Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(93,1300)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.93");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bn (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 | 93.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.93 |
Dual form | 1300.2.bn.a.657.1 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.133975 | + | 0.500000i | −0.0773503 | + | 0.288675i | −0.993756 | − | 0.111576i | \(-0.964410\pi\) |
0.916406 | + | 0.400251i | \(0.131077\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.23205 | − | 2.13397i | 0.465671 | − | 0.806567i | −0.533560 | − | 0.845762i | \(-0.679146\pi\) |
0.999232 | + | 0.0391956i | \(0.0124795\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −3.00000 | + | 2.00000i | −0.832050 | + | 0.554700i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.866025 | − | 0.232051i | 0.210042 | − | 0.0562806i | −0.152264 | − | 0.988340i | \(-0.548656\pi\) |
0.362306 | + | 0.932059i | \(0.381990\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.86603 | − | 0.767949i | 0.657511 | − | 0.176180i | 0.0853887 | − | 0.996348i | \(-0.472787\pi\) |
0.572123 | + | 0.820168i | \(0.306120\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.901924 | + | 0.901924i | 0.196816 | + | 0.196816i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.133975 | + | 0.0358984i | 0.0279356 | + | 0.00748533i | 0.272760 | − | 0.962082i | \(-0.412064\pi\) |
−0.244824 | + | 0.969567i | \(0.578730\pi\) | |||||||
\(24\) | 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 | −0.354221 | − | 0.935162i | \(-0.615254\pi\) |
0.632764 | + | 0.774345i | \(0.281920\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | −1.96410 | − | 1.13397i | −0.341906 | − | 0.197400i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.767949 | + | 1.33013i | 0.126250 | + | 0.218672i | 0.922221 | − | 0.386663i | \(-0.126372\pi\) |
−0.795971 | + | 0.605335i | \(0.793039\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 1.59808 | + | 5.96410i | 0.243704 | + | 0.909517i | 0.974030 | + | 0.226418i | \(0.0727016\pi\) |
−0.730326 | + | 0.683099i | \(0.760632\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9282 | 1.59404 | 0.797021 | − | 0.603951i | \(-0.206408\pi\) | ||||
0.797021 | + | 0.603951i | \(0.206408\pi\) | |||||||
\(48\) | 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 | 0.517321 | − | 0.855791i | \(-0.326929\pi\) |
−0.855791 | + | 0.517321i | \(0.826929\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.53590i | 0.203435i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.33013 | − | 8.69615i | −0.303357 | − | 1.13214i | −0.934351 | − | 0.356355i | \(-0.884019\pi\) |
0.630994 | − | 0.775788i | \(-0.282647\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 5.83013 | − | 3.36603i | 0.734527 | − | 0.424079i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.6244 | + | 6.13397i | −1.29797 | + | 0.749384i | −0.980053 | − | 0.198734i | \(-0.936317\pi\) |
−0.317918 | + | 0.948118i | \(0.602984\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 14.9282i | 1.74721i | 0.486632 | + | 0.873607i | \(0.338225\pi\) | ||||
−0.486632 | + | 0.873607i | \(0.661775\pi\) | |||||||
\(74\) | 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 | \(-0.990403\pi\) | ||
0.999545 | − | 0.0301466i | \(-0.00959743\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.33013 | + | 5.76795i | 0.370014 | + | 0.640883i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.92820 | −0.321412 | −0.160706 | − | 0.987002i | \(-0.551377\pi\) | ||||
−0.160706 | + | 0.987002i | \(0.551377\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.232051 | + | 0.866025i | 0.0248785 | + | 0.0928477i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.7942 | + | 3.96410i | 1.56819 | + | 0.420194i | 0.935243 | − | 0.354005i | \(-0.115181\pi\) |
0.632942 | + | 0.774199i | \(0.281847\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.571797 | + | 8.86603i | 0.0599406 | + | 0.929412i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.90192 | − | 3.29423i | −0.197220 | − | 0.341596i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.69615 | + | 3.86603i | 0.679891 | + | 0.392535i | 0.799814 | − | 0.600248i | \(-0.204931\pi\) |
−0.119923 | + | 0.992783i | \(0.538265\pi\) | |||||||
\(98\) | 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 | −0.109166 | + | 0.994024i | \(0.534818\pi\) |
−0.994024 | + | 0.109166i | \(0.965182\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.33013 | − | 1.96410i | −0.708630 | − | 0.189877i | −0.113537 | − | 0.993534i | \(-0.536218\pi\) |
−0.595093 | + | 0.803657i | \(0.702885\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.53590 | + | 3.53590i | 0.338678 | + | 0.338678i | 0.855869 | − | 0.517192i | \(-0.173023\pi\) |
−0.517192 | + | 0.855869i | \(0.673023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.767949 | + | 0.205771i | −0.0728905 | + | 0.0195310i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.86603 | − | 0.767949i | 0.269613 | − | 0.0722426i | −0.121480 | − | 0.992594i | \(-0.538764\pi\) |
0.391093 | + | 0.920351i | \(0.372097\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.83013 | + | 0.633975i | −0.908796 | + | 0.0586110i | ||||
\(118\) | 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 | ||||||||
\(123\) | −2.50000 | + | 4.33013i | −0.225417 | + | 0.390434i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.33013 | − | 19.8923i | 0.472972 | − | 1.76516i | −0.156029 | − | 0.987752i | \(-0.549869\pi\) |
0.629001 | − | 0.777404i | \(-0.283464\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 1.89230 | − | 7.06218i | 0.164084 | − | 0.612368i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.16025 | − | 12.4019i | 0.611742 | − | 1.05957i | −0.379205 | − | 0.925313i | \(-0.623802\pi\) |
0.990947 | − | 0.134255i | \(-0.0428642\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.50000 | + | 2.59808i | 0.381685 | + | 0.220366i | 0.678551 | − | 0.734553i | \(-0.262608\pi\) |
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.46410 | + | 5.46410i | −0.123300 | + | 0.460160i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.06218 | − | 14.9641i | −0.423321 | − | 1.25136i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.464102 | + | 0.124356i | −0.0382785 | + | 0.0102567i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.33013 | − | 0.892305i | 0.272815 | − | 0.0731005i | −0.119818 | − | 0.992796i | \(-0.538231\pi\) |
0.392633 | + | 0.919695i | \(0.371564\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 2.36603 | + | 0.633975i | 0.191282 | + | 0.0512538i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.46410 | + | 6.46410i | −0.515891 | + | 0.515891i | −0.916326 | − | 0.400434i | \(-0.868859\pi\) |
0.400434 | + | 0.916326i | \(0.368859\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | 2.76795 | + | 1.59808i | 0.216803 | + | 0.125171i | 0.604469 | − | 0.796629i | \(-0.293385\pi\) |
−0.387666 | + | 0.921800i | \(0.626719\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.23205 | − | 15.9904i | −0.714398 | − | 1.23737i | −0.963191 | − | 0.268816i | \(-0.913368\pi\) |
0.248794 | − | 0.968556i | \(-0.419966\pi\) | |||||||
\(168\) | 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 | ||||||||
\(173\) | 0.741670 | + | 2.76795i | 0.0563881 | + | 0.210443i | 0.988372 | − | 0.152057i | \(-0.0485898\pi\) |
−0.931984 | + | 0.362500i | \(0.881923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.66025 | 0.350286 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.96410 | − | 12.0622i | −0.520521 | − | 0.901570i | −0.999715 | − | 0.0238604i | \(-0.992404\pi\) |
0.479194 | − | 0.877709i | \(-0.340929\pi\) | |||||||
\(180\) | 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 | ||||||||
\(187\) | 3.92820i | 0.287259i | ||||||||
\(188\) | 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 | ||||||||
\(193\) | 22.1603 | − | 12.7942i | 1.59513 | − | 0.920949i | 0.602723 | − | 0.797950i | \(-0.294082\pi\) |
0.992407 | − | 0.122998i | \(-0.0392510\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.69615 | + | 2.13397i | −0.263340 | + | 0.152039i | −0.625857 | − | 0.779938i | \(-0.715251\pi\) |
0.362517 | + | 0.931977i | \(0.381917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.42820 | + | 16.3301i | −0.668348 | + | 1.15761i | 0.310018 | + | 0.950731i | \(0.399665\pi\) |
−0.978366 | + | 0.206881i | \(0.933669\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.64359 | − | 6.13397i | −0.115930 | − | 0.432657i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 4.26795i | − | 0.299551i | ||||||
\(204\) | 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 | ||||||||
\(213\) | −1.19615 | −0.0819590 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.68653 | + | 17.4904i | 0.318143 | + | 1.18732i | ||||
\(218\) | 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 | ||||||||
\(223\) | 0.767949 | + | 1.33013i | 0.0514257 | + | 0.0890719i | 0.890592 | − | 0.454802i | \(-0.150290\pi\) |
−0.839167 | + | 0.543874i | \(0.816957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.76795 | + | 1.59808i | 0.183715 | + | 0.106068i | 0.589037 | − | 0.808106i | \(-0.299507\pi\) |
−0.405322 | + | 0.914174i | \(0.632841\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.0717968 | + | 0.0717968i | −0.00474446 | + | 0.00474446i | −0.709475 | − | 0.704731i | \(-0.751068\pi\) |
0.704731 | + | 0.709475i | \(0.251068\pi\) | |||||||
\(230\) | 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 | \(-0.546930\pi\) |
0.989151 | + | 0.146900i | \(0.0469296\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.267949 | + | 0.0717968i | 0.0174052 | + | 0.00466370i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.6603 | − | 16.6603i | −1.07766 | − | 1.07766i | −0.996719 | − | 0.0809436i | \(-0.974207\pi\) |
−0.0809436 | − | 0.996719i | \(-0.525793\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | −11.9282 | + | 3.19615i | −0.765195 | + | 0.205033i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.06218 | + | 8.03590i | −0.449356 | + | 0.511312i | ||||
\(248\) | 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 | ||||||||
\(253\) | −0.303848 | + | 0.526279i | −0.0191027 | + | 0.0330869i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.79423 | + | 21.6244i | −0.361434 | + | 1.34889i | 0.510757 | + | 0.859725i | \(0.329365\pi\) |
−0.872191 | + | 0.489165i | \(0.837302\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.78461 | 0.235164 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.73205 | 0.292907 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.72243 | − | 13.8923i | 0.229535 | − | 0.856636i | −0.751002 | − | 0.660300i | \(-0.770429\pi\) |
0.980537 | − | 0.196336i | \(-0.0629043\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.96410 | + | 6.86603i | −0.242599 | + | 0.420194i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.8205 | − | 9.13397i | −0.964593 | − | 0.556908i | −0.0670097 | − | 0.997752i | \(-0.521346\pi\) |
−0.897584 | + | 0.440844i | \(0.854679\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | −4.50962 | − | 0.901924i | −0.272935 | − | 0.0545869i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.3301 | − | 2.76795i | 0.620677 | − | 0.166310i | 0.0652416 | − | 0.997869i | \(-0.479218\pi\) |
0.555436 | + | 0.831560i | \(0.312552\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −29.7224 | − | 7.96410i | −1.76682 | − | 0.473417i | −0.778735 | − | 0.627354i | \(-0.784138\pi\) |
−0.988081 | + | 0.153937i | \(0.950805\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | 17.7679 | + | 10.2583i | 1.03801 | + | 0.599298i | 0.919270 | − | 0.393627i | \(-0.128780\pi\) |
0.118744 | + | 0.992925i | \(0.462113\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.50000 | − | 11.2583i | −0.377168 | − | 0.653275i | ||||
\(298\) | 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 | ||||||||
\(303\) | −2.30385 | − | 8.59808i | −0.132353 | − | 0.493947i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.00000 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | 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 | 0.846035 | − | 0.533127i | \(-0.178983\pi\) |
−0.533127 | + | 0.846035i | \(0.678983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 18.9282i | − | 1.06311i | −0.847023 | − | 0.531557i | \(-0.821607\pi\) | ||
0.847023 | − | 0.531557i | \(-0.178393\pi\) | |||||||
\(318\) | 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 | ||||||||
\(323\) | 2.30385 | − | 1.33013i | 0.128190 | − | 0.0740102i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.24167 | + | 1.29423i | −0.123965 | + | 0.0715710i | ||||
\(328\) | 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 | ||||||||
\(333\) | 4.19615i | 0.229948i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.9282 | − | 15.9282i | −0.867665 | − | 0.867665i | 0.124549 | − | 0.992213i | \(-0.460252\pi\) |
−0.992213 | + | 0.124549i | \(0.960252\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.53590i | 0.0834185i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.0981 | − | 27.8827i | −0.871760 | − | 1.50993i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5359 | 1.05484 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.79423 | − | 10.4282i | −0.150002 | − | 0.559815i | −0.999482 | − | 0.0321938i | \(-0.989751\pi\) |
0.849480 | − | 0.527621i | \(-0.176916\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.86603 | + | 2.10770i | 0.421059 | + | 0.112822i | 0.463126 | − | 0.886292i | \(-0.346728\pi\) |
−0.0420673 | + | 0.999115i | \(0.513394\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.09808 | − | 10.4904i | 0.111987 | − | 0.559935i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.23205 | − | 9.06218i | −0.278474 | − | 0.482331i | 0.692532 | − | 0.721387i | \(-0.256495\pi\) |
−0.971006 | + | 0.239056i | \(0.923162\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.990381 | + | 0.571797i | 0.0524165 | + | 0.0302627i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.1962 | + | 13.1962i | −0.696466 | + | 0.696466i | −0.963647 | − | 0.267180i | \(-0.913908\pi\) |
0.267180 | + | 0.963647i | \(0.413908\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | −14.7942 | − | 3.96410i | −0.772252 | − | 0.206924i | −0.148886 | − | 0.988854i | \(-0.547569\pi\) |
−0.623366 | + | 0.781930i | \(0.714235\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | 19.7942 | − | 5.30385i | 1.02491 | − | 0.274623i | 0.293061 | − | 0.956094i | \(-0.405326\pi\) |
0.731845 | + | 0.681471i | \(0.238659\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.76795 | + | 5.59808i | −0.142557 | + | 0.288316i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.59808 | + | 9.69615i | −0.133454 | + | 0.498058i | −0.999999 | − | 0.00104063i | \(-0.999669\pi\) |
0.866545 | + | 0.499099i | \(0.166335\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.23205 | + | 5.33013i | 0.472972 | + | 0.273071i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.7679 | + | 22.1147i | −0.652412 | + | 1.13001i | 0.330124 | + | 0.943937i | \(0.392909\pi\) |
−0.982536 | + | 0.186073i | \(0.940424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.36603 | + | 16.2942i | −0.221938 | + | 0.828282i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0718 | 0.764170 | 0.382085 | − | 0.924127i | \(-0.375206\pi\) | ||||
0.382085 | + | 0.924127i | \(0.375206\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.124356 | 0.00628894 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.784610 | + | 2.92820i | −0.0395783 | + | 0.147708i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.69615 | − | 9.86603i | 0.285882 | − | 0.495162i | −0.686941 | − | 0.726713i | \(-0.741047\pi\) |
0.972823 | + | 0.231552i | \(0.0743802\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 5.19615 | − | 25.9808i | 0.258839 | − | 1.29419i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.50000 | + | 1.74167i | −0.322193 | + | 0.0863314i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.5263 | + | 4.96410i | −0.916066 | + | 0.245459i | −0.685903 | − | 0.727693i | \(-0.740593\pi\) |
−0.230163 | + | 0.973152i | \(0.573926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.24167 | + | 5.24167i | 0.258553 | + | 0.258553i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.4282 | − | 5.74167i | −1.05441 | − | 0.282529i | ||||
\(414\) | 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 | \(-0.318435\pi\) |
0.998905 | − | 0.0467865i | \(-0.0148981\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 25.8564 | + | 14.9282i | 1.25718 | + | 0.725834i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.0885 | − | 19.2058i | −0.536608 | − | 0.929432i | ||||
\(428\) | 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 | ||||||||
\(433\) | −8.72243 | − | 32.5526i | −0.419173 | − | 1.56438i | −0.776327 | − | 0.630330i | \(-0.782919\pi\) |
0.357154 | − | 0.934046i | \(-0.383747\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.411543 | 0.0196868 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.0358984 | − | 0.0621778i | −0.00171334 | − | 0.00296759i | 0.865167 | − | 0.501483i | \(-0.167212\pi\) |
−0.866881 | + | 0.498515i | \(0.833879\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.53590i | 0.120757i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.5885 | + | 15.5885i | 0.740630 | + | 0.740630i | 0.972699 | − | 0.232069i | \(-0.0745496\pi\) |
−0.232069 | + | 0.972699i | \(0.574550\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.78461i | 0.0844091i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.20577 | + | 19.4282i | 0.245676 | + | 0.916874i | 0.973043 | + | 0.230625i | \(0.0740771\pi\) |
−0.727367 | + | 0.686249i | \(0.759256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.1603 | + | 36.6506i | −0.996397 | + | 1.72581i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.169873 | − | 0.0980762i | 0.00798133 | − | 0.00460802i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.7679 | − | 6.79423i | 0.550481 | − | 0.317821i | −0.198835 | − | 0.980033i | \(-0.563716\pi\) |
0.749316 | + | 0.662212i | \(0.230382\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 21.6077i | 1.00419i | 0.864811 | + | 0.502097i | \(0.167438\pi\) | ||||
−0.864811 | + | 0.502097i | \(0.832562\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.6603 | + | 16.6603i | 0.770945 | + | 0.770945i | 0.978272 | − | 0.207327i | \(-0.0664764\pi\) |
−0.207327 | + | 0.978272i | \(0.566476\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.2295i | 1.39587i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.36603 | − | 4.09808i | −0.109021 | − | 0.188829i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.0526 | −1.24388 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.46410 | − | 9.19615i | −0.112823 | − | 0.421063i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.13397 | + | 0.839746i | 0.143195 | + | 0.0383690i | 0.329705 | − | 0.944084i | \(-0.393051\pi\) |
−0.186510 | + | 0.982453i | \(0.559718\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.96410 | − | 2.45448i | −0.226344 | − | 0.111915i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0884573 | + | 0.153212i | 0.00402495 | + | 0.00697141i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.37564 | − | 0.794229i | −0.0623364 | − | 0.0359899i | 0.468508 | − | 0.883459i | \(-0.344792\pi\) |
−0.530844 | + | 0.847469i | \(0.678125\pi\) | |||||||
\(488\) | 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 | ||||||||
\(497\) | 5.50000 | + | 1.47372i | 0.246709 | + | 0.0661054i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.2679 | − | 20.2679i | −0.907318 | − | 0.907318i | 0.0887371 | − | 0.996055i | \(-0.471717\pi\) |
−0.996055 | + | 0.0887371i | \(0.971717\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.23205 | − | 2.47372i | 0.412458 | − | 0.110518i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.5263 | + | 3.35641i | −0.558519 | + | 0.149655i | −0.527026 | − | 0.849849i | \(-0.676693\pi\) |
−0.0314933 | + | 0.999504i | \(0.510026\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.33013 | + | 4.10770i | 0.236719 | + | 0.182429i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.45448 | − | 27.8205i | 0.330414 | − | 1.23312i | −0.578342 | − | 0.815795i | \(-0.696300\pi\) |
0.908756 | − | 0.417328i | \(-0.137033\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.8564 | + | 18.3923i | 1.40924 | + | 0.813628i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.40192 | + | 7.62436i | −0.194350 | + | 0.336624i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.3923 | + | 46.2487i | −0.545013 | + | 2.03402i | ||||
\(518\) | 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 | ||||||||
\(523\) | 2.93782 | − | 10.9641i | 0.128462 | − | 0.479427i | −0.871477 | − | 0.490436i | \(-0.836838\pi\) |
0.999939 | + | 0.0110090i | \(0.00350433\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.29423 | + | 5.70577i | −0.143499 | + | 0.248547i | ||||
\(528\) | 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 | ||||||||
\(533\) | −32.9904 | + | 11.1603i | −1.42897 | + | 0.483404i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.96410 | − | 1.86603i | 0.300523 | − | 0.0805249i | ||||
\(538\) | 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 | ||||||||
\(543\) | 11.4641 | + | 3.07180i | 0.491972 | + | 0.131823i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.124356 | − | 0.124356i | 0.00531706 | − | 0.00531706i | −0.704443 | − | 0.709760i | \(-0.748803\pi\) |
0.709760 | + | 0.704443i | \(0.248803\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | −1.14359 | − | 0.660254i | −0.0486305 | − | 0.0280769i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.69615 | + | 13.3301i | 0.326096 | + | 0.564816i | 0.981734 | − | 0.190260i | \(-0.0609332\pi\) |
−0.655637 | + | 0.755076i | \(0.727600\pi\) | |||||||
\(558\) | 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 | ||||||||
\(563\) | 6.66987 | + | 24.8923i | 0.281102 | + | 1.04909i | 0.951641 | + | 0.307212i | \(0.0993960\pi\) |
−0.670540 | + | 0.741874i | \(0.733937\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.4115 | 0.689220 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.8205 | − | 32.5981i | −0.788997 | − | 1.36658i | −0.926582 | − | 0.376093i | \(-0.877267\pi\) |
0.137585 | − | 0.990490i | \(-0.456066\pi\) | |||||||
\(570\) | 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 | ||||||||
\(577\) | 20.7846i | 0.865275i | 0.901568 | + | 0.432637i | \(0.142417\pi\) | ||||
−0.901568 | + | 0.432637i | \(0.857583\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | 13.2224 | − | 7.63397i | 0.547617 | − | 0.316167i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.0885 | − | 23.7224i | 1.69590 | − | 0.979130i | 0.746333 | − | 0.665573i | \(-0.231813\pi\) |
0.949570 | − | 0.313556i | \(-0.101520\pi\) | |||||||
\(588\) | 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 | ||||||||
\(593\) | 30.9282i | 1.27007i | 0.772484 | + | 0.635035i | \(0.219014\pi\) | ||||
−0.772484 | + | 0.635035i | \(0.780986\pi\) | |||||||
\(594\) | 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 | \(-0.734569\pi\) | ||
0.672011 | − | 0.740541i | \(-0.265431\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | −33.5167 | −1.36490 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.813467 | + | 3.03590i | 0.0330176 | + | 0.123223i | 0.980468 | − | 0.196680i | \(-0.0630161\pi\) |
−0.947450 | + | 0.319904i | \(0.896349\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | 12.2321 | + | 21.1865i | 0.494048 | + | 0.855716i | 0.999976 | − | 0.00685934i | \(-0.00218341\pi\) |
−0.505929 | + | 0.862575i | \(0.668850\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.2321 | + | 8.79423i | 0.613219 | + | 0.354042i | 0.774224 | − | 0.632911i | \(-0.218140\pi\) |
−0.161005 | + | 0.986954i | \(0.551474\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.6603 | + | 14.6603i | −0.589245 | + | 0.589245i | −0.937427 | − | 0.348182i | \(-0.886799\pi\) |
0.348182 | + | 0.937427i | \(0.386799\pi\) | |||||||
\(620\) | 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 | ||||||||
\(627\) | −6.50000 | − | 1.74167i | −0.259585 | − | 0.0695556i | ||||
\(628\) | 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 | ||||||||
\(633\) | 2.96410 | − | 0.794229i | 0.117812 | − | 0.0315678i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00000 | − | 1.48334i | −0.118864 | − | 0.0587721i | ||||
\(638\) | 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 | ||||||||
\(643\) | −18.0885 | + | 31.3301i | −0.713339 | + | 1.23554i | 0.250258 | + | 0.968179i | \(0.419485\pi\) |
−0.963597 | + | 0.267360i | \(0.913849\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.669873 | + | 2.50000i | −0.0263354 | + | 0.0982851i | −0.977843 | − | 0.209341i | \(-0.932868\pi\) |
0.951507 | + | 0.307626i | \(0.0995347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 39.4449 | 1.54835 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.37307 | −0.367359 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.8468 | − | 47.9449i | 0.502734 | − | 1.87623i | 0.0212467 | − | 0.999774i | \(-0.493236\pi\) |
0.481487 | − | 0.876453i | \(-0.340097\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.3923 | + | 35.3205i | −0.795580 | + | 1.37798i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.4282 | + | 20.4545i | 1.38009 | + | 0.796794i | 0.992169 | − | 0.124901i | \(-0.0398612\pi\) |
0.387918 | + | 0.921694i | \(0.373195\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −0.928203 | − | 1.39230i | −0.0360484 | − | 0.0540726i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.232051 | − | 0.0621778i | 0.00898504 | − | 0.00240754i | ||||
\(668\) | 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 | ||||||||
\(673\) | −35.9186 | − | 9.62436i | −1.38456 | − | 0.370992i | −0.511784 | − | 0.859114i | \(-0.671015\pi\) |
−0.872775 | + | 0.488122i | \(0.837682\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.1769 | − | 28.1769i | 1.08293 | − | 1.08293i | 0.0866916 | − | 0.996235i | \(-0.472371\pi\) |
0.996235 | − | 0.0866916i | \(-0.0276295\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | −12.6962 | − | 7.33013i | −0.485805 | − | 0.280480i | 0.237028 | − | 0.971503i | \(-0.423827\pi\) |
−0.722832 | + | 0.691023i | \(0.757160\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.0262794 | − | 0.0455173i | −0.00100262 | − | 0.00173659i | ||||
\(688\) | 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 | ||||||||
\(693\) | 7.63397 | + | 28.4904i | 0.289991 | + | 1.08226i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.66025 | 0.328031 | ||||||||
\(698\) | 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 | ||||||||
\(707\) | 42.3731i | 1.59360i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.27757 | + | 15.9641i | 0.160647 | + | 0.599544i | 0.998555 | + | 0.0537328i | \(0.0171119\pi\) |
−0.837908 | + | 0.545812i | \(0.816221\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.732051 | − | 1.26795i | 0.0274541 | − | 0.0475518i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.882686 | + | 0.509619i | −0.0330568 | + | 0.0190854i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.5622 | − | 6.09808i | 0.394452 | − | 0.227737i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.9641 | − | 36.3109i | 0.781829 | − | 1.35417i | −0.149046 | − | 0.988830i | \(-0.547620\pi\) |
0.930875 | − | 0.365337i | \(-0.119046\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.0981 | + | 37.6865i | 0.376072 | + | 1.40352i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.07180i | 0.225813i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.5885 | − | 33.5885i | −1.24573 | − | 1.24573i | −0.957589 | − | 0.288138i | \(-0.906964\pi\) |
−0.288138 | − | 0.957589i | \(-0.593036\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5885i | 0.503276i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.76795 | + | 4.79423i | 0.102376 | + | 0.177321i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.7846 | −0.989312 | −0.494656 | − | 0.869089i | \(-0.664706\pi\) | ||||
−0.494656 | + | 0.869089i | \(0.664706\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.9115 | − | 51.9186i | −0.512438 | − | 1.91245i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.9186 | + | 10.1603i | 1.39486 | + | 0.373751i | 0.876495 | − | 0.481410i | \(-0.159875\pi\) |
0.518362 | + | 0.855161i | \(0.326542\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.07180 | − | 4.60770i | −0.112845 | − | 0.169268i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.1603 | + | 19.3301i | 0.409430 | + | 0.709154i | 0.994826 | − | 0.101594i | \(-0.0323943\pi\) |
−0.585396 | + | 0.810748i | \(0.699061\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.92820 | − | 4.00000i | −0.253490 | − | 0.146352i | ||||
\(748\) | 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 | ||||||||
\(757\) | −18.0622 | − | 4.83975i | −0.656481 | − | 0.175904i | −0.0848236 | − | 0.996396i | \(-0.527033\pi\) |
−0.571657 | + | 0.820492i | \(0.693699\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 11.9019 | − | 3.18911i | 0.430879 | − | 0.115454i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.3827 | + | 21.4282i | 0.880408 | + | 0.773728i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.47372 | + | 20.4282i | −0.197387 | + | 0.736660i | 0.794248 | + | 0.607593i | \(0.207865\pi\) |
−0.991636 | + | 0.129067i | \(0.958802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.0359 | − | 5.79423i | −0.361434 | − | 0.208674i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.83975 | − | 17.0429i | 0.353911 | − | 0.612992i | −0.633020 | − | 0.774136i | \(-0.718185\pi\) |
0.986931 | + | 0.161144i | \(0.0515182\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.507042 | + | 1.89230i | −0.0181900 | + | 0.0678861i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.6603 | 1.02686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.1244 | −0.362278 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.33013 | + | 4.96410i | −0.0475349 | + | 0.177403i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.6244 | − | 37.4545i | 0.770825 | − | 1.33511i | −0.166286 | − | 0.986078i | \(-0.553178\pi\) |
0.937111 | − | 0.349031i | \(-0.113489\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | 2.08846 | + | 32.3827i | 0.0741633 | + | 1.14994i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.9904 | + | 5.62436i | −0.743517 | + | 0.199225i | −0.610641 | − | 0.791908i | \(-0.709088\pi\) |
−0.132877 | + | 0.991133i | \(0.542421\pi\) | |||||||
\(798\) | 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 | ||||||||
\(803\) | −63.1769 | − | 16.9282i | −2.22946 | − | 0.597383i | ||||
\(804\) | 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 | −0.308189 | − | 0.951325i | \(-0.599723\pi\) |
0.669777 | + | 0.742562i | \(0.266390\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 7.50000 | + | 4.33013i | 0.263036 | + | 0.151864i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.16025 | + | 15.8660i | 0.320477 | + | 0.555082i | ||||
\(818\) | 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 | ||||||||
\(823\) | −6.40192 | − | 23.8923i | −0.223157 | − | 0.832833i | −0.983135 | − | 0.182884i | \(-0.941457\pi\) |
0.759977 | − | 0.649949i | \(-0.225210\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.8564 | 0.899115 | 0.449558 | − | 0.893251i | \(-0.351582\pi\) | ||||
0.449558 | + | 0.893251i | \(0.351582\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.42820 | − | 7.66987i | −0.153798 | − | 0.266386i | 0.778823 | − | 0.627244i | \(-0.215817\pi\) |
−0.932621 | + | 0.360858i | \(0.882484\pi\) | |||||||
\(830\) | 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 | ||||||||
\(837\) | − | 21.8038i | − | 0.753651i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.79423 | − | 29.0885i | −0.269087 | − | 1.00425i | −0.959701 | − | 0.281022i | \(-0.909327\pi\) |
0.690615 | − | 0.723223i | \(-0.257340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | + | 22.5167i | −0.448276 | + | 0.776437i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.4378 | − | 6.02628i | 0.359498 | − | 0.207556i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.4904 | + | 10.0981i | −0.600977 | + | 0.346974i | ||||
\(848\) | 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 | ||||||||
\(853\) | 53.8564i | 1.84401i | 0.387180 | + | 0.922004i | \(0.373449\pi\) | ||||
−0.387180 | + | 0.922004i | \(0.626551\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.2487 | − | 19.2487i | −0.657523 | − | 0.657523i | 0.297270 | − | 0.954793i | \(-0.403924\pi\) |
−0.954793 | + | 0.297270i | \(0.903924\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.39230i | 0.0816244i | 0.999167 | + | 0.0408122i | \(0.0129945\pi\) | ||||
−0.999167 | + | 0.0408122i | \(0.987005\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.16025 | + | 10.6699i | 0.209941 | + | 0.363628i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.14359 | 0.0729688 | 0.0364844 | − | 0.999334i | \(-0.488384\pi\) | ||||
0.0364844 | + | 0.999334i | \(0.488384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.16987 | − | 8.09808i | −0.0736927 | − | 0.275025i | ||||
\(868\) | 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 | ||||||||
\(873\) | 10.5622 | + | 18.2942i | 0.357476 | + | 0.619166i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.5526 | + | 18.7942i | 1.09922 | + | 0.634636i | 0.936017 | − | 0.351956i | \(-0.114483\pi\) |
0.163205 | + | 0.986592i | \(0.447817\pi\) | |||||||
\(878\) | 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 | \(-0.743911\pi\) |
0.720503 | + | 0.693452i | \(0.243911\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.133975 | + | 0.0358984i | 0.00449843 | + | 0.00120535i | 0.261068 | − | 0.965321i | \(-0.415925\pi\) |
−0.256569 | + | 0.966526i | \(0.582592\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | 31.3205 | − | 8.39230i | 1.04810 | − | 0.280838i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0166605 | − | 0.258330i | −0.000556278 | − | 0.00862540i | ||||
\(898\) | 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 | ||||||||
\(903\) | −3.93782 | + | 6.82051i | −0.131043 | + | 0.226972i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.3494 | + | 42.3564i | −0.376849 | + | 1.40642i | 0.473774 | + | 0.880646i | \(0.342891\pi\) |
−0.850624 | + | 0.525775i | \(0.823775\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | 3.32051 | − | 12.3923i | 0.109893 | − | 0.410125i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.21539 | − | 12.4974i | 0.238273 | − | 0.412701i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.1410 | + | 19.1340i | 1.09322 | + | 0.631172i | 0.934432 | − | 0.356141i | \(-0.115908\pi\) |
0.158789 | + | 0.987313i | \(0.449241\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.535898 | − | 2.00000i | 0.0176585 | − | 0.0659022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.25833 | − | 5.50000i | −0.205995 | − | 0.181035i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −41.7846 | + | 11.1962i | −1.37239 | + | 0.367730i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.9904 | + | 5.89230i | −0.721481 | + | 0.193320i | −0.600832 | − | 0.799375i | \(-0.705164\pi\) |
−0.120649 | + | 0.992695i | \(0.538497\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.94744 | + | 1.94744i | 0.0638248 | + | 0.0638248i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.73205 | − | 0.464102i | −0.0567048 | − | 0.0151940i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.85641 | + | 2.85641i | −0.0933147 | + | 0.0933147i | −0.752223 | − | 0.658908i | \(-0.771018\pi\) |
0.658908 | + | 0.752223i | \(0.271018\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 1.16025 | + | 0.669873i | 0.0377831 | + | 0.0218141i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.62436 | + | 4.54552i | 0.0852801 | + | 0.147709i | 0.905511 | − | 0.424324i | \(-0.139488\pi\) |
−0.820230 | + | 0.572033i | \(0.806155\pi\) | |||||||
\(948\) | 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 | ||||||||
\(953\) | 3.38269 | + | 12.6244i | 0.109576 | + | 0.408943i | 0.998824 | − | 0.0484822i | \(-0.0154384\pi\) |
−0.889248 | + | 0.457425i | \(0.848772\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.92820 | −0.126981 | ||||||||
\(958\) | 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 | ||||||||
\(967\) | 58.3923i | 1.87777i | 0.344231 | + | 0.938885i | \(0.388140\pi\) | ||||
−0.344231 | + | 0.938885i | \(0.611860\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | 11.0885 | − | 6.40192i | 0.355480 | − | 0.205236i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.2321 | − | 8.79423i | 0.487316 | − | 0.281352i | −0.236144 | − | 0.971718i | \(-0.575884\pi\) |
0.723461 | + | 0.690366i | \(0.242550\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | − | 1.60770i | − | 0.0512775i | −0.999671 | − | 0.0256388i | \(-0.991838\pi\) | ||
0.999671 | − | 0.0256388i | \(-0.00816196\pi\) | |||||||
\(984\) | 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 | ||||||||
\(993\) | −8.90897 | −0.282717 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.20577 | + | 8.23205i | 0.0698575 | + | 0.260712i | 0.992018 | − | 0.126095i | \(-0.0402446\pi\) |
−0.922161 | + | 0.386807i | \(0.873578\pi\) | |||||||
\(998\) | 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.bn.a.93.1 | 4 | ||
5.2 | odd | 4 | 1300.2.bs.b.457.1 | 4 | |||
5.3 | odd | 4 | 260.2.bk.a.197.1 | yes | 4 | ||
5.4 | even | 2 | 260.2.bf.b.93.1 | ✓ | 4 | ||
13.7 | odd | 12 | 1300.2.bs.b.293.1 | 4 | |||
65.7 | even | 12 | inner | 1300.2.bn.a.657.1 | 4 | ||
65.33 | even | 12 | 260.2.bf.b.137.1 | yes | 4 | ||
65.59 | odd | 12 | 260.2.bk.a.33.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.b.93.1 | ✓ | 4 | 5.4 | even | 2 | ||
260.2.bf.b.137.1 | yes | 4 | 65.33 | even | 12 | ||
260.2.bk.a.33.1 | yes | 4 | 65.59 | odd | 12 | ||
260.2.bk.a.197.1 | yes | 4 | 5.3 | odd | 4 | ||
1300.2.bn.a.93.1 | 4 | 1.1 | even | 1 | trivial | ||
1300.2.bn.a.657.1 | 4 | 65.7 | even | 12 | inner | ||
1300.2.bs.b.293.1 | 4 | 13.7 | odd | 12 | |||
1300.2.bs.b.457.1 | 4 | 5.2 | odd | 4 |