Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(101,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.p (of order \(6\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 10 x^{14} - 12 x^{13} + 6 x^{12} - 27 x^{11} - 585 x^{10} + 3618 x^{9} + \cdots + 43046721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{41}]\) |
Coefficient ring index: | \( 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 401.1 | ||
Root | \(-1.82249 - 2.38297i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.401 |
Dual form | 900.3.p.d.101.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.97496 | + | 0.386835i | −0.991652 | + | 0.128945i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.32731 | + | 4.03103i | 0.332474 | + | 0.575861i | 0.982996 | − | 0.183626i | \(-0.0587835\pi\) |
−0.650523 | + | 0.759487i | \(0.725450\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.70072 | − | 2.30163i | 0.966746 | − | 0.255737i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.4900 | + | 7.21110i | −1.13545 | + | 0.655554i | −0.945301 | − | 0.326200i | \(-0.894232\pi\) |
−0.190153 | + | 0.981755i | \(0.560898\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.2909 | − | 21.2885i | 0.945456 | − | 1.63758i | 0.190621 | − | 0.981664i | \(-0.438950\pi\) |
0.754835 | − | 0.655915i | \(-0.227717\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.56655i | − | 0.386268i | −0.981172 | − | 0.193134i | \(-0.938135\pi\) | ||
0.981172 | − | 0.193134i | \(-0.0618652\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −33.0870 | −1.74142 | −0.870711 | − | 0.491795i | \(-0.836341\pi\) | ||||
−0.870711 | + | 0.491795i | \(0.836341\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.48300 | − | 11.0918i | −0.403952 | − | 0.528183i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 31.9638 | + | 18.4543i | 1.38973 | + | 0.802361i | 0.993285 | − | 0.115697i | \(-0.0369100\pi\) |
0.396446 | + | 0.918058i | \(0.370243\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −24.9939 | + | 10.2130i | −0.925700 | + | 0.378259i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −17.4825 | + | 10.0935i | −0.602844 | + | 0.348052i | −0.770160 | − | 0.637851i | \(-0.779824\pi\) |
0.167315 | + | 0.985903i | \(0.446490\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.48775 | − | 11.2371i | 0.209282 | − | 0.362487i | −0.742206 | − | 0.670171i | \(-0.766221\pi\) |
0.951489 | + | 0.307684i | \(0.0995540\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 34.3676 | − | 26.2843i | 1.04144 | − | 0.796493i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −19.9373 | −0.538845 | −0.269423 | − | 0.963022i | \(-0.586833\pi\) | ||||
−0.269423 | + | 0.963022i | \(0.586833\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −28.3298 | + | 68.0870i | −0.726406 | + | 1.74582i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 44.9196 | + | 25.9344i | 1.09560 | + | 0.632546i | 0.935062 | − | 0.354484i | \(-0.115343\pi\) |
0.160539 | + | 0.987029i | \(0.448677\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.70519 | − | 6.41757i | −0.0861672 | − | 0.149246i | 0.819721 | − | 0.572763i | \(-0.194129\pi\) |
−0.905888 | + | 0.423517i | \(0.860795\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 23.7134 | − | 13.6910i | 0.504541 | − | 0.291297i | −0.226046 | − | 0.974117i | \(-0.572580\pi\) |
0.730587 | + | 0.682820i | \(0.239247\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.6672 | − | 23.6723i | 0.278923 | − | 0.483108i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.54017 | + | 19.5352i | 0.0498073 | + | 0.383043i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 79.3730i | − | 1.49760i | −0.662794 | − | 0.748802i | \(-0.730630\pi\) | ||
0.662794 | − | 0.748802i | \(-0.269370\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 98.4324 | − | 12.7992i | 1.72688 | − | 0.224548i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 63.3853 | + | 36.5955i | 1.07433 | + | 0.620263i | 0.929360 | − | 0.369174i | \(-0.120359\pi\) |
0.144966 | + | 0.989437i | \(0.453693\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.3357 | − | 21.3660i | −0.202224 | − | 0.350263i | 0.747020 | − | 0.664801i | \(-0.231484\pi\) |
−0.949245 | + | 0.314538i | \(0.898150\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 29.5273 | + | 29.7162i | 0.468687 | + | 0.471686i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20.4754 | − | 35.4645i | 0.305603 | − | 0.529321i | −0.671792 | − | 0.740740i | \(-0.734475\pi\) |
0.977396 | + | 0.211419i | \(0.0678085\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −102.230 | − | 42.5360i | −1.48159 | − | 0.616464i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 117.149i | − | 1.64998i | −0.565145 | − | 0.824992i | \(-0.691180\pi\) | ||
0.565145 | − | 0.824992i | \(-0.308820\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40.1824 | 0.550444 | 0.275222 | − | 0.961381i | \(-0.411249\pi\) | ||||
0.275222 | + | 0.961381i | \(0.411249\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −58.1363 | − | 33.5650i | −0.755016 | − | 0.435909i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.1389 | − | 19.2931i | −0.140998 | − | 0.244216i | 0.786874 | − | 0.617113i | \(-0.211698\pi\) |
−0.927873 | + | 0.372897i | \(0.878365\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 70.4050 | − | 40.0517i | 0.869197 | − | 0.494466i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 116.582 | − | 67.3085i | 1.40460 | − | 0.810945i | 0.409738 | − | 0.912203i | \(-0.365620\pi\) |
0.994860 | + | 0.101258i | \(0.0322866\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 48.1051 | − | 36.7906i | 0.552932 | − | 0.422880i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.69877i | − | 0.0527951i | −0.999652 | − | 0.0263976i | \(-0.991596\pi\) | ||
0.999652 | − | 0.0263976i | \(-0.00840358\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 114.419 | 1.25736 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.9538 | + | 35.9396i | −0.160794 | + | 0.386447i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 69.4664 | + | 120.319i | 0.716148 | + | 1.24040i | 0.962515 | + | 0.271228i | \(0.0874298\pi\) |
−0.246367 | + | 0.969177i | \(0.579237\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −92.0745 | + | 91.4891i | −0.930046 | + | 0.924132i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 83.0415 | − | 47.9440i | 0.822193 | − | 0.474693i | −0.0289792 | − | 0.999580i | \(-0.509226\pi\) |
0.851172 | + | 0.524887i | \(0.175892\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 64.4175 | − | 111.574i | 0.625413 | − | 1.08325i | −0.363048 | − | 0.931770i | \(-0.618264\pi\) |
0.988461 | − | 0.151476i | \(-0.0484027\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.4712i | 0.181974i | 0.995852 | + | 0.0909870i | \(0.0290022\pi\) | ||||
−0.995852 | + | 0.0909870i | \(0.970998\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −27.4421 | −0.251762 | −0.125881 | − | 0.992045i | \(-0.540176\pi\) | ||||
−0.125881 | + | 0.992045i | \(0.540176\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 59.3125 | − | 7.71243i | 0.534347 | − | 0.0694814i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 47.5616 | + | 27.4597i | 0.420899 | + | 0.243006i | 0.695462 | − | 0.718563i | \(-0.255200\pi\) |
−0.274563 | + | 0.961569i | \(0.588533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 57.9416 | − | 213.515i | 0.495227 | − | 1.82491i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26.4699 | − | 15.2824i | 0.222437 | − | 0.128424i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 43.4999 | − | 75.3440i | 0.359503 | − | 0.622677i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −143.666 | − | 59.7771i | −1.16802 | − | 0.485993i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 93.6328 | 0.737266 | 0.368633 | − | 0.929575i | \(-0.379826\pi\) | ||||
0.368633 | + | 0.929575i | \(0.379826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.5053 | + | 17.6587i | 0.104692 | + | 0.136889i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 161.160 | + | 93.0460i | 1.23023 | + | 0.710274i | 0.967078 | − | 0.254480i | \(-0.0819042\pi\) |
0.263153 | + | 0.964754i | \(0.415238\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −77.0039 | − | 133.375i | −0.578977 | − | 1.00282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −61.0773 | + | 35.2630i | −0.445820 | + | 0.257394i | −0.706063 | − | 0.708149i | \(-0.749531\pi\) |
0.260243 | + | 0.965543i | \(0.416197\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 24.3745 | − | 42.2179i | 0.175356 | − | 0.303726i | −0.764928 | − | 0.644116i | \(-0.777226\pi\) |
0.940285 | + | 0.340389i | \(0.110559\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −65.2503 | + | 49.9032i | −0.462768 | + | 0.353923i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 354.524i | 2.47919i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −31.5021 | + | 75.7110i | −0.214300 | + | 0.515041i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 125.457 | + | 72.4324i | 0.841990 | + | 0.486123i | 0.857940 | − | 0.513750i | \(-0.171744\pi\) |
−0.0159500 | + | 0.999873i | \(0.505077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −116.217 | − | 201.293i | −0.769647 | − | 1.33307i | −0.937755 | − | 0.347299i | \(-0.887099\pi\) |
0.168108 | − | 0.985769i | \(-0.446234\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.1138 | − | 57.1337i | −0.0987830 | − | 0.373423i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −30.8620 | + | 53.4545i | −0.196573 | + | 0.340474i | −0.947415 | − | 0.320007i | \(-0.896315\pi\) |
0.750842 | + | 0.660482i | \(0.229648\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 30.7042 | + | 236.131i | 0.193108 | + | 1.48510i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 171.796i | 1.06706i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 53.3693 | 0.327419 | 0.163710 | − | 0.986509i | \(-0.447654\pi\) | ||||
0.163710 | + | 0.986509i | \(0.447654\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −116.376 | − | 67.1898i | −0.696863 | − | 0.402334i | 0.109315 | − | 0.994007i | \(-0.465134\pi\) |
−0.806178 | + | 0.591673i | \(0.798468\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −217.634 | − | 376.953i | −1.28778 | − | 2.23049i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −287.881 | + | 76.1542i | −1.68351 | + | 0.445346i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 204.285 | − | 117.944i | 1.18084 | − | 0.681758i | 0.224630 | − | 0.974444i | \(-0.427883\pi\) |
0.956208 | + | 0.292686i | \(0.0945492\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −202.725 | − | 84.3503i | −1.14534 | − | 0.476556i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 324.935i | 1.81528i | 0.419752 | + | 0.907639i | \(0.362117\pi\) | ||||
−0.419752 | + | 0.907639i | \(0.637883\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −205.548 | −1.13563 | −0.567813 | − | 0.823158i | \(-0.692210\pi\) | ||||
−0.567813 | + | 0.823158i | \(0.692210\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 44.9633 | + | 58.7911i | 0.245701 | + | 0.321263i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 47.3520 | + | 82.0161i | 0.253219 | + | 0.438589i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −99.3375 | − | 76.9822i | −0.525595 | − | 0.407313i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −55.6781 | + | 32.1458i | −0.291508 | + | 0.168302i | −0.638622 | − | 0.769521i | \(-0.720495\pi\) |
0.347114 | + | 0.937823i | \(0.387162\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 65.9311 | − | 114.196i | 0.341612 | − | 0.591689i | −0.643120 | − | 0.765765i | \(-0.722361\pi\) |
0.984732 | + | 0.174076i | \(0.0556939\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 97.7058i | − | 0.495968i | −0.968764 | − | 0.247984i | \(-0.920232\pi\) | ||
0.968764 | − | 0.247984i | \(-0.0797681\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −67.9123 | −0.341268 | −0.170634 | − | 0.985334i | \(-0.554582\pi\) | ||||
−0.170634 | + | 0.985334i | \(0.554582\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −47.1946 | + | 113.426i | −0.234799 | + | 0.564308i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −81.3745 | − | 46.9816i | −0.400859 | − | 0.231436i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 320.583 | + | 86.9968i | 1.54871 | + | 0.420274i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 413.257 | − | 238.594i | 1.97730 | − | 1.14160i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.53364 | − | 7.85250i | 0.0214865 | − | 0.0372156i | −0.855082 | − | 0.518492i | \(-0.826493\pi\) |
0.876569 | + | 0.481277i | \(0.159827\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 45.3173 | + | 348.513i | 0.212757 | + | 1.63621i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 60.3961 | 0.278323 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −119.541 | + | 15.5440i | −0.545849 | + | 0.0709770i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −139.792 | − | 80.7090i | −0.632544 | − | 0.365199i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −64.1704 | − | 111.146i | −0.287760 | − | 0.498415i | 0.685515 | − | 0.728059i | \(-0.259577\pi\) |
−0.973275 | + | 0.229644i | \(0.926244\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −179.936 | + | 103.886i | −0.792671 | + | 0.457649i | −0.840902 | − | 0.541187i | \(-0.817975\pi\) |
0.0482311 | + | 0.998836i | \(0.484642\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 195.885 | − | 339.283i | 0.855394 | − | 1.48159i | −0.0208858 | − | 0.999782i | \(-0.506649\pi\) |
0.876279 | − | 0.481803i | \(-0.160018\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 185.937 | + | 77.3652i | 0.804922 | + | 0.334914i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 152.713i | − | 0.655419i | −0.944779 | − | 0.327709i | \(-0.893723\pi\) | ||
0.944779 | − | 0.327709i | \(-0.106277\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 40.6009 | + | 53.0872i | 0.171312 | + | 0.223997i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 63.4669 | + | 36.6426i | 0.265552 | + | 0.153316i | 0.626865 | − | 0.779128i | \(-0.284338\pi\) |
−0.361313 | + | 0.932445i | \(0.617671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 214.984 | + | 372.364i | 0.892051 | + | 1.54508i | 0.837413 | + | 0.546571i | \(0.184067\pi\) |
0.0546375 | + | 0.998506i | \(0.482600\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −193.958 | + | 146.387i | −0.798182 | + | 0.602417i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −406.670 | + | 704.374i | −1.64644 | + | 2.85172i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −320.788 | + | 245.338i | −1.28831 | + | 0.985291i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 165.235i | − | 0.658309i | −0.944276 | − | 0.329154i | \(-0.893236\pi\) | ||
0.944276 | − | 0.329154i | \(-0.106764\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −532.303 | −2.10397 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −405.971 | − | 234.388i | −1.57965 | − | 0.912014i | −0.994907 | − | 0.100798i | \(-0.967860\pi\) |
−0.584747 | − | 0.811216i | \(-0.698806\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −46.4003 | − | 80.3677i | −0.179152 | − | 0.310300i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −128.879 | + | 128.059i | −0.493788 | + | 0.490648i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.6821 | + | 17.7143i | −0.116662 | + | 0.0673549i | −0.557196 | − | 0.830381i | \(-0.688123\pi\) |
0.440533 | + | 0.897736i | \(0.354789\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.81765 | + | 13.9786i | 0.00680767 | + | 0.0523544i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 141.461i | 0.525876i | 0.964813 | + | 0.262938i | \(0.0846914\pi\) | ||||
−0.964813 | + | 0.262938i | \(0.915309\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −372.478 | −1.37446 | −0.687229 | − | 0.726441i | \(-0.741173\pi\) | ||||
−0.687229 | + | 0.726441i | \(0.741173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −340.393 | + | 44.2615i | −1.24686 | + | 0.162130i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −129.107 | − | 223.619i | −0.466089 | − | 0.807289i | 0.533161 | − | 0.846014i | \(-0.321004\pi\) |
−0.999250 | + | 0.0387244i | \(0.987671\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.5843 | − | 112.703i | 0.109621 | − | 0.403954i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −283.705 | + | 163.797i | −1.00963 | + | 0.582908i | −0.911082 | − | 0.412224i | \(-0.864752\pi\) |
−0.0985444 | + | 0.995133i | \(0.531419\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −207.142 | + | 358.781i | −0.731952 | + | 1.26778i | 0.224096 | + | 0.974567i | \(0.428057\pi\) |
−0.956048 | + | 0.293210i | \(0.905276\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 241.430i | 0.841219i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 245.880 | 0.850797 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −253.203 | − | 331.072i | −0.870113 | − | 1.13771i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 359.962 | + | 207.824i | 1.22854 | + | 0.709298i | 0.966724 | − | 0.255820i | \(-0.0823454\pi\) |
0.261816 | + | 0.965118i | \(0.415679\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 238.526 | − | 307.794i | 0.803119 | − | 1.03634i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 785.730 | − | 453.641i | 2.62786 | − | 1.51720i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.2463 | − | 29.8714i | 0.0572966 | − | 0.0992406i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −228.498 | + | 174.755i | −0.754120 | + | 0.576748i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −91.4750 | −0.297964 | −0.148982 | − | 0.988840i | \(-0.547600\pi\) | ||||
−0.148982 | + | 0.988840i | \(0.547600\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −148.478 | + | 356.848i | −0.480512 | + | 1.15485i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 385.023 | + | 222.293i | 1.23802 | + | 0.714769i | 0.968688 | − | 0.248280i | \(-0.0798652\pi\) |
0.269328 | + | 0.963049i | \(0.413199\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −67.6156 | − | 117.114i | −0.216024 | − | 0.374165i | 0.737565 | − | 0.675277i | \(-0.235976\pi\) |
−0.953589 | + | 0.301111i | \(0.902642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 297.699 | − | 171.876i | 0.939113 | − | 0.542197i | 0.0494307 | − | 0.998778i | \(-0.484259\pi\) |
0.889682 | + | 0.456580i | \(0.150926\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 145.571 | − | 252.136i | 0.456334 | − | 0.790394i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.53215 | − | 57.9260i | −0.0234646 | − | 0.180455i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 217.268i | 0.672655i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 81.6389 | − | 10.6156i | 0.249660 | − | 0.0324635i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 110.377 | + | 63.7263i | 0.335493 | + | 0.193697i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −269.871 | − | 467.430i | −0.815319 | − | 1.41217i | −0.909098 | − | 0.416581i | \(-0.863228\pi\) |
0.0937793 | − | 0.995593i | \(-0.470105\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −173.469 | + | 45.8883i | −0.520926 | + | 0.137803i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 274.336 | − | 475.164i | 0.814054 | − | 1.40998i | −0.0959512 | − | 0.995386i | \(-0.530589\pi\) |
0.910005 | − | 0.414597i | \(-0.136077\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −152.116 | − | 63.2929i | −0.448720 | − | 0.186705i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 187.135i | 0.548783i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 355.308 | 1.03588 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −100.553 | − | 58.0540i | −0.289777 | − | 0.167303i | 0.348064 | − | 0.937471i | \(-0.386839\pi\) |
−0.637841 | + | 0.770168i | \(0.720172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −119.155 | − | 206.383i | −0.341419 | − | 0.591355i | 0.643278 | − | 0.765633i | \(-0.277574\pi\) |
−0.984696 | + | 0.174278i | \(0.944241\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −89.7786 | + | 657.610i | −0.255779 | + | 1.87353i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −481.520 | + | 278.006i | −1.36408 | + | 0.787551i | −0.990164 | − | 0.139912i | \(-0.955318\pi\) |
−0.373915 | + | 0.927463i | \(0.621985\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −72.8351 | + | 55.7041i | −0.204020 | + | 0.156034i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 119.443i | − | 0.332710i | −0.986066 | − | 0.166355i | \(-0.946800\pi\) | ||
0.986066 | − | 0.166355i | \(-0.0531998\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 733.751 | 2.03255 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −100.264 | + | 240.972i | −0.276211 | + | 0.663835i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 287.355 | + | 497.713i | 0.782983 | + | 1.35617i | 0.930197 | + | 0.367062i | \(0.119636\pi\) |
−0.147214 | + | 0.989105i | \(0.547030\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 450.525 | + | 122.259i | 1.22093 | + | 0.331325i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 319.955 | − | 184.726i | 0.862411 | − | 0.497913i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 108.136 | − | 187.298i | 0.289910 | − | 0.502139i | −0.683878 | − | 0.729596i | \(-0.739708\pi\) |
0.973788 | + | 0.227458i | \(0.0730413\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 496.235i | 1.31627i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −252.187 | −0.665400 | −0.332700 | − | 0.943033i | \(-0.607960\pi\) | ||||
−0.332700 | + | 0.943033i | \(0.607960\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −278.553 | + | 36.2204i | −0.731111 | + | 0.0950668i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −111.402 | − | 64.3180i | −0.290867 | − | 0.167932i | 0.347466 | − | 0.937693i | \(-0.387042\pi\) |
−0.638333 | + | 0.769761i | \(0.720376\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −47.0087 | − | 47.3095i | −0.121470 | − | 0.122247i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −214.436 | + | 123.805i | −0.551250 | + | 0.318264i | −0.749626 | − | 0.661862i | \(-0.769767\pi\) |
0.198376 | + | 0.980126i | \(0.436433\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 121.181 | − | 209.892i | 0.309926 | − | 0.536808i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −515.438 | − | 214.465i | −1.31155 | − | 0.545713i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 123.266 | 0.310493 | 0.155246 | − | 0.987876i | \(-0.450383\pi\) | ||||
0.155246 | + | 0.987876i | \(0.450383\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 280.677 | + | 366.996i | 0.703452 | + | 0.919789i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 397.425 | + | 229.454i | 0.991085 | + | 0.572203i | 0.905599 | − | 0.424136i | \(-0.139422\pi\) |
0.0854868 | + | 0.996339i | \(0.472755\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −159.481 | − | 276.229i | −0.395734 | − | 0.685432i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 249.016 | − | 143.770i | 0.611833 | − | 0.353242i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −38.8984 | + | 67.3740i | −0.0951061 | + | 0.164729i | −0.909653 | − | 0.415369i | \(-0.863652\pi\) |
0.814547 | + | 0.580098i | \(0.196986\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 168.061 | − | 128.533i | 0.408908 | − | 0.312732i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 340.677i | 0.824884i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −56.1818 | + | 135.025i | −0.134728 | + | 0.323802i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 363.032 | + | 209.597i | 0.866425 | + | 0.500230i | 0.866158 | − | 0.499770i | \(-0.166582\pi\) |
0.000266138 | 1.00000i | \(0.499915\pi\) | ||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −41.7402 | − | 72.2962i | −0.0991454 | − | 0.171725i | 0.812186 | − | 0.583399i | \(-0.198278\pi\) |
−0.911331 | + | 0.411674i | \(0.864944\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 174.812 | − | 173.701i | 0.413268 | − | 0.410640i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 57.4181 | − | 99.4510i | 0.134469 | − | 0.232906i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −137.142 | − | 1054.69i | −0.319679 | − | 2.45850i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 464.864i | − | 1.07857i | −0.842123 | − | 0.539285i | \(-0.818694\pi\) | ||
0.842123 | − | 0.539285i | \(-0.181306\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −201.140 | −0.464525 | −0.232263 | − | 0.972653i | \(-0.574613\pi\) | ||||
−0.232263 | + | 0.972653i | \(0.574613\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1057.59 | − | 610.598i | −2.42011 | − | 1.39725i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −252.879 | − | 437.999i | −0.576033 | − | 0.997719i | −0.995929 | − | 0.0901465i | \(-0.971266\pi\) |
0.419895 | − | 0.907573i | \(-0.362067\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 64.4296 | − | 237.423i | 0.146099 | − | 0.538374i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 197.026 | − | 113.753i | 0.444755 | − | 0.256779i | −0.260858 | − | 0.965377i | \(-0.584005\pi\) |
0.705612 | + | 0.708598i | \(0.250672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −401.247 | − | 166.952i | −0.897644 | − | 0.373495i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 224.825i | 0.500724i | 0.968152 | + | 0.250362i | \(0.0805496\pi\) | ||||
−0.968152 | + | 0.250362i | \(0.919450\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −748.061 | −1.65867 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 423.607 | + | 553.881i | 0.935114 | + | 1.22270i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 308.178 | + | 533.780i | 0.674350 | + | 1.16801i | 0.976659 | + | 0.214798i | \(0.0689093\pi\) |
−0.302309 | + | 0.953210i | \(0.597757\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 67.0642 | + | 164.124i | 0.146109 | + | 0.357568i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −616.599 | + | 355.994i | −1.33753 | + | 0.772221i | −0.986440 | − | 0.164122i | \(-0.947521\pi\) |
−0.351086 | + | 0.936343i | \(0.614188\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 126.318 | − | 218.788i | 0.272824 | − | 0.472545i | −0.696760 | − | 0.717304i | \(-0.745376\pi\) |
0.969584 | + | 0.244759i | \(0.0787090\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 508.789i | 1.08948i | 0.838604 | + | 0.544742i | \(0.183372\pi\) | ||||
−0.838604 | + | 0.544742i | \(0.816628\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 190.611 | 0.406420 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 71.1349 | − | 170.963i | 0.151029 | − | 0.362979i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 92.5555 | + | 53.4370i | 0.195678 | + | 0.112975i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −182.687 | − | 690.602i | −0.382993 | − | 1.44780i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −683.840 | + | 394.815i | −1.42764 | + | 0.824249i | −0.996934 | − | 0.0782437i | \(-0.975069\pi\) |
−0.430706 | + | 0.902492i | \(0.641735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −245.048 | + | 424.435i | −0.509454 | + | 0.882401i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −66.4567 | − | 511.085i | −0.137592 | − | 1.05815i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −317.579 | −0.652112 | −0.326056 | − | 0.945350i | \(-0.605720\pi\) | ||||
−0.326056 | + | 0.945350i | \(0.605720\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −158.771 | + | 20.6451i | −0.324686 | + | 0.0422190i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −597.835 | − | 345.160i | −1.21759 | − | 0.702973i | −0.253185 | − | 0.967418i | \(-0.581478\pi\) |
−0.964401 | + | 0.264444i | \(0.914811\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 66.2796 | + | 114.800i | 0.134441 | + | 0.232859i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 472.230 | − | 272.642i | 0.950161 | − | 0.548576i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.6761 | − | 44.4723i | 0.0514550 | − | 0.0891228i | −0.839151 | − | 0.543899i | \(-0.816947\pi\) |
0.890606 | + | 0.454776i | \(0.150281\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 372.205 | + | 154.868i | 0.742924 | + | 0.309118i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 239.928i | − | 0.476994i | −0.971143 | − | 0.238497i | \(-0.923345\pi\) | ||
0.971143 | − | 0.238497i | \(-0.0766547\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 793.270 | + | 1037.23i | 1.56464 | + | 2.04582i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −440.034 | − | 254.054i | −0.864507 | − | 0.499123i | 0.00101197 | − | 0.999999i | \(-0.499678\pi\) |
−0.865519 | + | 0.500876i | \(0.833011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 93.5171 | + | 161.976i | 0.183008 | + | 0.316979i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 826.974 | − | 337.918i | 1.61203 | − | 0.658709i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −197.454 | + | 342.000i | −0.381922 | + | 0.661508i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −562.114 | + | 429.903i | −1.08307 | + | 0.828329i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 66.1586i | 0.126984i | 0.997982 | + | 0.0634920i | \(0.0202237\pi\) | ||||
−0.997982 | + | 0.0634920i | \(0.979776\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −133.503 | −0.255264 | −0.127632 | − | 0.991822i | \(-0.540738\pi\) | ||||
−0.127632 | + | 0.991822i | \(0.540738\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −73.7890 | − | 42.6021i | −0.140017 | − | 0.0808389i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 416.623 | + | 721.613i | 0.787568 | + | 1.36411i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 635.727 | + | 172.517i | 1.19723 | + | 0.324892i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1104.21 | − | 637.515i | 2.07169 | − | 1.19609i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −125.696 | − | 966.666i | −0.234071 | − | 1.80012i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 394.222i | 0.731396i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 263.866 | 0.487737 | 0.243868 | − | 0.969808i | \(-0.421584\pi\) | ||||
0.243868 | + | 0.969808i | \(0.421584\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 611.497 | − | 79.5133i | 1.12615 | − | 0.146433i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −302.353 | − | 523.690i | −0.552747 | − | 0.957386i | −0.998075 | − | 0.0620188i | \(-0.980246\pi\) |
0.445328 | − | 0.895368i | \(-0.353087\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −156.506 | − | 157.508i | −0.285075 | − | 0.286899i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 578.443 | − | 333.964i | 1.04981 | − | 0.606106i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 51.8473 | − | 89.8022i | 0.0937565 | − | 0.162391i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 510.522i | 0.916556i | 0.888809 | + | 0.458278i | \(0.151534\pi\) | ||||
−0.888809 | + | 0.458278i | \(0.848466\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −182.161 | −0.325869 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −172.597 | − | 225.677i | −0.307659 | − | 0.402276i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −333.774 | − | 192.705i | −0.592849 | − | 0.342282i | 0.173374 | − | 0.984856i | \(-0.444533\pi\) |
−0.766223 | + | 0.642574i | \(0.777866\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 325.304 | + | 190.591i | 0.573729 | + | 0.336140i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 192.215 | − | 110.975i | 0.337812 | − | 0.195036i | −0.321492 | − | 0.946912i | \(-0.604184\pi\) |
0.659304 | + | 0.751877i | \(0.270851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −187.067 | + | 324.010i | −0.327613 | + | 0.567443i | −0.982038 | − | 0.188685i | \(-0.939578\pi\) |
0.654425 | + | 0.756127i | \(0.272911\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 153.205 | − | 117.170i | 0.267373 | − | 0.204486i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 237.121 | 0.410955 | 0.205478 | − | 0.978662i | \(-0.434125\pi\) | ||||
0.205478 | + | 0.978662i | \(0.434125\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −151.967 | + | 365.232i | −0.262465 | + | 0.630799i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 542.645 | + | 313.296i | 0.933984 | + | 0.539236i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 572.366 | + | 991.367i | 0.981760 | + | 1.70046i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 820.431 | − | 473.676i | 1.39767 | − | 0.806944i | 0.403519 | − | 0.914971i | \(-0.367787\pi\) |
0.994148 | + | 0.108028i | \(0.0344535\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −214.660 | + | 371.802i | −0.364449 | + | 0.631243i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 37.7960 | + | 290.670i | 0.0639527 | + | 0.491828i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 744.224i | − | 1.25502i | −0.778610 | − | 0.627508i | \(-0.784075\pi\) | ||
0.778610 | − | 0.627508i | \(-0.215925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 202.036 | − | 26.2709i | 0.338419 | − | 0.0440048i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −532.457 | − | 307.414i | −0.888910 | − | 0.513212i | −0.0153242 | − | 0.999883i | \(-0.504878\pi\) |
−0.873586 | + | 0.486670i | \(0.838211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −156.574 | − | 271.195i | −0.260523 | − | 0.451239i | 0.705858 | − | 0.708353i | \(-0.250562\pi\) |
−0.966381 | + | 0.257114i | \(0.917228\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 96.5247 | − | 355.693i | 0.160074 | − | 0.589873i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 485.085 | − | 840.192i | 0.799152 | − | 1.38417i | −0.121018 | − | 0.992650i | \(-0.538616\pi\) |
0.920169 | − | 0.391521i | \(-0.128051\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 260.260 | + | 108.290i | 0.427356 | + | 0.177815i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 673.099i | − | 1.10163i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 758.446 | 1.23727 | 0.618635 | − | 0.785679i | \(-0.287686\pi\) | ||||
0.618635 | + | 0.785679i | \(0.287686\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 270.760 | + | 156.323i | 0.438833 | + | 0.253360i | 0.703102 | − | 0.711089i | \(-0.251798\pi\) |
−0.264270 | + | 0.964449i | \(0.585131\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 488.656 | + | 846.377i | 0.789428 | + | 1.36733i | 0.926318 | + | 0.376744i | \(0.122956\pi\) |
−0.136889 | + | 0.990586i | \(0.543710\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −987.374 | − | 134.799i | −1.58997 | − | 0.217067i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.9409 | − | 10.9355i | 0.0304027 | − | 0.0175530i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1137.12 | + | 869.668i | −1.81359 | + | 1.38703i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 130.919i | 0.208138i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 904.406 | 1.43329 | 0.716645 | − | 0.697438i | \(-0.245677\pi\) | ||||
0.716645 | + | 0.697438i | \(0.245677\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.4498 | + | 25.1146i | −0.0165083 | + | 0.0396755i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −335.966 | − | 581.910i | −0.527419 | − | 0.913516i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −269.634 | − | 1019.28i | −0.421962 | − | 1.59512i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −764.357 | + | 441.302i | −1.19245 | + | 0.688459i | −0.958860 | − | 0.283878i | \(-0.908379\pi\) |
−0.233585 | + | 0.972336i | \(0.575046\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 285.894 | − | 495.184i | 0.444626 | − | 0.770114i | −0.553400 | − | 0.832915i | \(-0.686670\pi\) |
0.998026 | + | 0.0628010i | \(0.0200033\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 113.496i | − | 0.175419i | −0.996146 | − | 0.0877096i | \(-0.972045\pi\) | ||
0.996146 | − | 0.0877096i | \(-0.0279547\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1055.58 | −1.62646 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −179.676 | + | 23.3633i | −0.276000 | + | 0.0358884i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −880.891 | − | 508.582i | −1.34899 | − | 0.778840i | −0.360884 | − | 0.932611i | \(-0.617525\pi\) |
−0.988106 | + | 0.153771i | \(0.950858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 349.616 | − | 92.4852i | 0.532140 | − | 0.140769i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 697.672 | − | 402.801i | 1.05868 | − | 0.611231i | 0.133615 | − | 0.991033i | \(-0.457341\pi\) |
0.925068 | + | 0.379802i | \(0.124008\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 491.116 | − | 850.638i | 0.742989 | − | 1.28690i | −0.208139 | − | 0.978099i | \(-0.566741\pi\) |
0.951128 | − | 0.308796i | \(-0.0999261\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 447.097 | + | 186.029i | 0.674354 | + | 0.280587i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −745.076 | −1.11705 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 233.900 | + | 305.832i | 0.349626 | + | 0.457149i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 308.145 | + | 177.908i | 0.459233 | + | 0.265138i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −142.183 | − | 246.268i | −0.211267 | − | 0.365926i | 0.740844 | − | 0.671677i | \(-0.234426\pi\) |
−0.952111 | + | 0.305751i | \(0.901092\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −222.141 | + | 128.253i | −0.328125 | + | 0.189443i | −0.655009 | − | 0.755621i | \(-0.727335\pi\) |
0.326883 | + | 0.945065i | \(0.394002\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −323.340 | + | 560.042i | −0.476200 | + | 0.824803i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 495.116 | − | 378.663i | 0.727042 | − | 0.556039i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1126.46i | 1.64928i | 0.565660 | + | 0.824639i | \(0.308622\pi\) | ||||
−0.565660 | + | 0.824639i | \(0.691378\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −451.503 | + | 1085.13i | −0.657210 | + | 1.57952i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1689.73 | − | 975.568i | −2.45244 | − | 1.41592i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 144.035 | + | 249.476i | 0.208444 | + | 0.361036i | 0.951225 | − | 0.308499i | \(-0.0998267\pi\) |
−0.742780 | + | 0.669535i | \(0.766493\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −583.081 | − | 158.231i | −0.841387 | − | 0.228328i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 170.299 | − | 294.967i | 0.244332 | − | 0.423195i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 59.0746 | + | 454.313i | 0.0845130 | + | 0.649947i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 854.593i | − | 1.21911i | −0.792745 | − | 0.609553i | \(-0.791349\pi\) | ||
0.792745 | − | 0.609553i | \(-0.208651\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 659.665 | 0.938357 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 386.527 | + | 223.162i | 0.546715 | + | 0.315646i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 183.387 | + | 317.636i | 0.258656 | + | 0.448006i | 0.965882 | − | 0.258982i | \(-0.0833870\pi\) |
−0.707226 | + | 0.706988i | \(0.750054\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −141.322 | − | 142.226i | −0.198765 | − | 0.200037i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 414.746 | − | 239.454i | 0.581692 | − | 0.335840i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −202.986 | − | 84.4590i | −0.283104 | − | 0.117795i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 167.078i | 0.232376i | 0.993227 | + | 0.116188i | \(0.0370675\pi\) | ||||
−0.993227 | + | 0.116188i | \(0.962932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 599.679 | 0.831733 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −783.612 | − | 1024.60i | −1.08383 | − | 1.41715i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −330.352 | − | 572.186i | −0.454404 | − | 0.787051i | 0.544250 | − | 0.838923i | \(-0.316814\pi\) |
−0.998654 | + | 0.0518723i | \(0.983481\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 520.389 | − | 510.525i | 0.713840 | − | 0.700309i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.1413 | + | 24.3303i | −0.0576489 | + | 0.0332836i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.6300 | + | 23.6078i | −0.0185947 | + | 0.0322071i | −0.875173 | − | 0.483810i | \(-0.839253\pi\) |
0.856578 | + | 0.516017i | \(0.172586\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 590.601i | 0.801359i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 549.148 | 0.743096 | 0.371548 | − | 0.928414i | \(-0.378827\pi\) | ||||
0.371548 | + | 0.928414i | \(0.378827\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 937.350 | − | 2252.80i | 1.26498 | − | 3.04021i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 152.537 | + | 88.0673i | 0.205299 | + | 0.118529i | 0.599125 | − | 0.800656i | \(-0.295515\pi\) |
−0.393826 | + | 0.919185i | \(0.628849\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 859.425 | − | 853.960i | 1.15050 | − | 1.14319i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −78.4890 | + | 45.3157i | −0.104792 | + | 0.0605016i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 108.231 | − | 187.462i | 0.144116 | − | 0.249616i | −0.784927 | − | 0.619589i | \(-0.787299\pi\) |
0.929043 | + | 0.369972i | \(0.120633\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 63.9189 | + | 491.568i | 0.0848856 | + | 0.652813i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1104.91 | 1.45959 | 0.729793 | − | 0.683668i | \(-0.239616\pi\) | ||||
0.729793 | + | 0.683668i | \(0.239616\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1583.58 | − | 205.914i | 2.08640 | − | 0.271296i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 774.245 | + | 447.011i | 1.01741 | + | 0.587399i | 0.913351 | − | 0.407173i | \(-0.133485\pi\) |
0.104054 | + | 0.994572i | \(0.466819\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −63.8663 | − | 110.620i | −0.0837042 | − | 0.144980i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1558.13 | − | 899.586i | 2.03146 | − | 1.17286i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −287.360 | + | 497.722i | −0.373680 | + | 0.647233i | −0.990129 | − | 0.140162i | \(-0.955238\pi\) |
0.616448 | + | 0.787395i | \(0.288571\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1298.42 | + | 540.249i | 1.68407 | + | 0.700711i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 71.2870i | 0.0922212i | 0.998936 | + | 0.0461106i | \(0.0146827\pi\) | ||||
−0.998936 | + | 0.0461106i | \(0.985317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 169.128 | + | 221.141i | 0.217668 | + | 0.284609i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1486.26 | − | 858.091i | −1.90790 | − | 1.10153i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 844.772 | + | 1463.19i | 1.08165 | + | 1.87348i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 333.870 | − | 430.825i | 0.426399 | − | 0.550223i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.4363 | + | 30.2005i | −0.0221554 | + | 0.0383742i | −0.876891 | − | 0.480690i | \(-0.840386\pi\) |
0.854735 | + | 0.519064i | \(0.173720\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 84.4254 | − | 64.5683i | 0.107003 | − | 0.0818356i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 255.629i | 0.323172i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −606.469 | −0.764777 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 782.440 | + | 451.742i | 0.981731 | + | 0.566803i | 0.902792 | − | 0.430077i | \(-0.141513\pi\) |
0.0789390 | + | 0.996879i | \(0.474847\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −89.9024 | − | 155.716i | −0.112519 | − | 0.194888i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.8148 | − | 40.8826i | −0.0135017 | − | 0.0510395i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −501.878 | + | 289.759i | −0.625004 | + | 0.360846i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −54.7219 | − | 420.839i | −0.0678090 | − | 0.521485i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1019.43i | 1.26011i | 0.776551 | + | 0.630054i | \(0.216967\pi\) | ||||
−0.776551 | + | 0.630054i | \(0.783033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1022.62 | −1.26093 | −0.630467 | − | 0.776216i | \(-0.717136\pi\) | ||||
−0.630467 | + | 0.776216i | \(0.717136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1108.11 | − | 144.088i | 1.36298 | − | 0.177229i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 122.594 | + | 212.338i | 0.150053 | + | 0.259900i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 995.531 | − | 263.352i | 1.21555 | − | 0.321553i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1352.85 | + | 781.066i | −1.64780 | + | 0.951359i | −0.669859 | + | 0.742488i | \(0.733646\pi\) |
−0.977943 | + | 0.208871i | \(0.933021\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −707.151 | + | 1224.82i | −0.859236 | + | 1.48824i | 0.0134224 | + | 0.999910i | \(0.495727\pi\) |
−0.872659 | + | 0.488331i | \(0.837606\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 949.074i | − | 1.14761i | −0.818992 | − | 0.573805i | \(-0.805467\pi\) | ||
0.818992 | − | 0.573805i | \(-0.194533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1144.99 | 1.38118 | 0.690588 | − | 0.723249i | \(-0.257352\pi\) | ||||
0.690588 | + | 0.723249i | \(0.257352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 470.590 | + | 615.314i | 0.566294 | + | 0.740450i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −155.445 | − | 89.7465i | −0.186609 | − | 0.107739i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −47.3895 | + | 347.118i | −0.0566182 | + | 0.414717i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −218.826 | + | 126.340i | −0.260818 | + | 0.150583i | −0.624708 | − | 0.780859i | \(-0.714782\pi\) |
0.363890 | + | 0.931442i | \(0.381449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −216.742 | + | 375.408i | −0.257719 | + | 0.446383i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 780.648 | − | 597.037i | 0.926035 | − | 0.708228i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 404.951 | 0.478101 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 477.450 | − | 1147.49i | 0.562368 | − | 1.35158i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −637.271 | − | 367.929i | −0.748849 | − | 0.432348i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −136.549 | − | 236.510i | −0.160081 | − | 0.277269i | 0.774816 | − | 0.632186i | \(-0.217842\pi\) |
−0.934898 | + | 0.354917i | \(0.884509\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −358.085 | + | 206.740i | −0.417835 | + | 0.241237i | −0.694151 | − | 0.719830i | \(-0.744220\pi\) |
0.276315 | + | 0.961067i | \(0.410887\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −664.377 | + | 1150.73i | −0.773431 | + | 1.33962i | 0.162242 | + | 0.986751i | \(0.448128\pi\) |
−0.935672 | + | 0.352870i | \(0.885206\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −93.3935 | − | 718.243i | −0.108471 | − | 0.834196i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 283.552i | 0.328565i | 0.986413 | + | 0.164283i | \(0.0525309\pi\) | ||||
−0.986413 | + | 0.164283i | \(0.947469\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −731.483 | + | 95.1152i | −0.843695 | + | 0.109706i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 278.249 | + | 160.647i | 0.320194 | + | 0.184864i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −503.324 | − | 871.783i | −0.577870 | − | 1.00090i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 881.338 | + | 886.978i | 1.00955 | + | 1.01601i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −229.117 | + | 396.843i | −0.261251 | + | 0.452500i | −0.966575 | − | 0.256385i | \(-0.917468\pi\) |
0.705323 | + | 0.708886i | \(0.250802\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1151.27 | − | 479.022i | −1.30974 | − | 0.544962i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1408.20i | − | 1.59841i | −0.601056 | − | 0.799207i | \(-0.705253\pi\) | ||
0.601056 | − | 0.799207i | \(-0.294747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −200.279 | −0.226817 | −0.113408 | − | 0.993548i | \(-0.536177\pi\) | ||||
−0.113408 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1026.67 | − | 592.748i | −1.15746 | − | 0.668262i | −0.206769 | − | 0.978390i | \(-0.566295\pi\) |
−0.950695 | + | 0.310128i | \(0.899628\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 217.913 | + | 377.436i | 0.245121 | + | 0.424563i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −590.540 | + | 1007.94i | −0.662784 | + | 1.13125i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −784.607 | + | 452.993i | −0.878620 | + | 0.507271i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2162.03 | + | 1653.51i | −2.41029 | + | 1.84338i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 261.937i | 0.291364i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −521.207 | −0.578476 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −39.7516 | + | 95.5376i | −0.0440217 | + | 0.105800i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −665.240 | − | 1152.23i | −0.733451 | − | 1.27037i | −0.955400 | − | 0.295316i | \(-0.904575\pi\) |
0.221949 | − | 0.975058i | \(-0.428758\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 612.171 | − | 608.278i | 0.673455 | − | 0.669173i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 311.564 | − | 179.882i | 0.342003 | − | 0.197455i | −0.319155 | − | 0.947703i | \(-0.603399\pi\) |
0.661157 | + | 0.750247i | \(0.270066\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −970.736 | + | 1681.36i | −1.06324 | + | 1.84158i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 866.189i | 0.944590i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 114.308 | 0.124383 | 0.0621913 | − | 0.998064i | \(-0.480191\pi\) | ||||
0.0621913 | + | 0.998064i | \(0.480191\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 272.134 | − | 35.3858i | 0.295477 | − | 0.0384210i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2493.93 | − | 1439.87i | −2.70198 | − | 1.55999i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 303.675 | − | 1119.04i | 0.327589 | − | 1.20717i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −692.105 | + | 399.587i | −0.745000 | + | 0.430126i | −0.823885 | − | 0.566758i | \(-0.808198\pi\) |
0.0788843 | + | 0.996884i | \(0.474864\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −452.207 | + | 783.246i | −0.485722 | + | 0.841296i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1231.42 | − | 512.372i | −1.31985 | − | 0.549166i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −937.387 | −1.00041 | −0.500206 | − | 0.865906i | \(-0.666743\pi\) | ||||
−0.500206 | + | 0.865906i | \(0.666743\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 246.457 | + | 322.252i | 0.262468 | + | 0.343186i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −490.911 | − | 283.428i | −0.521691 | − | 0.301198i | 0.215935 | − | 0.976408i | \(-0.430720\pi\) |
−0.737626 | + | 0.675209i | \(0.764053\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 957.202 | + | 1657.92i | 1.01506 | + | 1.75814i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 619.197 | − | 357.494i | 0.653851 | − | 0.377501i | −0.136079 | − | 0.990698i | \(-0.543450\pi\) |
0.789930 | + | 0.613197i | \(0.210117\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 493.880 | − | 855.424i | 0.520421 | − | 0.901396i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −819.153 | + | 626.485i | −0.861359 | + | 0.658765i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 918.880i | − | 0.964197i | −0.876117 | − | 0.482099i | \(-0.839875\pi\) | ||
0.876117 | − | 0.482099i | \(-0.160125\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −335.531 | + | 806.405i | −0.350607 | + | 0.842638i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −284.292 | − | 164.136i | −0.296447 | − | 0.171154i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 396.318 | + | 686.443i | 0.412402 | + | 0.714301i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 44.8156 | + | 169.414i | 0.0465375 | + | 0.175923i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.16023 | + | 15.8660i | −0.00947283 | + | 0.0164074i | −0.870723 | − | 0.491774i | \(-0.836349\pi\) |
0.861250 | + | 0.508181i | \(0.169682\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −84.0468 | − | 646.362i | −0.0867356 | − | 0.667040i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 35.9529i | − | 0.0370266i | −0.999829 | − | 0.0185133i | \(-0.994107\pi\) | ||
0.999829 | − | 0.0185133i | \(-0.00589331\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 226.909 | 0.233205 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 486.908 | + | 281.116i | 0.498370 | + | 0.287734i | 0.728040 | − | 0.685534i | \(-0.240431\pi\) |
−0.229670 | + | 0.973269i | \(0.573765\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.8833 | + | 58.6875i | 0.0346101 | + | 0.0599464i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −238.766 | + | 63.1616i | −0.243390 | + | 0.0643849i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −418.957 | + | 241.885i | −0.426202 | + | 0.246068i | −0.697727 | − | 0.716363i | \(-0.745805\pi\) |
0.271525 | + | 0.962431i | \(0.412472\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −353.019 | − | 146.885i | −0.357669 | − | 0.148820i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 273.507i | − | 0.276549i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1071.66 | −1.08139 | −0.540695 | − | 0.841219i | \(-0.681839\pi\) | ||||
−0.540695 | + | 0.841219i | \(0.681839\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 983.671 | + | 1286.19i | 0.990606 | + | 1.29525i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 155.387 | + | 269.139i | 0.155855 | + | 0.269949i | 0.933370 | − | 0.358916i | \(-0.116853\pi\) |
−0.777515 | + | 0.628864i | \(0.783520\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 498.310 | − | 203.619i | 0.498809 | − | 0.203823i |
(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 | 900.3.p.d.401.1 | yes | 16 | |
3.2 | odd | 2 | 2700.3.p.e.2501.6 | 16 | |||
5.2 | odd | 4 | 900.3.u.d.149.9 | 32 | |||
5.3 | odd | 4 | 900.3.u.d.149.8 | 32 | |||
5.4 | even | 2 | 900.3.p.e.401.8 | yes | 16 | ||
9.2 | odd | 6 | inner | 900.3.p.d.101.1 | ✓ | 16 | |
9.7 | even | 3 | 2700.3.p.e.1601.6 | 16 | |||
15.2 | even | 4 | 2700.3.u.d.449.6 | 32 | |||
15.8 | even | 4 | 2700.3.u.d.449.11 | 32 | |||
15.14 | odd | 2 | 2700.3.p.d.2501.3 | 16 | |||
45.2 | even | 12 | 900.3.u.d.749.8 | 32 | |||
45.7 | odd | 12 | 2700.3.u.d.2249.11 | 32 | |||
45.29 | odd | 6 | 900.3.p.e.101.8 | yes | 16 | ||
45.34 | even | 6 | 2700.3.p.d.1601.3 | 16 | |||
45.38 | even | 12 | 900.3.u.d.749.9 | 32 | |||
45.43 | odd | 12 | 2700.3.u.d.2249.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.p.d.101.1 | ✓ | 16 | 9.2 | odd | 6 | inner | |
900.3.p.d.401.1 | yes | 16 | 1.1 | even | 1 | trivial | |
900.3.p.e.101.8 | yes | 16 | 45.29 | odd | 6 | ||
900.3.p.e.401.8 | yes | 16 | 5.4 | even | 2 | ||
900.3.u.d.149.8 | 32 | 5.3 | odd | 4 | |||
900.3.u.d.149.9 | 32 | 5.2 | odd | 4 | |||
900.3.u.d.749.8 | 32 | 45.2 | even | 12 | |||
900.3.u.d.749.9 | 32 | 45.38 | even | 12 | |||
2700.3.p.d.1601.3 | 16 | 45.34 | even | 6 | |||
2700.3.p.d.2501.3 | 16 | 15.14 | odd | 2 | |||
2700.3.p.e.1601.6 | 16 | 9.7 | even | 3 | |||
2700.3.p.e.2501.6 | 16 | 3.2 | odd | 2 | |||
2700.3.u.d.449.6 | 32 | 15.2 | even | 4 | |||
2700.3.u.d.449.11 | 32 | 15.8 | even | 4 | |||
2700.3.u.d.2249.6 | 32 | 45.43 | odd | 12 | |||
2700.3.u.d.2249.11 | 32 | 45.7 | odd | 12 |