Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(361,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.961 |
Dual form | 980.2.i.l.361.1 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.207107 | − | 0.358719i | −0.119573 | − | 0.207107i | 0.800025 | − | 0.599966i | \(-0.204819\pi\) |
−0.919599 | + | 0.392859i | \(0.871486\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.41421 | − | 2.44949i | 0.471405 | − | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.91421 | + | 3.31552i | 0.577157 | + | 0.999665i | 0.995804 | + | 0.0915161i | \(0.0291713\pi\) |
−0.418646 | + | 0.908149i | \(0.637495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.58579 | −0.994518 | −0.497259 | − | 0.867602i | \(-0.665660\pi\) | ||||
−0.497259 | + | 0.867602i | \(0.665660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.414214 | 0.106949 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.20711 | + | 5.55487i | 0.777838 | + | 1.34725i | 0.933186 | + | 0.359395i | \(0.117017\pi\) |
−0.155348 | + | 0.987860i | \(0.549650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.82843 | − | 3.16693i | 0.419470 | − | 0.726543i | −0.576416 | − | 0.817156i | \(-0.695549\pi\) |
0.995886 | + | 0.0906130i | \(0.0288826\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.292893 | + | 0.507306i | −0.0610725 | + | 0.105781i | −0.894945 | − | 0.446176i | \(-0.852785\pi\) |
0.833873 | + | 0.551957i | \(0.186119\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.41421 | −0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.65685 | 1.23615 | 0.618073 | − | 0.786120i | \(-0.287913\pi\) | ||||
0.618073 | + | 0.786120i | \(0.287913\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.29289 | + | 3.97141i | 0.411816 | + | 0.713286i | 0.995088 | − | 0.0989906i | \(-0.0315614\pi\) |
−0.583273 | + | 0.812276i | \(0.698228\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.792893 | − | 1.37333i | 0.138025 | − | 0.239066i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.70711 | − | 2.95680i | 0.280647 | − | 0.486094i | −0.690898 | − | 0.722953i | \(-0.742784\pi\) |
0.971544 | + | 0.236858i | \(0.0761178\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.742641 | + | 1.28629i | 0.118918 | + | 0.205971i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.585786 | −0.0914845 | −0.0457422 | − | 0.998953i | \(-0.514565\pi\) | ||||
−0.0457422 | + | 0.998953i | \(0.514565\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.6569 | 1.77765 | 0.888827 | − | 0.458243i | \(-0.151521\pi\) | ||||
0.888827 | + | 0.458243i | \(0.151521\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.41421 | + | 2.44949i | 0.210819 | + | 0.365148i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.44975 | + | 7.70719i | −0.649062 | + | 1.12421i | 0.334285 | + | 0.942472i | \(0.391505\pi\) |
−0.983347 | + | 0.181737i | \(0.941828\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.32843 | − | 2.30090i | 0.186017 | − | 0.322191i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.87868 | + | 3.25397i | 0.258056 | + | 0.446967i | 0.965721 | − | 0.259581i | \(-0.0835846\pi\) |
−0.707665 | + | 0.706548i | \(0.750251\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.82843 | −0.516225 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.51472 | −0.200629 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.70711 | + | 2.95680i | 0.222246 | + | 0.384942i | 0.955490 | − | 0.295024i | \(-0.0953277\pi\) |
−0.733243 | + | 0.679966i | \(0.761994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.58579 | − | 4.47871i | 0.331076 | − | 0.573441i | −0.651647 | − | 0.758522i | \(-0.725922\pi\) |
0.982723 | + | 0.185082i | \(0.0592550\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.79289 | − | 3.10538i | 0.222381 | − | 0.385175i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.53553 | + | 9.58783i | 0.676273 | + | 1.17134i | 0.976095 | + | 0.217344i | \(0.0697394\pi\) |
−0.299822 | + | 0.953995i | \(0.596927\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.242641 | 0.0292105 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.48528 | 0.769661 | 0.384831 | − | 0.922987i | \(-0.374260\pi\) | ||||
0.384831 | + | 0.922987i | \(0.374260\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.58579 | + | 4.47871i | 0.302643 | + | 0.524194i | 0.976734 | − | 0.214455i | \(-0.0687975\pi\) |
−0.674090 | + | 0.738649i | \(0.735464\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.207107 | + | 0.358719i | −0.0239146 | + | 0.0414214i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.57107 | + | 11.3814i | −0.739303 | + | 1.28051i | 0.213507 | + | 0.976942i | \(0.431511\pi\) |
−0.952810 | + | 0.303569i | \(0.901822\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.74264 | − | 6.48244i | −0.415849 | − | 0.720272i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.41421 | −0.695719 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.37868 | − | 2.38794i | −0.147810 | − | 0.256014i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.48528 | − | 14.6969i | 0.899438 | − | 1.55787i | 0.0712241 | − | 0.997460i | \(-0.477309\pi\) |
0.828214 | − | 0.560412i | \(-0.189357\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.949747 | − | 1.64501i | 0.0984842 | − | 0.170580i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.82843 | + | 3.16693i | 0.187593 | + | 0.324920i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.7279 | −1.59693 | −0.798464 | − | 0.602042i | \(-0.794354\pi\) | ||||
−0.798464 | + | 0.602042i | \(0.794354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.8284 | 1.08830 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.41421 | − | 4.18154i | −0.240223 | − | 0.416079i | 0.720555 | − | 0.693398i | \(-0.243887\pi\) |
−0.960778 | + | 0.277319i | \(0.910554\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.792893 | − | 1.37333i | 0.0781261 | − | 0.135318i | −0.824315 | − | 0.566131i | \(-0.808440\pi\) |
0.902441 | + | 0.430813i | \(0.141773\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.41421 | − | 14.5738i | 0.813433 | − | 1.40891i | −0.0970151 | − | 0.995283i | \(-0.530930\pi\) |
0.910448 | − | 0.413624i | \(-0.135737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.50000 | − | 7.79423i | −0.431022 | − | 0.746552i | 0.565940 | − | 0.824447i | \(-0.308513\pi\) |
−0.996962 | + | 0.0778949i | \(0.975180\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.41421 | −0.134231 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.07107 | −0.477046 | −0.238523 | − | 0.971137i | \(-0.576663\pi\) | ||||
−0.238523 | + | 0.971137i | \(0.576663\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.292893 | − | 0.507306i | −0.0273124 | − | 0.0473065i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.07107 | + | 8.78335i | −0.468820 | + | 0.812021i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.82843 | + | 3.16693i | −0.166221 | + | 0.287903i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.121320 | + | 0.210133i | 0.0109391 | + | 0.0189471i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.8995 | −1.94327 | −0.971633 | − | 0.236494i | \(-0.924002\pi\) | ||||
−0.971633 | + | 0.236494i | \(0.924002\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.41421 | − | 4.18154i | −0.212560 | − | 0.368164i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.87868 | + | 10.1822i | −0.513623 | + | 0.889620i | 0.486253 | + | 0.873818i | \(0.338364\pi\) |
−0.999875 | + | 0.0158021i | \(0.994970\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.20711 | − | 2.09077i | 0.103891 | − | 0.179945i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.48528 | − | 11.2328i | −0.554075 | − | 0.959686i | −0.997975 | − | 0.0636096i | \(-0.979739\pi\) |
0.443900 | − | 0.896076i | \(-0.353595\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.8995 | 1.17894 | 0.589470 | − | 0.807790i | \(-0.299337\pi\) | ||||
0.589470 | + | 0.807790i | \(0.299337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.68629 | 0.310442 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.86396 | − | 11.8887i | −0.573993 | − | 0.994185i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.32843 | + | 5.76500i | −0.276411 | + | 0.478758i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.75736 | + | 3.04384i | −0.143968 | + | 0.249361i | −0.928988 | − | 0.370111i | \(-0.879320\pi\) |
0.785019 | + | 0.619472i | \(0.212653\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.91421 | + | 10.2437i | 0.481292 | + | 0.833622i | 0.999770 | − | 0.0214692i | \(-0.00683439\pi\) |
−0.518478 | + | 0.855091i | \(0.673501\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.1421 | 1.46670 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.58579 | −0.368339 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.24264 | + | 9.08052i | 0.418408 | + | 0.724704i | 0.995780 | − | 0.0917773i | \(-0.0292548\pi\) |
−0.577371 | + | 0.816482i | \(0.695921\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.778175 | − | 1.34784i | 0.0617133 | − | 0.106891i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.7782 | + | 18.6683i | −0.844212 | + | 1.46222i | 0.0420922 | + | 0.999114i | \(0.486598\pi\) |
−0.886304 | + | 0.463104i | \(0.846736\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.792893 | + | 1.37333i | 0.0617267 | + | 0.106914i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.41421 | −0.186817 | −0.0934087 | − | 0.995628i | \(-0.529776\pi\) | ||||
−0.0934087 | + | 0.995628i | \(0.529776\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.142136 | −0.0109335 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.17157 | − | 8.95743i | −0.395480 | − | 0.684992i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.27817 | − | 16.0703i | 0.705407 | − | 1.22180i | −0.261138 | − | 0.965301i | \(-0.584098\pi\) |
0.966545 | − | 0.256499i | \(-0.0825689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.707107 | − | 1.22474i | 0.0531494 | − | 0.0920575i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.24264 | − | 5.61642i | −0.242366 | − | 0.419791i | 0.719022 | − | 0.694988i | \(-0.244590\pi\) |
−0.961388 | + | 0.275197i | \(0.911257\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.75736 | −0.130623 | −0.0653117 | − | 0.997865i | \(-0.520804\pi\) | ||||
−0.0653117 | + | 0.997865i | \(0.520804\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.14214 | −0.158351 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.70711 | + | 2.95680i | 0.125509 | + | 0.217388i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.2782 | + | 21.2664i | −0.897869 | + | 1.55515i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.32843 | + | 14.4253i | −0.602624 | + | 1.04378i | 0.389798 | + | 0.920900i | \(0.372545\pi\) |
−0.992422 | + | 0.122875i | \(0.960789\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.82843 | − | 4.89898i | −0.203595 | − | 0.352636i | 0.746089 | − | 0.665846i | \(-0.231929\pi\) |
−0.949684 | + | 0.313210i | \(0.898596\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.48528 | −0.106363 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −27.5563 | −1.96331 | −0.981654 | − | 0.190669i | \(-0.938934\pi\) | ||||
−0.981654 | + | 0.190669i | \(0.938934\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.3640 | − | 23.1471i | −0.947346 | − | 1.64085i | −0.750984 | − | 0.660320i | \(-0.770421\pi\) |
−0.196362 | − | 0.980532i | \(-0.562913\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.29289 | − | 3.97141i | 0.161728 | − | 0.280121i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.292893 | − | 0.507306i | 0.0204565 | − | 0.0354318i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.828427 | + | 1.43488i | 0.0575797 | + | 0.0997309i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.0000 | 0.968400 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.3137 | −1.67382 | −0.836912 | − | 0.547337i | \(-0.815642\pi\) | ||||
−0.836912 | + | 0.547337i | \(0.815642\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.34315 | − | 2.32640i | −0.0920308 | − | 0.159402i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.82843 | + | 10.0951i | −0.397495 | + | 0.688482i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.07107 | − | 1.85514i | 0.0723761 | − | 0.125359i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.5000 | − | 19.9186i | −0.773574 | − | 1.33987i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.0711 | −1.61192 | −0.805959 | − | 0.591971i | \(-0.798350\pi\) | ||||
−0.805959 | + | 0.591971i | \(0.798350\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.82843 | −0.188562 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.86396 | + | 6.69258i | 0.256460 | + | 0.444202i | 0.965291 | − | 0.261176i | \(-0.0841104\pi\) |
−0.708831 | + | 0.705378i | \(0.750777\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.9497 | − | 20.6976i | 0.789662 | − | 1.36773i | −0.136513 | − | 0.990638i | \(-0.543589\pi\) |
0.926174 | − | 0.377096i | \(-0.123077\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.58579 | − | 7.94282i | 0.300425 | − | 0.520351i | −0.675807 | − | 0.737078i | \(-0.736205\pi\) |
0.976232 | + | 0.216727i | \(0.0695382\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.44975 | − | 7.70719i | −0.290270 | − | 0.502762i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.44365 | 0.353603 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.1716 | 0.916683 | 0.458341 | − | 0.888776i | \(-0.348444\pi\) | ||||
0.458341 | + | 0.888776i | \(0.348444\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.77817 | − | 3.07989i | −0.114542 | − | 0.198393i | 0.803054 | − | 0.595906i | \(-0.203207\pi\) |
−0.917597 | + | 0.397513i | \(0.869873\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.17157 | + | 8.95743i | −0.331757 | + | 0.574619i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.55635 | + | 11.3559i | −0.417171 | + | 0.722561i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.65685 | − | 2.86976i | −0.104999 | − | 0.181863i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.0711 | 1.70871 | 0.854355 | − | 0.519689i | \(-0.173952\pi\) | ||||
0.854355 | + | 0.519689i | \(0.173952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.24264 | −0.140994 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.32843 | + | 2.30090i | 0.0831893 | + | 0.144088i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.8995 | + | 22.3426i | −0.804648 | + | 1.39369i | 0.111880 | + | 0.993722i | \(0.464313\pi\) |
−0.916528 | + | 0.399970i | \(0.869020\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.41421 | − | 16.3059i | 0.582725 | − | 1.00931i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.00000 | − | 8.66025i | −0.308313 | − | 0.534014i | 0.669680 | − | 0.742650i | \(-0.266431\pi\) |
−0.977993 | + | 0.208635i | \(0.933098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.75736 | −0.230813 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.02944 | −0.430195 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.36396 | − | 14.4868i | −0.509960 | − | 0.883276i | −0.999933 | − | 0.0115389i | \(-0.996327\pi\) |
0.489974 | − | 0.871737i | \(-0.337006\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.4853 | − | 25.0892i | 0.879918 | − | 1.52406i | 0.0284886 | − | 0.999594i | \(-0.490931\pi\) |
0.851430 | − | 0.524469i | \(-0.175736\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.91421 | − | 3.31552i | 0.115431 | − | 0.199933i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.70711 | + | 6.42090i | 0.222738 | + | 0.385794i | 0.955639 | − | 0.294542i | \(-0.0951671\pi\) |
−0.732900 | + | 0.680336i | \(0.761834\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.9706 | 0.776527 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00000 | −0.0596550 | −0.0298275 | − | 0.999555i | \(-0.509496\pi\) | ||||
−0.0298275 | + | 0.999555i | \(0.509496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.37868 | − | 16.2443i | −0.557505 | − | 0.965626i | −0.997704 | − | 0.0677263i | \(-0.978426\pi\) |
0.440199 | − | 0.897900i | \(-0.354908\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.757359 | − | 1.31178i | 0.0448621 | − | 0.0777034i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0711 | + | 20.9077i | −0.710063 | + | 1.22986i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.25736 | + | 5.64191i | 0.190950 | + | 0.330735i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4142 | 0.842087 | 0.421044 | − | 0.907040i | \(-0.361664\pi\) | ||||
0.421044 | + | 0.907040i | \(0.361664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.41421 | −0.198783 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.62132 | − | 8.00436i | −0.268156 | − | 0.464460i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.05025 | − | 1.81909i | 0.0607377 | − | 0.105201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.00000 | + | 1.73205i | −0.0574485 | + | 0.0995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.58579 | + | 4.47871i | 0.148062 | + | 0.256450i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.58579 | −0.204652 | −0.102326 | − | 0.994751i | \(-0.532628\pi\) | ||||
−0.102326 | + | 0.994751i | \(0.532628\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.656854 | −0.0373671 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.48528 | + | 6.03668i | 0.197632 | + | 0.342309i | 0.947760 | − | 0.318984i | \(-0.103342\pi\) |
−0.750128 | + | 0.661293i | \(0.770008\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.27817 | − | 14.3382i | 0.467910 | − | 0.810444i | −0.531417 | − | 0.847110i | \(-0.678340\pi\) |
0.999328 | + | 0.0366660i | \(0.0116738\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.48528 | − | 12.9649i | 0.420415 | − | 0.728181i | −0.575565 | − | 0.817756i | \(-0.695218\pi\) |
0.995980 | + | 0.0895756i | \(0.0285511\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.7426 | + | 22.0709i | 0.713451 | + | 1.23573i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.97056 | −0.389059 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.4558 | 1.30512 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.79289 | + | 3.10538i | 0.0994518 | + | 0.172256i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.86396 | + | 3.22848i | −0.103077 | + | 0.178535i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.41421 | + | 4.18154i | −0.132697 | + | 0.229838i | −0.924715 | − | 0.380659i | \(-0.875697\pi\) |
0.792018 | + | 0.610497i | \(0.209030\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.82843 | − | 8.36308i | −0.264596 | − | 0.458294i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0711 | −0.604877 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.7279 | −1.02017 | −0.510087 | − | 0.860123i | \(-0.670387\pi\) | ||||
−0.510087 | + | 0.860123i | \(0.670387\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.05025 | + | 1.81909i | 0.0570419 | + | 0.0987994i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.77817 | + | 15.2042i | −0.475365 | + | 0.823356i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.121320 | + | 0.210133i | −0.00653167 | + | 0.0113132i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.70711 | + | 6.42090i | 0.199008 | + | 0.344692i | 0.948207 | − | 0.317653i | \(-0.102895\pi\) |
−0.749199 | + | 0.662345i | \(0.769561\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.0000 | −0.963518 | −0.481759 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481759 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.65685 | 0.462069 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.03553 | − | 1.79360i | −0.0551159 | − | 0.0954636i | 0.837151 | − | 0.546972i | \(-0.184219\pi\) |
−0.892267 | + | 0.451508i | \(0.850886\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.24264 | + | 5.61642i | −0.172101 | + | 0.298089i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.65685 | + | 9.79796i | −0.298557 | + | 0.517116i | −0.975806 | − | 0.218638i | \(-0.929839\pi\) |
0.677249 | + | 0.735754i | \(0.263172\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.81371 | + | 4.87349i | 0.148090 | + | 0.256499i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.51472 | 0.0795021 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.17157 | −0.270692 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.86396 | + | 17.0849i | 0.514895 | + | 0.891824i | 0.999851 | + | 0.0172850i | \(0.00550227\pi\) |
−0.484956 | + | 0.874539i | \(0.661164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.828427 | + | 1.43488i | −0.0431262 | + | 0.0746968i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.24264 | + | 14.2767i | −0.426788 | + | 0.739218i | −0.996586 | − | 0.0825669i | \(-0.973688\pi\) |
0.569798 | + | 0.821785i | \(0.307022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.207107 | − | 0.358719i | −0.0106949 | − | 0.0185242i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.8701 | −1.22937 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.0000 | 0.719132 | 0.359566 | − | 0.933120i | \(-0.382925\pi\) | ||||
0.359566 | + | 0.933120i | \(0.382925\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.53553 | + | 7.85578i | 0.232362 | + | 0.402464i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.75736 | + | 3.04384i | −0.0897969 | + | 0.155533i | −0.907425 | − | 0.420214i | \(-0.861955\pi\) |
0.817628 | + | 0.575746i | \(0.195288\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.4853 | − | 28.5533i | 0.837994 | − | 1.45145i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.57107 | − | 11.3814i | −0.333166 | − | 0.577061i | 0.649965 | − | 0.759965i | \(-0.274784\pi\) |
−0.983131 | + | 0.182903i | \(0.941450\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.75736 | −0.190018 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.87006 | 0.245662 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.57107 | − | 11.3814i | −0.330626 | − | 0.572662i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.20711 | − | 12.4831i | 0.361714 | − | 0.626508i | −0.626529 | − | 0.779398i | \(-0.715525\pi\) |
0.988243 | + | 0.152891i | \(0.0488582\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.257359 | + | 0.445759i | −0.0128519 | + | 0.0222602i | −0.872380 | − | 0.488829i | \(-0.837424\pi\) |
0.859528 | + | 0.511089i | \(0.170758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.22183 | − | 14.2406i | −0.409558 | − | 0.709376i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.48528 | 0.371947 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.0711 | 0.647909 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.4142 | + | 28.4303i | 0.811631 | + | 1.40579i | 0.911722 | + | 0.410807i | \(0.134753\pi\) |
−0.100092 | + | 0.994978i | \(0.531914\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.68629 | + | 4.65279i | −0.132505 | + | 0.229505i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | + | 6.92820i | −0.196352 | + | 0.340092i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.87868 | − | 4.98602i | −0.140970 | − | 0.244166i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.55635 | 0.466858 | 0.233429 | − | 0.972374i | \(-0.425005\pi\) | ||||
0.233429 | + | 0.972374i | \(0.425005\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3137 | 0.990030 | 0.495015 | − | 0.868885i | \(-0.335163\pi\) | ||||
0.495015 | + | 0.868885i | \(0.335163\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.5858 | + | 21.7992i | 0.611942 | + | 1.05991i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.20711 | − | 5.55487i | 0.155568 | − | 0.269451i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.84315 | + | 4.92447i | −0.137268 | + | 0.237756i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.91421 | + | 8.51167i | 0.236709 | + | 0.409993i | 0.959768 | − | 0.280794i | \(-0.0905978\pi\) |
−0.723059 | + | 0.690787i | \(0.757264\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.2843 | 1.07091 | 0.535457 | − | 0.844563i | \(-0.320139\pi\) | ||||
0.535457 | + | 0.844563i | \(0.320139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.75736 | 0.132205 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.07107 | + | 1.85514i | 0.0512361 | + | 0.0887436i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1213 | − | 20.9947i | 0.578519 | − | 1.00202i | −0.417130 | − | 0.908847i | \(-0.636964\pi\) |
0.995649 | − | 0.0931778i | \(-0.0297025\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.7279 | − | 30.7057i | 0.842279 | − | 1.45887i | −0.0456844 | − | 0.998956i | \(-0.514547\pi\) |
0.887963 | − | 0.459914i | \(-0.152120\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.48528 | + | 14.6969i | 0.402241 | + | 0.696702i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.45584 | 0.0688591 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.8284 | 1.12453 | 0.562267 | − | 0.826956i | \(-0.309930\pi\) | ||||
0.562267 | + | 0.826956i | \(0.309930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.12132 | − | 1.94218i | −0.0528009 | − | 0.0914539i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.44975 | − | 4.24309i | 0.115099 | − | 0.199358i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.53553 | − | 13.0519i | 0.352497 | − | 0.610543i | −0.634189 | − | 0.773178i | \(-0.718666\pi\) |
0.986686 | + | 0.162635i | \(0.0519992\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.74264 | − | 13.4106i | −0.361396 | − | 0.625955i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.3431 | −1.04062 | −0.520312 | − | 0.853976i | \(-0.674184\pi\) | ||||
−0.520312 | + | 0.853976i | \(0.674184\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.4558 | −0.625346 | −0.312673 | − | 0.949861i | \(-0.601224\pi\) | ||||
−0.312673 | + | 0.949861i | \(0.601224\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.949747 | + | 1.64501i | 0.0440435 | + | 0.0762856i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.449747 | − | 0.778985i | 0.0208118 | − | 0.0360471i | −0.855432 | − | 0.517915i | \(-0.826708\pi\) |
0.876244 | + | 0.481868i | \(0.160042\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.17157 | − | 3.76127i | 0.100061 | − | 0.173310i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.3137 | + | 38.6485i | 1.02599 | + | 1.77706i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.65685 | −0.167788 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.6274 | 0.486596 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.70711 | + | 8.15295i | 0.215073 | + | 0.372518i | 0.953295 | − | 0.302040i | \(-0.0976677\pi\) |
−0.738222 | + | 0.674558i | \(0.764334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.12132 | + | 10.6024i | −0.279108 | + | 0.483430i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.86396 | − | 13.6208i | 0.357084 | − | 0.618488i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.70711 | + | 6.42090i | 0.167985 | + | 0.290959i | 0.937711 | − | 0.347415i | \(-0.112941\pi\) |
−0.769726 | + | 0.638374i | \(0.779607\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.92893 | 0.403780 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.2843 | 0.780028 | 0.390014 | − | 0.920809i | \(-0.372470\pi\) | ||||
0.390014 | + | 0.920809i | \(0.372470\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.3492 | + | 36.9780i | 0.961522 | + | 1.66540i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.41421 | + | 9.37769i | −0.243351 | + | 0.421496i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.81371 | − | 11.8017i | 0.305023 | − | 0.528316i | −0.672243 | − | 0.740331i | \(-0.734669\pi\) |
0.977267 | + | 0.212014i | \(0.0680024\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.500000 | + | 0.866025i | 0.0223384 | + | 0.0386912i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.0416 | −1.74078 | −0.870390 | − | 0.492363i | \(-0.836133\pi\) | ||||
−0.870390 | + | 0.492363i | \(0.836133\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.82843 | 0.214862 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.0294373 | + | 0.0509868i | 0.00130735 | + | 0.00226440i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.5355 | + | 30.3724i | −0.777249 | + | 1.34623i | 0.156273 | + | 0.987714i | \(0.450052\pi\) |
−0.933522 | + | 0.358521i | \(0.883281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.41421 | + | 7.64564i | −0.194892 | + | 0.337563i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.792893 | + | 1.37333i | 0.0349390 | + | 0.0605162i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.0711 | −1.49844 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.68629 | −0.337391 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.34315 | + | 5.79050i | 0.146466 | + | 0.253686i | 0.929919 | − | 0.367765i | \(-0.119877\pi\) |
−0.783453 | + | 0.621451i | \(0.786543\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.928932 | − | 1.60896i | 0.0406194 | − | 0.0703548i | −0.845001 | − | 0.534765i | \(-0.820400\pi\) |
0.885620 | + | 0.464410i | \(0.153734\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.7071 | + | 25.4735i | −0.640652 | + | 1.10964i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3284 | + | 19.6214i | 0.492540 | + | 0.853105i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.65685 | 0.419072 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.10051 | 0.0909830 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.41421 | + | 14.5738i | 0.363778 | + | 0.630082i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.34315 | + | 2.32640i | −0.0579610 | + | 0.100391i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.98528 | + | 13.8309i | −0.343314 | + | 0.594637i | −0.985046 | − | 0.172292i | \(-0.944883\pi\) |
0.641732 | + | 0.766929i | \(0.278216\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.363961 | + | 0.630399i | 0.0156191 | + | 0.0270530i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.00000 | 0.385518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.51472 | 0.321306 | 0.160653 | − | 0.987011i | \(-0.448640\pi\) | ||||
0.160653 | + | 0.987011i | \(0.448640\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.31371 | − | 12.6677i | −0.312141 | − | 0.540645i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.1716 | − | 21.0818i | 0.518526 | − | 0.898114i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.707107 | − | 1.22474i | 0.0300150 | − | 0.0519875i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.89949 | + | 6.75412i | 0.165227 | + | 0.286181i | 0.936736 | − | 0.350037i | \(-0.113831\pi\) |
−0.771509 | + | 0.636218i | \(0.780498\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.7990 | −1.76791 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.1716 | 0.429444 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.3137 | − | 17.8639i | −0.434671 | − | 0.752872i | 0.562598 | − | 0.826731i | \(-0.309802\pi\) |
−0.997269 | + | 0.0738585i | \(0.976469\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.53553 | − | 4.39167i | 0.106671 | − | 0.184759i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.8995 | − | 27.5387i | 0.666542 | − | 1.15448i | −0.312323 | − | 0.949976i | \(-0.601107\pi\) |
0.978865 | − | 0.204508i | \(-0.0655594\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.41421 | − | 4.18154i | −0.101032 | − | 0.174992i | 0.811078 | − | 0.584938i | \(-0.198881\pi\) |
−0.912110 | + | 0.409946i | \(0.865548\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.89949 | 0.288231 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.585786 | 0.0244290 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.03553 | − | 12.1859i | −0.292893 | − | 0.507306i | 0.681599 | − | 0.731725i | \(-0.261285\pi\) |
−0.974493 | + | 0.224420i | \(0.927951\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.17157 | + | 2.02922i | −0.0486889 | + | 0.0843317i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.19239 | + | 12.4576i | −0.297878 | + | 0.515940i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.07107 | − | 8.78335i | −0.209663 | − | 0.363147i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.8284 | 1.27243 | 0.636213 | − | 0.771514i | \(-0.280500\pi\) | ||||
0.636213 | + | 0.771514i | \(0.280500\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.7696 | 0.690977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.70711 | + | 9.88500i | 0.234759 | + | 0.406615i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.86396 | − | 15.3528i | 0.363999 | − | 0.630465i | −0.624616 | − | 0.780932i | \(-0.714744\pi\) |
0.988615 | + | 0.150467i | \(0.0480777\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.53553 | + | 9.58783i | −0.226554 | + | 0.392404i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.39949 | + | 11.0843i | 0.261476 | + | 0.452890i | 0.966634 | − | 0.256160i | \(-0.0824573\pi\) |
−0.705158 | + | 0.709050i | \(0.749124\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.6569 | −1.61764 | −0.808818 | − | 0.588058i | \(-0.799892\pi\) | ||||
−0.808818 | + | 0.588058i | \(0.799892\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.3137 | 1.27519 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.82843 | − | 3.16693i | −0.0743361 | − | 0.128754i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.96447 | − | 12.0628i | 0.282679 | − | 0.489614i | −0.689365 | − | 0.724414i | \(-0.742110\pi\) |
0.972044 | + | 0.234800i | \(0.0754436\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.9558 | − | 27.6363i | 0.645504 | − | 1.11805i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.6569 | + | 35.7787i | 0.834322 | + | 1.44509i | 0.894581 | + | 0.446906i | \(0.147474\pi\) |
−0.0602584 | + | 0.998183i | \(0.519192\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.242641 | −0.00978422 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.8701 | 1.64537 | 0.822683 | − | 0.568500i | \(-0.192476\pi\) | ||||
0.822683 | + | 0.568500i | \(0.192476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.43503 | + | 9.41375i | 0.218452 | + | 0.378370i | 0.954335 | − | 0.298739i | \(-0.0965659\pi\) |
−0.735883 | + | 0.677109i | \(0.763233\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.707107 | − | 1.22474i | 0.0283752 | − | 0.0491473i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.89949 | − | 5.02207i | −0.115795 | − | 0.200562i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.8995 | 0.873190 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.4853 | −1.57188 | −0.785942 | − | 0.618300i | \(-0.787822\pi\) | ||||
−0.785942 | + | 0.618300i | \(0.787822\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.03553 | + | 8.72180i | 0.200145 | + | 0.346660i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.9497 | − | 18.9655i | 0.434527 | − | 0.752624i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.17157 | − | 15.8856i | 0.362822 | − | 0.628426i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.6569 | − | 34.0467i | −0.776399 | − | 1.34476i | −0.934005 | − | 0.357261i | \(-0.883711\pi\) |
0.157606 | − | 0.987502i | \(-0.449622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.21320 | −0.166153 | −0.0830763 | − | 0.996543i | \(-0.526475\pi\) | ||||
−0.0830763 | + | 0.996543i | \(0.526475\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.82843 | 0.190119 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.5563 | + | 30.4085i | 0.690211 | + | 1.19548i | 0.971768 | + | 0.235937i | \(0.0758158\pi\) |
−0.281557 | + | 0.959544i | \(0.590851\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.53553 | + | 11.3199i | −0.256542 | + | 0.444344i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.3431 | − | 23.1110i | 0.522158 | − | 0.904404i | −0.477510 | − | 0.878626i | \(-0.658461\pi\) |
0.999668 | − | 0.0257773i | \(-0.00820608\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.87868 | − | 10.1822i | −0.229699 | − | 0.397850i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6274 | 0.570670 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.6569 | −0.804677 | −0.402338 | − | 0.915491i | \(-0.631802\pi\) | ||||
−0.402338 | + | 0.915491i | \(0.631802\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0711 | − | 29.5680i | −0.663988 | − | 1.15006i | −0.979559 | − | 0.201158i | \(-0.935529\pi\) |
0.315571 | − | 0.948902i | \(-0.397804\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.76346 | + | 8.25055i | −0.184997 | + | 0.320425i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.94975 | + | 3.37706i | −0.0754945 | + | 0.130760i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.98528 | + | 8.63476i | 0.192742 | + | 0.333839i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.7990 | 0.764332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.5147 | −1.06061 | −0.530307 | − | 0.847806i | \(-0.677923\pi\) | ||||
−0.530307 | + | 0.847806i | \(0.677923\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.20711 | + | 2.09077i | 0.0464616 | + | 0.0804738i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.13604 | + | 8.89588i | −0.197394 | + | 0.341896i | −0.947683 | − | 0.319214i | \(-0.896581\pi\) |
0.750289 | + | 0.661110i | \(0.229914\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.60051 | − | 2.77216i | 0.0613315 | − | 0.106229i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.5563 | − | 30.4085i | −0.671775 | − | 1.16355i | −0.977400 | − | 0.211397i | \(-0.932199\pi\) |
0.305625 | − | 0.952152i | \(-0.401135\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9706 | 0.495580 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.89949 | −0.377689 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.73654 | − | 11.6680i | −0.256642 | − | 0.444517i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.75736 | − | 3.04384i | 0.0668531 | − | 0.115793i | −0.830661 | − | 0.556778i | \(-0.812037\pi\) |
0.897515 | + | 0.440985i | \(0.145371\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.94975 | + | 12.0373i | −0.263619 | + | 0.456601i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.87868 | − | 3.25397i | −0.0711601 | − | 0.123253i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.79899 | −0.143691 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.514719 | 0.0194407 | 0.00972033 | − | 0.999953i | \(-0.496906\pi\) | ||||
0.00972033 | + | 0.999953i | \(0.496906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.24264 | − | 10.8126i | −0.235446 | − | 0.407804i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.84315 | + | 3.19242i | −0.0694169 | + | 0.120234i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.81371 | + | 3.14144i | −0.0681153 | + | 0.117979i | −0.898072 | − | 0.439849i | \(-0.855032\pi\) |
0.829956 | + | 0.557828i | \(0.188365\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.5858 | + | 32.1915i | 0.697021 | + | 1.20728i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.68629 | −0.100602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.7279 | 0.513395 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.93503 | − | 5.08362i | −0.109611 | − | 0.189851i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.87868 | − | 13.6463i | 0.293825 | − | 0.508920i | −0.680886 | − | 0.732390i | \(-0.738405\pi\) |
0.974711 | + | 0.223470i | \(0.0717383\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.736544 | + | 1.27573i | −0.0273924 | + | 0.0474450i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.32843 | − | 5.76500i | −0.123615 | − | 0.214107i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.0000 | 0.667583 | 0.333792 | − | 0.942647i | \(-0.391672\pi\) | ||||
0.333792 | + | 0.942647i | \(0.391672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.3848 | + | 64.7523i | 1.38273 | + | 2.39495i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.3492 | + | 26.5857i | −0.566937 | + | 0.981964i | 0.429929 | + | 0.902863i | \(0.358538\pi\) |
−0.996867 | + | 0.0791015i | \(0.974795\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.1924 | + | 36.7063i | −0.780632 | + | 1.35209i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.3284 | − | 17.8894i | −0.379937 | − | 0.658071i | 0.611115 | − | 0.791541i | \(-0.290721\pi\) |
−0.991053 | + | 0.133471i | \(0.957388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.43146 | 0.199530 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.92893 | −0.327571 | −0.163785 | − | 0.986496i | \(-0.552370\pi\) | ||||
−0.163785 | + | 0.986496i | \(0.552370\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.75736 | − | 3.04384i | −0.0643847 | − | 0.111518i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.3137 | − | 19.5959i | 0.413947 | − | 0.716977i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.571068 | + | 0.989118i | −0.0208386 | + | 0.0360934i | −0.876257 | − | 0.481845i | \(-0.839967\pi\) |
0.855418 | + | 0.517938i | \(0.173300\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.60660 | − | 9.71092i | −0.204316 | − | 0.353886i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.8284 | −0.430481 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.1716 | 1.35102 | 0.675512 | − | 0.737349i | \(-0.263923\pi\) | ||||
0.675512 | + | 0.737349i | \(0.263923\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.464466 | + | 0.804479i | 0.0168591 | + | 0.0292007i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.43503 | + | 16.3419i | −0.342020 | + | 0.592395i | −0.984808 | − | 0.173649i | \(-0.944444\pi\) |
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.07107 | + | 15.7116i | −0.327965 | + | 0.568052i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.12132 | − | 10.6024i | −0.221028 | − | 0.382832i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.1421 | −1.01483 | −0.507416 | − | 0.861701i | \(-0.669399\pi\) | ||||
−0.507416 | + | 0.861701i | \(0.669399\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.6863 | 0.384857 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.8640 | − | 37.8695i | −0.786392 | − | 1.36207i | −0.928164 | − | 0.372172i | \(-0.878613\pi\) |
0.141772 | − | 0.989899i | \(-0.454720\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.29289 | − | 3.97141i | 0.0823632 | − | 0.142657i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.07107 | + | 1.85514i | −0.0383750 | + | 0.0664674i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.4142 | + | 21.5020i | 0.444215 | + | 0.769404i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.0711 | −0.574333 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.4853 | −0.374236 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.8640 | − | 37.8695i | −0.779366 | − | 1.34990i | −0.932308 | − | 0.361666i | \(-0.882208\pi\) |
0.152942 | − | 0.988235i | \(-0.451125\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.07107 | + | 3.58719i | −0.0737320 | + | 0.127708i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.27208 | + | 16.0597i | −0.329261 | + | 0.570297i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.778175 | + | 1.34784i | 0.0275990 | + | 0.0478029i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.3848 | 1.25339 | 0.626697 | − | 0.779263i | \(-0.284407\pi\) | ||||
0.626697 | + | 0.779263i | \(0.284407\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −57.0833 | −2.01946 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.0000 | − | 41.5692i | −0.847998 | − | 1.46878i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.89949 | + | 17.1464i | −0.349346 | + | 0.605084i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.46447 | + | 6.00063i | −0.121955 | + | 0.211232i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.01472 | − | 5.22165i | −0.105992 | − | 0.183583i | 0.808151 | − | 0.588975i | \(-0.200468\pi\) |
−0.914143 | + | 0.405392i | \(0.867135\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.5563 | 0.686716 | 0.343358 | − | 0.939205i | \(-0.388436\pi\) | ||||
0.343358 | + | 0.939205i | \(0.388436\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0000 | −0.420858 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.7782 | − | 18.6683i | −0.377543 | − | 0.653924i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.3137 | − | 36.9164i | 0.745672 | − | 1.29154i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.9142 | + | 41.4206i | −0.834612 | + | 1.44559i | 0.0597343 | + | 0.998214i | \(0.480975\pi\) |
−0.894346 | + | 0.447376i | \(0.852359\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.2635 | − | 31.6332i | −0.636624 | − | 1.10267i | −0.986169 | − | 0.165745i | \(-0.946997\pi\) |
0.349545 | − | 0.936920i | \(-0.386336\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.58579 | −0.0552100 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.0416 | −0.349182 | −0.174591 | − | 0.984641i | \(-0.555860\pi\) | ||||
−0.174591 | + | 0.984641i | \(0.555860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.3640 | + | 19.6830i | 0.394687 | + | 0.683617i | 0.993061 | − | 0.117599i | \(-0.0375198\pi\) |
−0.598374 | + | 0.801217i | \(0.704186\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.53553 | − | 2.65962i | 0.0532671 | − | 0.0922613i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.20711 | − | 2.09077i | 0.0417737 | − | 0.0723541i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.53553 | − | 9.58783i | −0.191336 | − | 0.331404i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.3848 | −0.772808 | −0.386404 | − | 0.922330i | \(-0.626283\pi\) | ||||
−0.386404 | + | 0.922330i | \(0.626283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.3137 | 0.528059 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.207107 | + | 0.358719i | 0.00713314 | + | 0.0123550i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.0710678 | − | 0.123093i | 0.00244481 | − | 0.00423453i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.88478 | + | 6.72863i | −0.133325 | + | 0.230926i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.00000 | + | 1.73205i | 0.0342796 | + | 0.0593739i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.2843 | 1.03691 | 0.518457 | − | 0.855104i | \(-0.326507\pi\) | ||||
0.518457 | + | 0.855104i | \(0.326507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.3431 | 0.353728 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.4142 | − | 18.0379i | −0.355743 | − | 0.616165i | 0.631502 | − | 0.775374i | \(-0.282439\pi\) |
−0.987245 | + | 0.159210i | \(0.949105\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.7279 | + | 39.3659i | −0.775467 | + | 1.34315i | 0.159065 | + | 0.987268i | \(0.449152\pi\) |
−0.934532 | + | 0.355880i | \(0.884181\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.87868 | − | 17.1104i | 0.336274 | − | 0.582444i | −0.647455 | − | 0.762104i | \(-0.724166\pi\) |
0.983729 | + | 0.179660i | \(0.0574998\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.27817 | + | 16.0703i | 0.315467 | + | 0.546406i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.0000 | 0.339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −50.3137 | −1.70678 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.8492 | − | 34.3799i | −0.672566 | − | 1.16492i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.2426 | + | 38.5254i | −0.752799 | + | 1.30389i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.34315 | + | 9.25460i | −0.180425 | + | 0.312506i | −0.942025 | − | 0.335542i | \(-0.891081\pi\) |
0.761600 | + | 0.648047i | \(0.224414\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.98528 | − | 5.17066i | −0.100691 | − | 0.174402i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.2843 | 1.89627 | 0.948133 | − | 0.317875i | \(-0.102969\pi\) | ||||
0.948133 | + | 0.317875i | \(0.102969\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.11270 | −0.239361 | −0.119681 | − | 0.992812i | \(-0.538187\pi\) | ||||
−0.119681 | + | 0.992812i | \(0.538187\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.707107 | + | 1.22474i | 0.0237691 | + | 0.0411693i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.7990 | − | 49.8813i | 0.966975 | − | 1.67485i | 0.262764 | − | 0.964860i | \(-0.415366\pi\) |
0.704211 | − | 0.709991i | \(-0.251301\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.3284 | − | 24.8176i | 0.480020 | − | 0.831420i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.2721 | + | 28.1841i | 0.544524 | + | 0.943144i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.48528 | 0.216779 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.870058 | −0.0290504 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.2635 | + | 26.4371i | 0.509065 | + | 0.881726i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0503 | + | 20.8716i | −0.401452 | + | 0.695335i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.878680 | − | 1.52192i | 0.0292083 | − | 0.0505903i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.2635 | − | 19.5089i | −0.373997 | − | 0.647782i | 0.616179 | − | 0.787606i | \(-0.288680\pi\) |
−0.990176 | + | 0.139824i | \(0.955346\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.6569 | −0.452969 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.5980 | −1.84204 | −0.921022 | − | 0.389511i | \(-0.872644\pi\) | ||||
−0.921022 | + | 0.389511i | \(0.872644\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.3137 | + | 26.5241i | 0.506810 | + | 0.877820i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.07107 | − | 1.85514i | 0.0354084 | − | 0.0613292i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.25736 | − | 16.0342i | 0.305372 | − | 0.528920i | −0.671972 | − | 0.740577i | \(-0.734552\pi\) |
0.977344 | + | 0.211657i | \(0.0678858\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.742641 | + | 1.28629i | 0.0244708 | + | 0.0423847i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.2548 | −0.765442 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.41421 | −0.112259 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.24264 | − | 3.88437i | −0.0736580 | − | 0.127579i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.6360 | + | 18.4222i | −0.348957 | + | 0.604411i | −0.986064 | − | 0.166364i | \(-0.946797\pi\) |
0.637107 | + | 0.770775i | \(0.280131\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.44365 | − | 2.50048i | 0.0472630 | − | 0.0818619i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.2782 | − | 21.2664i | −0.401539 | − | 0.695486i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.72792 | 0.252460 | 0.126230 | − | 0.992001i | \(-0.459712\pi\) | ||||
0.126230 | + | 0.992001i | \(0.459712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.85786 | −0.223798 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.00000 | − | 3.46410i | −0.0651981 | − | 0.112926i | 0.831584 | − | 0.555399i | \(-0.187435\pi\) |
−0.896782 | + | 0.442473i | \(0.854101\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.171573 | − | 0.297173i | 0.00558718 | − | 0.00967728i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.0208 | − | 27.7489i | 0.520607 | − | 0.901717i | −0.479106 | − | 0.877757i | \(-0.659039\pi\) |
0.999713 | − | 0.0239601i | \(-0.00762748\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.27208 | − | 16.0597i | −0.300984 | − | 0.521320i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.20101 | −0.201082 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.8701 | −1.25912 | −0.629562 | − | 0.776950i | \(-0.716766\pi\) | ||||
−0.629562 | + | 0.776950i | \(0.716766\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.32843 | − | 14.4253i | −0.269502 | − | 0.466790i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.27817 | − | 9.14207i | 0.170619 | − | 0.295521i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.98528 | − | 8.63476i | 0.160816 | − | 0.278541i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.7990 | − | 41.2211i | −0.766912 | − | 1.32833i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.65685 | 0.182101 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.45584 | −0.239764 | −0.119882 | − | 0.992788i | \(-0.538252\pi\) | ||||
−0.119882 | + | 0.992788i | \(0.538252\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.85786 | − | 8.41407i | −0.156057 | − | 0.270299i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.2635 | + | 19.5089i | −0.361462 | + | 0.626070i | −0.988202 | − | 0.153159i | \(-0.951055\pi\) |
0.626740 | + | 0.779228i | \(0.284389\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.742641 | − | 1.28629i | 0.0237835 | − | 0.0411943i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.07107 | + | 7.05130i | 0.130245 | + | 0.225591i | 0.923771 | − | 0.382945i | \(-0.125090\pi\) |
−0.793526 | + | 0.608536i | \(0.791757\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 64.9706 | 2.07647 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.4558 | −0.812743 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.0061 | − | 36.3836i | −0.669990 | − | 1.16046i | −0.977906 | − | 0.209044i | \(-0.932965\pi\) |
0.307916 | − | 0.951414i | \(-0.400368\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.7782 | − | 23.8645i | 0.439009 | − | 0.760386i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.41421 | + | 5.91359i | −0.108566 | + | 0.188041i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.6569 | − | 21.9223i | −0.402058 | − | 0.696385i | 0.591916 | − | 0.806000i | \(-0.298372\pi\) |
−0.993974 | + | 0.109614i | \(0.965038\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.00000 | 0.0634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.7279 | 0.847332 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.4203 | − | 44.0293i | −0.805069 | − | 1.39442i | −0.916244 | − | 0.400620i | \(-0.868795\pi\) |
0.111175 | − | 0.993801i | \(-0.464539\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.12132 | + | 7.13834i | −0.130393 | + | 0.225847i |
(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 | 980.2.i.l.961.1 | 4 | ||
7.2 | even | 3 | 980.2.a.j.1.2 | ✓ | 2 | ||
7.3 | odd | 6 | 980.2.i.k.361.2 | 4 | |||
7.4 | even | 3 | inner | 980.2.i.l.361.1 | 4 | ||
7.5 | odd | 6 | 980.2.a.k.1.1 | yes | 2 | ||
7.6 | odd | 2 | 980.2.i.k.961.2 | 4 | |||
21.2 | odd | 6 | 8820.2.a.bg.1.2 | 2 | |||
21.5 | even | 6 | 8820.2.a.bl.1.2 | 2 | |||
28.19 | even | 6 | 3920.2.a.bo.1.2 | 2 | |||
28.23 | odd | 6 | 3920.2.a.bx.1.1 | 2 | |||
35.2 | odd | 12 | 4900.2.e.q.2549.2 | 4 | |||
35.9 | even | 6 | 4900.2.a.z.1.1 | 2 | |||
35.12 | even | 12 | 4900.2.e.r.2549.3 | 4 | |||
35.19 | odd | 6 | 4900.2.a.x.1.2 | 2 | |||
35.23 | odd | 12 | 4900.2.e.q.2549.3 | 4 | |||
35.33 | even | 12 | 4900.2.e.r.2549.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
980.2.a.j.1.2 | ✓ | 2 | 7.2 | even | 3 | ||
980.2.a.k.1.1 | yes | 2 | 7.5 | odd | 6 | ||
980.2.i.k.361.2 | 4 | 7.3 | odd | 6 | |||
980.2.i.k.961.2 | 4 | 7.6 | odd | 2 | |||
980.2.i.l.361.1 | 4 | 7.4 | even | 3 | inner | ||
980.2.i.l.961.1 | 4 | 1.1 | even | 1 | trivial | ||
3920.2.a.bo.1.2 | 2 | 28.19 | even | 6 | |||
3920.2.a.bx.1.1 | 2 | 28.23 | odd | 6 | |||
4900.2.a.x.1.2 | 2 | 35.19 | odd | 6 | |||
4900.2.a.z.1.1 | 2 | 35.9 | even | 6 | |||
4900.2.e.q.2549.2 | 4 | 35.2 | odd | 12 | |||
4900.2.e.q.2549.3 | 4 | 35.23 | odd | 12 | |||
4900.2.e.r.2549.2 | 4 | 35.33 | even | 12 | |||
4900.2.e.r.2549.3 | 4 | 35.12 | even | 12 | |||
8820.2.a.bg.1.2 | 2 | 21.2 | odd | 6 | |||
8820.2.a.bl.1.2 | 2 | 21.5 | even | 6 |