Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), 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: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 136.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.136 |
Dual form | 405.2.e.i.271.1 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | + | 2.36603i | −0.965926 | + | 1.67303i | −0.258819 | + | 0.965926i | \(0.583333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.73205 | − | 4.73205i | −1.36603 | − | 2.36603i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.633975 | − | 1.09808i | 0.239620 | − | 0.415034i | −0.720985 | − | 0.692950i | \(-0.756311\pi\) |
0.960605 | + | 0.277916i | \(0.0896439\pi\) | |||||||
\(8\) | 9.46410 | 3.34607 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.73205 | −0.863950 | ||||||||
\(11\) | −1.13397 | + | 1.96410i | −0.341906 | + | 0.592199i | −0.984787 | − | 0.173768i | \(-0.944406\pi\) |
0.642880 | + | 0.765967i | \(0.277739\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.73205 | + | 4.73205i | 0.757735 | + | 1.31243i | 0.944003 | + | 0.329936i | \(0.107027\pi\) |
−0.186269 | + | 0.982499i | \(0.559640\pi\) | |||||||
\(14\) | 1.73205 | + | 3.00000i | 0.462910 | + | 0.801784i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.46410 | + | 12.9282i | −1.86603 | + | 3.23205i | ||||
\(17\) | −0.732051 | −0.177548 | −0.0887742 | − | 0.996052i | \(-0.528295\pi\) | ||||
−0.0887742 | + | 0.996052i | \(0.528295\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.46410 | −0.565304 | −0.282652 | − | 0.959223i | \(-0.591214\pi\) | ||||
−0.282652 | + | 0.959223i | \(0.591214\pi\) | |||||||
\(20\) | 2.73205 | − | 4.73205i | 0.610905 | − | 1.05812i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.09808 | − | 5.36603i | −0.660512 | − | 1.14404i | ||||
\(23\) | 1.73205 | + | 3.00000i | 0.361158 | + | 0.625543i | 0.988152 | − | 0.153481i | \(-0.0490483\pi\) |
−0.626994 | + | 0.779024i | \(0.715715\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −14.9282 | −2.92766 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.92820 | −1.30931 | ||||||||
\(29\) | −3.59808 | + | 6.23205i | −0.668146 | + | 1.15726i | 0.310276 | + | 0.950646i | \(0.399579\pi\) |
−0.978422 | + | 0.206616i | \(0.933755\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50000 | + | 2.59808i | 0.269408 | + | 0.466628i | 0.968709 | − | 0.248199i | \(-0.0798387\pi\) |
−0.699301 | + | 0.714827i | \(0.746505\pi\) | |||||||
\(32\) | −10.9282 | − | 18.9282i | −1.93185 | − | 3.34607i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.00000 | − | 1.73205i | 0.171499 | − | 0.297044i | ||||
\(35\) | 1.26795 | 0.214323 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.732051 | 0.120348 | 0.0601742 | − | 0.998188i | \(-0.480834\pi\) | ||||
0.0601742 | + | 0.998188i | \(0.480834\pi\) | |||||||
\(38\) | 3.36603 | − | 5.83013i | 0.546041 | − | 0.945771i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.73205 | + | 8.19615i | 0.748203 | + | 1.29593i | ||||
\(41\) | 1.59808 | + | 2.76795i | 0.249578 | + | 0.432281i | 0.963409 | − | 0.268037i | \(-0.0863749\pi\) |
−0.713831 | + | 0.700318i | \(0.753042\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.09808 | − | 8.83013i | 0.777449 | − | 1.34658i | −0.155958 | − | 0.987764i | \(-0.549847\pi\) |
0.933408 | − | 0.358818i | \(-0.116820\pi\) | |||||||
\(44\) | 12.3923 | 1.86821 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.46410 | −1.39541 | ||||||||
\(47\) | −2.63397 | + | 4.56218i | −0.384205 | + | 0.665462i | −0.991659 | − | 0.128893i | \(-0.958858\pi\) |
0.607454 | + | 0.794355i | \(0.292191\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.69615 | + | 4.66987i | 0.385165 | + | 0.667125i | ||||
\(50\) | −1.36603 | − | 2.36603i | −0.193185 | − | 0.334607i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 14.9282 | − | 25.8564i | 2.07017 | − | 3.58564i | ||||
\(53\) | −3.26795 | −0.448887 | −0.224444 | − | 0.974487i | \(-0.572056\pi\) | ||||
−0.224444 | + | 0.974487i | \(0.572056\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.26795 | −0.305810 | ||||||||
\(56\) | 6.00000 | − | 10.3923i | 0.801784 | − | 1.38873i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.83013 | − | 17.0263i | −1.29076 | − | 2.23566i | ||||
\(59\) | −5.86603 | − | 10.1603i | −0.763691 | − | 1.32275i | −0.940936 | − | 0.338585i | \(-0.890052\pi\) |
0.177244 | − | 0.984167i | \(-0.443282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | + | 3.46410i | −0.256074 | + | 0.443533i | −0.965187 | − | 0.261562i | \(-0.915762\pi\) |
0.709113 | + | 0.705095i | \(0.249096\pi\) | |||||||
\(62\) | −8.19615 | −1.04091 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 29.8564 | 3.73205 | ||||||||
\(65\) | −2.73205 | + | 4.73205i | −0.338869 | + | 0.586939i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.73205 | + | 3.00000i | 0.211604 | + | 0.366508i | 0.952217 | − | 0.305424i | \(-0.0987981\pi\) |
−0.740613 | + | 0.671932i | \(0.765465\pi\) | |||||||
\(68\) | 2.00000 | + | 3.46410i | 0.242536 | + | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.73205 | + | 3.00000i | −0.207020 | + | 0.358569i | ||||
\(71\) | 0.267949 | 0.0317997 | 0.0158999 | − | 0.999874i | \(-0.494939\pi\) | ||||
0.0158999 | + | 0.999874i | \(0.494939\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.66025 | 1.13065 | 0.565324 | − | 0.824869i | \(-0.308751\pi\) | ||||
0.565324 | + | 0.824869i | \(0.308751\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.73205 | + | 11.6603i | 0.772219 | + | 1.33752i | ||||
\(77\) | 1.43782 | + | 2.49038i | 0.163855 | + | 0.283805i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.26795 | + | 7.39230i | −0.480182 | + | 0.831699i | −0.999742 | − | 0.0227349i | \(-0.992763\pi\) |
0.519560 | + | 0.854434i | \(0.326096\pi\) | |||||||
\(80\) | −14.9282 | −1.66902 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.73205 | −0.964294 | ||||||||
\(83\) | −4.09808 | + | 7.09808i | −0.449822 | + | 0.779115i | −0.998374 | − | 0.0570015i | \(-0.981846\pi\) |
0.548552 | + | 0.836117i | \(0.315179\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.366025 | − | 0.633975i | −0.0397010 | − | 0.0687642i | ||||
\(86\) | 13.9282 | + | 24.1244i | 1.50192 | + | 2.60140i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.7321 | + | 18.5885i | −1.14404 | + | 1.98154i | ||||
\(89\) | 5.19615 | 0.550791 | 0.275396 | − | 0.961331i | \(-0.411191\pi\) | ||||
0.275396 | + | 0.961331i | \(0.411191\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.92820 | 0.726273 | ||||||||
\(92\) | 9.46410 | − | 16.3923i | 0.986701 | − | 1.70902i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.19615 | − | 12.4641i | −0.742226 | − | 1.28557i | ||||
\(95\) | −1.23205 | − | 2.13397i | −0.126406 | − | 0.218941i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.83013 | + | 6.63397i | −0.388890 | + | 0.673578i | −0.992301 | − | 0.123853i | \(-0.960475\pi\) |
0.603410 | + | 0.797431i | \(0.293808\pi\) | |||||||
\(98\) | −14.7321 | −1.48816 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.46410 | 0.546410 | ||||||||
\(101\) | 7.33013 | − | 12.6962i | 0.729375 | − | 1.26331i | −0.227773 | − | 0.973714i | \(-0.573144\pi\) |
0.957148 | − | 0.289600i | \(-0.0935223\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.73205 | + | 6.46410i | 0.367730 | + | 0.636927i | 0.989210 | − | 0.146503i | \(-0.0468018\pi\) |
−0.621480 | + | 0.783430i | \(0.713468\pi\) | |||||||
\(104\) | 25.8564 | + | 44.7846i | 2.53543 | + | 4.39149i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.46410 | − | 7.73205i | 0.433592 | − | 0.751003i | ||||
\(107\) | 15.4641 | 1.49497 | 0.747486 | − | 0.664278i | \(-0.231261\pi\) | ||||
0.747486 | + | 0.664278i | \(0.231261\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.9282 | −1.90878 | −0.954388 | − | 0.298570i | \(-0.903490\pi\) | ||||
−0.954388 | + | 0.298570i | \(0.903490\pi\) | |||||||
\(110\) | 3.09808 | − | 5.36603i | 0.295390 | − | 0.511630i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.46410 | + | 16.3923i | 0.894274 | + | 1.54893i | ||||
\(113\) | 2.56218 | + | 4.43782i | 0.241029 | + | 0.417475i | 0.961008 | − | 0.276521i | \(-0.0891816\pi\) |
−0.719978 | + | 0.693997i | \(0.755848\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.73205 | + | 3.00000i | −0.161515 | + | 0.279751i | ||||
\(116\) | 39.3205 | 3.65082 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 32.0526 | 2.95068 | ||||||||
\(119\) | −0.464102 | + | 0.803848i | −0.0425441 | + | 0.0736886i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.92820 | + | 5.07180i | 0.266200 | + | 0.461072i | ||||
\(122\) | −5.46410 | − | 9.46410i | −0.494697 | − | 0.856840i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.19615 | − | 14.1962i | 0.736036 | − | 1.27485i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.5885 | 1.47199 | 0.735994 | − | 0.676988i | \(-0.236715\pi\) | ||||
0.735994 | + | 0.676988i | \(0.236715\pi\) | |||||||
\(128\) | −18.9282 | + | 32.7846i | −1.67303 | + | 2.89778i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.46410 | − | 12.9282i | −0.654645 | − | 1.13388i | ||||
\(131\) | −7.79423 | − | 13.5000i | −0.680985 | − | 1.17950i | −0.974681 | − | 0.223602i | \(-0.928219\pi\) |
0.293696 | − | 0.955899i | \(-0.405115\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.56218 | + | 2.70577i | −0.135458 | + | 0.234620i | ||||
\(134\) | −9.46410 | −0.817574 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.92820 | −0.594089 | ||||||||
\(137\) | 4.73205 | − | 8.19615i | 0.404286 | − | 0.700245i | −0.589952 | − | 0.807439i | \(-0.700853\pi\) |
0.994238 | + | 0.107194i | \(0.0341866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.6962 | − | 18.5263i | −0.907236 | − | 1.57138i | −0.817888 | − | 0.575378i | \(-0.804855\pi\) |
−0.0893482 | − | 0.996000i | \(-0.528478\pi\) | |||||||
\(140\) | −3.46410 | − | 6.00000i | −0.292770 | − | 0.507093i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.366025 | + | 0.633975i | −0.0307162 | + | 0.0532020i | ||||
\(143\) | −12.3923 | −1.03630 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.19615 | −0.597608 | ||||||||
\(146\) | −13.1962 | + | 22.8564i | −1.09212 | + | 1.89161i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | − | 3.46410i | −0.164399 | − | 0.284747i | ||||
\(149\) | −4.00000 | − | 6.92820i | −0.327693 | − | 0.567581i | 0.654361 | − | 0.756182i | \(-0.272938\pi\) |
−0.982054 | + | 0.188602i | \(0.939604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.69615 | − | 13.3301i | 0.626304 | − | 1.08479i | −0.361983 | − | 0.932185i | \(-0.617900\pi\) |
0.988287 | − | 0.152606i | \(-0.0487665\pi\) | |||||||
\(152\) | −23.3205 | −1.89154 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.85641 | −0.633087 | ||||||||
\(155\) | −1.50000 | + | 2.59808i | −0.120483 | + | 0.208683i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.56218 | − | 4.43782i | −0.204484 | − | 0.354177i | 0.745484 | − | 0.666523i | \(-0.232218\pi\) |
−0.949968 | + | 0.312347i | \(0.898885\pi\) | |||||||
\(158\) | −11.6603 | − | 20.1962i | −0.927640 | − | 1.60672i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.9282 | − | 18.9282i | 0.863950 | − | 1.49641i | ||||
\(161\) | 4.39230 | 0.346162 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.26795 | 0.725922 | 0.362961 | − | 0.931804i | \(-0.381766\pi\) | ||||
0.362961 | + | 0.931804i | \(0.381766\pi\) | |||||||
\(164\) | 8.73205 | − | 15.1244i | 0.681859 | − | 1.18101i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.1962 | − | 19.3923i | −0.868990 | − | 1.50513i | ||||
\(167\) | −0.169873 | − | 0.294229i | −0.0131452 | − | 0.0227681i | 0.859378 | − | 0.511341i | \(-0.170851\pi\) |
−0.872523 | + | 0.488573i | \(0.837518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.42820 | + | 14.5981i | −0.648323 | + | 1.12293i | ||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −55.7128 | −4.24806 | ||||||||
\(173\) | 7.73205 | − | 13.3923i | 0.587857 | − | 1.01820i | −0.406656 | − | 0.913581i | \(-0.633305\pi\) |
0.994513 | − | 0.104617i | \(-0.0333615\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.633975 | + | 1.09808i | 0.0479240 | + | 0.0830068i | ||||
\(176\) | −16.9282 | − | 29.3205i | −1.27601 | − | 2.21012i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.09808 | + | 12.2942i | −0.532023 | + | 0.921491i | ||||
\(179\) | 16.1244 | 1.20519 | 0.602595 | − | 0.798047i | \(-0.294133\pi\) | ||||
0.602595 | + | 0.798047i | \(0.294133\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.5359 | 1.45209 | 0.726046 | − | 0.687646i | \(-0.241356\pi\) | ||||
0.726046 | + | 0.687646i | \(0.241356\pi\) | |||||||
\(182\) | −9.46410 | + | 16.3923i | −0.701526 | + | 1.21508i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 16.3923 | + | 28.3923i | 1.20846 | + | 2.09311i | ||||
\(185\) | 0.366025 | + | 0.633975i | 0.0269107 | + | 0.0466107i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.830127 | − | 1.43782i | 0.0607049 | − | 0.105144i | ||||
\(188\) | 28.7846 | 2.09933 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.73205 | 0.488394 | ||||||||
\(191\) | 8.06218 | − | 13.9641i | 0.583359 | − | 1.01041i | −0.411719 | − | 0.911311i | \(-0.635072\pi\) |
0.995078 | − | 0.0990961i | \(-0.0315951\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.36603 | + | 7.56218i | 0.314273 | + | 0.544337i | 0.979283 | − | 0.202498i | \(-0.0649058\pi\) |
−0.665009 | + | 0.746835i | \(0.731572\pi\) | |||||||
\(194\) | −10.4641 | − | 18.1244i | −0.751279 | − | 1.30125i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.7321 | − | 25.5167i | 1.05229 | − | 1.82262i | ||||
\(197\) | −13.8564 | −0.987228 | −0.493614 | − | 0.869681i | \(-0.664324\pi\) | ||||
−0.493614 | + | 0.869681i | \(0.664324\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | −4.73205 | + | 8.19615i | −0.334607 | + | 0.579555i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.0263 | + | 34.6865i | 1.40904 | + | 2.44054i | ||||
\(203\) | 4.56218 | + | 7.90192i | 0.320202 | + | 0.554606i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.59808 | + | 2.76795i | −0.111614 | + | 0.193322i | ||||
\(206\) | −20.3923 | −1.42080 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −81.5692 | −5.65581 | ||||||||
\(209\) | 2.79423 | − | 4.83975i | 0.193281 | − | 0.334772i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.42820 | − | 16.3301i | −0.649064 | − | 1.12421i | −0.983347 | − | 0.181739i | \(-0.941827\pi\) |
0.334282 | − | 0.942473i | \(-0.391506\pi\) | |||||||
\(212\) | 8.92820 | + | 15.4641i | 0.613192 | + | 1.06208i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −21.1244 | + | 36.5885i | −1.44403 | + | 2.50114i | ||||
\(215\) | 10.1962 | 0.695372 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.80385 | 0.258222 | ||||||||
\(218\) | 27.2224 | − | 47.1506i | 1.84374 | − | 3.19344i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.19615 | + | 10.7321i | 0.417745 | + | 0.723555i | ||||
\(221\) | −2.00000 | − | 3.46410i | −0.134535 | − | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3923 | − | 21.4641i | 0.829850 | − | 1.43734i | −0.0683053 | − | 0.997664i | \(-0.521759\pi\) |
0.898155 | − | 0.439678i | \(-0.144907\pi\) | |||||||
\(224\) | −27.7128 | −1.85164 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | 10.0263 | − | 17.3660i | 0.665468 | − | 1.15262i | −0.313691 | − | 0.949525i | \(-0.601566\pi\) |
0.979158 | − | 0.203098i | \(-0.0651011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000 | + | 10.3923i | 0.396491 | + | 0.686743i | 0.993290 | − | 0.115648i | \(-0.0368944\pi\) |
−0.596799 | + | 0.802391i | \(0.703561\pi\) | |||||||
\(230\) | −4.73205 | − | 8.19615i | −0.312022 | − | 0.540438i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −34.0526 | + | 58.9808i | −2.23566 | + | 3.87228i | ||||
\(233\) | −10.0526 | −0.658565 | −0.329283 | − | 0.944231i | \(-0.606807\pi\) | ||||
−0.329283 | + | 0.944231i | \(0.606807\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.26795 | −0.343643 | ||||||||
\(236\) | −32.0526 | + | 55.5167i | −2.08644 | + | 3.61383i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.26795 | − | 2.19615i | −0.0821889 | − | 0.142355i | ||||
\(239\) | −3.73205 | − | 6.46410i | −0.241406 | − | 0.418128i | 0.719709 | − | 0.694276i | \(-0.244275\pi\) |
−0.961115 | + | 0.276148i | \(0.910942\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.16025 | + | 15.8660i | −0.590064 | + | 1.02202i | 0.404159 | + | 0.914689i | \(0.367564\pi\) |
−0.994223 | + | 0.107332i | \(0.965769\pi\) | |||||||
\(242\) | −16.0000 | −1.02852 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 21.8564 | 1.39921 | ||||||||
\(245\) | −2.69615 | + | 4.66987i | −0.172251 | + | 0.298347i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.73205 | − | 11.6603i | −0.428350 | − | 0.741924i | ||||
\(248\) | 14.1962 | + | 24.5885i | 0.901457 | + | 1.56137i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.36603 | − | 2.36603i | 0.0863950 | − | 0.149641i | ||||
\(251\) | −10.3923 | −0.655956 | −0.327978 | − | 0.944685i | \(-0.606367\pi\) | ||||
−0.327978 | + | 0.944685i | \(0.606367\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.85641 | −0.493928 | ||||||||
\(254\) | −22.6603 | + | 39.2487i | −1.42183 | + | 2.46268i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −21.8564 | − | 37.8564i | −1.36603 | − | 2.36603i | ||||
\(257\) | −5.19615 | − | 9.00000i | −0.324127 | − | 0.561405i | 0.657208 | − | 0.753709i | \(-0.271737\pi\) |
−0.981335 | + | 0.192304i | \(0.938404\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.464102 | − | 0.803848i | 0.0288379 | − | 0.0499487i | ||||
\(260\) | 29.8564 | 1.85162 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 42.5885 | 2.63112 | ||||||||
\(263\) | −6.66025 | + | 11.5359i | −0.410689 | + | 0.711334i | −0.994965 | − | 0.100221i | \(-0.968045\pi\) |
0.584276 | + | 0.811555i | \(0.301378\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.63397 | − | 2.83013i | −0.100374 | − | 0.173853i | ||||
\(266\) | −4.26795 | − | 7.39230i | −0.261685 | − | 0.453251i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.46410 | − | 16.3923i | 0.578112 | − | 1.00132i | ||||
\(269\) | 6.66025 | 0.406083 | 0.203041 | − | 0.979170i | \(-0.434917\pi\) | ||||
0.203041 | + | 0.979170i | \(0.434917\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9282 | 0.663841 | 0.331921 | − | 0.943307i | \(-0.392303\pi\) | ||||
0.331921 | + | 0.943307i | \(0.392303\pi\) | |||||||
\(272\) | 5.46410 | − | 9.46410i | 0.331310 | − | 0.573845i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.9282 | + | 22.3923i | 0.781021 | + | 1.35277i | ||||
\(275\) | −1.13397 | − | 1.96410i | −0.0683812 | − | 0.118440i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.09808 | + | 12.2942i | −0.426482 | + | 0.738689i | −0.996558 | − | 0.0829037i | \(-0.973581\pi\) |
0.570075 | + | 0.821592i | \(0.306914\pi\) | |||||||
\(278\) | 58.4449 | 3.50529 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.0000 | 0.717137 | ||||||||
\(281\) | 4.26795 | − | 7.39230i | 0.254605 | − | 0.440988i | −0.710184 | − | 0.704017i | \(-0.751388\pi\) |
0.964788 | + | 0.263029i | \(0.0847214\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.66025 | − | 4.60770i | −0.158136 | − | 0.273899i | 0.776061 | − | 0.630658i | \(-0.217215\pi\) |
−0.934196 | + | 0.356759i | \(0.883882\pi\) | |||||||
\(284\) | −0.732051 | − | 1.26795i | −0.0434392 | − | 0.0752389i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.9282 | − | 29.3205i | 1.00099 | − | 1.73376i | ||||
\(287\) | 4.05256 | 0.239215 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4641 | −0.968477 | ||||||||
\(290\) | 9.83013 | − | 17.0263i | 0.577245 | − | 0.999818i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −26.3923 | − | 45.7128i | −1.54449 | − | 2.67514i | ||||
\(293\) | 12.6340 | + | 21.8827i | 0.738085 | + | 1.27840i | 0.953357 | + | 0.301846i | \(0.0976029\pi\) |
−0.215272 | + | 0.976554i | \(0.569064\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.86603 | − | 10.1603i | 0.341533 | − | 0.591553i | ||||
\(296\) | 6.92820 | 0.402694 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.8564 | 1.26611 | ||||||||
\(299\) | −9.46410 | + | 16.3923i | −0.547323 | + | 0.947991i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.46410 | − | 11.1962i | −0.372585 | − | 0.645335i | ||||
\(302\) | 21.0263 | + | 36.4186i | 1.20993 | + | 2.09565i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18.3923 | − | 31.8564i | 1.05487 | − | 1.82709i | ||||
\(305\) | −4.00000 | −0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.0526 | −1.37275 | −0.686376 | − | 0.727247i | \(-0.740800\pi\) | ||||
−0.686376 | + | 0.727247i | \(0.740800\pi\) | |||||||
\(308\) | 7.85641 | − | 13.6077i | 0.447660 | − | 0.775370i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.09808 | − | 7.09808i | −0.232755 | − | 0.403144i | ||||
\(311\) | 8.13397 | + | 14.0885i | 0.461235 | + | 0.798883i | 0.999023 | − | 0.0441973i | \(-0.0140730\pi\) |
−0.537787 | + | 0.843080i | \(0.680740\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.4641 | − | 19.8564i | 0.647989 | − | 1.12235i | −0.335613 | − | 0.942000i | \(-0.608943\pi\) |
0.983602 | − | 0.180351i | \(-0.0577232\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 46.6410 | 2.62376 | ||||||||
\(317\) | −2.09808 | + | 3.63397i | −0.117840 | + | 0.204104i | −0.918911 | − | 0.394464i | \(-0.870930\pi\) |
0.801072 | + | 0.598568i | \(0.204264\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.16025 | − | 14.1340i | −0.456887 | − | 0.791351i | ||||
\(320\) | 14.9282 | + | 25.8564i | 0.834512 | + | 1.44542i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.00000 | + | 10.3923i | −0.334367 | + | 0.579141i | ||||
\(323\) | 1.80385 | 0.100369 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.46410 | −0.303094 | ||||||||
\(326\) | −12.6603 | + | 21.9282i | −0.701187 | + | 1.21449i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.1244 | + | 26.1962i | 0.835103 | + | 1.44644i | ||||
\(329\) | 3.33975 | + | 5.78461i | 0.184126 | + | 0.318916i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.23205 | + | 5.59808i | −0.177650 | + | 0.307698i | −0.941075 | − | 0.338198i | \(-0.890183\pi\) |
0.763425 | + | 0.645896i | \(0.223516\pi\) | |||||||
\(332\) | 44.7846 | 2.45787 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.928203 | 0.0507890 | ||||||||
\(335\) | −1.73205 | + | 3.00000i | −0.0946320 | + | 0.163908i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.66025 | + | 6.33975i | 0.199387 | + | 0.345348i | 0.948330 | − | 0.317286i | \(-0.102772\pi\) |
−0.748943 | + | 0.662634i | \(0.769438\pi\) | |||||||
\(338\) | −23.0263 | − | 39.8827i | −1.25246 | − | 2.16933i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.00000 | + | 3.46410i | −0.108465 | + | 0.187867i | ||||
\(341\) | −6.80385 | −0.368449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7128 | 0.848412 | ||||||||
\(344\) | 48.2487 | − | 83.5692i | 2.60140 | − | 4.50575i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.1244 | + | 36.5885i | 1.13565 | + | 1.96701i | ||||
\(347\) | 1.29423 | + | 2.24167i | 0.0694778 | + | 0.120339i | 0.898672 | − | 0.438622i | \(-0.144533\pi\) |
−0.829194 | + | 0.558961i | \(0.811200\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.42820 | + | 7.66987i | −0.237036 | + | 0.410559i | −0.959863 | − | 0.280471i | \(-0.909509\pi\) |
0.722826 | + | 0.691030i | \(0.242843\pi\) | |||||||
\(350\) | −3.46410 | −0.185164 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 49.5692 | 2.64205 | ||||||||
\(353\) | −9.75833 | + | 16.9019i | −0.519384 | + | 0.899599i | 0.480363 | + | 0.877070i | \(0.340505\pi\) |
−0.999746 | + | 0.0225287i | \(0.992828\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.133975 | + | 0.232051i | 0.00711063 | + | 0.0123160i | ||||
\(356\) | −14.1962 | − | 24.5885i | −0.752395 | − | 1.30319i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.0263 | + | 38.1506i | −1.16413 | + | 2.01632i | ||||
\(359\) | −18.1244 | −0.956567 | −0.478283 | − | 0.878206i | \(-0.658741\pi\) | ||||
−0.478283 | + | 0.878206i | \(0.658741\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.9282 | −0.680432 | ||||||||
\(362\) | −26.6865 | + | 46.2224i | −1.40261 | + | 2.42940i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −18.9282 | − | 32.7846i | −0.992107 | − | 1.71838i | ||||
\(365\) | 4.83013 | + | 8.36603i | 0.252820 | + | 0.437898i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.5885 | − | 27.0000i | 0.813711 | − | 1.40939i | −0.0965390 | − | 0.995329i | \(-0.530777\pi\) |
0.910250 | − | 0.414059i | \(-0.135889\pi\) | |||||||
\(368\) | −51.7128 | −2.69572 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.00000 | −0.103975 | ||||||||
\(371\) | −2.07180 | + | 3.58846i | −0.107562 | + | 0.186303i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.02628 | + | 15.6340i | 0.467363 | + | 0.809497i | 0.999305 | − | 0.0372845i | \(-0.0118708\pi\) |
−0.531942 | + | 0.846781i | \(0.678537\pi\) | |||||||
\(374\) | 2.26795 | + | 3.92820i | 0.117273 | + | 0.203123i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.9282 | + | 43.1769i | −1.28557 | + | 2.22668i | ||||
\(377\) | −39.3205 | −2.02511 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.3923 | −0.944749 | −0.472375 | − | 0.881398i | \(-0.656603\pi\) | ||||
−0.472375 | + | 0.881398i | \(0.656603\pi\) | |||||||
\(380\) | −6.73205 | + | 11.6603i | −0.345347 | + | 0.598158i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.0263 | + | 38.1506i | 1.12696 | + | 1.95196i | ||||
\(383\) | 4.73205 | + | 8.19615i | 0.241797 | + | 0.418804i | 0.961226 | − | 0.275762i | \(-0.0889300\pi\) |
−0.719430 | + | 0.694565i | \(0.755597\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.43782 | + | 2.49038i | −0.0732782 | + | 0.126922i | ||||
\(386\) | −23.8564 | −1.21426 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 41.8564 | 2.12494 | ||||||||
\(389\) | 10.2679 | − | 17.7846i | 0.520606 | − | 0.901716i | −0.479107 | − | 0.877756i | \(-0.659040\pi\) |
0.999713 | − | 0.0239591i | \(-0.00762716\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.26795 | − | 2.19615i | −0.0641229 | − | 0.111064i | ||||
\(392\) | 25.5167 | + | 44.1962i | 1.28879 | + | 2.23224i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.9282 | − | 32.7846i | 0.953589 | − | 1.65166i | ||||
\(395\) | −8.53590 | −0.429488 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.39230 | −0.320821 | −0.160410 | − | 0.987050i | \(-0.551282\pi\) | ||||
−0.160410 | + | 0.987050i | \(0.551282\pi\) | |||||||
\(398\) | 2.73205 | − | 4.73205i | 0.136945 | − | 0.237196i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.46410 | − | 12.9282i | −0.373205 | − | 0.646410i | ||||
\(401\) | 5.53590 | + | 9.58846i | 0.276450 | + | 0.478825i | 0.970500 | − | 0.241102i | \(-0.0775088\pi\) |
−0.694050 | + | 0.719927i | \(0.744175\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.19615 | + | 14.1962i | −0.408279 | + | 0.707161i | ||||
\(404\) | −80.1051 | −3.98538 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24.9282 | −1.23717 | ||||||||
\(407\) | −0.830127 | + | 1.43782i | −0.0411479 | + | 0.0712702i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.92820 | − | 8.53590i | −0.243684 | − | 0.422073i | 0.718077 | − | 0.695964i | \(-0.245023\pi\) |
−0.961761 | + | 0.273891i | \(0.911689\pi\) | |||||||
\(410\) | −4.36603 | − | 7.56218i | −0.215623 | − | 0.373469i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 20.3923 | − | 35.3205i | 1.00466 | − | 1.74012i | ||||
\(413\) | −14.8756 | −0.731983 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.19615 | −0.402333 | ||||||||
\(416\) | 59.7128 | − | 103.426i | 2.92766 | − | 5.07086i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.63397 | + | 13.2224i | 0.373390 | + | 0.646730i | ||||
\(419\) | −0.196152 | − | 0.339746i | −0.00958267 | − | 0.0165977i | 0.861194 | − | 0.508276i | \(-0.169717\pi\) |
−0.870777 | + | 0.491678i | \(0.836384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.89230 | − | 6.74167i | 0.189699 | − | 0.328569i | −0.755451 | − | 0.655206i | \(-0.772582\pi\) |
0.945150 | + | 0.326637i | \(0.105915\pi\) | |||||||
\(422\) | 51.5167 | 2.50779 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30.9282 | −1.50201 | ||||||||
\(425\) | 0.366025 | − | 0.633975i | 0.0177548 | − | 0.0307523i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.53590 | + | 4.39230i | 0.122721 | + | 0.212559i | ||||
\(428\) | −42.2487 | − | 73.1769i | −2.04217 | − | 3.53714i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.9282 | + | 24.1244i | −0.671678 | + | 1.16338i | ||||
\(431\) | 38.6603 | 1.86220 | 0.931099 | − | 0.364765i | \(-0.118851\pi\) | ||||
0.931099 | + | 0.364765i | \(0.118851\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.5359 | −1.37135 | −0.685674 | − | 0.727909i | \(-0.740492\pi\) | ||||
−0.685674 | + | 0.727909i | \(0.740492\pi\) | |||||||
\(434\) | −5.19615 | + | 9.00000i | −0.249423 | + | 0.432014i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 54.4449 | + | 94.3013i | 2.60744 | + | 4.51621i | ||||
\(437\) | −4.26795 | − | 7.39230i | −0.204164 | − | 0.353622i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.69615 | − | 13.3301i | 0.367317 | − | 0.636212i | −0.621828 | − | 0.783154i | \(-0.713610\pi\) |
0.989145 | + | 0.146942i | \(0.0469430\pi\) | |||||||
\(440\) | −21.4641 | −1.02326 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.9282 | 0.519802 | ||||||||
\(443\) | −8.83013 | + | 15.2942i | −0.419532 | + | 0.726651i | −0.995892 | − | 0.0905449i | \(-0.971139\pi\) |
0.576360 | + | 0.817196i | \(0.304472\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.59808 | + | 4.50000i | 0.123161 | + | 0.213320i | ||||
\(446\) | 33.8564 | + | 58.6410i | 1.60315 | + | 2.77673i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.9282 | − | 32.7846i | 0.894274 | − | 1.54893i | ||||
\(449\) | 16.1244 | 0.760955 | 0.380478 | − | 0.924790i | \(-0.375760\pi\) | ||||
0.380478 | + | 0.924790i | \(0.375760\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.24871 | −0.341328 | ||||||||
\(452\) | 14.0000 | − | 24.2487i | 0.658505 | − | 1.14056i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.3923 | + | 47.4449i | 1.28558 | + | 2.22670i | ||||
\(455\) | 3.46410 | + | 6.00000i | 0.162400 | + | 0.281284i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.366025 | − | 0.633975i | 0.0171219 | − | 0.0296561i | −0.857337 | − | 0.514755i | \(-0.827883\pi\) |
0.874459 | + | 0.485099i | \(0.161216\pi\) | |||||||
\(458\) | −32.7846 | −1.53192 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.9282 | 0.882532 | ||||||||
\(461\) | 0.526279 | − | 0.911543i | 0.0245113 | − | 0.0424548i | −0.853510 | − | 0.521077i | \(-0.825530\pi\) |
0.878021 | + | 0.478622i | \(0.158864\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.19615 | − | 9.00000i | −0.241486 | − | 0.418265i | 0.719652 | − | 0.694335i | \(-0.244301\pi\) |
−0.961138 | + | 0.276069i | \(0.910968\pi\) | |||||||
\(464\) | −53.7128 | − | 93.0333i | −2.49355 | − | 4.31896i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.7321 | − | 23.7846i | 0.636125 | − | 1.10180i | ||||
\(467\) | 35.3731 | 1.63687 | 0.818435 | − | 0.574599i | \(-0.194842\pi\) | ||||
0.818435 | + | 0.574599i | \(0.194842\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.39230 | 0.202818 | ||||||||
\(470\) | 7.19615 | − | 12.4641i | 0.331934 | − | 0.574926i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −55.5167 | − | 96.1577i | −2.55536 | − | 4.42602i | ||||
\(473\) | 11.5622 | + | 20.0263i | 0.531630 | + | 0.920809i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.23205 | − | 2.13397i | 0.0565304 | − | 0.0979135i | ||||
\(476\) | 5.07180 | 0.232465 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 20.3923 | 0.932722 | ||||||||
\(479\) | −18.0622 | + | 31.2846i | −0.825282 | + | 1.42943i | 0.0764216 | + | 0.997076i | \(0.475650\pi\) |
−0.901704 | + | 0.432355i | \(0.857683\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | + | 3.46410i | 0.0911922 | + | 0.157949i | ||||
\(482\) | −25.0263 | − | 43.3468i | −1.13992 | − | 1.97439i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.0000 | − | 27.7128i | 0.727273 | − | 1.25967i | ||||
\(485\) | −7.66025 | −0.347834 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.60770 | 0.163480 | 0.0817401 | − | 0.996654i | \(-0.473952\pi\) | ||||
0.0817401 | + | 0.996654i | \(0.473952\pi\) | |||||||
\(488\) | −18.9282 | + | 32.7846i | −0.856840 | + | 1.48409i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.36603 | − | 12.7583i | −0.332763 | − | 0.576363i | ||||
\(491\) | −19.0622 | − | 33.0167i | −0.860264 | − | 1.49002i | −0.871674 | − | 0.490086i | \(-0.836965\pi\) |
0.0114100 | − | 0.999935i | \(-0.496368\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.63397 | − | 4.56218i | 0.118628 | − | 0.205470i | ||||
\(494\) | 36.7846 | 1.65502 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −44.7846 | −2.01089 | ||||||||
\(497\) | 0.169873 | − | 0.294229i | 0.00761984 | − | 0.0131980i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.16025 | + | 8.93782i | 0.231005 | + | 0.400112i | 0.958104 | − | 0.286420i | \(-0.0924654\pi\) |
−0.727099 | + | 0.686532i | \(0.759132\pi\) | |||||||
\(500\) | 2.73205 | + | 4.73205i | 0.122181 | + | 0.211624i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.1962 | − | 24.5885i | 0.633605 | − | 1.09744i | ||||
\(503\) | −27.3205 | −1.21816 | −0.609081 | − | 0.793108i | \(-0.708461\pi\) | ||||
−0.609081 | + | 0.793108i | \(0.708461\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.6603 | 0.652373 | ||||||||
\(506\) | 10.7321 | − | 18.5885i | 0.477098 | − | 0.826358i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −45.3205 | − | 78.4974i | −2.01077 | − | 3.48276i | ||||
\(509\) | 17.3923 | + | 30.1244i | 0.770900 | + | 1.33524i | 0.937070 | + | 0.349141i | \(0.113527\pi\) |
−0.166170 | + | 0.986097i | \(0.553140\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.12436 | − | 10.6077i | 0.270926 | − | 0.469257i | ||||
\(512\) | 43.7128 | 1.93185 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.3923 | 1.25233 | ||||||||
\(515\) | −3.73205 | + | 6.46410i | −0.164454 | + | 0.284842i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.97372 | − | 10.3468i | −0.262724 | − | 0.455051i | ||||
\(518\) | 1.26795 | + | 2.19615i | 0.0557105 | + | 0.0964934i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −25.8564 | + | 44.7846i | −1.13388 | + | 1.96394i | ||||
\(521\) | −12.5359 | −0.549208 | −0.274604 | − | 0.961557i | \(-0.588547\pi\) | ||||
−0.274604 | + | 0.961557i | \(0.588547\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.2487 | −1.14778 | −0.573888 | − | 0.818934i | \(-0.694566\pi\) | ||||
−0.573888 | + | 0.818934i | \(0.694566\pi\) | |||||||
\(524\) | −42.5885 | + | 73.7654i | −1.86049 | + | 3.22246i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.1962 | − | 31.5167i | −0.793390 | − | 1.37419i | ||||
\(527\) | −1.09808 | − | 1.90192i | −0.0478330 | − | 0.0828491i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.50000 | − | 9.52628i | 0.239130 | − | 0.414186i | ||||
\(530\) | 8.92820 | 0.387816 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 17.0718 | 0.740156 | ||||||||
\(533\) | −8.73205 | + | 15.1244i | −0.378227 | + | 0.655109i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.73205 | + | 13.3923i | 0.334286 | + | 0.579000i | ||||
\(536\) | 16.3923 | + | 28.3923i | 0.708040 | + | 1.22636i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.09808 | + | 15.7583i | −0.392246 | + | 0.679390i | ||||
\(539\) | −12.2295 | −0.526761 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5359 | −0.753927 | −0.376964 | − | 0.926228i | \(-0.623032\pi\) | ||||
−0.376964 | + | 0.926228i | \(0.623032\pi\) | |||||||
\(542\) | −14.9282 | + | 25.8564i | −0.641221 | + | 1.11063i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.00000 | + | 13.8564i | 0.342997 | + | 0.594089i | ||||
\(545\) | −9.96410 | − | 17.2583i | −0.426815 | − | 0.739266i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.07180 | − | 5.32051i | 0.131341 | − | 0.227488i | −0.792853 | − | 0.609413i | \(-0.791405\pi\) |
0.924194 | + | 0.381924i | \(0.124739\pi\) | |||||||
\(548\) | −51.7128 | −2.20906 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.19615 | 0.264205 | ||||||||
\(551\) | 8.86603 | − | 15.3564i | 0.377705 | − | 0.654205i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.41154 | + | 9.37307i | 0.230122 | + | 0.398583i | ||||
\(554\) | −19.3923 | − | 33.5885i | −0.823900 | − | 1.42704i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −58.4449 | + | 101.229i | −2.47861 | + | 4.29309i | ||||
\(557\) | 9.46410 | 0.401007 | 0.200503 | − | 0.979693i | \(-0.435742\pi\) | ||||
0.200503 | + | 0.979693i | \(0.435742\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 55.7128 | 2.35640 | ||||||||
\(560\) | −9.46410 | + | 16.3923i | −0.399931 | + | 0.692701i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.6603 | + | 20.1962i | 0.491858 | + | 0.851923i | ||||
\(563\) | −6.63397 | − | 11.4904i | −0.279589 | − | 0.484262i | 0.691694 | − | 0.722191i | \(-0.256865\pi\) |
−0.971283 | + | 0.237929i | \(0.923531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.56218 | + | 4.43782i | −0.107792 | + | 0.186701i | ||||
\(566\) | 14.5359 | 0.610989 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.53590 | 0.106404 | ||||||||
\(569\) | 16.4545 | − | 28.5000i | 0.689808 | − | 1.19478i | −0.282092 | − | 0.959387i | \(-0.591028\pi\) |
0.971900 | − | 0.235395i | \(-0.0756383\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.892305 | − | 1.54552i | −0.0373418 | − | 0.0646779i | 0.846750 | − | 0.531990i | \(-0.178556\pi\) |
−0.884092 | + | 0.467312i | \(0.845222\pi\) | |||||||
\(572\) | 33.8564 | + | 58.6410i | 1.41561 | + | 2.45190i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.53590 | + | 9.58846i | −0.231064 | + | 0.400214i | ||||
\(575\) | −3.46410 | −0.144463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.7321 | 0.779825 | 0.389913 | − | 0.920852i | \(-0.372505\pi\) | ||||
0.389913 | + | 0.920852i | \(0.372505\pi\) | |||||||
\(578\) | 22.4904 | − | 38.9545i | 0.935477 | − | 1.62029i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19.6603 | + | 34.0526i | 0.816348 | + | 1.41396i | ||||
\(581\) | 5.19615 | + | 9.00000i | 0.215573 | + | 0.373383i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.70577 | − | 6.41858i | 0.153477 | − | 0.265831i | ||||
\(584\) | 91.4256 | 3.78322 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −69.0333 | −2.85174 | ||||||||
\(587\) | 2.83013 | − | 4.90192i | 0.116812 | − | 0.202324i | −0.801691 | − | 0.597739i | \(-0.796066\pi\) |
0.918503 | + | 0.395415i | \(0.129399\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.69615 | − | 6.40192i | −0.152297 | − | 0.263787i | ||||
\(590\) | 16.0263 | + | 27.7583i | 0.659791 | + | 1.14279i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.46410 | + | 9.46410i | −0.224573 | + | 0.388972i | ||||
\(593\) | 27.8564 | 1.14393 | 0.571963 | − | 0.820280i | \(-0.306182\pi\) | ||||
0.571963 | + | 0.820280i | \(0.306182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.928203 | −0.0380526 | ||||||||
\(596\) | −21.8564 | + | 37.8564i | −0.895273 | + | 1.55066i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −25.8564 | − | 44.7846i | −1.05735 | − | 1.83138i | ||||
\(599\) | 8.40192 | + | 14.5526i | 0.343293 | + | 0.594601i | 0.985042 | − | 0.172313i | \(-0.0551242\pi\) |
−0.641749 | + | 0.766915i | \(0.721791\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.62436 | + | 14.9378i | −0.351795 | + | 0.609326i | −0.986564 | − | 0.163375i | \(-0.947762\pi\) |
0.634769 | + | 0.772702i | \(0.281095\pi\) | |||||||
\(602\) | 35.3205 | 1.43956 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −84.1051 | −3.42219 | ||||||||
\(605\) | −2.92820 | + | 5.07180i | −0.119048 | + | 0.206198i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.90192 | + | 5.02628i | 0.117785 | + | 0.204010i | 0.918890 | − | 0.394514i | \(-0.129087\pi\) |
−0.801104 | + | 0.598525i | \(0.795754\pi\) | |||||||
\(608\) | 26.9282 | + | 46.6410i | 1.09208 | + | 1.89154i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.46410 | − | 9.46410i | 0.221235 | − | 0.383190i | ||||
\(611\) | −28.7846 | −1.16450 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.46410 | −0.220693 | −0.110346 | − | 0.993893i | \(-0.535196\pi\) | ||||
−0.110346 | + | 0.993893i | \(0.535196\pi\) | |||||||
\(614\) | 32.8564 | − | 56.9090i | 1.32598 | − | 2.29666i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.6077 | + | 23.5692i | 0.548270 | + | 0.949631i | ||||
\(617\) | 3.46410 | + | 6.00000i | 0.139459 | + | 0.241551i | 0.927292 | − | 0.374338i | \(-0.122130\pi\) |
−0.787833 | + | 0.615889i | \(0.788797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.92820 | + | 13.7321i | −0.318661 | + | 0.551938i | −0.980209 | − | 0.197965i | \(-0.936567\pi\) |
0.661548 | + | 0.749903i | \(0.269900\pi\) | |||||||
\(620\) | 16.3923 | 0.658331 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −44.4449 | −1.78208 | ||||||||
\(623\) | 3.29423 | − | 5.70577i | 0.131980 | − | 0.228597i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 31.3205 | + | 54.2487i | 1.25182 | + | 2.16821i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.0000 | + | 24.2487i | −0.558661 | + | 0.967629i | ||||
\(629\) | −0.535898 | −0.0213677 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7128 | 0.904183 | 0.452091 | − | 0.891972i | \(-0.350678\pi\) | ||||
0.452091 | + | 0.891972i | \(0.350678\pi\) | |||||||
\(632\) | −40.3923 | + | 69.9615i | −1.60672 | + | 2.78292i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.73205 | − | 9.92820i | −0.227649 | − | 0.394299i | ||||
\(635\) | 8.29423 | + | 14.3660i | 0.329146 | + | 0.570098i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.7321 | + | 25.5167i | −0.583705 | + | 1.01101i | ||||
\(638\) | 44.5885 | 1.76527 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −37.8564 | −1.49641 | ||||||||
\(641\) | 13.3301 | − | 23.0885i | 0.526508 | − | 0.911939i | −0.473015 | − | 0.881055i | \(-0.656834\pi\) |
0.999523 | − | 0.0308846i | \(-0.00983245\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.1699 | − | 21.0788i | −0.479933 | − | 0.831268i | 0.519802 | − | 0.854287i | \(-0.326006\pi\) |
−0.999735 | + | 0.0230185i | \(0.992672\pi\) | |||||||
\(644\) | −12.0000 | − | 20.7846i | −0.472866 | − | 0.819028i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.46410 | + | 4.26795i | −0.0969488 | + | 0.167920i | ||||
\(647\) | −4.53590 | −0.178325 | −0.0891623 | − | 0.996017i | \(-0.528419\pi\) | ||||
−0.0891623 | + | 0.996017i | \(0.528419\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.6077 | 1.04444 | ||||||||
\(650\) | 7.46410 | − | 12.9282i | 0.292766 | − | 0.507086i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −25.3205 | − | 43.8564i | −0.991628 | − | 1.71755i | ||||
\(653\) | −5.26795 | − | 9.12436i | −0.206151 | − | 0.357064i | 0.744348 | − | 0.667792i | \(-0.232760\pi\) |
−0.950499 | + | 0.310728i | \(0.899427\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.79423 | − | 13.5000i | 0.304546 | − | 0.527489i | ||||
\(656\) | −47.7128 | −1.86287 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.2487 | −0.711409 | ||||||||
\(659\) | 2.73205 | − | 4.73205i | 0.106426 | − | 0.184335i | −0.807894 | − | 0.589328i | \(-0.799393\pi\) |
0.914320 | + | 0.404993i | \(0.132726\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.16025 | + | 14.1340i | 0.317397 | + | 0.549748i | 0.979944 | − | 0.199272i | \(-0.0638579\pi\) |
−0.662547 | + | 0.749020i | \(0.730525\pi\) | |||||||
\(662\) | −8.83013 | − | 15.2942i | −0.343193 | − | 0.594427i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −38.7846 | + | 67.1769i | −1.50513 | + | 2.60697i | ||||
\(665\) | −3.12436 | −0.121157 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.9282 | −0.965224 | ||||||||
\(668\) | −0.928203 | + | 1.60770i | −0.0359133 | + | 0.0622036i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.73205 | − | 8.19615i | −0.182815 | − | 0.316645i | ||||
\(671\) | −4.53590 | − | 7.85641i | −0.175106 | − | 0.303293i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.19615 | + | 9.00000i | −0.200297 | + | 0.346925i | −0.948624 | − | 0.316405i | \(-0.897524\pi\) |
0.748327 | + | 0.663330i | \(0.230857\pi\) | |||||||
\(674\) | −20.0000 | −0.770371 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 92.1051 | 3.54250 | ||||||||
\(677\) | −9.00000 | + | 15.5885i | −0.345898 | + | 0.599113i | −0.985517 | − | 0.169580i | \(-0.945759\pi\) |
0.639618 | + | 0.768693i | \(0.279092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.85641 | + | 8.41154i | 0.186372 | + | 0.322805i | ||||
\(680\) | −3.46410 | − | 6.00000i | −0.132842 | − | 0.230089i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.29423 | − | 16.0981i | 0.355894 | − | 0.616427i | ||||
\(683\) | 40.3923 | 1.54557 | 0.772784 | − | 0.634669i | \(-0.218863\pi\) | ||||
0.772784 | + | 0.634669i | \(0.218863\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.46410 | 0.361605 | ||||||||
\(686\) | −21.4641 | + | 37.1769i | −0.819503 | + | 1.41942i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 76.1051 | + | 131.818i | 2.90148 | + | 5.02551i | ||||
\(689\) | −8.92820 | − | 15.4641i | −0.340137 | − | 0.589135i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.8564 | + | 32.6603i | −0.717332 | + | 1.24245i | 0.244722 | + | 0.969593i | \(0.421303\pi\) |
−0.962053 | + | 0.272861i | \(0.912030\pi\) | |||||||
\(692\) | −84.4974 | −3.21211 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.07180 | −0.268442 | ||||||||
\(695\) | 10.6962 | − | 18.5263i | 0.405728 | − | 0.702742i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.16987 | − | 2.02628i | −0.0443121 | − | 0.0767508i | ||||
\(698\) | −12.0981 | − | 20.9545i | −0.457919 | − | 0.793139i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.46410 | − | 6.00000i | 0.130931 | − | 0.226779i | ||||
\(701\) | 31.1962 | 1.17826 | 0.589131 | − | 0.808037i | \(-0.299470\pi\) | ||||
0.589131 | + | 0.808037i | \(0.299470\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.80385 | −0.0680334 | ||||||||
\(704\) | −33.8564 | + | 58.6410i | −1.27601 | + | 2.21012i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.6603 | − | 46.1769i | −1.00337 | − | 1.73789i | ||||
\(707\) | −9.29423 | − | 16.0981i | −0.349545 | − | 0.605430i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.7321 | − | 25.5167i | 0.553274 | − | 0.958298i | −0.444762 | − | 0.895649i | \(-0.646712\pi\) |
0.998036 | − | 0.0626494i | \(-0.0199550\pi\) | |||||||
\(710\) | −0.732051 | −0.0274734 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 49.1769 | 1.84298 | ||||||||
\(713\) | −5.19615 | + | 9.00000i | −0.194597 | + | 0.337053i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.19615 | − | 10.7321i | −0.231723 | − | 0.401356i | ||||
\(716\) | −44.0526 | − | 76.3013i | −1.64632 | − | 2.85151i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.7583 | − | 42.8827i | 0.923973 | − | 1.60037i | ||||
\(719\) | −39.5885 | −1.47640 | −0.738200 | − | 0.674582i | \(-0.764324\pi\) | ||||
−0.738200 | + | 0.674582i | \(0.764324\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.46410 | 0.352462 | ||||||||
\(722\) | 17.6603 | − | 30.5885i | 0.657247 | − | 1.13838i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −53.3731 | − | 92.4449i | −1.98359 | − | 3.43569i | ||||
\(725\) | −3.59808 | − | 6.23205i | −0.133629 | − | 0.231453i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.19615 | + | 10.7321i | −0.229803 | + | 0.398030i | −0.957749 | − | 0.287604i | \(-0.907141\pi\) |
0.727947 | + | 0.685633i | \(0.240475\pi\) | |||||||
\(728\) | 65.5692 | 2.43016 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −26.3923 | −0.976823 | ||||||||
\(731\) | −3.73205 | + | 6.46410i | −0.138035 | + | 0.239083i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.39230 | + | 5.87564i | 0.125298 | + | 0.217022i | 0.921849 | − | 0.387549i | \(-0.126678\pi\) |
−0.796552 | + | 0.604571i | \(0.793345\pi\) | |||||||
\(734\) | 42.5885 | + | 73.7654i | 1.57197 | + | 2.72273i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 37.8564 | − | 65.5692i | 1.39541 | − | 2.41691i | ||||
\(737\) | −7.85641 | −0.289394 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.5359 | 0.571497 | 0.285749 | − | 0.958305i | \(-0.407758\pi\) | ||||
0.285749 | + | 0.958305i | \(0.407758\pi\) | |||||||
\(740\) | 2.00000 | − | 3.46410i | 0.0735215 | − | 0.127343i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.66025 | − | 9.80385i | −0.207794 | − | 0.359911i | ||||
\(743\) | −22.9545 | − | 39.7583i | −0.842118 | − | 1.45859i | −0.888100 | − | 0.459649i | \(-0.847975\pi\) |
0.0459822 | − | 0.998942i | \(-0.485358\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.00000 | − | 6.92820i | 0.146549 | − | 0.253830i | ||||
\(746\) | −49.3205 | −1.80575 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.07180 | −0.331698 | ||||||||
\(749\) | 9.80385 | − | 16.9808i | 0.358225 | − | 0.620464i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.60770 | − | 6.24871i | −0.131647 | − | 0.228019i | 0.792665 | − | 0.609658i | \(-0.208693\pi\) |
−0.924311 | + | 0.381639i | \(0.875360\pi\) | |||||||
\(752\) | −39.3205 | − | 68.1051i | −1.43387 | − | 2.48354i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 53.7128 | − | 93.0333i | 1.95611 | − | 3.38807i | ||||
\(755\) | 15.3923 | 0.560183 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.1769 | 1.93275 | 0.966374 | − | 0.257141i | \(-0.0827805\pi\) | ||||
0.966374 | + | 0.257141i | \(0.0827805\pi\) | |||||||
\(758\) | 25.1244 | − | 43.5167i | 0.912558 | − | 1.58060i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.6603 | − | 20.1962i | −0.422962 | − | 0.732591i | ||||
\(761\) | −17.7224 | − | 30.6962i | −0.642438 | − | 1.11273i | −0.984887 | − | 0.173198i | \(-0.944590\pi\) |
0.342449 | − | 0.939536i | \(-0.388744\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.6340 | + | 21.8827i | −0.457381 | + | 0.792206i | ||||
\(764\) | −88.1051 | −3.18753 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.8564 | −0.934230 | ||||||||
\(767\) | 32.0526 | − | 55.5167i | 1.15735 | − | 2.00459i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.23205 | + | 14.2583i | 0.296855 | + | 0.514169i | 0.975415 | − | 0.220377i | \(-0.0707287\pi\) |
−0.678559 | + | 0.734545i | \(0.737395\pi\) | |||||||
\(770\) | −3.92820 | − | 6.80385i | −0.141563 | − | 0.245194i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.8564 | − | 41.3205i | 0.858611 | − | 1.48716i | ||||
\(773\) | 43.5167 | 1.56519 | 0.782593 | − | 0.622534i | \(-0.213897\pi\) | ||||
0.782593 | + | 0.622534i | \(0.213897\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.00000 | −0.107763 | ||||||||
\(776\) | −36.2487 | + | 62.7846i | −1.30125 | + | 2.25384i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.0526 | + | 48.5885i | 1.00573 | + | 1.74198i | ||||
\(779\) | −3.93782 | − | 6.82051i | −0.141087 | − | 0.244370i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.303848 | + | 0.526279i | −0.0108725 | + | 0.0188318i | ||||
\(782\) | 6.92820 | 0.247752 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −80.4974 | −2.87491 | ||||||||
\(785\) | 2.56218 | − | 4.43782i | 0.0914480 | − | 0.158393i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.97372 | + | 8.61474i | 0.177294 | + | 0.307082i | 0.940953 | − | 0.338538i | \(-0.109932\pi\) |
−0.763659 | + | 0.645620i | \(0.776599\pi\) | |||||||
\(788\) | 37.8564 | + | 65.5692i | 1.34858 | + | 2.33581i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.6603 | − | 20.1962i | 0.414853 | − | 0.718547i | ||||
\(791\) | 6.49742 | 0.231022 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.8564 | −0.776144 | ||||||||
\(794\) | 8.73205 | − | 15.1244i | 0.309889 | − | 0.536743i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.46410 | + | 9.46410i | 0.193670 | + | 0.335446i | ||||
\(797\) | −18.1962 | − | 31.5167i | −0.644541 | − | 1.11638i | −0.984407 | − | 0.175904i | \(-0.943715\pi\) |
0.339867 | − | 0.940474i | \(-0.389618\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.92820 | − | 3.33975i | 0.0682149 | − | 0.118152i | ||||
\(800\) | 21.8564 | 0.772741 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30.2487 | −1.06812 | ||||||||
\(803\) | −10.9545 | + | 18.9737i | −0.386575 | + | 0.669568i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.19615 | + | 3.80385i | 0.0774042 | + | 0.134068i | ||||
\(806\) | −22.3923 | − | 38.7846i | −0.788735 | − | 1.36613i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 69.3731 | − | 120.158i | 2.44054 | − | 4.22713i | ||||
\(809\) | 13.4449 | 0.472696 | 0.236348 | − | 0.971668i | \(-0.424049\pi\) | ||||
0.236348 | + | 0.971668i | \(0.424049\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.5359 | −0.405080 | −0.202540 | − | 0.979274i | \(-0.564920\pi\) | ||||
−0.202540 | + | 0.979274i | \(0.564920\pi\) | |||||||
\(812\) | 24.9282 | − | 43.1769i | 0.874808 | − | 1.51521i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.26795 | − | 3.92820i | −0.0794916 | − | 0.137683i | ||||
\(815\) | 4.63397 | + | 8.02628i | 0.162321 | + | 0.281148i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.5622 | + | 21.7583i | −0.439495 | + | 0.761228i | ||||
\(818\) | 26.9282 | 0.941523 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.4641 | 0.609873 | ||||||||
\(821\) | −17.1340 | + | 29.6769i | −0.597980 | + | 1.03573i | 0.395139 | + | 0.918621i | \(0.370696\pi\) |
−0.993119 | + | 0.117110i | \(0.962637\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.9282 | + | 20.6603i | 0.415791 | + | 0.720171i | 0.995511 | − | 0.0946445i | \(-0.0301714\pi\) |
−0.579720 | + | 0.814816i | \(0.696838\pi\) | |||||||
\(824\) | 35.3205 | + | 61.1769i | 1.23045 | + | 2.13120i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.3205 | − | 35.1962i | 0.707041 | − | 1.22463i | ||||
\(827\) | 32.3923 | 1.12639 | 0.563195 | − | 0.826324i | \(-0.309572\pi\) | ||||
0.563195 | + | 0.826324i | \(0.309572\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.7846 | 0.617685 | 0.308843 | − | 0.951113i | \(-0.400058\pi\) | ||||
0.308843 | + | 0.951113i | \(0.400058\pi\) | |||||||
\(830\) | 11.1962 | − | 19.3923i | 0.388624 | − | 0.673117i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 81.5692 | + | 141.282i | 2.82790 | + | 4.89807i | ||||
\(833\) | −1.97372 | − | 3.41858i | −0.0683854 | − | 0.118447i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.169873 | − | 0.294229i | 0.00587870 | − | 0.0101822i | ||||
\(836\) | −30.5359 | −1.05611 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.07180 | 0.0370246 | ||||||||
\(839\) | 11.4019 | − | 19.7487i | 0.393638 | − | 0.681801i | −0.599288 | − | 0.800533i | \(-0.704550\pi\) |
0.992926 | + | 0.118732i | \(0.0378830\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.3923 | − | 19.7321i | −0.392838 | − | 0.680416i | ||||
\(842\) | 10.6340 | + | 18.4186i | 0.366471 | + | 0.634746i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −51.5167 | + | 89.2295i | −1.77328 | + | 3.07141i | ||||
\(845\) | −16.8564 | −0.579878 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.42563 | 0.255148 | ||||||||
\(848\) | 24.3923 | − | 42.2487i | 0.837635 | − | 1.45083i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.00000 | + | 1.73205i | 0.0342997 | + | 0.0594089i | ||||
\(851\) | 1.26795 | + | 2.19615i | 0.0434647 | + | 0.0752831i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.7583 | + | 48.0788i | −0.950427 | + | 1.64619i | −0.205925 | + | 0.978568i | \(0.566020\pi\) |
−0.744502 | + | 0.667620i | \(0.767313\pi\) | |||||||
\(854\) | −13.8564 | −0.474156 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 146.354 | 5.00227 | ||||||||
\(857\) | −26.2487 | + | 45.4641i | −0.896639 | + | 1.55302i | −0.0648758 | + | 0.997893i | \(0.520665\pi\) |
−0.831763 | + | 0.555131i | \(0.812668\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.50000 | + | 9.52628i | 0.187658 | + | 0.325032i | 0.944469 | − | 0.328601i | \(-0.106577\pi\) |
−0.756811 | + | 0.653633i | \(0.773244\pi\) | |||||||
\(860\) | −27.8564 | − | 48.2487i | −0.949896 | − | 1.64527i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −52.8109 | + | 91.4711i | −1.79875 | + | 3.11552i | ||||
\(863\) | −1.12436 | −0.0382735 | −0.0191368 | − | 0.999817i | \(-0.506092\pi\) | ||||
−0.0191368 | + | 0.999817i | \(0.506092\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.4641 | 0.525795 | ||||||||
\(866\) | 38.9808 | − | 67.5167i | 1.32462 | − | 2.29431i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.3923 | − | 18.0000i | −0.352738 | − | 0.610960i | ||||
\(869\) | −9.67949 | − | 16.7654i | −0.328354 | − | 0.568726i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.46410 | + | 16.3923i | −0.320679 | + | 0.555432i | ||||
\(872\) | −188.603 | −6.38689 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23.3205 | 0.788828 | ||||||||
\(875\) | −0.633975 | + | 1.09808i | −0.0214323 | + | 0.0371218i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.2679 | − | 22.9808i | −0.448027 | − | 0.776005i | 0.550231 | − | 0.835013i | \(-0.314540\pi\) |
−0.998258 | + | 0.0590075i | \(0.981206\pi\) | |||||||
\(878\) | 21.0263 | + | 36.4186i | 0.709603 | + | 1.22907i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 16.9282 | − | 29.3205i | 0.570650 | − | 0.988394i | ||||
\(881\) | 8.94744 | 0.301447 | 0.150723 | − | 0.988576i | \(-0.451840\pi\) | ||||
0.150723 | + | 0.988576i | \(0.451840\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.8038 | −0.666453 | −0.333226 | − | 0.942847i | \(-0.608137\pi\) | ||||
−0.333226 | + | 0.942847i | \(0.608137\pi\) | |||||||
\(884\) | −10.9282 | + | 18.9282i | −0.367555 | + | 0.636624i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.1244 | − | 41.7846i | −0.810474 | − | 1.40378i | ||||
\(887\) | 22.0981 | + | 38.2750i | 0.741981 | + | 1.28515i | 0.951592 | + | 0.307364i | \(0.0994468\pi\) |
−0.209611 | + | 0.977785i | \(0.567220\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.5167 | − | 18.2154i | 0.352717 | − | 0.610925i | ||||
\(890\) | −14.1962 | −0.475856 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −135.426 | −4.53439 | ||||||||
\(893\) | 6.49038 | − | 11.2417i | 0.217192 | − | 0.376188i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.06218 | + | 13.9641i | 0.269489 | + | 0.466768i | ||||
\(896\) | 24.0000 | + | 41.5692i | 0.801784 | + | 1.38873i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.0263 | + | 38.1506i | −0.735026 | + | 1.27310i | ||||
\(899\) | −21.5885 | −0.720015 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.39230 | 0.0796992 | ||||||||
\(902\) | 9.90192 | − | 17.1506i | 0.329698 | − | 0.571054i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.2487 | + | 42.0000i | 0.806500 | + | 1.39690i | ||||
\(905\) | 9.76795 | + | 16.9186i | 0.324698 | + | 0.562393i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.0000 | − | 25.9808i | 0.498067 | − | 0.862677i | −0.501931 | − | 0.864908i | \(-0.667377\pi\) |
0.999998 | + | 0.00223080i | \(0.000710087\pi\) | |||||||
\(908\) | −109.569 | −3.63618 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −18.9282 | −0.627464 | ||||||||
\(911\) | −3.79423 | + | 6.57180i | −0.125708 | + | 0.217733i | −0.922010 | − | 0.387167i | \(-0.873454\pi\) |
0.796301 | + | 0.604900i | \(0.206787\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.29423 | − | 16.0981i | −0.307594 | − | 0.532769i | ||||
\(914\) | 1.00000 | + | 1.73205i | 0.0330771 | + | 0.0572911i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 32.7846 | − | 56.7846i | 1.08323 | − | 1.87622i | ||||
\(917\) | −19.7654 | −0.652710 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.9615 | 1.54912 | 0.774559 | − | 0.632502i | \(-0.217972\pi\) | ||||
0.774559 | + | 0.632502i | \(0.217972\pi\) | |||||||
\(920\) | −16.3923 | + | 28.3923i | −0.540438 | + | 0.936067i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.43782 | + | 2.49038i | 0.0473522 | + | 0.0820163i | ||||
\(923\) | 0.732051 | + | 1.26795i | 0.0240957 | + | 0.0417351i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.366025 | + | 0.633975i | −0.0120348 | + | 0.0208450i | ||||
\(926\) | 28.3923 | 0.933029 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 157.282 | 5.16304 | ||||||||
\(929\) | 14.1865 | − | 24.5718i | 0.465445 | − | 0.806175i | −0.533776 | − | 0.845626i | \(-0.679228\pi\) |
0.999222 | + | 0.0394511i | \(0.0125609\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.64359 | − | 11.5070i | −0.217735 | − | 0.377128i | ||||
\(932\) | 27.4641 | + | 47.5692i | 0.899617 | + | 1.55818i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −48.3205 | + | 83.6936i | −1.58110 | + | 2.73854i | ||||
\(935\) | 1.66025 | 0.0542961 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.8564 | −1.04070 | −0.520352 | − | 0.853952i | \(-0.674199\pi\) | ||||
−0.520352 | + | 0.853952i | \(0.674199\pi\) | |||||||
\(938\) | −6.00000 | + | 10.3923i | −0.195907 | + | 0.339321i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14.3923 | + | 24.9282i | 0.469425 | + | 0.813068i | ||||
\(941\) | −13.5885 | − | 23.5359i | −0.442971 | − | 0.767248i | 0.554937 | − | 0.831892i | \(-0.312742\pi\) |
−0.997908 | + | 0.0646438i | \(0.979409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.53590 | + | 9.58846i | −0.180274 | + | 0.312243i | ||||
\(944\) | 175.138 | 5.70027 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −63.1769 | −2.05406 | ||||||||
\(947\) | −1.14359 | + | 1.98076i | −0.0371618 | + | 0.0643661i | −0.884008 | − | 0.467472i | \(-0.845165\pi\) |
0.846846 | + | 0.531838i | \(0.178498\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.3923 | + | 45.7128i | 0.856730 | + | 1.48390i | ||||
\(950\) | 3.36603 | + | 5.83013i | 0.109208 | + | 0.189154i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.39230 | + | 7.60770i | −0.142355 | + | 0.246567i | ||||
\(953\) | −15.6077 | −0.505583 | −0.252791 | − | 0.967521i | \(-0.581349\pi\) | ||||
−0.252791 | + | 0.967521i | \(0.581349\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.1244 | 0.521772 | ||||||||
\(956\) | −20.3923 | + | 35.3205i | −0.659534 | + | 1.14235i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −49.3468 | − | 85.4711i | −1.59432 | − | 2.76145i | ||||
\(959\) | −6.00000 | − | 10.3923i | −0.193750 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | −10.9282 | −0.352339 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 100.105 | 3.22417 | ||||||||
\(965\) | −4.36603 | + | 7.56218i | −0.140547 | + | 0.243435i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.0981 | + | 31.3468i | 0.581995 | + | 1.00804i | 0.995243 | + | 0.0974261i | \(0.0310610\pi\) |
−0.413248 | + | 0.910619i | \(0.635606\pi\) | |||||||
\(968\) | 27.7128 | + | 48.0000i | 0.890724 | + | 1.54278i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.4641 | − | 18.1244i | 0.335982 | − | 0.581938i | ||||
\(971\) | 41.4449 | 1.33003 | 0.665014 | − | 0.746830i | \(-0.268425\pi\) | ||||
0.665014 | + | 0.746830i | \(0.268425\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.1244 | −0.869567 | ||||||||
\(974\) | −4.92820 | + | 8.53590i | −0.157910 | + | 0.273508i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.8564 | − | 51.7128i | −0.955680 | − | 1.65529i | ||||
\(977\) | −0.732051 | − | 1.26795i | −0.0234204 | − | 0.0405653i | 0.854078 | − | 0.520145i | \(-0.174122\pi\) |
−0.877498 | + | 0.479580i | \(0.840789\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.89230 | + | 10.2058i | −0.188319 | + | 0.326178i | ||||
\(980\) | 29.4641 | 0.941196 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 104.158 | 3.32381 | ||||||||
\(983\) | 8.70577 | − | 15.0788i | 0.277671 | − | 0.480940i | −0.693135 | − | 0.720808i | \(-0.743771\pi\) |
0.970806 | + | 0.239868i | \(0.0771042\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.92820 | − | 12.0000i | −0.220751 | − | 0.382352i | ||||
\(986\) | 7.19615 | + | 12.4641i | 0.229172 | + | 0.396938i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −36.7846 | + | 63.7128i | −1.17027 | + | 2.02697i | ||||
\(989\) | 35.3205 | 1.12313 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.14359 | 0.0998595 | 0.0499298 | − | 0.998753i | \(-0.484100\pi\) | ||||
0.0499298 | + | 0.998753i | \(0.484100\pi\) | |||||||
\(992\) | 32.7846 | − | 56.7846i | 1.04091 | − | 1.80291i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.464102 | + | 0.803848i | 0.0147204 | + | 0.0254965i | ||||
\(995\) | −1.00000 | − | 1.73205i | −0.0317021 | − | 0.0549097i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.75833 | − | 16.9019i | 0.309049 | − | 0.535289i | −0.669105 | − | 0.743168i | \(-0.733322\pi\) |
0.978155 | + | 0.207878i | \(0.0666558\pi\) | |||||||
\(998\) | −28.1962 | −0.892534 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 405.2.e.i.136.1 | 4 | ||
3.2 | odd | 2 | 405.2.e.l.136.2 | 4 | |||
9.2 | odd | 6 | 405.2.a.g.1.1 | ✓ | 2 | ||
9.4 | even | 3 | inner | 405.2.e.i.271.1 | 4 | ||
9.5 | odd | 6 | 405.2.e.l.271.2 | 4 | |||
9.7 | even | 3 | 405.2.a.h.1.2 | yes | 2 | ||
36.7 | odd | 6 | 6480.2.a.bi.1.1 | 2 | |||
36.11 | even | 6 | 6480.2.a.br.1.1 | 2 | |||
45.2 | even | 12 | 2025.2.b.g.649.1 | 4 | |||
45.7 | odd | 12 | 2025.2.b.h.649.4 | 4 | |||
45.29 | odd | 6 | 2025.2.a.m.1.2 | 2 | |||
45.34 | even | 6 | 2025.2.a.g.1.1 | 2 | |||
45.38 | even | 12 | 2025.2.b.g.649.4 | 4 | |||
45.43 | odd | 12 | 2025.2.b.h.649.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.2.a.g.1.1 | ✓ | 2 | 9.2 | odd | 6 | ||
405.2.a.h.1.2 | yes | 2 | 9.7 | even | 3 | ||
405.2.e.i.136.1 | 4 | 1.1 | even | 1 | trivial | ||
405.2.e.i.271.1 | 4 | 9.4 | even | 3 | inner | ||
405.2.e.l.136.2 | 4 | 3.2 | odd | 2 | |||
405.2.e.l.271.2 | 4 | 9.5 | odd | 6 | |||
2025.2.a.g.1.1 | 2 | 45.34 | even | 6 | |||
2025.2.a.m.1.2 | 2 | 45.29 | odd | 6 | |||
2025.2.b.g.649.1 | 4 | 45.2 | even | 12 | |||
2025.2.b.g.649.4 | 4 | 45.38 | even | 12 | |||
2025.2.b.h.649.1 | 4 | 45.43 | odd | 12 | |||
2025.2.b.h.649.4 | 4 | 45.7 | odd | 12 | |||
6480.2.a.bi.1.1 | 2 | 36.7 | odd | 6 | |||
6480.2.a.br.1.1 | 2 | 36.11 | even | 6 |