Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(49,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.bv (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 312) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.49 |
Dual form | 624.2.bv.c.433.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.73205i | 0.774597i | 0.921954 | + | 0.387298i | \(0.126592\pi\) | ||||
−0.921954 | + | 0.387298i | \(0.873408\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.633975 | − | 0.366025i | −0.239620 | − | 0.138345i | 0.375382 | − | 0.926870i | \(-0.377511\pi\) |
−0.615002 | + | 0.788526i | \(0.710845\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.633975 | − | 0.366025i | 0.191151 | − | 0.110361i | −0.401371 | − | 0.915916i | \(-0.631466\pi\) |
0.592521 | + | 0.805555i | \(0.298133\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.59808 | + | 2.50000i | 0.720577 | + | 0.693375i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | − | 0.866025i | 0.387298 | − | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.86603 | + | 3.23205i | −0.452578 | + | 0.783887i | −0.998545 | − | 0.0539188i | \(-0.982829\pi\) |
0.545968 | + | 0.837806i | \(0.316162\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.09808 | + | 0.633975i | 0.251916 | + | 0.145444i | 0.620641 | − | 0.784095i | \(-0.286872\pi\) |
−0.368725 | + | 0.929538i | \(0.620206\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.732051i | 0.159747i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.09808 | + | 1.90192i | 0.228965 | + | 0.396579i | 0.957502 | − | 0.288428i | \(-0.0931326\pi\) |
−0.728537 | + | 0.685007i | \(0.759799\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.96410 | + | 5.13397i | 0.550420 | + | 0.953355i | 0.998244 | + | 0.0592336i | \(0.0188657\pi\) |
−0.447824 | + | 0.894122i | \(0.647801\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46410i | 0.981382i | 0.871334 | + | 0.490691i | \(0.163256\pi\) | ||||
−0.871334 | + | 0.490691i | \(0.836744\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.633975 | − | 0.366025i | −0.110361 | − | 0.0637168i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.633975 | − | 1.09808i | 0.107161 | − | 0.185609i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.33013 | − | 4.23205i | 1.20507 | − | 0.695745i | 0.243388 | − | 0.969929i | \(-0.421741\pi\) |
0.961677 | + | 0.274184i | \(0.0884078\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.866025 | − | 3.50000i | 0.138675 | − | 0.560449i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.33013 | + | 2.50000i | −0.676252 | + | 0.390434i | −0.798441 | − | 0.602072i | \(-0.794342\pi\) |
0.122189 | + | 0.992507i | \(0.461009\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.901924 | + | 1.56218i | −0.137542 | + | 0.238230i | −0.926566 | − | 0.376133i | \(-0.877254\pi\) |
0.789024 | + | 0.614363i | \(0.210587\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50000 | − | 0.866025i | −0.223607 | − | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.73205i | 0.981971i | 0.871168 | + | 0.490985i | \(0.163363\pi\) | ||||
−0.871168 | + | 0.490985i | \(0.836637\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.23205 | − | 5.59808i | −0.461722 | − | 0.799725i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.73205 | 0.522592 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.92820 | 0.814301 | 0.407151 | − | 0.913361i | \(-0.366522\pi\) | ||||
0.407151 | + | 0.913361i | \(0.366522\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.633975 | + | 1.09808i | 0.0854851 | + | 0.148065i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.26795i | − | 0.167944i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.86603 | − | 8.42820i | 0.623031 | − | 1.07912i | −0.365887 | − | 0.930659i | \(-0.619234\pi\) |
0.988918 | − | 0.148462i | \(-0.0474322\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.633975 | − | 0.366025i | 0.0798733 | − | 0.0461149i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.33013 | + | 4.50000i | −0.537086 | + | 0.558156i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.56218 | − | 2.63397i | 0.557359 | − | 0.321791i | −0.194726 | − | 0.980858i | \(-0.562382\pi\) |
0.752085 | + | 0.659066i | \(0.229048\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.09808 | − | 1.90192i | 0.132193 | − | 0.228965i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.09808 | + | 4.09808i | 0.842387 | + | 0.486352i | 0.858075 | − | 0.513525i | \(-0.171661\pi\) |
−0.0156881 | + | 0.999877i | \(0.504994\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.19615i | − | 0.139999i | −0.997547 | − | 0.0699995i | \(-0.977700\pi\) | ||
0.997547 | − | 0.0699995i | \(-0.0222998\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | − | 1.73205i | −0.115470 | − | 0.200000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.535898 | −0.0610713 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3923 | −1.39424 | −0.697122 | − | 0.716953i | \(-0.745536\pi\) | ||||
−0.697122 | + | 0.716953i | \(0.745536\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.6603i | 1.71894i | 0.511189 | + | 0.859468i | \(0.329205\pi\) | ||||
−0.511189 | + | 0.859468i | \(0.670795\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.59808 | − | 3.23205i | −0.607197 | − | 0.350565i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.96410 | − | 5.13397i | 0.317785 | − | 0.550420i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.19615 | + | 1.26795i | −0.232792 | + | 0.134402i | −0.611859 | − | 0.790967i | \(-0.709578\pi\) |
0.379068 | + | 0.925369i | \(0.376245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.732051 | − | 2.53590i | −0.0767398 | − | 0.265834i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.73205 | − | 2.73205i | 0.490691 | − | 0.283300i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.09808 | + | 1.90192i | −0.112660 | + | 0.195133i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.66025 | − | 5.00000i | −0.879316 | − | 0.507673i | −0.00888289 | − | 0.999961i | \(-0.502828\pi\) |
−0.870433 | + | 0.492287i | \(0.836161\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.732051i | 0.0735739i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.23205 | − | 12.5263i | −0.719616 | − | 1.24641i | −0.961152 | − | 0.276020i | \(-0.910985\pi\) |
0.241536 | − | 0.970392i | \(-0.422349\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.73205 | −0.269197 | −0.134598 | − | 0.990900i | \(-0.542974\pi\) | ||||
−0.134598 | + | 0.990900i | \(0.542974\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.26795 | −0.123739 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.56218 | − | 13.0981i | −0.731063 | − | 1.26624i | −0.956429 | − | 0.291965i | \(-0.905691\pi\) |
0.225366 | − | 0.974274i | \(-0.427642\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.392305i | 0.0375760i | 0.999823 | + | 0.0187880i | \(0.00598076\pi\) | ||||
−0.999823 | + | 0.0187880i | \(0.994019\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.33013 | − | 4.23205i | −0.695745 | − | 0.401688i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.33013 | + | 4.03590i | −0.219200 | + | 0.379665i | −0.954564 | − | 0.298007i | \(-0.903678\pi\) |
0.735364 | + | 0.677673i | \(0.237011\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.29423 | + | 1.90192i | −0.307188 | + | 0.177355i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.46410 | + | 1.00000i | −0.320256 | + | 0.0924500i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.36603 | − | 1.36603i | 0.216893 | − | 0.125223i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.23205 | + | 9.06218i | −0.475641 | + | 0.823834i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.33013 | + | 2.50000i | 0.390434 | + | 0.225417i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00000 | − | 3.46410i | −0.177471 | − | 0.307389i | 0.763542 | − | 0.645758i | \(-0.223458\pi\) |
−0.941014 | + | 0.338368i | \(0.890125\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.80385 | 0.158820 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.3205 | −1.68804 | −0.844020 | − | 0.536311i | \(-0.819817\pi\) | ||||
−0.844020 | + | 0.536311i | \(0.819817\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.464102 | − | 0.803848i | −0.0402427 | − | 0.0697024i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.73205i | 0.149071i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.7942 | − | 6.23205i | −0.922213 | − | 0.532440i | −0.0378727 | − | 0.999283i | \(-0.512058\pi\) |
−0.884340 | + | 0.466843i | \(0.845391\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000 | − | 17.3205i | 0.848189 | − | 1.46911i | −0.0346338 | − | 0.999400i | \(-0.511026\pi\) |
0.882823 | − | 0.469706i | \(-0.155640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.83013 | − | 3.36603i | 0.490985 | − | 0.283470i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.56218 | + | 0.633975i | 0.214260 | + | 0.0530156i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.89230 | + | 5.13397i | −0.738466 | + | 0.426353i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.23205 | + | 5.59808i | −0.266575 | + | 0.461722i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.30385 | + | 4.79423i | 0.680278 | + | 0.392759i | 0.799960 | − | 0.600054i | \(-0.204854\pi\) |
−0.119682 | + | 0.992812i | \(0.538187\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 20.7321i | − | 1.68715i | −0.537011 | − | 0.843575i | \(-0.680447\pi\) | ||
0.537011 | − | 0.843575i | \(-0.319553\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.86603 | − | 3.23205i | −0.150859 | − | 0.261296i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.46410 | −0.760175 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0526 | 1.20132 | 0.600662 | − | 0.799503i | \(-0.294904\pi\) | ||||
0.600662 | + | 0.799503i | \(0.294904\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.96410 | − | 5.13397i | −0.235069 | − | 0.407151i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.60770i | − | 0.126704i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.66025 | + | 3.26795i | 0.443345 | + | 0.255966i | 0.705016 | − | 0.709192i | \(-0.250940\pi\) |
−0.261670 | + | 0.965157i | \(0.584273\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.633975 | − | 1.09808i | 0.0493549 | − | 0.0854851i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.73205 | − | 2.73205i | 0.366177 | − | 0.211412i | −0.305610 | − | 0.952157i | \(-0.598860\pi\) |
0.671787 | + | 0.740744i | \(0.265527\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | + | 12.9904i | 0.0384615 | + | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.09808 | + | 0.633975i | −0.0839720 | + | 0.0484812i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.26795 | − | 9.12436i | 0.400515 | − | 0.693712i | −0.593273 | − | 0.805001i | \(-0.702165\pi\) |
0.993788 | + | 0.111289i | \(0.0354980\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.26795 | − | 0.732051i | −0.0958479 | − | 0.0553378i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.63397 | − | 14.9545i | −0.645334 | − | 1.11775i | −0.984224 | − | 0.176925i | \(-0.943385\pi\) |
0.338891 | − | 0.940826i | \(-0.389948\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.80385 | −0.654385 | −0.327192 | − | 0.944958i | \(-0.606103\pi\) | ||||
−0.327192 | + | 0.944958i | \(0.606103\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.73205 | −0.719414 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.33013 | + | 12.6962i | 0.538922 | + | 0.933440i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.73205i | 0.199787i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.633975 | − | 0.366025i | −0.0461149 | − | 0.0266244i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.535898 | + | 0.928203i | −0.0387762 | + | 0.0671624i | −0.884762 | − | 0.466043i | \(-0.845679\pi\) |
0.845986 | + | 0.533205i | \(0.179013\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.16025 | − | 4.13397i | 0.515406 | − | 0.297570i | −0.219647 | − | 0.975579i | \(-0.570490\pi\) |
0.735053 | + | 0.678009i | \(0.237157\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.06218 | + | 1.50000i | 0.434122 | + | 0.107417i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.9282 | − | 7.46410i | 0.921096 | − | 0.531795i | 0.0371117 | − | 0.999311i | \(-0.488184\pi\) |
0.883985 | + | 0.467516i | \(0.154851\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.83013 | − | 15.2942i | 0.625951 | − | 1.08418i | −0.362405 | − | 0.932021i | \(-0.618044\pi\) |
0.988356 | − | 0.152158i | \(-0.0486224\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.56218 | − | 2.63397i | −0.321791 | − | 0.185786i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 4.33975i | − | 0.304590i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.33013 | − | 7.50000i | −0.302429 | − | 0.523823i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.19615 | −0.152643 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.928203 | 0.0642052 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6603 | + | 20.1962i | 0.802725 | + | 1.39036i | 0.917816 | + | 0.397006i | \(0.129951\pi\) |
−0.115091 | + | 0.993355i | \(0.536716\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.19615i | − | 0.561591i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.70577 | − | 1.56218i | −0.184532 | − | 0.106540i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | − | 3.46410i | 0.135769 | − | 0.235159i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.03590 | + | 0.598076i | −0.0699995 | + | 0.0404142i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.9282 | + | 3.73205i | −0.869645 | + | 0.251045i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.4641 | − | 12.3923i | 1.43734 | − | 0.829850i | 0.439678 | − | 0.898155i | \(-0.355093\pi\) |
0.997664 | + | 0.0683053i | \(0.0217592\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | + | 1.73205i | −0.0666667 | + | 0.115470i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.9019 | + | 8.02628i | 0.922703 | + | 0.532723i | 0.884496 | − | 0.466547i | \(-0.154502\pi\) |
0.0382067 | + | 0.999270i | \(0.487835\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.8564i | 1.84080i | 0.390974 | + | 0.920402i | \(0.372138\pi\) | ||||
−0.390974 | + | 0.920402i | \(0.627862\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.267949 | + | 0.464102i | 0.0176298 | + | 0.0305356i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.00000 | 0.131024 | 0.0655122 | − | 0.997852i | \(-0.479132\pi\) | ||||
0.0655122 | + | 0.997852i | \(0.479132\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.6603 | −0.760631 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.19615 | + | 10.7321i | 0.402483 | + | 0.697122i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.7321i | 1.72915i | 0.502502 | + | 0.864576i | \(0.332413\pi\) | ||||
−0.502502 | + | 0.864576i | \(0.667587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.6244 | − | 11.3301i | −1.26412 | − | 0.729838i | −0.290248 | − | 0.956952i | \(-0.593738\pi\) |
−0.973868 | + | 0.227114i | \(0.927071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.69615 | − | 5.59808i | 0.619464 | − | 0.357648i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.26795 | + | 4.39230i | 0.0806777 | + | 0.279476i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.5622 | − | 7.83013i | 0.859468 | − | 0.496214i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.73205 | − | 8.19615i | 0.298684 | − | 0.517337i | −0.677151 | − | 0.735844i | \(-0.736786\pi\) |
0.975835 | + | 0.218508i | \(0.0701189\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.39230 | + | 0.803848i | 0.0875335 | + | 0.0505375i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.46410i | 0.404798i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.86603 | − | 15.3564i | −0.553047 | − | 0.957906i | −0.998053 | − | 0.0623783i | \(-0.980131\pi\) |
0.445005 | − | 0.895528i | \(-0.353202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.19615 | −0.385010 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.92820 | −0.366947 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.16987 | + | 10.6865i | 0.380451 | + | 0.658960i | 0.991127 | − | 0.132921i | \(-0.0424356\pi\) |
−0.610676 | + | 0.791881i | \(0.709102\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.2679i | 0.630755i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.19615 | + | 1.26795i | 0.134402 | + | 0.0775972i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.73205 | + | 8.19615i | −0.288518 | + | 0.499728i | −0.973456 | − | 0.228873i | \(-0.926496\pi\) |
0.684938 | + | 0.728601i | \(0.259829\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8564 | + | 8.00000i | −0.841717 | + | 0.485965i | −0.857847 | − | 0.513905i | \(-0.828199\pi\) |
0.0161307 | + | 0.999870i | \(0.494865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.83013 | + | 1.90192i | −0.110764 | + | 0.115110i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.26795 | − | 0.732051i | 0.0764602 | − | 0.0441443i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.06218 | + | 7.03590i | −0.244073 | + | 0.422746i | −0.961870 | − | 0.273505i | \(-0.911817\pi\) |
0.717798 | + | 0.696252i | \(0.245150\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.73205 | − | 2.73205i | −0.283300 | − | 0.163564i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.7128i | − | 1.47424i | −0.675760 | − | 0.737121i | \(-0.736185\pi\) | ||
0.675760 | − | 0.737121i | \(-0.263815\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.7583 | + | 18.6340i | 0.639516 | + | 1.10767i | 0.985539 | + | 0.169449i | \(0.0541987\pi\) |
−0.346023 | + | 0.938226i | \(0.612468\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.19615 | 0.130089 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.66025 | 0.216058 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.53590 | + | 2.66025i | 0.0903470 | + | 0.156486i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.0000i | 0.586210i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.83975 | − | 1.06218i | −0.107479 | − | 0.0620531i | 0.445297 | − | 0.895383i | \(-0.353098\pi\) |
−0.552776 | + | 0.833330i | \(0.686431\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.633975 | − | 0.366025i | 0.0367869 | − | 0.0212389i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.90192 | + | 7.68653i | −0.109991 | + | 0.444524i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.14359 | − | 0.660254i | 0.0659156 | − | 0.0380564i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.23205 | + | 12.5263i | −0.415470 | + | 0.719616i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.5981 | + | 8.42820i | 0.835883 | + | 0.482598i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.7321i | 0.612510i | 0.951949 | + | 0.306255i | \(0.0990761\pi\) | ||||
−0.951949 | + | 0.306255i | \(0.900924\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.36603 | + | 2.36603i | 0.0777105 | + | 0.134598i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.33975 | −0.246084 | −0.123042 | − | 0.992401i | \(-0.539265\pi\) | ||||
−0.123042 | + | 0.992401i | \(0.539265\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.32051 | 0.187686 | 0.0938431 | − | 0.995587i | \(-0.470085\pi\) | ||||
0.0938431 | + | 0.995587i | \(0.470085\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.633975 | + | 1.09808i | 0.0357204 | + | 0.0618696i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 11.1962i | − | 0.628839i | −0.949284 | − | 0.314419i | \(-0.898190\pi\) | ||
0.949284 | − | 0.314419i | \(-0.101810\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.75833 | + | 2.16987i | 0.210426 | + | 0.121490i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.56218 | + | 13.0981i | −0.422080 | + | 0.731063i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.09808 | + | 2.36603i | −0.228023 | + | 0.131649i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.19615 | + | 5.00000i | 0.288231 | + | 0.277350i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.339746 | − | 0.196152i | 0.0187880 | − | 0.0108473i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.46410 | − | 4.26795i | 0.135850 | − | 0.235300i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3923 | − | 6.00000i | −0.571213 | − | 0.329790i | 0.186421 | − | 0.982470i | \(-0.440311\pi\) |
−0.757634 | + | 0.652680i | \(0.773645\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.46410i | 0.463830i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.56218 | + | 7.90192i | 0.249258 | + | 0.431728i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.9282 | 0.976611 | 0.488306 | − | 0.872673i | \(-0.337615\pi\) | ||||
0.488306 | + | 0.872673i | \(0.337615\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.66025 | 0.253110 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | + | 3.46410i | 0.108306 | + | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.85641i | 0.532196i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.29423 | + | 1.90192i | 0.177355 | + | 0.102396i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.7583 | − | 23.8301i | 0.738586 | − | 1.27927i | −0.214546 | − | 0.976714i | \(-0.568827\pi\) |
0.953132 | − | 0.302554i | \(-0.0978394\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.26795 | + | 4.19615i | −0.389044 | + | 0.224615i | −0.681746 | − | 0.731589i | \(-0.738779\pi\) |
0.292702 | + | 0.956204i | \(0.405446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.59808 | + | 2.50000i | 0.138675 | + | 0.133440i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.1865 | − | 12.2321i | 1.12765 | − | 0.651046i | 0.184304 | − | 0.982869i | \(-0.440997\pi\) |
0.943342 | + | 0.331823i | \(0.107664\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.09808 | + | 12.2942i | −0.376727 | + | 0.652510i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.36603 | − | 1.36603i | −0.125223 | − | 0.0722977i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 19.5167i | − | 1.03005i | −0.857175 | − | 0.515025i | \(-0.827783\pi\) | ||
0.857175 | − | 0.515025i | \(-0.172217\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.69615 | − | 15.0622i | −0.457692 | − | 0.792746i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.4641 | 0.549223 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.07180 | 0.108443 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.5622 | + | 20.0263i | 0.603541 | + | 1.04536i | 0.992280 | + | 0.124016i | \(0.0395773\pi\) |
−0.388740 | + | 0.921348i | \(0.627089\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 5.00000i | − | 0.260290i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.75833 | − | 2.16987i | −0.195123 | − | 0.112654i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.66987 | − | 13.2846i | 0.397131 | − | 0.687851i | −0.596240 | − | 0.802806i | \(-0.703339\pi\) |
0.993371 | + | 0.114955i | \(0.0366725\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.5000 | − | 6.06218i | 0.542218 | − | 0.313050i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.13397 | + | 20.7487i | −0.264413 | + | 1.06861i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.5167 | − | 18.1962i | 1.61890 | − | 0.934674i | 0.631697 | − | 0.775215i | \(-0.282358\pi\) |
0.987205 | − | 0.159459i | \(-0.0509748\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.00000 | + | 3.46410i | −0.102463 | + | 0.177471i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.5885 | + | 17.6603i | 1.56300 | + | 0.902397i | 0.996952 | + | 0.0780229i | \(0.0248607\pi\) |
0.566046 | + | 0.824374i | \(0.308473\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 0.928203i | − | 0.0473056i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.901924 | − | 1.56218i | −0.0458474 | − | 0.0794100i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.4641 | −1.24038 | −0.620190 | − | 0.784452i | \(-0.712944\pi\) | ||||
−0.620190 | + | 0.784452i | \(0.712944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.19615 | −0.414497 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.66025 | + | 16.7321i | 0.487295 | + | 0.844020i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 21.4641i | − | 1.07998i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.12436 | − | 5.26795i | −0.457938 | − | 0.264391i | 0.253239 | − | 0.967404i | \(-0.418504\pi\) |
−0.711177 | + | 0.703013i | \(0.751838\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.464102 | + | 0.803848i | −0.0232341 | + | 0.0402427i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.4545 | − | 7.76795i | 0.671885 | − | 0.387913i | −0.124906 | − | 0.992169i | \(-0.539863\pi\) |
0.796790 | + | 0.604256i | \(0.206529\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.6603 | + | 14.1962i | −0.680466 | + | 0.707161i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.50000 | − | 0.866025i | 0.0745356 | − | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.09808 | − | 5.36603i | 0.153566 | − | 0.265984i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.7487 | + | 11.4019i | 0.976511 | + | 0.563789i | 0.901215 | − | 0.433372i | \(-0.142677\pi\) |
0.0752960 | + | 0.997161i | \(0.476010\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.4641i | 0.614809i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.1244 | −1.33148 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.0000 | −0.979404 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.1962 | − | 28.0526i | −0.791234 | − | 1.37046i | −0.925203 | − | 0.379472i | \(-0.876106\pi\) |
0.133970 | − | 0.990985i | \(-0.457228\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000i | 0.243685i | 0.992549 | + | 0.121843i | \(0.0388803\pi\) | ||||
−0.992549 | + | 0.121843i | \(0.961120\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.83013 | − | 3.36603i | −0.283470 | − | 0.163662i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.73205 | + | 6.46410i | −0.181031 | + | 0.313555i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.16987 | + | 3.56218i | −0.298581 | + | 0.172386i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.732051 | − | 2.53590i | −0.0353437 | − | 0.122434i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.70577 | − | 5.02628i | 0.419342 | − | 0.242107i | −0.275454 | − | 0.961314i | \(-0.588828\pi\) |
0.694796 | + | 0.719207i | \(0.255495\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.4282 | + | 26.7224i | −0.741432 | + | 1.28420i | 0.210411 | + | 0.977613i | \(0.432520\pi\) |
−0.951843 | + | 0.306585i | \(0.900814\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.89230 | + | 5.13397i | 0.426353 | + | 0.246155i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.78461i | 0.133206i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.0981 | − | 17.4904i | −0.481955 | − | 0.834770i | 0.517831 | − | 0.855483i | \(-0.326740\pi\) |
−0.999785 | + | 0.0207128i | \(0.993406\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.46410 | 0.307814 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.3205 | 0.727899 | 0.363950 | − | 0.931419i | \(-0.381428\pi\) | ||||
0.363950 | + | 0.931419i | \(0.381428\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.19615 | − | 3.80385i | −0.104108 | − | 0.180320i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 9.58846i | − | 0.453518i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.1244 | + | 15.6603i | 1.28008 | + | 0.739053i | 0.976862 | − | 0.213869i | \(-0.0686066\pi\) |
0.303215 | + | 0.952922i | \(0.401940\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.83013 | + | 3.16987i | −0.0861773 | + | 0.149263i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.9545 | + | 10.3660i | −0.843575 | + | 0.487038i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.39230 | − | 1.26795i | 0.205914 | − | 0.0594424i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.8397 | − | 9.72243i | 0.787730 | − | 0.454796i | −0.0514327 | − | 0.998676i | \(-0.516379\pi\) |
0.839163 | + | 0.543880i | \(0.183045\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.86603 | + | 3.23205i | −0.0870986 | + | 0.150859i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.08846 | − | 1.20577i | −0.0972692 | − | 0.0561584i | 0.450576 | − | 0.892738i | \(-0.351219\pi\) |
−0.547846 | + | 0.836580i | \(0.684552\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.6603i | 1.09959i | 0.835301 | + | 0.549793i | \(0.185293\pi\) | ||||
−0.835301 | + | 0.549793i | \(0.814707\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.73205 | + | 8.19615i | 0.219444 | + | 0.380087i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.66025 | −0.261925 | −0.130963 | − | 0.991387i | \(-0.541807\pi\) | ||||
−0.130963 | + | 0.991387i | \(0.541807\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.85641 | −0.178072 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.52628 | − | 13.0359i | −0.346793 | − | 0.600662i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.32051i | 0.0607170i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.19615 | + | 1.26795i | 0.100766 | + | 0.0581775i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.96410 | + | 5.13397i | −0.135717 | + | 0.235069i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.73205 | + | 2.73205i | −0.216213 | + | 0.124831i | −0.604195 | − | 0.796836i | \(-0.706505\pi\) |
0.387983 | + | 0.921667i | \(0.373172\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.6244 | + | 7.33013i | 1.35075 | + | 0.334225i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.39230 | + | 0.803848i | −0.0633521 | + | 0.0365763i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.66025 | − | 15.0000i | 0.393242 | − | 0.681115i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.4904 | − | 15.2942i | −1.20039 | − | 0.693048i | −0.239751 | − | 0.970834i | \(-0.577066\pi\) |
−0.960643 | + | 0.277787i | \(0.910399\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6.53590i | − | 0.295564i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.9545 | − | 34.5622i | −0.900533 | − | 1.55977i | −0.826803 | − | 0.562491i | \(-0.809843\pi\) |
−0.0737298 | − | 0.997278i | \(-0.523490\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.1244 | −0.996431 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.26795 | −0.0569901 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.00000 | − | 5.19615i | −0.134568 | − | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13.8564i | − | 0.620298i | −0.950688 | − | 0.310149i | \(-0.899621\pi\) | ||
0.950688 | − | 0.310149i | \(-0.100379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.73205 | − | 2.73205i | −0.211412 | − | 0.122059i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.36603 | − | 11.0263i | 0.283847 | − | 0.491638i | −0.688482 | − | 0.725254i | \(-0.741723\pi\) |
0.972329 | + | 0.233616i | \(0.0750559\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.6962 | − | 12.5263i | 0.965466 | − | 0.557412i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.0000 | − | 6.92820i | 0.488527 | − | 0.307692i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.37564 | − | 0.794229i | 0.0609744 | − | 0.0352036i | −0.469203 | − | 0.883090i | \(-0.655459\pi\) |
0.530177 | + | 0.847887i | \(0.322125\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.437822 | + | 0.758330i | −0.0193681 | + | 0.0335466i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.09808 | + | 0.633975i | 0.0484812 | + | 0.0279907i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 4.73205i | − | 0.208519i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.46410 | + | 4.26795i | 0.108371 | + | 0.187704i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.5359 | −0.462475 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.9808 | −1.40110 | −0.700551 | − | 0.713602i | \(-0.747063\pi\) | ||||
−0.700551 | + | 0.713602i | \(0.747063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.2942 | + | 19.5622i | 0.493862 | + | 0.855394i | 0.999975 | − | 0.00707295i | \(-0.00225141\pi\) |
−0.506113 | + | 0.862467i | \(0.668918\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.46410i | 0.0638986i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.6603 | − | 10.1962i | −0.769293 | − | 0.444151i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.08846 | − | 15.7417i | 0.395150 | − | 0.684420i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.5000 | − | 4.33013i | −0.758009 | − | 0.187559i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.6865 | − | 13.0981i | 0.980824 | − | 0.566279i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.63397 | + | 14.9545i | −0.372584 | + | 0.645334i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.09808 | − | 2.36603i | −0.176517 | − | 0.101912i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.39230i | 0.145847i | 0.997338 | + | 0.0729233i | \(0.0232328\pi\) | ||||
−0.997338 | + | 0.0729233i | \(0.976767\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.40192 | + | 7.62436i | 0.188905 | + | 0.327192i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.679492 | −0.0291062 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.0526 | −1.54150 | −0.770748 | − | 0.637140i | \(-0.780117\pi\) | ||||
−0.770748 | + | 0.637140i | \(0.780117\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.86603 | + | 8.42820i | 0.207677 | + | 0.359707i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.51666i | 0.320221i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.85641 | + | 4.53590i | 0.334088 | + | 0.192886i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.33013 | − | 12.6962i | 0.311147 | − | 0.538922i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.3564 | + | 15.7942i | −1.15913 | + | 0.669223i | −0.951095 | − | 0.308899i | \(-0.900040\pi\) |
−0.208033 | + | 0.978122i | \(0.566706\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.24871 | + | 1.80385i | −0.264292 | + | 0.0762946i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.36603 | − | 1.36603i | 0.0998937 | − | 0.0576736i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.53590 | − | 4.39230i | 0.106875 | − | 0.185114i | −0.807627 | − | 0.589693i | \(-0.799249\pi\) |
0.914503 | + | 0.404579i | \(0.132582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.99038 | − | 4.03590i | −0.294088 | − | 0.169792i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.732051i | 0.0307432i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.00000 | − | 13.8564i | −0.335377 | − | 0.580891i | 0.648180 | − | 0.761487i | \(-0.275531\pi\) |
−0.983557 | + | 0.180597i | \(0.942197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.66025 | 0.153177 | 0.0765884 | − | 0.997063i | \(-0.475597\pi\) | ||||
0.0765884 | + | 0.997063i | \(0.475597\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.07180 | 0.0447750 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.19615 | + | 3.80385i | 0.0915859 | + | 0.158631i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 5.58846i | − | 0.232651i | −0.993211 | − | 0.116325i | \(-0.962889\pi\) | ||
0.993211 | − | 0.116325i | \(-0.0371115\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.16025 | − | 4.13397i | −0.297570 | − | 0.171802i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.73205 | − | 9.92820i | 0.237806 | − | 0.411891i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.75833 | − | 2.16987i | 0.155654 | − | 0.0898670i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.73205 | − | 6.00000i | −0.0716115 | − | 0.248069i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.85641 | + | 1.07180i | −0.0766221 | + | 0.0442378i | −0.537822 | − | 0.843059i | \(-0.680753\pi\) |
0.461199 | + | 0.887296i | \(0.347419\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.46410 | + | 6.00000i | −0.142736 | + | 0.247226i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.9282 | − | 7.46410i | −0.531795 | − | 0.307032i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 34.1769i | − | 1.40348i | −0.712434 | − | 0.701739i | \(-0.752407\pi\) | ||
0.712434 | − | 0.701739i | \(-0.247593\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.36603 | + | 4.09808i | 0.0969976 | + | 0.168005i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.6603 | −0.722786 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.4641 | 1.36731 | 0.683653 | − | 0.729807i | \(-0.260390\pi\) | ||||
0.683653 | + | 0.729807i | \(0.260390\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.8205 | − | 23.9378i | −0.563750 | − | 0.976444i | −0.997165 | − | 0.0752494i | \(-0.976025\pi\) |
0.433414 | − | 0.901195i | \(-0.357309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.26795i | 0.214527i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.6962 | − | 9.06218i | −0.638139 | − | 0.368430i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.3923 | + | 35.3205i | −0.827698 | + | 1.43362i | 0.0721415 | + | 0.997394i | \(0.477017\pi\) |
−0.899840 | + | 0.436221i | \(0.856317\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.75833 | + | 2.16987i | −0.152295 | + | 0.0879277i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.8301 | + | 17.4904i | −0.680874 | + | 0.707585i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.45448 | + | 0.839746i | −0.0587460 | + | 0.0339170i | −0.529085 | − | 0.848569i | \(-0.677465\pi\) |
0.470339 | + | 0.882486i | \(0.344132\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.33013 | + | 7.50000i | −0.174608 | + | 0.302429i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.27757 | + | 1.89230i | 0.131950 | + | 0.0761813i | 0.564522 | − | 0.825418i | \(-0.309061\pi\) |
−0.432572 | + | 0.901599i | \(0.642394\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 23.6077i | − | 0.948873i | −0.880290 | − | 0.474437i | \(-0.842652\pi\) | ||
0.880290 | − | 0.474437i | \(-0.157348\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.09808 | + | 1.90192i | 0.0440643 | + | 0.0763216i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.85641 | 0.0743754 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.464102 | − | 0.803848i | −0.0185344 | − | 0.0321026i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.5885i | 1.25951i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.32051 | − | 3.07180i | −0.211806 | − | 0.122286i | 0.390344 | − | 0.920669i | \(-0.372356\pi\) |
−0.602150 | + | 0.798383i | \(0.705689\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.6603 | − | 20.1962i | 0.463453 | − | 0.802725i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.00000 | − | 3.46410i | 0.238103 | − | 0.137469i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.59808 | − | 22.6244i | 0.221804 | − | 0.896410i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.09808 | + | 4.09808i | −0.280796 | + | 0.162117i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.2583 | − | 28.1603i | 0.642165 | − | 1.11226i | −0.342783 | − | 0.939415i | \(-0.611370\pi\) |
0.984948 | − | 0.172849i | \(-0.0552971\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.0000 | + | 13.8564i | 0.946468 | + | 0.546443i | 0.891982 | − | 0.452071i | \(-0.149315\pi\) |
0.0544858 | + | 0.998515i | \(0.482648\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.12436i | 0.123021i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.1244 | − | 29.6603i | −0.673228 | − | 1.16606i | −0.976983 | − | 0.213315i | \(-0.931574\pi\) |
0.303756 | − | 0.952750i | \(-0.401759\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | −0.156772 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.2679 | − | 22.9808i | −0.519215 | − | 0.899307i | −0.999751 | − | 0.0223315i | \(-0.992891\pi\) |
0.480536 | − | 0.876975i | \(-0.340442\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 33.4641i | − | 1.30755i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.03590 | + | 0.598076i | 0.0404142 | + | 0.0233332i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.6603 | + | 37.5167i | −0.843764 | + | 1.46144i | 0.0429268 | + | 0.999078i | \(0.486332\pi\) |
−0.886691 | + | 0.462363i | \(0.847002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.3301 | + | 7.69615i | −0.518482 | + | 0.299346i | −0.736313 | − | 0.676641i | \(-0.763435\pi\) |
0.217831 | + | 0.975986i | \(0.430102\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.69615 | + | 9.33013i | 0.376567 | + | 0.362352i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.39230 | − | 0.803848i | 0.0539913 | − | 0.0311719i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.50962 | + | 11.2750i | −0.252053 | + | 0.436569i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.4641 | − | 12.3923i | −0.829850 | − | 0.479114i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.12436i | − | 0.275033i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.10770 | − | 5.38269i | −0.119793 | − | 0.207487i | 0.799893 | − | 0.600143i | \(-0.204890\pi\) |
−0.919685 | + | 0.392656i | \(0.871556\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.00000 | 0.0769800 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.5359 | 0.558660 | 0.279330 | − | 0.960195i | \(-0.409888\pi\) | ||||
0.279330 | + | 0.960195i | \(0.409888\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.66025 | + | 6.33975i | 0.140468 | + | 0.243297i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 16.0526i | − | 0.615135i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.78461 | − | 5.07180i | −0.336134 | − | 0.194067i | 0.322427 | − | 0.946594i | \(-0.395501\pi\) |
−0.658561 | + | 0.752527i | \(0.728835\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.7942 | − | 18.6962i | 0.412426 | − | 0.714343i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.1244 | − | 13.9282i | 0.920402 | − | 0.531394i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.4019 | + | 14.8205i | 0.586767 | + | 0.564616i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.95448 | + | 5.16987i | −0.340645 | + | 0.196671i | −0.660557 | − | 0.750776i | \(-0.729680\pi\) |
0.319912 | + | 0.947447i | \(0.396346\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.267949 | − | 0.464102i | 0.0101785 | − | 0.0176298i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.0000 | + | 17.3205i | 1.13796 | + | 0.657004i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 18.6603i | − | 0.706808i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.00000 | − | 1.73205i | −0.0378235 | − | 0.0655122i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.1051 | −1.21259 | −0.606297 | − | 0.795238i | \(-0.707346\pi\) | ||||
−0.606297 | + | 0.795238i | \(0.707346\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.7321 | 0.404767 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.83013 | + | 10.0981i | 0.219575 | + | 0.380316i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.5885i | 0.398220i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.1865 | − | 17.4282i | −1.13368 | − | 0.654530i | −0.188821 | − | 0.982011i | \(-0.560467\pi\) |
−0.944858 | + | 0.327482i | \(0.893800\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.19615 | − | 10.7321i | 0.232374 | − | 0.402483i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.3923 | + | 6.00000i | −0.389195 | + | 0.224702i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.09808 | + | 4.43782i | −0.0410657 | + | 0.165965i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.1506 | − | 13.3660i | 0.864576 | − | 0.499163i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.5885 | + | 32.1962i | −0.693232 | + | 1.20071i | 0.277540 | + | 0.960714i | \(0.410481\pi\) |
−0.970773 | + | 0.240000i | \(0.922853\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.73205 | + | 1.00000i | 0.0645049 | + | 0.0372419i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.6603i | 0.842744i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.92820 | + | 10.2679i | 0.220168 | + | 0.381342i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.26795 | 0.0470256 | 0.0235128 | − | 0.999724i | \(-0.492515\pi\) | ||||
0.0235128 | + | 0.999724i | \(0.492515\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.36603 | − | 5.83013i | −0.124497 | − | 0.215635i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.0000i | 1.29275i | 0.763018 | + | 0.646377i | \(0.223717\pi\) | ||||
−0.763018 | + | 0.646377i | \(0.776283\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.69615 | − | 5.59808i | −0.357648 | − | 0.206488i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.92820 | − | 3.33975i | 0.0710263 | − | 0.123021i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.4641 | − | 12.3923i | 0.789570 | − | 0.455858i | −0.0502413 | − | 0.998737i | \(-0.515999\pi\) |
0.839811 | + | 0.542879i | \(0.182666\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.16987 | − | 3.29423i | 0.116448 | − | 0.121017i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.8038 | + | 16.0526i | −1.02002 | + | 0.588911i | −0.914111 | − | 0.405464i | \(-0.867110\pi\) |
−0.105913 | + | 0.994375i | \(0.533777\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.30385 | + | 14.3827i | −0.304229 | + | 0.526941i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.5622 | − | 7.83013i | −0.496214 | − | 0.286489i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.0718i | 0.404555i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.830127 | + | 1.43782i | 0.0302918 | + | 0.0524669i | 0.880774 | − | 0.473537i | \(-0.157023\pi\) |
−0.850482 | + | 0.526004i | \(0.823690\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.46410 | −0.344891 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 35.9090 | 1.30686 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.3923 | − | 30.1244i | −0.632134 | − | 1.09489i | −0.987115 | − | 0.160015i | \(-0.948846\pi\) |
0.354981 | − | 0.934874i | \(-0.384487\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.60770i | − | 0.0583556i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.19615 | + | 4.73205i | 0.297110 | + | 0.171537i | 0.641144 | − | 0.767421i | \(-0.278460\pi\) |
−0.344034 | + | 0.938957i | \(0.611793\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.143594 | − | 0.248711i | 0.00519844 | − | 0.00900395i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.59808 | − | 3.23205i | 0.202399 | − | 0.116855i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.2679 | + | 19.7846i | −1.23573 | + | 0.713451i | −0.968219 | − | 0.250103i | \(-0.919536\pi\) |
−0.267515 | + | 0.963554i | \(0.586202\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.86603 | + | 15.3564i | −0.319302 | + | 0.553047i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.5167 | + | 23.3923i | 1.45728 | + | 0.841363i | 0.998877 | − | 0.0473801i | \(-0.0150872\pi\) |
0.458406 | + | 0.888743i | \(0.348421\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.9282i | 0.392553i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.09808 | + | 5.36603i | 0.111143 | + | 0.192505i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.33975 | −0.227145 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.96410 | + | 5.13397i | 0.105928 | + | 0.183473i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.0718i | 0.930542i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.51666 | + | 4.33975i | 0.267940 | + | 0.154695i | 0.627951 | − | 0.778253i | \(-0.283894\pi\) |
−0.360011 | + | 0.932948i | \(0.617227\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.16987 | − | 10.6865i | 0.219653 | − | 0.380451i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.95448 | − | 1.70577i | 0.105049 | − | 0.0606502i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.7128 | − | 9.73205i | 1.19718 | − | 0.345595i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.89230 | − | 5.13397i | 0.315378 | − | 0.182083i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.00000 | − | 5.19615i | 0.106265 | − | 0.184057i | −0.807989 | − | 0.589197i | \(-0.799444\pi\) |
0.914255 | + | 0.405140i | \(0.132777\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.7583 | − | 12.5622i | −0.769754 | − | 0.444418i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2.53590i | − | 0.0896016i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.437822 | − | 0.758330i | −0.0154504 | − | 0.0267609i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.78461 | 0.0981446 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.46410 | 0.333152 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.13397 | − | 1.96410i | −0.0398684 | − | 0.0690541i | 0.845403 | − | 0.534130i | \(-0.179361\pi\) |
−0.885271 | + | 0.465075i | \(0.846027\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 50.2487i | − | 1.76447i | −0.470808 | − | 0.882235i | \(-0.656038\pi\) | ||
0.470808 | − | 0.882235i | \(-0.343962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.8564 | + | 8.00000i | 0.485965 | + | 0.280572i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.66025 | + | 9.80385i | −0.198270 | + | 0.343414i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.98076 | + | 1.14359i | −0.0692981 | + | 0.0400093i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.56218 | + | 0.633975i | 0.0895297 | + | 0.0221529i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.0526 | − | 14.4641i | 0.874340 | − | 0.504801i | 0.00555219 | − | 0.999985i | \(-0.498233\pi\) |
0.868788 | + | 0.495184i | \(0.164899\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.0000 | − | 20.7846i | 0.418294 | − | 0.724506i | −0.577474 | − | 0.816409i | \(-0.695962\pi\) |
0.995768 | + | 0.0919029i | \(0.0292950\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.26795 | − | 0.732051i | −0.0441443 | − | 0.0254867i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.6077i | 1.23820i | 0.785312 | + | 0.619100i | \(0.212503\pi\) | ||||
−0.785312 | + | 0.619100i | \(0.787497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.1340 | + | 19.2846i | 0.386699 | + | 0.669782i | 0.992003 | − | 0.126212i | \(-0.0402819\pi\) |
−0.605304 | + | 0.795994i | \(0.706949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.12436 | 0.281831 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.1244 | 0.835859 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.73205 | + | 8.19615i | 0.163759 | + | 0.283640i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.46410i | 0.188867i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.53590 | − | 4.92820i | −0.294692 | − | 0.170140i | 0.345364 | − | 0.938469i | \(-0.387755\pi\) |
−0.640056 | + | 0.768328i | \(0.721089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.07180 | + | 5.32051i | −0.105924 | + | 0.183466i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.4019 | + | 12.3564i | −0.737121 | + | 0.425577i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.5000 | + | 0.866025i | −0.774024 | + | 0.0297922i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.63397 | − | 3.83013i | 0.227946 | − | 0.131605i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.7583 | − | 18.6340i | 0.369225 | − | 0.639516i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.0981 | + | 9.29423i | 0.551835 | + | 0.318602i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 56.0333i | 1.91854i | 0.282483 | + | 0.959272i | \(0.408842\pi\) | ||||
−0.282483 | + | 0.959272i | \(0.591158\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.09808 | − | 1.90192i | −0.0375534 | − | 0.0650444i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.5167 | −0.359242 | −0.179621 | − | 0.983736i | \(-0.557487\pi\) | ||||
−0.179621 | + | 0.983736i | \(0.557487\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.4449 | 0.834048 | 0.417024 | − | 0.908895i | \(-0.363073\pi\) | ||||
0.417024 | + | 0.908895i | \(0.363073\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.83013 | − | 3.16987i | −0.0623706 | − | 0.108029i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 10.3397i | − | 0.351969i | −0.984393 | − | 0.175985i | \(-0.943689\pi\) | ||
0.984393 | − | 0.175985i | \(-0.0563109\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.8038 | + | 9.12436i | 0.537347 | + | 0.310237i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.53590 | − | 2.66025i | 0.0521618 | − | 0.0903470i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.85641 | + | 4.53590i | −0.266510 | + | 0.153870i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.4378 | + | 4.56218i | 0.624742 | + | 0.154583i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.66025 | − | 5.00000i | 0.293105 | − | 0.169224i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.43782 | − | 7.68653i | 0.150026 | − | 0.259852i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.4545 | + | 9.50000i | 0.555628 | + | 0.320792i | 0.751389 | − | 0.659860i | \(-0.229384\pi\) |
−0.195761 | + | 0.980652i | \(0.562718\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.12436i | 0.0716527i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.2583 | + | 17.7679i | 0.345612 | + | 0.598617i | 0.985465 | − | 0.169880i | \(-0.0543380\pi\) |
−0.639853 | + | 0.768497i | \(0.721005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.7846 | 1.10329 | 0.551645 | − | 0.834079i | \(-0.314000\pi\) | ||||
0.551645 | + | 0.834079i | \(0.314000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.07180 | − | 1.85641i | −0.0359874 | − | 0.0623320i | 0.847471 | − | 0.530842i | \(-0.178124\pi\) |
−0.883458 | + | 0.468510i | \(0.844791\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.92820i | 0.0982088i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.633975 | − | 0.366025i | −0.0212389 | − | 0.0122623i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.26795 | + | 7.39230i | −0.142821 | + | 0.247374i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.9019 | − | 14.9545i | 0.865806 | − | 0.499873i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.60770 | − | 2.19615i | 0.254014 | − | 0.0733274i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.0526 | + | 16.1962i | −0.935605 | + | 0.540172i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.0622 | + | 19.1603i | −0.368535 | + | 0.638321i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.14359 | − | 0.660254i | −0.0380564 | − | 0.0219719i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 15.2487i | − | 0.506884i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.5167 | − | 33.8038i | −0.648040 | − | 1.12244i | −0.983590 | − | 0.180416i | \(-0.942256\pi\) |
0.335550 | − | 0.942022i | \(-0.391078\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.4641 | 0.479744 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.46410 | 0.313560 | 0.156780 | − | 0.987634i | \(-0.449889\pi\) | ||||
0.156780 | + | 0.987634i | \(0.449889\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.73205 | + | 9.92820i | 0.189703 | + | 0.328576i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 16.8564i | − | 0.557256i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.2487 | + | 7.07180i | 0.404488 | + | 0.233531i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.19615 | + | 7.26795i | −0.138418 | + | 0.239748i | −0.926898 | − | 0.375313i | \(-0.877535\pi\) |
0.788480 | + | 0.615061i | \(0.210869\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.29423 | − | 5.36603i | 0.306255 | − | 0.176817i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.19615 | + | 28.3923i | 0.269780 | + | 0.934544i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.6603 | − | 8.46410i | 0.482026 | − | 0.278298i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.36603 | − | 2.36603i | 0.0448662 | − | 0.0777105i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.5788 | + | 13.0359i | 0.740788 | + | 0.427694i | 0.822356 | − | 0.568974i | \(-0.192659\pi\) |
−0.0815680 | + | 0.996668i | \(0.525993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 8.19615i | − | 0.268618i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.16987 | + | 3.75833i | 0.0710385 | + | 0.123042i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.73205 | −0.154755 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.3205 | −1.77457 | −0.887287 | − | 0.461218i | \(-0.847413\pi\) | ||||
−0.887287 | + | 0.461218i | \(0.847413\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.66025 | − | 2.87564i | −0.0541803 | − | 0.0938431i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.7846i | 0.481965i | 0.970530 | + | 0.240982i | \(0.0774696\pi\) | ||||
−0.970530 | + | 0.240982i | \(0.922530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.50962 | − | 5.49038i | −0.309676 | − | 0.178791i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.633975 | − | 1.09808i | 0.0206232 | − | 0.0357204i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.3205 | − | 6.53590i | 0.367867 | − | 0.212388i | −0.304659 | − | 0.952461i | \(-0.598543\pi\) |
0.672526 | + | 0.740073i | \(0.265209\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.99038 | − | 3.10770i | 0.0970719 | − | 0.100880i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.69615 | + | 5.59808i | −0.314419 | + | 0.181530i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.39230 | + | 7.60770i | −0.142281 | + | 0.246437i | −0.928355 | − | 0.371694i | \(-0.878777\pi\) |
0.786074 | + | 0.618132i | \(0.212110\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.60770 | − | 0.928203i | −0.0520238 | − | 0.0300360i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 4.33975i | − | 0.140284i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.56218 | + | 7.90192i | 0.147320 | + | 0.255166i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.14359 | 0.0368901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.1244 | 0.487376 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.16025 | + | 12.4019i | 0.230497 | + | 0.399232i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.732051i | 0.0235412i | 0.999931 | + | 0.0117706i | \(0.00374678\pi\) | ||||
−0.999931 | + | 0.0117706i | \(0.996253\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.09808 | + | 2.36603i | 0.131649 | + | 0.0760077i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.1962 | + | 17.6603i | −0.327210 | + | 0.566745i | −0.981957 | − | 0.189104i | \(-0.939442\pi\) |
0.654747 | + | 0.755848i | \(0.272775\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.6795 | + | 7.32051i | −0.406486 | + | 0.234685i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.73205 | − | 7.00000i | 0.0554700 | − | 0.224179i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.5981 | + | 27.4808i | −1.52280 | + | 0.879187i | −0.523161 | + | 0.852234i | \(0.675247\pi\) |
−0.999637 | + | 0.0269534i | \(0.991419\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.928203 | + | 1.60770i | −0.0296655 | + | 0.0513822i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.339746 | − | 0.196152i | −0.0108473 | − | 0.00626266i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 26.6410i | − | 0.849716i | −0.905260 | − | 0.424858i | \(-0.860324\pi\) | ||
0.905260 | − | 0.424858i | \(-0.139676\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.9282 | + | 22.3923i | 0.411927 | + | 0.713478i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.92820 | −0.156866 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.96152 | −0.125969 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.43782 | − | 11.1506i | −0.204504 | − | 0.354212i | 0.745470 | − | 0.666539i | \(-0.232225\pi\) |
−0.949975 | + | 0.312327i | \(0.898892\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.0000i | 0.380808i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.4904 | + | 15.2942i | 0.839802 | + | 0.484860i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.9904 | − | 27.6962i | 0.506420 | − | 0.877146i | −0.493552 | − | 0.869716i | \(-0.664302\pi\) |
0.999972 | − | 0.00742963i | \(-0.00236495\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.33013 | − | 4.23205i | 0.231915 | − | 0.133896i |
(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 | 624.2.bv.c.49.2 | 4 | ||
3.2 | odd | 2 | 1872.2.by.g.1297.2 | 4 | |||
4.3 | odd | 2 | 312.2.bf.a.49.1 | ✓ | 4 | ||
12.11 | even | 2 | 936.2.bi.a.361.1 | 4 | |||
13.2 | odd | 12 | 8112.2.a.bw.1.2 | 2 | |||
13.4 | even | 6 | inner | 624.2.bv.c.433.2 | 4 | ||
13.11 | odd | 12 | 8112.2.a.br.1.1 | 2 | |||
39.17 | odd | 6 | 1872.2.by.g.433.2 | 4 | |||
52.3 | odd | 6 | 4056.2.c.k.337.4 | 4 | |||
52.11 | even | 12 | 4056.2.a.u.1.1 | 2 | |||
52.15 | even | 12 | 4056.2.a.t.1.2 | 2 | |||
52.23 | odd | 6 | 4056.2.c.k.337.1 | 4 | |||
52.43 | odd | 6 | 312.2.bf.a.121.1 | yes | 4 | ||
156.95 | even | 6 | 936.2.bi.a.433.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.bf.a.49.1 | ✓ | 4 | 4.3 | odd | 2 | ||
312.2.bf.a.121.1 | yes | 4 | 52.43 | odd | 6 | ||
624.2.bv.c.49.2 | 4 | 1.1 | even | 1 | trivial | ||
624.2.bv.c.433.2 | 4 | 13.4 | even | 6 | inner | ||
936.2.bi.a.361.1 | 4 | 12.11 | even | 2 | |||
936.2.bi.a.433.1 | 4 | 156.95 | even | 6 | |||
1872.2.by.g.433.2 | 4 | 39.17 | odd | 6 | |||
1872.2.by.g.1297.2 | 4 | 3.2 | odd | 2 | |||
4056.2.a.t.1.2 | 2 | 52.15 | even | 12 | |||
4056.2.a.u.1.1 | 2 | 52.11 | even | 12 | |||
4056.2.c.k.337.1 | 4 | 52.23 | odd | 6 | |||
4056.2.c.k.337.4 | 4 | 52.3 | odd | 6 | |||
8112.2.a.br.1.1 | 2 | 13.11 | odd | 12 | |||
8112.2.a.bw.1.2 | 2 | 13.2 | odd | 12 |