Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(499,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.499");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.o (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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.499 |
Dual form | 1050.2.o.e.949.1 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.59808 | + | 0.500000i | −0.981981 | + | 0.188982i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | 2.50000 | + | 0.866025i | 0.668153 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.59808 | + | 1.50000i | −0.630126 | + | 0.363803i | −0.780801 | − | 0.624780i | \(-0.785189\pi\) |
0.150675 | + | 0.988583i | \(0.451855\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | 1.00000 | − | 1.73205i | 0.229416 | − | 0.397360i | −0.728219 | − | 0.685344i | \(-0.759652\pi\) |
0.957635 | + | 0.287984i | \(0.0929851\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | + | 1.73205i | −0.436436 | + | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.59808 | − | 1.50000i | −0.541736 | − | 0.312772i | 0.204046 | − | 0.978961i | \(-0.434591\pi\) |
−0.745782 | + | 0.666190i | \(0.767924\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.00000 | + | 3.46410i | −0.392232 | + | 0.679366i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −1.73205 | − | 2.00000i | −0.327327 | − | 0.377964i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | + | 0.866025i | 0.0898027 | + | 0.155543i | 0.907428 | − | 0.420208i | \(-0.138043\pi\) |
−0.817625 | + | 0.575751i | \(0.804710\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.66025 | − | 5.00000i | −1.42374 | − | 0.821995i | −0.427121 | − | 0.904194i | \(-0.640472\pi\) |
−0.996616 | + | 0.0821995i | \(0.973806\pi\) | |||||||
\(38\) | −1.73205 | + | 1.00000i | −0.280976 | + | 0.162221i | ||||
\(39\) | −2.00000 | − | 3.46410i | −0.320256 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.00000 | −1.40556 | −0.702782 | − | 0.711405i | \(-0.748059\pi\) | ||||
−0.702782 | + | 0.711405i | \(0.748059\pi\) | |||||||
\(42\) | 2.59808 | − | 0.500000i | 0.400892 | − | 0.0771517i | ||||
\(43\) | − | 10.0000i | − | 1.52499i | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||
0.646997 | − | 0.762493i | \(-0.276025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.50000 | + | 2.59808i | 0.221163 | + | 0.383065i | ||||
\(47\) | −2.59808 | − | 1.50000i | −0.378968 | − | 0.218797i | 0.298401 | − | 0.954441i | \(-0.403547\pi\) |
−0.677369 | + | 0.735643i | \(0.736880\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 6.50000 | − | 2.59808i | 0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50000 | + | 2.59808i | −0.210042 | + | 0.363803i | ||||
\(52\) | 3.46410 | − | 2.00000i | 0.480384 | − | 0.277350i | ||||
\(53\) | −5.19615 | + | 3.00000i | −0.713746 | + | 0.412082i | −0.812447 | − | 0.583036i | \(-0.801865\pi\) |
0.0987002 | + | 0.995117i | \(0.468532\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.500000 | + | 2.59808i | 0.0668153 | + | 0.347183i | ||||
\(57\) | − | 2.00000i | − | 0.264906i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00000 | − | 5.19615i | −0.390567 | − | 0.676481i | 0.601958 | − | 0.798528i | \(-0.294388\pi\) |
−0.992524 | + | 0.122047i | \(0.961054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | − | 1.00000i | − | 0.127000i | ||||||
\(63\) | −0.866025 | + | 2.50000i | −0.109109 | + | 0.314970i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.46410 | − | 2.00000i | 0.423207 | − | 0.244339i | −0.273241 | − | 0.961946i | \(-0.588096\pi\) |
0.696449 | + | 0.717607i | \(0.254762\pi\) | |||||||
\(68\) | −2.59808 | − | 1.50000i | −0.315063 | − | 0.181902i | ||||
\(69\) | −3.00000 | −0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 12.1244 | − | 7.00000i | 1.41905 | − | 0.819288i | 0.422833 | − | 0.906208i | \(-0.361036\pi\) |
0.996215 | + | 0.0869195i | \(0.0277023\pi\) | |||||||
\(74\) | 5.00000 | + | 8.66025i | 0.581238 | + | 1.00673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.00000i | 0.452911i | ||||||||
\(79\) | 5.50000 | − | 9.52628i | 0.618798 | − | 1.07179i | −0.370907 | − | 0.928670i | \(-0.620953\pi\) |
0.989705 | − | 0.143120i | \(-0.0457135\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 7.79423 | + | 4.50000i | 0.860729 | + | 0.496942i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | −2.50000 | − | 0.866025i | −0.272772 | − | 0.0944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.00000 | + | 8.66025i | −0.539164 | + | 0.933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.50000 | + | 12.9904i | −0.794998 | + | 1.37698i | 0.127842 | + | 0.991795i | \(0.459195\pi\) |
−0.922840 | + | 0.385183i | \(0.874138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 10.3923i | 0.209657 | + | 1.08941i | ||||
\(92\) | − | 3.00000i | − | 0.312772i | ||||||
\(93\) | 0.866025 | + | 0.500000i | 0.0898027 | + | 0.0518476i | ||||
\(94\) | 1.50000 | + | 2.59808i | 0.154713 | + | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 7.00000i | 0.710742i | 0.934725 | + | 0.355371i | \(0.115646\pi\) | ||||
−0.934725 | + | 0.355371i | \(0.884354\pi\) | |||||||
\(98\) | −6.92820 | − | 1.00000i | −0.699854 | − | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | − | 15.5885i | −0.895533 | − | 1.55111i | −0.833143 | − | 0.553058i | \(-0.813461\pi\) |
−0.0623905 | − | 0.998052i | \(-0.519872\pi\) | |||||||
\(102\) | 2.59808 | − | 1.50000i | 0.257248 | − | 0.148522i | ||||
\(103\) | −4.33013 | − | 2.50000i | −0.426660 | − | 0.246332i | 0.271263 | − | 0.962505i | \(-0.412559\pi\) |
−0.697923 | + | 0.716173i | \(0.745892\pi\) | |||||||
\(104\) | −4.00000 | −0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | −15.5885 | − | 9.00000i | −1.50699 | − | 0.870063i | −0.999967 | − | 0.00813215i | \(-0.997411\pi\) |
−0.507026 | − | 0.861931i | \(-0.669255\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0000 | −0.949158 | ||||||||
\(112\) | 0.866025 | − | 2.50000i | 0.0818317 | − | 0.236228i | ||||
\(113\) | 21.0000i | 1.97551i | 0.156001 | + | 0.987757i | \(0.450140\pi\) | ||||
−0.156001 | + | 0.987757i | \(0.549860\pi\) | |||||||
\(114\) | −1.00000 | + | 1.73205i | −0.0936586 | + | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.46410 | − | 2.00000i | −0.320256 | − | 0.184900i | ||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | 6.00000 | − | 5.19615i | 0.550019 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | 6.92820 | − | 4.00000i | 0.627250 | − | 0.362143i | ||||
\(123\) | −7.79423 | + | 4.50000i | −0.702782 | + | 0.405751i | ||||
\(124\) | −0.500000 | + | 0.866025i | −0.0449013 | + | 0.0777714i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | − | 1.73205i | 0.178174 | − | 0.154303i | ||||
\(127\) | 16.0000i | 1.41977i | 0.704317 | + | 0.709885i | \(0.251253\pi\) | ||||
−0.704317 | + | 0.709885i | \(0.748747\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −5.00000 | − | 8.66025i | −0.440225 | − | 0.762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | − | 10.3923i | 0.524222 | − | 0.907980i | −0.475380 | − | 0.879781i | \(-0.657689\pi\) |
0.999602 | − | 0.0281993i | \(-0.00897729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.73205 | + | 5.00000i | −0.150188 | + | 0.433555i | ||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.50000 | + | 2.59808i | 0.128624 | + | 0.222783i | ||||
\(137\) | 7.79423 | − | 4.50000i | 0.665906 | − | 0.384461i | −0.128618 | − | 0.991694i | \(-0.541054\pi\) |
0.794524 | + | 0.607233i | \(0.207721\pi\) | |||||||
\(138\) | 2.59808 | + | 1.50000i | 0.221163 | + | 0.127688i | ||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | −2.59808 | − | 1.50000i | −0.218026 | − | 0.125877i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.0000 | −1.15865 | ||||||||
\(147\) | 4.33013 | − | 5.50000i | 0.357143 | − | 0.453632i | ||||
\(148\) | − | 10.0000i | − | 0.821995i | ||||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | − | 6.92820i | −0.325515 | − | 0.563809i | 0.656101 | − | 0.754673i | \(-0.272204\pi\) |
−0.981617 | + | 0.190864i | \(0.938871\pi\) | |||||||
\(152\) | −1.73205 | − | 1.00000i | −0.140488 | − | 0.0811107i | ||||
\(153\) | 3.00000i | 0.242536i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | − | 3.46410i | 0.160128 | − | 0.277350i | ||||
\(157\) | −6.92820 | + | 4.00000i | −0.552931 | + | 0.319235i | −0.750303 | − | 0.661094i | \(-0.770093\pi\) |
0.197372 | + | 0.980329i | \(0.436759\pi\) | |||||||
\(158\) | −9.52628 | + | 5.50000i | −0.757870 | + | 0.437557i | ||||
\(159\) | −3.00000 | + | 5.19615i | −0.237915 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.50000 | + | 2.59808i | 0.591083 | + | 0.204757i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | −6.92820 | − | 4.00000i | −0.542659 | − | 0.313304i | 0.203497 | − | 0.979076i | \(-0.434769\pi\) |
−0.746156 | + | 0.665771i | \(0.768103\pi\) | |||||||
\(164\) | −4.50000 | − | 7.79423i | −0.351391 | − | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.0000i | 1.85718i | 0.371113 | + | 0.928588i | \(0.378976\pi\) | ||||
−0.371113 | + | 0.928588i | \(0.621024\pi\) | |||||||
\(168\) | 1.73205 | + | 2.00000i | 0.133631 | + | 0.154303i | ||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | − | 1.73205i | −0.0764719 | − | 0.132453i | ||||
\(172\) | 8.66025 | − | 5.00000i | 0.660338 | − | 0.381246i | ||||
\(173\) | 15.5885 | + | 9.00000i | 1.18517 | + | 0.684257i | 0.957205 | − | 0.289412i | \(-0.0934598\pi\) |
0.227964 | + | 0.973670i | \(0.426793\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.19615 | − | 3.00000i | −0.390567 | − | 0.225494i | ||||
\(178\) | 12.9904 | − | 7.50000i | 0.973670 | − | 0.562149i | ||||
\(179\) | −3.00000 | − | 5.19615i | −0.224231 | − | 0.388379i | 0.731858 | − | 0.681457i | \(-0.238654\pi\) |
−0.956088 | + | 0.293079i | \(0.905320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 3.46410 | − | 10.0000i | 0.256776 | − | 0.741249i | ||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | −1.50000 | + | 2.59808i | −0.110581 | + | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.500000 | − | 0.866025i | −0.0366618 | − | 0.0635001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 3.00000i | − | 0.218797i | ||||||
\(189\) | 0.500000 | + | 2.59808i | 0.0363696 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5000 | − | 18.1865i | 0.759753 | − | 1.31593i | −0.183223 | − | 0.983071i | \(-0.558653\pi\) |
0.942976 | − | 0.332860i | \(-0.108014\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 14.7224 | − | 8.50000i | 1.05974 | − | 0.611843i | 0.134382 | − | 0.990930i | \(-0.457095\pi\) |
0.925361 | + | 0.379086i | \(0.123762\pi\) | |||||||
\(194\) | 3.50000 | − | 6.06218i | 0.251285 | − | 0.435239i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | + | 4.33013i | 0.392857 | + | 0.309295i | ||||
\(197\) | 12.0000i | 0.854965i | 0.904024 | + | 0.427482i | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.50000 | + | 9.52628i | 0.389885 | + | 0.675300i | 0.992434 | − | 0.122782i | \(-0.0391815\pi\) |
−0.602549 | + | 0.798082i | \(0.705848\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | − | 3.46410i | 0.141069 | − | 0.244339i | ||||
\(202\) | 18.0000i | 1.26648i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.00000 | −0.210042 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.50000 | + | 4.33013i | 0.174183 | + | 0.301694i | ||||
\(207\) | −2.59808 | + | 1.50000i | −0.180579 | + | 0.104257i | ||||
\(208\) | 3.46410 | + | 2.00000i | 0.240192 | + | 0.138675i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0000 | 0.963800 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(212\) | −5.19615 | − | 3.00000i | −0.356873 | − | 0.206041i | ||||
\(213\) | 2.59808 | − | 1.50000i | 0.178017 | − | 0.102778i | ||||
\(214\) | 9.00000 | + | 15.5885i | 0.615227 | + | 1.06561i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −1.73205 | − | 2.00000i | −0.117579 | − | 0.135769i | ||||
\(218\) | − | 2.00000i | − | 0.135457i | ||||||
\(219\) | 7.00000 | − | 12.1244i | 0.473016 | − | 0.819288i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | + | 10.3923i | 0.403604 | + | 0.699062i | ||||
\(222\) | 8.66025 | + | 5.00000i | 0.581238 | + | 0.335578i | ||||
\(223\) | − | 19.0000i | − | 1.27233i | −0.771551 | − | 0.636167i | \(-0.780519\pi\) | ||
0.771551 | − | 0.636167i | \(-0.219481\pi\) | |||||||
\(224\) | −2.00000 | + | 1.73205i | −0.133631 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.5000 | − | 18.1865i | 0.698450 | − | 1.20975i | ||||
\(227\) | 5.19615 | − | 3.00000i | 0.344881 | − | 0.199117i | −0.317547 | − | 0.948242i | \(-0.602859\pi\) |
0.662428 | + | 0.749125i | \(0.269526\pi\) | |||||||
\(228\) | 1.73205 | − | 1.00000i | 0.114708 | − | 0.0662266i | ||||
\(229\) | −2.00000 | + | 3.46410i | −0.132164 | + | 0.228914i | −0.924510 | − | 0.381157i | \(-0.875526\pi\) |
0.792347 | + | 0.610071i | \(0.208859\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.9808 | + | 15.0000i | 1.70206 | + | 0.982683i | 0.943676 | + | 0.330870i | \(0.107342\pi\) |
0.758380 | + | 0.651813i | \(0.225991\pi\) | |||||||
\(234\) | 2.00000 | + | 3.46410i | 0.130744 | + | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.00000 | − | 5.19615i | 0.195283 | − | 0.338241i | ||||
\(237\) | − | 11.0000i | − | 0.714527i | ||||||
\(238\) | −7.79423 | + | 1.50000i | −0.505225 | + | 0.0972306i | ||||
\(239\) | −15.0000 | −0.970269 | −0.485135 | − | 0.874439i | \(-0.661229\pi\) | ||||
−0.485135 | + | 0.874439i | \(0.661229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.00000 | − | 12.1244i | −0.450910 | − | 0.780998i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | −9.52628 | + | 5.50000i | −0.612372 | + | 0.353553i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −8.00000 | −0.512148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.00000 | 0.573819 | ||||||||
\(247\) | −6.92820 | − | 4.00000i | −0.440831 | − | 0.254514i | ||||
\(248\) | 0.866025 | − | 0.500000i | 0.0549927 | − | 0.0317500i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | −2.59808 | + | 0.500000i | −0.163663 | + | 0.0314970i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.00000 | − | 13.8564i | 0.501965 | − | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 25.9808 | + | 15.0000i | 1.62064 | + | 0.935674i | 0.986750 | + | 0.162247i | \(0.0518742\pi\) |
0.633885 | + | 0.773427i | \(0.281459\pi\) | |||||||
\(258\) | 10.0000i | 0.622573i | ||||||||
\(259\) | 25.0000 | + | 8.66025i | 1.55342 | + | 0.538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.3923 | + | 6.00000i | −0.642039 | + | 0.370681i | ||||
\(263\) | 7.79423 | − | 4.50000i | 0.480613 | − | 0.277482i | −0.240059 | − | 0.970758i | \(-0.577167\pi\) |
0.720672 | + | 0.693276i | \(0.243833\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.00000 | − | 3.46410i | 0.245256 | − | 0.212398i | ||||
\(267\) | 15.0000i | 0.917985i | ||||||||
\(268\) | 3.46410 | + | 2.00000i | 0.211604 | + | 0.122169i | ||||
\(269\) | −3.00000 | − | 5.19615i | −0.182913 | − | 0.316815i | 0.759958 | − | 0.649972i | \(-0.225219\pi\) |
−0.942871 | + | 0.333157i | \(0.891886\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.50000 | − | 6.06218i | 0.212610 | − | 0.368251i | −0.739921 | − | 0.672694i | \(-0.765137\pi\) |
0.952531 | + | 0.304443i | \(0.0984703\pi\) | |||||||
\(272\) | − | 3.00000i | − | 0.181902i | ||||||
\(273\) | 6.92820 | + | 8.00000i | 0.419314 | + | 0.484182i | ||||
\(274\) | −9.00000 | −0.543710 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.50000 | − | 2.59808i | −0.0902894 | − | 0.156386i | ||||
\(277\) | 24.2487 | − | 14.0000i | 1.45696 | − | 0.841178i | 0.458103 | − | 0.888899i | \(-0.348529\pi\) |
0.998861 | + | 0.0477206i | \(0.0151957\pi\) | |||||||
\(278\) | 1.73205 | + | 1.00000i | 0.103882 | + | 0.0599760i | ||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | 0.536895 | 0.268447 | − | 0.963294i | \(-0.413489\pi\) | ||||
0.268447 | + | 0.963294i | \(0.413489\pi\) | |||||||
\(282\) | 2.59808 | + | 1.50000i | 0.154713 | + | 0.0893237i | ||||
\(283\) | −3.46410 | + | 2.00000i | −0.205919 | + | 0.118888i | −0.599414 | − | 0.800439i | \(-0.704600\pi\) |
0.393494 | + | 0.919327i | \(0.371266\pi\) | |||||||
\(284\) | 1.50000 | + | 2.59808i | 0.0890086 | + | 0.154167i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.3827 | − | 4.50000i | 1.38024 | − | 0.265627i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.50000 | + | 6.06218i | 0.205174 | + | 0.355371i | ||||
\(292\) | 12.1244 | + | 7.00000i | 0.709524 | + | 0.409644i | ||||
\(293\) | − | 24.0000i | − | 1.40209i | −0.713115 | − | 0.701047i | \(-0.752716\pi\) | ||
0.713115 | − | 0.701047i | \(-0.247284\pi\) | |||||||
\(294\) | −6.50000 | + | 2.59808i | −0.379088 | + | 0.151523i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.00000 | + | 8.66025i | −0.290619 | + | 0.503367i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.19615 | − | 3.00000i | 0.301005 | − | 0.173785i | ||||
\(299\) | −6.00000 | + | 10.3923i | −0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.00000 | + | 25.9808i | 0.288195 | + | 1.49751i | ||||
\(302\) | 8.00000i | 0.460348i | ||||||||
\(303\) | −15.5885 | − | 9.00000i | −0.895533 | − | 0.517036i | ||||
\(304\) | 1.00000 | + | 1.73205i | 0.0573539 | + | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.50000 | − | 2.59808i | 0.0857493 | − | 0.148522i | ||||
\(307\) | 28.0000i | 1.59804i | 0.601302 | + | 0.799022i | \(0.294649\pi\) | ||||
−0.601302 | + | 0.799022i | \(0.705351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.00000 | −0.284440 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.50000 | − | 7.79423i | −0.255172 | − | 0.441970i | 0.709771 | − | 0.704433i | \(-0.248799\pi\) |
−0.964942 | + | 0.262463i | \(0.915465\pi\) | |||||||
\(312\) | −3.46410 | + | 2.00000i | −0.196116 | + | 0.113228i | ||||
\(313\) | −4.33013 | − | 2.50000i | −0.244753 | − | 0.141308i | 0.372606 | − | 0.927990i | \(-0.378464\pi\) |
−0.617359 | + | 0.786681i | \(0.711798\pi\) | |||||||
\(314\) | 8.00000 | 0.451466 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.0000 | 0.618798 | ||||||||
\(317\) | −15.5885 | − | 9.00000i | −0.875535 | − | 0.505490i | −0.00635137 | − | 0.999980i | \(-0.502022\pi\) |
−0.869184 | + | 0.494489i | \(0.835355\pi\) | |||||||
\(318\) | 5.19615 | − | 3.00000i | 0.291386 | − | 0.168232i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0000 | −1.00466 | ||||||||
\(322\) | −5.19615 | − | 6.00000i | −0.289570 | − | 0.334367i | ||||
\(323\) | 6.00000i | 0.333849i | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.00000 | + | 6.92820i | 0.221540 | + | 0.383718i | ||||
\(327\) | 1.73205 | + | 1.00000i | 0.0957826 | + | 0.0553001i | ||||
\(328\) | 9.00000i | 0.496942i | ||||||||
\(329\) | 7.50000 | + | 2.59808i | 0.413488 | + | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00000 | − | 8.66025i | 0.274825 | − | 0.476011i | −0.695266 | − | 0.718752i | \(-0.744713\pi\) |
0.970091 | + | 0.242742i | \(0.0780468\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.66025 | + | 5.00000i | −0.474579 | + | 0.273998i | ||||
\(334\) | 12.0000 | − | 20.7846i | 0.656611 | − | 1.13728i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.500000 | − | 2.59808i | −0.0272772 | − | 0.141737i | ||||
\(337\) | − | 11.0000i | − | 0.599208i | −0.954064 | − | 0.299604i | \(-0.903145\pi\) | ||
0.954064 | − | 0.299604i | \(-0.0968546\pi\) | |||||||
\(338\) | 2.59808 | + | 1.50000i | 0.141317 | + | 0.0815892i | ||||
\(339\) | 10.5000 | + | 18.1865i | 0.570282 | + | 0.987757i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.00000i | 0.108148i | ||||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | −10.0000 | −0.539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | − | 15.5885i | −0.483843 | − | 0.838041i | ||||
\(347\) | 31.1769 | − | 18.0000i | 1.67366 | − | 0.966291i | 0.708105 | − | 0.706107i | \(-0.249550\pi\) |
0.965559 | − | 0.260184i | \(-0.0837832\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.9904 | + | 7.50000i | −0.691408 | + | 0.399185i | −0.804139 | − | 0.594441i | \(-0.797373\pi\) |
0.112731 | + | 0.993626i | \(0.464040\pi\) | |||||||
\(354\) | 3.00000 | + | 5.19615i | 0.159448 | + | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.0000 | −0.794998 | ||||||||
\(357\) | 2.59808 | − | 7.50000i | 0.137505 | − | 0.396942i | ||||
\(358\) | 6.00000i | 0.317110i | ||||||||
\(359\) | 6.00000 | − | 10.3923i | 0.316668 | − | 0.548485i | −0.663123 | − | 0.748511i | \(-0.730769\pi\) |
0.979791 | + | 0.200026i | \(0.0641026\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | −6.92820 | − | 4.00000i | −0.364138 | − | 0.210235i | ||||
\(363\) | − | 11.0000i | − | 0.577350i | ||||||
\(364\) | −8.00000 | + | 6.92820i | −0.419314 | + | 0.363137i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.00000 | − | 6.92820i | 0.209083 | − | 0.362143i | ||||
\(367\) | −6.92820 | + | 4.00000i | −0.361649 | + | 0.208798i | −0.669804 | − | 0.742538i | \(-0.733622\pi\) |
0.308155 | + | 0.951336i | \(0.400289\pi\) | |||||||
\(368\) | 2.59808 | − | 1.50000i | 0.135434 | − | 0.0781929i | ||||
\(369\) | −4.50000 | + | 7.79423i | −0.234261 | + | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | − | 10.3923i | 0.623009 | − | 0.539542i | ||||
\(372\) | 1.00000i | 0.0518476i | ||||||||
\(373\) | 3.46410 | + | 2.00000i | 0.179364 | + | 0.103556i | 0.586994 | − | 0.809591i | \(-0.300311\pi\) |
−0.407630 | + | 0.913147i | \(0.633645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.50000 | + | 2.59808i | −0.0773566 | + | 0.133986i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.866025 | − | 2.50000i | 0.0445435 | − | 0.128586i | ||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | + | 13.8564i | 0.409852 | + | 0.709885i | ||||
\(382\) | −18.1865 | + | 10.5000i | −0.930504 | + | 0.537227i | ||||
\(383\) | −18.1865 | − | 10.5000i | −0.929288 | − | 0.536525i | −0.0427020 | − | 0.999088i | \(-0.513597\pi\) |
−0.886586 | + | 0.462563i | \(0.846930\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.0000 | −0.865277 | ||||||||
\(387\) | −8.66025 | − | 5.00000i | −0.440225 | − | 0.254164i | ||||
\(388\) | −6.06218 | + | 3.50000i | −0.307760 | + | 0.177686i | ||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | 0.455150 | ||||||||
\(392\) | −2.59808 | − | 6.50000i | −0.131223 | − | 0.328300i | ||||
\(393\) | − | 12.0000i | − | 0.605320i | ||||||
\(394\) | 6.00000 | − | 10.3923i | 0.302276 | − | 0.523557i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.0526 | − | 11.0000i | −0.956221 | − | 0.552074i | −0.0612128 | − | 0.998125i | \(-0.519497\pi\) |
−0.895008 | + | 0.446051i | \(0.852830\pi\) | |||||||
\(398\) | − | 11.0000i | − | 0.551380i | ||||||
\(399\) | 1.00000 | + | 5.19615i | 0.0500626 | + | 0.260133i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.00000 | + | 15.5885i | −0.449439 | + | 0.778450i | −0.998350 | − | 0.0574304i | \(-0.981709\pi\) |
0.548911 | + | 0.835881i | \(0.315043\pi\) | |||||||
\(402\) | −3.46410 | + | 2.00000i | −0.172774 | + | 0.0997509i | ||||
\(403\) | 3.46410 | − | 2.00000i | 0.172559 | − | 0.0996271i | ||||
\(404\) | 9.00000 | − | 15.5885i | 0.447767 | − | 0.775555i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.59808 | + | 1.50000i | 0.128624 | + | 0.0742611i | ||||
\(409\) | 2.50000 | + | 4.33013i | 0.123617 | + | 0.214111i | 0.921192 | − | 0.389109i | \(-0.127217\pi\) |
−0.797574 | + | 0.603220i | \(0.793884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.50000 | − | 7.79423i | 0.221969 | − | 0.384461i | ||||
\(412\) | − | 5.00000i | − | 0.246332i | ||||||
\(413\) | 10.3923 | + | 12.0000i | 0.511372 | + | 0.590481i | ||||
\(414\) | 3.00000 | 0.147442 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.00000 | − | 3.46410i | −0.0980581 | − | 0.169842i | ||||
\(417\) | −1.73205 | + | 1.00000i | −0.0848189 | + | 0.0489702i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.0000 | −0.879358 | −0.439679 | − | 0.898155i | \(-0.644908\pi\) | ||||
−0.439679 | + | 0.898155i | \(0.644908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.0000 | −1.94948 | −0.974740 | − | 0.223341i | \(-0.928304\pi\) | ||||
−0.974740 | + | 0.223341i | \(0.928304\pi\) | |||||||
\(422\) | −12.1244 | − | 7.00000i | −0.590204 | − | 0.340755i | ||||
\(423\) | −2.59808 | + | 1.50000i | −0.126323 | + | 0.0729325i | ||||
\(424\) | 3.00000 | + | 5.19615i | 0.145693 | + | 0.252347i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.00000 | −0.145350 | ||||||||
\(427\) | 6.92820 | − | 20.0000i | 0.335279 | − | 0.967868i | ||||
\(428\) | − | 18.0000i | − | 0.870063i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.5000 | + | 23.3827i | 0.650272 | + | 1.12630i | 0.983057 | + | 0.183301i | \(0.0586785\pi\) |
−0.332785 | + | 0.943003i | \(0.607988\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 29.0000i | 1.39365i | 0.717241 | + | 0.696826i | \(0.245405\pi\) | ||||
−0.717241 | + | 0.696826i | \(0.754595\pi\) | |||||||
\(434\) | 0.500000 | + | 2.59808i | 0.0240008 | + | 0.124712i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | + | 1.73205i | −0.0478913 | + | 0.0829502i | ||||
\(437\) | −5.19615 | + | 3.00000i | −0.248566 | + | 0.143509i | ||||
\(438\) | −12.1244 | + | 7.00000i | −0.579324 | + | 0.334473i | ||||
\(439\) | 2.50000 | − | 4.33013i | 0.119318 | − | 0.206666i | −0.800179 | − | 0.599761i | \(-0.795262\pi\) |
0.919498 | + | 0.393095i | \(0.128596\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | − | 6.92820i | 0.0476190 | − | 0.329914i | ||||
\(442\) | − | 12.0000i | − | 0.570782i | ||||||
\(443\) | 5.19615 | + | 3.00000i | 0.246877 | + | 0.142534i | 0.618333 | − | 0.785916i | \(-0.287808\pi\) |
−0.371457 | + | 0.928450i | \(0.621142\pi\) | |||||||
\(444\) | −5.00000 | − | 8.66025i | −0.237289 | − | 0.410997i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.50000 | + | 16.4545i | −0.449838 | + | 0.779142i | ||||
\(447\) | 6.00000i | 0.283790i | ||||||||
\(448\) | 2.59808 | − | 0.500000i | 0.122748 | − | 0.0236228i | ||||
\(449\) | 21.0000 | 0.991051 | 0.495526 | − | 0.868593i | \(-0.334975\pi\) | ||||
0.495526 | + | 0.868593i | \(0.334975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −18.1865 | + | 10.5000i | −0.855423 | + | 0.493878i | ||||
\(453\) | −6.92820 | − | 4.00000i | −0.325515 | − | 0.187936i | ||||
\(454\) | −6.00000 | −0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | 1.73205 | + | 1.00000i | 0.0810219 | + | 0.0467780i | 0.539964 | − | 0.841688i | \(-0.318438\pi\) |
−0.458942 | + | 0.888466i | \(0.651771\pi\) | |||||||
\(458\) | 3.46410 | − | 2.00000i | 0.161867 | − | 0.0934539i | ||||
\(459\) | 1.50000 | + | 2.59808i | 0.0700140 | + | 0.121268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0000 | −0.558896 | −0.279448 | − | 0.960161i | \(-0.590151\pi\) | ||||
−0.279448 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.00000i | 0.232370i | 0.993228 | + | 0.116185i | \(0.0370665\pi\) | ||||
−0.993228 | + | 0.116185i | \(0.962933\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.0000 | − | 25.9808i | −0.694862 | − | 1.20354i | ||||
\(467\) | 10.3923 | + | 6.00000i | 0.480899 | + | 0.277647i | 0.720791 | − | 0.693153i | \(-0.243779\pi\) |
−0.239892 | + | 0.970799i | \(0.577112\pi\) | |||||||
\(468\) | − | 4.00000i | − | 0.184900i | ||||||
\(469\) | −8.00000 | + | 6.92820i | −0.369406 | + | 0.319915i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.00000 | + | 6.92820i | −0.184310 | + | 0.319235i | ||||
\(472\) | −5.19615 | + | 3.00000i | −0.239172 | + | 0.138086i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.50000 | + | 9.52628i | −0.252623 | + | 0.437557i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.50000 | + | 2.59808i | 0.343762 | + | 0.119083i | ||||
\(477\) | 6.00000i | 0.274721i | ||||||||
\(478\) | 12.9904 | + | 7.50000i | 0.594166 | + | 0.343042i | ||||
\(479\) | −13.5000 | − | 23.3827i | −0.616831 | − | 1.06838i | −0.990060 | − | 0.140643i | \(-0.955083\pi\) |
0.373230 | − | 0.927739i | \(-0.378250\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | + | 34.6410i | −0.911922 | + | 1.57949i | ||||
\(482\) | 14.0000i | 0.637683i | ||||||||
\(483\) | 7.79423 | − | 1.50000i | 0.354650 | − | 0.0682524i | ||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 26.8468 | − | 15.5000i | 1.21654 | − | 0.702372i | 0.252367 | − | 0.967632i | \(-0.418791\pi\) |
0.964177 | + | 0.265260i | \(0.0854576\pi\) | |||||||
\(488\) | 6.92820 | + | 4.00000i | 0.313625 | + | 0.181071i | ||||
\(489\) | −8.00000 | −0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.00000 | −0.270776 | −0.135388 | − | 0.990793i | \(-0.543228\pi\) | ||||
−0.135388 | + | 0.990793i | \(0.543228\pi\) | |||||||
\(492\) | −7.79423 | − | 4.50000i | −0.351391 | − | 0.202876i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 4.00000 | + | 6.92820i | 0.179969 | + | 0.311715i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | −7.79423 | + | 1.50000i | −0.349619 | + | 0.0672842i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0000 | − | 27.7128i | 0.716258 | − | 1.24060i | −0.246214 | − | 0.969216i | \(-0.579187\pi\) |
0.962472 | − | 0.271380i | \(-0.0874801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | + | 20.7846i | 0.536120 | + | 0.928588i | ||||
\(502\) | −10.3923 | − | 6.00000i | −0.463831 | − | 0.267793i | ||||
\(503\) | − | 36.0000i | − | 1.60516i | −0.596544 | − | 0.802580i | \(-0.703460\pi\) | ||
0.596544 | − | 0.802580i | \(-0.296540\pi\) | |||||||
\(504\) | 2.50000 | + | 0.866025i | 0.111359 | + | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.59808 | + | 1.50000i | −0.115385 | + | 0.0666173i | ||||
\(508\) | −13.8564 | + | 8.00000i | −0.614779 | + | 0.354943i | ||||
\(509\) | −18.0000 | + | 31.1769i | −0.797836 | + | 1.38189i | 0.123187 | + | 0.992384i | \(0.460689\pi\) |
−0.921023 | + | 0.389509i | \(0.872645\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0000 | + | 24.2487i | −1.23865 | + | 1.07270i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −1.73205 | − | 1.00000i | −0.0764719 | − | 0.0441511i | ||||
\(514\) | −15.0000 | − | 25.9808i | −0.661622 | − | 1.14596i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.00000 | − | 8.66025i | 0.220113 | − | 0.381246i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −17.3205 | − | 20.0000i | −0.761019 | − | 0.878750i | ||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.50000 | − | 12.9904i | −0.328581 | − | 0.569119i | 0.653650 | − | 0.756797i | \(-0.273237\pi\) |
−0.982231 | + | 0.187678i | \(0.939904\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.7128 | − | 16.0000i | −1.21180 | − | 0.699631i | −0.248646 | − | 0.968594i | \(-0.579986\pi\) |
−0.963150 | + | 0.268963i | \(0.913319\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.00000 | −0.392419 | ||||||||
\(527\) | −2.59808 | − | 1.50000i | −0.113174 | − | 0.0653410i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | −5.19615 | + | 1.00000i | −0.225282 | + | 0.0433555i | ||||
\(533\) | 36.0000i | 1.55933i | ||||||||
\(534\) | 7.50000 | − | 12.9904i | 0.324557 | − | 0.562149i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.00000 | − | 3.46410i | −0.0863868 | − | 0.149626i | ||||
\(537\) | −5.19615 | − | 3.00000i | −0.224231 | − | 0.129460i | ||||
\(538\) | 6.00000i | 0.258678i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | − | 13.8564i | 0.343947 | − | 0.595733i | −0.641215 | − | 0.767361i | \(-0.721569\pi\) |
0.985162 | + | 0.171628i | \(0.0549027\pi\) | |||||||
\(542\) | −6.06218 | + | 3.50000i | −0.260393 | + | 0.150338i | ||||
\(543\) | 6.92820 | − | 4.00000i | 0.297318 | − | 0.171656i | ||||
\(544\) | −1.50000 | + | 2.59808i | −0.0643120 | + | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.00000 | − | 10.3923i | −0.0855921 | − | 0.444750i | ||||
\(547\) | − | 26.0000i | − | 1.11168i | −0.831289 | − | 0.555840i | \(-0.812397\pi\) | ||
0.831289 | − | 0.555840i | \(-0.187603\pi\) | |||||||
\(548\) | 7.79423 | + | 4.50000i | 0.332953 | + | 0.192230i | ||||
\(549\) | 4.00000 | + | 6.92820i | 0.170716 | + | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 3.00000i | 0.127688i | ||||||||
\(553\) | −9.52628 | + | 27.5000i | −0.405099 | + | 1.16942i | ||||
\(554\) | −28.0000 | −1.18961 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | − | 1.73205i | −0.0424094 | − | 0.0734553i | ||||
\(557\) | −5.19615 | + | 3.00000i | −0.220168 | + | 0.127114i | −0.606028 | − | 0.795443i | \(-0.707238\pi\) |
0.385860 | + | 0.922557i | \(0.373905\pi\) | |||||||
\(558\) | −0.866025 | − | 0.500000i | −0.0366618 | − | 0.0211667i | ||||
\(559\) | −40.0000 | −1.69182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.79423 | − | 4.50000i | −0.328780 | − | 0.189821i | ||||
\(563\) | −25.9808 | + | 15.0000i | −1.09496 | + | 0.632175i | −0.934892 | − | 0.354932i | \(-0.884504\pi\) |
−0.160066 | + | 0.987106i | \(0.551171\pi\) | |||||||
\(564\) | −1.50000 | − | 2.59808i | −0.0631614 | − | 0.109399i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | 1.73205 | + | 2.00000i | 0.0727393 | + | 0.0839921i | ||||
\(568\) | − | 3.00000i | − | 0.125877i | ||||||
\(569\) | 13.5000 | − | 23.3827i | 0.565949 | − | 0.980253i | −0.431011 | − | 0.902347i | \(-0.641843\pi\) |
0.996961 | − | 0.0779066i | \(-0.0248236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | − | 27.7128i | −0.669579 | − | 1.15975i | −0.978022 | − | 0.208502i | \(-0.933141\pi\) |
0.308443 | − | 0.951243i | \(-0.400192\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 21.0000i | − | 0.877288i | ||||||
\(574\) | −22.5000 | − | 7.79423i | −0.939132 | − | 0.325325i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −12.1244 | + | 7.00000i | −0.504744 | + | 0.291414i | −0.730670 | − | 0.682730i | \(-0.760792\pi\) |
0.225927 | + | 0.974144i | \(0.427459\pi\) | |||||||
\(578\) | 6.92820 | − | 4.00000i | 0.288175 | − | 0.166378i | ||||
\(579\) | 8.50000 | − | 14.7224i | 0.353248 | − | 0.611843i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 7.00000i | − | 0.290159i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −7.00000 | − | 12.1244i | −0.289662 | − | 0.501709i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.0000 | + | 20.7846i | −0.495715 | + | 0.858604i | ||||
\(587\) | − | 42.0000i | − | 1.73353i | −0.498721 | − | 0.866763i | \(-0.666197\pi\) | ||
0.498721 | − | 0.866763i | \(-0.333803\pi\) | |||||||
\(588\) | 6.92820 | + | 1.00000i | 0.285714 | + | 0.0412393i | ||||
\(589\) | 2.00000 | 0.0824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000 | + | 10.3923i | 0.246807 | + | 0.427482i | ||||
\(592\) | 8.66025 | − | 5.00000i | 0.355934 | − | 0.205499i | ||||
\(593\) | −18.1865 | − | 10.5000i | −0.746831 | − | 0.431183i | 0.0777165 | − | 0.996976i | \(-0.475237\pi\) |
−0.824548 | + | 0.565792i | \(0.808570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 9.52628 | + | 5.50000i | 0.389885 | + | 0.225100i | ||||
\(598\) | 10.3923 | − | 6.00000i | 0.424973 | − | 0.245358i | ||||
\(599\) | −1.50000 | − | 2.59808i | −0.0612883 | − | 0.106155i | 0.833753 | − | 0.552137i | \(-0.186188\pi\) |
−0.895042 | + | 0.445983i | \(0.852854\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 8.66025 | − | 25.0000i | 0.352966 | − | 1.01892i | ||||
\(603\) | − | 4.00000i | − | 0.162893i | ||||||
\(604\) | 4.00000 | − | 6.92820i | 0.162758 | − | 0.281905i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.00000 | + | 15.5885i | 0.365600 | + | 0.633238i | ||||
\(607\) | −6.06218 | − | 3.50000i | −0.246056 | − | 0.142061i | 0.371901 | − | 0.928272i | \(-0.378706\pi\) |
−0.617957 | + | 0.786212i | \(0.712039\pi\) | |||||||
\(608\) | − | 2.00000i | − | 0.0811107i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.00000 | + | 10.3923i | −0.242734 | + | 0.420428i | ||||
\(612\) | −2.59808 | + | 1.50000i | −0.105021 | + | 0.0606339i | ||||
\(613\) | −13.8564 | + | 8.00000i | −0.559655 | + | 0.323117i | −0.753007 | − | 0.658012i | \(-0.771397\pi\) |
0.193352 | + | 0.981129i | \(0.438064\pi\) | |||||||
\(614\) | 14.0000 | − | 24.2487i | 0.564994 | − | 0.978598i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.0000i | 0.603877i | 0.953327 | + | 0.301939i | \(0.0976338\pi\) | ||||
−0.953327 | + | 0.301939i | \(0.902366\pi\) | |||||||
\(618\) | 4.33013 | + | 2.50000i | 0.174183 | + | 0.100565i | ||||
\(619\) | 10.0000 | + | 17.3205i | 0.401934 | + | 0.696170i | 0.993959 | − | 0.109749i | \(-0.0350048\pi\) |
−0.592025 | + | 0.805919i | \(0.701671\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.50000 | + | 2.59808i | −0.0601929 | + | 0.104257i | ||||
\(622\) | 9.00000i | 0.360867i | ||||||||
\(623\) | 12.9904 | − | 37.5000i | 0.520449 | − | 1.50241i | ||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.50000 | + | 4.33013i | 0.0999201 | + | 0.173067i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.92820 | − | 4.00000i | −0.276465 | − | 0.159617i | ||||
\(629\) | 30.0000 | 1.19618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.0000 | −1.47295 | −0.736473 | − | 0.676467i | \(-0.763510\pi\) | ||||
−0.736473 | + | 0.676467i | \(0.763510\pi\) | |||||||
\(632\) | −9.52628 | − | 5.50000i | −0.378935 | − | 0.218778i | ||||
\(633\) | 12.1244 | − | 7.00000i | 0.481900 | − | 0.278225i | ||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | −10.3923 | − | 26.0000i | −0.411758 | − | 1.03016i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.50000 | − | 2.59808i | 0.0593391 | − | 0.102778i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5000 | + | 28.5788i | 0.651711 | + | 1.12880i | 0.982708 | + | 0.185164i | \(0.0592817\pi\) |
−0.330997 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(642\) | 15.5885 | + | 9.00000i | 0.615227 | + | 0.355202i | ||||
\(643\) | 38.0000i | 1.49857i | 0.662246 | + | 0.749287i | \(0.269604\pi\) | ||||
−0.662246 | + | 0.749287i | \(0.730396\pi\) | |||||||
\(644\) | 1.50000 | + | 7.79423i | 0.0591083 | + | 0.307136i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.00000 | − | 5.19615i | 0.118033 | − | 0.204440i | ||||
\(647\) | −20.7846 | + | 12.0000i | −0.817127 | + | 0.471769i | −0.849425 | − | 0.527710i | \(-0.823051\pi\) |
0.0322975 | + | 0.999478i | \(0.489718\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.50000 | − | 0.866025i | −0.0979827 | − | 0.0339422i | ||||
\(652\) | − | 8.00000i | − | 0.313304i | ||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | −1.00000 | − | 1.73205i | −0.0391031 | − | 0.0677285i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.50000 | − | 7.79423i | 0.175695 | − | 0.304314i | ||||
\(657\) | − | 14.0000i | − | 0.546192i | ||||||
\(658\) | −5.19615 | − | 6.00000i | −0.202567 | − | 0.233904i | ||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | + | 8.66025i | 0.194477 | + | 0.336845i | 0.946729 | − | 0.322031i | \(-0.104366\pi\) |
−0.752252 | + | 0.658876i | \(0.771032\pi\) | |||||||
\(662\) | −8.66025 | + | 5.00000i | −0.336590 | + | 0.194331i | ||||
\(663\) | 10.3923 | + | 6.00000i | 0.403604 | + | 0.233021i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.0000 | 0.387492 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −20.7846 | + | 12.0000i | −0.804181 | + | 0.464294i | ||||
\(669\) | −9.50000 | − | 16.4545i | −0.367291 | − | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.866025 | + | 2.50000i | −0.0334077 | + | 0.0964396i | ||||
\(673\) | − | 19.0000i | − | 0.732396i | −0.930537 | − | 0.366198i | \(-0.880659\pi\) | ||
0.930537 | − | 0.366198i | \(-0.119341\pi\) | |||||||
\(674\) | −5.50000 | + | 9.52628i | −0.211852 | + | 0.366939i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50000 | − | 2.59808i | −0.0576923 | − | 0.0999260i | ||||
\(677\) | −10.3923 | − | 6.00000i | −0.399409 | − | 0.230599i | 0.286820 | − | 0.957984i | \(-0.407402\pi\) |
−0.686229 | + | 0.727386i | \(0.740735\pi\) | |||||||
\(678\) | − | 21.0000i | − | 0.806500i | ||||||
\(679\) | −3.50000 | − | 18.1865i | −0.134318 | − | 0.697935i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.00000 | − | 5.19615i | 0.114960 | − | 0.199117i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.19615 | − | 3.00000i | 0.198825 | − | 0.114792i | −0.397282 | − | 0.917697i | \(-0.630047\pi\) |
0.596107 | + | 0.802905i | \(0.296713\pi\) | |||||||
\(684\) | 1.00000 | − | 1.73205i | 0.0382360 | − | 0.0662266i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.5000 | − | 0.866025i | 0.706333 | − | 0.0330650i | ||||
\(687\) | 4.00000i | 0.152610i | ||||||||
\(688\) | 8.66025 | + | 5.00000i | 0.330169 | + | 0.190623i | ||||
\(689\) | 12.0000 | + | 20.7846i | 0.457164 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.0000 | + | 17.3205i | −0.380418 | + | 0.658903i | −0.991122 | − | 0.132956i | \(-0.957553\pi\) |
0.610704 | + | 0.791859i | \(0.290887\pi\) | |||||||
\(692\) | 18.0000i | 0.684257i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.0000 | −1.36654 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.3827 | − | 13.5000i | 0.885682 | − | 0.511349i | ||||
\(698\) | 22.5167 | + | 13.0000i | 0.852268 | + | 0.492057i | ||||
\(699\) | 30.0000 | 1.13470 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0000 | −0.453234 | −0.226617 | − | 0.973984i | \(-0.572767\pi\) | ||||
−0.226617 | + | 0.973984i | \(0.572767\pi\) | |||||||
\(702\) | 3.46410 | + | 2.00000i | 0.130744 | + | 0.0754851i | ||||
\(703\) | −17.3205 | + | 10.0000i | −0.653255 | + | 0.377157i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.0000 | 0.564532 | ||||||||
\(707\) | 31.1769 | + | 36.0000i | 1.17253 | + | 1.35392i | ||||
\(708\) | − | 6.00000i | − | 0.225494i | ||||||
\(709\) | −17.0000 | + | 29.4449i | −0.638448 | + | 1.10583i | 0.347325 | + | 0.937745i | \(0.387090\pi\) |
−0.985773 | + | 0.168080i | \(0.946243\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.50000 | − | 9.52628i | −0.206266 | − | 0.357263i | ||||
\(712\) | 12.9904 | + | 7.50000i | 0.486835 | + | 0.281074i | ||||
\(713\) | − | 3.00000i | − | 0.112351i | ||||||
\(714\) | −6.00000 | + | 5.19615i | −0.224544 | + | 0.194461i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.00000 | − | 5.19615i | 0.112115 | − | 0.194189i | ||||
\(717\) | −12.9904 | + | 7.50000i | −0.485135 | + | 0.280093i | ||||
\(718\) | −10.3923 | + | 6.00000i | −0.387837 | + | 0.223918i | ||||
\(719\) | −13.5000 | + | 23.3827i | −0.503465 | + | 0.872027i | 0.496527 | + | 0.868021i | \(0.334608\pi\) |
−0.999992 | + | 0.00400572i | \(0.998725\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.5000 | + | 4.33013i | 0.465524 | + | 0.161262i | ||||
\(722\) | − | 15.0000i | − | 0.558242i | ||||||
\(723\) | −12.1244 | − | 7.00000i | −0.450910 | − | 0.260333i | ||||
\(724\) | 4.00000 | + | 6.92820i | 0.148659 | + | 0.257485i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.50000 | + | 9.52628i | −0.204124 | + | 0.353553i | ||||
\(727\) | 37.0000i | 1.37225i | 0.727482 | + | 0.686127i | \(0.240691\pi\) | ||||
−0.727482 | + | 0.686127i | \(0.759309\pi\) | |||||||
\(728\) | 10.3923 | − | 2.00000i | 0.385164 | − | 0.0741249i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.0000 | + | 25.9808i | 0.554795 | + | 0.960933i | ||||
\(732\) | −6.92820 | + | 4.00000i | −0.256074 | + | 0.147844i | ||||
\(733\) | −12.1244 | − | 7.00000i | −0.447823 | − | 0.258551i | 0.259087 | − | 0.965854i | \(-0.416578\pi\) |
−0.706910 | + | 0.707303i | \(0.749912\pi\) | |||||||
\(734\) | 8.00000 | 0.295285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 7.79423 | − | 4.50000i | 0.286910 | − | 0.165647i | ||||
\(739\) | 1.00000 | + | 1.73205i | 0.0367856 | + | 0.0637145i | 0.883832 | − | 0.467804i | \(-0.154955\pi\) |
−0.847046 | + | 0.531519i | \(0.821621\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | −15.5885 | + | 3.00000i | −0.572270 | + | 0.110133i | ||||
\(743\) | − | 51.0000i | − | 1.87101i | −0.353315 | − | 0.935504i | \(-0.614946\pi\) | ||
0.353315 | − | 0.935504i | \(-0.385054\pi\) | |||||||
\(744\) | 0.500000 | − | 0.866025i | 0.0183309 | − | 0.0317500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.00000 | − | 3.46410i | −0.0732252 | − | 0.126830i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.0000 | + | 15.5885i | 1.64426 | + | 0.569590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | − | 13.8564i | 0.291924 | − | 0.505627i | −0.682341 | − | 0.731034i | \(-0.739038\pi\) |
0.974265 | + | 0.225407i | \(0.0723712\pi\) | |||||||
\(752\) | 2.59808 | − | 1.50000i | 0.0947421 | − | 0.0546994i | ||||
\(753\) | 10.3923 | − | 6.00000i | 0.378717 | − | 0.218652i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.00000 | + | 1.73205i | −0.0727393 | + | 0.0629941i | ||||
\(757\) | 16.0000i | 0.581530i | 0.956795 | + | 0.290765i | \(0.0939098\pi\) | ||||
−0.956795 | + | 0.290765i | \(0.906090\pi\) | |||||||
\(758\) | −13.8564 | − | 8.00000i | −0.503287 | − | 0.290573i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.5000 | + | 23.3827i | −0.489375 | + | 0.847622i | −0.999925 | − | 0.0122260i | \(-0.996108\pi\) |
0.510551 | + | 0.859848i | \(0.329442\pi\) | |||||||
\(762\) | − | 16.0000i | − | 0.579619i | ||||||
\(763\) | −3.46410 | − | 4.00000i | −0.125409 | − | 0.144810i | ||||
\(764\) | 21.0000 | 0.759753 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.5000 | + | 18.1865i | 0.379380 | + | 0.657106i | ||||
\(767\) | −20.7846 | + | 12.0000i | −0.750489 | + | 0.433295i | ||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | −26.0000 | −0.937584 | −0.468792 | − | 0.883309i | \(-0.655311\pi\) | ||||
−0.468792 | + | 0.883309i | \(0.655311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.0000 | 1.08042 | ||||||||
\(772\) | 14.7224 | + | 8.50000i | 0.529872 | + | 0.305922i | ||||
\(773\) | 15.5885 | − | 9.00000i | 0.560678 | − | 0.323708i | −0.192740 | − | 0.981250i | \(-0.561737\pi\) |
0.753418 | + | 0.657542i | \(0.228404\pi\) | |||||||
\(774\) | 5.00000 | + | 8.66025i | 0.179721 | + | 0.311286i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.00000 | 0.251285 | ||||||||
\(777\) | 25.9808 | − | 5.00000i | 0.932055 | − | 0.179374i | ||||
\(778\) | − | 6.00000i | − | 0.215110i | ||||||
\(779\) | −9.00000 | + | 15.5885i | −0.322458 | + | 0.558514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −7.79423 | − | 4.50000i | −0.278721 | − | 0.160920i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | + | 6.92820i | −0.0357143 | + | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.00000 | + | 10.3923i | −0.214013 | + | 0.370681i | ||||
\(787\) | 19.0526 | − | 11.0000i | 0.679150 | − | 0.392108i | −0.120384 | − | 0.992727i | \(-0.538413\pi\) |
0.799535 | + | 0.600620i | \(0.205079\pi\) | |||||||
\(788\) | −10.3923 | + | 6.00000i | −0.370211 | + | 0.213741i | ||||
\(789\) | 4.50000 | − | 7.79423i | 0.160204 | − | 0.277482i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.5000 | − | 54.5596i | −0.373337 | − | 1.93992i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.7128 | + | 16.0000i | 0.984111 | + | 0.568177i | ||||
\(794\) | 11.0000 | + | 19.0526i | 0.390375 | + | 0.676150i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.50000 | + | 9.52628i | −0.194942 | + | 0.337650i | ||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 1.73205 | − | 5.00000i | 0.0613139 | − | 0.176998i | ||||
\(799\) | 9.00000 | 0.318397 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.50000 | + | 12.9904i | 0.264999 | + | 0.458993i | ||||
\(802\) | 15.5885 | − | 9.00000i | 0.550448 | − | 0.317801i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 4.00000 | 0.141069 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | −5.19615 | − | 3.00000i | −0.182913 | − | 0.105605i | ||||
\(808\) | −15.5885 | + | 9.00000i | −0.548400 | + | 0.316619i | ||||
\(809\) | 3.00000 | + | 5.19615i | 0.105474 | + | 0.182687i | 0.913932 | − | 0.405868i | \(-0.133031\pi\) |
−0.808458 | + | 0.588555i | \(0.799697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 56.0000 | 1.96643 | 0.983213 | − | 0.182462i | \(-0.0584065\pi\) | ||||
0.983213 | + | 0.182462i | \(0.0584065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 7.00000i | − | 0.245501i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.50000 | − | 2.59808i | −0.0525105 | − | 0.0909509i | ||||
\(817\) | −17.3205 | − | 10.0000i | −0.605968 | − | 0.349856i | ||||
\(818\) | − | 5.00000i | − | 0.174821i | ||||||
\(819\) | 10.0000 | + | 3.46410i | 0.349428 | + | 0.121046i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.0000 | − | 46.7654i | 0.942306 | − | 1.63212i | 0.181250 | − | 0.983437i | \(-0.441986\pi\) |
0.761056 | − | 0.648686i | \(-0.224681\pi\) | |||||||
\(822\) | −7.79423 | + | 4.50000i | −0.271855 | + | 0.156956i | ||||
\(823\) | 27.7128 | − | 16.0000i | 0.966008 | − | 0.557725i | 0.0679910 | − | 0.997686i | \(-0.478341\pi\) |
0.898017 | + | 0.439961i | \(0.145008\pi\) | |||||||
\(824\) | −2.50000 | + | 4.33013i | −0.0870916 | + | 0.150847i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.00000 | − | 15.5885i | −0.104383 | − | 0.542392i | ||||
\(827\) | − | 48.0000i | − | 1.66912i | −0.550914 | − | 0.834562i | \(-0.685721\pi\) | ||
0.550914 | − | 0.834562i | \(-0.314279\pi\) | |||||||
\(828\) | −2.59808 | − | 1.50000i | −0.0902894 | − | 0.0521286i | ||||
\(829\) | 1.00000 | + | 1.73205i | 0.0347314 | + | 0.0601566i | 0.882869 | − | 0.469620i | \(-0.155609\pi\) |
−0.848137 | + | 0.529777i | \(0.822276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.0000 | − | 24.2487i | 0.485655 | − | 0.841178i | ||||
\(832\) | 4.00000i | 0.138675i | ||||||||
\(833\) | −12.9904 | + | 16.5000i | −0.450090 | + | 0.571691i | ||||
\(834\) | 2.00000 | 0.0692543 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.866025 | − | 0.500000i | 0.0299342 | − | 0.0172825i | ||||
\(838\) | 15.5885 | + | 9.00000i | 0.538494 | + | 0.310900i | ||||
\(839\) | −27.0000 | −0.932144 | −0.466072 | − | 0.884747i | \(-0.654331\pi\) | ||||
−0.466072 | + | 0.884747i | \(0.654331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 34.6410 | + | 20.0000i | 1.19381 | + | 0.689246i | ||||
\(843\) | 7.79423 | − | 4.50000i | 0.268447 | − | 0.154988i | ||||
\(844\) | 7.00000 | + | 12.1244i | 0.240950 | + | 0.417338i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | −9.52628 | + | 27.5000i | −0.327327 | + | 0.944911i | ||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | −2.00000 | + | 3.46410i | −0.0686398 | + | 0.118888i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.0000 | + | 25.9808i | 0.514193 | + | 0.890609i | ||||
\(852\) | 2.59808 | + | 1.50000i | 0.0890086 | + | 0.0513892i | ||||
\(853\) | 26.0000i | 0.890223i | 0.895475 | + | 0.445112i | \(0.146836\pi\) | ||||
−0.895475 | + | 0.445112i | \(0.853164\pi\) | |||||||
\(854\) | −16.0000 | + | 13.8564i | −0.547509 | + | 0.474156i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.00000 | + | 15.5885i | −0.307614 | + | 0.532803i | ||||
\(857\) | −46.7654 | + | 27.0000i | −1.59747 | + | 0.922302i | −0.605503 | + | 0.795843i | \(0.707028\pi\) |
−0.991972 | + | 0.126459i | \(0.959639\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.00000 | + | 3.46410i | −0.0682391 | + | 0.118194i | −0.898126 | − | 0.439738i | \(-0.855071\pi\) |
0.829887 | + | 0.557931i | \(0.188405\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.0000 | − | 15.5885i | 0.613438 | − | 0.531253i | ||||
\(862\) | − | 27.0000i | − | 0.919624i | ||||||
\(863\) | 12.9904 | + | 7.50000i | 0.442198 | + | 0.255303i | 0.704529 | − | 0.709675i | \(-0.251158\pi\) |
−0.262332 | + | 0.964978i | \(0.584491\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.5000 | − | 25.1147i | 0.492730 | − | 0.853433i | ||||
\(867\) | 8.00000i | 0.271694i | ||||||||
\(868\) | 0.866025 | − | 2.50000i | 0.0293948 | − | 0.0848555i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | − | 13.8564i | −0.271070 | − | 0.469506i | ||||
\(872\) | 1.73205 | − | 1.00000i | 0.0586546 | − | 0.0338643i | ||||
\(873\) | 6.06218 | + | 3.50000i | 0.205174 | + | 0.118457i | ||||
\(874\) | 6.00000 | 0.202953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.0000 | 0.473016 | ||||||||
\(877\) | 32.9090 | + | 19.0000i | 1.11126 | + | 0.641584i | 0.939155 | − | 0.343495i | \(-0.111611\pi\) |
0.172102 | + | 0.985079i | \(0.444944\pi\) | |||||||
\(878\) | −4.33013 | + | 2.50000i | −0.146135 | + | 0.0843709i | ||||
\(879\) | −12.0000 | − | 20.7846i | −0.404750 | − | 0.701047i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.00000 | −0.101073 | −0.0505363 | − | 0.998722i | \(-0.516093\pi\) | ||||
−0.0505363 | + | 0.998722i | \(0.516093\pi\) | |||||||
\(882\) | −4.33013 | + | 5.50000i | −0.145803 | + | 0.185195i | ||||
\(883\) | 38.0000i | 1.27880i | 0.768874 | + | 0.639401i | \(0.220818\pi\) | ||||
−0.768874 | + | 0.639401i | \(0.779182\pi\) | |||||||
\(884\) | −6.00000 | + | 10.3923i | −0.201802 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.00000 | − | 5.19615i | −0.100787 | − | 0.174568i | ||||
\(887\) | 41.5692 | + | 24.0000i | 1.39576 | + | 0.805841i | 0.993945 | − | 0.109881i | \(-0.0350469\pi\) |
0.401813 | + | 0.915722i | \(0.368380\pi\) | |||||||
\(888\) | 10.0000i | 0.335578i | ||||||||
\(889\) | −8.00000 | − | 41.5692i | −0.268311 | − | 1.39419i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.4545 | − | 9.50000i | 0.550937 | − | 0.318084i | ||||
\(893\) | −5.19615 | + | 3.00000i | −0.173883 | + | 0.100391i | ||||
\(894\) | 3.00000 | − | 5.19615i | 0.100335 | − | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.50000 | − | 0.866025i | −0.0835191 | − | 0.0289319i | ||||
\(897\) | 12.0000i | 0.400668i | ||||||||
\(898\) | −18.1865 | − | 10.5000i | −0.606892 | − | 0.350390i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000 | − | 15.5885i | 0.299833 | − | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.3205 | + | 20.0000i | 0.576390 | + | 0.665558i | ||||
\(904\) | 21.0000 | 0.698450 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.00000 | + | 6.92820i | 0.132891 | + | 0.230174i | ||||
\(907\) | 13.8564 | − | 8.00000i | 0.460094 | − | 0.265636i | −0.251990 | − | 0.967730i | \(-0.581085\pi\) |
0.712084 | + | 0.702094i | \(0.247752\pi\) | |||||||
\(908\) | 5.19615 | + | 3.00000i | 0.172440 | + | 0.0995585i | ||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.0000 | 1.29213 | 0.646064 | − | 0.763283i | \(-0.276414\pi\) | ||||
0.646064 | + | 0.763283i | \(0.276414\pi\) | |||||||
\(912\) | 1.73205 | + | 1.00000i | 0.0573539 | + | 0.0331133i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −1.00000 | − | 1.73205i | −0.0330771 | − | 0.0572911i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.00000 | −0.132164 | ||||||||
\(917\) | −10.3923 | + | 30.0000i | −0.343184 | + | 0.990687i | ||||
\(918\) | − | 3.00000i | − | 0.0990148i | ||||||
\(919\) | −9.50000 | + | 16.4545i | −0.313376 | + | 0.542783i | −0.979091 | − | 0.203423i | \(-0.934793\pi\) |
0.665715 | + | 0.746206i | \(0.268127\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | + | 24.2487i | 0.461316 | + | 0.799022i | ||||
\(922\) | 10.3923 | + | 6.00000i | 0.342252 | + | 0.197599i | ||||
\(923\) | − | 12.0000i | − | 0.394985i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.50000 | − | 4.33013i | 0.0821551 | − | 0.142297i | ||||
\(927\) | −4.33013 | + | 2.50000i | −0.142220 | + | 0.0821108i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.00000 | − | 15.5885i | 0.295280 | − | 0.511441i | −0.679770 | − | 0.733426i | \(-0.737920\pi\) |
0.975050 | + | 0.221985i | \(0.0712536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | − | 13.8564i | 0.0655474 | − | 0.454125i | ||||
\(932\) | 30.0000i | 0.982683i | ||||||||
\(933\) | −7.79423 | − | 4.50000i | −0.255172 | − | 0.147323i | ||||
\(934\) | −6.00000 | − | 10.3923i | −0.196326 | − | 0.340047i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.00000 | + | 3.46410i | −0.0653720 | + | 0.113228i | ||||
\(937\) | − | 26.0000i | − | 0.849383i | −0.905338 | − | 0.424691i | \(-0.860383\pi\) | ||
0.905338 | − | 0.424691i | \(-0.139617\pi\) | |||||||
\(938\) | 10.3923 | − | 2.00000i | 0.339321 | − | 0.0653023i | ||||
\(939\) | −5.00000 | −0.163169 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.0000 | − | 25.9808i | −0.488986 | − | 0.846949i | 0.510934 | − | 0.859620i | \(-0.329300\pi\) |
−0.999920 | + | 0.0126715i | \(0.995966\pi\) | |||||||
\(942\) | 6.92820 | − | 4.00000i | 0.225733 | − | 0.130327i | ||||
\(943\) | 23.3827 | + | 13.5000i | 0.761445 | + | 0.439620i | ||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.5692 | − | 24.0000i | −1.35082 | − | 0.779895i | −0.362454 | − | 0.932002i | \(-0.618061\pi\) |
−0.988364 | + | 0.152106i | \(0.951394\pi\) | |||||||
\(948\) | 9.52628 | − | 5.50000i | 0.309399 | − | 0.178632i | ||||
\(949\) | −28.0000 | − | 48.4974i | −0.908918 | − | 1.57429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | −5.19615 | − | 6.00000i | −0.168408 | − | 0.194461i | ||||
\(953\) | 6.00000i | 0.194359i | 0.995267 | + | 0.0971795i | \(0.0309821\pi\) | ||||
−0.995267 | + | 0.0971795i | \(0.969018\pi\) | |||||||
\(954\) | 3.00000 | − | 5.19615i | 0.0971286 | − | 0.168232i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.50000 | − | 12.9904i | −0.242567 | − | 0.420139i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.0000i | 0.872330i | ||||||||
\(959\) | −18.0000 | + | 15.5885i | −0.581250 | + | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | − | 25.9808i | 0.483871 | − | 0.838089i | ||||
\(962\) | 34.6410 | − | 20.0000i | 1.11687 | − | 0.644826i | ||||
\(963\) | −15.5885 | + | 9.00000i | −0.502331 | + | 0.290021i | ||||
\(964\) | 7.00000 | − | 12.1244i | 0.225455 | − | 0.390499i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.50000 | − | 2.59808i | −0.241309 | − | 0.0835917i | ||||
\(967\) | 49.0000i | 1.57573i | 0.615846 | + | 0.787867i | \(0.288815\pi\) | ||||
−0.615846 | + | 0.787867i | \(0.711185\pi\) | |||||||
\(968\) | −9.52628 | − | 5.50000i | −0.306186 | − | 0.176777i | ||||
\(969\) | 3.00000 | + | 5.19615i | 0.0963739 | + | 0.166924i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000 | − | 31.1769i | 0.577647 | − | 1.00051i | −0.418101 | − | 0.908401i | \(-0.637304\pi\) |
0.995748 | − | 0.0921142i | \(-0.0293625\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 5.19615 | − | 1.00000i | 0.166581 | − | 0.0320585i | ||||
\(974\) | −31.0000 | −0.993304 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | − | 6.92820i | −0.128037 | − | 0.221766i | ||||
\(977\) | −23.3827 | + | 13.5000i | −0.748078 | + | 0.431903i | −0.824999 | − | 0.565134i | \(-0.808824\pi\) |
0.0769208 | + | 0.997037i | \(0.475491\pi\) | |||||||
\(978\) | 6.92820 | + | 4.00000i | 0.221540 | + | 0.127906i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 5.19615 | + | 3.00000i | 0.165816 | + | 0.0957338i | ||||
\(983\) | −10.3923 | + | 6.00000i | −0.331463 | + | 0.191370i | −0.656490 | − | 0.754334i | \(-0.727960\pi\) |
0.325027 | + | 0.945705i | \(0.394626\pi\) | |||||||
\(984\) | 4.50000 | + | 7.79423i | 0.143455 | + | 0.248471i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.79423 | − | 1.50000i | 0.248093 | − | 0.0477455i | ||||
\(988\) | − | 8.00000i | − | 0.254514i | ||||||
\(989\) | −15.0000 | + | 25.9808i | −0.476972 | + | 0.826140i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.5000 | − | 51.0955i | −0.937098 | − | 1.62310i | −0.770849 | − | 0.637018i | \(-0.780168\pi\) |
−0.166250 | − | 0.986084i | \(-0.553166\pi\) | |||||||
\(992\) | 0.866025 | + | 0.500000i | 0.0274963 | + | 0.0158750i | ||||
\(993\) | − | 10.0000i | − | 0.317340i | ||||||
\(994\) | 7.50000 | + | 2.59808i | 0.237886 | + | 0.0824060i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.6410 | − | 20.0000i | 1.09709 | − | 0.633406i | 0.161636 | − | 0.986850i | \(-0.448323\pi\) |
0.935456 | + | 0.353444i | \(0.114990\pi\) | |||||||
\(998\) | −27.7128 | + | 16.0000i | −0.877234 | + | 0.506471i | ||||
\(999\) | −5.00000 | + | 8.66025i | −0.158193 | + | 0.273998i |
(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 | 1050.2.o.e.499.1 | 4 | ||
5.2 | odd | 4 | 1050.2.i.m.751.1 | yes | 2 | ||
5.3 | odd | 4 | 1050.2.i.h.751.1 | yes | 2 | ||
5.4 | even | 2 | inner | 1050.2.o.e.499.2 | 4 | ||
7.4 | even | 3 | inner | 1050.2.o.e.949.2 | 4 | ||
35.2 | odd | 12 | 7350.2.a.bb.1.1 | 1 | |||
35.4 | even | 6 | inner | 1050.2.o.e.949.1 | 4 | ||
35.12 | even | 12 | 7350.2.a.n.1.1 | 1 | |||
35.18 | odd | 12 | 1050.2.i.h.151.1 | ✓ | 2 | ||
35.23 | odd | 12 | 7350.2.a.by.1.1 | 1 | |||
35.32 | odd | 12 | 1050.2.i.m.151.1 | yes | 2 | ||
35.33 | even | 12 | 7350.2.a.cq.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.i.h.151.1 | ✓ | 2 | 35.18 | odd | 12 | ||
1050.2.i.h.751.1 | yes | 2 | 5.3 | odd | 4 | ||
1050.2.i.m.151.1 | yes | 2 | 35.32 | odd | 12 | ||
1050.2.i.m.751.1 | yes | 2 | 5.2 | odd | 4 | ||
1050.2.o.e.499.1 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.o.e.499.2 | 4 | 5.4 | even | 2 | inner | ||
1050.2.o.e.949.1 | 4 | 35.4 | even | 6 | inner | ||
1050.2.o.e.949.2 | 4 | 7.4 | even | 3 | inner | ||
7350.2.a.n.1.1 | 1 | 35.12 | even | 12 | |||
7350.2.a.bb.1.1 | 1 | 35.2 | odd | 12 | |||
7350.2.a.by.1.1 | 1 | 35.23 | odd | 12 | |||
7350.2.a.cq.1.1 | 1 | 35.33 | even | 12 |