Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(49,1900)]
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, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.5 | ||
Root | \(1.65604 + 0.956115i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.349 |
Dual form | 1900.2.s.c.49.5 |
$q$-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 | ||||||||
\(3\) | 2.22469 | − | 1.28442i | 1.28442 | − | 0.741563i | 0.306771 | − | 0.951783i | \(-0.400751\pi\) |
0.977654 | + | 0.210220i | \(0.0674182\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.56885i | − | 1.34890i | −0.738321 | − | 0.674449i | \(-0.764381\pi\) | ||
0.738321 | − | 0.674449i | \(-0.235619\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.79949 | − | 3.11682i | 0.599831 | − | 1.03894i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.56885 | 1.37756 | 0.688780 | − | 0.724970i | \(-0.258147\pi\) | ||||
0.688780 | + | 0.724970i | \(0.258147\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.866025 | + | 0.500000i | 0.240192 | + | 0.138675i | 0.615265 | − | 0.788320i | \(-0.289049\pi\) |
−0.375073 | + | 0.926995i | \(0.622382\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.96812 | + | 2.86834i | −1.20495 | + | 0.695676i | −0.961651 | − | 0.274277i | \(-0.911562\pi\) |
−0.243295 | + | 0.969952i | \(0.578228\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35327 | + | 0.221364i | 0.998710 | + | 0.0507843i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.58392 | − | 7.93958i | −1.00029 | − | 1.73256i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.84887 | + | 2.79949i | 1.01106 | + | 0.583735i | 0.911501 | − | 0.411297i | \(-0.134924\pi\) |
0.0995571 | + | 0.995032i | \(0.468257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.53871i | − | 0.296125i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.38341 | − | 5.86024i | 0.628284 | − | 1.08822i | −0.359612 | − | 0.933102i | \(-0.617091\pi\) |
0.987896 | − | 0.155118i | \(-0.0495758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.59899 | 0.826003 | 0.413001 | − | 0.910730i | \(-0.364480\pi\) | ||||
0.413001 | + | 0.910730i | \(0.364480\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.1643 | − | 5.86834i | 1.76937 | − | 1.02155i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.56885i | − | 0.586715i | −0.956003 | − | 0.293358i | \(-0.905227\pi\) | ||
0.956003 | − | 0.293358i | \(-0.0947727\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.56885 | 0.411345 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.35327 | − | 9.27214i | −0.836041 | − | 1.44807i | −0.893180 | − | 0.449699i | \(-0.851531\pi\) |
0.0571390 | − | 0.998366i | \(-0.481802\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.79088 | + | 5.65277i | −1.49310 | + | 0.862039i | −0.999969 | − | 0.00791826i | \(-0.997480\pi\) |
−0.493127 | + | 0.869957i | \(0.664146\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.86024 | − | 3.38341i | −0.854804 | − | 0.493522i | 0.00746461 | − | 0.999972i | \(-0.497624\pi\) |
−0.862269 | + | 0.506451i | \(0.830957\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.73669 | −0.819527 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.36834 | + | 12.7623i | −1.03177 | + | 1.78709i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.94536 | + | 1.70051i | 0.404577 | + | 0.233582i | 0.688457 | − | 0.725277i | \(-0.258288\pi\) |
−0.283880 | + | 0.958860i | \(0.591622\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.96901 | − | 5.09899i | 1.32043 | − | 0.675378i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.38341 | − | 5.86024i | −0.440483 | − | 0.762939i | 0.557242 | − | 0.830350i | \(-0.311859\pi\) |
−0.997725 | + | 0.0674112i | \(0.978526\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.06885 | + | 7.04745i | −0.520963 | + | 0.902334i | 0.478740 | + | 0.877957i | \(0.341094\pi\) |
−0.999703 | + | 0.0243773i | \(0.992240\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.1234 | − | 6.42212i | −1.40142 | − | 0.809112i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.48686 | − | 3.16784i | −0.670326 | − | 0.387013i | 0.125874 | − | 0.992046i | \(-0.459826\pi\) |
−0.796200 | + | 0.605033i | \(0.793160\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.3830 | 1.73150 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.515069 | + | 0.892126i | 0.0611275 | + | 0.105876i | 0.894970 | − | 0.446127i | \(-0.147197\pi\) |
−0.833842 | + | 0.552003i | \(0.813864\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0303 | + | 6.36834i | −1.29100 | + | 0.745358i | −0.978831 | − | 0.204669i | \(-0.934388\pi\) |
−0.312167 | + | 0.950027i | \(0.601055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 16.3055i | − | 1.85819i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.43115 | + | 4.21088i | 0.273526 | + | 0.473761i | 0.969762 | − | 0.244052i | \(-0.0784768\pi\) |
−0.696236 | + | 0.717813i | \(0.745143\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.42212 | + | 5.92729i | 0.380236 | + | 0.658588i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 9.40101i | − | 1.03190i | −0.856620 | − | 0.515948i | \(-0.827440\pi\) | ||
0.856620 | − | 0.515948i | \(-0.172560\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 17.3830i | − | 1.86365i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.13770 | − | 10.6308i | 0.650595 | − | 1.12686i | −0.332384 | − | 0.943144i | \(-0.607853\pi\) |
0.982979 | − | 0.183719i | \(-0.0588137\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.78442 | − | 3.09071i | 0.187059 | − | 0.323995i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.2313 | − | 5.90705i | 1.06094 | − | 0.612533i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.27689 | + | 1.31456i | −0.231183 | + | 0.133474i | −0.611118 | − | 0.791540i | \(-0.709280\pi\) |
0.379935 | + | 0.925013i | \(0.375947\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.22162 | − | 14.2403i | 0.826304 | − | 1.43120i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.43719 | + | 7.68544i | −0.441517 | + | 0.764730i | −0.997802 | − | 0.0662612i | \(-0.978893\pi\) |
0.556285 | + | 0.830992i | \(0.312226\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.40101i | − | 0.433645i | −0.976211 | − | 0.216822i | \(-0.930431\pi\) | ||
0.976211 | − | 0.216822i | \(-0.0695692\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.9347i | 1.34711i | 0.739135 | + | 0.673557i | \(0.235235\pi\) | ||||
−0.739135 | + | 0.673557i | \(0.764765\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.91608 | + | 3.31875i | 0.183527 | + | 0.317879i | 0.943079 | − | 0.332568i | \(-0.107915\pi\) |
−0.759552 | + | 0.650447i | \(0.774582\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.58392 | − | 7.93958i | −0.435086 | − | 0.753592i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.70655i | − | 0.160539i | −0.996773 | − | 0.0802693i | \(-0.974422\pi\) | ||
0.996773 | − | 0.0802693i | \(-0.0255780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.11682 | − | 1.79949i | 0.288150 | − | 0.166363i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.2367 | + | 17.7305i | 0.938396 | + | 1.62535i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.87439 | 0.897672 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23.8187 | − | 13.7518i | −2.14766 | − | 1.23995i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.0574 | + | 7.53871i | 1.15866 | + | 0.668952i | 0.950982 | − | 0.309245i | \(-0.100076\pi\) |
0.207677 | + | 0.978197i | \(0.433410\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.5211 | + | 25.1513i | −1.27851 | + | 2.21445i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.78442 | + | 11.7510i | 0.592758 | + | 1.02669i | 0.993859 | + | 0.110653i | \(0.0352943\pi\) |
−0.401101 | + | 0.916034i | \(0.631372\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.790014 | − | 15.5362i | 0.0685029 | − | 1.34716i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.08828 | + | 3.51507i | 0.520157 | + | 0.300313i | 0.736999 | − | 0.675894i | \(-0.236242\pi\) |
−0.216842 | + | 0.976207i | \(0.569576\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.09899 | + | 10.5638i | −0.517309 | + | 0.896006i | 0.482488 | + | 0.875902i | \(0.339733\pi\) |
−0.999798 | + | 0.0201039i | \(0.993600\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.3830 | −1.46391 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.95674 | + | 2.28442i | 0.330879 | + | 0.191033i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.7623 | + | 7.36834i | −1.05262 | + | 0.607731i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.76936 | + | 8.26077i | 0.390721 | + | 0.676748i | 0.992545 | − | 0.121880i | \(-0.0388925\pi\) |
−0.601824 | + | 0.798629i | \(0.705559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4131 | 1.66119 | 0.830597 | − | 0.556874i | \(-0.187999\pi\) | ||||
0.830597 | + | 0.556874i | \(0.187999\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.6463i | 1.66915i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3890 | − | 7.15277i | 0.988747 | − | 0.570853i | 0.0838472 | − | 0.996479i | \(-0.473279\pi\) |
0.904899 | + | 0.425626i | \(0.139946\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.73669 | 0.692864 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.99097 | − | 17.3049i | 0.787399 | − | 1.36382i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.53871i | 0.198847i | 0.995045 | + | 0.0994236i | \(0.0316999\pi\) | ||||
−0.995045 | + | 0.0994236i | \(0.968300\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.7510 | − | 6.78442i | −0.909317 | − | 0.524995i | −0.0291058 | − | 0.999576i | \(-0.509266\pi\) |
−0.880211 | + | 0.474582i | \(0.842599\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | − | 10.3923i | −0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.52364 | − | 13.1700i | 0.651819 | − | 1.00714i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.05324 | − | 1.18544i | 0.156105 | − | 0.0901271i | −0.419913 | − | 0.907564i | \(-0.637939\pi\) |
0.576017 | + | 0.817437i | \(0.304606\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.0541 | − | 8.69148i | −1.13153 | − | 0.653292i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.8744 | −1.33599 | −0.667997 | − | 0.744164i | \(-0.732848\pi\) | ||||
−0.667997 | + | 0.744164i | \(0.732848\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.2065 | + | 22.8744i | −0.981635 | + | 1.70024i | −0.325607 | + | 0.945505i | \(0.605569\pi\) |
−0.656028 | + | 0.754737i | \(0.727765\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.9045i | 1.54531i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.6986 | + | 13.1050i | −1.65988 | + | 0.958335i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.49143 | −0.399443 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.526625 | 0.0381052 | 0.0190526 | − | 0.999818i | \(-0.493935\pi\) | ||||
0.0190526 | + | 0.999818i | \(0.493935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.62521 | + | 2.67037i | −0.332930 | + | 0.192217i | −0.657141 | − | 0.753767i | \(-0.728234\pi\) |
0.324211 | + | 0.945985i | \(0.394901\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.43115i | 0.315706i | 0.987463 | + | 0.157853i | \(0.0504573\pi\) | ||||
−0.987463 | + | 0.157853i | \(0.949543\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.08392 | − | 10.5377i | 0.431278 | − | 0.746995i | −0.565706 | − | 0.824607i | \(-0.691396\pi\) |
0.996984 | + | 0.0776123i | \(0.0247296\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.2754 | −1.14798 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.9143 | − | 12.0749i | −1.46790 | − | 0.847491i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.4510 | − | 10.0753i | 1.21293 | − | 0.700285i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.8895 | + | 1.01138i | 1.37578 | + | 0.0699584i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3357 | + | 17.9019i | 0.711537 | + | 1.23242i | 0.964280 | + | 0.264885i | \(0.0853341\pi\) |
−0.252743 | + | 0.967534i | \(0.581333\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.29174 | + | 1.32314i | 0.157027 | + | 0.0906598i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.4131i | − | 1.11419i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.3593 | + | 28.3352i | −1.10546 | + | 1.91471i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.73669 | −0.385891 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.90454 | − | 2.25429i | 0.261467 | − | 0.150958i | −0.363536 | − | 0.931580i | \(-0.618431\pi\) |
0.625004 | + | 0.780622i | \(0.285097\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.6714i | 1.10652i | 0.833010 | + | 0.553258i | \(0.186616\pi\) | ||||
−0.833010 | + | 0.553258i | \(0.813384\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.31060 | −0.350934 | −0.175467 | − | 0.984485i | \(-0.556144\pi\) | ||||
−0.175467 | + | 0.984485i | \(0.556144\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −20.9432 | − | 36.2747i | −1.37796 | − | 2.38670i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.40052 | + | 1.38594i | −0.157263 | + | 0.0907961i | −0.576566 | − | 0.817050i | \(-0.695608\pi\) |
0.419303 | + | 0.907846i | \(0.362274\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.8171 | + | 6.24526i | 0.702647 | + | 0.405673i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.59899 | 0.556222 | 0.278111 | − | 0.960549i | \(-0.410292\pi\) | ||||
0.278111 | + | 0.960549i | \(0.410292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.83216 | + | 4.90545i | −0.182436 | + | 0.315988i | −0.942709 | − | 0.333615i | \(-0.891731\pi\) |
0.760274 | + | 0.649603i | \(0.225065\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.2240 | + | 11.0990i | 1.23322 | + | 0.712000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.65936 | + | 2.36834i | 0.232840 | + | 0.150694i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0749 | − | 20.9143i | −0.765215 | − | 1.32539i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.5598 | − | 20.0222i | 0.729650 | − | 1.26379i | −0.227382 | − | 0.973806i | \(-0.573017\pi\) |
0.957031 | − | 0.289984i | \(-0.0936501\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.1537 | + | 12.7905i | 1.39279 | + | 0.804130i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.15289 | − | 5.28442i | −0.570942 | − | 0.329633i | 0.186584 | − | 0.982439i | \(-0.440258\pi\) |
−0.757525 | + | 0.652806i | \(0.773592\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.7367 | −0.791419 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.1769 | − | 21.0909i | −0.753729 | − | 1.30550i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.67498 | − | 4.43115i | 0.473259 | − | 0.273236i | −0.244344 | − | 0.969689i | \(-0.578573\pi\) |
0.717603 | + | 0.696452i | \(0.245239\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 31.5337i | − | 1.92983i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.66784 | + | 4.62083i | 0.162661 | + | 0.281737i | 0.935822 | − | 0.352472i | \(-0.114659\pi\) |
−0.773161 | + | 0.634210i | \(0.781326\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.23064 | − | 3.86359i | −0.135502 | − | 0.234696i | 0.790287 | − | 0.612737i | \(-0.209931\pi\) |
−0.925789 | + | 0.378040i | \(0.876598\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 9.16784i | − | 0.554863i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0774i | 1.38659i | 0.720655 | + | 0.693294i | \(0.243841\pi\) | ||||
−0.720655 | + | 0.693294i | \(0.756159\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.27585 | − | 14.3342i | 0.495462 | − | 0.858166i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.01507 | + | 3.49020i | −0.120209 | + | 0.208208i | −0.919850 | − | 0.392270i | \(-0.871690\pi\) |
0.799641 | + | 0.600478i | \(0.205023\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.5735 | − | 15.9196i | 1.63908 | − | 0.946322i | 0.657925 | − | 0.753083i | \(-0.271434\pi\) |
0.981152 | − | 0.193239i | \(-0.0618991\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33.0909 | + | 19.1050i | −1.95329 | + | 1.12773i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.95479 | − | 13.7781i | 0.467929 | − | 0.810477i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.37692 | + | 5.84899i | −0.197958 | + | 0.342874i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 18.6764i | − | 1.09109i | −0.838082 | − | 0.545544i | \(-0.816323\pi\) | ||
0.838082 | − | 0.545544i | \(-0.183677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 7.03014i | − | 0.407930i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.79949 | + | 4.84887i | 0.161899 | + | 0.280417i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.1739 | + | 34.9422i | 1.16280 | + | 2.01403i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.7970i | 1.30965i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.5318 | − | 15.8955i | 1.57132 | − | 0.907204i | 0.575316 | − | 0.817931i | \(-0.304879\pi\) |
0.996007 | − | 0.0892730i | \(-0.0284544\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.65277 | − | 9.79088i | −0.321575 | − | 0.556984i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.37087 | 0.134440 | 0.0672199 | − | 0.997738i | \(-0.478587\pi\) | ||||
0.0672199 | + | 0.997738i | \(0.478587\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5742 | + | 6.10503i | 0.597691 | + | 0.345077i | 0.768132 | − | 0.640291i | \(-0.221186\pi\) |
−0.170442 | + | 0.985368i | \(0.554520\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.6326 | + | 14.2216i | 1.38350 | + | 0.798766i | 0.992572 | − | 0.121655i | \(-0.0388200\pi\) |
0.390930 | + | 0.920420i | \(0.372153\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.4583 | − | 26.7746i | 0.865499 | − | 1.49909i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.8980 | + | 31.0003i | 0.998971 | + | 1.73027i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.2625 | + | 11.3869i | −1.23872 | + | 0.633586i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.52537 | + | 4.92212i | 0.471454 | + | 0.272194i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0749 | + | 20.9143i | −0.665710 | + | 1.15304i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.5930 | −1.79147 | −0.895737 | − | 0.444584i | \(-0.853352\pi\) | ||||
−0.895737 | + | 0.444584i | \(0.853352\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.1234 | − | 6.42212i | −0.609561 | − | 0.351930i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.1016 | + | 5.83216i | −0.550269 | + | 0.317698i | −0.749231 | − | 0.662309i | \(-0.769577\pi\) |
0.198961 | + | 0.980007i | \(0.436243\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.19193 | − | 3.79654i | −0.119049 | − | 0.206200i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.0121 | 1.13787 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 4.50857i | − | 0.243440i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.2602 | + | 15.1613i | −1.40972 | + | 0.813903i | −0.995361 | − | 0.0962092i | \(-0.969328\pi\) |
−0.414361 | + | 0.910113i | \(0.635995\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.44324 | −0.184312 | −0.0921561 | − | 0.995745i | \(-0.529376\pi\) | ||||
−0.0921561 | + | 0.995745i | \(0.529376\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.769355 | − | 1.33256i | 0.0410652 | − | 0.0711269i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6.53871i | − | 0.348020i | −0.984744 | − | 0.174010i | \(-0.944327\pi\) | ||
0.984744 | − | 0.174010i | \(-0.0556726\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 45.5469 | + | 26.2965i | 2.41060 | + | 1.39176i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.2392 | − | 19.4669i | −0.593183 | − | 1.02742i | −0.993801 | − | 0.111178i | \(-0.964538\pi\) |
0.400617 | − | 0.916245i | \(-0.368796\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9020 | + | 1.92731i | 0.994842 | + | 0.101438i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.9674 | − | 12.6829i | 1.15299 | − | 0.665680i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.44256 | + | 4.29696i | 0.388499 | + | 0.224300i | 0.681509 | − | 0.731809i | \(-0.261324\pi\) |
−0.293011 | + | 0.956109i | \(0.594657\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −38.5327 | −2.00593 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.06885 | − | 10.5116i | 0.315079 | − | 0.545733i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.2453i | 1.92849i | 0.265019 | + | 0.964243i | \(0.414622\pi\) | ||||
−0.265019 | + | 0.964243i | \(0.585378\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.86024 | − | 3.38341i | 0.301818 | − | 0.174255i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.1678 | −0.625020 | −0.312510 | − | 0.949914i | \(-0.601170\pi\) | ||||
−0.312510 | + | 0.949914i | \(0.601170\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 38.7316 | 1.98428 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.6977 | + | 12.5272i | −1.10870 | + | 0.640108i | −0.938492 | − | 0.345301i | \(-0.887777\pi\) |
−0.170207 | + | 0.985408i | \(0.554444\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 40.6885i | 2.06831i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.0211 | − | 19.0891i | 0.558793 | − | 0.967857i | −0.438805 | − | 0.898582i | \(-0.644598\pi\) |
0.997598 | − | 0.0692748i | \(-0.0220685\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.1196 | −1.62436 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.1865 | + | 17.4282i | 1.52271 | + | 0.879135i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.3327 | + | 18.0900i | −1.57254 | + | 0.907909i | −0.576689 | + | 0.816964i | \(0.695656\pi\) |
−0.995856 | + | 0.0909453i | \(0.971011\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.1975 | − | 35.5779i | −0.911016 | − | 1.78112i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.9583 | − | 24.1765i | −0.697045 | − | 1.20732i | −0.969487 | − | 0.245144i | \(-0.921165\pi\) |
0.272442 | − | 0.962172i | \(-0.412169\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.98284 | + | 2.29949i | 0.198399 | + | 0.114546i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 16.3055i | − | 0.808235i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.06281 | − | 7.03699i | 0.200893 | − | 0.347957i | −0.747924 | − | 0.663785i | \(-0.768949\pi\) |
0.948816 | + | 0.315828i | \(0.102282\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.0594 | 0.890803 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.9143 | + | 12.0749i | −1.02913 | + | 0.594167i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.3348i | 1.53447i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.87439 | 0.140423 | 0.0702115 | − | 0.997532i | \(-0.477633\pi\) | ||||
0.0702115 | + | 0.997532i | \(0.477633\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.48240 | + | 6.03170i | 0.169722 | + | 0.293967i | 0.938322 | − | 0.345763i | \(-0.112380\pi\) |
−0.768600 | + | 0.639729i | \(0.779046\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.0909 | + | 12.1769i | −1.02548 | + | 0.592059i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.1513 | + | 14.5211i | 1.21716 | + | 0.702726i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.7367 | 0.566653 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.08996 | − | 8.81607i | 0.245175 | − | 0.424655i | −0.717006 | − | 0.697067i | \(-0.754488\pi\) |
0.962181 | + | 0.272412i | \(0.0878213\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.1186 | + | 9.88341i | 0.822666 | + | 0.474967i | 0.851335 | − | 0.524622i | \(-0.175793\pi\) |
−0.0286689 | + | 0.999589i | \(0.509127\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.4887 | + | 13.2603i | 0.980109 | + | 0.634328i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.3266 | + | 33.4747i | 0.922411 | + | 1.59766i | 0.795673 | + | 0.605726i | \(0.207117\pi\) |
0.126737 | + | 0.991936i | \(0.459550\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.3231 | + | 17.8802i | −0.491578 | + | 0.851438i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.27214 | − | 5.35327i | −0.440533 | − | 0.254342i | 0.263291 | − | 0.964717i | \(-0.415192\pi\) |
−0.703824 | + | 0.710375i | \(0.748525\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.2207 | + | 12.2518i | 1.00370 | + | 0.579488i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.0724 | −1.08885 | −0.544426 | − | 0.838809i | \(-0.683253\pi\) | ||||
−0.544426 | + | 0.838809i | \(0.683253\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.4583 | − | 42.3630i | −1.15170 | − | 1.99480i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 45.4128 | − | 26.2191i | 2.13368 | − | 1.23188i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.87439i | 0.321570i | 0.986989 | + | 0.160785i | \(0.0514026\pi\) | ||||
−0.986989 | + | 0.160785i | \(0.948597\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.41355 | + | 7.64450i | 0.206007 | + | 0.356815i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.41355 | + | 2.44834i | 0.0658357 | + | 0.114031i | 0.897064 | − | 0.441900i | \(-0.145695\pi\) |
−0.831229 | + | 0.555931i | \(0.812362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.9347i | − | 1.11234i | −0.831069 | − | 0.556169i | \(-0.812271\pi\) | ||
0.831069 | − | 0.556169i | \(-0.187729\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 33.5508i | − | 1.55255i | −0.630397 | − | 0.776273i | \(-0.717108\pi\) | ||
0.630397 | − | 0.776273i | \(-0.282892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.3055 | + | 19.5818i | −0.522041 | + | 0.904202i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.3744 | − | 31.8254i | 0.846647 | − | 1.46644i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −44.7331 | + | 25.8266i | −2.05683 | + | 1.18751i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.6003 | − | 6.12010i | 0.485356 | − | 0.280220i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.4583 | + | 31.9707i | −0.843382 | + | 1.46078i | 0.0436379 | + | 0.999047i | \(0.486105\pi\) |
−0.887019 | + | 0.461732i | \(0.847228\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.78442 | − | 3.09071i | 0.0813628 | − | 0.140924i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 51.3306i | − | 2.33562i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.8744i | 0.583394i | 0.956511 | + | 0.291697i | \(0.0942199\pi\) | ||||
−0.956511 | + | 0.291697i | \(0.905780\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.26078 | + | 5.64784i | 0.147458 | + | 0.255404i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.3382 | + | 21.3704i | 0.556815 | + | 0.964433i | 0.997760 | + | 0.0668981i | \(0.0213103\pi\) |
−0.440944 | + | 0.897534i | \(0.645356\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.8192i | 1.74833i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.18386 | − | 1.83821i | 0.142816 | − | 0.0824548i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.7603 | + | 27.2977i | 0.705529 | + | 1.22201i | 0.966500 | + | 0.256666i | \(0.0826240\pi\) |
−0.260971 | + | 0.965347i | \(0.584043\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −34.8563 | −1.55727 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.5420 | − | 6.08645i | −0.470046 | − | 0.271381i | 0.246213 | − | 0.969216i | \(-0.420814\pi\) |
−0.716259 | + | 0.697834i | \(0.754147\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.6963 | − | 15.4131i | −1.18562 | − | 0.684520i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.70051 | + | 8.14151i | −0.208346 | + | 0.360866i | −0.951194 | − | 0.308594i | \(-0.900141\pi\) |
0.742847 | + | 0.669461i | \(0.233475\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.7277 | + | 39.3655i | 1.00541 | + | 1.74143i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.340615 | − | 6.69843i | 0.0150385 | − | 0.295743i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.7746 | − | 15.4583i | −1.17754 | − | 0.679856i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.04521 | − | 5.27446i | 0.133670 | − | 0.231523i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.49649 | 0.372238 | 0.186119 | − | 0.982527i | \(-0.440409\pi\) | ||||
0.186119 | + | 0.982527i | \(0.440409\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.4320 | − | 11.2191i | −0.849703 | − | 0.490577i | 0.0108473 | − | 0.999941i | \(-0.496547\pi\) |
−0.860551 | + | 0.509365i | \(0.829880\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.8483 | + | 13.1915i | −0.995288 | + | 0.574630i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.17434 | + | 7.23016i | 0.181493 | + | 0.314355i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.3537 | −1.05686 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.7065i | − | 0.463752i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −39.7650 | + | 22.9583i | −1.71598 | + | 0.990724i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.2101 | −1.12895 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.7603 | − | 23.8336i | 0.591603 | − | 1.02469i | −0.402414 | − | 0.915458i | \(-0.631829\pi\) |
0.994017 | − | 0.109228i | \(-0.0348379\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 67.8513i | 2.91178i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.736308 | − | 0.425107i | −0.0314822 | − | 0.0181763i | 0.484176 | − | 0.874970i | \(-0.339119\pi\) |
−0.515659 | + | 0.856794i | \(0.672453\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.6437 | + | 25.3637i | 0.624980 | + | 1.08250i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.0262 | − | 24.7623i | 0.682738 | − | 1.05491i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.0280 | − | 8.67641i | 0.639055 | − | 0.368958i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.1127 | − | 19.6950i | −1.44540 | − | 0.834504i | −0.447200 | − | 0.894434i | \(-0.647579\pi\) |
−0.998203 | + | 0.0599303i | \(0.980912\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.3055 | −0.478173 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.6649 | + | 58.3092i | −1.42133 | + | 2.46182i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 22.0774i | − | 0.930452i | −0.885192 | − | 0.465226i | \(-0.845973\pi\) | ||
0.885192 | − | 0.465226i | \(-0.154027\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.1536 | − | 12.2130i | 0.888368 | − | 0.512900i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.53365 | 0.315827 | 0.157914 | − | 0.987453i | \(-0.449523\pi\) | ||||
0.157914 | + | 0.987453i | \(0.449523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.2824 | −1.60207 | −0.801035 | − | 0.598618i | \(-0.795717\pi\) | ||||
−0.801035 | + | 0.598618i | \(0.795717\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.17158 | − | 0.676410i | 0.0489433 | − | 0.0282574i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.21006i | 0.133637i | 0.997765 | + | 0.0668183i | \(0.0212848\pi\) | ||||
−0.997765 | + | 0.0668183i | \(0.978715\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.85977 | + | 11.8815i | −0.285082 | + | 0.493777i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.5508 | −1.39192 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.4569 | + | 7.76936i | 0.557329 | + | 0.321774i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.16202 | − | 1.24824i | 0.0892361 | − | 0.0515205i | −0.454718 | − | 0.890636i | \(-0.650260\pi\) |
0.543954 | + | 0.839115i | \(0.316927\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0207 | + | 1.01805i | 0.824937 | + | 0.0419480i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.69148 | + | 9.85793i | 0.234116 | + | 0.405501i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.1766 | − | 7.03014i | −0.500031 | − | 0.288693i | 0.228695 | − | 0.973498i | \(-0.426554\pi\) |
−0.728726 | + | 0.684805i | \(0.759887\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 31.2573i | − | 1.27928i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.6678 | + | 20.2093i | −0.476735 | + | 0.825729i | −0.999645 | − | 0.0266590i | \(-0.991513\pi\) |
0.522910 | + | 0.852388i | \(0.324847\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.6111 | 1.90131 | 0.950653 | − | 0.310257i | \(-0.100415\pi\) | ||||
0.950653 | + | 0.310257i | \(0.100415\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.7471 | + | 11.4010i | −0.804165 | + | 0.464285i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 11.1929i | − | 0.454307i | −0.973859 | − | 0.227153i | \(-0.927058\pi\) | ||
0.973859 | − | 0.227153i | \(-0.0729418\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −62.0372 | −2.51387 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.38341 | − | 5.86024i | −0.136878 | − | 0.237080i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.4092 | − | 16.9794i | 1.18783 | − | 0.685792i | 0.230015 | − | 0.973187i | \(-0.426123\pi\) |
0.957812 | + | 0.287395i | \(0.0927892\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.3290 | + | 8.27287i | 0.576865 | + | 0.333053i | 0.759887 | − | 0.650056i | \(-0.225254\pi\) |
−0.183022 | + | 0.983109i | \(0.558588\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.4312 | −0.861391 | −0.430695 | − | 0.902497i | \(-0.641732\pi\) | ||||
−0.430695 | + | 0.902497i | \(0.641732\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.30761 | − | 7.46100i | 0.172859 | − | 0.299400i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −37.9398 | − | 21.9045i | −1.52002 | − | 0.877586i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 45.5469 | − | 23.2965i | 1.81897 | − | 0.930373i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.2367 | + | 17.7305i | 0.408163 | + | 0.706960i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.5035 | + | 18.1926i | −0.418138 | + | 0.724237i | −0.995752 | − | 0.0920733i | \(-0.970651\pi\) |
0.577614 | + | 0.816310i | \(0.303984\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.9873 | + | 26.5508i | 1.82783 | + | 1.05530i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.96812 | − | 2.86834i | −0.196844 | − | 0.113648i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.70746 | 0.146665 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.9106 | + | 27.5579i | 0.628430 | + | 1.08847i | 0.987867 | + | 0.155303i | \(0.0496353\pi\) |
−0.359437 | + | 0.933169i | \(0.617031\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.69670 | + | 4.44369i | −0.303528 | + | 0.175242i | −0.644027 | − | 0.765003i | \(-0.722737\pi\) |
0.340499 | + | 0.940245i | \(0.389404\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.37593i | − | 0.0540934i | −0.999634 | − | 0.0270467i | \(-0.991390\pi\) | ||
0.999634 | − | 0.0270467i | \(-0.00861029\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.4583 | − | 26.7746i | −0.606792 | − | 1.05099i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.0814 | − | 36.5140i | −0.826245 | − | 1.43110i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 24.7237i | − | 0.967513i | −0.875203 | − | 0.483756i | \(-0.839272\pi\) | ||
0.875203 | − | 0.483756i | \(-0.160728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 45.8392i | 1.78836i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.9020 | + | 36.2033i | −0.814226 | + | 1.41028i | 0.0956561 | + | 0.995414i | \(0.469505\pi\) |
−0.909882 | + | 0.414867i | \(0.863828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.5211 | − | 19.9552i | 0.448119 | − | 0.776165i | −0.550144 | − | 0.835070i | \(-0.685427\pi\) |
0.998264 | + | 0.0589041i | \(0.0187606\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.7623 | + | 7.36834i | −0.495648 | + | 0.286163i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.8114 | − | 18.9437i | 1.27046 | − | 0.733503i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.79092 | − | 10.0302i | 0.223890 | − | 0.387789i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.5900 | + | 32.1988i | −0.717658 | + | 1.24302i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.5156i | 1.13774i | 0.822427 | + | 0.568871i | \(0.192620\pi\) | ||||
−0.822427 | + | 0.568871i | \(0.807380\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 12.5035i | − | 0.480549i | −0.970705 | − | 0.240275i | \(-0.922763\pi\) | ||
0.970705 | − | 0.240275i | \(-0.0772375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.69148 | + | 8.12588i | 0.180042 | + | 0.311843i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.4131 | + | 37.0886i | 0.820552 | + | 1.42124i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.9045i | 0.493778i | 0.969044 | + | 0.246889i | \(0.0794083\pi\) | ||||
−0.969044 | + | 0.246889i | \(0.920592\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.8144 | + | 6.82106i | −0.450748 | + | 0.260240i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.70051 | + | 2.94536i | 0.0647841 | + | 0.112209i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.3779 | 0.889337 | 0.444669 | − | 0.895695i | \(-0.353321\pi\) | ||||
0.444669 | + | 0.895695i | \(0.353321\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −50.8213 | − | 29.3417i | −1.93054 | − | 1.11460i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 53.1914 | + | 30.7101i | 2.01477 | + | 1.16323i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.56028 | + | 6.16658i | −0.134662 | + | 0.233242i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.82314 | + | 10.0860i | 0.219937 | + | 0.380942i | 0.954788 | − | 0.297286i | \(-0.0960816\pi\) |
−0.734852 | + | 0.678228i | \(0.762748\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.790014 | − | 15.5362i | 0.0297959 | − | 0.585958i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.4282 | + | 15.8357i | 1.03154 | + | 0.595562i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.58645 | + | 11.4081i | −0.247359 | + | 0.428439i | −0.962792 | − | 0.270243i | \(-0.912896\pi\) |
0.715433 | + | 0.698681i | \(0.246229\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.4994 | 0.656277 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.2999 | + | 12.8748i | 0.835137 | + | 0.482167i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.1301 | − | 11.0448i | 0.714426 | − | 0.412474i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.43972 | − | 4.22572i | −0.0909863 | − | 0.157593i | 0.816940 | − | 0.576723i | \(-0.195669\pi\) |
−0.907926 | + | 0.419130i | \(0.862335\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.7065 | −0.584942 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.5508i | 0.541150i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.2813 | + | 24.9884i | −1.60521 | + | 0.926770i | −0.614792 | + | 0.788689i | \(0.710760\pi\) |
−0.990421 | + | 0.138081i | \(0.955907\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 36.4905 | 1.35150 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.4282 | − | 56.1672i | 1.19940 | − | 2.07742i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.0493i | − | 1.44232i | −0.692770 | − | 0.721159i | \(-0.743610\pi\) | ||
0.692770 | − | 0.721159i | \(-0.256390\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.0686 | − | 14.4734i | −0.923415 | − | 0.533134i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.4020 | − | 21.4809i | −0.456215 | − | 0.790187i | 0.542542 | − | 0.840028i | \(-0.317462\pi\) |
−0.998757 | + | 0.0498412i | \(0.984128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.1829 | + | 0.568650i | 0.410814 | + | 0.0208899i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.1961 | + | 9.92817i | −0.630863 | + | 0.364229i | −0.781086 | − | 0.624423i | \(-0.785334\pi\) |
0.150223 | + | 0.988652i | \(0.452001\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.3012 | − | 16.9171i | −1.07208 | − | 0.618963i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49.7307 | 1.81712 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.7191 | − | 23.7622i | 0.500617 | − | 0.867094i | −0.499383 | − | 0.866381i | \(-0.666440\pi\) |
1.00000 | 0.000712212i | \(-0.000226704\pi\) | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 59.3909i | − | 2.16432i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0033 | + | 5.77540i | −0.363576 | + | 0.209910i | −0.670648 | − | 0.741776i | \(-0.733984\pi\) |
0.307073 | + | 0.951686i | \(0.400651\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 65.7136 | 2.38525 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.9940 | −1.70353 | −0.851766 | − | 0.523922i | \(-0.824468\pi\) | ||||
−0.851766 | + | 0.523922i | \(0.824468\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.8441 | − | 6.83821i | 0.428786 | − | 0.247560i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.76683i | − | 0.244336i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.43719 | + | 11.1495i | −0.232131 | + | 0.402063i | −0.958435 | − | 0.285311i | \(-0.907903\pi\) |
0.726304 | + | 0.687374i | \(0.241237\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.1498 | −0.977776 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.2748 | + | 14.0151i | 0.873104 | + | 0.504087i | 0.868379 | − | 0.495902i | \(-0.165162\pi\) |
0.00472572 | + | 0.999989i | \(0.498496\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −28.3352 | + | 16.3593i | −1.01652 | + | 0.586887i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.2518 | − | 41.5492i | −0.761423 | − | 1.48865i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.35327 | + | 4.07599i | 0.0842068 | + | 0.145850i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.01722 | − | 5.20609i | −0.322249 | − | 0.186051i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 22.3478i | − | 0.796612i | −0.917253 | − | 0.398306i | \(-0.869598\pi\) | ||
0.917253 | − | 0.398306i | \(-0.130402\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.3830 | − | 19.7159i | 0.405244 | − | 0.701903i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.09042 | −0.216550 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.04745 | + | 4.06885i | −0.250262 | + | 0.144489i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 16.3176i | − | 0.578000i | −0.957329 | − | 0.289000i | \(-0.906677\pi\) | ||
0.957329 | − | 0.289000i | \(-0.0933227\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.8192 | 1.37332 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.0895 | − | 38.2601i | −0.780494 | − | 1.35186i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −50.3958 | + | 29.0960i | −1.77843 | + | 1.02678i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.8702 | + | 6.85327i | 0.417852 | + | 0.241247i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.1859 | 0.604224 | 0.302112 | − | 0.953272i | \(-0.402308\pi\) | ||||
0.302112 | + | 0.953272i | \(0.402308\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.5774 | + | 32.1770i | −0.652342 | + | 1.12989i | 0.330212 | + | 0.943907i | \(0.392880\pi\) |
−0.982553 | + | 0.185982i | \(0.940453\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.92498 | − | 5.73019i | −0.348084 | − | 0.200967i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43.8737 | + | 22.4407i | −1.53495 | + | 0.785101i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.42212 | − | 11.1234i | −0.224407 | − | 0.388685i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.7638 | − | 39.4281i | 0.794464 | − | 1.37605i | −0.128716 | − | 0.991682i | \(-0.541085\pi\) |
0.923179 | − | 0.384370i | \(-0.125581\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.8564 | + | 8.00000i | 0.483004 | + | 0.278862i | 0.721668 | − | 0.692240i | \(-0.243376\pi\) |
−0.238664 | + | 0.971102i | \(0.576709\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.4141 | − | 6.58996i | −0.396909 | − | 0.229155i | 0.288240 | − | 0.957558i | \(-0.406930\pi\) |
−0.685149 | + | 0.728403i | \(0.740263\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.4503 | 1.16178 | 0.580888 | − | 0.813984i | \(-0.302705\pi\) | ||||
0.580888 | + | 0.813984i | \(0.302705\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.6412 | + | 51.3401i | 1.02824 | + | 1.78097i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.5005 | − | 16.4548i | 0.987485 | − | 0.570125i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 7.07651i | − | 0.244600i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.6774 | − | 39.2784i | −0.782911 | − | 1.35604i | −0.930239 | − | 0.366953i | \(-0.880401\pi\) |
0.147329 | − | 0.989088i | \(-0.452932\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.39497 | − | 14.5405i | −0.289482 | − | 0.501397i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.3528i | 0.356570i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 35.2402i | − | 1.21087i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40.8950 | − | 70.8323i | 1.40351 | − | 2.43096i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.99097 | − | 17.3049i | 0.342486 | − | 0.593203i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.64115 | + | 5.56632i | −0.330107 | + | 0.190587i | −0.655888 | − | 0.754858i | \(-0.727706\pi\) |
0.325782 | + | 0.945445i | \(0.394373\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.6021 | − | 7.27585i | 0.430481 | − | 0.248538i | −0.269070 | − | 0.963120i | \(-0.586716\pi\) |
0.699552 | + | 0.714582i | \(0.253383\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.68797 | + | 9.85185i | −0.194071 | + | 0.336141i | −0.946596 | − | 0.322423i | \(-0.895503\pi\) |
0.752525 | + | 0.658564i | \(0.228836\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −49.0780 | + | 85.0055i | −1.67257 | + | 2.89698i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.778912i | 0.0265145i | 0.999912 | + | 0.0132572i | \(0.00422003\pi\) | ||||
−0.999912 | + | 0.0132572i | \(0.995780\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 40.8693i | − | 1.38800i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.1076 | + | 19.2389i | 0.376798 | + | 0.652634i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.16784 | − | 5.48686i | −0.107338 | − | 0.185915i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.46220i | 0.320247i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.86231 | − | 5.69401i | 0.333027 | − | 0.192273i | −0.324157 | − | 0.946003i | \(-0.605081\pi\) |
0.657184 | + | 0.753730i | \(0.271747\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.9884 | − | 41.5492i | −0.809110 | − | 1.40142i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.0171 | 1.17976 | 0.589879 | − | 0.807492i | \(-0.299176\pi\) | ||||
0.589879 | + | 0.807492i | \(0.299176\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.9941 | − | 17.3171i | −1.00938 | − | 0.582767i | −0.0983709 | − | 0.995150i | \(-0.531363\pi\) |
−0.911010 | + | 0.412383i | \(0.864696\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.38093 | + | 5.41608i | 0.314981 | + | 0.181854i | 0.649153 | − | 0.760658i | \(-0.275123\pi\) |
−0.334172 | + | 0.942512i | \(0.608457\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.9045 | − | 46.6000i | 0.902349 | − | 1.56291i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.6352 | + | 27.0809i | 0.523798 | + | 0.907245i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.7623 | − | 16.0262i | −0.828638 | − | 0.536295i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.4560 | + | 7.19148i | 0.415894 | + | 0.240117i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.5603 | − | 26.9512i | 0.518964 | − | 0.898873i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.5105 | −0.649990 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 89.7612 | + | 51.8237i | 2.98707 | + | 1.72458i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.66025 | − | 5.00000i | 0.287559 | − | 0.166022i | −0.349281 | − | 0.937018i | \(-0.613574\pi\) |
0.636841 | + | 0.770996i | \(0.280241\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.9694 | + | 27.6598i | 0.529672 | + | 0.917418i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.8794 | −1.35440 | −0.677198 | − | 0.735801i | \(-0.736806\pi\) | ||||
−0.677198 | + | 0.735801i | \(0.736806\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 42.9518i | − | 1.42150i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 41.9374 | − | 24.2126i | 1.38490 | − | 0.799570i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.1146 | 0.333649 | 0.166825 | − | 0.985987i | \(-0.446649\pi\) | ||||
0.166825 | + | 0.985987i | \(0.446649\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40.8331 | − | 70.7251i | 1.34550 | − | 2.33047i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.03014i | 0.0339074i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.7171 | − | 7.91959i | −0.450530 | − | 0.260114i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.16134 | + | 15.8679i | 0.300574 | + | 0.520609i | 0.976266 | − | 0.216575i | \(-0.0694885\pi\) |
−0.675692 | + | 0.737184i | \(0.736155\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.9734 | − | 1.26989i | −0.818469 | − | 0.0416191i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.27446 | − | 3.04521i | 0.172678 | − | 0.0996956i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.1505 | − | 7.01507i | −0.396938 | − | 0.229172i | 0.288224 | − | 0.957563i | \(-0.406935\pi\) |
−0.685162 | + | 0.728391i | \(0.740269\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.3658 | 1.02358 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.67641 | − | 11.5639i | 0.217645 | − | 0.376972i | −0.736443 | − | 0.676500i | \(-0.763496\pi\) |
0.954087 | + | 0.299528i | \(0.0968292\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 59.9458i | − | 1.95211i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.1182 | − | 13.9247i | 0.783736 | − | 0.452490i | −0.0540164 | − | 0.998540i | \(-0.517202\pi\) |
0.837753 | + | 0.546050i | \(0.183869\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.7367 | −0.413450 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 73.0664 | 2.36934 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.8068 | + | 23.5598i | −1.32186 | + | 0.763178i | −0.984026 | − | 0.178027i | \(-0.943028\pi\) |
−0.337837 | + | 0.941205i | \(0.609695\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 79.4201i | − | 2.56729i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.5448 | − | 21.7282i | 0.405091 | − | 0.701639i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.84931 | −0.317720 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 43.4318 | + | 25.0753i | 1.39957 | + | 0.808042i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.7352 | + | 6.19798i | −0.345221 | + | 0.199313i | −0.662578 | − | 0.748993i | \(-0.730538\pi\) |
0.317357 | + | 0.948306i | \(0.397205\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −34.9015 | + | 53.9269i | −1.12120 | + | 1.73238i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0925 | + | 41.7294i | 0.773165 | + | 1.33916i | 0.935820 | + | 0.352478i | \(0.114661\pi\) |
−0.162655 | + | 0.986683i | \(0.552006\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.7005 | + | 21.7664i | 1.20862 | + | 0.697798i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4.86736i | − | 0.155721i | −0.996964 | − | 0.0778603i | \(-0.975191\pi\) | ||
0.996964 | − | 0.0778603i | \(-0.0248088\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.0422 | − | 48.5706i | 0.896233 | − | 1.55232i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.7919 | 0.440342 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.3085 | − | 11.7251i | 0.647741 | − | 0.373974i | −0.139849 | − | 0.990173i | \(-0.544662\pi\) |
0.787590 | + | 0.616199i | \(0.211328\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 62.0372i | 1.97466i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −63.2996 | −2.01281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.5688 | − | 40.8224i | −0.748689 | − | 1.29677i | −0.948451 | − | 0.316923i | \(-0.897350\pi\) |
0.199762 | − | 0.979844i | \(-0.435983\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −72.5093 | + | 41.8633i | −2.30101 | + | 1.32849i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.1472 | − | 8.74526i | −0.479718 | − | 0.276965i | 0.240581 | − | 0.970629i | \(-0.422662\pi\) |
−0.720299 | + | 0.693664i | \(0.755995\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.49143 | −0.173741 |
(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.s.c.349.5 | 12 | ||
5.2 | odd | 4 | 380.2.i.b.121.1 | ✓ | 6 | ||
5.3 | odd | 4 | 1900.2.i.c.501.3 | 6 | |||
5.4 | even | 2 | inner | 1900.2.s.c.349.2 | 12 | ||
15.2 | even | 4 | 3420.2.t.v.1261.3 | 6 | |||
19.11 | even | 3 | inner | 1900.2.s.c.49.2 | 12 | ||
20.7 | even | 4 | 1520.2.q.i.881.3 | 6 | |||
95.7 | odd | 12 | 7220.2.a.n.1.3 | 3 | |||
95.12 | even | 12 | 7220.2.a.o.1.1 | 3 | |||
95.49 | even | 6 | inner | 1900.2.s.c.49.5 | 12 | ||
95.68 | odd | 12 | 1900.2.i.c.201.3 | 6 | |||
95.87 | odd | 12 | 380.2.i.b.201.1 | yes | 6 | ||
285.182 | even | 12 | 3420.2.t.v.3241.3 | 6 | |||
380.87 | even | 12 | 1520.2.q.i.961.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.b.121.1 | ✓ | 6 | 5.2 | odd | 4 | ||
380.2.i.b.201.1 | yes | 6 | 95.87 | odd | 12 | ||
1520.2.q.i.881.3 | 6 | 20.7 | even | 4 | |||
1520.2.q.i.961.3 | 6 | 380.87 | even | 12 | |||
1900.2.i.c.201.3 | 6 | 95.68 | odd | 12 | |||
1900.2.i.c.501.3 | 6 | 5.3 | odd | 4 | |||
1900.2.s.c.49.2 | 12 | 19.11 | even | 3 | inner | ||
1900.2.s.c.49.5 | 12 | 95.49 | even | 6 | inner | ||
1900.2.s.c.349.2 | 12 | 5.4 | even | 2 | inner | ||
1900.2.s.c.349.5 | 12 | 1.1 | even | 1 | trivial | ||
3420.2.t.v.1261.3 | 6 | 15.2 | even | 4 | |||
3420.2.t.v.3241.3 | 6 | 285.182 | even | 12 | |||
7220.2.a.n.1.3 | 3 | 95.7 | odd | 12 | |||
7220.2.a.o.1.1 | 3 | 95.12 | even | 12 |