Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,2,Mod(429,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.429");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.c (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: | \(5.76519902594\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.324000000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 20x^{4} + 25x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 429.2 | ||
Root | \(0.951057 - 1.64728i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.429 |
Dual form | 722.2.c.n.653.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).
\(n\) | \(363\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||
\(3\) | 0.221232 | − | 0.383185i | 0.127728 | − | 0.221232i | −0.795068 | − | 0.606520i | \(-0.792565\pi\) |
0.922796 | + | 0.385289i | \(0.125898\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.445746 | − | 0.772054i | 0.199344 | − | 0.345273i | −0.748972 | − | 0.662601i | \(-0.769452\pi\) |
0.948316 | + | 0.317328i | \(0.102786\pi\) | |||||||
\(6\) | −0.221232 | − | 0.383185i | −0.0903175 | − | 0.156434i | ||||
\(7\) | 2.52015 | 0.952526 | 0.476263 | − | 0.879303i | \(-0.341991\pi\) | ||||
0.476263 | + | 0.879303i | \(0.341991\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.40211 | + | 2.42853i | 0.467371 | + | 0.809510i | ||||
\(10\) | −0.445746 | − | 0.772054i | −0.140957 | − | 0.244145i | ||||
\(11\) | 1.95199 | 0.588547 | 0.294273 | − | 0.955721i | \(-0.404922\pi\) | ||||
0.294273 | + | 0.955721i | \(0.404922\pi\) | |||||||
\(12\) | −0.442463 | −0.127728 | ||||||||
\(13\) | 3.22982 | + | 5.59422i | 0.895792 | + | 1.55156i | 0.832821 | + | 0.553542i | \(0.186724\pi\) |
0.0629711 | + | 0.998015i | \(0.479942\pi\) | |||||||
\(14\) | 1.26007 | − | 2.18251i | 0.336769 | − | 0.583301i | ||||
\(15\) | −0.197226 | − | 0.341606i | −0.0509236 | − | 0.0882022i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.71113 | − | 2.96376i | 0.415010 | − | 0.718818i | −0.580420 | − | 0.814318i | \(-0.697111\pi\) |
0.995430 | + | 0.0954992i | \(0.0304447\pi\) | |||||||
\(18\) | 2.80423 | 0.660962 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.891491 | −0.199344 | ||||||||
\(21\) | 0.557537 | − | 0.965682i | 0.121664 | − | 0.210729i | ||||
\(22\) | 0.975994 | − | 1.69047i | 0.208083 | − | 0.360410i | ||||
\(23\) | −4.09252 | − | 7.08845i | −0.853349 | − | 1.47804i | −0.878168 | − | 0.478352i | \(-0.841234\pi\) |
0.0248186 | − | 0.999692i | \(-0.492099\pi\) | |||||||
\(24\) | −0.221232 | + | 0.383185i | −0.0451587 | + | 0.0782172i | ||||
\(25\) | 2.10262 | + | 3.64185i | 0.420524 | + | 0.728369i | ||||
\(26\) | 6.45965 | 1.26684 | ||||||||
\(27\) | 2.56816 | 0.494242 | ||||||||
\(28\) | −1.26007 | − | 2.18251i | −0.238132 | − | 0.412456i | ||||
\(29\) | −2.29032 | − | 3.96695i | −0.425302 | − | 0.736645i | 0.571146 | − | 0.820848i | \(-0.306499\pi\) |
−0.996449 | + | 0.0842032i | \(0.973166\pi\) | |||||||
\(30\) | −0.394452 | −0.0720168 | ||||||||
\(31\) | −8.79360 | −1.57938 | −0.789689 | − | 0.613507i | \(-0.789758\pi\) | ||||
−0.789689 | + | 0.613507i | \(0.789758\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0.431842 | − | 0.747972i | 0.0751740 | − | 0.130205i | ||||
\(34\) | −1.71113 | − | 2.96376i | −0.293456 | − | 0.508281i | ||||
\(35\) | 1.12334 | − | 1.94569i | 0.189880 | − | 0.328882i | ||||
\(36\) | 1.40211 | − | 2.42853i | 0.233686 | − | 0.404755i | ||||
\(37\) | −5.97980 | −0.983073 | −0.491536 | − | 0.870857i | \(-0.663564\pi\) | ||||
−0.491536 | + | 0.870857i | \(0.663564\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.85816 | 0.457672 | ||||||||
\(40\) | −0.445746 | + | 0.772054i | −0.0704786 | + | 0.122072i | ||||
\(41\) | 1.74466 | − | 3.02184i | 0.272470 | − | 0.471932i | −0.697024 | − | 0.717048i | \(-0.745493\pi\) |
0.969494 | + | 0.245116i | \(0.0788260\pi\) | |||||||
\(42\) | −0.557537 | − | 0.965682i | −0.0860298 | − | 0.149008i | ||||
\(43\) | 3.12334 | − | 5.40979i | 0.476306 | − | 0.824986i | −0.523326 | − | 0.852133i | \(-0.675309\pi\) |
0.999631 | + | 0.0271471i | \(0.00864226\pi\) | |||||||
\(44\) | −0.975994 | − | 1.69047i | −0.147137 | − | 0.254848i | ||||
\(45\) | 2.49994 | 0.372670 | ||||||||
\(46\) | −8.18504 | −1.20682 | ||||||||
\(47\) | 5.27491 | + | 9.13641i | 0.769425 | + | 1.33268i | 0.937875 | + | 0.346973i | \(0.112790\pi\) |
−0.168451 | + | 0.985710i | \(0.553876\pi\) | |||||||
\(48\) | 0.221232 | + | 0.383185i | 0.0319321 | + | 0.0553079i | ||||
\(49\) | −0.648859 | −0.0926941 | ||||||||
\(50\) | 4.20524 | 0.594711 | ||||||||
\(51\) | −0.757113 | − | 1.31136i | −0.106017 | − | 0.183627i | ||||
\(52\) | 3.22982 | − | 5.59422i | 0.447896 | − | 0.775779i | ||||
\(53\) | −1.88139 | − | 3.25866i | −0.258429 | − | 0.447612i | 0.707392 | − | 0.706821i | \(-0.249871\pi\) |
−0.965821 | + | 0.259209i | \(0.916538\pi\) | |||||||
\(54\) | 1.28408 | − | 2.22409i | 0.174741 | − | 0.302660i | ||||
\(55\) | 0.870091 | − | 1.50704i | 0.117323 | − | 0.203209i | ||||
\(56\) | −2.52015 | −0.336769 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.58064 | −0.601468 | ||||||||
\(59\) | −1.42081 | + | 2.46091i | −0.184973 | + | 0.320383i | −0.943568 | − | 0.331180i | \(-0.892553\pi\) |
0.758594 | + | 0.651563i | \(0.225887\pi\) | |||||||
\(60\) | −0.197226 | + | 0.341606i | −0.0254618 | + | 0.0441011i | ||||
\(61\) | 1.22747 | + | 2.12605i | 0.157162 | + | 0.272213i | 0.933844 | − | 0.357680i | \(-0.116432\pi\) |
−0.776682 | + | 0.629893i | \(0.783099\pi\) | |||||||
\(62\) | −4.39680 | + | 7.61548i | −0.558394 | + | 0.967168i | ||||
\(63\) | 3.53353 | + | 6.12026i | 0.445183 | + | 0.771080i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.75872 | 0.714282 | ||||||||
\(66\) | −0.431842 | − | 0.747972i | −0.0531561 | − | 0.0920690i | ||||
\(67\) | 1.33630 | + | 2.31455i | 0.163256 | + | 0.282767i | 0.936034 | − | 0.351908i | \(-0.114467\pi\) |
−0.772779 | + | 0.634675i | \(0.781134\pi\) | |||||||
\(68\) | −3.42226 | −0.415010 | ||||||||
\(69\) | −3.62158 | −0.435987 | ||||||||
\(70\) | −1.12334 | − | 1.94569i | −0.134265 | − | 0.232554i | ||||
\(71\) | −0.0282202 | + | 0.0488788i | −0.00334912 | + | 0.00580085i | −0.867695 | − | 0.497097i | \(-0.834399\pi\) |
0.864346 | + | 0.502898i | \(0.167733\pi\) | |||||||
\(72\) | −1.40211 | − | 2.42853i | −0.165241 | − | 0.286205i | ||||
\(73\) | 3.48459 | − | 6.03548i | 0.407840 | − | 0.706400i | −0.586807 | − | 0.809727i | \(-0.699615\pi\) |
0.994647 | + | 0.103327i | \(0.0329487\pi\) | |||||||
\(74\) | −2.98990 | + | 5.17866i | −0.347569 | + | 0.602007i | ||||
\(75\) | 1.86067 | 0.214851 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.91930 | 0.560606 | ||||||||
\(78\) | 1.42908 | − | 2.47524i | 0.161811 | − | 0.280266i | ||||
\(79\) | 4.56581 | − | 7.90821i | 0.513694 | − | 0.889743i | −0.486180 | − | 0.873859i | \(-0.661610\pi\) |
0.999874 | − | 0.0158848i | \(-0.00505650\pi\) | |||||||
\(80\) | 0.445746 | + | 0.772054i | 0.0498359 | + | 0.0863183i | ||||
\(81\) | −3.63818 | + | 6.30151i | −0.404242 | + | 0.700168i | ||||
\(82\) | −1.74466 | − | 3.02184i | −0.192666 | − | 0.333707i | ||||
\(83\) | −14.1239 | −1.55030 | −0.775150 | − | 0.631778i | \(-0.782326\pi\) | ||||
−0.775150 | + | 0.631778i | \(0.782326\pi\) | |||||||
\(84\) | −1.11507 | −0.121664 | ||||||||
\(85\) | −1.52546 | − | 2.64217i | −0.165459 | − | 0.286584i | ||||
\(86\) | −3.12334 | − | 5.40979i | −0.336799 | − | 0.583353i | ||||
\(87\) | −2.02677 | −0.217292 | ||||||||
\(88\) | −1.95199 | −0.208083 | ||||||||
\(89\) | −0.933870 | − | 1.61751i | −0.0989901 | − | 0.171456i | 0.812277 | − | 0.583272i | \(-0.198228\pi\) |
−0.911267 | + | 0.411816i | \(0.864895\pi\) | |||||||
\(90\) | 1.24997 | − | 2.16501i | 0.131759 | − | 0.228213i | ||||
\(91\) | 8.13963 | + | 14.0983i | 0.853265 | + | 1.47790i | ||||
\(92\) | −4.09252 | + | 7.08845i | −0.426675 | + | 0.739022i | ||||
\(93\) | −1.94542 | + | 3.36957i | −0.201731 | + | 0.349409i | ||||
\(94\) | 10.5498 | 1.08813 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.442463 | 0.0451587 | ||||||||
\(97\) | −3.91216 | + | 6.77606i | −0.397219 | + | 0.688004i | −0.993382 | − | 0.114860i | \(-0.963358\pi\) |
0.596162 | + | 0.802864i | \(0.296692\pi\) | |||||||
\(98\) | −0.324429 | + | 0.561928i | −0.0327723 | + | 0.0567633i | ||||
\(99\) | 2.73691 | + | 4.74047i | 0.275070 | + | 0.476435i | ||||
\(100\) | 2.10262 | − | 3.64185i | 0.210262 | − | 0.364185i | ||||
\(101\) | 2.69244 | + | 4.66343i | 0.267907 | + | 0.464029i | 0.968321 | − | 0.249708i | \(-0.0803346\pi\) |
−0.700414 | + | 0.713737i | \(0.747001\pi\) | |||||||
\(102\) | −1.51423 | −0.149931 | ||||||||
\(103\) | −4.69468 | −0.462580 | −0.231290 | − | 0.972885i | \(-0.574295\pi\) | ||||
−0.231290 | + | 0.972885i | \(0.574295\pi\) | |||||||
\(104\) | −3.22982 | − | 5.59422i | −0.316710 | − | 0.548558i | ||||
\(105\) | −0.497039 | − | 0.860897i | −0.0485060 | − | 0.0840149i | ||||
\(106\) | −3.76278 | −0.365473 | ||||||||
\(107\) | 16.0373 | 1.55038 | 0.775191 | − | 0.631727i | \(-0.217654\pi\) | ||||
0.775191 | + | 0.631727i | \(0.217654\pi\) | |||||||
\(108\) | −1.28408 | − | 2.22409i | −0.123561 | − | 0.214013i | ||||
\(109\) | −7.05040 | + | 12.2116i | −0.675305 | + | 1.16966i | 0.301074 | + | 0.953601i | \(0.402655\pi\) |
−0.976380 | + | 0.216063i | \(0.930678\pi\) | |||||||
\(110\) | −0.870091 | − | 1.50704i | −0.0829599 | − | 0.143691i | ||||
\(111\) | −1.32292 | + | 2.29137i | −0.125566 | + | 0.217487i | ||||
\(112\) | −1.26007 | + | 2.18251i | −0.119066 | + | 0.206228i | ||||
\(113\) | −12.7224 | −1.19682 | −0.598410 | − | 0.801190i | \(-0.704201\pi\) | ||||
−0.598410 | + | 0.801190i | \(0.704201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.29689 | −0.680439 | ||||||||
\(116\) | −2.29032 | + | 3.96695i | −0.212651 | + | 0.368322i | ||||
\(117\) | −9.05716 | + | 15.6875i | −0.837335 | + | 1.45031i | ||||
\(118\) | 1.42081 | + | 2.46091i | 0.130796 | + | 0.226545i | ||||
\(119\) | 4.31230 | − | 7.46912i | 0.395308 | − | 0.684693i | ||||
\(120\) | 0.197226 | + | 0.341606i | 0.0180042 | + | 0.0311842i | ||||
\(121\) | −7.18974 | −0.653613 | ||||||||
\(122\) | 2.45495 | 0.222261 | ||||||||
\(123\) | −0.771949 | − | 1.33705i | −0.0696043 | − | 0.120558i | ||||
\(124\) | 4.39680 | + | 7.61548i | 0.394844 | + | 0.683891i | ||||
\(125\) | 8.20640 | 0.734002 | ||||||||
\(126\) | 7.06706 | 0.629584 | ||||||||
\(127\) | −3.58721 | − | 6.21323i | −0.318313 | − | 0.551335i | 0.661823 | − | 0.749660i | \(-0.269783\pi\) |
−0.980136 | + | 0.198325i | \(0.936450\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −1.38197 | − | 2.39364i | −0.121675 | − | 0.210748i | ||||
\(130\) | 2.87936 | − | 4.98720i | 0.252537 | − | 0.437406i | ||||
\(131\) | 1.76133 | − | 3.05071i | 0.153888 | − | 0.266542i | −0.778766 | − | 0.627315i | \(-0.784154\pi\) |
0.932654 | + | 0.360773i | \(0.117487\pi\) | |||||||
\(132\) | −0.863684 | −0.0751740 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.67261 | 0.230878 | ||||||||
\(135\) | 1.14475 | − | 1.98276i | 0.0985240 | − | 0.170649i | ||||
\(136\) | −1.71113 | + | 2.96376i | −0.146728 | + | 0.254141i | ||||
\(137\) | 5.50177 | + | 9.52935i | 0.470048 | + | 0.814147i | 0.999413 | − | 0.0342466i | \(-0.0109032\pi\) |
−0.529365 | + | 0.848394i | \(0.677570\pi\) | |||||||
\(138\) | −1.81079 | + | 3.13638i | −0.154145 | + | 0.266987i | ||||
\(139\) | −10.8793 | − | 18.8435i | −0.922771 | − | 1.59829i | −0.795108 | − | 0.606468i | \(-0.792586\pi\) |
−0.127663 | − | 0.991818i | \(-0.540747\pi\) | |||||||
\(140\) | −2.24669 | −0.189880 | ||||||||
\(141\) | 4.66791 | 0.393109 | ||||||||
\(142\) | 0.0282202 | + | 0.0488788i | 0.00236819 | + | 0.00410182i | ||||
\(143\) | 6.30458 | + | 10.9199i | 0.527216 | + | 0.913164i | ||||
\(144\) | −2.80423 | −0.233686 | ||||||||
\(145\) | −4.08361 | −0.339125 | ||||||||
\(146\) | −3.48459 | − | 6.03548i | −0.288387 | − | 0.499500i | ||||
\(147\) | −0.143548 | + | 0.248633i | −0.0118397 | + | 0.0205069i | ||||
\(148\) | 2.98990 | + | 5.17866i | 0.245768 | + | 0.425683i | ||||
\(149\) | −7.19479 | + | 12.4617i | −0.589420 | + | 1.02090i | 0.404889 | + | 0.914366i | \(0.367310\pi\) |
−0.994309 | + | 0.106539i | \(0.966023\pi\) | |||||||
\(150\) | 0.930333 | − | 1.61138i | 0.0759614 | − | 0.131569i | ||||
\(151\) | 12.4068 | 1.00965 | 0.504824 | − | 0.863222i | \(-0.331557\pi\) | ||||
0.504824 | + | 0.863222i | \(0.331557\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.59679 | 0.775855 | ||||||||
\(154\) | 2.45965 | − | 4.26024i | 0.198204 | − | 0.343300i | ||||
\(155\) | −3.91971 | + | 6.78914i | −0.314839 | + | 0.545317i | ||||
\(156\) | −1.42908 | − | 2.47524i | −0.114418 | − | 0.198178i | ||||
\(157\) | 0.225610 | − | 0.390768i | 0.0180056 | − | 0.0311867i | −0.856882 | − | 0.515512i | \(-0.827602\pi\) |
0.874888 | + | 0.484326i | \(0.160935\pi\) | |||||||
\(158\) | −4.56581 | − | 7.90821i | −0.363236 | − | 0.629144i | ||||
\(159\) | −1.66489 | −0.132035 | ||||||||
\(160\) | 0.891491 | 0.0704786 | ||||||||
\(161\) | −10.3138 | − | 17.8639i | −0.812837 | − | 1.40788i | ||||
\(162\) | 3.63818 | + | 6.30151i | 0.285842 | + | 0.495094i | ||||
\(163\) | −0.0692542 | −0.00542441 | −0.00271220 | − | 0.999996i | \(-0.500863\pi\) | ||||
−0.00271220 | + | 0.999996i | \(0.500863\pi\) | |||||||
\(164\) | −3.48932 | −0.272470 | ||||||||
\(165\) | −0.384983 | − | 0.666811i | −0.0299709 | − | 0.0519111i | ||||
\(166\) | −7.06195 | + | 12.2317i | −0.548114 | + | 0.949361i | ||||
\(167\) | −1.08685 | − | 1.88248i | −0.0841032 | − | 0.145671i | 0.820906 | − | 0.571064i | \(-0.193469\pi\) |
−0.905009 | + | 0.425393i | \(0.860136\pi\) | |||||||
\(168\) | −0.557537 | + | 0.965682i | −0.0430149 | + | 0.0745040i | ||||
\(169\) | −14.3635 | + | 24.8784i | −1.10489 | + | 1.91372i | ||||
\(170\) | −3.05092 | −0.233995 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.24669 | −0.476306 | ||||||||
\(173\) | 8.42464 | − | 14.5919i | 0.640514 | − | 1.10940i | −0.344804 | − | 0.938675i | \(-0.612055\pi\) |
0.985318 | − | 0.170728i | \(-0.0546119\pi\) | |||||||
\(174\) | −1.01338 | + | 1.75523i | −0.0768244 | + | 0.133064i | ||||
\(175\) | 5.29892 | + | 9.17799i | 0.400560 | + | 0.693791i | ||||
\(176\) | −0.975994 | + | 1.69047i | −0.0735684 | + | 0.127424i | ||||
\(177\) | 0.628656 | + | 1.08886i | 0.0472526 | + | 0.0818440i | ||||
\(178\) | −1.86774 | −0.139993 | ||||||||
\(179\) | 18.9655 | 1.41755 | 0.708775 | − | 0.705435i | \(-0.249248\pi\) | ||||
0.708775 | + | 0.705435i | \(0.249248\pi\) | |||||||
\(180\) | −1.24997 | − | 2.16501i | −0.0931674 | − | 0.161371i | ||||
\(181\) | 0.993436 | + | 1.72068i | 0.0738415 | + | 0.127897i | 0.900582 | − | 0.434686i | \(-0.143141\pi\) |
−0.826740 | + | 0.562584i | \(0.809807\pi\) | |||||||
\(182\) | 16.2793 | 1.20670 | ||||||||
\(183\) | 1.08623 | 0.0802961 | ||||||||
\(184\) | 4.09252 | + | 7.08845i | 0.301705 | + | 0.522568i | ||||
\(185\) | −2.66547 | + | 4.61673i | −0.195969 | + | 0.339429i | ||||
\(186\) | 1.94542 | + | 3.36957i | 0.142645 | + | 0.247069i | ||||
\(187\) | 3.34011 | − | 5.78523i | 0.244253 | − | 0.423058i | ||||
\(188\) | 5.27491 | − | 9.13641i | 0.384712 | − | 0.666341i | ||||
\(189\) | 6.47214 | 0.470779 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.9259 | −1.51415 | −0.757074 | − | 0.653329i | \(-0.773372\pi\) | ||||
−0.757074 | + | 0.653329i | \(0.773372\pi\) | |||||||
\(192\) | 0.221232 | − | 0.383185i | 0.0159660 | − | 0.0276540i | ||||
\(193\) | −3.89440 | + | 6.74529i | −0.280325 | + | 0.485537i | −0.971465 | − | 0.237184i | \(-0.923775\pi\) |
0.691140 | + | 0.722721i | \(0.257109\pi\) | |||||||
\(194\) | 3.91216 | + | 6.77606i | 0.280877 | + | 0.486493i | ||||
\(195\) | 1.27401 | − | 2.20665i | 0.0912339 | − | 0.158022i | ||||
\(196\) | 0.324429 | + | 0.561928i | 0.0231735 | + | 0.0401377i | ||||
\(197\) | 1.82514 | 0.130036 | 0.0650180 | − | 0.997884i | \(-0.479290\pi\) | ||||
0.0650180 | + | 0.997884i | \(0.479290\pi\) | |||||||
\(198\) | 5.47382 | 0.389007 | ||||||||
\(199\) | −1.17963 | − | 2.04317i | −0.0836216 | − | 0.144837i | 0.821181 | − | 0.570667i | \(-0.193315\pi\) |
−0.904803 | + | 0.425830i | \(0.859982\pi\) | |||||||
\(200\) | −2.10262 | − | 3.64185i | −0.148678 | − | 0.257517i | ||||
\(201\) | 1.18253 | 0.0834094 | ||||||||
\(202\) | 5.38487 | 0.378878 | ||||||||
\(203\) | −5.77195 | − | 9.99731i | −0.405111 | − | 0.701674i | ||||
\(204\) | −0.757113 | + | 1.31136i | −0.0530085 | + | 0.0918134i | ||||
\(205\) | −1.55535 | − | 2.69395i | −0.108630 | − | 0.188153i | ||||
\(206\) | −2.34734 | + | 4.06571i | −0.163547 | + | 0.283271i | ||||
\(207\) | 11.4764 | − | 19.8776i | 0.797662 | − | 1.38159i | ||||
\(208\) | −6.45965 | −0.447896 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.994078 | −0.0685979 | ||||||||
\(211\) | 0.180525 | − | 0.312679i | 0.0124279 | − | 0.0215257i | −0.859745 | − | 0.510724i | \(-0.829377\pi\) |
0.872172 | + | 0.489199i | \(0.162711\pi\) | |||||||
\(212\) | −1.88139 | + | 3.25866i | −0.129214 | + | 0.223806i | ||||
\(213\) | 0.0124864 | + | 0.0216271i | 0.000855554 | + | 0.00148186i | ||||
\(214\) | 8.01864 | − | 13.8887i | 0.548143 | − | 0.949411i | ||||
\(215\) | −2.78444 | − | 4.82278i | −0.189897 | − | 0.328911i | ||||
\(216\) | −2.56816 | −0.174741 | ||||||||
\(217\) | −22.1612 | −1.50440 | ||||||||
\(218\) | 7.05040 | + | 12.2116i | 0.477513 | + | 0.827077i | ||||
\(219\) | −1.54180 | − | 2.67048i | −0.104185 | − | 0.180454i | ||||
\(220\) | −1.74018 | −0.117323 | ||||||||
\(221\) | 22.1066 | 1.48705 | ||||||||
\(222\) | 1.32292 | + | 2.29137i | 0.0887886 | + | 0.153786i | ||||
\(223\) | −9.02431 | + | 15.6306i | −0.604312 | + | 1.04670i | 0.387848 | + | 0.921724i | \(0.373219\pi\) |
−0.992160 | + | 0.124976i | \(0.960115\pi\) | |||||||
\(224\) | 1.26007 | + | 2.18251i | 0.0841922 | + | 0.145825i | ||||
\(225\) | −5.89623 | + | 10.2126i | −0.393082 | + | 0.680838i | ||||
\(226\) | −6.36119 | + | 11.0179i | −0.423140 | + | 0.732900i | ||||
\(227\) | 12.2845 | 0.815349 | 0.407675 | − | 0.913127i | \(-0.366340\pi\) | ||||
0.407675 | + | 0.913127i | \(0.366340\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.79174 | 0.448811 | 0.224405 | − | 0.974496i | \(-0.427956\pi\) | ||||
0.224405 | + | 0.974496i | \(0.427956\pi\) | |||||||
\(230\) | −3.64845 | + | 6.31929i | −0.240571 | + | 0.416682i | ||||
\(231\) | 1.08831 | − | 1.88500i | 0.0716052 | − | 0.124024i | ||||
\(232\) | 2.29032 | + | 3.96695i | 0.150367 | + | 0.260443i | ||||
\(233\) | −10.7147 | + | 18.5584i | −0.701942 | + | 1.21580i | 0.265842 | + | 0.964017i | \(0.414350\pi\) |
−0.967784 | + | 0.251782i | \(0.918983\pi\) | |||||||
\(234\) | 9.05716 | + | 15.6875i | 0.592085 | + | 1.02552i | ||||
\(235\) | 9.40507 | 0.613519 | ||||||||
\(236\) | 2.84162 | 0.184973 | ||||||||
\(237\) | −2.02020 | − | 3.49909i | −0.131226 | − | 0.227291i | ||||
\(238\) | −4.31230 | − | 7.46912i | −0.279525 | − | 0.484151i | ||||
\(239\) | −11.8376 | −0.765713 | −0.382856 | − | 0.923808i | \(-0.625060\pi\) | ||||
−0.382856 | + | 0.923808i | \(0.625060\pi\) | |||||||
\(240\) | 0.394452 | 0.0254618 | ||||||||
\(241\) | 10.8732 | + | 18.8329i | 0.700401 | + | 1.21313i | 0.968326 | + | 0.249691i | \(0.0803290\pi\) |
−0.267924 | + | 0.963440i | \(0.586338\pi\) | |||||||
\(242\) | −3.59487 | + | 6.22650i | −0.231087 | + | 0.400254i | ||||
\(243\) | 5.46200 | + | 9.46046i | 0.350387 | + | 0.606889i | ||||
\(244\) | 1.22747 | − | 2.12605i | 0.0785810 | − | 0.136106i | ||||
\(245\) | −0.289226 | + | 0.500954i | −0.0184780 | + | 0.0320048i | ||||
\(246\) | −1.54390 | −0.0984353 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.79360 | 0.558394 | ||||||||
\(249\) | −3.12465 | + | 5.41206i | −0.198017 | + | 0.342975i | ||||
\(250\) | 4.10320 | − | 7.10695i | 0.259509 | − | 0.449483i | ||||
\(251\) | −11.8205 | − | 20.4737i | −0.746104 | − | 1.29229i | −0.949677 | − | 0.313231i | \(-0.898589\pi\) |
0.203573 | − | 0.979060i | \(-0.434745\pi\) | |||||||
\(252\) | 3.53353 | − | 6.12026i | 0.222592 | − | 0.385540i | ||||
\(253\) | −7.98855 | − | 13.8366i | −0.502236 | − | 0.869898i | ||||
\(254\) | −7.17442 | −0.450163 | ||||||||
\(255\) | −1.34992 | −0.0845352 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0.461734 | + | 0.799748i | 0.0288022 | + | 0.0498869i | 0.880067 | − | 0.474849i | \(-0.157497\pi\) |
−0.851265 | + | 0.524736i | \(0.824164\pi\) | |||||||
\(258\) | −2.76393 | −0.172075 | ||||||||
\(259\) | −15.0700 | −0.936402 | ||||||||
\(260\) | −2.87936 | − | 4.98720i | −0.178570 | − | 0.309293i | ||||
\(261\) | 6.42258 | − | 11.1242i | 0.397548 | − | 0.688573i | ||||
\(262\) | −1.76133 | − | 3.05071i | −0.108815 | − | 0.188473i | ||||
\(263\) | −2.15984 | + | 3.74095i | −0.133181 | + | 0.230677i | −0.924901 | − | 0.380208i | \(-0.875853\pi\) |
0.791720 | + | 0.610884i | \(0.209186\pi\) | |||||||
\(264\) | −0.431842 | + | 0.747972i | −0.0265780 | + | 0.0460345i | ||||
\(265\) | −3.35449 | −0.206064 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.826407 | −0.0505753 | ||||||||
\(268\) | 1.33630 | − | 2.31455i | 0.0816278 | − | 0.141384i | ||||
\(269\) | 5.39768 | − | 9.34905i | 0.329102 | − | 0.570022i | −0.653232 | − | 0.757158i | \(-0.726587\pi\) |
0.982334 | + | 0.187136i | \(0.0599206\pi\) | |||||||
\(270\) | −1.14475 | − | 1.98276i | −0.0696670 | − | 0.120667i | ||||
\(271\) | −0.403622 | + | 0.699093i | −0.0245183 | + | 0.0424669i | −0.878024 | − | 0.478616i | \(-0.841139\pi\) |
0.853506 | + | 0.521083i | \(0.174472\pi\) | |||||||
\(272\) | 1.71113 | + | 2.96376i | 0.103752 | + | 0.179705i | ||||
\(273\) | 7.20298 | 0.435944 | ||||||||
\(274\) | 11.0035 | 0.664749 | ||||||||
\(275\) | 4.10429 | + | 7.10885i | 0.247498 | + | 0.428680i | ||||
\(276\) | 1.81079 | + | 3.13638i | 0.108997 | + | 0.188788i | ||||
\(277\) | −9.14869 | −0.549691 | −0.274846 | − | 0.961488i | \(-0.588627\pi\) | ||||
−0.274846 | + | 0.961488i | \(0.588627\pi\) | |||||||
\(278\) | −21.7586 | −1.30499 | ||||||||
\(279\) | −12.3296 | − | 21.3555i | −0.738155 | − | 1.27852i | ||||
\(280\) | −1.12334 | + | 1.94569i | −0.0671327 | + | 0.116277i | ||||
\(281\) | −10.6079 | − | 18.3734i | −0.632813 | − | 1.09606i | −0.986974 | − | 0.160880i | \(-0.948567\pi\) |
0.354161 | − | 0.935184i | \(-0.384766\pi\) | |||||||
\(282\) | 2.33395 | − | 4.04253i | 0.138985 | − | 0.240729i | ||||
\(283\) | −2.59493 | + | 4.49454i | −0.154252 | + | 0.267173i | −0.932787 | − | 0.360429i | \(-0.882630\pi\) |
0.778534 | + | 0.627602i | \(0.215964\pi\) | |||||||
\(284\) | 0.0564404 | 0.00334912 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.6092 | 0.745596 | ||||||||
\(287\) | 4.39680 | − | 7.61548i | 0.259535 | − | 0.449528i | ||||
\(288\) | −1.40211 | + | 2.42853i | −0.0826203 | + | 0.143103i | ||||
\(289\) | 2.64407 | + | 4.57966i | 0.155533 | + | 0.269392i | ||||
\(290\) | −2.04180 | + | 3.53651i | −0.119899 | + | 0.207671i | ||||
\(291\) | 1.73099 | + | 2.99816i | 0.101472 | + | 0.175755i | ||||
\(292\) | −6.96917 | −0.407840 | ||||||||
\(293\) | −17.5660 | −1.02621 | −0.513107 | − | 0.858324i | \(-0.671506\pi\) | ||||
−0.513107 | + | 0.858324i | \(0.671506\pi\) | |||||||
\(294\) | 0.143548 | + | 0.248633i | 0.00837190 | + | 0.0145006i | ||||
\(295\) | 1.26664 | + | 2.19388i | 0.0737465 | + | 0.127733i | ||||
\(296\) | 5.97980 | 0.347569 | ||||||||
\(297\) | 5.01302 | 0.290885 | ||||||||
\(298\) | 7.19479 | + | 12.4617i | 0.416783 | + | 0.721889i | ||||
\(299\) | 26.4362 | − | 45.7889i | 1.52885 | − | 2.64804i | ||||
\(300\) | −0.930333 | − | 1.61138i | −0.0537128 | − | 0.0930333i | ||||
\(301\) | 7.87129 | − | 13.6335i | 0.453693 | − | 0.785820i | ||||
\(302\) | 6.20338 | − | 10.7446i | 0.356964 | − | 0.618280i | ||||
\(303\) | 2.38261 | 0.136877 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.18857 | 0.125317 | ||||||||
\(306\) | 4.79840 | − | 8.31106i | 0.274306 | − | 0.475112i | ||||
\(307\) | 10.7842 | − | 18.6787i | 0.615486 | − | 1.06605i | −0.374813 | − | 0.927100i | \(-0.622293\pi\) |
0.990299 | − | 0.138952i | \(-0.0443734\pi\) | |||||||
\(308\) | −2.45965 | − | 4.26024i | −0.140152 | − | 0.242750i | ||||
\(309\) | −1.03861 | + | 1.79893i | −0.0590846 | + | 0.102337i | ||||
\(310\) | 3.91971 | + | 6.78914i | 0.222625 | + | 0.385597i | ||||
\(311\) | −2.57368 | −0.145940 | −0.0729701 | − | 0.997334i | \(-0.523248\pi\) | ||||
−0.0729701 | + | 0.997334i | \(0.523248\pi\) | |||||||
\(312\) | −2.85816 | −0.161811 | ||||||||
\(313\) | 2.59194 | + | 4.48938i | 0.146505 | + | 0.253755i | 0.929934 | − | 0.367728i | \(-0.119864\pi\) |
−0.783428 | + | 0.621482i | \(0.786531\pi\) | |||||||
\(314\) | −0.225610 | − | 0.390768i | −0.0127319 | − | 0.0220523i | ||||
\(315\) | 6.30023 | 0.354977 | ||||||||
\(316\) | −9.13162 | −0.513694 | ||||||||
\(317\) | 10.1281 | + | 17.5423i | 0.568850 | + | 0.985276i | 0.996680 | + | 0.0814174i | \(0.0259447\pi\) |
−0.427830 | + | 0.903859i | \(0.640722\pi\) | |||||||
\(318\) | −0.832446 | + | 1.44184i | −0.0466813 | + | 0.0808543i | ||||
\(319\) | −4.47068 | − | 7.74345i | −0.250310 | − | 0.433550i | ||||
\(320\) | 0.445746 | − | 0.772054i | 0.0249179 | − | 0.0431591i | ||||
\(321\) | 3.54795 | − | 6.14524i | 0.198028 | − | 0.342994i | ||||
\(322\) | −20.6275 | −1.14953 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 7.27636 | 0.404242 | ||||||||
\(325\) | −13.5822 | + | 23.5251i | −0.753405 | + | 1.30494i | ||||
\(326\) | −0.0346271 | + | 0.0599759i | −0.00191782 | + | 0.00332176i | ||||
\(327\) | 3.11954 | + | 5.40321i | 0.172511 | + | 0.298798i | ||||
\(328\) | −1.74466 | + | 3.02184i | −0.0963328 | + | 0.166853i | ||||
\(329\) | 13.2935 | + | 23.0251i | 0.732897 | + | 1.26941i | ||||
\(330\) | −0.769967 | −0.0423853 | ||||||||
\(331\) | −21.3280 | −1.17229 | −0.586146 | − | 0.810205i | \(-0.699356\pi\) | ||||
−0.586146 | + | 0.810205i | \(0.699356\pi\) | |||||||
\(332\) | 7.06195 | + | 12.2317i | 0.387575 | + | 0.671299i | ||||
\(333\) | −8.38435 | − | 14.5221i | −0.459460 | − | 0.795807i | ||||
\(334\) | −2.17371 | −0.118940 | ||||||||
\(335\) | 2.38261 | 0.130176 | ||||||||
\(336\) | 0.557537 | + | 0.965682i | 0.0304161 | + | 0.0526822i | ||||
\(337\) | 11.3637 | − | 19.6826i | 0.619022 | − | 1.07218i | −0.370642 | − | 0.928776i | \(-0.620862\pi\) |
0.989665 | − | 0.143402i | \(-0.0458042\pi\) | |||||||
\(338\) | 14.3635 | + | 24.8784i | 0.781273 | + | 1.35321i | ||||
\(339\) | −2.81459 | + | 4.87502i | −0.152868 | + | 0.264775i | ||||
\(340\) | −1.52546 | + | 2.64217i | −0.0827296 | + | 0.143292i | ||||
\(341\) | −17.1650 | −0.929538 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.2762 | −1.04082 | ||||||||
\(344\) | −3.12334 | + | 5.40979i | −0.168399 | + | 0.291676i | ||||
\(345\) | −1.61430 | + | 2.79606i | −0.0869112 | + | 0.150535i | ||||
\(346\) | −8.42464 | − | 14.5919i | −0.452912 | − | 0.784466i | ||||
\(347\) | 2.46428 | − | 4.26825i | 0.132289 | − | 0.229132i | −0.792269 | − | 0.610171i | \(-0.791101\pi\) |
0.924559 | + | 0.381040i | \(0.124434\pi\) | |||||||
\(348\) | 1.01338 | + | 1.75523i | 0.0543231 | + | 0.0940903i | ||||
\(349\) | 26.1615 | 1.40039 | 0.700197 | − | 0.713950i | \(-0.253096\pi\) | ||||
0.700197 | + | 0.713950i | \(0.253096\pi\) | |||||||
\(350\) | 10.5978 | 0.566478 | ||||||||
\(351\) | 8.29470 | + | 14.3668i | 0.442738 | + | 0.766845i | ||||
\(352\) | 0.975994 | + | 1.69047i | 0.0520207 | + | 0.0901025i | ||||
\(353\) | 2.70813 | 0.144139 | 0.0720697 | − | 0.997400i | \(-0.477040\pi\) | ||||
0.0720697 | + | 0.997400i | \(0.477040\pi\) | |||||||
\(354\) | 1.25731 | 0.0668253 | ||||||||
\(355\) | 0.0251581 | + | 0.0435750i | 0.00133525 | + | 0.00231272i | ||||
\(356\) | −0.933870 | + | 1.61751i | −0.0494950 | + | 0.0857279i | ||||
\(357\) | −1.90803 | − | 3.30481i | −0.100984 | − | 0.174909i | ||||
\(358\) | 9.48276 | − | 16.4246i | 0.501179 | − | 0.868068i | ||||
\(359\) | 4.65501 | − | 8.06272i | 0.245682 | − | 0.425534i | −0.716641 | − | 0.697442i | \(-0.754321\pi\) |
0.962323 | + | 0.271908i | \(0.0876547\pi\) | |||||||
\(360\) | −2.49994 | −0.131759 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 1.98687 | 0.104428 | ||||||||
\(363\) | −1.59060 | + | 2.75500i | −0.0834848 | + | 0.144600i | ||||
\(364\) | 8.13963 | − | 14.0983i | 0.426633 | − | 0.738950i | ||||
\(365\) | −3.10648 | − | 5.38058i | −0.162601 | − | 0.281632i | ||||
\(366\) | 0.543113 | − | 0.940699i | 0.0283890 | − | 0.0491711i | ||||
\(367\) | −3.87721 | − | 6.71552i | −0.202389 | − | 0.350548i | 0.746909 | − | 0.664926i | \(-0.231537\pi\) |
−0.949298 | + | 0.314379i | \(0.898204\pi\) | |||||||
\(368\) | 8.18504 | 0.426675 | ||||||||
\(369\) | 9.78485 | 0.509379 | ||||||||
\(370\) | 2.66547 | + | 4.61673i | 0.138571 | + | 0.240012i | ||||
\(371\) | −4.74138 | − | 8.21231i | −0.246160 | − | 0.426362i | ||||
\(372\) | 3.89085 | 0.201731 | ||||||||
\(373\) | −25.0124 | −1.29509 | −0.647546 | − | 0.762027i | \(-0.724205\pi\) | ||||
−0.647546 | + | 0.762027i | \(0.724205\pi\) | |||||||
\(374\) | −3.34011 | − | 5.78523i | −0.172713 | − | 0.299147i | ||||
\(375\) | 1.81552 | − | 3.14456i | 0.0937528 | − | 0.162385i | ||||
\(376\) | −5.27491 | − | 9.13641i | −0.272033 | − | 0.471174i | ||||
\(377\) | 14.7947 | − | 25.6251i | 0.761965 | − | 1.31976i | ||||
\(378\) | 3.23607 | − | 5.60503i | 0.166445 | − | 0.288292i | ||||
\(379\) | 19.1802 | 0.985222 | 0.492611 | − | 0.870250i | \(-0.336043\pi\) | ||||
0.492611 | + | 0.870250i | \(0.336043\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.17442 | −0.162630 | ||||||||
\(382\) | −10.4630 | + | 18.1224i | −0.535332 | + | 0.927222i | ||||
\(383\) | 2.41659 | − | 4.18566i | 0.123482 | − | 0.213877i | −0.797656 | − | 0.603112i | \(-0.793927\pi\) |
0.921139 | + | 0.389235i | \(0.127261\pi\) | |||||||
\(384\) | −0.221232 | − | 0.383185i | −0.0112897 | − | 0.0195543i | ||||
\(385\) | 2.19276 | − | 3.79797i | 0.111753 | − | 0.193562i | ||||
\(386\) | 3.89440 | + | 6.74529i | 0.198220 | + | 0.343326i | ||||
\(387\) | 17.5171 | 0.890446 | ||||||||
\(388\) | 7.82432 | 0.397219 | ||||||||
\(389\) | −10.8646 | − | 18.8180i | −0.550855 | − | 0.954109i | −0.998213 | − | 0.0597540i | \(-0.980968\pi\) |
0.447358 | − | 0.894355i | \(-0.352365\pi\) | |||||||
\(390\) | −1.27401 | − | 2.20665i | −0.0645121 | − | 0.111738i | ||||
\(391\) | −28.0113 | −1.41659 | ||||||||
\(392\) | 0.648859 | 0.0327723 | ||||||||
\(393\) | −0.779323 | − | 1.34983i | −0.0393116 | − | 0.0680898i | ||||
\(394\) | 0.912571 | − | 1.58062i | 0.0459747 | − | 0.0796304i | ||||
\(395\) | −4.07038 | − | 7.05010i | −0.204803 | − | 0.354729i | ||||
\(396\) | 2.73691 | − | 4.74047i | 0.137535 | − | 0.238217i | ||||
\(397\) | −5.85701 | + | 10.1446i | −0.293955 | + | 0.509145i | −0.974741 | − | 0.223337i | \(-0.928305\pi\) |
0.680786 | + | 0.732482i | \(0.261638\pi\) | |||||||
\(398\) | −2.35926 | −0.118259 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.20524 | −0.210262 | ||||||||
\(401\) | 5.90617 | − | 10.2298i | 0.294940 | − | 0.510851i | −0.680031 | − | 0.733183i | \(-0.738034\pi\) |
0.974971 | + | 0.222332i | \(0.0713670\pi\) | |||||||
\(402\) | 0.591266 | − | 1.02410i | 0.0294897 | − | 0.0510776i | ||||
\(403\) | −28.4018 | − | 49.1934i | −1.41479 | − | 2.45050i | ||||
\(404\) | 2.69244 | − | 4.66343i | 0.133954 | − | 0.232015i | ||||
\(405\) | 3.24341 | + | 5.61775i | 0.161166 | + | 0.279148i | ||||
\(406\) | −11.5439 | −0.572914 | ||||||||
\(407\) | −11.6725 | −0.578584 | ||||||||
\(408\) | 0.757113 | + | 1.31136i | 0.0374827 | + | 0.0649219i | ||||
\(409\) | −12.6331 | − | 21.8812i | −0.624668 | − | 1.08196i | −0.988605 | − | 0.150534i | \(-0.951901\pi\) |
0.363937 | − | 0.931424i | \(-0.381432\pi\) | |||||||
\(410\) | −3.11070 | −0.153627 | ||||||||
\(411\) | 4.86867 | 0.240154 | ||||||||
\(412\) | 2.34734 | + | 4.06571i | 0.115645 | + | 0.200303i | ||||
\(413\) | −3.58064 | + | 6.20186i | −0.176192 | + | 0.305173i | ||||
\(414\) | −11.4764 | − | 19.8776i | −0.564032 | − | 0.976932i | ||||
\(415\) | −6.29567 | + | 10.9044i | −0.309042 | + | 0.535277i | ||||
\(416\) | −3.22982 | + | 5.59422i | −0.158355 | + | 0.274279i | ||||
\(417\) | −9.62739 | −0.471455 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.6143 | 1.54446 | 0.772229 | − | 0.635344i | \(-0.219142\pi\) | ||||
0.772229 | + | 0.635344i | \(0.219142\pi\) | |||||||
\(420\) | −0.497039 | + | 0.860897i | −0.0242530 | + | 0.0420075i | ||||
\(421\) | 1.09486 | − | 1.89635i | 0.0533602 | − | 0.0924226i | −0.838112 | − | 0.545499i | \(-0.816340\pi\) |
0.891472 | + | 0.453076i | \(0.149674\pi\) | |||||||
\(422\) | −0.180525 | − | 0.312679i | −0.00878783 | − | 0.0152210i | ||||
\(423\) | −14.7920 | + | 25.6206i | −0.719214 | + | 1.24571i | ||||
\(424\) | 1.88139 | + | 3.25866i | 0.0913684 | + | 0.158255i | ||||
\(425\) | 14.3914 | 0.698087 | ||||||||
\(426\) | 0.0249728 | 0.00120994 | ||||||||
\(427\) | 3.09342 | + | 5.35796i | 0.149701 | + | 0.259290i | ||||
\(428\) | −8.01864 | − | 13.8887i | −0.387596 | − | 0.671335i | ||||
\(429\) | 5.57909 | 0.269361 | ||||||||
\(430\) | −5.56887 | −0.268555 | ||||||||
\(431\) | 0.901858 | + | 1.56206i | 0.0434410 | + | 0.0752420i | 0.886928 | − | 0.461907i | \(-0.152835\pi\) |
−0.843487 | + | 0.537149i | \(0.819501\pi\) | |||||||
\(432\) | −1.28408 | + | 2.22409i | −0.0617803 | + | 0.107007i | ||||
\(433\) | 3.28616 | + | 5.69180i | 0.157923 | + | 0.273531i | 0.934120 | − | 0.356960i | \(-0.116187\pi\) |
−0.776197 | + | 0.630491i | \(0.782854\pi\) | |||||||
\(434\) | −11.0806 | + | 19.1921i | −0.531885 | + | 0.921252i | ||||
\(435\) | −0.903423 | + | 1.56477i | −0.0433158 | + | 0.0750252i | ||||
\(436\) | 14.1008 | 0.675305 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −3.08361 | −0.147340 | ||||||||
\(439\) | 4.56530 | − | 7.90733i | 0.217890 | − | 0.377396i | −0.736273 | − | 0.676685i | \(-0.763416\pi\) |
0.954163 | + | 0.299289i | \(0.0967493\pi\) | |||||||
\(440\) | −0.870091 | + | 1.50704i | −0.0414799 | + | 0.0718454i | ||||
\(441\) | −0.909774 | − | 1.57577i | −0.0433226 | − | 0.0750369i | ||||
\(442\) | 11.0533 | − | 19.1449i | 0.525752 | − | 0.910629i | ||||
\(443\) | 13.7343 | + | 23.7885i | 0.652536 | + | 1.13023i | 0.982505 | + | 0.186235i | \(0.0596284\pi\) |
−0.329969 | + | 0.943992i | \(0.607038\pi\) | |||||||
\(444\) | 2.64584 | 0.125566 | ||||||||
\(445\) | −1.66508 | −0.0789321 | ||||||||
\(446\) | 9.02431 | + | 15.6306i | 0.427313 | + | 0.740128i | ||||
\(447\) | 3.18343 | + | 5.51386i | 0.150571 | + | 0.260797i | ||||
\(448\) | 2.52015 | 0.119066 | ||||||||
\(449\) | −7.57293 | −0.357389 | −0.178694 | − | 0.983905i | \(-0.557187\pi\) | ||||
−0.178694 | + | 0.983905i | \(0.557187\pi\) | |||||||
\(450\) | 5.89623 | + | 10.2126i | 0.277951 | + | 0.481425i | ||||
\(451\) | 3.40556 | − | 5.89860i | 0.160362 | − | 0.277754i | ||||
\(452\) | 6.36119 | + | 11.0179i | 0.299205 | + | 0.518238i | ||||
\(453\) | 2.74477 | − | 4.75408i | 0.128960 | − | 0.223366i | ||||
\(454\) | 6.14224 | − | 10.6387i | 0.288270 | − | 0.499297i | ||||
\(455\) | 14.5128 | 0.680372 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.7675 | −1.01824 | −0.509120 | − | 0.860696i | \(-0.670029\pi\) | ||||
−0.509120 | + | 0.860696i | \(0.670029\pi\) | |||||||
\(458\) | 3.39587 | − | 5.88182i | 0.158679 | − | 0.274839i | ||||
\(459\) | 4.39445 | − | 7.61141i | 0.205115 | − | 0.355270i | ||||
\(460\) | 3.64845 | + | 6.31929i | 0.170110 | + | 0.294639i | ||||
\(461\) | −5.97219 | + | 10.3441i | −0.278153 | + | 0.481775i | −0.970926 | − | 0.239381i | \(-0.923055\pi\) |
0.692773 | + | 0.721156i | \(0.256389\pi\) | |||||||
\(462\) | −1.08831 | − | 1.88500i | −0.0506325 | − | 0.0876981i | ||||
\(463\) | −8.75371 | −0.406819 | −0.203410 | − | 0.979094i | \(-0.565202\pi\) | ||||
−0.203410 | + | 0.979094i | \(0.565202\pi\) | |||||||
\(464\) | 4.58064 | 0.212651 | ||||||||
\(465\) | 1.73433 | + | 3.00395i | 0.0804276 | + | 0.139305i | ||||
\(466\) | 10.7147 | + | 18.5584i | 0.496348 | + | 0.859700i | ||||
\(467\) | 29.3568 | 1.35847 | 0.679236 | − | 0.733920i | \(-0.262311\pi\) | ||||
0.679236 | + | 0.733920i | \(0.262311\pi\) | |||||||
\(468\) | 18.1143 | 0.837335 | ||||||||
\(469\) | 3.36768 | + | 5.83300i | 0.155505 | + | 0.269343i | ||||
\(470\) | 4.70254 | − | 8.14503i | 0.216912 | − | 0.375702i | ||||
\(471\) | −0.0998242 | − | 0.172901i | −0.00459966 | − | 0.00796684i | ||||
\(472\) | 1.42081 | − | 2.46091i | 0.0653980 | − | 0.113273i | ||||
\(473\) | 6.09673 | − | 10.5599i | 0.280328 | − | 0.485543i | ||||
\(474\) | −4.04041 | −0.185582 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.62460 | −0.395308 | ||||||||
\(477\) | 5.27584 | − | 9.13803i | 0.241564 | − | 0.418401i | ||||
\(478\) | −5.91881 | + | 10.2517i | −0.270720 | + | 0.468901i | ||||
\(479\) | 12.4352 | + | 21.5385i | 0.568180 | + | 0.984117i | 0.996746 | + | 0.0806064i | \(0.0256857\pi\) |
−0.428566 | + | 0.903511i | \(0.640981\pi\) | |||||||
\(480\) | 0.197226 | − | 0.341606i | 0.00900210 | − | 0.0155921i | ||||
\(481\) | −19.3137 | − | 33.4523i | −0.880629 | − | 1.52529i | ||||
\(482\) | 21.7463 | 0.990517 | ||||||||
\(483\) | −9.12692 | −0.415289 | ||||||||
\(484\) | 3.59487 | + | 6.22650i | 0.163403 | + | 0.283023i | ||||
\(485\) | 3.48766 | + | 6.04080i | 0.158366 | + | 0.274298i | ||||
\(486\) | 10.9240 | 0.495523 | ||||||||
\(487\) | −8.53766 | −0.386878 | −0.193439 | − | 0.981112i | \(-0.561964\pi\) | ||||
−0.193439 | + | 0.981112i | \(0.561964\pi\) | |||||||
\(488\) | −1.22747 | − | 2.12605i | −0.0555652 | − | 0.0962417i | ||||
\(489\) | −0.0153212 | + | 0.0265371i | −0.000692850 | + | 0.00120005i | ||||
\(490\) | 0.289226 | + | 0.500954i | 0.0130659 | + | 0.0226308i | ||||
\(491\) | 5.76985 | − | 9.99368i | 0.260390 | − | 0.451008i | −0.705956 | − | 0.708256i | \(-0.749482\pi\) |
0.966346 | + | 0.257248i | \(0.0828156\pi\) | |||||||
\(492\) | −0.771949 | + | 1.33705i | −0.0348021 | + | 0.0602791i | ||||
\(493\) | −15.6762 | −0.706019 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.87986 | 0.219333 | ||||||||
\(496\) | 4.39680 | − | 7.61548i | 0.197422 | − | 0.341945i | ||||
\(497\) | −0.0711190 | + | 0.123182i | −0.00319013 | + | 0.00552546i | ||||
\(498\) | 3.12465 | + | 5.41206i | 0.140019 | + | 0.242520i | ||||
\(499\) | 14.8045 | − | 25.6422i | 0.662742 | − | 1.14790i | −0.317151 | − | 0.948375i | \(-0.602726\pi\) |
0.979892 | − | 0.199527i | \(-0.0639406\pi\) | |||||||
\(500\) | −4.10320 | − | 7.10695i | −0.183501 | − | 0.317832i | ||||
\(501\) | −0.961785 | −0.0429694 | ||||||||
\(502\) | −23.6410 | −1.05515 | ||||||||
\(503\) | −2.93414 | − | 5.08207i | −0.130827 | − | 0.226598i | 0.793169 | − | 0.609002i | \(-0.208430\pi\) |
−0.923995 | + | 0.382403i | \(0.875096\pi\) | |||||||
\(504\) | −3.53353 | − | 6.12026i | −0.157396 | − | 0.272618i | ||||
\(505\) | 4.80057 | 0.213622 | ||||||||
\(506\) | −15.9771 | −0.710269 | ||||||||
\(507\) | 6.35534 | + | 11.0078i | 0.282251 | + | 0.488872i | ||||
\(508\) | −3.58721 | + | 6.21323i | −0.159157 | + | 0.275667i | ||||
\(509\) | −12.7843 | − | 22.1431i | −0.566656 | − | 0.981477i | −0.996893 | − | 0.0787614i | \(-0.974903\pi\) |
0.430237 | − | 0.902716i | \(-0.358430\pi\) | |||||||
\(510\) | −0.674959 | + | 1.16906i | −0.0298877 | + | 0.0517670i | ||||
\(511\) | 8.78167 | − | 15.2103i | 0.388478 | − | 0.672864i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.923469 | 0.0407325 | ||||||||
\(515\) | −2.09263 | + | 3.62455i | −0.0922124 | + | 0.159717i | ||||
\(516\) | −1.38197 | + | 2.39364i | −0.0608377 | + | 0.105374i | ||||
\(517\) | 10.2966 | + | 17.8342i | 0.452842 | + | 0.784346i | ||||
\(518\) | −7.53498 | + | 13.0510i | −0.331068 | + | 0.573427i | ||||
\(519\) | −3.72760 | − | 6.45639i | −0.163623 | − | 0.283404i | ||||
\(520\) | −5.75872 | −0.252537 | ||||||||
\(521\) | 14.0332 | 0.614807 | 0.307403 | − | 0.951579i | \(-0.400540\pi\) | ||||
0.307403 | + | 0.951579i | \(0.400540\pi\) | |||||||
\(522\) | −6.42258 | − | 11.1242i | −0.281109 | − | 0.486895i | ||||
\(523\) | 15.5392 | + | 26.9147i | 0.679482 | + | 1.17690i | 0.975137 | + | 0.221602i | \(0.0711286\pi\) |
−0.295655 | + | 0.955295i | \(0.595538\pi\) | |||||||
\(524\) | −3.52265 | −0.153888 | ||||||||
\(525\) | 4.68915 | 0.204651 | ||||||||
\(526\) | 2.15984 | + | 3.74095i | 0.0941734 | + | 0.163113i | ||||
\(527\) | −15.0470 | + | 26.0622i | −0.655458 | + | 1.13529i | ||||
\(528\) | 0.431842 | + | 0.747972i | 0.0187935 | + | 0.0325513i | ||||
\(529\) | −21.9974 | + | 38.1007i | −0.956410 | + | 1.65655i | ||||
\(530\) | −1.67724 | + | 2.90507i | −0.0728548 | + | 0.126188i | ||||
\(531\) | −7.96853 | −0.345805 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.5398 | 0.976307 | ||||||||
\(534\) | −0.413204 | + | 0.715690i | −0.0178811 | + | 0.0309709i | ||||
\(535\) | 7.14855 | − | 12.3816i | 0.309059 | − | 0.535305i | ||||
\(536\) | −1.33630 | − | 2.31455i | −0.0577196 | − | 0.0999732i | ||||
\(537\) | 4.19577 | − | 7.26729i | 0.181061 | − | 0.313607i | ||||
\(538\) | −5.39768 | − | 9.34905i | −0.232710 | − | 0.403066i | ||||
\(539\) | −1.26657 | −0.0545548 | ||||||||
\(540\) | −2.28949 | −0.0985240 | ||||||||
\(541\) | −1.44804 | − | 2.50808i | −0.0622561 | − | 0.107831i | 0.833217 | − | 0.552945i | \(-0.186496\pi\) |
−0.895474 | + | 0.445115i | \(0.853163\pi\) | |||||||
\(542\) | 0.403622 | + | 0.699093i | 0.0173370 | + | 0.0300286i | ||||
\(543\) | 0.879118 | 0.0377266 | ||||||||
\(544\) | 3.42226 | 0.146728 | ||||||||
\(545\) | 6.28537 | + | 10.8866i | 0.269236 | + | 0.466330i | ||||
\(546\) | 3.60149 | − | 6.23796i | 0.154130 | − | 0.266960i | ||||
\(547\) | 15.1931 | + | 26.3151i | 0.649608 | + | 1.12515i | 0.983217 | + | 0.182443i | \(0.0584004\pi\) |
−0.333608 | + | 0.942712i | \(0.608266\pi\) | |||||||
\(548\) | 5.50177 | − | 9.52935i | 0.235024 | − | 0.407074i | ||||
\(549\) | −3.44212 | + | 5.96192i | −0.146906 | + | 0.254449i | ||||
\(550\) | 8.20859 | 0.350015 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 3.62158 | 0.154145 | ||||||||
\(553\) | 11.5065 | − | 19.9299i | 0.489306 | − | 0.847504i | ||||
\(554\) | −4.57434 | + | 7.92300i | −0.194345 | + | 0.336616i | ||||
\(555\) | 1.17937 | + | 2.04273i | 0.0500616 | + | 0.0867092i | ||||
\(556\) | −10.8793 | + | 18.8435i | −0.461385 | + | 0.799143i | ||||
\(557\) | 3.06706 | + | 5.31231i | 0.129956 | + | 0.225090i | 0.923659 | − | 0.383215i | \(-0.125183\pi\) |
−0.793704 | + | 0.608305i | \(0.791850\pi\) | |||||||
\(558\) | −24.6593 | −1.04391 | ||||||||
\(559\) | 40.3514 | 1.70668 | ||||||||
\(560\) | 1.12334 | + | 1.94569i | 0.0474700 | + | 0.0822204i | ||||
\(561\) | −1.47788 | − | 2.55976i | −0.0623959 | − | 0.108073i | ||||
\(562\) | −21.2158 | −0.894932 | ||||||||
\(563\) | 28.1917 | 1.18814 | 0.594069 | − | 0.804414i | \(-0.297521\pi\) | ||||
0.594069 | + | 0.804414i | \(0.297521\pi\) | |||||||
\(564\) | −2.33395 | − | 4.04253i | −0.0982772 | − | 0.170221i | ||||
\(565\) | −5.67094 | + | 9.82236i | −0.238578 | + | 0.413230i | ||||
\(566\) | 2.59493 | + | 4.49454i | 0.109073 | + | 0.188920i | ||||
\(567\) | −9.16875 | + | 15.8807i | −0.385051 | + | 0.666929i | ||||
\(568\) | 0.0282202 | − | 0.0488788i | 0.00118409 | − | 0.00205091i | ||||
\(569\) | 42.1145 | 1.76553 | 0.882766 | − | 0.469812i | \(-0.155678\pi\) | ||||
0.882766 | + | 0.469812i | \(0.155678\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.166927 | 0.00698566 | 0.00349283 | − | 0.999994i | \(-0.498888\pi\) | ||||
0.00349283 | + | 0.999994i | \(0.498888\pi\) | |||||||
\(572\) | 6.30458 | − | 10.9199i | 0.263608 | − | 0.456582i | ||||
\(573\) | −4.62948 | + | 8.01850i | −0.193399 | + | 0.334977i | ||||
\(574\) | −4.39680 | − | 7.61548i | −0.183519 | − | 0.317864i | ||||
\(575\) | 17.2100 | − | 29.8087i | 0.717708 | − | 1.24311i | ||||
\(576\) | 1.40211 | + | 2.42853i | 0.0584214 | + | 0.101189i | ||||
\(577\) | −19.9631 | −0.831076 | −0.415538 | − | 0.909576i | \(-0.636407\pi\) | ||||
−0.415538 | + | 0.909576i | \(0.636407\pi\) | |||||||
\(578\) | 5.28814 | 0.219957 | ||||||||
\(579\) | 1.72313 | + | 2.98455i | 0.0716108 | + | 0.124033i | ||||
\(580\) | 2.04180 | + | 3.53651i | 0.0847812 | + | 0.146845i | ||||
\(581\) | −35.5943 | −1.47670 | ||||||||
\(582\) | 3.46197 | 0.143503 | ||||||||
\(583\) | −3.67245 | − | 6.36087i | −0.152097 | − | 0.263440i | ||||
\(584\) | −3.48459 | + | 6.03548i | −0.144193 | + | 0.249750i | ||||
\(585\) | 8.07438 | + | 13.9852i | 0.333835 | + | 0.578218i | ||||
\(586\) | −8.78298 | + | 15.2126i | −0.362822 | + | 0.628426i | ||||
\(587\) | −5.07202 | + | 8.78499i | −0.209345 | + | 0.362595i | −0.951508 | − | 0.307623i | \(-0.900466\pi\) |
0.742164 | + | 0.670219i | \(0.233800\pi\) | |||||||
\(588\) | 0.287096 | 0.0118397 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 2.53328 | 0.104293 | ||||||||
\(591\) | 0.403779 | − | 0.699366i | 0.0166093 | − | 0.0287681i | ||||
\(592\) | 2.98990 | − | 5.17866i | 0.122884 | − | 0.212841i | ||||
\(593\) | −3.72658 | − | 6.45462i | −0.153032 | − | 0.265060i | 0.779309 | − | 0.626640i | \(-0.215570\pi\) |
−0.932341 | + | 0.361581i | \(0.882237\pi\) | |||||||
\(594\) | 2.50651 | − | 4.34140i | 0.102843 | − | 0.178130i | ||||
\(595\) | −3.84438 | − | 6.65866i | −0.157604 | − | 0.272978i | ||||
\(596\) | 14.3896 | 0.589420 | ||||||||
\(597\) | −1.04388 | −0.0427233 | ||||||||
\(598\) | −26.4362 | − | 45.7889i | −1.08106 | − | 1.87245i | ||||
\(599\) | −3.18571 | − | 5.51781i | −0.130164 | − | 0.225451i | 0.793575 | − | 0.608472i | \(-0.208217\pi\) |
−0.923740 | + | 0.383020i | \(0.874884\pi\) | |||||||
\(600\) | −1.86067 | −0.0759614 | ||||||||
\(601\) | −1.74631 | −0.0712333 | −0.0356166 | − | 0.999366i | \(-0.511340\pi\) | ||||
−0.0356166 | + | 0.999366i | \(0.511340\pi\) | |||||||
\(602\) | −7.87129 | − | 13.6335i | −0.320810 | − | 0.555659i | ||||
\(603\) | −3.74730 | + | 6.49052i | −0.152602 | + | 0.264314i | ||||
\(604\) | −6.20338 | − | 10.7446i | −0.252412 | − | 0.437190i | ||||
\(605\) | −3.20480 | + | 5.55087i | −0.130293 | + | 0.225675i | ||||
\(606\) | 1.19130 | − | 2.06340i | 0.0483934 | − | 0.0838199i | ||||
\(607\) | −32.1612 | −1.30538 | −0.652691 | − | 0.757624i | \(-0.726360\pi\) | ||||
−0.652691 | + | 0.757624i | \(0.726360\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.10775 | −0.206977 | ||||||||
\(610\) | 1.09428 | − | 1.89535i | 0.0443062 | − | 0.0767407i | ||||
\(611\) | −34.0741 | + | 59.0180i | −1.37849 | + | 2.38761i | ||||
\(612\) | −4.79840 | − | 8.31106i | −0.193964 | − | 0.335955i | ||||
\(613\) | −6.38223 | + | 11.0543i | −0.257776 | + | 0.446481i | −0.965646 | − | 0.259862i | \(-0.916323\pi\) |
0.707870 | + | 0.706343i | \(0.249656\pi\) | |||||||
\(614\) | −10.7842 | − | 18.6787i | −0.435214 | − | 0.753813i | ||||
\(615\) | −1.37637 | −0.0555007 | ||||||||
\(616\) | −4.91930 | −0.198204 | ||||||||
\(617\) | 0.841616 | + | 1.45772i | 0.0338822 | + | 0.0586856i | 0.882469 | − | 0.470370i | \(-0.155880\pi\) |
−0.848587 | + | 0.529056i | \(0.822546\pi\) | |||||||
\(618\) | 1.03861 | + | 1.79893i | 0.0417791 | + | 0.0723635i | ||||
\(619\) | 31.5285 | 1.26724 | 0.633618 | − | 0.773646i | \(-0.281569\pi\) | ||||
0.633618 | + | 0.773646i | \(0.281569\pi\) | |||||||
\(620\) | 7.83942 | 0.314839 | ||||||||
\(621\) | −10.5102 | − | 18.2043i | −0.421761 | − | 0.730512i | ||||
\(622\) | −1.28684 | + | 2.22887i | −0.0515976 | + | 0.0893697i | ||||
\(623\) | −2.35349 | − | 4.07637i | −0.0942906 | − | 0.163316i | ||||
\(624\) | −1.42908 | + | 2.47524i | −0.0572090 | + | 0.0990888i | ||||
\(625\) | −6.85514 | + | 11.8735i | −0.274206 | + | 0.474938i | ||||
\(626\) | 5.18389 | 0.207190 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.451220 | −0.0180056 | ||||||||
\(629\) | −10.2322 | + | 17.7227i | −0.407985 | + | 0.706651i | ||||
\(630\) | 3.15011 | − | 5.45616i | 0.125503 | − | 0.217378i | ||||
\(631\) | 15.8831 | + | 27.5103i | 0.632297 | + | 1.09517i | 0.987081 | + | 0.160222i | \(0.0512209\pi\) |
−0.354785 | + | 0.934948i | \(0.615446\pi\) | |||||||
\(632\) | −4.56581 | + | 7.90821i | −0.181618 | + | 0.314572i | ||||
\(633\) | −0.0798758 | − | 0.138349i | −0.00317478 | − | 0.00549888i | ||||
\(634\) | 20.2562 | 0.804475 | ||||||||
\(635\) | −6.39593 | −0.253815 | ||||||||
\(636\) | 0.832446 | + | 1.44184i | 0.0330086 | + | 0.0571726i | ||||
\(637\) | −2.09570 | − | 3.62986i | −0.0830347 | − | 0.143820i | ||||
\(638\) | −8.94137 | −0.353992 | ||||||||
\(639\) | −0.158272 | −0.00626113 | ||||||||
\(640\) | −0.445746 | − | 0.772054i | −0.0176196 | − | 0.0305181i | ||||
\(641\) | −20.2219 | + | 35.0253i | −0.798715 | + | 1.38342i | 0.121738 | + | 0.992562i | \(0.461153\pi\) |
−0.920453 | + | 0.390853i | \(0.872180\pi\) | |||||||
\(642\) | −3.54795 | − | 6.14524i | −0.140027 | − | 0.242533i | ||||
\(643\) | 13.0516 | − | 22.6061i | 0.514706 | − | 0.891497i | −0.485148 | − | 0.874432i | \(-0.661234\pi\) |
0.999854 | − | 0.0170651i | \(-0.00543224\pi\) | |||||||
\(644\) | −10.3138 | + | 17.8639i | −0.406419 | + | 0.703938i | ||||
\(645\) | −2.46402 | −0.0970208 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −48.7713 | −1.91740 | −0.958699 | − | 0.284423i | \(-0.908198\pi\) | ||||
−0.958699 | + | 0.284423i | \(0.908198\pi\) | |||||||
\(648\) | 3.63818 | − | 6.30151i | 0.142921 | − | 0.247547i | ||||
\(649\) | −2.77340 | + | 4.80367i | −0.108866 | + | 0.188561i | ||||
\(650\) | 13.5822 | + | 23.5251i | 0.532738 | + | 0.922729i | ||||
\(651\) | −4.90276 | + | 8.49182i | −0.192154 | + | 0.332821i | ||||
\(652\) | 0.0346271 | + | 0.0599759i | 0.00135610 | + | 0.00234884i | ||||
\(653\) | −43.1831 | −1.68988 | −0.844942 | − | 0.534858i | \(-0.820365\pi\) | ||||
−0.844942 | + | 0.534858i | \(0.820365\pi\) | |||||||
\(654\) | 6.23909 | 0.243968 | ||||||||
\(655\) | −1.57021 | − | 2.71968i | −0.0613531 | − | 0.106267i | ||||
\(656\) | 1.74466 | + | 3.02184i | 0.0681176 | + | 0.117983i | ||||
\(657\) | 19.5431 | 0.762451 | ||||||||
\(658\) | 26.5871 | 1.03647 | ||||||||
\(659\) | −7.13844 | − | 12.3641i | −0.278074 | − | 0.481638i | 0.692832 | − | 0.721099i | \(-0.256363\pi\) |
−0.970906 | + | 0.239461i | \(0.923029\pi\) | |||||||
\(660\) | −0.384983 | + | 0.666811i | −0.0149855 | + | 0.0259556i | ||||
\(661\) | 17.8748 | + | 30.9601i | 0.695251 | + | 1.20421i | 0.970096 | + | 0.242721i | \(0.0780399\pi\) |
−0.274846 | + | 0.961488i | \(0.588627\pi\) | |||||||
\(662\) | −10.6640 | + | 18.4706i | −0.414468 | + | 0.717880i | ||||
\(663\) | 4.89068 | − | 8.47091i | 0.189938 | − | 0.328983i | ||||
\(664\) | 14.1239 | 0.548114 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.7687 | −0.649774 | ||||||||
\(667\) | −18.7464 | + | 32.4697i | −0.725863 | + | 1.25723i | ||||
\(668\) | −1.08685 | + | 1.88248i | −0.0420516 | + | 0.0728355i | ||||
\(669\) | 3.99293 | + | 6.91595i | 0.154375 | + | 0.267386i | ||||
\(670\) | 1.19130 | − | 2.06340i | 0.0460241 | − | 0.0797161i | ||||
\(671\) | 2.39602 | + | 4.15002i | 0.0924972 | + | 0.160210i | ||||
\(672\) | 1.11507 | 0.0430149 | ||||||||
\(673\) | −10.3574 | −0.399248 | −0.199624 | − | 0.979873i | \(-0.563972\pi\) | ||||
−0.199624 | + | 0.979873i | \(0.563972\pi\) | |||||||
\(674\) | −11.3637 | − | 19.6826i | −0.437715 | − | 0.758144i | ||||
\(675\) | 5.39986 | + | 9.35284i | 0.207841 | + | 0.359991i | ||||
\(676\) | 28.7271 | 1.10489 | ||||||||
\(677\) | 10.7171 | 0.411891 | 0.205945 | − | 0.978564i | \(-0.433973\pi\) | ||||
0.205945 | + | 0.978564i | \(0.433973\pi\) | |||||||
\(678\) | 2.81459 | + | 4.87502i | 0.108094 | + | 0.187224i | ||||
\(679\) | −9.85921 | + | 17.0767i | −0.378362 | + | 0.655342i | ||||
\(680\) | 1.52546 | + | 2.64217i | 0.0584986 | + | 0.101323i | ||||
\(681\) | 2.71772 | − | 4.70722i | 0.104143 | − | 0.180381i | ||||
\(682\) | −8.58251 | + | 14.8653i | −0.328641 | + | 0.569223i | ||||
\(683\) | −0.122930 | −0.00470377 | −0.00235188 | − | 0.999997i | \(-0.500749\pi\) | ||||
−0.00235188 | + | 0.999997i | \(0.500749\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.80957 | 0.374804 | ||||||||
\(686\) | −9.63812 | + | 16.6937i | −0.367985 | + | 0.637369i | ||||
\(687\) | 1.50255 | − | 2.60249i | 0.0573258 | − | 0.0992912i | ||||
\(688\) | 3.12334 | + | 5.40979i | 0.119076 | + | 0.206246i | ||||
\(689\) | 12.1531 | − | 21.0498i | 0.462997 | − | 0.801934i | ||||
\(690\) | 1.61430 | + | 2.79606i | 0.0614555 | + | 0.106444i | ||||
\(691\) | −25.2815 | −0.961752 | −0.480876 | − | 0.876789i | \(-0.659681\pi\) | ||||
−0.480876 | + | 0.876789i | \(0.659681\pi\) | |||||||
\(692\) | −16.8493 | −0.640514 | ||||||||
\(693\) | 6.89741 | + | 11.9467i | 0.262011 | + | 0.453816i | ||||
\(694\) | −2.46428 | − | 4.26825i | −0.0935427 | − | 0.162021i | ||||
\(695\) | −19.3976 | −0.735793 | ||||||||
\(696\) | 2.02677 | 0.0768244 | ||||||||
\(697\) | −5.97068 | − | 10.3415i | −0.226156 | − | 0.391713i | ||||
\(698\) | 13.0808 | − | 22.6565i | 0.495114 | − | 0.857562i | ||||
\(699\) | 4.74085 | + | 8.21140i | 0.179316 | + | 0.310584i | ||||
\(700\) | 5.29892 | − | 9.17799i | 0.200280 | − | 0.346895i | ||||
\(701\) | 2.58643 | − | 4.47984i | 0.0976883 | − | 0.169201i | −0.813039 | − | 0.582209i | \(-0.802189\pi\) |
0.910727 | + | 0.413008i | \(0.135522\pi\) | |||||||
\(702\) | 16.5894 | 0.626127 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.95199 | 0.0735684 | ||||||||
\(705\) | 2.08070 | − | 3.60388i | 0.0783637 | − | 0.135730i | ||||
\(706\) | 1.35407 | − | 2.34531i | 0.0509610 | − | 0.0882670i | ||||
\(707\) | 6.78533 | + | 11.7525i | 0.255189 | + | 0.442000i | ||||
\(708\) | 0.628656 | − | 1.08886i | 0.0236263 | − | 0.0409220i | ||||
\(709\) | 14.9954 | + | 25.9727i | 0.563162 | + | 0.975426i | 0.997218 | + | 0.0745396i | \(0.0237487\pi\) |
−0.434056 | + | 0.900886i | \(0.642918\pi\) | |||||||
\(710\) | 0.0503161 | 0.00188833 | ||||||||
\(711\) | 25.6071 | 0.960342 | ||||||||
\(712\) | 0.933870 | + | 1.61751i | 0.0349983 | + | 0.0606188i | ||||
\(713\) | 35.9880 | + | 62.3330i | 1.34776 | + | 2.33439i | ||||
\(714\) | −3.81607 | −0.142813 | ||||||||
\(715\) | 11.2410 | 0.420388 | ||||||||
\(716\) | −9.48276 | − | 16.4246i | −0.354387 | − | 0.613817i | ||||
\(717\) | −2.61886 | + | 4.53600i | −0.0978031 | + | 0.169400i | ||||
\(718\) | −4.65501 | − | 8.06272i | −0.173723 | − | 0.300898i | ||||
\(719\) | 11.3516 | − | 19.6616i | 0.423344 | − | 0.733254i | −0.572920 | − | 0.819611i | \(-0.694189\pi\) |
0.996264 | + | 0.0863576i | \(0.0275228\pi\) | |||||||
\(720\) | −1.24997 | + | 2.16501i | −0.0465837 | + | 0.0806853i | ||||
\(721\) | −11.8313 | −0.440620 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.62195 | 0.357844 | ||||||||
\(724\) | 0.993436 | − | 1.72068i | 0.0369207 | − | 0.0639486i | ||||
\(725\) | 9.63136 | − | 16.6820i | 0.357700 | − | 0.619554i | ||||
\(726\) | 1.59060 | + | 2.75500i | 0.0590326 | + | 0.102248i | ||||
\(727\) | −18.2969 | + | 31.6911i | −0.678593 | + | 1.17536i | 0.296811 | + | 0.954936i | \(0.404077\pi\) |
−0.975405 | + | 0.220422i | \(0.929257\pi\) | |||||||
\(728\) | −8.13963 | − | 14.0983i | −0.301675 | − | 0.522516i | ||||
\(729\) | −16.9956 | −0.629467 | ||||||||
\(730\) | −6.21296 | −0.229952 | ||||||||
\(731\) | −10.6889 | − | 18.5137i | −0.395343 | − | 0.684754i | ||||
\(732\) | −0.543113 | − | 0.940699i | −0.0200740 | − | 0.0347692i | ||||
\(733\) | 21.1522 | 0.781275 | 0.390637 | − | 0.920545i | \(-0.372255\pi\) | ||||
0.390637 | + | 0.920545i | \(0.372255\pi\) | |||||||
\(734\) | −7.75442 | −0.286221 | ||||||||
\(735\) | 0.127972 | + | 0.221654i | 0.00472032 | + | 0.00817583i | ||||
\(736\) | 4.09252 | − | 7.08845i | 0.150852 | − | 0.261284i | ||||
\(737\) | 2.60845 | + | 4.51797i | 0.0960836 | + | 0.166422i | ||||
\(738\) | 4.89242 | − | 8.47393i | 0.180093 | − | 0.311930i | ||||
\(739\) | −24.1533 | + | 41.8348i | −0.888494 | + | 1.53892i | −0.0468384 | + | 0.998902i | \(0.514915\pi\) |
−0.841656 | + | 0.540014i | \(0.818419\pi\) | |||||||
\(740\) | 5.33094 | 0.195969 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.48276 | −0.348123 | ||||||||
\(743\) | 15.9299 | − | 27.5914i | 0.584412 | − | 1.01223i | −0.410536 | − | 0.911844i | \(-0.634659\pi\) |
0.994948 | − | 0.100387i | \(-0.0320082\pi\) | |||||||
\(744\) | 1.94542 | − | 3.36957i | 0.0713227 | − | 0.123535i | ||||
\(745\) | 6.41409 | + | 11.1095i | 0.234994 | + | 0.407022i | ||||
\(746\) | −12.5062 | + | 21.6614i | −0.457884 | + | 0.793078i | ||||
\(747\) | −19.8033 | − | 34.3003i | −0.724565 | − | 1.25498i | ||||
\(748\) | −6.68021 | −0.244253 | ||||||||
\(749\) | 40.4163 | 1.47678 | ||||||||
\(750\) | −1.81552 | − | 3.14456i | −0.0662932 | − | 0.114823i | ||||
\(751\) | −20.4981 | − | 35.5038i | −0.747987 | − | 1.29555i | −0.948786 | − | 0.315919i | \(-0.897687\pi\) |
0.200799 | − | 0.979632i | \(-0.435646\pi\) | |||||||
\(752\) | −10.5498 | −0.384712 | ||||||||
\(753\) | −10.4603 | −0.381194 | ||||||||
\(754\) | −14.7947 | − | 25.6251i | −0.538790 | − | 0.933212i | ||||
\(755\) | 5.53026 | − | 9.57869i | 0.201267 | − | 0.348604i | ||||
\(756\) | −3.23607 | − | 5.60503i | −0.117695 | − | 0.203853i | ||||
\(757\) | 6.41076 | − | 11.1038i | 0.233003 | − | 0.403573i | −0.725687 | − | 0.688025i | \(-0.758478\pi\) |
0.958690 | + | 0.284451i | \(0.0918114\pi\) | |||||||
\(758\) | 9.59011 | − | 16.6106i | 0.348329 | − | 0.603323i | ||||
\(759\) | −7.06929 | −0.256599 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.6382 | 1.29188 | 0.645942 | − | 0.763386i | \(-0.276465\pi\) | ||||
0.645942 | + | 0.763386i | \(0.276465\pi\) | |||||||
\(762\) | −1.58721 | + | 2.74913i | −0.0574985 | + | 0.0995903i | ||||
\(763\) | −17.7680 | + | 30.7751i | −0.643246 | + | 1.11413i | ||||
\(764\) | 10.4630 | + | 18.1224i | 0.378537 | + | 0.655645i | ||||
\(765\) | 4.27773 | − | 7.40924i | 0.154662 | − | 0.267882i | ||||
\(766\) | −2.41659 | − | 4.18566i | −0.0873151 | − | 0.151234i | ||||
\(767\) | −18.3558 | −0.662791 | ||||||||
\(768\) | −0.442463 | −0.0159660 | ||||||||
\(769\) | 2.78701 | + | 4.82723i | 0.100502 | + | 0.174075i | 0.911892 | − | 0.410431i | \(-0.134622\pi\) |
−0.811390 | + | 0.584506i | \(0.801288\pi\) | |||||||
\(770\) | −2.19276 | − | 3.79797i | −0.0790215 | − | 0.136869i | ||||
\(771\) | 0.408601 | 0.0147154 | ||||||||
\(772\) | 7.78879 | 0.280325 | ||||||||
\(773\) | −18.2060 | − | 31.5337i | −0.654823 | − | 1.13419i | −0.981938 | − | 0.189202i | \(-0.939410\pi\) |
0.327115 | − | 0.944984i | \(-0.393923\pi\) | |||||||
\(774\) | 8.75856 | − | 15.1703i | 0.314820 | − | 0.545284i | ||||
\(775\) | −18.4896 | − | 32.0250i | −0.664167 | − | 1.15037i | ||||
\(776\) | 3.91216 | − | 6.77606i | 0.140438 | − | 0.243246i | ||||
\(777\) | −3.33395 | + | 5.77458i | −0.119605 | + | 0.207162i | ||||
\(778\) | −21.7291 | −0.779027 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −2.54802 | −0.0912339 | ||||||||
\(781\) | −0.0550855 | + | 0.0954109i | −0.00197111 | + | 0.00341407i | ||||
\(782\) | −14.0057 | + | 24.2585i | −0.500842 | + | 0.867483i | ||||
\(783\) | −5.88191 | − | 10.1878i | −0.210202 | − | 0.364081i | ||||
\(784\) | 0.324429 | − | 0.561928i | 0.0115868 | − | 0.0200689i | ||||
\(785\) | −0.201129 | − | 0.348366i | −0.00717862 | − | 0.0124337i | ||||
\(786\) | −1.55865 | −0.0555951 | ||||||||
\(787\) | 31.9046 | 1.13728 | 0.568638 | − | 0.822588i | \(-0.307471\pi\) | ||||
0.568638 | + | 0.822588i | \(0.307471\pi\) | |||||||
\(788\) | −0.912571 | − | 1.58062i | −0.0325090 | − | 0.0563072i | ||||
\(789\) | 0.955649 | + | 1.65523i | 0.0340220 | + | 0.0589278i | ||||
\(790\) | −8.14076 | −0.289635 | ||||||||
\(791\) | −32.0622 | −1.14000 | ||||||||
\(792\) | −2.73691 | − | 4.74047i | −0.0972518 | − | 0.168445i | ||||
\(793\) | −7.92906 | + | 13.7335i | −0.281569 | + | 0.487692i | ||||
\(794\) | 5.85701 | + | 10.1446i | 0.207857 | + | 0.360020i | ||||
\(795\) | −0.742119 | + | 1.28539i | −0.0263202 | + | 0.0455880i | ||||
\(796\) | −1.17963 | + | 2.04317i | −0.0418108 | + | 0.0724184i | ||||
\(797\) | −2.09165 | −0.0740900 | −0.0370450 | − | 0.999314i | \(-0.511794\pi\) | ||||
−0.0370450 | + | 0.999314i | \(0.511794\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.1042 | 1.27728 | ||||||||
\(800\) | −2.10262 | + | 3.64185i | −0.0743389 | + | 0.128759i | ||||
\(801\) | 2.61878 | − | 4.53587i | 0.0925302 | − | 0.160267i | ||||
\(802\) | −5.90617 | − | 10.2298i | −0.208554 | − | 0.361226i | ||||
\(803\) | 6.80188 | − | 11.7812i | 0.240033 | − | 0.415749i | ||||
\(804\) | −0.591266 | − | 1.02410i | −0.0208523 | − | 0.0361173i | ||||
\(805\) | −18.3892 | −0.648136 | ||||||||
\(806\) | −56.8036 | −2.00082 | ||||||||
\(807\) | −2.38828 | − | 4.13661i | −0.0840713 | − | 0.145616i | ||||
\(808\) | −2.69244 | − | 4.66343i | −0.0947195 | − | 0.164059i | ||||
\(809\) | −30.0719 | −1.05727 | −0.528636 | − | 0.848849i | \(-0.677296\pi\) | ||||
−0.528636 | + | 0.848849i | \(0.677296\pi\) | |||||||
\(810\) | 6.48681 | 0.227923 | ||||||||
\(811\) | −0.411796 | − | 0.713252i | −0.0144601 | − | 0.0250457i | 0.858705 | − | 0.512471i | \(-0.171270\pi\) |
−0.873165 | + | 0.487425i | \(0.837936\pi\) | |||||||
\(812\) | −5.77195 | + | 9.99731i | −0.202556 | + | 0.350837i | ||||
\(813\) | 0.178588 | + | 0.309323i | 0.00626335 | + | 0.0108484i | ||||
\(814\) | −5.83625 | + | 10.1087i | −0.204560 | + | 0.354309i | ||||
\(815\) | −0.0308698 | + | 0.0534680i | −0.00108132 | + | 0.00187290i | ||||
\(816\) | 1.51423 | 0.0530085 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −25.2663 | −0.883414 | ||||||||
\(819\) | −22.8254 | + | 39.5347i | −0.797583 | + | 1.38145i | ||||
\(820\) | −1.55535 | + | 2.69395i | −0.0543152 | + | 0.0940767i | ||||
\(821\) | −3.85562 | − | 6.67813i | −0.134562 | − | 0.233068i | 0.790868 | − | 0.611987i | \(-0.209629\pi\) |
−0.925430 | + | 0.378918i | \(0.876296\pi\) | |||||||
\(822\) | 2.43433 | − | 4.21639i | 0.0849071 | − | 0.147063i | ||||
\(823\) | 12.4060 | + | 21.4879i | 0.432447 | + | 0.749019i | 0.997083 | − | 0.0763201i | \(-0.0243171\pi\) |
−0.564637 | + | 0.825339i | \(0.690984\pi\) | |||||||
\(824\) | 4.69468 | 0.163547 | ||||||||
\(825\) | 3.63200 | 0.126450 | ||||||||
\(826\) | 3.58064 | + | 6.20186i | 0.124587 | + | 0.215790i | ||||
\(827\) | −5.31424 | − | 9.20453i | −0.184794 | − | 0.320073i | 0.758713 | − | 0.651425i | \(-0.225828\pi\) |
−0.943507 | + | 0.331352i | \(0.892495\pi\) | |||||||
\(828\) | −22.9527 | −0.797662 | ||||||||
\(829\) | 21.4710 | 0.745718 | 0.372859 | − | 0.927888i | \(-0.378377\pi\) | ||||
0.372859 | + | 0.927888i | \(0.378377\pi\) | |||||||
\(830\) | 6.29567 | + | 10.9044i | 0.218526 | + | 0.378498i | ||||
\(831\) | −2.02398 | + | 3.50564i | −0.0702111 | + | 0.121609i | ||||
\(832\) | 3.22982 | + | 5.59422i | 0.111974 | + | 0.193945i | ||||
\(833\) | −1.11028 | + | 1.92307i | −0.0384690 | + | 0.0666303i | ||||
\(834\) | −4.81370 | + | 8.33756i | −0.166685 | + | 0.288706i | ||||
\(835\) | −1.93784 | −0.0670617 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.5834 | −0.780595 | ||||||||
\(838\) | 15.8071 | − | 27.3788i | 0.546048 | − | 0.945783i | ||||
\(839\) | 24.4119 | − | 42.2827i | 0.842794 | − | 1.45976i | −0.0447298 | − | 0.998999i | \(-0.514243\pi\) |
0.887524 | − | 0.460762i | \(-0.152424\pi\) | |||||||
\(840\) | 0.497039 | + | 0.860897i | 0.0171495 | + | 0.0297038i | ||||
\(841\) | 4.00885 | − | 6.94353i | 0.138236 | − | 0.239432i | ||||
\(842\) | −1.09486 | − | 1.89635i | −0.0377314 | − | 0.0653526i | ||||
\(843\) | −9.38720 | −0.323312 | ||||||||
\(844\) | −0.361050 | −0.0124279 | ||||||||
\(845\) | 12.8050 | + | 22.1789i | 0.440504 | + | 0.762976i | ||||
\(846\) | 14.7920 | + | 25.6206i | 0.508561 | + | 0.880853i | ||||
\(847\) | −18.1192 | −0.622583 | ||||||||
\(848\) | 3.76278 | 0.129214 | ||||||||
\(849\) | 1.14816 | + | 1.98867i | 0.0394047 | + | 0.0682510i | ||||
\(850\) | 7.19572 | − | 12.4633i | 0.246811 | − | 0.427489i | ||||
\(851\) | 24.4724 | + | 42.3875i | 0.838904 | + | 1.45302i | ||||
\(852\) | 0.0124864 | − | 0.0216271i | 0.000427777 | − | 0.000740932i | ||||
\(853\) | 10.5055 | − | 18.1961i | 0.359702 | − | 0.623022i | −0.628209 | − | 0.778045i | \(-0.716212\pi\) |
0.987911 | + | 0.155022i | \(0.0495450\pi\) | |||||||
\(854\) | 6.18683 | 0.211709 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.0373 | −0.548143 | ||||||||
\(857\) | −16.1196 | + | 27.9200i | −0.550635 | + | 0.953727i | 0.447594 | + | 0.894237i | \(0.352281\pi\) |
−0.998229 | + | 0.0594906i | \(0.981052\pi\) | |||||||
\(858\) | 2.78955 | − | 4.83164i | 0.0952336 | − | 0.164949i | ||||
\(859\) | 20.6137 | + | 35.7040i | 0.703331 | + | 1.21820i | 0.967291 | + | 0.253671i | \(0.0816380\pi\) |
−0.263960 | + | 0.964534i | \(0.585029\pi\) | |||||||
\(860\) | −2.78444 | + | 4.82278i | −0.0949485 | + | 0.164456i | ||||
\(861\) | −1.94542 | − | 3.36957i | −0.0662999 | − | 0.114835i | ||||
\(862\) | 1.80372 | 0.0614348 | ||||||||
\(863\) | −42.0649 | −1.43191 | −0.715953 | − | 0.698148i | \(-0.754008\pi\) | ||||
−0.715953 | + | 0.698148i | \(0.754008\pi\) | |||||||
\(864\) | 1.28408 | + | 2.22409i | 0.0436853 | + | 0.0756651i | ||||
\(865\) | −7.51050 | − | 13.0086i | −0.255365 | − | 0.442304i | ||||
\(866\) | 6.57233 | 0.223337 | ||||||||
\(867\) | 2.33981 | 0.0794640 | ||||||||
\(868\) | 11.0806 | + | 19.1921i | 0.376100 | + | 0.651424i | ||||
\(869\) | 8.91241 | − | 15.4367i | 0.302333 | − | 0.523656i | ||||
\(870\) | 0.903423 | + | 1.56477i | 0.0306289 | + | 0.0530508i | ||||
\(871\) | −8.63206 | + | 14.9512i | −0.292486 | + | 0.506601i | ||||
\(872\) | 7.05040 | − | 12.2116i | 0.238757 | − | 0.413538i | ||||
\(873\) | −21.9412 | −0.742596 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.6813 | 0.699156 | ||||||||
\(876\) | −1.54180 | + | 2.67048i | −0.0520927 | + | 0.0902272i | ||||
\(877\) | 1.17776 | − | 2.03993i | 0.0397700 | − | 0.0688837i | −0.845455 | − | 0.534046i | \(-0.820671\pi\) |
0.885225 | + | 0.465163i | \(0.154004\pi\) | |||||||
\(878\) | −4.56530 | − | 7.90733i | −0.154071 | − | 0.266859i | ||||
\(879\) | −3.88615 | + | 6.73101i | −0.131077 | + | 0.227031i | ||||
\(880\) | 0.870091 | + | 1.50704i | 0.0293308 | + | 0.0508024i | ||||
\(881\) | 23.1354 | 0.779450 | 0.389725 | − | 0.920931i | \(-0.372570\pi\) | ||||
0.389725 | + | 0.920931i | \(0.372570\pi\) | |||||||
\(882\) | −1.81955 | −0.0612673 | ||||||||
\(883\) | −3.50595 | − | 6.07249i | −0.117985 | − | 0.204356i | 0.800984 | − | 0.598685i | \(-0.204310\pi\) |
−0.918969 | + | 0.394330i | \(0.870977\pi\) | |||||||
\(884\) | −11.0533 | − | 19.1449i | −0.371763 | − | 0.643912i | ||||
\(885\) | 1.12088 | 0.0376780 | ||||||||
\(886\) | 27.4686 | 0.922826 | ||||||||
\(887\) | 24.4646 | + | 42.3740i | 0.821443 | + | 1.42278i | 0.904608 | + | 0.426244i | \(0.140164\pi\) |
−0.0831655 | + | 0.996536i | \(0.526503\pi\) | |||||||
\(888\) | 1.32292 | − | 2.29137i | 0.0443943 | − | 0.0768932i | ||||
\(889\) | −9.04029 | − | 15.6582i | −0.303202 | − | 0.525161i | ||||
\(890\) | −0.832538 | + | 1.44200i | −0.0279067 | + | 0.0483359i | ||||
\(891\) | −7.10169 | + | 12.3005i | −0.237916 | + | 0.412082i | ||||
\(892\) | 18.0486 | 0.604312 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 6.36686 | 0.212940 | ||||||||
\(895\) | 8.45380 | − | 14.6424i | 0.282579 | − | 0.489442i | ||||
\(896\) | 1.26007 | − | 2.18251i | 0.0420961 | − | 0.0729126i | ||||
\(897\) | −11.6971 | − | 20.2599i | −0.390554 | − | 0.676459i | ||||
\(898\) | −3.78646 | + | 6.55835i | −0.126356 | + | 0.218855i | ||||
\(899\) | 20.1402 | + | 34.8838i | 0.671713 | + | 1.16344i | ||||
\(900\) | 11.7925 | 0.393082 | ||||||||
\(901\) | −12.8772 | −0.429002 | ||||||||
\(902\) | −3.40556 | − | 5.89860i | −0.113393 | − | 0.196402i | ||||
\(903\) | −3.48276 | − | 6.03231i | −0.115899 | − | 0.200743i | ||||
\(904\) | 12.7224 | 0.423140 | ||||||||
\(905\) | 1.77128 | 0.0588793 | ||||||||
\(906\) | −2.74477 | − | 4.75408i | −0.0911888 | − | 0.157944i | ||||
\(907\) | −0.596520 | + | 1.03320i | −0.0198071 | + | 0.0343070i | −0.875759 | − | 0.482748i | \(-0.839639\pi\) |
0.855952 | + | 0.517055i | \(0.172972\pi\) | |||||||
\(908\) | −6.14224 | − | 10.6387i | −0.203837 | − | 0.353057i | ||||
\(909\) | −7.55020 | + | 13.0773i | −0.250424 | + | 0.433747i | ||||
\(910\) | 7.25641 | − | 12.5685i | 0.240548 | − | 0.416641i | ||||
\(911\) | −37.6344 | −1.24688 | −0.623442 | − | 0.781870i | \(-0.714266\pi\) | ||||
−0.623442 | + | 0.781870i | \(0.714266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.5697 | −0.912424 | ||||||||
\(914\) | −10.8837 | + | 18.8512i | −0.360002 | + | 0.623542i | ||||
\(915\) | 0.484180 | − | 0.838625i | 0.0160065 | − | 0.0277241i | ||||
\(916\) | −3.39587 | − | 5.88182i | −0.112203 | − | 0.194341i | ||||
\(917\) | 4.43880 | − | 7.68823i | 0.146582 | − | 0.253888i | ||||
\(918\) | −4.39445 | − | 7.61141i | −0.145039 | − | 0.251214i | ||||
\(919\) | 26.9476 | 0.888921 | 0.444460 | − | 0.895799i | \(-0.353395\pi\) | ||||
0.444460 | + | 0.895799i | \(0.353395\pi\) | |||||||
\(920\) | 7.29689 | 0.240571 | ||||||||
\(921\) | −4.77161 | − | 8.26466i | −0.157230 | − | 0.272330i | ||||
\(922\) | 5.97219 | + | 10.3441i | 0.196684 | + | 0.340666i | ||||
\(923\) | −0.364585 | −0.0120005 | ||||||||
\(924\) | −2.17661 | −0.0716052 | ||||||||
\(925\) | −12.5732 | − | 21.7775i | −0.413406 | − | 0.716040i | ||||
\(926\) | −4.37685 | + | 7.58093i | −0.143832 | + | 0.249125i | ||||
\(927\) | −6.58247 | − | 11.4012i | −0.216197 | − | 0.374464i | ||||
\(928\) | 2.29032 | − | 3.96695i | 0.0751835 | − | 0.130222i | ||||
\(929\) | 8.92750 | − | 15.4629i | 0.292902 | − | 0.507321i | −0.681593 | − | 0.731732i | \(-0.738712\pi\) |
0.974495 | + | 0.224411i | \(0.0720457\pi\) | |||||||
\(930\) | 3.46866 | 0.113742 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 21.4294 | 0.701942 | ||||||||
\(933\) | −0.569380 | + | 0.986196i | −0.0186407 | + | 0.0322866i | ||||
\(934\) | 14.6784 | − | 25.4238i | 0.480293 | − | 0.831891i | ||||
\(935\) | −2.97768 | − | 5.15749i | −0.0973804 | − | 0.168668i | ||||
\(936\) | 9.05716 | − | 15.6875i | 0.296042 | − | 0.512761i | ||||
\(937\) | 11.9163 | + | 20.6396i | 0.389288 | + | 0.674267i | 0.992354 | − | 0.123425i | \(-0.0393878\pi\) |
−0.603066 | + | 0.797691i | \(0.706054\pi\) | |||||||
\(938\) | 6.73537 | 0.219918 | ||||||||
\(939\) | 2.29368 | 0.0748514 | ||||||||
\(940\) | −4.70254 | − | 8.14503i | −0.153380 | − | 0.265662i | ||||
\(941\) | 10.1825 | + | 17.6367i | 0.331941 | + | 0.574939i | 0.982892 | − | 0.184181i | \(-0.0589632\pi\) |
−0.650951 | + | 0.759119i | \(0.725630\pi\) | |||||||
\(942\) | −0.199648 | −0.00650490 | ||||||||
\(943\) | −28.5602 | −0.930049 | ||||||||
\(944\) | −1.42081 | − | 2.46091i | −0.0462434 | − | 0.0800958i | ||||
\(945\) | 2.88493 | − | 4.99684i | 0.0938467 | − | 0.162547i | ||||
\(946\) | −6.09673 | − | 10.5599i | −0.198222 | − | 0.343330i | ||||
\(947\) | 1.70795 | − | 2.95825i | 0.0555009 | − | 0.0961304i | −0.836940 | − | 0.547294i | \(-0.815658\pi\) |
0.892441 | + | 0.451164i | \(0.148991\pi\) | |||||||
\(948\) | −2.02020 | + | 3.49909i | −0.0656132 | + | 0.113645i | ||||
\(949\) | 45.0184 | 1.46136 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.96261 | 0.290633 | ||||||||
\(952\) | −4.31230 | + | 7.46912i | −0.139762 | + | 0.242076i | ||||
\(953\) | −8.86967 | + | 15.3627i | −0.287317 | + | 0.497647i | −0.973168 | − | 0.230094i | \(-0.926097\pi\) |
0.685852 | + | 0.727741i | \(0.259430\pi\) | |||||||
\(954\) | −5.27584 | − | 9.13803i | −0.170812 | − | 0.295855i | ||||
\(955\) | −9.32765 | + | 16.1560i | −0.301836 | + | 0.522794i | ||||
\(956\) | 5.91881 | + | 10.2517i | 0.191428 | + | 0.331563i | ||||
\(957\) | −3.95623 | −0.127887 | ||||||||
\(958\) | 24.8705 | 0.803528 | ||||||||
\(959\) | 13.8653 | + | 24.0154i | 0.447733 | + | 0.775497i | ||||
\(960\) | −0.197226 | − | 0.341606i | −0.00636545 | − | 0.0110253i | ||||
\(961\) | 46.3275 | 1.49443 | ||||||||
\(962\) | −38.6274 | −1.24540 | ||||||||
\(963\) | 22.4861 | + | 38.9470i | 0.724604 | + | 1.25505i | ||||
\(964\) | 10.8732 | − | 18.8329i | 0.350201 | − | 0.606565i | ||||
\(965\) | 3.47182 | + | 6.01337i | 0.111762 | + | 0.193577i | ||||
\(966\) | −4.56346 | + | 7.90414i | −0.146827 | + | 0.254312i | ||||
\(967\) | 21.3776 | − | 37.0270i | 0.687456 | − | 1.19071i | −0.285202 | − | 0.958467i | \(-0.592061\pi\) |
0.972658 | − | 0.232242i | \(-0.0746060\pi\) | |||||||
\(968\) | 7.18974 | 0.231087 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.97531 | 0.223964 | ||||||||
\(971\) | 26.5243 | − | 45.9415i | 0.851207 | − | 1.47433i | −0.0289131 | − | 0.999582i | \(-0.509205\pi\) |
0.880120 | − | 0.474751i | \(-0.157462\pi\) | |||||||
\(972\) | 5.46200 | − | 9.46046i | 0.175194 | − | 0.303444i | ||||
\(973\) | −27.4174 | − | 47.4884i | −0.878963 | − | 1.52241i | ||||
\(974\) | −4.26883 | + | 7.39383i | −0.136782 | + | 0.236914i | ||||
\(975\) | 6.00963 | + | 10.4090i | 0.192462 | + | 0.333354i | ||||
\(976\) | −2.45495 | −0.0785810 | ||||||||
\(977\) | 12.3264 | 0.394356 | 0.197178 | − | 0.980368i | \(-0.436822\pi\) | ||||
0.197178 | + | 0.980368i | \(0.436822\pi\) | |||||||
\(978\) | 0.0153212 | + | 0.0265371i | 0.000489919 | + | 0.000848564i | ||||
\(979\) | −1.82290 | − | 3.15736i | −0.0582603 | − | 0.100910i | ||||
\(980\) | 0.578452 | 0.0184780 | ||||||||
\(981\) | −39.5418 | −1.26247 | ||||||||
\(982\) | −5.76985 | − | 9.99368i | −0.184123 | − | 0.318911i | ||||
\(983\) | −16.1277 | + | 27.9340i | −0.514394 | + | 0.890956i | 0.485467 | + | 0.874255i | \(0.338650\pi\) |
−0.999861 | + | 0.0167010i | \(0.994684\pi\) | |||||||
\(984\) | 0.771949 | + | 1.33705i | 0.0246088 | + | 0.0426237i | ||||
\(985\) | 0.813549 | − | 1.40911i | 0.0259218 | − | 0.0448979i | ||||
\(986\) | −7.83808 | + | 13.5759i | −0.249615 | + | 0.432346i | ||||
\(987\) | 11.7638 | 0.374446 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51.1294 | −1.62582 | ||||||||
\(990\) | 2.43993 | − | 4.22608i | 0.0775461 | − | 0.134314i | ||||
\(991\) | 13.9183 | − | 24.1072i | 0.442129 | − | 0.765790i | −0.555718 | − | 0.831371i | \(-0.687557\pi\) |
0.997847 | + | 0.0655808i | \(0.0208900\pi\) | |||||||
\(992\) | −4.39680 | − | 7.61548i | −0.139599 | − | 0.241792i | ||||
\(993\) | −4.71843 | + | 8.17256i | −0.149735 | + | 0.259348i | ||||
\(994\) | 0.0711190 | + | 0.123182i | 0.00225576 | + | 0.00390709i | ||||
\(995\) | −2.10326 | −0.0666777 | ||||||||
\(996\) | 6.24931 | 0.198017 | ||||||||
\(997\) | 21.6657 | + | 37.5260i | 0.686159 | + | 1.18846i | 0.973071 | + | 0.230505i | \(0.0740377\pi\) |
−0.286913 | + | 0.957957i | \(0.592629\pi\) | |||||||
\(998\) | −14.8045 | − | 25.6422i | −0.468629 | − | 0.811689i | ||||
\(999\) | −15.3571 | −0.485876 |
(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 | 722.2.c.n.429.2 | 8 | ||
19.2 | odd | 18 | 722.2.e.r.595.3 | 24 | |||
19.3 | odd | 18 | 722.2.e.r.99.2 | 24 | |||
19.4 | even | 9 | 722.2.e.s.423.3 | 24 | |||
19.5 | even | 9 | 722.2.e.s.389.3 | 24 | |||
19.6 | even | 9 | 722.2.e.s.415.2 | 24 | |||
19.7 | even | 3 | inner | 722.2.c.n.653.2 | 8 | ||
19.8 | odd | 6 | 722.2.a.n.1.2 | yes | 4 | ||
19.9 | even | 9 | 722.2.e.s.245.3 | 24 | |||
19.10 | odd | 18 | 722.2.e.r.245.2 | 24 | |||
19.11 | even | 3 | 722.2.a.m.1.3 | ✓ | 4 | ||
19.12 | odd | 6 | 722.2.c.m.653.3 | 8 | |||
19.13 | odd | 18 | 722.2.e.r.415.3 | 24 | |||
19.14 | odd | 18 | 722.2.e.r.389.2 | 24 | |||
19.15 | odd | 18 | 722.2.e.r.423.2 | 24 | |||
19.16 | even | 9 | 722.2.e.s.99.3 | 24 | |||
19.17 | even | 9 | 722.2.e.s.595.2 | 24 | |||
19.18 | odd | 2 | 722.2.c.m.429.3 | 8 | |||
57.8 | even | 6 | 6498.2.a.bx.1.2 | 4 | |||
57.11 | odd | 6 | 6498.2.a.ca.1.2 | 4 | |||
76.11 | odd | 6 | 5776.2.a.bv.1.2 | 4 | |||
76.27 | even | 6 | 5776.2.a.bt.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
722.2.a.m.1.3 | ✓ | 4 | 19.11 | even | 3 | ||
722.2.a.n.1.2 | yes | 4 | 19.8 | odd | 6 | ||
722.2.c.m.429.3 | 8 | 19.18 | odd | 2 | |||
722.2.c.m.653.3 | 8 | 19.12 | odd | 6 | |||
722.2.c.n.429.2 | 8 | 1.1 | even | 1 | trivial | ||
722.2.c.n.653.2 | 8 | 19.7 | even | 3 | inner | ||
722.2.e.r.99.2 | 24 | 19.3 | odd | 18 | |||
722.2.e.r.245.2 | 24 | 19.10 | odd | 18 | |||
722.2.e.r.389.2 | 24 | 19.14 | odd | 18 | |||
722.2.e.r.415.3 | 24 | 19.13 | odd | 18 | |||
722.2.e.r.423.2 | 24 | 19.15 | odd | 18 | |||
722.2.e.r.595.3 | 24 | 19.2 | odd | 18 | |||
722.2.e.s.99.3 | 24 | 19.16 | even | 9 | |||
722.2.e.s.245.3 | 24 | 19.9 | even | 9 | |||
722.2.e.s.389.3 | 24 | 19.5 | even | 9 | |||
722.2.e.s.415.2 | 24 | 19.6 | even | 9 | |||
722.2.e.s.423.3 | 24 | 19.4 | even | 9 | |||
722.2.e.s.595.2 | 24 | 19.17 | even | 9 | |||
5776.2.a.bt.1.3 | 4 | 76.27 | even | 6 | |||
5776.2.a.bv.1.2 | 4 | 76.11 | odd | 6 | |||
6498.2.a.bx.1.2 | 4 | 57.8 | even | 6 | |||
6498.2.a.ca.1.2 | 4 | 57.11 | odd | 6 |