Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.a (trivial) |
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: | yes |
Analytic conductor: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + \cdots - 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-1.94926\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.94926 | 1.37833 | 0.689166 | − | 0.724603i | \(-0.257977\pi\) | ||||
0.689166 | + | 0.724603i | \(0.257977\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.79960 | 0.899801 | ||||||||
\(5\) | −3.69296 | −1.65154 | −0.825770 | − | 0.564007i | \(-0.809259\pi\) | ||||
−0.825770 | + | 0.564007i | \(0.809259\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.45473 | −0.927801 | −0.463901 | − | 0.885887i | \(-0.653551\pi\) | ||||
−0.463901 | + | 0.885887i | \(0.653551\pi\) | |||||||
\(8\) | −0.390627 | −0.138107 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.19852 | −2.27637 | ||||||||
\(11\) | −4.43817 | −1.33816 | −0.669079 | − | 0.743192i | \(-0.733311\pi\) | ||||
−0.669079 | + | 0.743192i | \(0.733311\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.28535 | −1.18854 | −0.594271 | − | 0.804265i | \(-0.702559\pi\) | ||||
−0.594271 | + | 0.804265i | \(0.702559\pi\) | |||||||
\(14\) | −4.78490 | −1.27882 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.36064 | −1.09016 | ||||||||
\(17\) | 1.49875 | 0.363499 | 0.181750 | − | 0.983345i | \(-0.441824\pi\) | ||||
0.181750 | + | 0.983345i | \(0.441824\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.06731 | 0.244858 | 0.122429 | − | 0.992477i | \(-0.460932\pi\) | ||||
0.122429 | + | 0.992477i | \(0.460932\pi\) | |||||||
\(20\) | −6.64585 | −1.48606 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.65112 | −1.84443 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.63793 | 1.72759 | ||||||||
\(26\) | −8.35324 | −1.63821 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.41754 | −0.834837 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.48186 | 0.445755 | 0.222878 | − | 0.974846i | \(-0.428455\pi\) | ||||
0.222878 | + | 0.974846i | \(0.428455\pi\) | |||||||
\(32\) | −7.71875 | −1.36449 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.92144 | 0.501023 | ||||||||
\(35\) | 9.06522 | 1.53230 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.20872 | 0.527510 | 0.263755 | − | 0.964590i | \(-0.415039\pi\) | ||||
0.263755 | + | 0.964590i | \(0.415039\pi\) | |||||||
\(38\) | 2.08047 | 0.337496 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.44257 | 0.228090 | ||||||||
\(41\) | −4.57310 | −0.714199 | −0.357099 | − | 0.934066i | \(-0.616234\pi\) | ||||
−0.357099 | + | 0.934066i | \(0.616234\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.98441 | 0.912614 | 0.456307 | − | 0.889822i | \(-0.349172\pi\) | ||||
0.456307 | + | 0.889822i | \(0.349172\pi\) | |||||||
\(44\) | −7.98693 | −1.20408 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.94926 | −0.287402 | ||||||||
\(47\) | 4.84278 | 0.706392 | 0.353196 | − | 0.935549i | \(-0.385095\pi\) | ||||
0.353196 | + | 0.935549i | \(0.385095\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.974292 | −0.139185 | ||||||||
\(50\) | 16.8375 | 2.38119 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.71192 | −1.06945 | ||||||||
\(53\) | −4.65981 | −0.640074 | −0.320037 | − | 0.947405i | \(-0.603695\pi\) | ||||
−0.320037 | + | 0.947405i | \(0.603695\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.3900 | 2.21002 | ||||||||
\(56\) | 0.958884 | 0.128136 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.94926 | −0.255950 | ||||||||
\(59\) | −0.167254 | −0.0217746 | −0.0108873 | − | 0.999941i | \(-0.503466\pi\) | ||||
−0.0108873 | + | 0.999941i | \(0.503466\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.1401 | 1.68242 | 0.841212 | − | 0.540706i | \(-0.181843\pi\) | ||||
0.841212 | + | 0.540706i | \(0.181843\pi\) | |||||||
\(62\) | 4.83778 | 0.614399 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.32455 | −0.790568 | ||||||||
\(65\) | 15.8256 | 1.96292 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.9525 | 1.46023 | 0.730113 | − | 0.683327i | \(-0.239467\pi\) | ||||
0.730113 | + | 0.683327i | \(0.239467\pi\) | |||||||
\(68\) | 2.69715 | 0.327077 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 17.6704 | 2.11202 | ||||||||
\(71\) | −8.22431 | −0.976046 | −0.488023 | − | 0.872831i | \(-0.662282\pi\) | ||||
−0.488023 | + | 0.872831i | \(0.662282\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.4723 | −1.22569 | −0.612845 | − | 0.790203i | \(-0.709975\pi\) | ||||
−0.612845 | + | 0.790203i | \(0.709975\pi\) | |||||||
\(74\) | 6.25462 | 0.727084 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.92074 | 0.220324 | ||||||||
\(77\) | 10.8945 | 1.24154 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.909584 | 0.102336 | 0.0511681 | − | 0.998690i | \(-0.483706\pi\) | ||||
0.0511681 | + | 0.998690i | \(0.483706\pi\) | |||||||
\(80\) | 16.1036 | 1.80044 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.91415 | −0.984403 | ||||||||
\(83\) | 4.61155 | 0.506183 | 0.253092 | − | 0.967442i | \(-0.418553\pi\) | ||||
0.253092 | + | 0.967442i | \(0.418553\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.53480 | −0.600334 | ||||||||
\(86\) | 11.6652 | 1.25789 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.73367 | 0.184809 | ||||||||
\(89\) | −12.8616 | −1.36333 | −0.681664 | − | 0.731665i | \(-0.738744\pi\) | ||||
−0.681664 | + | 0.731665i | \(0.738744\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5194 | 1.10273 | ||||||||
\(92\) | −1.79960 | −0.187622 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.43982 | 0.973643 | ||||||||
\(95\) | −3.94154 | −0.404394 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.88580 | 0.191474 | 0.0957372 | − | 0.995407i | \(-0.469479\pi\) | ||||
0.0957372 | + | 0.995407i | \(0.469479\pi\) | |||||||
\(98\) | −1.89915 | −0.191843 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 15.5448 | 1.55448 | ||||||||
\(101\) | −5.40314 | −0.537633 | −0.268816 | − | 0.963191i | \(-0.586632\pi\) | ||||
−0.268816 | + | 0.963191i | \(0.586632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.14017 | −0.605009 | −0.302505 | − | 0.953148i | \(-0.597823\pi\) | ||||
−0.302505 | + | 0.953148i | \(0.597823\pi\) | |||||||
\(104\) | 1.67397 | 0.164146 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.08316 | −0.882234 | ||||||||
\(107\) | 3.00788 | 0.290783 | 0.145391 | − | 0.989374i | \(-0.453556\pi\) | ||||
0.145391 | + | 0.989374i | \(0.453556\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.3033 | −1.27423 | −0.637113 | − | 0.770771i | \(-0.719871\pi\) | ||||
−0.637113 | + | 0.770771i | \(0.719871\pi\) | |||||||
\(110\) | 31.9482 | 3.04614 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.7042 | 1.01145 | ||||||||
\(113\) | 18.0625 | 1.69918 | 0.849590 | − | 0.527443i | \(-0.176849\pi\) | ||||
0.849590 | + | 0.527443i | \(0.176849\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.69296 | 0.344370 | ||||||||
\(116\) | −1.79960 | −0.167089 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.326020 | −0.0300126 | ||||||||
\(119\) | −3.67902 | −0.337255 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.69731 | 0.790665 | ||||||||
\(122\) | 25.6135 | 2.31894 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.46636 | 0.401091 | ||||||||
\(125\) | −13.4347 | −1.20164 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.61372 | −0.586873 | −0.293436 | − | 0.955979i | \(-0.594799\pi\) | ||||
−0.293436 | + | 0.955979i | \(0.594799\pi\) | |||||||
\(128\) | 3.10933 | 0.274828 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 30.8482 | 2.70556 | ||||||||
\(131\) | 10.8669 | 0.949448 | 0.474724 | − | 0.880135i | \(-0.342548\pi\) | ||||
0.474724 | + | 0.880135i | \(0.342548\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.61997 | −0.227180 | ||||||||
\(134\) | 23.2984 | 2.01268 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.585450 | −0.0502019 | ||||||||
\(137\) | −19.4409 | −1.66095 | −0.830474 | − | 0.557057i | \(-0.811930\pi\) | ||||
−0.830474 | + | 0.557057i | \(0.811930\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.9146 | −1.26504 | −0.632520 | − | 0.774544i | \(-0.717979\pi\) | ||||
−0.632520 | + | 0.774544i | \(0.717979\pi\) | |||||||
\(140\) | 16.3138 | 1.37877 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.0313 | −1.34532 | ||||||||
\(143\) | 19.0191 | 1.59046 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.69296 | 0.306683 | ||||||||
\(146\) | −20.4132 | −1.68941 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.77442 | 0.474654 | ||||||||
\(149\) | 7.73831 | 0.633947 | 0.316974 | − | 0.948434i | \(-0.397333\pi\) | ||||
0.316974 | + | 0.948434i | \(0.397333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8699 | 1.04733 | 0.523667 | − | 0.851923i | \(-0.324564\pi\) | ||||
0.523667 | + | 0.851923i | \(0.324564\pi\) | |||||||
\(152\) | −0.416921 | −0.0338168 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 21.2362 | 1.71126 | ||||||||
\(155\) | −9.16540 | −0.736183 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.6332 | 1.00824 | 0.504120 | − | 0.863634i | \(-0.331817\pi\) | ||||
0.504120 | + | 0.863634i | \(0.331817\pi\) | |||||||
\(158\) | 1.77301 | 0.141053 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 28.5050 | 2.25352 | ||||||||
\(161\) | 2.45473 | 0.193460 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.96876 | −0.702488 | −0.351244 | − | 0.936284i | \(-0.614241\pi\) | ||||
−0.351244 | + | 0.936284i | \(0.614241\pi\) | |||||||
\(164\) | −8.22977 | −0.642637 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.98909 | 0.697689 | ||||||||
\(167\) | −12.9614 | −1.00298 | −0.501492 | − | 0.865162i | \(-0.667215\pi\) | ||||
−0.501492 | + | 0.865162i | \(0.667215\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.36420 | 0.412631 | ||||||||
\(170\) | −10.7888 | −0.827460 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.7696 | 0.821171 | ||||||||
\(173\) | 4.02670 | 0.306144 | 0.153072 | − | 0.988215i | \(-0.451083\pi\) | ||||
0.153072 | + | 0.988215i | \(0.451083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.2038 | −1.60286 | ||||||||
\(176\) | 19.3532 | 1.45880 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −25.0706 | −1.87912 | ||||||||
\(179\) | 0.565219 | 0.0422464 | 0.0211232 | − | 0.999777i | \(-0.493276\pi\) | ||||
0.0211232 | + | 0.999777i | \(0.493276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.4322 | 1.07274 | 0.536368 | − | 0.843984i | \(-0.319796\pi\) | ||||
0.536368 | + | 0.843984i | \(0.319796\pi\) | |||||||
\(182\) | 20.5050 | 1.51993 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.390627 | 0.0287974 | ||||||||
\(185\) | −11.8497 | −0.871204 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.65168 | −0.486419 | ||||||||
\(188\) | 8.71508 | 0.635612 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.68308 | −0.557389 | ||||||||
\(191\) | 11.1284 | 0.805223 | 0.402612 | − | 0.915371i | \(-0.368103\pi\) | ||||
0.402612 | + | 0.915371i | \(0.368103\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.0097 | −1.29637 | −0.648183 | − | 0.761485i | \(-0.724471\pi\) | ||||
−0.648183 | + | 0.761485i | \(0.724471\pi\) | |||||||
\(194\) | 3.67591 | 0.263915 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.75334 | −0.125238 | ||||||||
\(197\) | −22.4270 | −1.59786 | −0.798930 | − | 0.601424i | \(-0.794600\pi\) | ||||
−0.798930 | + | 0.601424i | \(0.794600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.8224 | 1.90139 | 0.950694 | − | 0.310129i | \(-0.100372\pi\) | ||||
0.950694 | + | 0.310129i | \(0.100372\pi\) | |||||||
\(200\) | −3.37421 | −0.238592 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.5321 | −0.741037 | ||||||||
\(203\) | 2.45473 | 0.172288 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.8883 | 1.17953 | ||||||||
\(206\) | −11.9688 | −0.833904 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18.6868 | 1.29570 | ||||||||
\(209\) | −4.73691 | −0.327659 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.39698 | 0.646915 | 0.323457 | − | 0.946243i | \(-0.395155\pi\) | ||||
0.323457 | + | 0.946243i | \(0.395155\pi\) | |||||||
\(212\) | −8.38580 | −0.575939 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.86313 | 0.400795 | ||||||||
\(215\) | −22.1002 | −1.50722 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.09230 | −0.413572 | ||||||||
\(218\) | −25.9316 | −1.75631 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 29.4954 | 1.98858 | ||||||||
\(221\) | −6.42265 | −0.432034 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.7193 | 0.985681 | 0.492840 | − | 0.870120i | \(-0.335959\pi\) | ||||
0.492840 | + | 0.870120i | \(0.335959\pi\) | |||||||
\(224\) | 18.9475 | 1.26598 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 35.2085 | 2.34204 | ||||||||
\(227\) | −25.3440 | −1.68214 | −0.841070 | − | 0.540927i | \(-0.818074\pi\) | ||||
−0.841070 | + | 0.540927i | \(0.818074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.2652 | 1.47133 | 0.735664 | − | 0.677347i | \(-0.236870\pi\) | ||||
0.735664 | + | 0.677347i | \(0.236870\pi\) | |||||||
\(230\) | 7.19852 | 0.474656 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.390627 | 0.0256459 | ||||||||
\(233\) | −5.91632 | −0.387591 | −0.193796 | − | 0.981042i | \(-0.562080\pi\) | ||||
−0.193796 | + | 0.981042i | \(0.562080\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.8842 | −1.16664 | ||||||||
\(236\) | −0.300990 | −0.0195928 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.17135 | −0.464850 | ||||||||
\(239\) | −15.1516 | −0.980072 | −0.490036 | − | 0.871702i | \(-0.663016\pi\) | ||||
−0.490036 | + | 0.871702i | \(0.663016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.07716 | −0.0693858 | −0.0346929 | − | 0.999398i | \(-0.511045\pi\) | ||||
−0.0346929 | + | 0.999398i | \(0.511045\pi\) | |||||||
\(242\) | 16.9533 | 1.08980 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 23.6470 | 1.51385 | ||||||||
\(245\) | 3.59802 | 0.229869 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.57381 | −0.291024 | ||||||||
\(248\) | −0.969481 | −0.0615621 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −26.1877 | −1.65626 | ||||||||
\(251\) | −26.7693 | −1.68966 | −0.844832 | − | 0.535032i | \(-0.820299\pi\) | ||||
−0.844832 | + | 0.535032i | \(0.820299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.43817 | 0.279025 | ||||||||
\(254\) | −12.8918 | −0.808906 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.7100 | 1.16937 | ||||||||
\(257\) | 19.8433 | 1.23779 | 0.618897 | − | 0.785472i | \(-0.287580\pi\) | ||||
0.618897 | + | 0.785472i | \(0.287580\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.87654 | −0.489425 | ||||||||
\(260\) | 28.4798 | 1.76624 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.1824 | 1.30866 | ||||||||
\(263\) | 16.6065 | 1.02400 | 0.512002 | − | 0.858984i | \(-0.328904\pi\) | ||||
0.512002 | + | 0.858984i | \(0.328904\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.2085 | 1.05711 | ||||||||
\(266\) | −5.10699 | −0.313130 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21.5097 | 1.31391 | ||||||||
\(269\) | 17.7138 | 1.08003 | 0.540015 | − | 0.841655i | \(-0.318418\pi\) | ||||
0.540015 | + | 0.841655i | \(0.318418\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0182 | 0.851544 | 0.425772 | − | 0.904830i | \(-0.360003\pi\) | ||||
0.425772 | + | 0.904830i | \(0.360003\pi\) | |||||||
\(272\) | −6.53548 | −0.396272 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −37.8953 | −2.28934 | ||||||||
\(275\) | −38.3366 | −2.31178 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.0263 | 0.602425 | 0.301212 | − | 0.953557i | \(-0.402609\pi\) | ||||
0.301212 | + | 0.953557i | \(0.402609\pi\) | |||||||
\(278\) | −29.0724 | −1.74364 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.54112 | −0.211622 | ||||||||
\(281\) | 18.4255 | 1.09917 | 0.549587 | − | 0.835437i | \(-0.314785\pi\) | ||||
0.549587 | + | 0.835437i | \(0.314785\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.7278 | −1.52936 | −0.764680 | − | 0.644411i | \(-0.777103\pi\) | ||||
−0.764680 | + | 0.644411i | \(0.777103\pi\) | |||||||
\(284\) | −14.8005 | −0.878248 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 37.0731 | 2.19218 | ||||||||
\(287\) | 11.2257 | 0.662635 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.7538 | −0.867868 | ||||||||
\(290\) | 7.19852 | 0.422712 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −18.8460 | −1.10288 | ||||||||
\(293\) | 24.2334 | 1.41573 | 0.707865 | − | 0.706348i | \(-0.249659\pi\) | ||||
0.707865 | + | 0.706348i | \(0.249659\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.617660 | 0.0359616 | ||||||||
\(296\) | −1.25341 | −0.0728531 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.0840 | 0.873790 | ||||||||
\(299\) | 4.28535 | 0.247828 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.6901 | −0.846725 | ||||||||
\(302\) | 25.0867 | 1.44357 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.65416 | −0.266935 | ||||||||
\(305\) | −48.5260 | −2.77859 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.93632 | −0.452950 | −0.226475 | − | 0.974017i | \(-0.572720\pi\) | ||||
−0.226475 | + | 0.974017i | \(0.572720\pi\) | |||||||
\(308\) | 19.6058 | 1.11714 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.8657 | −1.01470 | ||||||||
\(311\) | 10.8054 | 0.612717 | 0.306358 | − | 0.951916i | \(-0.400889\pi\) | ||||
0.306358 | + | 0.951916i | \(0.400889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.0705 | −1.41707 | −0.708535 | − | 0.705675i | \(-0.750644\pi\) | ||||
−0.708535 | + | 0.705675i | \(0.750644\pi\) | |||||||
\(314\) | 24.6254 | 1.38969 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.63689 | 0.0920822 | ||||||||
\(317\) | 14.5292 | 0.816041 | 0.408021 | − | 0.912973i | \(-0.366219\pi\) | ||||
0.408021 | + | 0.912973i | \(0.366219\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.43817 | 0.248490 | ||||||||
\(320\) | 23.3563 | 1.30566 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.78490 | 0.266652 | ||||||||
\(323\) | 1.59963 | 0.0890058 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −37.0165 | −2.05331 | ||||||||
\(326\) | −17.4824 | −0.968262 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.78638 | 0.0986361 | ||||||||
\(329\) | −11.8877 | −0.655392 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.56900 | −0.141205 | −0.0706026 | − | 0.997505i | \(-0.522492\pi\) | ||||
−0.0706026 | + | 0.997505i | \(0.522492\pi\) | |||||||
\(332\) | 8.29895 | 0.455464 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −25.2651 | −1.38245 | ||||||||
\(335\) | −44.1399 | −2.41162 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.1666 | −1.47986 | −0.739930 | − | 0.672683i | \(-0.765142\pi\) | ||||
−0.739930 | + | 0.672683i | \(0.765142\pi\) | |||||||
\(338\) | 10.4562 | 0.568743 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.96044 | −0.540181 | ||||||||
\(341\) | −11.0149 | −0.596490 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5747 | 1.05694 | ||||||||
\(344\) | −2.33767 | −0.126039 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.84907 | 0.421968 | ||||||||
\(347\) | −24.3805 | −1.30881 | −0.654406 | − | 0.756143i | \(-0.727081\pi\) | ||||
−0.654406 | + | 0.756143i | \(0.727081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.6829 | −1.37478 | −0.687388 | − | 0.726290i | \(-0.741243\pi\) | ||||
−0.687388 | + | 0.726290i | \(0.741243\pi\) | |||||||
\(350\) | −41.3317 | −2.20927 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 34.2571 | 1.82591 | ||||||||
\(353\) | 27.0213 | 1.43820 | 0.719100 | − | 0.694907i | \(-0.244555\pi\) | ||||
0.719100 | + | 0.694907i | \(0.244555\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.3720 | 1.61198 | ||||||||
\(356\) | −23.1458 | −1.22672 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.10176 | 0.0582296 | ||||||||
\(359\) | −14.3872 | −0.759326 | −0.379663 | − | 0.925125i | \(-0.623960\pi\) | ||||
−0.379663 | + | 0.925125i | \(0.623960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8608 | −0.940044 | ||||||||
\(362\) | 28.1320 | 1.47859 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18.9307 | 0.992238 | ||||||||
\(365\) | 38.6738 | 2.02428 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.3059 | 0.694564 | 0.347282 | − | 0.937761i | \(-0.387105\pi\) | ||||
0.347282 | + | 0.937761i | \(0.387105\pi\) | |||||||
\(368\) | 4.36064 | 0.227314 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −23.0980 | −1.20081 | ||||||||
\(371\) | 11.4386 | 0.593861 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.9296 | 1.08370 | 0.541848 | − | 0.840477i | \(-0.317725\pi\) | ||||
0.541848 | + | 0.840477i | \(0.317725\pi\) | |||||||
\(374\) | −12.9658 | −0.670447 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.89172 | −0.0975580 | ||||||||
\(377\) | 4.28535 | 0.220707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6614 | 0.907206 | 0.453603 | − | 0.891204i | \(-0.350138\pi\) | ||||
0.453603 | + | 0.891204i | \(0.350138\pi\) | |||||||
\(380\) | −7.09321 | −0.363874 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.6921 | 1.10987 | ||||||||
\(383\) | 24.2702 | 1.24015 | 0.620076 | − | 0.784542i | \(-0.287102\pi\) | ||||
0.620076 | + | 0.784542i | \(0.287102\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −40.2329 | −2.05046 | ||||||||
\(386\) | −35.1055 | −1.78682 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.39370 | 0.172289 | ||||||||
\(389\) | 17.6760 | 0.896208 | 0.448104 | − | 0.893981i | \(-0.352099\pi\) | ||||
0.448104 | + | 0.893981i | \(0.352099\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.49875 | −0.0757948 | ||||||||
\(392\) | 0.380585 | 0.0192224 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −43.7161 | −2.20238 | ||||||||
\(395\) | −3.35905 | −0.169012 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.88374 | −0.0945421 | −0.0472711 | − | 0.998882i | \(-0.515052\pi\) | ||||
−0.0472711 | + | 0.998882i | \(0.515052\pi\) | |||||||
\(398\) | 52.2837 | 2.62075 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −37.6669 | −1.88334 | ||||||||
\(401\) | −21.3807 | −1.06770 | −0.533849 | − | 0.845580i | \(-0.679255\pi\) | ||||
−0.533849 | + | 0.845580i | \(0.679255\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.6356 | −0.529798 | ||||||||
\(404\) | −9.72351 | −0.483763 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.78490 | 0.237471 | ||||||||
\(407\) | −14.2408 | −0.705891 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.6232 | −1.16809 | −0.584045 | − | 0.811721i | \(-0.698531\pi\) | ||||
−0.584045 | + | 0.811721i | \(0.698531\pi\) | |||||||
\(410\) | 32.9196 | 1.62578 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.0499 | −0.544388 | ||||||||
\(413\) | 0.410563 | 0.0202025 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.0302 | −0.835982 | ||||||||
\(416\) | 33.0775 | 1.62176 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.23346 | −0.451623 | ||||||||
\(419\) | −8.32610 | −0.406757 | −0.203378 | − | 0.979100i | \(-0.565192\pi\) | ||||
−0.203378 | + | 0.979100i | \(0.565192\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.2050 | 0.594835 | 0.297417 | − | 0.954748i | \(-0.403875\pi\) | ||||
0.297417 | + | 0.954748i | \(0.403875\pi\) | |||||||
\(422\) | 18.3171 | 0.891663 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.82024 | 0.0883989 | ||||||||
\(425\) | 12.9461 | 0.627976 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −32.2555 | −1.56095 | ||||||||
\(428\) | 5.41299 | 0.261647 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −43.0789 | −2.07745 | ||||||||
\(431\) | 0.126584 | 0.00609733 | 0.00304867 | − | 0.999995i | \(-0.499030\pi\) | ||||
0.00304867 | + | 0.999995i | \(0.499030\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.4809 | 1.56093 | 0.780467 | − | 0.625197i | \(-0.214981\pi\) | ||||
0.780467 | + | 0.625197i | \(0.214981\pi\) | |||||||
\(434\) | −11.8755 | −0.570040 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.9407 | −1.14655 | ||||||||
\(437\) | −1.06731 | −0.0510565 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.2416 | 1.34790 | 0.673950 | − | 0.738777i | \(-0.264596\pi\) | ||||
0.673950 | + | 0.738777i | \(0.264596\pi\) | |||||||
\(440\) | −6.40235 | −0.305220 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.5194 | −0.595486 | ||||||||
\(443\) | 7.98359 | 0.379312 | 0.189656 | − | 0.981851i | \(-0.439263\pi\) | ||||
0.189656 | + | 0.981851i | \(0.439263\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 47.4974 | 2.25159 | ||||||||
\(446\) | 28.6918 | 1.35860 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 15.5251 | 0.733490 | ||||||||
\(449\) | 21.4781 | 1.01361 | 0.506807 | − | 0.862059i | \(-0.330826\pi\) | ||||
0.506807 | + | 0.862059i | \(0.330826\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.2962 | 0.955710 | ||||||||
\(452\) | 32.5054 | 1.52892 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −49.4019 | −2.31855 | ||||||||
\(455\) | −38.8476 | −1.82120 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.5058 | −0.725332 | −0.362666 | − | 0.931919i | \(-0.618133\pi\) | ||||
−0.362666 | + | 0.931919i | \(0.618133\pi\) | |||||||
\(458\) | 43.4006 | 2.02798 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.64585 | 0.309865 | ||||||||
\(461\) | 39.6350 | 1.84599 | 0.922993 | − | 0.384817i | \(-0.125735\pi\) | ||||
0.922993 | + | 0.384817i | \(0.125735\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.779361 | −0.0362200 | −0.0181100 | − | 0.999836i | \(-0.505765\pi\) | ||||
−0.0181100 | + | 0.999836i | \(0.505765\pi\) | |||||||
\(464\) | 4.36064 | 0.202437 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.5324 | −0.534230 | ||||||||
\(467\) | −26.1858 | −1.21173 | −0.605867 | − | 0.795566i | \(-0.707174\pi\) | ||||
−0.605867 | + | 0.795566i | \(0.707174\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.3401 | −1.35480 | ||||||||
\(470\) | −34.8609 | −1.60801 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.0653337 | 0.00300723 | ||||||||
\(473\) | −26.5598 | −1.22122 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.21938 | 0.423014 | ||||||||
\(476\) | −6.62077 | −0.303462 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −29.5343 | −1.35087 | ||||||||
\(479\) | −15.1362 | −0.691589 | −0.345794 | − | 0.938310i | \(-0.612390\pi\) | ||||
−0.345794 | + | 0.938310i | \(0.612390\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.7505 | −0.626968 | ||||||||
\(482\) | −2.09966 | −0.0956367 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.6517 | 0.711441 | ||||||||
\(485\) | −6.96419 | −0.316228 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.2117 | 1.23308 | 0.616540 | − | 0.787323i | \(-0.288534\pi\) | ||||
0.616540 | + | 0.787323i | \(0.288534\pi\) | |||||||
\(488\) | −5.13289 | −0.232355 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.01346 | 0.316836 | ||||||||
\(491\) | 35.7369 | 1.61279 | 0.806393 | − | 0.591380i | \(-0.201417\pi\) | ||||
0.806393 | + | 0.591380i | \(0.201417\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.49875 | −0.0675001 | ||||||||
\(494\) | −8.91552 | −0.401128 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.8225 | −0.485944 | ||||||||
\(497\) | 20.1885 | 0.905577 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.79653 | −0.125190 | −0.0625950 | − | 0.998039i | \(-0.519938\pi\) | ||||
−0.0625950 | + | 0.998039i | \(0.519938\pi\) | |||||||
\(500\) | −24.1772 | −1.08124 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −52.1802 | −2.32892 | ||||||||
\(503\) | 1.52256 | 0.0678877 | 0.0339438 | − | 0.999424i | \(-0.489193\pi\) | ||||
0.0339438 | + | 0.999424i | \(0.489193\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.9536 | 0.887922 | ||||||||
\(506\) | 8.65112 | 0.384589 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.9021 | −0.528069 | ||||||||
\(509\) | 20.7212 | 0.918449 | 0.459225 | − | 0.888320i | \(-0.348127\pi\) | ||||
0.459225 | + | 0.888320i | \(0.348127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.7067 | 1.13720 | ||||||||
\(512\) | 30.2519 | 1.33696 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 38.6798 | 1.70609 | ||||||||
\(515\) | 22.6754 | 0.999197 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.4931 | −0.945264 | ||||||||
\(518\) | −15.3534 | −0.674590 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.18190 | −0.271094 | ||||||||
\(521\) | 38.9143 | 1.70486 | 0.852432 | − | 0.522837i | \(-0.175127\pi\) | ||||
0.852432 | + | 0.522837i | \(0.175127\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.1164 | −1.01081 | −0.505405 | − | 0.862882i | \(-0.668657\pi\) | ||||
−0.505405 | + | 0.862882i | \(0.668657\pi\) | |||||||
\(524\) | 19.5562 | 0.854314 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.3704 | 1.41142 | ||||||||
\(527\) | 3.71968 | 0.162032 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 33.5437 | 1.45705 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.71490 | −0.204417 | ||||||||
\(533\) | 19.5973 | 0.848855 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.1080 | −0.480239 | ||||||||
\(536\) | −4.66895 | −0.201668 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.5288 | 1.48864 | ||||||||
\(539\) | 4.32407 | 0.186251 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.05558 | −0.0453827 | −0.0226914 | − | 0.999743i | \(-0.507224\pi\) | ||||
−0.0226914 | + | 0.999743i | \(0.507224\pi\) | |||||||
\(542\) | 27.3250 | 1.17371 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −11.5684 | −0.495993 | ||||||||
\(545\) | 49.1285 | 2.10444 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.3543 | 0.528231 | 0.264115 | − | 0.964491i | \(-0.414920\pi\) | ||||
0.264115 | + | 0.964491i | \(0.414920\pi\) | |||||||
\(548\) | −34.9859 | −1.49452 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −74.7278 | −3.18640 | ||||||||
\(551\) | −1.06731 | −0.0454691 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.23278 | −0.0949477 | ||||||||
\(554\) | 19.5439 | 0.830342 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.8403 | −1.13828 | ||||||||
\(557\) | −37.8043 | −1.60182 | −0.800909 | − | 0.598786i | \(-0.795650\pi\) | ||||
−0.800909 | + | 0.598786i | \(0.795650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.6453 | −1.08468 | ||||||||
\(560\) | −39.5301 | −1.67045 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 35.9161 | 1.51503 | ||||||||
\(563\) | 5.16163 | 0.217537 | 0.108768 | − | 0.994067i | \(-0.465309\pi\) | ||||
0.108768 | + | 0.994067i | \(0.465309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −66.7042 | −2.80627 | ||||||||
\(566\) | −50.1501 | −2.10797 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.21264 | 0.134799 | ||||||||
\(569\) | 3.91406 | 0.164086 | 0.0820429 | − | 0.996629i | \(-0.473856\pi\) | ||||
0.0820429 | + | 0.996629i | \(0.473856\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.6511 | −1.28271 | −0.641355 | − | 0.767245i | \(-0.721627\pi\) | ||||
−0.641355 | + | 0.767245i | \(0.721627\pi\) | |||||||
\(572\) | 34.2268 | 1.43109 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 21.8819 | 0.913331 | ||||||||
\(575\) | −8.63793 | −0.360227 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.4740 | −1.64333 | −0.821663 | − | 0.569974i | \(-0.806953\pi\) | ||||
−0.821663 | + | 0.569974i | \(0.806953\pi\) | |||||||
\(578\) | −28.7589 | −1.19621 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.64585 | 0.275954 | ||||||||
\(581\) | −11.3201 | −0.469637 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.6810 | 0.856519 | ||||||||
\(584\) | 4.09076 | 0.169277 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 47.2371 | 1.95135 | ||||||||
\(587\) | −3.03610 | −0.125313 | −0.0626567 | − | 0.998035i | \(-0.519957\pi\) | ||||
−0.0626567 | + | 0.998035i | \(0.519957\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.64892 | 0.109147 | ||||||||
\(590\) | 1.20398 | 0.0495670 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13.9921 | −0.575070 | ||||||||
\(593\) | 18.8795 | 0.775289 | 0.387644 | − | 0.921809i | \(-0.373289\pi\) | ||||
0.387644 | + | 0.921809i | \(0.373289\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.5865 | 0.556990 | ||||||||
\(596\) | 13.9259 | 0.570426 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.35324 | 0.341589 | ||||||||
\(599\) | 12.7183 | 0.519657 | 0.259828 | − | 0.965655i | \(-0.416334\pi\) | ||||
0.259828 | + | 0.965655i | \(0.416334\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.5436 | 0.552456 | 0.276228 | − | 0.961092i | \(-0.410916\pi\) | ||||
0.276228 | + | 0.961092i | \(0.410916\pi\) | |||||||
\(602\) | −28.6348 | −1.16707 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.1606 | 0.942392 | ||||||||
\(605\) | −32.1188 | −1.30581 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.2819 | −0.985573 | −0.492786 | − | 0.870150i | \(-0.664022\pi\) | ||||
−0.492786 | + | 0.870150i | \(0.664022\pi\) | |||||||
\(608\) | −8.23832 | −0.334108 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −94.5896 | −3.82982 | ||||||||
\(611\) | −20.7530 | −0.839576 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.0334 | 1.57654 | 0.788272 | − | 0.615327i | \(-0.210976\pi\) | ||||
0.788272 | + | 0.615327i | \(0.210976\pi\) | |||||||
\(614\) | −15.4699 | −0.624315 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.25569 | −0.171466 | ||||||||
\(617\) | −0.677906 | −0.0272915 | −0.0136457 | − | 0.999907i | \(-0.504344\pi\) | ||||
−0.0136457 | + | 0.999907i | \(0.504344\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0270 | −0.563794 | −0.281897 | − | 0.959445i | \(-0.590964\pi\) | ||||
−0.281897 | + | 0.959445i | \(0.590964\pi\) | |||||||
\(620\) | −16.4941 | −0.662418 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.0625 | 0.844527 | ||||||||
\(623\) | 31.5718 | 1.26490 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.42419 | 0.256968 | ||||||||
\(626\) | −48.8689 | −1.95319 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.7348 | 0.907216 | ||||||||
\(629\) | 4.80905 | 0.191749 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.52595 | −0.140366 | −0.0701829 | − | 0.997534i | \(-0.522358\pi\) | ||||
−0.0701829 | + | 0.997534i | \(0.522358\pi\) | |||||||
\(632\) | −0.355308 | −0.0141334 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.3211 | 1.12478 | ||||||||
\(635\) | 24.4242 | 0.969245 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.17518 | 0.165427 | ||||||||
\(638\) | 8.65112 | 0.342501 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.4826 | −0.453890 | ||||||||
\(641\) | 32.2414 | 1.27346 | 0.636729 | − | 0.771088i | \(-0.280287\pi\) | ||||
0.636729 | + | 0.771088i | \(0.280287\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.2087 | 0.599772 | 0.299886 | − | 0.953975i | \(-0.403051\pi\) | ||||
0.299886 | + | 0.953975i | \(0.403051\pi\) | |||||||
\(644\) | 4.41754 | 0.174075 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.11809 | 0.122680 | ||||||||
\(647\) | 8.38839 | 0.329781 | 0.164891 | − | 0.986312i | \(-0.447273\pi\) | ||||
0.164891 | + | 0.986312i | \(0.447273\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.742299 | 0.0291378 | ||||||||
\(650\) | −72.1547 | −2.83014 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.1402 | −0.632099 | ||||||||
\(653\) | −3.35936 | −0.131462 | −0.0657309 | − | 0.997837i | \(-0.520938\pi\) | ||||
−0.0657309 | + | 0.997837i | \(0.520938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40.1311 | −1.56805 | ||||||||
\(656\) | 19.9416 | 0.778590 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −23.1722 | −0.903348 | ||||||||
\(659\) | 21.5018 | 0.837591 | 0.418796 | − | 0.908080i | \(-0.362452\pi\) | ||||
0.418796 | + | 0.908080i | \(0.362452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.8099 | 0.809412 | 0.404706 | − | 0.914447i | \(-0.367374\pi\) | ||||
0.404706 | + | 0.914447i | \(0.367374\pi\) | |||||||
\(662\) | −5.00764 | −0.194628 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.80139 | −0.0699076 | ||||||||
\(665\) | 9.67543 | 0.375197 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −23.3254 | −0.902487 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −86.0401 | −3.32402 | ||||||||
\(671\) | −58.3181 | −2.25135 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.9922 | −0.462267 | −0.231133 | − | 0.972922i | \(-0.574243\pi\) | ||||
−0.231133 | + | 0.972922i | \(0.574243\pi\) | |||||||
\(674\) | −52.9547 | −2.03974 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.65343 | 0.371286 | ||||||||
\(677\) | 40.8268 | 1.56910 | 0.784551 | − | 0.620064i | \(-0.212893\pi\) | ||||
0.784551 | + | 0.620064i | \(0.212893\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.62914 | −0.177650 | ||||||||
\(680\) | 2.16204 | 0.0829105 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21.4709 | −0.822162 | ||||||||
\(683\) | −23.2310 | −0.888909 | −0.444454 | − | 0.895801i | \(-0.646602\pi\) | ||||
−0.444454 | + | 0.895801i | \(0.646602\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 71.7944 | 2.74312 | ||||||||
\(686\) | 38.1562 | 1.45681 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.0958 | −0.994895 | ||||||||
\(689\) | 19.9689 | 0.760754 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.77244 | −0.219594 | −0.109797 | − | 0.993954i | \(-0.535020\pi\) | ||||
−0.109797 | + | 0.993954i | \(0.535020\pi\) | |||||||
\(692\) | 7.24645 | 0.275469 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −47.5238 | −1.80398 | ||||||||
\(695\) | 55.0789 | 2.08926 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.85392 | −0.259611 | ||||||||
\(698\) | −50.0627 | −1.89490 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −38.1584 | −1.44225 | ||||||||
\(701\) | −0.668564 | −0.0252513 | −0.0126256 | − | 0.999920i | \(-0.504019\pi\) | ||||
−0.0126256 | + | 0.999920i | \(0.504019\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.42471 | 0.129165 | ||||||||
\(704\) | 28.0694 | 1.05790 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 52.6715 | 1.98232 | ||||||||
\(707\) | 13.2633 | 0.498816 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.21463 | −0.308507 | −0.154253 | − | 0.988031i | \(-0.549297\pi\) | ||||
−0.154253 | + | 0.988031i | \(0.549297\pi\) | |||||||
\(710\) | 59.2029 | 2.22185 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.02409 | 0.188286 | ||||||||
\(713\) | −2.48186 | −0.0929464 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −70.2366 | −2.62670 | ||||||||
\(716\) | 1.01717 | 0.0380134 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.0443 | −1.04660 | ||||||||
\(719\) | −21.6313 | −0.806710 | −0.403355 | − | 0.915044i | \(-0.632156\pi\) | ||||
−0.403355 | + | 0.915044i | \(0.632156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0725 | 0.561329 | ||||||||
\(722\) | −34.8154 | −1.29569 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 25.9722 | 0.965249 | ||||||||
\(725\) | −8.63793 | −0.320805 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.4681 | −0.722031 | −0.361016 | − | 0.932560i | \(-0.617570\pi\) | ||||
−0.361016 | + | 0.932560i | \(0.617570\pi\) | |||||||
\(728\) | −4.10915 | −0.152295 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 75.3851 | 2.79013 | ||||||||
\(731\) | 8.96911 | 0.331735 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.4969 | −1.60659 | −0.803297 | − | 0.595578i | \(-0.796923\pi\) | ||||
−0.803297 | + | 0.595578i | \(0.796923\pi\) | |||||||
\(734\) | 25.9367 | 0.957340 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.71875 | 0.284517 | ||||||||
\(737\) | −53.0470 | −1.95401 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.06700 | 0.223178 | 0.111589 | − | 0.993754i | \(-0.464406\pi\) | ||||
0.111589 | + | 0.993754i | \(0.464406\pi\) | |||||||
\(740\) | −21.3247 | −0.783911 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22.2967 | 0.818538 | ||||||||
\(743\) | −9.80597 | −0.359746 | −0.179873 | − | 0.983690i | \(-0.557569\pi\) | ||||
−0.179873 | + | 0.983690i | \(0.557569\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.5773 | −1.04699 | ||||||||
\(746\) | 40.7972 | 1.49369 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.9704 | −0.437680 | ||||||||
\(749\) | −7.38354 | −0.269789 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.4182 | −0.635599 | −0.317799 | − | 0.948158i | \(-0.602944\pi\) | ||||
−0.317799 | + | 0.948158i | \(0.602944\pi\) | |||||||
\(752\) | −21.1176 | −0.770080 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.35324 | 0.304207 | ||||||||
\(755\) | −47.5278 | −1.72971 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.99421 | 0.254209 | 0.127104 | − | 0.991889i | \(-0.459432\pi\) | ||||
0.127104 | + | 0.991889i | \(0.459432\pi\) | |||||||
\(758\) | 34.4266 | 1.25043 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.53967 | 0.0558498 | ||||||||
\(761\) | 22.9466 | 0.831813 | 0.415906 | − | 0.909407i | \(-0.363464\pi\) | ||||
0.415906 | + | 0.909407i | \(0.363464\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.6560 | 1.18223 | ||||||||
\(764\) | 20.0267 | 0.724541 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 47.3089 | 1.70934 | ||||||||
\(767\) | 0.716740 | 0.0258800 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.9447 | −0.466798 | −0.233399 | − | 0.972381i | \(-0.574985\pi\) | ||||
−0.233399 | + | 0.972381i | \(0.574985\pi\) | |||||||
\(770\) | −78.4243 | −2.82622 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −32.4103 | −1.16647 | ||||||||
\(773\) | −25.9962 | −0.935020 | −0.467510 | − | 0.883988i | \(-0.654849\pi\) | ||||
−0.467510 | + | 0.883988i | \(0.654849\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.4381 | 0.770080 | ||||||||
\(776\) | −0.736645 | −0.0264440 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.4550 | 1.23527 | ||||||||
\(779\) | −4.88093 | −0.174878 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.5009 | 1.30610 | ||||||||
\(782\) | −2.92144 | −0.104470 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.24853 | 0.151733 | ||||||||
\(785\) | −46.6539 | −1.66515 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 55.5880 | 1.98150 | 0.990750 | − | 0.135701i | \(-0.0433286\pi\) | ||||
0.990750 | + | 0.135701i | \(0.0433286\pi\) | |||||||
\(788\) | −40.3597 | −1.43776 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.54766 | −0.232955 | ||||||||
\(791\) | −44.3387 | −1.57650 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.3101 | −1.99963 | ||||||||
\(794\) | −3.67189 | −0.130311 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 48.2696 | 1.71087 | ||||||||
\(797\) | 4.13366 | 0.146422 | 0.0732110 | − | 0.997316i | \(-0.476675\pi\) | ||||
0.0732110 | + | 0.997316i | \(0.476675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.25810 | 0.256773 | ||||||||
\(800\) | −66.6740 | −2.35728 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −41.6764 | −1.47164 | ||||||||
\(803\) | 46.4778 | 1.64017 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.06522 | −0.319507 | ||||||||
\(806\) | −20.7316 | −0.730239 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.11061 | 0.0742511 | ||||||||
\(809\) | −27.6896 | −0.973514 | −0.486757 | − | 0.873537i | \(-0.661820\pi\) | ||||
−0.486757 | + | 0.873537i | \(0.661820\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.07695 | −0.0378168 | −0.0189084 | − | 0.999821i | \(-0.506019\pi\) | ||||
−0.0189084 | + | 0.999821i | \(0.506019\pi\) | |||||||
\(812\) | 4.41754 | 0.155025 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.7590 | −0.972953 | ||||||||
\(815\) | 33.1213 | 1.16019 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.38724 | 0.223461 | ||||||||
\(818\) | −46.0476 | −1.61002 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30.3922 | 1.06134 | ||||||||
\(821\) | −41.8221 | −1.45960 | −0.729800 | − | 0.683660i | \(-0.760387\pi\) | ||||
−0.729800 | + | 0.683660i | \(0.760387\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.1258 | −0.562109 | −0.281055 | − | 0.959692i | \(-0.590684\pi\) | ||||
−0.281055 | + | 0.959692i | \(0.590684\pi\) | |||||||
\(824\) | 2.39852 | 0.0835563 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.800292 | 0.0278457 | ||||||||
\(827\) | 19.5277 | 0.679046 | 0.339523 | − | 0.940598i | \(-0.389734\pi\) | ||||
0.339523 | + | 0.940598i | \(0.389734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.6037 | −0.750327 | −0.375163 | − | 0.926959i | \(-0.622413\pi\) | ||||
−0.375163 | + | 0.926959i | \(0.622413\pi\) | |||||||
\(830\) | −33.1963 | −1.15226 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 27.1029 | 0.939623 | ||||||||
\(833\) | −1.46022 | −0.0505935 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 47.8660 | 1.65647 | ||||||||
\(836\) | −8.52456 | −0.294828 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.2297 | −0.560646 | ||||||||
\(839\) | 41.4413 | 1.43071 | 0.715357 | − | 0.698759i | \(-0.246264\pi\) | ||||
0.715357 | + | 0.698759i | \(0.246264\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 23.7907 | 0.819880 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.9108 | 0.582094 | ||||||||
\(845\) | −19.8098 | −0.681477 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.3496 | −0.733580 | ||||||||
\(848\) | 20.3197 | 0.697782 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 25.2352 | 0.865560 | ||||||||
\(851\) | −3.20872 | −0.109993 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.19307 | −0.212047 | −0.106023 | − | 0.994364i | \(-0.533812\pi\) | ||||
−0.106023 | + | 0.994364i | \(0.533812\pi\) | |||||||
\(854\) | −62.8743 | −2.15152 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.17496 | −0.0401592 | ||||||||
\(857\) | 46.6836 | 1.59468 | 0.797340 | − | 0.603530i | \(-0.206240\pi\) | ||||
0.797340 | + | 0.603530i | \(0.206240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.7061 | 1.18416 | 0.592079 | − | 0.805880i | \(-0.298307\pi\) | ||||
0.592079 | + | 0.805880i | \(0.298307\pi\) | |||||||
\(860\) | −39.7715 | −1.35620 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.246745 | 0.00840416 | ||||||||
\(863\) | −11.5543 | −0.393312 | −0.196656 | − | 0.980473i | \(-0.563008\pi\) | ||||
−0.196656 | + | 0.980473i | \(0.563008\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.8704 | −0.505609 | ||||||||
\(866\) | 63.3137 | 2.15149 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.9637 | −0.372133 | ||||||||
\(869\) | −4.03688 | −0.136942 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −51.2205 | −1.73554 | ||||||||
\(872\) | 5.19663 | 0.175980 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.08047 | −0.0703729 | ||||||||
\(875\) | 32.9786 | 1.11488 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.6949 | 1.00273 | 0.501363 | − | 0.865237i | \(-0.332832\pi\) | ||||
0.501363 | + | 0.865237i | \(0.332832\pi\) | |||||||
\(878\) | 55.0502 | 1.85785 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −71.4706 | −2.40927 | ||||||||
\(881\) | 2.14823 | 0.0723756 | 0.0361878 | − | 0.999345i | \(-0.488479\pi\) | ||||
0.0361878 | + | 0.999345i | \(0.488479\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0264 | 0.404720 | 0.202360 | − | 0.979311i | \(-0.435139\pi\) | ||||
0.202360 | + | 0.979311i | \(0.435139\pi\) | |||||||
\(884\) | −11.5582 | −0.388745 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.5621 | 0.522818 | ||||||||
\(887\) | 47.0278 | 1.57904 | 0.789520 | − | 0.613725i | \(-0.210329\pi\) | ||||
0.789520 | + | 0.613725i | \(0.210329\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.2349 | 0.544502 | ||||||||
\(890\) | 92.5846 | 3.10344 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.4890 | 0.886916 | ||||||||
\(893\) | 5.16876 | 0.172966 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.08733 | −0.0697717 | ||||||||
\(896\) | −7.63256 | −0.254986 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 41.8663 | 1.39710 | ||||||||
\(899\) | −2.48186 | −0.0827747 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.98386 | −0.232666 | ||||||||
\(902\) | 39.5625 | 1.31729 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.05571 | −0.234669 | ||||||||
\(905\) | −53.2974 | −1.77167 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.1405 | 1.16682 | 0.583411 | − | 0.812177i | \(-0.301718\pi\) | ||||
0.583411 | + | 0.812177i | \(0.301718\pi\) | |||||||
\(908\) | −45.6091 | −1.51359 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −75.7240 | −2.51023 | ||||||||
\(911\) | −43.8758 | −1.45367 | −0.726835 | − | 0.686812i | \(-0.759010\pi\) | ||||
−0.726835 | + | 0.686812i | \(0.759010\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.4668 | −0.677353 | ||||||||
\(914\) | −30.2249 | −0.999749 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 40.0685 | 1.32390 | ||||||||
\(917\) | −26.6754 | −0.880899 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.6219 | −1.50493 | −0.752463 | − | 0.658634i | \(-0.771135\pi\) | ||||
−0.752463 | + | 0.658634i | \(0.771135\pi\) | |||||||
\(920\) | −1.44257 | −0.0475600 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 77.2588 | 2.54438 | ||||||||
\(923\) | 35.2440 | 1.16007 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.7167 | 0.911319 | ||||||||
\(926\) | −1.51918 | −0.0499232 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.71875 | 0.253380 | ||||||||
\(929\) | −30.1167 | −0.988096 | −0.494048 | − | 0.869435i | \(-0.664483\pi\) | ||||
−0.494048 | + | 0.869435i | \(0.664483\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.03987 | −0.0340805 | ||||||||
\(932\) | −10.6470 | −0.348755 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −51.0428 | −1.67017 | ||||||||
\(935\) | 24.5644 | 0.803341 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −57.7787 | −1.88755 | −0.943773 | − | 0.330594i | \(-0.892751\pi\) | ||||
−0.943773 | + | 0.330594i | \(0.892751\pi\) | |||||||
\(938\) | −57.1914 | −1.86736 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −32.1844 | −1.04974 | ||||||||
\(941\) | −4.84815 | −0.158045 | −0.0790226 | − | 0.996873i | \(-0.525180\pi\) | ||||
−0.0790226 | + | 0.996873i | \(0.525180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.57310 | 0.148921 | ||||||||
\(944\) | 0.729332 | 0.0237377 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −51.7719 | −1.68325 | ||||||||
\(947\) | 24.7151 | 0.803134 | 0.401567 | − | 0.915830i | \(-0.368466\pi\) | ||||
0.401567 | + | 0.915830i | \(0.368466\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.8774 | 1.45678 | ||||||||
\(950\) | 17.9709 | 0.583054 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.43712 | 0.0465774 | ||||||||
\(953\) | −32.7211 | −1.05994 | −0.529970 | − | 0.848016i | \(-0.677797\pi\) | ||||
−0.529970 | + | 0.848016i | \(0.677797\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −41.0967 | −1.32986 | ||||||||
\(956\) | −27.2668 | −0.881870 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −29.5043 | −0.953239 | ||||||||
\(959\) | 47.7222 | 1.54103 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8404 | −0.801302 | ||||||||
\(962\) | −26.8032 | −0.864170 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.93845 | −0.0624334 | ||||||||
\(965\) | 66.5090 | 2.14100 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.3079 | −1.19974 | −0.599870 | − | 0.800097i | \(-0.704781\pi\) | ||||
−0.599870 | + | 0.800097i | \(0.704781\pi\) | |||||||
\(968\) | −3.39740 | −0.109197 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.5750 | −0.435867 | ||||||||
\(971\) | −27.8228 | −0.892876 | −0.446438 | − | 0.894815i | \(-0.647308\pi\) | ||||
−0.446438 | + | 0.894815i | \(0.647308\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.6113 | 1.17371 | ||||||||
\(974\) | 53.0426 | 1.69960 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −57.2994 | −1.83411 | ||||||||
\(977\) | 54.0284 | 1.72852 | 0.864260 | − | 0.503045i | \(-0.167787\pi\) | ||||
0.864260 | + | 0.503045i | \(0.167787\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 57.0820 | 1.82435 | ||||||||
\(980\) | 6.47500 | 0.206836 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 69.6605 | 2.22296 | ||||||||
\(983\) | 15.2109 | 0.485154 | 0.242577 | − | 0.970132i | \(-0.422007\pi\) | ||||
0.242577 | + | 0.970132i | \(0.422007\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 82.8221 | 2.63893 | ||||||||
\(986\) | −2.92144 | −0.0930376 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.23103 | −0.261864 | ||||||||
\(989\) | −5.98441 | −0.190293 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.74186 | 0.0553321 | 0.0276660 | − | 0.999617i | \(-0.491193\pi\) | ||||
0.0276660 | + | 0.999617i | \(0.491193\pi\) | |||||||
\(992\) | −19.1568 | −0.608230 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 39.3525 | 1.24819 | ||||||||
\(995\) | −99.0539 | −3.14022 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.9495 | −0.536797 | −0.268398 | − | 0.963308i | \(-0.586494\pi\) | ||||
−0.268398 | + | 0.963308i | \(0.586494\pi\) | |||||||
\(998\) | −5.45116 | −0.172553 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.s.1.16 | 20 | ||
3.2 | odd | 2 | 2001.2.a.o.1.5 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.o.1.5 | ✓ | 20 | 3.2 | odd | 2 | ||
6003.2.a.s.1.16 | 20 | 1.1 | even | 1 | trivial |