Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(201,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.i (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: | \(15.1715763840\) |
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: | \( x^{12} - 3 x^{11} + 15 x^{10} - 16 x^{9} + 79 x^{8} - 65 x^{7} + 298 x^{6} + 13 x^{5} + 233 x^{4} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 501.6 | ||
Root | \(1.42323 + 2.46510i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.501 |
Dual form | 1900.2.i.e.201.6 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.923228 | + | 1.59908i | 0.533026 | + | 0.923228i | 0.999256 | + | 0.0385649i | \(0.0122786\pi\) |
−0.466230 | + | 0.884664i | \(0.654388\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.72830 | 0.653234 | 0.326617 | − | 0.945157i | \(-0.394091\pi\) | ||||
0.326617 | + | 0.945157i | \(0.394091\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.204702 | + | 0.354554i | −0.0682339 | + | 0.118185i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.66366 | 0.803123 | 0.401562 | − | 0.915832i | \(-0.368468\pi\) | ||||
0.401562 | + | 0.915832i | \(0.368468\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.544662 | + | 0.943382i | −0.151062 | + | 0.261647i | −0.931618 | − | 0.363439i | \(-0.881603\pi\) |
0.780556 | + | 0.625086i | \(0.214936\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.660249 | − | 1.14358i | −0.160134 | − | 0.277360i | 0.774783 | − | 0.632228i | \(-0.217859\pi\) |
−0.934917 | + | 0.354868i | \(0.884526\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.41510 | − | 3.62868i | 0.554061 | − | 0.832476i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.59561 | + | 2.76368i | 0.348191 | + | 0.603085i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.704108 | + | 1.21955i | −0.146817 | + | 0.254294i | −0.930049 | − | 0.367435i | \(-0.880236\pi\) |
0.783233 | + | 0.621729i | \(0.213569\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.78343 | 0.920571 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0446618 | − | 0.0773564i | 0.00829348 | − | 0.0143647i | −0.861849 | − | 0.507165i | \(-0.830693\pi\) |
0.870142 | + | 0.492800i | \(0.164027\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.90368 | 1.59915 | 0.799574 | − | 0.600568i | \(-0.205059\pi\) | ||||
0.799574 | + | 0.600568i | \(0.205059\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.45917 | + | 4.25940i | 0.428086 | + | 0.741466i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.32732 | 0.547008 | 0.273504 | − | 0.961871i | \(-0.411817\pi\) | ||||
0.273504 | + | 0.961871i | \(0.411817\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.01139 | −0.322080 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.296903 | − | 0.514251i | −0.0463685 | − | 0.0803126i | 0.841910 | − | 0.539618i | \(-0.181432\pi\) |
−0.888278 | + | 0.459306i | \(0.848098\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.31334 | + | 2.27477i | 0.200282 | + | 0.346898i | 0.948619 | − | 0.316420i | \(-0.102481\pi\) |
−0.748337 | + | 0.663318i | \(0.769148\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.51092 | + | 6.08109i | −0.512120 | + | 0.887018i | 0.487781 | + | 0.872966i | \(0.337806\pi\) |
−0.999901 | + | 0.0140521i | \(0.995527\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.01299 | −0.573285 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.21912 | − | 2.11158i | 0.170711 | − | 0.295680i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.275627 | − | 0.477400i | 0.0378602 | − | 0.0655759i | −0.846474 | − | 0.532429i | \(-0.821279\pi\) |
0.884335 | + | 0.466854i | \(0.154612\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.03223 | + | 0.511833i | 1.06389 | + | 0.0677939i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.07268 | − | 7.05408i | −0.530217 | − | 0.918364i | −0.999378 | − | 0.0352509i | \(-0.988777\pi\) |
0.469161 | − | 0.883113i | \(-0.344556\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.207276 | + | 0.359013i | −0.0265390 | + | 0.0459669i | −0.878990 | − | 0.476840i | \(-0.841782\pi\) |
0.852451 | + | 0.522807i | \(0.175115\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.353785 | + | 0.612774i | −0.0445727 | + | 0.0772022i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.11271 | + | 3.65932i | −0.258108 | + | 0.447057i | −0.965735 | − | 0.259529i | \(-0.916433\pi\) |
0.707627 | + | 0.706586i | \(0.249766\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.60021 | −0.313028 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.36672 | + | 2.36723i | 0.162200 | + | 0.280939i | 0.935657 | − | 0.352910i | \(-0.114808\pi\) |
−0.773457 | + | 0.633848i | \(0.781474\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.53139 | + | 7.84860i | 0.530359 | + | 0.918609i | 0.999373 | + | 0.0354182i | \(0.0112763\pi\) |
−0.469013 | + | 0.883191i | \(0.655390\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.60359 | 0.524628 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.86470 | − | 10.1580i | −0.659831 | − | 1.14286i | −0.980659 | − | 0.195723i | \(-0.937295\pi\) |
0.320829 | − | 0.947137i | \(-0.396039\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.03030 | + | 8.71273i | 0.558922 | + | 0.968082i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.76556 | 0.852381 | 0.426190 | − | 0.904633i | \(-0.359855\pi\) | ||||
0.426190 | + | 0.904633i | \(0.359855\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.164932 | 0.0176826 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.132475 | + | 0.229454i | −0.0140423 | + | 0.0243221i | −0.872961 | − | 0.487790i | \(-0.837803\pi\) |
0.858919 | + | 0.512112i | \(0.171137\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.941337 | + | 1.63044i | −0.0986789 | + | 0.170917i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.22013 | + | 14.2377i | 0.852387 | + | 1.47638i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.843674 | − | 1.46129i | −0.0856621 | − | 0.148371i | 0.820011 | − | 0.572348i | \(-0.193967\pi\) |
−0.905673 | + | 0.423977i | \(0.860634\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.545256 | + | 0.944410i | −0.0548002 | + | 0.0949168i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.80562 | + | 8.32358i | −0.478177 | + | 0.828227i | −0.999687 | − | 0.0250179i | \(-0.992036\pi\) |
0.521510 | + | 0.853245i | \(0.325369\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.41108 | 0.533169 | 0.266585 | − | 0.963812i | \(-0.414105\pi\) | ||||
0.266585 | + | 0.963812i | \(0.414105\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.99613 | −0.676341 | −0.338171 | − | 0.941085i | \(-0.609808\pi\) | ||||
−0.338171 | + | 0.941085i | \(0.609808\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.05095 | − | 3.55235i | −0.196445 | − | 0.340253i | 0.750928 | − | 0.660384i | \(-0.229607\pi\) |
−0.947373 | + | 0.320131i | \(0.896273\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.07187 | + | 5.32064i | 0.291569 | + | 0.505013i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.9414 | 1.21742 | 0.608710 | − | 0.793393i | \(-0.291687\pi\) | ||||
0.608710 | + | 0.793393i | \(0.291687\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.222986 | − | 0.386224i | −0.0206151 | − | 0.0357064i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.14110 | − | 1.97645i | −0.104605 | − | 0.181181i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.90492 | −0.354993 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.548219 | − | 0.949543i | 0.0494312 | − | 0.0856174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.90009 | + | 10.2192i | −0.523548 | + | 0.906812i | 0.476076 | + | 0.879404i | \(0.342059\pi\) |
−0.999624 | + | 0.0274077i | \(0.991275\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.42502 | + | 4.20026i | −0.213511 | + | 0.369812i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.25635 | − | 3.90811i | −0.197138 | − | 0.341453i | 0.750461 | − | 0.660915i | \(-0.229831\pi\) |
−0.947599 | + | 0.319461i | \(0.896498\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.17400 | − | 6.27143i | 0.361932 | − | 0.543802i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.63770 | − | 2.83658i | 0.139918 | − | 0.242345i | −0.787547 | − | 0.616254i | \(-0.788649\pi\) |
0.927465 | + | 0.373909i | \(0.121983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.84162 | + | 6.65388i | −0.325842 | + | 0.564375i | −0.981682 | − | 0.190525i | \(-0.938981\pi\) |
0.655840 | + | 0.754900i | \(0.272314\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.9655 | −1.09189 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.45079 | + | 2.51285i | −0.121321 | + | 0.210135i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.70491 | − | 6.41709i | −0.305576 | − | 0.529273i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.15941 | + | 2.00816i | 0.0949828 | + | 0.164515i | 0.909601 | − | 0.415482i | \(-0.136387\pi\) |
−0.814619 | + | 0.579997i | \(0.803054\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.18280 | 0.259012 | 0.129506 | − | 0.991579i | \(-0.458661\pi\) | ||||
0.129506 | + | 0.991579i | \(0.458661\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.540616 | 0.0437062 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.981487 | + | 1.69999i | 0.0783312 | + | 0.135674i | 0.902530 | − | 0.430627i | \(-0.141708\pi\) |
−0.824199 | + | 0.566300i | \(0.808374\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.01787 | 0.0807220 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.21691 | + | 2.10774i | −0.0959057 | + | 0.166114i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.63601 | 0.128142 | 0.0640711 | − | 0.997945i | \(-0.479592\pi\) | ||||
0.0640711 | + | 0.997945i | \(0.479592\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.5824 | + | 21.7934i | −0.973658 | + | 1.68642i | −0.289363 | + | 0.957219i | \(0.593443\pi\) |
−0.684295 | + | 0.729205i | \(0.739890\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.90669 | + | 10.2307i | 0.454361 | + | 0.786976i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.792187 | + | 1.59908i | 0.0605800 | + | 0.122285i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.01277 | + | 12.1465i | 0.533171 | + | 0.923479i | 0.999249 | + | 0.0387355i | \(0.0123330\pi\) |
−0.466079 | + | 0.884743i | \(0.654334\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.52002 | − | 13.0251i | 0.565240 | − | 0.979024i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.7004 | −1.77145 | −0.885727 | − | 0.464207i | \(-0.846339\pi\) | ||||
−0.885727 | + | 0.464207i | \(0.846339\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.91555 | + | 6.78193i | −0.291040 | + | 0.504097i | −0.974056 | − | 0.226307i | \(-0.927335\pi\) |
0.683016 | + | 0.730404i | \(0.260668\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.765453 | −0.0565839 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.75868 | − | 3.04612i | −0.128607 | − | 0.222754i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.26717 | 0.601348 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.03698 | 0.436820 | 0.218410 | − | 0.975857i | \(-0.429913\pi\) | ||||
0.218410 | + | 0.975857i | \(0.429913\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.51822 | − | 13.0219i | −0.541173 | − | 0.937339i | −0.998837 | − | 0.0482141i | \(-0.984647\pi\) |
0.457664 | − | 0.889125i | \(-0.348686\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.45409 | 0.103599 | 0.0517996 | − | 0.998657i | \(-0.483504\pi\) | ||||
0.0517996 | + | 0.998657i | \(0.483504\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0696 | − | 20.9051i | 0.855590 | − | 1.48193i | −0.0205062 | − | 0.999790i | \(-0.506528\pi\) |
0.876096 | − | 0.482136i | \(-0.160139\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.80205 | −0.550314 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0771887 | − | 0.133695i | 0.00541759 | − | 0.00938354i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.288264 | − | 0.499288i | −0.0200357 | − | 0.0347029i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.43300 | − | 9.66556i | 0.444980 | − | 0.668581i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.63568 | − | 13.2254i | −0.525662 | − | 0.910473i | −0.999553 | − | 0.0298898i | \(-0.990484\pi\) |
0.473891 | − | 0.880583i | \(-0.342849\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.52359 | + | 4.37099i | −0.172914 | + | 0.299496i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.3882 | 1.04462 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.36702 | + | 14.4921i | −0.565391 | + | 0.979286i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.43845 | 0.0967605 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.72194 | − | 2.98248i | −0.115309 | − | 0.199722i | 0.802594 | − | 0.596526i | \(-0.203453\pi\) |
−0.917903 | + | 0.396804i | \(0.870119\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.9955 | −1.65901 | −0.829504 | − | 0.558501i | \(-0.811377\pi\) | ||||
−0.829504 | + | 0.558501i | \(0.811377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.35855 | 0.354103 | 0.177051 | − | 0.984202i | \(-0.443344\pi\) | ||||
0.177051 | + | 0.984202i | \(0.443344\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.25017 | + | 7.36150i | 0.279640 | + | 0.484351i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.50466 | − | 11.2664i | −0.426135 | − | 0.738087i | 0.570391 | − | 0.821373i | \(-0.306792\pi\) |
−0.996526 | + | 0.0832864i | \(0.973458\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.8289 | − | 18.7562i | 0.703414 | − | 1.21835i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.48487 | −0.548841 | −0.274420 | − | 0.961610i | \(-0.588486\pi\) | ||||
−0.274420 | + | 0.961610i | \(0.588486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0131746 | − | 0.0228190i | 0.000848648 | − | 0.00146990i | −0.865601 | − | 0.500735i | \(-0.833063\pi\) |
0.866449 | + | 0.499265i | \(0.166397\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.11309 | + | 3.65999i | −0.135555 | + | 0.234788i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.10782 | + | 4.25476i | 0.134117 | + | 0.270724i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.16939 | + | 12.4177i | 0.454341 | + | 0.786942i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.82041 | − | 17.0094i | 0.619859 | − | 1.07363i | −0.369653 | − | 0.929170i | \(-0.620523\pi\) |
0.989511 | − | 0.144457i | \(-0.0461434\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.87550 | + | 3.24847i | −0.117912 | + | 0.204229i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.76869 | + | 8.25962i | −0.297463 | + | 0.515221i | −0.975555 | − | 0.219756i | \(-0.929474\pi\) |
0.678092 | + | 0.734977i | \(0.262807\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.75059 | 0.357324 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0182847 | + | 0.0316700i | 0.00113179 | + | 0.00196032i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.64831 | − | 9.78317i | −0.348290 | − | 0.603256i | 0.637656 | − | 0.770321i | \(-0.279904\pi\) |
−0.985946 | + | 0.167065i | \(0.946571\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.489220 | −0.0299398 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.18113 | − | 14.1701i | −0.498812 | − | 0.863968i | 0.501187 | − | 0.865339i | \(-0.332897\pi\) |
−0.999999 | + | 0.00137116i | \(0.999564\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.25370 | + | 3.90352i | 0.136903 | + | 0.237122i | 0.926323 | − | 0.376731i | \(-0.122952\pi\) |
−0.789420 | + | 0.613853i | \(0.789619\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.47628 | −0.210394 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.7914 | 1.60974 | 0.804871 | − | 0.593450i | \(-0.202235\pi\) | ||||
0.804871 | + | 0.593450i | \(0.202235\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.82260 | + | 3.15683i | −0.109116 | + | 0.188995i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.65081 | − | 16.7157i | 0.575719 | − | 0.997174i | −0.420244 | − | 0.907411i | \(-0.638056\pi\) |
0.995963 | − | 0.0897633i | \(-0.0286111\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.15440 | + | 1.99948i | 0.0686221 | + | 0.118857i | 0.898295 | − | 0.439393i | \(-0.144806\pi\) |
−0.829673 | + | 0.558250i | \(0.811473\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.513136 | − | 0.888778i | −0.0302895 | − | 0.0524629i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.62814 | − | 13.2123i | 0.448714 | − | 0.777196i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.55781 | − | 2.69820i | 0.0913203 | − | 0.158171i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.5156 | −1.19854 | −0.599268 | − | 0.800549i | \(-0.704541\pi\) | ||||
−0.599268 | + | 0.800549i | \(0.704541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.7414 | 0.739332 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.767001 | − | 1.32849i | −0.0443568 | − | 0.0768283i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.26983 | + | 3.93147i | 0.130831 | + | 0.226606i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.7468 | −1.01952 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.03655 | + | 3.52742i | 0.116232 | + | 0.201320i | 0.918272 | − | 0.395951i | \(-0.129585\pi\) |
−0.802039 | + | 0.597271i | \(0.796252\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.99566 | + | 8.65274i | 0.284193 | + | 0.492237i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.1999 | 0.635087 | 0.317543 | − | 0.948244i | \(-0.397142\pi\) | ||||
0.317543 | + | 0.948244i | \(0.397142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.0281 | − | 22.5654i | 0.736393 | − | 1.27547i | −0.217717 | − | 0.976012i | \(-0.569861\pi\) |
0.954110 | − | 0.299458i | \(-0.0968057\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.9315 | + | 24.1300i | −0.782469 | + | 1.35528i | 0.148030 | + | 0.988983i | \(0.452707\pi\) |
−0.930499 | + | 0.366294i | \(0.880627\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.118964 | − | 0.206051i | 0.00666069 | − | 0.0115367i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.45902 | − | 11.1874i | −0.360508 | − | 0.624417i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.74426 | − | 0.366038i | −0.319619 | − | 0.0203669i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.78699 | − | 6.55926i | 0.209421 | − | 0.362728i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.06791 | + | 10.5099i | −0.334534 | + | 0.579431i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.9379 | −1.15085 | −0.575426 | − | 0.817854i | \(-0.695164\pi\) | ||||
−0.575426 | + | 0.817854i | \(0.695164\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.681108 | + | 1.17971i | −0.0373245 | + | 0.0646479i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.75456 | − | 13.4313i | −0.422418 | − | 0.731649i | 0.573758 | − | 0.819025i | \(-0.305485\pi\) |
−0.996175 | + | 0.0873761i | \(0.972152\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.9478 | + | 20.6942i | 0.648917 | + | 1.12396i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.7164 | 1.28431 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.0337 | −1.02772 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.5770 | − | 30.4443i | −0.943584 | − | 1.63434i | −0.758561 | − | 0.651602i | \(-0.774097\pi\) |
−0.185023 | − | 0.982734i | \(-0.559236\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.5120 | 1.57974 | 0.789870 | − | 0.613274i | \(-0.210148\pi\) | ||||
0.789870 | + | 0.613274i | \(0.210148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.60535 | + | 4.51260i | −0.139063 | + | 0.240865i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.0179 | −1.65092 | −0.825458 | − | 0.564463i | \(-0.809083\pi\) | ||||
−0.825458 | + | 0.564463i | \(0.809083\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.10700 | − | 3.64943i | 0.111514 | − | 0.193148i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.5956 | + | 28.7444i | 0.875882 | + | 1.51707i | 0.855820 | + | 0.517274i | \(0.173053\pi\) |
0.0200625 | + | 0.999799i | \(0.493613\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.33460 | − | 17.5272i | −0.386032 | − | 0.922485i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.60513 | − | 6.24428i | −0.189220 | − | 0.327739i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.46462 | − | 12.9291i | 0.389650 | − | 0.674894i | −0.602752 | − | 0.797928i | \(-0.705929\pi\) |
0.992402 | + | 0.123035i | \(0.0392626\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.243106 | 0.0126556 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.476365 | − | 0.825088i | 0.0247316 | − | 0.0428364i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.129504 | −0.00670546 | −0.00335273 | − | 0.999994i | \(-0.501067\pi\) | ||||
−0.00335273 | + | 0.999994i | \(0.501067\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0486511 | + | 0.0842662i | 0.00250566 | + | 0.00433993i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.91054 | 0.509070 | 0.254535 | − | 0.967064i | \(-0.418078\pi\) | ||||
0.254535 | + | 0.967064i | \(0.418078\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.7885 | −1.11626 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.1930 | − | 31.5112i | −0.929619 | − | 1.61015i | −0.783960 | − | 0.620812i | \(-0.786803\pi\) |
−0.145659 | − | 0.989335i | \(-0.546530\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.07537 | −0.0546641 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.3433 | − | 19.6472i | 0.575129 | − | 0.996153i | −0.420898 | − | 0.907108i | \(-0.638285\pi\) |
0.996028 | − | 0.0890454i | \(-0.0283816\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.85954 | 0.0940412 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.16625 | − | 7.21616i | 0.210160 | − | 0.364007i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.67149 | − | 16.7515i | −0.485398 | − | 0.840734i | 0.514461 | − | 0.857514i | \(-0.327992\pi\) |
−0.999859 | + | 0.0167797i | \(0.994659\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.8821 | + | 0.884599i | 0.694973 | + | 0.0442853i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.11006 | − | 1.92268i | −0.0554337 | − | 0.0960140i | 0.836977 | − | 0.547238i | \(-0.184321\pi\) |
−0.892411 | + | 0.451224i | \(0.850987\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.84949 | + | 8.39957i | −0.241570 | + | 0.418412i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.86284 | 0.439315 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.19101 | + | 8.99110i | −0.256679 | + | 0.444581i | −0.965350 | − | 0.260958i | \(-0.915962\pi\) |
0.708671 | + | 0.705539i | \(0.249295\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.04788 | 0.298320 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.03879 | − | 12.1915i | −0.346356 | − | 0.599907i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.1868 | −0.694730 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.0958 | −0.737479 | −0.368740 | − | 0.929533i | \(-0.620211\pi\) | ||||
−0.368740 | + | 0.929533i | \(0.620211\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.47485 | − | 11.2148i | −0.315565 | − | 0.546574i | 0.663993 | − | 0.747739i | \(-0.268861\pi\) |
−0.979557 | + | 0.201165i | \(0.935527\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.43738 | − | 2.48962i | −0.0698879 | − | 0.121049i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.358235 | + | 0.620480i | −0.0173362 | + | 0.0300272i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.35765 | −0.258670 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0654 | − | 26.0940i | 0.725674 | − | 1.25690i | −0.233022 | − | 0.972472i | \(-0.574861\pi\) |
0.958696 | − | 0.284433i | \(-0.0918053\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.9281 | − | 22.3922i | 0.621287 | − | 1.07610i | −0.367959 | − | 0.929842i | \(-0.619943\pi\) |
0.989246 | − | 0.146259i | \(-0.0467232\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.72487 | + | 5.50031i | 0.130348 | + | 0.263116i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.35016 | + | 7.53469i | 0.207622 | + | 0.359611i | 0.950965 | − | 0.309299i | \(-0.100094\pi\) |
−0.743343 | + | 0.668910i | \(0.766761\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.821467 | − | 1.42282i | 0.0391175 | − | 0.0677534i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.0822 | + | 26.1231i | −0.716575 | + | 1.24114i | 0.245774 | + | 0.969327i | \(0.420958\pi\) |
−0.962349 | + | 0.271817i | \(0.912375\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.14081 | + | 3.70798i | −0.101257 | + | 0.175382i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.7821 | 1.12235 | 0.561173 | − | 0.827699i | \(-0.310350\pi\) | ||||
0.561173 | + | 0.827699i | \(0.310350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.790849 | − | 1.36979i | −0.0372396 | − | 0.0645009i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.93845 | + | 5.08954i | 0.138060 | + | 0.239128i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.5258 | 1.24082 | 0.620412 | − | 0.784276i | \(-0.286966\pi\) | ||||
0.620412 | + | 0.784276i | \(0.286966\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.15825 | − | 5.47025i | −0.147414 | − | 0.255329i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.34402 | + | 12.7202i | 0.342045 | + | 0.592439i | 0.984812 | − | 0.173622i | \(-0.0555472\pi\) |
−0.642767 | + | 0.766061i | \(0.722214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.22167 | 0.428567 | 0.214284 | − | 0.976771i | \(-0.431258\pi\) | ||||
0.214284 | + | 0.976771i | \(0.431258\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.3069 | −1.44871 | −0.724355 | − | 0.689427i | \(-0.757862\pi\) | ||||
−0.724355 | + | 0.689427i | \(0.757862\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.65139 | + | 6.32439i | −0.168605 | + | 0.292033i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.81227 | + | 3.13895i | −0.0835051 | + | 0.144635i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.49828 | + | 6.05920i | 0.160851 | + | 0.278602i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.112843 | + | 0.195449i | 0.00516671 | + | 0.00894900i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.0062 | + | 27.7236i | −0.731344 | + | 1.26672i | 0.224966 | + | 0.974367i | \(0.427773\pi\) |
−0.956309 | + | 0.292357i | \(0.905560\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.81226 | + | 3.13893i | −0.0826321 | + | 0.143123i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.49393 | −0.204481 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.19899 | 0.0996456 | 0.0498228 | − | 0.998758i | \(-0.484134\pi\) | ||||
0.0498228 | + | 0.998758i | \(0.484134\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.51041 | + | 2.61611i | 0.0683031 | + | 0.118304i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.78283 | − | 11.7482i | −0.306105 | − | 0.530189i | 0.671402 | − | 0.741094i | \(-0.265693\pi\) |
−0.977507 | + | 0.210904i | \(0.932359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.117951 | −0.00531227 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.36210 | + | 4.09128i | 0.105955 | + | 0.183519i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.20880 | − | 10.7540i | −0.277944 | − | 0.481413i | 0.692930 | − | 0.721005i | \(-0.256320\pi\) |
−0.970874 | + | 0.239592i | \(0.922986\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −46.4658 | −2.07594 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.43957 | − | 14.6178i | 0.376302 | − | 0.651774i | −0.614219 | − | 0.789136i | \(-0.710529\pi\) |
0.990521 | + | 0.137361i | \(0.0438622\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.9064 | + | 18.8905i | −0.484372 | + | 0.838957i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.4081 | − | 21.4915i | 0.549981 | − | 0.952594i | −0.448295 | − | 0.893886i | \(-0.647968\pi\) |
0.998275 | − | 0.0587085i | \(-0.0186983\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.83159 | + | 13.5647i | 0.346449 | + | 0.600067i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.5524 | − | 17.3575i | 0.510053 | − | 0.766353i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.35189 | + | 16.1979i | −0.411296 | + | 0.712385i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.9488 | + | 22.4279i | −0.568388 | + | 0.984477i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.6549 | −1.43064 | −0.715318 | − | 0.698799i | \(-0.753718\pi\) | ||||
−0.715318 | + | 0.698799i | \(0.753718\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.72603 | + | 2.98957i | −0.0754741 | + | 0.130725i | −0.901292 | − | 0.433211i | \(-0.857380\pi\) |
0.825818 | + | 0.563936i | \(0.190714\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.87864 | − | 10.1821i | −0.256078 | − | 0.443539i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.5085 | + | 18.2012i | 0.456890 | + | 0.791356i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.33474 | 0.144715 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.646847 | 0.0280181 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.8809 | − | 37.8989i | −0.944231 | − | 1.63546i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.6892 | −0.460418 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.69787 | + | 6.40490i | −0.158984 | + | 0.275368i | −0.934503 | − | 0.355956i | \(-0.884155\pi\) |
0.775519 | + | 0.631325i | \(0.217488\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.4598 | −0.620529 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.74778 | + | 6.49134i | −0.160243 | + | 0.277550i | −0.934956 | − | 0.354764i | \(-0.884561\pi\) |
0.774713 | + | 0.632314i | \(0.217895\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0848596 | − | 0.146981i | −0.00362172 | − | 0.00627300i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.172839 | − | 0.348887i | −0.00736319 | − | 0.0148631i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.1359 | − | 17.5560i | −0.431024 | − | 0.746556i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.1744 | + | 22.8187i | −0.558217 | + | 0.966859i | 0.439429 | + | 0.898277i | \(0.355181\pi\) |
−0.997645 | + | 0.0685820i | \(0.978153\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.86130 | −0.121020 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.24732 | − | 5.62453i | 0.137102 | − | 0.237468i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.8731 | −0.458247 | −0.229123 | − | 0.973397i | \(-0.573586\pi\) | ||||
−0.229123 | + | 0.973397i | \(0.573586\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.69385 | + | 15.0582i | 0.365107 | + | 0.632384i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.8171 | −0.788853 | −0.394427 | − | 0.918927i | \(-0.629057\pi\) | ||||
−0.394427 | + | 0.918927i | \(0.629057\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.0661 | −1.21638 | −0.608189 | − | 0.793792i | \(-0.708104\pi\) | ||||
−0.608189 | + | 0.793792i | \(0.708104\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.57351 | + | 9.65360i | 0.232837 | + | 0.403285i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.6665 | 0.735468 | 0.367734 | − | 0.929931i | \(-0.380134\pi\) | ||||
0.367734 | + | 0.929931i | \(0.380134\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.8821 | − | 24.0444i | 0.576919 | − | 0.999253i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.4212 | 0.556804 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.734176 | − | 1.27163i | 0.0304065 | − | 0.0526655i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.2815 | − | 26.4684i | −0.630736 | − | 1.09247i | −0.987402 | − | 0.158234i | \(-0.949420\pi\) |
0.356666 | − | 0.934232i | \(-0.383913\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.5032 | − | 32.3086i | 0.886026 | − | 1.33125i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.34245 | + | 2.32520i | 0.0552211 | + | 0.0956458i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.0606 | − | 19.1576i | 0.454206 | − | 0.786707i | −0.544437 | − | 0.838802i | \(-0.683257\pi\) |
0.998642 | + | 0.0520949i | \(0.0165898\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 44.5719 | 1.82421 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.0909 | + | 24.4062i | −0.575740 | + | 0.997210i | 0.420221 | + | 0.907422i | \(0.361952\pi\) |
−0.995961 | + | 0.0897885i | \(0.971381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.7927 | −1.33764 | −0.668821 | − | 0.743424i | \(-0.733201\pi\) | ||||
−0.668821 | + | 0.743424i | \(0.733201\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.864950 | − | 1.49814i | −0.0352235 | − | 0.0610089i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.2403 | −1.55213 | −0.776063 | − | 0.630656i | \(-0.782786\pi\) | ||||
−0.776063 | + | 0.630656i | \(0.782786\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.285051 | 0.0115509 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.82453 | − | 6.62427i | −0.154724 | − | 0.267989i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.72203 | − | 6.44674i | −0.150331 | − | 0.260381i | 0.781018 | − | 0.624509i | \(-0.214701\pi\) |
−0.931349 | + | 0.364127i | \(0.881367\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.23294 | + | 7.33167i | −0.170412 | + | 0.295162i | −0.938564 | − | 0.345106i | \(-0.887843\pi\) |
0.768152 | + | 0.640267i | \(0.221176\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.1940 | −1.41457 | −0.707283 | − | 0.706931i | \(-0.750079\pi\) | ||||
−0.707283 | + | 0.706931i | \(0.750079\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.36805 | + | 5.83363i | −0.135155 | + | 0.234095i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.228956 | + | 0.396564i | −0.00917294 | + | 0.0158880i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.3951 | + | 1.36335i | 0.854439 | + | 0.0544469i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.19686 | − | 3.80507i | −0.0875944 | − | 0.151718i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.23316 | + | 9.06410i | −0.208329 | + | 0.360836i | −0.951188 | − | 0.308611i | \(-0.900136\pi\) |
0.742859 | + | 0.669447i | \(0.233469\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.0990 | − | 24.4201i | 0.560383 | − | 0.970612i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.18572 | − | 3.78579i | 0.0866016 | − | 0.149998i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.11908 | −0.0442702 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.85836 | + | 4.95082i | 0.112898 | + | 0.195546i | 0.916938 | − | 0.399030i | \(-0.130653\pi\) |
−0.804039 | + | 0.594576i | \(0.797320\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.5249 | + | 30.3540i | 0.691114 | + | 1.19705i | 0.971473 | + | 0.237150i | \(0.0762133\pi\) |
−0.280359 | + | 0.959895i | \(0.590453\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.40523 | 0.330444 | 0.165222 | − | 0.986256i | \(-0.447166\pi\) | ||||
0.165222 | + | 0.986256i | \(0.447166\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.8482 | − | 18.7897i | −0.425830 | − | 0.737559i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.2068 | + | 24.6069i | 0.556809 | + | 0.964421i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.586740 | −0.0229609 | −0.0114805 | − | 0.999934i | \(-0.503654\pi\) | ||||
−0.0114805 | + | 0.999934i | \(0.503654\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.71034 | −0.144754 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.16313 | + | 7.21076i | −0.162173 | + | 0.280891i | −0.935648 | − | 0.352936i | \(-0.885183\pi\) |
0.773475 | + | 0.633827i | \(0.218517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.564657 | − | 0.978014i | 0.0219626 | − | 0.0380403i | −0.854835 | − | 0.518900i | \(-0.826342\pi\) |
0.876798 | + | 0.480859i | \(0.159675\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.32802 | + | 2.30019i | 0.0515759 | + | 0.0893321i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0628934 | + | 0.108935i | 0.00243524 | + | 0.00421796i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.17948 | − | 5.50703i | 0.122926 | − | 0.212914i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.552113 | + | 0.956288i | −0.0213141 | + | 0.0369171i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.90978 | 0.381994 | 0.190997 | − | 0.981591i | \(-0.438828\pi\) | ||||
0.190997 | + | 0.981591i | \(0.438828\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.9039 | −1.26460 | −0.632301 | − | 0.774723i | \(-0.717889\pi\) | ||||
−0.632301 | + | 0.774723i | \(0.717889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.45812 | − | 2.52553i | −0.0559574 | − | 0.0969211i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.0765 | − | 39.9697i | −0.884295 | − | 1.53164i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.22470 | 0.123390 | 0.0616949 | − | 0.998095i | \(-0.480349\pi\) | ||||
0.0616949 | + | 0.998095i | \(0.480349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.94716 | + | 8.56874i | 0.188746 | + | 0.326918i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.300247 | + | 0.520043i | 0.0114385 | + | 0.0198120i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.98569 | −0.341832 | −0.170916 | − | 0.985286i | \(-0.554673\pi\) | ||||
−0.170916 | + | 0.985286i | \(0.554673\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.942363 | + | 1.63222i | −0.0357974 | + | 0.0620029i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.392060 | + | 0.679067i | −0.0148503 | + | 0.0257215i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.0106 | − | 20.8029i | 0.454282 | − | 0.786839i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.62340 | + | 13.2041i | 0.287932 | + | 0.498713i | 0.973316 | − | 0.229469i | \(-0.0736990\pi\) |
−0.685384 | + | 0.728182i | \(0.740366\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.03580 | − | 12.0738i | 0.303076 | − | 0.455371i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.30554 | + | 14.3856i | −0.312362 | + | 0.541027i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.6736 | + | 30.6116i | −0.663746 | + | 1.14964i | 0.315878 | + | 0.948800i | \(0.397701\pi\) |
−0.979624 | + | 0.200841i | \(0.935632\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.80206 | 0.180091 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.26915 | + | 10.8585i | −0.234781 | + | 0.406653i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.83347 | − | 13.5680i | −0.292546 | − | 0.506705i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.9566 | + | 25.9056i | 0.557787 | + | 0.966115i | 0.997681 | + | 0.0680651i | \(0.0216826\pi\) |
−0.439894 | + | 0.898050i | \(0.644984\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.35194 | 0.348284 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.0486525 | 0.00180941 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.1230 | − | 33.1220i | −0.709232 | − | 1.22843i | −0.965142 | − | 0.261725i | \(-0.915709\pi\) |
0.255911 | − | 0.966700i | \(-0.417625\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.3783 | 0.828827 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.73426 | − | 3.00382i | 0.0641438 | − | 0.111100i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.55553 | 0.0574549 | 0.0287274 | − | 0.999587i | \(-0.490855\pi\) | ||||
0.0287274 | + | 0.999587i | \(0.490855\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.62754 | + | 9.74718i | −0.207293 | + | 0.359042i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.5945 | + | 23.5464i | 0.500083 | + | 0.866169i | 1.00000 | 9.57964e-5i | \(3.04929e-5\pi\) | |
−0.499917 | + | 0.866073i | \(0.666636\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.85770 | + | 7.29868i | −0.178452 | + | 0.268124i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.54725 | + | 16.5363i | 0.350255 | + | 0.606659i | 0.986294 | − | 0.164998i | \(-0.0527617\pi\) |
−0.636039 | + | 0.771657i | \(0.719428\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.58962 | + | 2.75331i | −0.0581613 | + | 0.100738i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0914 | −0.441809 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.08150 | + | 1.87321i | −0.0394644 | + | 0.0683544i | −0.885083 | − | 0.465433i | \(-0.845899\pi\) |
0.845619 | + | 0.533788i | \(0.179232\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.2659 | 1.32160 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.1677 | + | 41.8598i | 0.878392 | + | 1.52142i | 0.853105 | + | 0.521739i | \(0.174716\pi\) |
0.0252862 | + | 0.999680i | \(0.491950\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.92607 | −0.251401 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.4377 | 1.79211 | 0.896057 | − | 0.443939i | \(-0.146419\pi\) | ||||
0.896057 | + | 0.443939i | \(0.146419\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.54465 | − | 6.13951i | −0.128325 | − | 0.222265i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.87293 | 0.320383 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.7781 | − | 18.6682i | 0.388667 | − | 0.673192i | −0.603603 | − | 0.797285i | \(-0.706269\pi\) |
0.992271 | + | 0.124093i | \(0.0396022\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.6104 | −0.634222 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.9699 | + | 39.7850i | −0.826169 | + | 1.43097i | 0.0748533 | + | 0.997195i | \(0.476151\pi\) |
−0.901022 | + | 0.433772i | \(0.857182\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.30911 | + | 9.19564i | 0.190463 | + | 0.329892i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.58310 | − | 0.164602i | −0.0925493 | − | 0.00589746i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.64048 | + | 6.30550i | 0.130267 | + | 0.225629i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.213636 | − | 0.370029i | 0.00763473 | − | 0.0132237i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.7925 | 1.56103 | 0.780517 | − | 0.625135i | \(-0.214956\pi\) | ||||
0.780517 | + | 0.625135i | \(0.214956\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.4294 | − | 18.0642i | 0.371295 | − | 0.643102i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.3665 | 0.795261 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.225791 | − | 0.391081i | −0.00801807 | − | 0.0138877i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.8269 | −1.58785 | −0.793925 | − | 0.608016i | \(-0.791966\pi\) | ||||
−0.793925 | + | 0.608016i | \(0.791966\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.27232 | 0.328031 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0542358 | − | 0.0939392i | −0.00191633 | − | 0.00331918i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.0701 | + | 20.9060i | 0.425944 | + | 0.737757i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.1061 | − | 26.1645i | 0.531760 | − | 0.921035i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −47.3024 | −1.66307 | −0.831533 | − | 0.555476i | \(-0.812536\pi\) | ||||
−0.831533 | + | 0.555476i | \(0.812536\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.5474 | − | 44.2493i | 0.897089 | − | 1.55380i | 0.0658911 | − | 0.997827i | \(-0.479011\pi\) |
0.831198 | − | 0.555977i | \(-0.187656\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.16136 | + | 7.20769i | −0.145945 | + | 0.252785i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.4262 | + | 0.728107i | 0.399753 | + | 0.0254732i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.385386 | − | 0.667509i | −0.0134665 | − | 0.0233246i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.9827 | + | 25.9508i | −0.522901 | + | 0.905690i | 0.476744 | + | 0.879042i | \(0.341817\pi\) |
−0.999645 | + | 0.0266484i | \(0.991517\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.2210 | + | 43.6840i | −0.879148 | + | 1.52273i | −0.0268715 | + | 0.999639i | \(0.508555\pi\) |
−0.852277 | + | 0.523091i | \(0.824779\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.04814 | + | 1.81544i | −0.0364475 | + | 0.0631290i | −0.883674 | − | 0.468103i | \(-0.844938\pi\) |
0.847226 | + | 0.531232i | \(0.178271\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.82967 | 0.306667 | 0.153334 | − | 0.988174i | \(-0.450999\pi\) | ||||
0.153334 | + | 0.988174i | \(0.450999\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.7346 | + | 42.8416i | 0.858034 | + | 1.48616i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.64957 | + | 4.58920i | 0.0918023 | + | 0.159006i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 42.5901 | 1.47213 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.8735 | − | 24.0295i | −0.478965 | − | 0.829592i | 0.520744 | − | 0.853713i | \(-0.325655\pi\) |
−0.999709 | + | 0.0241209i | \(0.992321\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4960 | + | 25.1078i | 0.499862 | + | 0.865787i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 35.6396 | 1.22749 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.74886 | −0.231893 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.13155 | + | 3.69196i | −0.0731547 | + | 0.126708i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.34279 | + | 4.05783i | −0.0803098 | + | 0.139101i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.0668 | + | 31.2926i | 0.618595 | + | 1.07144i | 0.989742 | + | 0.142864i | \(0.0456312\pi\) |
−0.371147 | + | 0.928574i | \(0.621035\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.7728 | + | 18.6590i | 0.367991 | + | 0.637379i | 0.989251 | − | 0.146225i | \(-0.0467125\pi\) |
−0.621261 | + | 0.783604i | \(0.713379\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0122 | − | 19.0736i | 0.375730 | − | 0.650784i | −0.614706 | − | 0.788756i | \(-0.710725\pi\) |
0.990436 | + | 0.137973i | \(0.0440586\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.947484 | − | 1.64109i | 0.0322902 | − | 0.0559282i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.06081 | −0.138231 | −0.0691157 | − | 0.997609i | \(-0.522018\pi\) | ||||
−0.0691157 | + | 0.997609i | \(0.522018\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.1701 | 0.956706 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.6216 | − | 27.0574i | −0.529925 | − | 0.917858i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.30142 | − | 3.98618i | −0.0779808 | − | 0.135067i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.690806 | 0.0233802 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.13257 | − | 8.88987i | −0.173315 | − | 0.300190i | 0.766262 | − | 0.642528i | \(-0.222114\pi\) |
−0.939577 | + | 0.342338i | \(0.888781\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.9406 | − | 32.8061i | −0.638851 | − | 1.10652i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.4838 | 1.80191 | 0.900957 | − | 0.433909i | \(-0.142866\pi\) | ||||
0.900957 | + | 0.433909i | \(0.142866\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.5511 | − | 35.5955i | 0.691598 | − | 1.19788i | −0.279716 | − | 0.960083i | \(-0.590240\pi\) |
0.971314 | − | 0.237800i | \(-0.0764263\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.68891 | + | 15.0496i | −0.291745 | + | 0.505317i | −0.974222 | − | 0.225590i | \(-0.927569\pi\) |
0.682478 | + | 0.730907i | \(0.260903\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.1971 | + | 17.6619i | −0.341999 | + | 0.592360i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.3990 | + | 23.2078i | 0.448883 | + | 0.777489i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.5871 | + | 27.4264i | 0.454675 | + | 0.917790i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.41623 | − | 2.45299i | 0.0472867 | − | 0.0819030i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.397654 | − | 0.688757i | 0.0132625 | − | 0.0229713i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.727929 | −0.0242508 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.19115 | + | 7.25928i | −0.139473 | + | 0.241574i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.08357 | − | 15.7332i | −0.301615 | − | 0.522413i | 0.674887 | − | 0.737921i | \(-0.264192\pi\) |
−0.976502 | + | 0.215509i | \(0.930859\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.96744 | − | 3.40770i | −0.0652558 | − | 0.113026i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.0630 | 1.69179 | 0.845897 | − | 0.533347i | \(-0.179066\pi\) | ||||
0.845897 | + | 0.533347i | \(0.179066\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.6848 | 0.684567 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.89964 | − | 6.75437i | −0.128777 | − | 0.223049i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.9920 | −0.494541 | −0.247271 | − | 0.968946i | \(-0.579534\pi\) | ||||
−0.247271 | + | 0.968946i | \(0.579534\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.76041 | + | 6.51322i | −0.123910 | + | 0.214618i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.97761 | −0.0980091 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.10766 | + | 1.91852i | −0.0363802 | + | 0.0630124i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.71605 | + | 11.6325i | 0.220347 | + | 0.381651i | 0.954913 | − | 0.296885i | \(-0.0959479\pi\) |
−0.734567 | + | 0.678537i | \(0.762615\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.69177 | + | 14.5619i | −0.317635 | + | 0.477246i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.3400 | + | 17.9095i | 0.338518 | + | 0.586330i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.1700 | − | 21.0790i | 0.397576 | − | 0.688622i | −0.595850 | − | 0.803096i | \(-0.703185\pi\) |
0.993426 | + | 0.114473i | \(0.0365180\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 48.1117 | 1.57007 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.2200 | − | 31.5579i | 0.593954 | − | 1.02876i | −0.399739 | − | 0.916629i | \(-0.630899\pi\) |
0.993694 | − | 0.112130i | \(-0.0357673\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.836207 | 0.0272307 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.21884 | + | 15.9675i | 0.299572 | + | 0.518874i | 0.976038 | − | 0.217600i | \(-0.0698228\pi\) |
−0.676466 | + | 0.736474i | \(0.736489\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.87230 | −0.320469 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −51.4477 | −1.66831 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.05532 | + | 12.2202i | 0.228544 | + | 0.395850i | 0.957377 | − | 0.288842i | \(-0.0932701\pi\) |
−0.728833 | + | 0.684692i | \(0.759937\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.439323 | 0.0142013 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.83043 | − | 4.90245i | 0.0913993 | − | 0.158308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.2754 | 1.55727 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.43212 | − | 2.48050i | 0.0461494 | − | 0.0799331i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.5122 | + | 45.9205i | 0.852576 | + | 1.47670i | 0.878876 | + | 0.477051i | \(0.158294\pi\) |
−0.0262999 | + | 0.999654i | \(0.508372\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.71794 | − | 9.52347i | −0.151562 | − | 0.305938i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.12809 | − | 3.68596i | −0.0682937 | − | 0.118288i | 0.829857 | − | 0.557977i | \(-0.188422\pi\) |
−0.898150 | + | 0.439689i | \(0.855089\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.63946 | + | 11.4999i | −0.212851 | + | 0.368669i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.5984 | 1.04292 | 0.521458 | − | 0.853277i | \(-0.325388\pi\) | ||||
0.521458 | + | 0.853277i | \(0.325388\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.352869 | + | 0.611187i | −0.0112777 | + | 0.0195336i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.67933 | 0.0536169 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.23872 | − | 9.07372i | −0.167089 | − | 0.289407i | 0.770306 | − | 0.637674i | \(-0.220103\pi\) |
−0.937395 | + | 0.348268i | \(0.886770\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.4083 | −0.713263 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.69892 | −0.117619 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00924 | + | 6.94421i | 0.127358 | + | 0.220590i | 0.922652 | − | 0.385633i | \(-0.126017\pi\) |
−0.795294 | + | 0.606224i | \(0.792684\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.3305 | − | 33.4814i | −0.613434 | − | 1.06250i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.3481 | − | 35.2440i | 0.644432 | − | 1.11619i | −0.340001 | − | 0.940425i | \(-0.610427\pi\) |
0.984432 | − | 0.175763i | \(-0.0562393\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.9160 | 0.503559 |
(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 | 1900.2.i.e.501.6 | yes | 12 | |
5.2 | odd | 4 | 1900.2.s.e.349.10 | 24 | |||
5.3 | odd | 4 | 1900.2.s.e.349.3 | 24 | |||
5.4 | even | 2 | 1900.2.i.f.501.1 | yes | 12 | ||
19.11 | even | 3 | inner | 1900.2.i.e.201.6 | ✓ | 12 | |
95.49 | even | 6 | 1900.2.i.f.201.1 | yes | 12 | ||
95.68 | odd | 12 | 1900.2.s.e.49.10 | 24 | |||
95.87 | odd | 12 | 1900.2.s.e.49.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.i.e.201.6 | ✓ | 12 | 19.11 | even | 3 | inner | |
1900.2.i.e.501.6 | yes | 12 | 1.1 | even | 1 | trivial | |
1900.2.i.f.201.1 | yes | 12 | 95.49 | even | 6 | ||
1900.2.i.f.501.1 | yes | 12 | 5.4 | even | 2 | ||
1900.2.s.e.49.3 | 24 | 95.87 | odd | 12 | |||
1900.2.s.e.49.10 | 24 | 95.68 | odd | 12 | |||
1900.2.s.e.349.3 | 24 | 5.3 | odd | 4 | |||
1900.2.s.e.349.10 | 24 | 5.2 | odd | 4 |