Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(529,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.3 | ||
Root | \(-0.623490 + 1.07992i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.991 |
Dual form | 1014.2.e.n.529.3 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 4.29590 | 1.92118 | 0.960592 | − | 0.277963i | \(-0.0896593\pi\) | ||||
0.960592 | + | 0.277963i | \(0.0896593\pi\) | |||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 2.17845 | − | 3.77318i | 0.823376 | − | 1.42613i | −0.0797783 | − | 0.996813i | \(-0.525421\pi\) |
0.903154 | − | 0.429316i | \(-0.141245\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 2.14795 | + | 3.72036i | 0.679241 | + | 1.17648i | ||||
\(11\) | −0.579417 | − | 1.00358i | −0.174701 | − | 0.302591i | 0.765357 | − | 0.643606i | \(-0.222562\pi\) |
−0.940058 | + | 0.341016i | \(0.889229\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.35690 | 1.16443 | ||||||||
\(15\) | 2.14795 | + | 3.72036i | 0.554598 | + | 0.960592i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.246980 | + | 0.427781i | −0.0599014 | + | 0.103752i | −0.894421 | − | 0.447226i | \(-0.852412\pi\) |
0.834520 | + | 0.550978i | \(0.185745\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −0.890084 | + | 1.54167i | −0.204199 | + | 0.353683i | −0.949877 | − | 0.312623i | \(-0.898792\pi\) |
0.745678 | + | 0.666306i | \(0.232126\pi\) | |||||||
\(20\) | −2.14795 | + | 3.72036i | −0.480296 | + | 0.831897i | ||||
\(21\) | 4.35690 | 0.950753 | ||||||||
\(22\) | 0.579417 | − | 1.00358i | 0.123532 | − | 0.213964i | ||||
\(23\) | −1.69202 | − | 2.93067i | −0.352811 | − | 0.611086i | 0.633930 | − | 0.773391i | \(-0.281441\pi\) |
−0.986741 | + | 0.162304i | \(0.948107\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 13.4547 | 2.69095 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.17845 | + | 3.77318i | 0.411688 | + | 0.713064i | ||||
\(29\) | −3.46950 | − | 6.00935i | −0.644270 | − | 1.11591i | −0.984470 | − | 0.175555i | \(-0.943828\pi\) |
0.340200 | − | 0.940353i | \(-0.389505\pi\) | |||||||
\(30\) | −2.14795 | + | 3.72036i | −0.392160 | + | 0.679241i | ||||
\(31\) | −2.22521 | −0.399659 | −0.199830 | − | 0.979831i | \(-0.564039\pi\) | ||||
−0.199830 | + | 0.979831i | \(0.564039\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0.579417 | − | 1.00358i | 0.100864 | − | 0.174701i | ||||
\(34\) | −0.493959 | −0.0847133 | ||||||||
\(35\) | 9.35839 | − | 16.2092i | 1.58186 | − | 2.73986i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 1.93900 | + | 3.35845i | 0.318770 | + | 0.552126i | 0.980232 | − | 0.197853i | \(-0.0633970\pi\) |
−0.661462 | + | 0.749979i | \(0.730064\pi\) | |||||||
\(38\) | −1.78017 | −0.288781 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.29590 | −0.679241 | ||||||||
\(41\) | 3.15883 | + | 5.47126i | 0.493327 | + | 0.854467i | 0.999970 | − | 0.00768834i | \(-0.00244730\pi\) |
−0.506644 | + | 0.862156i | \(0.669114\pi\) | |||||||
\(42\) | 2.17845 | + | 3.77318i | 0.336142 | + | 0.582215i | ||||
\(43\) | −3.69202 | + | 6.39477i | −0.563028 | + | 0.975193i | 0.434202 | + | 0.900815i | \(0.357030\pi\) |
−0.997230 | + | 0.0743776i | \(0.976303\pi\) | |||||||
\(44\) | 1.15883 | 0.174701 | ||||||||
\(45\) | −2.14795 | + | 3.72036i | −0.320197 | + | 0.554598i | ||||
\(46\) | 1.69202 | − | 2.93067i | 0.249475 | − | 0.432103i | ||||
\(47\) | −1.78017 | −0.259664 | −0.129832 | − | 0.991536i | \(-0.541444\pi\) | ||||
−0.129832 | + | 0.991536i | \(0.541444\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −5.99127 | − | 10.3772i | −0.855896 | − | 1.48246i | ||||
\(50\) | 6.72737 | + | 11.6521i | 0.951393 | + | 1.64786i | ||||
\(51\) | −0.493959 | −0.0691681 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.51573 | −0.345562 | −0.172781 | − | 0.984960i | \(-0.555275\pi\) | ||||
−0.172781 | + | 0.984960i | \(0.555275\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −2.48911 | − | 4.31127i | −0.335632 | − | 0.581332i | ||||
\(56\) | −2.17845 | + | 3.77318i | −0.291107 | + | 0.504213i | ||||
\(57\) | −1.78017 | −0.235789 | ||||||||
\(58\) | 3.46950 | − | 6.00935i | 0.455568 | − | 0.789066i | ||||
\(59\) | −3.31551 | + | 5.74263i | −0.431643 | + | 0.747627i | −0.997015 | − | 0.0772087i | \(-0.975399\pi\) |
0.565372 | + | 0.824836i | \(0.308733\pi\) | |||||||
\(60\) | −4.29590 | −0.554598 | ||||||||
\(61\) | −5.24698 | + | 9.08804i | −0.671807 | + | 1.16360i | 0.305584 | + | 0.952165i | \(0.401148\pi\) |
−0.977391 | + | 0.211439i | \(0.932185\pi\) | |||||||
\(62\) | −1.11260 | − | 1.92709i | −0.141301 | − | 0.244740i | ||||
\(63\) | 2.17845 | + | 3.77318i | 0.274459 | + | 0.475376i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.15883 | 0.142643 | ||||||||
\(67\) | −2.04892 | − | 3.54883i | −0.250315 | − | 0.433558i | 0.713297 | − | 0.700861i | \(-0.247201\pi\) |
−0.963613 | + | 0.267303i | \(0.913868\pi\) | |||||||
\(68\) | −0.246980 | − | 0.427781i | −0.0299507 | − | 0.0518761i | ||||
\(69\) | 1.69202 | − | 2.93067i | 0.203695 | − | 0.352811i | ||||
\(70\) | 18.7168 | 2.23708 | ||||||||
\(71\) | −4.69202 | + | 8.12682i | −0.556841 | + | 0.964476i | 0.440917 | + | 0.897548i | \(0.354653\pi\) |
−0.997758 | + | 0.0669283i | \(0.978680\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 0.374354 | 0.0438149 | 0.0219074 | − | 0.999760i | \(-0.493026\pi\) | ||||
0.0219074 | + | 0.999760i | \(0.493026\pi\) | |||||||
\(74\) | −1.93900 | + | 3.35845i | −0.225404 | + | 0.390412i | ||||
\(75\) | 6.72737 | + | 11.6521i | 0.776809 | + | 1.34547i | ||||
\(76\) | −0.890084 | − | 1.54167i | −0.102100 | − | 0.176842i | ||||
\(77\) | −5.04892 | −0.575378 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.65519 | 0.298732 | 0.149366 | − | 0.988782i | \(-0.452277\pi\) | ||||
0.149366 | + | 0.988782i | \(0.452277\pi\) | |||||||
\(80\) | −2.14795 | − | 3.72036i | −0.240148 | − | 0.415948i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −3.15883 | + | 5.47126i | −0.348835 | + | 0.604200i | ||||
\(83\) | −14.2784 | −1.56726 | −0.783631 | − | 0.621226i | \(-0.786635\pi\) | ||||
−0.783631 | + | 0.621226i | \(0.786635\pi\) | |||||||
\(84\) | −2.17845 | + | 3.77318i | −0.237688 | + | 0.411688i | ||||
\(85\) | −1.06100 | + | 1.83770i | −0.115081 | + | 0.199327i | ||||
\(86\) | −7.38404 | −0.796242 | ||||||||
\(87\) | 3.46950 | − | 6.00935i | 0.371970 | − | 0.644270i | ||||
\(88\) | 0.579417 | + | 1.00358i | 0.0617660 | + | 0.106982i | ||||
\(89\) | −0.417895 | − | 0.723815i | −0.0442968 | − | 0.0767242i | 0.843027 | − | 0.537871i | \(-0.180771\pi\) |
−0.887324 | + | 0.461147i | \(0.847438\pi\) | |||||||
\(90\) | −4.29590 | −0.452827 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.38404 | 0.352811 | ||||||||
\(93\) | −1.11260 | − | 1.92709i | −0.115372 | − | 0.199830i | ||||
\(94\) | −0.890084 | − | 1.54167i | −0.0918051 | − | 0.159011i | ||||
\(95\) | −3.82371 | + | 6.62286i | −0.392304 | + | 0.679491i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −9.19687 | + | 15.9294i | −0.933800 | + | 1.61739i | −0.157041 | + | 0.987592i | \(0.550195\pi\) |
−0.776759 | + | 0.629797i | \(0.783138\pi\) | |||||||
\(98\) | 5.99127 | − | 10.3772i | 0.605210 | − | 1.04825i | ||||
\(99\) | 1.15883 | 0.116467 | ||||||||
\(100\) | −6.72737 | + | 11.6521i | −0.672737 | + | 1.16521i | ||||
\(101\) | 2.73341 | + | 4.73440i | 0.271984 | + | 0.471090i | 0.969370 | − | 0.245606i | \(-0.0789869\pi\) |
−0.697386 | + | 0.716696i | \(0.745654\pi\) | |||||||
\(102\) | −0.246980 | − | 0.427781i | −0.0244546 | − | 0.0423567i | ||||
\(103\) | 7.00969 | 0.690685 | 0.345343 | − | 0.938477i | \(-0.387763\pi\) | ||||
0.345343 | + | 0.938477i | \(0.387763\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 18.7168 | 1.82657 | ||||||||
\(106\) | −1.25786 | − | 2.17869i | −0.122175 | − | 0.211613i | ||||
\(107\) | 0.958615 | + | 1.66037i | 0.0926728 | + | 0.160514i | 0.908635 | − | 0.417591i | \(-0.137126\pi\) |
−0.815962 | + | 0.578105i | \(0.803792\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 18.7681 | 1.79766 | 0.898828 | − | 0.438301i | \(-0.144420\pi\) | ||||
0.898828 | + | 0.438301i | \(0.144420\pi\) | |||||||
\(110\) | 2.48911 | − | 4.31127i | 0.237328 | − | 0.411064i | ||||
\(111\) | −1.93900 | + | 3.35845i | −0.184042 | + | 0.318770i | ||||
\(112\) | −4.35690 | −0.411688 | ||||||||
\(113\) | −5.20775 | + | 9.02009i | −0.489904 | + | 0.848539i | −0.999932 | − | 0.0116189i | \(-0.996302\pi\) |
0.510028 | + | 0.860158i | \(0.329635\pi\) | |||||||
\(114\) | −0.890084 | − | 1.54167i | −0.0833640 | − | 0.144391i | ||||
\(115\) | −7.26875 | − | 12.5898i | −0.677814 | − | 1.17401i | ||||
\(116\) | 6.93900 | 0.644270 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.63102 | −0.610435 | ||||||||
\(119\) | 1.07606 | + | 1.86380i | 0.0986427 | + | 0.170854i | ||||
\(120\) | −2.14795 | − | 3.72036i | −0.196080 | − | 0.339620i | ||||
\(121\) | 4.82855 | − | 8.36330i | 0.438959 | − | 0.760300i | ||||
\(122\) | −10.4940 | −0.950078 | ||||||||
\(123\) | −3.15883 | + | 5.47126i | −0.284822 | + | 0.493327i | ||||
\(124\) | 1.11260 | − | 1.92709i | 0.0999148 | − | 0.173058i | ||||
\(125\) | 36.3207 | 3.24862 | ||||||||
\(126\) | −2.17845 | + | 3.77318i | −0.194072 | + | 0.336142i | ||||
\(127\) | −4.19687 | − | 7.26918i | −0.372412 | − | 0.645036i | 0.617524 | − | 0.786552i | \(-0.288136\pi\) |
−0.989936 | + | 0.141516i | \(0.954802\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −7.38404 | −0.650129 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.5036 | −1.17982 | −0.589910 | − | 0.807469i | \(-0.700837\pi\) | ||||
−0.589910 | + | 0.807469i | \(0.700837\pi\) | |||||||
\(132\) | 0.579417 | + | 1.00358i | 0.0504318 | + | 0.0873504i | ||||
\(133\) | 3.87800 | + | 6.71690i | 0.336265 | + | 0.582429i | ||||
\(134\) | 2.04892 | − | 3.54883i | 0.176999 | − | 0.306572i | ||||
\(135\) | −4.29590 | −0.369732 | ||||||||
\(136\) | 0.246980 | − | 0.427781i | 0.0211783 | − | 0.0366819i | ||||
\(137\) | −2.00000 | + | 3.46410i | −0.170872 | + | 0.295958i | −0.938725 | − | 0.344668i | \(-0.887992\pi\) |
0.767853 | + | 0.640626i | \(0.221325\pi\) | |||||||
\(138\) | 3.38404 | 0.288069 | ||||||||
\(139\) | 7.51573 | − | 13.0176i | 0.637476 | − | 1.10414i | −0.348509 | − | 0.937305i | \(-0.613312\pi\) |
0.985985 | − | 0.166835i | \(-0.0533548\pi\) | |||||||
\(140\) | 9.35839 | + | 16.2092i | 0.790928 | + | 1.36993i | ||||
\(141\) | −0.890084 | − | 1.54167i | −0.0749586 | − | 0.129832i | ||||
\(142\) | −9.38404 | −0.787491 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −14.9046 | − | 25.8156i | −1.23776 | − | 2.14387i | ||||
\(146\) | 0.187177 | + | 0.324200i | 0.0154909 | + | 0.0268310i | ||||
\(147\) | 5.99127 | − | 10.3772i | 0.494152 | − | 0.855896i | ||||
\(148\) | −3.87800 | −0.318770 | ||||||||
\(149\) | 1.96346 | − | 3.40081i | 0.160853 | − | 0.278605i | −0.774322 | − | 0.632792i | \(-0.781909\pi\) |
0.935175 | + | 0.354187i | \(0.115242\pi\) | |||||||
\(150\) | −6.72737 | + | 11.6521i | −0.549287 | + | 0.951393i | ||||
\(151\) | 9.62863 | 0.783567 | 0.391783 | − | 0.920057i | \(-0.371858\pi\) | ||||
0.391783 | + | 0.920057i | \(0.371858\pi\) | |||||||
\(152\) | 0.890084 | − | 1.54167i | 0.0721953 | − | 0.125046i | ||||
\(153\) | −0.246980 | − | 0.427781i | −0.0199671 | − | 0.0345841i | ||||
\(154\) | −2.52446 | − | 4.37249i | −0.203427 | − | 0.352345i | ||||
\(155\) | −9.55927 | −0.767819 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.3840 | −1.38740 | −0.693699 | − | 0.720265i | \(-0.744020\pi\) | ||||
−0.693699 | + | 0.720265i | \(0.744020\pi\) | |||||||
\(158\) | 1.32759 | + | 2.29946i | 0.105618 | + | 0.182935i | ||||
\(159\) | −1.25786 | − | 2.17869i | −0.0997552 | − | 0.172781i | ||||
\(160\) | 2.14795 | − | 3.72036i | 0.169810 | − | 0.294120i | ||||
\(161\) | −14.7439 | −1.16198 | ||||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | 11.2349 | − | 19.4594i | 0.879985 | − | 1.52418i | 0.0286294 | − | 0.999590i | \(-0.490886\pi\) |
0.851356 | − | 0.524589i | \(-0.175781\pi\) | |||||||
\(164\) | −6.31767 | −0.493327 | ||||||||
\(165\) | 2.48911 | − | 4.31127i | 0.193777 | − | 0.335632i | ||||
\(166\) | −7.13922 | − | 12.3655i | −0.554111 | − | 0.959748i | ||||
\(167\) | 0.417895 | + | 0.723815i | 0.0323377 | + | 0.0560105i | 0.881741 | − | 0.471733i | \(-0.156371\pi\) |
−0.849404 | + | 0.527744i | \(0.823038\pi\) | |||||||
\(168\) | −4.35690 | −0.336142 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.12200 | −0.162750 | ||||||||
\(171\) | −0.890084 | − | 1.54167i | −0.0680664 | − | 0.117894i | ||||
\(172\) | −3.69202 | − | 6.39477i | −0.281514 | − | 0.487597i | ||||
\(173\) | 2.08546 | − | 3.61212i | 0.158554 | − | 0.274624i | −0.775793 | − | 0.630987i | \(-0.782650\pi\) |
0.934348 | + | 0.356363i | \(0.115983\pi\) | |||||||
\(174\) | 6.93900 | 0.526044 | ||||||||
\(175\) | 29.3104 | − | 50.7672i | 2.21566 | − | 3.83764i | ||||
\(176\) | −0.579417 | + | 1.00358i | −0.0436752 | + | 0.0756476i | ||||
\(177\) | −6.63102 | −0.498418 | ||||||||
\(178\) | 0.417895 | − | 0.723815i | 0.0313225 | − | 0.0542522i | ||||
\(179\) | −11.4438 | − | 19.8213i | −0.855353 | − | 1.48152i | −0.876317 | − | 0.481735i | \(-0.840007\pi\) |
0.0209638 | − | 0.999780i | \(-0.493327\pi\) | |||||||
\(180\) | −2.14795 | − | 3.72036i | −0.160099 | − | 0.277299i | ||||
\(181\) | 11.6039 | 0.862509 | 0.431255 | − | 0.902230i | \(-0.358071\pi\) | ||||
0.431255 | + | 0.902230i | \(0.358071\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.4940 | −0.775736 | ||||||||
\(184\) | 1.69202 | + | 2.93067i | 0.124737 | + | 0.216052i | ||||
\(185\) | 8.32975 | + | 14.4275i | 0.612415 | + | 1.06073i | ||||
\(186\) | 1.11260 | − | 1.92709i | 0.0815801 | − | 0.141301i | ||||
\(187\) | 0.572417 | 0.0418592 | ||||||||
\(188\) | 0.890084 | − | 1.54167i | 0.0649160 | − | 0.112438i | ||||
\(189\) | −2.17845 | + | 3.77318i | −0.158459 | + | 0.274459i | ||||
\(190\) | −7.64742 | −0.554802 | ||||||||
\(191\) | −8.34481 | + | 14.4536i | −0.603810 | + | 1.04583i | 0.388429 | + | 0.921479i | \(0.373018\pi\) |
−0.992238 | + | 0.124350i | \(0.960315\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 4.82371 | + | 8.35491i | 0.347218 | + | 0.601399i | 0.985754 | − | 0.168193i | \(-0.0537930\pi\) |
−0.638536 | + | 0.769592i | \(0.720460\pi\) | |||||||
\(194\) | −18.3937 | −1.32059 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.9825 | 0.855896 | ||||||||
\(197\) | 9.81916 | + | 17.0073i | 0.699586 | + | 1.21172i | 0.968610 | + | 0.248585i | \(0.0799656\pi\) |
−0.269024 | + | 0.963133i | \(0.586701\pi\) | |||||||
\(198\) | 0.579417 | + | 1.00358i | 0.0411774 | + | 0.0713213i | ||||
\(199\) | 9.21044 | − | 15.9529i | 0.652911 | − | 1.13087i | −0.329502 | − | 0.944155i | \(-0.606881\pi\) |
0.982413 | − | 0.186720i | \(-0.0597857\pi\) | |||||||
\(200\) | −13.4547 | −0.951393 | ||||||||
\(201\) | 2.04892 | − | 3.54883i | 0.144519 | − | 0.250315i | ||||
\(202\) | −2.73341 | + | 4.73440i | −0.192322 | + | 0.333111i | ||||
\(203\) | −30.2325 | −2.12191 | ||||||||
\(204\) | 0.246980 | − | 0.427781i | 0.0172920 | − | 0.0299507i | ||||
\(205\) | 13.5700 | + | 23.5040i | 0.947772 | + | 1.64159i | ||||
\(206\) | 3.50484 | + | 6.07057i | 0.244194 | + | 0.422957i | ||||
\(207\) | 3.38404 | 0.235207 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.06292 | 0.142695 | ||||||||
\(210\) | 9.35839 | + | 16.2092i | 0.645790 | + | 1.11854i | ||||
\(211\) | −7.96077 | − | 13.7885i | −0.548042 | − | 0.949237i | −0.998409 | − | 0.0563930i | \(-0.982040\pi\) |
0.450367 | − | 0.892844i | \(-0.351293\pi\) | |||||||
\(212\) | 1.25786 | − | 2.17869i | 0.0863905 | − | 0.149633i | ||||
\(213\) | −9.38404 | −0.642984 | ||||||||
\(214\) | −0.958615 | + | 1.66037i | −0.0655296 | + | 0.113501i | ||||
\(215\) | −15.8605 | + | 27.4713i | −1.08168 | + | 1.87352i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −4.84750 | + | 8.39612i | −0.329070 | + | 0.569966i | ||||
\(218\) | 9.38404 | + | 16.2536i | 0.635568 | + | 1.10084i | ||||
\(219\) | 0.187177 | + | 0.324200i | 0.0126483 | + | 0.0219074i | ||||
\(220\) | 4.97823 | 0.335632 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.87800 | −0.260274 | ||||||||
\(223\) | −2.59179 | − | 4.48912i | −0.173559 | − | 0.300614i | 0.766102 | − | 0.642719i | \(-0.222194\pi\) |
−0.939662 | + | 0.342105i | \(0.888860\pi\) | |||||||
\(224\) | −2.17845 | − | 3.77318i | −0.145554 | − | 0.252106i | ||||
\(225\) | −6.72737 | + | 11.6521i | −0.448491 | + | 0.776809i | ||||
\(226\) | −10.4155 | −0.692829 | ||||||||
\(227\) | 7.44385 | − | 12.8931i | 0.494065 | − | 0.855746i | −0.505911 | − | 0.862586i | \(-0.668844\pi\) |
0.999977 | + | 0.00683921i | \(0.00217701\pi\) | |||||||
\(228\) | 0.890084 | − | 1.54167i | 0.0589472 | − | 0.102100i | ||||
\(229\) | −23.4577 | −1.55013 | −0.775065 | − | 0.631882i | \(-0.782283\pi\) | ||||
−0.775065 | + | 0.631882i | \(0.782283\pi\) | |||||||
\(230\) | 7.26875 | − | 12.5898i | 0.479287 | − | 0.830150i | ||||
\(231\) | −2.52446 | − | 4.37249i | −0.166097 | − | 0.287689i | ||||
\(232\) | 3.46950 | + | 6.00935i | 0.227784 | + | 0.394533i | ||||
\(233\) | −11.8780 | −0.778154 | −0.389077 | − | 0.921205i | \(-0.627206\pi\) | ||||
−0.389077 | + | 0.921205i | \(0.627206\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.64742 | −0.498862 | ||||||||
\(236\) | −3.31551 | − | 5.74263i | −0.215821 | − | 0.373814i | ||||
\(237\) | 1.32759 | + | 2.29946i | 0.0862364 | + | 0.149366i | ||||
\(238\) | −1.07606 | + | 1.86380i | −0.0697509 | + | 0.120812i | ||||
\(239\) | 25.3599 | 1.64039 | 0.820197 | − | 0.572081i | \(-0.193864\pi\) | ||||
0.820197 | + | 0.572081i | \(0.193864\pi\) | |||||||
\(240\) | 2.14795 | − | 3.72036i | 0.138649 | − | 0.240148i | ||||
\(241\) | 6.01089 | − | 10.4112i | 0.387195 | − | 0.670642i | −0.604876 | − | 0.796320i | \(-0.706777\pi\) |
0.992071 | + | 0.125678i | \(0.0401106\pi\) | |||||||
\(242\) | 9.65710 | 0.620782 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −5.24698 | − | 9.08804i | −0.335903 | − | 0.581802i | ||||
\(245\) | −25.7379 | − | 44.5793i | −1.64433 | − | 2.84807i | ||||
\(246\) | −6.31767 | −0.402800 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.22521 | 0.141301 | ||||||||
\(249\) | −7.13922 | − | 12.3655i | −0.452430 | − | 0.783631i | ||||
\(250\) | 18.1603 | + | 31.4546i | 1.14856 | + | 1.98936i | ||||
\(251\) | 7.67241 | − | 13.2890i | 0.484278 | − | 0.838794i | −0.515559 | − | 0.856854i | \(-0.672416\pi\) |
0.999837 | + | 0.0180600i | \(0.00574899\pi\) | |||||||
\(252\) | −4.35690 | −0.274459 | ||||||||
\(253\) | −1.96077 | + | 3.39616i | −0.123273 | + | 0.213514i | ||||
\(254\) | 4.19687 | − | 7.26918i | 0.263335 | − | 0.456109i | ||||
\(255\) | −2.12200 | −0.132885 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.75302 | + | 6.50042i | 0.234107 | + | 0.405485i | 0.959013 | − | 0.283363i | \(-0.0914501\pi\) |
−0.724906 | + | 0.688848i | \(0.758117\pi\) | |||||||
\(258\) | −3.69202 | − | 6.39477i | −0.229855 | − | 0.398121i | ||||
\(259\) | 16.8961 | 1.04987 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.93900 | 0.429513 | ||||||||
\(262\) | −6.75182 | − | 11.6945i | −0.417129 | − | 0.722489i | ||||
\(263\) | 6.11529 | + | 10.5920i | 0.377085 | + | 0.653131i | 0.990637 | − | 0.136524i | \(-0.0435931\pi\) |
−0.613552 | + | 0.789655i | \(0.710260\pi\) | |||||||
\(264\) | −0.579417 | + | 1.00358i | −0.0356606 | + | 0.0617660i | ||||
\(265\) | −10.8073 | −0.663888 | ||||||||
\(266\) | −3.87800 | + | 6.71690i | −0.237776 | + | 0.411839i | ||||
\(267\) | 0.417895 | − | 0.723815i | 0.0255747 | − | 0.0442968i | ||||
\(268\) | 4.09783 | 0.250315 | ||||||||
\(269\) | −1.35809 | + | 2.35228i | −0.0828044 | + | 0.143421i | −0.904453 | − | 0.426572i | \(-0.859721\pi\) |
0.821649 | + | 0.569994i | \(0.193054\pi\) | |||||||
\(270\) | −2.14795 | − | 3.72036i | −0.130720 | − | 0.226414i | ||||
\(271\) | 6.19687 | + | 10.7333i | 0.376433 | + | 0.652001i | 0.990540 | − | 0.137222i | \(-0.0438172\pi\) |
−0.614108 | + | 0.789222i | \(0.710484\pi\) | |||||||
\(272\) | 0.493959 | 0.0299507 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.00000 | −0.241649 | ||||||||
\(275\) | −7.79590 | − | 13.5029i | −0.470110 | − | 0.814255i | ||||
\(276\) | 1.69202 | + | 2.93067i | 0.101848 | + | 0.176405i | ||||
\(277\) | 12.0640 | − | 20.8954i | 0.724854 | − | 1.25548i | −0.234179 | − | 0.972193i | \(-0.575240\pi\) |
0.959034 | − | 0.283291i | \(-0.0914264\pi\) | |||||||
\(278\) | 15.0315 | 0.901527 | ||||||||
\(279\) | 1.11260 | − | 1.92709i | 0.0666099 | − | 0.115372i | ||||
\(280\) | −9.35839 | + | 16.2092i | −0.559271 | + | 0.968685i | ||||
\(281\) | −12.8358 | −0.765719 | −0.382860 | − | 0.923807i | \(-0.625061\pi\) | ||||
−0.382860 | + | 0.923807i | \(0.625061\pi\) | |||||||
\(282\) | 0.890084 | − | 1.54167i | 0.0530037 | − | 0.0918051i | ||||
\(283\) | −2.82371 | − | 4.89081i | −0.167852 | − | 0.290728i | 0.769812 | − | 0.638270i | \(-0.220350\pi\) |
−0.937664 | + | 0.347542i | \(0.887016\pi\) | |||||||
\(284\) | −4.69202 | − | 8.12682i | −0.278420 | − | 0.482238i | ||||
\(285\) | −7.64742 | −0.452994 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.5254 | 1.62477 | ||||||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | 8.37800 | + | 14.5111i | 0.492824 | + | 0.853596i | ||||
\(290\) | 14.9046 | − | 25.8156i | 0.875229 | − | 1.51594i | ||||
\(291\) | −18.3937 | −1.07826 | ||||||||
\(292\) | −0.187177 | + | 0.324200i | −0.0109537 | + | 0.0189724i | ||||
\(293\) | 10.6826 | − | 18.5029i | 0.624086 | − | 1.08095i | −0.364631 | − | 0.931152i | \(-0.618805\pi\) |
0.988717 | − | 0.149796i | \(-0.0478618\pi\) | |||||||
\(294\) | 11.9825 | 0.698836 | ||||||||
\(295\) | −14.2431 | + | 24.6698i | −0.829265 | + | 1.43633i | ||||
\(296\) | −1.93900 | − | 3.35845i | −0.112702 | − | 0.195206i | ||||
\(297\) | 0.579417 | + | 1.00358i | 0.0336212 | + | 0.0582336i | ||||
\(298\) | 3.92692 | 0.227480 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −13.4547 | −0.776809 | ||||||||
\(301\) | 16.0858 | + | 27.8613i | 0.927167 | + | 1.60590i | ||||
\(302\) | 4.81431 | + | 8.33864i | 0.277033 | + | 0.479835i | ||||
\(303\) | −2.73341 | + | 4.73440i | −0.157030 | + | 0.271984i | ||||
\(304\) | 1.78017 | 0.102100 | ||||||||
\(305\) | −22.5405 | + | 39.0413i | −1.29066 | + | 2.23550i | ||||
\(306\) | 0.246980 | − | 0.427781i | 0.0141189 | − | 0.0244546i | ||||
\(307\) | 28.8853 | 1.64857 | 0.824286 | − | 0.566174i | \(-0.191577\pi\) | ||||
0.824286 | + | 0.566174i | \(0.191577\pi\) | |||||||
\(308\) | 2.52446 | − | 4.37249i | 0.143844 | − | 0.249146i | ||||
\(309\) | 3.50484 | + | 6.07057i | 0.199384 | + | 0.345343i | ||||
\(310\) | −4.77963 | − | 8.27857i | −0.271465 | − | 0.470191i | ||||
\(311\) | 3.38404 | 0.191891 | 0.0959457 | − | 0.995387i | \(-0.469412\pi\) | ||||
0.0959457 | + | 0.995387i | \(0.469412\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3502 | 0.811121 | 0.405560 | − | 0.914068i | \(-0.367076\pi\) | ||||
0.405560 | + | 0.914068i | \(0.367076\pi\) | |||||||
\(314\) | −8.69202 | − | 15.0550i | −0.490519 | − | 0.849604i | ||||
\(315\) | 9.35839 | + | 16.2092i | 0.527285 | + | 0.913285i | ||||
\(316\) | −1.32759 | + | 2.29946i | −0.0746829 | + | 0.129355i | ||||
\(317\) | 18.5332 | 1.04093 | 0.520464 | − | 0.853884i | \(-0.325759\pi\) | ||||
0.520464 | + | 0.853884i | \(0.325759\pi\) | |||||||
\(318\) | 1.25786 | − | 2.17869i | 0.0705376 | − | 0.122175i | ||||
\(319\) | −4.02057 | + | 6.96384i | −0.225109 | + | 0.389900i | ||||
\(320\) | 4.29590 | 0.240148 | ||||||||
\(321\) | −0.958615 | + | 1.66037i | −0.0535047 | + | 0.0926728i | ||||
\(322\) | −7.37196 | − | 12.7686i | −0.410823 | − | 0.711567i | ||||
\(323\) | −0.439665 | − | 0.761522i | −0.0244636 | − | 0.0423722i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.4698 | 1.24449 | ||||||||
\(327\) | 9.38404 | + | 16.2536i | 0.518939 | + | 0.898828i | ||||
\(328\) | −3.15883 | − | 5.47126i | −0.174417 | − | 0.302100i | ||||
\(329\) | −3.87800 | + | 6.71690i | −0.213801 | + | 0.370315i | ||||
\(330\) | 4.97823 | 0.274043 | ||||||||
\(331\) | 3.93900 | − | 6.82255i | 0.216507 | − | 0.375001i | −0.737231 | − | 0.675641i | \(-0.763867\pi\) |
0.953738 | + | 0.300640i | \(0.0972002\pi\) | |||||||
\(332\) | 7.13922 | − | 12.3655i | 0.391816 | − | 0.678644i | ||||
\(333\) | −3.87800 | −0.212513 | ||||||||
\(334\) | −0.417895 | + | 0.723815i | −0.0228662 | + | 0.0396054i | ||||
\(335\) | −8.80194 | − | 15.2454i | −0.480901 | − | 0.832945i | ||||
\(336\) | −2.17845 | − | 3.77318i | −0.118844 | − | 0.205844i | ||||
\(337\) | −13.7265 | −0.747728 | −0.373864 | − | 0.927484i | \(-0.621967\pi\) | ||||
−0.373864 | + | 0.927484i | \(0.621967\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.4155 | −0.565692 | ||||||||
\(340\) | −1.06100 | − | 1.83770i | −0.0575407 | − | 0.0996635i | ||||
\(341\) | 1.28932 | + | 2.23317i | 0.0698208 | + | 0.120933i | ||||
\(342\) | 0.890084 | − | 1.54167i | 0.0481302 | − | 0.0833640i | ||||
\(343\) | −21.7084 | −1.17214 | ||||||||
\(344\) | 3.69202 | − | 6.39477i | 0.199060 | − | 0.344783i | ||||
\(345\) | 7.26875 | − | 12.5898i | 0.391336 | − | 0.677814i | ||||
\(346\) | 4.17092 | 0.224230 | ||||||||
\(347\) | 2.42543 | − | 4.20096i | 0.130204 | − | 0.225520i | −0.793551 | − | 0.608503i | \(-0.791770\pi\) |
0.923755 | + | 0.382984i | \(0.125104\pi\) | |||||||
\(348\) | 3.46950 | + | 6.00935i | 0.185985 | + | 0.322135i | ||||
\(349\) | −14.1739 | − | 24.5499i | −0.758711 | − | 1.31413i | −0.943508 | − | 0.331350i | \(-0.892496\pi\) |
0.184797 | − | 0.982777i | \(-0.440837\pi\) | |||||||
\(350\) | 58.6209 | 3.13342 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.15883 | −0.0617660 | ||||||||
\(353\) | −14.2228 | − | 24.6346i | −0.757004 | − | 1.31117i | −0.944372 | − | 0.328880i | \(-0.893329\pi\) |
0.187368 | − | 0.982290i | \(-0.440004\pi\) | |||||||
\(354\) | −3.31551 | − | 5.74263i | −0.176217 | − | 0.305218i | ||||
\(355\) | −20.1564 | + | 34.9120i | −1.06979 | + | 1.85294i | ||||
\(356\) | 0.835790 | 0.0442968 | ||||||||
\(357\) | −1.07606 | + | 1.86380i | −0.0569514 | + | 0.0986427i | ||||
\(358\) | 11.4438 | − | 19.8213i | 0.604826 | − | 1.04759i | ||||
\(359\) | −11.2271 | −0.592545 | −0.296273 | − | 0.955103i | \(-0.595744\pi\) | ||||
−0.296273 | + | 0.955103i | \(0.595744\pi\) | |||||||
\(360\) | 2.14795 | − | 3.72036i | 0.113207 | − | 0.196080i | ||||
\(361\) | 7.91550 | + | 13.7101i | 0.416605 | + | 0.721582i | ||||
\(362\) | 5.80194 | + | 10.0493i | 0.304943 | + | 0.528177i | ||||
\(363\) | 9.65710 | 0.506867 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.60819 | 0.0841764 | ||||||||
\(366\) | −5.24698 | − | 9.08804i | −0.274264 | − | 0.475039i | ||||
\(367\) | −8.41335 | − | 14.5723i | −0.439173 | − | 0.760670i | 0.558453 | − | 0.829536i | \(-0.311395\pi\) |
−0.997626 | + | 0.0688662i | \(0.978062\pi\) | |||||||
\(368\) | −1.69202 | + | 2.93067i | −0.0882027 | + | 0.152772i | ||||
\(369\) | −6.31767 | −0.328885 | ||||||||
\(370\) | −8.32975 | + | 14.4275i | −0.433043 | + | 0.750053i | ||||
\(371\) | −5.48039 | + | 9.49231i | −0.284527 | + | 0.492816i | ||||
\(372\) | 2.22521 | 0.115372 | ||||||||
\(373\) | 13.2664 | − | 22.9780i | 0.686906 | − | 1.18976i | −0.285928 | − | 0.958251i | \(-0.592302\pi\) |
0.972834 | − | 0.231505i | \(-0.0743649\pi\) | |||||||
\(374\) | 0.286208 | + | 0.495727i | 0.0147995 | + | 0.0256334i | ||||
\(375\) | 18.1603 | + | 31.4546i | 0.937795 | + | 1.62431i | ||||
\(376\) | 1.78017 | 0.0918051 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.35690 | −0.224095 | ||||||||
\(379\) | 10.9879 | + | 19.0316i | 0.564411 | + | 0.977589i | 0.997104 | + | 0.0760479i | \(0.0242302\pi\) |
−0.432693 | + | 0.901541i | \(0.642436\pi\) | |||||||
\(380\) | −3.82371 | − | 6.62286i | −0.196152 | − | 0.339745i | ||||
\(381\) | 4.19687 | − | 7.26918i | 0.215012 | − | 0.372412i | ||||
\(382\) | −16.6896 | −0.853916 | ||||||||
\(383\) | −0.307979 | + | 0.533434i | −0.0157370 | + | 0.0272572i | −0.873787 | − | 0.486309i | \(-0.838343\pi\) |
0.858050 | + | 0.513567i | \(0.171676\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | −21.6896 | −1.10541 | ||||||||
\(386\) | −4.82371 | + | 8.35491i | −0.245520 | + | 0.425254i | ||||
\(387\) | −3.69202 | − | 6.39477i | −0.187676 | − | 0.325064i | ||||
\(388\) | −9.19687 | − | 15.9294i | −0.466900 | − | 0.808695i | ||||
\(389\) | −35.5260 | −1.80124 | −0.900620 | − | 0.434607i | \(-0.856887\pi\) | ||||
−0.900620 | + | 0.434607i | \(0.856887\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.67158 | 0.0845354 | ||||||||
\(392\) | 5.99127 | + | 10.3772i | 0.302605 | + | 0.524127i | ||||
\(393\) | −6.75182 | − | 11.6945i | −0.340584 | − | 0.589910i | ||||
\(394\) | −9.81916 | + | 17.0073i | −0.494682 | + | 0.856815i | ||||
\(395\) | 11.4064 | 0.573918 | ||||||||
\(396\) | −0.579417 | + | 1.00358i | −0.0291168 | + | 0.0504318i | ||||
\(397\) | −8.03923 | + | 13.9244i | −0.403477 | + | 0.698843i | −0.994143 | − | 0.108073i | \(-0.965532\pi\) |
0.590666 | + | 0.806916i | \(0.298865\pi\) | |||||||
\(398\) | 18.4209 | 0.923355 | ||||||||
\(399\) | −3.87800 | + | 6.71690i | −0.194143 | + | 0.336265i | ||||
\(400\) | −6.72737 | − | 11.6521i | −0.336368 | − | 0.582607i | ||||
\(401\) | 11.4547 | + | 19.8402i | 0.572022 | + | 0.990771i | 0.996358 | + | 0.0852664i | \(0.0271741\pi\) |
−0.424336 | + | 0.905505i | \(0.639493\pi\) | |||||||
\(402\) | 4.09783 | 0.204381 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.46681 | −0.271984 | ||||||||
\(405\) | −2.14795 | − | 3.72036i | −0.106732 | − | 0.184866i | ||||
\(406\) | −15.1163 | − | 26.1821i | −0.750207 | − | 1.29940i | ||||
\(407\) | 2.24698 | − | 3.89188i | 0.111379 | − | 0.192913i | ||||
\(408\) | 0.493959 | 0.0244546 | ||||||||
\(409\) | −0.623490 | + | 1.07992i | −0.0308296 | + | 0.0533984i | −0.881029 | − | 0.473063i | \(-0.843148\pi\) |
0.850199 | + | 0.526462i | \(0.176482\pi\) | |||||||
\(410\) | −13.5700 | + | 23.5040i | −0.670176 | + | 1.16078i | ||||
\(411\) | −4.00000 | −0.197305 | ||||||||
\(412\) | −3.50484 | + | 6.07057i | −0.172671 | + | 0.299075i | ||||
\(413\) | 14.4453 | + | 25.0201i | 0.710809 | + | 1.23116i | ||||
\(414\) | 1.69202 | + | 2.93067i | 0.0831583 | + | 0.144034i | ||||
\(415\) | −61.3387 | −3.01100 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.0315 | 0.736094 | ||||||||
\(418\) | 1.03146 | + | 1.78654i | 0.0504503 | + | 0.0873825i | ||||
\(419\) | −14.7315 | − | 25.5158i | −0.719683 | − | 1.24653i | −0.961125 | − | 0.276112i | \(-0.910954\pi\) |
0.241442 | − | 0.970415i | \(-0.422380\pi\) | |||||||
\(420\) | −9.35839 | + | 16.2092i | −0.456643 | + | 0.790928i | ||||
\(421\) | 17.3491 | 0.845545 | 0.422772 | − | 0.906236i | \(-0.361057\pi\) | ||||
0.422772 | + | 0.906236i | \(0.361057\pi\) | |||||||
\(422\) | 7.96077 | − | 13.7885i | 0.387524 | − | 0.671212i | ||||
\(423\) | 0.890084 | − | 1.54167i | 0.0432774 | − | 0.0749586i | ||||
\(424\) | 2.51573 | 0.122175 | ||||||||
\(425\) | −3.32304 | + | 5.75568i | −0.161191 | + | 0.279192i | ||||
\(426\) | −4.69202 | − | 8.12682i | −0.227329 | − | 0.393746i | ||||
\(427\) | 22.8605 | + | 39.5956i | 1.10630 | + | 1.91617i | ||||
\(428\) | −1.91723 | −0.0926728 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −31.7211 | −1.52973 | ||||||||
\(431\) | 12.6920 | + | 21.9832i | 0.611353 | + | 1.05889i | 0.991013 | + | 0.133768i | \(0.0427078\pi\) |
−0.379659 | + | 0.925126i | \(0.623959\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −10.0027 | + | 17.3252i | −0.480699 | + | 0.832594i | −0.999755 | − | 0.0221458i | \(-0.992950\pi\) |
0.519056 | + | 0.854740i | \(0.326284\pi\) | |||||||
\(434\) | −9.69501 | −0.465375 | ||||||||
\(435\) | 14.9046 | − | 25.8156i | 0.714622 | − | 1.23776i | ||||
\(436\) | −9.38404 | + | 16.2536i | −0.449414 | + | 0.778408i | ||||
\(437\) | 6.02416 | 0.288175 | ||||||||
\(438\) | −0.187177 | + | 0.324200i | −0.00894367 | + | 0.0154909i | ||||
\(439\) | −0.271971 | − | 0.471067i | −0.0129805 | − | 0.0224828i | 0.859462 | − | 0.511199i | \(-0.170799\pi\) |
−0.872443 | + | 0.488716i | \(0.837465\pi\) | |||||||
\(440\) | 2.48911 | + | 4.31127i | 0.118664 | + | 0.205532i | ||||
\(441\) | 11.9825 | 0.570597 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.1360 | −0.861667 | −0.430834 | − | 0.902431i | \(-0.641780\pi\) | ||||
−0.430834 | + | 0.902431i | \(0.641780\pi\) | |||||||
\(444\) | −1.93900 | − | 3.35845i | −0.0920209 | − | 0.159385i | ||||
\(445\) | −1.79523 | − | 3.10943i | −0.0851022 | − | 0.147401i | ||||
\(446\) | 2.59179 | − | 4.48912i | 0.122725 | − | 0.212566i | ||||
\(447\) | 3.92692 | 0.185737 | ||||||||
\(448\) | 2.17845 | − | 3.77318i | 0.102922 | − | 0.178266i | ||||
\(449\) | 14.6896 | − | 25.4432i | 0.693246 | − | 1.20074i | −0.277522 | − | 0.960719i | \(-0.589513\pi\) |
0.970768 | − | 0.240019i | \(-0.0771536\pi\) | |||||||
\(450\) | −13.4547 | −0.634262 | ||||||||
\(451\) | 3.66056 | − | 6.34028i | 0.172369 | − | 0.298552i | ||||
\(452\) | −5.20775 | − | 9.02009i | −0.244952 | − | 0.424269i | ||||
\(453\) | 4.81431 | + | 8.33864i | 0.226196 | + | 0.391783i | ||||
\(454\) | 14.8877 | 0.698714 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.78017 | 0.0833640 | ||||||||
\(457\) | −4.17360 | − | 7.22889i | −0.195233 | − | 0.338153i | 0.751744 | − | 0.659455i | \(-0.229213\pi\) |
−0.946977 | + | 0.321302i | \(0.895880\pi\) | |||||||
\(458\) | −11.7289 | − | 20.3150i | −0.548054 | − | 0.949257i | ||||
\(459\) | 0.246980 | − | 0.427781i | 0.0115280 | − | 0.0199671i | ||||
\(460\) | 14.5375 | 0.677814 | ||||||||
\(461\) | 10.7485 | − | 18.6169i | 0.500606 | − | 0.867075i | −0.499394 | − | 0.866375i | \(-0.666444\pi\) |
1.00000 | 0.000700154i | \(-0.000222866\pi\) | ||||||||
\(462\) | 2.52446 | − | 4.37249i | 0.117448 | − | 0.203427i | ||||
\(463\) | −26.1715 | −1.21629 | −0.608147 | − | 0.793825i | \(-0.708087\pi\) | ||||
−0.608147 | + | 0.793825i | \(0.708087\pi\) | |||||||
\(464\) | −3.46950 | + | 6.00935i | −0.161068 | + | 0.278977i | ||||
\(465\) | −4.77963 | − | 8.27857i | −0.221650 | − | 0.383910i | ||||
\(466\) | −5.93900 | − | 10.2867i | −0.275119 | − | 0.476520i | ||||
\(467\) | −9.81269 | −0.454077 | −0.227039 | − | 0.973886i | \(-0.572904\pi\) | ||||
−0.227039 | + | 0.973886i | \(0.572904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.8538 | −0.824414 | ||||||||
\(470\) | −3.82371 | − | 6.62286i | −0.176374 | − | 0.305490i | ||||
\(471\) | −8.69202 | − | 15.0550i | −0.400507 | − | 0.693699i | ||||
\(472\) | 3.31551 | − | 5.74263i | 0.152609 | − | 0.264326i | ||||
\(473\) | 8.55688 | 0.393446 | ||||||||
\(474\) | −1.32759 | + | 2.29946i | −0.0609784 | + | 0.105618i | ||||
\(475\) | −11.9758 | + | 20.7428i | −0.549489 | + | 0.951743i | ||||
\(476\) | −2.15213 | −0.0986427 | ||||||||
\(477\) | 1.25786 | − | 2.17869i | 0.0575937 | − | 0.0997552i | ||||
\(478\) | 12.6799 | + | 21.9623i | 0.579967 | + | 1.00453i | ||||
\(479\) | 8.64071 | + | 14.9662i | 0.394804 | + | 0.683821i | 0.993076 | − | 0.117472i | \(-0.0374791\pi\) |
−0.598272 | + | 0.801293i | \(0.704146\pi\) | |||||||
\(480\) | 4.29590 | 0.196080 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 12.0218 | 0.547577 | ||||||||
\(483\) | −7.37196 | − | 12.7686i | −0.335436 | − | 0.580992i | ||||
\(484\) | 4.82855 | + | 8.36330i | 0.219480 | + | 0.380150i | ||||
\(485\) | −39.5088 | + | 68.4312i | −1.79400 | + | 3.10730i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −15.8443 | + | 27.4431i | −0.717973 | + | 1.24357i | 0.243829 | + | 0.969818i | \(0.421597\pi\) |
−0.961802 | + | 0.273747i | \(0.911737\pi\) | |||||||
\(488\) | 5.24698 | − | 9.08804i | 0.237520 | − | 0.411396i | ||||
\(489\) | 22.4698 | 1.01612 | ||||||||
\(490\) | 25.7379 | − | 44.5793i | 1.16272 | − | 2.01389i | ||||
\(491\) | −1.15183 | − | 1.99503i | −0.0519815 | − | 0.0900346i | 0.838864 | − | 0.544341i | \(-0.183220\pi\) |
−0.890845 | + | 0.454307i | \(0.849887\pi\) | |||||||
\(492\) | −3.15883 | − | 5.47126i | −0.142411 | − | 0.246663i | ||||
\(493\) | 3.42758 | 0.154371 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.97823 | 0.223755 | ||||||||
\(496\) | 1.11260 | + | 1.92709i | 0.0499574 | + | 0.0865288i | ||||
\(497\) | 20.4426 | + | 35.4077i | 0.916978 | + | 1.58825i | ||||
\(498\) | 7.13922 | − | 12.3655i | 0.319916 | − | 0.554111i | ||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | −18.1603 | + | 31.4546i | −0.812154 | + | 1.40669i | ||||
\(501\) | −0.417895 | + | 0.723815i | −0.0186702 | + | 0.0323377i | ||||
\(502\) | 15.3448 | 0.684873 | ||||||||
\(503\) | 17.6843 | − | 30.6300i | 0.788502 | − | 1.36573i | −0.138383 | − | 0.990379i | \(-0.544190\pi\) |
0.926885 | − | 0.375346i | \(-0.122476\pi\) | |||||||
\(504\) | −2.17845 | − | 3.77318i | −0.0970358 | − | 0.168071i | ||||
\(505\) | 11.7424 | + | 20.3385i | 0.522531 | + | 0.905051i | ||||
\(506\) | −3.92154 | −0.174334 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.39373 | 0.372412 | ||||||||
\(509\) | 14.3056 | + | 24.7780i | 0.634084 | + | 1.09827i | 0.986708 | + | 0.162501i | \(0.0519560\pi\) |
−0.352624 | + | 0.935765i | \(0.614711\pi\) | |||||||
\(510\) | −1.06100 | − | 1.83770i | −0.0469818 | − | 0.0813749i | ||||
\(511\) | 0.815511 | − | 1.41251i | 0.0360761 | − | 0.0624856i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.890084 | − | 1.54167i | 0.0392982 | − | 0.0680664i | ||||
\(514\) | −3.75302 | + | 6.50042i | −0.165539 | + | 0.286721i | ||||
\(515\) | 30.1129 | 1.32693 | ||||||||
\(516\) | 3.69202 | − | 6.39477i | 0.162532 | − | 0.281514i | ||||
\(517\) | 1.03146 | + | 1.78654i | 0.0453635 | + | 0.0785719i | ||||
\(518\) | 8.44803 | + | 14.6324i | 0.371185 | + | 0.642911i | ||||
\(519\) | 4.17092 | 0.183083 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.1594 | −0.751768 | −0.375884 | − | 0.926667i | \(-0.622661\pi\) | ||||
−0.375884 | + | 0.926667i | \(0.622661\pi\) | |||||||
\(522\) | 3.46950 | + | 6.00935i | 0.151856 | + | 0.263022i | ||||
\(523\) | −8.25667 | − | 14.3010i | −0.361039 | − | 0.625338i | 0.627093 | − | 0.778944i | \(-0.284245\pi\) |
−0.988132 | + | 0.153607i | \(0.950911\pi\) | |||||||
\(524\) | 6.75182 | − | 11.6945i | 0.294955 | − | 0.510877i | ||||
\(525\) | 58.6209 | 2.55842 | ||||||||
\(526\) | −6.11529 | + | 10.5920i | −0.266639 | + | 0.461833i | ||||
\(527\) | 0.549581 | − | 0.951903i | 0.0239401 | − | 0.0414655i | ||||
\(528\) | −1.15883 | −0.0504318 | ||||||||
\(529\) | 5.77413 | − | 10.0011i | 0.251049 | − | 0.434830i | ||||
\(530\) | −5.40366 | − | 9.35941i | −0.234720 | − | 0.406547i | ||||
\(531\) | −3.31551 | − | 5.74263i | −0.143881 | − | 0.249209i | ||||
\(532\) | −7.75600 | −0.336265 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.835790 | 0.0361682 | ||||||||
\(535\) | 4.11811 | + | 7.13278i | 0.178042 | + | 0.308377i | ||||
\(536\) | 2.04892 | + | 3.54883i | 0.0884997 | + | 0.153286i | ||||
\(537\) | 11.4438 | − | 19.8213i | 0.493838 | − | 0.855353i | ||||
\(538\) | −2.71618 | −0.117103 | ||||||||
\(539\) | −6.94289 | + | 12.0254i | −0.299051 | + | 0.517972i | ||||
\(540\) | 2.14795 | − | 3.72036i | 0.0924330 | − | 0.160099i | ||||
\(541\) | 25.0858 | 1.07852 | 0.539260 | − | 0.842139i | \(-0.318704\pi\) | ||||
0.539260 | + | 0.842139i | \(0.318704\pi\) | |||||||
\(542\) | −6.19687 | + | 10.7333i | −0.266178 | + | 0.461034i | ||||
\(543\) | 5.80194 | + | 10.0493i | 0.248985 | + | 0.431255i | ||||
\(544\) | 0.246980 | + | 0.427781i | 0.0105892 | + | 0.0183410i | ||||
\(545\) | 80.6258 | 3.45363 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.1594 | 1.33228 | 0.666140 | − | 0.745826i | \(-0.267945\pi\) | ||||
0.666140 | + | 0.745826i | \(0.267945\pi\) | |||||||
\(548\) | −2.00000 | − | 3.46410i | −0.0854358 | − | 0.147979i | ||||
\(549\) | −5.24698 | − | 9.08804i | −0.223936 | − | 0.387868i | ||||
\(550\) | 7.79590 | − | 13.5029i | 0.332418 | − | 0.575765i | ||||
\(551\) | 12.3526 | 0.526238 | ||||||||
\(552\) | −1.69202 | + | 2.93067i | −0.0720172 | + | 0.124737i | ||||
\(553\) | 5.78418 | − | 10.0185i | 0.245969 | − | 0.426030i | ||||
\(554\) | 24.1280 | 1.02510 | ||||||||
\(555\) | −8.32975 | + | 14.4275i | −0.353578 | + | 0.612415i | ||||
\(556\) | 7.51573 | + | 13.0176i | 0.318738 | + | 0.552070i | ||||
\(557\) | 1.98792 | + | 3.44318i | 0.0842308 | + | 0.145892i | 0.905063 | − | 0.425277i | \(-0.139823\pi\) |
−0.820832 | + | 0.571169i | \(0.806490\pi\) | |||||||
\(558\) | 2.22521 | 0.0942006 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −18.7168 | −0.790928 | ||||||||
\(561\) | 0.286208 | + | 0.495727i | 0.0120837 | + | 0.0209296i | ||||
\(562\) | −6.41789 | − | 11.1161i | −0.270723 | − | 0.468905i | ||||
\(563\) | −0.301405 | + | 0.522049i | −0.0127027 | + | 0.0220018i | −0.872307 | − | 0.488959i | \(-0.837377\pi\) |
0.859604 | + | 0.510961i | \(0.170710\pi\) | |||||||
\(564\) | 1.78017 | 0.0749586 | ||||||||
\(565\) | −22.3720 | + | 38.7494i | −0.941195 | + | 1.63020i | ||||
\(566\) | 2.82371 | − | 4.89081i | 0.118689 | − | 0.205576i | ||||
\(567\) | −4.35690 | −0.182972 | ||||||||
\(568\) | 4.69202 | − | 8.12682i | 0.196873 | − | 0.340994i | ||||
\(569\) | −1.10992 | − | 1.92243i | −0.0465301 | − | 0.0805925i | 0.841822 | − | 0.539755i | \(-0.181483\pi\) |
−0.888352 | + | 0.459162i | \(0.848150\pi\) | |||||||
\(570\) | −3.82371 | − | 6.62286i | −0.160158 | − | 0.277401i | ||||
\(571\) | 24.4155 | 1.02176 | 0.510878 | − | 0.859653i | \(-0.329320\pi\) | ||||
0.510878 | + | 0.859653i | \(0.329320\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.6896 | −0.697219 | ||||||||
\(574\) | 13.7627 | + | 23.8377i | 0.574444 | + | 0.994967i | ||||
\(575\) | −22.7657 | − | 39.4313i | −0.949395 | − | 1.64440i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 20.7375 | 0.863313 | 0.431656 | − | 0.902038i | \(-0.357929\pi\) | ||||
0.431656 | + | 0.902038i | \(0.357929\pi\) | |||||||
\(578\) | −8.37800 | + | 14.5111i | −0.348479 | + | 0.603583i | ||||
\(579\) | −4.82371 | + | 8.35491i | −0.200466 | + | 0.347218i | ||||
\(580\) | 29.8092 | 1.23776 | ||||||||
\(581\) | −31.1048 | + | 53.8752i | −1.29045 | + | 2.23512i | ||||
\(582\) | −9.19687 | − | 15.9294i | −0.381222 | − | 0.660296i | ||||
\(583\) | 1.45766 | + | 2.52473i | 0.0603699 | + | 0.104564i | ||||
\(584\) | −0.374354 | −0.0154909 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.3653 | 0.882591 | ||||||||
\(587\) | −5.68396 | − | 9.84490i | −0.234602 | − | 0.406343i | 0.724555 | − | 0.689217i | \(-0.242045\pi\) |
−0.959157 | + | 0.282874i | \(0.908712\pi\) | |||||||
\(588\) | 5.99127 | + | 10.3772i | 0.247076 | + | 0.427948i | ||||
\(589\) | 1.98062 | − | 3.43054i | 0.0816101 | − | 0.141353i | ||||
\(590\) | −28.4862 | −1.17276 | ||||||||
\(591\) | −9.81916 | + | 17.0073i | −0.403906 | + | 0.699586i | ||||
\(592\) | 1.93900 | − | 3.35845i | 0.0796925 | − | 0.138031i | ||||
\(593\) | −36.7198 | −1.50790 | −0.753950 | − | 0.656932i | \(-0.771854\pi\) | ||||
−0.753950 | + | 0.656932i | \(0.771854\pi\) | |||||||
\(594\) | −0.579417 | + | 1.00358i | −0.0237738 | + | 0.0411774i | ||||
\(595\) | 4.62266 | + | 8.00669i | 0.189511 | + | 0.328242i | ||||
\(596\) | 1.96346 | + | 3.40081i | 0.0804264 | + | 0.139303i | ||||
\(597\) | 18.4209 | 0.753916 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −47.4965 | −1.94065 | −0.970327 | − | 0.241798i | \(-0.922263\pi\) | ||||
−0.970327 | + | 0.241798i | \(0.922263\pi\) | |||||||
\(600\) | −6.72737 | − | 11.6521i | −0.274644 | − | 0.475697i | ||||
\(601\) | −3.87531 | − | 6.71224i | −0.158077 | − | 0.273798i | 0.776098 | − | 0.630612i | \(-0.217196\pi\) |
−0.934175 | + | 0.356814i | \(0.883863\pi\) | |||||||
\(602\) | −16.0858 | + | 27.8613i | −0.655606 | + | 1.13554i | ||||
\(603\) | 4.09783 | 0.166877 | ||||||||
\(604\) | −4.81431 | + | 8.33864i | −0.195892 | + | 0.339294i | ||||
\(605\) | 20.7430 | − | 35.9279i | 0.843321 | − | 1.46068i | ||||
\(606\) | −5.46681 | −0.222074 | ||||||||
\(607\) | −1.82155 | + | 3.15502i | −0.0739345 | + | 0.128058i | −0.900622 | − | 0.434602i | \(-0.856889\pi\) |
0.826688 | + | 0.562661i | \(0.190222\pi\) | |||||||
\(608\) | 0.890084 | + | 1.54167i | 0.0360977 | + | 0.0625230i | ||||
\(609\) | −15.1163 | − | 26.1821i | −0.612541 | − | 1.06095i | ||||
\(610\) | −45.0810 | −1.82528 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.493959 | 0.0199671 | ||||||||
\(613\) | −15.2131 | − | 26.3499i | −0.614452 | − | 1.06426i | −0.990480 | − | 0.137654i | \(-0.956044\pi\) |
0.376028 | − | 0.926608i | \(-0.377290\pi\) | |||||||
\(614\) | 14.4426 | + | 25.0154i | 0.582858 | + | 1.00954i | ||||
\(615\) | −13.5700 | + | 23.5040i | −0.547196 | + | 0.947772i | ||||
\(616\) | 5.04892 | 0.203427 | ||||||||
\(617\) | 4.08277 | − | 7.07156i | 0.164366 | − | 0.284690i | −0.772064 | − | 0.635545i | \(-0.780775\pi\) |
0.936430 | + | 0.350854i | \(0.114109\pi\) | |||||||
\(618\) | −3.50484 | + | 6.07057i | −0.140986 | + | 0.244194i | ||||
\(619\) | −7.95646 | −0.319797 | −0.159899 | − | 0.987133i | \(-0.551117\pi\) | ||||
−0.159899 | + | 0.987133i | \(0.551117\pi\) | |||||||
\(620\) | 4.77963 | − | 8.27857i | 0.191955 | − | 0.332475i | ||||
\(621\) | 1.69202 | + | 2.93067i | 0.0678985 | + | 0.117604i | ||||
\(622\) | 1.69202 | + | 2.93067i | 0.0678439 | + | 0.117509i | ||||
\(623\) | −3.64145 | −0.145892 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 88.7561 | 3.55024 | ||||||||
\(626\) | 7.17510 | + | 12.4276i | 0.286774 | + | 0.496708i | ||||
\(627\) | 1.03146 | + | 1.78654i | 0.0411925 | + | 0.0713475i | ||||
\(628\) | 8.69202 | − | 15.0550i | 0.346849 | − | 0.600761i | ||||
\(629\) | −1.91557 | −0.0763790 | ||||||||
\(630\) | −9.35839 | + | 16.2092i | −0.372847 | + | 0.645790i | ||||
\(631\) | −7.61679 | + | 13.1927i | −0.303219 | + | 0.525191i | −0.976863 | − | 0.213865i | \(-0.931395\pi\) |
0.673644 | + | 0.739056i | \(0.264728\pi\) | |||||||
\(632\) | −2.65519 | −0.105618 | ||||||||
\(633\) | 7.96077 | − | 13.7885i | 0.316412 | − | 0.548042i | ||||
\(634\) | 9.26659 | + | 16.0502i | 0.368023 | + | 0.637435i | ||||
\(635\) | −18.0293 | − | 31.2277i | −0.715471 | − | 1.23923i | ||||
\(636\) | 2.51573 | 0.0997552 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.04115 | −0.318352 | ||||||||
\(639\) | −4.69202 | − | 8.12682i | −0.185614 | − | 0.321492i | ||||
\(640\) | 2.14795 | + | 3.72036i | 0.0849051 | + | 0.147060i | ||||
\(641\) | 7.09544 | − | 12.2897i | 0.280253 | − | 0.485413i | −0.691194 | − | 0.722669i | \(-0.742915\pi\) |
0.971447 | + | 0.237257i | \(0.0762483\pi\) | |||||||
\(642\) | −1.91723 | −0.0756671 | ||||||||
\(643\) | −11.2784 | + | 19.5348i | −0.444778 | + | 0.770378i | −0.998037 | − | 0.0626312i | \(-0.980051\pi\) |
0.553259 | + | 0.833010i | \(0.313384\pi\) | |||||||
\(644\) | 7.37196 | − | 12.7686i | 0.290496 | − | 0.503154i | ||||
\(645\) | −31.7211 | −1.24902 | ||||||||
\(646\) | 0.439665 | − | 0.761522i | 0.0172984 | − | 0.0299617i | ||||
\(647\) | 18.4523 | + | 31.9604i | 0.725436 | + | 1.25649i | 0.958794 | + | 0.284102i | \(0.0916953\pi\) |
−0.233358 | + | 0.972391i | \(0.574971\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 7.68425 | 0.301633 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.69501 | −0.379977 | ||||||||
\(652\) | 11.2349 | + | 19.4594i | 0.439993 | + | 0.762089i | ||||
\(653\) | 0.924764 | + | 1.60174i | 0.0361888 | + | 0.0626808i | 0.883553 | − | 0.468332i | \(-0.155145\pi\) |
−0.847364 | + | 0.531013i | \(0.821812\pi\) | |||||||
\(654\) | −9.38404 | + | 16.2536i | −0.366945 | + | 0.635568i | ||||
\(655\) | −58.0103 | −2.26665 | ||||||||
\(656\) | 3.15883 | − | 5.47126i | 0.123332 | − | 0.213617i | ||||
\(657\) | −0.187177 | + | 0.324200i | −0.00730248 | + | 0.0126483i | ||||
\(658\) | −7.75600 | −0.302361 | ||||||||
\(659\) | −9.13922 | + | 15.8296i | −0.356013 | + | 0.616633i | −0.987291 | − | 0.158924i | \(-0.949198\pi\) |
0.631277 | + | 0.775557i | \(0.282531\pi\) | |||||||
\(660\) | 2.48911 | + | 4.31127i | 0.0968887 | + | 0.167816i | ||||
\(661\) | −1.81700 | − | 3.14714i | −0.0706732 | − | 0.122410i | 0.828523 | − | 0.559955i | \(-0.189181\pi\) |
−0.899197 | + | 0.437545i | \(0.855848\pi\) | |||||||
\(662\) | 7.87800 | 0.306187 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.2784 | 0.554111 | ||||||||
\(665\) | 16.6595 | + | 28.8551i | 0.646028 | + | 1.11895i | ||||
\(666\) | −1.93900 | − | 3.35845i | −0.0751348 | − | 0.130137i | ||||
\(667\) | −11.7409 | + | 20.3359i | −0.454611 | + | 0.787409i | ||||
\(668\) | −0.835790 | −0.0323377 | ||||||||
\(669\) | 2.59179 | − | 4.48912i | 0.100205 | − | 0.173559i | ||||
\(670\) | 8.80194 | − | 15.2454i | 0.340049 | − | 0.588981i | ||||
\(671\) | 12.1608 | 0.469461 | ||||||||
\(672\) | 2.17845 | − | 3.77318i | 0.0840355 | − | 0.145554i | ||||
\(673\) | 3.07391 | + | 5.32417i | 0.118490 | + | 0.205232i | 0.919170 | − | 0.393862i | \(-0.128861\pi\) |
−0.800679 | + | 0.599093i | \(0.795528\pi\) | |||||||
\(674\) | −6.86323 | − | 11.8875i | −0.264362 | − | 0.457888i | ||||
\(675\) | −13.4547 | −0.517873 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.2892 | −0.702911 | −0.351455 | − | 0.936205i | \(-0.614313\pi\) | ||||
−0.351455 | + | 0.936205i | \(0.614313\pi\) | |||||||
\(678\) | −5.20775 | − | 9.02009i | −0.200002 | − | 0.346414i | ||||
\(679\) | 40.0698 | + | 69.4029i | 1.53774 | + | 2.66344i | ||||
\(680\) | 1.06100 | − | 1.83770i | 0.0406875 | − | 0.0704727i | ||||
\(681\) | 14.8877 | 0.570498 | ||||||||
\(682\) | −1.28932 | + | 2.23317i | −0.0493708 | + | 0.0855127i | ||||
\(683\) | −1.79643 | + | 3.11151i | −0.0687385 | + | 0.119059i | −0.898346 | − | 0.439288i | \(-0.855231\pi\) |
0.829608 | + | 0.558347i | \(0.188564\pi\) | |||||||
\(684\) | 1.78017 | 0.0680664 | ||||||||
\(685\) | −8.59179 | + | 14.8814i | −0.328276 | + | 0.568590i | ||||
\(686\) | −10.8542 | − | 18.8000i | −0.414416 | − | 0.717789i | ||||
\(687\) | −11.7289 | − | 20.3150i | −0.447484 | − | 0.775065i | ||||
\(688\) | 7.38404 | 0.281514 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 14.5375 | 0.553433 | ||||||||
\(691\) | 9.90946 | + | 17.1637i | 0.376974 | + | 0.652938i | 0.990620 | − | 0.136643i | \(-0.0436314\pi\) |
−0.613647 | + | 0.789581i | \(0.710298\pi\) | |||||||
\(692\) | 2.08546 | + | 3.61212i | 0.0792772 | + | 0.137312i | ||||
\(693\) | 2.52446 | − | 4.37249i | 0.0958963 | − | 0.166097i | ||||
\(694\) | 4.85086 | 0.184136 | ||||||||
\(695\) | 32.2868 | − | 55.9224i | 1.22471 | − | 2.12126i | ||||
\(696\) | −3.46950 | + | 6.00935i | −0.131511 | + | 0.227784i | ||||
\(697\) | −3.12067 | −0.118204 | ||||||||
\(698\) | 14.1739 | − | 24.5499i | 0.536490 | − | 0.929228i | ||||
\(699\) | −5.93900 | − | 10.2867i | −0.224634 | − | 0.389077i | ||||
\(700\) | 29.3104 | + | 50.7672i | 1.10783 | + | 1.91882i | ||||
\(701\) | 5.25608 | 0.198519 | 0.0992596 | − | 0.995062i | \(-0.468353\pi\) | ||||
0.0992596 | + | 0.995062i | \(0.468353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.90349 | −0.260370 | ||||||||
\(704\) | −0.579417 | − | 1.00358i | −0.0218376 | − | 0.0378238i | ||||
\(705\) | −3.82371 | − | 6.62286i | −0.144009 | − | 0.249431i | ||||
\(706\) | 14.2228 | − | 24.6346i | 0.535283 | − | 0.927137i | ||||
\(707\) | 23.8183 | 0.895781 | ||||||||
\(708\) | 3.31551 | − | 5.74263i | 0.124605 | − | 0.215821i | ||||
\(709\) | −13.0489 | + | 22.6014i | −0.490062 | + | 0.848813i | −0.999935 | − | 0.0114372i | \(-0.996359\pi\) |
0.509872 | + | 0.860250i | \(0.329693\pi\) | |||||||
\(710\) | −40.3129 | −1.51292 | ||||||||
\(711\) | −1.32759 | + | 2.29946i | −0.0497886 | + | 0.0862364i | ||||
\(712\) | 0.417895 | + | 0.723815i | 0.0156613 | + | 0.0271261i | ||||
\(713\) | 3.76510 | + | 6.52135i | 0.141004 | + | 0.244226i | ||||
\(714\) | −2.15213 | −0.0805414 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.8877 | 0.855353 | ||||||||
\(717\) | 12.6799 | + | 21.9623i | 0.473541 | + | 0.820197i | ||||
\(718\) | −5.61356 | − | 9.72298i | −0.209496 | − | 0.362858i | ||||
\(719\) | −25.4155 | + | 44.0209i | −0.947838 | + | 1.64170i | −0.197872 | + | 0.980228i | \(0.563403\pi\) |
−0.749966 | + | 0.661476i | \(0.769930\pi\) | |||||||
\(720\) | 4.29590 | 0.160099 | ||||||||
\(721\) | 15.2702 | − | 26.4488i | 0.568694 | − | 0.985006i | ||||
\(722\) | −7.91550 | + | 13.7101i | −0.294584 | + | 0.510235i | ||||
\(723\) | 12.0218 | 0.447094 | ||||||||
\(724\) | −5.80194 | + | 10.0493i | −0.215627 | + | 0.373477i | ||||
\(725\) | −46.6812 | − | 80.8542i | −1.73370 | − | 3.00285i | ||||
\(726\) | 4.82855 | + | 8.36330i | 0.179204 | + | 0.310391i | ||||
\(727\) | −20.5042 | −0.760460 | −0.380230 | − | 0.924892i | \(-0.624155\pi\) | ||||
−0.380230 | + | 0.924892i | \(0.624155\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.804094 | + | 1.39273i | 0.0297608 | + | 0.0515473i | ||||
\(731\) | −1.82371 | − | 3.15875i | −0.0674523 | − | 0.116831i | ||||
\(732\) | 5.24698 | − | 9.08804i | 0.193934 | − | 0.335903i | ||||
\(733\) | 3.26205 | 0.120486 | 0.0602432 | − | 0.998184i | \(-0.480812\pi\) | ||||
0.0602432 | + | 0.998184i | \(0.480812\pi\) | |||||||
\(734\) | 8.41335 | − | 14.5723i | 0.310542 | − | 0.537875i | ||||
\(735\) | 25.7379 | − | 44.5793i | 0.949356 | − | 1.64433i | ||||
\(736\) | −3.38404 | −0.124737 | ||||||||
\(737\) | −2.37435 | + | 4.11250i | −0.0874605 | + | 0.151486i | ||||
\(738\) | −3.15883 | − | 5.47126i | −0.116278 | − | 0.201400i | ||||
\(739\) | 16.4101 | + | 28.4232i | 0.603656 | + | 1.04556i | 0.992262 | + | 0.124159i | \(0.0396234\pi\) |
−0.388606 | + | 0.921404i | \(0.627043\pi\) | |||||||
\(740\) | −16.6595 | −0.612415 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.9608 | −0.402383 | ||||||||
\(743\) | −17.4765 | − | 30.2702i | −0.641151 | − | 1.11051i | −0.985176 | − | 0.171545i | \(-0.945124\pi\) |
0.344026 | − | 0.938960i | \(-0.388209\pi\) | |||||||
\(744\) | 1.11260 | + | 1.92709i | 0.0407901 | + | 0.0706505i | ||||
\(745\) | 8.43482 | − | 14.6095i | 0.309028 | − | 0.535252i | ||||
\(746\) | 26.5327 | 0.971432 | ||||||||
\(747\) | 7.13922 | − | 12.3655i | 0.261210 | − | 0.452430i | ||||
\(748\) | −0.286208 | + | 0.495727i | −0.0104648 | + | 0.0181256i | ||||
\(749\) | 8.35317 | 0.305218 | ||||||||
\(750\) | −18.1603 | + | 31.4546i | −0.663121 | + | 1.14856i | ||||
\(751\) | 5.08306 | + | 8.80413i | 0.185484 | + | 0.321267i | 0.943739 | − | 0.330690i | \(-0.107281\pi\) |
−0.758256 | + | 0.651957i | \(0.773948\pi\) | |||||||
\(752\) | 0.890084 | + | 1.54167i | 0.0324580 | + | 0.0562189i | ||||
\(753\) | 15.3448 | 0.559196 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41.3636 | 1.50538 | ||||||||
\(756\) | −2.17845 | − | 3.77318i | −0.0792294 | − | 0.137229i | ||||
\(757\) | 1.23191 | + | 2.13374i | 0.0447747 | + | 0.0775520i | 0.887544 | − | 0.460723i | \(-0.152410\pi\) |
−0.842770 | + | 0.538275i | \(0.819076\pi\) | |||||||
\(758\) | −10.9879 | + | 19.0316i | −0.399099 | + | 0.691260i | ||||
\(759\) | −3.92154 | −0.142343 | ||||||||
\(760\) | 3.82371 | − | 6.62286i | 0.138700 | − | 0.240236i | ||||
\(761\) | −21.4034 | + | 37.0718i | −0.775873 | + | 1.34385i | 0.158429 | + | 0.987370i | \(0.449357\pi\) |
−0.934302 | + | 0.356482i | \(0.883976\pi\) | |||||||
\(762\) | 8.39373 | 0.304073 | ||||||||
\(763\) | 40.8853 | − | 70.8154i | 1.48015 | − | 2.56369i | ||||
\(764\) | −8.34481 | − | 14.4536i | −0.301905 | − | 0.522914i | ||||
\(765\) | −1.06100 | − | 1.83770i | −0.0383605 | − | 0.0664423i | ||||
\(766\) | −0.615957 | −0.0222554 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 12.7017 | + | 22.0000i | 0.458035 | + | 0.793341i | 0.998857 | − | 0.0477967i | \(-0.0152200\pi\) |
−0.540822 | + | 0.841137i | \(0.681887\pi\) | |||||||
\(770\) | −10.8448 | − | 18.7838i | −0.390820 | − | 0.676920i | ||||
\(771\) | −3.75302 | + | 6.50042i | −0.135162 | + | 0.234107i | ||||
\(772\) | −9.64742 | −0.347218 | ||||||||
\(773\) | 2.23945 | − | 3.87884i | 0.0805473 | − | 0.139512i | −0.822938 | − | 0.568131i | \(-0.807667\pi\) |
0.903485 | + | 0.428619i | \(0.141000\pi\) | |||||||
\(774\) | 3.69202 | − | 6.39477i | 0.132707 | − | 0.229855i | ||||
\(775\) | −29.9396 | −1.07546 | ||||||||
\(776\) | 9.19687 | − | 15.9294i | 0.330148 | − | 0.571834i | ||||
\(777\) | 8.44803 | + | 14.6324i | 0.303071 | + | 0.524935i | ||||
\(778\) | −17.7630 | − | 30.7664i | −0.636835 | − | 1.10303i | ||||
\(779\) | −11.2465 | −0.402948 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.8745 | 0.389122 | ||||||||
\(782\) | 0.835790 | + | 1.44763i | 0.0298878 | + | 0.0517671i | ||||
\(783\) | 3.46950 | + | 6.00935i | 0.123990 | + | 0.214757i | ||||
\(784\) | −5.99127 | + | 10.3772i | −0.213974 | + | 0.370614i | ||||
\(785\) | −74.6801 | −2.66545 | ||||||||
\(786\) | 6.75182 | − | 11.6945i | 0.240830 | − | 0.417129i | ||||
\(787\) | 4.71917 | − | 8.17384i | 0.168220 | − | 0.291366i | −0.769574 | − | 0.638558i | \(-0.779531\pi\) |
0.937794 | + | 0.347192i | \(0.112865\pi\) | |||||||
\(788\) | −19.6383 | −0.699586 | ||||||||
\(789\) | −6.11529 | + | 10.5920i | −0.217710 | + | 0.377085i | ||||
\(790\) | 5.70320 | + | 9.87824i | 0.202911 | + | 0.351452i | ||||
\(791\) | 22.6896 | + | 39.2996i | 0.806750 | + | 1.39733i | ||||
\(792\) | −1.15883 | −0.0411774 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −16.0785 | −0.570603 | ||||||||
\(795\) | −5.40366 | − | 9.35941i | −0.191648 | − | 0.331944i | ||||
\(796\) | 9.21044 | + | 15.9529i | 0.326455 | + | 0.565437i | ||||
\(797\) | 12.6230 | − | 21.8636i | 0.447128 | − | 0.774449i | −0.551070 | − | 0.834459i | \(-0.685780\pi\) |
0.998198 | + | 0.0600107i | \(0.0191135\pi\) | |||||||
\(798\) | −7.75600 | −0.274560 | ||||||||
\(799\) | 0.439665 | − | 0.761522i | 0.0155542 | − | 0.0269407i | ||||
\(800\) | 6.72737 | − | 11.6521i | 0.237848 | − | 0.411965i | ||||
\(801\) | 0.835790 | 0.0295312 | ||||||||
\(802\) | −11.4547 | + | 19.8402i | −0.404481 | + | 0.700581i | ||||
\(803\) | −0.216907 | − | 0.375694i | −0.00765449 | − | 0.0132580i | ||||
\(804\) | 2.04892 | + | 3.54883i | 0.0722597 | + | 0.125158i | ||||
\(805\) | −63.3384 | −2.23238 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.71618 | −0.0956142 | ||||||||
\(808\) | −2.73341 | − | 4.73440i | −0.0961609 | − | 0.166556i | ||||
\(809\) | −5.85325 | − | 10.1381i | −0.205789 | − | 0.356437i | 0.744595 | − | 0.667517i | \(-0.232643\pi\) |
−0.950384 | + | 0.311079i | \(0.899309\pi\) | |||||||
\(810\) | 2.14795 | − | 3.72036i | 0.0754712 | − | 0.130720i | ||||
\(811\) | −30.5628 | −1.07321 | −0.536603 | − | 0.843835i | \(-0.680293\pi\) | ||||
−0.536603 | + | 0.843835i | \(0.680293\pi\) | |||||||
\(812\) | 15.1163 | − | 26.1821i | 0.530476 | − | 0.918812i | ||||
\(813\) | −6.19687 | + | 10.7333i | −0.217334 | + | 0.376433i | ||||
\(814\) | 4.49396 | 0.157513 | ||||||||
\(815\) | 48.2640 | − | 83.5956i | 1.69061 | − | 2.92823i | ||||
\(816\) | 0.246980 | + | 0.427781i | 0.00864602 | + | 0.0149753i | ||||
\(817\) | −6.57242 | − | 11.3838i | −0.229940 | − | 0.398267i | ||||
\(818\) | −1.24698 | −0.0435996 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.1400 | −0.947772 | ||||||||
\(821\) | −11.2796 | − | 19.5369i | −0.393662 | − | 0.681843i | 0.599267 | − | 0.800549i | \(-0.295459\pi\) |
−0.992929 | + | 0.118706i | \(0.962125\pi\) | |||||||
\(822\) | −2.00000 | − | 3.46410i | −0.0697580 | − | 0.120824i | ||||
\(823\) | 7.28836 | − | 12.6238i | 0.254056 | − | 0.440039i | −0.710582 | − | 0.703614i | \(-0.751568\pi\) |
0.964639 | + | 0.263575i | \(0.0849018\pi\) | |||||||
\(824\) | −7.00969 | −0.244194 | ||||||||
\(825\) | 7.79590 | − | 13.5029i | 0.271418 | − | 0.470110i | ||||
\(826\) | −14.4453 | + | 25.0201i | −0.502618 | + | 0.870559i | ||||
\(827\) | −20.3666 | −0.708216 | −0.354108 | − | 0.935205i | \(-0.615215\pi\) | ||||
−0.354108 | + | 0.935205i | \(0.615215\pi\) | |||||||
\(828\) | −1.69202 | + | 2.93067i | −0.0588018 | + | 0.101848i | ||||
\(829\) | −16.2054 | − | 28.0685i | −0.562835 | − | 0.974859i | −0.997247 | − | 0.0741452i | \(-0.976377\pi\) |
0.434412 | − | 0.900714i | \(-0.356956\pi\) | |||||||
\(830\) | −30.6694 | − | 53.1209i | −1.06455 | − | 1.84385i | ||||
\(831\) | 24.1280 | 0.836990 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.91889 | 0.205077 | ||||||||
\(834\) | 7.51573 | + | 13.0176i | 0.260248 | + | 0.450763i | ||||
\(835\) | 1.79523 | + | 3.10943i | 0.0621266 | + | 0.107606i | ||||
\(836\) | −1.03146 | + | 1.78654i | −0.0356738 | + | 0.0617888i | ||||
\(837\) | 2.22521 | 0.0769145 | ||||||||
\(838\) | 14.7315 | − | 25.5158i | 0.508893 | − | 0.881428i | ||||
\(839\) | −14.9705 | + | 25.9296i | −0.516838 | + | 0.895189i | 0.482971 | + | 0.875636i | \(0.339558\pi\) |
−0.999809 | + | 0.0195528i | \(0.993776\pi\) | |||||||
\(840\) | −18.7168 | −0.645790 | ||||||||
\(841\) | −9.57487 | + | 16.5842i | −0.330168 | + | 0.571868i | ||||
\(842\) | 8.67456 | + | 15.0248i | 0.298945 | + | 0.517788i | ||||
\(843\) | −6.41789 | − | 11.1161i | −0.221044 | − | 0.382860i | ||||
\(844\) | 15.9215 | 0.548042 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.78017 | 0.0612034 | ||||||||
\(847\) | −21.0375 | − | 36.4380i | −0.722857 | − | 1.25203i | ||||
\(848\) | 1.25786 | + | 2.17869i | 0.0431953 | + | 0.0748164i | ||||
\(849\) | 2.82371 | − | 4.89081i | 0.0969094 | − | 0.167852i | ||||
\(850\) | −6.64609 | −0.227959 | ||||||||
\(851\) | 6.56166 | − | 11.3651i | 0.224931 | − | 0.389592i | ||||
\(852\) | 4.69202 | − | 8.12682i | 0.160746 | − | 0.278420i | ||||
\(853\) | 41.8780 | 1.43388 | 0.716938 | − | 0.697137i | \(-0.245543\pi\) | ||||
0.716938 | + | 0.697137i | \(0.245543\pi\) | |||||||
\(854\) | −22.8605 | + | 39.5956i | −0.782272 | + | 1.35493i | ||||
\(855\) | −3.82371 | − | 6.62286i | −0.130768 | − | 0.226497i | ||||
\(856\) | −0.958615 | − | 1.66037i | −0.0327648 | − | 0.0567503i | ||||
\(857\) | 25.2137 | 0.861284 | 0.430642 | − | 0.902523i | \(-0.358287\pi\) | ||||
0.430642 | + | 0.902523i | \(0.358287\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.9939 | −1.60341 | −0.801705 | − | 0.597719i | \(-0.796074\pi\) | ||||
−0.801705 | + | 0.597719i | \(0.796074\pi\) | |||||||
\(860\) | −15.8605 | − | 27.4713i | −0.540840 | − | 0.936762i | ||||
\(861\) | 13.7627 | + | 23.8377i | 0.469032 | + | 0.812387i | ||||
\(862\) | −12.6920 | + | 21.9832i | −0.432292 | + | 0.748752i | ||||
\(863\) | 43.6969 | 1.48746 | 0.743730 | − | 0.668480i | \(-0.233055\pi\) | ||||
0.743730 | + | 0.668480i | \(0.233055\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 8.95891 | − | 15.5173i | 0.304612 | − | 0.527604i | ||||
\(866\) | −20.0054 | −0.679810 | ||||||||
\(867\) | −8.37800 | + | 14.5111i | −0.284532 | + | 0.492824i | ||||
\(868\) | −4.84750 | − | 8.39612i | −0.164535 | − | 0.284983i | ||||
\(869\) | −1.53846 | − | 2.66469i | −0.0521887 | − | 0.0903934i | ||||
\(870\) | 29.8092 | 1.01063 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −18.7681 | −0.635568 | ||||||||
\(873\) | −9.19687 | − | 15.9294i | −0.311267 | − | 0.539130i | ||||
\(874\) | 3.01208 | + | 5.21708i | 0.101885 | + | 0.176470i | ||||
\(875\) | 79.1226 | − | 137.044i | 2.67483 | − | 4.63295i | ||||
\(876\) | −0.374354 | −0.0126483 | ||||||||
\(877\) | −6.44504 | + | 11.1631i | −0.217634 | + | 0.376952i | −0.954084 | − | 0.299539i | \(-0.903167\pi\) |
0.736450 | + | 0.676491i | \(0.236500\pi\) | |||||||
\(878\) | 0.271971 | − | 0.471067i | 0.00917857 | − | 0.0158977i | ||||
\(879\) | 21.3653 | 0.720632 | ||||||||
\(880\) | −2.48911 | + | 4.31127i | −0.0839080 | + | 0.145333i | ||||
\(881\) | 7.47889 | + | 12.9538i | 0.251970 | + | 0.436425i | 0.964068 | − | 0.265655i | \(-0.0855881\pi\) |
−0.712098 | + | 0.702080i | \(0.752255\pi\) | |||||||
\(882\) | 5.99127 | + | 10.3772i | 0.201737 | + | 0.349418i | ||||
\(883\) | −20.6896 | −0.696261 | −0.348131 | − | 0.937446i | \(-0.613183\pi\) | ||||
−0.348131 | + | 0.937446i | \(0.613183\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −28.4862 | −0.957553 | ||||||||
\(886\) | −9.06800 | − | 15.7062i | −0.304645 | − | 0.527661i | ||||
\(887\) | −12.0925 | − | 20.9448i | −0.406025 | − | 0.703256i | 0.588415 | − | 0.808559i | \(-0.299752\pi\) |
−0.994440 | + | 0.105303i | \(0.966419\pi\) | |||||||
\(888\) | 1.93900 | − | 3.35845i | 0.0650686 | − | 0.112702i | ||||
\(889\) | −36.5706 | −1.22654 | ||||||||
\(890\) | 1.79523 | − | 3.10943i | 0.0601763 | − | 0.104228i | ||||
\(891\) | −0.579417 | + | 1.00358i | −0.0194112 | + | 0.0336212i | ||||
\(892\) | 5.18359 | 0.173559 | ||||||||
\(893\) | 1.58450 | − | 2.74443i | 0.0530232 | − | 0.0918389i | ||||
\(894\) | 1.96346 | + | 3.40081i | 0.0656679 | + | 0.113740i | ||||
\(895\) | −49.1616 | − | 85.1504i | −1.64329 | − | 2.84626i | ||||
\(896\) | 4.35690 | 0.145554 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.3793 | 0.980399 | ||||||||
\(899\) | 7.72037 | + | 13.3721i | 0.257489 | + | 0.445983i | ||||
\(900\) | −6.72737 | − | 11.6521i | −0.224246 | − | 0.388405i | ||||
\(901\) | 0.621334 | − | 1.07618i | 0.0206996 | − | 0.0358528i | ||||
\(902\) | 7.32113 | 0.243767 | ||||||||
\(903\) | −16.0858 | + | 27.8613i | −0.535300 | + | 0.927167i | ||||
\(904\) | 5.20775 | − | 9.02009i | 0.173207 | − | 0.300004i | ||||
\(905\) | 49.8491 | 1.65704 | ||||||||
\(906\) | −4.81431 | + | 8.33864i | −0.159945 | + | 0.277033i | ||||
\(907\) | −13.6353 | − | 23.6171i | −0.452754 | − | 0.784193i | 0.545802 | − | 0.837914i | \(-0.316225\pi\) |
−0.998556 | + | 0.0537214i | \(0.982892\pi\) | |||||||
\(908\) | 7.44385 | + | 12.8931i | 0.247033 | + | 0.427873i | ||||
\(909\) | −5.46681 | −0.181323 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.2766 | 1.50008 | 0.750041 | − | 0.661391i | \(-0.230034\pi\) | ||||
0.750041 | + | 0.661391i | \(0.230034\pi\) | |||||||
\(912\) | 0.890084 | + | 1.54167i | 0.0294736 | + | 0.0510498i | ||||
\(913\) | 8.27317 | + | 14.3295i | 0.273802 | + | 0.474239i | ||||
\(914\) | 4.17360 | − | 7.22889i | 0.138051 | − | 0.239111i | ||||
\(915\) | −45.0810 | −1.49033 | ||||||||
\(916\) | 11.7289 | − | 20.3150i | 0.387532 | − | 0.671226i | ||||
\(917\) | −29.4170 | + | 50.9517i | −0.971435 | + | 1.68257i | ||||
\(918\) | 0.493959 | 0.0163031 | ||||||||
\(919\) | −2.34063 | + | 4.05410i | −0.0772104 | + | 0.133732i | −0.902045 | − | 0.431641i | \(-0.857935\pi\) |
0.824835 | + | 0.565374i | \(0.191268\pi\) | |||||||
\(920\) | 7.26875 | + | 12.5898i | 0.239644 | + | 0.415075i | ||||
\(921\) | 14.4426 | + | 25.0154i | 0.475901 | + | 0.824286i | ||||
\(922\) | 21.4969 | 0.707964 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 5.04892 | 0.166097 | ||||||||
\(925\) | 26.0887 | + | 45.1870i | 0.857792 | + | 1.48574i | ||||
\(926\) | −13.0858 | − | 22.6652i | −0.430025 | − | 0.744824i | ||||
\(927\) | −3.50484 | + | 6.07057i | −0.115114 | + | 0.199384i | ||||
\(928\) | −6.93900 | −0.227784 | ||||||||
\(929\) | 1.64550 | − | 2.85008i | 0.0539870 | − | 0.0935082i | −0.837769 | − | 0.546025i | \(-0.816140\pi\) |
0.891756 | + | 0.452517i | \(0.149474\pi\) | |||||||
\(930\) | 4.77963 | − | 8.27857i | 0.156730 | − | 0.271465i | ||||
\(931\) | 21.3309 | 0.699093 | ||||||||
\(932\) | 5.93900 | − | 10.2867i | 0.194538 | − | 0.336950i | ||||
\(933\) | 1.69202 | + | 2.93067i | 0.0553943 | + | 0.0959457i | ||||
\(934\) | −4.90635 | − | 8.49804i | −0.160541 | − | 0.278064i | ||||
\(935\) | 2.45904 | 0.0804193 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.67563 | 0.218083 | 0.109042 | − | 0.994037i | \(-0.465222\pi\) | ||||
0.109042 | + | 0.994037i | \(0.465222\pi\) | |||||||
\(938\) | −8.92692 | − | 15.4619i | −0.291474 | − | 0.504848i | ||||
\(939\) | 7.17510 | + | 12.4276i | 0.234150 | + | 0.405560i | ||||
\(940\) | 3.82371 | − | 6.62286i | 0.124716 | − | 0.216014i | ||||
\(941\) | −38.9778 | −1.27064 | −0.635319 | − | 0.772250i | \(-0.719131\pi\) | ||||
−0.635319 | + | 0.772250i | \(0.719131\pi\) | |||||||
\(942\) | 8.69202 | − | 15.0550i | 0.283201 | − | 0.490519i | ||||
\(943\) | 10.6896 | − | 18.5150i | 0.348102 | − | 0.602931i | ||||
\(944\) | 6.63102 | 0.215821 | ||||||||
\(945\) | −9.35839 | + | 16.2092i | −0.304428 | + | 0.527285i | ||||
\(946\) | 4.27844 | + | 7.41047i | 0.139104 | + | 0.240935i | ||||
\(947\) | −20.3339 | − | 35.2194i | −0.660764 | − | 1.14448i | −0.980415 | − | 0.196941i | \(-0.936899\pi\) |
0.319651 | − | 0.947535i | \(-0.396434\pi\) | |||||||
\(948\) | −2.65519 | −0.0862364 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −23.9517 | −0.777095 | ||||||||
\(951\) | 9.26659 | + | 16.0502i | 0.300490 | + | 0.520464i | ||||
\(952\) | −1.07606 | − | 1.86380i | −0.0348754 | − | 0.0604060i | ||||
\(953\) | 22.4252 | − | 38.8416i | 0.726423 | − | 1.25820i | −0.231962 | − | 0.972725i | \(-0.574515\pi\) |
0.958386 | − | 0.285477i | \(-0.0921520\pi\) | |||||||
\(954\) | 2.51573 | 0.0814497 | ||||||||
\(955\) | −35.8485 | + | 62.0914i | −1.16003 | + | 2.00923i | ||||
\(956\) | −12.6799 | + | 21.9623i | −0.410099 | + | 0.710312i | ||||
\(957\) | −8.04115 | −0.259933 | ||||||||
\(958\) | −8.64071 | + | 14.9662i | −0.279169 | + | 0.483534i | ||||
\(959\) | 8.71379 | + | 15.0927i | 0.281383 | + | 0.487370i | ||||
\(960\) | 2.14795 | + | 3.72036i | 0.0693247 | + | 0.120074i | ||||
\(961\) | −26.0484 | −0.840272 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.91723 | −0.0617819 | ||||||||
\(964\) | 6.01089 | + | 10.4112i | 0.193598 | + | 0.335321i | ||||
\(965\) | 20.7222 | + | 35.8918i | 0.667070 | + | 1.15540i | ||||
\(966\) | 7.37196 | − | 12.7686i | 0.237189 | − | 0.410823i | ||||
\(967\) | 22.4704 | 0.722599 | 0.361299 | − | 0.932450i | \(-0.382333\pi\) | ||||
0.361299 | + | 0.932450i | \(0.382333\pi\) | |||||||
\(968\) | −4.82855 | + | 8.36330i | −0.155196 | + | 0.268807i | ||||
\(969\) | 0.439665 | − | 0.761522i | 0.0141241 | − | 0.0244636i | ||||
\(970\) | −79.0176 | −2.53710 | ||||||||
\(971\) | −16.9218 | + | 29.3095i | −0.543048 | + | 0.940586i | 0.455679 | + | 0.890144i | \(0.349396\pi\) |
−0.998727 | + | 0.0504421i | \(0.983937\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −32.7453 | − | 56.7164i | −1.04976 | − | 1.81825i | ||||
\(974\) | −31.6886 | −1.01537 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.4940 | 0.335903 | ||||||||
\(977\) | −13.6069 | − | 23.5678i | −0.435322 | − | 0.754000i | 0.562000 | − | 0.827137i | \(-0.310032\pi\) |
−0.997322 | + | 0.0731375i | \(0.976699\pi\) | |||||||
\(978\) | 11.2349 | + | 19.4594i | 0.359252 | + | 0.622243i | ||||
\(979\) | −0.484271 | + | 0.838781i | −0.0154774 | + | 0.0268076i | ||||
\(980\) | 51.4758 | 1.64433 | ||||||||
\(981\) | −9.38404 | + | 16.2536i | −0.299609 | + | 0.518939i | ||||
\(982\) | 1.15183 | − | 1.99503i | 0.0367565 | − | 0.0636641i | ||||
\(983\) | −50.9965 | −1.62654 | −0.813269 | − | 0.581889i | \(-0.802314\pi\) | ||||
−0.813269 | + | 0.581889i | \(0.802314\pi\) | |||||||
\(984\) | 3.15883 | − | 5.47126i | 0.100700 | − | 0.174417i | ||||
\(985\) | 42.1821 | + | 73.0615i | 1.34403 | + | 2.32793i | ||||
\(986\) | 1.71379 | + | 2.96837i | 0.0545782 | + | 0.0945323i | ||||
\(987\) | −7.75600 | −0.246876 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.9879 | 0.794570 | ||||||||
\(990\) | 2.48911 | + | 4.31127i | 0.0791093 | + | 0.137021i | ||||
\(991\) | 12.1402 | + | 21.0274i | 0.385645 | + | 0.667958i | 0.991859 | − | 0.127345i | \(-0.0406455\pi\) |
−0.606213 | + | 0.795302i | \(0.707312\pi\) | |||||||
\(992\) | −1.11260 | + | 1.92709i | −0.0353252 | + | 0.0611851i | ||||
\(993\) | 7.87800 | 0.250001 | ||||||||
\(994\) | −20.4426 | + | 35.4077i | −0.648401 | + | 1.12306i | ||||
\(995\) | 39.5671 | − | 68.5322i | 1.25436 | − | 2.17262i | ||||
\(996\) | 14.2784 | 0.452430 | ||||||||
\(997\) | 2.03252 | − | 3.52043i | 0.0643707 | − | 0.111493i | −0.832044 | − | 0.554710i | \(-0.812829\pi\) |
0.896415 | + | 0.443216i | \(0.146163\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.93900 | − | 3.35845i | −0.0613473 | − | 0.106257i |
(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 | 1014.2.e.n.991.3 | 6 | ||
13.2 | odd | 12 | 1014.2.b.f.337.4 | 6 | |||
13.3 | even | 3 | 1014.2.a.l.1.3 | ✓ | 3 | ||
13.4 | even | 6 | 1014.2.e.l.529.1 | 6 | |||
13.5 | odd | 4 | 1014.2.i.h.361.4 | 12 | |||
13.6 | odd | 12 | 1014.2.i.h.823.1 | 12 | |||
13.7 | odd | 12 | 1014.2.i.h.823.6 | 12 | |||
13.8 | odd | 4 | 1014.2.i.h.361.3 | 12 | |||
13.9 | even | 3 | inner | 1014.2.e.n.529.3 | 6 | ||
13.10 | even | 6 | 1014.2.a.n.1.1 | yes | 3 | ||
13.11 | odd | 12 | 1014.2.b.f.337.3 | 6 | |||
13.12 | even | 2 | 1014.2.e.l.991.1 | 6 | |||
39.2 | even | 12 | 3042.2.b.o.1351.3 | 6 | |||
39.11 | even | 12 | 3042.2.b.o.1351.4 | 6 | |||
39.23 | odd | 6 | 3042.2.a.ba.1.3 | 3 | |||
39.29 | odd | 6 | 3042.2.a.bh.1.1 | 3 | |||
52.3 | odd | 6 | 8112.2.a.cj.1.3 | 3 | |||
52.23 | odd | 6 | 8112.2.a.cm.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.l.1.3 | ✓ | 3 | 13.3 | even | 3 | ||
1014.2.a.n.1.1 | yes | 3 | 13.10 | even | 6 | ||
1014.2.b.f.337.3 | 6 | 13.11 | odd | 12 | |||
1014.2.b.f.337.4 | 6 | 13.2 | odd | 12 | |||
1014.2.e.l.529.1 | 6 | 13.4 | even | 6 | |||
1014.2.e.l.991.1 | 6 | 13.12 | even | 2 | |||
1014.2.e.n.529.3 | 6 | 13.9 | even | 3 | inner | ||
1014.2.e.n.991.3 | 6 | 1.1 | even | 1 | trivial | ||
1014.2.i.h.361.3 | 12 | 13.8 | odd | 4 | |||
1014.2.i.h.361.4 | 12 | 13.5 | odd | 4 | |||
1014.2.i.h.823.1 | 12 | 13.6 | odd | 12 | |||
1014.2.i.h.823.6 | 12 | 13.7 | odd | 12 | |||
3042.2.a.ba.1.3 | 3 | 39.23 | odd | 6 | |||
3042.2.a.bh.1.1 | 3 | 39.29 | odd | 6 | |||
3042.2.b.o.1351.3 | 6 | 39.2 | even | 12 | |||
3042.2.b.o.1351.4 | 6 | 39.11 | even | 12 | |||
8112.2.a.cj.1.3 | 3 | 52.3 | odd | 6 | |||
8112.2.a.cm.1.1 | 3 | 52.23 | odd | 6 |