Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(13,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 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("280.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.s (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.40282095616.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 8x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 237.1 | ||
Root | \(1.71331 - 0.254137i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.237 |
Dual form | 280.2.s.a.13.1 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.707107 | − | 0.707107i | ||||
\(3\) | −1.96744 | + | 1.96744i | −1.13590 | + | 1.13590i | −0.146726 | + | 0.989177i | \(0.546874\pi\) |
−0.989177 | + | 0.146726i | \(0.953126\pi\) | |||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | 0.254137 | − | 2.22158i | 0.113654 | − | 0.993520i | ||||
\(6\) | 3.93488 | 1.60641 | ||||||||
\(7\) | 1.87083 | + | 1.87083i | 0.707107 | + | 0.707107i | ||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | − | 4.74166i | − | 1.58055i | ||||||
\(10\) | −2.47572 | + | 1.96744i | −0.782890 | + | 0.622160i | ||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | −3.93488 | − | 3.93488i | −1.13590 | − | 1.13590i | ||||
\(13\) | −4.88578 | + | 4.88578i | −1.35507 | + | 1.35507i | −0.475185 | + | 0.879886i | \(0.657619\pi\) |
−0.879886 | + | 0.475185i | \(0.842381\pi\) | |||||||
\(14\) | − | 3.74166i | − | 1.00000i | ||||||
\(15\) | 3.87083 | + | 4.87083i | 0.999444 | + | 1.25764i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | −4.74166 | + | 4.74166i | −1.11762 | + | 1.11762i | ||||
\(19\) | 2.41006i | 0.552906i | 0.961027 | + | 0.276453i | \(0.0891590\pi\) | ||||
−0.961027 | + | 0.276453i | \(0.910841\pi\) | |||||||
\(20\) | 4.44316 | + | 0.508274i | 0.993520 | + | 0.113654i | ||||
\(21\) | −7.36149 | −1.60641 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.74166 | + | 6.74166i | −1.40573 | + | 1.40573i | −0.625543 | + | 0.780189i | \(0.715123\pi\) |
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 7.86977i | 1.60641i | ||||||||
\(25\) | −4.87083 | − | 1.12917i | −0.974166 | − | 0.225834i | ||||
\(26\) | 9.77156 | 1.91636 | ||||||||
\(27\) | 3.42661 | + | 3.42661i | 0.659451 | + | 0.659451i | ||||
\(28\) | −3.74166 | + | 3.74166i | −0.707107 | + | 0.707107i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 1.00000 | − | 8.74166i | 0.182574 | − | 1.59600i | ||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 4.00000 | + | 4.00000i | 0.707107 | + | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.63164 | − | 3.68075i | 0.782890 | − | 0.622160i | ||||
\(36\) | 9.48331 | 1.58055 | ||||||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | 2.41006 | − | 2.41006i | 0.390964 | − | 0.390964i | ||||
\(39\) | − | 19.2250i | − | 3.07846i | ||||||
\(40\) | −3.93488 | − | 4.95143i | −0.622160 | − | 0.782890i | ||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 7.36149 | + | 7.36149i | 1.13590 | + | 1.13590i | ||||
\(43\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.5340 | − | 1.20503i | −1.57031 | − | 0.179635i | ||||
\(46\) | 13.4833 | 1.98801 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 7.86977 | − | 7.86977i | 1.13590 | − | 1.13590i | ||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 3.74166 | + | 6.00000i | 0.529150 | + | 0.848528i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.77156 | − | 9.77156i | −1.35507 | − | 1.35507i | ||||
\(53\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(54\) | − | 6.85322i | − | 0.932605i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.48331 | 1.00000 | ||||||||
\(57\) | −4.74166 | − | 4.74166i | −0.628048 | − | 0.628048i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.4111i | 1.35541i | 0.735332 | + | 0.677707i | \(0.237026\pi\) | ||||
−0.735332 | + | 0.677707i | \(0.762974\pi\) | |||||||
\(60\) | −9.74166 | + | 7.74166i | −1.25764 | + | 0.999444i | ||||
\(61\) | 6.47626 | 0.829199 | 0.414600 | − | 0.910004i | \(-0.363922\pi\) | ||||
0.414600 | + | 0.910004i | \(0.363922\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.87083 | − | 8.87083i | 1.11762 | − | 1.11762i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 9.61249 | + | 12.0958i | 1.19228 | + | 1.50030i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 26.5276i | − | 3.19355i | ||||||
\(70\) | −8.31239 | − | 0.950894i | −0.993520 | − | 0.113654i | ||||
\(71\) | −15.2250 | −1.80687 | −0.903436 | − | 0.428723i | \(-0.858964\pi\) | ||||
−0.903436 | + | 0.428723i | \(0.858964\pi\) | |||||||
\(72\) | −9.48331 | − | 9.48331i | −1.11762 | − | 1.11762i | ||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.8047 | − | 7.36149i | 1.36308 | − | 0.850032i | ||||
\(76\) | −4.82012 | −0.552906 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −19.2250 | + | 19.2250i | −2.17680 | + | 2.17680i | ||||
\(79\) | 8.25834i | 0.929136i | 0.885537 | + | 0.464568i | \(0.153790\pi\) | ||||
−0.885537 | + | 0.464568i | \(0.846210\pi\) | |||||||
\(80\) | −1.01655 | + | 8.88632i | −0.113654 | + | 0.993520i | ||||
\(81\) | 0.741657 | 0.0824064 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.2473 | − | 12.2473i | 1.34431 | − | 1.34431i | 0.452598 | − | 0.891715i | \(-0.350497\pi\) |
0.891715 | − | 0.452598i | \(-0.149503\pi\) | |||||||
\(84\) | − | 14.7230i | − | 1.60641i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 9.32894 | + | 11.7390i | 0.983356 | + | 1.23740i | ||||
\(91\) | −18.2809 | −1.91636 | ||||||||
\(92\) | −13.4833 | − | 13.4833i | −1.40573 | − | 1.40573i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.35414 | + | 0.612486i | 0.549324 | + | 0.0628397i | ||||
\(96\) | −15.7395 | −1.60641 | ||||||||
\(97\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(98\) | 7.00000 | − | 7.00000i | 0.707107 | − | 0.707107i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.25834 | − | 9.74166i | 0.225834 | − | 0.974166i | ||||
\(101\) | 1.39351 | 0.138660 | 0.0693299 | − | 0.997594i | \(-0.477914\pi\) | ||||
0.0693299 | + | 0.997594i | \(0.477914\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(104\) | 19.5431i | 1.91636i | ||||||||
\(105\) | −1.87083 | + | 16.3541i | −0.182574 | + | 1.59600i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | −6.85322 | + | 6.85322i | −0.659451 | + | 0.659451i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.48331 | − | 7.48331i | −0.707107 | − | 0.707107i | ||||
\(113\) | 11.2250 | − | 11.2250i | 1.05596 | − | 1.05596i | 0.0576178 | − | 0.998339i | \(-0.481650\pi\) |
0.998339 | − | 0.0576178i | \(-0.0183505\pi\) | |||||||
\(114\) | 9.48331i | 0.888194i | ||||||||
\(115\) | 13.2638 | + | 16.6904i | 1.23686 | + | 1.55639i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 23.1667 | + | 23.1667i | 2.14176 | + | 2.14176i | ||||
\(118\) | 10.4111 | − | 10.4111i | 0.958423 | − | 0.958423i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 17.4833 | + | 2.00000i | 1.59600 | + | 0.182574i | ||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | −6.47626 | − | 6.47626i | −0.586333 | − | 0.586333i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.74640 | + | 10.5340i | −0.335088 | + | 0.942187i | ||||
\(126\) | −17.7417 | −1.58055 | ||||||||
\(127\) | 10.2250 | + | 10.2250i | 0.907320 | + | 0.907320i | 0.996055 | − | 0.0887357i | \(-0.0282826\pi\) |
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.707107 | + | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.48331 | − | 21.7083i | 0.217801 | − | 1.90394i | ||||
\(131\) | 12.3129 | 1.07579 | 0.537893 | − | 0.843013i | \(-0.319221\pi\) | ||||
0.537893 | + | 0.843013i | \(0.319221\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.50881 | + | 4.50881i | −0.390964 | + | 0.390964i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.48331 | − | 6.74166i | 0.730127 | − | 0.580229i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.51669 | + | 1.51669i | 0.129579 | + | 0.129579i | 0.768922 | − | 0.639343i | \(-0.220793\pi\) |
−0.639343 | + | 0.768922i | \(0.720793\pi\) | |||||||
\(138\) | −26.5276 | + | 26.5276i | −2.25818 | + | 2.25818i | ||||
\(139\) | 5.32840i | 0.451949i | 0.974133 | + | 0.225974i | \(0.0725566\pi\) | ||||
−0.974133 | + | 0.225974i | \(0.927443\pi\) | |||||||
\(140\) | 7.36149 | + | 9.26328i | 0.622160 | + | 0.782890i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.2250 | + | 15.2250i | 1.27765 | + | 1.27765i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 18.9666i | 1.58055i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.7721 | − | 13.7721i | −1.13590 | − | 1.13590i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | −19.1661 | − | 4.44316i | −1.56491 | − | 0.362782i | ||||
\(151\) | −22.4499 | −1.82695 | −0.913475 | − | 0.406894i | \(-0.866612\pi\) | ||||
−0.913475 | + | 0.406894i | \(0.866612\pi\) | |||||||
\(152\) | 4.82012 | + | 4.82012i | 0.390964 | + | 0.390964i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 38.4499 | 3.07846 | ||||||||
\(157\) | −16.3135 | − | 16.3135i | −1.30196 | − | 1.30196i | −0.927071 | − | 0.374885i | \(-0.877682\pi\) |
−0.374885 | − | 0.927071i | \(-0.622318\pi\) | |||||||
\(158\) | 8.25834 | − | 8.25834i | 0.656998 | − | 0.656998i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.90287 | − | 7.86977i | 0.782890 | − | 0.622160i | ||||
\(161\) | −25.2250 | −1.98801 | ||||||||
\(162\) | −0.741657 | − | 0.741657i | −0.0582701 | − | 0.0582701i | ||||
\(163\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −24.4945 | −1.90115 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | −14.7230 | + | 14.7230i | −1.13590 | + | 1.13590i | ||||
\(169\) | − | 34.7417i | − | 2.67244i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.4277 | 0.873897 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.573929 | − | 0.573929i | 0.0436350 | − | 0.0436350i | −0.684953 | − | 0.728588i | \(-0.740177\pi\) |
0.728588 | + | 0.684953i | \(0.240177\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.00000 | − | 11.2250i | −0.529150 | − | 0.848528i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.4833 | − | 20.4833i | −1.53962 | − | 1.53962i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 2.41006 | − | 21.0679i | 0.179635 | − | 1.57031i | ||||
\(181\) | 26.9046 | 1.99980 | 0.999902 | − | 0.0140098i | \(-0.00445961\pi\) | ||||
0.999902 | + | 0.0140098i | \(0.00445961\pi\) | |||||||
\(182\) | 18.2809 | + | 18.2809i | 1.35507 | + | 1.35507i | ||||
\(183\) | −12.7417 | + | 12.7417i | −0.941890 | + | 0.941890i | ||||
\(184\) | 26.9666i | 1.98801i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.8212i | 0.932605i | ||||||||
\(190\) | −4.74166 | − | 5.96663i | −0.343996 | − | 0.432865i | ||||
\(191\) | 4.77503 | 0.345509 | 0.172754 | − | 0.984965i | \(-0.444733\pi\) | ||||
0.172754 | + | 0.984965i | \(0.444733\pi\) | |||||||
\(192\) | 15.7395 | + | 15.7395i | 1.13590 | + | 1.13590i | ||||
\(193\) | −6.00000 | + | 6.00000i | −0.431889 | + | 0.431889i | −0.889271 | − | 0.457381i | \(-0.848787\pi\) |
0.457381 | + | 0.889271i | \(0.348787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −42.7098 | − | 4.88578i | −3.05851 | − | 0.349878i | ||||
\(196\) | −14.0000 | −1.00000 | ||||||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −12.0000 | + | 7.48331i | −0.848528 | + | 0.529150i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.39351 | − | 1.39351i | −0.0980473 | − | 0.0980473i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 31.9666 | + | 31.9666i | 2.22183 | + | 2.22183i | ||||
\(208\) | 19.5431 | − | 19.5431i | 1.35507 | − | 1.35507i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 18.2250 | − | 14.4833i | 1.25764 | − | 0.999444i | ||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 29.9543 | − | 29.9543i | 2.05243 | − | 2.05243i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.7064 | 0.932605 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(224\) | 14.9666i | 1.00000i | ||||||||
\(225\) | −5.35414 | + | 23.0958i | −0.356943 | + | 1.53972i | ||||
\(226\) | −22.4499 | −1.49335 | ||||||||
\(227\) | −17.0674 | − | 17.0674i | −1.13280 | − | 1.13280i | −0.989709 | − | 0.143094i | \(-0.954295\pi\) |
−0.143094 | − | 0.989709i | \(-0.545705\pi\) | |||||||
\(228\) | 9.48331 | − | 9.48331i | 0.628048 | − | 0.628048i | ||||
\(229\) | 30.0856i | 1.98811i | 0.108880 | + | 0.994055i | \(0.465274\pi\) | ||||
−0.108880 | + | 0.994055i | \(0.534726\pi\) | |||||||
\(230\) | 3.42661 | − | 29.9543i | 0.225944 | − | 1.97512i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.9666 | − | 11.9666i | 0.783960 | − | 0.783960i | −0.196537 | − | 0.980497i | \(-0.562969\pi\) |
0.980497 | + | 0.196537i | \(0.0629694\pi\) | |||||||
\(234\) | − | 46.3334i | − | 3.02891i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −20.8223 | −1.35541 | ||||||||
\(237\) | −16.2478 | − | 16.2478i | −1.05541 | − | 1.05541i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.48331i | − | 0.484055i | −0.970269 | − | 0.242028i | \(-0.922188\pi\) | ||
0.970269 | − | 0.242028i | \(-0.0778125\pi\) | |||||||
\(240\) | −15.4833 | − | 19.4833i | −0.999444 | − | 1.25764i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −11.0000 | − | 11.0000i | −0.707107 | − | 0.707107i | ||||
\(243\) | −11.7390 | + | 11.7390i | −0.753057 | + | 0.753057i | ||||
\(244\) | 12.9525i | 0.829199i | ||||||||
\(245\) | 15.5511 | + | 1.77896i | 0.993520 | + | 0.113654i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.7750 | − | 11.7750i | −0.749227 | − | 0.749227i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 48.1916i | 3.05402i | ||||||||
\(250\) | 14.2804 | − | 6.78757i | 0.903170 | − | 0.429283i | ||||
\(251\) | −13.1982 | −0.833061 | −0.416530 | − | 0.909122i | \(-0.636754\pi\) | ||||
−0.416530 | + | 0.909122i | \(0.636754\pi\) | |||||||
\(252\) | 17.7417 | + | 17.7417i | 1.11762 | + | 1.11762i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 20.4499i | − | 1.28314i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −24.1916 | + | 19.2250i | −1.50030 | + | 1.19228i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.3129 | − | 12.3129i | −0.760695 | − | 0.760695i | ||||
\(263\) | 11.2250 | − | 11.2250i | 0.692161 | − | 0.692161i | −0.270546 | − | 0.962707i | \(-0.587204\pi\) |
0.962707 | + | 0.270546i | \(0.0872041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.01763 | 0.552906 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.0017i | 1.03661i | 0.855194 | + | 0.518307i | \(0.173438\pi\) | ||||
−0.855194 | + | 0.518307i | \(0.826562\pi\) | |||||||
\(270\) | −15.2250 | − | 1.74166i | −0.926562 | − | 0.105994i | ||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 35.9666 | − | 35.9666i | 2.17680 | − | 2.17680i | ||||
\(274\) | − | 3.03337i | − | 0.183253i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 53.0553 | 3.19355 | ||||||||
\(277\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(278\) | 5.32840 | − | 5.32840i | 0.319576 | − | 0.319576i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.90179 | − | 16.6248i | 0.113654 | − | 0.993520i | ||||
\(281\) | 14.9666 | 0.892834 | 0.446417 | − | 0.894825i | \(-0.352700\pi\) | ||||
0.446417 | + | 0.894825i | \(0.352700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.34441 | + | 2.34441i | −0.139361 | + | 0.139361i | −0.773345 | − | 0.633985i | \(-0.781418\pi\) |
0.633985 | + | 0.773345i | \(0.281418\pi\) | |||||||
\(284\) | − | 30.4499i | − | 1.80687i | ||||||
\(285\) | −11.7390 | + | 9.32894i | −0.695358 | + | 0.552599i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 18.9666 | − | 18.9666i | 1.11762 | − | 1.11762i | ||||
\(289\) | 17.0000i | 1.00000i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.1832 | + | 24.1832i | −1.41280 | + | 1.41280i | −0.674788 | + | 0.738011i | \(0.735765\pi\) |
−0.738011 | + | 0.674788i | \(0.764235\pi\) | |||||||
\(294\) | 27.5442i | 1.60641i | ||||||||
\(295\) | 23.1292 | + | 2.64586i | 1.34663 | + | 0.154048i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 65.8765i | − | 3.80974i | ||||||
\(300\) | 14.7230 | + | 23.6093i | 0.850032 | + | 1.36308i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 22.4499 | + | 22.4499i | 1.29185 | + | 1.29185i | ||||
\(303\) | −2.74166 | + | 2.74166i | −0.157504 | + | 0.157504i | ||||
\(304\) | − | 9.64025i | − | 0.552906i | ||||||
\(305\) | 1.64586 | − | 14.3875i | 0.0942415 | − | 0.823827i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.1987 | + | 17.1987i | 0.981582 | + | 0.981582i | 0.999833 | − | 0.0182515i | \(-0.00580994\pi\) |
−0.0182515 | + | 0.999833i | \(0.505810\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | −38.4499 | − | 38.4499i | −2.17680 | − | 2.17680i | ||||
\(313\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(314\) | 32.6269i | 1.84124i | ||||||||
\(315\) | −17.4528 | − | 21.9617i | −0.983356 | − | 1.23740i | ||||
\(316\) | −16.5167 | −0.929136 | ||||||||
\(317\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −17.7726 | − | 2.03310i | −0.993520 | − | 0.113654i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 25.2250 | + | 25.2250i | 1.40573 | + | 1.40573i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.48331i | 0.0824064i | ||||||||
\(325\) | 29.3147 | − | 18.2809i | 1.62609 | − | 1.01404i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 24.4945 | + | 24.4945i | 1.34431 | + | 1.34431i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 29.4460 | 1.60641 | ||||||||
\(337\) | 18.0000 | + | 18.0000i | 0.980522 | + | 0.980522i | 0.999814 | − | 0.0192914i | \(-0.00614103\pi\) |
−0.0192914 | + | 0.999814i | \(0.506141\pi\) | |||||||
\(338\) | −34.7417 | + | 34.7417i | −1.88970 | + | 1.88970i | ||||
\(339\) | 44.1690i | 2.39893i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −11.4277 | − | 11.4277i | −0.617939 | − | 0.617939i | ||||
\(343\) | −13.0958 | + | 13.0958i | −0.707107 | + | 0.707107i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −58.9333 | − | 6.74166i | −3.17286 | − | 0.362959i | ||||
\(346\) | −1.14786 | −0.0617092 | ||||||||
\(347\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 17.2644i | − | 0.924140i | −0.886843 | − | 0.462070i | \(-0.847107\pi\) | ||
0.886843 | − | 0.462070i | \(-0.152893\pi\) | |||||||
\(350\) | −4.22497 | + | 18.2250i | −0.225834 | + | 0.974166i | ||||
\(351\) | −33.4833 | −1.78721 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(354\) | 40.9666i | 2.17735i | ||||||||
\(355\) | −3.86923 | + | 33.8235i | −0.205357 | + | 1.79516i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.00000i | − | 0.316668i | −0.987386 | − | 0.158334i | \(-0.949388\pi\) | ||
0.987386 | − | 0.158334i | \(-0.0506123\pi\) | |||||||
\(360\) | −23.4780 | + | 18.6579i | −1.23740 | + | 0.983356i | ||||
\(361\) | 13.1916 | 0.694295 | ||||||||
\(362\) | −26.9046 | − | 26.9046i | −1.41407 | − | 1.41407i | ||||
\(363\) | −21.6419 | + | 21.6419i | −1.13590 | + | 1.13590i | ||||
\(364\) | − | 36.5618i | − | 1.91636i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 25.4833 | 1.33203 | ||||||||
\(367\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(368\) | 26.9666 | − | 26.9666i | 1.40573 | − | 1.40573i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.3541 | − | 28.0958i | −0.689605 | − | 1.45086i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 12.8212 | − | 12.8212i | 0.659451 | − | 0.659451i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | −1.22497 | + | 10.7083i | −0.0628397 | + | 0.549324i | ||||
\(381\) | −40.2341 | −2.06125 | ||||||||
\(382\) | −4.77503 | − | 4.77503i | −0.244312 | − | 0.244312i | ||||
\(383\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(384\) | − | 31.4791i | − | 1.60641i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.0000 | 0.610784 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 37.8240 | + | 47.5956i | 1.91529 | + | 2.41010i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 14.0000 | + | 14.0000i | 0.707107 | + | 0.707107i | ||||
\(393\) | −24.2250 | + | 24.2250i | −1.22199 | + | 1.22199i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.3466 | + | 2.09875i | 0.923116 | + | 0.105600i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.1181 | + | 28.1181i | 1.41121 | + | 1.41121i | 0.751680 | + | 0.659528i | \(0.229244\pi\) |
0.659528 | + | 0.751680i | \(0.270756\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 17.7417i | − | 0.888194i | ||||||
\(400\) | 19.4833 | + | 4.51669i | 0.974166 | + | 0.225834i | ||||
\(401\) | 14.7750 | 0.737830 | 0.368915 | − | 0.929463i | \(-0.379729\pi\) | ||||
0.368915 | + | 0.929463i | \(0.379729\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.78703i | 0.138660i | ||||||||
\(405\) | 0.188483 | − | 1.64765i | 0.00936578 | − | 0.0818724i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.96798 | −0.294379 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.4775 | + | 19.4775i | −0.958423 | + | 0.958423i | ||||
\(414\) | − | 63.9333i | − | 3.14215i | ||||||
\(415\) | −24.0958 | − | 30.3208i | −1.18282 | − | 1.48839i | ||||
\(416\) | −39.0862 | −1.91636 | ||||||||
\(417\) | −10.4833 | − | 10.4833i | −0.513370 | − | 0.513370i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 26.7733i | − | 1.30796i | −0.756511 | − | 0.653981i | \(-0.773098\pi\) | ||
0.756511 | − | 0.653981i | \(-0.226902\pi\) | |||||||
\(420\) | −32.7083 | − | 3.74166i | −1.59600 | − | 0.182574i | ||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −59.9085 | −2.90258 | ||||||||
\(427\) | 12.1160 | + | 12.1160i | 0.586333 | + | 0.586333i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.0000 | −0.867029 | −0.433515 | − | 0.901146i | \(-0.642727\pi\) | ||||
−0.433515 | + | 0.901146i | \(0.642727\pi\) | |||||||
\(432\) | −13.7064 | − | 13.7064i | −0.659451 | − | 0.659451i | ||||
\(433\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.2478 | − | 16.2478i | −0.777238 | − | 0.777238i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 33.1916 | 1.58055 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14.9666 | − | 14.9666i | 0.707107 | − | 0.707107i | ||||
\(449\) | 29.9333i | 1.41264i | 0.707894 | + | 0.706319i | \(0.249646\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 28.4499 | − | 17.7417i | 1.34114 | − | 0.836350i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 22.4499 | + | 22.4499i | 1.05596 | + | 1.05596i | ||||
\(453\) | 44.1690 | − | 44.1690i | 2.07524 | − | 2.07524i | ||||
\(454\) | 34.1348i | 1.60203i | ||||||||
\(455\) | −4.64586 | + | 40.6125i | −0.217801 | + | 1.90394i | ||||
\(456\) | −18.9666 | −0.888194 | ||||||||
\(457\) | 3.74166 | + | 3.74166i | 0.175027 | + | 0.175027i | 0.789184 | − | 0.614157i | \(-0.210504\pi\) |
−0.614157 | + | 0.789184i | \(0.710504\pi\) | |||||||
\(458\) | 30.0856 | − | 30.0856i | 1.40581 | − | 1.40581i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −33.3809 | + | 26.5276i | −1.55639 | + | 1.23686i | ||||
\(461\) | −41.6276 | −1.93879 | −0.969395 | − | 0.245505i | \(-0.921046\pi\) | ||||
−0.969395 | + | 0.245505i | \(0.921046\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0000 | − | 24.0000i | 1.11537 | − | 1.11537i | 0.122963 | − | 0.992411i | \(-0.460760\pi\) |
0.992411 | − | 0.122963i | \(-0.0392398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.9333 | −1.10869 | ||||||||
\(467\) | −18.8548 | − | 18.8548i | −0.872498 | − | 0.872498i | 0.120246 | − | 0.992744i | \(-0.461632\pi\) |
−0.992744 | + | 0.120246i | \(0.961632\pi\) | |||||||
\(468\) | −46.3334 | + | 46.3334i | −2.14176 | + | 2.14176i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 64.1916 | 2.95779 | ||||||||
\(472\) | 20.8223 | + | 20.8223i | 0.958423 | + | 0.958423i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 32.4956i | 1.49257i | ||||||||
\(475\) | 2.72137 | − | 11.7390i | 0.124865 | − | 0.538622i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.48331 | + | 7.48331i | −0.342279 | + | 0.342279i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | −4.00000 | + | 34.9666i | −0.182574 | + | 1.59600i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 49.6287 | − | 49.6287i | 2.25818 | − | 2.25818i | ||||
\(484\) | 22.0000i | 1.00000i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 23.4780 | 1.06498 | ||||||||
\(487\) | 30.2250 | + | 30.2250i | 1.36962 | + | 1.36962i | 0.860972 | + | 0.508652i | \(0.169856\pi\) |
0.508652 | + | 0.860972i | \(0.330144\pi\) | |||||||
\(488\) | 12.9525 | − | 12.9525i | 0.586333 | − | 0.586333i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.7721 | − | 17.3300i | −0.622160 | − | 0.782890i | ||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 23.5501i | 1.05957i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −28.4833 | − | 28.4833i | −1.27765 | − | 1.27765i | ||||
\(498\) | 48.1916 | − | 48.1916i | 2.15952 | − | 2.15952i | ||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | −21.0679 | − | 7.49280i | −0.942187 | − | 0.335088i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.1982 | + | 13.1982i | 0.589063 | + | 0.589063i | ||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | − | 35.4833i | − | 1.58055i | ||||||
\(505\) | 0.354143 | − | 3.09580i | 0.0157592 | − | 0.137761i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 68.3522 | + | 68.3522i | 3.03563 | + | 3.03563i | ||||
\(508\) | −20.4499 | + | 20.4499i | −0.907320 | + | 0.907320i | ||||
\(509\) | 25.0028i | 1.10823i | 0.832440 | + | 0.554115i | \(0.186943\pi\) | ||||
−0.832440 | + | 0.554115i | \(0.813057\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | −8.25834 | + | 8.25834i | −0.364615 | + | 0.364615i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.25834i | 0.0991302i | ||||||||
\(520\) | 43.4166 | + | 4.96663i | 1.90394 | + | 0.217801i | ||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.7246 | + | 26.7246i | −1.16859 | + | 1.16859i | −0.186044 | + | 0.982541i | \(0.559567\pi\) |
−0.982541 | + | 0.186044i | \(0.940433\pi\) | |||||||
\(524\) | 24.6259i | 1.07579i | ||||||||
\(525\) | 35.8566 | + | 8.31239i | 1.56491 | + | 0.362782i | ||||
\(526\) | −22.4499 | −0.978864 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 67.8999i | − | 2.95217i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 49.3661 | 2.14230 | ||||||||
\(532\) | −9.01763 | − | 9.01763i | −0.390964 | − | 0.390964i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.0017 | − | 17.0017i | 0.732997 | − | 0.732997i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 13.4833 | + | 16.9666i | 0.580229 | + | 0.730127i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −52.9333 | + | 52.9333i | −2.27158 | + | 2.27158i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −71.9333 | −3.07846 | ||||||||
\(547\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(548\) | −3.03337 | + | 3.03337i | −0.129579 | + | 0.129579i | ||||
\(549\) | − | 30.7082i | − | 1.31059i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −53.0553 | − | 53.0553i | −2.25818 | − | 2.25818i | ||||
\(553\) | −15.4499 | + | 15.4499i | −0.656998 | + | 0.656998i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.6568 | −0.451949 | ||||||||
\(557\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −18.5266 | + | 14.7230i | −0.782890 | + | 0.622160i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.9666 | − | 14.9666i | −0.631329 | − | 0.631329i | ||||
\(563\) | −7.05018 | + | 7.05018i | −0.297130 | + | 0.297130i | −0.839889 | − | 0.542759i | \(-0.817380\pi\) |
0.542759 | + | 0.839889i | \(0.317380\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.0845 | − | 27.7898i | −0.929101 | − | 1.16913i | ||||
\(566\) | 4.68881 | 0.197086 | ||||||||
\(567\) | 1.38751 | + | 1.38751i | 0.0582701 | + | 0.0582701i | ||||
\(568\) | −30.4499 | + | 30.4499i | −1.27765 | + | 1.27765i | ||||
\(569\) | 35.6749i | 1.49557i | 0.663941 | + | 0.747785i | \(0.268883\pi\) | ||||
−0.663941 | + | 0.747785i | \(0.731117\pi\) | |||||||
\(570\) | 21.0679 | + | 2.41006i | 0.882439 | + | 0.100946i | ||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.39459 | + | 9.39459i | −0.392465 | + | 0.392465i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 40.4499 | − | 25.2250i | 1.68688 | − | 1.05195i | ||||
\(576\) | −37.9333 | −1.58055 | ||||||||
\(577\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(578\) | 17.0000 | − | 17.0000i | 0.707107 | − | 0.707107i | ||||
\(579\) | − | 23.6093i | − | 0.981169i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 45.8251 | 1.90115 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 57.3541 | − | 45.5791i | 2.37130 | − | 1.88446i | ||||
\(586\) | 48.3665 | 1.99800 | ||||||||
\(587\) | 30.6595 | + | 30.6595i | 1.26545 | + | 1.26545i | 0.948412 | + | 0.317041i | \(0.102689\pi\) |
0.317041 | + | 0.948412i | \(0.397311\pi\) | |||||||
\(588\) | 27.5442 | − | 27.5442i | 1.13590 | − | 1.13590i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −20.4833 | − | 25.7750i | −0.843285 | − | 1.06114i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −65.8765 | + | 65.8765i | −2.69389 | + | 2.69389i | ||||
\(599\) | 25.6749i | 1.04905i | 0.851395 | + | 0.524524i | \(0.175757\pi\) | ||||
−0.851395 | + | 0.524524i | \(0.824243\pi\) | |||||||
\(600\) | 8.88632 | − | 38.3323i | 0.362782 | − | 1.56491i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 44.8999i | − | 1.82695i | ||||||
\(605\) | 2.79551 | − | 24.4374i | 0.113654 | − | 0.993520i | ||||
\(606\) | 5.48331 | 0.222744 | ||||||||
\(607\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(608\) | −9.64025 | + | 9.64025i | −0.390964 | + | 0.390964i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.0334 | + | 12.7417i | −0.649172 | + | 0.515895i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(614\) | − | 34.3974i | − | 1.38817i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.6749 | − | 33.6749i | −1.35570 | − | 1.35570i | −0.879143 | − | 0.476558i | \(-0.841884\pi\) |
−0.476558 | − | 0.879143i | \(-0.658116\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.9377i | − | 1.16310i | −0.813509 | − | 0.581552i | \(-0.802446\pi\) | ||
0.813509 | − | 0.581552i | \(-0.197554\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −46.2021 | −1.85402 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 76.8999i | 3.07846i | ||||||||
\(625\) | 22.4499 | + | 11.0000i | 0.897998 | + | 0.440000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 32.6269 | − | 32.6269i | 1.30196 | − | 1.30196i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −4.50881 | + | 39.4145i | −0.179635 | + | 1.57031i | ||||
\(631\) | 2.19160 | 0.0872463 | 0.0436231 | − | 0.999048i | \(-0.486110\pi\) | ||||
0.0436231 | + | 0.999048i | \(0.486110\pi\) | |||||||
\(632\) | 16.5167 | + | 16.5167i | 0.656998 | + | 0.656998i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.3141 | − | 20.1170i | 1.00456 | − | 0.798320i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.2004 | − | 34.2004i | −1.35507 | − | 1.35507i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 72.1916i | 2.85586i | ||||||||
\(640\) | 15.7395 | + | 19.8057i | 0.622160 | + | 0.782890i | ||||
\(641\) | −45.2250 | −1.78628 | −0.893140 | − | 0.449780i | \(-0.851502\pi\) | ||||
−0.893140 | + | 0.449780i | \(0.851502\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.11530 | − | 3.11530i | 0.122855 | − | 0.122855i | −0.643006 | − | 0.765861i | \(-0.722313\pi\) |
0.765861 | + | 0.643006i | \(0.222313\pi\) | |||||||
\(644\) | − | 50.4499i | − | 1.98801i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | 1.48331 | − | 1.48331i | 0.0582701 | − | 0.0582701i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −47.5956 | − | 11.0338i | −1.86685 | − | 0.432780i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.12917 | − | 27.3541i | 0.122267 | − | 1.06881i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.4442 | −0.484025 | −0.242012 | − | 0.970273i | \(-0.577807\pi\) | ||||
−0.242012 | + | 0.970273i | \(0.577807\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 48.9891i | − | 1.90115i | ||||||
\(665\) | 8.87083 | + | 11.1625i | 0.343996 | + | 0.432865i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −29.4460 | − | 29.4460i | −1.13590 | − | 1.13590i | ||||
\(673\) | −35.4499 | + | 35.4499i | −1.36649 | + | 1.36649i | −0.501113 | + | 0.865382i | \(0.667076\pi\) |
−0.865382 | + | 0.501113i | \(0.832924\pi\) | |||||||
\(674\) | − | 36.0000i | − | 1.38667i | ||||||
\(675\) | −12.8212 | − | 20.5597i | −0.493488 | − | 0.791342i | ||||
\(676\) | 69.4833 | 2.67244 | ||||||||
\(677\) | −35.9879 | − | 35.9879i | −1.38313 | − | 1.38313i | −0.839008 | − | 0.544119i | \(-0.816864\pi\) |
−0.544119 | − | 0.839008i | \(-0.683136\pi\) | |||||||
\(678\) | 44.1690 | − | 44.1690i | 1.69630 | − | 1.69630i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 67.1582 | 2.57351 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(684\) | 22.8554i | 0.873897i | ||||||||
\(685\) | 3.75488 | − | 2.98399i | 0.143467 | − | 0.114012i | ||||
\(686\) | 26.1916 | 1.00000 | ||||||||
\(687\) | −59.1916 | − | 59.1916i | −2.25830 | − | 2.25830i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 52.1916 | + | 65.6749i | 1.98690 | + | 2.50020i | ||||
\(691\) | 46.5790 | 1.77195 | 0.885975 | − | 0.463733i | \(-0.153490\pi\) | ||||
0.885975 | + | 0.463733i | \(0.153490\pi\) | |||||||
\(692\) | 1.14786 | + | 1.14786i | 0.0436350 | + | 0.0436350i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.8375 | + | 1.35414i | 0.449020 | + | 0.0513656i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −17.2644 | + | 17.2644i | −0.653466 | + | 0.653466i | ||||
\(699\) | 47.0873i | 1.78101i | ||||||||
\(700\) | 22.4499 | − | 14.0000i | 0.848528 | − | 0.529150i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 33.4833 | + | 33.4833i | 1.26375 | + | 1.26375i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.60703 | + | 2.60703i | 0.0980473 | + | 0.0980473i | ||||
\(708\) | 40.9666 | − | 40.9666i | 1.53962 | − | 1.53962i | ||||
\(709\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | 37.6927 | − | 29.9543i | 1.41458 | − | 1.12416i | ||||
\(711\) | 39.1582 | 1.46855 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.7230 | + | 14.7230i | 0.549840 | + | 0.549840i | ||||
\(718\) | −6.00000 | + | 6.00000i | −0.223918 | + | 0.223918i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 42.1359 | + | 4.82012i | 1.57031 | + | 0.179635i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −13.1916 | − | 13.1916i | −0.490941 | − | 0.490941i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 53.8092i | 1.99980i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 43.2837 | 1.60641 | ||||||||
\(727\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(728\) | −36.5618 | + | 36.5618i | −1.35507 | + | 1.35507i | ||||
\(729\) | − | 43.9666i | − | 1.62839i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −25.4833 | − | 25.4833i | −0.941890 | − | 0.941890i | ||||
\(733\) | −19.1005 | + | 19.1005i | −0.705493 | + | 0.705493i | −0.965584 | − | 0.260091i | \(-0.916247\pi\) |
0.260091 | + | 0.965584i | \(0.416247\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −34.0958 | + | 27.0958i | −1.25764 | + | 0.999444i | ||||
\(736\) | −53.9333 | −1.98801 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 46.3334 | 1.70210 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.2583 | − | 23.2583i | 0.853266 | − | 0.853266i | −0.137268 | − | 0.990534i | \(-0.543832\pi\) |
0.990534 | + | 0.137268i | \(0.0438322\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −58.0724 | − | 58.0724i | −2.12476 | − | 2.12476i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −14.7417 | + | 41.4499i | −0.538289 | + | 1.51354i | ||||
\(751\) | −22.4499 | −0.819210 | −0.409605 | − | 0.912263i | \(-0.634333\pi\) | ||||
−0.409605 | + | 0.912263i | \(0.634333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.9666 | − | 25.9666i | 0.946277 | − | 0.946277i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.70536 | + | 49.8743i | −0.207639 | + | 1.81511i | ||||
\(756\) | −25.6424 | −0.932605 | ||||||||
\(757\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.9333 | − | 9.48331i | 0.432865 | − | 0.343996i | ||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 40.2341 | + | 40.2341i | 1.45753 | + | 1.45753i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 9.55006i | 0.345509i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −50.8665 | − | 50.8665i | −1.83668 | − | 1.83668i | ||||
\(768\) | −31.4791 | + | 31.4791i | −1.13590 | + | 1.13590i | ||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.0000 | − | 12.0000i | −0.431889 | − | 0.431889i | ||||
\(773\) | −39.1519 | + | 39.1519i | −1.40820 | + | 1.40820i | −0.638932 | + | 0.769263i | \(0.720624\pi\) |
−0.769263 | + | 0.638932i | \(0.779376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 9.77156 | − | 85.4196i | 0.349878 | − | 3.05851i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 28.0000i | − | 1.00000i | ||||||
\(785\) | −40.3875 | + | 32.0958i | −1.44149 | + | 1.14555i | ||||
\(786\) | 48.4499 | 1.72815 | ||||||||
\(787\) | −38.5293 | − | 38.5293i | −1.37342 | − | 1.37342i | −0.855321 | − | 0.518099i | \(-0.826640\pi\) |
−0.518099 | − | 0.855321i | \(-0.673360\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 44.1690i | 1.57246i | ||||||||
\(790\) | −16.2478 | − | 20.4453i | −0.578071 | − | 0.727412i | ||||
\(791\) | 42.0000 | 1.49335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.6415 | + | 31.6415i | −1.12362 | + | 1.12362i | ||||
\(794\) | − | 56.2362i | − | 1.99575i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.3318 | + | 34.3318i | 1.21609 | + | 1.21609i | 0.968989 | + | 0.247104i | \(0.0794790\pi\) |
0.247104 | + | 0.968989i | \(0.420521\pi\) | |||||||
\(798\) | −17.7417 | + | 17.7417i | −0.628048 | + | 0.628048i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −14.9666 | − | 24.0000i | −0.529150 | − | 0.848528i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.7750 | − | 14.7750i | −0.521724 | − | 0.521724i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.41060 | + | 56.0393i | −0.225944 | + | 1.97512i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −33.4499 | − | 33.4499i | −1.17749 | − | 1.17749i | ||||
\(808\) | 2.78703 | − | 2.78703i | 0.0980473 | − | 0.0980473i | ||||
\(809\) | 55.6749i | 1.95743i | 0.205234 | + | 0.978713i | \(0.434204\pi\) | ||||
−0.205234 | + | 0.978713i | \(0.565796\pi\) | |||||||
\(810\) | −1.83613 | + | 1.45917i | −0.0645151 | + | 0.0512699i | ||||
\(811\) | −56.2193 | −1.97413 | −0.987063 | − | 0.160333i | \(-0.948743\pi\) | ||||
−0.987063 | + | 0.160333i | \(0.948743\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 86.6818i | 3.02891i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 5.96798 | + | 5.96798i | 0.208157 | + | 0.208157i | ||||
\(823\) | −36.0000 | + | 36.0000i | −1.25488 | + | 1.25488i | −0.301376 | + | 0.953506i | \(0.597446\pi\) |
−0.953506 | + | 0.301376i | \(0.902554\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 38.9549 | 1.35541 | ||||||||
\(827\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(828\) | −63.9333 | + | 63.9333i | −2.22183 | + | 2.22183i | ||||
\(829\) | − | 53.6949i | − | 1.86490i | −0.361299 | − | 0.932450i | \(-0.617667\pi\) | ||
0.361299 | − | 0.932450i | \(-0.382333\pi\) | |||||||
\(830\) | −6.22497 | + | 54.4166i | −0.216072 | + | 1.88883i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 39.0862 | + | 39.0862i | 1.35507 | + | 1.35507i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 20.9666i | 0.726015i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −26.7733 | + | 26.7733i | −0.924868 | + | 0.924868i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 28.9666 | + | 36.4499i | 0.999444 | + | 1.25764i | ||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29.4460 | + | 29.4460i | −1.01417 | + | 1.01417i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −77.1813 | − | 8.82914i | −2.65512 | − | 0.303732i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.5791 | + | 20.5791i | 0.707107 | + | 0.707107i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 9.22497i | − | 0.316600i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 59.9085 | + | 59.9085i | 2.05243 | + | 2.05243i | ||||
\(853\) | 39.9228 | − | 39.9228i | 1.36693 | − | 1.36693i | 0.502148 | − | 0.864782i | \(-0.332543\pi\) |
0.864782 | − | 0.502148i | \(-0.167457\pi\) | |||||||
\(854\) | − | 24.2319i | − | 0.829199i | ||||||
\(855\) | 2.90420 | − | 25.3875i | 0.0993215 | − | 0.868235i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.7589i | 1.42480i | 0.701776 | + | 0.712398i | \(0.252391\pi\) | ||||
−0.701776 | + | 0.712398i | \(0.747609\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0000 | + | 18.0000i | 0.613082 | + | 0.613082i | ||||
\(863\) | 11.2250 | − | 11.2250i | 0.382102 | − | 0.382102i | −0.489757 | − | 0.871859i | \(-0.662914\pi\) |
0.871859 | + | 0.489757i | \(0.162914\pi\) | |||||||
\(864\) | 27.4129i | 0.932605i | ||||||||
\(865\) | −1.12917 | − | 1.42088i | −0.0383930 | − | 0.0483115i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.4465 | − | 33.4465i | −1.13590 | − | 1.13590i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.4956i | 1.09918i | ||||||||
\(875\) | −26.7161 | + | 12.6984i | −0.903170 | + | 0.429283i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 95.1582i | − | 3.20961i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −33.1916 | − | 33.1916i | −1.11762 | − | 1.11762i | ||||
\(883\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −50.7109 | + | 40.2997i | −1.70463 | + | 1.35466i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.2583i | 1.28314i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −29.9333 | −1.00000 | ||||||||
\(897\) | 129.608 | + | 129.608i | 4.32749 | + | 4.32749i | ||||
\(898\) | 29.9333 | − | 29.9333i | 0.998886 | − | 0.998886i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −46.1916 | − | 10.7083i | −1.53972 | − | 0.356943i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 44.8999i | − | 1.49335i | ||||||
\(905\) | 6.83746 | − | 59.7707i | 0.227285 | − | 1.98685i | ||||
\(906\) | −88.3379 | −2.93483 | ||||||||
\(907\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(908\) | 34.1348 | − | 34.1348i | 1.13280 | − | 1.13280i | ||||
\(909\) | − | 6.60756i | − | 0.219159i | ||||||
\(910\) | 45.2583 | − | 35.9666i | 1.50030 | − | 1.19228i | ||||
\(911\) | 52.3832 | 1.73553 | 0.867766 | − | 0.496972i | \(-0.165555\pi\) | ||||
0.867766 | + | 0.496972i | \(0.165555\pi\) | |||||||
\(912\) | 18.9666 | + | 18.9666i | 0.628048 | + | 0.628048i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 7.48331i | − | 0.247526i | ||||||
\(915\) | 25.0685 | + | 31.5447i | 0.828738 | + | 1.04284i | ||||
\(916\) | −60.1711 | −1.98811 | ||||||||
\(917\) | 23.0354 | + | 23.0354i | 0.760695 | + | 0.760695i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 29.1582i | − | 0.961841i | −0.876764 | − | 0.480921i | \(-0.840303\pi\) | ||
0.876764 | − | 0.480921i | \(-0.159697\pi\) | |||||||
\(920\) | 59.9085 | + | 6.85322i | 1.97512 | + | 0.225944i | ||||
\(921\) | −67.6749 | −2.22996 | ||||||||
\(922\) | 41.6276 | + | 41.6276i | 1.37093 | + | 1.37093i | ||||
\(923\) | 74.3858 | − | 74.3858i | 2.44844 | − | 2.44844i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −48.0000 | −1.57738 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.8704 | −0.552906 | ||||||||
\(932\) | 23.9333 | + | 23.9333i | 0.783960 | + | 0.783960i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37.7097i | 1.23390i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 92.6667 | 3.02891 | ||||||||
\(937\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 61.1707 | 1.99411 | 0.997054 | − | 0.0767020i | \(-0.0244390\pi\) | ||||
0.997054 | + | 0.0767020i | \(0.0244390\pi\) | |||||||
\(942\) | −64.1916 | − | 64.1916i | −2.09148 | − | 2.09148i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 41.6446i | − | 1.35541i | ||||||
\(945\) | 28.4833 | + | 3.25834i | 0.926562 | + | 0.105994i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(948\) | 32.4956 | − | 32.4956i | 1.05541 | − | 1.05541i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −14.4604 | + | 9.01763i | −0.469156 | + | 0.292570i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.9666 | − | 41.9666i | 1.35943 | − | 1.35943i | 0.484817 | − | 0.874616i | \(-0.338886\pi\) |
0.874616 | − | 0.484817i | \(-0.161114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.21351 | − | 10.6081i | 0.0392683 | − | 0.343270i | ||||
\(956\) | 14.9666 | 0.484055 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.67492i | 0.183253i | ||||||||
\(960\) | 38.9666 | − | 30.9666i | 1.25764 | − | 0.999444i | ||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.8047 | + | 14.8543i | 0.380005 | + | 0.478177i | ||||
\(966\) | −99.2573 | −3.19355 | ||||||||
\(967\) | 40.2250 | + | 40.2250i | 1.29355 | + | 1.29355i | 0.932577 | + | 0.360971i | \(0.117555\pi\) |
0.360971 | + | 0.932577i | \(0.382445\pi\) | |||||||
\(968\) | 22.0000 | − | 22.0000i | 0.707107 | − | 0.707107i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57.6298 | −1.84943 | −0.924713 | − | 0.380664i | \(-0.875695\pi\) | ||||
−0.924713 | + | 0.380664i | \(0.875695\pi\) | |||||||
\(972\) | −23.4780 | − | 23.4780i | −0.753057 | − | 0.753057i | ||||
\(973\) | −9.96852 | + | 9.96852i | −0.319576 | + | 0.319576i | ||||
\(974\) | − | 60.4499i | − | 1.93694i | ||||||
\(975\) | −21.7083 | + | 93.6415i | −0.695222 | + | 2.99893i | ||||
\(976\) | −25.9050 | −0.829199 | ||||||||
\(977\) | 38.9333 | + | 38.9333i | 1.24559 | + | 1.24559i | 0.957650 | + | 0.287936i | \(0.0929689\pi\) |
0.287936 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.55792 | + | 31.1021i | −0.113654 | + | 0.993520i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.5501 | − | 23.5501i | 0.749227 | − | 0.749227i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 62.1916 | 1.97558 | 0.987791 | − | 0.155787i | \(-0.0497914\pi\) | ||||
0.987791 | + | 0.155787i | \(0.0497914\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 56.9666i | 1.80687i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −96.3832 | −3.05402 | ||||||||
\(997\) | 19.7401 | + | 19.7401i | 0.625174 | + | 0.625174i | 0.946850 | − | 0.321675i | \(-0.104246\pi\) |
−0.321675 | + | 0.946850i | \(0.604246\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 280.2.s.a.237.1 | yes | 8 | |
4.3 | odd | 2 | 1120.2.w.a.657.4 | 8 | |||
5.3 | odd | 4 | inner | 280.2.s.a.13.1 | ✓ | 8 | |
7.6 | odd | 2 | inner | 280.2.s.a.237.4 | yes | 8 | |
8.3 | odd | 2 | 1120.2.w.a.657.1 | 8 | |||
8.5 | even | 2 | inner | 280.2.s.a.237.4 | yes | 8 | |
20.3 | even | 4 | 1120.2.w.a.433.4 | 8 | |||
28.27 | even | 2 | 1120.2.w.a.657.1 | 8 | |||
35.13 | even | 4 | inner | 280.2.s.a.13.4 | yes | 8 | |
40.3 | even | 4 | 1120.2.w.a.433.1 | 8 | |||
40.13 | odd | 4 | inner | 280.2.s.a.13.4 | yes | 8 | |
56.13 | odd | 2 | CM | 280.2.s.a.237.1 | yes | 8 | |
56.27 | even | 2 | 1120.2.w.a.657.4 | 8 | |||
140.83 | odd | 4 | 1120.2.w.a.433.1 | 8 | |||
280.13 | even | 4 | inner | 280.2.s.a.13.1 | ✓ | 8 | |
280.83 | odd | 4 | 1120.2.w.a.433.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.s.a.13.1 | ✓ | 8 | 5.3 | odd | 4 | inner | |
280.2.s.a.13.1 | ✓ | 8 | 280.13 | even | 4 | inner | |
280.2.s.a.13.4 | yes | 8 | 35.13 | even | 4 | inner | |
280.2.s.a.13.4 | yes | 8 | 40.13 | odd | 4 | inner | |
280.2.s.a.237.1 | yes | 8 | 1.1 | even | 1 | trivial | |
280.2.s.a.237.1 | yes | 8 | 56.13 | odd | 2 | CM | |
280.2.s.a.237.4 | yes | 8 | 7.6 | odd | 2 | inner | |
280.2.s.a.237.4 | yes | 8 | 8.5 | even | 2 | inner | |
1120.2.w.a.433.1 | 8 | 40.3 | even | 4 | |||
1120.2.w.a.433.1 | 8 | 140.83 | odd | 4 | |||
1120.2.w.a.433.4 | 8 | 20.3 | even | 4 | |||
1120.2.w.a.433.4 | 8 | 280.83 | odd | 4 | |||
1120.2.w.a.657.1 | 8 | 8.3 | odd | 2 | |||
1120.2.w.a.657.1 | 8 | 28.27 | even | 2 | |||
1120.2.w.a.657.4 | 8 | 4.3 | odd | 2 | |||
1120.2.w.a.657.4 | 8 | 56.27 | even | 2 |