Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [102,3,Mod(47,102)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(102, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("102.47");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 102 = 2 \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 102.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.77929869648\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 89.2 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 102.89 |
Dual form | 102.3.e.a.47.2 |
$q$-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 \(\left(\mathbb{Z}/102\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | −2.12132 | − | 2.12132i | −0.707107 | − | 0.707107i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | −4.94975 | − | 4.94975i | −0.989949 | − | 0.989949i | 0.0100005 | − | 0.999950i | \(-0.496817\pi\) |
−0.999950 | + | 0.0100005i | \(0.996817\pi\) | |||||||
\(6\) | −3.00000 | − | 3.00000i | −0.500000 | − | 0.500000i | ||||
\(7\) | −5.00000 | − | 5.00000i | −0.714286 | − | 0.714286i | 0.253143 | − | 0.967429i | \(-0.418536\pi\) |
−0.967429 | + | 0.253143i | \(0.918536\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 9.00000i | 1.00000i | ||||||||
\(10\) | −7.00000 | − | 7.00000i | −0.700000 | − | 0.700000i | ||||
\(11\) | 3.53553 | − | 3.53553i | 0.321412 | − | 0.321412i | −0.527897 | − | 0.849309i | \(-0.677019\pi\) |
0.849309 | + | 0.527897i | \(0.177019\pi\) | |||||||
\(12\) | −4.24264 | − | 4.24264i | −0.353553 | − | 0.353553i | ||||
\(13\) | 15.0000 | 1.15385 | 0.576923 | − | 0.816798i | \(-0.304253\pi\) | ||||
0.576923 | + | 0.816798i | \(0.304253\pi\) | |||||||
\(14\) | −7.07107 | − | 7.07107i | −0.505076 | − | 0.505076i | ||||
\(15\) | 21.0000i | 1.40000i | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 4.94975 | − | 16.2635i | 0.291162 | − | 0.956674i | ||||
\(18\) | 12.7279i | 0.707107i | ||||||||
\(19\) | − | 5.00000i | − | 0.263158i | −0.991306 | − | 0.131579i | \(-0.957995\pi\) | ||
0.991306 | − | 0.131579i | \(-0.0420047\pi\) | |||||||
\(20\) | −9.89949 | − | 9.89949i | −0.494975 | − | 0.494975i | ||||
\(21\) | 21.2132i | 1.01015i | ||||||||
\(22\) | 5.00000 | − | 5.00000i | 0.227273 | − | 0.227273i | ||||
\(23\) | −14.8492 | + | 14.8492i | −0.645619 | + | 0.645619i | −0.951931 | − | 0.306312i | \(-0.900905\pi\) |
0.306312 | + | 0.951931i | \(0.400905\pi\) | |||||||
\(24\) | −6.00000 | − | 6.00000i | −0.250000 | − | 0.250000i | ||||
\(25\) | 24.0000i | 0.960000i | ||||||||
\(26\) | 21.2132 | 0.815892 | ||||||||
\(27\) | 19.0919 | − | 19.0919i | 0.707107 | − | 0.707107i | ||||
\(28\) | −10.0000 | − | 10.0000i | −0.357143 | − | 0.357143i | ||||
\(29\) | 28.2843 | + | 28.2843i | 0.975320 | + | 0.975320i | 0.999703 | − | 0.0243830i | \(-0.00776212\pi\) |
−0.0243830 | + | 0.999703i | \(0.507762\pi\) | |||||||
\(30\) | 29.6985i | 0.989949i | ||||||||
\(31\) | 24.0000 | − | 24.0000i | 0.774194 | − | 0.774194i | −0.204643 | − | 0.978837i | \(-0.565603\pi\) |
0.978837 | + | 0.204643i | \(0.0656034\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | −15.0000 | −0.454545 | ||||||||
\(34\) | 7.00000 | − | 23.0000i | 0.205882 | − | 0.676471i | ||||
\(35\) | 49.4975i | 1.41421i | ||||||||
\(36\) | 18.0000i | 0.500000i | ||||||||
\(37\) | −15.0000 | + | 15.0000i | −0.405405 | + | 0.405405i | −0.880133 | − | 0.474727i | \(-0.842547\pi\) |
0.474727 | + | 0.880133i | \(0.342547\pi\) | |||||||
\(38\) | − | 7.07107i | − | 0.186081i | ||||||
\(39\) | −31.8198 | − | 31.8198i | −0.815892 | − | 0.815892i | ||||
\(40\) | −14.0000 | − | 14.0000i | −0.350000 | − | 0.350000i | ||||
\(41\) | −38.8909 | + | 38.8909i | −0.948558 | + | 0.948558i | −0.998740 | − | 0.0501822i | \(-0.984020\pi\) |
0.0501822 | + | 0.998740i | \(0.484020\pi\) | |||||||
\(42\) | 30.0000i | 0.714286i | ||||||||
\(43\) | − | 75.0000i | − | 1.74419i | −0.489340 | − | 0.872093i | \(-0.662762\pi\) | ||
0.489340 | − | 0.872093i | \(-0.337238\pi\) | |||||||
\(44\) | 7.07107 | − | 7.07107i | 0.160706 | − | 0.160706i | ||||
\(45\) | 44.5477 | − | 44.5477i | 0.989949 | − | 0.989949i | ||||
\(46\) | −21.0000 | + | 21.0000i | −0.456522 | + | 0.456522i | ||||
\(47\) | − | 11.3137i | − | 0.240717i | −0.992730 | − | 0.120359i | \(-0.961596\pi\) | ||
0.992730 | − | 0.120359i | \(-0.0384044\pi\) | |||||||
\(48\) | −8.48528 | − | 8.48528i | −0.176777 | − | 0.176777i | ||||
\(49\) | 1.00000i | 0.0204082i | ||||||||
\(50\) | 33.9411i | 0.678823i | ||||||||
\(51\) | −45.0000 | + | 24.0000i | −0.882353 | + | 0.470588i | ||||
\(52\) | 30.0000 | 0.576923 | ||||||||
\(53\) | 67.8823 | 1.28080 | 0.640399 | − | 0.768043i | \(-0.278769\pi\) | ||||
0.640399 | + | 0.768043i | \(0.278769\pi\) | |||||||
\(54\) | 27.0000 | − | 27.0000i | 0.500000 | − | 0.500000i | ||||
\(55\) | −35.0000 | −0.636364 | ||||||||
\(56\) | −14.1421 | − | 14.1421i | −0.252538 | − | 0.252538i | ||||
\(57\) | −10.6066 | + | 10.6066i | −0.186081 | + | 0.186081i | ||||
\(58\) | 40.0000 | + | 40.0000i | 0.689655 | + | 0.689655i | ||||
\(59\) | −63.6396 | −1.07864 | −0.539319 | − | 0.842102i | \(-0.681318\pi\) | ||||
−0.539319 | + | 0.842102i | \(0.681318\pi\) | |||||||
\(60\) | 42.0000i | 0.700000i | ||||||||
\(61\) | 71.0000 | + | 71.0000i | 1.16393 | + | 1.16393i | 0.983607 | + | 0.180328i | \(0.0577159\pi\) |
0.180328 | + | 0.983607i | \(0.442284\pi\) | |||||||
\(62\) | 33.9411 | − | 33.9411i | 0.547438 | − | 0.547438i | ||||
\(63\) | 45.0000 | − | 45.0000i | 0.714286 | − | 0.714286i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −74.2462 | − | 74.2462i | −1.14225 | − | 1.14225i | ||||
\(66\) | −21.2132 | −0.321412 | ||||||||
\(67\) | −80.0000 | −1.19403 | −0.597015 | − | 0.802230i | \(-0.703647\pi\) | ||||
−0.597015 | + | 0.802230i | \(0.703647\pi\) | |||||||
\(68\) | 9.89949 | − | 32.5269i | 0.145581 | − | 0.478337i | ||||
\(69\) | 63.0000 | 0.913043 | ||||||||
\(70\) | 70.0000i | 1.00000i | ||||||||
\(71\) | −28.2843 | − | 28.2843i | −0.398370 | − | 0.398370i | 0.479288 | − | 0.877658i | \(-0.340895\pi\) |
−0.877658 | + | 0.479288i | \(0.840895\pi\) | |||||||
\(72\) | 25.4558i | 0.353553i | ||||||||
\(73\) | 80.0000 | − | 80.0000i | 1.09589 | − | 1.09589i | 0.101004 | − | 0.994886i | \(-0.467794\pi\) |
0.994886 | − | 0.101004i | \(-0.0322056\pi\) | |||||||
\(74\) | −21.2132 | + | 21.2132i | −0.286665 | + | 0.286665i | ||||
\(75\) | 50.9117 | − | 50.9117i | 0.678823 | − | 0.678823i | ||||
\(76\) | − | 10.0000i | − | 0.131579i | ||||||
\(77\) | −35.3553 | −0.459160 | ||||||||
\(78\) | −45.0000 | − | 45.0000i | −0.576923 | − | 0.576923i | ||||
\(79\) | −11.0000 | − | 11.0000i | −0.139241 | − | 0.139241i | 0.634051 | − | 0.773291i | \(-0.281391\pi\) |
−0.773291 | + | 0.634051i | \(0.781391\pi\) | |||||||
\(80\) | −19.7990 | − | 19.7990i | −0.247487 | − | 0.247487i | ||||
\(81\) | −81.0000 | −1.00000 | ||||||||
\(82\) | −55.0000 | + | 55.0000i | −0.670732 | + | 0.670732i | ||||
\(83\) | 124.451 | 1.49941 | 0.749704 | − | 0.661774i | \(-0.230196\pi\) | ||||
0.749704 | + | 0.661774i | \(0.230196\pi\) | |||||||
\(84\) | 42.4264i | 0.505076i | ||||||||
\(85\) | −105.000 | + | 56.0000i | −1.23529 | + | 0.658824i | ||||
\(86\) | − | 106.066i | − | 1.23333i | ||||||
\(87\) | − | 120.000i | − | 1.37931i | ||||||
\(88\) | 10.0000 | − | 10.0000i | 0.113636 | − | 0.113636i | ||||
\(89\) | − | 21.2132i | − | 0.238351i | −0.992873 | − | 0.119175i | \(-0.961975\pi\) | ||
0.992873 | − | 0.119175i | \(-0.0380251\pi\) | |||||||
\(90\) | 63.0000 | − | 63.0000i | 0.700000 | − | 0.700000i | ||||
\(91\) | −75.0000 | − | 75.0000i | −0.824176 | − | 0.824176i | ||||
\(92\) | −29.6985 | + | 29.6985i | −0.322810 | + | 0.322810i | ||||
\(93\) | −101.823 | −1.09488 | ||||||||
\(94\) | − | 16.0000i | − | 0.170213i | ||||||
\(95\) | −24.7487 | + | 24.7487i | −0.260513 | + | 0.260513i | ||||
\(96\) | −12.0000 | − | 12.0000i | −0.125000 | − | 0.125000i | ||||
\(97\) | −80.0000 | + | 80.0000i | −0.824742 | + | 0.824742i | −0.986784 | − | 0.162042i | \(-0.948192\pi\) |
0.162042 | + | 0.986784i | \(0.448192\pi\) | |||||||
\(98\) | 1.41421i | 0.0144308i | ||||||||
\(99\) | 31.8198 | + | 31.8198i | 0.321412 | + | 0.321412i | ||||
\(100\) | 48.0000i | 0.480000i | ||||||||
\(101\) | 56.5685i | 0.560085i | 0.959988 | + | 0.280042i | \(0.0903485\pi\) | ||||
−0.959988 | + | 0.280042i | \(0.909652\pi\) | |||||||
\(102\) | −63.6396 | + | 33.9411i | −0.623918 | + | 0.332756i | ||||
\(103\) | −5.00000 | −0.0485437 | −0.0242718 | − | 0.999705i | \(-0.507727\pi\) | ||||
−0.0242718 | + | 0.999705i | \(0.507727\pi\) | |||||||
\(104\) | 42.4264 | 0.407946 | ||||||||
\(105\) | 105.000 | − | 105.000i | 1.00000 | − | 1.00000i | ||||
\(106\) | 96.0000 | 0.905660 | ||||||||
\(107\) | 144.957 | + | 144.957i | 1.35474 | + | 1.35474i | 0.880277 | + | 0.474460i | \(0.157357\pi\) |
0.474460 | + | 0.880277i | \(0.342643\pi\) | |||||||
\(108\) | 38.1838 | − | 38.1838i | 0.353553 | − | 0.353553i | ||||
\(109\) | 104.000 | + | 104.000i | 0.954128 | + | 0.954128i | 0.998993 | − | 0.0448646i | \(-0.0142857\pi\) |
−0.0448646 | + | 0.998993i | \(0.514286\pi\) | |||||||
\(110\) | −49.4975 | −0.449977 | ||||||||
\(111\) | 63.6396 | 0.573330 | ||||||||
\(112\) | −20.0000 | − | 20.0000i | −0.178571 | − | 0.178571i | ||||
\(113\) | 45.9619 | − | 45.9619i | 0.406743 | − | 0.406743i | −0.473858 | − | 0.880601i | \(-0.657139\pi\) |
0.880601 | + | 0.473858i | \(0.157139\pi\) | |||||||
\(114\) | −15.0000 | + | 15.0000i | −0.131579 | + | 0.131579i | ||||
\(115\) | 147.000 | 1.27826 | ||||||||
\(116\) | 56.5685 | + | 56.5685i | 0.487660 | + | 0.487660i | ||||
\(117\) | 135.000i | 1.15385i | ||||||||
\(118\) | −90.0000 | −0.762712 | ||||||||
\(119\) | −106.066 | + | 56.5685i | −0.891311 | + | 0.475366i | ||||
\(120\) | 59.3970i | 0.494975i | ||||||||
\(121\) | 96.0000i | 0.793388i | ||||||||
\(122\) | 100.409 | + | 100.409i | 0.823026 | + | 0.823026i | ||||
\(123\) | 165.000 | 1.34146 | ||||||||
\(124\) | 48.0000 | − | 48.0000i | 0.387097 | − | 0.387097i | ||||
\(125\) | −4.94975 | + | 4.94975i | −0.0395980 | + | 0.0395980i | ||||
\(126\) | 63.6396 | − | 63.6396i | 0.505076 | − | 0.505076i | ||||
\(127\) | 125.000i | 0.984252i | 0.870524 | + | 0.492126i | \(0.163780\pi\) | ||||
−0.870524 | + | 0.492126i | \(0.836220\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | −159.099 | + | 159.099i | −1.23333 | + | 1.23333i | ||||
\(130\) | −105.000 | − | 105.000i | −0.807692 | − | 0.807692i | ||||
\(131\) | −3.53553 | − | 3.53553i | −0.0269888 | − | 0.0269888i | 0.693484 | − | 0.720472i | \(-0.256075\pi\) |
−0.720472 | + | 0.693484i | \(0.756075\pi\) | |||||||
\(132\) | −30.0000 | −0.227273 | ||||||||
\(133\) | −25.0000 | + | 25.0000i | −0.187970 | + | 0.187970i | ||||
\(134\) | −113.137 | −0.844307 | ||||||||
\(135\) | −189.000 | −1.40000 | ||||||||
\(136\) | 14.0000 | − | 46.0000i | 0.102941 | − | 0.338235i | ||||
\(137\) | − | 123.037i | − | 0.898077i | −0.893512 | − | 0.449039i | \(-0.851767\pi\) | ||
0.893512 | − | 0.449039i | \(-0.148233\pi\) | |||||||
\(138\) | 89.0955 | 0.645619 | ||||||||
\(139\) | −19.0000 | + | 19.0000i | −0.136691 | + | 0.136691i | −0.772141 | − | 0.635451i | \(-0.780814\pi\) |
0.635451 | + | 0.772141i | \(0.280814\pi\) | |||||||
\(140\) | 98.9949i | 0.707107i | ||||||||
\(141\) | −24.0000 | + | 24.0000i | −0.170213 | + | 0.170213i | ||||
\(142\) | −40.0000 | − | 40.0000i | −0.281690 | − | 0.281690i | ||||
\(143\) | 53.0330 | − | 53.0330i | 0.370860 | − | 0.370860i | ||||
\(144\) | 36.0000i | 0.250000i | ||||||||
\(145\) | − | 280.000i | − | 1.93103i | ||||||
\(146\) | 113.137 | − | 113.137i | 0.774912 | − | 0.774912i | ||||
\(147\) | 2.12132 | − | 2.12132i | 0.0144308 | − | 0.0144308i | ||||
\(148\) | −30.0000 | + | 30.0000i | −0.202703 | + | 0.202703i | ||||
\(149\) | − | 77.7817i | − | 0.522025i | −0.965335 | − | 0.261013i | \(-0.915944\pi\) | ||
0.965335 | − | 0.261013i | \(-0.0840564\pi\) | |||||||
\(150\) | 72.0000 | − | 72.0000i | 0.480000 | − | 0.480000i | ||||
\(151\) | 248.000i | 1.64238i | 0.570652 | + | 0.821192i | \(0.306691\pi\) | ||||
−0.570652 | + | 0.821192i | \(0.693309\pi\) | |||||||
\(152\) | − | 14.1421i | − | 0.0930404i | ||||||
\(153\) | 146.371 | + | 44.5477i | 0.956674 | + | 0.291162i | ||||
\(154\) | −50.0000 | −0.324675 | ||||||||
\(155\) | −237.588 | −1.53283 | ||||||||
\(156\) | −63.6396 | − | 63.6396i | −0.407946 | − | 0.407946i | ||||
\(157\) | −55.0000 | −0.350318 | −0.175159 | − | 0.984540i | \(-0.556044\pi\) | ||||
−0.175159 | + | 0.984540i | \(0.556044\pi\) | |||||||
\(158\) | −15.5563 | − | 15.5563i | −0.0984579 | − | 0.0984579i | ||||
\(159\) | −144.000 | − | 144.000i | −0.905660 | − | 0.905660i | ||||
\(160\) | −28.0000 | − | 28.0000i | −0.175000 | − | 0.175000i | ||||
\(161\) | 148.492 | 0.922313 | ||||||||
\(162\) | −114.551 | −0.707107 | ||||||||
\(163\) | 120.000 | + | 120.000i | 0.736196 | + | 0.736196i | 0.971840 | − | 0.235643i | \(-0.0757197\pi\) |
−0.235643 | + | 0.971840i | \(0.575720\pi\) | |||||||
\(164\) | −77.7817 | + | 77.7817i | −0.474279 | + | 0.474279i | ||||
\(165\) | 74.2462 | + | 74.2462i | 0.449977 | + | 0.449977i | ||||
\(166\) | 176.000 | 1.06024 | ||||||||
\(167\) | −81.3173 | − | 81.3173i | −0.486930 | − | 0.486930i | 0.420406 | − | 0.907336i | \(-0.361888\pi\) |
−0.907336 | + | 0.420406i | \(0.861888\pi\) | |||||||
\(168\) | 60.0000i | 0.357143i | ||||||||
\(169\) | 56.0000 | 0.331361 | ||||||||
\(170\) | −148.492 | + | 79.1960i | −0.873485 | + | 0.465859i | ||||
\(171\) | 45.0000 | 0.263158 | ||||||||
\(172\) | − | 150.000i | − | 0.872093i | ||||||
\(173\) | −17.6777 | − | 17.6777i | −0.102183 | − | 0.102183i | 0.654167 | − | 0.756350i | \(-0.273019\pi\) |
−0.756350 | + | 0.654167i | \(0.773019\pi\) | |||||||
\(174\) | − | 169.706i | − | 0.975320i | ||||||
\(175\) | 120.000 | − | 120.000i | 0.685714 | − | 0.685714i | ||||
\(176\) | 14.1421 | − | 14.1421i | 0.0803530 | − | 0.0803530i | ||||
\(177\) | 135.000 | + | 135.000i | 0.762712 | + | 0.762712i | ||||
\(178\) | − | 30.0000i | − | 0.168539i | ||||||
\(179\) | 56.5685 | 0.316025 | 0.158013 | − | 0.987437i | \(-0.449491\pi\) | ||||
0.158013 | + | 0.987437i | \(0.449491\pi\) | |||||||
\(180\) | 89.0955 | − | 89.0955i | 0.494975 | − | 0.494975i | ||||
\(181\) | −79.0000 | − | 79.0000i | −0.436464 | − | 0.436464i | 0.454356 | − | 0.890820i | \(-0.349869\pi\) |
−0.890820 | + | 0.454356i | \(0.849869\pi\) | |||||||
\(182\) | −106.066 | − | 106.066i | −0.582780 | − | 0.582780i | ||||
\(183\) | − | 301.227i | − | 1.64605i | ||||||
\(184\) | −42.0000 | + | 42.0000i | −0.228261 | + | 0.228261i | ||||
\(185\) | 148.492 | 0.802662 | ||||||||
\(186\) | −144.000 | −0.774194 | ||||||||
\(187\) | −40.0000 | − | 75.0000i | −0.213904 | − | 0.401070i | ||||
\(188\) | − | 22.6274i | − | 0.120359i | ||||||
\(189\) | −190.919 | −1.01015 | ||||||||
\(190\) | −35.0000 | + | 35.0000i | −0.184211 | + | 0.184211i | ||||
\(191\) | 63.6396i | 0.333192i | 0.986025 | + | 0.166596i | \(0.0532775\pi\) | ||||
−0.986025 | + | 0.166596i | \(0.946722\pi\) | |||||||
\(192\) | −16.9706 | − | 16.9706i | −0.0883883 | − | 0.0883883i | ||||
\(193\) | −240.000 | − | 240.000i | −1.24352 | − | 1.24352i | −0.958529 | − | 0.284994i | \(-0.908008\pi\) |
−0.284994 | − | 0.958529i | \(-0.591992\pi\) | |||||||
\(194\) | −113.137 | + | 113.137i | −0.583181 | + | 0.583181i | ||||
\(195\) | 315.000i | 1.61538i | ||||||||
\(196\) | 2.00000i | 0.0102041i | ||||||||
\(197\) | 57.2756 | − | 57.2756i | 0.290739 | − | 0.290739i | −0.546633 | − | 0.837372i | \(-0.684091\pi\) |
0.837372 | + | 0.546633i | \(0.184091\pi\) | |||||||
\(198\) | 45.0000 | + | 45.0000i | 0.227273 | + | 0.227273i | ||||
\(199\) | 104.000 | − | 104.000i | 0.522613 | − | 0.522613i | −0.395747 | − | 0.918360i | \(-0.629514\pi\) |
0.918360 | + | 0.395747i | \(0.129514\pi\) | |||||||
\(200\) | 67.8823i | 0.339411i | ||||||||
\(201\) | 169.706 | + | 169.706i | 0.844307 | + | 0.844307i | ||||
\(202\) | 80.0000i | 0.396040i | ||||||||
\(203\) | − | 282.843i | − | 1.39331i | ||||||
\(204\) | −90.0000 | + | 48.0000i | −0.441176 | + | 0.235294i | ||||
\(205\) | 385.000 | 1.87805 | ||||||||
\(206\) | −7.07107 | −0.0343256 | ||||||||
\(207\) | −133.643 | − | 133.643i | −0.645619 | − | 0.645619i | ||||
\(208\) | 60.0000 | 0.288462 | ||||||||
\(209\) | −17.6777 | − | 17.6777i | −0.0845822 | − | 0.0845822i | ||||
\(210\) | 148.492 | − | 148.492i | 0.707107 | − | 0.707107i | ||||
\(211\) | −216.000 | − | 216.000i | −1.02370 | − | 1.02370i | −0.999712 | − | 0.0239843i | \(-0.992365\pi\) |
−0.0239843 | − | 0.999712i | \(-0.507635\pi\) | |||||||
\(212\) | 135.765 | 0.640399 | ||||||||
\(213\) | 120.000i | 0.563380i | ||||||||
\(214\) | 205.000 | + | 205.000i | 0.957944 | + | 0.957944i | ||||
\(215\) | −371.231 | + | 371.231i | −1.72666 | + | 1.72666i | ||||
\(216\) | 54.0000 | − | 54.0000i | 0.250000 | − | 0.250000i | ||||
\(217\) | −240.000 | −1.10599 | ||||||||
\(218\) | 147.078 | + | 147.078i | 0.674671 | + | 0.674671i | ||||
\(219\) | −339.411 | −1.54982 | ||||||||
\(220\) | −70.0000 | −0.318182 | ||||||||
\(221\) | 74.2462 | − | 243.952i | 0.335956 | − | 1.10385i | ||||
\(222\) | 90.0000 | 0.405405 | ||||||||
\(223\) | 155.000i | 0.695067i | 0.937668 | + | 0.347534i | \(0.112981\pi\) | ||||
−0.937668 | + | 0.347534i | \(0.887019\pi\) | |||||||
\(224\) | −28.2843 | − | 28.2843i | −0.126269 | − | 0.126269i | ||||
\(225\) | −216.000 | −0.960000 | ||||||||
\(226\) | 65.0000 | − | 65.0000i | 0.287611 | − | 0.287611i | ||||
\(227\) | 109.602 | − | 109.602i | 0.482826 | − | 0.482826i | −0.423207 | − | 0.906033i | \(-0.639096\pi\) |
0.906033 | + | 0.423207i | \(0.139096\pi\) | |||||||
\(228\) | −21.2132 | + | 21.2132i | −0.0930404 | + | 0.0930404i | ||||
\(229\) | − | 40.0000i | − | 0.174672i | −0.996179 | − | 0.0873362i | \(-0.972165\pi\) | ||
0.996179 | − | 0.0873362i | \(-0.0278355\pi\) | |||||||
\(230\) | 207.889 | 0.903867 | ||||||||
\(231\) | 75.0000 | + | 75.0000i | 0.324675 | + | 0.324675i | ||||
\(232\) | 80.0000 | + | 80.0000i | 0.344828 | + | 0.344828i | ||||
\(233\) | 112.430 | + | 112.430i | 0.482532 | + | 0.482532i | 0.905939 | − | 0.423407i | \(-0.139166\pi\) |
−0.423407 | + | 0.905939i | \(0.639166\pi\) | |||||||
\(234\) | 190.919i | 0.815892i | ||||||||
\(235\) | −56.0000 | + | 56.0000i | −0.238298 | + | 0.238298i | ||||
\(236\) | −127.279 | −0.539319 | ||||||||
\(237\) | 46.6690i | 0.196916i | ||||||||
\(238\) | −150.000 | + | 80.0000i | −0.630252 | + | 0.336134i | ||||
\(239\) | 282.843i | 1.18344i | 0.806143 | + | 0.591721i | \(0.201551\pi\) | ||||
−0.806143 | + | 0.591721i | \(0.798449\pi\) | |||||||
\(240\) | 84.0000i | 0.350000i | ||||||||
\(241\) | 279.000 | − | 279.000i | 1.15768 | − | 1.15768i | 0.172702 | − | 0.984974i | \(-0.444750\pi\) |
0.984974 | − | 0.172702i | \(-0.0552498\pi\) | |||||||
\(242\) | 135.765i | 0.561010i | ||||||||
\(243\) | 171.827 | + | 171.827i | 0.707107 | + | 0.707107i | ||||
\(244\) | 142.000 | + | 142.000i | 0.581967 | + | 0.581967i | ||||
\(245\) | 4.94975 | − | 4.94975i | 0.0202031 | − | 0.0202031i | ||||
\(246\) | 233.345 | 0.948558 | ||||||||
\(247\) | − | 75.0000i | − | 0.303644i | ||||||
\(248\) | 67.8823 | − | 67.8823i | 0.273719 | − | 0.273719i | ||||
\(249\) | −264.000 | − | 264.000i | −1.06024 | − | 1.06024i | ||||
\(250\) | −7.00000 | + | 7.00000i | −0.0280000 | + | 0.0280000i | ||||
\(251\) | − | 63.6396i | − | 0.253544i | −0.991932 | − | 0.126772i | \(-0.959538\pi\) | ||
0.991932 | − | 0.126772i | \(-0.0404617\pi\) | |||||||
\(252\) | 90.0000 | − | 90.0000i | 0.357143 | − | 0.357143i | ||||
\(253\) | 105.000i | 0.415020i | ||||||||
\(254\) | 176.777i | 0.695971i | ||||||||
\(255\) | 341.533 | + | 103.945i | 1.33934 | + | 0.407626i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −159.806 | −0.621814 | −0.310907 | − | 0.950440i | \(-0.600633\pi\) | ||||
−0.310907 | + | 0.950440i | \(0.600633\pi\) | |||||||
\(258\) | −225.000 | + | 225.000i | −0.872093 | + | 0.872093i | ||||
\(259\) | 150.000 | 0.579151 | ||||||||
\(260\) | −148.492 | − | 148.492i | −0.571125 | − | 0.571125i | ||||
\(261\) | −254.558 | + | 254.558i | −0.975320 | + | 0.975320i | ||||
\(262\) | −5.00000 | − | 5.00000i | −0.0190840 | − | 0.0190840i | ||||
\(263\) | 391.737 | 1.48949 | 0.744747 | − | 0.667346i | \(-0.232570\pi\) | ||||
0.744747 | + | 0.667346i | \(0.232570\pi\) | |||||||
\(264\) | −42.4264 | −0.160706 | ||||||||
\(265\) | −336.000 | − | 336.000i | −1.26792 | − | 1.26792i | ||||
\(266\) | −35.3553 | + | 35.3553i | −0.132915 | + | 0.132915i | ||||
\(267\) | −45.0000 | + | 45.0000i | −0.168539 | + | 0.168539i | ||||
\(268\) | −160.000 | −0.597015 | ||||||||
\(269\) | −130.815 | − | 130.815i | −0.486300 | − | 0.486300i | 0.420836 | − | 0.907137i | \(-0.361737\pi\) |
−0.907137 | + | 0.420836i | \(0.861737\pi\) | |||||||
\(270\) | −267.286 | −0.989949 | ||||||||
\(271\) | −115.000 | −0.424354 | −0.212177 | − | 0.977231i | \(-0.568055\pi\) | ||||
−0.212177 | + | 0.977231i | \(0.568055\pi\) | |||||||
\(272\) | 19.7990 | − | 65.0538i | 0.0727904 | − | 0.239168i | ||||
\(273\) | 318.198i | 1.16556i | ||||||||
\(274\) | − | 174.000i | − | 0.635036i | ||||||
\(275\) | 84.8528 | + | 84.8528i | 0.308556 | + | 0.308556i | ||||
\(276\) | 126.000 | 0.456522 | ||||||||
\(277\) | 280.000 | − | 280.000i | 1.01083 | − | 1.01083i | 0.0108896 | − | 0.999941i | \(-0.496534\pi\) |
0.999941 | − | 0.0108896i | \(-0.00346634\pi\) | |||||||
\(278\) | −26.8701 | + | 26.8701i | −0.0966549 | + | 0.0966549i | ||||
\(279\) | 216.000 | + | 216.000i | 0.774194 | + | 0.774194i | ||||
\(280\) | 140.000i | 0.500000i | ||||||||
\(281\) | −35.3553 | −0.125820 | −0.0629099 | − | 0.998019i | \(-0.520038\pi\) | ||||
−0.0629099 | + | 0.998019i | \(0.520038\pi\) | |||||||
\(282\) | −33.9411 | + | 33.9411i | −0.120359 | + | 0.120359i | ||||
\(283\) | 155.000 | + | 155.000i | 0.547703 | + | 0.547703i | 0.925776 | − | 0.378073i | \(-0.123413\pi\) |
−0.378073 | + | 0.925776i | \(0.623413\pi\) | |||||||
\(284\) | −56.5685 | − | 56.5685i | −0.199185 | − | 0.199185i | ||||
\(285\) | 105.000 | 0.368421 | ||||||||
\(286\) | 75.0000 | − | 75.0000i | 0.262238 | − | 0.262238i | ||||
\(287\) | 388.909 | 1.35508 | ||||||||
\(288\) | 50.9117i | 0.176777i | ||||||||
\(289\) | −240.000 | − | 161.000i | −0.830450 | − | 0.557093i | ||||
\(290\) | − | 395.980i | − | 1.36545i | ||||||
\(291\) | 339.411 | 1.16636 | ||||||||
\(292\) | 160.000 | − | 160.000i | 0.547945 | − | 0.547945i | ||||
\(293\) | − | 46.6690i | − | 0.159280i | −0.996824 | − | 0.0796400i | \(-0.974623\pi\) | ||
0.996824 | − | 0.0796400i | \(-0.0253771\pi\) | |||||||
\(294\) | 3.00000 | − | 3.00000i | 0.0102041 | − | 0.0102041i | ||||
\(295\) | 315.000 | + | 315.000i | 1.06780 | + | 1.06780i | ||||
\(296\) | −42.4264 | + | 42.4264i | −0.143332 | + | 0.143332i | ||||
\(297\) | − | 135.000i | − | 0.454545i | ||||||
\(298\) | − | 110.000i | − | 0.369128i | ||||||
\(299\) | −222.739 | + | 222.739i | −0.744945 | + | 0.744945i | ||||
\(300\) | 101.823 | − | 101.823i | 0.339411 | − | 0.339411i | ||||
\(301\) | −375.000 | + | 375.000i | −1.24585 | + | 1.24585i | ||||
\(302\) | 350.725i | 1.16134i | ||||||||
\(303\) | 120.000 | − | 120.000i | 0.396040 | − | 0.396040i | ||||
\(304\) | − | 20.0000i | − | 0.0657895i | ||||||
\(305\) | − | 702.864i | − | 2.30447i | ||||||
\(306\) | 207.000 | + | 63.0000i | 0.676471 | + | 0.205882i | ||||
\(307\) | −320.000 | −1.04235 | −0.521173 | − | 0.853451i | \(-0.674505\pi\) | ||||
−0.521173 | + | 0.853451i | \(0.674505\pi\) | |||||||
\(308\) | −70.7107 | −0.229580 | ||||||||
\(309\) | 10.6066 | + | 10.6066i | 0.0343256 | + | 0.0343256i | ||||
\(310\) | −336.000 | −1.08387 | ||||||||
\(311\) | −84.8528 | − | 84.8528i | −0.272839 | − | 0.272839i | 0.557403 | − | 0.830242i | \(-0.311798\pi\) |
−0.830242 | + | 0.557403i | \(0.811798\pi\) | |||||||
\(312\) | −90.0000 | − | 90.0000i | −0.288462 | − | 0.288462i | ||||
\(313\) | 160.000 | + | 160.000i | 0.511182 | + | 0.511182i | 0.914889 | − | 0.403706i | \(-0.132278\pi\) |
−0.403706 | + | 0.914889i | \(0.632278\pi\) | |||||||
\(314\) | −77.7817 | −0.247713 | ||||||||
\(315\) | −445.477 | −1.41421 | ||||||||
\(316\) | −22.0000 | − | 22.0000i | −0.0696203 | − | 0.0696203i | ||||
\(317\) | −141.421 | + | 141.421i | −0.446124 | + | 0.446124i | −0.894064 | − | 0.447940i | \(-0.852158\pi\) |
0.447940 | + | 0.894064i | \(0.352158\pi\) | |||||||
\(318\) | −203.647 | − | 203.647i | −0.640399 | − | 0.640399i | ||||
\(319\) | 200.000 | 0.626959 | ||||||||
\(320\) | −39.5980 | − | 39.5980i | −0.123744 | − | 0.123744i | ||||
\(321\) | − | 615.000i | − | 1.91589i | ||||||
\(322\) | 210.000 | 0.652174 | ||||||||
\(323\) | −81.3173 | − | 24.7487i | −0.251756 | − | 0.0766215i | ||||
\(324\) | −162.000 | −0.500000 | ||||||||
\(325\) | 360.000i | 1.10769i | ||||||||
\(326\) | 169.706 | + | 169.706i | 0.520569 | + | 0.520569i | ||||
\(327\) | − | 441.235i | − | 1.34934i | ||||||
\(328\) | −110.000 | + | 110.000i | −0.335366 | + | 0.335366i | ||||
\(329\) | −56.5685 | + | 56.5685i | −0.171941 | + | 0.171941i | ||||
\(330\) | 105.000 | + | 105.000i | 0.318182 | + | 0.318182i | ||||
\(331\) | − | 45.0000i | − | 0.135952i | −0.997687 | − | 0.0679758i | \(-0.978346\pi\) | ||
0.997687 | − | 0.0679758i | \(-0.0216541\pi\) | |||||||
\(332\) | 248.902 | 0.749704 | ||||||||
\(333\) | −135.000 | − | 135.000i | −0.405405 | − | 0.405405i | ||||
\(334\) | −115.000 | − | 115.000i | −0.344311 | − | 0.344311i | ||||
\(335\) | 395.980 | + | 395.980i | 1.18203 | + | 1.18203i | ||||
\(336\) | 84.8528i | 0.252538i | ||||||||
\(337\) | −95.0000 | + | 95.0000i | −0.281899 | + | 0.281899i | −0.833866 | − | 0.551967i | \(-0.813877\pi\) |
0.551967 | + | 0.833866i | \(0.313877\pi\) | |||||||
\(338\) | 79.1960 | 0.234308 | ||||||||
\(339\) | −195.000 | −0.575221 | ||||||||
\(340\) | −210.000 | + | 112.000i | −0.617647 | + | 0.329412i | ||||
\(341\) | − | 169.706i | − | 0.497670i | ||||||
\(342\) | 63.6396 | 0.186081 | ||||||||
\(343\) | −240.000 | + | 240.000i | −0.699708 | + | 0.699708i | ||||
\(344\) | − | 212.132i | − | 0.616663i | ||||||
\(345\) | −311.834 | − | 311.834i | −0.903867 | − | 0.903867i | ||||
\(346\) | −25.0000 | − | 25.0000i | −0.0722543 | − | 0.0722543i | ||||
\(347\) | −113.137 | + | 113.137i | −0.326043 | + | 0.326043i | −0.851080 | − | 0.525036i | \(-0.824052\pi\) |
0.525036 | + | 0.851080i | \(0.324052\pi\) | |||||||
\(348\) | − | 240.000i | − | 0.689655i | ||||||
\(349\) | 473.000i | 1.35530i | 0.735384 | + | 0.677650i | \(0.237002\pi\) | ||||
−0.735384 | + | 0.677650i | \(0.762998\pi\) | |||||||
\(350\) | 169.706 | − | 169.706i | 0.484873 | − | 0.484873i | ||||
\(351\) | 286.378 | − | 286.378i | 0.815892 | − | 0.815892i | ||||
\(352\) | 20.0000 | − | 20.0000i | 0.0568182 | − | 0.0568182i | ||||
\(353\) | − | 9.89949i | − | 0.0280439i | −0.999902 | − | 0.0140219i | \(-0.995537\pi\) | ||
0.999902 | − | 0.0140219i | \(-0.00446347\pi\) | |||||||
\(354\) | 190.919 | + | 190.919i | 0.539319 | + | 0.539319i | ||||
\(355\) | 280.000i | 0.788732i | ||||||||
\(356\) | − | 42.4264i | − | 0.119175i | ||||||
\(357\) | 345.000 | + | 105.000i | 0.966387 | + | 0.294118i | ||||
\(358\) | 80.0000 | 0.223464 | ||||||||
\(359\) | −120.208 | −0.334842 | −0.167421 | − | 0.985886i | \(-0.553544\pi\) | ||||
−0.167421 | + | 0.985886i | \(0.553544\pi\) | |||||||
\(360\) | 126.000 | − | 126.000i | 0.350000 | − | 0.350000i | ||||
\(361\) | 336.000 | 0.930748 | ||||||||
\(362\) | −111.723 | − | 111.723i | −0.308627 | − | 0.308627i | ||||
\(363\) | 203.647 | − | 203.647i | 0.561010 | − | 0.561010i | ||||
\(364\) | −150.000 | − | 150.000i | −0.412088 | − | 0.412088i | ||||
\(365\) | −791.960 | −2.16975 | ||||||||
\(366\) | − | 426.000i | − | 1.16393i | ||||||
\(367\) | −75.0000 | − | 75.0000i | −0.204360 | − | 0.204360i | 0.597505 | − | 0.801865i | \(-0.296159\pi\) |
−0.801865 | + | 0.597505i | \(0.796159\pi\) | |||||||
\(368\) | −59.3970 | + | 59.3970i | −0.161405 | + | 0.161405i | ||||
\(369\) | −350.018 | − | 350.018i | −0.948558 | − | 0.948558i | ||||
\(370\) | 210.000 | 0.567568 | ||||||||
\(371\) | −339.411 | − | 339.411i | −0.914855 | − | 0.914855i | ||||
\(372\) | −203.647 | −0.547438 | ||||||||
\(373\) | 440.000 | 1.17962 | 0.589812 | − | 0.807540i | \(-0.299202\pi\) | ||||
0.589812 | + | 0.807540i | \(0.299202\pi\) | |||||||
\(374\) | −56.5685 | − | 106.066i | −0.151253 | − | 0.283599i | ||||
\(375\) | 21.0000 | 0.0560000 | ||||||||
\(376\) | − | 32.0000i | − | 0.0851064i | ||||||
\(377\) | 424.264 | + | 424.264i | 1.12537 | + | 1.12537i | ||||
\(378\) | −270.000 | −0.714286 | ||||||||
\(379\) | −171.000 | + | 171.000i | −0.451187 | + | 0.451187i | −0.895748 | − | 0.444561i | \(-0.853360\pi\) |
0.444561 | + | 0.895748i | \(0.353360\pi\) | |||||||
\(380\) | −49.4975 | + | 49.4975i | −0.130257 | + | 0.130257i | ||||
\(381\) | 265.165 | − | 265.165i | 0.695971 | − | 0.695971i | ||||
\(382\) | 90.0000i | 0.235602i | ||||||||
\(383\) | −497.803 | −1.29975 | −0.649874 | − | 0.760042i | \(-0.725178\pi\) | ||||
−0.649874 | + | 0.760042i | \(0.725178\pi\) | |||||||
\(384\) | −24.0000 | − | 24.0000i | −0.0625000 | − | 0.0625000i | ||||
\(385\) | 175.000 | + | 175.000i | 0.454545 | + | 0.454545i | ||||
\(386\) | −339.411 | − | 339.411i | −0.879304 | − | 0.879304i | ||||
\(387\) | 675.000 | 1.74419 | ||||||||
\(388\) | −160.000 | + | 160.000i | −0.412371 | + | 0.412371i | ||||
\(389\) | 700.036 | 1.79958 | 0.899789 | − | 0.436326i | \(-0.143720\pi\) | ||||
0.899789 | + | 0.436326i | \(0.143720\pi\) | |||||||
\(390\) | 445.477i | 1.14225i | ||||||||
\(391\) | 168.000 | + | 315.000i | 0.429668 | + | 0.805627i | ||||
\(392\) | 2.82843i | 0.00721538i | ||||||||
\(393\) | 15.0000i | 0.0381679i | ||||||||
\(394\) | 81.0000 | − | 81.0000i | 0.205584 | − | 0.205584i | ||||
\(395\) | 108.894i | 0.275682i | ||||||||
\(396\) | 63.6396 | + | 63.6396i | 0.160706 | + | 0.160706i | ||||
\(397\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(398\) | 147.078 | − | 147.078i | 0.369543 | − | 0.369543i | ||||
\(399\) | 106.066 | 0.265830 | ||||||||
\(400\) | 96.0000i | 0.240000i | ||||||||
\(401\) | −321.734 | + | 321.734i | −0.802328 | + | 0.802328i | −0.983459 | − | 0.181131i | \(-0.942024\pi\) |
0.181131 | + | 0.983459i | \(0.442024\pi\) | |||||||
\(402\) | 240.000 | + | 240.000i | 0.597015 | + | 0.597015i | ||||
\(403\) | 360.000 | − | 360.000i | 0.893300 | − | 0.893300i | ||||
\(404\) | 113.137i | 0.280042i | ||||||||
\(405\) | 400.930 | + | 400.930i | 0.989949 | + | 0.989949i | ||||
\(406\) | − | 400.000i | − | 0.985222i | ||||||
\(407\) | 106.066i | 0.260604i | ||||||||
\(408\) | −127.279 | + | 67.8823i | −0.311959 | + | 0.166378i | ||||
\(409\) | −345.000 | −0.843521 | −0.421760 | − | 0.906707i | \(-0.638588\pi\) | ||||
−0.421760 | + | 0.906707i | \(0.638588\pi\) | |||||||
\(410\) | 544.472 | 1.32798 | ||||||||
\(411\) | −261.000 | + | 261.000i | −0.635036 | + | 0.635036i | ||||
\(412\) | −10.0000 | −0.0242718 | ||||||||
\(413\) | 318.198 | + | 318.198i | 0.770455 | + | 0.770455i | ||||
\(414\) | −189.000 | − | 189.000i | −0.456522 | − | 0.456522i | ||||
\(415\) | −616.000 | − | 616.000i | −1.48434 | − | 1.48434i | ||||
\(416\) | 84.8528 | 0.203973 | ||||||||
\(417\) | 80.6102 | 0.193310 | ||||||||
\(418\) | −25.0000 | − | 25.0000i | −0.0598086 | − | 0.0598086i | ||||
\(419\) | 226.274 | − | 226.274i | 0.540034 | − | 0.540034i | −0.383505 | − | 0.923539i | \(-0.625283\pi\) |
0.923539 | + | 0.383505i | \(0.125283\pi\) | |||||||
\(420\) | 210.000 | − | 210.000i | 0.500000 | − | 0.500000i | ||||
\(421\) | −695.000 | −1.65083 | −0.825416 | − | 0.564525i | \(-0.809059\pi\) | ||||
−0.825416 | + | 0.564525i | \(0.809059\pi\) | |||||||
\(422\) | −305.470 | − | 305.470i | −0.723863 | − | 0.723863i | ||||
\(423\) | 101.823 | 0.240717 | ||||||||
\(424\) | 192.000 | 0.452830 | ||||||||
\(425\) | 390.323 | + | 118.794i | 0.918407 | + | 0.279515i | ||||
\(426\) | 169.706i | 0.398370i | ||||||||
\(427\) | − | 710.000i | − | 1.66276i | ||||||
\(428\) | 289.914 | + | 289.914i | 0.677369 | + | 0.677369i | ||||
\(429\) | −225.000 | −0.524476 | ||||||||
\(430\) | −525.000 | + | 525.000i | −1.22093 | + | 1.22093i | ||||
\(431\) | −197.990 | + | 197.990i | −0.459373 | + | 0.459373i | −0.898450 | − | 0.439076i | \(-0.855306\pi\) |
0.439076 | + | 0.898450i | \(0.355306\pi\) | |||||||
\(432\) | 76.3675 | − | 76.3675i | 0.176777 | − | 0.176777i | ||||
\(433\) | − | 305.000i | − | 0.704388i | −0.935927 | − | 0.352194i | \(-0.885436\pi\) | ||
0.935927 | − | 0.352194i | \(-0.114564\pi\) | |||||||
\(434\) | −339.411 | −0.782054 | ||||||||
\(435\) | −593.970 | + | 593.970i | −1.36545 | + | 1.36545i | ||||
\(436\) | 208.000 | + | 208.000i | 0.477064 | + | 0.477064i | ||||
\(437\) | 74.2462 | + | 74.2462i | 0.169900 | + | 0.169900i | ||||
\(438\) | −480.000 | −1.09589 | ||||||||
\(439\) | −64.0000 | + | 64.0000i | −0.145786 | + | 0.145786i | −0.776233 | − | 0.630447i | \(-0.782872\pi\) |
0.630447 | + | 0.776233i | \(0.282872\pi\) | |||||||
\(440\) | −98.9949 | −0.224989 | ||||||||
\(441\) | −9.00000 | −0.0204082 | ||||||||
\(442\) | 105.000 | − | 345.000i | 0.237557 | − | 0.780543i | ||||
\(443\) | − | 441.235i | − | 0.996015i | −0.867173 | − | 0.498007i | \(-0.834065\pi\) | ||
0.867173 | − | 0.498007i | \(-0.165935\pi\) | |||||||
\(444\) | 127.279 | 0.286665 | ||||||||
\(445\) | −105.000 | + | 105.000i | −0.235955 | + | 0.235955i | ||||
\(446\) | 219.203i | 0.491487i | ||||||||
\(447\) | −165.000 | + | 165.000i | −0.369128 | + | 0.369128i | ||||
\(448\) | −40.0000 | − | 40.0000i | −0.0892857 | − | 0.0892857i | ||||
\(449\) | −360.624 | + | 360.624i | −0.803173 | + | 0.803173i | −0.983590 | − | 0.180418i | \(-0.942255\pi\) |
0.180418 | + | 0.983590i | \(0.442255\pi\) | |||||||
\(450\) | −305.470 | −0.678823 | ||||||||
\(451\) | 275.000i | 0.609756i | ||||||||
\(452\) | 91.9239 | − | 91.9239i | 0.203371 | − | 0.203371i | ||||
\(453\) | 526.087 | − | 526.087i | 1.16134 | − | 1.16134i | ||||
\(454\) | 155.000 | − | 155.000i | 0.341410 | − | 0.341410i | ||||
\(455\) | 742.462i | 1.63178i | ||||||||
\(456\) | −30.0000 | + | 30.0000i | −0.0657895 | + | 0.0657895i | ||||
\(457\) | − | 265.000i | − | 0.579869i | −0.957047 | − | 0.289934i | \(-0.906367\pi\) | ||
0.957047 | − | 0.289934i | \(-0.0936335\pi\) | |||||||
\(458\) | − | 56.5685i | − | 0.123512i | ||||||
\(459\) | −216.000 | − | 405.000i | −0.470588 | − | 0.882353i | ||||
\(460\) | 294.000 | 0.639130 | ||||||||
\(461\) | 148.492 | 0.322109 | 0.161055 | − | 0.986945i | \(-0.448510\pi\) | ||||
0.161055 | + | 0.986945i | \(0.448510\pi\) | |||||||
\(462\) | 106.066 | + | 106.066i | 0.229580 | + | 0.229580i | ||||
\(463\) | 360.000 | 0.777538 | 0.388769 | − | 0.921335i | \(-0.372900\pi\) | ||||
0.388769 | + | 0.921335i | \(0.372900\pi\) | |||||||
\(464\) | 113.137 | + | 113.137i | 0.243830 | + | 0.243830i | ||||
\(465\) | 504.000 | + | 504.000i | 1.08387 | + | 1.08387i | ||||
\(466\) | 159.000 | + | 159.000i | 0.341202 | + | 0.341202i | ||||
\(467\) | −490.732 | −1.05082 | −0.525409 | − | 0.850850i | \(-0.676088\pi\) | ||||
−0.525409 | + | 0.850850i | \(0.676088\pi\) | |||||||
\(468\) | 270.000i | 0.576923i | ||||||||
\(469\) | 400.000 | + | 400.000i | 0.852878 | + | 0.852878i | ||||
\(470\) | −79.1960 | + | 79.1960i | −0.168502 | + | 0.168502i | ||||
\(471\) | 116.673 | + | 116.673i | 0.247713 | + | 0.247713i | ||||
\(472\) | −180.000 | −0.381356 | ||||||||
\(473\) | −265.165 | − | 265.165i | −0.560603 | − | 0.560603i | ||||
\(474\) | 66.0000i | 0.139241i | ||||||||
\(475\) | 120.000 | 0.252632 | ||||||||
\(476\) | −212.132 | + | 113.137i | −0.445656 | + | 0.237683i | ||||
\(477\) | 610.940i | 1.28080i | ||||||||
\(478\) | 400.000i | 0.836820i | ||||||||
\(479\) | −166.170 | − | 166.170i | −0.346910 | − | 0.346910i | 0.512047 | − | 0.858957i | \(-0.328887\pi\) |
−0.858957 | + | 0.512047i | \(0.828887\pi\) | |||||||
\(480\) | 118.794i | 0.247487i | ||||||||
\(481\) | −225.000 | + | 225.000i | −0.467775 | + | 0.467775i | ||||
\(482\) | 394.566 | − | 394.566i | 0.818601 | − | 0.818601i | ||||
\(483\) | −315.000 | − | 315.000i | −0.652174 | − | 0.652174i | ||||
\(484\) | 192.000i | 0.396694i | ||||||||
\(485\) | 791.960 | 1.63291 | ||||||||
\(486\) | 243.000 | + | 243.000i | 0.500000 | + | 0.500000i | ||||
\(487\) | 195.000 | + | 195.000i | 0.400411 | + | 0.400411i | 0.878378 | − | 0.477967i | \(-0.158626\pi\) |
−0.477967 | + | 0.878378i | \(0.658626\pi\) | |||||||
\(488\) | 200.818 | + | 200.818i | 0.411513 | + | 0.411513i | ||||
\(489\) | − | 509.117i | − | 1.04114i | ||||||
\(490\) | 7.00000 | − | 7.00000i | 0.0142857 | − | 0.0142857i | ||||
\(491\) | 565.685 | 1.15211 | 0.576054 | − | 0.817411i | \(-0.304592\pi\) | ||||
0.576054 | + | 0.817411i | \(0.304592\pi\) | |||||||
\(492\) | 330.000 | 0.670732 | ||||||||
\(493\) | 600.000 | − | 320.000i | 1.21704 | − | 0.649087i | ||||
\(494\) | − | 106.066i | − | 0.214709i | ||||||
\(495\) | − | 315.000i | − | 0.636364i | ||||||
\(496\) | 96.0000 | − | 96.0000i | 0.193548 | − | 0.193548i | ||||
\(497\) | 282.843i | 0.569100i | ||||||||
\(498\) | −373.352 | − | 373.352i | −0.749704 | − | 0.749704i | ||||
\(499\) | 336.000 | + | 336.000i | 0.673347 | + | 0.673347i | 0.958486 | − | 0.285139i | \(-0.0920399\pi\) |
−0.285139 | + | 0.958486i | \(0.592040\pi\) | |||||||
\(500\) | −9.89949 | + | 9.89949i | −0.0197990 | + | 0.0197990i | ||||
\(501\) | 345.000i | 0.688623i | ||||||||
\(502\) | − | 90.0000i | − | 0.179283i | ||||||
\(503\) | 477.297 | − | 477.297i | 0.948901 | − | 0.948901i | −0.0498557 | − | 0.998756i | \(-0.515876\pi\) |
0.998756 | + | 0.0498557i | \(0.0158761\pi\) | |||||||
\(504\) | 127.279 | − | 127.279i | 0.252538 | − | 0.252538i | ||||
\(505\) | 280.000 | − | 280.000i | 0.554455 | − | 0.554455i | ||||
\(506\) | 148.492i | 0.293463i | ||||||||
\(507\) | −118.794 | − | 118.794i | −0.234308 | − | 0.234308i | ||||
\(508\) | 250.000i | 0.492126i | ||||||||
\(509\) | 226.274i | 0.444547i | 0.974984 | + | 0.222273i | \(0.0713477\pi\) | ||||
−0.974984 | + | 0.222273i | \(0.928652\pi\) | |||||||
\(510\) | 483.000 | + | 147.000i | 0.947059 | + | 0.288235i | ||||
\(511\) | −800.000 | −1.56556 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −95.4594 | − | 95.4594i | −0.186081 | − | 0.186081i | ||||
\(514\) | −226.000 | −0.439689 | ||||||||
\(515\) | 24.7487 | + | 24.7487i | 0.0480558 | + | 0.0480558i | ||||
\(516\) | −318.198 | + | 318.198i | −0.616663 | + | 0.616663i | ||||
\(517\) | −40.0000 | − | 40.0000i | −0.0773694 | − | 0.0773694i | ||||
\(518\) | 212.132 | 0.409521 | ||||||||
\(519\) | 75.0000i | 0.144509i | ||||||||
\(520\) | −210.000 | − | 210.000i | −0.403846 | − | 0.403846i | ||||
\(521\) | −441.942 | + | 441.942i | −0.848257 | + | 0.848257i | −0.989916 | − | 0.141659i | \(-0.954756\pi\) |
0.141659 | + | 0.989916i | \(0.454756\pi\) | |||||||
\(522\) | −360.000 | + | 360.000i | −0.689655 | + | 0.689655i | ||||
\(523\) | −240.000 | −0.458891 | −0.229446 | − | 0.973322i | \(-0.573691\pi\) | ||||
−0.229446 | + | 0.973322i | \(0.573691\pi\) | |||||||
\(524\) | −7.07107 | − | 7.07107i | −0.0134944 | − | 0.0134944i | ||||
\(525\) | −509.117 | −0.969746 | ||||||||
\(526\) | 554.000 | 1.05323 | ||||||||
\(527\) | −271.529 | − | 509.117i | −0.515235 | − | 0.966066i | ||||
\(528\) | −60.0000 | −0.113636 | ||||||||
\(529\) | 88.0000i | 0.166352i | ||||||||
\(530\) | −475.176 | − | 475.176i | −0.896558 | − | 0.896558i | ||||
\(531\) | − | 572.756i | − | 1.07864i | ||||||
\(532\) | −50.0000 | + | 50.0000i | −0.0939850 | + | 0.0939850i | ||||
\(533\) | −583.363 | + | 583.363i | −1.09449 | + | 1.09449i | ||||
\(534\) | −63.6396 | + | 63.6396i | −0.119175 | + | 0.119175i | ||||
\(535\) | − | 1435.00i | − | 2.68224i | ||||||
\(536\) | −226.274 | −0.422153 | ||||||||
\(537\) | −120.000 | − | 120.000i | −0.223464 | − | 0.223464i | ||||
\(538\) | −185.000 | − | 185.000i | −0.343866 | − | 0.343866i | ||||
\(539\) | 3.53553 | + | 3.53553i | 0.00655943 | + | 0.00655943i | ||||
\(540\) | −378.000 | −0.700000 | ||||||||
\(541\) | 321.000 | − | 321.000i | 0.593346 | − | 0.593346i | −0.345188 | − | 0.938534i | \(-0.612185\pi\) |
0.938534 | + | 0.345188i | \(0.112185\pi\) | |||||||
\(542\) | −162.635 | −0.300064 | ||||||||
\(543\) | 335.169i | 0.617253i | ||||||||
\(544\) | 28.0000 | − | 92.0000i | 0.0514706 | − | 0.169118i | ||||
\(545\) | − | 1029.55i | − | 1.88908i | ||||||
\(546\) | 450.000i | 0.824176i | ||||||||
\(547\) | −395.000 | + | 395.000i | −0.722121 | + | 0.722121i | −0.969037 | − | 0.246916i | \(-0.920583\pi\) |
0.246916 | + | 0.969037i | \(0.420583\pi\) | |||||||
\(548\) | − | 246.073i | − | 0.449039i | ||||||
\(549\) | −639.000 | + | 639.000i | −1.16393 | + | 1.16393i | ||||
\(550\) | 120.000 | + | 120.000i | 0.218182 | + | 0.218182i | ||||
\(551\) | 141.421 | − | 141.421i | 0.256663 | − | 0.256663i | ||||
\(552\) | 178.191 | 0.322810 | ||||||||
\(553\) | 110.000i | 0.198915i | ||||||||
\(554\) | 395.980 | − | 395.980i | 0.714765 | − | 0.714765i | ||||
\(555\) | −315.000 | − | 315.000i | −0.567568 | − | 0.567568i | ||||
\(556\) | −38.0000 | + | 38.0000i | −0.0683453 | + | 0.0683453i | ||||
\(557\) | − | 929.138i | − | 1.66811i | −0.551680 | − | 0.834056i | \(-0.686013\pi\) | ||
0.551680 | − | 0.834056i | \(-0.313987\pi\) | |||||||
\(558\) | 305.470 | + | 305.470i | 0.547438 | + | 0.547438i | ||||
\(559\) | − | 1125.00i | − | 2.01252i | ||||||
\(560\) | 197.990i | 0.353553i | ||||||||
\(561\) | −74.2462 | + | 243.952i | −0.132346 | + | 0.434852i | ||||
\(562\) | −50.0000 | −0.0889680 | ||||||||
\(563\) | −101.823 | −0.180859 | −0.0904293 | − | 0.995903i | \(-0.528824\pi\) | ||||
−0.0904293 | + | 0.995903i | \(0.528824\pi\) | |||||||
\(564\) | −48.0000 | + | 48.0000i | −0.0851064 | + | 0.0851064i | ||||
\(565\) | −455.000 | −0.805310 | ||||||||
\(566\) | 219.203 | + | 219.203i | 0.387285 | + | 0.387285i | ||||
\(567\) | 405.000 | + | 405.000i | 0.714286 | + | 0.714286i | ||||
\(568\) | −80.0000 | − | 80.0000i | −0.140845 | − | 0.140845i | ||||
\(569\) | 395.980 | 0.695922 | 0.347961 | − | 0.937509i | \(-0.386874\pi\) | ||||
0.347961 | + | 0.937509i | \(0.386874\pi\) | |||||||
\(570\) | 148.492 | 0.260513 | ||||||||
\(571\) | −104.000 | − | 104.000i | −0.182137 | − | 0.182137i | 0.610150 | − | 0.792286i | \(-0.291109\pi\) |
−0.792286 | + | 0.610150i | \(0.791109\pi\) | |||||||
\(572\) | 106.066 | − | 106.066i | 0.185430 | − | 0.185430i | ||||
\(573\) | 135.000 | − | 135.000i | 0.235602 | − | 0.235602i | ||||
\(574\) | 550.000 | 0.958188 | ||||||||
\(575\) | −356.382 | − | 356.382i | −0.619794 | − | 0.619794i | ||||
\(576\) | 72.0000i | 0.125000i | ||||||||
\(577\) | −185.000 | −0.320624 | −0.160312 | − | 0.987066i | \(-0.551250\pi\) | ||||
−0.160312 | + | 0.987066i | \(0.551250\pi\) | |||||||
\(578\) | −339.411 | − | 227.688i | −0.587217 | − | 0.393925i | ||||
\(579\) | 1018.23i | 1.75861i | ||||||||
\(580\) | − | 560.000i | − | 0.965517i | ||||||
\(581\) | −622.254 | − | 622.254i | −1.07101 | − | 1.07101i | ||||
\(582\) | 480.000 | 0.824742 | ||||||||
\(583\) | 240.000 | − | 240.000i | 0.411664 | − | 0.411664i | ||||
\(584\) | 226.274 | − | 226.274i | 0.387456 | − | 0.387456i | ||||
\(585\) | 668.216 | − | 668.216i | 1.14225 | − | 1.14225i | ||||
\(586\) | − | 66.0000i | − | 0.112628i | ||||||
\(587\) | 497.803 | 0.848046 | 0.424023 | − | 0.905651i | \(-0.360618\pi\) | ||||
0.424023 | + | 0.905651i | \(0.360618\pi\) | |||||||
\(588\) | 4.24264 | − | 4.24264i | 0.00721538 | − | 0.00721538i | ||||
\(589\) | −120.000 | − | 120.000i | −0.203735 | − | 0.203735i | ||||
\(590\) | 445.477 | + | 445.477i | 0.755046 | + | 0.755046i | ||||
\(591\) | −243.000 | −0.411168 | ||||||||
\(592\) | −60.0000 | + | 60.0000i | −0.101351 | + | 0.101351i | ||||
\(593\) | −916.410 | −1.54538 | −0.772690 | − | 0.634784i | \(-0.781089\pi\) | ||||
−0.772690 | + | 0.634784i | \(0.781089\pi\) | |||||||
\(594\) | − | 190.919i | − | 0.321412i | ||||||
\(595\) | 805.000 | + | 245.000i | 1.35294 | + | 0.411765i | ||||
\(596\) | − | 155.563i | − | 0.261013i | ||||||
\(597\) | −441.235 | −0.739086 | ||||||||
\(598\) | −315.000 | + | 315.000i | −0.526756 | + | 0.526756i | ||||
\(599\) | 615.183i | 1.02702i | 0.858085 | + | 0.513508i | \(0.171654\pi\) | ||||
−0.858085 | + | 0.513508i | \(0.828346\pi\) | |||||||
\(600\) | 144.000 | − | 144.000i | 0.240000 | − | 0.240000i | ||||
\(601\) | −56.0000 | − | 56.0000i | −0.0931780 | − | 0.0931780i | 0.658981 | − | 0.752159i | \(-0.270988\pi\) |
−0.752159 | + | 0.658981i | \(0.770988\pi\) | |||||||
\(602\) | −530.330 | + | 530.330i | −0.880947 | + | 0.880947i | ||||
\(603\) | − | 720.000i | − | 1.19403i | ||||||
\(604\) | 496.000i | 0.821192i | ||||||||
\(605\) | 475.176 | − | 475.176i | 0.785414 | − | 0.785414i | ||||
\(606\) | 169.706 | − | 169.706i | 0.280042 | − | 0.280042i | ||||
\(607\) | −645.000 | + | 645.000i | −1.06260 | + | 1.06260i | −0.0646981 | + | 0.997905i | \(0.520608\pi\) |
−0.997905 | + | 0.0646981i | \(0.979392\pi\) | |||||||
\(608\) | − | 28.2843i | − | 0.0465202i | ||||||
\(609\) | −600.000 | + | 600.000i | −0.985222 | + | 0.985222i | ||||
\(610\) | − | 994.000i | − | 1.62951i | ||||||
\(611\) | − | 169.706i | − | 0.277751i | ||||||
\(612\) | 292.742 | + | 89.0955i | 0.478337 | + | 0.145581i | ||||
\(613\) | 495.000 | 0.807504 | 0.403752 | − | 0.914868i | \(-0.367706\pi\) | ||||
0.403752 | + | 0.914868i | \(0.367706\pi\) | |||||||
\(614\) | −452.548 | −0.737049 | ||||||||
\(615\) | −816.708 | − | 816.708i | −1.32798 | − | 1.32798i | ||||
\(616\) | −100.000 | −0.162338 | ||||||||
\(617\) | 56.5685 | + | 56.5685i | 0.0916832 | + | 0.0916832i | 0.751461 | − | 0.659778i | \(-0.229350\pi\) |
−0.659778 | + | 0.751461i | \(0.729350\pi\) | |||||||
\(618\) | 15.0000 | + | 15.0000i | 0.0242718 | + | 0.0242718i | ||||
\(619\) | 261.000 | + | 261.000i | 0.421648 | + | 0.421648i | 0.885771 | − | 0.464123i | \(-0.153630\pi\) |
−0.464123 | + | 0.885771i | \(0.653630\pi\) | |||||||
\(620\) | −475.176 | −0.766413 | ||||||||
\(621\) | 567.000i | 0.913043i | ||||||||
\(622\) | −120.000 | − | 120.000i | −0.192926 | − | 0.192926i | ||||
\(623\) | −106.066 | + | 106.066i | −0.170250 | + | 0.170250i | ||||
\(624\) | −127.279 | − | 127.279i | −0.203973 | − | 0.203973i | ||||
\(625\) | 649.000 | 1.03840 | ||||||||
\(626\) | 226.274 | + | 226.274i | 0.361460 | + | 0.361460i | ||||
\(627\) | 75.0000i | 0.119617i | ||||||||
\(628\) | −110.000 | −0.175159 | ||||||||
\(629\) | 169.706 | + | 318.198i | 0.269802 | + | 0.505879i | ||||
\(630\) | −630.000 | −1.00000 | ||||||||
\(631\) | 213.000i | 0.337559i | 0.985654 | + | 0.168780i | \(0.0539826\pi\) | ||||
−0.985654 | + | 0.168780i | \(0.946017\pi\) | |||||||
\(632\) | −31.1127 | − | 31.1127i | −0.0492290 | − | 0.0492290i | ||||
\(633\) | 916.410i | 1.44773i | ||||||||
\(634\) | −200.000 | + | 200.000i | −0.315457 | + | 0.315457i | ||||
\(635\) | 618.718 | − | 618.718i | 0.974360 | − | 0.974360i | ||||
\(636\) | −288.000 | − | 288.000i | −0.452830 | − | 0.452830i | ||||
\(637\) | 15.0000i | 0.0235479i | ||||||||
\(638\) | 282.843 | 0.443327 | ||||||||
\(639\) | 254.558 | − | 254.558i | 0.398370 | − | 0.398370i | ||||
\(640\) | −56.0000 | − | 56.0000i | −0.0875000 | − | 0.0875000i | ||||
\(641\) | 236.881 | + | 236.881i | 0.369549 | + | 0.369549i | 0.867313 | − | 0.497764i | \(-0.165845\pi\) |
−0.497764 | + | 0.867313i | \(0.665845\pi\) | |||||||
\(642\) | − | 869.741i | − | 1.35474i | ||||||
\(643\) | 520.000 | − | 520.000i | 0.808709 | − | 0.808709i | −0.175729 | − | 0.984439i | \(-0.556228\pi\) |
0.984439 | + | 0.175729i | \(0.0562284\pi\) | |||||||
\(644\) | 296.985 | 0.461157 | ||||||||
\(645\) | 1575.00 | 2.44186 | ||||||||
\(646\) | −115.000 | − | 35.0000i | −0.178019 | − | 0.0541796i | ||||
\(647\) | 1056.42i | 1.63279i | 0.577491 | + | 0.816397i | \(0.304032\pi\) | ||||
−0.577491 | + | 0.816397i | \(0.695968\pi\) | |||||||
\(648\) | −229.103 | −0.353553 | ||||||||
\(649\) | −225.000 | + | 225.000i | −0.346687 | + | 0.346687i | ||||
\(650\) | 509.117i | 0.783257i | ||||||||
\(651\) | 509.117 | + | 509.117i | 0.782054 | + | 0.782054i | ||||
\(652\) | 240.000 | + | 240.000i | 0.368098 | + | 0.368098i | ||||
\(653\) | −894.490 | + | 894.490i | −1.36982 | + | 1.36982i | −0.509122 | + | 0.860694i | \(0.670030\pi\) |
−0.860694 | + | 0.509122i | \(0.829970\pi\) | |||||||
\(654\) | − | 624.000i | − | 0.954128i | ||||||
\(655\) | 35.0000i | 0.0534351i | ||||||||
\(656\) | −155.563 | + | 155.563i | −0.237139 | + | 0.237139i | ||||
\(657\) | 720.000 | + | 720.000i | 1.09589 | + | 1.09589i | ||||
\(658\) | −80.0000 | + | 80.0000i | −0.121581 | + | 0.121581i | ||||
\(659\) | 7.07107i | 0.0107300i | 0.999986 | + | 0.00536500i | \(0.00170774\pi\) | ||||
−0.999986 | + | 0.00536500i | \(0.998292\pi\) | |||||||
\(660\) | 148.492 | + | 148.492i | 0.224989 | + | 0.224989i | ||||
\(661\) | 535.000i | 0.809380i | 0.914454 | + | 0.404690i | \(0.132621\pi\) | ||||
−0.914454 | + | 0.404690i | \(0.867379\pi\) | |||||||
\(662\) | − | 63.6396i | − | 0.0961323i | ||||||
\(663\) | −675.000 | + | 360.000i | −1.01810 | + | 0.542986i | ||||
\(664\) | 352.000 | 0.530120 | ||||||||
\(665\) | 247.487 | 0.372161 | ||||||||
\(666\) | −190.919 | − | 190.919i | −0.286665 | − | 0.286665i | ||||
\(667\) | −840.000 | −1.25937 | ||||||||
\(668\) | −162.635 | − | 162.635i | −0.243465 | − | 0.243465i | ||||
\(669\) | 328.805 | − | 328.805i | 0.491487 | − | 0.491487i | ||||
\(670\) | 560.000 | + | 560.000i | 0.835821 | + | 0.835821i | ||||
\(671\) | 502.046 | 0.748205 | ||||||||
\(672\) | 120.000i | 0.178571i | ||||||||
\(673\) | −480.000 | − | 480.000i | −0.713224 | − | 0.713224i | 0.253984 | − | 0.967208i | \(-0.418259\pi\) |
−0.967208 | + | 0.253984i | \(0.918259\pi\) | |||||||
\(674\) | −134.350 | + | 134.350i | −0.199333 | + | 0.199333i | ||||
\(675\) | 458.205 | + | 458.205i | 0.678823 | + | 0.678823i | ||||
\(676\) | 112.000 | 0.165680 | ||||||||
\(677\) | 333.047 | + | 333.047i | 0.491946 | + | 0.491946i | 0.908919 | − | 0.416973i | \(-0.136909\pi\) |
−0.416973 | + | 0.908919i | \(0.636909\pi\) | |||||||
\(678\) | −275.772 | −0.406743 | ||||||||
\(679\) | 800.000 | 1.17820 | ||||||||
\(680\) | −296.985 | + | 158.392i | −0.436742 | + | 0.232929i | ||||
\(681\) | −465.000 | −0.682819 | ||||||||
\(682\) | − | 240.000i | − | 0.351906i | ||||||
\(683\) | 533.866 | + | 533.866i | 0.781648 | + | 0.781648i | 0.980109 | − | 0.198461i | \(-0.0635942\pi\) |
−0.198461 | + | 0.980109i | \(0.563594\pi\) | |||||||
\(684\) | 90.0000 | 0.131579 | ||||||||
\(685\) | −609.000 | + | 609.000i | −0.889051 | + | 0.889051i | ||||
\(686\) | −339.411 | + | 339.411i | −0.494769 | + | 0.494769i | ||||
\(687\) | −84.8528 | + | 84.8528i | −0.123512 | + | 0.123512i | ||||
\(688\) | − | 300.000i | − | 0.436047i | ||||||
\(689\) | 1018.23 | 1.47784 | ||||||||
\(690\) | −441.000 | − | 441.000i | −0.639130 | − | 0.639130i | ||||
\(691\) | 304.000 | + | 304.000i | 0.439942 | + | 0.439942i | 0.891992 | − | 0.452050i | \(-0.149307\pi\) |
−0.452050 | + | 0.891992i | \(0.649307\pi\) | |||||||
\(692\) | −35.3553 | − | 35.3553i | −0.0510915 | − | 0.0510915i | ||||
\(693\) | − | 318.198i | − | 0.459160i | ||||||
\(694\) | −160.000 | + | 160.000i | −0.230548 | + | 0.230548i | ||||
\(695\) | 188.090 | 0.270634 | ||||||||
\(696\) | − | 339.411i | − | 0.487660i | ||||||
\(697\) | 440.000 | + | 825.000i | 0.631277 | + | 1.18364i | ||||
\(698\) | 668.923i | 0.958342i | ||||||||
\(699\) | − | 477.000i | − | 0.682403i | ||||||
\(700\) | 240.000 | − | 240.000i | 0.342857 | − | 0.342857i | ||||
\(701\) | 169.706i | 0.242091i | 0.992647 | + | 0.121045i | \(0.0386247\pi\) | ||||
−0.992647 | + | 0.121045i | \(0.961375\pi\) | |||||||
\(702\) | 405.000 | − | 405.000i | 0.576923 | − | 0.576923i | ||||
\(703\) | 75.0000 | + | 75.0000i | 0.106686 | + | 0.106686i | ||||
\(704\) | 28.2843 | − | 28.2843i | 0.0401765 | − | 0.0401765i | ||||
\(705\) | 237.588 | 0.337004 | ||||||||
\(706\) | − | 14.0000i | − | 0.0198300i | ||||||
\(707\) | 282.843 | − | 282.843i | 0.400060 | − | 0.400060i | ||||
\(708\) | 270.000 | + | 270.000i | 0.381356 | + | 0.381356i | ||||
\(709\) | 344.000 | − | 344.000i | 0.485190 | − | 0.485190i | −0.421594 | − | 0.906785i | \(-0.638529\pi\) |
0.906785 | + | 0.421594i | \(0.138529\pi\) | |||||||
\(710\) | 395.980i | 0.557718i | ||||||||
\(711\) | 99.0000 | − | 99.0000i | 0.139241 | − | 0.139241i | ||||
\(712\) | − | 60.0000i | − | 0.0842697i | ||||||
\(713\) | 712.764i | 0.999668i | ||||||||
\(714\) | 487.904 | + | 148.492i | 0.683338 | + | 0.207973i | ||||
\(715\) | −525.000 | −0.734266 | ||||||||
\(716\) | 113.137 | 0.158013 | ||||||||
\(717\) | 600.000 | − | 600.000i | 0.836820 | − | 0.836820i | ||||
\(718\) | −170.000 | −0.236769 | ||||||||
\(719\) | −194.454 | − | 194.454i | −0.270451 | − | 0.270451i | 0.558831 | − | 0.829282i | \(-0.311250\pi\) |
−0.829282 | + | 0.558831i | \(0.811250\pi\) | |||||||
\(720\) | 178.191 | − | 178.191i | 0.247487 | − | 0.247487i | ||||
\(721\) | 25.0000 | + | 25.0000i | 0.0346741 | + | 0.0346741i | ||||
\(722\) | 475.176 | 0.658138 | ||||||||
\(723\) | −1183.70 | −1.63720 | ||||||||
\(724\) | −158.000 | − | 158.000i | −0.218232 | − | 0.218232i | ||||
\(725\) | −678.823 | + | 678.823i | −0.936307 | + | 0.936307i | ||||
\(726\) | 288.000 | − | 288.000i | 0.396694 | − | 0.396694i | ||||
\(727\) | −1310.00 | −1.80193 | −0.900963 | − | 0.433896i | \(-0.857138\pi\) | ||||
−0.900963 | + | 0.433896i | \(0.857138\pi\) | |||||||
\(728\) | −212.132 | − | 212.132i | −0.291390 | − | 0.291390i | ||||
\(729\) | − | 729.000i | − | 1.00000i | ||||||
\(730\) | −1120.00 | −1.53425 | ||||||||
\(731\) | −1219.76 | − | 371.231i | −1.66862 | − | 0.507840i | ||||
\(732\) | − | 602.455i | − | 0.823026i | ||||||
\(733\) | 520.000i | 0.709413i | 0.934978 | + | 0.354707i | \(0.115419\pi\) | ||||
−0.934978 | + | 0.354707i | \(0.884581\pi\) | |||||||
\(734\) | −106.066 | − | 106.066i | −0.144504 | − | 0.144504i | ||||
\(735\) | −21.0000 | −0.0285714 | ||||||||
\(736\) | −84.0000 | + | 84.0000i | −0.114130 | + | 0.114130i | ||||
\(737\) | −282.843 | + | 282.843i | −0.383776 | + | 0.383776i | ||||
\(738\) | −495.000 | − | 495.000i | −0.670732 | − | 0.670732i | ||||
\(739\) | 1197.00i | 1.61976i | 0.586598 | + | 0.809878i | \(0.300467\pi\) | ||||
−0.586598 | + | 0.809878i | \(0.699533\pi\) | |||||||
\(740\) | 296.985 | 0.401331 | ||||||||
\(741\) | −159.099 | + | 159.099i | −0.214709 | + | 0.214709i | ||||
\(742\) | −480.000 | − | 480.000i | −0.646900 | − | 0.646900i | ||||
\(743\) | −318.198 | − | 318.198i | −0.428261 | − | 0.428261i | 0.459775 | − | 0.888036i | \(-0.347930\pi\) |
−0.888036 | + | 0.459775i | \(0.847930\pi\) | |||||||
\(744\) | −288.000 | −0.387097 | ||||||||
\(745\) | −385.000 | + | 385.000i | −0.516779 | + | 0.516779i | ||||
\(746\) | 622.254 | 0.834121 | ||||||||
\(747\) | 1120.06i | 1.49941i | ||||||||
\(748\) | −80.0000 | − | 150.000i | −0.106952 | − | 0.200535i | ||||
\(749\) | − | 1449.57i | − | 1.93534i | ||||||
\(750\) | 29.6985 | 0.0395980 | ||||||||
\(751\) | 216.000 | − | 216.000i | 0.287617 | − | 0.287617i | −0.548521 | − | 0.836137i | \(-0.684809\pi\) |
0.836137 | + | 0.548521i | \(0.184809\pi\) | |||||||
\(752\) | − | 45.2548i | − | 0.0601793i | ||||||
\(753\) | −135.000 | + | 135.000i | −0.179283 | + | 0.179283i | ||||
\(754\) | 600.000 | + | 600.000i | 0.795756 | + | 0.795756i | ||||
\(755\) | 1227.54 | − | 1227.54i | 1.62588 | − | 1.62588i | ||||
\(756\) | −381.838 | −0.505076 | ||||||||
\(757\) | − | 1105.00i | − | 1.45971i | −0.683602 | − | 0.729855i | \(-0.739588\pi\) | ||
0.683602 | − | 0.729855i | \(-0.260412\pi\) | |||||||
\(758\) | −241.831 | + | 241.831i | −0.319038 | + | 0.319038i | ||||
\(759\) | 222.739 | − | 222.739i | 0.293463 | − | 0.293463i | ||||
\(760\) | −70.0000 | + | 70.0000i | −0.0921053 | + | 0.0921053i | ||||
\(761\) | − | 1074.80i | − | 1.41236i | −0.708035 | − | 0.706178i | \(-0.750418\pi\) | ||
0.708035 | − | 0.706178i | \(-0.249582\pi\) | |||||||
\(762\) | 375.000 | − | 375.000i | 0.492126 | − | 0.492126i | ||||
\(763\) | − | 1040.00i | − | 1.36304i | ||||||
\(764\) | 127.279i | 0.166596i | ||||||||
\(765\) | −504.000 | − | 945.000i | −0.658824 | − | 1.23529i | ||||
\(766\) | −704.000 | −0.919060 | ||||||||
\(767\) | −954.594 | −1.24458 | ||||||||
\(768\) | −33.9411 | − | 33.9411i | −0.0441942 | − | 0.0441942i | ||||
\(769\) | 287.000 | 0.373212 | 0.186606 | − | 0.982435i | \(-0.440251\pi\) | ||||
0.186606 | + | 0.982435i | \(0.440251\pi\) | |||||||
\(770\) | 247.487 | + | 247.487i | 0.321412 | + | 0.321412i | ||||
\(771\) | 339.000 | + | 339.000i | 0.439689 | + | 0.439689i | ||||
\(772\) | −480.000 | − | 480.000i | −0.621762 | − | 0.621762i | ||||
\(773\) | −520.431 | −0.673261 | −0.336630 | − | 0.941637i | \(-0.609287\pi\) | ||||
−0.336630 | + | 0.941637i | \(0.609287\pi\) | |||||||
\(774\) | 954.594 | 1.23333 | ||||||||
\(775\) | 576.000 | + | 576.000i | 0.743226 | + | 0.743226i | ||||
\(776\) | −226.274 | + | 226.274i | −0.291590 | + | 0.291590i | ||||
\(777\) | −318.198 | − | 318.198i | −0.409521 | − | 0.409521i | ||||
\(778\) | 990.000 | 1.27249 | ||||||||
\(779\) | 194.454 | + | 194.454i | 0.249620 | + | 0.249620i | ||||
\(780\) | 630.000i | 0.807692i | ||||||||
\(781\) | −200.000 | −0.256082 | ||||||||
\(782\) | 237.588 | + | 445.477i | 0.303821 | + | 0.569664i | ||||
\(783\) | 1080.00 | 1.37931 | ||||||||
\(784\) | 4.00000i | 0.00510204i | ||||||||
\(785\) | 272.236 | + | 272.236i | 0.346798 | + | 0.346798i | ||||
\(786\) | 21.2132i | 0.0269888i | ||||||||
\(787\) | −720.000 | + | 720.000i | −0.914867 | + | 0.914867i | −0.996650 | − | 0.0817835i | \(-0.973938\pi\) |
0.0817835 | + | 0.996650i | \(0.473938\pi\) | |||||||
\(788\) | 114.551 | − | 114.551i | 0.145370 | − | 0.145370i | ||||
\(789\) | −831.000 | − | 831.000i | −1.05323 | − | 1.05323i | ||||
\(790\) | 154.000i | 0.194937i | ||||||||
\(791\) | −459.619 | −0.581061 | ||||||||
\(792\) | 90.0000 | + | 90.0000i | 0.113636 | + | 0.113636i | ||||
\(793\) | 1065.00 | + | 1065.00i | 1.34300 | + | 1.34300i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1425.53i | 1.79312i | ||||||||
\(796\) | 208.000 | − | 208.000i | 0.261307 | − | 0.261307i | ||||
\(797\) | −237.588 | −0.298103 | −0.149051 | − | 0.988829i | \(-0.547622\pi\) | ||||
−0.149051 | + | 0.988829i | \(0.547622\pi\) | |||||||
\(798\) | 150.000 | 0.187970 | ||||||||
\(799\) | −184.000 | − | 56.0000i | −0.230288 | − | 0.0700876i | ||||
\(800\) | 135.765i | 0.169706i | ||||||||
\(801\) | 190.919 | 0.238351 | ||||||||
\(802\) | −455.000 | + | 455.000i | −0.567332 | + | 0.567332i | ||||
\(803\) | − | 565.685i | − | 0.704465i | ||||||
\(804\) | 339.411 | + | 339.411i | 0.422153 | + | 0.422153i | ||||
\(805\) | −735.000 | − | 735.000i | −0.913043 | − | 0.913043i | ||||
\(806\) | 509.117 | − | 509.117i | 0.631659 | − | 0.631659i | ||||
\(807\) | 555.000i | 0.687732i | ||||||||
\(808\) | 160.000i | 0.198020i | ||||||||
\(809\) | 123.744 | − | 123.744i | 0.152959 | − | 0.152959i | −0.626479 | − | 0.779438i | \(-0.715505\pi\) |
0.779438 | + | 0.626479i | \(0.215505\pi\) | |||||||
\(810\) | 567.000 | + | 567.000i | 0.700000 | + | 0.700000i | ||||
\(811\) | 824.000 | − | 824.000i | 1.01603 | − | 1.01603i | 0.0161602 | − | 0.999869i | \(-0.494856\pi\) |
0.999869 | − | 0.0161602i | \(-0.00514417\pi\) | |||||||
\(812\) | − | 565.685i | − | 0.696657i | ||||||
\(813\) | 243.952 | + | 243.952i | 0.300064 | + | 0.300064i | ||||
\(814\) | 150.000i | 0.184275i | ||||||||
\(815\) | − | 1187.94i | − | 1.45759i | ||||||
\(816\) | −180.000 | + | 96.0000i | −0.220588 | + | 0.117647i | ||||
\(817\) | −375.000 | −0.458996 | ||||||||
\(818\) | −487.904 | −0.596459 | ||||||||
\(819\) | 675.000 | − | 675.000i | 0.824176 | − | 0.824176i | ||||
\(820\) | 770.000 | 0.939024 | ||||||||
\(821\) | 300.520 | + | 300.520i | 0.366042 | + | 0.366042i | 0.866031 | − | 0.499990i | \(-0.166663\pi\) |
−0.499990 | + | 0.866031i | \(0.666663\pi\) | |||||||
\(822\) | −369.110 | + | 369.110i | −0.449039 | + | 0.449039i | ||||
\(823\) | 1005.00 | + | 1005.00i | 1.22114 | + | 1.22114i | 0.967226 | + | 0.253916i | \(0.0817186\pi\) |
0.253916 | + | 0.967226i | \(0.418281\pi\) | |||||||
\(824\) | −14.1421 | −0.0171628 | ||||||||
\(825\) | − | 360.000i | − | 0.436364i | ||||||
\(826\) | 450.000 | + | 450.000i | 0.544794 | + | 0.544794i | ||||
\(827\) | 586.192 | − | 586.192i | 0.708817 | − | 0.708817i | −0.257470 | − | 0.966286i | \(-0.582889\pi\) |
0.966286 | + | 0.257470i | \(0.0828887\pi\) | |||||||
\(828\) | −267.286 | − | 267.286i | −0.322810 | − | 0.322810i | ||||
\(829\) | 8.00000 | 0.00965018 | 0.00482509 | − | 0.999988i | \(-0.498464\pi\) | ||||
0.00482509 | + | 0.999988i | \(0.498464\pi\) | |||||||
\(830\) | −871.156 | − | 871.156i | −1.04959 | − | 1.04959i | ||||
\(831\) | −1187.94 | −1.42953 | ||||||||
\(832\) | 120.000 | 0.144231 | ||||||||
\(833\) | 16.2635 | + | 4.94975i | 0.0195240 | + | 0.00594207i | ||||
\(834\) | 114.000 | 0.136691 | ||||||||
\(835\) | 805.000i | 0.964072i | ||||||||
\(836\) | −35.3553 | − | 35.3553i | −0.0422911 | − | 0.0422911i | ||||
\(837\) | − | 916.410i | − | 1.09488i | ||||||
\(838\) | 320.000 | − | 320.000i | 0.381862 | − | 0.381862i | ||||
\(839\) | 512.652 | − | 512.652i | 0.611028 | − | 0.611028i | −0.332186 | − | 0.943214i | \(-0.607786\pi\) |
0.943214 | + | 0.332186i | \(0.107786\pi\) | |||||||
\(840\) | 296.985 | − | 296.985i | 0.353553 | − | 0.353553i | ||||
\(841\) | 759.000i | 0.902497i | ||||||||
\(842\) | −982.878 | −1.16731 | ||||||||
\(843\) | 75.0000 | + | 75.0000i | 0.0889680 | + | 0.0889680i | ||||
\(844\) | −432.000 | − | 432.000i | −0.511848 | − | 0.511848i | ||||
\(845\) | −277.186 | − | 277.186i | −0.328031 | − | 0.328031i | ||||
\(846\) | 144.000 | 0.170213 | ||||||||
\(847\) | 480.000 | − | 480.000i | 0.566706 | − | 0.566706i | ||||
\(848\) | 271.529 | 0.320199 | ||||||||
\(849\) | − | 657.609i | − | 0.774569i | ||||||
\(850\) | 552.000 | + | 168.000i | 0.649412 | + | 0.197647i | ||||
\(851\) | − | 445.477i | − | 0.523475i | ||||||
\(852\) | 240.000i | 0.281690i | ||||||||
\(853\) | −905.000 | + | 905.000i | −1.06096 | + | 1.06096i | −0.0629443 | + | 0.998017i | \(0.520049\pi\) |
−0.998017 | + | 0.0629443i | \(0.979951\pi\) | |||||||
\(854\) | − | 1004.09i | − | 1.17575i | ||||||
\(855\) | −222.739 | − | 222.739i | −0.260513 | − | 0.260513i | ||||
\(856\) | 410.000 | + | 410.000i | 0.478972 | + | 0.478972i | ||||
\(857\) | −610.940 | + | 610.940i | −0.712882 | + | 0.712882i | −0.967137 | − | 0.254255i | \(-0.918170\pi\) |
0.254255 | + | 0.967137i | \(0.418170\pi\) | |||||||
\(858\) | −318.198 | −0.370860 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | −742.462 | + | 742.462i | −0.863328 | + | 0.863328i | ||||
\(861\) | −825.000 | − | 825.000i | −0.958188 | − | 0.958188i | ||||
\(862\) | −280.000 | + | 280.000i | −0.324826 | + | 0.324826i | ||||
\(863\) | 230.517i | 0.267111i | 0.991041 | + | 0.133556i | \(0.0426394\pi\) | ||||
−0.991041 | + | 0.133556i | \(0.957361\pi\) | |||||||
\(864\) | 108.000 | − | 108.000i | 0.125000 | − | 0.125000i | ||||
\(865\) | 175.000i | 0.202312i | ||||||||
\(866\) | − | 431.335i | − | 0.498078i | ||||||
\(867\) | 167.584 | + | 850.649i | 0.193292 | + | 0.981141i | ||||
\(868\) | −480.000 | −0.552995 | ||||||||
\(869\) | −77.7817 | −0.0895072 | ||||||||
\(870\) | −840.000 | + | 840.000i | −0.965517 | + | 0.965517i | ||||
\(871\) | −1200.00 | −1.37773 | ||||||||
\(872\) | 294.156 | + | 294.156i | 0.337335 | + | 0.337335i | ||||
\(873\) | −720.000 | − | 720.000i | −0.824742 | − | 0.824742i | ||||
\(874\) | 105.000 | + | 105.000i | 0.120137 | + | 0.120137i | ||||
\(875\) | 49.4975 | 0.0565685 | ||||||||
\(876\) | −678.823 | −0.774912 | ||||||||
\(877\) | −815.000 | − | 815.000i | −0.929304 | − | 0.929304i | 0.0683565 | − | 0.997661i | \(-0.478224\pi\) |
−0.997661 | + | 0.0683565i | \(0.978224\pi\) | |||||||
\(878\) | −90.5097 | + | 90.5097i | −0.103086 | + | 0.103086i | ||||
\(879\) | −99.0000 | + | 99.0000i | −0.112628 | + | 0.112628i | ||||
\(880\) | −140.000 | −0.159091 | ||||||||
\(881\) | 883.883 | + | 883.883i | 1.00327 | + | 1.00327i | 0.999995 | + | 0.00327833i | \(0.00104353\pi\) |
0.00327833 | + | 0.999995i | \(0.498956\pi\) | |||||||
\(882\) | −12.7279 | −0.0144308 | ||||||||
\(883\) | −645.000 | −0.730464 | −0.365232 | − | 0.930916i | \(-0.619010\pi\) | ||||
−0.365232 | + | 0.930916i | \(0.619010\pi\) | |||||||
\(884\) | 148.492 | − | 487.904i | 0.167978 | − | 0.551927i | ||||
\(885\) | − | 1336.43i | − | 1.51009i | ||||||
\(886\) | − | 624.000i | − | 0.704289i | ||||||
\(887\) | 529.623 | + | 529.623i | 0.597095 | + | 0.597095i | 0.939538 | − | 0.342444i | \(-0.111255\pi\) |
−0.342444 | + | 0.939538i | \(0.611255\pi\) | |||||||
\(888\) | 180.000 | 0.202703 | ||||||||
\(889\) | 625.000 | − | 625.000i | 0.703037 | − | 0.703037i | ||||
\(890\) | −148.492 | + | 148.492i | −0.166845 | + | 0.166845i | ||||
\(891\) | −286.378 | + | 286.378i | −0.321412 | + | 0.321412i | ||||
\(892\) | 310.000i | 0.347534i | ||||||||
\(893\) | −56.5685 | −0.0633466 | ||||||||
\(894\) | −233.345 | + | 233.345i | −0.261013 | + | 0.261013i | ||||
\(895\) | −280.000 | − | 280.000i | −0.312849 | − | 0.312849i | ||||
\(896\) | −56.5685 | − | 56.5685i | −0.0631345 | − | 0.0631345i | ||||
\(897\) | 945.000 | 1.05351 | ||||||||
\(898\) | −510.000 | + | 510.000i | −0.567929 | + | 0.567929i | ||||
\(899\) | 1357.65 | 1.51017 | ||||||||
\(900\) | −432.000 | −0.480000 | ||||||||
\(901\) | 336.000 | − | 1104.00i | 0.372919 | − | 1.22531i | ||||
\(902\) | 388.909i | 0.431163i | ||||||||
\(903\) | 1590.99 | 1.76189 | ||||||||
\(904\) | 130.000 | − | 130.000i | 0.143805 | − | 0.143805i | ||||
\(905\) | 782.060i | 0.864155i | ||||||||
\(906\) | 744.000 | − | 744.000i | 0.821192 | − | 0.821192i | ||||
\(907\) | −685.000 | − | 685.000i | −0.755237 | − | 0.755237i | 0.220214 | − | 0.975451i | \(-0.429324\pi\) |
−0.975451 | + | 0.220214i | \(0.929324\pi\) | |||||||
\(908\) | 219.203 | − | 219.203i | 0.241413 | − | 0.241413i | ||||
\(909\) | −509.117 | −0.560085 | ||||||||
\(910\) | 1050.00i | 1.15385i | ||||||||
\(911\) | −936.916 | + | 936.916i | −1.02845 | + | 1.02845i | −0.0288651 | + | 0.999583i | \(0.509189\pi\) |
−0.999583 | + | 0.0288651i | \(0.990811\pi\) | |||||||
\(912\) | −42.4264 | + | 42.4264i | −0.0465202 | + | 0.0465202i | ||||
\(913\) | 440.000 | − | 440.000i | 0.481928 | − | 0.481928i | ||||
\(914\) | − | 374.767i | − | 0.410029i | ||||||
\(915\) | −1491.00 | + | 1491.00i | −1.62951 | + | 1.62951i | ||||
\(916\) | − | 80.0000i | − | 0.0873362i | ||||||
\(917\) | 35.3553i | 0.0385554i | ||||||||
\(918\) | −305.470 | − | 572.756i | −0.332756 | − | 0.623918i | ||||
\(919\) | 1235.00 | 1.34385 | 0.671926 | − | 0.740618i | \(-0.265467\pi\) | ||||
0.671926 | + | 0.740618i | \(0.265467\pi\) | |||||||
\(920\) | 415.779 | 0.451933 | ||||||||
\(921\) | 678.823 | + | 678.823i | 0.737049 | + | 0.737049i | ||||
\(922\) | 210.000 | 0.227766 | ||||||||
\(923\) | −424.264 | − | 424.264i | −0.459658 | − | 0.459658i | ||||
\(924\) | 150.000 | + | 150.000i | 0.162338 | + | 0.162338i | ||||
\(925\) | −360.000 | − | 360.000i | −0.389189 | − | 0.389189i | ||||
\(926\) | 509.117 | 0.549802 | ||||||||
\(927\) | − | 45.0000i | − | 0.0485437i | ||||||
\(928\) | 160.000 | + | 160.000i | 0.172414 | + | 0.172414i | ||||
\(929\) | 979.343 | − | 979.343i | 1.05419 | − | 1.05419i | 0.0557454 | − | 0.998445i | \(-0.482246\pi\) |
0.998445 | − | 0.0557454i | \(-0.0177535\pi\) | |||||||
\(930\) | 712.764 | + | 712.764i | 0.766413 | + | 0.766413i | ||||
\(931\) | 5.00000 | 0.00537057 | ||||||||
\(932\) | 224.860 | + | 224.860i | 0.241266 | + | 0.241266i | ||||
\(933\) | 360.000i | 0.385852i | ||||||||
\(934\) | −694.000 | −0.743041 | ||||||||
\(935\) | −173.241 | + | 569.221i | −0.185285 | + | 0.608792i | ||||
\(936\) | 381.838i | 0.407946i | ||||||||
\(937\) | 530.000i | 0.565635i | 0.959174 | + | 0.282818i | \(0.0912691\pi\) | ||||
−0.959174 | + | 0.282818i | \(0.908731\pi\) | |||||||
\(938\) | 565.685 | + | 565.685i | 0.603076 | + | 0.603076i | ||||
\(939\) | − | 678.823i | − | 0.722921i | ||||||
\(940\) | −112.000 | + | 112.000i | −0.119149 | + | 0.119149i | ||||
\(941\) | −593.970 | + | 593.970i | −0.631211 | + | 0.631211i | −0.948372 | − | 0.317161i | \(-0.897271\pi\) |
0.317161 | + | 0.948372i | \(0.397271\pi\) | |||||||
\(942\) | 165.000 | + | 165.000i | 0.175159 | + | 0.175159i | ||||
\(943\) | − | 1155.00i | − | 1.22481i | ||||||
\(944\) | −254.558 | −0.269659 | ||||||||
\(945\) | 945.000 | + | 945.000i | 1.00000 | + | 1.00000i | ||||
\(946\) | −375.000 | − | 375.000i | −0.396406 | − | 0.396406i | ||||
\(947\) | −950.352 | − | 950.352i | −1.00354 | − | 1.00354i | −0.999994 | − | 0.00354537i | \(-0.998871\pi\) |
−0.00354537 | − | 0.999994i | \(-0.501129\pi\) | |||||||
\(948\) | 93.3381i | 0.0984579i | ||||||||
\(949\) | 1200.00 | − | 1200.00i | 1.26449 | − | 1.26449i | ||||
\(950\) | 169.706 | 0.178638 | ||||||||
\(951\) | 600.000 | 0.630915 | ||||||||
\(952\) | −300.000 | + | 160.000i | −0.315126 | + | 0.168067i | ||||
\(953\) | − | 45.2548i | − | 0.0474867i | −0.999718 | − | 0.0237434i | \(-0.992442\pi\) | ||
0.999718 | − | 0.0237434i | \(-0.00755845\pi\) | |||||||
\(954\) | 864.000i | 0.905660i | ||||||||
\(955\) | 315.000 | − | 315.000i | 0.329843 | − | 0.329843i | ||||
\(956\) | 565.685i | 0.591721i | ||||||||
\(957\) | −424.264 | − | 424.264i | −0.443327 | − | 0.443327i | ||||
\(958\) | −235.000 | − | 235.000i | −0.245303 | − | 0.245303i | ||||
\(959\) | −615.183 | + | 615.183i | −0.641484 | + | 0.641484i | ||||
\(960\) | 168.000i | 0.175000i | ||||||||
\(961\) | − | 191.000i | − | 0.198751i | ||||||
\(962\) | −318.198 | + | 318.198i | −0.330767 | + | 0.330767i | ||||
\(963\) | −1304.61 | + | 1304.61i | −1.35474 | + | 1.35474i | ||||
\(964\) | 558.000 | − | 558.000i | 0.578838 | − | 0.578838i | ||||
\(965\) | 2375.88i | 2.46205i | ||||||||
\(966\) | −445.477 | − | 445.477i | −0.461157 | − | 0.461157i | ||||
\(967\) | 1115.00i | 1.15305i | 0.817079 | + | 0.576525i | \(0.195592\pi\) | ||||
−0.817079 | + | 0.576525i | \(0.804408\pi\) | |||||||
\(968\) | 271.529i | 0.280505i | ||||||||
\(969\) | 120.000 | + | 225.000i | 0.123839 | + | 0.232198i | ||||
\(970\) | 1120.00 | 1.15464 | ||||||||
\(971\) | 1866.76 | 1.92251 | 0.961257 | − | 0.275652i | \(-0.0888938\pi\) | ||||
0.961257 | + | 0.275652i | \(0.0888938\pi\) | |||||||
\(972\) | 343.654 | + | 343.654i | 0.353553 | + | 0.353553i | ||||
\(973\) | 190.000 | 0.195272 | ||||||||
\(974\) | 275.772 | + | 275.772i | 0.283133 | + | 0.283133i | ||||
\(975\) | 763.675 | − | 763.675i | 0.783257 | − | 0.783257i | ||||
\(976\) | 284.000 | + | 284.000i | 0.290984 | + | 0.290984i | ||||
\(977\) | −612.354 | −0.626770 | −0.313385 | − | 0.949626i | \(-0.601463\pi\) | ||||
−0.313385 | + | 0.949626i | \(0.601463\pi\) | |||||||
\(978\) | − | 720.000i | − | 0.736196i | ||||||
\(979\) | −75.0000 | − | 75.0000i | −0.0766088 | − | 0.0766088i | ||||
\(980\) | 9.89949 | − | 9.89949i | 0.0101015 | − | 0.0101015i | ||||
\(981\) | −936.000 | + | 936.000i | −0.954128 | + | 0.954128i | ||||
\(982\) | 800.000 | 0.814664 | ||||||||
\(983\) | −823.779 | − | 823.779i | −0.838026 | − | 0.838026i | 0.150573 | − | 0.988599i | \(-0.451888\pi\) |
−0.988599 | + | 0.150573i | \(0.951888\pi\) | |||||||
\(984\) | 466.690 | 0.474279 | ||||||||
\(985\) | −567.000 | −0.575635 | ||||||||
\(986\) | 848.528 | − | 452.548i | 0.860576 | − | 0.458974i | ||||
\(987\) | 240.000 | 0.243161 | ||||||||
\(988\) | − | 150.000i | − | 0.151822i | ||||||
\(989\) | 1113.69 | + | 1113.69i | 1.12608 | + | 1.12608i | ||||
\(990\) | − | 445.477i | − | 0.449977i | ||||||
\(991\) | 1024.00 | − | 1024.00i | 1.03330 | − | 1.03330i | 0.0338736 | − | 0.999426i | \(-0.489216\pi\) |
0.999426 | − | 0.0338736i | \(-0.0107844\pi\) | |||||||
\(992\) | 135.765 | − | 135.765i | 0.136859 | − | 0.136859i | ||||
\(993\) | −95.4594 | + | 95.4594i | −0.0961323 | + | 0.0961323i | ||||
\(994\) | 400.000i | 0.402414i | ||||||||
\(995\) | −1029.55 | −1.03472 | ||||||||
\(996\) | −528.000 | − | 528.000i | −0.530120 | − | 0.530120i | ||||
\(997\) | −1065.00 | − | 1065.00i | −1.06820 | − | 1.06820i | −0.997497 | − | 0.0707075i | \(-0.977474\pi\) |
−0.0707075 | − | 0.997497i | \(-0.522526\pi\) | |||||||
\(998\) | 475.176 | + | 475.176i | 0.476128 | + | 0.476128i | ||||
\(999\) | 572.756i | 0.573330i |
(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 | 102.3.e.a.89.2 | yes | 4 | |
3.2 | odd | 2 | inner | 102.3.e.a.89.1 | yes | 4 | |
17.13 | even | 4 | inner | 102.3.e.a.47.1 | ✓ | 4 | |
51.47 | odd | 4 | inner | 102.3.e.a.47.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
102.3.e.a.47.1 | ✓ | 4 | 17.13 | even | 4 | inner | |
102.3.e.a.47.2 | yes | 4 | 51.47 | odd | 4 | inner | |
102.3.e.a.89.1 | yes | 4 | 3.2 | odd | 2 | inner | |
102.3.e.a.89.2 | yes | 4 | 1.1 | even | 1 | trivial |