Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(201,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 10x^{8} - 12x^{7} + 85x^{6} - 70x^{5} + 186x^{4} - 110x^{3} + 285x^{2} - 150x + 100 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 501.3 | ||
Root | \(0.341187 + 0.590953i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.501 |
Dual form | 950.2.e.n.201.3 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.341187 | + | 0.590953i | 0.196984 | + | 0.341187i | 0.947549 | − | 0.319610i | \(-0.103552\pi\) |
−0.750565 | + | 0.660797i | \(0.770218\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.341187 | − | 0.590953i | 0.139289 | − | 0.241256i | ||||
\(7\) | −0.317626 | −0.120051 | −0.0600256 | − | 0.998197i | \(-0.519118\pi\) | ||||
−0.0600256 | + | 0.998197i | \(0.519118\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.26718 | − | 2.19482i | 0.422394 | − | 0.731608i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.31087 | −1.29978 | −0.649889 | − | 0.760029i | \(-0.725184\pi\) | ||||
−0.649889 | + | 0.760029i | \(0.725184\pi\) | |||||||
\(12\) | −0.682374 | −0.196984 | ||||||||
\(13\) | −3.14836 | + | 5.45312i | −0.873198 | + | 1.51242i | −0.0145275 | + | 0.999894i | \(0.504624\pi\) |
−0.858670 | + | 0.512528i | \(0.828709\pi\) | |||||||
\(14\) | 0.158813 | + | 0.275072i | 0.0424445 | + | 0.0735161i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.0669268 | + | 0.115921i | 0.0162321 | + | 0.0281149i | 0.874027 | − | 0.485877i | \(-0.161500\pi\) |
−0.857795 | + | 0.513992i | \(0.828166\pi\) | |||||||
\(18\) | −2.53437 | −0.597356 | ||||||||
\(19\) | −4.05310 | + | 1.60387i | −0.929844 | + | 0.367953i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.108370 | − | 0.187702i | −0.0236482 | − | 0.0409599i | ||||
\(22\) | 2.15544 | + | 3.73333i | 0.459541 | + | 0.795948i | ||||
\(23\) | −1.98955 | + | 3.44600i | −0.414849 | + | 0.718540i | −0.995413 | − | 0.0956753i | \(-0.969499\pi\) |
0.580564 | + | 0.814215i | \(0.302832\pi\) | |||||||
\(24\) | 0.341187 | + | 0.590953i | 0.0696445 | + | 0.120628i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.29672 | 1.23489 | ||||||||
\(27\) | 3.77651 | 0.726789 | ||||||||
\(28\) | 0.158813 | − | 0.275072i | 0.0300128 | − | 0.0519837i | ||||
\(29\) | 4.57435 | − | 7.92301i | 0.849436 | − | 1.47127i | −0.0322757 | − | 0.999479i | \(-0.510275\pi\) |
0.881712 | − | 0.471788i | \(-0.156391\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.98584 | −0.536274 | −0.268137 | − | 0.963381i | \(-0.586408\pi\) | ||||
−0.268137 | + | 0.963381i | \(0.586408\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.47081 | − | 2.54753i | −0.256036 | − | 0.443467i | ||||
\(34\) | 0.0669268 | − | 0.115921i | 0.0114778 | − | 0.0198802i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.26718 | + | 2.19482i | 0.211197 | + | 0.365804i | ||||
\(37\) | −5.07323 | −0.834033 | −0.417017 | − | 0.908899i | \(-0.636924\pi\) | ||||
−0.417017 | + | 0.908899i | \(0.636924\pi\) | |||||||
\(38\) | 3.41554 | + | 2.70815i | 0.554074 | + | 0.439320i | ||||
\(39\) | −4.29672 | −0.688026 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.433073 | + | 0.750105i | 0.0676347 | + | 0.117147i | 0.897860 | − | 0.440282i | \(-0.145121\pi\) |
−0.830225 | + | 0.557428i | \(0.811788\pi\) | |||||||
\(42\) | −0.108370 | + | 0.187702i | −0.0167218 | + | 0.0289631i | ||||
\(43\) | −2.85199 | − | 4.93979i | −0.434925 | − | 0.753311i | 0.562365 | − | 0.826889i | \(-0.309892\pi\) |
−0.997289 | + | 0.0735777i | \(0.976558\pi\) | |||||||
\(44\) | 2.15544 | − | 3.73333i | 0.324944 | − | 0.562820i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.97909 | 0.586685 | ||||||||
\(47\) | −6.48617 | + | 11.2344i | −0.946105 | + | 1.63870i | −0.192582 | + | 0.981281i | \(0.561686\pi\) |
−0.753523 | + | 0.657421i | \(0.771647\pi\) | |||||||
\(48\) | 0.341187 | − | 0.590953i | 0.0492461 | − | 0.0852968i | ||||
\(49\) | −6.89911 | −0.985588 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0456691 | + | 0.0791012i | −0.00639495 | + | 0.0110764i | ||||
\(52\) | −3.14836 | − | 5.45312i | −0.436599 | − | 0.756211i | ||||
\(53\) | −3.96261 | + | 6.86344i | −0.544306 | + | 0.942766i | 0.454344 | + | 0.890826i | \(0.349874\pi\) |
−0.998650 | + | 0.0519397i | \(0.983460\pi\) | |||||||
\(54\) | −1.88825 | − | 3.27055i | −0.256959 | − | 0.445066i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.317626 | −0.0424445 | ||||||||
\(57\) | −2.33068 | − | 1.84797i | −0.308706 | − | 0.244770i | ||||
\(58\) | −9.14871 | −1.20128 | ||||||||
\(59\) | 4.80717 | + | 8.32627i | 0.625841 | + | 1.08399i | 0.988378 | + | 0.152018i | \(0.0485772\pi\) |
−0.362537 | + | 0.931969i | \(0.618089\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.08711 | + | 5.34704i | −0.395264 | + | 0.684618i | −0.993135 | − | 0.116975i | \(-0.962680\pi\) |
0.597871 | + | 0.801593i | \(0.296014\pi\) | |||||||
\(62\) | 1.49292 | + | 2.58582i | 0.189601 | + | 0.328399i | ||||
\(63\) | −0.402490 | + | 0.697133i | −0.0507090 | + | 0.0878305i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.47081 | + | 2.54753i | −0.181045 | + | 0.313579i | ||||
\(67\) | 0.295518 | − | 0.511852i | 0.0361033 | − | 0.0625327i | −0.847409 | − | 0.530940i | \(-0.821839\pi\) |
0.883512 | + | 0.468408i | \(0.155172\pi\) | |||||||
\(68\) | −0.133854 | −0.0162321 | ||||||||
\(69\) | −2.71523 | −0.326875 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.83073 | − | 10.0991i | −0.691981 | − | 1.19855i | −0.971188 | − | 0.238315i | \(-0.923405\pi\) |
0.279207 | − | 0.960231i | \(-0.409928\pi\) | |||||||
\(72\) | 1.26718 | − | 2.19482i | 0.149339 | − | 0.258663i | ||||
\(73\) | 4.13048 | + | 7.15420i | 0.483436 | + | 0.837335i | 0.999819 | − | 0.0190222i | \(-0.00605532\pi\) |
−0.516383 | + | 0.856358i | \(0.672722\pi\) | |||||||
\(74\) | 2.53661 | + | 4.39354i | 0.294875 | + | 0.510739i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.637555 | − | 4.31202i | 0.0731326 | − | 0.494623i | ||||
\(77\) | 1.36924 | 0.156040 | ||||||||
\(78\) | 2.14836 | + | 3.72107i | 0.243254 | + | 0.421328i | ||||
\(79\) | 1.66112 | + | 2.87714i | 0.186890 | + | 0.323703i | 0.944212 | − | 0.329339i | \(-0.106826\pi\) |
−0.757322 | + | 0.653042i | \(0.773492\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.51305 | − | 4.35273i | −0.279228 | − | 0.483637i | ||||
\(82\) | 0.433073 | − | 0.750105i | 0.0478249 | − | 0.0828352i | ||||
\(83\) | −4.20708 | −0.461787 | −0.230894 | − | 0.972979i | \(-0.574165\pi\) | ||||
−0.230894 | + | 0.972979i | \(0.574165\pi\) | |||||||
\(84\) | 0.216740 | 0.0236482 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.85199 | + | 4.93979i | −0.307538 | + | 0.532672i | ||||
\(87\) | 6.24284 | 0.669303 | ||||||||
\(88\) | −4.31087 | −0.459541 | ||||||||
\(89\) | 1.85992 | − | 3.22147i | 0.197151 | − | 0.341476i | −0.750453 | − | 0.660924i | \(-0.770164\pi\) |
0.947604 | + | 0.319449i | \(0.103498\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | − | 1.73205i | 0.104828 | − | 0.181568i | ||||
\(92\) | −1.98955 | − | 3.44600i | −0.207425 | − | 0.359270i | ||||
\(93\) | −1.01873 | − | 1.76450i | −0.105638 | − | 0.182970i | ||||
\(94\) | 12.9723 | 1.33799 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.682374 | −0.0696445 | ||||||||
\(97\) | −2.42830 | − | 4.20594i | −0.246556 | − | 0.427048i | 0.716012 | − | 0.698088i | \(-0.245966\pi\) |
−0.962568 | + | 0.271040i | \(0.912632\pi\) | |||||||
\(98\) | 3.44956 | + | 5.97481i | 0.348458 | + | 0.603547i | ||||
\(99\) | −5.46266 | + | 9.46161i | −0.549018 | + | 0.950928i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.25638 | − | 2.17611i | 0.125014 | − | 0.216531i | −0.796724 | − | 0.604343i | \(-0.793436\pi\) |
0.921739 | + | 0.387812i | \(0.126769\pi\) | |||||||
\(102\) | 0.0913382 | 0.00904383 | ||||||||
\(103\) | −4.03297 | −0.397380 | −0.198690 | − | 0.980062i | \(-0.563669\pi\) | ||||
−0.198690 | + | 0.980062i | \(0.563669\pi\) | |||||||
\(104\) | −3.14836 | + | 5.45312i | −0.308722 | + | 0.534722i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.92522 | 0.769765 | ||||||||
\(107\) | −10.0000 | −0.966736 | −0.483368 | − | 0.875417i | \(-0.660587\pi\) | ||||
−0.483368 | + | 0.875417i | \(0.660587\pi\) | |||||||
\(108\) | −1.88825 | + | 3.27055i | −0.181697 | + | 0.314709i | ||||
\(109\) | 2.93197 | + | 5.07832i | 0.280832 | + | 0.486415i | 0.971590 | − | 0.236671i | \(-0.0760564\pi\) |
−0.690758 | + | 0.723086i | \(0.742723\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.73092 | − | 2.99804i | −0.164292 | − | 0.284561i | ||||
\(112\) | 0.158813 | + | 0.275072i | 0.0150064 | + | 0.0259919i | ||||
\(113\) | 18.0853 | 1.70132 | 0.850660 | − | 0.525716i | \(-0.176202\pi\) | ||||
0.850660 | + | 0.525716i | \(0.176202\pi\) | |||||||
\(114\) | −0.435051 | + | 2.94241i | −0.0407463 | + | 0.275582i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.57435 | + | 7.92301i | 0.424718 | + | 0.735633i | ||||
\(117\) | 7.97909 | + | 13.8202i | 0.737667 | + | 1.27768i | ||||
\(118\) | 4.80717 | − | 8.32627i | 0.442536 | − | 0.766495i | ||||
\(119\) | −0.0212577 | − | 0.0368194i | −0.00194869 | − | 0.00337523i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.58363 | 0.689421 | ||||||||
\(122\) | 6.17422 | 0.558988 | ||||||||
\(123\) | −0.295518 | + | 0.511852i | −0.0266460 | + | 0.0461522i | ||||
\(124\) | 1.49292 | − | 2.58582i | 0.134068 | − | 0.232213i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.804980 | 0.0717133 | ||||||||
\(127\) | 8.94845 | − | 15.4992i | 0.794047 | − | 1.37533i | −0.129396 | − | 0.991593i | \(-0.541304\pi\) |
0.923443 | − | 0.383736i | \(-0.125363\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.94613 | − | 3.37079i | 0.171347 | − | 0.296781i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.90509 | + | 10.2279i | 0.515930 | + | 0.893617i | 0.999829 | + | 0.0184931i | \(0.00588686\pi\) |
−0.483899 | + | 0.875124i | \(0.660780\pi\) | |||||||
\(132\) | 2.94163 | 0.256036 | ||||||||
\(133\) | 1.28737 | − | 0.509431i | 0.111629 | − | 0.0441733i | ||||
\(134\) | −0.591036 | −0.0510577 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.0669268 | + | 0.115921i | 0.00573892 | + | 0.00994011i | ||||
\(137\) | 7.91554 | − | 13.7101i | 0.676270 | − | 1.17133i | −0.299825 | − | 0.953994i | \(-0.596928\pi\) |
0.976096 | − | 0.217341i | \(-0.0697382\pi\) | |||||||
\(138\) | 1.35762 | + | 2.35146i | 0.115568 | + | 0.200169i | ||||
\(139\) | −0.583681 | + | 1.01096i | −0.0495071 | + | 0.0857489i | −0.889717 | − | 0.456512i | \(-0.849098\pi\) |
0.840210 | + | 0.542261i | \(0.182432\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.85199 | −0.745472 | ||||||||
\(142\) | −5.83073 | + | 10.0991i | −0.489304 | + | 0.847500i | ||||
\(143\) | 13.5722 | − | 23.5077i | 1.13496 | − | 1.96581i | ||||
\(144\) | −2.53437 | −0.211197 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.13048 | − | 7.15420i | 0.341841 | − | 0.592086i | ||||
\(147\) | −2.35389 | − | 4.07705i | −0.194145 | − | 0.336270i | ||||
\(148\) | 2.53661 | − | 4.39354i | 0.208508 | − | 0.361147i | ||||
\(149\) | 6.07575 | + | 10.5235i | 0.497745 | + | 0.862120i | 0.999997 | − | 0.00260182i | \(-0.000828187\pi\) |
−0.502252 | + | 0.864722i | \(0.667495\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.3803 | −1.65853 | −0.829263 | − | 0.558859i | \(-0.811239\pi\) | ||||
−0.829263 | + | 0.558859i | \(0.811239\pi\) | |||||||
\(152\) | −4.05310 | + | 1.60387i | −0.328750 | + | 0.130091i | ||||
\(153\) | 0.339234 | 0.0274254 | ||||||||
\(154\) | −0.684622 | − | 1.18580i | −0.0551684 | − | 0.0955545i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.14836 | − | 3.72107i | 0.172006 | − | 0.297924i | ||||
\(157\) | −2.46121 | − | 4.26294i | −0.196426 | − | 0.340220i | 0.750941 | − | 0.660369i | \(-0.229600\pi\) |
−0.947367 | + | 0.320149i | \(0.896267\pi\) | |||||||
\(158\) | 1.66112 | − | 2.87714i | 0.132151 | − | 0.228893i | ||||
\(159\) | −5.40796 | −0.428879 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.631931 | − | 1.09454i | 0.0498032 | − | 0.0862616i | ||||
\(162\) | −2.51305 | + | 4.35273i | −0.197444 | + | 0.341983i | ||||
\(163\) | −1.43727 | −0.112576 | −0.0562880 | − | 0.998415i | \(-0.517927\pi\) | ||||
−0.0562880 | + | 0.998415i | \(0.517927\pi\) | |||||||
\(164\) | −0.866146 | −0.0676347 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.10354 | + | 3.64344i | 0.163266 | + | 0.282786i | ||||
\(167\) | −4.68750 | + | 8.11899i | −0.362730 | + | 0.628266i | −0.988409 | − | 0.151814i | \(-0.951488\pi\) |
0.625680 | + | 0.780080i | \(0.284822\pi\) | |||||||
\(168\) | −0.108370 | − | 0.187702i | −0.00836091 | − | 0.0144815i | ||||
\(169\) | −13.3243 | − | 23.0784i | −1.02495 | − | 1.77526i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.61580 | + | 10.9282i | −0.123563 | + | 0.835703i | ||||
\(172\) | 5.70398 | 0.434925 | ||||||||
\(173\) | −3.88263 | − | 6.72491i | −0.295191 | − | 0.511286i | 0.679838 | − | 0.733362i | \(-0.262050\pi\) |
−0.975029 | + | 0.222076i | \(0.928717\pi\) | |||||||
\(174\) | −3.12142 | − | 5.40646i | −0.236634 | − | 0.409863i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.15544 | + | 3.73333i | 0.162472 | + | 0.281410i | ||||
\(177\) | −3.28029 | + | 5.68163i | −0.246562 | + | 0.427057i | ||||
\(178\) | −3.71984 | −0.278814 | ||||||||
\(179\) | −1.12249 | −0.0838992 | −0.0419496 | − | 0.999120i | \(-0.513357\pi\) | ||||
−0.0419496 | + | 0.999120i | \(0.513357\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.89198 | + | 13.6693i | −0.586606 | + | 1.01603i | 0.408067 | + | 0.912952i | \(0.366203\pi\) |
−0.994673 | + | 0.103080i | \(0.967130\pi\) | |||||||
\(182\) | −2.00000 | −0.148250 | ||||||||
\(183\) | −4.21313 | −0.311444 | ||||||||
\(184\) | −1.98955 | + | 3.44600i | −0.146671 | + | 0.254042i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.01873 | + | 1.76450i | −0.0746970 | + | 0.129379i | ||||
\(187\) | −0.288513 | − | 0.499719i | −0.0210982 | − | 0.0365431i | ||||
\(188\) | −6.48617 | − | 11.2344i | −0.473053 | − | 0.819351i | ||||
\(189\) | −1.19952 | −0.0872520 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.2974 | 1.32395 | 0.661977 | − | 0.749524i | \(-0.269717\pi\) | ||||
0.661977 | + | 0.749524i | \(0.269717\pi\) | |||||||
\(192\) | 0.341187 | + | 0.590953i | 0.0246231 | + | 0.0426484i | ||||
\(193\) | −0.558777 | − | 0.967830i | −0.0402216 | − | 0.0696659i | 0.845214 | − | 0.534428i | \(-0.179473\pi\) |
−0.885435 | + | 0.464762i | \(0.846140\pi\) | |||||||
\(194\) | −2.42830 | + | 4.20594i | −0.174342 | + | 0.301969i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.44956 | − | 5.97481i | 0.246397 | − | 0.426772i | ||||
\(197\) | 16.2594 | 1.15843 | 0.579217 | − | 0.815173i | \(-0.303358\pi\) | ||||
0.579217 | + | 0.815173i | \(0.303358\pi\) | |||||||
\(198\) | 10.9253 | 0.776429 | ||||||||
\(199\) | 6.89911 | − | 11.9496i | 0.489065 | − | 0.847086i | −0.510856 | − | 0.859667i | \(-0.670671\pi\) |
0.999921 | + | 0.0125807i | \(0.00400467\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.403308 | 0.0284471 | ||||||||
\(202\) | −2.51276 | −0.176797 | ||||||||
\(203\) | −1.45293 | + | 2.51655i | −0.101976 | + | 0.176627i | ||||
\(204\) | −0.0456691 | − | 0.0791012i | −0.00319748 | − | 0.00553819i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.01648 | + | 3.49265i | 0.140495 | + | 0.243345i | ||||
\(207\) | 5.04224 | + | 8.73341i | 0.350460 | + | 0.607014i | ||||
\(208\) | 6.29672 | 0.436599 | ||||||||
\(209\) | 17.4724 | − | 6.91409i | 1.20859 | − | 0.478257i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.584458 | + | 1.01231i | 0.0402358 | + | 0.0696904i | 0.885442 | − | 0.464750i | \(-0.153856\pi\) |
−0.845206 | + | 0.534440i | \(0.820522\pi\) | |||||||
\(212\) | −3.96261 | − | 6.86344i | −0.272153 | − | 0.471383i | ||||
\(213\) | 3.97874 | − | 6.89138i | 0.272619 | − | 0.472190i | ||||
\(214\) | 5.00000 | + | 8.66025i | 0.341793 | + | 0.592003i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.77651 | 0.256959 | ||||||||
\(217\) | 0.948381 | 0.0643803 | ||||||||
\(218\) | 2.93197 | − | 5.07832i | 0.198578 | − | 0.343947i | ||||
\(219\) | −2.81853 | + | 4.88184i | −0.190459 | + | 0.329884i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.842838 | −0.0566954 | ||||||||
\(222\) | −1.73092 | + | 2.99804i | −0.116172 | + | 0.201215i | ||||
\(223\) | −3.15881 | − | 5.47122i | −0.211530 | − | 0.366380i | 0.740664 | − | 0.671876i | \(-0.234511\pi\) |
−0.952193 | + | 0.305496i | \(0.901178\pi\) | |||||||
\(224\) | 0.158813 | − | 0.275072i | 0.0106111 | − | 0.0183790i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.04264 | − | 15.6623i | −0.601508 | − | 1.04184i | ||||
\(227\) | 3.77942 | 0.250849 | 0.125424 | − | 0.992103i | \(-0.459971\pi\) | ||||
0.125424 | + | 0.992103i | \(0.459971\pi\) | |||||||
\(228\) | 2.76573 | − | 1.09444i | 0.183165 | − | 0.0724811i | ||||
\(229\) | 5.43628 | 0.359239 | 0.179620 | − | 0.983736i | \(-0.442513\pi\) | ||||
0.179620 | + | 0.983736i | \(0.442513\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.467169 | + | 0.809160i | 0.0307374 | + | 0.0532388i | ||||
\(232\) | 4.57435 | − | 7.92301i | 0.300321 | − | 0.520171i | ||||
\(233\) | −1.22461 | − | 2.12109i | −0.0802270 | − | 0.138957i | 0.823120 | − | 0.567867i | \(-0.192231\pi\) |
−0.903347 | + | 0.428910i | \(0.858898\pi\) | |||||||
\(234\) | 7.97909 | − | 13.8202i | 0.521610 | − | 0.903454i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.61434 | −0.625841 | ||||||||
\(237\) | −1.13350 | + | 1.96329i | −0.0736289 | + | 0.127529i | ||||
\(238\) | −0.0212577 | + | 0.0368194i | −0.00137793 | + | 0.00238664i | ||||
\(239\) | −9.45899 | −0.611851 | −0.305926 | − | 0.952055i | \(-0.598966\pi\) | ||||
−0.305926 | + | 0.952055i | \(0.598966\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.43540 | − | 14.6105i | 0.543372 | − | 0.941148i | −0.455335 | − | 0.890320i | \(-0.650481\pi\) |
0.998707 | − | 0.0508279i | \(-0.0161860\pi\) | |||||||
\(242\) | −3.79182 | − | 6.56762i | −0.243747 | − | 0.422183i | ||||
\(243\) | 7.37960 | − | 12.7819i | 0.473402 | − | 0.819956i | ||||
\(244\) | −3.08711 | − | 5.34704i | −0.197632 | − | 0.342309i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.591036 | 0.0376831 | ||||||||
\(247\) | 4.01451 | − | 27.1516i | 0.255437 | − | 1.72761i | ||||
\(248\) | −2.98584 | −0.189601 | ||||||||
\(249\) | −1.43540 | − | 2.48619i | −0.0909649 | − | 0.157556i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.32814 | + | 2.30040i | −0.0838311 | + | 0.145200i | −0.904893 | − | 0.425640i | \(-0.860049\pi\) |
0.821061 | + | 0.570840i | \(0.193382\pi\) | |||||||
\(252\) | −0.402490 | − | 0.697133i | −0.0253545 | − | 0.0439152i | ||||
\(253\) | 8.57668 | − | 14.8553i | 0.539211 | − | 0.933942i | ||||
\(254\) | −17.8969 | −1.12295 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1.12373 | + | 1.94635i | −0.0700961 | + | 0.121410i | −0.898943 | − | 0.438065i | \(-0.855664\pi\) |
0.828847 | + | 0.559475i | \(0.188997\pi\) | |||||||
\(258\) | −3.89225 | −0.242321 | ||||||||
\(259\) | 1.61139 | 0.100127 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.5931 | − | 20.0798i | −0.717594 | − | 1.24291i | ||||
\(262\) | 5.90509 | − | 10.2279i | 0.364818 | − | 0.631883i | ||||
\(263\) | 15.9289 | + | 27.5897i | 0.982219 | + | 1.70125i | 0.653695 | + | 0.756758i | \(0.273218\pi\) |
0.328524 | + | 0.944496i | \(0.393449\pi\) | |||||||
\(264\) | −1.47081 | − | 2.54753i | −0.0905224 | − | 0.156789i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.08486 | − | 0.860178i | −0.0665173 | − | 0.0527409i | ||||
\(267\) | 2.53832 | 0.155343 | ||||||||
\(268\) | 0.295518 | + | 0.511852i | 0.0180516 | + | 0.0312663i | ||||
\(269\) | 5.44763 | + | 9.43558i | 0.332148 | + | 0.575297i | 0.982933 | − | 0.183965i | \(-0.0588933\pi\) |
−0.650785 | + | 0.759262i | \(0.725560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.96631 | + | 10.3340i | 0.362428 | + | 0.627743i | 0.988360 | − | 0.152134i | \(-0.0486147\pi\) |
−0.625932 | + | 0.779877i | \(0.715281\pi\) | |||||||
\(272\) | 0.0669268 | − | 0.115921i | 0.00405803 | − | 0.00702872i | ||||
\(273\) | 1.36475 | 0.0825983 | ||||||||
\(274\) | −15.8311 | −0.956391 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.35762 | − | 2.35146i | 0.0817188 | − | 0.141541i | ||||
\(277\) | −15.9065 | −0.955730 | −0.477865 | − | 0.878433i | \(-0.658589\pi\) | ||||
−0.477865 | + | 0.878433i | \(0.658589\pi\) | |||||||
\(278\) | 1.16736 | 0.0700137 | ||||||||
\(279\) | −3.78361 | + | 6.55341i | −0.226519 | + | 0.392342i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.4921 | − | 18.1729i | 0.625909 | − | 1.08411i | −0.362455 | − | 0.932001i | \(-0.618062\pi\) |
0.988364 | − | 0.152105i | \(-0.0486052\pi\) | |||||||
\(282\) | 4.42600 | + | 7.66605i | 0.263564 | + | 0.456507i | ||||
\(283\) | 6.43083 | + | 11.1385i | 0.382273 | + | 0.662116i | 0.991387 | − | 0.130967i | \(-0.0418081\pi\) |
−0.609114 | + | 0.793083i | \(0.708475\pi\) | |||||||
\(284\) | 11.6615 | 0.691981 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −27.1444 | −1.60508 | ||||||||
\(287\) | −0.137555 | − | 0.238253i | −0.00811963 | − | 0.0140636i | ||||
\(288\) | 1.26718 | + | 2.19482i | 0.0746695 | + | 0.129331i | ||||
\(289\) | 8.49104 | − | 14.7069i | 0.499473 | − | 0.865113i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.65701 | − | 2.87002i | 0.0971356 | − | 0.168244i | ||||
\(292\) | −8.26096 | −0.483436 | ||||||||
\(293\) | −12.1278 | −0.708511 | −0.354255 | − | 0.935149i | \(-0.615266\pi\) | ||||
−0.354255 | + | 0.935149i | \(0.615266\pi\) | |||||||
\(294\) | −2.35389 | + | 4.07705i | −0.137282 | + | 0.237779i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.07323 | −0.294875 | ||||||||
\(297\) | −16.2801 | −0.944664 | ||||||||
\(298\) | 6.07575 | − | 10.5235i | 0.351959 | − | 0.609611i | ||||
\(299\) | −12.5276 | − | 21.6985i | −0.724491 | − | 1.25485i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.905866 | + | 1.56901i | 0.0522132 | + | 0.0904360i | ||||
\(302\) | 10.1902 | + | 17.6499i | 0.586377 | + | 1.01564i | ||||
\(303\) | 1.71464 | 0.0985035 | ||||||||
\(304\) | 3.41554 | + | 2.70815i | 0.195895 | + | 0.155323i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.169617 | − | 0.293785i | −0.00969635 | − | 0.0167946i | ||||
\(307\) | −9.08409 | − | 15.7341i | −0.518456 | − | 0.897992i | −0.999770 | − | 0.0214442i | \(-0.993174\pi\) |
0.481314 | − | 0.876548i | \(-0.340160\pi\) | |||||||
\(308\) | −0.684622 | + | 1.18580i | −0.0390100 | + | 0.0675673i | ||||
\(309\) | −1.37600 | − | 2.38330i | −0.0782777 | − | 0.135581i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.4766 | 1.10442 | 0.552210 | − | 0.833705i | \(-0.313785\pi\) | ||||
0.552210 | + | 0.833705i | \(0.313785\pi\) | |||||||
\(312\) | −4.29672 | −0.243254 | ||||||||
\(313\) | 5.98987 | − | 10.3748i | 0.338568 | − | 0.586416i | −0.645596 | − | 0.763679i | \(-0.723391\pi\) |
0.984164 | + | 0.177263i | \(0.0567243\pi\) | |||||||
\(314\) | −2.46121 | + | 4.26294i | −0.138894 | + | 0.240572i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.32223 | −0.186890 | ||||||||
\(317\) | 0.564654 | − | 0.978009i | 0.0317141 | − | 0.0549305i | −0.849733 | − | 0.527214i | \(-0.823237\pi\) |
0.881447 | + | 0.472283i | \(0.156570\pi\) | |||||||
\(318\) | 2.70398 | + | 4.68343i | 0.151632 | + | 0.262634i | ||||
\(319\) | −19.7195 | + | 34.1551i | −1.10408 | + | 1.91232i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.41187 | − | 5.90953i | −0.190432 | − | 0.329838i | ||||
\(322\) | −1.26386 | −0.0704323 | ||||||||
\(323\) | −0.457182 | − | 0.362495i | −0.0254383 | − | 0.0201698i | ||||
\(324\) | 5.02610 | 0.279228 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.718637 | + | 1.24472i | 0.0398016 | + | 0.0689385i | ||||
\(327\) | −2.00070 | + | 3.46532i | −0.110639 | + | 0.191632i | ||||
\(328\) | 0.433073 | + | 0.750105i | 0.0239125 | + | 0.0414176i | ||||
\(329\) | 2.06017 | − | 3.56833i | 0.113581 | − | 0.196728i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.3080 | −0.786437 | −0.393218 | − | 0.919445i | \(-0.628638\pi\) | ||||
−0.393218 | + | 0.919445i | \(0.628638\pi\) | |||||||
\(332\) | 2.10354 | − | 3.64344i | 0.115447 | − | 0.199960i | ||||
\(333\) | −6.42871 | + | 11.1348i | −0.352291 | + | 0.610186i | ||||
\(334\) | 9.37500 | 0.512977 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.108370 | + | 0.187702i | −0.00591206 | + | 0.0102400i | ||||
\(337\) | −13.8589 | − | 24.0043i | −0.754941 | − | 1.30760i | −0.945404 | − | 0.325901i | \(-0.894332\pi\) |
0.190463 | − | 0.981694i | \(-0.439001\pi\) | |||||||
\(338\) | −13.3243 | + | 23.0784i | −0.724748 | + | 1.25530i | ||||
\(339\) | 6.17047 | + | 10.6876i | 0.335134 | + | 0.580469i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.8716 | 0.697036 | ||||||||
\(342\) | 10.2720 | − | 4.06480i | 0.555448 | − | 0.219799i | ||||
\(343\) | 4.41472 | 0.238372 | ||||||||
\(344\) | −2.85199 | − | 4.93979i | −0.153769 | − | 0.266336i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.88263 | + | 6.72491i | −0.208731 | + | 0.361534i | ||||
\(347\) | 15.7098 | + | 27.2102i | 0.843346 | + | 1.46072i | 0.887050 | + | 0.461673i | \(0.152751\pi\) |
−0.0437044 | + | 0.999045i | \(0.513916\pi\) | |||||||
\(348\) | −3.12142 | + | 5.40646i | −0.167326 | + | 0.289817i | ||||
\(349\) | 23.4539 | 1.25546 | 0.627729 | − | 0.778432i | \(-0.283985\pi\) | ||||
0.627729 | + | 0.778432i | \(0.283985\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.8898 | + | 20.5937i | −0.634631 | + | 1.09921i | ||||
\(352\) | 2.15544 | − | 3.73333i | 0.114885 | − | 0.198987i | ||||
\(353\) | −17.3468 | −0.923277 | −0.461638 | − | 0.887068i | \(-0.652738\pi\) | ||||
−0.461638 | + | 0.887068i | \(0.652738\pi\) | |||||||
\(354\) | 6.56058 | 0.348691 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.85992 | + | 3.22147i | 0.0985755 | + | 0.170738i | ||||
\(357\) | 0.0145057 | − | 0.0251246i | 0.000767722 | − | 0.00132973i | ||||
\(358\) | 0.561247 | + | 0.972108i | 0.0296628 | + | 0.0513775i | ||||
\(359\) | −0.402934 | − | 0.697902i | −0.0212660 | − | 0.0368339i | 0.855197 | − | 0.518304i | \(-0.173436\pi\) |
−0.876463 | + | 0.481470i | \(0.840103\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.8552 | − | 13.0013i | 0.729221 | − | 0.684279i | ||||
\(362\) | 15.7840 | 0.829587 | ||||||||
\(363\) | 2.58744 | + | 4.48157i | 0.135805 | + | 0.235222i | ||||
\(364\) | 1.00000 | + | 1.73205i | 0.0524142 | + | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.10657 | + | 3.64868i | 0.110112 | + | 0.190720i | ||||
\(367\) | −1.26908 | + | 2.19811i | −0.0662455 | + | 0.114740i | −0.897246 | − | 0.441531i | \(-0.854435\pi\) |
0.831000 | + | 0.556272i | \(0.187769\pi\) | |||||||
\(368\) | 3.97909 | 0.207425 | ||||||||
\(369\) | 2.19513 | 0.114274 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.25863 | − | 2.18001i | 0.0653446 | − | 0.113180i | ||||
\(372\) | 2.03746 | 0.105638 | ||||||||
\(373\) | −12.4012 | −0.642110 | −0.321055 | − | 0.947060i | \(-0.604038\pi\) | ||||
−0.321055 | + | 0.947060i | \(0.604038\pi\) | |||||||
\(374\) | −0.288513 | + | 0.499719i | −0.0149186 | + | 0.0258399i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.48617 | + | 11.2344i | −0.334499 | + | 0.579369i | ||||
\(377\) | 28.8034 | + | 49.8890i | 1.48345 | + | 2.56941i | ||||
\(378\) | 0.599758 | + | 1.03881i | 0.0308482 | + | 0.0534307i | ||||
\(379\) | −12.6756 | −0.651100 | −0.325550 | − | 0.945525i | \(-0.605549\pi\) | ||||
−0.325550 | + | 0.945525i | \(0.605549\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.2124 | 0.625660 | ||||||||
\(382\) | −9.14871 | − | 15.8460i | −0.468089 | − | 0.810753i | ||||
\(383\) | −7.97632 | − | 13.8154i | −0.407571 | − | 0.705934i | 0.587046 | − | 0.809554i | \(-0.300291\pi\) |
−0.994617 | + | 0.103620i | \(0.966957\pi\) | |||||||
\(384\) | 0.341187 | − | 0.590953i | 0.0174111 | − | 0.0301570i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.558777 | + | 0.967830i | −0.0284410 | + | 0.0492612i | ||||
\(387\) | −14.4560 | −0.734839 | ||||||||
\(388\) | 4.85660 | 0.246556 | ||||||||
\(389\) | 13.0991 | − | 22.6883i | 0.664150 | − | 1.15034i | −0.315365 | − | 0.948971i | \(-0.602127\pi\) |
0.979515 | − | 0.201372i | \(-0.0645399\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.532616 | −0.0269355 | ||||||||
\(392\) | −6.89911 | −0.348458 | ||||||||
\(393\) | −4.02948 | + | 6.97926i | −0.203260 | + | 0.352057i | ||||
\(394\) | −8.12970 | − | 14.0811i | −0.409568 | − | 0.709393i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.46266 | − | 9.46161i | −0.274509 | − | 0.475464i | ||||
\(397\) | 15.0639 | + | 26.0914i | 0.756034 | + | 1.30949i | 0.944858 | + | 0.327479i | \(0.106199\pi\) |
−0.188824 | + | 0.982011i | \(0.560468\pi\) | |||||||
\(398\) | −13.7982 | −0.691643 | ||||||||
\(399\) | 0.740283 | + | 0.586963i | 0.0370605 | + | 0.0293849i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.08591 | + | 1.88085i | 0.0542278 | + | 0.0939254i | 0.891865 | − | 0.452302i | \(-0.149397\pi\) |
−0.837637 | + | 0.546227i | \(0.816064\pi\) | |||||||
\(402\) | −0.201654 | − | 0.349275i | −0.0100576 | − | 0.0174202i | ||||
\(403\) | 9.40051 | − | 16.2822i | 0.468273 | − | 0.811072i | ||||
\(404\) | 1.25638 | + | 2.17611i | 0.0625072 | + | 0.108266i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.90587 | 0.144216 | ||||||||
\(407\) | 21.8700 | 1.08406 | ||||||||
\(408\) | −0.0456691 | + | 0.0791012i | −0.00226096 | + | 0.00391609i | ||||
\(409\) | −16.0832 | + | 27.8569i | −0.795262 | + | 1.37743i | 0.127410 | + | 0.991850i | \(0.459333\pi\) |
−0.922673 | + | 0.385584i | \(0.874000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.8027 | 0.532859 | ||||||||
\(412\) | 2.01648 | − | 3.49265i | 0.0993450 | − | 0.172071i | ||||
\(413\) | −1.52688 | − | 2.64464i | −0.0751329 | − | 0.130134i | ||||
\(414\) | 5.04224 | − | 8.73341i | 0.247812 | − | 0.429224i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.14836 | − | 5.45312i | −0.154361 | − | 0.267361i | ||||
\(417\) | −0.796577 | −0.0390085 | ||||||||
\(418\) | −14.7240 | − | 11.6745i | −0.720173 | − | 0.571018i | ||||
\(419\) | −9.99674 | −0.488373 | −0.244186 | − | 0.969728i | \(-0.578521\pi\) | ||||
−0.244186 | + | 0.969728i | \(0.578521\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0856 | + | 33.0572i | 0.930173 | + | 1.61111i | 0.783023 | + | 0.621993i | \(0.213677\pi\) |
0.147150 | + | 0.989114i | \(0.452990\pi\) | |||||||
\(422\) | 0.584458 | − | 1.01231i | 0.0284510 | − | 0.0492785i | ||||
\(423\) | 16.4383 | + | 28.4720i | 0.799259 | + | 1.38436i | ||||
\(424\) | −3.96261 | + | 6.86344i | −0.192441 | + | 0.333318i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.95748 | −0.385541 | ||||||||
\(427\) | 0.980546 | − | 1.69836i | 0.0474520 | − | 0.0821892i | ||||
\(428\) | 5.00000 | − | 8.66025i | 0.241684 | − | 0.418609i | ||||
\(429\) | 18.5226 | 0.894280 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.73649 | + | 3.00769i | −0.0836437 | + | 0.144875i | −0.904812 | − | 0.425810i | \(-0.859989\pi\) |
0.821169 | + | 0.570685i | \(0.193322\pi\) | |||||||
\(432\) | −1.88825 | − | 3.27055i | −0.0908487 | − | 0.157355i | ||||
\(433\) | 5.54742 | − | 9.60841i | 0.266592 | − | 0.461751i | −0.701388 | − | 0.712780i | \(-0.747436\pi\) |
0.967979 | + | 0.251029i | \(0.0807691\pi\) | |||||||
\(434\) | −0.474191 | − | 0.821322i | −0.0227619 | − | 0.0394247i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.86394 | −0.280832 | ||||||||
\(437\) | 2.53689 | − | 17.1579i | 0.121356 | − | 0.820775i | ||||
\(438\) | 5.63706 | 0.269349 | ||||||||
\(439\) | 6.51914 | + | 11.2915i | 0.311141 | + | 0.538913i | 0.978610 | − | 0.205725i | \(-0.0659554\pi\) |
−0.667468 | + | 0.744638i | \(0.732622\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.74244 | + | 15.1423i | −0.416307 | + | 0.721064i | ||||
\(442\) | 0.421419 | + | 0.729919i | 0.0200449 | + | 0.0347187i | ||||
\(443\) | −7.51250 | + | 13.0120i | −0.356930 | + | 0.618221i | −0.987446 | − | 0.157955i | \(-0.949510\pi\) |
0.630516 | + | 0.776176i | \(0.282843\pi\) | |||||||
\(444\) | 3.46184 | 0.164292 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.15881 | + | 5.47122i | −0.149574 | + | 0.259070i | ||||
\(447\) | −4.14594 | + | 7.18097i | −0.196096 | + | 0.339648i | ||||
\(448\) | −0.317626 | −0.0150064 | ||||||||
\(449\) | 14.4251 | 0.680761 | 0.340381 | − | 0.940288i | \(-0.389444\pi\) | ||||
0.340381 | + | 0.940288i | \(0.389444\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.86692 | − | 3.23361i | −0.0879100 | − | 0.152265i | ||||
\(452\) | −9.04264 | + | 15.6623i | −0.425330 | + | 0.736693i | ||||
\(453\) | −6.95350 | − | 12.0438i | −0.326704 | − | 0.565868i | ||||
\(454\) | −1.88971 | − | 3.27307i | −0.0886884 | − | 0.153613i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.33068 | − | 1.84797i | −0.109144 | − | 0.0865392i | ||||
\(457\) | −32.1773 | −1.50519 | −0.752596 | − | 0.658483i | \(-0.771199\pi\) | ||||
−0.752596 | + | 0.658483i | \(0.771199\pi\) | |||||||
\(458\) | −2.71814 | − | 4.70795i | −0.127010 | − | 0.219988i | ||||
\(459\) | 0.252750 | + | 0.437775i | 0.0117973 | + | 0.0204336i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.75530 | + | 13.4326i | 0.361200 | + | 0.625617i | 0.988159 | − | 0.153435i | \(-0.0490337\pi\) |
−0.626958 | + | 0.779053i | \(0.715700\pi\) | |||||||
\(462\) | 0.467169 | − | 0.809160i | 0.0217347 | − | 0.0376455i | ||||
\(463\) | −30.1477 | −1.40108 | −0.700541 | − | 0.713612i | \(-0.747058\pi\) | ||||
−0.700541 | + | 0.713612i | \(0.747058\pi\) | |||||||
\(464\) | −9.14871 | −0.424718 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.22461 | + | 2.12109i | −0.0567290 | + | 0.0982576i | ||||
\(467\) | −34.5731 | −1.59985 | −0.799927 | − | 0.600098i | \(-0.795128\pi\) | ||||
−0.799927 | + | 0.600098i | \(0.795128\pi\) | |||||||
\(468\) | −15.9582 | −0.737667 | ||||||||
\(469\) | −0.0938641 | + | 0.162577i | −0.00433424 | + | 0.00750713i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.67947 | − | 2.90892i | 0.0773858 | − | 0.134036i | ||||
\(472\) | 4.80717 | + | 8.32627i | 0.221268 | + | 0.383247i | ||||
\(473\) | 12.2946 | + | 21.2948i | 0.565305 | + | 0.979137i | ||||
\(474\) | 2.26701 | 0.104127 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.0425153 | 0.00194869 | ||||||||
\(477\) | 10.0427 | + | 17.3945i | 0.459824 | + | 0.796438i | ||||
\(478\) | 4.72950 | + | 8.19173i | 0.216322 | + | 0.374681i | ||||
\(479\) | −15.4238 | + | 26.7148i | −0.704732 | + | 1.22063i | 0.262056 | + | 0.965053i | \(0.415600\pi\) |
−0.966788 | + | 0.255579i | \(0.917734\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.9723 | − | 27.6649i | 0.728276 | − | 1.26141i | ||||
\(482\) | −16.8708 | −0.768444 | ||||||||
\(483\) | 0.862427 | 0.0392418 | ||||||||
\(484\) | −3.79182 | + | 6.56762i | −0.172355 | + | 0.298528i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14.7592 | −0.669491 | ||||||||
\(487\) | −30.7745 | −1.39453 | −0.697263 | − | 0.716815i | \(-0.745599\pi\) | ||||
−0.697263 | + | 0.716815i | \(0.745599\pi\) | |||||||
\(488\) | −3.08711 | + | 5.34704i | −0.139747 | + | 0.242049i | ||||
\(489\) | −0.490380 | − | 0.849362i | −0.0221757 | − | 0.0384095i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.8571 | + | 22.2692i | 0.580234 | + | 1.00499i | 0.995451 | + | 0.0952719i | \(0.0303720\pi\) |
−0.415218 | + | 0.909722i | \(0.636295\pi\) | |||||||
\(492\) | −0.295518 | − | 0.511852i | −0.0133230 | − | 0.0230761i | ||||
\(493\) | 1.22459 | 0.0551526 | ||||||||
\(494\) | −25.5212 | + | 10.0991i | −1.14825 | + | 0.454381i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.49292 | + | 2.58582i | 0.0670342 | + | 0.116107i | ||||
\(497\) | 1.85199 | + | 3.20774i | 0.0830732 | + | 0.143887i | ||||
\(498\) | −1.43540 | + | 2.48619i | −0.0643219 | + | 0.111409i | ||||
\(499\) | 0.201106 | + | 0.348326i | 0.00900274 | + | 0.0155932i | 0.870492 | − | 0.492183i | \(-0.163801\pi\) |
−0.861489 | + | 0.507776i | \(0.830468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.39726 | −0.285808 | ||||||||
\(502\) | 2.65627 | 0.118555 | ||||||||
\(503\) | −20.2327 | + | 35.0441i | −0.902133 | + | 1.56254i | −0.0774136 | + | 0.996999i | \(0.524666\pi\) |
−0.824720 | + | 0.565542i | \(0.808667\pi\) | |||||||
\(504\) | −0.402490 | + | 0.697133i | −0.0179283 | + | 0.0310528i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −17.1534 | −0.762560 | ||||||||
\(507\) | 9.09218 | − | 15.7481i | 0.403798 | − | 0.699399i | ||||
\(508\) | 8.94845 | + | 15.4992i | 0.397023 | + | 0.687665i | ||||
\(509\) | 5.72694 | − | 9.91935i | 0.253842 | − | 0.439668i | −0.710738 | − | 0.703457i | \(-0.751639\pi\) |
0.964580 | + | 0.263789i | \(0.0849723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.31195 | − | 2.27236i | −0.0580371 | − | 0.100523i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −15.3066 | + | 6.05703i | −0.675801 | + | 0.267425i | ||||
\(514\) | 2.24745 | 0.0991308 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.94613 | + | 3.37079i | 0.0856734 | + | 0.148391i | ||||
\(517\) | 27.9611 | − | 48.4300i | 1.22973 | − | 2.12995i | ||||
\(518\) | −0.805694 | − | 1.39550i | −0.0354002 | − | 0.0613149i | ||||
\(519\) | 2.64941 | − | 4.58891i | 0.116296 | − | 0.201431i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.66822 | 0.0730860 | 0.0365430 | − | 0.999332i | \(-0.488365\pi\) | ||||
0.0365430 | + | 0.999332i | \(0.488365\pi\) | |||||||
\(522\) | −11.5931 | + | 20.0798i | −0.507416 | + | 0.878870i | ||||
\(523\) | −21.9775 | + | 38.0662i | −0.961011 | + | 1.66452i | −0.241039 | + | 0.970515i | \(0.577488\pi\) |
−0.719971 | + | 0.694004i | \(0.755845\pi\) | |||||||
\(524\) | −11.8102 | −0.515930 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.9289 | − | 27.5897i | 0.694534 | − | 1.20297i | ||||
\(527\) | −0.199833 | − | 0.346121i | −0.00870486 | − | 0.0150773i | ||||
\(528\) | −1.47081 | + | 2.54753i | −0.0640090 | + | 0.110867i | ||||
\(529\) | 3.58341 | + | 6.20665i | 0.155800 | + | 0.269854i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.3663 | 1.05741 | ||||||||
\(532\) | −0.202504 | + | 1.36961i | −0.00877966 | + | 0.0593801i | ||||
\(533\) | −5.45388 | −0.236234 | ||||||||
\(534\) | −1.26916 | − | 2.19825i | −0.0549220 | − | 0.0951276i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.295518 | − | 0.511852i | 0.0127644 | − | 0.0221086i | ||||
\(537\) | −0.382981 | − | 0.663342i | −0.0165268 | − | 0.0286253i | ||||
\(538\) | 5.44763 | − | 9.43558i | 0.234864 | − | 0.406797i | ||||
\(539\) | 29.7412 | 1.28104 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7202 | − | 25.4961i | 0.632870 | − | 1.09616i | −0.354092 | − | 0.935211i | \(-0.615210\pi\) |
0.986962 | − | 0.160953i | \(-0.0514567\pi\) | |||||||
\(542\) | 5.96631 | − | 10.3340i | 0.256275 | − | 0.443881i | ||||
\(543\) | −10.7706 | −0.462209 | ||||||||
\(544\) | −0.133854 | −0.00573892 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.682374 | − | 1.18191i | −0.0292029 | − | 0.0505809i | ||||
\(547\) | −10.2026 | + | 17.6714i | −0.436231 | + | 0.755574i | −0.997395 | − | 0.0721302i | \(-0.977020\pi\) |
0.561164 | + | 0.827704i | \(0.310354\pi\) | |||||||
\(548\) | 7.91554 | + | 13.7101i | 0.338135 | + | 0.585667i | ||||
\(549\) | 7.82387 | + | 13.5513i | 0.333915 | + | 0.578357i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.83281 | + | 39.4494i | −0.248486 | + | 1.68060i | ||||
\(552\) | −2.71523 | −0.115568 | ||||||||
\(553\) | −0.527613 | − | 0.913853i | −0.0224364 | − | 0.0388610i | ||||
\(554\) | 7.95326 | + | 13.7754i | 0.337902 | + | 0.585263i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.583681 | − | 1.01096i | −0.0247536 | − | 0.0428744i | ||||
\(557\) | 2.30575 | − | 3.99368i | 0.0976977 | − | 0.169217i | −0.813034 | − | 0.582217i | \(-0.802185\pi\) |
0.910731 | + | 0.412999i | \(0.135519\pi\) | |||||||
\(558\) | 7.56722 | 0.320346 | ||||||||
\(559\) | 35.9164 | 1.51910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.196874 | − | 0.340995i | 0.00831202 | − | 0.0143968i | ||||
\(562\) | −20.9843 | −0.885169 | ||||||||
\(563\) | −5.13495 | −0.216412 | −0.108206 | − | 0.994128i | \(-0.534511\pi\) | ||||
−0.108206 | + | 0.994128i | \(0.534511\pi\) | |||||||
\(564\) | 4.42600 | − | 7.66605i | 0.186368 | − | 0.322799i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.43083 | − | 11.1385i | 0.270308 | − | 0.468187i | ||||
\(567\) | 0.798210 | + | 1.38254i | 0.0335217 | + | 0.0580612i | ||||
\(568\) | −5.83073 | − | 10.0991i | −0.244652 | − | 0.423750i | ||||
\(569\) | −23.0698 | −0.967135 | −0.483568 | − | 0.875307i | \(-0.660659\pi\) | ||||
−0.483568 | + | 0.875307i | \(0.660659\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.7009 | −1.03370 | −0.516850 | − | 0.856076i | \(-0.672896\pi\) | ||||
−0.516850 | + | 0.856076i | \(0.672896\pi\) | |||||||
\(572\) | 13.5722 | + | 23.5077i | 0.567481 | + | 0.982906i | ||||
\(573\) | 6.24284 | + | 10.8129i | 0.260799 | + | 0.451716i | ||||
\(574\) | −0.137555 | + | 0.238253i | −0.00574144 | + | 0.00994447i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.26718 | − | 2.19482i | 0.0527993 | − | 0.0914510i | ||||
\(577\) | −34.0569 | −1.41781 | −0.708903 | − | 0.705306i | \(-0.750810\pi\) | ||||
−0.708903 | + | 0.705306i | \(0.750810\pi\) | |||||||
\(578\) | −16.9821 | −0.706362 | ||||||||
\(579\) | 0.381295 | − | 0.660422i | 0.0158461 | − | 0.0274462i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.33628 | 0.0554381 | ||||||||
\(582\) | −3.31402 | −0.137370 | ||||||||
\(583\) | 17.0823 | − | 29.5874i | 0.707477 | − | 1.22539i | ||||
\(584\) | 4.13048 | + | 7.15420i | 0.170920 | + | 0.296043i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.06388 | + | 10.5029i | 0.250496 | + | 0.433873i | ||||
\(587\) | −18.9701 | − | 32.8572i | −0.782981 | − | 1.35616i | −0.930198 | − | 0.367059i | \(-0.880365\pi\) |
0.147216 | − | 0.989104i | \(-0.452969\pi\) | |||||||
\(588\) | 4.70778 | 0.194145 | ||||||||
\(589\) | 12.1019 | − | 4.78891i | 0.498651 | − | 0.197324i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.54750 | + | 9.60855i | 0.228194 | + | 0.395243i | ||||
\(592\) | 2.53661 | + | 4.39354i | 0.104254 | + | 0.180574i | ||||
\(593\) | −4.85602 | + | 8.41087i | −0.199413 | + | 0.345393i | −0.948338 | − | 0.317261i | \(-0.897237\pi\) |
0.748925 | + | 0.662654i | \(0.230570\pi\) | |||||||
\(594\) | 8.14003 | + | 14.0989i | 0.333989 | + | 0.578486i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.1515 | −0.497745 | ||||||||
\(597\) | 9.41556 | 0.385353 | ||||||||
\(598\) | −12.5276 | + | 21.6985i | −0.512292 | + | 0.887316i | ||||
\(599\) | 7.71001 | − | 13.3541i | 0.315023 | − | 0.545635i | −0.664420 | − | 0.747360i | \(-0.731321\pi\) |
0.979442 | + | 0.201725i | \(0.0646546\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.9383 | −0.894881 | −0.447441 | − | 0.894314i | \(-0.647664\pi\) | ||||
−0.447441 | + | 0.894314i | \(0.647664\pi\) | |||||||
\(602\) | 0.905866 | − | 1.56901i | 0.0369203 | − | 0.0639479i | ||||
\(603\) | −0.748951 | − | 1.29722i | −0.0304996 | − | 0.0528269i | ||||
\(604\) | 10.1902 | − | 17.6499i | 0.414631 | − | 0.718163i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.857320 | − | 1.48492i | −0.0348263 | − | 0.0603209i | ||||
\(607\) | 22.2900 | 0.904724 | 0.452362 | − | 0.891834i | \(-0.350582\pi\) | ||||
0.452362 | + | 0.891834i | \(0.350582\pi\) | |||||||
\(608\) | 0.637555 | − | 4.31202i | 0.0258563 | − | 0.174876i | ||||
\(609\) | −1.98289 | −0.0803507 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40.8416 | − | 70.7397i | −1.65227 | − | 2.86182i | ||||
\(612\) | −0.169617 | + | 0.293785i | −0.00685636 | + | 0.0118756i | ||||
\(613\) | 12.6028 | + | 21.8287i | 0.509023 | + | 0.881654i | 0.999945 | + | 0.0104504i | \(0.00332654\pi\) |
−0.490922 | + | 0.871203i | \(0.663340\pi\) | |||||||
\(614\) | −9.08409 | + | 15.7341i | −0.366604 | + | 0.634977i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.36924 | 0.0551684 | ||||||||
\(617\) | −9.51333 | + | 16.4776i | −0.382992 | + | 0.663362i | −0.991488 | − | 0.130195i | \(-0.958440\pi\) |
0.608496 | + | 0.793557i | \(0.291773\pi\) | |||||||
\(618\) | −1.37600 | + | 2.38330i | −0.0553507 | + | 0.0958702i | ||||
\(619\) | −33.9075 | −1.36286 | −0.681429 | − | 0.731884i | \(-0.738641\pi\) | ||||
−0.681429 | + | 0.731884i | \(0.738641\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.51354 | + | 13.0138i | −0.301508 | + | 0.522227i | ||||
\(622\) | −9.73832 | − | 16.8673i | −0.390471 | − | 0.676316i | ||||
\(623\) | −0.590758 | + | 1.02322i | −0.0236682 | + | 0.0409946i | ||||
\(624\) | 2.14836 | + | 3.72107i | 0.0860032 | + | 0.148962i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.9797 | −0.478807 | ||||||||
\(627\) | 10.0473 | + | 7.96637i | 0.401249 | + | 0.318146i | ||||
\(628\) | 4.92242 | 0.196426 | ||||||||
\(629\) | −0.339535 | − | 0.588091i | −0.0135381 | − | 0.0234487i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.27169 | + | 7.39878i | −0.170053 | + | 0.294541i | −0.938438 | − | 0.345447i | \(-0.887727\pi\) |
0.768385 | + | 0.639988i | \(0.221061\pi\) | |||||||
\(632\) | 1.66112 | + | 2.87714i | 0.0660757 | + | 0.114446i | ||||
\(633\) | −0.398819 | + | 0.690775i | −0.0158516 | + | 0.0274558i | ||||
\(634\) | −1.12931 | −0.0448505 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.70398 | − | 4.68343i | 0.107220 | − | 0.185710i | ||||
\(637\) | 21.7209 | − | 37.6217i | 0.860613 | − | 1.49063i | ||||
\(638\) | 39.4389 | 1.56140 | ||||||||
\(639\) | −29.5544 | −1.16915 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.86302 | − | 3.22684i | −0.0735847 | − | 0.127453i | 0.826885 | − | 0.562371i | \(-0.190111\pi\) |
−0.900470 | + | 0.434918i | \(0.856777\pi\) | |||||||
\(642\) | −3.41187 | + | 5.90953i | −0.134656 | + | 0.233231i | ||||
\(643\) | −16.1350 | − | 27.9466i | −0.636300 | − | 1.10210i | −0.986238 | − | 0.165332i | \(-0.947131\pi\) |
0.349938 | − | 0.936773i | \(-0.386203\pi\) | |||||||
\(644\) | 0.631931 | + | 1.09454i | 0.0249016 | + | 0.0431308i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.0853390 | + | 0.577179i | −0.00335762 | + | 0.0227088i | ||||
\(647\) | 48.1241 | 1.89195 | 0.945977 | − | 0.324234i | \(-0.105107\pi\) | ||||
0.945977 | + | 0.324234i | \(0.105107\pi\) | |||||||
\(648\) | −2.51305 | − | 4.35273i | −0.0987220 | − | 0.170992i | ||||
\(649\) | −20.7231 | − | 35.8935i | −0.813453 | − | 1.40894i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.323575 | + | 0.560449i | 0.0126819 | + | 0.0219657i | ||||
\(652\) | 0.718637 | − | 1.24472i | 0.0281440 | − | 0.0487469i | ||||
\(653\) | 13.9774 | 0.546979 | 0.273489 | − | 0.961875i | \(-0.411822\pi\) | ||||
0.273489 | + | 0.961875i | \(0.411822\pi\) | |||||||
\(654\) | 4.00140 | 0.156467 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.433073 | − | 0.750105i | 0.0169087 | − | 0.0292867i | ||||
\(657\) | 20.9363 | 0.816802 | ||||||||
\(658\) | −4.12035 | −0.160628 | ||||||||
\(659\) | 6.24517 | − | 10.8170i | 0.243277 | − | 0.421369i | −0.718369 | − | 0.695663i | \(-0.755111\pi\) |
0.961646 | + | 0.274294i | \(0.0884441\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.2429 | + | 24.6695i | −0.553986 | + | 0.959531i | 0.443996 | + | 0.896029i | \(0.353560\pi\) |
−0.997982 | + | 0.0635024i | \(0.979773\pi\) | |||||||
\(662\) | 7.15398 | + | 12.3911i | 0.278047 | + | 0.481592i | ||||
\(663\) | −0.287566 | − | 0.498078i | −0.0111681 | − | 0.0193438i | ||||
\(664\) | −4.20708 | −0.163266 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.8574 | 0.498215 | ||||||||
\(667\) | 18.2018 | + | 31.5264i | 0.704776 | + | 1.22071i | ||||
\(668\) | −4.68750 | − | 8.11899i | −0.181365 | − | 0.314133i | ||||
\(669\) | 2.15549 | − | 3.73342i | 0.0833362 | − | 0.144342i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.3082 | − | 23.0504i | 0.513755 | − | 0.889851i | ||||
\(672\) | 0.216740 | 0.00836091 | ||||||||
\(673\) | 31.6748 | 1.22097 | 0.610486 | − | 0.792027i | \(-0.290974\pi\) | ||||
0.610486 | + | 0.792027i | \(0.290974\pi\) | |||||||
\(674\) | −13.8589 | + | 24.0043i | −0.533824 | + | 0.924610i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26.6487 | 1.02495 | ||||||||
\(677\) | −49.3049 | −1.89494 | −0.947470 | − | 0.319844i | \(-0.896369\pi\) | ||||
−0.947470 | + | 0.319844i | \(0.896369\pi\) | |||||||
\(678\) | 6.17047 | − | 10.6876i | 0.236975 | − | 0.410453i | ||||
\(679\) | 0.771290 | + | 1.33591i | 0.0295994 | + | 0.0512677i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.28949 | + | 2.23346i | 0.0494133 | + | 0.0855863i | ||||
\(682\) | −6.43580 | − | 11.1471i | −0.246440 | − | 0.426846i | ||||
\(683\) | −4.26771 | −0.163299 | −0.0816496 | − | 0.996661i | \(-0.526019\pi\) | ||||
−0.0816496 | + | 0.996661i | \(0.526019\pi\) | |||||||
\(684\) | −8.65623 | − | 6.86344i | −0.330979 | − | 0.262430i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.20736 | − | 3.82326i | −0.0842773 | − | 0.145973i | ||||
\(687\) | 1.85479 | + | 3.21259i | 0.0707645 | + | 0.122568i | ||||
\(688\) | −2.85199 | + | 4.93979i | −0.108731 | + | 0.188328i | ||||
\(689\) | −24.9514 | − | 43.2172i | −0.950574 | − | 1.64644i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.249546 | 0.00949319 | 0.00474659 | − | 0.999989i | \(-0.498489\pi\) | ||||
0.00474659 | + | 0.999989i | \(0.498489\pi\) | |||||||
\(692\) | 7.76526 | 0.295191 | ||||||||
\(693\) | 1.73508 | − | 3.00525i | 0.0659104 | − | 0.114160i | ||||
\(694\) | 15.7098 | − | 27.2102i | 0.596335 | − | 1.03288i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.24284 | 0.236634 | ||||||||
\(697\) | −0.0579684 | + | 0.100404i | −0.00219571 | + | 0.00380308i | ||||
\(698\) | −11.7269 | − | 20.3117i | −0.443871 | − | 0.768808i | ||||
\(699\) | 0.835643 | − | 1.44738i | 0.0316069 | − | 0.0547448i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.08961 | − | 7.08341i | −0.154462 | − | 0.267537i | 0.778401 | − | 0.627768i | \(-0.216031\pi\) |
−0.932863 | + | 0.360231i | \(0.882698\pi\) | |||||||
\(702\) | 23.7796 | 0.897504 | ||||||||
\(703\) | 20.5623 | − | 8.13680i | 0.775521 | − | 0.306885i | ||||
\(704\) | −4.31087 | −0.162472 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.67340 | + | 15.0228i | 0.326428 | + | 0.565389i | ||||
\(707\) | −0.399058 | + | 0.691189i | −0.0150081 | + | 0.0259948i | ||||
\(708\) | −3.28029 | − | 5.68163i | −0.123281 | − | 0.213529i | ||||
\(709\) | 6.85226 | − | 11.8685i | 0.257342 | − | 0.445730i | −0.708187 | − | 0.706025i | \(-0.750487\pi\) |
0.965529 | + | 0.260295i | \(0.0838200\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.41975 | 0.315765 | ||||||||
\(712\) | 1.85992 | − | 3.22147i | 0.0697034 | − | 0.120730i | ||||
\(713\) | 5.94048 | − | 10.2892i | 0.222473 | − | 0.385334i | ||||
\(714\) | −0.0290114 | −0.00108572 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.561247 | − | 0.972108i | 0.0209748 | − | 0.0363294i | ||||
\(717\) | −3.22729 | − | 5.58982i | −0.120525 | − | 0.208756i | ||||
\(718\) | −0.402934 | + | 0.697902i | −0.0150374 | + | 0.0260455i | ||||
\(719\) | −13.4178 | − | 23.2403i | −0.500398 | − | 0.866715i | −1.00000 | 0.000460027i | \(-0.999854\pi\) | |
0.499602 | − | 0.866255i | \(-0.333480\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.28097 | 0.0477060 | ||||||||
\(722\) | −18.1870 | − | 5.49830i | −0.676852 | − | 0.204626i | ||||
\(723\) | 11.5122 | 0.428143 | ||||||||
\(724\) | −7.89198 | − | 13.6693i | −0.293303 | − | 0.508016i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.58744 | − | 4.48157i | 0.0960288 | − | 0.166327i | ||||
\(727\) | 14.5299 | + | 25.1665i | 0.538883 | + | 0.933373i | 0.998965 | + | 0.0454961i | \(0.0144869\pi\) |
−0.460081 | + | 0.887877i | \(0.652180\pi\) | |||||||
\(728\) | 1.00000 | − | 1.73205i | 0.0370625 | − | 0.0641941i | ||||
\(729\) | −5.00701 | −0.185445 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.381749 | − | 0.661209i | 0.0141195 | − | 0.0244557i | ||||
\(732\) | 2.10657 | − | 3.64868i | 0.0778609 | − | 0.134859i | ||||
\(733\) | −30.8850 | −1.14076 | −0.570381 | − | 0.821380i | \(-0.693204\pi\) | ||||
−0.570381 | + | 0.821380i | \(0.693204\pi\) | |||||||
\(734\) | 2.53816 | 0.0936852 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.98955 | − | 3.44600i | −0.0733357 | − | 0.127021i | ||||
\(737\) | −1.27394 | + | 2.20653i | −0.0469262 | + | 0.0812786i | ||||
\(738\) | −1.09757 | − | 1.90104i | −0.0404020 | − | 0.0699782i | ||||
\(739\) | 17.9491 | + | 31.0887i | 0.660267 | + | 1.14362i | 0.980545 | + | 0.196292i | \(0.0628901\pi\) |
−0.320279 | + | 0.947323i | \(0.603777\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.4150 | − | 6.89138i | 0.639757 | − | 0.253161i | ||||
\(742\) | −2.51725 | −0.0924113 | ||||||||
\(743\) | 3.15432 | + | 5.46344i | 0.115721 | + | 0.200434i | 0.918068 | − | 0.396424i | \(-0.129749\pi\) |
−0.802347 | + | 0.596858i | \(0.796416\pi\) | |||||||
\(744\) | −1.01873 | − | 1.76450i | −0.0373485 | − | 0.0646895i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.20061 | + | 10.7398i | 0.227020 | + | 0.393211i | ||||
\(747\) | −5.33114 | + | 9.23380i | −0.195056 | + | 0.337847i | ||||
\(748\) | 0.577026 | 0.0210982 | ||||||||
\(749\) | 3.17626 | 0.116058 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.3945 | − | 35.3242i | 0.744204 | − | 1.28900i | −0.206361 | − | 0.978476i | \(-0.566162\pi\) |
0.950566 | − | 0.310524i | \(-0.100505\pi\) | |||||||
\(752\) | 12.9723 | 0.473053 | ||||||||
\(753\) | −1.81257 | −0.0660537 | ||||||||
\(754\) | 28.8034 | − | 49.8890i | 1.04896 | − | 1.81685i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.599758 | − | 1.03881i | 0.0218130 | − | 0.0377812i | ||||
\(757\) | 9.72687 | + | 16.8474i | 0.353529 | + | 0.612330i | 0.986865 | − | 0.161547i | \(-0.0516482\pi\) |
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(758\) | 6.33778 | + | 10.9774i | 0.230199 | + | 0.398716i | ||||
\(759\) | 11.7050 | 0.424865 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.1465 | −0.694058 | −0.347029 | − | 0.937854i | \(-0.612810\pi\) | ||||
−0.347029 | + | 0.937854i | \(0.612810\pi\) | |||||||
\(762\) | −6.10619 | − | 10.5762i | −0.221204 | − | 0.383137i | ||||
\(763\) | −0.931269 | − | 1.61301i | −0.0337142 | − | 0.0583947i | ||||
\(764\) | −9.14871 | + | 15.8460i | −0.330989 | + | 0.573289i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.97632 | + | 13.8154i | −0.288196 | + | 0.499170i | ||||
\(767\) | −60.5388 | −2.18593 | ||||||||
\(768\) | −0.682374 | −0.0246231 | ||||||||
\(769\) | −13.3405 | + | 23.1064i | −0.481070 | + | 0.833238i | −0.999764 | − | 0.0217222i | \(-0.993085\pi\) |
0.518694 | + | 0.854960i | \(0.326418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.53360 | −0.0552314 | ||||||||
\(772\) | 1.11755 | 0.0402216 | ||||||||
\(773\) | 11.8521 | − | 20.5284i | 0.426290 | − | 0.738356i | −0.570250 | − | 0.821471i | \(-0.693154\pi\) |
0.996540 | + | 0.0831151i | \(0.0264869\pi\) | |||||||
\(774\) | 7.22799 | + | 12.5192i | 0.259805 | + | 0.449995i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.42830 | − | 4.20594i | −0.0871709 | − | 0.150984i | ||||
\(777\) | 0.549785 | + | 0.952255i | 0.0197234 | + | 0.0341620i | ||||
\(778\) | −26.1982 | −0.939250 | ||||||||
\(779\) | −2.95836 | − | 2.34565i | −0.105994 | − | 0.0840418i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.1356 | + | 43.5361i | 0.899421 | + | 1.55784i | ||||
\(782\) | 0.266308 | + | 0.461259i | 0.00952315 | + | 0.0164946i | ||||
\(783\) | 17.2751 | − | 29.9213i | 0.617361 | − | 1.06930i | ||||
\(784\) | 3.44956 | + | 5.97481i | 0.123198 | + | 0.213386i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.05896 | 0.287454 | ||||||||
\(787\) | 30.3141 | 1.08058 | 0.540291 | − | 0.841478i | \(-0.318314\pi\) | ||||
0.540291 | + | 0.841478i | \(0.318314\pi\) | |||||||
\(788\) | −8.12970 | + | 14.0811i | −0.289609 | + | 0.501617i | ||||
\(789\) | −10.8695 | + | 18.8265i | −0.386964 | + | 0.670241i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.74435 | −0.204246 | ||||||||
\(792\) | −5.46266 | + | 9.46161i | −0.194107 | + | 0.336204i | ||||
\(793\) | −19.4387 | − | 33.6688i | −0.690288 | − | 1.19561i | ||||
\(794\) | 15.0639 | − | 26.0914i | 0.534597 | − | 0.925949i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.89911 | + | 11.9496i | 0.244533 | + | 0.423543i | ||||
\(797\) | 0.460092 | 0.0162973 | 0.00814865 | − | 0.999967i | \(-0.497406\pi\) | ||||
0.00814865 | + | 0.999967i | \(0.497406\pi\) | |||||||
\(798\) | 0.138183 | − | 0.934586i | 0.00489164 | − | 0.0330840i | ||||
\(799\) | −1.73639 | −0.0614292 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.71371 | − | 8.16439i | −0.166551 | − | 0.288475i | ||||
\(802\) | 1.08591 | − | 1.88085i | 0.0383449 | − | 0.0664153i | ||||
\(803\) | −17.8060 | − | 30.8408i | −0.628359 | − | 1.08835i | ||||
\(804\) | −0.201654 | + | 0.349275i | −0.00711178 | + | 0.0123180i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.8010 | −0.662238 | ||||||||
\(807\) | −3.71733 | + | 6.43860i | −0.130856 | + | 0.226649i | ||||
\(808\) | 1.25638 | − | 2.17611i | 0.0441992 | − | 0.0765553i | ||||
\(809\) | 43.3070 | 1.52259 | 0.761296 | − | 0.648404i | \(-0.224563\pi\) | ||||
0.761296 | + | 0.648404i | \(0.224563\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.9700 | + | 27.6609i | −0.560783 | + | 0.971305i | 0.436645 | + | 0.899634i | \(0.356166\pi\) |
−0.997428 | + | 0.0716709i | \(0.977167\pi\) | |||||||
\(812\) | −1.45293 | − | 2.51655i | −0.0509880 | − | 0.0883137i | ||||
\(813\) | −4.07126 | + | 7.05162i | −0.142785 | + | 0.247311i | ||||
\(814\) | −10.9350 | − | 18.9400i | −0.383272 | − | 0.663847i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.0913382 | 0.00319748 | ||||||||
\(817\) | 19.4822 | + | 15.4472i | 0.681596 | + | 0.540430i | ||||
\(818\) | 32.1664 | 1.12467 | ||||||||
\(819\) | −2.53437 | − | 4.38965i | −0.0885579 | − | 0.153387i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.55092 | + | 16.5427i | −0.333329 | + | 0.577344i | −0.983162 | − | 0.182733i | \(-0.941505\pi\) |
0.649833 | + | 0.760077i | \(0.274839\pi\) | |||||||
\(822\) | −5.40136 | − | 9.35543i | −0.188394 | − | 0.326308i | ||||
\(823\) | −8.43860 | + | 14.6161i | −0.294151 | + | 0.509485i | −0.974787 | − | 0.223137i | \(-0.928370\pi\) |
0.680636 | + | 0.732622i | \(0.261704\pi\) | |||||||
\(824\) | −4.03297 | −0.140495 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.52688 | + | 2.64464i | −0.0531270 | + | 0.0920187i | ||||
\(827\) | 11.9233 | − | 20.6518i | 0.414615 | − | 0.718134i | −0.580773 | − | 0.814065i | \(-0.697250\pi\) |
0.995388 | + | 0.0959317i | \(0.0305830\pi\) | |||||||
\(828\) | −10.0845 | −0.350460 | ||||||||
\(829\) | −34.6508 | −1.20347 | −0.601735 | − | 0.798696i | \(-0.705524\pi\) | ||||
−0.601735 | + | 0.798696i | \(0.705524\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.42710 | − | 9.40001i | −0.188264 | − | 0.326083i | ||||
\(832\) | −3.14836 | + | 5.45312i | −0.109150 | + | 0.189053i | ||||
\(833\) | −0.461735 | − | 0.799749i | −0.0159982 | − | 0.0277097i | ||||
\(834\) | 0.398289 | + | 0.689856i | 0.0137916 | + | 0.0238878i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.74842 | + | 18.5886i | −0.0950561 | + | 0.642899i | ||||
\(837\) | −11.2761 | −0.389758 | ||||||||
\(838\) | 4.99837 | + | 8.65743i | 0.172666 | + | 0.299066i | ||||
\(839\) | 4.08140 | + | 7.06919i | 0.140906 | + | 0.244056i | 0.927838 | − | 0.372984i | \(-0.121665\pi\) |
−0.786932 | + | 0.617039i | \(0.788332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3494 | − | 47.3706i | −0.943084 | − | 1.63347i | ||||
\(842\) | 19.0856 | − | 33.0572i | 0.657732 | − | 1.13922i | ||||
\(843\) | 14.3191 | 0.493177 | ||||||||
\(844\) | −1.16892 | −0.0402358 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 16.4383 | − | 28.4720i | 0.565161 | − | 0.978888i | ||||
\(847\) | −2.40876 | −0.0827659 | ||||||||
\(848\) | 7.92522 | 0.272153 | ||||||||
\(849\) | −4.38823 | + | 7.60064i | −0.150604 | + | 0.260853i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.0934 | − | 17.4823i | 0.345998 | − | 0.599286i | ||||
\(852\) | 3.97874 | + | 6.89138i | 0.136309 | + | 0.236095i | ||||
\(853\) | 11.6611 | + | 20.1976i | 0.399269 | + | 0.691554i | 0.993636 | − | 0.112640i | \(-0.0359306\pi\) |
−0.594367 | + | 0.804194i | \(0.702597\pi\) | |||||||
\(854\) | −1.96109 | −0.0671072 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.0000 | −0.341793 | ||||||||
\(857\) | −16.7728 | − | 29.0514i | −0.572949 | − | 0.992377i | −0.996261 | − | 0.0863933i | \(-0.972466\pi\) |
0.423312 | − | 0.905984i | \(-0.360867\pi\) | |||||||
\(858\) | −9.26131 | − | 16.0411i | −0.316176 | − | 0.547632i | ||||
\(859\) | −8.96416 | + | 15.5264i | −0.305853 | + | 0.529753i | −0.977451 | − | 0.211163i | \(-0.932275\pi\) |
0.671598 | + | 0.740916i | \(0.265608\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0938641 | − | 0.162577i | 0.00319888 | − | 0.00554062i | ||||
\(862\) | 3.47298 | 0.118290 | ||||||||
\(863\) | 40.9267 | 1.39316 | 0.696580 | − | 0.717479i | \(-0.254704\pi\) | ||||
0.696580 | + | 0.717479i | \(0.254704\pi\) | |||||||
\(864\) | −1.88825 | + | 3.27055i | −0.0642397 | + | 0.111266i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.0948 | −0.377018 | ||||||||
\(867\) | 11.5881 | 0.393554 | ||||||||
\(868\) | −0.474191 | + | 0.821322i | −0.0160951 | + | 0.0278775i | ||||
\(869\) | −7.16086 | − | 12.4030i | −0.242916 | − | 0.420742i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.86079 | + | 3.22299i | 0.0630506 | + | 0.109207i | ||||
\(872\) | 2.93197 | + | 5.07832i | 0.0992890 | + | 0.171974i | ||||
\(873\) | −12.3084 | −0.416576 | ||||||||
\(874\) | −16.1276 | + | 6.38195i | −0.545526 | + | 0.215873i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.81853 | − | 4.88184i | −0.0952294 | − | 0.164942i | ||||
\(877\) | −5.72299 | − | 9.91251i | −0.193252 | − | 0.334722i | 0.753074 | − | 0.657935i | \(-0.228570\pi\) |
−0.946326 | + | 0.323214i | \(0.895237\pi\) | |||||||
\(878\) | 6.51914 | − | 11.2915i | 0.220010 | − | 0.381069i | ||||
\(879\) | −4.13783 | − | 7.16694i | −0.139566 | − | 0.241735i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.5970 | −0.592860 | −0.296430 | − | 0.955055i | \(-0.595796\pi\) | ||||
−0.296430 | + | 0.955055i | \(0.595796\pi\) | |||||||
\(882\) | 17.4849 | 0.588746 | ||||||||
\(883\) | 11.6528 | − | 20.1832i | 0.392147 | − | 0.679218i | −0.600586 | − | 0.799560i | \(-0.705066\pi\) |
0.992732 | + | 0.120342i | \(0.0383992\pi\) | |||||||
\(884\) | 0.421419 | − | 0.729919i | 0.0141739 | − | 0.0245498i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.0250 | 0.504775 | ||||||||
\(887\) | 2.19763 | − | 3.80640i | 0.0737891 | − | 0.127806i | −0.826770 | − | 0.562540i | \(-0.809824\pi\) |
0.900559 | + | 0.434734i | \(0.143158\pi\) | |||||||
\(888\) | −1.73092 | − | 2.99804i | −0.0580859 | − | 0.100608i | ||||
\(889\) | −2.84226 | + | 4.92294i | −0.0953263 | + | 0.165110i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.8335 | + | 18.7641i | 0.362934 | + | 0.628621i | ||||
\(892\) | 6.31763 | 0.211530 | ||||||||
\(893\) | 8.27058 | − | 55.9370i | 0.276765 | − | 1.87186i | ||||
\(894\) | 8.29187 | 0.277322 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.158813 | + | 0.275072i | 0.00530557 | + | 0.00918951i | ||||
\(897\) | 8.54852 | − | 14.8065i | 0.285427 | − | 0.494374i | ||||
\(898\) | −7.21254 | − | 12.4925i | −0.240686 | − | 0.416880i | ||||
\(899\) | −13.6583 | + | 23.6569i | −0.455530 | + | 0.789002i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.06082 | −0.0353410 | ||||||||
\(902\) | −1.86692 | + | 3.23361i | −0.0621618 | + | 0.107667i | ||||
\(903\) | −0.618140 | + | 1.07065i | −0.0205704 | + | 0.0356290i | ||||
\(904\) | 18.0853 | 0.601508 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.95350 | + | 12.0438i | −0.231014 | + | 0.400129i | ||||
\(907\) | −26.9577 | − | 46.6921i | −0.895115 | − | 1.55039i | −0.833662 | − | 0.552275i | \(-0.813760\pi\) |
−0.0614534 | − | 0.998110i | \(-0.519574\pi\) | |||||||
\(908\) | −1.88971 | + | 3.27307i | −0.0627122 | + | 0.108621i | ||||
\(909\) | −3.18412 | − | 5.51506i | −0.105611 | − | 0.182923i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.8496 | −1.41967 | −0.709835 | − | 0.704368i | \(-0.751231\pi\) | ||||
−0.709835 | + | 0.704368i | \(0.751231\pi\) | |||||||
\(912\) | −0.435051 | + | 2.94241i | −0.0144060 | + | 0.0974330i | ||||
\(913\) | 18.1362 | 0.600220 | ||||||||
\(914\) | 16.0887 | + | 27.8664i | 0.532166 | + | 0.921738i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.71814 | + | 4.70795i | −0.0898098 | + | 0.155555i | ||||
\(917\) | −1.87561 | − | 3.24865i | −0.0619380 | − | 0.107280i | ||||
\(918\) | 0.252750 | − | 0.437775i | 0.00834198 | − | 0.0144487i | ||||
\(919\) | 40.6599 | 1.34124 | 0.670622 | − | 0.741799i | \(-0.266027\pi\) | ||||
0.670622 | + | 0.741799i | \(0.266027\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.19875 | − | 10.7365i | 0.204256 | − | 0.353781i | ||||
\(922\) | 7.75530 | − | 13.4326i | 0.255407 | − | 0.442378i | ||||
\(923\) | 73.4290 | 2.41694 | ||||||||
\(924\) | −0.934337 | −0.0307374 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.0739 | + | 26.1087i | 0.495358 | + | 0.857985i | ||||
\(927\) | −5.11051 | + | 8.85166i | −0.167851 | + | 0.290727i | ||||
\(928\) | 4.57435 | + | 7.92301i | 0.150161 | + | 0.260086i | ||||
\(929\) | 14.3215 | + | 24.8056i | 0.469874 | + | 0.813846i | 0.999407 | − | 0.0344435i | \(-0.0109659\pi\) |
−0.529532 | + | 0.848290i | \(0.677633\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.9628 | − | 11.0653i | 0.916443 | − | 0.362650i | ||||
\(932\) | 2.44922 | 0.0802270 | ||||||||
\(933\) | 6.64518 | + | 11.5098i | 0.217553 | + | 0.376814i | ||||
\(934\) | 17.2866 | + | 29.9412i | 0.565634 | + | 0.979706i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.97909 | + | 13.8202i | 0.260805 | + | 0.451727i | ||||
\(937\) | 13.9548 | − | 24.1704i | 0.455884 | − | 0.789614i | −0.542855 | − | 0.839827i | \(-0.682657\pi\) |
0.998739 | + | 0.0502128i | \(0.0159899\pi\) | |||||||
\(938\) | 0.187728 | 0.00612955 | ||||||||
\(939\) | 8.17467 | 0.266770 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.3706 | + | 24.8907i | −0.468470 | + | 0.811413i | −0.999351 | − | 0.0360331i | \(-0.988528\pi\) |
0.530881 | + | 0.847446i | \(0.321861\pi\) | |||||||
\(942\) | −3.35893 | −0.109440 | ||||||||
\(943\) | −3.44648 | −0.112233 | ||||||||
\(944\) | 4.80717 | − | 8.32627i | 0.156460 | − | 0.270997i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.2946 | − | 21.2948i | 0.399731 | − | 0.692355i | ||||
\(947\) | 15.2939 | + | 26.4899i | 0.496986 | + | 0.860804i | 0.999994 | − | 0.00347712i | \(-0.00110680\pi\) |
−0.503008 | + | 0.864282i | \(0.667773\pi\) | |||||||
\(948\) | −1.13350 | − | 1.96329i | −0.0368145 | − | 0.0637645i | ||||
\(949\) | −52.0169 | −1.68854 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.770611 | 0.0249888 | ||||||||
\(952\) | −0.0212577 | − | 0.0368194i | −0.000688965 | − | 0.00119332i | ||||
\(953\) | 11.7597 | + | 20.3684i | 0.380933 | + | 0.659796i | 0.991196 | − | 0.132403i | \(-0.0422694\pi\) |
−0.610263 | + | 0.792199i | \(0.708936\pi\) | |||||||
\(954\) | 10.0427 | − | 17.3945i | 0.325144 | − | 0.563167i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.72950 | − | 8.19173i | 0.152963 | − | 0.264939i | ||||
\(957\) | −26.9121 | −0.869945 | ||||||||
\(958\) | 30.8476 | 0.996642 | ||||||||
\(959\) | −2.51418 | + | 4.35469i | −0.0811871 | + | 0.140620i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0847 | −0.712411 | ||||||||
\(962\) | −31.9447 | −1.02994 | ||||||||
\(963\) | −12.6718 | + | 21.9482i | −0.408344 | + | 0.707272i | ||||
\(964\) | 8.43540 | + | 14.6105i | 0.271686 | + | 0.470574i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.431214 | − | 0.746884i | −0.0138741 | − | 0.0240306i | ||||
\(967\) | −0.318277 | − | 0.551272i | −0.0102351 | − | 0.0177277i | 0.860862 | − | 0.508838i | \(-0.169925\pi\) |
−0.871098 | + | 0.491110i | \(0.836591\pi\) | |||||||
\(968\) | 7.58363 | 0.243747 | ||||||||
\(969\) | 0.0582332 | − | 0.393852i | 0.00187072 | − | 0.0126524i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.9491 | − | 20.6965i | −0.383466 | − | 0.664182i | 0.608089 | − | 0.793869i | \(-0.291936\pi\) |
−0.991555 | + | 0.129686i | \(0.958603\pi\) | |||||||
\(972\) | 7.37960 | + | 12.7819i | 0.236701 | + | 0.409978i | ||||
\(973\) | 0.185392 | − | 0.321108i | 0.00594339 | − | 0.0102943i | ||||
\(974\) | 15.3873 | + | 26.6515i | 0.493040 | + | 0.853970i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.17422 | 0.197632 | ||||||||
\(977\) | 7.29767 | 0.233473 | 0.116737 | − | 0.993163i | \(-0.462757\pi\) | ||||
0.116737 | + | 0.993163i | \(0.462757\pi\) | |||||||
\(978\) | −0.490380 | + | 0.849362i | −0.0156806 | + | 0.0271596i | ||||
\(979\) | −8.01788 | + | 13.8874i | −0.256252 | + | 0.443842i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.8614 | 0.474487 | ||||||||
\(982\) | 12.8571 | − | 22.2692i | 0.410287 | − | 0.710638i | ||||
\(983\) | −24.6949 | − | 42.7727i | −0.787644 | − | 1.36424i | −0.927407 | − | 0.374054i | \(-0.877968\pi\) |
0.139763 | − | 0.990185i | \(-0.455366\pi\) | |||||||
\(984\) | −0.295518 | + | 0.511852i | −0.00942077 | + | 0.0163173i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.612294 | − | 1.06052i | −0.0194994 | − | 0.0337740i | ||||
\(987\) | 2.81162 | 0.0894949 | ||||||||
\(988\) | 21.5067 | + | 17.0525i | 0.684219 | + | 0.542511i | ||||
\(989\) | 22.6967 | 0.721712 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.14580 | + | 12.3769i | 0.226994 | + | 0.393165i | 0.956916 | − | 0.290366i | \(-0.0937769\pi\) |
−0.729922 | + | 0.683531i | \(0.760444\pi\) | |||||||
\(992\) | 1.49292 | − | 2.58582i | 0.0474003 | − | 0.0820998i | ||||
\(993\) | −4.88169 | − | 8.45534i | −0.154916 | − | 0.268322i | ||||
\(994\) | 1.85199 | − | 3.20774i | 0.0587416 | − | 0.101743i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.87080 | 0.0909649 | ||||||||
\(997\) | −29.4280 | + | 50.9707i | −0.931993 | + | 1.61426i | −0.152084 | + | 0.988368i | \(0.548598\pi\) |
−0.779910 | + | 0.625892i | \(0.784735\pi\) | |||||||
\(998\) | 0.201106 | − | 0.348326i | 0.00636590 | − | 0.0110261i | ||||
\(999\) | −19.1591 | −0.606167 |
(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 | 950.2.e.n.501.3 | 10 | ||
5.2 | odd | 4 | 190.2.i.a.159.8 | yes | 20 | ||
5.3 | odd | 4 | 190.2.i.a.159.3 | yes | 20 | ||
5.4 | even | 2 | 950.2.e.o.501.3 | 10 | |||
15.2 | even | 4 | 1710.2.t.d.919.3 | 20 | |||
15.8 | even | 4 | 1710.2.t.d.919.10 | 20 | |||
19.11 | even | 3 | inner | 950.2.e.n.201.3 | 10 | ||
95.49 | even | 6 | 950.2.e.o.201.3 | 10 | |||
95.68 | odd | 12 | 190.2.i.a.49.8 | yes | 20 | ||
95.87 | odd | 12 | 190.2.i.a.49.3 | ✓ | 20 | ||
285.68 | even | 12 | 1710.2.t.d.1189.3 | 20 | |||
285.182 | even | 12 | 1710.2.t.d.1189.10 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.i.a.49.3 | ✓ | 20 | 95.87 | odd | 12 | ||
190.2.i.a.49.8 | yes | 20 | 95.68 | odd | 12 | ||
190.2.i.a.159.3 | yes | 20 | 5.3 | odd | 4 | ||
190.2.i.a.159.8 | yes | 20 | 5.2 | odd | 4 | ||
950.2.e.n.201.3 | 10 | 19.11 | even | 3 | inner | ||
950.2.e.n.501.3 | 10 | 1.1 | even | 1 | trivial | ||
950.2.e.o.201.3 | 10 | 95.49 | even | 6 | |||
950.2.e.o.501.3 | 10 | 5.4 | even | 2 | |||
1710.2.t.d.919.3 | 20 | 15.2 | even | 4 | |||
1710.2.t.d.919.10 | 20 | 15.8 | even | 4 | |||
1710.2.t.d.1189.3 | 20 | 285.68 | even | 12 | |||
1710.2.t.d.1189.10 | 20 | 285.182 | even | 12 |