Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(193,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bs (of order \(12\), degree \(4\), 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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 457.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.457 |
Dual form | 1300.2.bs.b.293.1 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | + | 0.133975i | 0.288675 | + | 0.0773503i | 0.400251 | − | 0.916406i | \(-0.368923\pi\) |
−0.111576 | + | 0.993756i | \(0.535590\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.13397 | + | 1.23205i | 0.806567 | + | 0.465671i | 0.845762 | − | 0.533560i | \(-0.179146\pi\) |
−0.0391956 | + | 0.999232i | \(0.512480\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.36603 | − | 1.36603i | −0.788675 | − | 0.455342i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.13397 | + | 4.23205i | −0.341906 | + | 1.27601i | 0.554279 | + | 0.832331i | \(0.312994\pi\) |
−0.896185 | + | 0.443680i | \(0.853673\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | + | 3.00000i | 0.554700 | + | 0.832050i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.232051 | + | 0.866025i | 0.0562806 | + | 0.210042i | 0.988340 | − | 0.152264i | \(-0.0486563\pi\) |
−0.932059 | + | 0.362306i | \(0.881990\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.86603 | + | 0.767949i | −0.657511 | + | 0.176180i | −0.572123 | − | 0.820168i | \(-0.693880\pi\) |
−0.0853887 | + | 0.996348i | \(0.527213\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.901924 | + | 0.901924i | 0.196816 | + | 0.196816i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0358984 | − | 0.133975i | 0.00748533 | − | 0.0279356i | −0.962082 | − | 0.272760i | \(-0.912064\pi\) |
0.969567 | + | 0.244824i | \(0.0787302\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.09808 | − | 2.09808i | −0.403775 | − | 0.403775i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | + | 0.866025i | −0.278543 | + | 0.160817i | −0.632764 | − | 0.774345i | \(-0.718080\pi\) |
0.354221 | + | 0.935162i | \(0.384746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.19615 | + | 5.19615i | −0.933257 | + | 0.933257i | −0.997908 | − | 0.0646514i | \(-0.979406\pi\) |
0.0646514 | + | 0.997908i | \(0.479406\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.13397 | + | 1.96410i | −0.197400 | + | 0.341906i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.33013 | + | 0.767949i | −0.218672 | + | 0.126250i | −0.605335 | − | 0.795971i | \(-0.706961\pi\) |
0.386663 | + | 0.922221i | \(0.373628\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.598076 | + | 1.76795i | 0.0957688 | + | 0.283098i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.33013 | + | 2.50000i | 1.45712 | + | 0.390434i | 0.898494 | − | 0.438985i | \(-0.144662\pi\) |
0.558627 | + | 0.829419i | \(0.311329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.96410 | − | 1.59808i | 0.909517 | − | 0.243704i | 0.226418 | − | 0.974030i | \(-0.427298\pi\) |
0.683099 | + | 0.730326i | \(0.260632\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9282i | 1.59404i | 0.603951 | + | 0.797021i | \(0.293592\pi\) | ||||
−0.603951 | + | 0.797021i | \(0.706408\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.464102 | − | 0.803848i | −0.0663002 | − | 0.114835i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.464102i | 0.0649872i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.46410 | + | 2.46410i | −0.338470 | + | 0.338470i | −0.855791 | − | 0.517321i | \(-0.826929\pi\) |
0.517321 | + | 0.855791i | \(0.326929\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.53590 | −0.203435 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.33013 | + | 8.69615i | 0.303357 | + | 1.13214i | 0.934351 | + | 0.356355i | \(0.115981\pi\) |
−0.630994 | + | 0.775788i | \(0.717353\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.50000 | − | 7.79423i | 0.576166 | − | 0.997949i | −0.419748 | − | 0.907641i | \(-0.637882\pi\) |
0.995914 | − | 0.0903080i | \(-0.0287851\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.36603 | − | 5.83013i | −0.424079 | − | 0.734527i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.13397 | − | 10.6244i | −0.749384 | − | 1.29797i | −0.948118 | − | 0.317918i | \(-0.897016\pi\) |
0.198734 | − | 0.980053i | \(-0.436317\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0358984 | − | 0.0621778i | 0.00432166 | − | 0.00748533i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.598076 | + | 2.23205i | 0.0709786 | + | 0.264896i | 0.992291 | − | 0.123927i | \(-0.0395487\pi\) |
−0.921313 | + | 0.388822i | \(0.872882\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.9282 | 1.74721 | 0.873607 | − | 0.486632i | \(-0.161775\pi\) | ||||
0.873607 | + | 0.486632i | \(0.161775\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.63397 | + | 7.63397i | −0.869972 | + | 0.869972i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.535898i | 0.0602933i | 0.999545 | + | 0.0301466i | \(0.00959743\pi\) | ||||
−0.999545 | + | 0.0301466i | \(0.990403\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.33013 | + | 5.76795i | 0.370014 | + | 0.640883i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.92820i | 0.321412i | 0.987002 | + | 0.160706i | \(0.0513771\pi\) | ||||
−0.987002 | + | 0.160706i | \(0.948623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.866025 | + | 0.232051i | −0.0928477 | + | 0.0248785i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7942 | − | 3.96410i | −1.56819 | − | 0.420194i | −0.632942 | − | 0.774199i | \(-0.718153\pi\) |
−0.935243 | + | 0.354005i | \(0.884819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.571797 | + | 8.86603i | 0.0599406 | + | 0.929412i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.29423 | + | 1.90192i | −0.341596 | + | 0.197220i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.86603 | + | 6.69615i | −0.392535 | + | 0.679891i | −0.992783 | − | 0.119923i | \(-0.961735\pi\) |
0.600248 | + | 0.799814i | \(0.295069\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.46410 | − | 8.46410i | 0.850674 | − | 0.850674i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.8923 | + | 8.59808i | −1.48184 | + | 0.855541i | −0.999788 | − | 0.0206021i | \(-0.993442\pi\) |
−0.482052 | + | 0.876143i | \(0.660108\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.1962 | + | 11.1962i | 1.10319 | + | 1.10319i | 0.994024 | + | 0.109166i | \(0.0348181\pi\) |
0.109166 | + | 0.994024i | \(0.465182\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.96410 | − | 7.33013i | 0.189877 | − | 0.708630i | −0.803657 | − | 0.595093i | \(-0.797115\pi\) |
0.993534 | − | 0.113537i | \(-0.0362181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.53590 | − | 3.53590i | −0.338678 | − | 0.338678i | 0.517192 | − | 0.855869i | \(-0.326977\pi\) |
−0.855869 | + | 0.517192i | \(0.826977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.767949 | + | 0.205771i | −0.0728905 | + | 0.0195310i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.767949 | − | 2.86603i | −0.0722426 | − | 0.269613i | 0.920351 | − | 0.391093i | \(-0.127903\pi\) |
−0.992594 | + | 0.121480i | \(0.961236\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.633975 | − | 9.83013i | −0.0586110 | − | 0.908796i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.571797 | + | 2.13397i | −0.0524165 | + | 0.195621i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.09808 | − | 4.09808i | −0.645280 | − | 0.372552i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.33013 | + | 2.50000i | 0.390434 | + | 0.225417i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.8923 | + | 5.33013i | 1.76516 | + | 0.472972i | 0.987752 | − | 0.156029i | \(-0.0498694\pi\) |
0.777404 | + | 0.629001i | \(0.216536\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.19615 | 0.281406 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.85641 | 0.511677 | 0.255838 | − | 0.966720i | \(-0.417649\pi\) | ||||
0.255838 | + | 0.966720i | \(0.417649\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.06218 | − | 1.89230i | −0.612368 | − | 0.164084i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.4019 | + | 7.16025i | 1.05957 | + | 0.611742i | 0.925313 | − | 0.379205i | \(-0.123802\pi\) |
0.134255 | + | 0.990947i | \(0.457136\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.50000 | − | 2.59808i | −0.381685 | − | 0.220366i | 0.296866 | − | 0.954919i | \(-0.404058\pi\) |
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.46410 | + | 5.46410i | −0.123300 | + | 0.460160i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.9641 | + | 5.06218i | −1.25136 | + | 0.423321i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.124356 | − | 0.464102i | −0.0102567 | − | 0.0382785i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.33013 | + | 0.892305i | −0.272815 | + | 0.0731005i | −0.392633 | − | 0.919695i | \(-0.628436\pi\) |
0.119818 | + | 0.992796i | \(0.461769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.267949 | − | 0.267949i | −0.0218054 | − | 0.0218054i | 0.696120 | − | 0.717925i | \(-0.254908\pi\) |
−0.717925 | + | 0.696120i | \(0.754908\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.633975 | − | 2.36603i | 0.0512538 | − | 0.191282i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.46410 | − | 6.46410i | −0.515891 | − | 0.515891i | 0.400434 | − | 0.916326i | \(-0.368859\pi\) |
−0.916326 | + | 0.400434i | \(0.868859\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.56218 | + | 0.901924i | −0.123889 | + | 0.0715272i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.241670 | − | 0.241670i | 0.0190462 | − | 0.0190462i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.59808 | − | 2.76795i | 0.125171 | − | 0.216803i | −0.796629 | − | 0.604469i | \(-0.793385\pi\) |
0.921800 | + | 0.387666i | \(0.126719\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.9904 | − | 9.23205i | 1.23737 | − | 0.714398i | 0.268816 | − | 0.963191i | \(-0.413368\pi\) |
0.968556 | + | 0.248794i | \(0.0800342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | + | 12.0000i | −0.384615 | + | 0.923077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.83013 | + | 2.09808i | 0.598785 | + | 0.160444i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.76795 | − | 0.741670i | 0.210443 | − | 0.0563881i | −0.152057 | − | 0.988372i | \(-0.548590\pi\) |
0.362500 | + | 0.931984i | \(0.381923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.66025i | 0.350286i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.96410 | + | 12.0622i | 0.520521 | + | 0.901570i | 0.999715 | + | 0.0238604i | \(0.00759573\pi\) |
−0.479194 | + | 0.877709i | \(0.659071\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.9282i | − | 1.70424i | −0.523347 | − | 0.852120i | \(-0.675317\pi\) | ||
0.523347 | − | 0.852120i | \(-0.324683\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.29423 | − | 3.29423i | 0.243516 | − | 0.243516i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.92820 | −0.287259 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.89230 | − | 7.06218i | −0.137645 | − | 0.513698i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.50000 | − | 12.9904i | 0.542681 | − | 0.939951i | −0.456068 | − | 0.889945i | \(-0.650743\pi\) |
0.998749 | − | 0.0500060i | \(-0.0159241\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.7942 | − | 22.1603i | −0.920949 | − | 1.59513i | −0.797950 | − | 0.602723i | \(-0.794082\pi\) |
−0.122998 | − | 0.992407i | \(-0.539251\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.13397 | − | 3.69615i | −0.152039 | − | 0.263340i | 0.779938 | − | 0.625857i | \(-0.215251\pi\) |
−0.931977 | + | 0.362517i | \(0.881917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.42820 | − | 16.3301i | 0.668348 | − | 1.15761i | −0.310018 | − | 0.950731i | \(-0.600335\pi\) |
0.978366 | − | 0.206881i | \(-0.0663314\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.64359 | − | 6.13397i | −0.115930 | − | 0.432657i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.26795 | −0.299551 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.267949 | + | 0.267949i | −0.0186238 | + | 0.0186238i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 13.0000i | − | 0.899229i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.96410 | − | 5.13397i | −0.204057 | − | 0.353437i | 0.745775 | − | 0.666198i | \(-0.232080\pi\) |
−0.949832 | + | 0.312761i | \(0.898746\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.19615i | 0.0819590i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.4904 | + | 4.68653i | −1.18732 | + | 0.318143i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.46410 | + | 2.00000i | 0.504377 | + | 0.135147i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.13397 | + | 2.42820i | −0.143547 | + | 0.163339i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.33013 | − | 0.767949i | 0.0890719 | − | 0.0514257i | −0.454802 | − | 0.890592i | \(-0.650290\pi\) |
0.543874 | + | 0.839167i | \(0.316957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.59808 | + | 2.76795i | −0.106068 | + | 0.183715i | −0.914174 | − | 0.405322i | \(-0.867159\pi\) |
0.808106 | + | 0.589037i | \(0.200493\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.0717968 | − | 0.0717968i | 0.00474446 | − | 0.00474446i | −0.704731 | − | 0.709475i | \(-0.748932\pi\) |
0.709475 | + | 0.704731i | \(0.248932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.83975 | + | 2.79423i | −0.318432 | + | 0.183847i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.8564 | − | 12.8564i | −0.842251 | − | 0.842251i | 0.146900 | − | 0.989151i | \(-0.453070\pi\) |
−0.989151 | + | 0.146900i | \(0.953070\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.0717968 | + | 0.267949i | −0.00466370 | + | 0.0174052i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.6603 | + | 16.6603i | 1.07766 | + | 1.07766i | 0.996719 | + | 0.0809436i | \(0.0257934\pi\) |
0.0809436 | + | 0.996719i | \(0.474207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3301 | − | 3.03590i | 0.729838 | − | 0.195559i | 0.125281 | − | 0.992121i | \(-0.460017\pi\) |
0.604557 | + | 0.796562i | \(0.293350\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.19615 | + | 11.9282i | 0.205033 | + | 0.765195i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.03590 | − | 7.06218i | −0.511312 | − | 0.449356i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.392305 | + | 1.46410i | −0.0248613 | + | 0.0927837i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.3564 | − | 8.86603i | −0.969288 | − | 0.559619i | −0.0702687 | − | 0.997528i | \(-0.522386\pi\) |
−0.899019 | + | 0.437910i | \(0.855719\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.526279 | + | 0.303848i | 0.0330869 | + | 0.0191027i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.6244 | − | 5.79423i | −1.34889 | − | 0.361434i | −0.489165 | − | 0.872191i | \(-0.662698\pi\) |
−0.859725 | + | 0.510757i | \(0.829365\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.78461 | −0.235164 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.73205 | 0.292907 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.8923 | − | 3.72243i | −0.856636 | − | 0.229535i | −0.196336 | − | 0.980537i | \(-0.562904\pi\) |
−0.660300 | + | 0.751002i | \(0.729571\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.86603 | − | 3.96410i | −0.420194 | − | 0.242599i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.8205 | + | 9.13397i | 0.964593 | + | 0.556908i | 0.897584 | − | 0.440844i | \(-0.145321\pi\) |
0.0670097 | + | 0.997752i | \(0.478654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.33013 | − | 16.1603i | 0.263036 | − | 0.981666i | −0.700405 | − | 0.713746i | \(-0.746997\pi\) |
0.963441 | − | 0.267920i | \(-0.0863362\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.901924 | + | 4.50962i | −0.0545869 | + | 0.272935i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.76795 | + | 10.3301i | 0.166310 | + | 0.620677i | 0.997869 | + | 0.0652416i | \(0.0207818\pi\) |
−0.831560 | + | 0.555436i | \(0.812552\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.3923 | − | 5.19615i | 1.16099 | − | 0.311086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4641 | − | 16.4641i | −0.982166 | − | 0.982166i | 0.0176778 | − | 0.999844i | \(-0.494373\pi\) |
−0.999844 | + | 0.0176778i | \(0.994373\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.96410 | + | 29.7224i | −0.473417 | + | 1.76682i | 0.153937 | + | 0.988081i | \(0.450805\pi\) |
−0.627354 | + | 0.778735i | \(0.715862\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.8301 | + | 16.8301i | 0.993451 | + | 0.993451i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.0263 | − | 8.09808i | 0.825075 | − | 0.476357i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.83013 | + | 2.83013i | −0.165905 | + | 0.165905i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2583 | − | 17.7679i | 0.599298 | − | 1.03801i | −0.393627 | − | 0.919270i | \(-0.628780\pi\) |
0.992925 | − | 0.118744i | \(-0.0378869\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.2583 | − | 6.50000i | 0.653275 | − | 0.377168i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.473721 | − | 0.160254i | 0.0273960 | − | 0.00926773i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.6962 | + | 3.93782i | 0.847072 | + | 0.226972i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.59808 | + | 2.30385i | −0.493947 | + | 0.132353i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.00000i | − | 0.228292i | −0.993464 | − | 0.114146i | \(-0.963587\pi\) | ||
0.993464 | − | 0.114146i | \(-0.0364132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.09808 | + | 7.09808i | 0.233131 | + | 0.403795i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.46410i | 0.196431i | 0.995165 | + | 0.0982156i | \(0.0313135\pi\) | ||||
−0.995165 | + | 0.0982156i | \(0.968687\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.53590 | − | 5.53590i | 0.312907 | − | 0.312907i | −0.533127 | − | 0.846035i | \(-0.678983\pi\) |
0.846035 | + | 0.533127i | \(0.178983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.9282 | 1.06311 | 0.531557 | − | 0.847023i | \(-0.321607\pi\) | ||||
0.531557 | + | 0.847023i | \(0.321607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.96410 | − | 7.33013i | −0.109969 | − | 0.410408i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.96410 | − | 3.40192i | 0.109625 | − | 0.189877i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.33013 | − | 2.30385i | −0.0740102 | − | 0.128190i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.29423 | − | 2.24167i | −0.0715710 | − | 0.123965i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.4641 | + | 23.3205i | −0.742300 | + | 1.28570i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.45448 | + | 16.6244i | 0.244841 | + | 0.913757i | 0.973464 | + | 0.228842i | \(0.0734940\pi\) |
−0.728623 | + | 0.684915i | \(0.759839\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.19615 | 0.229948 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.9282 | − | 15.9282i | 0.867665 | − | 0.867665i | −0.124549 | − | 0.992213i | \(-0.539748\pi\) |
0.992213 | + | 0.124549i | \(0.0397484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 1.53590i | − | 0.0834185i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.0981 | − | 27.8827i | −0.871760 | − | 1.50993i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.5359i | − | 1.05484i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.4282 | − | 2.79423i | 0.559815 | − | 0.150002i | 0.0321938 | − | 0.999482i | \(-0.489751\pi\) |
0.527621 | + | 0.849480i | \(0.323084\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.86603 | − | 2.10770i | −0.421059 | − | 0.112822i | 0.0420673 | − | 0.999115i | \(-0.486606\pi\) |
−0.463126 | + | 0.886292i | \(0.653272\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.09808 | − | 10.4904i | 0.111987 | − | 0.559935i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.06218 | + | 5.23205i | −0.482331 | + | 0.278474i | −0.721387 | − | 0.692532i | \(-0.756495\pi\) |
0.239056 | + | 0.971006i | \(0.423162\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.571797 | + | 0.990381i | −0.0302627 | + | 0.0524165i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.1962 | − | 13.1962i | 0.696466 | − | 0.696466i | −0.267180 | − | 0.963647i | \(-0.586092\pi\) |
0.963647 | + | 0.267180i | \(0.0860919\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.83013 | + | 5.09808i | −0.464744 | + | 0.268320i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.00000 | − | 3.00000i | −0.157459 | − | 0.157459i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.96410 | − | 14.7942i | 0.206924 | − | 0.772252i | −0.781930 | − | 0.623366i | \(-0.785765\pi\) |
0.988854 | − | 0.148886i | \(-0.0475688\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.6603 | − | 18.6603i | −0.971414 | − | 0.971414i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.29423 | + | 2.22243i | −0.430615 | + | 0.115383i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.30385 | − | 19.7942i | −0.274623 | − | 1.02491i | −0.956094 | − | 0.293061i | \(-0.905326\pi\) |
0.681471 | − | 0.731845i | \(-0.261341\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.59808 | − | 2.76795i | −0.288316 | − | 0.142557i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.59808 | − | 9.69615i | 0.133454 | − | 0.498058i | −0.866545 | − | 0.499099i | \(-0.833665\pi\) |
0.999999 | + | 0.00104063i | \(0.000331242\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.23205 | + | 5.33013i | 0.472972 | + | 0.273071i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.1147 | + | 12.7679i | 1.13001 | + | 0.652412i | 0.943937 | − | 0.330124i | \(-0.107091\pi\) |
0.186073 | + | 0.982536i | \(0.440424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.2942 | − | 4.36603i | −0.828282 | − | 0.221938i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0718 | −0.764170 | −0.382085 | − | 0.924127i | \(-0.624794\pi\) | ||||
−0.382085 | + | 0.924127i | \(0.624794\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.124356 | 0.00628894 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.92820 | + | 0.784610i | 0.147708 | + | 0.0395783i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.86603 | + | 5.69615i | 0.495162 | + | 0.285882i | 0.726713 | − | 0.686941i | \(-0.241047\pi\) |
−0.231552 | + | 0.972823i | \(0.574380\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.27757 | − | 1.89230i | −0.164084 | − | 0.0947337i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.66987 | − | 9.96410i | 0.133327 | − | 0.497583i | −0.866672 | − | 0.498878i | \(-0.833745\pi\) |
0.999999 | + | 0.00129478i | \(0.000412141\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.9808 | − | 5.19615i | −1.29419 | − | 0.258839i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.74167 | − | 6.50000i | −0.0863314 | − | 0.322193i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.5263 | − | 4.96410i | 0.916066 | − | 0.245459i | 0.230163 | − | 0.973152i | \(-0.426074\pi\) |
0.685903 | + | 0.727693i | \(0.259407\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.24167 | + | 5.24167i | 0.258553 | + | 0.258553i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.74167 | + | 21.4282i | −0.282529 | + | 1.05441i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.90192 | − | 1.90192i | −0.0931376 | − | 0.0931376i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.5000 | + | 18.1865i | −1.53888 | + | 0.888470i | −0.539971 | + | 0.841684i | \(0.681565\pi\) |
−0.998905 | + | 0.0467865i | \(0.985102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.85641 | − | 6.85641i | 0.334161 | − | 0.334161i | −0.520003 | − | 0.854164i | \(-0.674069\pi\) |
0.854164 | + | 0.520003i | \(0.174069\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.9282 | − | 25.8564i | 0.725834 | − | 1.25718i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.2058 | − | 11.0885i | 0.929432 | − | 0.536608i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.16025 | + | 0.526279i | −0.393981 | + | 0.0254090i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.2583 | − | 6.23205i | −1.12031 | − | 0.300187i | −0.349304 | − | 0.937010i | \(-0.613582\pi\) |
−0.771011 | + | 0.636822i | \(0.780249\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.5526 | + | 8.72243i | −1.56438 | + | 0.419173i | −0.934046 | − | 0.357154i | \(-0.883747\pi\) |
−0.630330 | + | 0.776327i | \(0.717081\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.411543i | 0.0196868i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.0358984 | + | 0.0621778i | 0.00171334 | + | 0.00296759i | 0.866881 | − | 0.498515i | \(-0.166121\pi\) |
−0.865167 | + | 0.501483i | \(0.832788\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.53590i | 0.120757i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.5885 | − | 15.5885i | 0.740630 | − | 0.740630i | −0.232069 | − | 0.972699i | \(-0.574550\pi\) |
0.972699 | + | 0.232069i | \(0.0745496\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.78461 | −0.0844091 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.20577 | − | 19.4282i | −0.245676 | − | 0.916874i | −0.973043 | − | 0.230625i | \(-0.925923\pi\) |
0.727367 | − | 0.686249i | \(-0.240744\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.1603 | + | 36.6506i | −0.996397 | + | 1.72581i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.0980762 | − | 0.169873i | −0.00460802 | − | 0.00798133i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.79423 | + | 11.7679i | 0.317821 | + | 0.550481i | 0.980033 | − | 0.198835i | \(-0.0637157\pi\) |
−0.662212 | + | 0.749316i | \(0.730382\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.33013 | − | 2.30385i | 0.0620850 | − | 0.107534i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.813467 | + | 3.03590i | 0.0378869 | + | 0.141396i | 0.982279 | − | 0.187427i | \(-0.0600148\pi\) |
−0.944392 | + | 0.328823i | \(0.893348\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.6077 | 1.00419 | 0.502097 | − | 0.864811i | \(-0.332562\pi\) | ||||
0.502097 | + | 0.864811i | \(0.332562\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.6603 | + | 16.6603i | −0.770945 | + | 0.770945i | −0.978272 | − | 0.207327i | \(-0.933524\pi\) |
0.207327 | + | 0.978272i | \(0.433524\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 30.2295i | − | 1.39587i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.36603 | − | 4.09808i | −0.109021 | − | 0.188829i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.0526i | 1.24388i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.19615 | − | 2.46410i | 0.421063 | − | 0.112823i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.13397 | − | 0.839746i | −0.143195 | − | 0.0383690i | 0.186510 | − | 0.982453i | \(-0.440282\pi\) |
−0.329705 | + | 0.944084i | \(0.606949\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.96410 | − | 2.45448i | −0.226344 | − | 0.111915i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.153212 | − | 0.0884573i | 0.00697141 | − | 0.00402495i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.794229 | − | 1.37564i | 0.0359899 | − | 0.0623364i | −0.847469 | − | 0.530844i | \(-0.821875\pi\) |
0.883459 | + | 0.468508i | \(0.155208\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.16987 | − | 1.16987i | 0.0529035 | − | 0.0529035i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.89230 | − | 3.40192i | 0.265916 | − | 0.153527i | −0.361114 | − | 0.932522i | \(-0.617604\pi\) |
0.627030 | + | 0.778995i | \(0.284270\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.09808 | − | 1.09808i | −0.0494549 | − | 0.0494549i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.47372 | + | 5.50000i | −0.0661054 | + | 0.246709i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.2679 | + | 20.2679i | 0.907318 | + | 0.907318i | 0.996055 | − | 0.0887371i | \(-0.0282831\pi\) |
−0.0887371 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.23205 | − | 2.47372i | 0.412458 | − | 0.110518i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.35641 | + | 12.5263i | 0.149655 | + | 0.558519i | 0.999504 | + | 0.0314933i | \(0.0100263\pi\) |
−0.849849 | + | 0.527026i | \(0.823307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.10770 | + | 5.33013i | −0.182429 | + | 0.236719i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.45448 | + | 27.8205i | −0.330414 | + | 1.23312i | 0.578342 | + | 0.815795i | \(0.303700\pi\) |
−0.908756 | + | 0.417328i | \(0.862967\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.8564 | + | 18.3923i | 1.40924 | + | 0.813628i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.62436 | + | 4.40192i | 0.336624 | + | 0.194350i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −46.2487 | − | 12.3923i | −2.03402 | − | 0.545013i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.48334 | 0.0651114 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.85641 | −0.344195 | −0.172098 | − | 0.985080i | \(-0.555054\pi\) | ||||
−0.172098 | + | 0.985080i | \(0.555054\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.9641 | − | 2.93782i | −0.479427 | − | 0.128462i | 0.0110090 | − | 0.999939i | \(-0.496496\pi\) |
−0.490436 | + | 0.871477i | \(0.663162\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.70577 | − | 3.29423i | −0.248547 | − | 0.143499i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9019 | + | 11.4904i | 0.865301 | + | 0.499582i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.36603 | − | 23.7583i | 0.276262 | − | 1.03102i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.1603 | + | 32.9904i | 0.483404 | + | 1.42897i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.86603 | + | 6.96410i | 0.0805249 | + | 0.300523i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.92820 | − | 1.05256i | 0.169200 | − | 0.0453369i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.7846 | + | 21.7846i | 0.936594 | + | 0.936594i | 0.998106 | − | 0.0615128i | \(-0.0195925\pi\) |
−0.0615128 | + | 0.998106i | \(0.519592\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.07180 | − | 11.4641i | 0.131823 | − | 0.491972i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.124356 | + | 0.124356i | 0.00531706 | + | 0.00531706i | 0.709760 | − | 0.704443i | \(-0.248803\pi\) |
−0.704443 | + | 0.709760i | \(0.748803\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.2942 | + | 12.2942i | −0.908816 | + | 0.524705i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.63397 | − | 3.63397i | 0.154813 | − | 0.154813i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.660254 | + | 1.14359i | −0.0280769 | + | 0.0486305i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.3301 | + | 7.69615i | −0.564816 | + | 0.326096i | −0.755076 | − | 0.655637i | \(-0.772400\pi\) |
0.190260 | + | 0.981734i | \(0.439067\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.7224 | + | 14.6962i | 0.707284 | + | 0.621581i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.96410 | − | 0.526279i | −0.0829244 | − | 0.0222195i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.8923 | − | 6.66987i | 1.04909 | − | 0.281102i | 0.307212 | − | 0.951641i | \(-0.400604\pi\) |
0.741874 | + | 0.670540i | \(0.233937\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.4115i | 0.689220i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.8205 | + | 32.5981i | 0.788997 | + | 1.36658i | 0.926582 | + | 0.376093i | \(0.122733\pi\) |
−0.137585 | + | 0.990490i | \(0.543934\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.6077i | 0.904254i | 0.891954 | + | 0.452127i | \(0.149335\pi\) | ||||
−0.891954 | + | 0.452127i | \(0.850665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.49038 | − | 5.49038i | 0.229364 | − | 0.229364i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.7846 | −0.865275 | −0.432637 | − | 0.901568i | \(-0.642417\pi\) | ||||
−0.432637 | + | 0.901568i | \(0.642417\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.42820 | − | 12.7942i | −0.142471 | − | 0.531710i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.60770 | + | 6.24871i | −0.149672 | + | 0.259240i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.63397 | − | 13.2224i | −0.316167 | − | 0.547617i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.7224 | + | 41.0885i | 0.979130 | + | 1.69590i | 0.665573 | + | 0.746333i | \(0.268187\pi\) |
0.313556 | + | 0.949570i | \(0.398480\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.9019 | − | 18.8827i | 0.449206 | − | 0.778048i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.571797 | − | 2.13397i | −0.0235206 | − | 0.0877800i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.9282 | 1.27007 | 0.635035 | − | 0.772484i | \(-0.280986\pi\) | ||||
0.635035 | + | 0.772484i | \(0.280986\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.90192 | − | 6.90192i | 0.282477 | − | 0.282477i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.2487i | 1.48108i | 0.672011 | + | 0.740541i | \(0.265431\pi\) | ||||
−0.672011 | + | 0.740541i | \(0.734569\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.42820 | + | 12.8660i | 0.303003 | + | 0.524816i | 0.976815 | − | 0.214087i | \(-0.0686775\pi\) |
−0.673812 | + | 0.738903i | \(0.735344\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.5167i | 1.36490i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.03590 | + | 0.813467i | −0.123223 | + | 0.0330176i | −0.319904 | − | 0.947450i | \(-0.603651\pi\) |
0.196680 | + | 0.980468i | \(0.436984\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.13397 | − | 0.571797i | −0.0864730 | − | 0.0231704i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.7846 | + | 21.8564i | −1.32632 | + | 0.884216i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.1865 | − | 12.2321i | 0.855716 | − | 0.494048i | −0.00685934 | − | 0.999976i | \(-0.502183\pi\) |
0.862575 | + | 0.505929i | \(0.168850\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.79423 | + | 15.2321i | −0.354042 | + | 0.613219i | −0.986954 | − | 0.161005i | \(-0.948526\pi\) |
0.632911 | + | 0.774224i | \(0.281860\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.6603 | − | 14.6603i | 0.589245 | − | 0.589245i | −0.348182 | − | 0.937427i | \(-0.613201\pi\) |
0.937427 | + | 0.348182i | \(0.113201\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.356406 | + | 0.205771i | −0.0143021 | + | 0.00825732i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26.6865 | − | 26.6865i | −1.06917 | − | 1.06917i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.74167 | − | 6.50000i | 0.0695556 | − | 0.259585i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.973721 | − | 0.973721i | −0.0388248 | − | 0.0388248i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.6506 | − | 11.1603i | 1.65809 | − | 0.444283i | 0.696225 | − | 0.717823i | \(-0.254862\pi\) |
0.961860 | + | 0.273541i | \(0.0881948\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.794229 | − | 2.96410i | −0.0315678 | − | 0.117812i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.48334 | − | 3.00000i | 0.0587721 | − | 0.118864i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.63397 | − | 6.09808i | 0.0646390 | − | 0.241236i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.64359 | + | 3.25833i | 0.222909 | + | 0.128696i | 0.607296 | − | 0.794475i | \(-0.292254\pi\) |
−0.384388 | + | 0.923172i | \(0.625587\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.3301 | + | 18.0885i | 1.23554 | + | 0.713339i | 0.968179 | − | 0.250258i | \(-0.0805153\pi\) |
0.267360 | + | 0.963597i | \(0.413849\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.50000 | − | 0.669873i | −0.0982851 | − | 0.0263354i | 0.209341 | − | 0.977843i | \(-0.432868\pi\) |
−0.307626 | + | 0.951507i | \(0.599535\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.4449 | −1.54835 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.37307 | −0.367359 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −47.9449 | − | 12.8468i | −1.87623 | − | 0.502734i | −0.999774 | − | 0.0212467i | \(-0.993236\pi\) |
−0.876453 | − | 0.481487i | \(-0.840097\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −35.3205 | − | 20.3923i | −1.37798 | − | 0.795580i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.4282 | − | 20.4545i | −1.38009 | − | 0.796794i | −0.387918 | − | 0.921694i | \(-0.626805\pi\) |
−0.992169 | + | 0.124901i | \(0.960139\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.794229 | + | 2.96410i | −0.0308919 | + | 0.115290i | −0.979650 | − | 0.200713i | \(-0.935674\pi\) |
0.948758 | + | 0.316003i | \(0.102341\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.39230 | + | 0.928203i | −0.0540726 | + | 0.0360484i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0621778 | + | 0.232051i | 0.00240754 | + | 0.00898504i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.767949 | − | 0.205771i | 0.0296906 | − | 0.00795558i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.8827 | + | 27.8827i | 1.07640 | + | 1.07640i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.62436 | + | 35.9186i | −0.370992 | + | 1.38456i | 0.488122 | + | 0.872775i | \(0.337682\pi\) |
−0.859114 | + | 0.511784i | \(0.828985\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.1769 | + | 28.1769i | 1.08293 | + | 1.08293i | 0.996235 | + | 0.0866916i | \(0.0276295\pi\) |
0.0866916 | + | 0.996235i | \(0.472371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.5000 | + | 9.52628i | −0.633212 | + | 0.365585i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.16987 | + | 1.16987i | −0.0448296 | + | 0.0448296i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.33013 | + | 12.6962i | −0.280480 | + | 0.485805i | −0.971503 | − | 0.237028i | \(-0.923827\pi\) |
0.691023 | + | 0.722832i | \(0.257160\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.0455173 | − | 0.0262794i | 0.00173659 | − | 0.00100262i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.3205 | − | 2.46410i | −0.469374 | − | 0.0938748i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.6506 | − | 10.0885i | −1.43230 | − | 0.383783i | −0.542468 | − | 0.840076i | \(-0.682510\pi\) |
−0.889829 | + | 0.456293i | \(0.849177\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28.4904 | − | 7.63397i | 1.08226 | − | 0.289991i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.66025i | 0.328031i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.70577 | − | 8.15064i | −0.177989 | − | 0.308285i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.0718i | 0.795871i | 0.917413 | + | 0.397935i | \(0.130273\pi\) | ||||
−0.917413 | + | 0.397935i | \(0.869727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.22243 | − | 3.22243i | 0.121536 | − | 0.121536i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −42.3731 | −1.59360 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.27757 | − | 15.9641i | −0.160647 | − | 0.599544i | −0.998555 | − | 0.0537328i | \(-0.982888\pi\) |
0.837908 | − | 0.545812i | \(-0.183779\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.732051 | − | 1.26795i | 0.0274541 | − | 0.0475518i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.509619 | + | 0.882686i | 0.0190854 | + | 0.0330568i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.09808 | + | 10.5622i | 0.227737 | + | 0.394452i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.9641 | + | 36.3109i | −0.781829 | + | 1.35417i | 0.149046 | + | 0.988830i | \(0.452380\pi\) |
−0.930875 | + | 0.365337i | \(0.880954\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.0981 | + | 37.6865i | 0.376072 | + | 1.40352i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.07180 | 0.225813 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.5885 | − | 33.5885i | 1.24573 | − | 1.24573i | 0.288138 | − | 0.957589i | \(-0.406964\pi\) |
0.957589 | − | 0.288138i | \(-0.0930362\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 13.5885i | − | 0.503276i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.76795 | + | 4.79423i | 0.102376 | + | 0.177321i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.7846i | 0.989312i | 0.869089 | + | 0.494656i | \(0.164706\pi\) | ||||
−0.869089 | + | 0.494656i | \(0.835294\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 51.9186 | − | 13.9115i | 1.91245 | − | 0.512438i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.9186 | − | 10.1603i | −1.39486 | − | 0.373751i | −0.518362 | − | 0.855161i | \(-0.673458\pi\) |
−0.876495 | + | 0.481410i | \(0.840125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.07180 | − | 4.60770i | −0.112845 | − | 0.169268i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.3301 | − | 11.1603i | 0.709154 | − | 0.409430i | −0.101594 | − | 0.994826i | \(-0.532394\pi\) |
0.810748 | + | 0.585396i | \(0.199061\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.00000 | − | 6.92820i | 0.146352 | − | 0.253490i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.2224 | − | 13.2224i | 0.483137 | − | 0.483137i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.6436 | − | 10.1865i | 0.643824 | − | 0.371712i | −0.142262 | − | 0.989829i | \(-0.545438\pi\) |
0.786086 | + | 0.618117i | \(0.212104\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.49038 | − | 6.49038i | −0.236523 | − | 0.236523i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.83975 | − | 18.0622i | 0.175904 | − | 0.656481i | −0.820492 | − | 0.571657i | \(-0.806301\pi\) |
0.996396 | − | 0.0848236i | \(-0.0270327\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.222432 | + | 0.222432i | 0.00807377 | + | 0.00807377i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.669873 | + | 0.179492i | −0.0242829 | + | 0.00650658i | −0.270940 | − | 0.962596i | \(-0.587335\pi\) |
0.246657 | + | 0.969103i | \(0.420668\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.18911 | − | 11.9019i | −0.115454 | − | 0.430879i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.4282 | + | 24.3827i | −0.773728 | + | 0.880408i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.47372 | − | 20.4282i | 0.197387 | − | 0.736660i | −0.794248 | − | 0.607593i | \(-0.792135\pi\) |
0.991636 | − | 0.129067i | \(-0.0411982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.0359 | − | 5.79423i | −0.361434 | − | 0.208674i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.0429 | − | 9.83975i | −0.612992 | − | 0.353911i | 0.161144 | − | 0.986931i | \(-0.448482\pi\) |
−0.774136 | + | 0.633020i | \(0.781815\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.89230 | − | 0.507042i | −0.0678861 | − | 0.0181900i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.6603 | −1.02686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.1244 | −0.362278 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.96410 | + | 1.33013i | 0.177403 | + | 0.0475349i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.4545 | + | 21.6244i | 1.33511 | + | 0.770825i | 0.986078 | − | 0.166286i | \(-0.0531776\pi\) |
0.349031 | + | 0.937111i | \(0.386511\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.44744 | − | 3.72243i | −0.229535 | − | 0.132522i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.89230 | − | 7.06218i | 0.0672826 | − | 0.251102i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.3827 | − | 2.08846i | 1.14994 | − | 0.0741633i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.62436 | − | 20.9904i | −0.199225 | − | 0.743517i | −0.991133 | − | 0.132877i | \(-0.957579\pi\) |
0.791908 | − | 0.610641i | \(-0.209088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.46410 | + | 2.53590i | −0.334816 | + | 0.0897136i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.5885 | + | 29.5885i | 1.04546 | + | 1.04546i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.9282 | + | 63.1769i | −0.597383 | + | 2.22946i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.68653 | + | 6.68653i | 0.235377 | + | 0.235377i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.2846 | + | 5.93782i | −0.361588 | + | 0.208763i | −0.669777 | − | 0.742562i | \(-0.733610\pi\) |
0.308189 | + | 0.951325i | \(0.400277\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.0526 | + | 23.0526i | −0.809485 | + | 0.809485i | −0.984556 | − | 0.175071i | \(-0.943985\pi\) |
0.175071 | + | 0.984556i | \(0.443985\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.33013 | − | 7.50000i | 0.151864 | − | 0.263036i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.8660 | + | 9.16025i | −0.555082 | + | 0.320477i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.7583 | − | 21.7583i | 0.375926 | − | 0.760298i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.4545 | − | 7.35641i | −0.958168 | − | 0.256740i | −0.254343 | − | 0.967114i | \(-0.581859\pi\) |
−0.703825 | + | 0.710374i | \(0.748526\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.8923 | + | 6.40192i | −0.832833 | + | 0.223157i | −0.649949 | − | 0.759977i | \(-0.725210\pi\) |
−0.182884 | + | 0.983135i | \(0.558543\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.8564i | 0.899115i | 0.893251 | + | 0.449558i | \(0.148418\pi\) | ||||
−0.893251 | + | 0.449558i | \(0.851582\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.42820 | + | 7.66987i | 0.153798 | + | 0.266386i | 0.932621 | − | 0.360858i | \(-0.117516\pi\) |
−0.778823 | + | 0.627244i | \(0.784183\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.53590i | 0.192038i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.588457 | − | 0.588457i | 0.0203888 | − | 0.0203888i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.8038 | 0.753651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.79423 | + | 29.0885i | 0.269087 | + | 1.00425i | 0.959701 | + | 0.281022i | \(0.0906734\pi\) |
−0.690615 | + | 0.723223i | \(0.742660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | + | 22.5167i | −0.448276 | + | 0.776437i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.02628 | − | 10.4378i | −0.207556 | − | 0.359498i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.0981 | − | 17.4904i | −0.346974 | − | 0.600977i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.96410 | + | 13.7942i | −0.273327 | + | 0.473417i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0551363 | + | 0.205771i | 0.00189005 | + | 0.00705375i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 53.8564 | 1.84401 | 0.922004 | − | 0.387180i | \(-0.126551\pi\) | ||||
0.922004 | + | 0.387180i | \(0.126551\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.2487 | − | 19.2487i | 0.657523 | − | 0.657523i | −0.297270 | − | 0.954793i | \(-0.596076\pi\) |
0.954793 | + | 0.297270i | \(0.0960761\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.39230i | − | 0.0816244i | −0.999167 | − | 0.0408122i | \(-0.987005\pi\) | ||
0.999167 | − | 0.0408122i | \(-0.0129945\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.16025 | + | 10.6699i | 0.209941 | + | 0.363628i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.14359i | − | 0.0729688i | −0.999334 | − | 0.0364844i | \(-0.988384\pi\) | ||
0.999334 | − | 0.0364844i | \(-0.0116159\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.09808 | − | 2.16987i | 0.275025 | − | 0.0736927i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.26795 | − | 0.607695i | −0.0769349 | − | 0.0206146i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.6051 | − | 39.6506i | 0.664294 | − | 1.34351i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.2942 | − | 10.5622i | 0.619166 | − | 0.357476i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.7942 | + | 32.5526i | −0.634636 | + | 1.09922i | 0.351956 | + | 0.936017i | \(0.385517\pi\) |
−0.986592 | + | 0.163205i | \(0.947817\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.50962 | − | 7.50962i | 0.253293 | − | 0.253293i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.96410 | − | 2.86603i | 0.167245 | − | 0.0965588i | −0.414041 | − | 0.910258i | \(-0.635883\pi\) |
0.581286 | + | 0.813699i | \(0.302550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.803848 | − | 0.803848i | −0.0270516 | − | 0.0270516i | 0.693452 | − | 0.720503i | \(-0.256089\pi\) |
−0.720503 | + | 0.693452i | \(0.756089\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.0358984 | + | 0.133975i | −0.00120535 | + | 0.00449843i | −0.966526 | − | 0.256569i | \(-0.917408\pi\) |
0.965321 | + | 0.261068i | \(0.0840745\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.8827 | + | 35.8827i | 1.20347 | + | 1.20347i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.1865 | + | 7.55256i | −0.944284 | + | 0.253020i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.39230 | − | 31.3205i | −0.280838 | − | 1.04810i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.258330 | − | 0.0166605i | 0.00862540 | − | 0.000556278i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.29423 | − | 12.2942i | 0.109869 | − | 0.410035i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.70577 | − | 1.56218i | −0.0901423 | − | 0.0520437i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.82051 | + | 3.93782i | 0.226972 | + | 0.131043i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.3564 | − | 11.3494i | −1.40642 | − | 0.376849i | −0.525775 | − | 0.850624i | \(-0.676225\pi\) |
−0.880646 | + | 0.473774i | \(0.842891\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 46.9808 | 1.55825 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.5692 | 0.847146 | 0.423573 | − | 0.905862i | \(-0.360776\pi\) | ||||
0.423573 | + | 0.905862i | \(0.360776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.3923 | − | 3.32051i | −0.410125 | − | 0.109893i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.4974 | + | 7.21539i | 0.412701 | + | 0.238273i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.1410 | − | 19.1340i | −1.09322 | − | 0.631172i | −0.158789 | − | 0.987313i | \(-0.550759\pi\) |
−0.934432 | + | 0.356141i | \(0.884092\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.535898 | − | 2.00000i | 0.0176585 | − | 0.0659022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.50000 | + | 6.25833i | −0.181035 | + | 0.205995i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.1962 | − | 41.7846i | −0.367730 | − | 1.37239i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.9904 | − | 5.89230i | 0.721481 | − | 0.193320i | 0.120649 | − | 0.992695i | \(-0.461503\pi\) |
0.600832 | + | 0.799375i | \(0.294836\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.94744 | + | 1.94744i | 0.0638248 | + | 0.0638248i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.464102 | + | 1.73205i | −0.0151940 | + | 0.0567048i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.85641 | − | 2.85641i | −0.0933147 | − | 0.0933147i | 0.658908 | − | 0.752223i | \(-0.271018\pi\) |
−0.752223 | + | 0.658908i | \(0.771018\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.50962 | − | 2.02628i | 0.114532 | − | 0.0661251i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.85641 | − | 6.85641i | 0.223512 | − | 0.223512i | −0.586463 | − | 0.809976i | \(-0.699480\pi\) |
0.809976 | + | 0.586463i | \(0.199480\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.669873 | − | 1.16025i | 0.0218141 | − | 0.0377831i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.54552 | + | 2.62436i | −0.147709 | + | 0.0852801i | −0.572033 | − | 0.820230i | \(-0.693845\pi\) |
0.424324 | + | 0.905511i | \(0.360512\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.8564 | + | 44.7846i | 0.969180 | + | 1.45377i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.46410 | + | 2.53590i | 0.306895 | + | 0.0822321i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.6244 | − | 3.38269i | 0.408943 | − | 0.109576i | −0.0484822 | − | 0.998824i | \(-0.515438\pi\) |
0.457425 | + | 0.889248i | \(0.348772\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.92820i | − | 0.126981i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.6436 | + | 30.5596i | 0.569741 | + | 0.986821i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 23.0000i | − | 0.741935i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.6603 | + | 14.6603i | −0.472420 | + | 0.472420i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −58.3923 | −1.87777 | −0.938885 | − | 0.344231i | \(-0.888140\pi\) | ||||
−0.938885 | + | 0.344231i | \(0.888140\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.356406 | − | 1.33013i | −0.0114494 | − | 0.0427298i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.8923 | − | 30.9904i | 0.574191 | − | 0.994529i | −0.421938 | − | 0.906625i | \(-0.638650\pi\) |
0.996129 | − | 0.0879038i | \(-0.0280168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.40192 | − | 11.0885i | −0.205236 | − | 0.355480i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.79423 | + | 15.2321i | 0.281352 | + | 0.487316i | 0.971718 | − | 0.236144i | \(-0.0758837\pi\) |
−0.690366 | + | 0.723461i | \(0.742550\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.5526 | − | 58.1147i | 1.07234 | − | 1.85736i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.53590 | + | 13.1962i | 0.112893 | + | 0.421321i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.60770 | −0.0512775 | −0.0256388 | − | 0.999671i | \(-0.508162\pi\) | ||||
−0.0256388 | + | 0.999671i | \(0.508162\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.85641 | + | 9.85641i | −0.313733 | + | 0.313733i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 0.856406i | − | 0.0272321i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.8205 | − | 36.0622i | −0.661385 | − | 1.14555i | −0.980252 | − | 0.197753i | \(-0.936636\pi\) |
0.318867 | − | 0.947800i | \(-0.396698\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.90897i | 0.282717i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.23205 | + | 2.20577i | −0.260712 | + | 0.0698575i | −0.386807 | − | 0.922161i | \(-0.626422\pi\) |
0.126095 | + | 0.992018i | \(0.459755\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.40192 | + | 1.17949i | 0.139271 | + | 0.0373175i |
(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 | 1300.2.bs.b.457.1 | 4 | ||
5.2 | odd | 4 | 260.2.bf.b.93.1 | ✓ | 4 | ||
5.3 | odd | 4 | 1300.2.bn.a.93.1 | 4 | |||
5.4 | even | 2 | 260.2.bk.a.197.1 | yes | 4 | ||
13.7 | odd | 12 | 1300.2.bn.a.657.1 | 4 | |||
65.7 | even | 12 | 260.2.bk.a.33.1 | yes | 4 | ||
65.33 | even | 12 | inner | 1300.2.bs.b.293.1 | 4 | ||
65.59 | odd | 12 | 260.2.bf.b.137.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.b.93.1 | ✓ | 4 | 5.2 | odd | 4 | ||
260.2.bf.b.137.1 | yes | 4 | 65.59 | odd | 12 | ||
260.2.bk.a.33.1 | yes | 4 | 65.7 | even | 12 | ||
260.2.bk.a.197.1 | yes | 4 | 5.4 | even | 2 | ||
1300.2.bn.a.93.1 | 4 | 5.3 | odd | 4 | |||
1300.2.bn.a.657.1 | 4 | 13.7 | odd | 12 | |||
1300.2.bs.b.293.1 | 4 | 65.33 | even | 12 | inner | ||
1300.2.bs.b.457.1 | 4 | 1.1 | even | 1 | trivial |