Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.q (of order \(3\), 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: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.11337408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 18x^{4} + 81x^{2} + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.2 | ||
Root | \(3.17656i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.961 |
Dual form | 1960.2.q.w.361.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.352860 | + | 0.611171i | 0.203724 | + | 0.352860i | 0.949725 | − | 0.313084i | \(-0.101362\pi\) |
−0.746002 | + | 0.665944i | \(0.768029\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.25098 | − | 2.16676i | 0.416993 | − | 0.722254i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.25098 | + | 3.89881i | 0.678696 | + | 1.17554i | 0.975374 | + | 0.220558i | \(0.0707879\pi\) |
−0.296678 | + | 0.954978i | \(0.595879\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.09052 | −1.41186 | −0.705928 | − | 0.708283i | \(-0.749470\pi\) | ||||
−0.705928 | + | 0.708283i | \(0.749470\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.705720 | 0.182216 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | + | 1.73205i | 0.242536 | + | 0.420084i | 0.961436 | − | 0.275029i | \(-0.0886875\pi\) |
−0.718900 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.54526 | + | 2.67647i | −0.354507 | + | 0.614024i | −0.987033 | − | 0.160515i | \(-0.948685\pi\) |
0.632526 | + | 0.774539i | \(0.282018\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.89812 | + | 5.01969i | −0.604300 | + | 1.04668i | 0.387862 | + | 0.921717i | \(0.373214\pi\) |
−0.992162 | + | 0.124960i | \(0.960120\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.88284 | 0.747253 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.50196 | 1.76447 | 0.882235 | − | 0.470810i | \(-0.156038\pi\) | ||||
0.882235 | + | 0.470810i | \(0.156038\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.70572 | + | 4.68644i | 0.485962 | + | 0.841710i | 0.999870 | − | 0.0161350i | \(-0.00513615\pi\) |
−0.513908 | + | 0.857845i | \(0.671803\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.58856 | + | 2.75147i | −0.276533 | + | 0.478969i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.54526 | + | 6.14057i | −0.582837 | + | 1.00950i | 0.412304 | + | 0.911046i | \(0.364724\pi\) |
−0.995141 | + | 0.0984573i | \(0.968609\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.79624 | − | 3.11118i | −0.287629 | − | 0.498187i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.59248 | 1.02957 | 0.514786 | − | 0.857319i | \(-0.327871\pi\) | ||||
0.514786 | + | 0.857319i | \(0.327871\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.70572 | 0.717616 | 0.358808 | − | 0.933411i | \(-0.383183\pi\) | ||||
0.358808 | + | 0.933411i | \(0.383183\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.25098 | − | 2.16676i | −0.186485 | − | 0.323002i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.04722 | − | 8.74204i | 0.736213 | − | 1.27516i | −0.217977 | − | 0.975954i | \(-0.569946\pi\) |
0.954189 | − | 0.299204i | \(-0.0967210\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.705720 | + | 1.22234i | −0.0988205 | + | 0.171162i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.95670 | − | 8.58526i | −0.680855 | − | 1.17928i | −0.974720 | − | 0.223429i | \(-0.928275\pi\) |
0.293865 | − | 0.955847i | \(-0.405058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.50196 | 0.607044 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.18104 | −0.288886 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | + | 6.92820i | 0.520756 | + | 0.901975i | 0.999709 | + | 0.0241347i | \(0.00768307\pi\) |
−0.478953 | + | 0.877841i | \(0.658984\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.45670 | + | 7.71923i | −0.570622 | + | 0.988346i | 0.425880 | + | 0.904780i | \(0.359964\pi\) |
−0.996502 | + | 0.0835666i | \(0.973369\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.54526 | + | 4.40852i | −0.315701 | + | 0.546810i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.0585795 | + | 0.101463i | 0.00715662 | + | 0.0123956i | 0.869582 | − | 0.493789i | \(-0.164389\pi\) |
−0.862425 | + | 0.506185i | \(0.831055\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.09052 | −0.492441 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.09052 | + | 7.08499i | 0.478759 | + | 0.829235i | 0.999703 | − | 0.0243555i | \(-0.00775336\pi\) |
−0.520944 | + | 0.853591i | \(0.674420\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.352860 | − | 0.611171i | 0.0407447 | − | 0.0705720i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.09052 | − | 12.2811i | 0.797746 | − | 1.38174i | −0.123335 | − | 0.992365i | \(-0.539359\pi\) |
0.921081 | − | 0.389371i | \(-0.127308\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.38284 | − | 4.12720i | −0.264760 | − | 0.458578i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.7057 | 1.17511 | 0.587553 | − | 0.809186i | \(-0.300091\pi\) | ||||
0.587553 | + | 0.809186i | \(0.300091\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.35286 | + | 5.80732i | 0.359464 | + | 0.622610i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.04526 | − | 3.54249i | 0.216797 | − | 0.375504i | −0.737030 | − | 0.675860i | \(-0.763772\pi\) |
0.953827 | + | 0.300356i | \(0.0971056\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.90948 | + | 3.30732i | −0.198004 | + | 0.342953i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.54526 | + | 2.67647i | 0.158540 | + | 0.274600i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.2637 | 1.13205 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.66046 | − | 2.87600i | −0.165222 | − | 0.286173i | 0.771512 | − | 0.636215i | \(-0.219501\pi\) |
−0.936734 | + | 0.350042i | \(0.886167\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.44338 | + | 9.42821i | −0.536352 | + | 0.928989i | 0.462744 | + | 0.886492i | \(0.346865\pi\) |
−0.999097 | + | 0.0424975i | \(0.986469\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.94142 | + | 3.36264i | −0.187684 | + | 0.325079i | −0.944478 | − | 0.328575i | \(-0.893431\pi\) |
0.756794 | + | 0.653654i | \(0.226765\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.13578 | + | 8.89543i | 0.491919 | + | 0.852028i | 0.999957 | − | 0.00930661i | \(-0.00296243\pi\) |
−0.508038 | + | 0.861335i | \(0.669629\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.00392 | −0.474951 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.82288 | 0.265554 | 0.132777 | − | 0.991146i | \(-0.457611\pi\) | ||||
0.132777 | + | 0.991146i | \(0.457611\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.89812 | + | 5.01969i | 0.270251 | + | 0.468089i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.36814 | + | 11.0299i | −0.588735 | + | 1.01972i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.63382 | + | 8.02601i | −0.421256 | + | 0.729638i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.32622 | + | 4.02913i | 0.209748 | + | 0.363295i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.73236 | −0.153722 | −0.0768610 | − | 0.997042i | \(-0.524490\pi\) | ||||
−0.0768610 | + | 0.997042i | \(0.524490\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.66046 | + | 2.87600i | 0.146195 | + | 0.253218i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.36814 | + | 11.0299i | −0.556387 | + | 0.963690i | 0.441407 | + | 0.897307i | \(0.354479\pi\) |
−0.997794 | + | 0.0663835i | \(0.978854\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.94142 | − | 3.36264i | 0.167091 | − | 0.289410i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | − | 3.46410i | −0.170872 | − | 0.295958i | 0.767853 | − | 0.640626i | \(-0.221325\pi\) |
−0.938725 | + | 0.344668i | \(0.887992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.41144 | 0.119717 | 0.0598584 | − | 0.998207i | \(-0.480935\pi\) | ||||
0.0598584 | + | 0.998207i | \(0.480935\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.12384 | 0.599936 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.4587 | − | 19.8470i | −0.958221 | − | 1.65969i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.75098 | − | 8.22894i | 0.394547 | − | 0.683376i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.5472 | + | 20.0004i | −0.945985 | + | 1.63849i | −0.192218 | + | 0.981352i | \(0.561568\pi\) |
−0.753767 | + | 0.657142i | \(0.771765\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.203760 | + | 0.352922i | 0.0165817 | + | 0.0287204i | 0.874197 | − | 0.485571i | \(-0.161388\pi\) |
−0.857615 | + | 0.514291i | \(0.828055\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.00392 | 0.404543 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.41144 | 0.434657 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.04722 | − | 12.2061i | −0.562429 | − | 0.974156i | −0.997284 | − | 0.0736555i | \(-0.976533\pi\) |
0.434854 | − | 0.900501i | \(-0.356800\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.49804 | − | 6.05878i | 0.277413 | − | 0.480493i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.09052 | − | 14.0132i | 0.633698 | − | 1.09760i | −0.353091 | − | 0.935589i | \(-0.614869\pi\) |
0.986789 | − | 0.162009i | \(-0.0517973\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.58856 | + | 2.75147i | 0.123669 | + | 0.214201i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.79624 | −0.603291 | −0.301646 | − | 0.953420i | \(-0.597536\pi\) | ||||
−0.301646 | + | 0.953420i | \(0.597536\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9134 | 0.993338 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.86618 | + | 6.69642i | 0.295654 | + | 0.512088i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.45474 | + | 7.71584i | −0.338688 | + | 0.586624i | −0.984186 | − | 0.177137i | \(-0.943316\pi\) |
0.645499 | + | 0.763762i | \(0.276650\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.82288 | + | 4.88937i | −0.212181 | + | 0.367507i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.839541 | − | 1.45413i | −0.0627502 | − | 0.108687i | 0.832944 | − | 0.553358i | \(-0.186654\pi\) |
−0.895694 | + | 0.444671i | \(0.853320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.5059 | −0.929555 | −0.464777 | − | 0.885428i | \(-0.653866\pi\) | ||||
−0.464777 | + | 0.885428i | \(0.653866\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.29036 | −0.464997 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.54526 | + | 6.14057i | 0.260653 | + | 0.451464i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.50196 | + | 7.79762i | −0.329216 | + | 0.570219i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.29428 | + | 5.70586i | −0.238366 | + | 0.412862i | −0.960245 | − | 0.279157i | \(-0.909945\pi\) |
0.721880 | + | 0.692019i | \(0.243278\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.91340 | − | 15.4385i | −0.641601 | − | 1.11128i | −0.985075 | − | 0.172123i | \(-0.944937\pi\) |
0.343475 | − | 0.939162i | \(-0.388396\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.59248 | −0.257263 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.09052 | 0.362685 | 0.181342 | − | 0.983420i | \(-0.441956\pi\) | ||||
0.181342 | + | 0.983420i | \(0.441956\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.1810 | + | 21.0982i | 0.863491 | + | 1.49561i | 0.868538 | + | 0.495623i | \(0.165060\pi\) |
−0.00504654 | + | 0.999987i | \(0.501606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.0413407 | + | 0.0716041i | −0.00291595 | + | 0.00505057i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.29624 | − | 5.70926i | 0.230219 | − | 0.398752i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.25098 | + | 12.5591i | 0.503978 | + | 0.872915i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.9134 | −0.962410 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.26764 | −0.569168 | −0.284584 | − | 0.958651i | \(-0.591855\pi\) | ||||
−0.284584 | + | 0.958651i | \(0.591855\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.35286 | − | 4.07527i | 0.160464 | − | 0.277931i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.88676 | + | 5.00002i | −0.195069 | + | 0.337870i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.09052 | − | 8.81704i | −0.342425 | − | 0.593098i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8268 | 1.19377 | 0.596885 | − | 0.802327i | \(-0.296405\pi\) | ||||
0.596885 | + | 0.802327i | \(0.296405\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.50196 | −0.166797 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.67908 | + | 4.64030i | 0.177817 | + | 0.307988i | 0.941133 | − | 0.338038i | \(-0.109763\pi\) |
−0.763316 | + | 0.646026i | \(0.776430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0905 | − | 20.9414i | 0.798964 | − | 1.38385i | −0.121327 | − | 0.992613i | \(-0.538715\pi\) |
0.920291 | − | 0.391234i | \(-0.127952\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.00000 | + | 15.5885i | −0.589610 | + | 1.02123i | 0.404674 | + | 0.914461i | \(0.367385\pi\) |
−0.994283 | + | 0.106773i | \(0.965948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.04722 | − | 8.74204i | −0.329244 | − | 0.570268i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.0078 | 0.650079 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.7696 | −0.825997 | −0.412998 | − | 0.910732i | \(-0.635519\pi\) | ||||
−0.412998 | + | 0.910732i | \(0.635519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.0472 | − | 19.1343i | −0.711614 | − | 1.23255i | −0.964251 | − | 0.264990i | \(-0.914631\pi\) |
0.252637 | − | 0.967561i | \(-0.418702\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.50588 | − | 13.0006i | 0.481502 | − | 0.833987i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.86618 | − | 13.6246i | 0.500513 | − | 0.866914i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.77762 | + | 6.54303i | 0.239397 | + | 0.414647i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5059 | 0.852484 | 0.426242 | − | 0.904609i | \(-0.359837\pi\) | ||||
0.426242 | + | 0.904609i | \(0.359837\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.0944 | −1.64054 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.705720 | + | 1.22234i | 0.0441939 | + | 0.0765460i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.18104 | + | 14.1700i | −0.510319 | + | 0.883899i | 0.489609 | + | 0.871942i | \(0.337139\pi\) |
−0.999929 | + | 0.0119570i | \(0.996194\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.8868 | − | 20.5885i | 0.735772 | − | 1.27439i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.55662 | − | 7.89230i | −0.280973 | − | 0.486660i | 0.690651 | − | 0.723188i | \(-0.257324\pi\) |
−0.971625 | + | 0.236528i | \(0.923991\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.91340 | −0.608975 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.88676 | 0.176667 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.45670 | + | 7.71923i | 0.271730 | + | 0.470650i | 0.969305 | − | 0.245862i | \(-0.0790710\pi\) |
−0.697575 | + | 0.716512i | \(0.745738\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.18104 | − | 14.1700i | 0.496963 | − | 0.860765i | −0.503031 | − | 0.864268i | \(-0.667782\pi\) |
0.999994 | + | 0.00350346i | \(0.00111519\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.25098 | − | 3.89881i | 0.135739 | − | 0.235107i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.58856 | − | 9.67967i | −0.335784 | − | 0.581595i | 0.647851 | − | 0.761767i | \(-0.275668\pi\) |
−0.983635 | + | 0.180172i | \(0.942335\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.5392 | 0.810571 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.2755 | −1.68677 | −0.843387 | − | 0.537307i | \(-0.819442\pi\) | ||||
−0.843387 | + | 0.537307i | \(0.819442\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.41144 | − | 11.1049i | −0.381121 | − | 0.660120i | 0.610102 | − | 0.792323i | \(-0.291128\pi\) |
−0.991223 | + | 0.132203i | \(0.957795\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.09052 | + | 1.88884i | −0.0645969 | + | 0.111885i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.705720 | + | 1.22234i | 0.0413700 | + | 0.0716550i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.90948 | −0.520497 | −0.260249 | − | 0.965542i | \(-0.583805\pi\) | ||||
−0.260249 | + | 0.965542i | \(0.583805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.74020 | + | 15.1385i | 0.507158 | + | 0.878423i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.7529 | − | 25.5528i | 0.853185 | − | 1.47776i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.17182 | − | 2.02965i | 0.0673192 | − | 0.116600i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.45670 | + | 7.71923i | 0.255190 | + | 0.442002i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.12108 | 0.520567 | 0.260284 | − | 0.965532i | \(-0.416184\pi\) | ||||
0.260284 | + | 0.965532i | \(0.416184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.68300 | −0.437071 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.58856 | − | 11.4117i | −0.373603 | − | 0.647099i | 0.616514 | − | 0.787344i | \(-0.288544\pi\) |
−0.990117 | + | 0.140245i | \(0.955211\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.76960 | + | 15.1894i | −0.495687 | + | 0.858555i | −0.999988 | − | 0.00497286i | \(-0.998417\pi\) |
0.504300 | + | 0.863528i | \(0.331750\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.59248 | − | 11.4185i | 0.370271 | − | 0.641327i | −0.619336 | − | 0.785126i | \(-0.712598\pi\) |
0.989607 | + | 0.143798i | \(0.0459316\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.3887 | + | 37.0464i | 1.19754 | + | 2.07420i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.74020 | −0.152943 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.18104 | −0.343922 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.54526 | + | 4.40852i | 0.141186 | + | 0.244541i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.62442 | + | 6.27768i | −0.200431 | + | 0.347157i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.25098 | + | 7.36291i | −0.233655 | + | 0.404702i | −0.958881 | − | 0.283809i | \(-0.908402\pi\) |
0.725226 | + | 0.688511i | \(0.241735\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.87010 | + | 15.3635i | 0.486078 | + | 0.841913i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.117159 | 0.00640108 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.1889 | 1.53555 | 0.767773 | − | 0.640722i | \(-0.221365\pi\) | ||||
0.767773 | + | 0.640722i | \(0.221365\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.996080 | + | 1.72526i | 0.0540997 | + | 0.0937034i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.1810 | + | 21.0982i | −0.659640 | + | 1.14253i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.04526 | + | 3.54249i | −0.110113 | + | 0.190722i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.35286 | − | 2.34322i | −0.0726253 | − | 0.125791i | 0.827426 | − | 0.561575i | \(-0.189804\pi\) |
−0.900051 | + | 0.435784i | \(0.856471\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6830 | 0.732434 | 0.366217 | − | 0.930529i | \(-0.380653\pi\) | ||||
0.366217 | + | 0.930529i | \(0.380653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.7657 | −1.05501 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.1810 | − | 17.6341i | −0.541882 | − | 0.938567i | −0.998796 | − | 0.0490565i | \(-0.984379\pi\) |
0.456914 | − | 0.889511i | \(-0.348955\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.20768 | − | 15.9482i | 0.485963 | − | 0.841712i | −0.513907 | − | 0.857846i | \(-0.671802\pi\) |
0.999870 | + | 0.0161337i | \(0.00513574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.72434 | + | 8.18280i | 0.248650 | + | 0.430674i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.54036 | −0.343280 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.18104 | 0.428215 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.8115 | − | 22.1902i | −0.668756 | − | 1.15832i | −0.978252 | − | 0.207419i | \(-0.933494\pi\) |
0.309496 | − | 0.950901i | \(-0.399840\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.24706 | − | 14.2843i | 0.429325 | − | 0.743612i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0944 | + | 24.4123i | −0.729782 | + | 1.26402i | 0.227193 | + | 0.973850i | \(0.427045\pi\) |
−0.956975 | + | 0.290170i | \(0.906288\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.352860 | − | 0.611171i | −0.0182216 | − | 0.0315607i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −48.3699 | −2.49118 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.7402 | 1.11672 | 0.558359 | − | 0.829599i | \(-0.311431\pi\) | ||||
0.558359 | + | 0.829599i | \(0.311431\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.611280 | − | 1.05877i | −0.0313168 | − | 0.0542423i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.1058 | + | 17.5038i | −0.516382 | + | 0.894400i | 0.483437 | + | 0.875379i | \(0.339388\pi\) |
−0.999819 | + | 0.0190210i | \(0.993945\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.88676 | − | 10.1962i | 0.299241 | − | 0.518300i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.91340 | − | 11.9744i | −0.350523 | − | 0.607124i | 0.635818 | − | 0.771839i | \(-0.280663\pi\) |
−0.986341 | + | 0.164715i | \(0.947330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.5925 | −0.586257 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.98824 | −0.453397 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.09052 | − | 12.2811i | −0.356763 | − | 0.617931i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.1850 | − | 31.4973i | 0.912677 | − | 1.58080i | 0.102410 | − | 0.994742i | \(-0.467345\pi\) |
0.810267 | − | 0.586061i | \(-0.199322\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.40948 | − | 5.90539i | 0.170261 | − | 0.294901i | −0.768250 | − | 0.640150i | \(-0.778872\pi\) |
0.938511 | + | 0.345249i | \(0.112205\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.7735 | − | 23.8564i | −0.686108 | − | 1.18837i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.76568 | −0.236809 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.9212 | −1.58228 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.93202 | − | 15.4707i | −0.441660 | − | 0.764978i | 0.556153 | − | 0.831080i | \(-0.312277\pi\) |
−0.997813 | + | 0.0661025i | \(0.978944\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.41144 | − | 2.44468i | 0.0696212 | − | 0.120587i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.35286 | − | 9.27143i | 0.262762 | − | 0.455116i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.498040 | + | 0.862631i | 0.0243891 | + | 0.0422432i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.4487 | −0.901277 | −0.450639 | − | 0.892706i | \(-0.648804\pi\) | ||||
−0.450639 | + | 0.892706i | \(0.648804\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.7324 | −0.523063 | −0.261532 | − | 0.965195i | \(-0.584228\pi\) | ||||
−0.261532 | + | 0.965195i | \(0.584228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.6279 | − | 21.8722i | −0.613992 | − | 1.06346i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | − | 1.73205i | 0.0485071 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.08660 | − | 14.0064i | 0.390425 | − | 0.676236i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.29428 | − | 5.70586i | −0.158680 | − | 0.274842i | 0.775713 | − | 0.631086i | \(-0.217390\pi\) |
−0.934393 | + | 0.356244i | \(0.884057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.17712 | −0.248797 | −0.124398 | − | 0.992232i | \(-0.539700\pi\) | ||||
−0.124398 | + | 0.992232i | \(0.539700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.70572 | 0.321515 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.95670 | − | 15.5135i | −0.428457 | − | 0.742109i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.5059 | − | 26.8570i | 0.740055 | − | 1.28181i | −0.212414 | − | 0.977180i | \(-0.568133\pi\) |
0.952470 | − | 0.304634i | \(-0.0985340\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.43946 | + | 4.22527i | −0.115902 | + | 0.200749i | −0.918140 | − | 0.396256i | \(-0.870309\pi\) |
0.802238 | + | 0.597005i | \(0.203643\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.04526 | − | 3.54249i | −0.0969546 | − | 0.167930i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.2982 | −0.770878 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.7696 | 1.31053 | 0.655264 | − | 0.755400i | \(-0.272557\pi\) | ||||
0.655264 | + | 0.755400i | \(0.272557\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.8395 | + | 25.7028i | 0.698767 | + | 1.21030i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.143797 | + | 0.249064i | −0.00675619 | + | 0.0117021i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.5020 | − | 21.6540i | 0.584817 | − | 1.01293i | −0.410081 | − | 0.912049i | \(-0.634500\pi\) |
0.994898 | − | 0.100884i | \(-0.0321670\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.88284 | + | 6.72528i | 0.181236 | + | 0.313909i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.00784 | 0.186664 | 0.0933318 | − | 0.995635i | \(-0.470248\pi\) | ||||
0.0933318 | + | 0.995635i | \(0.470248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.8002 | −1.71025 | −0.855124 | − | 0.518423i | \(-0.826519\pi\) | ||||
−0.855124 | + | 0.518423i | \(0.826519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.90948 | + | 3.30732i | 0.0885500 | + | 0.153373i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.7377 | + | 20.3302i | −0.543154 | + | 0.940771i | 0.455566 | + | 0.890202i | \(0.349437\pi\) |
−0.998721 | + | 0.0505688i | \(0.983897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.97336 | − | 8.61411i | 0.229160 | − | 0.396917i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.5925 | + | 18.3467i | 0.487043 | + | 0.843583i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.09052 | 0.141803 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.8029 | −1.13565 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.8868 | − | 32.7128i | −0.862958 | − | 1.49469i | −0.869060 | − | 0.494706i | \(-0.835276\pi\) |
0.00610232 | − | 0.999981i | \(-0.498058\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0472 | − | 31.2587i | 0.822882 | − | 1.42527i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.00000 | − | 1.73205i | 0.0454077 | − | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.08660 | + | 5.34615i | 0.139867 | + | 0.242257i | 0.927446 | − | 0.373957i | \(-0.121999\pi\) |
−0.787579 | + | 0.616214i | \(0.788666\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.4193 | 0.516398 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.7814 | 1.79531 | 0.897654 | − | 0.440701i | \(-0.145270\pi\) | ||||
0.897654 | + | 0.440701i | \(0.145270\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.50196 | + | 16.4579i | 0.427947 | + | 0.741226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.63186 | − | 9.75467i | 0.253133 | − | 0.438440i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.88284 | + | 3.26118i | −0.0842875 | + | 0.145990i | −0.905087 | − | 0.425226i | \(-0.860195\pi\) |
0.820800 | + | 0.571216i | \(0.193528\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.75098 | − | 4.76484i | −0.122905 | − | 0.212877i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.7057 | −0.834047 | −0.417023 | − | 0.908896i | \(-0.636927\pi\) | ||||
−0.417023 | + | 0.908896i | \(0.636927\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.32092 | −0.147779 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.55662 | + | 7.89230i | 0.202367 | + | 0.350509i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.16242 | − | 10.6736i | 0.273144 | − | 0.473100i | −0.696521 | − | 0.717537i | \(-0.745270\pi\) |
0.969665 | + | 0.244437i | \(0.0786030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.00000 | + | 10.3923i | −0.264906 | + | 0.458831i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.44338 | + | 9.42821i | 0.239864 | + | 0.415457i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.4448 | 1.99866 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.28759 | −0.275995 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.7796 | − | 25.5990i | −0.647505 | − | 1.12151i | −0.983717 | − | 0.179725i | \(-0.942479\pi\) |
0.336212 | − | 0.941786i | \(-0.390854\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.5020 | + | 37.2425i | −0.940215 | + | 1.62850i | −0.175155 | + | 0.984541i | \(0.556043\pi\) |
−0.765060 | + | 0.643959i | \(0.777291\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.41144 | + | 9.37289i | −0.235726 | + | 0.408289i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.29820 | − | 9.17675i | −0.230357 | − | 0.398989i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.0157 | 0.868606 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.5592 | −1.45361 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.94142 | + | 3.36264i | 0.0839349 | + | 0.145380i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.592480 | − | 1.02621i | 0.0255674 | − | 0.0442841i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.48334 | − | 4.30127i | 0.106767 | − | 0.184926i | −0.807692 | − | 0.589605i | \(-0.799283\pi\) |
0.914459 | + | 0.404679i | \(0.132617\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.41282 | − | 7.64323i | −0.189372 | − | 0.328003i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.2716 | 0.439985 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.1250 | −0.945997 | −0.472998 | − | 0.881063i | \(-0.656828\pi\) | ||||
−0.472998 | + | 0.881063i | \(0.656828\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.1505 | + | 19.3132i | 0.475891 | + | 0.824267i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.6830 | + | 25.4317i | −0.625517 | + | 1.08343i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.50196 | + | 4.33352i | −0.106202 | + | 0.183948i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.77958 | − | 4.81437i | −0.117775 | − | 0.203991i | 0.801111 | − | 0.598516i | \(-0.204243\pi\) |
−0.918885 | + | 0.394524i | \(0.870909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.9546 | −1.01317 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.35424 | −0.268276 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.74158 | + | 8.21266i | 0.199834 | + | 0.346122i | 0.948474 | − | 0.316854i | \(-0.102626\pi\) |
−0.748641 | + | 0.662976i | \(0.769293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.41144 | − | 2.44468i | 0.0593797 | − | 0.102849i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.1417 | − | 29.6902i | 0.718616 | − | 1.24468i | −0.242933 | − | 0.970043i | \(-0.578109\pi\) |
0.961548 | − | 0.274636i | \(-0.0885573\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.7735 | + | 27.3205i | 0.660101 | + | 1.14333i | 0.980589 | + | 0.196076i | \(0.0628200\pi\) |
−0.320487 | + | 0.947253i | \(0.603847\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.64968 | −0.194243 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.79624 | 0.241720 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.32092 | − | 9.21610i | −0.221513 | − | 0.383671i | 0.733755 | − | 0.679414i | \(-0.237766\pi\) |
−0.955268 | + | 0.295743i | \(0.904433\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.29036 | − | 10.8952i | 0.261418 | − | 0.452790i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.3149 | − | 38.6505i | 0.924187 | − | 1.60074i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.36814 | + | 11.0299i | 0.263290 | + | 0.456032i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.64184 | −0.274138 | −0.137069 | − | 0.990562i | \(-0.543768\pi\) | ||||
−0.137069 | + | 0.990562i | \(0.543768\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.7242 | −0.689107 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.79624 | + | 3.11118i | 0.0738874 | + | 0.127977i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.76960 | − | 11.7253i | 0.277994 | − | 0.481500i | −0.692892 | − | 0.721041i | \(-0.743664\pi\) |
0.970886 | + | 0.239541i | \(0.0769971\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.59640 | + | 14.8894i | −0.351827 | + | 0.609383i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.0905 | − | 22.6734i | −0.534864 | − | 0.926412i | −0.999170 | − | 0.0407369i | \(-0.987029\pi\) |
0.464306 | − | 0.885675i | \(-0.346304\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.0078 | 1.46879 | 0.734395 | − | 0.678722i | \(-0.237466\pi\) | ||||
0.734395 | + | 0.678722i | \(0.237466\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.293127 | 0.0119371 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.63382 | + | 8.02601i | 0.188392 | + | 0.326304i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.8715 | − | 20.5620i | 0.481849 | − | 0.834586i | −0.517934 | − | 0.855420i | \(-0.673299\pi\) |
0.999783 | + | 0.0208341i | \(0.00663219\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.6930 | + | 44.5015i | −1.03943 | + | 1.80034i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.77958 | + | 8.27847i | 0.193045 | + | 0.334364i | 0.946258 | − | 0.323413i | \(-0.104830\pi\) |
−0.753213 | + | 0.657777i | \(0.771497\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.65244 | 0.187605 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.8268 | −0.798197 | −0.399098 | − | 0.916908i | \(-0.630677\pi\) | ||||
−0.399098 | + | 0.916908i | \(0.630677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.5758 | + | 23.5140i | 0.545658 | + | 0.945108i | 0.998565 | + | 0.0535500i | \(0.0170536\pi\) |
−0.452907 | + | 0.891558i | \(0.649613\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.2529 | + | 19.4907i | −0.451565 | + | 0.782133i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.90948 | − | 8.50347i | −0.196066 | − | 0.339596i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.1810 | −0.565435 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −49.7735 | −1.98145 | −0.990726 | − | 0.135873i | \(-0.956616\pi\) | ||||
−0.990726 | + | 0.135873i | \(0.956616\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.91732 | − | 5.05294i | −0.115953 | − | 0.200836i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.866179 | + | 1.50027i | −0.0343733 | + | 0.0595362i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.1152 | − | 17.5200i | −0.399526 | − | 0.692000i | 0.594141 | − | 0.804361i | \(-0.297492\pi\) |
−0.993667 | + | 0.112361i | \(0.964159\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.1850 | 0.993198 | 0.496599 | − | 0.867980i | \(-0.334582\pi\) | ||||
0.496599 | + | 0.867980i | \(0.334582\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.32092 | 0.130761 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.78488 | + | 16.9479i | 0.384683 | + | 0.666291i | 0.991725 | − | 0.128379i | \(-0.0409773\pi\) |
−0.607042 | + | 0.794670i | \(0.707644\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.0078 | + | 31.1905i | −0.706870 | + | 1.22433i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.13382 | + | 15.8202i | −0.357434 | + | 0.619094i | −0.987531 | − | 0.157422i | \(-0.949682\pi\) |
0.630097 | + | 0.776516i | \(0.283015\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.36814 | + | 11.0299i | 0.248824 | + | 0.430975i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.4686 | 0.798558 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 46.0078 | 1.79221 | 0.896105 | − | 0.443841i | \(-0.146385\pi\) | ||||
0.896105 | + | 0.443841i | \(0.146385\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.2302 | − | 41.9680i | −0.942446 | − | 1.63236i | −0.760785 | − | 0.649004i | \(-0.775186\pi\) |
−0.181661 | − | 0.983361i | \(-0.558147\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.59248 | − | 6.22236i | 0.139520 | − | 0.241656i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.5378 | + | 47.6969i | −1.06627 | + | 1.84683i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.29036 | + | 10.8952i | 0.243199 | + | 0.421234i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40.1278 | −1.54912 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.0118 | −0.578661 | −0.289330 | − | 0.957229i | \(-0.593433\pi\) | ||||
−0.289330 | + | 0.957229i | \(0.593433\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.94142 | − | 3.36264i | −0.0747253 | − | 0.129428i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.95670 | − | 6.85320i | 0.152068 | − | 0.263390i | −0.779919 | − | 0.625880i | \(-0.784740\pi\) |
0.931988 | + | 0.362490i | \(0.118073\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.89068 | + | 3.27475i | −0.0724510 | + | 0.125489i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.8548 | − | 25.7293i | −0.568404 | − | 0.984504i | −0.996724 | − | 0.0808774i | \(-0.974228\pi\) |
0.428320 | − | 0.903627i | \(-0.359106\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.00000 | −0.152832 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.0650 | 0.651072 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.2322 | + | 43.7034i | 0.961270 | + | 1.66497i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.8868 | + | 18.8564i | −0.414152 | + | 0.717332i | −0.995339 | − | 0.0964378i | \(-0.969255\pi\) |
0.581187 | + | 0.813770i | \(0.302588\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.705720 | − | 1.22234i | 0.0267695 | − | 0.0463661i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.59248 | + | 11.4185i | 0.249708 | + | 0.432507i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.7030 | −0.480470 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.0905 | 0.909886 | 0.454943 | − | 0.890520i | \(-0.349660\pi\) | ||||
0.454943 | + | 0.890520i | \(0.349660\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.9567 | − | 18.9776i | −0.413240 | − | 0.715752i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.56192 | − | 6.16943i | 0.134150 | − | 0.232354i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.0186 | − | 20.8169i | 0.451369 | − | 0.781794i | −0.547103 | − | 0.837066i | \(-0.684269\pi\) |
0.998471 | + | 0.0552719i | \(0.0176026\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.7402 | − | 30.7269i | −0.665309 | − | 1.15235i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.3660 | −1.17467 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.9173 | −0.857059 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.50588 | − | 7.80441i | −0.168275 | − | 0.291461i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.117159 | + | 0.202925i | −0.00436929 | + | 0.00756783i | −0.868202 | − | 0.496211i | \(-0.834724\pi\) |
0.863832 | + | 0.503779i | \(0.168057\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.79624 | − | 13.5035i | 0.289945 | − | 0.502200i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.75098 | − | 8.22894i | −0.176447 | − | 0.305615i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.44200 | −0.350184 | −0.175092 | − | 0.984552i | \(-0.556022\pi\) | ||||
−0.175092 | + | 0.984552i | \(0.556022\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.70295 | −0.137146 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.70572 | + | 8.15055i | 0.174047 | + | 0.301459i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.3721 | + | 24.8931i | −0.530844 | + | 0.919449i | 0.468508 | + | 0.883459i | \(0.344792\pi\) |
−0.999352 | + | 0.0359897i | \(0.988542\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.263722 | + | 0.456781i | −0.00971434 | + | 0.0168257i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.0739 | + | 22.6446i | 0.480930 | + | 0.832995i | 0.999761 | − | 0.0218823i | \(-0.00696591\pi\) |
−0.518831 | + | 0.854877i | \(0.673633\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.1026 | 0.407865 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.7547 | 1.20165 | 0.600827 | − | 0.799379i | \(-0.294838\pi\) | ||||
0.600827 | + | 0.799379i | \(0.294838\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.5472 | + | 20.0004i | 0.423057 | + | 0.732757i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.3926 | − | 23.1967i | 0.490011 | − | 0.848724i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0905 | + | 22.6734i | −0.477680 | + | 0.827366i | −0.999673 | − | 0.0255841i | \(-0.991855\pi\) |
0.521993 | + | 0.852950i | \(0.325189\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.76568 | + | 8.25440i | 0.173671 | + | 0.300807i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.407520 | 0.0148312 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.8229 | 0.611438 | 0.305719 | − | 0.952122i | \(-0.401103\pi\) | ||||
0.305719 | + | 0.952122i | \(0.401103\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.20768 | − | 15.9482i | −0.334218 | − | 0.578882i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.95278 | + | 5.11436i | −0.107038 | + | 0.185396i | −0.914569 | − | 0.404430i | \(-0.867470\pi\) |
0.807531 | + | 0.589825i | \(0.200803\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.50196 | − | 4.33352i | 0.0904585 | − | 0.156679i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.3621 | − | 35.2682i | −0.735232 | − | 1.27346i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.275481 | −0.00993410 | −0.00496705 | − | 0.999988i | \(-0.501581\pi\) | ||||
−0.00496705 | + | 0.999988i | \(0.501581\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.5470 | −0.415857 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.68906 | + | 6.38964i | 0.132686 | + | 0.229819i | 0.924711 | − | 0.380669i | \(-0.124306\pi\) |
−0.792025 | + | 0.610489i | \(0.790973\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.70572 | − | 4.68644i | 0.0971923 | − | 0.168342i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.1871 | + | 17.6446i | −0.364991 | + | 0.632182i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 36.8946 | 1.31851 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.0944 | −0.503052 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.33014 | − | 16.1603i | −0.332584 | − | 0.576052i | 0.650434 | − | 0.759563i | \(-0.274587\pi\) |
−0.983018 | + | 0.183511i | \(0.941254\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.21570 | − | 5.56975i | 0.114482 | − | 0.198288i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.6869 | − | 39.2949i | 0.805636 | − | 1.39540i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.49804 | − | 6.05878i | −0.124063 | − | 0.214883i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.81896 | −0.347805 | −0.173903 | − | 0.984763i | \(-0.555638\pi\) | ||||
−0.173903 | + | 0.984763i | \(0.555638\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.1889 | 0.714231 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.11716 | − | 8.86318i | −0.180806 | − | 0.313165i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.4154 | + | 31.8963i | −0.649864 | + | 1.12560i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.14518 | + | 5.44761i | −0.110716 | + | 0.191765i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.0020 | + | 27.7162i | 0.562599 | + | 0.974450i | 0.997269 | + | 0.0738600i | \(0.0235318\pi\) |
−0.434670 | + | 0.900590i | \(0.643135\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.5137 | −1.52797 | −0.763987 | − | 0.645232i | \(-0.776761\pi\) | ||||
−0.763987 | + | 0.645232i | \(0.776761\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.5470 | 0.404972 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.09052 | − | 14.0132i | −0.283399 | − | 0.490861i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.27156 | + | 12.5947i | −0.254400 | + | 0.440633i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.3621 | − | 30.0720i | 0.605941 | − | 1.04952i | −0.385961 | − | 0.922515i | \(-0.626130\pi\) |
0.991902 | − | 0.127005i | \(-0.0405365\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.6511 | + | 20.1802i | 0.406130 | + | 0.703439i | 0.994452 | − | 0.105188i | \(-0.0335445\pi\) |
−0.588322 | + | 0.808627i | \(0.700211\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.17712 | 0.110613 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.2943 | 0.392741 | 0.196370 | − | 0.980530i | \(-0.437085\pi\) | ||||
0.196370 | + | 0.980530i | \(0.437085\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0039 | + | 17.3273i | 0.347450 | + | 0.601802i | 0.985796 | − | 0.167948i | \(-0.0537141\pi\) |
−0.638345 | + | 0.769750i | \(0.720381\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.94396 | − | 6.83113i | 0.136814 | − | 0.236969i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.89812 | + | 6.75174i | −0.134900 | + | 0.233654i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.5059 | + | 18.1967i | 0.363136 | + | 0.628971i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.5846 | −0.468994 | −0.234497 | − | 0.972117i | \(-0.575344\pi\) | ||||
−0.234497 | + | 0.972117i | \(0.575344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61.2872 | 2.11335 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.97728 | − | 17.2812i | −0.343636 | − | 0.595195i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.45670 | − | 11.1833i | 0.222117 | − | 0.384718i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.52468 | − | 7.83697i | 0.155287 | − | 0.268964i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.5492 | − | 35.5922i | −0.704417 | − | 1.22009i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6336 | 1.01464 | 0.507318 | − | 0.861759i | \(-0.330637\pi\) | ||||
0.507318 | + | 0.861759i | \(0.330637\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.73236 | 0.264441 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.41536 | − | 16.3079i | −0.321623 | − | 0.557067i | 0.659200 | − | 0.751967i | \(-0.270895\pi\) |
−0.980823 | + | 0.194901i | \(0.937562\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000 | − | 6.92820i | 0.136478 | − | 0.236387i | −0.789683 | − | 0.613515i | \(-0.789755\pi\) |
0.926161 | + | 0.377128i | \(0.123088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.92868 | + | 17.1970i | −0.337976 | + | 0.585392i | −0.984052 | − | 0.177881i | \(-0.943076\pi\) |
0.646076 | + | 0.763273i | \(0.276409\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.45474 | + | 7.71584i | 0.151466 | + | 0.262346i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.17436 | 0.311577 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 63.8425 | 2.16571 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.298200 | − | 0.516497i | −0.0101041 | − | 0.0175008i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.50196 | − | 4.33352i | 0.0846785 | − | 0.146667i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.77566 | − | 11.7358i | 0.228798 | − | 0.396289i | −0.728654 | − | 0.684882i | \(-0.759854\pi\) |
0.957452 | + | 0.288592i | \(0.0931872\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.14380 | − | 5.44522i | −0.106038 | − | 0.183663i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.5964 | 1.60356 | 0.801782 | − | 0.597617i | \(-0.203886\pi\) | ||||
0.801782 | + | 0.597617i | \(0.203886\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.6497 | 1.23336 | 0.616680 | − | 0.787214i | \(-0.288477\pi\) | ||||
0.616680 | + | 0.787214i | \(0.288477\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.82288 | + | 4.88937i | 0.0948900 | + | 0.164354i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.0625 | − | 39.9454i | 0.774363 | − | 1.34124i | −0.160789 | − | 0.986989i | \(-0.551404\pi\) |
0.935152 | − | 0.354247i | \(-0.115263\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.7275 | − | 18.5805i | 0.359383 | − | 0.622470i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.5985 | + | 27.0175i | 0.521985 | + | 0.904105i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.67908 | −0.0561255 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.8229 | 0.695256 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.7096 | + | 44.5304i | 0.857464 | + | 1.48517i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.91340 | − | 17.1705i | 0.330263 | − | 0.572033i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.25294 | + | 10.8304i | −0.207855 | + | 0.360015i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.53390 | + | 4.38884i | 0.0841368 | + | 0.145729i | 0.905023 | − | 0.425363i | \(-0.139853\pi\) |
−0.820886 | + | 0.571092i | \(0.806520\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.30881 | −0.275586 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.41536 | −0.0800244 | −0.0400122 | − | 0.999199i | \(-0.512740\pi\) | ||||
−0.0400122 | + | 0.999199i | \(0.512740\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0984 | + | 41.7396i | 0.797539 | + | 1.38138i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.14518 | + | 5.44761i | −0.103976 | + | 0.180093i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.2755 | + | 31.6541i | −0.602852 | + | 1.04417i | 0.389534 | + | 0.921012i | \(0.372636\pi\) |
−0.992387 | + | 0.123159i | \(0.960697\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.21846 | + | 5.57454i | 0.106052 | + | 0.183687i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.09052 | 0.233135 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.6191 | + | 23.5890i | 0.447311 | + | 0.774765i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.11520 | + | 14.0559i | −0.266251 | + | 0.461160i | −0.967891 | − | 0.251372i | \(-0.919118\pi\) |
0.701640 | + | 0.712532i | \(0.252452\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.64968 | − | 8.05348i | 0.152224 | − | 0.263659i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.50196 | + | 7.79762i | 0.147230 | + | 0.255010i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.1889 | 1.44359 | 0.721794 | − | 0.692108i | \(-0.243318\pi\) | ||||
0.721794 | + | 0.692108i | \(0.243318\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.3778 | −0.403933 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.7363 | + | 20.3278i | 0.382592 | + | 0.662668i | 0.991432 | − | 0.130625i | \(-0.0416983\pi\) |
−0.608840 | + | 0.793293i | \(0.708365\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.1058 | + | 33.0922i | −0.622170 | + | 1.07763i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.0359 | + | 48.5595i | −0.911043 | + | 1.57797i | −0.0984495 | + | 0.995142i | \(0.531388\pi\) |
−0.812594 | + | 0.582831i | \(0.801945\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.8229 | − | 36.0663i | −0.675939 | − | 1.17076i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.30489 | 0.301732 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.7163 | −0.735854 | −0.367927 | − | 0.929855i | \(-0.619932\pi\) | ||||
−0.367927 | + | 0.929855i | \(0.619932\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.29428 | + | 5.70586i | 0.106600 | + | 0.184637i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.0944 | + | 26.1443i | −0.487934 | + | 0.845126i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.858162 | − | 1.48638i | 0.0276827 | − | 0.0479478i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.85736 | + | 8.41319i | 0.156526 | + | 0.271111i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.8268 | −0.573865 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.9400 | 0.351808 | 0.175904 | − | 0.984407i | \(-0.443715\pi\) | ||||
0.175904 | + | 0.984407i | \(0.443715\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.18104 | − | 3.77767i | −0.0700651 | − | 0.121356i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.8701 | − | 22.2917i | 0.413021 | − | 0.715374i | −0.582197 | − | 0.813048i | \(-0.697807\pi\) |
0.995218 | + | 0.0976739i | \(0.0311402\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.79624 | + | 3.11118i | −0.0575257 | + | 0.0996375i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.41144 | − | 14.5690i | −0.269106 | − | 0.466105i | 0.699525 | − | 0.714608i | \(-0.253395\pi\) |
−0.968631 | + | 0.248503i | \(0.920061\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.4154 | 0.588557 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.6990 | 0.820507 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.9926 | − | 38.0922i | −0.701454 | − | 1.21495i | −0.967956 | − | 0.251119i | \(-0.919201\pi\) |
0.266502 | − | 0.963834i | \(-0.414132\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.54526 | − | 4.40852i | 0.0810987 | − | 0.140467i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.6377 | + | 23.6213i | −0.433655 | + | 0.751112i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.1172 | + | 38.3080i | 0.702575 | + | 1.21690i | 0.967560 | + | 0.252643i | \(0.0812997\pi\) |
−0.264985 | + | 0.964253i | \(0.585367\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.00000 | −0.190404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.3621 | 0.772330 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.0984 | + | 29.6152i | 0.541510 | + | 0.937924i | 0.998818 | + | 0.0486148i | \(0.0154807\pi\) |
−0.457307 | + | 0.889309i | \(0.651186\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.7657 | + | 23.8429i | −0.435527 | + | 0.754355i |
(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 | 1960.2.q.w.961.2 | 6 | ||
7.2 | even | 3 | 1960.2.a.v.1.2 | 3 | |||
7.3 | odd | 6 | 280.2.q.e.81.2 | ✓ | 6 | ||
7.4 | even | 3 | inner | 1960.2.q.w.361.2 | 6 | ||
7.5 | odd | 6 | 1960.2.a.w.1.2 | 3 | |||
7.6 | odd | 2 | 280.2.q.e.121.2 | yes | 6 | ||
21.17 | even | 6 | 2520.2.bi.q.361.2 | 6 | |||
21.20 | even | 2 | 2520.2.bi.q.1801.2 | 6 | |||
28.3 | even | 6 | 560.2.q.l.81.2 | 6 | |||
28.19 | even | 6 | 3920.2.a.cc.1.2 | 3 | |||
28.23 | odd | 6 | 3920.2.a.cb.1.2 | 3 | |||
28.27 | even | 2 | 560.2.q.l.401.2 | 6 | |||
35.3 | even | 12 | 1400.2.bh.i.249.3 | 12 | |||
35.9 | even | 6 | 9800.2.a.cf.1.2 | 3 | |||
35.13 | even | 4 | 1400.2.bh.i.849.4 | 12 | |||
35.17 | even | 12 | 1400.2.bh.i.249.4 | 12 | |||
35.19 | odd | 6 | 9800.2.a.ce.1.2 | 3 | |||
35.24 | odd | 6 | 1400.2.q.j.1201.2 | 6 | |||
35.27 | even | 4 | 1400.2.bh.i.849.3 | 12 | |||
35.34 | odd | 2 | 1400.2.q.j.401.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.e.81.2 | ✓ | 6 | 7.3 | odd | 6 | ||
280.2.q.e.121.2 | yes | 6 | 7.6 | odd | 2 | ||
560.2.q.l.81.2 | 6 | 28.3 | even | 6 | |||
560.2.q.l.401.2 | 6 | 28.27 | even | 2 | |||
1400.2.q.j.401.2 | 6 | 35.34 | odd | 2 | |||
1400.2.q.j.1201.2 | 6 | 35.24 | odd | 6 | |||
1400.2.bh.i.249.3 | 12 | 35.3 | even | 12 | |||
1400.2.bh.i.249.4 | 12 | 35.17 | even | 12 | |||
1400.2.bh.i.849.3 | 12 | 35.27 | even | 4 | |||
1400.2.bh.i.849.4 | 12 | 35.13 | even | 4 | |||
1960.2.a.v.1.2 | 3 | 7.2 | even | 3 | |||
1960.2.a.w.1.2 | 3 | 7.5 | odd | 6 | |||
1960.2.q.w.361.2 | 6 | 7.4 | even | 3 | inner | ||
1960.2.q.w.961.2 | 6 | 1.1 | even | 1 | trivial | ||
2520.2.bi.q.361.2 | 6 | 21.17 | even | 6 | |||
2520.2.bi.q.1801.2 | 6 | 21.20 | even | 2 | |||
3920.2.a.cb.1.2 | 3 | 28.23 | odd | 6 | |||
3920.2.a.cc.1.2 | 3 | 28.19 | even | 6 | |||
9800.2.a.ce.1.2 | 3 | 35.19 | odd | 6 | |||
9800.2.a.cf.1.2 | 3 | 35.9 | even | 6 |