Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,2,Mod(295,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.295");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.f (of order \(3\), 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: | \(7.04280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.31116960000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} - 8x^{4} + 9x^{2} + 81 \) |
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 | 295.2 | ||
Root | \(1.62968 - 0.586627i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.295 |
Dual form | 882.2.f.r.589.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||
\(3\) | −0.306808 | + | 1.70466i | −0.177136 | + | 0.984186i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.62968 | + | 2.82269i | 0.728817 | + | 1.26235i | 0.957384 | + | 0.288819i | \(0.0932627\pi\) |
−0.228567 | + | 0.973528i | \(0.573404\pi\) | |||||||
\(6\) | 1.32288 | + | 1.11803i | 0.540062 | + | 0.456435i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.81174 | − | 1.04601i | −0.937246 | − | 0.348669i | ||||
\(10\) | 3.25937 | 1.03070 | ||||||||
\(11\) | −2.81174 | + | 4.87007i | −0.847771 | + | 1.46838i | 0.0354222 | + | 0.999372i | \(0.488722\pi\) |
−0.883193 | + | 0.469010i | \(0.844611\pi\) | |||||||
\(12\) | 1.62968 | − | 0.586627i | 0.470449 | − | 0.169345i | ||||
\(13\) | 0.613616 | + | 1.06281i | 0.170186 | + | 0.294772i | 0.938485 | − | 0.345320i | \(-0.112230\pi\) |
−0.768298 | + | 0.640092i | \(0.778896\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.31174 | + | 1.91203i | −1.37148 | + | 0.493685i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −5.90512 | −1.43220 | −0.716101 | − | 0.697997i | \(-0.754075\pi\) | ||||
−0.716101 | + | 0.697997i | \(0.754075\pi\) | |||||||
\(18\) | −2.31174 | + | 1.91203i | −0.544882 | + | 0.450670i | ||||
\(19\) | 2.64575 | 0.606977 | 0.303488 | − | 0.952835i | \(-0.401849\pi\) | ||||
0.303488 | + | 0.952835i | \(0.401849\pi\) | |||||||
\(20\) | 1.62968 | − | 2.82269i | 0.364408 | − | 0.631174i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.81174 | + | 4.87007i | 0.599464 | + | 1.03830i | ||||
\(23\) | −3.31174 | − | 5.73610i | −0.690545 | − | 1.19606i | −0.971660 | − | 0.236385i | \(-0.924037\pi\) |
0.281114 | − | 0.959674i | \(-0.409296\pi\) | |||||||
\(24\) | 0.306808 | − | 1.70466i | 0.0626269 | − | 0.347962i | ||||
\(25\) | −2.81174 | + | 4.87007i | −0.562348 | + | 0.974015i | ||||
\(26\) | 1.22723 | 0.240680 | ||||||||
\(27\) | 2.64575 | − | 4.47214i | 0.509175 | − | 0.860663i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | − | 3.46410i | 0.371391 | − | 0.643268i | −0.618389 | − | 0.785872i | \(-0.712214\pi\) |
0.989780 | + | 0.142605i | \(0.0455477\pi\) | |||||||
\(30\) | −1.00000 | + | 5.55612i | −0.182574 | + | 1.01440i | ||||
\(31\) | −0.613616 | − | 1.06281i | −0.110209 | − | 0.190887i | 0.805646 | − | 0.592398i | \(-0.201819\pi\) |
−0.915854 | + | 0.401511i | \(0.868485\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −7.43916 | − | 6.28724i | −1.29499 | − | 1.09447i | ||||
\(34\) | −2.95256 | + | 5.11398i | −0.506360 | + | 0.877041i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 2.95804i | 0.0833333 | + | 0.493007i | ||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 1.32288 | − | 2.29129i | 0.214599 | − | 0.371696i | ||||
\(39\) | −2.00000 | + | 0.719927i | −0.320256 | + | 0.115281i | ||||
\(40\) | −1.62968 | − | 2.82269i | −0.257676 | − | 0.446307i | ||||
\(41\) | 2.95256 | + | 5.11398i | 0.461112 | + | 0.798670i | 0.999017 | − | 0.0443359i | \(-0.0141172\pi\) |
−0.537904 | + | 0.843006i | \(0.680784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.81174 | + | 6.60212i | −0.581285 | + | 1.00681i | 0.414043 | + | 0.910257i | \(0.364116\pi\) |
−0.995327 | + | 0.0965570i | \(0.969217\pi\) | |||||||
\(44\) | 5.62348 | 0.847771 | ||||||||
\(45\) | −1.62968 | − | 9.64134i | −0.242939 | − | 1.43725i | ||||
\(46\) | −6.62348 | −0.976578 | ||||||||
\(47\) | −5.29150 | + | 9.16515i | −0.771845 | + | 1.33687i | 0.164706 | + | 0.986343i | \(0.447333\pi\) |
−0.936551 | + | 0.350532i | \(0.886001\pi\) | |||||||
\(48\) | −1.32288 | − | 1.11803i | −0.190941 | − | 0.161374i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.81174 | + | 4.87007i | 0.397640 | + | 0.688732i | ||||
\(51\) | 1.81174 | − | 10.0662i | 0.253694 | − | 1.40955i | ||||
\(52\) | 0.613616 | − | 1.06281i | 0.0850932 | − | 0.147386i | ||||
\(53\) | −4.00000 | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | −2.55011 | − | 4.52736i | −0.347026 | − | 0.616095i | ||||
\(55\) | −18.3290 | −2.47148 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.811738 | + | 4.51011i | −0.107517 | + | 0.597379i | ||||
\(58\) | −2.00000 | − | 3.46410i | −0.262613 | − | 0.454859i | ||||
\(59\) | 7.43916 | + | 12.8850i | 0.968496 | + | 1.67748i | 0.699914 | + | 0.714227i | \(0.253222\pi\) |
0.268582 | + | 0.963257i | \(0.413445\pi\) | |||||||
\(60\) | 4.31174 | + | 3.64408i | 0.556643 | + | 0.470449i | ||||
\(61\) | 2.24330 | − | 3.88551i | 0.287225 | − | 0.497488i | −0.685921 | − | 0.727676i | \(-0.740601\pi\) |
0.973146 | + | 0.230187i | \(0.0739339\pi\) | |||||||
\(62\) | −1.22723 | −0.155859 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | + | 3.46410i | −0.248069 | + | 0.429669i | ||||
\(66\) | −9.16449 | + | 3.29888i | −1.12807 | + | 0.406064i | ||||
\(67\) | 2.81174 | + | 4.87007i | 0.343508 | + | 0.594974i | 0.985082 | − | 0.172088i | \(-0.0550513\pi\) |
−0.641573 | + | 0.767062i | \(0.721718\pi\) | |||||||
\(68\) | 2.95256 | + | 5.11398i | 0.358050 | + | 0.620162i | ||||
\(69\) | 10.7942 | − | 3.88551i | 1.29947 | − | 0.467760i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6235 | −1.26077 | −0.630387 | − | 0.776281i | \(-0.717104\pi\) | ||||
−0.630387 | + | 0.776281i | \(0.717104\pi\) | |||||||
\(72\) | 2.81174 | + | 1.04601i | 0.331366 | + | 0.123273i | ||||
\(73\) | 11.1966 | 1.31047 | 0.655233 | − | 0.755427i | \(-0.272571\pi\) | ||||
0.655233 | + | 0.755427i | \(0.272571\pi\) | |||||||
\(74\) | 3.00000 | − | 5.19615i | 0.348743 | − | 0.604040i | ||||
\(75\) | −7.43916 | − | 6.28724i | −0.859000 | − | 0.725988i | ||||
\(76\) | −1.32288 | − | 2.29129i | −0.151744 | − | 0.262829i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.376525 | + | 2.09201i | −0.0426330 | + | 0.236874i | ||||
\(79\) | −1.68826 | + | 2.92416i | −0.189944 | + | 0.328993i | −0.945231 | − | 0.326401i | \(-0.894164\pi\) |
0.755287 | + | 0.655394i | \(0.227497\pi\) | |||||||
\(80\) | −3.25937 | −0.364408 | ||||||||
\(81\) | 6.81174 | + | 5.88220i | 0.756860 | + | 0.653577i | ||||
\(82\) | 5.90512 | 0.652111 | ||||||||
\(83\) | 3.87298 | − | 6.70820i | 0.425115 | − | 0.736321i | −0.571316 | − | 0.820730i | \(-0.693567\pi\) |
0.996431 | + | 0.0844091i | \(0.0269003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.62348 | − | 16.6683i | −1.04381 | − | 1.80794i | ||||
\(86\) | 3.81174 | + | 6.60212i | 0.411030 | + | 0.711925i | ||||
\(87\) | 5.29150 | + | 4.47214i | 0.567309 | + | 0.479463i | ||||
\(88\) | 2.81174 | − | 4.87007i | 0.299732 | − | 0.519151i | ||||
\(89\) | 8.97320 | 0.951157 | 0.475579 | − | 0.879673i | \(-0.342239\pi\) | ||||
0.475579 | + | 0.879673i | \(0.342239\pi\) | |||||||
\(90\) | −9.16449 | − | 3.40932i | −0.966022 | − | 0.359374i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.31174 | + | 5.73610i | −0.345273 | + | 0.598030i | ||||
\(93\) | 2.00000 | − | 0.719927i | 0.207390 | − | 0.0746530i | ||||
\(94\) | 5.29150 | + | 9.16515i | 0.545777 | + | 0.945313i | ||||
\(95\) | 4.31174 | + | 7.46815i | 0.442375 | + | 0.766216i | ||||
\(96\) | −1.62968 | + | 0.586627i | −0.166329 | + | 0.0598724i | ||||
\(97\) | −1.53404 | + | 2.65704i | −0.155758 | + | 0.269781i | −0.933335 | − | 0.359007i | \(-0.883115\pi\) |
0.777577 | + | 0.628788i | \(0.216449\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.0000 | − | 10.7523i | 1.30655 | − | 1.08064i | ||||
\(100\) | 5.62348 | 0.562348 | ||||||||
\(101\) | −6.30757 | + | 10.9250i | −0.627627 | + | 1.08708i | 0.360400 | + | 0.932798i | \(0.382640\pi\) |
−0.988027 | + | 0.154283i | \(0.950693\pi\) | |||||||
\(102\) | −7.81174 | − | 6.60212i | −0.773477 | − | 0.653708i | ||||
\(103\) | 4.67789 | + | 8.10234i | 0.460926 | + | 0.798347i | 0.999007 | − | 0.0445458i | \(-0.0141841\pi\) |
−0.538081 | + | 0.842893i | \(0.680851\pi\) | |||||||
\(104\) | −0.613616 | − | 1.06281i | −0.0601700 | − | 0.104217i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | + | 3.46410i | −0.194257 | + | 0.336463i | ||||
\(107\) | 0.376525 | 0.0364000 | 0.0182000 | − | 0.999834i | \(-0.494206\pi\) | ||||
0.0182000 | + | 0.999834i | \(0.494206\pi\) | |||||||
\(108\) | −5.19586 | − | 0.0552199i | −0.499972 | − | 0.00531353i | ||||
\(109\) | 11.2470 | 1.07726 | 0.538631 | − | 0.842542i | \(-0.318942\pi\) | ||||
0.538631 | + | 0.842542i | \(0.318942\pi\) | |||||||
\(110\) | −9.16449 | + | 15.8734i | −0.873799 | + | 1.51347i | ||||
\(111\) | −1.84085 | + | 10.2280i | −0.174726 | + | 0.970796i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.68826 | + | 6.38826i | 0.346963 | + | 0.600957i | 0.985708 | − | 0.168461i | \(-0.0538798\pi\) |
−0.638746 | + | 0.769418i | \(0.720546\pi\) | |||||||
\(114\) | 3.50000 | + | 2.95804i | 0.327805 | + | 0.277046i | ||||
\(115\) | 10.7942 | − | 18.6961i | 1.00656 | − | 1.74342i | ||||
\(116\) | −4.00000 | −0.371391 | ||||||||
\(117\) | −0.613616 | − | 3.63020i | −0.0567288 | − | 0.335612i | ||||
\(118\) | 14.8783 | 1.36966 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.31174 | − | 1.91203i | 0.484893 | − | 0.174544i | ||||
\(121\) | −10.3117 | − | 17.8605i | −0.937431 | − | 1.62368i | ||||
\(122\) | −2.24330 | − | 3.88551i | −0.203099 | − | 0.351777i | ||||
\(123\) | −9.62348 | + | 3.46410i | −0.867720 | + | 0.312348i | ||||
\(124\) | −0.613616 | + | 1.06281i | −0.0551043 | + | 0.0954435i | ||||
\(125\) | −2.03214 | −0.181760 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.37652 | 0.122147 | 0.0610734 | − | 0.998133i | \(-0.480548\pi\) | ||||
0.0610734 | + | 0.998133i | \(0.480548\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −10.0849 | − | 8.52330i | −0.887927 | − | 0.750435i | ||||
\(130\) | 2.00000 | + | 3.46410i | 0.175412 | + | 0.303822i | ||||
\(131\) | 2.85692 | + | 4.94832i | 0.249610 | + | 0.432337i | 0.963418 | − | 0.268005i | \(-0.0863643\pi\) |
−0.713808 | + | 0.700342i | \(0.753031\pi\) | |||||||
\(132\) | −1.72533 | + | 9.58612i | −0.150170 | + | 0.834365i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.62348 | 0.485794 | ||||||||
\(135\) | 16.9352 | + | 0.179982i | 1.45755 | + | 0.0154904i | ||||
\(136\) | 5.90512 | 0.506360 | ||||||||
\(137\) | 10.4352 | − | 18.0743i | 0.891540 | − | 1.54419i | 0.0535117 | − | 0.998567i | \(-0.482959\pi\) |
0.838029 | − | 0.545626i | \(-0.183708\pi\) | |||||||
\(138\) | 2.03214 | − | 11.2908i | 0.172987 | − | 0.961135i | ||||
\(139\) | −3.96863 | − | 6.87386i | −0.336615 | − | 0.583033i | 0.647179 | − | 0.762338i | \(-0.275949\pi\) |
−0.983794 | + | 0.179305i | \(0.942615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.0000 | − | 11.8322i | −1.17901 | − | 0.996448i | ||||
\(142\) | −5.31174 | + | 9.20020i | −0.445751 | + | 0.772064i | ||||
\(143\) | −6.90131 | −0.577116 | ||||||||
\(144\) | 2.31174 | − | 1.91203i | 0.192645 | − | 0.159336i | ||||
\(145\) | 13.0375 | 1.08270 | ||||||||
\(146\) | 5.59831 | − | 9.69656i | 0.463319 | − | 0.802493i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.00000 | − | 5.19615i | −0.246598 | − | 0.427121i | ||||
\(149\) | 2.62348 | + | 4.54399i | 0.214923 | + | 0.372258i | 0.953249 | − | 0.302186i | \(-0.0977165\pi\) |
−0.738325 | + | 0.674445i | \(0.764383\pi\) | |||||||
\(150\) | −9.16449 | + | 3.29888i | −0.748277 | + | 0.269353i | ||||
\(151\) | 4.31174 | − | 7.46815i | 0.350884 | − | 0.607749i | −0.635520 | − | 0.772084i | \(-0.719214\pi\) |
0.986405 | + | 0.164335i | \(0.0525477\pi\) | |||||||
\(152\) | −2.64575 | −0.214599 | ||||||||
\(153\) | 16.6036 | + | 6.17680i | 1.34233 | + | 0.499364i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | − | 3.46410i | 0.160644 | − | 0.278243i | ||||
\(156\) | 1.62348 | + | 1.37209i | 0.129982 | + | 0.109855i | ||||
\(157\) | −8.14842 | − | 14.1135i | −0.650315 | − | 1.12638i | −0.983046 | − | 0.183356i | \(-0.941304\pi\) |
0.332732 | − | 0.943021i | \(-0.392030\pi\) | |||||||
\(158\) | 1.68826 | + | 2.92416i | 0.134311 | + | 0.232633i | ||||
\(159\) | 1.22723 | − | 6.81864i | 0.0973258 | − | 0.540754i | ||||
\(160\) | −1.62968 | + | 2.82269i | −0.128838 | + | 0.223154i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.50000 | − | 2.95804i | 0.667823 | − | 0.232406i | ||||
\(163\) | −1.24695 | −0.0976687 | −0.0488344 | − | 0.998807i | \(-0.515551\pi\) | ||||
−0.0488344 | + | 0.998807i | \(0.515551\pi\) | |||||||
\(164\) | 2.95256 | − | 5.11398i | 0.230556 | − | 0.399335i | ||||
\(165\) | 5.62348 | − | 31.2447i | 0.437787 | − | 2.43240i | ||||
\(166\) | −3.87298 | − | 6.70820i | −0.300602 | − | 0.520658i | ||||
\(167\) | 3.25937 | + | 5.64539i | 0.252217 | + | 0.436853i | 0.964136 | − | 0.265409i | \(-0.0855069\pi\) |
−0.711919 | + | 0.702262i | \(0.752174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.74695 | − | 9.95401i | 0.442073 | − | 0.765693i | ||||
\(170\) | −19.2470 | −1.47617 | ||||||||
\(171\) | −7.43916 | − | 2.76748i | −0.568887 | − | 0.211634i | ||||
\(172\) | 7.62348 | 0.581285 | ||||||||
\(173\) | −0.613616 | + | 1.06281i | −0.0466524 | + | 0.0808043i | −0.888409 | − | 0.459053i | \(-0.848189\pi\) |
0.841756 | + | 0.539858i | \(0.181522\pi\) | |||||||
\(174\) | 6.51873 | − | 2.34651i | 0.494184 | − | 0.177888i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.81174 | − | 4.87007i | −0.211943 | − | 0.367096i | ||||
\(177\) | −24.2470 | + | 8.72802i | −1.82251 | + | 0.656038i | ||||
\(178\) | 4.48660 | − | 7.77102i | 0.336285 | − | 0.582462i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | −7.53480 | + | 6.23202i | −0.561611 | + | 0.464507i | ||||
\(181\) | −4.48660 | −0.333486 | −0.166743 | − | 0.986000i | \(-0.553325\pi\) | ||||
−0.166743 | + | 0.986000i | \(0.553325\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.93521 | + | 5.01617i | 0.438744 | + | 0.370806i | ||||
\(184\) | 3.31174 | + | 5.73610i | 0.244145 | + | 0.422871i | ||||
\(185\) | 9.77810 | + | 16.9362i | 0.718900 | + | 1.24517i | ||||
\(186\) | 0.376525 | − | 2.09201i | 0.0276081 | − | 0.153394i | ||||
\(187\) | 16.6036 | − | 28.7584i | 1.21418 | − | 2.10302i | ||||
\(188\) | 10.5830 | 0.771845 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.62348 | 0.625613 | ||||||||
\(191\) | −2.68826 | + | 4.65621i | −0.194516 | + | 0.336911i | −0.946742 | − | 0.321994i | \(-0.895647\pi\) |
0.752226 | + | 0.658905i | \(0.228980\pi\) | |||||||
\(192\) | −0.306808 | + | 1.70466i | −0.0221420 | + | 0.123023i | ||||
\(193\) | −6.74695 | − | 11.6861i | −0.485656 | − | 0.841181i | 0.514208 | − | 0.857666i | \(-0.328086\pi\) |
−0.999864 | + | 0.0164844i | \(0.994753\pi\) | |||||||
\(194\) | 1.53404 | + | 2.65704i | 0.110138 | + | 0.190764i | ||||
\(195\) | −5.29150 | − | 4.47214i | −0.378932 | − | 0.320256i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.24695 | 0.516324 | 0.258162 | − | 0.966102i | \(-0.416883\pi\) | ||||
0.258162 | + | 0.966102i | \(0.416883\pi\) | |||||||
\(198\) | −2.81174 | − | 16.6345i | −0.199821 | − | 1.18216i | ||||
\(199\) | −10.2004 | −0.723089 | −0.361545 | − | 0.932355i | \(-0.617751\pi\) | ||||
−0.361545 | + | 0.932355i | \(0.617751\pi\) | |||||||
\(200\) | 2.81174 | − | 4.87007i | 0.198820 | − | 0.344366i | ||||
\(201\) | −9.16449 | + | 3.29888i | −0.646413 | + | 0.232685i | ||||
\(202\) | 6.30757 | + | 10.9250i | 0.443799 | + | 0.768683i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −9.62348 | + | 3.46410i | −0.673778 | + | 0.242536i | ||||
\(205\) | −9.62348 | + | 16.6683i | −0.672133 | + | 1.16417i | ||||
\(206\) | 9.35577 | 0.651848 | ||||||||
\(207\) | 3.31174 | + | 19.5925i | 0.230182 | + | 1.36177i | ||||
\(208\) | −1.22723 | −0.0850932 | ||||||||
\(209\) | −7.43916 | + | 12.8850i | −0.514577 | + | 0.891274i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.62348 | + | 4.54399i | 0.180607 | + | 0.312821i | 0.942088 | − | 0.335367i | \(-0.108860\pi\) |
−0.761480 | + | 0.648188i | \(0.775527\pi\) | |||||||
\(212\) | 2.00000 | + | 3.46410i | 0.137361 | + | 0.237915i | ||||
\(213\) | 3.25937 | − | 18.1094i | 0.223328 | − | 1.24084i | ||||
\(214\) | 0.188262 | − | 0.326080i | 0.0128693 | − | 0.0222904i | ||||
\(215\) | −24.8477 | −1.69460 | ||||||||
\(216\) | −2.64575 | + | 4.47214i | −0.180021 | + | 0.304290i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.62348 | − | 9.74015i | 0.380870 | − | 0.659686i | ||||
\(219\) | −3.43521 | + | 19.0864i | −0.232130 | + | 1.28974i | ||||
\(220\) | 9.16449 | + | 15.8734i | 0.617870 | + | 1.07018i | ||||
\(221\) | −3.62348 | − | 6.27604i | −0.243741 | − | 0.422172i | ||||
\(222\) | 7.93725 | + | 6.70820i | 0.532714 | + | 0.450225i | ||||
\(223\) | 3.25937 | − | 5.64539i | 0.218263 | − | 0.378043i | −0.736014 | − | 0.676967i | \(-0.763294\pi\) |
0.954277 | + | 0.298923i | \(0.0966275\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.0000 | − | 10.7523i | 0.866667 | − | 0.716818i | ||||
\(226\) | 7.37652 | 0.490679 | ||||||||
\(227\) | −14.3603 | + | 24.8728i | −0.953130 | + | 1.65087i | −0.214538 | + | 0.976716i | \(0.568825\pi\) |
−0.738592 | + | 0.674153i | \(0.764509\pi\) | |||||||
\(228\) | 4.31174 | − | 1.55207i | 0.285552 | − | 0.102788i | ||||
\(229\) | 13.4399 | + | 23.2786i | 0.888135 | + | 1.53829i | 0.842078 | + | 0.539356i | \(0.181332\pi\) |
0.0460572 | + | 0.998939i | \(0.485334\pi\) | |||||||
\(230\) | −10.7942 | − | 18.6961i | −0.711746 | − | 1.23278i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.00000 | + | 3.46410i | −0.131306 | + | 0.227429i | ||||
\(233\) | 17.0000 | 1.11371 | 0.556854 | − | 0.830611i | \(-0.312008\pi\) | ||||
0.556854 | + | 0.830611i | \(0.312008\pi\) | |||||||
\(234\) | −3.45065 | − | 1.28369i | −0.225576 | − | 0.0839177i | ||||
\(235\) | −34.4939 | −2.25013 | ||||||||
\(236\) | 7.43916 | − | 12.8850i | 0.484248 | − | 0.838742i | ||||
\(237\) | −4.46672 | − | 3.77507i | −0.290145 | − | 0.245217i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.31174 | − | 10.9323i | −0.408272 | − | 0.707148i | 0.586424 | − | 0.810004i | \(-0.300535\pi\) |
−0.994696 | + | 0.102856i | \(0.967202\pi\) | |||||||
\(240\) | 1.00000 | − | 5.55612i | 0.0645497 | − | 0.358646i | ||||
\(241\) | −13.3443 | + | 23.1130i | −0.859580 | + | 1.48884i | 0.0127491 | + | 0.999919i | \(0.495942\pi\) |
−0.872330 | + | 0.488918i | \(0.837392\pi\) | |||||||
\(242\) | −20.6235 | −1.32573 | ||||||||
\(243\) | −12.1170 | + | 9.80700i | −0.777309 | + | 0.629119i | ||||
\(244\) | −4.48660 | −0.287225 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.81174 | + | 10.0662i | −0.115512 | + | 0.641799i | ||||
\(247\) | 1.62348 | + | 2.81194i | 0.103299 | + | 0.178920i | ||||
\(248\) | 0.613616 | + | 1.06281i | 0.0389647 | + | 0.0674888i | ||||
\(249\) | 10.2470 | + | 8.66025i | 0.649374 | + | 0.548821i | ||||
\(250\) | −1.01607 | + | 1.75988i | −0.0642618 | + | 0.111305i | ||||
\(251\) | −5.10022 | −0.321923 | −0.160961 | − | 0.986961i | \(-0.551459\pi\) | ||||
−0.160961 | + | 0.986961i | \(0.551459\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.2470 | 2.34170 | ||||||||
\(254\) | 0.688262 | − | 1.19211i | 0.0431854 | − | 0.0747993i | ||||
\(255\) | 31.3664 | − | 11.2908i | 1.96424 | − | 0.707056i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0.498095 | + | 0.862726i | 0.0310703 | + | 0.0538154i | 0.881142 | − | 0.472851i | \(-0.156775\pi\) |
−0.850072 | + | 0.526666i | \(0.823442\pi\) | |||||||
\(258\) | −12.4239 | + | 4.47214i | −0.773475 | + | 0.278423i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | −9.24695 | + | 7.64813i | −0.572372 | + | 0.473407i | ||||
\(262\) | 5.71383 | 0.353002 | ||||||||
\(263\) | 1.68826 | − | 2.92416i | 0.104103 | − | 0.180311i | −0.809269 | − | 0.587439i | \(-0.800136\pi\) |
0.913371 | + | 0.407128i | \(0.133470\pi\) | |||||||
\(264\) | 7.43916 | + | 6.28724i | 0.457849 | + | 0.386953i | ||||
\(265\) | −6.51873 | − | 11.2908i | −0.400443 | − | 0.693587i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.75305 | + | 15.2963i | −0.168484 | + | 0.936116i | ||||
\(268\) | 2.81174 | − | 4.87007i | 0.171754 | − | 0.297487i | ||||
\(269\) | 24.0428 | 1.46592 | 0.732958 | − | 0.680274i | \(-0.238139\pi\) | ||||
0.732958 | + | 0.680274i | \(0.238139\pi\) | |||||||
\(270\) | 8.62348 | − | 14.5763i | 0.524808 | − | 0.887087i | ||||
\(271\) | 2.83704 | 0.172338 | 0.0861689 | − | 0.996281i | \(-0.472538\pi\) | ||||
0.0861689 | + | 0.996281i | \(0.472538\pi\) | |||||||
\(272\) | 2.95256 | − | 5.11398i | 0.179025 | − | 0.310081i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.4352 | − | 18.0743i | −0.630414 | − | 1.09191i | ||||
\(275\) | −15.8117 | − | 27.3867i | −0.953484 | − | 1.65148i | ||||
\(276\) | −8.76203 | − | 7.40527i | −0.527412 | − | 0.445745i | ||||
\(277\) | 14.2470 | − | 24.6764i | 0.856016 | − | 1.48266i | −0.0196827 | − | 0.999806i | \(-0.506266\pi\) |
0.875699 | − | 0.482857i | \(-0.160401\pi\) | |||||||
\(278\) | −7.93725 | −0.476045 | ||||||||
\(279\) | 0.613616 | + | 3.63020i | 0.0367362 | + | 0.217334i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9352 | − | 22.4044i | 0.771650 | − | 1.33654i | −0.165008 | − | 0.986292i | \(-0.552765\pi\) |
0.936658 | − | 0.350245i | \(-0.113902\pi\) | |||||||
\(282\) | −17.2470 | + | 6.20828i | −1.02704 | + | 0.369697i | ||||
\(283\) | −3.66182 | − | 6.34246i | −0.217673 | − | 0.377020i | 0.736423 | − | 0.676521i | \(-0.236513\pi\) |
−0.954096 | + | 0.299501i | \(0.903180\pi\) | |||||||
\(284\) | 5.31174 | + | 9.20020i | 0.315194 | + | 0.545931i | ||||
\(285\) | −14.0535 | + | 5.05876i | −0.832460 | + | 0.299655i | ||||
\(286\) | −3.45065 | + | 5.97671i | −0.204041 | + | 0.353410i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.500000 | − | 2.95804i | −0.0294628 | − | 0.174304i | ||||
\(289\) | 17.8704 | 1.05120 | ||||||||
\(290\) | 6.51873 | − | 11.2908i | 0.382793 | − | 0.663017i | ||||
\(291\) | −4.05869 | − | 3.43022i | −0.237925 | − | 0.201083i | ||||
\(292\) | −5.59831 | − | 9.69656i | −0.327616 | − | 0.567448i | ||||
\(293\) | −12.8263 | − | 22.2158i | −0.749321 | − | 1.29786i | −0.948149 | − | 0.317827i | \(-0.897047\pi\) |
0.198828 | − | 0.980034i | \(-0.436287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.2470 | + | 41.9970i | −1.41171 | + | 2.44516i | ||||
\(296\) | −6.00000 | −0.348743 | ||||||||
\(297\) | 14.3405 | + | 25.4595i | 0.832118 | + | 1.47731i | ||||
\(298\) | 5.24695 | 0.303948 | ||||||||
\(299\) | 4.06427 | − | 7.03952i | 0.235043 | − | 0.407106i | ||||
\(300\) | −1.72533 | + | 9.58612i | −0.0996118 | + | 0.553455i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.31174 | − | 7.46815i | −0.248113 | − | 0.429744i | ||||
\(303\) | −16.6883 | − | 14.1042i | −0.958716 | − | 0.810263i | ||||
\(304\) | −1.32288 | + | 2.29129i | −0.0758721 | + | 0.131414i | ||||
\(305\) | 14.6235 | 0.837338 | ||||||||
\(306\) | 13.6511 | − | 11.2908i | 0.780381 | − | 0.645451i | ||||
\(307\) | 13.2288 | 0.755005 | 0.377503 | − | 0.926009i | \(-0.376783\pi\) | ||||
0.377503 | + | 0.926009i | \(0.376783\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.2470 | + | 5.48835i | −0.867369 | + | 0.312221i | ||||
\(310\) | −2.00000 | − | 3.46410i | −0.113592 | − | 0.196748i | ||||
\(311\) | −10.3917 | − | 17.9990i | −0.589260 | − | 1.02063i | −0.994330 | − | 0.106343i | \(-0.966086\pi\) |
0.405069 | − | 0.914286i | \(-0.367247\pi\) | |||||||
\(312\) | 2.00000 | − | 0.719927i | 0.113228 | − | 0.0407579i | ||||
\(313\) | −10.8898 | + | 18.8617i | −0.615529 | + | 1.06613i | 0.374763 | + | 0.927121i | \(0.377724\pi\) |
−0.990292 | + | 0.139006i | \(0.955609\pi\) | |||||||
\(314\) | −16.2968 | −0.919684 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.37652 | 0.189944 | ||||||||
\(317\) | −3.62348 | + | 6.27604i | −0.203515 | + | 0.352498i | −0.949658 | − | 0.313287i | \(-0.898570\pi\) |
0.746144 | + | 0.665785i | \(0.231903\pi\) | |||||||
\(318\) | −5.29150 | − | 4.47214i | −0.296733 | − | 0.250785i | ||||
\(319\) | 11.2470 | + | 19.4803i | 0.629708 | + | 1.09069i | ||||
\(320\) | 1.62968 | + | 2.82269i | 0.0911021 | + | 0.157793i | ||||
\(321\) | −0.115521 | + | 0.641847i | −0.00644774 | + | 0.0358244i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.6235 | −0.869313 | ||||||||
\(324\) | 1.68826 | − | 8.84024i | 0.0937924 | − | 0.491124i | ||||
\(325\) | −6.90131 | −0.382816 | ||||||||
\(326\) | −0.623475 | + | 1.07989i | −0.0345311 | + | 0.0598096i | ||||
\(327\) | −3.45065 | + | 19.1722i | −0.190822 | + | 1.06023i | ||||
\(328\) | −2.95256 | − | 5.11398i | −0.163028 | − | 0.282372i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −24.2470 | − | 20.4924i | −1.33475 | − | 1.12807i | ||||
\(331\) | −4.00000 | + | 6.92820i | −0.219860 | + | 0.380808i | −0.954765 | − | 0.297361i | \(-0.903893\pi\) |
0.734905 | + | 0.678170i | \(0.237227\pi\) | |||||||
\(332\) | −7.74597 | −0.425115 | ||||||||
\(333\) | −16.8704 | − | 6.27604i | −0.924494 | − | 0.343925i | ||||
\(334\) | 6.51873 | 0.356689 | ||||||||
\(335\) | −9.16449 | + | 15.8734i | −0.500709 | + | 0.867254i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.56479 | − | 2.71029i | −0.0852394 | − | 0.147639i | 0.820254 | − | 0.572000i | \(-0.193832\pi\) |
−0.905493 | + | 0.424361i | \(0.860499\pi\) | |||||||
\(338\) | −5.74695 | − | 9.95401i | −0.312593 | − | 0.541427i | ||||
\(339\) | −12.0214 | + | 4.32727i | −0.652913 | + | 0.235025i | ||||
\(340\) | −9.62348 | + | 16.6683i | −0.521906 | + | 0.903968i | ||||
\(341\) | 6.90131 | 0.373727 | ||||||||
\(342\) | −6.11628 | + | 5.05876i | −0.330731 | + | 0.273547i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.81174 | − | 6.60212i | 0.205515 | − | 0.355963i | ||||
\(345\) | 28.5587 | + | 24.1365i | 1.53755 | + | 1.29947i | ||||
\(346\) | 0.613616 | + | 1.06281i | 0.0329882 | + | 0.0571372i | ||||
\(347\) | 1.81174 | + | 3.13802i | 0.0972592 | + | 0.168458i | 0.910549 | − | 0.413401i | \(-0.135659\pi\) |
−0.813290 | + | 0.581858i | \(0.802326\pi\) | |||||||
\(348\) | 1.22723 | − | 6.81864i | 0.0657865 | − | 0.365518i | ||||
\(349\) | 13.6511 | − | 23.6444i | 0.730726 | − | 1.26565i | −0.225848 | − | 0.974163i | \(-0.572515\pi\) |
0.956573 | − | 0.291492i | \(-0.0941515\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.37652 | + | 0.0677676i | 0.340354 | + | 0.00361717i | ||||
\(352\) | −5.62348 | −0.299732 | ||||||||
\(353\) | 2.95256 | − | 5.11398i | 0.157149 | − | 0.272190i | −0.776691 | − | 0.629882i | \(-0.783103\pi\) |
0.933839 | + | 0.357693i | \(0.116436\pi\) | |||||||
\(354\) | −4.56479 | + | 25.3625i | −0.242616 | + | 1.34800i | ||||
\(355\) | −17.3129 | − | 29.9868i | −0.918874 | − | 1.59154i | ||||
\(356\) | −4.48660 | − | 7.77102i | −0.237789 | − | 0.411863i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.1174 | 1.64231 | 0.821156 | − | 0.570704i | \(-0.193329\pi\) | ||||
0.821156 | + | 0.570704i | \(0.193329\pi\) | |||||||
\(360\) | 1.62968 | + | 9.64134i | 0.0858919 | + | 0.508143i | ||||
\(361\) | −12.0000 | −0.631579 | ||||||||
\(362\) | −2.24330 | + | 3.88551i | −0.117905 | + | 0.204218i | ||||
\(363\) | 33.6097 | − | 12.0983i | 1.76405 | − | 0.634995i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.2470 | + | 31.6046i | 0.955089 | + | 1.65426i | ||||
\(366\) | 7.31174 | − | 2.63196i | 0.382191 | − | 0.137575i | ||||
\(367\) | 3.45065 | − | 5.97671i | 0.180123 | − | 0.311982i | −0.761799 | − | 0.647813i | \(-0.775684\pi\) |
0.941922 | + | 0.335831i | \(0.109017\pi\) | |||||||
\(368\) | 6.62348 | 0.345273 | ||||||||
\(369\) | −2.95256 | − | 17.4676i | −0.153704 | − | 0.909326i | ||||
\(370\) | 19.5562 | 1.01668 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.62348 | − | 1.37209i | −0.0841733 | − | 0.0711394i | ||||
\(373\) | −5.62348 | − | 9.74015i | −0.291173 | − | 0.504326i | 0.682915 | − | 0.730498i | \(-0.260712\pi\) |
−0.974087 | + | 0.226172i | \(0.927379\pi\) | |||||||
\(374\) | −16.6036 | − | 28.7584i | −0.858554 | − | 1.48706i | ||||
\(375\) | 0.623475 | − | 3.46410i | 0.0321961 | − | 0.178885i | ||||
\(376\) | 5.29150 | − | 9.16515i | 0.272888 | − | 0.472657i | ||||
\(377\) | 4.90893 | 0.252823 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.6235 | 0.802524 | 0.401262 | − | 0.915963i | \(-0.368572\pi\) | ||||
0.401262 | + | 0.915963i | \(0.368572\pi\) | |||||||
\(380\) | 4.31174 | − | 7.46815i | 0.221187 | − | 0.383108i | ||||
\(381\) | −0.422329 | + | 2.34651i | −0.0216366 | + | 0.120215i | ||||
\(382\) | 2.68826 | + | 4.65621i | 0.137543 | + | 0.238232i | ||||
\(383\) | −13.8424 | − | 23.9757i | −0.707312 | − | 1.22510i | −0.965851 | − | 0.259100i | \(-0.916574\pi\) |
0.258538 | − | 0.966001i | \(-0.416759\pi\) | |||||||
\(384\) | 1.32288 | + | 1.11803i | 0.0675077 | + | 0.0570544i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.4939 | −0.686822 | ||||||||
\(387\) | 17.6235 | − | 14.5763i | 0.895852 | − | 0.740957i | ||||
\(388\) | 3.06808 | 0.155758 | ||||||||
\(389\) | −18.6235 | + | 32.2568i | −0.944248 | + | 1.63548i | −0.186997 | + | 0.982360i | \(0.559876\pi\) |
−0.757251 | + | 0.653125i | \(0.773458\pi\) | |||||||
\(390\) | −6.51873 | + | 2.34651i | −0.330089 | + | 0.118820i | ||||
\(391\) | 19.5562 | + | 33.8723i | 0.989000 | + | 1.71300i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.31174 | + | 3.35189i | −0.469715 | + | 0.169080i | ||||
\(394\) | 3.62348 | − | 6.27604i | 0.182548 | − | 0.316183i | ||||
\(395\) | −11.0053 | −0.553738 | ||||||||
\(396\) | −15.8117 | − | 5.88220i | −0.794570 | − | 0.295591i | ||||
\(397\) | −9.35577 | −0.469553 | −0.234776 | − | 0.972049i | \(-0.575436\pi\) | ||||
−0.234776 | + | 0.972049i | \(0.575436\pi\) | |||||||
\(398\) | −5.10022 | + | 8.83383i | −0.255651 | + | 0.442800i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.81174 | − | 4.87007i | −0.140587 | − | 0.243504i | ||||
\(401\) | 7.50000 | + | 12.9904i | 0.374532 | + | 0.648709i | 0.990257 | − | 0.139253i | \(-0.0444700\pi\) |
−0.615725 | + | 0.787961i | \(0.711137\pi\) | |||||||
\(402\) | −1.72533 | + | 9.58612i | −0.0860515 | + | 0.478112i | ||||
\(403\) | 0.753049 | − | 1.30432i | 0.0375121 | − | 0.0649728i | ||||
\(404\) | 12.6151 | 0.627627 | ||||||||
\(405\) | −5.50267 | + | 28.8136i | −0.273430 | + | 1.43176i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.8704 | + | 29.2204i | −0.836236 | + | 1.44840i | ||||
\(408\) | −1.81174 | + | 10.0662i | −0.0896944 | + | 0.498352i | ||||
\(409\) | −1.11171 | − | 1.92554i | −0.0549706 | − | 0.0952118i | 0.837231 | − | 0.546850i | \(-0.184173\pi\) |
−0.892201 | + | 0.451638i | \(0.850840\pi\) | |||||||
\(410\) | 9.62348 | + | 16.6683i | 0.475270 | + | 0.823191i | ||||
\(411\) | 27.6090 | + | 23.3338i | 1.36185 | + | 1.15097i | ||||
\(412\) | 4.67789 | − | 8.10234i | 0.230463 | − | 0.399174i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 18.6235 | + | 6.92820i | 0.915294 | + | 0.340503i | ||||
\(415\) | 25.2470 | 1.23932 | ||||||||
\(416\) | −0.613616 | + | 1.06281i | −0.0300850 | + | 0.0521087i | ||||
\(417\) | 12.9352 | − | 4.65621i | 0.633440 | − | 0.228015i | ||||
\(418\) | 7.43916 | + | 12.8850i | 0.363861 | + | 0.630226i | ||||
\(419\) | −0.402452 | − | 0.697067i | −0.0196610 | − | 0.0340539i | 0.856027 | − | 0.516930i | \(-0.172925\pi\) |
−0.875689 | + | 0.482876i | \(0.839592\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(422\) | 5.24695 | 0.255418 | ||||||||
\(423\) | 24.4651 | − | 20.2351i | 1.18954 | − | 0.983862i | ||||
\(424\) | 4.00000 | 0.194257 | ||||||||
\(425\) | 16.6036 | − | 28.7584i | 0.805395 | − | 1.39499i | ||||
\(426\) | −14.0535 | − | 11.8774i | −0.680896 | − | 0.575462i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.188262 | − | 0.326080i | −0.00910000 | − | 0.0157617i | ||||
\(429\) | 2.11738 | − | 11.7644i | 0.102228 | − | 0.567990i | ||||
\(430\) | −12.4239 | + | 21.5187i | −0.599131 | + | 1.03773i | ||||
\(431\) | −8.00000 | −0.385346 | −0.192673 | − | 0.981263i | \(-0.561716\pi\) | ||||
−0.192673 | + | 0.981263i | \(0.561716\pi\) | |||||||
\(432\) | 2.55011 | + | 4.52736i | 0.122692 | + | 0.217823i | ||||
\(433\) | −7.13235 | −0.342759 | −0.171379 | − | 0.985205i | \(-0.554822\pi\) | ||||
−0.171379 | + | 0.985205i | \(0.554822\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.00000 | + | 22.2245i | −0.191785 | + | 1.06558i | ||||
\(436\) | −5.62348 | − | 9.74015i | −0.269316 | − | 0.466468i | ||||
\(437\) | −8.76203 | − | 15.1763i | −0.419145 | − | 0.725980i | ||||
\(438\) | 14.8117 | + | 12.5182i | 0.707732 | + | 0.598143i | ||||
\(439\) | −15.4919 | + | 26.8328i | −0.739390 | + | 1.28066i | 0.213381 | + | 0.976969i | \(0.431552\pi\) |
−0.952770 | + | 0.303691i | \(0.901781\pi\) | |||||||
\(440\) | 18.3290 | 0.873799 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.24695 | −0.344702 | ||||||||
\(443\) | −10.1883 | + | 17.6466i | −0.484059 | + | 0.838415i | −0.999832 | − | 0.0183103i | \(-0.994171\pi\) |
0.515773 | + | 0.856725i | \(0.327505\pi\) | |||||||
\(444\) | 9.77810 | − | 3.51976i | 0.464048 | − | 0.167040i | ||||
\(445\) | 14.6235 | + | 25.3286i | 0.693219 | + | 1.20069i | ||||
\(446\) | −3.25937 | − | 5.64539i | −0.154336 | − | 0.267317i | ||||
\(447\) | −8.55087 | + | 3.07800i | −0.404442 | + | 0.145585i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | −2.81174 | − | 16.6345i | −0.132547 | − | 0.784156i | ||||
\(451\) | −33.2073 | −1.56367 | ||||||||
\(452\) | 3.68826 | − | 6.38826i | 0.173481 | − | 0.300478i | ||||
\(453\) | 11.4078 | + | 9.64134i | 0.535985 | + | 0.452990i | ||||
\(454\) | 14.3603 | + | 24.8728i | 0.673964 | + | 1.16734i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.811738 | − | 4.51011i | 0.0380131 | − | 0.211205i | ||||
\(457\) | −5.50000 | + | 9.52628i | −0.257279 | + | 0.445621i | −0.965512 | − | 0.260358i | \(-0.916159\pi\) |
0.708233 | + | 0.705979i | \(0.249493\pi\) | |||||||
\(458\) | 26.8798 | 1.25601 | ||||||||
\(459\) | −15.6235 | + | 26.4085i | −0.729241 | + | 1.23264i | ||||
\(460\) | −21.5883 | −1.00656 | ||||||||
\(461\) | −4.88905 | + | 8.46808i | −0.227706 | + | 0.394398i | −0.957128 | − | 0.289666i | \(-0.906456\pi\) |
0.729422 | + | 0.684064i | \(0.239789\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.6883 | − | 21.9767i | −0.589674 | − | 1.02134i | −0.994275 | − | 0.106851i | \(-0.965923\pi\) |
0.404601 | − | 0.914493i | \(-0.367410\pi\) | |||||||
\(464\) | 2.00000 | + | 3.46410i | 0.0928477 | + | 0.160817i | ||||
\(465\) | 5.29150 | + | 4.47214i | 0.245388 | + | 0.207390i | ||||
\(466\) | 8.50000 | − | 14.7224i | 0.393755 | − | 0.682003i | ||||
\(467\) | 11.1966 | 0.518118 | 0.259059 | − | 0.965862i | \(-0.416588\pi\) | ||||
0.259059 | + | 0.965862i | \(0.416588\pi\) | |||||||
\(468\) | −2.83704 | + | 2.34651i | −0.131142 | + | 0.108467i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −17.2470 | + | 29.8726i | −0.795543 | + | 1.37792i | ||||
\(471\) | 26.5587 | − | 9.56016i | 1.22376 | − | 0.440509i | ||||
\(472\) | −7.43916 | − | 12.8850i | −0.342415 | − | 0.593080i | ||||
\(473\) | −21.4352 | − | 37.1269i | −0.985592 | − | 1.70710i | ||||
\(474\) | −5.50267 | + | 1.98076i | −0.252746 | + | 0.0909793i | ||||
\(475\) | −7.43916 | + | 12.8850i | −0.341332 | + | 0.591204i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.2470 | + | 4.18403i | 0.514962 | + | 0.191574i | ||||
\(478\) | −12.6235 | −0.577384 | ||||||||
\(479\) | −7.74597 | + | 13.4164i | −0.353922 | + | 0.613011i | −0.986933 | − | 0.161132i | \(-0.948486\pi\) |
0.633011 | + | 0.774143i | \(0.281819\pi\) | |||||||
\(480\) | −4.31174 | − | 3.64408i | −0.196803 | − | 0.166329i | ||||
\(481\) | 3.68170 | + | 6.37688i | 0.167871 | + | 0.290761i | ||||
\(482\) | 13.3443 | + | 23.1130i | 0.607815 | + | 1.05277i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.3117 | + | 17.8605i | −0.468715 | + | 0.811839i | ||||
\(485\) | −10.0000 | −0.454077 | ||||||||
\(486\) | 2.43459 | + | 15.3972i | 0.110435 | + | 0.698430i | ||||
\(487\) | 4.62348 | 0.209510 | 0.104755 | − | 0.994498i | \(-0.466594\pi\) | ||||
0.104755 | + | 0.994498i | \(0.466594\pi\) | |||||||
\(488\) | −2.24330 | + | 3.88551i | −0.101549 | + | 0.175889i | ||||
\(489\) | 0.382574 | − | 2.12563i | 0.0173006 | − | 0.0961242i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.0587 | + | 31.2786i | 0.814977 | + | 1.41158i | 0.909344 | + | 0.416044i | \(0.136584\pi\) |
−0.0943671 | + | 0.995537i | \(0.530083\pi\) | |||||||
\(492\) | 7.81174 | + | 6.60212i | 0.352180 | + | 0.297647i | ||||
\(493\) | −11.8102 | + | 20.4559i | −0.531906 | + | 0.921289i | ||||
\(494\) | 3.24695 | 0.146087 | ||||||||
\(495\) | 51.5363 | + | 19.1722i | 2.31638 | + | 0.861728i | ||||
\(496\) | 1.22723 | 0.0551043 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.6235 | − | 4.54399i | 0.565671 | − | 0.203621i | ||||
\(499\) | −4.18826 | − | 7.25428i | −0.187492 | − | 0.324746i | 0.756921 | − | 0.653506i | \(-0.226703\pi\) |
−0.944414 | + | 0.328760i | \(0.893369\pi\) | |||||||
\(500\) | 1.01607 | + | 1.75988i | 0.0454399 | + | 0.0787043i | ||||
\(501\) | −10.6235 | + | 3.82407i | −0.474622 | + | 0.170847i | ||||
\(502\) | −2.55011 | + | 4.41692i | −0.113817 | + | 0.197137i | ||||
\(503\) | 20.7834 | 0.926688 | 0.463344 | − | 0.886179i | \(-0.346650\pi\) | ||||
0.463344 | + | 0.886179i | \(0.346650\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −41.1174 | −1.82970 | ||||||||
\(506\) | 18.6235 | − | 32.2568i | 0.827914 | − | 1.43399i | ||||
\(507\) | 15.2050 | + | 12.8506i | 0.675278 | + | 0.570714i | ||||
\(508\) | −0.688262 | − | 1.19211i | −0.0305367 | − | 0.0528911i | ||||
\(509\) | −8.35958 | − | 14.4792i | −0.370532 | − | 0.641780i | 0.619115 | − | 0.785300i | \(-0.287491\pi\) |
−0.989647 | + | 0.143520i | \(0.954158\pi\) | |||||||
\(510\) | 5.90512 | − | 32.8095i | 0.261483 | − | 1.45283i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.00000 | − | 11.8322i | 0.309058 | − | 0.522403i | ||||
\(514\) | 0.996190 | 0.0439401 | ||||||||
\(515\) | −15.2470 | + | 26.4085i | −0.671861 | + | 1.16370i | ||||
\(516\) | −2.33894 | + | 12.9954i | −0.102966 | + | 0.572092i | ||||
\(517\) | −29.7566 | − | 51.5400i | −1.30870 | − | 2.26673i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.62348 | − | 1.37209i | −0.0712627 | − | 0.0602279i | ||||
\(520\) | 2.00000 | − | 3.46410i | 0.0877058 | − | 0.151911i | ||||
\(521\) | 31.1354 | 1.36407 | 0.682033 | − | 0.731321i | \(-0.261096\pi\) | ||||
0.682033 | + | 0.731321i | \(0.261096\pi\) | |||||||
\(522\) | 2.00000 | + | 11.8322i | 0.0875376 | + | 0.517880i | ||||
\(523\) | 12.2326 | 0.534893 | 0.267446 | − | 0.963573i | \(-0.413820\pi\) | ||||
0.267446 | + | 0.963573i | \(0.413820\pi\) | |||||||
\(524\) | 2.85692 | − | 4.94832i | 0.124805 | − | 0.216169i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.68826 | − | 2.92416i | −0.0736117 | − | 0.127499i | ||||
\(527\) | 3.62348 | + | 6.27604i | 0.157841 | + | 0.273389i | ||||
\(528\) | 9.16449 | − | 3.29888i | 0.398833 | − | 0.143565i | ||||
\(529\) | −10.4352 | + | 18.0743i | −0.453705 | + | 0.785840i | ||||
\(530\) | −13.0375 | −0.566311 | ||||||||
\(531\) | −7.43916 | − | 44.0107i | −0.322832 | − | 1.90990i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.62348 | + | 6.27604i | −0.156950 | + | 0.271846i | ||||
\(534\) | 11.8704 | + | 10.0323i | 0.513684 | + | 0.434142i | ||||
\(535\) | 0.613616 | + | 1.06281i | 0.0265289 | + | 0.0459495i | ||||
\(536\) | −2.81174 | − | 4.87007i | −0.121449 | − | 0.210355i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.0214 | − | 20.8217i | 0.518279 | − | 0.897686i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.31174 | − | 14.7563i | −0.357680 | − | 0.635011i | ||||
\(541\) | 4.00000 | 0.171973 | 0.0859867 | − | 0.996296i | \(-0.472596\pi\) | ||||
0.0859867 | + | 0.996296i | \(0.472596\pi\) | |||||||
\(542\) | 1.41852 | − | 2.45695i | 0.0609306 | − | 0.105535i | ||||
\(543\) | 1.37652 | − | 7.64813i | 0.0590723 | − | 0.328213i | ||||
\(544\) | −2.95256 | − | 5.11398i | −0.126590 | − | 0.219260i | ||||
\(545\) | 18.3290 | + | 31.7467i | 0.785127 | + | 1.35988i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.81174 | + | 16.9944i | −0.419520 | + | 0.726629i | −0.995891 | − | 0.0905585i | \(-0.971135\pi\) |
0.576372 | + | 0.817188i | \(0.304468\pi\) | |||||||
\(548\) | −20.8704 | −0.891540 | ||||||||
\(549\) | −10.3718 | + | 8.57852i | −0.442659 | + | 0.366123i | ||||
\(550\) | −31.6235 | −1.34843 | ||||||||
\(551\) | 5.29150 | − | 9.16515i | 0.225426 | − | 0.390449i | ||||
\(552\) | −10.7942 | + | 3.88551i | −0.459430 | + | 0.165378i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.2470 | − | 24.6764i | −0.605295 | − | 1.04840i | ||||
\(555\) | −31.8704 | + | 11.4722i | −1.35282 | + | 0.486968i | ||||
\(556\) | −3.96863 | + | 6.87386i | −0.168307 | + | 0.291517i | ||||
\(557\) | 22.7530 | 0.964078 | 0.482039 | − | 0.876150i | \(-0.339896\pi\) | ||||
0.482039 | + | 0.876150i | \(0.339896\pi\) | |||||||
\(558\) | 3.45065 | + | 1.28369i | 0.146078 | + | 0.0543431i | ||||
\(559\) | −9.35577 | −0.395707 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 43.9291 | + | 37.1269i | 1.85469 | + | 1.56750i | ||||
\(562\) | −12.9352 | − | 22.4044i | −0.545639 | − | 0.945075i | ||||
\(563\) | −2.74139 | − | 4.74824i | −0.115536 | − | 0.200114i | 0.802458 | − | 0.596709i | \(-0.203525\pi\) |
−0.917994 | + | 0.396595i | \(0.870192\pi\) | |||||||
\(564\) | −3.24695 | + | 18.0404i | −0.136721 | + | 0.759639i | ||||
\(565\) | −12.0214 | + | 20.8217i | −0.505744 | + | 0.875975i | ||||
\(566\) | −7.32364 | −0.307835 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.6235 | 0.445751 | ||||||||
\(569\) | −14.4352 | + | 25.0025i | −0.605156 | + | 1.04816i | 0.386871 | + | 0.922134i | \(0.373556\pi\) |
−0.992027 | + | 0.126027i | \(0.959778\pi\) | |||||||
\(570\) | −2.64575 | + | 14.7001i | −0.110818 | + | 0.615719i | ||||
\(571\) | 4.18826 | + | 7.25428i | 0.175273 | + | 0.303582i | 0.940256 | − | 0.340469i | \(-0.110586\pi\) |
−0.764983 | + | 0.644051i | \(0.777252\pi\) | |||||||
\(572\) | 3.45065 | + | 5.97671i | 0.144279 | + | 0.249899i | ||||
\(573\) | −7.11247 | − | 6.01114i | −0.297128 | − | 0.251119i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 37.2470 | 1.55331 | ||||||||
\(576\) | −2.81174 | − | 1.04601i | −0.117156 | − | 0.0435836i | ||||
\(577\) | −16.4881 | −0.686410 | −0.343205 | − | 0.939261i | \(-0.611512\pi\) | ||||
−0.343205 | + | 0.939261i | \(0.611512\pi\) | |||||||
\(578\) | 8.93521 | − | 15.4762i | 0.371656 | − | 0.643727i | ||||
\(579\) | 21.9908 | − | 7.91589i | 0.913906 | − | 0.328973i | ||||
\(580\) | −6.51873 | − | 11.2908i | −0.270676 | − | 0.468824i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.00000 | + | 1.79982i | −0.207257 | + | 0.0746049i | ||||
\(583\) | 11.2470 | − | 19.4803i | 0.465801 | − | 0.806791i | ||||
\(584\) | −11.1966 | −0.463319 | ||||||||
\(585\) | 9.24695 | − | 7.64813i | 0.382314 | − | 0.316211i | ||||
\(586\) | −25.6526 | −1.05970 | ||||||||
\(587\) | −1.51416 | + | 2.62261i | −0.0624962 | + | 0.108247i | −0.895581 | − | 0.444899i | \(-0.853239\pi\) |
0.833084 | + | 0.553146i | \(0.186573\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.62348 | − | 2.81194i | −0.0668941 | − | 0.115864i | ||||
\(590\) | 24.2470 | + | 41.9970i | 0.998231 | + | 1.72899i | ||||
\(591\) | −2.22342 | + | 12.3536i | −0.0914594 | + | 0.508159i | ||||
\(592\) | −3.00000 | + | 5.19615i | −0.123299 | + | 0.213561i | ||||
\(593\) | 12.1928 | 0.500699 | 0.250349 | − | 0.968156i | \(-0.419455\pi\) | ||||
0.250349 | + | 0.968156i | \(0.419455\pi\) | |||||||
\(594\) | 29.2188 | + | 0.310528i | 1.19886 | + | 0.0127411i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.62348 | − | 4.54399i | 0.107462 | − | 0.186129i | ||||
\(597\) | 3.12957 | − | 17.3883i | 0.128085 | − | 0.711655i | ||||
\(598\) | −4.06427 | − | 7.03952i | −0.166200 | − | 0.287868i | ||||
\(599\) | 1.24695 | + | 2.15978i | 0.0509490 | + | 0.0882463i | 0.890375 | − | 0.455227i | \(-0.150442\pi\) |
−0.839426 | + | 0.543474i | \(0.817109\pi\) | |||||||
\(600\) | 7.43916 | + | 6.28724i | 0.303702 | + | 0.256675i | ||||
\(601\) | −19.8630 | + | 34.4037i | −0.810229 | + | 1.40336i | 0.102474 | + | 0.994736i | \(0.467324\pi\) |
−0.912704 | + | 0.408622i | \(0.866009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.81174 | − | 16.6345i | −0.114503 | − | 0.677408i | ||||
\(604\) | −8.62348 | −0.350884 | ||||||||
\(605\) | 33.6097 | − | 58.2138i | 1.36643 | − | 2.36673i | ||||
\(606\) | −20.5587 | + | 7.40038i | −0.835140 | + | 0.300620i | ||||
\(607\) | −13.8424 | − | 23.9757i | −0.561845 | − | 0.973143i | −0.997336 | − | 0.0729503i | \(-0.976759\pi\) |
0.435491 | − | 0.900193i | \(-0.356575\pi\) | |||||||
\(608\) | 1.32288 | + | 2.29129i | 0.0536497 | + | 0.0929240i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.31174 | − | 12.6643i | 0.296044 | − | 0.512763i | ||||
\(611\) | −12.9878 | −0.525430 | ||||||||
\(612\) | −2.95256 | − | 17.4676i | −0.119350 | − | 0.706085i | ||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | 6.61438 | − | 11.4564i | 0.266935 | − | 0.462344i | ||||
\(615\) | −25.4613 | − | 21.5187i | −1.02670 | − | 0.867720i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.0587 | − | 34.7427i | −0.807532 | − | 1.39869i | −0.914568 | − | 0.404432i | \(-0.867469\pi\) |
0.107036 | − | 0.994255i | \(-0.465864\pi\) | |||||||
\(618\) | −2.87043 | + | 15.9484i | −0.115465 | + | 0.641540i | ||||
\(619\) | 17.0061 | − | 29.4554i | 0.683533 | − | 1.18391i | −0.290363 | − | 0.956917i | \(-0.593776\pi\) |
0.973896 | − | 0.226997i | \(-0.0728907\pi\) | |||||||
\(620\) | −4.00000 | −0.160644 | ||||||||
\(621\) | −34.4146 | − | 0.365747i | −1.38101 | − | 0.0146769i | ||||
\(622\) | −20.7834 | −0.833340 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.376525 | − | 2.09201i | 0.0150730 | − | 0.0837476i | ||||
\(625\) | 10.7470 | + | 18.6143i | 0.429878 | + | 0.744571i | ||||
\(626\) | 10.8898 | + | 18.8617i | 0.435244 | + | 0.753866i | ||||
\(627\) | −19.6822 | − | 16.6345i | −0.786030 | − | 0.664317i | ||||
\(628\) | −8.14842 | + | 14.1135i | −0.325157 | + | 0.563189i | ||||
\(629\) | −35.4307 | −1.41271 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.6235 | 1.21910 | 0.609551 | − | 0.792747i | \(-0.291350\pi\) | ||||
0.609551 | + | 0.792747i | \(0.291350\pi\) | |||||||
\(632\) | 1.68826 | − | 2.92416i | 0.0671555 | − | 0.116317i | ||||
\(633\) | −8.55087 | + | 3.07800i | −0.339867 | + | 0.122340i | ||||
\(634\) | 3.62348 | + | 6.27604i | 0.143907 | + | 0.249254i | ||||
\(635\) | 2.24330 | + | 3.88551i | 0.0890226 | + | 0.154192i | ||||
\(636\) | −6.51873 | + | 2.34651i | −0.258485 | + | 0.0930451i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.4939 | 0.890542 | ||||||||
\(639\) | 29.8704 | + | 11.1122i | 1.18166 | + | 0.439593i | ||||
\(640\) | 3.25937 | 0.128838 | ||||||||
\(641\) | 12.7470 | − | 22.0784i | 0.503474 | − | 0.872043i | −0.496518 | − | 0.868027i | \(-0.665388\pi\) |
0.999992 | − | 0.00401642i | \(-0.00127847\pi\) | |||||||
\(642\) | 0.498095 | + | 0.420967i | 0.0196583 | + | 0.0166143i | ||||
\(643\) | 6.82554 | + | 11.8222i | 0.269173 | + | 0.466222i | 0.968649 | − | 0.248435i | \(-0.0799163\pi\) |
−0.699475 | + | 0.714657i | \(0.746583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.62348 | − | 42.3569i | 0.300174 | − | 1.66780i | ||||
\(646\) | −7.81174 | + | 13.5303i | −0.307349 | + | 0.532344i | ||||
\(647\) | −35.0481 | −1.37788 | −0.688942 | − | 0.724816i | \(-0.741925\pi\) | ||||
−0.688942 | + | 0.724816i | \(0.741925\pi\) | |||||||
\(648\) | −6.81174 | − | 5.88220i | −0.267590 | − | 0.231074i | ||||
\(649\) | −83.6679 | −3.28425 | ||||||||
\(650\) | −3.45065 | + | 5.97671i | −0.135346 | + | 0.234426i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.623475 | + | 1.07989i | 0.0244172 | + | 0.0422918i | ||||
\(653\) | −19.6235 | − | 33.9889i | −0.767926 | − | 1.33009i | −0.938686 | − | 0.344774i | \(-0.887956\pi\) |
0.170760 | − | 0.985313i | \(-0.445378\pi\) | |||||||
\(654\) | 14.8783 | + | 12.5745i | 0.581788 | + | 0.491701i | ||||
\(655\) | −9.31174 | + | 16.1284i | −0.363840 | + | 0.630189i | ||||
\(656\) | −5.90512 | −0.230556 | ||||||||
\(657\) | −31.4820 | − | 11.7117i | −1.22823 | − | 0.456919i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.24695 | − | 9.08799i | 0.204392 | − | 0.354018i | −0.745547 | − | 0.666453i | \(-0.767812\pi\) |
0.949939 | + | 0.312436i | \(0.101145\pi\) | |||||||
\(660\) | −29.8704 | + | 10.7523i | −1.16270 | + | 0.418531i | ||||
\(661\) | 1.43840 | + | 2.49138i | 0.0559471 | + | 0.0969033i | 0.892643 | − | 0.450765i | \(-0.148849\pi\) |
−0.836695 | + | 0.547669i | \(0.815516\pi\) | |||||||
\(662\) | 4.00000 | + | 6.92820i | 0.155464 | + | 0.269272i | ||||
\(663\) | 11.8102 | − | 4.25126i | 0.458672 | − | 0.165105i | ||||
\(664\) | −3.87298 | + | 6.70820i | −0.150301 | + | 0.260329i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.8704 | + | 11.4722i | −0.537468 | + | 0.444539i | ||||
\(667\) | −26.4939 | −1.02585 | ||||||||
\(668\) | 3.25937 | − | 5.64539i | 0.126109 | − | 0.218427i | ||||
\(669\) | 8.62348 | + | 7.28817i | 0.333403 | + | 0.281777i | ||||
\(670\) | 9.16449 | + | 15.8734i | 0.354055 | + | 0.613241i | ||||
\(671\) | 12.6151 | + | 21.8501i | 0.487002 | + | 0.843512i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.68826 | + | 16.7806i | −0.373455 | + | 0.646843i | −0.990095 | − | 0.140403i | \(-0.955160\pi\) |
0.616639 | + | 0.787246i | \(0.288494\pi\) | |||||||
\(674\) | −3.12957 | −0.120547 | ||||||||
\(675\) | 14.3405 | + | 25.4595i | 0.551965 | + | 0.979936i | ||||
\(676\) | −11.4939 | −0.442073 | ||||||||
\(677\) | 21.3971 | − | 37.0608i | 0.822356 | − | 1.42436i | −0.0815682 | − | 0.996668i | \(-0.525993\pi\) |
0.903924 | − | 0.427694i | \(-0.140674\pi\) | |||||||
\(678\) | −2.26318 | + | 12.5745i | −0.0869168 | + | 0.482920i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 9.62348 | + | 16.6683i | 0.369043 | + | 0.639202i | ||||
\(681\) | −37.9939 | − | 32.1107i | −1.45593 | − | 1.23048i | ||||
\(682\) | 3.45065 | − | 5.97671i | 0.132132 | − | 0.228860i | ||||
\(683\) | −27.3643 | −1.04707 | −0.523533 | − | 0.852005i | \(-0.675386\pi\) | ||||
−0.523533 | + | 0.852005i | \(0.675386\pi\) | |||||||
\(684\) | 1.32288 | + | 7.82624i | 0.0505814 | + | 0.299244i | ||||
\(685\) | 68.0244 | 2.59908 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.8056 | + | 15.7684i | −1.67129 | + | 0.601603i | ||||
\(688\) | −3.81174 | − | 6.60212i | −0.145321 | − | 0.251704i | ||||
\(689\) | −2.45446 | − | 4.25126i | −0.0935076 | − | 0.161960i | ||||
\(690\) | 35.1822 | − | 12.6643i | 1.33936 | − | 0.482122i | ||||
\(691\) | −7.34352 | + | 12.7193i | −0.279360 | + | 0.483867i | −0.971226 | − | 0.238160i | \(-0.923456\pi\) |
0.691865 | + | 0.722026i | \(0.256789\pi\) | |||||||
\(692\) | 1.22723 | 0.0466524 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.62348 | 0.137545 | ||||||||
\(695\) | 12.9352 | − | 22.4044i | 0.490661 | − | 0.849849i | ||||
\(696\) | −5.29150 | − | 4.47214i | −0.200574 | − | 0.169516i | ||||
\(697\) | −17.4352 | − | 30.1987i | −0.660406 | − | 1.14386i | ||||
\(698\) | −13.6511 | − | 23.6444i | −0.516701 | − | 0.894953i | ||||
\(699\) | −5.21574 | + | 28.9792i | −0.197277 | + | 1.09610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.2470 | −0.802486 | −0.401243 | − | 0.915972i | \(-0.631422\pi\) | ||||
−0.401243 | + | 0.915972i | \(0.631422\pi\) | |||||||
\(702\) | 3.24695 | − | 5.48835i | 0.122548 | − | 0.207144i | ||||
\(703\) | 15.8745 | 0.598718 | ||||||||
\(704\) | −2.81174 | + | 4.87007i | −0.105971 | + | 0.183548i | ||||
\(705\) | 10.5830 | − | 58.8004i | 0.398579 | − | 2.21455i | ||||
\(706\) | −2.95256 | − | 5.11398i | −0.111121 | − | 0.192467i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 19.6822 | + | 16.6345i | 0.739701 | + | 0.625161i | ||||
\(709\) | −9.24695 | + | 16.0162i | −0.347277 | + | 0.601501i | −0.985765 | − | 0.168131i | \(-0.946227\pi\) |
0.638488 | + | 0.769632i | \(0.279560\pi\) | |||||||
\(710\) | −34.6258 | −1.29948 | ||||||||
\(711\) | 7.80564 | − | 6.45603i | 0.292734 | − | 0.242120i | ||||
\(712\) | −8.97320 | −0.336285 | ||||||||
\(713\) | −4.06427 | + | 7.03952i | −0.152208 | + | 0.263632i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.2470 | − | 19.4803i | −0.420612 | − | 0.728522i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.5723 | − | 7.40527i | 0.768286 | − | 0.276555i | ||||
\(718\) | 15.5587 | − | 26.9484i | 0.580645 | − | 1.00571i | ||||
\(719\) | −11.8102 | −0.440448 | −0.220224 | − | 0.975449i | \(-0.570679\pi\) | ||||
−0.220224 | + | 0.975449i | \(0.570679\pi\) | |||||||
\(720\) | 9.16449 | + | 3.40932i | 0.341540 | + | 0.127058i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.00000 | + | 10.3923i | −0.223297 | + | 0.386762i | ||||
\(723\) | −35.3056 | − | 29.8387i | −1.31303 | − | 1.10971i | ||||
\(724\) | 2.24330 | + | 3.88551i | 0.0833716 | + | 0.144404i | ||||
\(725\) | 11.2470 | + | 19.4803i | 0.417701 | + | 0.723480i | ||||
\(726\) | 6.32745 | − | 35.1560i | 0.234834 | − | 1.30476i | ||||
\(727\) | 22.2020 | − | 38.4549i | 0.823425 | − | 1.42621i | −0.0796922 | − | 0.996820i | \(-0.525394\pi\) |
0.903117 | − | 0.429394i | \(-0.141273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | − | 23.6643i | −0.481481 | − | 0.876456i | ||||
\(730\) | 36.4939 | 1.35070 | ||||||||
\(731\) | 22.5088 | − | 38.9863i | 0.832517 | − | 1.44196i | ||||
\(732\) | 1.37652 | − | 7.64813i | 0.0508778 | − | 0.282683i | ||||
\(733\) | 4.08415 | + | 7.07395i | 0.150851 | + | 0.261282i | 0.931541 | − | 0.363637i | \(-0.118465\pi\) |
−0.780689 | + | 0.624919i | \(0.785132\pi\) | |||||||
\(734\) | −3.45065 | − | 5.97671i | −0.127366 | − | 0.220604i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.31174 | − | 5.73610i | 0.122072 | − | 0.211435i | ||||
\(737\) | −31.6235 | −1.16487 | ||||||||
\(738\) | −16.6036 | − | 6.17680i | −0.611189 | − | 0.227371i | ||||
\(739\) | 20.8704 | 0.767731 | 0.383866 | − | 0.923389i | \(-0.374593\pi\) | ||||
0.383866 | + | 0.923389i | \(0.374593\pi\) | |||||||
\(740\) | 9.77810 | − | 16.9362i | 0.359450 | − | 0.622586i | ||||
\(741\) | −5.29150 | + | 1.90475i | −0.194388 | + | 0.0699727i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.6235 | − | 27.0607i | −0.573170 | − | 0.992759i | −0.996238 | − | 0.0866612i | \(-0.972380\pi\) |
0.423068 | − | 0.906098i | \(-0.360953\pi\) | |||||||
\(744\) | −2.00000 | + | 0.719927i | −0.0733236 | + | 0.0263938i | ||||
\(745\) | −8.55087 | + | 14.8105i | −0.313280 | + | 0.542616i | ||||
\(746\) | −11.2470 | −0.411780 | ||||||||
\(747\) | −17.9066 | + | 14.8105i | −0.655170 | + | 0.541889i | ||||
\(748\) | −33.2073 | −1.21418 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.68826 | − | 2.27200i | −0.0981615 | − | 0.0829616i | ||||
\(751\) | 5.68826 | + | 9.85236i | 0.207568 | + | 0.359518i | 0.950948 | − | 0.309351i | \(-0.100112\pi\) |
−0.743380 | + | 0.668869i | \(0.766779\pi\) | |||||||
\(752\) | −5.29150 | − | 9.16515i | −0.192961 | − | 0.334219i | ||||
\(753\) | 1.56479 | − | 8.69414i | 0.0570240 | − | 0.316832i | ||||
\(754\) | 2.45446 | − | 4.25126i | 0.0893863 | − | 0.154822i | ||||
\(755\) | 28.1071 | 1.02292 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.7409 | 1.58979 | 0.794894 | − | 0.606748i | \(-0.207526\pi\) | ||||
0.794894 | + | 0.606748i | \(0.207526\pi\) | |||||||
\(758\) | 7.81174 | − | 13.5303i | 0.283735 | − | 0.491444i | ||||
\(759\) | −11.4277 | + | 63.4934i | −0.414798 | + | 2.30467i | ||||
\(760\) | −4.31174 | − | 7.46815i | −0.156403 | − | 0.270898i | ||||
\(761\) | 2.83704 | + | 4.91389i | 0.102843 | + | 0.178129i | 0.912855 | − | 0.408285i | \(-0.133873\pi\) |
−0.810012 | + | 0.586413i | \(0.800540\pi\) | |||||||
\(762\) | 1.82097 | + | 1.53900i | 0.0659668 | + | 0.0557521i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.37652 | 0.194516 | ||||||||
\(765\) | 9.62348 | + | 56.9332i | 0.347937 | + | 2.05843i | ||||
\(766\) | −27.6847 | −1.00029 | ||||||||
\(767\) | −9.12957 | + | 15.8129i | −0.329650 | + | 0.570970i | ||||
\(768\) | 1.62968 | − | 0.586627i | 0.0588061 | − | 0.0211681i | ||||
\(769\) | 0.422329 | + | 0.731495i | 0.0152296 | + | 0.0263784i | 0.873540 | − | 0.486753i | \(-0.161819\pi\) |
−0.858310 | + | 0.513131i | \(0.828485\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.62348 | + | 0.584392i | −0.0584680 | + | 0.0210464i | ||||
\(772\) | −6.74695 | + | 11.6861i | −0.242828 | + | 0.420591i | ||||
\(773\) | −13.4598 | −0.484115 | −0.242058 | − | 0.970262i | \(-0.577822\pi\) | ||||
−0.242058 | + | 0.970262i | \(0.577822\pi\) | |||||||
\(774\) | −3.81174 | − | 22.5505i | −0.137010 | − | 0.810563i | ||||
\(775\) | 6.90131 | 0.247902 | ||||||||
\(776\) | 1.53404 | − | 2.65704i | 0.0550688 | − | 0.0953820i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.6235 | + | 32.2568i | 0.667684 | + | 1.15646i | ||||
\(779\) | 7.81174 | + | 13.5303i | 0.279885 | + | 0.484774i | ||||
\(780\) | −1.22723 | + | 6.81864i | −0.0439420 | + | 0.244147i | ||||
\(781\) | 29.8704 | − | 51.7371i | 1.06885 | − | 1.85130i | ||||
\(782\) | 39.1124 | 1.39866 | ||||||||
\(783\) | −10.2004 | − | 18.1094i | −0.364534 | − | 0.647178i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.5587 | − | 46.0010i | 0.947920 | − | 1.64185i | ||||
\(786\) | −1.75305 | + | 9.74015i | −0.0625292 | + | 0.347419i | ||||
\(787\) | 13.2288 | + | 22.9129i | 0.471554 | + | 0.816756i | 0.999470 | − | 0.0325406i | \(-0.0103598\pi\) |
−0.527916 | + | 0.849296i | \(0.677026\pi\) | |||||||
\(788\) | −3.62348 | − | 6.27604i | −0.129081 | − | 0.223575i | ||||
\(789\) | 4.46672 | + | 3.77507i | 0.159020 | + | 0.134396i | ||||
\(790\) | −5.50267 | + | 9.53090i | −0.195776 | + | 0.339094i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −13.0000 | + | 10.7523i | −0.461935 | + | 0.382065i | ||||
\(793\) | 5.50610 | 0.195527 | ||||||||
\(794\) | −4.67789 | + | 8.10234i | −0.166012 | + | 0.287541i | ||||
\(795\) | 21.2470 | − | 7.64813i | 0.753552 | − | 0.271251i | ||||
\(796\) | 5.10022 | + | 8.83383i | 0.180772 | + | 0.313107i | ||||
\(797\) | 8.76203 | + | 15.1763i | 0.310367 | + | 0.537572i | 0.978442 | − | 0.206523i | \(-0.0662147\pi\) |
−0.668075 | + | 0.744094i | \(0.732881\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.2470 | − | 54.1213i | 1.10544 | − | 1.91467i | ||||
\(800\) | −5.62348 | −0.198820 | ||||||||
\(801\) | −25.2303 | − | 9.38603i | −0.891468 | − | 0.331639i | ||||
\(802\) | 15.0000 | 0.529668 | ||||||||
\(803\) | −31.4820 | + | 54.5284i | −1.11097 | + | 1.92426i | ||||
\(804\) | 7.43916 | + | 6.28724i | 0.262359 | + | 0.221734i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.753049 | − | 1.30432i | −0.0265250 | − | 0.0459427i | ||||
\(807\) | −7.37652 | + | 40.9848i | −0.259666 | + | 1.44273i | ||||
\(808\) | 6.30757 | − | 10.9250i | 0.221900 | − | 0.384341i | ||||
\(809\) | 24.1174 | 0.847922 | 0.423961 | − | 0.905680i | \(-0.360639\pi\) | ||||
0.423961 | + | 0.905680i | \(0.360639\pi\) | |||||||
\(810\) | 22.2020 | + | 19.1722i | 0.780097 | + | 0.673644i | ||||
\(811\) | −7.51493 | −0.263885 | −0.131942 | − | 0.991257i | \(-0.542121\pi\) | ||||
−0.131942 | + | 0.991257i | \(0.542121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.870426 | + | 4.83619i | −0.0305272 | + | 0.169613i | ||||
\(814\) | 16.8704 | + | 29.2204i | 0.591308 | + | 1.02418i | ||||
\(815\) | −2.03214 | − | 3.51976i | −0.0711826 | − | 0.123292i | ||||
\(816\) | 7.81174 | + | 6.60212i | 0.273466 | + | 0.231121i | ||||
\(817\) | −10.0849 | + | 17.4676i | −0.352826 | + | 0.611113i | ||||
\(818\) | −2.22342 | −0.0777401 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.2470 | 0.672133 | ||||||||
\(821\) | 18.8704 | − | 32.6845i | 0.658582 | − | 1.14070i | −0.322400 | − | 0.946603i | \(-0.604490\pi\) |
0.980983 | − | 0.194095i | \(-0.0621769\pi\) | |||||||
\(822\) | 34.0122 | − | 12.2432i | 1.18631 | − | 0.427029i | ||||
\(823\) | −12.8704 | − | 22.2922i | −0.448635 | − | 0.777058i | 0.549663 | − | 0.835387i | \(-0.314756\pi\) |
−0.998297 | + | 0.0583284i | \(0.981423\pi\) | |||||||
\(824\) | −4.67789 | − | 8.10234i | −0.162962 | − | 0.282258i | ||||
\(825\) | 51.5363 | − | 18.5512i | 1.79426 | − | 0.645869i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.2470 | 0.877922 | 0.438961 | − | 0.898506i | \(-0.355347\pi\) | ||||
0.438961 | + | 0.898506i | \(0.355347\pi\) | |||||||
\(828\) | 15.3117 | − | 12.6643i | 0.532120 | − | 0.440115i | ||||
\(829\) | 4.90893 | 0.170494 | 0.0852471 | − | 0.996360i | \(-0.472832\pi\) | ||||
0.0852471 | + | 0.996360i | \(0.472832\pi\) | |||||||
\(830\) | 12.6235 | − | 21.8645i | 0.438167 | − | 0.758928i | ||||
\(831\) | 37.6939 | + | 31.8572i | 1.30759 | + | 1.10511i | ||||
\(832\) | 0.613616 | + | 1.06281i | 0.0212733 | + | 0.0368465i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.43521 | − | 13.5303i | 0.0843245 | − | 0.468517i | ||||
\(835\) | −10.6235 | + | 18.4004i | −0.367641 | + | 0.636772i | ||||
\(836\) | 14.8783 | 0.514577 | ||||||||
\(837\) | −6.37652 | − | 0.0677676i | −0.220405 | − | 0.00234239i | ||||
\(838\) | −0.804903 | −0.0278049 | ||||||||
\(839\) | 17.9066 | − | 31.0152i | 0.618206 | − | 1.07076i | −0.371607 | − | 0.928390i | \(-0.621193\pi\) |
0.989813 | − | 0.142374i | \(-0.0454736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | + | 11.2583i | 0.224138 | + | 0.388218i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.2234 | + | 28.9240i | 1.17872 | + | 0.996196i | ||||
\(844\) | 2.62348 | − | 4.54399i | 0.0903037 | − | 0.156411i | ||||
\(845\) | 37.4628 | 1.28876 | ||||||||
\(846\) | −5.29150 | − | 31.3050i | −0.181926 | − | 1.07629i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.00000 | − | 3.46410i | 0.0686803 | − | 0.118958i | ||||
\(849\) | 11.9352 | − | 4.29624i | 0.409615 | − | 0.147447i | ||||
\(850\) | −16.6036 | − | 28.7584i | −0.569500 | − | 0.986403i | ||||
\(851\) | −19.8704 | − | 34.4166i | −0.681149 | − | 1.17979i | ||||
\(852\) | −17.3129 | + | 6.23202i | −0.593130 | + | 0.213505i | ||||
\(853\) | −16.0857 | + | 27.8612i | −0.550763 | + | 0.953949i | 0.447457 | + | 0.894306i | \(0.352330\pi\) |
−0.998220 | + | 0.0596438i | \(0.981004\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.31174 | − | 25.5086i | −0.147458 | − | 0.872375i | ||||
\(856\) | −0.376525 | −0.0128693 | ||||||||
\(857\) | 6.09641 | − | 10.5593i | 0.208249 | − | 0.360698i | −0.742914 | − | 0.669387i | \(-0.766557\pi\) |
0.951163 | + | 0.308689i | \(0.0998901\pi\) | |||||||
\(858\) | −9.12957 | − | 7.71590i | −0.311679 | − | 0.263416i | ||||
\(859\) | −4.98469 | − | 8.63374i | −0.170076 | − | 0.294580i | 0.768371 | − | 0.640005i | \(-0.221068\pi\) |
−0.938446 | + | 0.345426i | \(0.887735\pi\) | |||||||
\(860\) | 12.4239 | + | 21.5187i | 0.423650 | + | 0.733783i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.00000 | + | 6.92820i | −0.136241 | + | 0.235976i | ||||
\(863\) | 37.8704 | 1.28912 | 0.644562 | − | 0.764552i | \(-0.277040\pi\) | ||||
0.644562 | + | 0.764552i | \(0.277040\pi\) | |||||||
\(864\) | 5.19586 | + | 0.0552199i | 0.176767 | + | 0.00187862i | ||||
\(865\) | −4.00000 | −0.136004 | ||||||||
\(866\) | −3.56618 | + | 6.17680i | −0.121184 | + | 0.209896i | ||||
\(867\) | −5.48279 | + | 30.4630i | −0.186205 | + | 1.03458i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.49390 | − | 16.4439i | −0.322059 | − | 0.557822i | ||||
\(870\) | 17.2470 | + | 14.5763i | 0.584726 | + | 0.494184i | ||||
\(871\) | −3.45065 | + | 5.97671i | −0.116921 | + | 0.202513i | ||||
\(872\) | −11.2470 | −0.380870 | ||||||||
\(873\) | 7.09260 | − | 5.86627i | 0.240048 | − | 0.198543i | ||||
\(874\) | −17.5241 | −0.592760 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 18.2470 | − | 6.56824i | 0.616507 | − | 0.221920i | ||||
\(877\) | −6.00000 | − | 10.3923i | −0.202606 | − | 0.350923i | 0.746762 | − | 0.665092i | \(-0.231608\pi\) |
−0.949367 | + | 0.314169i | \(0.898274\pi\) | |||||||
\(878\) | 15.4919 | + | 26.8328i | 0.522827 | + | 0.905564i | ||||
\(879\) | 41.8056 | − | 15.0485i | 1.41007 | − | 0.507574i | ||||
\(880\) | 9.16449 | − | 15.8734i | 0.308935 | − | 0.535091i | ||||
\(881\) | −4.90893 | −0.165386 | −0.0826930 | − | 0.996575i | \(-0.526352\pi\) | ||||
−0.0826930 | + | 0.996575i | \(0.526352\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.12957 | −0.105319 | −0.0526593 | − | 0.998613i | \(-0.516770\pi\) | ||||
−0.0526593 | + | 0.998613i | \(0.516770\pi\) | |||||||
\(884\) | −3.62348 | + | 6.27604i | −0.121871 | + | 0.211086i | ||||
\(885\) | −64.1514 | − | 54.2178i | −2.15643 | − | 1.82251i | ||||
\(886\) | 10.1883 | + | 17.6466i | 0.342281 | + | 0.592849i | ||||
\(887\) | 13.6511 | + | 23.6444i | 0.458359 | + | 0.793900i | 0.998874 | − | 0.0474335i | \(-0.0151042\pi\) |
−0.540516 | + | 0.841334i | \(0.681771\pi\) | |||||||
\(888\) | 1.84085 | − | 10.2280i | 0.0617748 | − | 0.343228i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 29.2470 | 0.980360 | ||||||||
\(891\) | −47.7995 | + | 16.6345i | −1.60134 | + | 0.557276i | ||||
\(892\) | −6.51873 | −0.218263 | ||||||||
\(893\) | −14.0000 | + | 24.2487i | −0.468492 | + | 0.811452i | ||||
\(894\) | −1.60981 | + | 8.94427i | −0.0538400 | + | 0.299141i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.7530 | + | 9.08799i | 0.359034 | + | 0.303439i | ||||
\(898\) | −7.50000 | + | 12.9904i | −0.250278 | + | 0.433495i | ||||
\(899\) | −4.90893 | −0.163722 | ||||||||
\(900\) | −15.8117 | − | 5.88220i | −0.527058 | − | 0.196073i | ||||
\(901\) | 23.6205 | 0.786912 | ||||||||
\(902\) | −16.6036 | + | 28.7584i | −0.552841 | + | 0.957549i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.68826 | − | 6.38826i | −0.122670 | − | 0.212470i | ||||
\(905\) | −7.31174 | − | 12.6643i | −0.243050 | − | 0.420976i | ||||
\(906\) | 14.0535 | − | 5.05876i | 0.466897 | − | 0.168066i | ||||
\(907\) | −9.18826 | + | 15.9145i | −0.305091 | + | 0.528434i | −0.977282 | − | 0.211945i | \(-0.932020\pi\) |
0.672190 | + | 0.740378i | \(0.265354\pi\) | |||||||
\(908\) | 28.7207 | 0.953130 | ||||||||
\(909\) | 29.1629 | − | 24.1206i | 0.967272 | − | 0.800028i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.0648 | + | 17.4327i | −0.333461 | + | 0.577572i | −0.983188 | − | 0.182596i | \(-0.941550\pi\) |
0.649727 | + | 0.760168i | \(0.274883\pi\) | |||||||
\(912\) | −3.50000 | − | 2.95804i | −0.115897 | − | 0.0979505i | ||||
\(913\) | 21.7796 | + | 37.7234i | 0.720800 | + | 1.24846i | ||||
\(914\) | 5.50000 | + | 9.52628i | 0.181924 | + | 0.315101i | ||||
\(915\) | −4.48660 | + | 24.9281i | −0.148322 | + | 0.824096i | ||||
\(916\) | 13.4399 | − | 23.2786i | 0.444067 | − | 0.769147i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 15.0587 | + | 26.7346i | 0.497011 | + | 0.882372i | ||||
\(919\) | 22.3643 | 0.737731 | 0.368866 | − | 0.929483i | \(-0.379746\pi\) | ||||
0.368866 | + | 0.929483i | \(0.379746\pi\) | |||||||
\(920\) | −10.7942 | + | 18.6961i | −0.355873 | + | 0.616391i | ||||
\(921\) | −4.05869 | + | 22.5505i | −0.133738 | + | 0.743066i | ||||
\(922\) | 4.88905 | + | 8.46808i | 0.161012 | + | 0.278882i | ||||
\(923\) | −6.51873 | − | 11.2908i | −0.214567 | − | 0.371641i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.8704 | + | 29.2204i | −0.554696 | + | 0.960762i | ||||
\(926\) | −25.3765 | −0.833924 | ||||||||
\(927\) | −4.67789 | − | 27.6748i | −0.153642 | − | 0.908958i | ||||
\(928\) | 4.00000 | 0.131306 | ||||||||
\(929\) | −6.09641 | + | 10.5593i | −0.200017 | + | 0.346439i | −0.948533 | − | 0.316677i | \(-0.897433\pi\) |
0.748517 | + | 0.663116i | \(0.230766\pi\) | |||||||
\(930\) | 6.51873 | − | 2.34651i | 0.213758 | − | 0.0769450i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.50000 | − | 14.7224i | −0.278427 | − | 0.482249i | ||||
\(933\) | 33.8704 | − | 12.1921i | 1.10887 | − | 0.399152i | ||||
\(934\) | 5.59831 | − | 9.69656i | 0.183182 | − | 0.317281i | ||||
\(935\) | 108.235 | 3.53965 | ||||||||
\(936\) | 0.613616 | + | 3.63020i | 0.0200567 | + | 0.118657i | ||||
\(937\) | 8.12854 | 0.265548 | 0.132774 | − | 0.991146i | \(-0.457612\pi\) | ||||
0.132774 | + | 0.991146i | \(0.457612\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.8117 | − | 24.3504i | −0.940236 | − | 0.794644i | ||||
\(940\) | 17.2470 | + | 29.8726i | 0.562534 | + | 0.974337i | ||||
\(941\) | 9.14461 | + | 15.8389i | 0.298106 | + | 0.516334i | 0.975703 | − | 0.219099i | \(-0.0703119\pi\) |
−0.677597 | + | 0.735434i | \(0.736979\pi\) | |||||||
\(942\) | 5.00000 | − | 27.7806i | 0.162909 | − | 0.905140i | ||||
\(943\) | 19.5562 | − | 33.8723i | 0.636838 | − | 1.10304i | ||||
\(944\) | −14.8783 | −0.484248 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −42.8704 | −1.39384 | ||||||||
\(947\) | −25.6822 | + | 44.4828i | −0.834558 | + | 1.44550i | 0.0598315 | + | 0.998208i | \(0.480944\pi\) |
−0.894390 | + | 0.447289i | \(0.852390\pi\) | |||||||
\(948\) | −1.03594 | + | 5.75583i | −0.0336459 | + | 0.186941i | ||||
\(949\) | 6.87043 | + | 11.8999i | 0.223023 | + | 0.386288i | ||||
\(950\) | 7.43916 | + | 12.8850i | 0.241358 | + | 0.418045i | ||||
\(951\) | −9.58681 | − | 8.10234i | −0.310874 | − | 0.262736i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.62348 | −0.311735 | −0.155867 | − | 0.987778i | \(-0.549817\pi\) | ||||
−0.155867 | + | 0.987778i | \(0.549817\pi\) | |||||||
\(954\) | 9.24695 | − | 7.64813i | 0.299381 | − | 0.247617i | ||||
\(955\) | −17.5241 | −0.567066 | ||||||||
\(956\) | −6.31174 | + | 10.9323i | −0.204136 | + | 0.353574i | ||||
\(957\) | −36.6579 | + | 13.1955i | −1.18498 | + | 0.426551i | ||||
\(958\) | 7.74597 | + | 13.4164i | 0.250261 | + | 0.433464i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.31174 | + | 1.91203i | −0.171436 | + | 0.0617106i | ||||
\(961\) | 14.7470 | − | 25.5425i | 0.475708 | − | 0.823951i | ||||
\(962\) | 7.36339 | 0.237405 | ||||||||
\(963\) | −1.05869 | − | 0.393847i | −0.0341158 | − | 0.0126916i | ||||
\(964\) | 26.6886 | 0.859580 | ||||||||
\(965\) | 21.9908 | − | 38.0892i | 0.707909 | − | 1.22613i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.55869 | − | 6.16383i | −0.114440 | − | 0.198215i | 0.803116 | − | 0.595823i | \(-0.203174\pi\) |
−0.917556 | + | 0.397607i | \(0.869841\pi\) | |||||||
\(968\) | 10.3117 | + | 17.8605i | 0.331432 | + | 0.574057i | ||||
\(969\) | 4.79341 | − | 26.6327i | 0.153986 | − | 0.855566i | ||||
\(970\) | −5.00000 | + | 8.66025i | −0.160540 | + | 0.278064i | ||||
\(971\) | −43.1369 | −1.38433 | −0.692165 | − | 0.721739i | \(-0.743343\pi\) | ||||
−0.692165 | + | 0.721739i | \(0.743343\pi\) | |||||||
\(972\) | 14.5516 | + | 5.59017i | 0.466744 | + | 0.179305i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.31174 | − | 4.00405i | 0.0740729 | − | 0.128298i | ||||
\(975\) | 2.11738 | − | 11.7644i | 0.0678103 | − | 0.376762i | ||||
\(976\) | 2.24330 | + | 3.88551i | 0.0718063 | + | 0.124372i | ||||
\(977\) | −20.8117 | − | 36.0470i | −0.665826 | − | 1.15325i | −0.979061 | − | 0.203569i | \(-0.934746\pi\) |
0.313234 | − | 0.949676i | \(-0.398588\pi\) | |||||||
\(978\) | −1.64956 | − | 1.39413i | −0.0527471 | − | 0.0445795i | ||||
\(979\) | −25.2303 | + | 43.7001i | −0.806363 | + | 1.39666i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.6235 | − | 11.7644i | −1.00966 | − | 0.375608i | ||||
\(982\) | 36.1174 | 1.15255 | ||||||||
\(983\) | −8.97320 | + | 15.5420i | −0.286201 | + | 0.495714i | −0.972900 | − | 0.231228i | \(-0.925726\pi\) |
0.686699 | + | 0.726942i | \(0.259059\pi\) | |||||||
\(984\) | 9.62348 | − | 3.46410i | 0.306785 | − | 0.110432i | ||||
\(985\) | 11.8102 | + | 20.4559i | 0.376305 | + | 0.651780i | ||||
\(986\) | 11.8102 | + | 20.4559i | 0.376115 | + | 0.651450i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.62348 | − | 2.81194i | 0.0516496 | − | 0.0894598i | ||||
\(989\) | 50.4939 | 1.60561 | ||||||||
\(990\) | 42.3718 | − | 35.0456i | 1.34666 | − | 1.11382i | ||||
\(991\) | 36.9878 | 1.17496 | 0.587478 | − | 0.809240i | \(-0.300121\pi\) | ||||
0.587478 | + | 0.809240i | \(0.300121\pi\) | |||||||
\(992\) | 0.613616 | − | 1.06281i | 0.0194823 | − | 0.0337444i | ||||
\(993\) | −10.5830 | − | 8.94427i | −0.335842 | − | 0.283838i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.6235 | − | 28.7927i | −0.527000 | − | 0.912790i | ||||
\(996\) | 2.37652 | − | 13.2042i | 0.0753031 | − | 0.418393i | ||||
\(997\) | −19.9587 | + | 34.5694i | −0.632097 | + | 1.09482i | 0.355025 | + | 0.934857i | \(0.384472\pi\) |
−0.987122 | + | 0.159967i | \(0.948861\pi\) | |||||||
\(998\) | −8.37652 | −0.265154 | ||||||||
\(999\) | 15.8745 | − | 26.8328i | 0.502247 | − | 0.848953i |
(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 | 882.2.f.r.295.2 | ✓ | 8 | |
3.2 | odd | 2 | 2646.2.f.p.883.1 | 8 | |||
7.2 | even | 3 | 882.2.e.r.655.1 | 8 | |||
7.3 | odd | 6 | 882.2.h.s.79.1 | 8 | |||
7.4 | even | 3 | 882.2.h.s.79.4 | 8 | |||
7.5 | odd | 6 | 882.2.e.r.655.4 | 8 | |||
7.6 | odd | 2 | inner | 882.2.f.r.295.3 | yes | 8 | |
9.2 | odd | 6 | 7938.2.a.cq.1.4 | 4 | |||
9.4 | even | 3 | inner | 882.2.f.r.589.2 | yes | 8 | |
9.5 | odd | 6 | 2646.2.f.p.1765.1 | 8 | |||
9.7 | even | 3 | 7938.2.a.ch.1.1 | 4 | |||
21.2 | odd | 6 | 2646.2.e.s.2125.1 | 8 | |||
21.5 | even | 6 | 2646.2.e.s.2125.4 | 8 | |||
21.11 | odd | 6 | 2646.2.h.r.667.4 | 8 | |||
21.17 | even | 6 | 2646.2.h.r.667.1 | 8 | |||
21.20 | even | 2 | 2646.2.f.p.883.4 | 8 | |||
63.4 | even | 3 | 882.2.e.r.373.2 | 8 | |||
63.5 | even | 6 | 2646.2.h.r.361.1 | 8 | |||
63.13 | odd | 6 | inner | 882.2.f.r.589.3 | yes | 8 | |
63.20 | even | 6 | 7938.2.a.cq.1.1 | 4 | |||
63.23 | odd | 6 | 2646.2.h.r.361.4 | 8 | |||
63.31 | odd | 6 | 882.2.e.r.373.3 | 8 | |||
63.32 | odd | 6 | 2646.2.e.s.1549.1 | 8 | |||
63.34 | odd | 6 | 7938.2.a.ch.1.4 | 4 | |||
63.40 | odd | 6 | 882.2.h.s.67.1 | 8 | |||
63.41 | even | 6 | 2646.2.f.p.1765.4 | 8 | |||
63.58 | even | 3 | 882.2.h.s.67.4 | 8 | |||
63.59 | even | 6 | 2646.2.e.s.1549.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.e.r.373.2 | 8 | 63.4 | even | 3 | |||
882.2.e.r.373.3 | 8 | 63.31 | odd | 6 | |||
882.2.e.r.655.1 | 8 | 7.2 | even | 3 | |||
882.2.e.r.655.4 | 8 | 7.5 | odd | 6 | |||
882.2.f.r.295.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
882.2.f.r.295.3 | yes | 8 | 7.6 | odd | 2 | inner | |
882.2.f.r.589.2 | yes | 8 | 9.4 | even | 3 | inner | |
882.2.f.r.589.3 | yes | 8 | 63.13 | odd | 6 | inner | |
882.2.h.s.67.1 | 8 | 63.40 | odd | 6 | |||
882.2.h.s.67.4 | 8 | 63.58 | even | 3 | |||
882.2.h.s.79.1 | 8 | 7.3 | odd | 6 | |||
882.2.h.s.79.4 | 8 | 7.4 | even | 3 | |||
2646.2.e.s.1549.1 | 8 | 63.32 | odd | 6 | |||
2646.2.e.s.1549.4 | 8 | 63.59 | even | 6 | |||
2646.2.e.s.2125.1 | 8 | 21.2 | odd | 6 | |||
2646.2.e.s.2125.4 | 8 | 21.5 | even | 6 | |||
2646.2.f.p.883.1 | 8 | 3.2 | odd | 2 | |||
2646.2.f.p.883.4 | 8 | 21.20 | even | 2 | |||
2646.2.f.p.1765.1 | 8 | 9.5 | odd | 6 | |||
2646.2.f.p.1765.4 | 8 | 63.41 | even | 6 | |||
2646.2.h.r.361.1 | 8 | 63.5 | even | 6 | |||
2646.2.h.r.361.4 | 8 | 63.23 | odd | 6 | |||
2646.2.h.r.667.1 | 8 | 21.17 | even | 6 | |||
2646.2.h.r.667.4 | 8 | 21.11 | odd | 6 | |||
7938.2.a.ch.1.1 | 4 | 9.7 | even | 3 | |||
7938.2.a.ch.1.4 | 4 | 63.34 | odd | 6 | |||
7938.2.a.cq.1.1 | 4 | 63.20 | even | 6 | |||
7938.2.a.cq.1.4 | 4 | 9.2 | odd | 6 |