Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(159,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.159");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.m (of order \(6\), degree \(2\), 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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 37x^{14} + 559x^{12} + 4431x^{10} + 19684x^{8} + 48248x^{6} + 58656x^{4} + 25392x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.8 | ||
Root | \(2.85998i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.249 |
Dual form | 370.2.m.d.159.8 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 2.47681 | − | 1.42999i | 1.42999 | − | 0.825604i | 0.432869 | − | 0.901457i | \(-0.357501\pi\) |
0.997119 | + | 0.0758530i | \(0.0241680\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.654464 | − | 2.13815i | −0.292685 | − | 0.956209i | ||||
\(6\) | − | 2.85998i | − | 1.16758i | ||||||
\(7\) | −4.15112 | + | 2.39665i | −1.56897 | + | 0.905848i | −0.572686 | + | 0.819775i | \(0.694099\pi\) |
−0.996289 | + | 0.0860730i | \(0.972568\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.58973 | − | 4.48555i | 0.863244 | − | 1.49518i | ||||
\(10\) | −2.17892 | − | 0.502291i | −0.689036 | − | 0.158838i | ||||
\(11\) | 2.72666 | 0.822120 | 0.411060 | − | 0.911608i | \(-0.365159\pi\) | ||||
0.411060 | + | 0.911608i | \(0.365159\pi\) | |||||||
\(12\) | −2.47681 | − | 1.42999i | −0.714994 | − | 0.412802i | ||||
\(13\) | −0.608891 | − | 1.05463i | −0.168876 | − | 0.292502i | 0.769149 | − | 0.639070i | \(-0.220680\pi\) |
−0.938025 | + | 0.346568i | \(0.887347\pi\) | |||||||
\(14\) | 4.79330i | 1.28106i | ||||||||
\(15\) | −4.67851 | − | 4.35991i | −1.20799 | − | 1.12572i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.226399 | + | 0.392135i | −0.0549098 | + | 0.0951066i | −0.892174 | − | 0.451692i | \(-0.850820\pi\) |
0.837264 | + | 0.546799i | \(0.184154\pi\) | |||||||
\(18\) | −2.58973 | − | 4.48555i | −0.610405 | − | 1.05725i | ||||
\(19\) | 6.47189 | − | 3.73655i | 1.48475 | − | 0.857223i | 0.484905 | − | 0.874567i | \(-0.338854\pi\) |
0.999850 | + | 0.0173439i | \(0.00552102\pi\) | |||||||
\(20\) | −1.52446 | + | 1.63586i | −0.340879 | + | 0.365789i | ||||
\(21\) | −6.85436 | + | 11.8721i | −1.49574 | + | 2.59070i | ||||
\(22\) | 1.36333 | − | 2.36136i | 0.290663 | − | 0.503444i | ||||
\(23\) | 7.02428 | 1.46466 | 0.732332 | − | 0.680948i | \(-0.238432\pi\) | ||||
0.732332 | + | 0.680948i | \(0.238432\pi\) | |||||||
\(24\) | −2.47681 | + | 1.42999i | −0.505577 | + | 0.291895i | ||||
\(25\) | −4.14335 | + | 2.79868i | −0.828671 | + | 0.559737i | ||||
\(26\) | −1.21778 | −0.238827 | ||||||||
\(27\) | − | 6.23321i | − | 1.19958i | ||||||
\(28\) | 4.15112 | + | 2.39665i | 0.784487 | + | 0.452924i | ||||
\(29\) | 8.17947i | 1.51889i | 0.650572 | + | 0.759445i | \(0.274529\pi\) | ||||
−0.650572 | + | 0.759445i | \(0.725471\pi\) | |||||||
\(30\) | −6.11505 | + | 1.87175i | −1.11645 | + | 0.341734i | ||||
\(31\) | − | 1.53078i | − | 0.274936i | −0.990506 | − | 0.137468i | \(-0.956104\pi\) | ||
0.990506 | − | 0.137468i | \(-0.0438965\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 6.75343 | − | 3.89910i | 1.17562 | − | 0.678745i | ||||
\(34\) | 0.226399 | + | 0.392135i | 0.0388271 | + | 0.0672506i | ||||
\(35\) | 7.84115 | + | 7.30718i | 1.32540 | + | 1.23514i | ||||
\(36\) | −5.17946 | −0.863244 | ||||||||
\(37\) | 5.22148 | + | 3.12028i | 0.858406 | + | 0.512971i | ||||
\(38\) | − | 7.47310i | − | 1.21230i | ||||||
\(39\) | −3.01622 | − | 1.74141i | −0.482981 | − | 0.278849i | ||||
\(40\) | 0.654464 | + | 2.13815i | 0.103480 | + | 0.338071i | ||||
\(41\) | 2.40568 | + | 4.16675i | 0.375704 | + | 0.650738i | 0.990432 | − | 0.138001i | \(-0.0440678\pi\) |
−0.614729 | + | 0.788739i | \(0.710734\pi\) | |||||||
\(42\) | 6.85436 | + | 11.8721i | 1.05765 | + | 1.83190i | ||||
\(43\) | −7.62420 | −1.16268 | −0.581340 | − | 0.813661i | \(-0.697471\pi\) | ||||
−0.581340 | + | 0.813661i | \(0.697471\pi\) | |||||||
\(44\) | −1.36333 | − | 2.36136i | −0.205530 | − | 0.355988i | ||||
\(45\) | −11.2856 | − | 2.60160i | −1.68236 | − | 0.387823i | ||||
\(46\) | 3.51214 | − | 6.08320i | 0.517837 | − | 0.896920i | ||||
\(47\) | 2.87372i | 0.419175i | 0.977790 | + | 0.209588i | \(0.0672122\pi\) | ||||
−0.977790 | + | 0.209588i | \(0.932788\pi\) | |||||||
\(48\) | 2.85998i | 0.412802i | ||||||||
\(49\) | 7.98785 | − | 13.8354i | 1.14112 | − | 1.97648i | ||||
\(50\) | 0.352054 | + | 4.98759i | 0.0497880 | + | 0.705352i | ||||
\(51\) | 1.29499i | 0.181335i | ||||||||
\(52\) | −0.608891 | + | 1.05463i | −0.0844380 | + | 0.146251i | ||||
\(53\) | −5.93485 | − | 3.42649i | −0.815215 | − | 0.470664i | 0.0335488 | − | 0.999437i | \(-0.489319\pi\) |
−0.848763 | + | 0.528773i | \(0.822652\pi\) | |||||||
\(54\) | −5.39812 | − | 3.11660i | −0.734591 | − | 0.424116i | ||||
\(55\) | −1.78450 | − | 5.83001i | −0.240622 | − | 0.786118i | ||||
\(56\) | 4.15112 | − | 2.39665i | 0.554716 | − | 0.320266i | ||||
\(57\) | 10.6864 | − | 18.5095i | 1.41545 | − | 2.45164i | ||||
\(58\) | 7.08363 | + | 4.08974i | 0.930126 | + | 0.537009i | ||||
\(59\) | −8.91923 | − | 5.14952i | −1.16118 | − | 0.670410i | −0.209597 | − | 0.977788i | \(-0.567215\pi\) |
−0.951588 | + | 0.307378i | \(0.900548\pi\) | |||||||
\(60\) | −1.43654 | + | 6.23167i | −0.185457 | + | 0.804505i | ||||
\(61\) | −5.44953 | + | 3.14629i | −0.697741 | + | 0.402841i | −0.806505 | − | 0.591227i | \(-0.798644\pi\) |
0.108765 | + | 0.994068i | \(0.465311\pi\) | |||||||
\(62\) | −1.32569 | − | 0.765390i | −0.168363 | − | 0.0972047i | ||||
\(63\) | 24.8267i | 3.12787i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.85646 | + | 1.99212i | −0.230265 | + | 0.247092i | ||||
\(66\) | − | 7.79819i | − | 0.959891i | ||||||
\(67\) | −0.0243958 | + | 0.0140849i | −0.00298042 | + | 0.00172074i | −0.501489 | − | 0.865164i | \(-0.667214\pi\) |
0.498509 | + | 0.866884i | \(0.333881\pi\) | |||||||
\(68\) | 0.452798 | 0.0549098 | ||||||||
\(69\) | 17.3978 | − | 10.0446i | 2.09445 | − | 1.20923i | ||||
\(70\) | 10.2488 | − | 3.13704i | 1.22496 | − | 0.374948i | ||||
\(71\) | −0.101250 | − | 0.175370i | −0.0120162 | − | 0.0208126i | 0.859955 | − | 0.510370i | \(-0.170492\pi\) |
−0.871971 | + | 0.489558i | \(0.837158\pi\) | |||||||
\(72\) | −2.58973 | + | 4.48555i | −0.305203 | + | 0.528627i | ||||
\(73\) | 1.18787i | 0.139030i | 0.997581 | + | 0.0695150i | \(0.0221452\pi\) | ||||
−0.997581 | + | 0.0695150i | \(0.977855\pi\) | |||||||
\(74\) | 5.31298 | − | 2.96180i | 0.617622 | − | 0.344302i | ||||
\(75\) | −6.26022 | + | 12.8568i | −0.722868 | + | 1.48457i | ||||
\(76\) | −6.47189 | − | 3.73655i | −0.742377 | − | 0.428612i | ||||
\(77\) | −11.3187 | + | 6.53485i | −1.28989 | + | 0.744716i | ||||
\(78\) | −3.01622 | + | 1.74141i | −0.341519 | + | 0.197176i | ||||
\(79\) | −8.91394 | + | 5.14647i | −1.00290 | + | 0.579023i | −0.909104 | − | 0.416569i | \(-0.863232\pi\) |
−0.0937929 | + | 0.995592i | \(0.529899\pi\) | |||||||
\(80\) | 2.17892 | + | 0.502291i | 0.243611 | + | 0.0561579i | ||||
\(81\) | −1.14422 | − | 1.98185i | −0.127135 | − | 0.220205i | ||||
\(82\) | 4.81135 | 0.531325 | ||||||||
\(83\) | −5.78633 | − | 3.34074i | −0.635132 | − | 0.366694i | 0.147605 | − | 0.989046i | \(-0.452844\pi\) |
−0.782737 | + | 0.622353i | \(0.786177\pi\) | |||||||
\(84\) | 13.7087 | 1.49574 | ||||||||
\(85\) | 0.986612 | + | 0.227437i | 0.107013 | + | 0.0246690i | ||||
\(86\) | −3.81210 | + | 6.60275i | −0.411070 | + | 0.711993i | ||||
\(87\) | 11.6965 | + | 20.2590i | 1.25400 | + | 2.17199i | ||||
\(88\) | −2.72666 | −0.290663 | ||||||||
\(89\) | 3.24928 | + | 1.87597i | 0.344423 | + | 0.198853i | 0.662226 | − | 0.749304i | \(-0.269612\pi\) |
−0.317803 | + | 0.948157i | \(0.602945\pi\) | |||||||
\(90\) | −7.89587 | + | 8.47286i | −0.832298 | + | 0.893118i | ||||
\(91\) | 5.05516 | + | 2.91860i | 0.529925 | + | 0.305952i | ||||
\(92\) | −3.51214 | − | 6.08320i | −0.366166 | − | 0.634218i | ||||
\(93\) | −2.18900 | − | 3.79146i | −0.226988 | − | 0.393156i | ||||
\(94\) | 2.48872 | + | 1.43686i | 0.256691 | + | 0.148201i | ||||
\(95\) | −12.2249 | − | 11.3924i | −1.25425 | − | 1.16884i | ||||
\(96\) | 2.47681 | + | 1.42999i | 0.252789 | + | 0.145948i | ||||
\(97\) | 15.7903 | 1.60326 | 0.801630 | − | 0.597820i | \(-0.203966\pi\) | ||||
0.801630 | + | 0.597820i | \(0.203966\pi\) | |||||||
\(98\) | −7.98785 | − | 13.8354i | −0.806894 | − | 1.39758i | ||||
\(99\) | 7.06132 | − | 12.2306i | 0.709690 | − | 1.22922i | ||||
\(100\) | 4.49541 | + | 2.18891i | 0.449541 | + | 0.218891i | ||||
\(101\) | −6.29744 | −0.626619 | −0.313310 | − | 0.949651i | \(-0.601438\pi\) | ||||
−0.313310 | + | 0.949651i | \(0.601438\pi\) | |||||||
\(102\) | 1.12150 | + | 0.647496i | 0.111045 | + | 0.0641117i | ||||
\(103\) | 8.52688 | 0.840179 | 0.420089 | − | 0.907483i | \(-0.361999\pi\) | ||||
0.420089 | + | 0.907483i | \(0.361999\pi\) | |||||||
\(104\) | 0.608891 | + | 1.05463i | 0.0597067 | + | 0.103415i | ||||
\(105\) | 29.8702 | + | 6.88577i | 2.91504 | + | 0.671982i | ||||
\(106\) | −5.93485 | + | 3.42649i | −0.576444 | + | 0.332810i | ||||
\(107\) | −5.73095 | + | 3.30877i | −0.554032 | + | 0.319871i | −0.750747 | − | 0.660590i | \(-0.770306\pi\) |
0.196715 | + | 0.980461i | \(0.436973\pi\) | |||||||
\(108\) | −5.39812 | + | 3.11660i | −0.519434 | + | 0.299895i | ||||
\(109\) | 12.9732 | + | 7.49007i | 1.24261 | + | 0.717418i | 0.969624 | − | 0.244601i | \(-0.0786570\pi\) |
0.272981 | + | 0.962019i | \(0.411990\pi\) | |||||||
\(110\) | −5.94119 | − | 1.36958i | −0.566470 | − | 0.130584i | ||||
\(111\) | 17.3946 | + | 0.261690i | 1.65102 | + | 0.0248385i | ||||
\(112\) | − | 4.79330i | − | 0.452924i | ||||||
\(113\) | 0.726663 | − | 1.25862i | 0.0683588 | − | 0.118401i | −0.829820 | − | 0.558031i | \(-0.811557\pi\) |
0.898179 | + | 0.439630i | \(0.144890\pi\) | |||||||
\(114\) | −10.6864 | − | 18.5095i | −1.00088 | − | 1.73357i | ||||
\(115\) | −4.59714 | − | 15.0189i | −0.428686 | − | 1.40052i | ||||
\(116\) | 7.08363 | − | 4.08974i | 0.657698 | − | 0.379722i | ||||
\(117\) | −6.30746 | −0.583125 | ||||||||
\(118\) | −8.91923 | + | 5.14952i | −0.821081 | + | 0.474052i | ||||
\(119\) | − | 2.17040i | − | 0.198960i | ||||||
\(120\) | 4.67851 | + | 4.35991i | 0.427088 | + | 0.398004i | ||||
\(121\) | −3.56531 | −0.324119 | ||||||||
\(122\) | 6.29258i | 0.569703i | ||||||||
\(123\) | 11.9168 | + | 6.88018i | 1.07450 | + | 0.620365i | ||||
\(124\) | −1.32569 | + | 0.765390i | −0.119051 | + | 0.0687341i | ||||
\(125\) | 8.69568 | + | 7.02746i | 0.777765 | + | 0.628555i | ||||
\(126\) | 21.5006 | + | 12.4133i | 1.91542 | + | 1.10587i | ||||
\(127\) | −11.5987 | − | 6.69650i | −1.02922 | − | 0.594218i | −0.112456 | − | 0.993657i | \(-0.535872\pi\) |
−0.916760 | + | 0.399438i | \(0.869205\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −18.8837 | + | 10.9025i | −1.66262 | + | 0.959913i | ||||
\(130\) | 0.796995 | + | 2.60380i | 0.0699011 | + | 0.228368i | ||||
\(131\) | −5.49133 | − | 3.17042i | −0.479780 | − | 0.277001i | 0.240545 | − | 0.970638i | \(-0.422674\pi\) |
−0.720325 | + | 0.693637i | \(0.756007\pi\) | |||||||
\(132\) | −6.75343 | − | 3.89910i | −0.587811 | − | 0.339373i | ||||
\(133\) | −17.9104 | + | 31.0217i | −1.55303 | + | 2.68992i | ||||
\(134\) | 0.0281698i | 0.00243350i | ||||||||
\(135\) | −13.3275 | + | 4.07941i | −1.14705 | + | 0.351100i | ||||
\(136\) | 0.226399 | − | 0.392135i | 0.0194136 | − | 0.0336253i | ||||
\(137\) | 9.41845i | 0.804673i | 0.915492 | + | 0.402336i | \(0.131802\pi\) | ||||
−0.915492 | + | 0.402336i | \(0.868198\pi\) | |||||||
\(138\) | − | 20.0893i | − | 1.71011i | ||||||
\(139\) | −4.32653 | + | 7.49376i | −0.366971 | + | 0.635613i | −0.989090 | − | 0.147310i | \(-0.952939\pi\) |
0.622119 | + | 0.782922i | \(0.286272\pi\) | |||||||
\(140\) | 2.40763 | − | 10.4442i | 0.203482 | − | 0.882698i | ||||
\(141\) | 4.10939 | + | 7.11767i | 0.346073 | + | 0.599416i | ||||
\(142\) | −0.202500 | −0.0169934 | ||||||||
\(143\) | −1.66024 | − | 2.87562i | −0.138836 | − | 0.240472i | ||||
\(144\) | 2.58973 | + | 4.48555i | 0.215811 | + | 0.373795i | ||||
\(145\) | 17.4889 | − | 5.35317i | 1.45238 | − | 0.444557i | ||||
\(146\) | 1.02873 | + | 0.593937i | 0.0851382 | + | 0.0491545i | ||||
\(147\) | − | 45.6901i | − | 3.76846i | ||||||
\(148\) | 0.0915007 | − | 6.08207i | 0.00752131 | − | 0.499943i | ||||
\(149\) | 4.30003 | 0.352272 | 0.176136 | − | 0.984366i | \(-0.443640\pi\) | ||||
0.176136 | + | 0.984366i | \(0.443640\pi\) | |||||||
\(150\) | 8.00417 | + | 11.8499i | 0.653537 | + | 0.967539i | ||||
\(151\) | −0.465325 | − | 0.805967i | −0.0378677 | − | 0.0655887i | 0.846470 | − | 0.532436i | \(-0.178723\pi\) |
−0.884338 | + | 0.466847i | \(0.845390\pi\) | |||||||
\(152\) | −6.47189 | + | 3.73655i | −0.524940 | + | 0.303074i | ||||
\(153\) | 1.17263 | + | 2.03105i | 0.0948012 | + | 0.164200i | ||||
\(154\) | 13.0697i | 1.05319i | ||||||||
\(155\) | −3.27304 | + | 1.00184i | −0.262897 | + | 0.0804698i | ||||
\(156\) | 3.48283i | 0.278849i | ||||||||
\(157\) | 0.603380 | + | 0.348361i | 0.0481549 | + | 0.0278023i | 0.523884 | − | 0.851789i | \(-0.324482\pi\) |
−0.475729 | + | 0.879592i | \(0.657816\pi\) | |||||||
\(158\) | 10.2929i | 0.818862i | ||||||||
\(159\) | −19.5993 | −1.55433 | ||||||||
\(160\) | 1.52446 | − | 1.63586i | 0.120519 | − | 0.129326i | ||||
\(161\) | −29.1586 | + | 16.8347i | −2.29802 | + | 1.32676i | ||||
\(162\) | −2.28844 | −0.179797 | ||||||||
\(163\) | −4.94299 | + | 8.56151i | −0.387165 | + | 0.670589i | −0.992067 | − | 0.125711i | \(-0.959879\pi\) |
0.604902 | + | 0.796300i | \(0.293212\pi\) | |||||||
\(164\) | 2.40568 | − | 4.16675i | 0.187852 | − | 0.325369i | ||||
\(165\) | −12.7567 | − | 11.8880i | −0.993110 | − | 0.925481i | ||||
\(166\) | −5.78633 | + | 3.34074i | −0.449106 | + | 0.259292i | ||||
\(167\) | 7.01504 | + | 12.1504i | 0.542840 | + | 0.940227i | 0.998739 | + | 0.0501957i | \(0.0159845\pi\) |
−0.455899 | + | 0.890032i | \(0.650682\pi\) | |||||||
\(168\) | 6.85436 | − | 11.8721i | 0.528825 | − | 0.915952i | ||||
\(169\) | 5.75850 | − | 9.97402i | 0.442962 | − | 0.767232i | ||||
\(170\) | 0.690272 | − | 0.740713i | 0.0529414 | − | 0.0568101i | ||||
\(171\) | − | 38.7066i | − | 2.95997i | ||||||
\(172\) | 3.81210 | + | 6.60275i | 0.290670 | + | 0.503455i | ||||
\(173\) | −3.44700 | − | 1.99013i | −0.262071 | − | 0.151307i | 0.363208 | − | 0.931708i | \(-0.381681\pi\) |
−0.625279 | + | 0.780401i | \(0.715015\pi\) | |||||||
\(174\) | 23.3931 | 1.77343 | ||||||||
\(175\) | 10.4921 | − | 21.5478i | 0.793127 | − | 1.62886i | ||||
\(176\) | −1.36333 | + | 2.36136i | −0.102765 | + | 0.177994i | ||||
\(177\) | −29.4550 | −2.21397 | ||||||||
\(178\) | 3.24928 | − | 1.87597i | 0.243544 | − | 0.140610i | ||||
\(179\) | 8.01227i | 0.598866i | 0.954117 | + | 0.299433i | \(0.0967974\pi\) | ||||
−0.954117 | + | 0.299433i | \(0.903203\pi\) | |||||||
\(180\) | 3.38977 | + | 11.0745i | 0.252659 | + | 0.825441i | ||||
\(181\) | −12.3988 | − | 21.4754i | −0.921599 | − | 1.59626i | −0.796942 | − | 0.604055i | \(-0.793551\pi\) |
−0.124656 | − | 0.992200i | \(-0.539783\pi\) | |||||||
\(182\) | 5.05516 | − | 2.91860i | 0.374713 | − | 0.216341i | ||||
\(183\) | −8.99831 | + | 15.5855i | −0.665174 | + | 1.15212i | ||||
\(184\) | −7.02428 | −0.517837 | ||||||||
\(185\) | 3.25435 | − | 13.2064i | 0.239264 | − | 0.970954i | ||||
\(186\) | −4.37800 | −0.321010 | ||||||||
\(187\) | −0.617314 | + | 1.06922i | −0.0451425 | + | 0.0781891i | ||||
\(188\) | 2.48872 | − | 1.43686i | 0.181508 | − | 0.104794i | ||||
\(189\) | 14.9388 | + | 25.8748i | 1.08664 | + | 1.88211i | ||||
\(190\) | −15.9786 | + | 4.89088i | −1.15921 | + | 0.354821i | ||||
\(191\) | − | 6.28982i | − | 0.455116i | −0.973765 | − | 0.227558i | \(-0.926926\pi\) | ||
0.973765 | − | 0.227558i | \(-0.0730741\pi\) | |||||||
\(192\) | 2.47681 | − | 1.42999i | 0.178748 | − | 0.103200i | ||||
\(193\) | 14.8233 | 1.06701 | 0.533503 | − | 0.845798i | \(-0.320875\pi\) | ||||
0.533503 | + | 0.845798i | \(0.320875\pi\) | |||||||
\(194\) | 7.89514 | − | 13.6748i | 0.566838 | − | 0.981793i | ||||
\(195\) | −1.74939 | + | 7.58881i | −0.125277 | + | 0.543446i | ||||
\(196\) | −15.9757 | −1.14112 | ||||||||
\(197\) | −16.3592 | − | 9.44497i | −1.16554 | − | 0.672926i | −0.212916 | − | 0.977070i | \(-0.568296\pi\) |
−0.952626 | + | 0.304145i | \(0.901629\pi\) | |||||||
\(198\) | −7.06132 | − | 12.2306i | −0.501826 | − | 0.869189i | ||||
\(199\) | − | 17.7101i | − | 1.25544i | −0.778441 | − | 0.627718i | \(-0.783989\pi\) | ||
0.778441 | − | 0.627718i | \(-0.216011\pi\) | |||||||
\(200\) | 4.14335 | − | 2.79868i | 0.292979 | − | 0.197897i | ||||
\(201\) | −0.0402825 | + | 0.0697713i | −0.00284131 | + | 0.00492129i | ||||
\(202\) | −3.14872 | + | 5.45375i | −0.221543 | + | 0.383724i | ||||
\(203\) | −19.6033 | − | 33.9539i | −1.37588 | − | 2.38310i | ||||
\(204\) | 1.12150 | − | 0.647496i | 0.0785204 | − | 0.0453338i | ||||
\(205\) | 7.33471 | − | 7.87068i | 0.512278 | − | 0.549712i | ||||
\(206\) | 4.26344 | − | 7.38450i | 0.297048 | − | 0.514502i | ||||
\(207\) | 18.1910 | − | 31.5077i | 1.26436 | − | 2.18994i | ||||
\(208\) | 1.21778 | 0.0844380 | ||||||||
\(209\) | 17.6467 | − | 10.1883i | 1.22065 | − | 0.704740i | ||||
\(210\) | 20.8984 | − | 22.4255i | 1.44212 | − | 1.54751i | ||||
\(211\) | −8.54618 | −0.588344 | −0.294172 | − | 0.955753i | \(-0.595044\pi\) | ||||
−0.294172 | + | 0.955753i | \(0.595044\pi\) | |||||||
\(212\) | 6.85298i | 0.470664i | ||||||||
\(213\) | −0.501555 | − | 0.289573i | −0.0343660 | − | 0.0198412i | ||||
\(214\) | 6.61753i | 0.452365i | ||||||||
\(215\) | 4.98977 | + | 16.3017i | 0.340299 | + | 1.11177i | ||||
\(216\) | 6.23321i | 0.424116i | ||||||||
\(217\) | 3.66874 | + | 6.35445i | 0.249051 | + | 0.431368i | ||||
\(218\) | 12.9732 | − | 7.49007i | 0.878654 | − | 0.507291i | ||||
\(219\) | 1.69864 | + | 2.94214i | 0.114784 | + | 0.198811i | ||||
\(220\) | −4.15668 | + | 4.46043i | −0.280244 | + | 0.300722i | ||||
\(221\) | 0.551410 | 0.0370918 | ||||||||
\(222\) | 8.92392 | − | 14.9333i | 0.598934 | − | 1.00226i | ||||
\(223\) | − | 23.2869i | − | 1.55940i | −0.626150 | − | 0.779702i | \(-0.715370\pi\) | ||
0.626150 | − | 0.779702i | \(-0.284630\pi\) | |||||||
\(224\) | −4.15112 | − | 2.39665i | −0.277358 | − | 0.160133i | ||||
\(225\) | 1.82345 | + | 25.8330i | 0.121563 | + | 1.72220i | ||||
\(226\) | −0.726663 | − | 1.25862i | −0.0483369 | − | 0.0837220i | ||||
\(227\) | 1.50747 | + | 2.61101i | 0.100054 | + | 0.173299i | 0.911707 | − | 0.410842i | \(-0.134765\pi\) |
−0.811653 | + | 0.584140i | \(0.801432\pi\) | |||||||
\(228\) | −21.3729 | −1.41545 | ||||||||
\(229\) | −0.804843 | − | 1.39403i | −0.0531855 | − | 0.0921201i | 0.838207 | − | 0.545352i | \(-0.183604\pi\) |
−0.891392 | + | 0.453232i | \(0.850271\pi\) | |||||||
\(230\) | −15.3054 | − | 3.52823i | −1.00921 | − | 0.232645i | ||||
\(231\) | −18.6895 | + | 32.3712i | −1.22968 | + | 2.12987i | ||||
\(232\) | − | 8.17947i | − | 0.537009i | ||||||
\(233\) | 19.5213i | 1.27888i | 0.768839 | + | 0.639442i | \(0.220835\pi\) | ||||
−0.768839 | + | 0.639442i | \(0.779165\pi\) | |||||||
\(234\) | −3.15373 | + | 5.46242i | −0.206166 | + | 0.357090i | ||||
\(235\) | 6.14444 | − | 1.88075i | 0.400819 | − | 0.122686i | ||||
\(236\) | 10.2990i | 0.670410i | ||||||||
\(237\) | −14.7188 | + | 25.4937i | −0.956087 | + | 1.65599i | ||||
\(238\) | −1.87962 | − | 1.08520i | −0.121838 | − | 0.0703429i | ||||
\(239\) | −5.67805 | − | 3.27822i | −0.367282 | − | 0.212051i | 0.304988 | − | 0.952356i | \(-0.401347\pi\) |
−0.672271 | + | 0.740306i | \(0.734681\pi\) | |||||||
\(240\) | 6.11505 | − | 1.87175i | 0.394725 | − | 0.120821i | ||||
\(241\) | 8.41117 | − | 4.85619i | 0.541811 | − | 0.312815i | −0.204002 | − | 0.978971i | \(-0.565395\pi\) |
0.745813 | + | 0.666156i | \(0.232061\pi\) | |||||||
\(242\) | −1.78265 | + | 3.08765i | −0.114593 | + | 0.198481i | ||||
\(243\) | 10.5263 | + | 6.07737i | 0.675264 | + | 0.389864i | ||||
\(244\) | 5.44953 | + | 3.14629i | 0.348870 | + | 0.201420i | ||||
\(245\) | −34.8098 | − | 8.02445i | −2.22392 | − | 0.512663i | ||||
\(246\) | 11.9168 | − | 6.88018i | 0.759788 | − | 0.438664i | ||||
\(247\) | −7.88136 | − | 4.55030i | −0.501479 | − | 0.289529i | ||||
\(248\) | 1.53078i | 0.0972047i | ||||||||
\(249\) | −19.1089 | −1.21098 | ||||||||
\(250\) | 10.4338 | − | 4.01694i | 0.659891 | − | 0.254054i | ||||
\(251\) | 17.8028i | 1.12371i | 0.827237 | + | 0.561853i | \(0.189911\pi\) | ||||
−0.827237 | + | 0.561853i | \(0.810089\pi\) | |||||||
\(252\) | 21.5006 | − | 12.4133i | 1.35441 | − | 0.781967i | ||||
\(253\) | 19.1528 | 1.20413 | ||||||||
\(254\) | −11.5987 | + | 6.69650i | −0.727766 | + | 0.420176i | ||||
\(255\) | 2.76888 | − | 0.847526i | 0.173394 | − | 0.0530741i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −10.3090 | + | 17.8557i | −0.643058 | + | 1.11381i | 0.341688 | + | 0.939813i | \(0.389001\pi\) |
−0.984746 | + | 0.173996i | \(0.944332\pi\) | |||||||
\(258\) | 21.8050i | 1.35752i | ||||||||
\(259\) | −29.1532 | − | 0.438590i | −1.81149 | − | 0.0272527i | ||||
\(260\) | 2.65345 | + | 0.611681i | 0.164560 | + | 0.0379349i | ||||
\(261\) | 36.6894 | + | 21.1826i | 2.27102 | + | 1.31117i | ||||
\(262\) | −5.49133 | + | 3.17042i | −0.339255 | + | 0.195869i | ||||
\(263\) | 24.0090 | − | 13.8616i | 1.48046 | − | 0.854743i | 0.480704 | − | 0.876883i | \(-0.340381\pi\) |
0.999755 | + | 0.0221398i | \(0.00704789\pi\) | |||||||
\(264\) | −6.75343 | + | 3.89910i | −0.415645 | + | 0.239973i | ||||
\(265\) | −3.44219 | + | 14.9321i | −0.211452 | + | 0.917272i | ||||
\(266\) | 17.9104 | + | 31.0217i | 1.09816 | + | 1.90206i | ||||
\(267\) | 10.7305 | 0.656694 | ||||||||
\(268\) | 0.0243958 | + | 0.0140849i | 0.00149021 | + | 0.000860372i | ||||
\(269\) | −15.7739 | −0.961749 | −0.480875 | − | 0.876789i | \(-0.659681\pi\) | ||||
−0.480875 | + | 0.876789i | \(0.659681\pi\) | |||||||
\(270\) | −3.13089 | + | 13.5817i | −0.190540 | + | 0.826555i | ||||
\(271\) | 12.0183 | − | 20.8164i | 0.730063 | − | 1.26451i | −0.226793 | − | 0.973943i | \(-0.572824\pi\) |
0.956856 | − | 0.290563i | \(-0.0938424\pi\) | |||||||
\(272\) | −0.226399 | − | 0.392135i | −0.0137275 | − | 0.0237767i | ||||
\(273\) | 16.6942 | 1.01038 | ||||||||
\(274\) | 8.15662 | + | 4.70923i | 0.492759 | + | 0.284495i | ||||
\(275\) | −11.2975 | + | 7.63107i | −0.681267 | + | 0.460171i | ||||
\(276\) | −17.3978 | − | 10.0446i | −1.04723 | − | 0.604616i | ||||
\(277\) | 8.49982 | + | 14.7221i | 0.510705 | + | 0.884567i | 0.999923 | + | 0.0124054i | \(0.00394888\pi\) |
−0.489218 | + | 0.872161i | \(0.662718\pi\) | |||||||
\(278\) | 4.32653 | + | 7.49376i | 0.259488 | + | 0.449446i | ||||
\(279\) | −6.86639 | − | 3.96431i | −0.411080 | − | 0.237337i | ||||
\(280\) | −7.84115 | − | 7.30718i | −0.468598 | − | 0.436688i | ||||
\(281\) | 16.1845 | + | 9.34413i | 0.965486 | + | 0.557424i | 0.897857 | − | 0.440287i | \(-0.145123\pi\) |
0.0676291 | + | 0.997711i | \(0.478457\pi\) | |||||||
\(282\) | 8.21877 | 0.489421 | ||||||||
\(283\) | 0.220942 | + | 0.382682i | 0.0131336 | + | 0.0227481i | 0.872518 | − | 0.488583i | \(-0.162486\pi\) |
−0.859384 | + | 0.511331i | \(0.829153\pi\) | |||||||
\(284\) | −0.101250 | + | 0.175370i | −0.00600809 | + | 0.0104063i | ||||
\(285\) | −46.5699 | − | 10.7354i | −2.75856 | − | 0.635911i | ||||
\(286\) | −3.32048 | −0.196344 | ||||||||
\(287\) | −19.9725 | − | 11.5311i | −1.17894 | − | 0.680661i | ||||
\(288\) | 5.17946 | 0.305203 | ||||||||
\(289\) | 8.39749 | + | 14.5449i | 0.493970 | + | 0.855581i | ||||
\(290\) | 4.10848 | − | 17.8224i | 0.241258 | − | 1.04657i | ||||
\(291\) | 39.1096 | − | 22.5799i | 2.29264 | − | 1.32366i | ||||
\(292\) | 1.02873 | − | 0.593937i | 0.0602018 | − | 0.0347575i | ||||
\(293\) | 4.12530 | − | 2.38174i | 0.241003 | − | 0.139143i | −0.374635 | − | 0.927172i | \(-0.622232\pi\) |
0.615637 | + | 0.788030i | \(0.288899\pi\) | |||||||
\(294\) | −39.5688 | − | 22.8450i | −2.30770 | − | 1.33235i | ||||
\(295\) | −5.17311 | + | 22.4408i | −0.301190 | + | 1.30655i | ||||
\(296\) | −5.22148 | − | 3.12028i | −0.303492 | − | 0.181363i | ||||
\(297\) | − | 16.9959i | − | 0.986200i | ||||||
\(298\) | 2.15001 | − | 3.72393i | 0.124547 | − | 0.215722i | ||||
\(299\) | −4.27702 | − | 7.40802i | −0.247347 | − | 0.428417i | ||||
\(300\) | 14.2644 | − | 1.00687i | 0.823555 | − | 0.0581315i | ||||
\(301\) | 31.6490 | − | 18.2725i | 1.82422 | − | 1.05321i | ||||
\(302\) | −0.930651 | −0.0535529 | ||||||||
\(303\) | −15.5976 | + | 9.00527i | −0.896058 | + | 0.517339i | ||||
\(304\) | 7.47310i | 0.428612i | ||||||||
\(305\) | 10.2938 | + | 9.59277i | 0.589419 | + | 0.549280i | ||||
\(306\) | 2.34525 | 0.134069 | ||||||||
\(307\) | − | 2.96816i | − | 0.169402i | −0.996406 | − | 0.0847009i | \(-0.973007\pi\) | ||
0.996406 | − | 0.0847009i | \(-0.0269935\pi\) | |||||||
\(308\) | 11.3187 | + | 6.53485i | 0.644943 | + | 0.372358i | ||||
\(309\) | 21.1195 | − | 12.1933i | 1.20145 | − | 0.693655i | ||||
\(310\) | −0.768898 | + | 3.33545i | −0.0436704 | + | 0.189441i | ||||
\(311\) | −21.7036 | − | 12.5306i | −1.23070 | − | 0.710544i | −0.263523 | − | 0.964653i | \(-0.584884\pi\) |
−0.967176 | + | 0.254109i | \(0.918218\pi\) | |||||||
\(312\) | 3.01622 | + | 1.74141i | 0.170760 | + | 0.0985882i | ||||
\(313\) | 8.91834 | − | 15.4470i | 0.504095 | − | 0.873117i | −0.495894 | − | 0.868383i | \(-0.665160\pi\) |
0.999989 | − | 0.00473445i | \(-0.00150703\pi\) | |||||||
\(314\) | 0.603380 | − | 0.348361i | 0.0340507 | − | 0.0196592i | ||||
\(315\) | 53.0832 | − | 16.2482i | 2.99090 | − | 0.915482i | ||||
\(316\) | 8.91394 | + | 5.14647i | 0.501449 | + | 0.289511i | ||||
\(317\) | −3.90982 | − | 2.25733i | −0.219597 | − | 0.126785i | 0.386167 | − | 0.922429i | \(-0.373799\pi\) |
−0.605764 | + | 0.795645i | \(0.707132\pi\) | |||||||
\(318\) | −9.79967 | + | 16.9735i | −0.549538 | + | 0.951829i | ||||
\(319\) | 22.3027i | 1.24871i | ||||||||
\(320\) | −0.654464 | − | 2.13815i | −0.0365857 | − | 0.119526i | ||||
\(321\) | −9.46299 | + | 16.3904i | −0.528173 | + | 0.914822i | ||||
\(322\) | 33.6695i | 1.87633i | ||||||||
\(323\) | 3.38381i | 0.188280i | ||||||||
\(324\) | −1.14422 | + | 1.98185i | −0.0635677 | + | 0.110103i | ||||
\(325\) | 5.47443 | + | 2.66561i | 0.303667 | + | 0.147862i | ||||
\(326\) | 4.94299 | + | 8.56151i | 0.273767 | + | 0.474178i | ||||
\(327\) | 42.8428 | 2.36921 | ||||||||
\(328\) | −2.40568 | − | 4.16675i | −0.132831 | − | 0.230070i | ||||
\(329\) | −6.88730 | − | 11.9292i | −0.379709 | − | 0.657676i | ||||
\(330\) | −16.6737 | + | 5.10364i | −0.917856 | + | 0.280946i | ||||
\(331\) | −19.8565 | − | 11.4642i | −1.09141 | − | 0.630127i | −0.157460 | − | 0.987525i | \(-0.550330\pi\) |
−0.933952 | + | 0.357399i | \(0.883664\pi\) | |||||||
\(332\) | 6.68148i | 0.366694i | ||||||||
\(333\) | 27.5184 | − | 15.3405i | 1.50800 | − | 0.840654i | ||||
\(334\) | 14.0301 | 0.767692 | ||||||||
\(335\) | 0.0460818 | + | 0.0429437i | 0.00251772 | + | 0.00234626i | ||||
\(336\) | −6.85436 | − | 11.8721i | −0.373936 | − | 0.647676i | ||||
\(337\) | −9.93107 | + | 5.73371i | −0.540980 | + | 0.312335i | −0.745476 | − | 0.666532i | \(-0.767778\pi\) |
0.204496 | + | 0.978867i | \(0.434444\pi\) | |||||||
\(338\) | −5.75850 | − | 9.97402i | −0.313221 | − | 0.542515i | ||||
\(339\) | − | 4.15648i | − | 0.225749i | ||||||
\(340\) | −0.296340 | − | 0.968150i | −0.0160713 | − | 0.0525053i | ||||
\(341\) | − | 4.17392i | − | 0.226031i | ||||||
\(342\) | −33.5209 | − | 19.3533i | −1.81260 | − | 1.04651i | ||||
\(343\) | 43.0232i | 2.32303i | ||||||||
\(344\) | 7.62420 | 0.411070 | ||||||||
\(345\) | −32.8632 | − | 30.6253i | −1.76929 | − | 1.64881i | ||||
\(346\) | −3.44700 | + | 1.99013i | −0.185312 | + | 0.106990i | ||||
\(347\) | 11.3700 | 0.610373 | 0.305187 | − | 0.952293i | \(-0.401281\pi\) | ||||
0.305187 | + | 0.952293i | \(0.401281\pi\) | |||||||
\(348\) | 11.6965 | − | 20.2590i | 0.627001 | − | 1.08600i | ||||
\(349\) | 2.53073 | − | 4.38336i | 0.135467 | − | 0.234636i | −0.790309 | − | 0.612709i | \(-0.790080\pi\) |
0.925776 | + | 0.378073i | \(0.123413\pi\) | |||||||
\(350\) | −13.4149 | − | 19.8603i | −0.717058 | − | 1.06158i | ||||
\(351\) | −6.57373 | + | 3.79535i | −0.350880 | + | 0.202581i | ||||
\(352\) | 1.36333 | + | 2.36136i | 0.0726658 | + | 0.125861i | ||||
\(353\) | −10.0780 | + | 17.4557i | −0.536400 | + | 0.929072i | 0.462694 | + | 0.886518i | \(0.346883\pi\) |
−0.999094 | + | 0.0425542i | \(0.986450\pi\) | |||||||
\(354\) | −14.7275 | + | 25.5088i | −0.782758 | + | 1.35578i | ||||
\(355\) | −0.308703 | + | 0.331262i | −0.0163843 | + | 0.0175815i | ||||
\(356\) | − | 3.75194i | − | 0.198853i | ||||||
\(357\) | −3.10364 | − | 5.37566i | −0.164262 | − | 0.284510i | ||||
\(358\) | 6.93883 | + | 4.00614i | 0.366729 | + | 0.211731i | ||||
\(359\) | −4.76781 | −0.251635 | −0.125818 | − | 0.992053i | \(-0.540155\pi\) | ||||
−0.125818 | + | 0.992053i | \(0.540155\pi\) | |||||||
\(360\) | 11.2856 | + | 2.60160i | 0.594806 | + | 0.137116i | ||||
\(361\) | 18.4236 | − | 31.9106i | 0.969663 | − | 1.67951i | ||||
\(362\) | −24.7977 | −1.30334 | ||||||||
\(363\) | −8.83059 | + | 5.09834i | −0.463486 | + | 0.267594i | ||||
\(364\) | − | 5.83719i | − | 0.305952i | ||||||
\(365\) | 2.53985 | − | 0.777421i | 0.132942 | − | 0.0406921i | ||||
\(366\) | 8.99831 | + | 15.5855i | 0.470349 | + | 0.814668i | ||||
\(367\) | −19.0638 | + | 11.0065i | −0.995123 | + | 0.574535i | −0.906802 | − | 0.421557i | \(-0.861484\pi\) |
−0.0883215 | + | 0.996092i | \(0.528150\pi\) | |||||||
\(368\) | −3.51214 | + | 6.08320i | −0.183083 | + | 0.317109i | ||||
\(369\) | 24.9202 | 1.29729 | ||||||||
\(370\) | −9.80991 | − | 9.42155i | −0.509993 | − | 0.489803i | ||||
\(371\) | 32.8484 | 1.70540 | ||||||||
\(372\) | −2.18900 | + | 3.79146i | −0.113494 | + | 0.196578i | ||||
\(373\) | −0.696232 | + | 0.401970i | −0.0360495 | + | 0.0208132i | −0.517916 | − | 0.855431i | \(-0.673292\pi\) |
0.481867 | + | 0.876244i | \(0.339959\pi\) | |||||||
\(374\) | 0.617314 | + | 1.06922i | 0.0319206 | + | 0.0552880i | ||||
\(375\) | 31.5867 | + | 4.97099i | 1.63113 | + | 0.256701i | ||||
\(376\) | − | 2.87372i | − | 0.148201i | ||||||
\(377\) | 8.62632 | − | 4.98041i | 0.444278 | − | 0.256504i | ||||
\(378\) | 29.8776 | 1.53674 | ||||||||
\(379\) | 0.189378 | − | 0.328013i | 0.00972771 | − | 0.0168489i | −0.861121 | − | 0.508401i | \(-0.830237\pi\) |
0.870848 | + | 0.491552i | \(0.163570\pi\) | |||||||
\(380\) | −3.75367 | + | 16.2833i | −0.192559 | + | 0.835316i | ||||
\(381\) | −38.3037 | −1.96236 | ||||||||
\(382\) | −5.44715 | − | 3.14491i | −0.278700 | − | 0.160908i | ||||
\(383\) | 0.359573 | + | 0.622798i | 0.0183733 | + | 0.0318235i | 0.875066 | − | 0.484004i | \(-0.160818\pi\) |
−0.856693 | + | 0.515827i | \(0.827485\pi\) | |||||||
\(384\) | − | 2.85998i | − | 0.145948i | ||||||
\(385\) | 21.3802 | + | 19.9242i | 1.08963 | + | 1.01543i | ||||
\(386\) | 7.41166 | − | 12.8374i | 0.377243 | − | 0.653405i | ||||
\(387\) | −19.7446 | + | 34.1987i | −1.00368 | + | 1.73842i | ||||
\(388\) | −7.89514 | − | 13.6748i | −0.400815 | − | 0.694232i | ||||
\(389\) | −11.8245 | + | 6.82689i | −0.599527 | + | 0.346137i | −0.768855 | − | 0.639423i | \(-0.779173\pi\) |
0.169328 | + | 0.985560i | \(0.445840\pi\) | |||||||
\(390\) | 5.69741 | + | 5.30943i | 0.288500 | + | 0.268853i | ||||
\(391\) | −1.59029 | + | 2.75446i | −0.0804244 | + | 0.139299i | ||||
\(392\) | −7.98785 | + | 13.8354i | −0.403447 | + | 0.698791i | ||||
\(393\) | −18.1346 | −0.914772 | ||||||||
\(394\) | −16.3592 | + | 9.44497i | −0.824163 | + | 0.475831i | ||||
\(395\) | 16.8378 | + | 15.6912i | 0.847200 | + | 0.789507i | ||||
\(396\) | −14.1226 | −0.709690 | ||||||||
\(397\) | 15.3780i | 0.771802i | 0.922540 | + | 0.385901i | \(0.126109\pi\) | ||||
−0.922540 | + | 0.385901i | \(0.873891\pi\) | |||||||
\(398\) | −15.3374 | − | 8.85505i | −0.768794 | − | 0.443863i | ||||
\(399\) | 102.447i | 5.12874i | ||||||||
\(400\) | −0.352054 | − | 4.98759i | −0.0176027 | − | 0.249380i | ||||
\(401\) | − | 30.7247i | − | 1.53432i | −0.641457 | − | 0.767159i | \(-0.721670\pi\) | ||
0.641457 | − | 0.767159i | \(-0.278330\pi\) | |||||||
\(402\) | 0.0402825 | + | 0.0697713i | 0.00200911 | + | 0.00347988i | ||||
\(403\) | −1.61441 | + | 0.932079i | −0.0804194 | + | 0.0464302i | ||||
\(404\) | 3.14872 | + | 5.45375i | 0.156655 | + | 0.271334i | ||||
\(405\) | −3.48863 | + | 3.74356i | −0.173351 | + | 0.186019i | ||||
\(406\) | −39.2066 | −1.94579 | ||||||||
\(407\) | 14.2372 | + | 8.50795i | 0.705713 | + | 0.421723i | ||||
\(408\) | − | 1.29499i | − | 0.0641117i | ||||||
\(409\) | −7.04079 | − | 4.06500i | −0.348144 | − | 0.201001i | 0.315723 | − | 0.948851i | \(-0.397753\pi\) |
−0.663868 | + | 0.747850i | \(0.731086\pi\) | |||||||
\(410\) | −3.14886 | − | 10.2874i | −0.155511 | − | 0.508058i | ||||
\(411\) | 13.4683 | + | 23.3277i | 0.664341 | + | 1.15067i | ||||
\(412\) | −4.26344 | − | 7.38450i | −0.210045 | − | 0.363808i | ||||
\(413\) | 49.3663 | 2.42916 | ||||||||
\(414\) | −18.1910 | − | 31.5077i | −0.894038 | − | 1.54852i | ||||
\(415\) | −3.35605 | + | 14.5584i | −0.164742 | + | 0.714645i | ||||
\(416\) | 0.608891 | − | 1.05463i | 0.0298534 | − | 0.0517075i | ||||
\(417\) | 24.7475i | 1.21189i | ||||||||
\(418\) | − | 20.3766i | − | 0.996653i | ||||||
\(419\) | −5.36246 | + | 9.28806i | −0.261973 | + | 0.453751i | −0.966766 | − | 0.255662i | \(-0.917707\pi\) |
0.704793 | + | 0.709413i | \(0.251040\pi\) | |||||||
\(420\) | −8.97186 | − | 29.3113i | −0.437782 | − | 1.43024i | ||||
\(421\) | 35.7769i | 1.74366i | 0.489809 | + | 0.871830i | \(0.337066\pi\) | ||||
−0.489809 | + | 0.871830i | \(0.662934\pi\) | |||||||
\(422\) | −4.27309 | + | 7.40121i | −0.208011 | + | 0.360285i | ||||
\(423\) | 12.8902 | + | 7.44216i | 0.626743 | + | 0.361850i | ||||
\(424\) | 5.93485 | + | 3.42649i | 0.288222 | + | 0.166405i | ||||
\(425\) | −0.159410 | − | 2.25837i | −0.00773250 | − | 0.109547i | ||||
\(426\) | −0.501555 | + | 0.289573i | −0.0243004 | + | 0.0140299i | ||||
\(427\) | 15.0811 | − | 26.1212i | 0.729825 | − | 1.26409i | ||||
\(428\) | 5.73095 | + | 3.30877i | 0.277016 | + | 0.159935i | ||||
\(429\) | −8.22421 | − | 4.74825i | −0.397069 | − | 0.229248i | ||||
\(430\) | 16.6126 | + | 3.82957i | 0.801128 | + | 0.184678i | ||||
\(431\) | −2.13125 | + | 1.23048i | −0.102659 | + | 0.0592700i | −0.550450 | − | 0.834868i | \(-0.685544\pi\) |
0.447792 | + | 0.894138i | \(0.352211\pi\) | |||||||
\(432\) | 5.39812 | + | 3.11660i | 0.259717 | + | 0.149948i | ||||
\(433\) | − | 31.2629i | − | 1.50240i | −0.660075 | − | 0.751200i | \(-0.729475\pi\) | ||
0.660075 | − | 0.751200i | \(-0.270525\pi\) | |||||||
\(434\) | 7.33749 | 0.352211 | ||||||||
\(435\) | 35.6618 | − | 38.2677i | 1.70985 | − | 1.83480i | ||||
\(436\) | − | 14.9801i | − | 0.717418i | ||||||
\(437\) | 45.4604 | − | 26.2466i | 2.17467 | − | 1.25554i | ||||
\(438\) | 3.39729 | 0.162329 | ||||||||
\(439\) | 19.8174 | − | 11.4416i | 0.945835 | − | 0.546078i | 0.0540505 | − | 0.998538i | \(-0.482787\pi\) |
0.891785 | + | 0.452460i | \(0.149453\pi\) | |||||||
\(440\) | 1.78450 | + | 5.83001i | 0.0850729 | + | 0.277935i | ||||
\(441\) | −41.3727 | − | 71.6597i | −1.97013 | − | 3.41237i | ||||
\(442\) | 0.275705 | − | 0.477535i | 0.0131139 | − | 0.0227140i | ||||
\(443\) | 1.49918i | 0.0712281i | 0.999366 | + | 0.0356141i | \(0.0113387\pi\) | ||||
−0.999366 | + | 0.0356141i | \(0.988661\pi\) | |||||||
\(444\) | −8.47066 | − | 15.1950i | −0.402000 | − | 0.721123i | ||||
\(445\) | 1.88457 | − | 8.17520i | 0.0893371 | − | 0.387541i | ||||
\(446\) | −20.1670 | − | 11.6434i | −0.954936 | − | 0.551333i | ||||
\(447\) | 10.6504 | − | 6.14898i | 0.503744 | − | 0.290837i | ||||
\(448\) | −4.15112 | + | 2.39665i | −0.196122 | + | 0.113231i | ||||
\(449\) | −22.7095 | + | 13.1113i | −1.07173 | + | 0.618761i | −0.928653 | − | 0.370951i | \(-0.879032\pi\) |
−0.143074 | + | 0.989712i | \(0.545699\pi\) | |||||||
\(450\) | 23.2838 | + | 11.3374i | 1.09761 | + | 0.534448i | ||||
\(451\) | 6.55947 | + | 11.3613i | 0.308873 | + | 0.534984i | ||||
\(452\) | −1.45333 | −0.0683588 | ||||||||
\(453\) | −2.30505 | − | 1.33082i | −0.108301 | − | 0.0625274i | ||||
\(454\) | 3.01493 | 0.141498 | ||||||||
\(455\) | 2.93197 | − | 12.7188i | 0.137453 | − | 0.596266i | ||||
\(456\) | −10.6864 | + | 18.5095i | −0.500438 | + | 0.866785i | ||||
\(457\) | −16.2116 | − | 28.0793i | −0.758346 | − | 1.31349i | −0.943693 | − | 0.330821i | \(-0.892674\pi\) |
0.185347 | − | 0.982673i | \(-0.440659\pi\) | |||||||
\(458\) | −1.60969 | −0.0752157 | ||||||||
\(459\) | 2.44426 | + | 1.41119i | 0.114088 | + | 0.0658688i | ||||
\(460\) | −10.7082 | + | 11.4907i | −0.499273 | + | 0.535757i | ||||
\(461\) | 6.96252 | + | 4.01982i | 0.324277 | + | 0.187221i | 0.653297 | − | 0.757101i | \(-0.273385\pi\) |
−0.329020 | + | 0.944323i | \(0.606718\pi\) | |||||||
\(462\) | 18.6895 | + | 32.3712i | 0.869515 | + | 1.50604i | ||||
\(463\) | −8.11837 | − | 14.0614i | −0.377293 | − | 0.653490i | 0.613375 | − | 0.789792i | \(-0.289812\pi\) |
−0.990667 | + | 0.136302i | \(0.956478\pi\) | |||||||
\(464\) | −7.08363 | − | 4.08974i | −0.328849 | − | 0.189861i | ||||
\(465\) | −6.67407 | + | 7.16177i | −0.309503 | + | 0.332119i | ||||
\(466\) | 16.9060 | + | 9.76067i | 0.783154 | + | 0.452154i | ||||
\(467\) | 3.44377 | 0.159358 | 0.0796792 | − | 0.996821i | \(-0.474610\pi\) | ||||
0.0796792 | + | 0.996821i | \(0.474610\pi\) | |||||||
\(468\) | 3.15373 | + | 5.46242i | 0.145781 | + | 0.252500i | ||||
\(469\) | 0.0675131 | − | 0.116936i | 0.00311747 | − | 0.00539961i | ||||
\(470\) | 1.44344 | − | 6.26162i | 0.0665811 | − | 0.288827i | ||||
\(471\) | 1.99261 | 0.0918147 | ||||||||
\(472\) | 8.91923 | + | 5.14952i | 0.410541 | + | 0.237026i | ||||
\(473\) | −20.7886 | −0.955863 | ||||||||
\(474\) | 14.7188 | + | 25.4937i | 0.676056 | + | 1.17096i | ||||
\(475\) | −16.3579 | + | 33.5946i | −0.750553 | + | 1.54143i | ||||
\(476\) | −1.87962 | + | 1.08520i | −0.0861522 | + | 0.0497400i | ||||
\(477\) | −30.7393 | + | 17.7474i | −1.40746 | + | 0.812596i | ||||
\(478\) | −5.67805 | + | 3.27822i | −0.259708 | + | 0.149942i | ||||
\(479\) | 5.67506 | + | 3.27650i | 0.259300 | + | 0.149707i | 0.624015 | − | 0.781412i | \(-0.285500\pi\) |
−0.364715 | + | 0.931119i | \(0.618834\pi\) | |||||||
\(480\) | 1.43654 | − | 6.23167i | 0.0655688 | − | 0.284435i | ||||
\(481\) | 0.111428 | − | 7.40664i | 0.00508068 | − | 0.337714i | ||||
\(482\) | − | 9.71238i | − | 0.442387i | ||||||
\(483\) | −48.1469 | + | 83.3929i | −2.19076 | + | 3.79451i | ||||
\(484\) | 1.78265 | + | 3.08765i | 0.0810297 | + | 0.140348i | ||||
\(485\) | −10.3342 | − | 33.7620i | −0.469251 | − | 1.53305i | ||||
\(486\) | 10.5263 | − | 6.07737i | 0.477483 | − | 0.275675i | ||||
\(487\) | −4.97590 | −0.225479 | −0.112740 | − | 0.993625i | \(-0.535963\pi\) | ||||
−0.112740 | + | 0.993625i | \(0.535963\pi\) | |||||||
\(488\) | 5.44953 | − | 3.14629i | 0.246689 | − | 0.142426i | ||||
\(489\) | 28.2736i | 1.27858i | ||||||||
\(490\) | −24.3543 | + | 26.1339i | −1.10021 | + | 1.18061i | ||||
\(491\) | −13.1607 | −0.593934 | −0.296967 | − | 0.954888i | \(-0.595975\pi\) | ||||
−0.296967 | + | 0.954888i | \(0.595975\pi\) | |||||||
\(492\) | − | 13.7604i | − | 0.620365i | ||||||
\(493\) | −3.20745 | − | 1.85182i | −0.144456 | − | 0.0834020i | ||||
\(494\) | −7.88136 | + | 4.55030i | −0.354599 | + | 0.204728i | ||||
\(495\) | −30.7722 | − | 7.09368i | −1.38311 | − | 0.318837i | ||||
\(496\) | 1.32569 | + | 0.765390i | 0.0595255 | + | 0.0343670i | ||||
\(497\) | 0.840602 | + | 0.485322i | 0.0377062 | + | 0.0217697i | ||||
\(498\) | −9.55443 | + | 16.5488i | −0.428144 | + | 0.741568i | ||||
\(499\) | −11.2307 | + | 6.48407i | −0.502757 | + | 0.290267i | −0.729851 | − | 0.683606i | \(-0.760411\pi\) |
0.227094 | + | 0.973873i | \(0.427077\pi\) | |||||||
\(500\) | 1.73812 | − | 11.0444i | 0.0777312 | − | 0.493921i | ||||
\(501\) | 34.7499 | + | 20.0629i | 1.55251 | + | 0.896342i | ||||
\(502\) | 15.4177 | + | 8.90142i | 0.688127 | + | 0.397290i | ||||
\(503\) | 21.2832 | − | 36.8636i | 0.948971 | − | 1.64367i | 0.201372 | − | 0.979515i | \(-0.435460\pi\) |
0.747598 | − | 0.664151i | \(-0.231207\pi\) | |||||||
\(504\) | − | 24.8267i | − | 1.10587i | ||||||
\(505\) | 4.12145 | + | 13.4649i | 0.183402 | + | 0.599179i | ||||
\(506\) | 9.57642 | − | 16.5869i | 0.425724 | − | 0.737375i | ||||
\(507\) | − | 32.9384i | − | 1.46284i | ||||||
\(508\) | 13.3930i | 0.594218i | ||||||||
\(509\) | −8.09471 | + | 14.0204i | −0.358791 | + | 0.621445i | −0.987759 | − | 0.155986i | \(-0.950144\pi\) |
0.628968 | + | 0.777431i | \(0.283478\pi\) | |||||||
\(510\) | 0.650463 | − | 2.82169i | 0.0288030 | − | 0.124946i | ||||
\(511\) | −2.84691 | − | 4.93100i | −0.125940 | − | 0.218135i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −23.2907 | − | 40.3407i | −1.02831 | − | 1.78108i | ||||
\(514\) | 10.3090 | + | 17.8557i | 0.454711 | + | 0.787582i | ||||
\(515\) | −5.58054 | − | 18.2317i | −0.245908 | − | 0.803386i | ||||
\(516\) | 18.8837 | + | 10.9025i | 0.831309 | + | 0.479957i | ||||
\(517\) | 7.83567i | 0.344612i | ||||||||
\(518\) | −14.9564 | + | 25.0281i | −0.657148 | + | 1.09967i | ||||
\(519\) | −11.3834 | −0.499677 | ||||||||
\(520\) | 1.85646 | − | 1.99212i | 0.0814111 | − | 0.0873602i | ||||
\(521\) | 0.175072 | + | 0.303234i | 0.00767006 | + | 0.0132849i | 0.869835 | − | 0.493343i | \(-0.164225\pi\) |
−0.862165 | + | 0.506628i | \(0.830892\pi\) | |||||||
\(522\) | 36.6894 | − | 21.1826i | 1.60585 | − | 0.927138i | ||||
\(523\) | −7.81043 | − | 13.5281i | −0.341526 | − | 0.591541i | 0.643190 | − | 0.765706i | \(-0.277610\pi\) |
−0.984716 | + | 0.174166i | \(0.944277\pi\) | |||||||
\(524\) | 6.34084i | 0.277001i | ||||||||
\(525\) | −4.82621 | − | 68.3734i | −0.210633 | − | 2.98406i | ||||
\(526\) | − | 27.7232i | − | 1.20879i | ||||||
\(527\) | 0.600272 | + | 0.346567i | 0.0261483 | + | 0.0150967i | ||||
\(528\) | 7.79819i | 0.339373i | ||||||||
\(529\) | 26.3405 | 1.14524 | ||||||||
\(530\) | 11.2105 | + | 10.4471i | 0.486953 | + | 0.453792i | ||||
\(531\) | −46.1968 | + | 26.6717i | −2.00477 | + | 1.15745i | ||||
\(532\) | 35.8208 | 1.55303 | ||||||||
\(533\) | 2.92959 | − | 5.07420i | 0.126895 | − | 0.219788i | ||||
\(534\) | 5.36524 | − | 9.29286i | 0.232176 | − | 0.402141i | ||||
\(535\) | 10.8253 | + | 10.0882i | 0.468020 | + | 0.436149i | ||||
\(536\) | 0.0243958 | − | 0.0140849i | 0.00105374 | − | 0.000608375i | ||||
\(537\) | 11.4575 | + | 19.8449i | 0.494426 | + | 0.856370i | ||||
\(538\) | −7.88693 | + | 13.6606i | −0.340030 | + | 0.588949i | ||||
\(539\) | 21.7802 | − | 37.7244i | 0.938138 | − | 1.62490i | ||||
\(540\) | 10.1966 | + | 9.50226i | 0.438793 | + | 0.408912i | ||||
\(541\) | 20.4656i | 0.879886i | 0.898026 | + | 0.439943i | \(0.145001\pi\) | ||||
−0.898026 | + | 0.439943i | \(0.854999\pi\) | |||||||
\(542\) | −12.0183 | − | 20.8164i | −0.516232 | − | 0.894140i | ||||
\(543\) | −61.4192 | − | 35.4604i | −2.63575 | − | 1.52175i | ||||
\(544\) | −0.452798 | −0.0194136 | ||||||||
\(545\) | 7.52439 | − | 32.6406i | 0.322309 | − | 1.39817i | ||||
\(546\) | 8.34712 | − | 14.4576i | 0.357224 | − | 0.618729i | ||||
\(547\) | 2.51196 | 0.107404 | 0.0537018 | − | 0.998557i | \(-0.482898\pi\) | ||||
0.0537018 | + | 0.998557i | \(0.482898\pi\) | |||||||
\(548\) | 8.15662 | − | 4.70923i | 0.348434 | − | 0.201168i | ||||
\(549\) | 32.5922i | 1.39100i | ||||||||
\(550\) | 0.959934 | + | 13.5995i | 0.0409317 | + | 0.579884i | ||||
\(551\) | 30.5630 | + | 52.9367i | 1.30203 | + | 2.25518i | ||||
\(552\) | −17.3978 | + | 10.0446i | −0.740500 | + | 0.427528i | ||||
\(553\) | 24.6685 | − | 42.7272i | 1.04901 | − | 1.81694i | ||||
\(554\) | 16.9996 | 0.722246 | ||||||||
\(555\) | −10.8246 | − | 37.3635i | −0.459479 | − | 1.58599i | ||||
\(556\) | 8.65305 | 0.366971 | ||||||||
\(557\) | 12.6417 | − | 21.8961i | 0.535646 | − | 0.927766i | −0.463486 | − | 0.886104i | \(-0.653402\pi\) |
0.999132 | − | 0.0416616i | \(-0.0132651\pi\) | |||||||
\(558\) | −6.86639 | + | 3.96431i | −0.290677 | + | 0.167823i | ||||
\(559\) | 4.64231 | + | 8.04072i | 0.196349 | + | 0.340086i | ||||
\(560\) | −10.2488 | + | 3.13704i | −0.433090 | + | 0.132564i | ||||
\(561\) | 3.53101i | 0.149079i | ||||||||
\(562\) | 16.1845 | − | 9.34413i | 0.682702 | − | 0.394158i | ||||
\(563\) | −7.66929 | −0.323222 | −0.161611 | − | 0.986855i | \(-0.551669\pi\) | ||||
−0.161611 | + | 0.986855i | \(0.551669\pi\) | |||||||
\(564\) | 4.10939 | − | 7.11767i | 0.173036 | − | 0.299708i | ||||
\(565\) | −3.16669 | − | 0.729993i | −0.133224 | − | 0.0307110i | ||||
\(566\) | 0.441884 | 0.0185738 | ||||||||
\(567\) | 9.49957 | + | 5.48458i | 0.398945 | + | 0.230331i | ||||
\(568\) | 0.101250 | + | 0.175370i | 0.00424836 | + | 0.00735838i | ||||
\(569\) | 14.3157i | 0.600147i | 0.953916 | + | 0.300074i | \(0.0970113\pi\) | ||||
−0.953916 | + | 0.300074i | \(0.902989\pi\) | |||||||
\(570\) | −32.5821 | + | 34.9630i | −1.36471 | + | 1.46444i | ||||
\(571\) | 19.3284 | − | 33.4777i | 0.808867 | − | 1.40100i | −0.104782 | − | 0.994495i | \(-0.533415\pi\) |
0.913649 | − | 0.406504i | \(-0.133252\pi\) | |||||||
\(572\) | −1.66024 | + | 2.87562i | −0.0694182 | + | 0.120236i | ||||
\(573\) | −8.99437 | − | 15.5787i | −0.375745 | − | 0.650810i | ||||
\(574\) | −19.9725 | + | 11.5311i | −0.833635 | + | 0.481300i | ||||
\(575\) | −29.1041 | + | 19.6587i | −1.21372 | + | 0.819826i | ||||
\(576\) | 2.58973 | − | 4.48555i | 0.107905 | − | 0.186898i | ||||
\(577\) | −11.0994 | + | 19.2247i | −0.462073 | + | 0.800335i | −0.999064 | − | 0.0432535i | \(-0.986228\pi\) |
0.536991 | + | 0.843588i | \(0.319561\pi\) | |||||||
\(578\) | 16.7950 | 0.698579 | ||||||||
\(579\) | 36.7146 | − | 21.1972i | 1.52581 | − | 0.880924i | ||||
\(580\) | −13.3804 | − | 12.4693i | −0.555593 | − | 0.517758i | ||||
\(581\) | 32.0263 | 1.32868 | ||||||||
\(582\) | − | 45.1598i | − | 1.87194i | ||||||
\(583\) | −16.1823 | − | 9.34288i | −0.670204 | − | 0.386943i | ||||
\(584\) | − | 1.18787i | − | 0.0491545i | ||||||
\(585\) | 4.12801 | + | 13.4863i | 0.170672 | + | 0.557589i | ||||
\(586\) | − | 4.76349i | − | 0.196778i | ||||||
\(587\) | 6.18890 | + | 10.7195i | 0.255443 | + | 0.442441i | 0.965016 | − | 0.262192i | \(-0.0844452\pi\) |
−0.709572 | + | 0.704632i | \(0.751112\pi\) | |||||||
\(588\) | −39.5688 | + | 22.8450i | −1.63179 | + | 0.942114i | ||||
\(589\) | −5.71984 | − | 9.90705i | −0.235682 | − | 0.408213i | ||||
\(590\) | 16.8477 | + | 15.7005i | 0.693611 | + | 0.646377i | ||||
\(591\) | −54.0248 | −2.22228 | ||||||||
\(592\) | −5.31298 | + | 2.96180i | −0.218362 | + | 0.121729i | ||||
\(593\) | 44.0752i | 1.80995i | 0.425463 | + | 0.904976i | \(0.360111\pi\) | ||||
−0.425463 | + | 0.904976i | \(0.639889\pi\) | |||||||
\(594\) | −14.7188 | − | 8.49793i | −0.603922 | − | 0.348674i | ||||
\(595\) | −4.64063 | + | 1.42045i | −0.190247 | + | 0.0582326i | ||||
\(596\) | −2.15001 | − | 3.72393i | −0.0880679 | − | 0.152538i | ||||
\(597\) | −25.3252 | − | 43.8646i | −1.03649 | − | 1.79526i | ||||
\(598\) | −8.55405 | −0.349801 | ||||||||
\(599\) | −20.8173 | − | 36.0565i | −0.850570 | − | 1.47323i | −0.880695 | − | 0.473685i | \(-0.842924\pi\) |
0.0301245 | − | 0.999546i | \(-0.490410\pi\) | |||||||
\(600\) | 6.26022 | − | 12.8568i | 0.255572 | − | 0.524875i | ||||
\(601\) | −2.02155 | + | 3.50143i | −0.0824607 | + | 0.142826i | −0.904306 | − | 0.426884i | \(-0.859611\pi\) |
0.821846 | + | 0.569710i | \(0.192945\pi\) | |||||||
\(602\) | − | 36.5451i | − | 1.48947i | ||||||
\(603\) | 0.145904i | 0.00594169i | ||||||||
\(604\) | −0.465325 | + | 0.805967i | −0.0189338 | + | 0.0327943i | ||||
\(605\) | 2.33337 | + | 7.62315i | 0.0948648 | + | 0.309925i | ||||
\(606\) | 18.0105i | 0.731628i | ||||||||
\(607\) | 12.6098 | − | 21.8408i | 0.511815 | − | 0.886490i | −0.488091 | − | 0.872793i | \(-0.662307\pi\) |
0.999906 | − | 0.0136974i | \(-0.00436017\pi\) | |||||||
\(608\) | 6.47189 | + | 3.73655i | 0.262470 | + | 0.151537i | ||||
\(609\) | −97.1074 | − | 56.0650i | −3.93499 | − | 2.27187i | ||||
\(610\) | 13.4545 | − | 4.11827i | 0.544755 | − | 0.166744i | ||||
\(611\) | 3.03071 | − | 1.74978i | 0.122610 | − | 0.0707887i | ||||
\(612\) | 1.17263 | − | 2.03105i | 0.0474006 | − | 0.0821002i | ||||
\(613\) | −33.6551 | − | 19.4308i | −1.35932 | − | 0.784802i | −0.369785 | − | 0.929117i | \(-0.620569\pi\) |
−0.989532 | + | 0.144315i | \(0.953902\pi\) | |||||||
\(614\) | −2.57050 | − | 1.48408i | −0.103737 | − | 0.0598926i | ||||
\(615\) | 6.91170 | − | 29.9827i | 0.278707 | − | 1.20902i | ||||
\(616\) | 11.3187 | − | 6.53485i | 0.456043 | − | 0.263297i | ||||
\(617\) | 35.5323 | + | 20.5146i | 1.43048 | + | 0.825886i | 0.997157 | − | 0.0753540i | \(-0.0240087\pi\) |
0.433320 | + | 0.901240i | \(0.357342\pi\) | |||||||
\(618\) | − | 24.3867i | − | 0.980976i | ||||||
\(619\) | 35.0195 | 1.40755 | 0.703775 | − | 0.710423i | \(-0.251496\pi\) | ||||
0.703775 | + | 0.710423i | \(0.251496\pi\) | |||||||
\(620\) | 2.50414 | + | 2.33361i | 0.100569 | + | 0.0937201i | ||||
\(621\) | − | 43.7838i | − | 1.75698i | ||||||
\(622\) | −21.7036 | + | 12.5306i | −0.870235 | + | 0.502430i | ||||
\(623\) | −17.9842 | −0.720521 | ||||||||
\(624\) | 3.01622 | − | 1.74141i | 0.120745 | − | 0.0697124i | ||||
\(625\) | 9.33474 | − | 23.1919i | 0.373390 | − | 0.927675i | ||||
\(626\) | −8.91834 | − | 15.4470i | −0.356449 | − | 0.617387i | ||||
\(627\) | 29.1383 | − | 50.4691i | 1.16367 | − | 2.01554i | ||||
\(628\) | − | 0.696723i | − | 0.0278023i | ||||||
\(629\) | −2.40571 | + | 1.34110i | −0.0959219 | + | 0.0534730i | ||||
\(630\) | 12.4702 | − | 54.0955i | 0.496826 | − | 2.15521i | ||||
\(631\) | −10.5341 | − | 6.08185i | −0.419355 | − | 0.242115i | 0.275446 | − | 0.961316i | \(-0.411174\pi\) |
−0.694801 | + | 0.719202i | \(0.744508\pi\) | |||||||
\(632\) | 8.91394 | − | 5.14647i | 0.354578 | − | 0.204715i | ||||
\(633\) | −21.1673 | + | 12.2209i | −0.841324 | + | 0.485739i | ||||
\(634\) | −3.90982 | + | 2.25733i | −0.155279 | + | 0.0896502i | ||||
\(635\) | −6.72719 | + | 29.1823i | −0.266960 | + | 1.15806i | ||||
\(636\) | 9.79967 | + | 16.9735i | 0.388582 | + | 0.673044i | ||||
\(637\) | −19.4549 | −0.770832 | ||||||||
\(638\) | 19.3147 | + | 11.1513i | 0.764675 | + | 0.441485i | ||||
\(639\) | −1.04884 | −0.0414916 | ||||||||
\(640\) | −2.17892 | − | 0.502291i | −0.0861295 | − | 0.0198548i | ||||
\(641\) | −5.79442 | + | 10.0362i | −0.228866 | + | 0.396407i | −0.957472 | − | 0.288525i | \(-0.906835\pi\) |
0.728606 | + | 0.684933i | \(0.240168\pi\) | |||||||
\(642\) | 9.46299 | + | 16.3904i | 0.373475 | + | 0.646877i | ||||
\(643\) | 41.4828 | 1.63592 | 0.817962 | − | 0.575273i | \(-0.195104\pi\) | ||||
0.817962 | + | 0.575273i | \(0.195104\pi\) | |||||||
\(644\) | 29.1586 | + | 16.8347i | 1.14901 | + | 0.663381i | ||||
\(645\) | 35.6699 | + | 33.2409i | 1.40450 | + | 1.30886i | ||||
\(646\) | 2.93046 | + | 1.69190i | 0.115297 | + | 0.0665670i | ||||
\(647\) | 15.5065 | + | 26.8580i | 0.609622 | + | 1.05590i | 0.991303 | + | 0.131602i | \(0.0420120\pi\) |
−0.381681 | + | 0.924294i | \(0.624655\pi\) | |||||||
\(648\) | 1.14422 | + | 1.98185i | 0.0449492 | + | 0.0778543i | ||||
\(649\) | −24.3197 | − | 14.0410i | −0.954633 | − | 0.551158i | ||||
\(650\) | 5.04570 | − | 3.40819i | 0.197909 | − | 0.133680i | ||||
\(651\) | 18.1736 | + | 10.4925i | 0.712278 | + | 0.411234i | ||||
\(652\) | 9.88597 | 0.387165 | ||||||||
\(653\) | −4.23528 | − | 7.33571i | −0.165739 | − | 0.287069i | 0.771178 | − | 0.636619i | \(-0.219668\pi\) |
−0.936918 | + | 0.349551i | \(0.886334\pi\) | |||||||
\(654\) | 21.4214 | − | 37.1030i | 0.837643 | − | 1.45084i | ||||
\(655\) | −3.18495 | + | 13.8162i | −0.124446 | + | 0.539844i | ||||
\(656\) | −4.81135 | −0.187852 | ||||||||
\(657\) | 5.32826 | + | 3.07627i | 0.207875 | + | 0.120017i | ||||
\(658\) | −13.7746 | −0.536990 | ||||||||
\(659\) | −6.79380 | − | 11.7672i | −0.264649 | − | 0.458385i | 0.702823 | − | 0.711365i | \(-0.251923\pi\) |
−0.967472 | + | 0.252980i | \(0.918589\pi\) | |||||||
\(660\) | −3.91696 | + | 16.9917i | −0.152468 | + | 0.661399i | ||||
\(661\) | 21.0739 | − | 12.1670i | 0.819679 | − | 0.473242i | −0.0306266 | − | 0.999531i | \(-0.509750\pi\) |
0.850306 | + | 0.526289i | \(0.176417\pi\) | |||||||
\(662\) | −19.8565 | + | 11.4642i | −0.771745 | + | 0.445567i | ||||
\(663\) | 1.36574 | − | 0.788509i | 0.0530409 | − | 0.0306232i | ||||
\(664\) | 5.78633 | + | 3.34074i | 0.224553 | + | 0.129646i | ||||
\(665\) | 78.0507 | + | 17.9925i | 3.02668 | + | 0.697718i | ||||
\(666\) | 0.473924 | − | 31.5019i | 0.0183642 | − | 1.22067i | ||||
\(667\) | 57.4549i | 2.22466i | ||||||||
\(668\) | 7.01504 | − | 12.1504i | 0.271420 | − | 0.470114i | ||||
\(669\) | −33.3000 | − | 57.6772i | −1.28745 | − | 2.22993i | ||||
\(670\) | 0.0602312 | − | 0.0184361i | 0.00232693 | − | 0.000712250i | ||||
\(671\) | −14.8590 | + | 8.57887i | −0.573627 | + | 0.331184i | ||||
\(672\) | −13.7087 | −0.528825 | ||||||||
\(673\) | −39.5674 | + | 22.8442i | −1.52521 | + | 0.880580i | −0.525656 | + | 0.850697i | \(0.676180\pi\) |
−0.999553 | + | 0.0298833i | \(0.990486\pi\) | |||||||
\(674\) | 11.4674i | 0.441708i | ||||||||
\(675\) | 17.4448 | + | 25.8264i | 0.671450 | + | 0.994058i | ||||
\(676\) | −11.5170 | −0.442962 | ||||||||
\(677\) | 34.8450i | 1.33920i | 0.742722 | + | 0.669600i | \(0.233535\pi\) | ||||
−0.742722 | + | 0.669600i | \(0.766465\pi\) | |||||||
\(678\) | −3.59962 | − | 2.07824i | −0.138242 | − | 0.0798143i | ||||
\(679\) | −65.5473 | + | 37.8438i | −2.51548 | + | 1.45231i | ||||
\(680\) | −0.986612 | − | 0.227437i | −0.0378349 | − | 0.00872179i | ||||
\(681\) | 7.46742 | + | 4.31132i | 0.286152 | + | 0.165210i | ||||
\(682\) | −3.61472 | − | 2.08696i | −0.138415 | − | 0.0799139i | ||||
\(683\) | −1.96909 | + | 3.41056i | −0.0753450 | + | 0.130501i | −0.901236 | − | 0.433328i | \(-0.857339\pi\) |
0.825891 | + | 0.563829i | \(0.190672\pi\) | |||||||
\(684\) | −33.5209 | + | 19.3533i | −1.28170 | + | 0.739992i | ||||
\(685\) | 20.1380 | − | 6.16404i | 0.769435 | − | 0.235516i | ||||
\(686\) | 37.2592 | + | 21.5116i | 1.42256 | + | 0.821316i | ||||
\(687\) | −3.98689 | − | 2.30183i | −0.152109 | − | 0.0878204i | ||||
\(688\) | 3.81210 | − | 6.60275i | 0.145335 | − | 0.251728i | ||||
\(689\) | 8.34544i | 0.317936i | ||||||||
\(690\) | −42.9538 | + | 13.1477i | −1.63522 | + | 0.500525i | ||||
\(691\) | 4.62702 | − | 8.01424i | 0.176020 | − | 0.304876i | −0.764494 | − | 0.644631i | \(-0.777011\pi\) |
0.940514 | + | 0.339755i | \(0.110344\pi\) | |||||||
\(692\) | 3.98026i | 0.151307i | ||||||||
\(693\) | 67.6940i | 2.57148i | ||||||||
\(694\) | 5.68500 | − | 9.84670i | 0.215800 | − | 0.373776i | ||||
\(695\) | 18.8543 | + | 4.34635i | 0.715186 | + | 0.164867i | ||||
\(696\) | −11.6965 | − | 20.2590i | −0.443356 | − | 0.767916i | ||||
\(697\) | −2.17857 | −0.0825193 | ||||||||
\(698\) | −2.53073 | − | 4.38336i | −0.0957896 | − | 0.165913i | ||||
\(699\) | 27.9153 | + | 48.3507i | 1.05585 | + | 1.82879i | ||||
\(700\) | −23.9070 | + | 1.68750i | −0.903600 | + | 0.0637816i | ||||
\(701\) | 27.8917 | + | 16.1033i | 1.05346 | + | 0.608213i | 0.923615 | − | 0.383321i | \(-0.125220\pi\) |
0.129841 | + | 0.991535i | \(0.458553\pi\) | |||||||
\(702\) | 7.59069i | 0.286492i | ||||||||
\(703\) | 45.4519 | + | 0.683794i | 1.71425 | + | 0.0257898i | ||||
\(704\) | 2.72666 | 0.102765 | ||||||||
\(705\) | 12.5292 | − | 13.4447i | 0.471876 | − | 0.506358i | ||||
\(706\) | 10.0780 | + | 17.4557i | 0.379292 | + | 0.656953i | ||||
\(707\) | 26.1414 | − | 15.0928i | 0.983150 | − | 0.567622i | ||||
\(708\) | 14.7275 | + | 25.5088i | 0.553493 | + | 0.958678i | ||||
\(709\) | − | 2.61309i | − | 0.0981367i | −0.998795 | − | 0.0490683i | \(-0.984375\pi\) | ||
0.998795 | − | 0.0490683i | \(-0.0156252\pi\) | |||||||
\(710\) | 0.132529 | + | 0.432976i | 0.00497373 | + | 0.0162493i | ||||
\(711\) | 53.3119i | 1.99935i | ||||||||
\(712\) | −3.24928 | − | 1.87597i | −0.121772 | − | 0.0703050i | ||||
\(713\) | − | 10.7526i | − | 0.402689i | ||||||
\(714\) | −6.20728 | −0.232302 | ||||||||
\(715\) | −5.06194 | + | 5.43184i | −0.189306 | + | 0.203139i | ||||
\(716\) | 6.93883 | − | 4.00614i | 0.259316 | − | 0.149716i | ||||
\(717\) | −18.7513 | −0.700279 | ||||||||
\(718\) | −2.38391 | + | 4.12905i | −0.0889666 | + | 0.154095i | ||||
\(719\) | −5.84379 | + | 10.1217i | −0.217937 | + | 0.377477i | −0.954177 | − | 0.299243i | \(-0.903266\pi\) |
0.736240 | + | 0.676720i | \(0.236599\pi\) | |||||||
\(720\) | 7.89587 | − | 8.47286i | 0.294262 | − | 0.315765i | ||||
\(721\) | −35.3961 | + | 20.4359i | −1.31822 | + | 0.761074i | ||||
\(722\) | −18.4236 | − | 31.9106i | −0.685655 | − | 1.18759i | ||||
\(723\) | 13.8886 | − | 24.0557i | 0.516522 | − | 0.894643i | ||||
\(724\) | −12.3988 | + | 21.4754i | −0.460799 | + | 0.798128i | ||||
\(725\) | −22.8917 | − | 33.8904i | −0.850178 | − | 1.25866i | ||||
\(726\) | 10.1967i | 0.378435i | ||||||||
\(727\) | 10.9295 | + | 18.9305i | 0.405354 | + | 0.702093i | 0.994363 | − | 0.106033i | \(-0.0338150\pi\) |
−0.589009 | + | 0.808127i | \(0.700482\pi\) | |||||||
\(728\) | −5.05516 | − | 2.91860i | −0.187357 | − | 0.108170i | ||||
\(729\) | 41.6276 | 1.54176 | ||||||||
\(730\) | 0.596658 | − | 2.58828i | 0.0220833 | − | 0.0957967i | ||||
\(731\) | 1.72611 | − | 2.98972i | 0.0638426 | − | 0.110579i | ||||
\(732\) | 17.9966 | 0.665174 | ||||||||
\(733\) | −2.21236 | + | 1.27731i | −0.0817153 | + | 0.0471784i | −0.540301 | − | 0.841472i | \(-0.681690\pi\) |
0.458586 | + | 0.888650i | \(0.348356\pi\) | |||||||
\(734\) | 22.0130i | 0.812515i | ||||||||
\(735\) | −97.6922 | + | 29.9025i | −3.60343 | + | 1.10297i | ||||
\(736\) | 3.51214 | + | 6.08320i | 0.129459 | + | 0.224230i | ||||
\(737\) | −0.0665190 | + | 0.0384048i | −0.00245026 | + | 0.00141466i | ||||
\(738\) | 12.4601 | − | 21.5815i | 0.458663 | − | 0.794427i | ||||
\(739\) | −9.05174 | −0.332974 | −0.166487 | − | 0.986044i | \(-0.553242\pi\) | ||||
−0.166487 | + | 0.986044i | \(0.553242\pi\) | |||||||
\(740\) | −13.0643 | + | 3.78486i | −0.480252 | + | 0.139134i | ||||
\(741\) | −26.0275 | −0.956145 | ||||||||
\(742\) | 16.4242 | − | 28.4475i | 0.602950 | − | 1.04434i | ||||
\(743\) | 13.0291 | − | 7.52236i | 0.477992 | − | 0.275969i | −0.241587 | − | 0.970379i | \(-0.577668\pi\) |
0.719579 | + | 0.694410i | \(0.244335\pi\) | |||||||
\(744\) | 2.18900 | + | 3.79146i | 0.0802526 | + | 0.139001i | ||||
\(745\) | −2.81421 | − | 9.19409i | −0.103105 | − | 0.336845i | ||||
\(746\) | 0.803940i | 0.0294343i | ||||||||
\(747\) | −29.9701 | + | 17.3032i | −1.09655 | + | 0.633092i | ||||
\(748\) | 1.23463 | 0.0451425 | ||||||||
\(749\) | 15.8599 | − | 27.4702i | 0.579508 | − | 1.00374i | ||||
\(750\) | 20.0984 | − | 24.8694i | 0.733889 | − | 0.908103i | ||||
\(751\) | −53.5679 | −1.95472 | −0.977360 | − | 0.211582i | \(-0.932139\pi\) | ||||
−0.977360 | + | 0.211582i | \(0.932139\pi\) | |||||||
\(752\) | −2.48872 | − | 1.43686i | −0.0907541 | − | 0.0523969i | ||||
\(753\) | 25.4579 | + | 44.0943i | 0.927736 | + | 1.60689i | ||||
\(754\) | − | 9.96082i | − | 0.362752i | ||||||
\(755\) | −1.41874 | + | 1.52241i | −0.0516332 | + | 0.0554062i | ||||
\(756\) | 14.9388 | − | 25.8748i | 0.543319 | − | 0.941056i | ||||
\(757\) | 9.72544 | − | 16.8450i | 0.353477 | − | 0.612241i | −0.633379 | − | 0.773842i | \(-0.718333\pi\) |
0.986856 | + | 0.161601i | \(0.0516658\pi\) | |||||||
\(758\) | −0.189378 | − | 0.328013i | −0.00687853 | − | 0.0119140i | ||||
\(759\) | 47.4380 | − | 27.3883i | 1.72189 | − | 0.994134i | ||||
\(760\) | 12.2249 | + | 11.3924i | 0.443444 | + | 0.413247i | ||||
\(761\) | −16.5499 | + | 28.6652i | −0.599932 | + | 1.03911i | 0.392898 | + | 0.919582i | \(0.371472\pi\) |
−0.992830 | + | 0.119531i | \(0.961861\pi\) | |||||||
\(762\) | −19.1518 | + | 33.1719i | −0.693798 | + | 1.20169i | ||||
\(763\) | −71.8042 | −2.59949 | ||||||||
\(764\) | −5.44715 | + | 3.14491i | −0.197071 | + | 0.113779i | ||||
\(765\) | 3.57524 | − | 3.83649i | 0.129263 | − | 0.138709i | ||||
\(766\) | 0.719146 | 0.0259838 | ||||||||
\(767\) | 12.5420i | 0.452865i | ||||||||
\(768\) | −2.47681 | − | 1.42999i | −0.0893742 | − | 0.0516002i | ||||
\(769\) | 6.77792i | 0.244418i | 0.992504 | + | 0.122209i | \(0.0389978\pi\) | ||||
−0.992504 | + | 0.122209i | \(0.961002\pi\) | |||||||
\(770\) | 27.9450 | − | 8.55366i | 1.00707 | − | 0.308252i | ||||
\(771\) | 58.9670i | 2.12365i | ||||||||
\(772\) | −7.41166 | − | 12.8374i | −0.266751 | − | 0.462027i | ||||
\(773\) | 23.2941 | − | 13.4489i | 0.837831 | − | 0.483722i | −0.0186952 | − | 0.999825i | \(-0.505951\pi\) |
0.856526 | + | 0.516103i | \(0.172618\pi\) | |||||||
\(774\) | 19.7446 | + | 34.1987i | 0.709706 | + | 1.22925i | ||||
\(775\) | 4.28417 | + | 6.34256i | 0.153892 | + | 0.227832i | ||||
\(776\) | −15.7903 | −0.566838 | ||||||||
\(777\) | −72.8341 | + | 40.6024i | −2.61291 | + | 1.45660i | ||||
\(778\) | 13.6538i | 0.489512i | ||||||||
\(779\) | 31.1386 | + | 17.9779i | 1.11565 | + | 0.644124i | ||||
\(780\) | 7.44680 | − | 2.27939i | 0.266638 | − | 0.0816152i | ||||
\(781\) | −0.276075 | − | 0.478176i | −0.00987874 | − | 0.0171105i | ||||
\(782\) | 1.59029 | + | 2.75446i | 0.0568687 | + | 0.0984994i | ||||
\(783\) | 50.9843 | 1.82203 | ||||||||
\(784\) | 7.98785 | + | 13.8354i | 0.285280 | + | 0.494120i | ||||
\(785\) | 0.349958 | − | 1.51811i | 0.0124905 | − | 0.0541835i | ||||
\(786\) | −9.06732 | + | 15.7051i | −0.323421 | + | 0.560181i | ||||
\(787\) | − | 32.7991i | − | 1.16916i | −0.811335 | − | 0.584581i | \(-0.801259\pi\) | ||
0.811335 | − | 0.584581i | \(-0.198741\pi\) | |||||||
\(788\) | 18.8899i | 0.672926i | ||||||||
\(789\) | 39.6439 | − | 68.6652i | 1.41136 | − | 2.44454i | ||||
\(790\) | 22.0078 | − | 6.73636i | 0.783003 | − | 0.239669i | ||||
\(791\) | 6.96623i | 0.247691i | ||||||||
\(792\) | −7.06132 | + | 12.2306i | −0.250913 | + | 0.434594i | ||||
\(793\) | 6.63634 | + | 3.83149i | 0.235663 | + | 0.136060i | ||||
\(794\) | 13.3178 | + | 7.68902i | 0.472630 | + | 0.272873i | ||||
\(795\) | 12.8271 | + | 41.9063i | 0.454929 | + | 1.48626i | ||||
\(796\) | −15.3374 | + | 8.85505i | −0.543619 | + | 0.313859i | ||||
\(797\) | −18.6926 | + | 32.3766i | −0.662127 | + | 1.14684i | 0.317929 | + | 0.948115i | \(0.397013\pi\) |
−0.980056 | + | 0.198723i | \(0.936321\pi\) | |||||||
\(798\) | 88.7213 | + | 51.2233i | 3.14070 | + | 1.81328i | ||||
\(799\) | −1.12689 | − | 0.650608i | −0.0398664 | − | 0.0230169i | ||||
\(800\) | −4.49541 | − | 2.18891i | −0.158937 | − | 0.0773896i | ||||
\(801\) | 16.8295 | − | 9.71653i | 0.594642 | − | 0.343317i | ||||
\(802\) | −26.6084 | − | 15.3624i | −0.939574 | − | 0.542463i | ||||
\(803\) | 3.23893i | 0.114299i | ||||||||
\(804\) | 0.0805650 | 0.00284131 | ||||||||
\(805\) | 55.0784 | + | 51.3277i | 1.94126 | + | 1.80906i | ||||
\(806\) | 1.86416i | 0.0656622i | ||||||||
\(807\) | −39.0689 | + | 22.5564i | −1.37529 | + | 0.794024i | ||||
\(808\) | 6.29744 | 0.221543 | ||||||||
\(809\) | 3.73688 | − | 2.15749i | 0.131382 | − | 0.0758533i | −0.432869 | − | 0.901457i | \(-0.642499\pi\) |
0.564250 | + | 0.825604i | \(0.309165\pi\) | |||||||
\(810\) | 1.49770 | + | 4.89302i | 0.0526239 | + | 0.171923i | ||||
\(811\) | −12.2356 | − | 21.1926i | −0.429649 | − | 0.744173i | 0.567193 | − | 0.823585i | \(-0.308029\pi\) |
−0.996842 | + | 0.0794116i | \(0.974696\pi\) | |||||||
\(812\) | −19.6033 | + | 33.9539i | −0.687942 | + | 1.19155i | ||||
\(813\) | − | 68.7444i | − | 2.41097i | ||||||
\(814\) | 14.4867 | − | 8.07582i | 0.507759 | − | 0.283057i | ||||
\(815\) | 21.5408 | + | 4.96564i | 0.754540 | + | 0.173939i | ||||
\(816\) | −1.12150 | − | 0.647496i | −0.0392602 | − | 0.0226669i | ||||
\(817\) | −49.3430 | + | 28.4882i | −1.72629 | + | 0.996676i | ||||
\(818\) | −7.04079 | + | 4.06500i | −0.246175 | + | 0.142129i | ||||
\(819\) | 26.1830 | − | 15.1168i | 0.914908 | − | 0.528222i | ||||
\(820\) | −10.4836 | − | 2.41670i | −0.366102 | − | 0.0843948i | ||||
\(821\) | 4.53720 | + | 7.85866i | 0.158349 | + | 0.274269i | 0.934274 | − | 0.356557i | \(-0.116049\pi\) |
−0.775924 | + | 0.630826i | \(0.782716\pi\) | |||||||
\(822\) | 26.9365 | 0.939520 | ||||||||
\(823\) | 18.6688 | + | 10.7784i | 0.650753 | + | 0.375712i | 0.788745 | − | 0.614721i | \(-0.210731\pi\) |
−0.137992 | + | 0.990433i | \(0.544065\pi\) | |||||||
\(824\) | −8.52688 | −0.297048 | ||||||||
\(825\) | −17.0695 | + | 35.0560i | −0.594284 | + | 1.22049i | ||||
\(826\) | 24.6832 | − | 42.7525i | 0.858837 | − | 1.48755i | ||||
\(827\) | −26.5009 | − | 45.9009i | −0.921526 | − | 1.59613i | −0.797055 | − | 0.603907i | \(-0.793610\pi\) |
−0.124471 | − | 0.992223i | \(-0.539723\pi\) | |||||||
\(828\) | −36.3820 | −1.26436 | ||||||||
\(829\) | −17.8018 | − | 10.2779i | −0.618283 | − | 0.356966i | 0.157917 | − | 0.987452i | \(-0.449522\pi\) |
−0.776200 | + | 0.630487i | \(0.782855\pi\) | |||||||
\(830\) | 10.9299 | + | 10.1856i | 0.379384 | + | 0.353549i | ||||
\(831\) | 42.1049 | + | 24.3093i | 1.46060 | + | 0.843280i | ||||
\(832\) | −0.608891 | − | 1.05463i | −0.0211095 | − | 0.0365627i | ||||
\(833\) | 3.61688 | + | 6.26462i | 0.125318 | + | 0.217056i | ||||
\(834\) | 21.4320 | + | 12.3738i | 0.742129 | + | 0.428468i | ||||
\(835\) | 21.3883 | − | 22.9512i | 0.740172 | − | 0.794260i | ||||
\(836\) | −17.6467 | − | 10.1883i | −0.610323 | − | 0.352370i | ||||
\(837\) | −9.54167 | −0.329808 | ||||||||
\(838\) | 5.36246 | + | 9.28806i | 0.185243 | + | 0.320851i | ||||
\(839\) | 22.5116 | − | 38.9912i | 0.777186 | − | 1.34612i | −0.156372 | − | 0.987698i | \(-0.549980\pi\) |
0.933558 | − | 0.358427i | \(-0.116687\pi\) | |||||||
\(840\) | −29.8702 | − | 6.88577i | −1.03062 | − | 0.237581i | ||||
\(841\) | −37.9037 | −1.30703 | ||||||||
\(842\) | 30.9837 | + | 17.8884i | 1.06777 | + | 0.616477i | ||||
\(843\) | 53.4479 | 1.84085 | ||||||||
\(844\) | 4.27309 | + | 7.40121i | 0.147086 | + | 0.254760i | ||||
\(845\) | −25.0947 | − | 5.78489i | −0.863283 | − | 0.199006i | ||||
\(846\) | 12.8902 | − | 7.44216i | 0.443174 | − | 0.255867i | ||||
\(847\) | 14.8000 | − | 8.54479i | 0.508534 | − | 0.293602i | ||||
\(848\) | 5.93485 | − | 3.42649i | 0.203804 | − | 0.117666i | ||||
\(849\) | 1.09446 | + | 0.631888i | 0.0375619 | + | 0.0216864i | ||||
\(850\) | −2.03551 | − | 0.991133i | −0.0698175 | − | 0.0339956i | ||||
\(851\) | 36.6771 | + | 21.9177i | 1.25728 | + | 0.751329i | ||||
\(852\) | 0.579146i | 0.0198412i | ||||||||
\(853\) | −8.02858 | + | 13.9059i | −0.274893 | + | 0.476129i | −0.970108 | − | 0.242673i | \(-0.921976\pi\) |
0.695215 | + | 0.718802i | \(0.255309\pi\) | |||||||
\(854\) | −15.0811 | − | 26.1212i | −0.516064 | − | 0.893850i | ||||
\(855\) | −82.7605 | + | 25.3321i | −2.83035 | + | 0.866340i | ||||
\(856\) | 5.73095 | − | 3.30877i | 0.195880 | − | 0.113091i | ||||
\(857\) | 50.9495 | 1.74040 | 0.870202 | − | 0.492696i | \(-0.163988\pi\) | ||||
0.870202 | + | 0.492696i | \(0.163988\pi\) | |||||||
\(858\) | −8.22421 | + | 4.74825i | −0.280770 | + | 0.162103i | ||||
\(859\) | − | 40.2983i | − | 1.37496i | −0.726203 | − | 0.687480i | \(-0.758717\pi\) | ||
0.726203 | − | 0.687480i | \(-0.241283\pi\) | |||||||
\(860\) | 11.6228 | − | 12.4721i | 0.396334 | − | 0.425295i | ||||
\(861\) | −65.9575 | −2.24782 | ||||||||
\(862\) | 2.46095i | 0.0838205i | ||||||||
\(863\) | 2.94309 | + | 1.69919i | 0.100184 | + | 0.0578411i | 0.549255 | − | 0.835655i | \(-0.314912\pi\) |
−0.449071 | + | 0.893496i | \(0.648245\pi\) | |||||||
\(864\) | 5.39812 | − | 3.11660i | 0.183648 | − | 0.106029i | ||||
\(865\) | −1.99925 | + | 8.67267i | −0.0679764 | + | 0.294880i | ||||
\(866\) | −27.0745 | − | 15.6315i | −0.920028 | − | 0.531178i | ||||
\(867\) | 41.5980 | + | 24.0166i | 1.41274 | + | 0.815647i | ||||
\(868\) | 3.66874 | − | 6.35445i | 0.124525 | − | 0.215684i | ||||
\(869\) | −24.3053 | + | 14.0327i | −0.824502 | + | 0.476026i | ||||
\(870\) | −15.3099 | − | 50.0179i | −0.519056 | − | 1.69577i | ||||
\(871\) | 0.0297087 | + | 0.0171523i | 0.00100664 | + | 0.000581185i | ||||
\(872\) | −12.9732 | − | 7.49007i | −0.439327 | − | 0.253646i | ||||
\(873\) | 40.8926 | − | 70.8280i | 1.38400 | − | 2.39717i | ||||
\(874\) | − | 52.4931i | − | 1.77561i | ||||||
\(875\) | −52.9391 | − | 8.33134i | −1.78967 | − | 0.281651i | ||||
\(876\) | 1.69864 | − | 2.94214i | 0.0573919 | − | 0.0994056i | ||||
\(877\) | − | 24.2792i | − | 0.819851i | −0.912119 | − | 0.409925i | \(-0.865555\pi\) | ||
0.912119 | − | 0.409925i | \(-0.134445\pi\) | |||||||
\(878\) | − | 22.8832i | − | 0.772271i | ||||||
\(879\) | 6.81173 | − | 11.7983i | 0.229754 | − | 0.397945i | ||||
\(880\) | 5.94119 | + | 1.36958i | 0.200277 | + | 0.0461685i | ||||
\(881\) | −27.2517 | − | 47.2013i | −0.918132 | − | 1.59025i | −0.802251 | − | 0.596987i | \(-0.796364\pi\) |
−0.115881 | − | 0.993263i | \(-0.536969\pi\) | |||||||
\(882\) | −82.7455 | −2.78619 | ||||||||
\(883\) | 1.62873 | + | 2.82104i | 0.0548111 | + | 0.0949356i | 0.892129 | − | 0.451781i | \(-0.149211\pi\) |
−0.837318 | + | 0.546716i | \(0.815878\pi\) | |||||||
\(884\) | −0.275705 | − | 0.477535i | −0.00927296 | − | 0.0160612i | ||||
\(885\) | 19.2772 | + | 62.9791i | 0.647997 | + | 2.11702i | ||||
\(886\) | 1.29833 | + | 0.749589i | 0.0436181 | + | 0.0251829i | ||||
\(887\) | 34.5745i | 1.16090i | 0.814296 | + | 0.580450i | \(0.197123\pi\) | ||||
−0.814296 | + | 0.580450i | \(0.802877\pi\) | |||||||
\(888\) | −17.3946 | − | 0.261690i | −0.583724 | − | 0.00878174i | ||||
\(889\) | 64.1966 | 2.15309 | ||||||||
\(890\) | −6.13764 | − | 5.71968i | −0.205734 | − | 0.191724i | ||||
\(891\) | −3.11990 | − | 5.40383i | −0.104521 | − | 0.181035i | ||||
\(892\) | −20.1670 | + | 11.6434i | −0.675242 | + | 0.389851i | ||||
\(893\) | 10.7378 | + | 18.5984i | 0.359327 | + | 0.622372i | ||||
\(894\) | − | 12.2980i | − | 0.411306i | ||||||
\(895\) | 17.1314 | − | 5.24375i | 0.572640 | − | 0.175279i | ||||
\(896\) | 4.79330i | 0.160133i | ||||||||
\(897\) | −21.1868 | − | 12.2322i | −0.707405 | − | 0.408421i | ||||
\(898\) | 26.2226i | 0.875061i | ||||||||
\(899\) | 12.5210 | 0.417598 | ||||||||
\(900\) | 21.4603 | − | 14.4957i | 0.715345 | − | 0.483189i | ||||
\(901\) | 2.68729 | − | 1.55151i | 0.0895266 | − | 0.0516882i | ||||
\(902\) | 13.1189 | 0.436813 | ||||||||
\(903\) | 52.2590 | − | 90.5153i | 1.73907 | − | 3.01216i | ||||
\(904\) | −0.726663 | + | 1.25862i | −0.0241685 | + | 0.0418610i | ||||
\(905\) | −37.8030 | + | 40.5655i | −1.25662 | + | 1.34844i | ||||
\(906\) | −2.30505 | + | 1.33082i | −0.0765801 | + | 0.0442135i | ||||
\(907\) | −15.9340 | − | 27.5984i | −0.529078 | − | 0.916390i | −0.999425 | − | 0.0339085i | \(-0.989205\pi\) |
0.470347 | − | 0.882482i | \(-0.344129\pi\) | |||||||
\(908\) | 1.50747 | − | 2.61101i | 0.0500270 | − | 0.0866493i | ||||
\(909\) | −16.3087 | + | 28.2475i | −0.540925 | + | 0.936910i | ||||
\(910\) | −9.54881 | − | 8.89856i | −0.316540 | − | 0.294984i | ||||
\(911\) | − | 16.4317i | − | 0.544406i | −0.962240 | − | 0.272203i | \(-0.912248\pi\) | ||
0.962240 | − | 0.272203i | \(-0.0877523\pi\) | |||||||
\(912\) | 10.6864 | + | 18.5095i | 0.353863 | + | 0.612909i | ||||
\(913\) | −15.7774 | − | 9.10907i | −0.522155 | − | 0.301466i | ||||
\(914\) | −32.4232 | −1.07246 | ||||||||
\(915\) | 39.2132 | + | 9.03954i | 1.29635 | + | 0.298838i | ||||
\(916\) | −0.804843 | + | 1.39403i | −0.0265928 | + | 0.0460600i | ||||
\(917\) | 30.3935 | 1.00368 | ||||||||
\(918\) | 2.44426 | − | 1.41119i | 0.0806725 | − | 0.0465763i | ||||
\(919\) | 41.6667i | 1.37446i | 0.726440 | + | 0.687229i | \(0.241173\pi\) | ||||
−0.726440 | + | 0.687229i | \(0.758827\pi\) | |||||||
\(920\) | 4.59714 | + | 15.0189i | 0.151563 | + | 0.495160i | ||||
\(921\) | −4.24443 | − | 7.35157i | −0.139859 | − | 0.242243i | ||||
\(922\) | 6.96252 | − | 4.01982i | 0.229299 | − | 0.132386i | ||||
\(923\) | −0.123301 | + | 0.213563i | −0.00405849 | + | 0.00702951i | ||||
\(924\) | 37.3790 | 1.22968 | ||||||||
\(925\) | −30.3671 | + | 1.68485i | −0.998464 | + | 0.0553976i | ||||
\(926\) | −16.2367 | −0.533572 | ||||||||
\(927\) | 22.0823 | − | 38.2477i | 0.725279 | − | 1.25622i | ||||
\(928\) | −7.08363 | + | 4.08974i | −0.232532 | + | 0.134252i | ||||
\(929\) | 8.74165 | + | 15.1410i | 0.286804 | + | 0.496760i | 0.973045 | − | 0.230615i | \(-0.0740737\pi\) |
−0.686241 | + | 0.727374i | \(0.740740\pi\) | |||||||
\(930\) | 2.86524 | + | 9.36080i | 0.0939550 | + | 0.306953i | ||||
\(931\) | − | 119.388i | − | 3.91278i | ||||||
\(932\) | 16.9060 | − | 9.76067i | 0.553773 | − | 0.319721i | ||||
\(933\) | −71.6743 | −2.34651 | ||||||||
\(934\) | 1.72188 | − | 2.98239i | 0.0563417 | − | 0.0975867i | ||||
\(935\) | 2.69016 | + | 0.620143i | 0.0879776 | + | 0.0202808i | ||||
\(936\) | 6.30746 | 0.206166 | ||||||||
\(937\) | 5.78313 | + | 3.33889i | 0.188927 | + | 0.109077i | 0.591480 | − | 0.806320i | \(-0.298544\pi\) |
−0.402553 | + | 0.915397i | \(0.631877\pi\) | |||||||
\(938\) | −0.0675131 | − | 0.116936i | −0.00220438 | − | 0.00381810i | ||||
\(939\) | − | 51.0125i | − | 1.66473i | ||||||
\(940\) | −4.70100 | − | 4.38087i | −0.153330 | − | 0.142888i | ||||
\(941\) | −9.59102 | + | 16.6121i | −0.312658 | + | 0.541540i | −0.978937 | − | 0.204163i | \(-0.934553\pi\) |
0.666279 | + | 0.745703i | \(0.267886\pi\) | |||||||
\(942\) | 0.996305 | − | 1.72565i | 0.0324614 | − | 0.0562248i | ||||
\(943\) | 16.8981 | + | 29.2684i | 0.550279 | + | 0.953112i | ||||
\(944\) | 8.91923 | − | 5.14952i | 0.290296 | − | 0.167603i | ||||
\(945\) | 45.5472 | − | 48.8755i | 1.48165 | − | 1.58992i | ||||
\(946\) | −10.3943 | + | 18.0035i | −0.337948 | + | 0.585344i | ||||
\(947\) | −6.35306 | + | 11.0038i | −0.206447 | + | 0.357576i | −0.950593 | − | 0.310441i | \(-0.899523\pi\) |
0.744146 | + | 0.668017i | \(0.232857\pi\) | |||||||
\(948\) | 29.4375 | 0.956087 | ||||||||
\(949\) | 1.25277 | − | 0.723286i | 0.0406666 | − | 0.0234788i | ||||
\(950\) | 20.9148 | + | 30.9637i | 0.678567 | + | 1.00459i | ||||
\(951\) | −12.9118 | −0.418695 | ||||||||
\(952\) | 2.17040i | 0.0703429i | ||||||||
\(953\) | −7.63027 | − | 4.40534i | −0.247169 | − | 0.142703i | 0.371298 | − | 0.928514i | \(-0.378913\pi\) |
−0.618467 | + | 0.785811i | \(0.712246\pi\) | |||||||
\(954\) | 35.4947i | 1.14918i | ||||||||
\(955\) | −13.4486 | + | 4.11647i | −0.435186 | + | 0.133206i | ||||
\(956\) | 6.55644i | 0.212051i | ||||||||
\(957\) | 31.8925 | + | 55.2395i | 1.03094 | + | 1.78564i | ||||
\(958\) | 5.67506 | − | 3.27650i | 0.183353 | − | 0.105859i | ||||
\(959\) | −22.5727 | − | 39.0971i | −0.728911 | − | 1.26251i | ||||
\(960\) | −4.67851 | − | 4.35991i | −0.150998 | − | 0.140716i | ||||
\(961\) | 28.6567 | 0.924410 | ||||||||
\(962\) | −6.35863 | − | 3.79982i | −0.205010 | − | 0.122511i | ||||
\(963\) | 34.2753i | 1.10450i | ||||||||
\(964\) | −8.41117 | − | 4.85619i | −0.270905 | − | 0.156407i | ||||
\(965\) | −9.70133 | − | 31.6944i | −0.312297 | − | 1.02028i | ||||
\(966\) | 48.1469 | + | 83.3929i | 1.54910 | + | 2.68312i | ||||
\(967\) | −28.7222 | − | 49.7484i | −0.923645 | − | 1.59980i | −0.793727 | − | 0.608275i | \(-0.791862\pi\) |
−0.129918 | − | 0.991525i | \(-0.541471\pi\) | |||||||
\(968\) | 3.56531 | 0.114593 | ||||||||
\(969\) | 4.83880 | + | 8.38105i | 0.155445 | + | 0.269238i | ||||
\(970\) | −34.4058 | − | 7.93132i | −1.10470 | − | 0.254659i | ||||
\(971\) | 1.39588 | − | 2.41774i | 0.0447959 | − | 0.0775888i | −0.842758 | − | 0.538292i | \(-0.819070\pi\) |
0.887554 | + | 0.460704i | \(0.152403\pi\) | |||||||
\(972\) | − | 12.1547i | − | 0.389864i | ||||||
\(973\) | − | 41.4766i | − | 1.32968i | ||||||
\(974\) | −2.48795 | + | 4.30925i | −0.0797190 | + | 0.138077i | ||||
\(975\) | 17.3709 | − | 1.22615i | 0.556315 | − | 0.0392681i | ||||
\(976\) | − | 6.29258i | − | 0.201420i | ||||||
\(977\) | 5.86092 | − | 10.1514i | 0.187507 | − | 0.324772i | −0.756911 | − | 0.653518i | \(-0.773292\pi\) |
0.944419 | + | 0.328745i | \(0.106626\pi\) | |||||||
\(978\) | 24.4857 | + | 14.1368i | 0.782966 | + | 0.452046i | ||||
\(979\) | 8.85969 | + | 5.11514i | 0.283157 | + | 0.163481i | ||||
\(980\) | 10.4555 | + | 34.1584i | 0.333989 | + | 1.09115i | ||||
\(981\) | 67.1941 | − | 38.7945i | 2.14534 | − | 1.23861i | ||||
\(982\) | −6.58035 | + | 11.3975i | −0.209987 | + | 0.363709i | ||||
\(983\) | 20.6403 | + | 11.9167i | 0.658324 | + | 0.380083i | 0.791638 | − | 0.610990i | \(-0.209229\pi\) |
−0.133314 | + | 0.991074i | \(0.542562\pi\) | |||||||
\(984\) | −11.9168 | − | 6.88018i | −0.379894 | − | 0.219332i | ||||
\(985\) | −9.48825 | + | 41.1597i | −0.302321 | + | 1.31146i | ||||
\(986\) | −3.20745 | + | 1.85182i | −0.102146 | + | 0.0589741i | ||||
\(987\) | −34.1171 | − | 19.6975i | −1.08596 | − | 0.626979i | ||||
\(988\) | 9.10061i | 0.289529i | ||||||||
\(989\) | −53.5545 | −1.70294 | ||||||||
\(990\) | −21.5294 | + | 23.1026i | −0.684249 | + | 0.734250i | ||||
\(991\) | − | 22.9383i | − | 0.728660i | −0.931270 | − | 0.364330i | \(-0.881298\pi\) | ||
0.931270 | − | 0.364330i | \(-0.118702\pi\) | |||||||
\(992\) | 1.32569 | − | 0.765390i | 0.0420909 | − | 0.0243012i | ||||
\(993\) | −65.5744 | −2.08094 | ||||||||
\(994\) | 0.840602 | − | 0.485322i | 0.0266623 | − | 0.0153935i | ||||
\(995\) | −37.8668 | + | 11.5906i | −1.20046 | + | 0.367448i | ||||
\(996\) | 9.55443 | + | 16.5488i | 0.302744 | + | 0.524368i | ||||
\(997\) | 12.0633 | − | 20.8943i | 0.382050 | − | 0.661730i | −0.609305 | − | 0.792936i | \(-0.708552\pi\) |
0.991355 | + | 0.131206i | \(0.0418849\pi\) | |||||||
\(998\) | 12.9681i | 0.410499i | ||||||||
\(999\) | 19.4493 | − | 32.5466i | 0.615350 | − | 1.02973i |
(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 | 370.2.m.d.249.8 | yes | 16 | |
5.4 | even | 2 | 370.2.m.c.249.1 | yes | 16 | ||
37.11 | even | 6 | 370.2.m.c.159.1 | ✓ | 16 | ||
185.159 | even | 6 | inner | 370.2.m.d.159.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.m.c.159.1 | ✓ | 16 | 37.11 | even | 6 | ||
370.2.m.c.249.1 | yes | 16 | 5.4 | even | 2 | ||
370.2.m.d.159.8 | yes | 16 | 185.159 | even | 6 | inner | |
370.2.m.d.249.8 | yes | 16 | 1.1 | even | 1 | trivial |