.3588 | + | 9.44473i | 0.729401 | + | 0.421120i | 0.818203 | − | 0.574930i | \(-0.194971\pi\) |
−0.0888021 | + | 0.996049i | \(0.528304\pi\) | |||||||
\(504\) | 2.29099 | + | 3.96812i | 0.102049 | + | 0.176754i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.85544 | 0.0824846 | ||||||||
\(507\) | 12.6791 | + | 2.87057i | 0.563099 | + | 0.127486i | ||||
\(508\) | 8.96062i | 0.397563i | ||||||||
\(509\) | −16.2075 | + | 9.35742i | −0.718386 | + | 0.414761i | −0.814158 | − | 0.580643i | \(-0.802801\pi\) |
0.0957722 | + | 0.995403i | \(0.469468\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.40237 | − | 4.16102i | 0.106274 | − | 0.184073i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.44829 | + | 2.50851i | −0.0639436 | + | 0.110754i | ||||
\(514\) | −5.97280 | − | 3.44840i | −0.263449 | − | 0.152102i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.85747 | − | 6.68133i | 0.169815 | − | 0.294129i | ||||
\(517\) | −1.17630 | + | 0.679140i | −0.0517338 | + | 0.0298685i | ||||
\(518\) | 10.6042 | + | 18.3670i | 0.465920 | + | 0.806998i | ||||
\(519\) | 6.70184 | 0.294178 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.9556 | 1.79430 | 0.897149 | − | 0.441729i | \(-0.145635\pi\) | ||||
0.897149 | + | 0.441729i | \(0.145635\pi\) | |||||||
\(522\) | 4.78243 | + | 8.28342i | 0.209321 | + | 0.362555i | ||||
\(523\) | −35.0978 | + | 20.2637i | −1.53472 | + | 0.886072i | −0.535587 | + | 0.844480i | \(0.679909\pi\) |
−0.999135 | + | 0.0415914i | \(0.986757\pi\) | |||||||
\(524\) | 4.24027 | − | 7.34436i | 0.185237 | − | 0.320840i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.10511 | + | 4.10214i | 0.309798 | + | 0.178862i | ||||
\(527\) | 9.78050 | − | 16.9403i | 0.426045 | − | 0.737932i | ||||
\(528\) | 0.651048 | 0.0283332 | ||||||||
\(529\) | −7.43893 | + | 12.8846i | −0.323432 | + | 0.560200i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.47663 | + | 3.73928i | −0.281062 | + | 0.162271i | ||||
\(532\) | 13.2721i | 0.575418i | ||||||||
\(533\) | 12.4803 | − | 1.89229i | 0.540583 | − | 0.0819641i | ||||
\(534\) | −8.19889 | −0.354801 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.58365 | − | 7.93912i | −0.197984 | − | 0.342918i | ||||
\(537\) | −17.2881 | − | 9.98128i | −0.746036 | − | 0.430724i | ||||
\(538\) | 25.0171 | 1.07857 | ||||||||
\(539\) | 7.89049 | + | 4.55558i | 0.339868 | + | 0.196223i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.2949i | 1.13050i | 0.824918 | + | 0.565252i | \(0.191221\pi\) | ||||
−0.824918 | + | 0.565252i | \(0.808779\pi\) | |||||||
\(542\) | −0.233654 | − | 0.134900i | −0.0100363 | − | 0.00579445i | ||||
\(543\) | −2.77032 | + | 1.59944i | −0.118886 | + | 0.0686387i | ||||
\(544\) | −3.03194 | + | 1.75049i | −0.129993 | + | 0.0750517i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −16.3339 | + | 2.47657i | −0.699027 | + | 0.105987i | ||||
\(547\) | − | 33.5445i | − | 1.43426i | −0.696940 | − | 0.717130i | \(-0.745455\pi\) | ||
0.696940 | − | 0.717130i | \(-0.254545\pi\) | |||||||
\(548\) | −6.97859 | − | 12.0873i | −0.298110 | − | 0.516342i | ||||
\(549\) | −3.31432 | − | 5.74056i | −0.141452 | − | 0.245001i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.7054i | 1.18029i | ||||||||
\(552\) | 1.42497 | − | 2.46812i | 0.0606507 | − | 0.105050i | ||||
\(553\) | −7.93045 | + | 13.7359i | −0.337237 | + | 0.584112i | ||||
\(554\) | − | 15.9723i | − | 0.678599i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.91182 | + | 8.50753i | 0.208308 | + | 0.360799i | ||||
\(557\) | 6.56478 | + | 11.3705i | 0.278159 | + | 0.481785i | 0.970927 | − | 0.239375i | \(-0.0769425\pi\) |
−0.692768 | + | 0.721160i | \(0.743609\pi\) | |||||||
\(558\) | 5.58728i | 0.236529i | ||||||||
\(559\) | 17.3624 | + | 21.7327i | 0.734351 | + | 0.919194i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.97394 | + | 1.13965i | −0.0833397 | + | 0.0481162i | ||||
\(562\) | 4.84041 | − | 2.79461i | 0.204180 | − | 0.117884i | ||||
\(563\) | −17.0622 | − | 9.85086i | −0.719086 | − | 0.415164i | 0.0953304 | − | 0.995446i | \(-0.469609\pi\) |
−0.814416 | + | 0.580281i | \(0.802943\pi\) | |||||||
\(564\) | 2.08630i | 0.0878490i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.45566 | + | 4.88188i | 0.355418 | + | 0.205201i | ||||
\(567\) | 4.58199 | 0.192425 | ||||||||
\(568\) | −11.2778 | − | 6.51127i | −0.473208 | − | 0.273207i | ||||
\(569\) | −10.1979 | − | 17.6633i | −0.427519 | − | 0.740485i | 0.569133 | − | 0.822246i | \(-0.307279\pi\) |
−0.996652 | + | 0.0817607i | \(0.973946\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.7935 | −0.828333 | −0.414167 | − | 0.910201i | \(-0.635927\pi\) | ||||
−0.414167 | + | 0.910201i | \(0.635927\pi\) | |||||||
\(572\) | −0.855682 | + | 2.18587i | −0.0357779 | + | 0.0913958i | ||||
\(573\) | − | 25.0732i | − | 1.04745i | ||||||
\(574\) | −13.8923 | + | 8.02073i | −0.579854 | + | 0.334779i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 14.1729 | 0.590024 | 0.295012 | − | 0.955493i | \(-0.404676\pi\) | ||||
0.295012 | + | 0.955493i | \(0.404676\pi\) | |||||||
\(578\) | −2.37155 | + | 4.10765i | −0.0986436 | + | 0.170856i | ||||
\(579\) | −7.78636 | − | 4.49546i | −0.323590 | − | 0.186825i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.2209 | − | 41.9518i | 1.00485 | − | 1.74046i | ||||
\(582\) | 12.5030 | − | 7.21861i | 0.518266 | − | 0.299221i | ||||
\(583\) | −1.81879 | − | 3.15024i | −0.0753267 | − | 0.130470i | ||||
\(584\) | −1.04861 | −0.0433919 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.0136 | −0.620206 | ||||||||
\(587\) | −10.7608 | − | 18.6382i | −0.444145 | − | 0.769281i | 0.553847 | − | 0.832618i | \(-0.313159\pi\) |
−0.997992 | + | 0.0633369i | \(0.979826\pi\) | |||||||
\(588\) | 12.1197 | − | 6.99731i | 0.499808 | − | 0.288564i | ||||
\(589\) | −8.09201 | + | 14.0158i | −0.333425 | + | 0.577510i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.8660 | − | 10.8923i | −0.776043 | − | 0.448049i | ||||
\(592\) | 2.31432 | − | 4.00851i | 0.0951178 | − | 0.164749i | ||||
\(593\) | −37.9368 | −1.55788 | −0.778938 | − | 0.627101i | \(-0.784241\pi\) | ||||
−0.778938 | + | 0.627101i | \(0.784241\pi\) | |||||||
\(594\) | 0.325524 | − | 0.563824i | 0.0133564 | − | 0.0231340i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.6473 | + | 10.1887i | −0.722862 | + | 0.417345i | ||||
\(597\) | 0.591076i | 0.0241911i | ||||||||
\(598\) | 6.41376 | + | 8.02817i | 0.262278 | + | 0.328296i | ||||
\(599\) | 22.4129 | 0.915765 | 0.457883 | − | 0.889013i | \(-0.348608\pi\) | ||||
0.457883 | + | 0.889013i | \(0.348608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.6804 | − | 28.8913i | −0.680407 | − | 1.17850i | −0.974857 | − | 0.222832i | \(-0.928470\pi\) |
0.294450 | − | 0.955667i | \(-0.404863\pi\) | |||||||
\(602\) | −30.6138 | − | 17.6749i | −1.24772 | − | 0.720373i | ||||
\(603\) | −9.16730 | −0.373321 | ||||||||
\(604\) | −19.5583 | − | 11.2920i | −0.795816 | − | 0.459465i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 8.26277i | − | 0.335652i | ||||||
\(607\) | 13.9037 | + | 8.02733i | 0.564335 | + | 0.325819i | 0.754884 | − | 0.655859i | \(-0.227693\pi\) |
−0.190548 | + | 0.981678i | \(0.561027\pi\) | |||||||
\(608\) | 2.50851 | − | 1.44829i | 0.101734 | − | 0.0587359i | ||||
\(609\) | 37.9545 | − | 21.9131i | 1.53799 | − | 0.887962i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.00467 | − | 2.74206i | −0.283379 | − | 0.110932i | ||||
\(612\) | 3.50098i | 0.141519i | ||||||||
\(613\) | 19.0929 | + | 33.0698i | 0.771154 | + | 1.33568i | 0.936931 | + | 0.349514i | \(0.113653\pi\) |
−0.165777 | + | 0.986163i | \(0.553013\pi\) | |||||||
\(614\) | 3.15380 | + | 5.46254i | 0.127277 | + | 0.220450i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 2.98309i | − | 0.120192i | ||||||
\(617\) | 21.5003 | − | 37.2397i | 0.865571 | − | 1.49921i | −0.000908306 | − | 1.00000i | \(-0.500289\pi\) |
0.866479 | − | 0.499213i | \(-0.166378\pi\) | |||||||
\(618\) | −9.86041 | + | 17.0787i | −0.396644 | + | 0.687007i | ||||
\(619\) | − | 6.35493i | − | 0.255426i | −0.991811 | − | 0.127713i | \(-0.959236\pi\) | ||
0.991811 | − | 0.127713i | \(-0.0407636\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.42497 | − | 2.46812i | −0.0571820 | − | 0.0990422i | ||||
\(622\) | 13.4851 | + | 23.3570i | 0.540705 | + | 0.936529i | ||||
\(623\) | 37.5672i | 1.50510i | ||||||||
\(624\) | 2.25049 | + | 2.81696i | 0.0900918 | + | 0.112769i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.9996 | + | 9.23735i | −0.639471 | + | 0.369199i | ||||
\(627\) | 1.63316 | − | 0.942906i | 0.0652222 | − | 0.0376560i | ||||
\(628\) | −5.66593 | − | 3.27123i | −0.226095 | − | 0.130536i | ||||
\(629\) | 16.2048i | 0.646126i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.08250 | − | 1.77968i | −0.122713 | − | 0.0708481i | 0.437387 | − | 0.899273i | \(-0.355904\pi\) |
−0.560100 | + | 0.828425i | \(0.689237\pi\) | |||||||
\(632\) | 3.46158 | 0.137694 | ||||||||
\(633\) | −10.5598 | − | 6.09671i | −0.419715 | − | 0.242322i | ||||
\(634\) | 1.42766 | + | 2.47279i | 0.0566997 | + | 0.0982068i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.58728 | −0.221550 | ||||||||
\(637\) | 7.56411 | + | 49.8881i | 0.299701 | + | 1.97664i | ||||
\(638\) | − | 6.22718i | − | 0.246537i | ||||||
\(639\) | −11.2778 | + | 6.51127i | −0.446145 | + | 0.257582i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.4394 | − | 33.6701i | 0.767812 | − | 1.32989i | −0.170935 | − | 0.985282i | \(-0.554679\pi\) |
0.938747 | − | 0.344607i | \(-0.111988\pi\) | |||||||
\(642\) | 2.56096 | 0.101073 | ||||||||
\(643\) | 7.50930 | − | 13.0065i | 0.296138 | − | 0.512926i | −0.679111 | − | 0.734035i | \(-0.737635\pi\) |
0.975249 | + | 0.221110i | \(0.0709679\pi\) | |||||||
\(644\) | −11.3089 | − | 6.52919i | −0.445632 | − | 0.257286i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.07044 | + | 8.78226i | −0.199494 | + | 0.345534i | ||||
\(647\) | 25.8429 | − | 14.9204i | 1.01599 | − | 0.586581i | 0.103049 | − | 0.994676i | \(-0.467140\pi\) |
0.912939 | + | 0.408095i | \(0.133807\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 4.86890 | 0.191121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.6009 | 1.00338 | ||||||||
\(652\) | −7.09944 | − | 12.2966i | −0.278036 | − | 0.481572i | ||||
\(653\) | 2.67950 | − | 1.54701i | 0.104857 | − | 0.0605393i | −0.446654 | − | 0.894707i | \(-0.647385\pi\) |
0.551511 | + | 0.834167i | \(0.314051\pi\) | |||||||
\(654\) | −6.85845 | + | 11.8792i | −0.268187 | + | 0.464513i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.03194 | + | 1.75049i | 0.118377 | + | 0.0683452i | ||||
\(657\) | −0.524307 | + | 0.908126i | −0.0204552 | + | 0.0354294i | ||||
\(658\) | 9.55939 | 0.372664 | ||||||||
\(659\) | 2.65012 | − | 4.59015i | 0.103234 | − | 0.178807i | −0.809781 | − | 0.586732i | \(-0.800414\pi\) |
0.913015 | + | 0.407925i | \(0.133748\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.0453 | + | 15.6146i | −1.05194 | + | 0.607337i | −0.923191 | − | 0.384340i | \(-0.874429\pi\) |
−0.128747 | + | 0.991677i | \(0.541096\pi\) | |||||||
\(662\) | 4.85375i | 0.188646i | ||||||||
\(663\) | −11.7544 | − | 4.60140i | −0.456504 | − | 0.178704i | ||||
\(664\) | −10.5722 | −0.410282 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.31432 | − | 4.00851i | −0.0896779 | − | 0.155327i | ||||
\(667\) | −23.6072 | − | 13.6296i | −0.914075 | − | 0.527742i | ||||
\(668\) | 2.84994 | 0.110267 | ||||||||
\(669\) | 11.3838 | + | 6.57244i | 0.440123 | + | 0.254105i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.31556i | 0.166600i | ||||||||
\(672\) | −3.96812 | − | 2.29099i | −0.153073 | − | 0.0883770i | ||||
\(673\) | −31.2197 | + | 18.0247i | −1.20343 | + | 0.694801i | −0.961316 | − | 0.275447i | \(-0.911174\pi\) |
−0.242114 | + | 0.970248i | \(0.577841\pi\) | |||||||
\(674\) | 5.38479 | − | 3.10891i | 0.207414 | − | 0.119751i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.4157 | + | 3.85357i | −0.477528 | + | 0.148214i | ||||
\(677\) | 23.2219i | 0.892491i | 0.894911 | + | 0.446245i | \(0.147239\pi\) | ||||
−0.894911 | + | 0.446245i | \(0.852761\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.0756 | − | 57.2886i | −1.26932 | − | 2.19853i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.5235i | 0.863103i | ||||||||
\(682\) | 1.81879 | − | 3.15024i | 0.0696452 | − | 0.120629i | ||||
\(683\) | −14.8652 | + | 25.7473i | −0.568802 | + | 0.985195i | 0.427882 | + | 0.903834i | \(0.359260\pi\) |
−0.996685 | + | 0.0813602i | \(0.974074\pi\) | |||||||
\(684\) | − | 2.89658i | − | 0.110754i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.0246 | − | 27.7554i | −0.611822 | − | 1.05971i | ||||
\(687\) | −11.2639 | − | 19.5097i | −0.429746 | − | 0.744342i | ||||
\(688\) | 7.71493i | 0.294129i | ||||||||
\(689\) | 7.34346 | − | 18.7591i | 0.279763 | − | 0.714665i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.7614 | + | 11.4092i | −0.751758 | + | 0.434028i | −0.826329 | − | 0.563188i | \(-0.809575\pi\) |
0.0745709 | + | 0.997216i | \(0.476241\pi\) | |||||||
\(692\) | −5.80397 | + | 3.35092i | −0.220634 | + | 0.127383i | ||||
\(693\) | −2.58343 | − | 1.49155i | −0.0981365 | − | 0.0566592i | ||||
\(694\) | − | 8.43916i | − | 0.320346i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.28342 | − | 4.78243i | −0.313982 | − | 0.181278i | ||||
\(697\) | −12.2569 | −0.464263 | ||||||||
\(698\) | −18.9617 | − | 10.9476i | −0.717712 | − | 0.414371i | ||||
\(699\) | 7.93624 | + | 13.7460i | 0.300176 | + | 0.519920i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.2728 | 1.63439 | 0.817196 | − | 0.576359i | \(-0.195527\pi\) | ||||
0.817196 | + | 0.576359i | \(0.195527\pi\) | |||||||
\(702\) | 3.56481 | − | 0.540502i | 0.134545 | − | 0.0203999i | ||||
\(703\) | − | 13.4072i | − | 0.505662i | ||||||
\(704\) | −0.563824 | + | 0.325524i | −0.0212499 | + | 0.0122686i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.45302 | − | 7.71285i | 0.167592 | − | 0.290277i | ||||
\(707\) | −37.8599 | −1.42387 | ||||||||
\(708\) | 3.73928 | − | 6.47663i | 0.140531 | − | 0.243407i | ||||
\(709\) | −15.8342 | − | 9.14186i | −0.594664 | − | 0.343330i | 0.172275 | − | 0.985049i | \(-0.444888\pi\) |
−0.766940 | + | 0.641719i | \(0.778221\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.73079 | − | 2.99781i | 0.0649096 | − | 0.112427i | ||||
\(712\) | 7.10045 | − | 4.09944i | 0.266100 | − | 0.153633i | ||||
\(713\) | −7.96170 | − | 13.7901i | −0.298168 | − | 0.516442i | ||||
\(714\) | 16.0415 | 0.600337 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.9626 | 0.746036 | ||||||||
\(717\) | 10.4851 | + | 18.1608i | 0.391575 | + | 0.678228i | ||||
\(718\) | 32.0401 | − | 18.4983i | 1.19572 | − | 0.690352i | ||||
\(719\) | −13.6420 | + | 23.6287i | −0.508762 | + | 0.881201i | 0.491187 | + | 0.871054i | \(0.336563\pi\) |
−0.999949 | + | 0.0101468i | \(0.996770\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 78.2545 | + | 45.1803i | 2.91435 | + | 1.68260i | ||||
\(722\) | −5.30491 | + | 9.18837i | −0.197428 | + | 0.341956i | ||||
\(723\) | −6.24809 | −0.232369 | ||||||||
\(724\) | 1.59944 | − | 2.77032i | 0.0594429 | − | 0.102958i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.15920 | − | 5.28807i | 0.339930 | − | 0.196259i | ||||
\(727\) | − | 17.0453i | − | 0.632176i | −0.948730 | − | 0.316088i | \(-0.897631\pi\) | ||
0.948730 | − | 0.316088i | \(-0.102369\pi\) | |||||||
\(728\) | 12.9073 | − | 10.3117i | 0.478376 | − | 0.382178i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.5049 | − | 23.3912i | −0.499498 | − | 0.865155i | ||||
\(732\) | 5.74056 | + | 3.31432i | 0.212177 | + | 0.122501i | ||||
\(733\) | 11.2472 | 0.415424 | 0.207712 | − | 0.978190i | \(-0.433398\pi\) | ||||
0.207712 | + | 0.978190i | \(0.433398\pi\) | |||||||
\(734\) | −17.3875 | − | 10.0387i | −0.641786 | − | 0.370535i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.84994i | 0.105050i | ||||||||
\(737\) | 5.16874 | + | 2.98418i | 0.190393 | + | 0.109924i | ||||
\(738\) | 3.03194 | − | 1.75049i | 0.111607 | − | 0.0644365i | ||||
\(739\) | −9.24885 | + | 5.33982i | −0.340224 | + | 0.196429i | −0.660371 | − | 0.750939i | \(-0.729601\pi\) |
0.320147 | + | 0.947368i | \(0.396268\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.72517 | + | 3.80702i | 0.357263 | + | 0.139854i | ||||
\(742\) | 25.6009i | 0.939837i | ||||||||
\(743\) | 13.5160 | + | 23.4105i | 0.495855 | + | 0.858847i | 0.999989 | − | 0.00477910i | \(-0.00152124\pi\) |
−0.504133 | + | 0.863626i | \(0.668188\pi\) | |||||||
\(744\) | −2.79364 | − | 4.83873i | −0.102420 | − | 0.177396i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 33.3306i | 1.22032i | ||||||||
\(747\) | −5.28611 | + | 9.15582i | −0.193409 | + | 0.334994i | ||||
\(748\) | 1.13965 | − | 1.97394i | 0.0416699 | − | 0.0721743i | ||||
\(749\) | − | 11.7343i | − | 0.428761i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.7159 | + | 22.0246i | 0.464010 | + | 0.803688i | 0.999156 | − | 0.0410709i | \(-0.0130769\pi\) |
−0.535147 | + | 0.844759i | \(0.679744\pi\) | |||||||
\(752\) | −1.04315 | − | 1.80679i | −0.0380397 | − | 0.0658868i | ||||
\(753\) | 25.9518i | 0.945736i | ||||||||
\(754\) | 26.9439 | − | 21.5257i | 0.981238 | − | 0.783918i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.96812 | + | 2.29099i | −0.144319 | + | 0.0833226i | ||||
\(757\) | −37.5693 | + | 21.6906i | −1.36548 | + | 0.788359i | −0.990347 | − | 0.138612i | \(-0.955736\pi\) |
−0.375132 | + | 0.926971i | \(0.622403\pi\) | |||||||
\(758\) | −1.43619 | − | 0.829184i | −0.0521648 | − | 0.0301173i | ||||
\(759\) | 1.85544i | 0.0673484i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.5138 | − | 8.95691i | −0.562376 | − | 0.324688i | 0.191723 | − | 0.981449i | \(-0.438593\pi\) |
−0.754099 | + | 0.656761i | \(0.771926\pi\) | |||||||
\(762\) | −8.96062 | −0.324609 | ||||||||
\(763\) | 54.4303 | + | 31.4253i | 1.97051 | + | 1.13767i | ||||
\(764\) | 12.5366 | + | 21.7141i | 0.453559 | + | 0.785587i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.5932 | −0.924722 | ||||||||
\(767\) | 16.8305 | + | 21.0669i | 0.607713 | + | 0.760680i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −6.17619 | + | 3.56583i | −0.222719 | + | 0.128587i | −0.607209 | − | 0.794542i | \(-0.707711\pi\) |
0.384490 | + | 0.923129i | \(0.374377\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.44840 | − | 5.97280i | 0.124191 | − | 0.215105i | ||||
\(772\) | 8.99091 | 0.323590 | ||||||||
\(773\) | −17.9169 | + | 31.0330i | −0.644427 | + | 1.11618i | 0.340006 | + | 0.940423i | \(0.389571\pi\) |
−0.984434 | + | 0.175757i | \(0.943763\pi\) | |||||||
\(774\) | 6.68133 | + | 3.85747i | 0.240155 | + | 0.138654i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.21861 | + | 12.5030i | −0.259133 | + | 0.448832i | ||||
\(777\) | −18.3670 | + | 10.6042i | −0.658911 | + | 0.380422i | ||||
\(778\) | −4.78243 | − | 8.28342i | −0.171459 | − | 0.296975i | ||||
\(779\) | 10.1409 | 0.363335 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.47829 | 0.303377 | ||||||||
\(782\) | −4.98879 | − | 8.64084i | −0.178399 | − | 0.308996i | ||||
\(783\) | −8.28342 | + | 4.78243i | −0.296025 | + | 0.170910i | ||||
\(784\) | −6.99731 | + | 12.1197i | −0.249904 | + | 0.432846i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.34436 | + | 4.24027i | 0.261965 | + | 0.151245i | ||||
\(787\) | 8.71109 | − | 15.0880i | 0.310517 | − | 0.537831i | −0.667958 | − | 0.744199i | \(-0.732831\pi\) |
0.978474 | + | 0.206369i | \(0.0661646\pi\) | |||||||
\(788\) | 21.7846 | 0.776043 | ||||||||
\(789\) | −4.10214 | + | 7.10511i | −0.146040 | + | 0.252949i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.651048i | 0.0231340i | ||||||||
\(793\) | −18.6726 | + | 14.9177i | −0.663084 | + | 0.529743i | ||||
\(794\) | −0.463855 | −0.0164616 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.295538 | − | 0.511887i | −0.0104751 | − | 0.0181433i | ||||
\(797\) | −22.2653 | − | 12.8548i | −0.788676 | − | 0.455342i | 0.0508204 | − | 0.998708i | \(-0.483816\pi\) |
−0.839496 | + | 0.543366i | \(0.817150\pi\) | |||||||
\(798\) | −13.2721 | −0.469827 | ||||||||
\(799\) | 6.32554 | + | 3.65205i | 0.223781 | + | 0.129200i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 8.19889i | − | 0.289694i | ||||||
\(802\) | −17.6992 | − | 10.2187i | −0.624981 | − | 0.360833i | ||||
\(803\) | 0.591233 | − | 0.341349i | 0.0208642 | − | 0.0120459i | ||||
\(804\) | 7.93912 | − | 4.58365i | 0.279991 | − | 0.161653i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19.9176 | − | 3.01994i | 0.701567 | − | 0.106373i | ||||
\(807\) | 25.0171i | 0.880645i | ||||||||
\(808\) | 4.13139 | + | 7.15577i | 0.145342 | + | 0.251739i | ||||
\(809\) | 1.44563 | + | 2.50390i | 0.0508255 | + | 0.0880323i | 0.890319 | − | 0.455338i | \(-0.150481\pi\) |
−0.839493 | + | 0.543370i | \(0.817148\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.4396i | 1.66583i | 0.553400 | + | 0.832916i | \(0.313330\pi\) | ||||
−0.553400 | + | 0.832916i | \(0.686670\pi\) | |||||||
\(812\) | −21.9131 | + | 37.9545i | −0.768997 | + | 1.33194i | ||||
\(813\) | 0.134900 | − | 0.233654i | 0.00473115 | − | 0.00819459i | ||||
\(814\) | 3.01346i | 0.105622i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.75049 | − | 3.03194i | −0.0612795 | − | 0.106139i | ||||
\(817\) | 11.1735 | + | 19.3530i | 0.390910 | + | 0.677076i | ||||
\(818\) | − | 10.5688i | − | 0.369529i | ||||||
\(819\) | −2.47657 | − | 16.3339i | −0.0865384 | − | 0.570753i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.7086 | + | 15.4202i | −0.932135 | + | 0.538168i | −0.887486 | − | 0.460834i | \(-0.847550\pi\) |
−0.0446489 | + | 0.999003i | \(0.514217\pi\) | |||||||
\(822\) | 12.0873 | − | 6.97859i | 0.421592 | − | 0.243406i | ||||
\(823\) | −19.7529 | − | 11.4043i | −0.688542 | − | 0.397530i | 0.114523 | − | 0.993421i | \(-0.463466\pi\) |
−0.803066 | + | 0.595890i | \(0.796799\pi\) | |||||||
\(824\) | − | 19.7208i | − | 0.687007i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −29.6758 | − | 17.1334i | −1.03255 | − | 0.596146i | ||||
\(827\) | −43.7321 | −1.52071 | −0.760357 | − | 0.649506i | \(-0.774976\pi\) | ||||
−0.760357 | + | 0.649506i | \(0.774976\pi\) | |||||||
\(828\) | 2.46812 | + | 1.42497i | 0.0857730 | + | 0.0495211i | ||||
\(829\) | −7.34530 | − | 12.7224i | −0.255113 | − | 0.441869i | 0.709813 | − | 0.704390i | \(-0.248779\pi\) |
−0.964926 | + | 0.262521i | \(0.915446\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.9723 | 0.554073 | ||||||||
\(832\) | −3.35747 | − | 1.31432i | −0.116399 | − | 0.0455657i | ||||
\(833\) | − | 48.9949i | − | 1.69757i | ||||||
\(834\) | −8.50753 | + | 4.91182i | −0.294592 | + | 0.170082i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.942906 | + | 1.63316i | −0.0326111 | + | 0.0564841i | ||||
\(837\) | −5.58728 | −0.193125 | ||||||||
\(838\) | 14.2835 | − | 24.7397i | 0.493414 | − | 0.854618i | ||||
\(839\) | −11.8808 | − | 6.85939i | −0.410171 | − | 0.236812i | 0.280692 | − | 0.959798i | \(-0.409436\pi\) |
−0.690863 | + | 0.722985i | \(0.742769\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31.2433 | + | 54.1151i | −1.07736 | + | 1.86604i | ||||
\(842\) | −33.2716 | + | 19.2094i | −1.14661 | + | 0.661998i | ||||
\(843\) | 2.79461 | + | 4.84041i | 0.0962516 | + | 0.166713i | ||||
\(844\) | 12.1934 | 0.419715 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.08630 | −0.0717284 | ||||||||
\(847\) | −24.2299 | − | 41.9674i | −0.832548 | − | 1.44202i | ||||
\(848\) | 4.83873 | − | 2.79364i | 0.166163 | − | 0.0959340i | ||||
\(849\) | −4.88188 | + | 8.45566i | −0.167546 | + | 0.290198i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4240 | + | 6.59565i | 0.391610 | + | 0.226096i | ||||
\(852\) | 6.51127 | − | 11.2778i | 0.223072 | − | 0.386373i | ||||
\(853\) | 5.80880 | 0.198890 | 0.0994448 | − | 0.995043i | \(-0.468293\pi\) | ||||
0.0994448 | + | 0.995043i | \(0.468293\pi\) | |||||||
\(854\) | 15.1862 | − | 26.3032i | 0.519660 | − | 0.900077i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.21785 | + | 1.28048i | −0.0758047 | + | 0.0437658i | ||||
\(857\) | 49.9085i | 1.70484i | 0.522855 | + | 0.852421i | \(0.324867\pi\) | ||||
−0.522855 | + | 0.852421i | \(0.675133\pi\) | |||||||
\(858\) | −2.18587 | − | 0.855682i | −0.0746244 | − | 0.0292125i | ||||
\(859\) | 5.11251 | 0.174436 | 0.0872182 | − | 0.996189i | \(-0.472202\pi\) | ||||
0.0872182 | + | 0.996189i | \(0.472202\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.02073 | − | 13.8923i | −0.273346 | − | 0.473449i | ||||
\(862\) | 6.84351 | + | 3.95111i | 0.233091 | + | 0.134575i | ||||
\(863\) | −18.5089 | −0.630051 | −0.315025 | − | 0.949083i | \(-0.602013\pi\) | ||||
−0.315025 | + | 0.949083i | \(0.602013\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.6624i | 0.566211i | ||||||||
\(867\) | −4.10765 | − | 2.37155i | −0.139503 | − | 0.0805422i | ||||
\(868\) | −22.1710 | + | 12.8004i | −0.752533 | + | 0.434475i | ||||
\(869\) | −1.95172 | + | 1.12683i | −0.0662076 | + | 0.0382250i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.95494 | + | 32.6797i | 0.167892 | + | 1.10731i | ||||
\(872\) | − | 13.7169i | − | 0.464513i | ||||||
\(873\) | 7.21861 | + | 12.5030i | 0.244313 | + | 0.423162i | ||||
\(874\) | 4.12754 | + | 7.14910i | 0.139616 | + | 0.241822i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 1.04861i | − | 0.0354294i | ||||||
\(877\) | 1.97186 | − | 3.41536i | 0.0665850 | − | 0.115329i | −0.830811 | − | 0.556555i | \(-0.812123\pi\) |
0.897396 | + | 0.441226i | \(0.145456\pi\) | |||||||
\(878\) | 11.1728 | − | 19.3519i | 0.377065 | − | 0.653095i | ||||
\(879\) | − | 15.0136i | − | 0.506396i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.2883 | + | 31.6762i | 0.616147 | + | 1.06720i | 0.990182 | + | 0.139784i | \(0.0446407\pi\) |
−0.374035 | + | 0.927415i | \(0.622026\pi\) | |||||||
\(882\) | 6.99731 | + | 12.1197i | 0.235612 | + | 0.408091i | ||||
\(883\) | − | 22.7956i | − | 0.767134i | −0.923513 | − | 0.383567i | \(-0.874696\pi\) | ||
0.923513 | − | 0.383567i | \(-0.125304\pi\) | |||||||
\(884\) | 12.4803 | − | 1.89229i | 0.419759 | − | 0.0636445i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.1727 | + | 8.75998i | −0.509738 | + | 0.294297i | ||||
\(887\) | 9.83830 | − | 5.68015i | 0.330338 | − | 0.190721i | −0.325653 | − | 0.945489i | \(-0.605584\pi\) |
0.655991 | + | 0.754769i | \(0.272251\pi\) | |||||||
\(888\) | 4.00851 | + | 2.31432i | 0.134517 | + | 0.0776634i | ||||
\(889\) | 41.0574i | 1.37702i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.563824 | + | 0.325524i | 0.0188888 | + | 0.0109055i | ||||
\(892\) | −13.1449 | −0.440123 | ||||||||
\(893\) | −5.23351 | − | 3.02157i | −0.175133 | − | 0.101113i | ||||
\(894\) | −10.1887 | − | 17.6473i | −0.340761 | − | 0.590215i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.58199 | 0.153073 | ||||||||
\(897\) | −8.02817 | + | 6.41376i | −0.268053 | + | 0.214149i | ||||
\(898\) | − | 19.5804i | − | 0.653406i | ||||||
\(899\) | −46.2818 | + | 26.7208i | −1.54358 | + | 0.891189i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.78050 | + | 16.9403i | −0.325836 | + | 0.564364i | ||||
\(902\) | −2.27931 | −0.0758926 | ||||||||
\(903\) | 17.6749 | − | 30.6138i | 0.588182 | − | 1.01876i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.2920 | − | 19.5583i | 0.375151 | − | 0.649781i | ||||
\(907\) | −28.9626 | + | 16.7215i | −0.961686 | + | 0.555230i | −0.896692 | − | 0.442656i | \(-0.854036\pi\) |
−0.0649947 | + | 0.997886i | \(0.520703\pi\) | |||||||
\(908\) | −11.2618 | − | 19.5059i | −0.373735 | − | 0.647327i | ||||
\(909\) | 8.26277 | 0.274059 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.9855 | 1.35791 | 0.678956 | − | 0.734179i | \(-0.262433\pi\) | ||||
0.678956 | + | 0.734179i | \(0.262433\pi\) | |||||||
\(912\) | 1.44829 | + | 2.50851i | 0.0479577 | + | 0.0830652i | ||||
\(913\) | 5.96087 | − | 3.44151i | 0.197276 | − | 0.113897i | ||||
\(914\) | −11.3375 | + | 19.6371i | −0.375011 | + | 0.649538i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.5097 | + | 11.2639i | 0.644619 | + | 0.372171i | ||||
\(917\) | 19.4289 | − | 33.6518i | 0.641597 | − | 1.11128i | ||||
\(918\) | −3.50098 | −0.115550 | ||||||||
\(919\) | 6.47104 | − | 11.2082i | 0.213460 | − | 0.369724i | −0.739335 | − | 0.673338i | \(-0.764860\pi\) |
0.952795 | + | 0.303614i | \(0.0981933\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.46254 | + | 3.15380i | −0.179997 | + | 0.103921i | ||||
\(922\) | − | 32.8053i | − | 1.08038i | ||||||
\(923\) | 29.3071 | + | 36.6840i | 0.964655 | + | 1.20747i | ||||
\(924\) | 2.98309 | 0.0981365 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10.3236 | − | 17.8810i | −0.339254 | − | 0.587605i | ||||
\(927\) | −17.0787 | − | 9.86041i | −0.560939 | − | 0.323858i | ||||
\(928\) | 9.56487 | 0.313982 | ||||||||
\(929\) | 29.1850 | + | 16.8500i | 0.957529 | + | 0.552830i | 0.895412 | − | 0.445239i | \(-0.146881\pi\) |
0.0621173 | + | 0.998069i | \(0.480215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.5365i | 1.32853i | ||||||||
\(932\) | −13.7460 | − | 7.93624i | −0.450264 | − | 0.259960i | ||||
\(933\) | −23.3570 | + | 13.4851i | −0.764672 | + | 0.441484i | ||||
\(934\) | −6.73020 | + | 3.88568i | −0.220219 | + | 0.127143i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.81696 | + | 2.25049i | −0.0920753 | + | 0.0735596i | ||||
\(937\) | 12.3888i | 0.404724i | 0.979311 | + | 0.202362i | \(0.0648618\pi\) | ||||
−0.979311 | + | 0.202362i | \(0.935138\pi\) | |||||||
\(938\) | −21.0022 | − | 36.3769i | −0.685747 | − | 1.18775i | ||||
\(939\) | −9.23735 | − | 15.9996i | −0.301449 | − | 0.522126i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 5.26120i | − | 0.171510i | −0.996316 | − | 0.0857551i | \(-0.972670\pi\) | ||
0.996316 | − | 0.0857551i | \(-0.0273303\pi\) | |||||||
\(942\) | 3.27123 | − | 5.66593i | 0.106582 | − | 0.184606i | ||||
\(943\) | −4.98879 | + | 8.64084i | −0.162457 | + | 0.281385i | ||||
\(944\) | 7.47857i | 0.243407i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.51139 | − | 4.34986i | −0.0816525 | − | 0.141426i | ||||
\(947\) | 3.34711 | + | 5.79737i | 0.108766 | + | 0.188389i | 0.915271 | − | 0.402839i | \(-0.131977\pi\) |
−0.806504 | + | 0.591228i | \(0.798643\pi\) | |||||||
\(948\) | 3.46158i | 0.112427i | ||||||||
\(949\) | 3.52068 | + | 1.37821i | 0.114286 | + | 0.0447386i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.47279 | + | 1.42766i | −0.0801856 | + | 0.0462952i | ||||
\(952\) | −13.8923 | + | 8.02073i | −0.450253 | + | 0.259953i | ||||
\(953\) | −35.2569 | − | 20.3556i | −1.14208 | − | 0.659382i | −0.195137 | − | 0.980776i | \(-0.562515\pi\) |
−0.946945 | + | 0.321394i | \(0.895848\pi\) | |||||||
\(954\) | − | 5.58728i | − | 0.180895i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.1608 | − | 10.4851i | −0.587362 | − | 0.339114i | ||||
\(957\) | 6.22718 | 0.201296 | ||||||||
\(958\) | 15.1745 | + | 8.76102i | 0.490267 | + | 0.283056i | ||||
\(959\) | −31.9758 | − | 55.3837i | −1.03255 | − | 1.78843i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.217731 | −0.00702359 | ||||||||
\(962\) | −13.0387 | + | 10.4167i | −0.420384 | + | 0.335848i | ||||
\(963\) | 2.56096i | 0.0825257i | ||||||||
\(964\) | 5.41101 | − | 3.12405i | 0.174277 | − | 0.100619i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.52919 | − | 11.3089i | 0.210073 | − | 0.363857i | ||||
\(967\) | −60.9859 | −1.96117 | −0.980587 | − | 0.196085i | \(-0.937177\pi\) | ||||
−0.980587 | + | 0.196085i | \(0.937177\pi\) | |||||||
\(968\) | −5.28807 | + | 9.15920i | −0.169965 | + | 0.294388i | ||||
\(969\) | −8.78226 | − | 5.07044i | −0.282127 | − | 0.162886i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.2702 | − | 40.3052i | 0.746776 | − | 1.29345i | −0.202584 | − | 0.979265i | \(-0.564934\pi\) |
0.949360 | − | 0.314189i | \(-0.101733\pi\) | |||||||
\(972\) | 0.866025 | − | 0.500000i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | 22.5059 | + | 38.9814i | 0.721506 | + | 1.24969i | ||||
\(974\) | −20.8824 | −0.669114 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.62863 | −0.212177 | ||||||||
\(977\) | 18.8296 | + | 32.6138i | 0.602413 | + | 1.04341i | 0.992455 | + | 0.122612i | \(0.0391271\pi\) |
−0.390042 | + | 0.920797i | \(0.627540\pi\) | |||||||
\(978\) | 12.2966 | − | 7.09944i | 0.393202 | − | 0.227015i | ||||
\(979\) | −2.66893 | + | 4.62273i | −0.0852995 | + | 0.147743i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.8792 | − | 6.85845i | −0.379273 | − | 0.218973i | ||||
\(982\) | −7.97312 | + | 13.8098i | −0.254432 | + | 0.440690i | ||||
\(983\) | −32.9140 | −1.04979 | −0.524896 | − | 0.851166i | \(-0.675896\pi\) | ||||
−0.524896 | + | 0.851166i | \(0.675896\pi\) | |||||||
\(984\) | −1.75049 | + | 3.03194i | −0.0558037 | + | 0.0966548i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −29.0001 | + | 16.7432i | −0.923552 | + | 0.533213i | ||||
\(987\) | 9.55939i | 0.304279i | ||||||||
\(988\) | −10.3258 | + | 1.56561i | −0.328506 | + | 0.0498086i | ||||
\(989\) | −21.9871 | −0.699148 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.9561 | − | 51.8855i | −0.951588 | − | 1.64820i | −0.741991 | − | 0.670410i | \(-0.766118\pi\) |
−0.209597 | − | 0.977788i | \(-0.567215\pi\) | |||||||
\(992\) | 4.83873 | + | 2.79364i | 0.153630 | + | 0.0886982i | ||||
\(993\) | −4.85375 | −0.154029 | ||||||||
\(994\) | −51.6749 | − | 29.8345i | −1.63903 | − | 0.946294i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 10.5722i | − | 0.334994i | ||||||
\(997\) | 46.1811 | + | 26.6627i | 1.46257 | + | 0.844416i | 0.999130 | − | 0.0417112i | \(-0.0132809\pi\) |
0.463442 | + | 0.886127i | \(0.346614\pi\) | |||||||
\(998\) | −16.6250 | + | 9.59847i | −0.526256 | + | 0.303834i | ||||
\(999\) | 4.00851 | − | 2.31432i | 0.126824 | − | 0.0732217i |
(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.y.m.49.4 | 12 | ||
5.2 | odd | 4 | 1950.2.bc.h.751.4 | ✓ | 12 | ||
5.3 | odd | 4 | 1950.2.bc.k.751.3 | yes | 12 | ||
5.4 | even | 2 | 1950.2.y.n.49.3 | 12 | |||
13.4 | even | 6 | 1950.2.y.n.199.3 | 12 | |||
65.4 | even | 6 | inner | 1950.2.y.m.199.4 | 12 | ||
65.17 | odd | 12 | 1950.2.bc.h.901.4 | yes | 12 | ||
65.43 | odd | 12 | 1950.2.bc.k.901.3 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.m.49.4 | 12 | 1.1 | even | 1 | trivial | ||
1950.2.y.m.199.4 | 12 | 65.4 | even | 6 | inner | ||
1950.2.y.n.49.3 | 12 | 5.4 | even | 2 | |||
1950.2.y.n.199.3 | 12 | 13.4 | even | 6 | |||
1950.2.bc.h.751.4 | ✓ | 12 | 5.2 | odd | 4 | ||
1950.2.bc.h.901.4 | yes | 12 | 65.17 | odd | 12 | ||
1950.2.bc.k.751.3 | yes | 12 | 5.3 | odd | 4 | ||
1950.2.bc.k.901.3 | yes | 12 | 65.43 | odd | 12 |