Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,3,Mod(124,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.124");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3052138789\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 124.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.124 |
Dual form | 525.3.s.b.199.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.433013 | + | 0.250000i | 0.700629 | − | 0.713525i | \(-0.252903\pi\) |
−0.267617 | + | 0.963525i | \(0.586236\pi\) | |||||||
\(3\) | 0.866025 | + | 1.50000i | 0.288675 | + | 0.500000i | ||||
\(4\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.73205i | 0.288675i | ||||||||
\(7\) | 4.33013 | − | 5.50000i | 0.618590 | − | 0.785714i | ||||
\(8\) | − | 7.00000i | − | 0.875000i | ||||||
\(9\) | −1.50000 | + | 2.59808i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | − | 3.46410i | −0.181818 | − | 0.314918i | 0.760682 | − | 0.649125i | \(-0.224865\pi\) |
−0.942500 | + | 0.334207i | \(0.891532\pi\) | |||||||
\(12\) | 2.59808 | − | 4.50000i | 0.216506 | − | 0.375000i | ||||
\(13\) | −17.3205 | −1.33235 | −0.666173 | − | 0.745797i | \(-0.732069\pi\) | ||||
−0.666173 | + | 0.745797i | \(0.732069\pi\) | |||||||
\(14\) | 6.50000 | − | 2.59808i | 0.464286 | − | 0.185577i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.50000 | + | 4.33013i | −0.156250 | + | 0.270633i | ||||
\(17\) | −4.33013 | − | 7.50000i | −0.254713 | − | 0.441176i | 0.710104 | − | 0.704097i | \(-0.248648\pi\) |
−0.964818 | + | 0.262920i | \(0.915314\pi\) | |||||||
\(18\) | −2.59808 | + | 1.50000i | −0.144338 | + | 0.0833333i | ||||
\(19\) | −6.00000 | − | 3.46410i | −0.315789 | − | 0.182321i | 0.333725 | − | 0.942671i | \(-0.391694\pi\) |
−0.649514 | + | 0.760349i | \(0.725028\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.0000 | + | 1.73205i | 0.571429 | + | 0.0824786i | ||||
\(22\) | − | 4.00000i | − | 0.181818i | ||||||
\(23\) | −26.8468 | − | 15.5000i | −1.16725 | − | 0.673913i | −0.214220 | − | 0.976785i | \(-0.568721\pi\) |
−0.953031 | + | 0.302872i | \(0.902054\pi\) | |||||||
\(24\) | 10.5000 | − | 6.06218i | 0.437500 | − | 0.252591i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −15.0000 | − | 8.66025i | −0.576923 | − | 0.333087i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −20.7846 | − | 3.00000i | −0.742307 | − | 0.107143i | ||||
\(29\) | −10.0000 | −0.344828 | −0.172414 | − | 0.985025i | \(-0.555157\pi\) | ||||
−0.172414 | + | 0.985025i | \(0.555157\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 25.5000 | − | 14.7224i | 0.822581 | − | 0.474917i | −0.0287249 | − | 0.999587i | \(-0.509145\pi\) |
0.851306 | + | 0.524670i | \(0.175811\pi\) | |||||||
\(32\) | −28.5788 | + | 16.5000i | −0.893089 | + | 0.515625i | ||||
\(33\) | 3.46410 | − | 6.00000i | 0.104973 | − | 0.181818i | ||||
\(34\) | − | 8.66025i | − | 0.254713i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.00000 | 0.250000 | ||||||||
\(37\) | 43.3013 | + | 25.0000i | 1.17030 | + | 0.675676i | 0.953752 | − | 0.300595i | \(-0.0971853\pi\) |
0.216553 | + | 0.976271i | \(0.430519\pi\) | |||||||
\(38\) | −3.46410 | − | 6.00000i | −0.0911606 | − | 0.157895i | ||||
\(39\) | −15.0000 | − | 25.9808i | −0.384615 | − | 0.666173i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 53.6936i | − | 1.30960i | −0.755802 | − | 0.654800i | \(-0.772753\pi\) | ||
0.755802 | − | 0.654800i | \(-0.227247\pi\) | |||||||
\(42\) | 9.52628 | + | 7.50000i | 0.226816 | + | 0.178571i | ||||
\(43\) | − | 34.0000i | − | 0.790698i | −0.918531 | − | 0.395349i | \(-0.870624\pi\) | ||
0.918531 | − | 0.395349i | \(-0.129376\pi\) | |||||||
\(44\) | −6.00000 | + | 10.3923i | −0.136364 | + | 0.236189i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −15.5000 | − | 26.8468i | −0.336957 | − | 0.583626i | ||||
\(47\) | 21.6506 | − | 37.5000i | 0.460652 | − | 0.797872i | −0.538342 | − | 0.842727i | \(-0.680949\pi\) |
0.998994 | + | 0.0448543i | \(0.0142824\pi\) | |||||||
\(48\) | −8.66025 | −0.180422 | ||||||||
\(49\) | −11.5000 | − | 47.6314i | −0.234694 | − | 0.972069i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.50000 | − | 12.9904i | 0.147059 | − | 0.254713i | ||||
\(52\) | 25.9808 | + | 45.0000i | 0.499630 | + | 0.865385i | ||||
\(53\) | −43.3013 | + | 25.0000i | −0.817005 | + | 0.471698i | −0.849383 | − | 0.527778i | \(-0.823025\pi\) |
0.0323775 | + | 0.999476i | \(0.489692\pi\) | |||||||
\(54\) | −4.50000 | − | 2.59808i | −0.0833333 | − | 0.0481125i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −38.5000 | − | 30.3109i | −0.687500 | − | 0.541266i | ||||
\(57\) | − | 12.0000i | − | 0.210526i | ||||||
\(58\) | −8.66025 | − | 5.00000i | −0.149315 | − | 0.0862069i | ||||
\(59\) | 48.0000 | − | 27.7128i | 0.813559 | − | 0.469709i | −0.0346311 | − | 0.999400i | \(-0.511026\pi\) |
0.848190 | + | 0.529691i | \(0.177692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 21.0000 | + | 12.1244i | 0.344262 | + | 0.198760i | 0.662155 | − | 0.749367i | \(-0.269642\pi\) |
−0.317893 | + | 0.948127i | \(0.602975\pi\) | |||||||
\(62\) | 29.4449 | 0.474917 | ||||||||
\(63\) | 7.79423 | + | 19.5000i | 0.123718 | + | 0.309524i | ||||
\(64\) | −13.0000 | −0.203125 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.00000 | − | 3.46410i | 0.0909091 | − | 0.0524864i | ||||
\(67\) | −43.3013 | + | 25.0000i | −0.646288 | + | 0.373134i | −0.787032 | − | 0.616912i | \(-0.788384\pi\) |
0.140745 | + | 0.990046i | \(0.455050\pi\) | |||||||
\(68\) | −12.9904 | + | 22.5000i | −0.191035 | + | 0.330882i | ||||
\(69\) | − | 53.6936i | − | 0.778168i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 97.0000 | 1.36620 | 0.683099 | − | 0.730326i | \(-0.260632\pi\) | ||||
0.683099 | + | 0.730326i | \(0.260632\pi\) | |||||||
\(72\) | 18.1865 | + | 10.5000i | 0.252591 | + | 0.145833i | ||||
\(73\) | 24.2487 | + | 42.0000i | 0.332174 | + | 0.575342i | 0.982938 | − | 0.183938i | \(-0.0588845\pi\) |
−0.650764 | + | 0.759280i | \(0.725551\pi\) | |||||||
\(74\) | 25.0000 | + | 43.3013i | 0.337838 | + | 0.585152i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.7846i | 0.273482i | ||||||||
\(77\) | −27.7128 | − | 4.00000i | −0.359907 | − | 0.0519481i | ||||
\(78\) | − | 30.0000i | − | 0.384615i | ||||||
\(79\) | −3.50000 | + | 6.06218i | −0.0443038 | + | 0.0767364i | −0.887327 | − | 0.461141i | \(-0.847440\pi\) |
0.843023 | + | 0.537877i | \(0.180774\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 26.8468 | − | 46.5000i | 0.327400 | − | 0.567073i | ||||
\(83\) | −152.420 | −1.83639 | −0.918196 | − | 0.396127i | \(-0.870354\pi\) | ||||
−0.918196 | + | 0.396127i | \(0.870354\pi\) | |||||||
\(84\) | −13.5000 | − | 33.7750i | −0.160714 | − | 0.402083i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 17.0000 | − | 29.4449i | 0.197674 | − | 0.342382i | ||||
\(87\) | −8.66025 | − | 15.0000i | −0.0995431 | − | 0.172414i | ||||
\(88\) | −24.2487 | + | 14.0000i | −0.275554 | + | 0.159091i | ||||
\(89\) | 136.500 | + | 78.8083i | 1.53371 | + | 0.885487i | 0.999186 | + | 0.0403318i | \(0.0128415\pi\) |
0.534522 | + | 0.845155i | \(0.320492\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −75.0000 | + | 95.2628i | −0.824176 | + | 1.04684i | ||||
\(92\) | 93.0000i | 1.01087i | ||||||||
\(93\) | 44.1673 | + | 25.5000i | 0.474917 | + | 0.274194i | ||||
\(94\) | 37.5000 | − | 21.6506i | 0.398936 | − | 0.230326i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −49.5000 | − | 28.5788i | −0.515625 | − | 0.297696i | ||||
\(97\) | 112.583 | 1.16065 | 0.580326 | − | 0.814384i | \(-0.302925\pi\) | ||||
0.580326 | + | 0.814384i | \(0.302925\pi\) | |||||||
\(98\) | 13.8564 | − | 47.0000i | 0.141392 | − | 0.479592i | ||||
\(99\) | 12.0000 | 0.121212 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.0000 | + | 10.3923i | −0.178218 | + | 0.102894i | −0.586455 | − | 0.809982i | \(-0.699477\pi\) |
0.408237 | + | 0.912876i | \(0.366144\pi\) | |||||||
\(102\) | 12.9904 | − | 7.50000i | 0.127357 | − | 0.0735294i | ||||
\(103\) | 49.3634 | − | 85.5000i | 0.479257 | − | 0.830097i | −0.520460 | − | 0.853886i | \(-0.674240\pi\) |
0.999717 | + | 0.0237888i | \(0.00757293\pi\) | |||||||
\(104\) | 121.244i | 1.16580i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −50.0000 | −0.471698 | ||||||||
\(107\) | −152.420 | − | 88.0000i | −1.42449 | − | 0.822430i | −0.427812 | − | 0.903868i | \(-0.640715\pi\) |
−0.996678 | + | 0.0814379i | \(0.974049\pi\) | |||||||
\(108\) | 7.79423 | + | 13.5000i | 0.0721688 | + | 0.125000i | ||||
\(109\) | −2.00000 | − | 3.46410i | −0.0183486 | − | 0.0317807i | 0.856705 | − | 0.515806i | \(-0.172508\pi\) |
−0.875054 | + | 0.484025i | \(0.839174\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 86.6025i | 0.780203i | ||||||||
\(112\) | 12.9904 | + | 32.5000i | 0.115986 | + | 0.290179i | ||||
\(113\) | 115.000i | 1.01770i | 0.860855 | + | 0.508850i | \(0.169929\pi\) | ||||
−0.860855 | + | 0.508850i | \(0.830071\pi\) | |||||||
\(114\) | 6.00000 | − | 10.3923i | 0.0526316 | − | 0.0911606i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.0000 | + | 25.9808i | 0.129310 | + | 0.223972i | ||||
\(117\) | 25.9808 | − | 45.0000i | 0.222058 | − | 0.384615i | ||||
\(118\) | 55.4256 | 0.469709 | ||||||||
\(119\) | −60.0000 | − | 8.66025i | −0.504202 | − | 0.0727752i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 52.5000 | − | 90.9327i | 0.433884 | − | 0.751510i | ||||
\(122\) | 12.1244 | + | 21.0000i | 0.0993800 | + | 0.172131i | ||||
\(123\) | 80.5404 | − | 46.5000i | 0.654800 | − | 0.378049i | ||||
\(124\) | −76.5000 | − | 44.1673i | −0.616935 | − | 0.356188i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.00000 | + | 20.7846i | −0.0238095 | + | 0.164957i | ||||
\(127\) | − | 62.0000i | − | 0.488189i | −0.969751 | − | 0.244094i | \(-0.921509\pi\) | ||
0.969751 | − | 0.244094i | \(-0.0784907\pi\) | |||||||
\(128\) | 103.057 | + | 59.5000i | 0.805133 | + | 0.464844i | ||||
\(129\) | 51.0000 | − | 29.4449i | 0.395349 | − | 0.228255i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −27.0000 | − | 15.5885i | −0.206107 | − | 0.118996i | 0.393394 | − | 0.919370i | \(-0.371301\pi\) |
−0.599501 | + | 0.800374i | \(0.704634\pi\) | |||||||
\(132\) | −20.7846 | −0.157459 | ||||||||
\(133\) | −45.0333 | + | 18.0000i | −0.338596 | + | 0.135338i | ||||
\(134\) | −50.0000 | −0.373134 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −52.5000 | + | 30.3109i | −0.386029 | + | 0.222874i | ||||
\(137\) | −193.124 | + | 111.500i | −1.40966 | + | 0.813869i | −0.995355 | − | 0.0962688i | \(-0.969309\pi\) |
−0.414306 | + | 0.910137i | \(0.635976\pi\) | |||||||
\(138\) | 26.8468 | − | 46.5000i | 0.194542 | − | 0.336957i | ||||
\(139\) | − | 79.6743i | − | 0.573197i | −0.958051 | − | 0.286598i | \(-0.907475\pi\) | ||
0.958051 | − | 0.286598i | \(-0.0925245\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 75.0000 | 0.531915 | ||||||||
\(142\) | 84.0045 | + | 48.5000i | 0.591581 | + | 0.341549i | ||||
\(143\) | 34.6410 | + | 60.0000i | 0.242245 | + | 0.419580i | ||||
\(144\) | −7.50000 | − | 12.9904i | −0.0520833 | − | 0.0902110i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 48.4974i | 0.332174i | ||||||||
\(147\) | 61.4878 | − | 58.5000i | 0.418284 | − | 0.397959i | ||||
\(148\) | − | 150.000i | − | 1.01351i | ||||||
\(149\) | −106.000 | + | 183.597i | −0.711409 | + | 1.23220i | 0.252919 | + | 0.967488i | \(0.418609\pi\) |
−0.964328 | + | 0.264710i | \(0.914724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 119.000 | + | 206.114i | 0.788079 | + | 1.36499i | 0.927142 | + | 0.374710i | \(0.122258\pi\) |
−0.139063 | + | 0.990284i | \(0.544409\pi\) | |||||||
\(152\) | −24.2487 | + | 42.0000i | −0.159531 | + | 0.276316i | ||||
\(153\) | 25.9808 | 0.169809 | ||||||||
\(154\) | −22.0000 | − | 17.3205i | −0.142857 | − | 0.112471i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −45.0000 | + | 77.9423i | −0.288462 | + | 0.499630i | ||||
\(157\) | −126.440 | − | 219.000i | −0.805348 | − | 1.39490i | −0.916056 | − | 0.401051i | \(-0.868645\pi\) |
0.110707 | − | 0.993853i | \(-0.464688\pi\) | |||||||
\(158\) | −6.06218 | + | 3.50000i | −0.0383682 | + | 0.0221519i | ||||
\(159\) | −75.0000 | − | 43.3013i | −0.471698 | − | 0.272335i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −201.500 | + | 80.5404i | −1.25155 | + | 0.500251i | ||||
\(162\) | − | 9.00000i | − | 0.0555556i | ||||||
\(163\) | 252.879 | + | 146.000i | 1.55141 | + | 0.895706i | 0.998028 | + | 0.0627765i | \(0.0199955\pi\) |
0.553380 | + | 0.832929i | \(0.313338\pi\) | |||||||
\(164\) | −139.500 | + | 80.5404i | −0.850610 | + | 0.491100i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −132.000 | − | 76.2102i | −0.795181 | − | 0.459098i | ||||
\(167\) | −131.636 | −0.788239 | −0.394119 | − | 0.919059i | \(-0.628950\pi\) | ||||
−0.394119 | + | 0.919059i | \(0.628950\pi\) | |||||||
\(168\) | 12.1244 | − | 84.0000i | 0.0721688 | − | 0.500000i | ||||
\(169\) | 131.000 | 0.775148 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.0000 | − | 10.3923i | 0.105263 | − | 0.0607737i | ||||
\(172\) | −88.3346 | + | 51.0000i | −0.513573 | + | 0.296512i | ||||
\(173\) | 74.4782 | − | 129.000i | 0.430510 | − | 0.745665i | −0.566407 | − | 0.824125i | \(-0.691667\pi\) |
0.996917 | + | 0.0784606i | \(0.0250005\pi\) | |||||||
\(174\) | − | 17.3205i | − | 0.0995431i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 20.0000 | 0.113636 | ||||||||
\(177\) | 83.1384 | + | 48.0000i | 0.469709 | + | 0.271186i | ||||
\(178\) | 78.8083 | + | 136.500i | 0.442743 | + | 0.766854i | ||||
\(179\) | 95.0000 | + | 164.545i | 0.530726 | + | 0.919245i | 0.999357 | + | 0.0358508i | \(0.0114141\pi\) |
−0.468631 | + | 0.883394i | \(0.655253\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.7846i | − | 0.114832i | −0.998350 | − | 0.0574160i | \(-0.981714\pi\) | ||
0.998350 | − | 0.0574160i | \(-0.0182862\pi\) | |||||||
\(182\) | −112.583 | + | 45.0000i | −0.618590 | + | 0.247253i | ||||
\(183\) | 42.0000i | 0.229508i | ||||||||
\(184\) | −108.500 | + | 187.928i | −0.589674 | + | 1.02135i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 25.5000 | + | 44.1673i | 0.137097 | + | 0.237459i | ||||
\(187\) | −17.3205 | + | 30.0000i | −0.0926230 | + | 0.160428i | ||||
\(188\) | −129.904 | −0.690978 | ||||||||
\(189\) | −22.5000 | + | 28.5788i | −0.119048 | + | 0.151211i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 134.500 | − | 232.961i | 0.704188 | − | 1.21969i | −0.262795 | − | 0.964852i | \(-0.584644\pi\) |
0.966984 | − | 0.254839i | \(-0.0820223\pi\) | |||||||
\(192\) | −11.2583 | − | 19.5000i | −0.0586371 | − | 0.101562i | ||||
\(193\) | 25.1147 | − | 14.5000i | 0.130128 | − | 0.0751295i | −0.433523 | − | 0.901143i | \(-0.642730\pi\) |
0.563651 | + | 0.826013i | \(0.309396\pi\) | |||||||
\(194\) | 97.5000 | + | 56.2917i | 0.502577 | + | 0.290163i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −106.500 | + | 101.325i | −0.543367 | + | 0.516964i | ||||
\(197\) | − | 52.0000i | − | 0.263959i | −0.991252 | − | 0.131980i | \(-0.957867\pi\) | ||
0.991252 | − | 0.131980i | \(-0.0421334\pi\) | |||||||
\(198\) | 10.3923 | + | 6.00000i | 0.0524864 | + | 0.0303030i | ||||
\(199\) | −154.500 | + | 89.2006i | −0.776382 | + | 0.448244i | −0.835147 | − | 0.550028i | \(-0.814617\pi\) |
0.0587646 | + | 0.998272i | \(0.481284\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −75.0000 | − | 43.3013i | −0.373134 | − | 0.215429i | ||||
\(202\) | −20.7846 | −0.102894 | ||||||||
\(203\) | −43.3013 | + | 55.0000i | −0.213307 | + | 0.270936i | ||||
\(204\) | −45.0000 | −0.220588 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 85.5000 | − | 49.3634i | 0.415049 | − | 0.239628i | ||||
\(207\) | 80.5404 | − | 46.5000i | 0.389084 | − | 0.224638i | ||||
\(208\) | 43.3013 | − | 75.0000i | 0.208179 | − | 0.360577i | ||||
\(209\) | 27.7128i | 0.132597i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 344.000 | 1.63033 | 0.815166 | − | 0.579228i | \(-0.196646\pi\) | ||||
0.815166 | + | 0.579228i | \(0.196646\pi\) | |||||||
\(212\) | 129.904 | + | 75.0000i | 0.612754 | + | 0.353774i | ||||
\(213\) | 84.0045 | + | 145.500i | 0.394387 | + | 0.683099i | ||||
\(214\) | −88.0000 | − | 152.420i | −0.411215 | − | 0.712245i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 36.3731i | 0.168394i | ||||||||
\(217\) | 29.4449 | − | 204.000i | 0.135691 | − | 0.940092i | ||||
\(218\) | − | 4.00000i | − | 0.0183486i | ||||||
\(219\) | −42.0000 | + | 72.7461i | −0.191781 | + | 0.332174i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 75.0000 | + | 129.904i | 0.339367 | + | 0.587800i | ||||
\(222\) | −43.3013 | + | 75.0000i | −0.195051 | + | 0.337838i | ||||
\(223\) | 219.970 | 0.986415 | 0.493207 | − | 0.869912i | \(-0.335824\pi\) | ||||
0.493207 | + | 0.869912i | \(0.335824\pi\) | |||||||
\(224\) | −33.0000 | + | 228.631i | −0.147321 | + | 1.02067i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −57.5000 | + | 99.5929i | −0.254425 | + | 0.440677i | ||||
\(227\) | 41.5692 | + | 72.0000i | 0.183124 | + | 0.317181i | 0.942943 | − | 0.332955i | \(-0.108046\pi\) |
−0.759819 | + | 0.650135i | \(0.774712\pi\) | |||||||
\(228\) | −31.1769 | + | 18.0000i | −0.136741 | + | 0.0789474i | ||||
\(229\) | 108.000 | + | 62.3538i | 0.471616 | + | 0.272287i | 0.716916 | − | 0.697160i | \(-0.245553\pi\) |
−0.245300 | + | 0.969447i | \(0.578887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.0000 | − | 45.0333i | −0.0779221 | − | 0.194949i | ||||
\(232\) | 70.0000i | 0.301724i | ||||||||
\(233\) | 168.009 | + | 97.0000i | 0.721068 | + | 0.416309i | 0.815146 | − | 0.579256i | \(-0.196657\pi\) |
−0.0940774 | + | 0.995565i | \(0.529990\pi\) | |||||||
\(234\) | 45.0000 | − | 25.9808i | 0.192308 | − | 0.111029i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −144.000 | − | 83.1384i | −0.610169 | − | 0.352282i | ||||
\(237\) | −12.1244 | −0.0511576 | ||||||||
\(238\) | −47.6314 | − | 37.5000i | −0.200132 | − | 0.157563i | ||||
\(239\) | 155.000 | 0.648536 | 0.324268 | − | 0.945965i | \(-0.394882\pi\) | ||||
0.324268 | + | 0.945965i | \(0.394882\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 234.000 | − | 135.100i | 0.970954 | − | 0.560581i | 0.0714273 | − | 0.997446i | \(-0.477245\pi\) |
0.899527 | + | 0.436865i | \(0.143911\pi\) | |||||||
\(242\) | 90.9327 | − | 52.5000i | 0.375755 | − | 0.216942i | ||||
\(243\) | 7.79423 | − | 13.5000i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | − | 72.7461i | − | 0.298140i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 93.0000 | 0.378049 | ||||||||
\(247\) | 103.923 | + | 60.0000i | 0.420741 | + | 0.242915i | ||||
\(248\) | −103.057 | − | 178.500i | −0.415553 | − | 0.719758i | ||||
\(249\) | −132.000 | − | 228.631i | −0.530120 | − | 0.918196i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 207.846i | 0.828072i | 0.910260 | + | 0.414036i | \(0.135881\pi\) | ||||
−0.910260 | + | 0.414036i | \(0.864119\pi\) | |||||||
\(252\) | 38.9711 | − | 49.5000i | 0.154647 | − | 0.196429i | ||||
\(253\) | 124.000i | 0.490119i | ||||||||
\(254\) | 31.0000 | − | 53.6936i | 0.122047 | − | 0.211392i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 85.5000 | + | 148.090i | 0.333984 | + | 0.578478i | ||||
\(257\) | 239.023 | − | 414.000i | 0.930051 | − | 1.61089i | 0.146820 | − | 0.989163i | \(-0.453096\pi\) |
0.783230 | − | 0.621732i | \(-0.213571\pi\) | |||||||
\(258\) | 58.8897 | 0.228255 | ||||||||
\(259\) | 325.000 | − | 129.904i | 1.25483 | − | 0.501559i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.0000 | − | 25.9808i | 0.0574713 | − | 0.0995431i | ||||
\(262\) | −15.5885 | − | 27.0000i | −0.0594979 | − | 0.103053i | ||||
\(263\) | −51.0955 | + | 29.5000i | −0.194279 | + | 0.112167i | −0.593984 | − | 0.804477i | \(-0.702446\pi\) |
0.399705 | + | 0.916644i | \(0.369113\pi\) | |||||||
\(264\) | −42.0000 | − | 24.2487i | −0.159091 | − | 0.0918512i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −48.0000 | − | 6.92820i | −0.180451 | − | 0.0260459i | ||||
\(267\) | 273.000i | 1.02247i | ||||||||
\(268\) | 129.904 | + | 75.0000i | 0.484716 | + | 0.279851i | ||||
\(269\) | 6.00000 | − | 3.46410i | 0.0223048 | − | 0.0128777i | −0.488806 | − | 0.872392i | \(-0.662567\pi\) |
0.511111 | + | 0.859515i | \(0.329234\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −223.500 | − | 129.038i | −0.824723 | − | 0.476154i | 0.0273193 | − | 0.999627i | \(-0.491303\pi\) |
−0.852043 | + | 0.523473i | \(0.824636\pi\) | |||||||
\(272\) | 43.3013 | 0.159196 | ||||||||
\(273\) | −207.846 | − | 30.0000i | −0.761341 | − | 0.109890i | ||||
\(274\) | −223.000 | −0.813869 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −139.500 | + | 80.5404i | −0.505435 | + | 0.291813i | ||||
\(277\) | −188.794 | + | 109.000i | −0.681565 | + | 0.393502i | −0.800444 | − | 0.599407i | \(-0.795403\pi\) |
0.118879 | + | 0.992909i | \(0.462070\pi\) | |||||||
\(278\) | 39.8372 | − | 69.0000i | 0.143299 | − | 0.248201i | ||||
\(279\) | 88.3346i | 0.316611i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −389.000 | −1.38434 | −0.692171 | − | 0.721734i | \(-0.743346\pi\) | ||||
−0.692171 | + | 0.721734i | \(0.743346\pi\) | |||||||
\(282\) | 64.9519 | + | 37.5000i | 0.230326 | + | 0.132979i | ||||
\(283\) | −107.387 | − | 186.000i | −0.379460 | − | 0.657244i | 0.611524 | − | 0.791226i | \(-0.290557\pi\) |
−0.990984 | + | 0.133982i | \(0.957224\pi\) | |||||||
\(284\) | −145.500 | − | 252.013i | −0.512324 | − | 0.887371i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 69.2820i | 0.242245i | ||||||||
\(287\) | −295.315 | − | 232.500i | −1.02897 | − | 0.810105i | ||||
\(288\) | − | 99.0000i | − | 0.343750i | ||||||
\(289\) | 107.000 | − | 185.329i | 0.370242 | − | 0.641278i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 97.5000 | + | 168.875i | 0.335052 | + | 0.580326i | ||||
\(292\) | 72.7461 | − | 126.000i | 0.249131 | − | 0.431507i | ||||
\(293\) | −491.902 | −1.67885 | −0.839424 | − | 0.543477i | \(-0.817107\pi\) | ||||
−0.839424 | + | 0.543477i | \(0.817107\pi\) | |||||||
\(294\) | 82.5000 | − | 19.9186i | 0.280612 | − | 0.0677503i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 175.000 | − | 303.109i | 0.591216 | − | 1.02402i | ||||
\(297\) | 10.3923 | + | 18.0000i | 0.0349909 | + | 0.0606061i | ||||
\(298\) | −183.597 | + | 106.000i | −0.616099 | + | 0.355705i | ||||
\(299\) | 465.000 | + | 268.468i | 1.55518 | + | 0.897886i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −187.000 | − | 147.224i | −0.621262 | − | 0.489117i | ||||
\(302\) | 238.000i | 0.788079i | ||||||||
\(303\) | −31.1769 | − | 18.0000i | −0.102894 | − | 0.0594059i | ||||
\(304\) | 30.0000 | − | 17.3205i | 0.0986842 | − | 0.0569754i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 22.5000 | + | 12.9904i | 0.0735294 | + | 0.0424522i | ||||
\(307\) | −145.492 | −0.473916 | −0.236958 | − | 0.971520i | \(-0.576150\pi\) | ||||
−0.236958 | + | 0.971520i | \(0.576150\pi\) | |||||||
\(308\) | 31.1769 | + | 78.0000i | 0.101224 | + | 0.253247i | ||||
\(309\) | 171.000 | 0.553398 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −277.500 | + | 160.215i | −0.892283 | + | 0.515160i | −0.874689 | − | 0.484685i | \(-0.838934\pi\) |
−0.0175944 | + | 0.999845i | \(0.505601\pi\) | |||||||
\(312\) | −181.865 | + | 105.000i | −0.582902 | + | 0.336538i | ||||
\(313\) | −25.1147 | + | 43.5000i | −0.0802388 | + | 0.138978i | −0.903352 | − | 0.428899i | \(-0.858902\pi\) |
0.823114 | + | 0.567877i | \(0.192235\pi\) | |||||||
\(314\) | − | 252.879i | − | 0.805348i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.0000 | 0.0664557 | ||||||||
\(317\) | 117.779 | + | 68.0000i | 0.371544 | + | 0.214511i | 0.674133 | − | 0.738610i | \(-0.264518\pi\) |
−0.302589 | + | 0.953121i | \(0.597851\pi\) | |||||||
\(318\) | −43.3013 | − | 75.0000i | −0.136168 | − | 0.235849i | ||||
\(319\) | 20.0000 | + | 34.6410i | 0.0626959 | + | 0.108593i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 304.841i | − | 0.949660i | ||||||
\(322\) | −214.774 | − | 31.0000i | −0.667001 | − | 0.0962733i | ||||
\(323\) | 60.0000i | 0.185759i | ||||||||
\(324\) | −13.5000 | + | 23.3827i | −0.0416667 | + | 0.0721688i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 146.000 | + | 252.879i | 0.447853 | + | 0.775704i | ||||
\(327\) | 3.46410 | − | 6.00000i | 0.0105936 | − | 0.0183486i | ||||
\(328\) | −375.855 | −1.14590 | ||||||||
\(329\) | −112.500 | − | 281.458i | −0.341945 | − | 0.855496i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 221.000 | − | 382.783i | 0.667674 | − | 1.15644i | −0.310879 | − | 0.950449i | \(-0.600623\pi\) |
0.978553 | − | 0.205995i | \(-0.0660432\pi\) | |||||||
\(332\) | 228.631 | + | 396.000i | 0.688647 | + | 1.19277i | ||||
\(333\) | −129.904 | + | 75.0000i | −0.390102 | + | 0.225225i | ||||
\(334\) | −114.000 | − | 65.8179i | −0.341317 | − | 0.197060i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −37.5000 | + | 47.6314i | −0.111607 | + | 0.141760i | ||||
\(337\) | 331.000i | 0.982196i | 0.871104 | + | 0.491098i | \(0.163404\pi\) | ||||
−0.871104 | + | 0.491098i | \(0.836596\pi\) | |||||||
\(338\) | 113.449 | + | 65.5000i | 0.335649 | + | 0.193787i | ||||
\(339\) | −172.500 | + | 99.5929i | −0.508850 | + | 0.293784i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −102.000 | − | 58.8897i | −0.299120 | − | 0.172697i | ||||
\(342\) | 20.7846 | 0.0607737 | ||||||||
\(343\) | −311.769 | − | 143.000i | −0.908948 | − | 0.416910i | ||||
\(344\) | −238.000 | −0.691860 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 129.000 | − | 74.4782i | 0.372832 | − | 0.215255i | ||||
\(347\) | 105.655 | − | 61.0000i | 0.304482 | − | 0.175793i | −0.339973 | − | 0.940435i | \(-0.610418\pi\) |
0.644454 | + | 0.764643i | \(0.277085\pi\) | |||||||
\(348\) | −25.9808 | + | 45.0000i | −0.0746574 | + | 0.129310i | ||||
\(349\) | − | 367.195i | − | 1.05213i | −0.850443 | − | 0.526067i | \(-0.823666\pi\) | ||
0.850443 | − | 0.526067i | \(-0.176334\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 90.0000 | 0.256410 | ||||||||
\(352\) | 114.315 | + | 66.0000i | 0.324760 | + | 0.187500i | ||||
\(353\) | −59.7558 | − | 103.500i | −0.169280 | − | 0.293201i | 0.768887 | − | 0.639385i | \(-0.220811\pi\) |
−0.938167 | + | 0.346183i | \(0.887477\pi\) | |||||||
\(354\) | 48.0000 | + | 83.1384i | 0.135593 | + | 0.234854i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 472.850i | − | 1.32823i | ||||||
\(357\) | −38.9711 | − | 97.5000i | −0.109163 | − | 0.273109i | ||||
\(358\) | 190.000i | 0.530726i | ||||||||
\(359\) | 119.000 | − | 206.114i | 0.331476 | − | 0.574134i | −0.651325 | − | 0.758799i | \(-0.725787\pi\) |
0.982802 | + | 0.184665i | \(0.0591200\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −156.500 | − | 271.066i | −0.433518 | − | 0.750875i | ||||
\(362\) | 10.3923 | − | 18.0000i | 0.0287080 | − | 0.0497238i | ||||
\(363\) | 181.865 | 0.501006 | ||||||||
\(364\) | 360.000 | + | 51.9615i | 0.989011 | + | 0.142751i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −21.0000 | + | 36.3731i | −0.0573770 | + | 0.0993800i | ||||
\(367\) | 114.315 | + | 198.000i | 0.311486 | + | 0.539510i | 0.978684 | − | 0.205371i | \(-0.0658400\pi\) |
−0.667198 | + | 0.744880i | \(0.732507\pi\) | |||||||
\(368\) | 134.234 | − | 77.5000i | 0.364766 | − | 0.210598i | ||||
\(369\) | 139.500 | + | 80.5404i | 0.378049 | + | 0.218267i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −50.0000 | + | 346.410i | −0.134771 | + | 0.933720i | ||||
\(372\) | − | 153.000i | − | 0.411290i | ||||||
\(373\) | −178.401 | − | 103.000i | −0.478287 | − | 0.276139i | 0.241415 | − | 0.970422i | \(-0.422388\pi\) |
−0.719703 | + | 0.694283i | \(0.755722\pi\) | |||||||
\(374\) | −30.0000 | + | 17.3205i | −0.0802139 | + | 0.0463115i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −262.500 | − | 151.554i | −0.698138 | − | 0.403070i | ||||
\(377\) | 173.205 | 0.459430 | ||||||||
\(378\) | −33.7750 | + | 13.5000i | −0.0893518 | + | 0.0357143i | ||||
\(379\) | 430.000 | 1.13456 | 0.567282 | − | 0.823523i | \(-0.307995\pi\) | ||||
0.567282 | + | 0.823523i | \(0.307995\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 93.0000 | − | 53.6936i | 0.244094 | − | 0.140928i | ||||
\(382\) | 232.961 | − | 134.500i | 0.609845 | − | 0.352094i | ||||
\(383\) | 283.190 | − | 490.500i | 0.739400 | − | 1.28068i | −0.213365 | − | 0.976972i | \(-0.568442\pi\) |
0.952766 | − | 0.303706i | \(-0.0982242\pi\) | |||||||
\(384\) | 206.114i | 0.536755i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 29.0000 | 0.0751295 | ||||||||
\(387\) | 88.3346 | + | 51.0000i | 0.228255 | + | 0.131783i | ||||
\(388\) | −168.875 | − | 292.500i | −0.435245 | − | 0.753866i | ||||
\(389\) | −280.000 | − | 484.974i | −0.719794 | − | 1.24672i | −0.961081 | − | 0.276267i | \(-0.910903\pi\) |
0.241287 | − | 0.970454i | \(-0.422431\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 268.468i | 0.686619i | ||||||||
\(392\) | −333.420 | + | 80.5000i | −0.850561 | + | 0.205357i | ||||
\(393\) | − | 54.0000i | − | 0.137405i | ||||||
\(394\) | 26.0000 | − | 45.0333i | 0.0659898 | − | 0.114298i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −18.0000 | − | 31.1769i | −0.0454545 | − | 0.0787296i | ||||
\(397\) | 315.233 | − | 546.000i | 0.794038 | − | 1.37531i | −0.129410 | − | 0.991591i | \(-0.541308\pi\) |
0.923448 | − | 0.383724i | \(-0.125358\pi\) | |||||||
\(398\) | −178.401 | −0.448244 | ||||||||
\(399\) | −66.0000 | − | 51.9615i | −0.165414 | − | 0.130229i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 277.000 | − | 479.778i | 0.690773 | − | 1.19645i | −0.280812 | − | 0.959763i | \(-0.590604\pi\) |
0.971585 | − | 0.236691i | \(-0.0760630\pi\) | |||||||
\(402\) | −43.3013 | − | 75.0000i | −0.107715 | − | 0.186567i | ||||
\(403\) | −441.673 | + | 255.000i | −1.09596 | + | 0.632754i | ||||
\(404\) | 54.0000 | + | 31.1769i | 0.133663 | + | 0.0771706i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −65.0000 | + | 25.9808i | −0.160099 | + | 0.0639920i | ||||
\(407\) | − | 200.000i | − | 0.491400i | ||||||
\(408\) | −90.9327 | − | 52.5000i | −0.222874 | − | 0.128676i | ||||
\(409\) | −601.500 | + | 347.276i | −1.47066 | + | 0.849086i | −0.999457 | − | 0.0329389i | \(-0.989513\pi\) |
−0.471203 | + | 0.882025i | \(0.656180\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −334.500 | − | 193.124i | −0.813869 | − | 0.469887i | ||||
\(412\) | −296.181 | −0.718885 | ||||||||
\(413\) | 55.4256 | − | 384.000i | 0.134202 | − | 0.929782i | ||||
\(414\) | 93.0000 | 0.224638 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 495.000 | − | 285.788i | 1.18990 | − | 0.686991i | ||||
\(417\) | 119.512 | − | 69.0000i | 0.286598 | − | 0.165468i | ||||
\(418\) | −13.8564 | + | 24.0000i | −0.0331493 | + | 0.0574163i | ||||
\(419\) | − | 647.787i | − | 1.54603i | −0.634387 | − | 0.773016i | \(-0.718747\pi\) | ||
0.634387 | − | 0.773016i | \(-0.281253\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 638.000 | 1.51544 | 0.757720 | − | 0.652580i | \(-0.226313\pi\) | ||||
0.757720 | + | 0.652580i | \(0.226313\pi\) | |||||||
\(422\) | 297.913 | + | 172.000i | 0.705954 | + | 0.407583i | ||||
\(423\) | 64.9519 | + | 112.500i | 0.153551 | + | 0.265957i | ||||
\(424\) | 175.000 | + | 303.109i | 0.412736 | + | 0.714879i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 168.009i | 0.394387i | ||||||||
\(427\) | 157.617 | − | 63.0000i | 0.369126 | − | 0.147541i | ||||
\(428\) | 528.000i | 1.23364i | ||||||||
\(429\) | −60.0000 | + | 103.923i | −0.139860 | + | 0.242245i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 287.500 | + | 497.965i | 0.667053 | + | 1.15537i | 0.978724 | + | 0.205180i | \(0.0657780\pi\) |
−0.311671 | + | 0.950190i | \(0.600889\pi\) | |||||||
\(432\) | 12.9904 | − | 22.5000i | 0.0300703 | − | 0.0520833i | ||||
\(433\) | 368.927 | 0.852025 | 0.426012 | − | 0.904717i | \(-0.359918\pi\) | ||||
0.426012 | + | 0.904717i | \(0.359918\pi\) | |||||||
\(434\) | 127.500 | − | 161.947i | 0.293779 | − | 0.373149i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.00000 | + | 10.3923i | −0.0137615 | + | 0.0238356i | ||||
\(437\) | 107.387 | + | 186.000i | 0.245737 | + | 0.425629i | ||||
\(438\) | −72.7461 | + | 42.0000i | −0.166087 | + | 0.0958904i | ||||
\(439\) | −115.500 | − | 66.6840i | −0.263098 | − | 0.151900i | 0.362649 | − | 0.931926i | \(-0.381872\pi\) |
−0.625747 | + | 0.780026i | \(0.715206\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 141.000 | + | 41.5692i | 0.319728 | + | 0.0942613i | ||||
\(442\) | 150.000i | 0.339367i | ||||||||
\(443\) | −232.095 | − | 134.000i | −0.523916 | − | 0.302483i | 0.214619 | − | 0.976698i | \(-0.431149\pi\) |
−0.738535 | + | 0.674215i | \(0.764482\pi\) | |||||||
\(444\) | 225.000 | − | 129.904i | 0.506757 | − | 0.292576i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 190.500 | + | 109.985i | 0.427130 | + | 0.246604i | ||||
\(447\) | −367.195 | −0.821465 | ||||||||
\(448\) | −56.2917 | + | 71.5000i | −0.125651 | + | 0.159598i | ||||
\(449\) | −685.000 | −1.52561 | −0.762806 | − | 0.646627i | \(-0.776179\pi\) | ||||
−0.762806 | + | 0.646627i | \(0.776179\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −186.000 | + | 107.387i | −0.412417 | + | 0.238109i | ||||
\(452\) | 298.779 | − | 172.500i | 0.661015 | − | 0.381637i | ||||
\(453\) | −206.114 | + | 357.000i | −0.454998 | + | 0.788079i | ||||
\(454\) | 83.1384i | 0.183124i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −84.0000 | −0.184211 | ||||||||
\(457\) | 282.324 | + | 163.000i | 0.617777 | + | 0.356674i | 0.776003 | − | 0.630729i | \(-0.217244\pi\) |
−0.158226 | + | 0.987403i | \(0.550577\pi\) | |||||||
\(458\) | 62.3538 | + | 108.000i | 0.136144 | + | 0.235808i | ||||
\(459\) | 22.5000 | + | 38.9711i | 0.0490196 | + | 0.0849045i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.1051i | 0.0826575i | 0.999146 | + | 0.0413288i | \(0.0131591\pi\) | ||||
−0.999146 | + | 0.0413288i | \(0.986841\pi\) | |||||||
\(462\) | 6.92820 | − | 48.0000i | 0.0149961 | − | 0.103896i | ||||
\(463\) | − | 115.000i | − | 0.248380i | −0.992258 | − | 0.124190i | \(-0.960367\pi\) | ||
0.992258 | − | 0.124190i | \(-0.0396333\pi\) | |||||||
\(464\) | 25.0000 | − | 43.3013i | 0.0538793 | − | 0.0933217i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 97.0000 | + | 168.009i | 0.208155 | + | 0.360534i | ||||
\(467\) | −174.937 | + | 303.000i | −0.374598 | + | 0.648822i | −0.990267 | − | 0.139183i | \(-0.955553\pi\) |
0.615669 | + | 0.788005i | \(0.288886\pi\) | |||||||
\(468\) | −155.885 | −0.333087 | ||||||||
\(469\) | −50.0000 | + | 346.410i | −0.106610 | + | 0.738614i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 219.000 | − | 379.319i | 0.464968 | − | 0.805348i | ||||
\(472\) | −193.990 | − | 336.000i | −0.410995 | − | 0.711864i | ||||
\(473\) | −117.779 | + | 68.0000i | −0.249005 | + | 0.143763i | ||||
\(474\) | −10.5000 | − | 6.06218i | −0.0221519 | − | 0.0127894i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 67.5000 | + | 168.875i | 0.141807 | + | 0.354779i | ||||
\(477\) | − | 150.000i | − | 0.314465i | ||||||
\(478\) | 134.234 | + | 77.5000i | 0.280824 | + | 0.162134i | ||||
\(479\) | 265.500 | − | 153.286i | 0.554280 | − | 0.320014i | −0.196567 | − | 0.980490i | \(-0.562979\pi\) |
0.750846 | + | 0.660477i | \(0.229646\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −750.000 | − | 433.013i | −1.55925 | − | 0.900234i | ||||
\(482\) | 270.200 | 0.560581 | ||||||||
\(483\) | −295.315 | − | 232.500i | −0.611418 | − | 0.481366i | ||||
\(484\) | −315.000 | −0.650826 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13.5000 | − | 7.79423i | 0.0277778 | − | 0.0160375i | ||||
\(487\) | −347.276 | + | 200.500i | −0.713093 | + | 0.411704i | −0.812205 | − | 0.583372i | \(-0.801733\pi\) |
0.0991123 | + | 0.995076i | \(0.468400\pi\) | |||||||
\(488\) | 84.8705 | − | 147.000i | 0.173915 | − | 0.301230i | ||||
\(489\) | 505.759i | 1.03427i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −218.000 | −0.443992 | −0.221996 | − | 0.975048i | \(-0.571257\pi\) | ||||
−0.221996 | + | 0.975048i | \(0.571257\pi\) | |||||||
\(492\) | −241.621 | − | 139.500i | −0.491100 | − | 0.283537i | ||||
\(493\) | 43.3013 | + | 75.0000i | 0.0878322 | + | 0.152130i | ||||
\(494\) | 60.0000 | + | 103.923i | 0.121457 | + | 0.210371i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 147.224i | 0.296823i | ||||||||
\(497\) | 420.022 | − | 533.500i | 0.845115 | − | 1.07344i | ||||
\(498\) | − | 264.000i | − | 0.530120i | ||||||
\(499\) | −437.000 | + | 756.906i | −0.875752 | + | 1.51685i | −0.0197915 | + | 0.999804i | \(0.506300\pi\) |
−0.855960 | + | 0.517042i | \(0.827033\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −114.000 | − | 197.454i | −0.227545 | − | 0.394119i | ||||
\(502\) | −103.923 | + | 180.000i | −0.207018 | + | 0.358566i | ||||
\(503\) | 498.831 | 0.991711 | 0.495855 | − | 0.868405i | \(-0.334855\pi\) | ||||
0.495855 | + | 0.868405i | \(0.334855\pi\) | |||||||
\(504\) | 136.500 | − | 54.5596i | 0.270833 | − | 0.108253i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −62.0000 | + | 107.387i | −0.122530 | + | 0.212228i | ||||
\(507\) | 113.449 | + | 196.500i | 0.223766 | + | 0.387574i | ||||
\(508\) | −161.081 | + | 93.0000i | −0.317088 | + | 0.183071i | ||||
\(509\) | −558.000 | − | 322.161i | −1.09627 | − | 0.632930i | −0.161029 | − | 0.986950i | \(-0.551481\pi\) |
−0.935238 | + | 0.354019i | \(0.884815\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 336.000 | + | 48.4974i | 0.657534 | + | 0.0949069i | ||||
\(512\) | − | 305.000i | − | 0.595703i | ||||||
\(513\) | 31.1769 | + | 18.0000i | 0.0607737 | + | 0.0350877i | ||||
\(514\) | 414.000 | − | 239.023i | 0.805447 | − | 0.465025i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −153.000 | − | 88.3346i | −0.296512 | − | 0.171191i | ||||
\(517\) | −173.205 | −0.335019 | ||||||||
\(518\) | 346.410 | + | 50.0000i | 0.668745 | + | 0.0965251i | ||||
\(519\) | 258.000 | 0.497110 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.50000 | + | 0.866025i | −0.00287908 | + | 0.00166224i | −0.501439 | − | 0.865193i | \(-0.667196\pi\) |
0.498560 | + | 0.866855i | \(0.333862\pi\) | |||||||
\(522\) | 25.9808 | − | 15.0000i | 0.0497716 | − | 0.0287356i | ||||
\(523\) | 479.778 | − | 831.000i | 0.917358 | − | 1.58891i | 0.113945 | − | 0.993487i | \(-0.463651\pi\) |
0.803412 | − | 0.595423i | \(-0.203016\pi\) | |||||||
\(524\) | 93.5307i | 0.178494i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −59.0000 | −0.112167 | ||||||||
\(527\) | −220.836 | − | 127.500i | −0.419045 | − | 0.241935i | ||||
\(528\) | 17.3205 | + | 30.0000i | 0.0328040 | + | 0.0568182i | ||||
\(529\) | 216.000 | + | 374.123i | 0.408318 | + | 0.707227i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 166.277i | 0.313139i | ||||||||
\(532\) | 114.315 | + | 90.0000i | 0.214878 | + | 0.169173i | ||||
\(533\) | 930.000i | 1.74484i | ||||||||
\(534\) | −136.500 | + | 236.425i | −0.255618 | + | 0.442743i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 175.000 | + | 303.109i | 0.326493 | + | 0.565502i | ||||
\(537\) | −164.545 | + | 285.000i | −0.306415 | + | 0.530726i | ||||
\(538\) | 6.92820 | 0.0128777 | ||||||||
\(539\) | −142.000 | + | 135.100i | −0.263451 | + | 0.250649i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 146.000 | − | 252.879i | 0.269871 | − | 0.467430i | −0.698958 | − | 0.715163i | \(-0.746352\pi\) |
0.968828 | + | 0.247733i | \(0.0796857\pi\) | |||||||
\(542\) | −129.038 | − | 223.500i | −0.238077 | − | 0.412362i | ||||
\(543\) | 31.1769 | − | 18.0000i | 0.0574160 | − | 0.0331492i | ||||
\(544\) | 247.500 | + | 142.894i | 0.454963 | + | 0.262673i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −165.000 | − | 129.904i | −0.302198 | − | 0.237919i | ||||
\(547\) | 316.000i | 0.577697i | 0.957375 | + | 0.288848i | \(0.0932723\pi\) | ||||
−0.957375 | + | 0.288848i | \(0.906728\pi\) | |||||||
\(548\) | 579.371 | + | 334.500i | 1.05725 | + | 0.610401i | ||||
\(549\) | −63.0000 | + | 36.3731i | −0.114754 | + | 0.0662533i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 60.0000 | + | 34.6410i | 0.108893 | + | 0.0628694i | ||||
\(552\) | −375.855 | −0.680897 | ||||||||
\(553\) | 18.1865 | + | 45.5000i | 0.0328870 | + | 0.0822785i | ||||
\(554\) | −218.000 | −0.393502 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −207.000 | + | 119.512i | −0.372302 | + | 0.214949i | ||||
\(557\) | −424.352 | + | 245.000i | −0.761854 | + | 0.439856i | −0.829961 | − | 0.557822i | \(-0.811637\pi\) |
0.0681073 | + | 0.997678i | \(0.478304\pi\) | |||||||
\(558\) | −44.1673 | + | 76.5000i | −0.0791529 | + | 0.137097i | ||||
\(559\) | 588.897i | 1.05348i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −60.0000 | −0.106952 | ||||||||
\(562\) | −336.884 | − | 194.500i | −0.599438 | − | 0.346085i | ||||
\(563\) | −17.3205 | − | 30.0000i | −0.0307647 | − | 0.0532860i | 0.850233 | − | 0.526406i | \(-0.176461\pi\) |
−0.880998 | + | 0.473120i | \(0.843128\pi\) | |||||||
\(564\) | −112.500 | − | 194.856i | −0.199468 | − | 0.345489i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 214.774i | − | 0.379460i | ||||||
\(567\) | −62.3538 | − | 9.00000i | −0.109971 | − | 0.0158730i | ||||
\(568\) | − | 679.000i | − | 1.19542i | ||||||
\(569\) | 252.500 | − | 437.343i | 0.443761 | − | 0.768617i | −0.554204 | − | 0.832381i | \(-0.686977\pi\) |
0.997965 | + | 0.0637643i | \(0.0203106\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 62.0000 | + | 107.387i | 0.108581 | + | 0.188069i | 0.915196 | − | 0.403009i | \(-0.132036\pi\) |
−0.806614 | + | 0.591078i | \(0.798703\pi\) | |||||||
\(572\) | 103.923 | − | 180.000i | 0.181684 | − | 0.314685i | ||||
\(573\) | 465.922 | 0.813127 | ||||||||
\(574\) | −139.500 | − | 349.008i | −0.243031 | − | 0.608028i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 19.5000 | − | 33.7750i | 0.0338542 | − | 0.0586371i | ||||
\(577\) | 79.6743 | + | 138.000i | 0.138084 | + | 0.239168i | 0.926771 | − | 0.375626i | \(-0.122572\pi\) |
−0.788687 | + | 0.614794i | \(0.789239\pi\) | |||||||
\(578\) | 185.329 | − | 107.000i | 0.320639 | − | 0.185121i | ||||
\(579\) | 43.5000 | + | 25.1147i | 0.0751295 | + | 0.0433761i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −660.000 | + | 838.313i | −1.13597 | + | 1.44288i | ||||
\(582\) | 195.000i | 0.335052i | ||||||||
\(583\) | 173.205 | + | 100.000i | 0.297093 | + | 0.171527i | ||||
\(584\) | 294.000 | − | 169.741i | 0.503425 | − | 0.290652i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −426.000 | − | 245.951i | −0.726962 | − | 0.419712i | ||||
\(587\) | 329.090 | 0.560630 | 0.280315 | − | 0.959908i | \(-0.409561\pi\) | ||||
0.280315 | + | 0.959908i | \(0.409561\pi\) | |||||||
\(588\) | −244.219 | − | 72.0000i | −0.415339 | − | 0.122449i | ||||
\(589\) | −204.000 | −0.346350 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 78.0000 | − | 45.0333i | 0.131980 | − | 0.0761985i | ||||
\(592\) | −216.506 | + | 125.000i | −0.365720 | + | 0.211149i | ||||
\(593\) | 317.831 | − | 550.500i | 0.535972 | − | 0.928331i | −0.463144 | − | 0.886283i | \(-0.653279\pi\) |
0.999116 | − | 0.0420473i | \(-0.0133880\pi\) | |||||||
\(594\) | 20.7846i | 0.0349909i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 636.000 | 1.06711 | ||||||||
\(597\) | −267.602 | − | 154.500i | −0.448244 | − | 0.258794i | ||||
\(598\) | 268.468 | + | 465.000i | 0.448943 | + | 0.777592i | ||||
\(599\) | −23.5000 | − | 40.7032i | −0.0392321 | − | 0.0679519i | 0.845743 | − | 0.533591i | \(-0.179158\pi\) |
−0.884975 | + | 0.465639i | \(0.845824\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1157.01i | 1.92514i | 0.271031 | + | 0.962571i | \(0.412635\pi\) | ||||
−0.271031 | + | 0.962571i | \(0.587365\pi\) | |||||||
\(602\) | −88.3346 | − | 221.000i | −0.146735 | − | 0.367110i | ||||
\(603\) | − | 150.000i | − | 0.248756i | ||||||
\(604\) | 357.000 | − | 618.342i | 0.591060 | − | 1.02375i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −18.0000 | − | 31.1769i | −0.0297030 | − | 0.0514471i | ||||
\(607\) | −226.033 | + | 391.500i | −0.372377 | + | 0.644975i | −0.989931 | − | 0.141553i | \(-0.954790\pi\) |
0.617554 | + | 0.786528i | \(0.288124\pi\) | |||||||
\(608\) | 228.631 | 0.376037 | ||||||||
\(609\) | −120.000 | − | 17.3205i | −0.197044 | − | 0.0284409i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −375.000 | + | 649.519i | −0.613748 | + | 1.06304i | ||||
\(612\) | −38.9711 | − | 67.5000i | −0.0636783 | − | 0.110294i | ||||
\(613\) | −788.083 | + | 455.000i | −1.28562 | + | 0.742251i | −0.977869 | − | 0.209217i | \(-0.932909\pi\) |
−0.307748 | + | 0.951468i | \(0.599575\pi\) | |||||||
\(614\) | −126.000 | − | 72.7461i | −0.205212 | − | 0.118479i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −28.0000 | + | 193.990i | −0.0454545 | + | 0.314918i | ||||
\(617\) | − | 313.000i | − | 0.507293i | −0.967297 | − | 0.253647i | \(-0.918370\pi\) | ||
0.967297 | − | 0.253647i | \(-0.0816301\pi\) | |||||||
\(618\) | 148.090 | + | 85.5000i | 0.239628 | + | 0.138350i | ||||
\(619\) | −657.000 | + | 379.319i | −1.06139 | + | 0.612793i | −0.925816 | − | 0.377974i | \(-0.876621\pi\) |
−0.135573 | + | 0.990767i | \(0.543288\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 139.500 | + | 80.5404i | 0.224638 | + | 0.129695i | ||||
\(622\) | −320.429 | −0.515160 | ||||||||
\(623\) | 1024.51 | − | 409.500i | 1.64448 | − | 0.657303i | ||||
\(624\) | 150.000 | 0.240385 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −43.5000 | + | 25.1147i | −0.0694888 | + | 0.0401194i | ||||
\(627\) | −41.5692 | + | 24.0000i | −0.0662986 | + | 0.0382775i | ||||
\(628\) | −379.319 | + | 657.000i | −0.604011 | + | 1.04618i | ||||
\(629\) | − | 433.013i | − | 0.688414i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −793.000 | −1.25674 | −0.628368 | − | 0.777916i | \(-0.716277\pi\) | ||||
−0.628368 | + | 0.777916i | \(0.716277\pi\) | |||||||
\(632\) | 42.4352 | + | 24.5000i | 0.0671444 | + | 0.0387658i | ||||
\(633\) | 297.913 | + | 516.000i | 0.470636 | + | 0.815166i | ||||
\(634\) | 68.0000 | + | 117.779i | 0.107256 | + | 0.185772i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 259.808i | 0.408503i | ||||||||
\(637\) | 199.186 | + | 825.000i | 0.312694 | + | 1.29513i | ||||
\(638\) | 40.0000i | 0.0626959i | ||||||||
\(639\) | −145.500 | + | 252.013i | −0.227700 | + | 0.394387i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 68.5000 | + | 118.645i | 0.106864 | + | 0.185094i | 0.914498 | − | 0.404590i | \(-0.132586\pi\) |
−0.807634 | + | 0.589684i | \(0.799252\pi\) | |||||||
\(642\) | 152.420 | − | 264.000i | 0.237415 | − | 0.411215i | ||||
\(643\) | 1073.87 | 1.67010 | 0.835048 | − | 0.550177i | \(-0.185440\pi\) | ||||
0.835048 | + | 0.550177i | \(0.185440\pi\) | |||||||
\(644\) | 511.500 | + | 402.702i | 0.794255 | + | 0.625313i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30.0000 | + | 51.9615i | −0.0464396 | + | 0.0804358i | ||||
\(647\) | 169.741 | + | 294.000i | 0.262351 | + | 0.454405i | 0.966866 | − | 0.255284i | \(-0.0821689\pi\) |
−0.704515 | + | 0.709689i | \(0.748836\pi\) | |||||||
\(648\) | −54.5596 | + | 31.5000i | −0.0841969 | + | 0.0486111i | ||||
\(649\) | −192.000 | − | 110.851i | −0.295840 | − | 0.170803i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 331.500 | − | 132.502i | 0.509217 | − | 0.203536i | ||||
\(652\) | − | 876.000i | − | 1.34356i | ||||||
\(653\) | −860.829 | − | 497.000i | −1.31827 | − | 0.761103i | −0.334818 | − | 0.942283i | \(-0.608675\pi\) |
−0.983450 | + | 0.181180i | \(0.942008\pi\) | |||||||
\(654\) | 6.00000 | − | 3.46410i | 0.00917431 | − | 0.00529679i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 232.500 | + | 134.234i | 0.354421 | + | 0.204625i | ||||
\(657\) | −145.492 | −0.221449 | ||||||||
\(658\) | 43.3013 | − | 300.000i | 0.0658074 | − | 0.455927i | ||||
\(659\) | −226.000 | −0.342944 | −0.171472 | − | 0.985189i | \(-0.554852\pi\) | ||||
−0.171472 | + | 0.985189i | \(0.554852\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −447.000 | + | 258.076i | −0.676248 | + | 0.390432i | −0.798440 | − | 0.602074i | \(-0.794341\pi\) |
0.122192 | + | 0.992507i | \(0.461008\pi\) | |||||||
\(662\) | 382.783 | − | 221.000i | 0.578222 | − | 0.333837i | ||||
\(663\) | −129.904 | + | 225.000i | −0.195933 | + | 0.339367i | ||||
\(664\) | 1066.94i | 1.60684i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −150.000 | −0.225225 | ||||||||
\(667\) | 268.468 | + | 155.000i | 0.402501 | + | 0.232384i | ||||
\(668\) | 197.454 | + | 342.000i | 0.295590 | + | 0.511976i | ||||
\(669\) | 190.500 | + | 329.956i | 0.284753 | + | 0.493207i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 96.9948i | − | 0.144553i | ||||||
\(672\) | −371.525 | + | 148.500i | −0.552864 | + | 0.220982i | ||||
\(673\) | 755.000i | 1.12184i | 0.827869 | + | 0.560921i | \(0.189553\pi\) | ||||
−0.827869 | + | 0.560921i | \(0.810447\pi\) | |||||||
\(674\) | −165.500 | + | 286.654i | −0.245549 | + | 0.425303i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −196.500 | − | 340.348i | −0.290680 | − | 0.503473i | ||||
\(677\) | −12.1244 | + | 21.0000i | −0.0179089 | + | 0.0310192i | −0.874841 | − | 0.484410i | \(-0.839034\pi\) |
0.856932 | + | 0.515429i | \(0.172368\pi\) | |||||||
\(678\) | −199.186 | −0.293784 | ||||||||
\(679\) | 487.500 | − | 619.208i | 0.717968 | − | 0.911941i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −72.0000 | + | 124.708i | −0.105727 | + | 0.183124i | ||||
\(682\) | −58.8897 | − | 102.000i | −0.0863486 | − | 0.149560i | ||||
\(683\) | 928.379 | − | 536.000i | 1.35927 | − | 0.784773i | 0.369742 | − | 0.929135i | \(-0.379446\pi\) |
0.989525 | + | 0.144361i | \(0.0461128\pi\) | |||||||
\(684\) | −54.0000 | − | 31.1769i | −0.0789474 | − | 0.0455803i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −198.500 | − | 279.726i | −0.289359 | − | 0.407764i | ||||
\(687\) | 216.000i | 0.314410i | ||||||||
\(688\) | 147.224 | + | 85.0000i | 0.213989 | + | 0.123547i | ||||
\(689\) | 750.000 | − | 433.013i | 1.08853 | − | 0.628465i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1110.00 | + | 640.859i | 1.60637 | + | 0.927437i | 0.990174 | + | 0.139842i | \(0.0446595\pi\) |
0.616194 | + | 0.787595i | \(0.288674\pi\) | |||||||
\(692\) | −446.869 | −0.645765 | ||||||||
\(693\) | 51.9615 | − | 66.0000i | 0.0749806 | − | 0.0952381i | ||||
\(694\) | 122.000 | 0.175793 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −105.000 | + | 60.6218i | −0.150862 | + | 0.0871003i | ||||
\(697\) | −402.702 | + | 232.500i | −0.577764 | + | 0.333572i | ||||
\(698\) | 183.597 | − | 318.000i | 0.263034 | − | 0.455587i | ||||
\(699\) | 336.018i | 0.480712i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1070.00 | −1.52639 | −0.763195 | − | 0.646168i | \(-0.776371\pi\) | ||||
−0.763195 | + | 0.646168i | \(0.776371\pi\) | |||||||
\(702\) | 77.9423 | + | 45.0000i | 0.111029 | + | 0.0641026i | ||||
\(703\) | −173.205 | − | 300.000i | −0.246380 | − | 0.426743i | ||||
\(704\) | 26.0000 | + | 45.0333i | 0.0369318 | + | 0.0639678i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 119.512i | − | 0.169280i | ||||||
\(707\) | −20.7846 | + | 144.000i | −0.0293983 | + | 0.203678i | ||||
\(708\) | − | 288.000i | − | 0.406780i | ||||||
\(709\) | −167.000 | + | 289.252i | −0.235543 | + | 0.407972i | −0.959430 | − | 0.281946i | \(-0.909020\pi\) |
0.723887 | + | 0.689918i | \(0.242354\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.5000 | − | 18.1865i | −0.0147679 | − | 0.0255788i | ||||
\(712\) | 551.658 | − | 955.500i | 0.774801 | − | 1.34199i | ||||
\(713\) | −912.791 | −1.28021 | ||||||||
\(714\) | 15.0000 | − | 103.923i | 0.0210084 | − | 0.145550i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 285.000 | − | 493.634i | 0.398045 | − | 0.689434i | ||||
\(717\) | 134.234 | + | 232.500i | 0.187216 | + | 0.324268i | ||||
\(718\) | 206.114 | − | 119.000i | 0.287067 | − | 0.165738i | ||||
\(719\) | 1054.50 | + | 608.816i | 1.46662 | + | 0.846754i | 0.999303 | − | 0.0373359i | \(-0.0118872\pi\) |
0.467318 | + | 0.884090i | \(0.345220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −256.500 | − | 641.725i | −0.355756 | − | 0.890048i | ||||
\(722\) | − | 313.000i | − | 0.433518i | ||||||
\(723\) | 405.300 | + | 234.000i | 0.560581 | + | 0.323651i | ||||
\(724\) | −54.0000 | + | 31.1769i | −0.0745856 | + | 0.0430620i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 157.500 | + | 90.9327i | 0.216942 | + | 0.125252i | ||||
\(727\) | 455.529 | 0.626588 | 0.313294 | − | 0.949656i | \(-0.398567\pi\) | ||||
0.313294 | + | 0.949656i | \(0.398567\pi\) | |||||||
\(728\) | 666.840 | + | 525.000i | 0.915988 | + | 0.721154i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −255.000 | + | 147.224i | −0.348837 | + | 0.201401i | ||||
\(732\) | 109.119 | − | 63.0000i | 0.149070 | − | 0.0860656i | ||||
\(733\) | −644.323 | + | 1116.00i | −0.879022 | + | 1.52251i | −0.0266057 | + | 0.999646i | \(0.508470\pi\) |
−0.852416 | + | 0.522864i | \(0.824863\pi\) | |||||||
\(734\) | 228.631i | 0.311486i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1023.00 | 1.38995 | ||||||||
\(737\) | 173.205 | + | 100.000i | 0.235014 | + | 0.135685i | ||||
\(738\) | 80.5404 | + | 139.500i | 0.109133 | + | 0.189024i | ||||
\(739\) | 337.000 | + | 583.701i | 0.456022 | + | 0.789853i | 0.998746 | − | 0.0500580i | \(-0.0159406\pi\) |
−0.542725 | + | 0.839911i | \(0.682607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 207.846i | 0.280494i | ||||||||
\(742\) | −216.506 | + | 275.000i | −0.291788 | + | 0.370620i | ||||
\(743\) | 1123.00i | 1.51144i | 0.654895 | + | 0.755720i | \(0.272713\pi\) | ||||
−0.654895 | + | 0.755720i | \(0.727287\pi\) | |||||||
\(744\) | 178.500 | − | 309.171i | 0.239919 | − | 0.415553i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −103.000 | − | 178.401i | −0.138070 | − | 0.239144i | ||||
\(747\) | 228.631 | − | 396.000i | 0.306065 | − | 0.530120i | ||||
\(748\) | 103.923 | 0.138935 | ||||||||
\(749\) | −1144.00 | + | 457.261i | −1.52737 | + | 0.610496i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 317.000 | − | 549.060i | 0.422104 | − | 0.731105i | −0.574041 | − | 0.818826i | \(-0.694625\pi\) |
0.996145 | + | 0.0877211i | \(0.0279584\pi\) | |||||||
\(752\) | 108.253 | + | 187.500i | 0.143954 | + | 0.249335i | ||||
\(753\) | −311.769 | + | 180.000i | −0.414036 | + | 0.239044i | ||||
\(754\) | 150.000 | + | 86.6025i | 0.198939 | + | 0.114857i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 108.000 | + | 15.5885i | 0.142857 | + | 0.0206197i | ||||
\(757\) | 100.000i | 0.132100i | 0.997816 | + | 0.0660502i | \(0.0210397\pi\) | ||||
−0.997816 | + | 0.0660502i | \(0.978960\pi\) | |||||||
\(758\) | 372.391 | + | 215.000i | 0.491281 | + | 0.283641i | ||||
\(759\) | −186.000 | + | 107.387i | −0.245059 | + | 0.141485i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 193.500 | + | 111.717i | 0.254271 | + | 0.146803i | 0.621718 | − | 0.783241i | \(-0.286435\pi\) |
−0.367448 | + | 0.930044i | \(0.619768\pi\) | |||||||
\(762\) | 107.387 | 0.140928 | ||||||||
\(763\) | −27.7128 | − | 4.00000i | −0.0363209 | − | 0.00524246i | ||||
\(764\) | −807.000 | −1.05628 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 490.500 | − | 283.190i | 0.640339 | − | 0.369700i | ||||
\(767\) | −831.384 | + | 480.000i | −1.08394 | + | 0.625815i | ||||
\(768\) | −148.090 | + | 256.500i | −0.192826 | + | 0.333984i | ||||
\(769\) | − | 921.451i | − | 1.19825i | −0.800657 | − | 0.599123i | \(-0.795516\pi\) | ||
0.800657 | − | 0.599123i | \(-0.204484\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 828.000 | 1.07393 | ||||||||
\(772\) | −75.3442 | − | 43.5000i | −0.0975961 | − | 0.0563472i | ||||
\(773\) | −403.568 | − | 699.000i | −0.522080 | − | 0.904269i | −0.999670 | − | 0.0256863i | \(-0.991823\pi\) |
0.477590 | − | 0.878583i | \(-0.341510\pi\) | |||||||
\(774\) | 51.0000 | + | 88.3346i | 0.0658915 | + | 0.114127i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 788.083i | − | 1.01557i | ||||||
\(777\) | 476.314 | + | 375.000i | 0.613017 | + | 0.482625i | ||||
\(778\) | − | 560.000i | − | 0.719794i | ||||||
\(779\) | −186.000 | + | 322.161i | −0.238768 | + | 0.413558i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −194.000 | − | 336.018i | −0.248399 | − | 0.430241i | ||||
\(782\) | −134.234 | + | 232.500i | −0.171655 | + | 0.297315i | ||||
\(783\) | 51.9615 | 0.0663621 | ||||||||
\(784\) | 235.000 | + | 69.2820i | 0.299745 | + | 0.0883699i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 27.0000 | − | 46.7654i | 0.0343511 | − | 0.0594979i | ||||
\(787\) | 60.6218 | + | 105.000i | 0.0770289 | + | 0.133418i | 0.901967 | − | 0.431805i | \(-0.142123\pi\) |
−0.824938 | + | 0.565223i | \(0.808790\pi\) | |||||||
\(788\) | −135.100 | + | 78.0000i | −0.171447 | + | 0.0989848i | ||||
\(789\) | −88.5000 | − | 51.0955i | −0.112167 | − | 0.0647598i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 632.500 | + | 497.965i | 0.799621 | + | 0.629538i | ||||
\(792\) | − | 84.0000i | − | 0.106061i | ||||||
\(793\) | −363.731 | − | 210.000i | −0.458677 | − | 0.264817i | ||||
\(794\) | 546.000 | − | 315.233i | 0.687657 | − | 0.397019i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 463.500 | + | 267.602i | 0.582286 | + | 0.336183i | ||||
\(797\) | 585.433 | 0.734546 | 0.367273 | − | 0.930113i | \(-0.380291\pi\) | ||||
0.367273 | + | 0.930113i | \(0.380291\pi\) | |||||||
\(798\) | −31.1769 | − | 78.0000i | −0.0390688 | − | 0.0977444i | ||||
\(799\) | −375.000 | −0.469337 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −409.500 | + | 236.425i | −0.511236 | + | 0.295162i | ||||
\(802\) | 479.778 | − | 277.000i | 0.598227 | − | 0.345387i | ||||
\(803\) | 96.9948 | − | 168.000i | 0.120791 | − | 0.209215i | ||||
\(804\) | 259.808i | 0.323144i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −510.000 | −0.632754 | ||||||||
\(807\) | 10.3923 | + | 6.00000i | 0.0128777 | + | 0.00743494i | ||||
\(808\) | 72.7461 | + | 126.000i | 0.0900323 | + | 0.155941i | ||||
\(809\) | −265.000 | − | 458.993i | −0.327565 | − | 0.567359i | 0.654463 | − | 0.756094i | \(-0.272895\pi\) |
−0.982028 | + | 0.188735i | \(0.939561\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 176.669i | 0.217841i | 0.994050 | + | 0.108921i | \(0.0347394\pi\) | ||||
−0.994050 | + | 0.108921i | \(0.965261\pi\) | |||||||
\(812\) | 207.846 | + | 30.0000i | 0.255968 | + | 0.0369458i | ||||
\(813\) | − | 447.000i | − | 0.549815i | ||||||
\(814\) | 100.000 | − | 173.205i | 0.122850 | − | 0.212783i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 37.5000 | + | 64.9519i | 0.0459559 | + | 0.0795979i | ||||
\(817\) | −117.779 | + | 204.000i | −0.144161 | + | 0.249694i | ||||
\(818\) | −694.552 | −0.849086 | ||||||||
\(819\) | −135.000 | − | 337.750i | −0.164835 | − | 0.412393i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −356.000 | + | 616.610i | −0.433618 | + | 0.751048i | −0.997182 | − | 0.0750247i | \(-0.976096\pi\) |
0.563564 | + | 0.826072i | \(0.309430\pi\) | |||||||
\(822\) | −193.124 | − | 334.500i | −0.234944 | − | 0.406934i | ||||
\(823\) | 968.216 | − | 559.000i | 1.17645 | − | 0.679222i | 0.221258 | − | 0.975215i | \(-0.428984\pi\) |
0.955190 | + | 0.295993i | \(0.0956505\pi\) | |||||||
\(824\) | −598.500 | − | 345.544i | −0.726335 | − | 0.419350i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 240.000 | − | 304.841i | 0.290557 | − | 0.369057i | ||||
\(827\) | − | 196.000i | − | 0.237001i | −0.992954 | − | 0.118501i | \(-0.962191\pi\) | ||
0.992954 | − | 0.118501i | \(-0.0378088\pi\) | |||||||
\(828\) | −241.621 | − | 139.500i | −0.291813 | − | 0.168478i | ||||
\(829\) | 354.000 | − | 204.382i | 0.427021 | − | 0.246540i | −0.271056 | − | 0.962564i | \(-0.587373\pi\) |
0.698077 | + | 0.716023i | \(0.254040\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −327.000 | − | 188.794i | −0.393502 | − | 0.227188i | ||||
\(832\) | 225.167 | 0.270633 | ||||||||
\(833\) | −307.439 | + | 292.500i | −0.369074 | + | 0.351140i | ||||
\(834\) | 138.000 | 0.165468 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 72.0000 | − | 41.5692i | 0.0861244 | − | 0.0497239i | ||||
\(837\) | −132.502 | + | 76.5000i | −0.158306 | + | 0.0913978i | ||||
\(838\) | 323.894 | − | 561.000i | 0.386508 | − | 0.669451i | ||||
\(839\) | − | 282.324i | − | 0.336501i | −0.985744 | − | 0.168250i | \(-0.946188\pi\) | ||
0.985744 | − | 0.168250i | \(-0.0538117\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −741.000 | −0.881094 | ||||||||
\(842\) | 552.524 | + | 319.000i | 0.656205 | + | 0.378860i | ||||
\(843\) | −336.884 | − | 583.500i | −0.399625 | − | 0.692171i | ||||
\(844\) | −516.000 | − | 893.738i | −0.611374 | − | 1.05893i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 129.904i | 0.153551i | ||||||||
\(847\) | −272.798 | − | 682.500i | −0.322076 | − | 0.805785i | ||||
\(848\) | − | 250.000i | − | 0.294811i | ||||||
\(849\) | 186.000 | − | 322.161i | 0.219081 | − | 0.379460i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −775.000 | − | 1342.34i | −0.910693 | − | 1.57737i | ||||
\(852\) | 252.013 | − | 436.500i | 0.295790 | − | 0.512324i | ||||
\(853\) | 38.1051 | 0.0446719 | 0.0223359 | − | 0.999751i | \(-0.492890\pi\) | ||||
0.0223359 | + | 0.999751i | \(0.492890\pi\) | |||||||
\(854\) | 168.000 | + | 24.2487i | 0.196721 | + | 0.0283943i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −616.000 | + | 1066.94i | −0.719626 | + | 1.24643i | ||||
\(857\) | −436.477 | − | 756.000i | −0.509308 | − | 0.882147i | −0.999942 | − | 0.0107813i | \(-0.996568\pi\) |
0.490634 | − | 0.871366i | \(-0.336765\pi\) | |||||||
\(858\) | −103.923 | + | 60.0000i | −0.121122 | + | 0.0699301i | ||||
\(859\) | −477.000 | − | 275.396i | −0.555297 | − | 0.320601i | 0.195959 | − | 0.980612i | \(-0.437218\pi\) |
−0.751256 | + | 0.660011i | \(0.770551\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 93.0000 | − | 644.323i | 0.108014 | − | 0.748343i | ||||
\(862\) | 575.000i | 0.667053i | ||||||||
\(863\) | −1201.18 | − | 693.500i | −1.39186 | − | 0.803592i | −0.398341 | − | 0.917237i | \(-0.630414\pi\) |
−0.993521 | + | 0.113645i | \(0.963747\pi\) | |||||||
\(864\) | 148.500 | − | 85.7365i | 0.171875 | − | 0.0992321i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 319.500 | + | 184.463i | 0.368938 | + | 0.213006i | ||||
\(867\) | 370.659 | 0.427519 | ||||||||
\(868\) | −574.175 | + | 229.500i | −0.661492 | + | 0.264401i | ||||
\(869\) | 28.0000 | 0.0322209 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 750.000 | − | 433.013i | 0.861079 | − | 0.497144i | ||||
\(872\) | −24.2487 | + | 14.0000i | −0.0278082 | + | 0.0160550i | ||||
\(873\) | −168.875 | + | 292.500i | −0.193442 | + | 0.335052i | ||||
\(874\) | 214.774i | 0.245737i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 252.000 | 0.287671 | ||||||||
\(877\) | −658.179 | − | 380.000i | −0.750490 | − | 0.433295i | 0.0753812 | − | 0.997155i | \(-0.475983\pi\) |
−0.825871 | + | 0.563859i | \(0.809316\pi\) | |||||||
\(878\) | −66.6840 | − | 115.500i | −0.0759498 | − | 0.131549i | ||||
\(879\) | −426.000 | − | 737.854i | −0.484642 | − | 0.839424i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 524.811i | − | 0.595700i | −0.954613 | − | 0.297850i | \(-0.903731\pi\) | ||
0.954613 | − | 0.297850i | \(-0.0962695\pi\) | |||||||
\(882\) | 101.325 | + | 106.500i | 0.114881 | + | 0.120748i | ||||
\(883\) | − | 1324.00i | − | 1.49943i | −0.661759 | − | 0.749717i | \(-0.730190\pi\) | ||
0.661759 | − | 0.749717i | \(-0.269810\pi\) | |||||||
\(884\) | 225.000 | − | 389.711i | 0.254525 | − | 0.440850i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −134.000 | − | 232.095i | −0.151242 | − | 0.261958i | ||||
\(887\) | −758.638 | + | 1314.00i | −0.855286 | + | 1.48140i | 0.0210944 | + | 0.999777i | \(0.493285\pi\) |
−0.876380 | + | 0.481620i | \(0.840048\pi\) | |||||||
\(888\) | 606.218 | 0.682678 | ||||||||
\(889\) | −341.000 | − | 268.468i | −0.383577 | − | 0.301989i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.0000 | + | 31.1769i | −0.0202020 | + | 0.0349909i | ||||
\(892\) | −329.956 | − | 571.500i | −0.369905 | − | 0.640695i | ||||
\(893\) | −259.808 | + | 150.000i | −0.290938 | + | 0.167973i | ||||
\(894\) | −318.000 | − | 183.597i | −0.355705 | − | 0.205366i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 773.500 | − | 309.171i | 0.863281 | − | 0.345057i | ||||
\(897\) | 930.000i | 1.03679i | ||||||||
\(898\) | −593.227 | − | 342.500i | −0.660610 | − | 0.381403i | ||||
\(899\) | −255.000 | + | 147.224i | −0.283648 | + | 0.163765i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 375.000 | + | 216.506i | 0.416204 | + | 0.240296i | ||||
\(902\) | −214.774 | −0.238109 | ||||||||
\(903\) | 58.8897 | − | 408.000i | 0.0652156 | − | 0.451827i | ||||
\(904\) | 805.000 | 0.890487 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −357.000 | + | 206.114i | −0.394040 | + | 0.227499i | ||||
\(907\) | −32.9090 | + | 19.0000i | −0.0362833 | + | 0.0209482i | −0.518032 | − | 0.855361i | \(-0.673335\pi\) |
0.481749 | + | 0.876309i | \(0.340002\pi\) | |||||||
\(908\) | 124.708 | − | 216.000i | 0.137343 | − | 0.237885i | ||||
\(909\) | − | 62.3538i | − | 0.0685961i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −611.000 | −0.670692 | −0.335346 | − | 0.942095i | \(-0.608853\pi\) | ||||
−0.335346 | + | 0.942095i | \(0.608853\pi\) | |||||||
\(912\) | 51.9615 | + | 30.0000i | 0.0569754 | + | 0.0328947i | ||||
\(913\) | 304.841 | + | 528.000i | 0.333889 | + | 0.578313i | ||||
\(914\) | 163.000 | + | 282.324i | 0.178337 | + | 0.308889i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 374.123i | − | 0.408431i | ||||||
\(917\) | −202.650 | + | 81.0000i | −0.220992 | + | 0.0883315i | ||||
\(918\) | 45.0000i | 0.0490196i | ||||||||
\(919\) | 155.500 | − | 269.334i | 0.169206 | − | 0.293073i | −0.768935 | − | 0.639327i | \(-0.779213\pi\) |
0.938141 | + | 0.346254i | \(0.112546\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −126.000 | − | 218.238i | −0.136808 | − | 0.236958i | ||||
\(922\) | −19.0526 | + | 33.0000i | −0.0206644 | + | 0.0357918i | ||||
\(923\) | −1680.09 | −1.82025 | ||||||||
\(924\) | −90.0000 | + | 114.315i | −0.0974026 | + | 0.123718i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 57.5000 | − | 99.5929i | 0.0620950 | − | 0.107552i | ||||
\(927\) | 148.090 | + | 256.500i | 0.159752 | + | 0.276699i | ||||
\(928\) | 285.788 | − | 165.000i | 0.307962 | − | 0.177802i | ||||
\(929\) | 948.000 | + | 547.328i | 1.02045 | + | 0.589158i | 0.914235 | − | 0.405185i | \(-0.132793\pi\) |
0.106217 | + | 0.994343i | \(0.466126\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −96.0000 | + | 325.626i | −0.103115 | + | 0.349759i | ||||
\(932\) | − | 582.000i | − | 0.624464i | ||||||
\(933\) | −480.644 | − | 277.500i | −0.515160 | − | 0.297428i | ||||
\(934\) | −303.000 | + | 174.937i | −0.324411 | + | 0.187299i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −315.000 | − | 181.865i | −0.336538 | − | 0.194301i | ||||
\(937\) | 519.615 | 0.554552 | 0.277276 | − | 0.960790i | \(-0.410568\pi\) | ||||
0.277276 | + | 0.960790i | \(0.410568\pi\) | |||||||
\(938\) | −216.506 | + | 275.000i | −0.230817 | + | 0.293177i | ||||
\(939\) | −87.0000 | −0.0926518 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1437.00 | − | 829.652i | 1.52710 | − | 0.881671i | 0.527617 | − | 0.849482i | \(-0.323086\pi\) |
0.999482 | − | 0.0321886i | \(-0.0102477\pi\) | |||||||
\(942\) | 379.319 | − | 219.000i | 0.402674 | − | 0.232484i | ||||
\(943\) | −832.250 | + | 1441.50i | −0.882556 | + | 1.52863i | ||||
\(944\) | 277.128i | 0.293568i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −136.000 | −0.143763 | ||||||||
\(947\) | 762.102 | + | 440.000i | 0.804754 | + | 0.464625i | 0.845131 | − | 0.534559i | \(-0.179522\pi\) |
−0.0403766 | + | 0.999185i | \(0.512856\pi\) | |||||||
\(948\) | 18.1865 | + | 31.5000i | 0.0191841 | + | 0.0332278i | ||||
\(949\) | −420.000 | − | 727.461i | −0.442571 | − | 0.766556i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 235.559i | 0.247696i | ||||||||
\(952\) | −60.6218 | + | 420.000i | −0.0636783 | + | 0.441176i | ||||
\(953\) | 910.000i | 0.954879i | 0.878665 | + | 0.477440i | \(0.158435\pi\) | ||||
−0.878665 | + | 0.477440i | \(0.841565\pi\) | |||||||
\(954\) | 75.0000 | − | 129.904i | 0.0786164 | − | 0.136168i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −232.500 | − | 402.702i | −0.243201 | − | 0.421236i | ||||
\(957\) | −34.6410 | + | 60.0000i | −0.0361975 | + | 0.0626959i | ||||
\(958\) | 306.573 | 0.320014 | ||||||||
\(959\) | −223.000 | + | 1544.99i | −0.232534 | + | 1.61104i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −47.0000 | + | 81.4064i | −0.0489074 | + | 0.0847101i | ||||
\(962\) | −433.013 | − | 750.000i | −0.450117 | − | 0.779626i | ||||
\(963\) | 457.261 | − | 264.000i | 0.474830 | − | 0.274143i | ||||
\(964\) | −702.000 | − | 405.300i | −0.728216 | − | 0.420436i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −139.500 | − | 349.008i | −0.144410 | − | 0.361292i | ||||
\(967\) | − | 473.000i | − | 0.489142i | −0.969631 | − | 0.244571i | \(-0.921353\pi\) | ||
0.969631 | − | 0.244571i | \(-0.0786471\pi\) | |||||||
\(968\) | −636.529 | − | 367.500i | −0.657571 | − | 0.379649i | ||||
\(969\) | −90.0000 | + | 51.9615i | −0.0928793 | + | 0.0536239i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 777.000 | + | 448.601i | 0.800206 | + | 0.461999i | 0.843543 | − | 0.537061i | \(-0.180466\pi\) |
−0.0433372 | + | 0.999061i | \(0.513799\pi\) | |||||||
\(972\) | −46.7654 | −0.0481125 | ||||||||
\(973\) | −438.209 | − | 345.000i | −0.450369 | − | 0.354573i | ||||
\(974\) | −401.000 | −0.411704 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −105.000 | + | 60.6218i | −0.107582 | + | 0.0621125i | ||||
\(977\) | 196.588 | − | 113.500i | 0.201216 | − | 0.116172i | −0.396007 | − | 0.918248i | \(-0.629604\pi\) |
0.597222 | + | 0.802076i | \(0.296271\pi\) | |||||||
\(978\) | −252.879 | + | 438.000i | −0.258568 | + | 0.447853i | ||||
\(979\) | − | 630.466i | − | 0.643990i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.0000 | 0.0122324 | ||||||||
\(982\) | −188.794 | − | 109.000i | −0.192254 | − | 0.110998i | ||||
\(983\) | −758.638 | − | 1314.00i | −0.771758 | − | 1.33672i | −0.936599 | − | 0.350404i | \(-0.886044\pi\) |
0.164840 | − | 0.986320i | \(-0.447289\pi\) | |||||||
\(984\) | −325.500 | − | 563.783i | −0.330793 | − | 0.572950i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 86.6025i | 0.0878322i | ||||||||
\(987\) | 324.760 | − | 412.500i | 0.329037 | − | 0.417933i | ||||
\(988\) | − | 360.000i | − | 0.364372i | ||||||
\(989\) | −527.000 | + | 912.791i | −0.532861 | + | 0.922943i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −902.500 | − | 1563.18i | −0.910696 | − | 1.57737i | −0.813083 | − | 0.582148i | \(-0.802213\pi\) |
−0.0976133 | − | 0.995224i | \(-0.531121\pi\) | |||||||
\(992\) | −485.840 | + | 841.500i | −0.489758 | + | 0.848286i | ||||
\(993\) | 765.566 | 0.770963 | ||||||||
\(994\) | 630.500 | − | 252.013i | 0.634306 | − | 0.253535i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −396.000 | + | 685.892i | −0.397590 | + | 0.688647i | ||||
\(997\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(998\) | −756.906 | + | 437.000i | −0.758423 | + | 0.437876i | ||||
\(999\) | −225.000 | − | 129.904i | −0.225225 | − | 0.130034i |
(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 | 525.3.s.b.124.2 | 4 | ||
5.2 | odd | 4 | 525.3.o.d.376.1 | ✓ | 2 | ||
5.3 | odd | 4 | 525.3.o.e.376.1 | yes | 2 | ||
5.4 | even | 2 | inner | 525.3.s.b.124.1 | 4 | ||
7.3 | odd | 6 | inner | 525.3.s.b.199.1 | 4 | ||
35.3 | even | 12 | 525.3.o.e.451.1 | yes | 2 | ||
35.17 | even | 12 | 525.3.o.d.451.1 | yes | 2 | ||
35.24 | odd | 6 | inner | 525.3.s.b.199.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.3.o.d.376.1 | ✓ | 2 | 5.2 | odd | 4 | ||
525.3.o.d.451.1 | yes | 2 | 35.17 | even | 12 | ||
525.3.o.e.376.1 | yes | 2 | 5.3 | odd | 4 | ||
525.3.o.e.451.1 | yes | 2 | 35.3 | even | 12 | ||
525.3.s.b.124.1 | 4 | 5.4 | even | 2 | inner | ||
525.3.s.b.124.2 | 4 | 1.1 | even | 1 | trivial | ||
525.3.s.b.199.1 | 4 | 7.3 | odd | 6 | inner | ||
525.3.s.b.199.2 | 4 | 35.24 | odd | 6 | inner |