Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(406,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.406");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.k (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: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 13 x^{10} - 10 x^{9} + 44 x^{8} - 20 x^{7} + 119 x^{6} + 13 x^{5} + 83 x^{4} + 14 x^{3} + 46 x^{2} + 12 x + 4 \) |
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 | 676.4 | ||
Root | \(-0.156312 + 0.270740i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.676 |
Dual form | 855.2.k.k.406.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.656312 | − | 1.13677i | 0.464082 | − | 0.803814i | −0.535077 | − | 0.844803i | \(-0.679717\pi\) |
0.999160 | + | 0.0409889i | \(0.0130508\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.138510 | + | 0.239907i | 0.0692550 | + | 0.119953i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.11486 | 1.17731 | 0.588653 | − | 0.808386i | \(-0.299658\pi\) | ||||
0.588653 | + | 0.808386i | \(0.299658\pi\) | |||||||
\(8\) | 2.98887 | 1.05672 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.656312 | − | 1.13677i | −0.207544 | − | 0.359477i | ||||
\(11\) | −0.692973 | −0.208939 | −0.104470 | − | 0.994528i | \(-0.533314\pi\) | ||||
−0.104470 | + | 0.994528i | \(0.533314\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.07262 | + | 3.58988i | 0.574841 | + | 0.995653i | 0.996059 | + | 0.0886938i | \(0.0282693\pi\) |
−0.421218 | + | 0.906959i | \(0.638397\pi\) | |||||||
\(14\) | 2.04432 | − | 3.54086i | 0.546367 | − | 0.946336i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.68461 | − | 2.91783i | 0.421152 | − | 0.729457i | ||||
\(17\) | −1.40392 | + | 2.43165i | −0.340500 | + | 0.589763i | −0.984526 | − | 0.175241i | \(-0.943930\pi\) |
0.644026 | + | 0.765004i | \(0.277263\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.62820 | + | 4.04339i | −0.373534 | + | 0.927616i | ||||
\(20\) | 0.277020 | 0.0619436 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.454806 | + | 0.787748i | −0.0969650 | + | 0.167948i | ||||
\(23\) | −1.51519 | − | 2.62438i | −0.315938 | − | 0.547221i | 0.663698 | − | 0.748000i | \(-0.268986\pi\) |
−0.979637 | + | 0.200779i | \(0.935653\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 5.44113 | 1.06709 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.431440 | + | 0.747275i | 0.0815344 | + | 0.141222i | ||||
\(29\) | −1.93613 | − | 3.35348i | −0.359530 | − | 0.622725i | 0.628352 | − | 0.777929i | \(-0.283730\pi\) |
−0.987882 | + | 0.155204i | \(0.950396\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.374753 | 0.0673077 | 0.0336539 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336539 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(32\) | 0.777612 | + | 1.34686i | 0.137464 | + | 0.238094i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.84281 | + | 3.19185i | 0.316040 | + | 0.547397i | ||||
\(35\) | 1.55743 | − | 2.69755i | 0.263254 | − | 0.455969i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.34678 | −0.221410 | −0.110705 | − | 0.993853i | \(-0.535311\pi\) | ||||
−0.110705 | + | 0.993853i | \(0.535311\pi\) | |||||||
\(38\) | 3.52778 | + | 4.50460i | 0.572281 | + | 0.730742i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.49443 | − | 2.58844i | 0.236291 | − | 0.409268i | ||||
\(41\) | 4.77223 | − | 8.26575i | 0.745297 | − | 1.29089i | −0.204759 | − | 0.978812i | \(-0.565641\pi\) |
0.950056 | − | 0.312080i | \(-0.101026\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.32486 | − | 4.02677i | 0.354538 | − | 0.614077i | −0.632501 | − | 0.774560i | \(-0.717972\pi\) |
0.987039 | + | 0.160482i | \(0.0513049\pi\) | |||||||
\(44\) | −0.0959838 | − | 0.166249i | −0.0144701 | − | 0.0250629i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.97774 | −0.586486 | ||||||||
\(47\) | −0.0650711 | − | 0.112706i | −0.00949159 | − | 0.0164399i | 0.861241 | − | 0.508197i | \(-0.169688\pi\) |
−0.870732 | + | 0.491758i | \(0.836355\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.70235 | 0.386051 | ||||||||
\(50\) | −1.31262 | −0.185633 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.574157 | + | 0.994469i | −0.0796212 | + | 0.137908i | ||||
\(53\) | −0.442770 | − | 0.766900i | −0.0608191 | − | 0.105342i | 0.834013 | − | 0.551745i | \(-0.186038\pi\) |
−0.894832 | + | 0.446403i | \(0.852705\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.346487 | + | 0.600132i | −0.0467202 | + | 0.0809218i | ||||
\(56\) | 9.30991 | 1.24409 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.08282 | −0.667407 | ||||||||
\(59\) | −0.719490 | + | 1.24619i | −0.0936697 | + | 0.162241i | −0.909053 | − | 0.416681i | \(-0.863193\pi\) |
0.815383 | + | 0.578922i | \(0.196526\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.63574 | − | 2.83319i | −0.209435 | − | 0.362753i | 0.742101 | − | 0.670288i | \(-0.233829\pi\) |
−0.951537 | + | 0.307535i | \(0.900496\pi\) | |||||||
\(62\) | 0.245955 | − | 0.426007i | 0.0312363 | − | 0.0541029i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.77986 | 1.09748 | ||||||||
\(65\) | 4.14523 | 0.514153 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.44562 | − | 9.43209i | −0.665288 | − | 1.15231i | −0.979207 | − | 0.202864i | \(-0.934975\pi\) |
0.313919 | − | 0.949450i | \(-0.398358\pi\) | |||||||
\(68\) | −0.777826 | −0.0943253 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.04432 | − | 3.54086i | −0.244343 | − | 0.423214i | ||||
\(71\) | 5.75724 | − | 9.97184i | 0.683259 | − | 1.18344i | −0.290721 | − | 0.956808i | \(-0.593895\pi\) |
0.973981 | − | 0.226632i | \(-0.0727714\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.37964 | + | 4.12166i | −0.278516 | + | 0.482404i | −0.971016 | − | 0.239014i | \(-0.923176\pi\) |
0.692500 | + | 0.721418i | \(0.256509\pi\) | |||||||
\(74\) | −0.883908 | + | 1.53097i | −0.102752 | + | 0.177972i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.19556 | + | 0.169435i | −0.137140 | + | 0.0194355i | ||||
\(77\) | −2.15851 | −0.245986 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.37760 | + | 9.31428i | −0.605027 | + | 1.04794i | 0.387020 | + | 0.922071i | \(0.373504\pi\) |
−0.992047 | + | 0.125867i | \(0.959829\pi\) | |||||||
\(80\) | −1.68461 | − | 2.91783i | −0.188345 | − | 0.326223i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.26414 | − | 10.8498i | −0.691759 | − | 1.19816i | ||||
\(83\) | −0.386145 | −0.0423850 | −0.0211925 | − | 0.999775i | \(-0.506746\pi\) | ||||
−0.0211925 | + | 0.999775i | \(0.506746\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.40392 | + | 2.43165i | 0.152276 | + | 0.263750i | ||||
\(86\) | −3.05166 | − | 5.28564i | −0.329069 | − | 0.569965i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.07121 | −0.220791 | ||||||||
\(89\) | 3.37096 | + | 5.83867i | 0.357321 | + | 0.618898i | 0.987512 | − | 0.157542i | \(-0.0503569\pi\) |
−0.630191 | + | 0.776440i | \(0.717024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.45591 | + | 11.1820i | 0.676763 | + | 1.17219i | ||||
\(92\) | 0.419737 | − | 0.727006i | 0.0437606 | − | 0.0757957i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.170828 | −0.0176195 | ||||||||
\(95\) | 2.68758 | + | 3.43175i | 0.275740 | + | 0.352090i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.16484 | − | 3.74962i | 0.219807 | − | 0.380716i | −0.734942 | − | 0.678130i | \(-0.762791\pi\) |
0.954749 | + | 0.297414i | \(0.0961240\pi\) | |||||||
\(98\) | 1.77359 | − | 3.07194i | 0.179159 | − | 0.310313i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.138510 | − | 0.239907i | 0.0138510 | − | 0.0239907i | ||||
\(101\) | −0.498699 | − | 0.863773i | −0.0496224 | − | 0.0859486i | 0.840147 | − | 0.542358i | \(-0.182468\pi\) |
−0.889770 | + | 0.456410i | \(0.849135\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.52737 | −0.446095 | −0.223047 | − | 0.974808i | \(-0.571600\pi\) | ||||
−0.223047 | + | 0.974808i | \(0.571600\pi\) | |||||||
\(104\) | 6.19478 | + | 10.7297i | 0.607448 | + | 1.05213i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.16238 | −0.112900 | ||||||||
\(107\) | −18.6472 | −1.80270 | −0.901348 | − | 0.433096i | \(-0.857421\pi\) | ||||
−0.901348 | + | 0.433096i | \(0.857421\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.72633 | + | 9.91830i | −0.548483 | + | 0.950000i | 0.449896 | + | 0.893081i | \(0.351461\pi\) |
−0.998379 | + | 0.0569194i | \(0.981872\pi\) | |||||||
\(110\) | 0.454806 | + | 0.787748i | 0.0433641 | + | 0.0751088i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.24732 | − | 9.08863i | 0.495825 | − | 0.858795i | ||||
\(113\) | −18.2976 | −1.72130 | −0.860649 | − | 0.509199i | \(-0.829942\pi\) | ||||
−0.860649 | + | 0.509199i | \(0.829942\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.03037 | −0.282584 | ||||||||
\(116\) | 0.536347 | − | 0.928980i | 0.0497986 | − | 0.0862537i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.944420 | + | 1.63578i | 0.0869409 | + | 0.150586i | ||||
\(119\) | −4.37300 | + | 7.57427i | −0.400873 | + | 0.694332i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5198 | −0.956344 | ||||||||
\(122\) | −4.29423 | −0.388781 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.0519071 | + | 0.0899058i | 0.00466140 | + | 0.00807378i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.94672 | − | 10.3000i | −0.527686 | − | 0.913979i | −0.999479 | − | 0.0322694i | \(-0.989727\pi\) |
0.471793 | − | 0.881709i | \(-0.343607\pi\) | |||||||
\(128\) | 4.20710 | − | 7.28691i | 0.371859 | − | 0.644078i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.72057 | − | 4.71216i | 0.238609 | − | 0.413284i | ||||
\(131\) | −6.09045 | + | 10.5490i | −0.532125 | + | 0.921668i | 0.467172 | + | 0.884167i | \(0.345273\pi\) |
−0.999297 | + | 0.0375009i | \(0.988060\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.07161 | + | 12.5946i | −0.439764 | + | 1.09209i | ||||
\(134\) | −14.2961 | −1.23499 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.19612 | + | 7.26790i | −0.359815 | + | 0.623217i | ||||
\(137\) | 8.40697 | + | 14.5613i | 0.718256 | + | 1.24406i | 0.961690 | + | 0.274138i | \(0.0883925\pi\) |
−0.243435 | + | 0.969917i | \(0.578274\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.952762 | − | 1.65023i | −0.0808122 | − | 0.139971i | 0.822787 | − | 0.568350i | \(-0.192418\pi\) |
−0.903599 | + | 0.428379i | \(0.859085\pi\) | |||||||
\(140\) | 0.862879 | 0.0729266 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.55709 | − | 13.0893i | −0.634177 | − | 1.09843i | ||||
\(143\) | −1.43627 | − | 2.48769i | −0.120107 | − | 0.208031i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.87226 | −0.321574 | ||||||||
\(146\) | 3.12358 | + | 5.41019i | 0.258509 | + | 0.447751i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.186543 | − | 0.323102i | −0.0153337 | − | 0.0265588i | ||||
\(149\) | −0.145728 | + | 0.252409i | −0.0119385 | + | 0.0206782i | −0.871933 | − | 0.489625i | \(-0.837134\pi\) |
0.859994 | + | 0.510303i | \(0.170467\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.5750 | 1.51161 | 0.755807 | − | 0.654794i | \(-0.227245\pi\) | ||||
0.755807 | + | 0.654794i | \(0.227245\pi\) | |||||||
\(152\) | −4.86647 | + | 12.0852i | −0.394723 | + | 0.980236i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.41666 | + | 2.45372i | −0.114158 | + | 0.197727i | ||||
\(155\) | 0.187377 | − | 0.324546i | 0.0150505 | − | 0.0260682i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.88718 | − | 17.1251i | 0.789083 | − | 1.36673i | −0.137446 | − | 0.990509i | \(-0.543890\pi\) |
0.926529 | − | 0.376222i | \(-0.122777\pi\) | |||||||
\(158\) | 7.05876 | + | 12.2261i | 0.561565 | + | 0.972659i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.55522 | 0.122951 | ||||||||
\(161\) | −4.71960 | − | 8.17458i | −0.371956 | − | 0.644247i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7513 | 1.23374 | 0.616868 | − | 0.787066i | \(-0.288401\pi\) | ||||
0.616868 | + | 0.787066i | \(0.288401\pi\) | |||||||
\(164\) | 2.64401 | 0.206462 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.253432 | + | 0.438957i | −0.0196701 | + | 0.0340696i | ||||
\(167\) | −1.83465 | − | 3.17771i | −0.141970 | − | 0.245898i | 0.786269 | − | 0.617885i | \(-0.212010\pi\) |
−0.928238 | + | 0.371986i | \(0.878677\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.09148 | + | 3.62255i | −0.160883 | + | 0.278658i | ||||
\(170\) | 3.68563 | 0.282675 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.28807 | 0.0982141 | ||||||||
\(173\) | 3.50081 | − | 6.06357i | 0.266161 | − | 0.461005i | −0.701706 | − | 0.712467i | \(-0.747578\pi\) |
0.967867 | + | 0.251462i | \(0.0809113\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.55743 | − | 2.69755i | −0.117731 | − | 0.203915i | ||||
\(176\) | −1.16739 | + | 2.02198i | −0.0879953 | + | 0.152412i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.84960 | 0.663305 | ||||||||
\(179\) | −18.4828 | −1.38147 | −0.690735 | − | 0.723108i | \(-0.742713\pi\) | ||||
−0.690735 | + | 0.723108i | \(0.742713\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.77997 | + | 13.4753i | 0.578281 | + | 1.00161i | 0.995677 | + | 0.0928869i | \(0.0296095\pi\) |
−0.417396 | + | 0.908725i | \(0.637057\pi\) | |||||||
\(182\) | 16.9484 | 1.25630 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.52870 | − | 7.84393i | −0.333860 | − | 0.578262i | ||||
\(185\) | −0.673391 | + | 1.16635i | −0.0495087 | + | 0.0857515i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.972876 | − | 1.68507i | 0.0711438 | − | 0.123225i | ||||
\(188\) | 0.0180260 | − | 0.0312220i | 0.00131468 | − | 0.00227710i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.66499 | − | 0.802844i | 0.410981 | − | 0.0582444i | ||||
\(191\) | 6.07892 | 0.439855 | 0.219928 | − | 0.975516i | \(-0.429418\pi\) | ||||
0.219928 | + | 0.975516i | \(0.429418\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.37309 | + | 11.0385i | −0.458745 | + | 0.794570i | −0.998895 | − | 0.0469988i | \(-0.985034\pi\) |
0.540150 | + | 0.841569i | \(0.318368\pi\) | |||||||
\(194\) | −2.84162 | − | 4.92184i | −0.204017 | − | 0.353367i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.374303 | + | 0.648312i | 0.0267359 | + | 0.0463080i | ||||
\(197\) | −26.8916 | −1.91595 | −0.957975 | − | 0.286851i | \(-0.907391\pi\) | ||||
−0.957975 | + | 0.286851i | \(0.907391\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7248 | + | 20.3079i | 0.831148 | + | 1.43959i | 0.897129 | + | 0.441769i | \(0.145649\pi\) |
−0.0659811 | + | 0.997821i | \(0.521018\pi\) | |||||||
\(200\) | −1.49443 | − | 2.58844i | −0.105672 | − | 0.183030i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.30921 | −0.0921156 | ||||||||
\(203\) | −6.03077 | − | 10.4456i | −0.423277 | − | 0.733138i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.77223 | − | 8.26575i | −0.333307 | − | 0.577305i | ||||
\(206\) | −2.97136 | + | 5.14655i | −0.207025 | + | 0.358577i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.9662 | 0.968382 | ||||||||
\(209\) | 1.12830 | − | 2.80196i | 0.0780459 | − | 0.193815i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.77527 | − | 8.27101i | 0.328743 | − | 0.569400i | −0.653520 | − | 0.756910i | \(-0.726708\pi\) |
0.982263 | + | 0.187510i | \(0.0600416\pi\) | |||||||
\(212\) | 0.122656 | − | 0.212447i | 0.00842406 | − | 0.0145909i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.2384 | + | 21.1975i | −0.836599 | + | 1.44903i | ||||
\(215\) | −2.32486 | − | 4.02677i | −0.158554 | − | 0.274624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.16730 | 0.0792418 | ||||||||
\(218\) | 7.51651 | + | 13.0190i | 0.509083 | + | 0.881757i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.191968 | −0.0129424 | ||||||||
\(221\) | −11.6391 | −0.782932 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.59965 | − | 11.4309i | 0.441945 | − | 0.765471i | −0.555889 | − | 0.831257i | \(-0.687622\pi\) |
0.997834 | + | 0.0657855i | \(0.0209553\pi\) | |||||||
\(224\) | 2.42215 | + | 4.19529i | 0.161837 | + | 0.280310i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.0090 | + | 20.8001i | −0.798824 | + | 1.38360i | ||||
\(227\) | −8.69848 | −0.577339 | −0.288669 | − | 0.957429i | \(-0.593213\pi\) | ||||
−0.288669 | + | 0.957429i | \(0.593213\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.6107 | 1.29591 | 0.647955 | − | 0.761679i | \(-0.275624\pi\) | ||||
0.647955 | + | 0.761679i | \(0.275624\pi\) | |||||||
\(230\) | −1.98887 | + | 3.44482i | −0.131142 | + | 0.227145i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.78684 | − | 10.0231i | −0.379925 | − | 0.658049i | ||||
\(233\) | −13.9062 | + | 24.0863i | −0.911027 | + | 1.57795i | −0.0984108 | + | 0.995146i | \(0.531376\pi\) |
−0.812616 | + | 0.582799i | \(0.801957\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.130142 | −0.00848954 | ||||||||
\(236\) | −0.398627 | −0.0259484 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.74011 | + | 9.94216i | 0.372076 | + | 0.644454i | ||||
\(239\) | 23.5071 | 1.52055 | 0.760275 | − | 0.649601i | \(-0.225064\pi\) | ||||
0.760275 | + | 0.649601i | \(0.225064\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.2817 | − | 21.2725i | −0.791132 | − | 1.37028i | −0.925266 | − | 0.379318i | \(-0.876159\pi\) |
0.134134 | − | 0.990963i | \(-0.457175\pi\) | |||||||
\(242\) | −6.90426 | + | 11.9585i | −0.443823 | + | 0.768723i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.453134 | − | 0.784851i | 0.0290089 | − | 0.0502449i | ||||
\(245\) | 1.35118 | − | 2.34031i | 0.0863235 | − | 0.149517i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.8899 | + | 2.53536i | −1.13831 | + | 0.161321i | ||||
\(248\) | 1.12009 | 0.0711257 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.656312 | + | 1.13677i | −0.0415088 | + | 0.0718953i | ||||
\(251\) | −5.17195 | − | 8.95808i | −0.326451 | − | 0.565429i | 0.655354 | − | 0.755322i | \(-0.272519\pi\) |
−0.981805 | + | 0.189893i | \(0.939186\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.04998 | + | 1.81863i | 0.0660119 | + | 0.114336i | ||||
\(254\) | −15.6116 | −0.979559 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.25752 | + | 5.64219i | 0.203595 | + | 0.352637i | ||||
\(257\) | 1.34568 | + | 2.33079i | 0.0839413 | + | 0.145391i | 0.904940 | − | 0.425540i | \(-0.139916\pi\) |
−0.820998 | + | 0.570931i | \(0.806583\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.19504 | −0.260667 | ||||||||
\(260\) | 0.574157 | + | 0.994469i | 0.0356077 | + | 0.0616743i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.99447 | + | 13.8468i | 0.493900 | + | 0.855459i | ||||
\(263\) | −7.57261 | + | 13.1161i | −0.466947 | + | 0.808776i | −0.999287 | − | 0.0377547i | \(-0.987979\pi\) |
0.532340 | + | 0.846531i | \(0.321313\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.885540 | −0.0543983 | ||||||||
\(266\) | 10.9885 | + | 14.0312i | 0.673750 | + | 0.860308i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.50855 | − | 2.61288i | 0.0921492 | − | 0.159607i | ||||
\(269\) | −5.03811 | + | 8.72626i | −0.307179 | + | 0.532050i | −0.977744 | − | 0.209801i | \(-0.932718\pi\) |
0.670565 | + | 0.741851i | \(0.266052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.60942 | − | 16.6440i | 0.583730 | − | 1.01105i | −0.411302 | − | 0.911499i | \(-0.634926\pi\) |
0.995032 | − | 0.0995516i | \(-0.0317408\pi\) | |||||||
\(272\) | 4.73010 | + | 8.19278i | 0.286805 | + | 0.496760i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.0704 | 1.33332 | ||||||||
\(275\) | 0.346487 | + | 0.600132i | 0.0208939 | + | 0.0361893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3594 | 0.862771 | 0.431386 | − | 0.902168i | \(-0.358025\pi\) | ||||
0.431386 | + | 0.902168i | \(0.358025\pi\) | |||||||
\(278\) | −2.50123 | −0.150014 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.65496 | − | 8.06262i | 0.278187 | − | 0.481834i | ||||
\(281\) | 9.65362 | + | 16.7206i | 0.575887 | + | 0.997465i | 0.995945 | + | 0.0899676i | \(0.0286764\pi\) |
−0.420058 | + | 0.907497i | \(0.637990\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.2313 | + | 28.1134i | −0.964850 | + | 1.67117i | −0.254831 | + | 0.966986i | \(0.582020\pi\) |
−0.710018 | + | 0.704183i | \(0.751313\pi\) | |||||||
\(284\) | 3.18975 | 0.189277 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.77056 | −0.222958 | ||||||||
\(287\) | 14.8648 | − | 25.7466i | 0.877443 | − | 1.51978i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.55804 | + | 7.89475i | 0.268120 | + | 0.464397i | ||||
\(290\) | −2.54141 | + | 4.40185i | −0.149237 | + | 0.258486i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.31842 | −0.0771546 | ||||||||
\(293\) | −7.22833 | −0.422283 | −0.211142 | − | 0.977455i | \(-0.567718\pi\) | ||||
−0.211142 | + | 0.977455i | \(0.567718\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.719490 | + | 1.24619i | 0.0418904 | + | 0.0725562i | ||||
\(296\) | −4.02535 | −0.233969 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.191287 | + | 0.331318i | 0.0110809 | + | 0.0191927i | ||||
\(299\) | 6.28080 | − | 10.8787i | 0.363228 | − | 0.629130i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.24161 | − | 12.5428i | 0.417400 | − | 0.722957i | ||||
\(302\) | 12.1910 | − | 21.1155i | 0.701514 | − | 1.21506i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.05504 | + | 11.5623i | 0.519342 | + | 0.663145i | ||||
\(305\) | −3.27149 | −0.187325 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.69667 | − | 11.5990i | 0.382199 | − | 0.661989i | −0.609177 | − | 0.793034i | \(-0.708500\pi\) |
0.991376 | + | 0.131046i | \(0.0418334\pi\) | |||||||
\(308\) | −0.298976 | − | 0.517842i | −0.0170357 | − | 0.0295068i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.245955 | − | 0.426007i | −0.0139693 | − | 0.0241956i | ||||
\(311\) | −19.0587 | −1.08072 | −0.540361 | − | 0.841433i | \(-0.681712\pi\) | ||||
−0.540361 | + | 0.841433i | \(0.681712\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.47738 | − | 9.48711i | −0.309600 | − | 0.536243i | 0.668675 | − | 0.743555i | \(-0.266862\pi\) |
−0.978275 | + | 0.207312i | \(0.933528\pi\) | |||||||
\(314\) | −12.9781 | − | 22.4788i | −0.732399 | − | 1.26855i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.97941 | −0.167605 | ||||||||
\(317\) | 5.04659 | + | 8.74096i | 0.283445 | + | 0.490941i | 0.972231 | − | 0.234024i | \(-0.0751893\pi\) |
−0.688786 | + | 0.724965i | \(0.741856\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.34169 | + | 2.32387i | 0.0751200 | + | 0.130112i | ||||
\(320\) | 4.38993 | − | 7.60358i | 0.245405 | − | 0.425053i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.3901 | −0.690473 | ||||||||
\(323\) | −7.54627 | − | 9.63579i | −0.419886 | − | 0.536150i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.07262 | − | 3.58988i | 0.114968 | − | 0.199131i | ||||
\(326\) | 10.3378 | − | 17.9055i | 0.572556 | − | 0.991695i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.2636 | − | 24.7052i | 0.787574 | − | 1.36412i | ||||
\(329\) | −0.202687 | − | 0.351065i | −0.0111745 | − | 0.0193548i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.50229 | −0.0825736 | −0.0412868 | − | 0.999147i | \(-0.513146\pi\) | ||||
−0.0412868 | + | 0.999147i | \(0.513146\pi\) | |||||||
\(332\) | −0.0534850 | − | 0.0926388i | −0.00293537 | − | 0.00508421i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.81641 | −0.263542 | ||||||||
\(335\) | −10.8912 | −0.595052 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.46673 | − | 2.54045i | 0.0798980 | − | 0.138387i | −0.823308 | − | 0.567595i | \(-0.807874\pi\) |
0.903206 | + | 0.429208i | \(0.141207\pi\) | |||||||
\(338\) | 2.74533 | + | 4.75505i | 0.149326 | + | 0.258641i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.388913 | + | 0.673617i | −0.0210918 | + | 0.0365320i | ||||
\(341\) | −0.259694 | −0.0140632 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.3866 | −0.722807 | ||||||||
\(344\) | 6.94870 | − | 12.0355i | 0.374649 | − | 0.648911i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.59524 | − | 7.95919i | −0.247042 | − | 0.427889i | ||||
\(347\) | 4.86657 | − | 8.42915i | 0.261251 | − | 0.452501i | −0.705323 | − | 0.708886i | \(-0.749198\pi\) |
0.966575 | + | 0.256385i | \(0.0825315\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0493 | 0.644987 | 0.322493 | − | 0.946572i | \(-0.395479\pi\) | ||||
0.322493 | + | 0.946572i | \(0.395479\pi\) | |||||||
\(350\) | −4.08864 | −0.218547 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.538864 | − | 0.933340i | −0.0287215 | − | 0.0497472i | ||||
\(353\) | 26.1484 | 1.39174 | 0.695870 | − | 0.718168i | \(-0.255019\pi\) | ||||
0.695870 | + | 0.718168i | \(0.255019\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.75724 | − | 9.97184i | −0.305563 | − | 0.529250i | ||||
\(356\) | −0.933824 | + | 1.61743i | −0.0494926 | + | 0.0857236i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.1305 | + | 21.0106i | −0.641116 | + | 1.11045i | ||||
\(359\) | 16.6763 | − | 28.8843i | 0.880144 | − | 1.52445i | 0.0289631 | − | 0.999580i | \(-0.490779\pi\) |
0.851181 | − | 0.524873i | \(-0.175887\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.6979 | − | 13.1669i | −0.720945 | − | 0.692993i | ||||
\(362\) | 20.4243 | 1.07348 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.78842 | + | 3.09763i | −0.0937386 | + | 0.162360i | ||||
\(365\) | 2.37964 | + | 4.12166i | 0.124556 | + | 0.215738i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.49560 | − | 11.2507i | −0.339068 | − | 0.587283i | 0.645190 | − | 0.764022i | \(-0.276778\pi\) |
−0.984258 | + | 0.176740i | \(0.943445\pi\) | |||||||
\(368\) | −10.2100 | −0.532233 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.883908 | + | 1.53097i | 0.0459522 | + | 0.0795916i | ||||
\(371\) | −1.37917 | − | 2.38879i | −0.0716028 | − | 0.124020i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −36.5438 | −1.89216 | −0.946082 | − | 0.323926i | \(-0.894997\pi\) | ||||
−0.946082 | + | 0.323926i | \(0.894997\pi\) | |||||||
\(374\) | −1.27702 | − | 2.21186i | −0.0660331 | − | 0.114373i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.194489 | − | 0.336865i | −0.0100300 | − | 0.0173725i | ||||
\(377\) | 8.02571 | − | 13.9009i | 0.413345 | − | 0.715935i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.7622 | −1.68288 | −0.841441 | − | 0.540350i | \(-0.818292\pi\) | ||||
−0.841441 | + | 0.540350i | \(0.818292\pi\) | |||||||
\(380\) | −0.451043 | + | 1.12010i | −0.0231380 | + | 0.0574599i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.98967 | − | 6.91030i | 0.204129 | − | 0.353562i | ||||
\(383\) | 19.3221 | − | 33.4669i | 0.987315 | − | 1.71008i | 0.356153 | − | 0.934428i | \(-0.384088\pi\) |
0.631162 | − | 0.775651i | \(-0.282578\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.07926 | + | 1.86933i | −0.0550040 | + | 0.0952698i | ||||
\(386\) | 8.36547 | + | 14.4894i | 0.425791 | + | 0.737492i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.19941 | 0.0608909 | ||||||||
\(389\) | 17.7295 | + | 30.7085i | 0.898923 | + | 1.55698i | 0.828873 | + | 0.559437i | \(0.188983\pi\) |
0.0700500 | + | 0.997543i | \(0.477684\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.50878 | 0.430308 | ||||||||
\(392\) | 8.07698 | 0.407949 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.6493 | + | 30.5695i | −0.889159 | + | 1.54007i | ||||
\(395\) | 5.37760 | + | 9.31428i | 0.270576 | + | 0.468652i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.08814 | + | 10.5450i | −0.305555 | + | 0.529237i | −0.977385 | − | 0.211469i | \(-0.932175\pi\) |
0.671830 | + | 0.740706i | \(0.265509\pi\) | |||||||
\(398\) | 30.7804 | 1.54288 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.36922 | −0.168461 | ||||||||
\(401\) | −15.4557 | + | 26.7701i | −0.771822 | + | 1.33684i | 0.164741 | + | 0.986337i | \(0.447321\pi\) |
−0.936563 | + | 0.350498i | \(0.886012\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.776720 | + | 1.34532i | 0.0386912 | + | 0.0670151i | ||||
\(404\) | 0.138150 | − | 0.239282i | 0.00687321 | − | 0.0119047i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.8323 | −0.785742 | ||||||||
\(407\) | 0.933283 | 0.0462611 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.96184 | − | 12.0583i | −0.344241 | − | 0.596243i | 0.640975 | − | 0.767562i | \(-0.278530\pi\) |
−0.985216 | + | 0.171319i | \(0.945197\pi\) | |||||||
\(410\) | −12.5283 | −0.618728 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.627086 | − | 1.08614i | −0.0308943 | − | 0.0535105i | ||||
\(413\) | −2.24111 | + | 3.88172i | −0.110278 | + | 0.191007i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.193073 | + | 0.334412i | −0.00947757 | + | 0.0164156i | ||||
\(416\) | −3.22338 | + | 5.58306i | −0.158039 | + | 0.273732i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.44465 | − | 3.12157i | −0.119572 | − | 0.152681i | ||||
\(419\) | 19.7638 | 0.965525 | 0.482763 | − | 0.875751i | \(-0.339633\pi\) | ||||
0.482763 | + | 0.875751i | \(0.339633\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.07302 | − | 1.85853i | 0.0522959 | − | 0.0905791i | −0.838692 | − | 0.544605i | \(-0.816679\pi\) |
0.890988 | + | 0.454026i | \(0.150013\pi\) | |||||||
\(422\) | −6.26813 | − | 10.8567i | −0.305128 | − | 0.528497i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.32338 | − | 2.29216i | −0.0642691 | − | 0.111317i | ||||
\(425\) | 2.80783 | 0.136200 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.09511 | − | 8.82499i | −0.246570 | − | 0.427071i | ||||
\(428\) | −2.58283 | − | 4.47359i | −0.124846 | − | 0.216239i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.10333 | −0.294329 | ||||||||
\(431\) | −14.0250 | − | 24.2920i | −0.675559 | − | 1.17010i | −0.976305 | − | 0.216398i | \(-0.930569\pi\) |
0.300746 | − | 0.953704i | \(-0.402764\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.38799 | + | 9.33227i | 0.258930 | + | 0.448480i | 0.965956 | − | 0.258708i | \(-0.0832967\pi\) |
−0.707025 | + | 0.707188i | \(0.749963\pi\) | |||||||
\(434\) | 0.766116 | − | 1.32695i | 0.0367747 | − | 0.0636957i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.17262 | −0.151941 | ||||||||
\(437\) | 13.0784 | − | 1.85348i | 0.625625 | − | 0.0886638i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.03536 | − | 15.6497i | 0.431234 | − | 0.746920i | −0.565745 | − | 0.824580i | \(-0.691412\pi\) |
0.996980 | + | 0.0776600i | \(0.0247449\pi\) | |||||||
\(440\) | −1.03560 | + | 1.79372i | −0.0493704 | + | 0.0855121i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.63889 | + | 13.2310i | −0.363345 | + | 0.629332i | ||||
\(443\) | 1.78684 | + | 3.09491i | 0.0848956 | + | 0.147043i | 0.905347 | − | 0.424673i | \(-0.139611\pi\) |
−0.820451 | + | 0.571717i | \(0.806278\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.74192 | 0.319598 | ||||||||
\(446\) | −8.66285 | − | 15.0045i | −0.410198 | − | 0.710483i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 27.3480 | 1.29207 | ||||||||
\(449\) | 12.7199 | 0.600291 | 0.300145 | − | 0.953893i | \(-0.402965\pi\) | ||||
0.300145 | + | 0.953893i | \(0.402965\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.30703 | + | 5.72794i | −0.155722 | + | 0.269718i | ||||
\(452\) | −2.53441 | − | 4.38972i | −0.119209 | − | 0.206475i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.70892 | + | 9.88813i | −0.267933 | + | 0.464073i | ||||
\(455\) | 12.9118 | 0.605316 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.7579 | 1.39202 | 0.696008 | − | 0.718034i | \(-0.254958\pi\) | ||||
0.696008 | + | 0.718034i | \(0.254958\pi\) | |||||||
\(458\) | 12.8707 | − | 22.2927i | 0.601409 | − | 1.04167i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.419737 | − | 0.727006i | −0.0195704 | − | 0.0338969i | ||||
\(461\) | −17.2888 | + | 29.9450i | −0.805218 | + | 1.39468i | 0.110926 | + | 0.993829i | \(0.464618\pi\) |
−0.916144 | + | 0.400850i | \(0.868715\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.783874 | 0.0364297 | 0.0182149 | − | 0.999834i | \(-0.494202\pi\) | ||||
0.0182149 | + | 0.999834i | \(0.494202\pi\) | |||||||
\(464\) | −13.0465 | −0.605668 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.2536 | + | 31.6162i | 0.845583 | + | 1.46459i | ||||
\(467\) | 14.2134 | 0.657720 | 0.328860 | − | 0.944379i | \(-0.393336\pi\) | ||||
0.328860 | + | 0.944379i | \(0.393336\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.9623 | − | 29.3796i | −0.783248 | − | 1.35663i | ||||
\(470\) | −0.0854138 | + | 0.147941i | −0.00393985 | + | 0.00682401i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.15046 | + | 3.72471i | −0.0989831 | + | 0.171444i | ||||
\(473\) | −1.61107 | + | 2.79045i | −0.0740769 | + | 0.128305i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.31577 | − | 0.611633i | 0.198021 | − | 0.0280637i | ||||
\(476\) | −2.42282 | −0.111050 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.4280 | − | 26.7221i | 0.705660 | − | 1.22224i | ||||
\(479\) | −9.33951 | − | 16.1765i | −0.426733 | − | 0.739123i | 0.569848 | − | 0.821750i | \(-0.307002\pi\) |
−0.996581 | + | 0.0826272i | \(0.973669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.79136 | − | 4.83478i | −0.127275 | − | 0.220447i | ||||
\(482\) | −32.2424 | −1.46860 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.45710 | − | 2.52377i | −0.0662317 | − | 0.114717i | ||||
\(485\) | −2.16484 | − | 3.74962i | −0.0983005 | − | 0.170261i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.6054 | −0.661833 | −0.330916 | − | 0.943660i | \(-0.607358\pi\) | ||||
−0.330916 | + | 0.943660i | \(0.607358\pi\) | |||||||
\(488\) | −4.88902 | − | 8.46804i | −0.221316 | − | 0.383330i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.77359 | − | 3.07194i | −0.0801225 | − | 0.138776i | ||||
\(491\) | 1.65767 | − | 2.87116i | 0.0748094 | − | 0.129574i | −0.826194 | − | 0.563386i | \(-0.809499\pi\) |
0.901003 | + | 0.433812i | \(0.142832\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.8727 | 0.489680 | ||||||||
\(494\) | −8.85923 | + | 22.0006i | −0.398596 | + | 0.989854i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.631313 | − | 1.09347i | 0.0283468 | − | 0.0490981i | ||||
\(497\) | 17.9330 | − | 31.0609i | 0.804405 | − | 1.39327i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.63324 | − | 8.02501i | 0.207412 | − | 0.359249i | −0.743486 | − | 0.668751i | \(-0.766829\pi\) |
0.950899 | + | 0.309502i | \(0.100162\pi\) | |||||||
\(500\) | −0.138510 | − | 0.239907i | −0.00619436 | − | 0.0107289i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.5776 | −0.606000 | ||||||||
\(503\) | −16.6005 | − | 28.7530i | −0.740181 | − | 1.28203i | −0.952413 | − | 0.304812i | \(-0.901406\pi\) |
0.212231 | − | 0.977219i | \(-0.431927\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.997399 | −0.0443837 | ||||||||
\(506\) | 2.75647 | 0.122540 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.64736 | − | 2.85331i | 0.0730898 | − | 0.126595i | ||||
\(509\) | 18.3832 | + | 31.8406i | 0.814820 | + | 1.41131i | 0.909457 | + | 0.415798i | \(0.136498\pi\) |
−0.0946365 | + | 0.995512i | \(0.530169\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.41226 | + | 12.8384i | −0.327899 | + | 0.567938i | ||||
\(512\) | 25.3802 | 1.12166 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.53274 | 0.155823 | ||||||||
\(515\) | −2.26368 | + | 3.92081i | −0.0997498 | + | 0.172772i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0450925 | + | 0.0781025i | 0.00198317 | + | 0.00343495i | ||||
\(518\) | −2.75325 | + | 4.76877i | −0.120971 | + | 0.209528i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.3896 | 0.543318 | ||||||||
\(521\) | 5.40142 | 0.236640 | 0.118320 | − | 0.992975i | \(-0.462249\pi\) | ||||
0.118320 | + | 0.992975i | \(0.462249\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.04334 | − | 8.73533i | −0.220530 | − | 0.381969i | 0.734439 | − | 0.678675i | \(-0.237445\pi\) |
−0.954969 | + | 0.296705i | \(0.904112\pi\) | |||||||
\(524\) | −3.37435 | −0.147409 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.93998 | + | 17.2166i | 0.433404 | + | 0.750677i | ||||
\(527\) | −0.526123 | + | 0.911271i | −0.0229183 | + | 0.0396956i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.90842 | − | 11.9657i | 0.300366 | − | 0.520249i | ||||
\(530\) | −0.581190 | + | 1.00665i | −0.0252453 | + | 0.0437261i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.72399 | + | 0.527765i | −0.161455 | + | 0.0228815i | ||||
\(533\) | 39.5640 | 1.71371 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.32362 | + | 16.1490i | −0.403095 | + | 0.698181i | ||||
\(536\) | −16.2763 | − | 28.1913i | −0.703027 | − | 1.21768i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.61314 | + | 11.4543i | 0.285113 | + | 0.493830i | ||||
\(539\) | −1.87266 | −0.0806611 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.85048 | − | 8.40128i | −0.208538 | − | 0.361199i | 0.742716 | − | 0.669607i | \(-0.233537\pi\) |
−0.951254 | + | 0.308407i | \(0.900204\pi\) | |||||||
\(542\) | −12.6135 | − | 21.8473i | −0.541798 | − | 0.938422i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.36681 | −0.187225 | ||||||||
\(545\) | 5.72633 | + | 9.91830i | 0.245289 | + | 0.424853i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.05849 | − | 3.56540i | −0.0880145 | − | 0.152446i | 0.818657 | − | 0.574282i | \(-0.194719\pi\) |
−0.906672 | + | 0.421837i | \(0.861386\pi\) | |||||||
\(548\) | −2.32890 | + | 4.03377i | −0.0994857 | + | 0.172314i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.909613 | 0.0387860 | ||||||||
\(551\) | 16.7118 | − | 2.36840i | 0.711947 | − | 0.100897i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.7505 | + | 29.0127i | −0.712302 | + | 1.23374i | ||||
\(554\) | 9.42422 | − | 16.3232i | 0.400397 | − | 0.693508i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.263934 | − | 0.457147i | 0.0111933 | − | 0.0193874i | ||||
\(557\) | 16.8094 | + | 29.1147i | 0.712237 | + | 1.23363i | 0.964016 | + | 0.265846i | \(0.0856512\pi\) |
−0.251779 | + | 0.967785i | \(0.581015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.2742 | 0.815211 | ||||||||
\(560\) | −5.24732 | − | 9.08863i | −0.221740 | − | 0.384065i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25.3431 | 1.06904 | ||||||||
\(563\) | −34.8168 | −1.46735 | −0.733677 | − | 0.679498i | \(-0.762198\pi\) | ||||
−0.733677 | + | 0.679498i | \(0.762198\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.14882 | + | 15.8462i | −0.384894 | + | 0.666656i | ||||
\(566\) | 21.3056 | + | 36.9023i | 0.895539 | + | 1.55112i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17.2076 | − | 29.8045i | 0.722017 | − | 1.25057i | ||||
\(569\) | 35.0377 | 1.46886 | 0.734429 | − | 0.678686i | \(-0.237450\pi\) | ||||
0.734429 | + | 0.678686i | \(0.237450\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.7203 | 1.49485 | 0.747424 | − | 0.664347i | \(-0.231290\pi\) | ||||
0.747424 | + | 0.664347i | \(0.231290\pi\) | |||||||
\(572\) | 0.397875 | − | 0.689140i | 0.0166360 | − | 0.0288144i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.5119 | − | 33.7956i | −0.814412 | − | 1.41060i | ||||
\(575\) | −1.51519 | + | 2.62438i | −0.0631877 | + | 0.109444i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.5678 | 1.18929 | 0.594647 | − | 0.803987i | \(-0.297292\pi\) | ||||
0.594647 | + | 0.803987i | \(0.297292\pi\) | |||||||
\(578\) | 11.9660 | 0.497719 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.536347 | − | 0.928980i | −0.0222706 | − | 0.0385738i | ||||
\(581\) | −1.20279 | −0.0499001 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.306828 | + | 0.531441i | 0.0127075 | + | 0.0220100i | ||||
\(584\) | −7.11245 | + | 12.3191i | −0.294315 | + | 0.509769i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.74404 | + | 8.21691i | −0.195974 | + | 0.339437i | ||||
\(587\) | 10.8661 | − | 18.8206i | 0.448492 | − | 0.776811i | −0.549796 | − | 0.835299i | \(-0.685295\pi\) |
0.998288 | + | 0.0584879i | \(0.0186279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.610173 | + | 1.51527i | −0.0251417 | + | 0.0624357i | ||||
\(590\) | 1.88884 | 0.0777623 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.26880 | + | 3.92968i | −0.0932472 | + | 0.161509i | ||||
\(593\) | −4.15459 | − | 7.19595i | −0.170608 | − | 0.295502i | 0.768024 | − | 0.640421i | \(-0.221240\pi\) |
−0.938633 | + | 0.344918i | \(0.887907\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.37300 | + | 7.57427i | 0.179276 | + | 0.310515i | ||||
\(596\) | −0.0807395 | −0.00330722 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.24433 | − | 14.2796i | −0.337136 | − | 0.583936i | ||||
\(599\) | −7.98082 | − | 13.8232i | −0.326087 | − | 0.564800i | 0.655644 | − | 0.755070i | \(-0.272397\pi\) |
−0.981732 | + | 0.190270i | \(0.939064\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.2096 | 0.416457 | 0.208228 | − | 0.978080i | \(-0.433230\pi\) | ||||
0.208228 | + | 0.978080i | \(0.433230\pi\) | |||||||
\(602\) | −9.50551 | − | 16.4640i | −0.387416 | − | 0.671024i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.57283 | + | 4.45627i | 0.104687 | + | 0.181323i | ||||
\(605\) | −5.25989 | + | 9.11040i | −0.213845 | + | 0.370391i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.4506 | −0.464764 | −0.232382 | − | 0.972625i | \(-0.574652\pi\) | ||||
−0.232382 | + | 0.972625i | \(0.574652\pi\) | |||||||
\(608\) | −6.71199 | + | 0.951226i | −0.272207 | + | 0.0385773i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.14711 | + | 3.71891i | −0.0869341 | + | 0.150574i | ||||
\(611\) | 0.269735 | − | 0.467195i | 0.0109123 | − | 0.0189007i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.0849 | − | 22.6637i | 0.528494 | − | 0.915378i | −0.470954 | − | 0.882158i | \(-0.656090\pi\) |
0.999448 | − | 0.0332202i | \(-0.0105763\pi\) | |||||||
\(614\) | −8.79021 | − | 15.2251i | −0.354744 | − | 0.614435i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.45152 | −0.259939 | ||||||||
\(617\) | 15.2975 | + | 26.4961i | 0.615854 | + | 1.06669i | 0.990234 | + | 0.139416i | \(0.0445224\pi\) |
−0.374379 | + | 0.927276i | \(0.622144\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.4931 | 1.14523 | 0.572616 | − | 0.819823i | \(-0.305928\pi\) | ||||
0.572616 | + | 0.819823i | \(0.305928\pi\) | |||||||
\(620\) | 0.103814 | 0.00416928 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.5085 | + | 21.6653i | −0.501544 | + | 0.868700i | ||||
\(623\) | 10.5001 | + | 18.1866i | 0.420676 | + | 0.728633i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −14.3795 | −0.574720 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.47790 | 0.218592 | ||||||||
\(629\) | 1.89077 | − | 3.27491i | 0.0753899 | − | 0.130579i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.50411 | + | 9.53340i | 0.219115 | + | 0.379518i | 0.954538 | − | 0.298090i | \(-0.0963496\pi\) |
−0.735423 | + | 0.677609i | \(0.763016\pi\) | |||||||
\(632\) | −16.0729 | + | 27.8392i | −0.639347 | + | 1.10738i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.2486 | 0.526167 | ||||||||
\(635\) | −11.8934 | −0.471976 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.60094 | + | 9.70112i | 0.221918 | + | 0.384372i | ||||
\(638\) | 3.52226 | 0.139447 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.20710 | − | 7.28691i | −0.166300 | − | 0.288041i | ||||
\(641\) | 11.0021 | − | 19.0562i | 0.434557 | − | 0.752675i | −0.562702 | − | 0.826660i | \(-0.690238\pi\) |
0.997259 | + | 0.0739847i | \(0.0235716\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.4637 | + | 40.6403i | −0.925319 | + | 1.60270i | −0.134271 | + | 0.990945i | \(0.542869\pi\) |
−0.791048 | + | 0.611754i | \(0.790464\pi\) | |||||||
\(644\) | 1.30742 | − | 2.26452i | 0.0515197 | − | 0.0892347i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.9063 | + | 2.25425i | −0.625826 | + | 0.0886924i | ||||
\(647\) | 0.973639 | 0.0382777 | 0.0191389 | − | 0.999817i | \(-0.493908\pi\) | ||||
0.0191389 | + | 0.999817i | \(0.493908\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.498588 | − | 0.863579i | 0.0195713 | − | 0.0338984i | ||||
\(650\) | −2.72057 | − | 4.71216i | −0.106709 | − | 0.184826i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.18171 | + | 3.77884i | 0.0854425 | + | 0.147991i | ||||
\(653\) | −43.3819 | −1.69766 | −0.848832 | − | 0.528662i | \(-0.822694\pi\) | ||||
−0.848832 | + | 0.528662i | \(0.822694\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.09045 | + | 10.5490i | 0.237974 | + | 0.412182i | ||||
\(656\) | −16.0787 | − | 27.8491i | −0.627767 | − | 1.08733i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.532104 | −0.0207436 | ||||||||
\(659\) | −1.95482 | − | 3.38584i | −0.0761489 | − | 0.131894i | 0.825436 | − | 0.564495i | \(-0.190929\pi\) |
−0.901585 | + | 0.432601i | \(0.857596\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.3249 | + | 33.4717i | 0.751652 | + | 1.30190i | 0.947022 | + | 0.321169i | \(0.104076\pi\) |
−0.195370 | + | 0.980730i | \(0.562591\pi\) | |||||||
\(662\) | −0.985973 | + | 1.70776i | −0.0383209 | + | 0.0663738i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.15414 | −0.0447892 | ||||||||
\(665\) | 8.37143 | + | 10.6894i | 0.324630 | + | 0.414518i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.86720 | + | 10.1623i | −0.227179 | + | 0.393485i | ||||
\(668\) | 0.508235 | − | 0.880289i | 0.0196642 | − | 0.0340594i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.14805 | + | 12.3808i | −0.276153 | + | 0.478311i | ||||
\(671\) | 1.13353 | + | 1.96332i | 0.0437593 | + | 0.0757933i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.0257 | −0.733387 | −0.366693 | − | 0.930342i | \(-0.619510\pi\) | ||||
−0.366693 | + | 0.930342i | \(0.619510\pi\) | |||||||
\(674\) | −1.92527 | − | 3.33466i | −0.0741585 | − | 0.128446i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.15877 | −0.0445679 | ||||||||
\(677\) | 3.39483 | 0.130474 | 0.0652369 | − | 0.997870i | \(-0.479220\pi\) | ||||
0.0652369 | + | 0.997870i | \(0.479220\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.74319 | − | 11.6795i | 0.258780 | − | 0.448220i | ||||
\(680\) | 4.19612 | + | 7.26790i | 0.160914 | + | 0.278711i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.170440 | + | 0.295211i | −0.00652649 | + | 0.0113042i | ||||
\(683\) | −6.42057 | −0.245676 | −0.122838 | − | 0.992427i | \(-0.539200\pi\) | ||||
−0.122838 | + | 0.992427i | \(0.539200\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.8139 | 0.642427 | ||||||||
\(686\) | −8.78576 | + | 15.2174i | −0.335442 | + | 0.581002i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.83296 | − | 13.5671i | −0.298629 | − | 0.517240i | ||||
\(689\) | 1.83539 | − | 3.17898i | 0.0699226 | − | 0.121110i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.32092 | 0.354584 | 0.177292 | − | 0.984158i | \(-0.443266\pi\) | ||||
0.177292 | + | 0.984158i | \(0.443266\pi\) | |||||||
\(692\) | 1.93959 | 0.0737321 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.38798 | − | 11.0643i | −0.242484 | − | 0.419995i | ||||
\(695\) | −1.90552 | −0.0722806 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.3996 | + | 23.2088i | 0.507547 | + | 0.879097i | ||||
\(698\) | 7.90813 | − | 13.6973i | 0.299327 | − | 0.518450i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.431440 | − | 0.747275i | 0.0163069 | − | 0.0282443i | ||||
\(701\) | −12.1943 | + | 21.1211i | −0.460572 | + | 0.797735i | −0.998990 | − | 0.0449438i | \(-0.985689\pi\) |
0.538417 | + | 0.842678i | \(0.319022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.19283 | − | 5.44556i | 0.0827040 | − | 0.205383i | ||||
\(704\) | −6.08421 | −0.229307 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.1615 | − | 29.7246i | 0.645882 | − | 1.11870i | ||||
\(707\) | −1.55338 | − | 2.69053i | −0.0584208 | − | 0.101188i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.78866 | − | 15.2224i | −0.330065 | − | 0.571689i | 0.652459 | − | 0.757824i | \(-0.273737\pi\) |
−0.982524 | + | 0.186135i | \(0.940404\pi\) | |||||||
\(710\) | −15.1142 | −0.567225 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.0754 | + | 17.4510i | 0.377590 | + | 0.654005i | ||||
\(713\) | −0.567822 | − | 0.983496i | −0.0212651 | − | 0.0368322i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.87254 | −0.107427 | ||||||||
\(716\) | −2.56006 | − | 4.43415i | −0.0956738 | − | 0.165712i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.8898 | − | 37.9142i | −0.816918 | − | 1.41494i | ||||
\(719\) | 9.54695 | − | 16.5358i | 0.356041 | − | 0.616681i | −0.631255 | − | 0.775576i | \(-0.717460\pi\) |
0.987296 | + | 0.158895i | \(0.0507930\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.1021 | −0.525190 | ||||||||
\(722\) | −23.9577 | + | 6.92979i | −0.891615 | + | 0.257900i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.15521 | + | 3.73293i | −0.0800977 | + | 0.138733i | ||||
\(725\) | −1.93613 | + | 3.35348i | −0.0719061 | + | 0.124545i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.846286 | + | 1.46581i | −0.0313870 | + | 0.0543639i | −0.881292 | − | 0.472572i | \(-0.843326\pi\) |
0.849905 | + | 0.526936i | \(0.176659\pi\) | |||||||
\(728\) | 19.2959 | + | 33.4214i | 0.715153 | + | 1.23868i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.24715 | 0.231217 | ||||||||
\(731\) | 6.52782 | + | 11.3065i | 0.241440 | + | 0.418186i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.4707 | −0.682233 | −0.341116 | − | 0.940021i | \(-0.610805\pi\) | ||||
−0.341116 | + | 0.940021i | \(0.610805\pi\) | |||||||
\(734\) | −17.0526 | −0.629422 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.35645 | − | 4.08150i | 0.0868601 | − | 0.150446i | ||||
\(737\) | 3.77367 | + | 6.53619i | 0.139005 | + | 0.240763i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.97295 | − | 15.5416i | 0.330075 | − | 0.571707i | −0.652451 | − | 0.757831i | \(-0.726259\pi\) |
0.982526 | + | 0.186124i | \(0.0595925\pi\) | |||||||
\(740\) | −0.373086 | −0.0137149 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.62065 | −0.132918 | ||||||||
\(743\) | −15.3279 | + | 26.5486i | −0.562324 | + | 0.973975i | 0.434969 | + | 0.900446i | \(0.356759\pi\) |
−0.997293 | + | 0.0735289i | \(0.976574\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.145728 | + | 0.252409i | 0.00533908 | + | 0.00924756i | ||||
\(746\) | −23.9841 | + | 41.5417i | −0.878120 | + | 1.52095i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.539013 | 0.0197083 | ||||||||
\(749\) | −58.0835 | −2.12233 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.8978 | − | 24.0717i | −0.507139 | − | 0.878390i | −0.999966 | − | 0.00826290i | \(-0.997370\pi\) |
0.492827 | − | 0.870127i | \(-0.335964\pi\) | |||||||
\(752\) | −0.438478 | −0.0159896 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.5347 | − | 18.2467i | −0.383652 | − | 0.664506i | ||||
\(755\) | 9.28752 | − | 16.0865i | 0.338007 | − | 0.585446i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.66800 | − | 6.35317i | 0.133316 | − | 0.230910i | −0.791637 | − | 0.610992i | \(-0.790771\pi\) |
0.924953 | + | 0.380082i | \(0.124104\pi\) | |||||||
\(758\) | −21.5022 | + | 37.2429i | −0.780996 | + | 1.35272i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.03282 | + | 10.2571i | 0.291381 | + | 0.372063i | ||||
\(761\) | 32.6306 | 1.18286 | 0.591430 | − | 0.806356i | \(-0.298564\pi\) | ||||
0.591430 | + | 0.806356i | \(0.298564\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.8367 | + | 30.8941i | −0.645733 | + | 1.11844i | ||||
\(764\) | 0.841992 | + | 1.45837i | 0.0304622 | + | 0.0527621i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.3627 | − | 43.9294i | −0.916391 | − | 1.58724i | ||||
\(767\) | −5.96491 | −0.215381 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.2386 | + | 26.3941i | 0.549519 | + | 0.951796i | 0.998307 | + | 0.0581573i | \(0.0185225\pi\) |
−0.448788 | + | 0.893638i | \(0.648144\pi\) | |||||||
\(770\) | 1.41666 | + | 2.45372i | 0.0510528 | + | 0.0884261i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.53095 | −0.127082 | ||||||||
\(773\) | 19.9777 | + | 34.6024i | 0.718548 | + | 1.24456i | 0.961575 | + | 0.274542i | \(0.0885263\pi\) |
−0.243027 | + | 0.970020i | \(0.578140\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.187377 | − | 0.324546i | −0.00673077 | − | 0.0116580i | ||||
\(776\) | 6.47044 | − | 11.2071i | 0.232275 | − | 0.402312i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 46.5444 | 1.66870 | ||||||||
\(779\) | 25.6515 | + | 32.7542i | 0.919059 | + | 1.17354i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.98961 | + | 6.91022i | −0.142760 | + | 0.247267i | ||||
\(782\) | 5.58441 | − | 9.67249i | 0.199698 | − | 0.345888i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.55241 | − | 7.88501i | 0.162586 | − | 0.281607i | ||||
\(785\) | −9.88718 | − | 17.1251i | −0.352889 | − | 0.611221i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.4665 | 0.836492 | 0.418246 | − | 0.908334i | \(-0.362645\pi\) | ||||
0.418246 | + | 0.908334i | \(0.362645\pi\) | |||||||
\(788\) | −3.72476 | − | 6.45148i | −0.132689 | − | 0.229824i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.1175 | 0.502279 | ||||||||
\(791\) | −56.9946 | −2.02650 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.78054 | − | 11.7442i | 0.240784 | − | 0.417050i | ||||
\(794\) | 7.99143 | + | 13.8416i | 0.283605 | + | 0.491219i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.24800 | + | 5.62570i | −0.115122 | + | 0.199398i | ||||
\(797\) | −29.1427 | −1.03229 | −0.516145 | − | 0.856502i | \(-0.672633\pi\) | ||||
−0.516145 | + | 0.856502i | \(0.672633\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.365418 | 0.0129275 | ||||||||
\(800\) | 0.777612 | − | 1.34686i | 0.0274927 | − | 0.0476188i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.2875 | + | 35.1391i | 0.716378 | + | 1.24080i | ||||
\(803\) | 1.64903 | − | 2.85620i | 0.0581930 | − | 0.100793i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.43919 | −0.332688 | ||||||||
\(806\) | 2.03908 | 0.0718236 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.49055 | − | 2.58170i | −0.0524373 | − | 0.0908240i | ||||
\(809\) | −29.6241 | −1.04153 | −0.520765 | − | 0.853700i | \(-0.674353\pi\) | ||||
−0.520765 | + | 0.853700i | \(0.674353\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.40989 | + | 12.8343i | 0.260196 | + | 0.450673i | 0.966294 | − | 0.257441i | \(-0.0828793\pi\) |
−0.706098 | + | 0.708115i | \(0.749546\pi\) | |||||||
\(812\) | 1.67065 | − | 2.89364i | 0.0586282 | − | 0.101547i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.612525 | − | 1.06092i | 0.0214690 | − | 0.0371854i | ||||
\(815\) | 7.87565 | − | 13.6410i | 0.275872 | − | 0.477824i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.4965 | + | 15.9567i | 0.437196 | + | 0.558254i | ||||
\(818\) | −18.2766 | −0.639025 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.32200 | − | 2.28978i | 0.0461664 | − | 0.0799625i | ||||
\(821\) | 13.1421 | + | 22.7628i | 0.458663 | + | 0.794427i | 0.998891 | − | 0.0470915i | \(-0.0149952\pi\) |
−0.540228 | + | 0.841519i | \(0.681662\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.43263 | + | 16.3378i | 0.328801 | + | 0.569500i | 0.982274 | − | 0.187450i | \(-0.0600222\pi\) |
−0.653473 | + | 0.756950i | \(0.726689\pi\) | |||||||
\(824\) | −13.5317 | −0.471399 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.94174 | + | 5.09524i | 0.102356 | + | 0.177286i | ||||
\(827\) | −11.0170 | − | 19.0820i | −0.383098 | − | 0.663546i | 0.608405 | − | 0.793627i | \(-0.291810\pi\) |
−0.991503 | + | 0.130081i | \(0.958476\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.6976 | −0.788320 | −0.394160 | − | 0.919042i | \(-0.628964\pi\) | ||||
−0.394160 | + | 0.919042i | \(0.628964\pi\) | |||||||
\(830\) | 0.253432 | + | 0.438957i | 0.00879674 | + | 0.0152364i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 18.1973 | + | 31.5186i | 0.630878 | + | 1.09271i | ||||
\(833\) | −3.79388 | + | 6.57119i | −0.131450 | + | 0.227678i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.66930 | −0.126981 | ||||||||
\(836\) | 0.828488 | − | 0.117414i | 0.0286539 | − | 0.00406084i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.9712 | − | 22.4668i | 0.448083 | − | 0.776103i | ||||
\(839\) | −14.7891 | + | 25.6155i | −0.510577 | + | 0.884345i | 0.489348 | + | 0.872089i | \(0.337235\pi\) |
−0.999925 | + | 0.0122566i | \(0.996099\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00280 | − | 12.1292i | 0.241476 | − | 0.418249i | ||||
\(842\) | −1.40847 | − | 2.43955i | −0.0485392 | − | 0.0840723i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.64569 | 0.0910685 | ||||||||
\(845\) | 2.09148 | + | 3.62255i | 0.0719492 | + | 0.124620i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.7677 | −1.12591 | ||||||||
\(848\) | −2.98358 | −0.102457 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.84281 | − | 3.19185i | 0.0632080 | − | 0.109479i | ||||
\(851\) | 2.04063 | + | 3.53447i | 0.0699518 | + | 0.121160i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.21421 | − | 12.4954i | 0.247010 | − | 0.427834i | −0.715685 | − | 0.698423i | \(-0.753885\pi\) |
0.962695 | + | 0.270590i | \(0.0872187\pi\) | |||||||
\(854\) | −13.3759 | −0.457715 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −55.7341 | −1.90495 | ||||||||
\(857\) | −3.93716 | + | 6.81937i | −0.134491 | + | 0.232945i | −0.925403 | − | 0.378985i | \(-0.876273\pi\) |
0.790912 | + | 0.611930i | \(0.209607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.789249 | + | 1.36702i | 0.0269288 | + | 0.0466421i | 0.879176 | − | 0.476498i | \(-0.158094\pi\) |
−0.852247 | + | 0.523140i | \(0.824761\pi\) | |||||||
\(860\) | 0.644033 | − | 1.11550i | 0.0219613 | − | 0.0380382i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.8190 | −1.25406 | ||||||||
\(863\) | 24.2826 | 0.826591 | 0.413295 | − | 0.910597i | \(-0.364378\pi\) | ||||
0.413295 | + | 0.910597i | \(0.364378\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.50081 | − | 6.06357i | −0.119031 | − | 0.206168i | ||||
\(866\) | 14.1448 | 0.480660 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.161683 | + | 0.280044i | 0.00548789 | + | 0.00950531i | ||||
\(869\) | 3.72653 | − | 6.45454i | 0.126414 | − | 0.218955i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.5734 | − | 39.0982i | 0.764870 | − | 1.32479i | ||||
\(872\) | −17.1153 | + | 29.6445i | −0.579596 | + | 1.00389i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.47654 | − | 16.0835i | 0.219072 | − | 0.544034i | ||||
\(875\) | −3.11486 | −0.105301 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.1997 | + | 26.3266i | −0.513256 | + | 0.888986i | 0.486625 | + | 0.873611i | \(0.338228\pi\) |
−0.999882 | + | 0.0153754i | \(0.995106\pi\) | |||||||
\(878\) | −11.8600 | − | 20.5422i | −0.400257 | − | 0.693265i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.16739 | + | 2.02198i | 0.0393527 | + | 0.0681608i | ||||
\(881\) | −3.60055 | −0.121306 | −0.0606529 | − | 0.998159i | \(-0.519318\pi\) | ||||
−0.0606529 | + | 0.998159i | \(0.519318\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.99273 | − | 15.5759i | −0.302630 | − | 0.524170i | 0.674101 | − | 0.738639i | \(-0.264531\pi\) |
−0.976731 | + | 0.214469i | \(0.931198\pi\) | |||||||
\(884\) | −1.61214 | − | 2.79230i | −0.0542220 | − | 0.0939153i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.69091 | 0.157594 | ||||||||
\(887\) | 7.74011 | + | 13.4063i | 0.259888 | + | 0.450138i | 0.966212 | − | 0.257750i | \(-0.0829812\pi\) |
−0.706324 | + | 0.707889i | \(0.749648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.5232 | − | 32.0831i | −0.621248 | − | 1.07603i | ||||
\(890\) | 4.42480 | − | 7.66398i | 0.148320 | − | 0.256897i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.65647 | 0.122428 | ||||||||
\(893\) | 0.561664 | − | 0.0795993i | 0.0187954 | − | 0.00266369i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.24141 | + | 16.0066i | −0.308906 | + | 0.535041i | ||||
\(896\) | 13.1045 | − | 22.6977i | 0.437792 | − | 0.758278i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.34824 | − | 14.4596i | 0.278584 | − | 0.482522i | ||||
\(899\) | −0.725571 | − | 1.25673i | −0.0241992 | − | 0.0419142i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.48645 | 0.0828356 | ||||||||
\(902\) | 4.34088 | + | 7.51863i | 0.144536 | + | 0.250343i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −54.6893 | −1.81894 | ||||||||
\(905\) | 15.5599 | 0.517230 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.40551 | − | 16.2908i | 0.312305 | − | 0.540928i | −0.666556 | − | 0.745455i | \(-0.732232\pi\) |
0.978861 | + | 0.204527i | \(0.0655657\pi\) | |||||||
\(908\) | −1.20483 | − | 2.08682i | −0.0399836 | − | 0.0692537i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.47418 | − | 14.6777i | 0.280916 | − | 0.486561i | ||||
\(911\) | 12.4666 | 0.413038 | 0.206519 | − | 0.978443i | \(-0.433786\pi\) | ||||
0.206519 | + | 0.978443i | \(0.433786\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.267588 | 0.00885588 | ||||||||
\(914\) | 19.5305 | − | 33.8278i | 0.646011 | − | 1.11892i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.71628 | + | 4.70473i | 0.0897483 | + | 0.155449i | ||||
\(917\) | −18.9709 | + | 32.8586i | −0.626474 | + | 1.08509i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.4751 | −0.411515 | −0.205757 | − | 0.978603i | \(-0.565966\pi\) | ||||
−0.205757 | + | 0.978603i | \(0.565966\pi\) | |||||||
\(920\) | −9.05739 | −0.298613 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.6936 | + | 39.3065i | 0.747375 | + | 1.29449i | ||||
\(923\) | 47.7302 | 1.57106 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.673391 | + | 1.16635i | 0.0221410 | + | 0.0383493i | ||||
\(926\) | 0.514466 | − | 0.891081i | 0.0169064 | − | 0.0292827i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.01111 | − | 5.21540i | 0.0988447 | − | 0.171204i | ||||
\(929\) | 26.5510 | − | 45.9876i | 0.871109 | − | 1.50880i | 0.0102579 | − | 0.999947i | \(-0.496735\pi\) |
0.860851 | − | 0.508857i | \(-0.169932\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.39996 | + | 10.9267i | −0.144203 | + | 0.358107i | ||||
\(932\) | −7.70461 | −0.252373 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.32845 | − | 16.1573i | 0.305236 | − | 0.528685i | ||||
\(935\) | −0.972876 | − | 1.68507i | −0.0318165 | − | 0.0551077i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.04507 | + | 5.27422i | 0.0994782 | + | 0.172301i | 0.911469 | − | 0.411369i | \(-0.134949\pi\) |
−0.811991 | + | 0.583671i | \(0.801616\pi\) | |||||||
\(938\) | −44.5303 | −1.45397 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.0180260 | − | 0.0312220i | −0.000587943 | − | 0.00101835i | ||||
\(941\) | 7.55084 | + | 13.0784i | 0.246150 | + | 0.426345i | 0.962454 | − | 0.271443i | \(-0.0875010\pi\) |
−0.716304 | + | 0.697788i | \(0.754168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.9233 | −0.941872 | ||||||||
\(944\) | 2.42412 | + | 4.19870i | 0.0788984 | + | 0.136656i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.11472 | + | 3.66281i | 0.0687555 | + | 0.119088i | ||||
\(947\) | −19.0664 | + | 33.0240i | −0.619576 | + | 1.07314i | 0.369988 | + | 0.929037i | \(0.379362\pi\) |
−0.989563 | + | 0.144100i | \(0.953971\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.7284 | −0.640410 | ||||||||
\(950\) | 2.13721 | − | 5.30744i | 0.0693402 | − | 0.172196i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.0703 | + | 22.6385i | −0.423612 | + | 0.733718i | ||||
\(953\) | 23.0367 | − | 39.9008i | 0.746233 | − | 1.29251i | −0.203383 | − | 0.979099i | \(-0.565194\pi\) |
0.949616 | − | 0.313415i | \(-0.101473\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.03946 | − | 5.26450i | 0.0983546 | − | 0.170355i | ||||
\(956\) | 3.25597 | + | 5.63951i | 0.105306 | + | 0.182395i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.5185 | −0.792157 | ||||||||
\(959\) | 26.1865 | + | 45.3564i | 0.845607 | + | 1.46463i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8596 | −0.995470 | ||||||||
\(962\) | −7.32802 | −0.236265 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.40227 | − | 5.89291i | 0.109580 | − | 0.189798i | ||||
\(965\) | 6.37309 | + | 11.0385i | 0.205157 | + | 0.355343i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.8881 | + | 48.3036i | −0.896821 | + | 1.55334i | −0.0652862 | + | 0.997867i | \(0.520796\pi\) |
−0.831535 | + | 0.555473i | \(0.812537\pi\) | |||||||
\(968\) | −31.4423 | −1.01059 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.68325 | −0.182478 | ||||||||
\(971\) | 20.9238 | − | 36.2410i | 0.671476 | − | 1.16303i | −0.306010 | − | 0.952028i | \(-0.598994\pi\) |
0.977486 | − | 0.211002i | \(-0.0676725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.96772 | − | 5.14024i | −0.0951407 | − | 0.164789i | ||||
\(974\) | −9.58568 | + | 16.6029i | −0.307145 | + | 0.531991i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.0224 | −0.352817 | ||||||||
\(977\) | −35.9635 | −1.15057 | −0.575287 | − | 0.817952i | \(-0.695110\pi\) | ||||
−0.575287 | + | 0.817952i | \(0.695110\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.33598 | − | 4.04604i | −0.0746584 | − | 0.129312i | ||||
\(980\) | 0.748607 | 0.0239134 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.17589 | − | 3.76875i | −0.0694354 | − | 0.120266i | ||||
\(983\) | 1.03321 | − | 1.78956i | 0.0329541 | − | 0.0570782i | −0.849078 | − | 0.528268i | \(-0.822842\pi\) |
0.882032 | + | 0.471189i | \(0.156175\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.4458 | + | 23.2888i | −0.428419 | + | 0.742044i | ||||
\(986\) | 7.13585 | − | 12.3597i | 0.227252 | − | 0.393612i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.08618 | − | 3.94073i | −0.0981845 | − | 0.125371i | ||||
\(989\) | −14.0904 | −0.448048 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9425 | − | 24.1491i | 0.442898 | − | 0.767121i | −0.555006 | − | 0.831847i | \(-0.687284\pi\) |
0.997903 | + | 0.0647256i | \(0.0206172\pi\) | |||||||
\(992\) | 0.291413 | + | 0.504742i | 0.00925236 | + | 0.0160256i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −23.5393 | − | 40.7712i | −0.746621 | − | 1.29319i | ||||
\(995\) | 23.4496 | 0.743401 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.6627 | + | 49.6453i | 0.907758 | + | 1.57228i | 0.817171 | + | 0.576395i | \(0.195541\pi\) |
0.0905868 | + | 0.995889i | \(0.471126\pi\) | |||||||
\(998\) | −6.08170 | − | 10.5338i | −0.192513 | − | 0.333442i | ||||
\(999\) | 0 | 0 |
(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 | 855.2.k.k.676.4 | yes | 12 | |
3.2 | odd | 2 | 855.2.k.j.676.3 | yes | 12 | ||
19.7 | even | 3 | inner | 855.2.k.k.406.4 | yes | 12 | |
57.26 | odd | 6 | 855.2.k.j.406.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
855.2.k.j.406.3 | ✓ | 12 | 57.26 | odd | 6 | ||
855.2.k.j.676.3 | yes | 12 | 3.2 | odd | 2 | ||
855.2.k.k.406.4 | yes | 12 | 19.7 | even | 3 | inner | |
855.2.k.k.676.4 | yes | 12 | 1.1 | even | 1 | trivial |