Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(401,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.i (of order \(3\), degree \(2\), 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: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.2702336256.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 56x^{4} + 225x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 501.4 | ||
Root | \(0.656712 + 2.13746i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.501 |
Dual form | 700.2.i.f.401.4 |
$q$-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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.866025 | − | 1.50000i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.209313 | + | 2.63746i | −0.0791130 | + | 0.996866i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.13746 | + | 1.97014i | −0.342957 | + | 0.594018i | −0.984980 | − | 0.172666i | \(-0.944762\pi\) |
0.642024 | + | 0.766685i | \(0.278095\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.09095 | 1.68933 | 0.844663 | − | 0.535299i | \(-0.179801\pi\) | ||||
0.844663 | + | 0.535299i | \(0.179801\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.38876 | − | 4.13746i | 0.579360 | − | 1.00348i | −0.416193 | − | 0.909276i | \(-0.636636\pi\) |
0.995553 | − | 0.0942047i | \(-0.0300308\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.13746 | + | 3.70219i | 0.490367 | + | 0.849340i | 0.999939 | − | 0.0110882i | \(-0.00352954\pi\) |
−0.509572 | + | 0.860428i | \(0.670196\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.77492 | + | 2.59808i | 0.823754 | + | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.447399 | + | 0.774917i | 0.0932891 | + | 0.161581i | 0.908893 | − | 0.417029i | \(-0.136929\pi\) |
−0.815604 | + | 0.578610i | \(0.803595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.27492 | −0.608137 | −0.304068 | − | 0.952650i | \(-0.598345\pi\) | ||||
−0.304068 | + | 0.952650i | \(0.598345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.13746 | − | 3.70219i | 0.383899 | − | 0.664932i | −0.607717 | − | 0.794154i | \(-0.707914\pi\) |
0.991616 | + | 0.129221i | \(0.0412478\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.97014 | + | 3.41238i | 0.342957 | + | 0.594018i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.80739 | − | 4.86254i | −0.461532 | − | 0.799397i | 0.537506 | − | 0.843260i | \(-0.319367\pi\) |
−0.999038 | + | 0.0438633i | \(0.986033\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.27492 | − | 9.13642i | 0.844663 | − | 1.46300i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.2749 | −1.76085 | −0.880423 | − | 0.474189i | \(-0.842741\pi\) | ||||
−0.880423 | + | 0.474189i | \(0.842741\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.50958 | 0.992701 | 0.496351 | − | 0.868122i | \(-0.334673\pi\) | ||||
0.496351 | + | 0.868122i | \(0.334673\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.07534 | + | 1.86254i | 0.156854 | + | 0.271680i | 0.933733 | − | 0.357971i | \(-0.116531\pi\) |
−0.776878 | + | 0.629651i | \(0.783198\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.91238 | − | 1.10411i | −0.987482 | − | 0.157730i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.13746 | − | 7.16629i | −0.579360 | − | 1.00348i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.70219 | − | 6.41238i | 0.508534 | − | 0.880808i | −0.491417 | − | 0.870925i | \(-0.663521\pi\) |
0.999951 | − | 0.00988297i | \(-0.00314590\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.40437 | 0.980733 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.13746 | + | 3.70219i | −0.278273 | + | 0.481984i | −0.970956 | − | 0.239259i | \(-0.923095\pi\) |
0.692682 | + | 0.721243i | \(0.256429\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.774917 | − | 1.34220i | −0.0992180 | − | 0.171851i | 0.812143 | − | 0.583458i | \(-0.198301\pi\) |
−0.911361 | + | 0.411608i | \(0.864967\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.95698 | + | 12.0498i | −0.849930 | + | 1.47212i | 0.0313404 | + | 0.999509i | \(0.490022\pi\) |
−0.881270 | + | 0.472613i | \(0.843311\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.54983 | 0.186578 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5498 | 1.25204 | 0.626018 | − | 0.779809i | \(-0.284684\pi\) | ||||
0.626018 | + | 0.779809i | \(0.284684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.07534 | − | 1.86254i | 0.125859 | − | 0.217994i | −0.796209 | − | 0.605021i | \(-0.793165\pi\) |
0.922068 | + | 0.387027i | \(0.126498\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.95807 | − | 3.41238i | −0.565024 | − | 0.388876i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.137459 | + | 0.238085i | 0.0154653 | + | 0.0267867i | 0.873654 | − | 0.486547i | \(-0.161744\pi\) |
−0.858189 | + | 0.513334i | \(0.828410\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.67232 | −0.622618 | −0.311309 | − | 0.950309i | \(-0.600767\pi\) | ||||
−0.311309 | + | 0.950309i | \(0.600767\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.83616 | + | 4.91238i | −0.304068 | + | 0.526662i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.50000 | + | 6.06218i | 0.370999 | + | 0.642590i | 0.989720 | − | 0.143022i | \(-0.0456819\pi\) |
−0.618720 | + | 0.785611i | \(0.712349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.27492 | + | 16.0646i | −0.133648 | + | 1.68403i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.70219 | − | 6.41238i | −0.383899 | − | 0.664932i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.92820 | 0.703452 | 0.351726 | − | 0.936103i | \(-0.385595\pi\) | ||||
0.351726 | + | 0.936103i | \(0.385595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.774917 | + | 1.34220i | −0.0771071 | + | 0.133553i | −0.902001 | − | 0.431735i | \(-0.857902\pi\) |
0.824894 | + | 0.565288i | \(0.191235\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.28465 | + | 2.22508i | 0.126581 | + | 0.219244i | 0.922350 | − | 0.386356i | \(-0.126266\pi\) |
−0.795769 | + | 0.605600i | \(0.792933\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.95698 | − | 12.0498i | −0.672556 | − | 1.16490i | −0.977177 | − | 0.212428i | \(-0.931863\pi\) |
0.304621 | − | 0.952474i | \(-0.401470\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.77492 | + | 3.07425i | −0.170006 | + | 0.294459i | −0.938422 | − | 0.345492i | \(-0.887712\pi\) |
0.768416 | + | 0.639951i | \(0.221045\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.72508 | −0.923064 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.0192 | −1.22474 | −0.612369 | − | 0.790572i | \(-0.709783\pi\) | ||||
−0.612369 | + | 0.790572i | \(0.709783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.4124 | + | 7.16629i | 0.954501 | + | 0.656933i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.91238 | + | 5.04438i | 0.264761 | + | 0.458580i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.76436 | + | 16.9124i | −0.880423 | + | 1.52494i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.78959 | −0.158801 | −0.0794004 | − | 0.996843i | \(-0.525301\pi\) | ||||
−0.0794004 | + | 0.996843i | \(0.525301\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.63746 | − | 9.76436i | 0.496351 | − | 0.859704i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.13746 | + | 15.8265i | 0.798343 | + | 1.38277i | 0.920694 | + | 0.390285i | \(0.127623\pi\) |
−0.122351 | + | 0.992487i | \(0.539043\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.2118 | + | 4.86254i | −0.885472 | + | 0.421636i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.59698 | − | 7.96221i | 0.392747 | − | 0.680258i | −0.600064 | − | 0.799952i | \(-0.704858\pi\) |
0.992811 | + | 0.119695i | \(0.0381915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.0997 | −1.45037 | −0.725187 | − | 0.688551i | \(-0.758247\pi\) | ||||
−0.725187 | + | 0.688551i | \(0.758247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.72508 | 0.313709 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.92820 | + | 12.0000i | −0.579365 | + | 1.00349i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.64246 | + | 9.41238i | −0.630339 | + | 0.776320i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.77492 | − | 6.53835i | −0.309253 | − | 0.535642i | 0.668946 | − | 0.743311i | \(-0.266746\pi\) |
−0.978199 | + | 0.207669i | \(0.933412\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1375 | − | 17.5586i | 0.824975 | − | 1.42890i | −0.0769640 | − | 0.997034i | \(-0.524523\pi\) |
0.901939 | − | 0.431864i | \(-0.142144\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.43424 | − | 9.41238i | 0.433699 | − | 0.751189i | −0.563489 | − | 0.826123i | \(-0.690541\pi\) |
0.997188 | + | 0.0749341i | \(0.0238747\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.41238 | − | 11.1066i | −0.508534 | − | 0.880808i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.13746 | + | 1.01779i | −0.168455 | + | 0.0802135i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.70219 | − | 6.41238i | −0.289978 | − | 0.502256i | 0.683826 | − | 0.729645i | \(-0.260315\pi\) |
−0.973804 | + | 0.227389i | \(0.926981\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.6005 | −0.975058 | −0.487529 | − | 0.873107i | \(-0.662102\pi\) | ||||
−0.487529 | + | 0.873107i | \(0.662102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.0997 | 1.85382 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.37451 | − | 16.2371i | −0.712731 | − | 1.23449i | −0.963828 | − | 0.266524i | \(-0.914125\pi\) |
0.251097 | − | 0.967962i | \(-0.419209\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.70219 | + | 6.41238i | 0.278273 | + | 0.481984i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.137459 | + | 0.238085i | −0.0102741 | + | 0.0177953i | −0.871117 | − | 0.491076i | \(-0.836604\pi\) |
0.860843 | + | 0.508871i | \(0.169937\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.7251 | −1.24317 | −0.621583 | − | 0.783348i | \(-0.713510\pi\) | ||||
−0.621583 | + | 0.783348i | \(0.713510\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.68439 | −0.198436 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.43424 | + | 9.41238i | 0.397391 | + | 0.688301i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.08762 | + | 13.7046i | −0.0791130 | + | 0.996866i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.4124 | − | 19.7668i | −0.825771 | − | 1.43028i | −0.901329 | − | 0.433135i | \(-0.857407\pi\) |
0.0755585 | − | 0.997141i | \(-0.475926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.59698 | + | 7.96221i | −0.330898 | + | 0.573132i | −0.982688 | − | 0.185267i | \(-0.940685\pi\) |
0.651790 | + | 0.758399i | \(0.274018\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.0383 | −1.85515 | −0.927576 | − | 0.373634i | \(-0.878112\pi\) | ||||
−0.927576 | + | 0.373634i | \(0.878112\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.86254 | + | 8.42217i | −0.344696 | + | 0.597032i | −0.985299 | − | 0.170841i | \(-0.945351\pi\) |
0.640602 | + | 0.767873i | \(0.278685\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0498 | + | 20.8709i | 0.849930 | + | 1.47212i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.685484 | − | 8.63746i | 0.0481115 | − | 0.606231i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.72508 | −0.672698 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.6495 | −1.35273 | −0.676364 | − | 0.736568i | \(-0.736445\pi\) | ||||
−0.676364 | + | 0.736568i | \(0.736445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.13642 | − | 15.8248i | 0.626018 | − | 1.08429i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.31697 | + | 6.41238i | 0.632477 | + | 0.435300i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.86254 | − | 3.22602i | −0.125859 | − | 0.217994i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.5498 | − | 25.2011i | 0.978728 | − | 1.69521i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.71780 | −0.583787 | −0.291893 | − | 0.956451i | \(-0.594285\pi\) | ||||
−0.291893 | + | 0.956451i | \(0.594285\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.22602 | + | 5.58762i | −0.214118 | + | 0.370864i | −0.952999 | − | 0.302972i | \(-0.902021\pi\) |
0.738881 | + | 0.673836i | \(0.235354\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.13746 | + | 3.70219i | 0.141247 | + | 0.244647i | 0.927967 | − | 0.372663i | \(-0.121555\pi\) |
−0.786719 | + | 0.617311i | \(0.788222\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.41238 | + | 4.48190i | −0.619289 | + | 0.294887i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.31697 | + | 16.1375i | 0.610375 | + | 1.05720i | 0.991177 | + | 0.132544i | \(0.0423145\pi\) |
−0.380802 | + | 0.924656i | \(0.624352\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.476171 | 0.0309306 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.5498 | −0.941151 | −0.470575 | − | 0.882360i | \(-0.655954\pi\) | ||||
−0.470575 | + | 0.882360i | \(0.655954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.41238 | − | 11.1066i | 0.413057 | − | 0.715436i | −0.582165 | − | 0.813071i | \(-0.697794\pi\) |
0.995222 | + | 0.0976343i | \(0.0311275\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.0192 | + | 22.5498i | 0.828389 | + | 1.43481i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.91238 | + | 8.50848i | −0.311309 | + | 0.539203i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.45017 | −0.344011 | −0.172006 | − | 0.985096i | \(-0.555025\pi\) | ||||
−0.172006 | + | 0.985096i | \(0.555025\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.03559 | −0.127976 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.3624 | − | 21.4124i | −0.771148 | − | 1.33567i | −0.936934 | − | 0.349506i | \(-0.886350\pi\) |
0.165786 | − | 0.986162i | \(-0.446984\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.4124 | − | 6.38658i | 0.833404 | − | 0.396843i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.4666 | − | 23.3248i | 0.830383 | − | 1.43827i | −0.0673516 | − | 0.997729i | \(-0.521455\pi\) |
0.897735 | − | 0.440536i | \(-0.145212\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1244 | 0.741999 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.7749 | − | 25.5909i | 0.900843 | − | 1.56031i | 0.0744400 | − | 0.997225i | \(-0.476283\pi\) |
0.826403 | − | 0.563080i | \(-0.190384\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.41238 | + | 11.1066i | 0.389524 | + | 0.674676i | 0.992386 | − | 0.123170i | \(-0.0393062\pi\) |
−0.602861 | + | 0.797846i | \(0.705973\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.9928 | + | 15.8248i | 1.39159 | + | 0.957758i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.31697 | − | 16.1375i | 0.559802 | − | 0.969606i | −0.437710 | − | 0.899116i | \(-0.644210\pi\) |
0.997512 | − | 0.0704898i | \(-0.0224562\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.79314 | + | 16.9622i | −0.582142 | + | 1.00830i | 0.413084 | + | 0.910693i | \(0.364452\pi\) |
−0.995225 | + | 0.0976056i | \(0.968882\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.35999 | − | 29.7371i | 0.139306 | − | 1.75533i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.91238 | − | 5.04438i | −0.171316 | − | 0.296728i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | − | 10.3923i | 0.351726 | − | 0.609208i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.92820 | −0.404750 | −0.202375 | − | 0.979308i | \(-0.564866\pi\) | ||||
−0.202375 | + | 0.979308i | \(0.564866\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.91041 | + | 10.2371i | −0.342957 | + | 0.594018i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.72508 | + | 4.71998i | 0.157596 | + | 0.272964i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.36254 | + | 17.1687i | −0.0785356 | + | 0.989590i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.34220 | + | 2.32475i | 0.0771071 | + | 0.133553i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.99782 | 0.228167 | 0.114084 | − | 0.993471i | \(-0.463607\pi\) | ||||
0.114084 | + | 0.993471i | \(0.463607\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.45017 | 0.253161 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.41238 | + | 11.1066i | −0.363612 | + | 0.629795i | −0.988552 | − | 0.150878i | \(-0.951790\pi\) |
0.624940 | + | 0.780673i | \(0.285123\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.22383 | + | 12.5120i | 0.408315 | + | 0.707223i | 0.994701 | − | 0.102809i | \(-0.0327831\pi\) |
−0.586386 | + | 0.810032i | \(0.699450\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.91259 | + | 3.31271i | 0.107422 | + | 0.186060i | 0.914725 | − | 0.404077i | \(-0.132407\pi\) |
−0.807303 | + | 0.590137i | \(0.799074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.72508 | − | 6.45203i | 0.208565 | − | 0.361244i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0997 | −1.34511 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.4235 | 1.13640 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.07425 | + | 5.32475i | 0.170006 | + | 0.294459i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.13746 | + | 2.44631i | −0.283237 | + | 0.134869i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.41238 | + | 4.17836i | 0.132596 | + | 0.229663i | 0.924677 | − | 0.380753i | \(-0.124335\pi\) |
−0.792080 | + | 0.610417i | \(0.791002\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0192 | 0.709198 | 0.354599 | − | 0.935018i | \(-0.384617\pi\) | ||||
0.354599 | + | 0.935018i | \(0.384617\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.2749 | + | 19.5287i | −0.612369 | + | 1.06065i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.86254 | + | 8.42217i | 0.263321 | + | 0.456086i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.35890 | − | 18.0000i | 0.235358 | − | 0.971909i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.06218 | − | 10.5000i | 0.325435 | − | 0.563670i | −0.656165 | − | 0.754617i | \(-0.727823\pi\) |
0.981600 | + | 0.190947i | \(0.0611560\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.2749 | −0.603532 | −0.301766 | − | 0.953382i | \(-0.597576\pi\) | ||||
−0.301766 | + | 0.953382i | \(0.597576\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 31.6495 | 1.68933 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6304 | − | 18.4124i | 0.565799 | − | 0.979992i | −0.431176 | − | 0.902268i | \(-0.641901\pi\) |
0.996975 | − | 0.0777242i | \(-0.0247654\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.7668 | − | 9.41238i | 1.04617 | − | 0.498156i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.687293 | + | 1.19043i | 0.0362739 | + | 0.0628283i | 0.883592 | − | 0.468257i | \(-0.155118\pi\) |
−0.847318 | + | 0.531085i | \(0.821784\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.362541 | − | 0.627940i | 0.0190811 | − | 0.0330495i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.0888 | 0.529523 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.37560 | + | 12.7749i | −0.385003 | + | 0.666845i | −0.991770 | − | 0.128035i | \(-0.959133\pi\) |
0.606766 | + | 0.794880i | \(0.292466\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.1375 | + | 11.1066i | 0.837815 | + | 0.576624i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.80739 | + | 4.86254i | 0.145361 | + | 0.251773i | 0.929508 | − | 0.368803i | \(-0.120232\pi\) |
−0.784146 | + | 0.620576i | \(0.786899\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.9474 | −1.02734 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.6495 | 1.21479 | 0.607397 | − | 0.794399i | \(-0.292214\pi\) | ||||
0.607397 | + | 0.794399i | \(0.292214\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.54983 | + | 2.68439i | −0.0794004 | + | 0.137526i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.0025 | + | 17.3248i | 0.511101 | + | 0.885253i | 0.999917 | + | 0.0128665i | \(0.00409564\pi\) |
−0.488816 | + | 0.872387i | \(0.662571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.68729 | − | 4.65453i | 0.136251 | − | 0.235994i | −0.789824 | − | 0.613334i | \(-0.789828\pi\) |
0.926075 | + | 0.377340i | \(0.123161\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.27492 | 0.216192 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.6531 | 1.59669 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.58492 | + | 13.1375i | 0.380676 | + | 0.659350i | 0.991159 | − | 0.132679i | \(-0.0423580\pi\) |
−0.610483 | + | 0.792029i | \(0.709025\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.54983 | + | 19.5287i | −0.0775888 | + | 0.977659i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | − | 2.59808i | −0.0749064 | − | 0.129742i | 0.826139 | − | 0.563466i | \(-0.190532\pi\) |
−0.901046 | + | 0.433724i | \(0.857199\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.0192 | − | 22.5498i | 0.648530 | − | 1.12329i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.7732 | 0.633142 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.04983 | + | 8.74657i | −0.249698 | + | 0.432490i | −0.963442 | − | 0.267917i | \(-0.913665\pi\) |
0.713744 | + | 0.700407i | \(0.246998\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.96221 | − | 13.7910i | −0.392747 | − | 0.680258i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.31697 | − | 6.41238i | −0.458458 | − | 0.315532i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.8087 | + | 25.6495i | −0.725187 | + | 1.25606i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.0997 | 0.835373 | 0.417687 | − | 0.908591i | \(-0.362841\pi\) | ||||
0.417687 | + | 0.908591i | \(0.362841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.27492 | 0.159610 | 0.0798048 | − | 0.996811i | \(-0.474570\pi\) | ||||
0.0798048 | + | 0.996811i | \(0.474570\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.70219 | − | 1.76287i | 0.179161 | − | 0.0853114i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.0000 | + | 20.7846i | 0.579365 | + | 1.00349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.68729 | + | 16.7789i | −0.466620 | + | 0.808210i | −0.999273 | − | 0.0381236i | \(-0.987862\pi\) |
0.532653 | + | 0.846334i | \(0.321195\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.8756 | 1.29156 | 0.645778 | − | 0.763525i | \(-0.276533\pi\) | ||||
0.645778 | + | 0.763525i | \(0.276533\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.91259 | + | 3.31271i | −0.0914917 | + | 0.158468i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.587624 | − | 1.01779i | −0.0280458 | − | 0.0485767i | 0.851662 | − | 0.524092i | \(-0.175595\pi\) |
−0.879708 | + | 0.475515i | \(0.842262\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.06218 | − | 10.5000i | −0.288023 | − | 0.498870i | 0.685315 | − | 0.728247i | \(-0.259665\pi\) |
−0.973338 | + | 0.229377i | \(0.926331\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.0767 | −0.618507 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.8248 | −1.21875 | −0.609373 | − | 0.792884i | \(-0.708579\pi\) | ||||
−0.609373 | + | 0.792884i | \(0.708579\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.8248 | − | 22.2131i | 0.603894 | − | 1.04598i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.5586 | − | 30.4124i | −0.824975 | − | 1.42890i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.2118 | + | 17.6873i | 0.477686 | + | 0.827377i | 0.999673 | − | 0.0255769i | \(-0.00814228\pi\) |
−0.521987 | + | 0.852954i | \(0.674809\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.4124 | − | 21.4989i | 0.579360 | − | 1.00348i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.50958 | −0.302526 | −0.151263 | − | 0.988494i | \(-0.548334\pi\) | ||||
−0.151263 | + | 0.988494i | \(0.548334\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.58382 | − | 16.5997i | −0.443486 | − | 0.768141i | 0.554459 | − | 0.832211i | \(-0.312925\pi\) |
−0.997945 | + | 0.0640700i | \(0.979592\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.3248 | − | 20.8709i | −1.40027 | − | 0.963730i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.41238 | − | 16.3027i | −0.433699 | − | 0.751189i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.40437 | + | 12.8248i | −0.340453 | + | 0.589683i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.41238 | − | 11.1066i | 0.292989 | − | 0.507472i | −0.681526 | − | 0.731794i | \(-0.738683\pi\) |
0.974515 | + | 0.224322i | \(0.0720168\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.0997 | − | 29.6175i | −0.779678 | − | 1.35044i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.324401 | + | 4.08762i | −0.0147608 | + | 0.185993i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.7213 | − | 28.9622i | 0.757716 | − | 1.31240i | −0.186296 | − | 0.982494i | \(-0.559648\pi\) |
0.944013 | − | 0.329909i | \(-0.107018\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.8248 | −0.579955 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4502 | −0.606997 | −0.303499 | − | 0.952832i | \(-0.598155\pi\) | ||||
−0.303499 | + | 0.952832i | \(0.598155\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.82300 | + | 13.5498i | −0.352330 | + | 0.610254i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.20822 | + | 27.8248i | −0.0990523 | + | 1.24811i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.6873 | − | 34.0994i | −0.881324 | − | 1.52650i | −0.849869 | − | 0.526993i | \(-0.823319\pi\) |
−0.0314548 | − | 0.999505i | \(-0.510014\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.9124 | + | 18.9008i | −0.487529 | + | 0.844425i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.1797 | 0.721418 | 0.360709 | − | 0.932678i | \(-0.382535\pi\) | ||||
0.360709 | + | 0.932678i | \(0.382535\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.8709 | − | 36.1495i | 0.926910 | − | 1.60546i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.7749 | + | 25.5909i | 0.654887 | + | 1.13430i | 0.981922 | + | 0.189285i | \(0.0606170\pi\) |
−0.327036 | + | 0.945012i | \(0.606050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.68729 | + | 3.22602i | 0.207354 | + | 0.142711i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.1066 | + | 19.2371i | 0.490367 | + | 0.849340i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.89261 | −0.215177 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.4743 | −1.42546 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.41238 | − | 11.1066i | 0.280931 | − | 0.486587i | −0.690683 | − | 0.723158i | \(-0.742690\pi\) |
0.971614 | + | 0.236570i | \(0.0760234\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.85286 | + | 10.1375i | 0.255928 | + | 0.443280i | 0.965147 | − | 0.261708i | \(-0.0842857\pi\) |
−0.709219 | + | 0.704988i | \(0.750952\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.2118 | − | 17.6873i | −0.444831 | − | 0.770471i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0997 | − | 19.2252i | 0.482594 | − | 0.835878i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −68.6750 | −2.97464 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.238085 | + | 0.412376i | 0.0102741 | + | 0.0177953i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.0378 | − | 12.3624i | 0.432358 | − | 0.532488i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.22508 | + | 2.12191i | 0.0526704 | + | 0.0912278i | 0.891159 | − | 0.453692i | \(-0.149893\pi\) |
−0.838488 | + | 0.544920i | \(0.816560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.4843 | + | 25.0876i | −0.621583 | + | 1.07661i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.1271 | −1.54468 | −0.772341 | − | 0.635208i | \(-0.780914\pi\) | ||||
−0.772341 | + | 0.635208i | \(0.780914\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.00000 | − | 12.1244i | −0.298210 | − | 0.516515i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.656712 | + | 0.312707i | −0.0279262 | + | 0.0132977i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.80739 | − | 4.86254i | 0.118953 | − | 0.206032i | −0.800400 | − | 0.599466i | \(-0.795380\pi\) |
0.919353 | + | 0.393434i | \(0.128713\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.6495 | 1.67700 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.8248 | 0.794782 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.11972 | − | 10.5997i | 0.257916 | − | 0.446723i | −0.707768 | − | 0.706445i | \(-0.750298\pi\) |
0.965683 | + | 0.259722i | \(0.0836310\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.6150 | + | 13.5000i | 0.823754 | + | 0.566947i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.6873 | + | 25.4391i | 0.615723 | + | 1.06646i | 0.990257 | + | 0.139251i | \(0.0444694\pi\) |
−0.374534 | + | 0.927213i | \(0.622197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.137459 | − | 0.238085i | 0.00575246 | − | 0.00996356i | −0.863135 | − | 0.504974i | \(-0.831502\pi\) |
0.868887 | + | 0.495010i | \(0.164836\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −39.5336 | −1.65154 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.12081 | + | 7.13746i | −0.171552 | + | 0.297136i | −0.938963 | − | 0.344019i | \(-0.888211\pi\) |
0.767411 | + | 0.641156i | \(0.221545\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.96221 | + | 13.7910i | 0.330898 | + | 0.573132i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.18729 | − | 14.9605i | 0.0492572 | − | 0.620667i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.42217 | + | 14.5876i | 0.348811 | + | 0.604158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.9715 | 0.576665 | 0.288333 | − | 0.957530i | \(-0.406899\pi\) | ||||
0.288333 | + | 0.957530i | \(0.406899\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.2749 | 0.753005 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.5498 | + | 39.0575i | −0.927576 | + | 1.60661i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.1542 | + | 17.5876i | 0.416984 | + | 0.722237i | 0.995634 | − | 0.0933384i | \(-0.0297538\pi\) |
−0.578651 | + | 0.815576i | \(0.696421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.42217 | + | 14.5876i | 0.344696 | + | 0.597032i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.13746 | − | 1.97014i | 0.0464753 | − | 0.0804976i | −0.841852 | − | 0.539709i | \(-0.818534\pi\) |
0.888327 | + | 0.459211i | \(0.151868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0934 | − | 27.8746i | −0.653211 | − | 1.13139i | −0.982339 | − | 0.187109i | \(-0.940088\pi\) |
0.329128 | − | 0.944285i | \(-0.393245\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.3625 | − | 8.50848i | −0.500955 | − | 0.344781i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.54983 | + | 11.3446i | 0.264978 | + | 0.458955i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.5109 | − | 32.0619i | 0.747650 | − | 1.29497i | −0.201297 | − | 0.979530i | \(-0.564516\pi\) |
0.948947 | − | 0.315437i | \(-0.102151\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.57919 | −0.144093 | −0.0720464 | − | 0.997401i | \(-0.522953\pi\) | ||||
−0.0720464 | + | 0.997401i | \(0.522953\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.9622 | + | 38.0397i | −0.882736 | + | 1.52894i | −0.0344487 | + | 0.999406i | \(0.510968\pi\) |
−0.848287 | + | 0.529537i | \(0.822366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.32475 | + | 4.02659i | 0.0932891 | + | 0.161581i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.7213 | + | 7.96221i | −0.669926 | + | 0.318999i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.42217 | + | 14.5876i | −0.336349 | + | 0.582574i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.8248 | −1.06957 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.90033 | 0.115460 | 0.0577302 | − | 0.998332i | \(-0.481614\pi\) | ||||
0.0577302 | + | 0.998332i | \(0.481614\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.0170 | + | 29.4743i | −0.676364 | + | 1.17150i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −42.1029 | − | 6.72508i | −1.66818 | − | 0.266457i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.0498 | + | 24.3350i | −0.554935 | + | 0.961176i | 0.442973 | + | 0.896535i | \(0.353924\pi\) |
−0.997909 | + | 0.0646411i | \(0.979410\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.3353 | −1.51180 | −0.755898 | − | 0.654689i | \(-0.772800\pi\) | ||||
−0.755898 | + | 0.654689i | \(0.772800\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.389855 | − | 0.675248i | 0.0153268 | − | 0.0265468i | −0.858260 | − | 0.513215i | \(-0.828454\pi\) |
0.873587 | + | 0.486668i | \(0.161788\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.86254 | − | 8.42217i | −0.190871 | − | 0.330599i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.6873 | − | 8.42217i | 0.693220 | − | 0.330091i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.5109 | − | 32.0619i | −0.724389 | − | 1.25468i | −0.959225 | − | 0.282643i | \(-0.908789\pi\) |
0.234836 | − | 0.972035i | \(-0.424545\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.4502 | −0.991398 | −0.495699 | − | 0.868494i | \(-0.665088\pi\) | ||||
−0.495699 | + | 0.868494i | \(0.665088\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.77492 | − | 13.4666i | 0.302409 | − | 0.523788i | −0.674272 | − | 0.738483i | \(-0.735542\pi\) |
0.976681 | + | 0.214695i | \(0.0688758\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −25.2011 | − | 43.6495i | −0.978728 | − | 1.69521i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.46519 | − | 2.53779i | −0.0567325 | − | 0.0982636i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.54983 | + | 13.0767i | −0.291893 | + | 0.505574i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.52575 | 0.136110 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.57919 | −0.137968 | −0.0689838 | − | 0.997618i | \(-0.521976\pi\) | ||||
−0.0689838 | + | 0.997618i | \(0.521976\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.3049 | + | 21.3127i | 0.472916 | + | 0.819114i | 0.999519 | − | 0.0309969i | \(-0.00986821\pi\) |
−0.526604 | + | 0.850111i | \(0.676535\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.45017 | + | 18.2728i | −0.0556522 | + | 0.701248i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.58762 | + | 9.67805i | 0.214118 | + | 0.370864i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.85177 | + | 13.5997i | −0.300440 | + | 0.520377i | −0.976236 | − | 0.216712i | \(-0.930467\pi\) |
0.675796 | + | 0.737089i | \(0.263800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.40437 | 0.282494 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.5498 | − | 39.0575i | 0.859080 | − | 1.48797i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.68729 | + | 6.38658i | 0.140271 | + | 0.242957i | 0.927599 | − | 0.373578i | \(-0.121869\pi\) |
−0.787327 | + | 0.616535i | \(0.788536\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.9331 | + | 46.6495i | −1.02016 | + | 1.76698i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 32.2749 | 1.22075 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.8248 | −0.522154 | −0.261077 | − | 0.965318i | \(-0.584078\pi\) | ||||
−0.261077 | + | 0.965318i | \(0.584078\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0014 | − | 20.7870i | 0.452640 | − | 0.783995i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.37779 | − | 2.32475i | −0.127035 | − | 0.0874313i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.7749 | + | 22.1268i | 0.479772 | + | 0.830990i | 0.999731 | − | 0.0232018i | \(-0.00738601\pi\) |
−0.519959 | + | 0.854191i | \(0.674053\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.82518 | 0.143254 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.6005 | + | 21.8248i | −0.470575 | + | 0.815060i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.68729 | − | 6.38658i | −0.137513 | − | 0.238179i | 0.789042 | − | 0.614340i | \(-0.210577\pi\) |
−0.926555 | + | 0.376160i | \(0.877244\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.13746 | + | 2.92248i | −0.228571 | + | 0.108839i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.1066 | − | 19.2371i | −0.413057 | − | 0.715436i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.6915 | 0.693228 | 0.346614 | − | 0.938008i | \(-0.387331\pi\) | ||||
0.346614 | + | 0.938008i | \(0.387331\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.5498 | − | 26.9331i | 0.575131 | − | 0.996157i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.6638 | + | 28.8625i | 0.615491 | + | 1.06606i | 0.990298 | + | 0.138959i | \(0.0443757\pi\) |
−0.374807 | + | 0.927103i | \(0.622291\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.8265 | − | 27.4124i | −0.582978 | − | 1.00975i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.9622 | + | 27.6474i | −0.587179 | + | 1.01702i | 0.407420 | + | 0.913241i | \(0.366428\pi\) |
−0.994600 | + | 0.103784i | \(0.966905\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 45.0997 | 1.65678 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.5287 | 0.716440 | 0.358220 | − | 0.933637i | \(-0.383384\pi\) | ||||
0.358220 | + | 0.933637i | \(0.383384\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.2371 | − | 15.8265i | 1.21446 | − | 0.578289i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.1375 | + | 19.2906i | 0.406412 | + | 0.703926i | 0.994485 | − | 0.104882i | \(-0.0334466\pi\) |
−0.588073 | + | 0.808808i | \(0.700113\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.71998 | + | 8.17525i | −0.172006 | + | 0.297923i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.43996 | −0.343101 | −0.171551 | − | 0.985175i | \(-0.554878\pi\) | ||||
−0.171551 | + | 0.985175i | \(0.554878\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.76287 | + | 3.05338i | −0.0639882 | + | 0.110831i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9622 | + | 25.9153i | 0.542380 | + | 0.939429i | 0.998767 | + | 0.0496479i | \(0.0158099\pi\) |
−0.456387 | + | 0.889781i | \(0.650857\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.73668 | − | 5.32475i | −0.280087 | − | 0.192769i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.0192 | + | 22.5498i | −0.470094 | + | 0.814227i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −42.8248 | −1.54230 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.6183 | + | 23.5876i | −0.489817 | + | 0.848388i | −0.999931 | − | 0.0117187i | \(-0.996270\pi\) |
0.510114 | + | 0.860107i | \(0.329603\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.03559 | − | 25.6495i | 0.0730264 | − | 0.920171i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.0997 | − | 41.7419i | −0.863460 | − | 1.49556i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0000 | + | 20.7846i | −0.429394 | + | 0.743732i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.0170 | −0.608137 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.866025 | + | 1.50000i | −0.0308705 | + | 0.0534692i | −0.881048 | − | 0.473027i | \(-0.843161\pi\) |
0.850177 | + | 0.526496i | \(0.176495\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.3248 | − | 40.3997i | −0.830383 | − | 1.43827i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.72508 | − | 34.3375i | 0.0968928 | − | 1.22090i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.71998 | − | 8.17525i | −0.167611 | − | 0.290312i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.3873 | 1.04095 | 0.520476 | − | 0.853876i | \(-0.325754\pi\) | ||||
0.520476 | + | 0.853876i | \(0.325754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.2749 | 0.363500 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.44631 | + | 4.23713i | 0.0863283 | + | 0.149525i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.5909 | − | 44.3248i | −0.900843 | − | 1.56031i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.5997 | + | 37.4117i | −0.759404 | + | 1.31533i | 0.183751 | + | 0.982973i | \(0.441176\pi\) |
−0.943155 | + | 0.332353i | \(0.892157\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.5498 | 0.791832 | 0.395916 | − | 0.918287i | \(-0.370427\pi\) | ||||
0.395916 | + | 0.918287i | \(0.370427\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.2131 | 0.779048 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.9140 | + | 24.0997i | 0.486788 | + | 0.843141i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.68729 | − | 15.0468i | −0.303189 | − | 0.525138i | 0.673668 | − | 0.739034i | \(-0.264718\pi\) |
−0.976856 | + | 0.213896i | \(0.931385\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.1509 | + | 27.9743i | −0.562987 | + | 0.975121i | 0.434247 | + | 0.900794i | \(0.357014\pi\) |
−0.997234 | + | 0.0743276i | \(0.976319\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.5670 | 1.58452 | 0.792261 | − | 0.610183i | \(-0.208904\pi\) | ||||
0.792261 | + | 0.610183i | \(0.208904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.962210 | + | 1.66660i | −0.0334189 | + | 0.0578833i | −0.882251 | − | 0.470779i | \(-0.843973\pi\) |
0.848832 | + | 0.528662i | \(0.177306\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.1375 | − | 27.9509i | −0.559802 | − | 0.969606i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.0802 | + | 25.9622i | −0.730387 | + | 0.899537i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.1066 | − | 19.2371i | 0.383899 | − | 0.664932i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.9003 | 0.376321 | 0.188161 | − | 0.982138i | \(-0.439747\pi\) | ||||
0.188161 | + | 0.982138i | \(0.439747\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.2749 | −0.630170 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.19615 | − | 9.00000i | 0.178965 | − | 0.309976i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.9140 | + | 6.62541i | −0.478089 | + | 0.227652i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.9622 | + | 29.3794i | 0.582142 | + | 1.00830i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.51204 | − | 4.35099i | 0.0861118 | − | 0.149150i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.4547 | 1.04275 | 0.521375 | − | 0.853327i | \(-0.325419\pi\) | ||||
0.521375 | + | 0.853327i | \(0.325419\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.6638 | − | 28.8625i | 0.569224 | − | 0.985926i | −0.427418 | − | 0.904054i | \(-0.640577\pi\) |
0.996643 | − | 0.0818717i | \(-0.0260898\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.6873 | − | 30.6353i | −0.603483 | − | 1.04526i | −0.992289 | − | 0.123943i | \(-0.960446\pi\) |
0.388807 | − | 0.921319i | \(-0.372887\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −42.5619 | − | 29.2931i | −1.45050 | − | 0.998306i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.5718 | − | 21.7749i | −0.427947 | − | 0.741227i | 0.568743 | − | 0.822515i | \(-0.307430\pi\) |
−0.996691 | + | 0.0812884i | \(0.974097\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.0888 | −0.342632 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.625414 | −0.0212157 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42.3746 | + | 73.3949i | −1.43581 | + | 2.48689i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.3361 | − | 38.6873i | −0.754237 | − | 1.30638i | −0.945753 | − | 0.324887i | \(-0.894674\pi\) |
0.191516 | − | 0.981490i | \(-0.438660\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.00000 | + | 10.3923i | −0.202375 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.0241 | 1.34845 | 0.674223 | − | 0.738528i | \(-0.264479\pi\) | ||||
0.674223 | + | 0.738528i | \(0.264479\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.6695 | −0.695585 | −0.347792 | − | 0.937572i | \(-0.613069\pi\) | ||||
−0.347792 | + | 0.937572i | \(0.613069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.6150 | + | 33.9743i | 0.658609 | + | 1.14074i | 0.980976 | + | 0.194129i | \(0.0621881\pi\) |
−0.322367 | + | 0.946615i | \(0.604479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.374586 | − | 4.71998i | 0.0125632 | − | 0.158303i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.2371 | + | 17.7312i | 0.342957 | + | 0.594018i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.59698 | + | 7.96221i | −0.153832 | + | 0.266445i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.43996 | 0.315191 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.00000 | + | 12.1244i | −0.233463 | + | 0.404370i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.6873 | − | 30.6353i | −0.589249 | − | 1.02061i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.5731 | + | 16.9124i | 0.817742 | + | 0.562809i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.6605 | − | 39.2492i | 0.752430 | − | 1.30325i | −0.194212 | − | 0.980960i | \(-0.562215\pi\) |
0.946642 | − | 0.322288i | \(-0.104452\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.09967 | 0.168960 | 0.0844798 | − | 0.996425i | \(-0.473077\pi\) | ||||
0.0844798 | + | 0.996425i | \(0.473077\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.45203 | − | 11.1752i | 0.213531 | − | 0.369847i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −43.6544 | + | 20.7870i | −1.44160 | + | 0.686446i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.96221 | − | 5.13070i | −0.0977143 | − | 0.169246i | 0.813024 | − | 0.582230i | \(-0.197820\pi\) |
−0.910738 | + | 0.412984i | \(0.864486\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.46221 | − | 5.99672i | 0.114084 | − | 0.197599i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 64.2585 | 2.11509 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.95017 | + | 15.5021i | 0.293645 | + | 0.508609i | 0.974669 | − | 0.223653i | \(-0.0717982\pi\) |
−0.681023 | + | 0.732262i | \(0.738465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.6873 | − | 27.9509i | −0.350262 | − | 0.916054i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.1066 | + | 19.2371i | 0.363612 | + | 0.629795i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.5074 | 0.343262 | 0.171631 | − | 0.985161i | \(-0.445096\pi\) | ||||
0.171631 | + | 0.985161i | \(0.445096\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.0241 | 0.816630 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.13746 | + | 3.70219i | −0.0696792 | + | 0.120688i | −0.898760 | − | 0.438441i | \(-0.855531\pi\) |
0.829081 | + | 0.559129i | \(0.188864\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.04438 | − | 8.73713i | −0.164268 | − | 0.284520i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.8709 | + | 36.1495i | 0.678214 | + | 1.17470i | 0.975518 | + | 0.219918i | \(0.0705791\pi\) |
−0.297304 | + | 0.954783i | \(0.596088\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.54983 | − | 11.3446i | 0.212617 | − | 0.368263i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.62541 | 0.214844 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.6175 | 0.959405 | 0.479702 | − | 0.877431i | \(-0.340745\pi\) | ||||
0.479702 | + | 0.877431i | \(0.340745\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.45203 | − | 11.1752i | −0.208565 | − | 0.361244i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.0378 | + | 13.7910i | 0.647054 | + | 0.445333i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.36254 | + | 11.0202i | 0.205243 | + | 0.355492i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.50958 | 0.209334 | 0.104667 | − | 0.994507i | \(-0.466622\pi\) | ||||
0.104667 | + | 0.994507i | \(0.466622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.6873 | − | 30.6353i | 0.568198 | − | 0.984147i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.96221 | − | 13.7910i | −0.255519 | − | 0.442573i | 0.709517 | − | 0.704688i | \(-0.248913\pi\) |
−0.965036 | + | 0.262116i | \(0.915580\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.57919 | − | 45.0997i | 0.114744 | − | 1.44583i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.42217 | + | 14.5876i | −0.269449 | + | 0.466699i | −0.968720 | − | 0.248158i | \(-0.920175\pi\) |
0.699271 | + | 0.714857i | \(0.253508\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.9244 | −0.508947 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.6052 | − | 32.2251i | 0.593412 | − | 1.02782i | −0.400356 | − | 0.916360i | \(-0.631114\pi\) |
0.993769 | − | 0.111461i | \(-0.0355530\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.779710 | + | 9.82475i | −0.0248184 | + | 0.312725i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.91238 | + | 5.04438i | 0.0926082 | + | 0.160402i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.2371 | − | 29.8556i | 0.547555 | − | 0.948394i | −0.450886 | − | 0.892582i | \(-0.648892\pi\) |
0.998441 | − | 0.0558122i | \(-0.0177748\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.35671 | 0.265192 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.38876 | − | 4.13746i | 0.0756529 | − | 0.131035i | −0.825717 | − | 0.564084i | \(-0.809229\pi\) |
0.901370 | + | 0.433050i | \(0.142563\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.5876 | − | 25.2665i | −0.461532 | − | 0.799397i |
(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 | 700.2.i.f.501.4 | 8 | ||
5.2 | odd | 4 | 140.2.q.a.109.1 | yes | 4 | ||
5.3 | odd | 4 | 140.2.q.b.109.1 | yes | 4 | ||
5.4 | even | 2 | inner | 700.2.i.f.501.1 | 8 | ||
7.2 | even | 3 | inner | 700.2.i.f.401.4 | 8 | ||
7.3 | odd | 6 | 4900.2.a.bf.1.4 | 4 | |||
7.4 | even | 3 | 4900.2.a.be.1.2 | 4 | |||
15.2 | even | 4 | 1260.2.bm.a.109.2 | 4 | |||
15.8 | even | 4 | 1260.2.bm.b.109.2 | 4 | |||
20.3 | even | 4 | 560.2.bw.a.529.1 | 4 | |||
20.7 | even | 4 | 560.2.bw.e.529.1 | 4 | |||
35.2 | odd | 12 | 140.2.q.b.9.2 | yes | 4 | ||
35.3 | even | 12 | 980.2.e.c.589.3 | 4 | |||
35.4 | even | 6 | 4900.2.a.be.1.4 | 4 | |||
35.9 | even | 6 | inner | 700.2.i.f.401.1 | 8 | ||
35.12 | even | 12 | 980.2.q.b.569.1 | 4 | |||
35.13 | even | 4 | 980.2.q.b.949.2 | 4 | |||
35.17 | even | 12 | 980.2.e.c.589.1 | 4 | |||
35.18 | odd | 12 | 980.2.e.f.589.2 | 4 | |||
35.23 | odd | 12 | 140.2.q.a.9.1 | ✓ | 4 | ||
35.24 | odd | 6 | 4900.2.a.bf.1.2 | 4 | |||
35.27 | even | 4 | 980.2.q.g.949.2 | 4 | |||
35.32 | odd | 12 | 980.2.e.f.589.4 | 4 | |||
35.33 | even | 12 | 980.2.q.g.569.2 | 4 | |||
105.2 | even | 12 | 1260.2.bm.b.289.1 | 4 | |||
105.23 | even | 12 | 1260.2.bm.a.289.2 | 4 | |||
140.23 | even | 12 | 560.2.bw.e.289.1 | 4 | |||
140.107 | even | 12 | 560.2.bw.a.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.q.a.9.1 | ✓ | 4 | 35.23 | odd | 12 | ||
140.2.q.a.109.1 | yes | 4 | 5.2 | odd | 4 | ||
140.2.q.b.9.2 | yes | 4 | 35.2 | odd | 12 | ||
140.2.q.b.109.1 | yes | 4 | 5.3 | odd | 4 | ||
560.2.bw.a.289.2 | 4 | 140.107 | even | 12 | |||
560.2.bw.a.529.1 | 4 | 20.3 | even | 4 | |||
560.2.bw.e.289.1 | 4 | 140.23 | even | 12 | |||
560.2.bw.e.529.1 | 4 | 20.7 | even | 4 | |||
700.2.i.f.401.1 | 8 | 35.9 | even | 6 | inner | ||
700.2.i.f.401.4 | 8 | 7.2 | even | 3 | inner | ||
700.2.i.f.501.1 | 8 | 5.4 | even | 2 | inner | ||
700.2.i.f.501.4 | 8 | 1.1 | even | 1 | trivial | ||
980.2.e.c.589.1 | 4 | 35.17 | even | 12 | |||
980.2.e.c.589.3 | 4 | 35.3 | even | 12 | |||
980.2.e.f.589.2 | 4 | 35.18 | odd | 12 | |||
980.2.e.f.589.4 | 4 | 35.32 | odd | 12 | |||
980.2.q.b.569.1 | 4 | 35.12 | even | 12 | |||
980.2.q.b.949.2 | 4 | 35.13 | even | 4 | |||
980.2.q.g.569.2 | 4 | 35.33 | even | 12 | |||
980.2.q.g.949.2 | 4 | 35.27 | even | 4 | |||
1260.2.bm.a.109.2 | 4 | 15.2 | even | 4 | |||
1260.2.bm.a.289.2 | 4 | 105.23 | even | 12 | |||
1260.2.bm.b.109.2 | 4 | 15.8 | even | 4 | |||
1260.2.bm.b.289.1 | 4 | 105.2 | even | 12 | |||
4900.2.a.be.1.2 | 4 | 7.4 | even | 3 | |||
4900.2.a.be.1.4 | 4 | 35.4 | even | 6 | |||
4900.2.a.bf.1.2 | 4 | 35.24 | odd | 6 | |||
4900.2.a.bf.1.4 | 4 | 7.3 | odd | 6 |