Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(49,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.u (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.1952986685049.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 241.1 | ||
Root | \(0.500000 - 1.00210i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.241 |
Dual form | 432.2.u.c.337.1 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.210069 | + | 1.71926i | 0.121284 | + | 0.992618i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0713060 | − | 0.0598329i | 0.0318890 | − | 0.0267581i | −0.626704 | − | 0.779258i | \(-0.715596\pi\) |
0.658593 | + | 0.752499i | \(0.271152\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.544891 | + | 0.198324i | −0.205950 | + | 0.0749595i | −0.442935 | − | 0.896554i | \(-0.646063\pi\) |
0.236986 | + | 0.971513i | \(0.423841\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.91174 | + | 0.722330i | −0.970581 | + | 0.240777i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.36944 | + | 1.98820i | 0.714413 | + | 0.599464i | 0.925834 | − | 0.377932i | \(-0.123365\pi\) |
−0.211421 | + | 0.977395i | \(0.567809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.729623 | + | 4.13790i | 0.202361 | + | 1.14765i | 0.901539 | + | 0.432699i | \(0.142439\pi\) |
−0.699178 | + | 0.714948i | \(0.746450\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.117848 | + | 0.110025i | 0.0304282 | + | 0.0284083i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.995493 | + | 1.72424i | 0.241443 | + | 0.418191i | 0.961125 | − | 0.276112i | \(-0.0890461\pi\) |
−0.719683 | + | 0.694303i | \(0.755713\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.92271 | + | 3.33023i | −0.441100 | + | 0.764008i | −0.997771 | − | 0.0667249i | \(-0.978745\pi\) |
0.556671 | + | 0.830733i | \(0.312078\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.455437 | − | 0.895151i | −0.0993845 | − | 0.195338i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.18428 | − | 1.52295i | −0.872482 | − | 0.317558i | −0.133310 | − | 0.991074i | \(-0.542561\pi\) |
−0.739172 | + | 0.673517i | \(0.764783\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.866736 | + | 4.91551i | −0.173347 | + | 0.983101i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.85354 | − | 4.85432i | −0.356715 | − | 0.934213i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.11126 | − | 6.30229i | 0.206356 | − | 1.17031i | −0.688935 | − | 0.724823i | \(-0.741921\pi\) |
0.895291 | − | 0.445482i | \(-0.146968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.55754 | + | 0.566898i | 0.279743 | + | 0.101818i | 0.478081 | − | 0.878316i | \(-0.341332\pi\) |
−0.198339 | + | 0.980134i | \(0.563555\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.92049 | + | 4.49135i | −0.508392 | + | 0.781844i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0269877 | + | 0.0467441i | −0.00456176 | + | 0.00790120i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.01505 | − | 3.49016i | −0.331272 | − | 0.573779i | 0.651490 | − | 0.758657i | \(-0.274144\pi\) |
−0.982761 | + | 0.184878i | \(0.940811\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.96087 | + | 2.12366i | −1.11463 | + | 0.340058i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.190345 | − | 1.07950i | −0.0297270 | − | 0.168590i | 0.966330 | − | 0.257306i | \(-0.0828348\pi\) |
−0.996057 | + | 0.0887159i | \(0.971724\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.28657 | + | 4.43596i | 0.806194 | + | 0.676477i | 0.949696 | − | 0.313173i | \(-0.101392\pi\) |
−0.143502 | + | 0.989650i | \(0.545836\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.164406 | + | 0.225724i | −0.0245082 | + | 0.0336490i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.37650 | − | 1.22894i | 0.492513 | − | 0.179260i | −0.0838106 | − | 0.996482i | \(-0.526709\pi\) |
0.576323 | + | 0.817222i | \(0.304487\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.10474 | + | 4.28338i | −0.729248 | + | 0.611912i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.75531 | + | 2.07373i | −0.385821 | + | 0.290380i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.40034 | 0.741793 | 0.370897 | − | 0.928674i | \(-0.379050\pi\) | ||||
0.370897 | + | 0.928674i | \(0.379050\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.287915 | 0.0388224 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.12946 | − | 2.60607i | −0.811866 | − | 0.345182i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.87850 | − | 6.61085i | 1.02569 | − | 0.860659i | 0.0353615 | − | 0.999375i | \(-0.488742\pi\) |
0.990332 | + | 0.138715i | \(0.0442973\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4005 | − | 4.51341i | 1.58772 | − | 0.577883i | 0.610855 | − | 0.791742i | \(-0.290826\pi\) |
0.976864 | + | 0.213860i | \(0.0686036\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.44333 | − | 0.971060i | 0.181842 | − | 0.122342i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.299609 | + | 0.251402i | 0.0371619 | + | 0.0311825i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.53458 | + | 8.70304i | 0.187479 | + | 1.06324i | 0.922729 | + | 0.385449i | \(0.125954\pi\) |
−0.735250 | + | 0.677796i | \(0.762935\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.73937 | − | 7.51381i | 0.209396 | − | 0.904556i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.572473 | + | 0.991553i | 0.0679401 | + | 0.117676i | 0.897994 | − | 0.440007i | \(-0.145024\pi\) |
−0.830054 | + | 0.557683i | \(0.811691\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.0977361 | + | 0.169284i | −0.0114391 | + | 0.0198132i | −0.871688 | − | 0.490061i | \(-0.836975\pi\) |
0.860249 | + | 0.509874i | \(0.170308\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.63313 | − | 0.457552i | −0.996868 | − | 0.0528336i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.68539 | − | 0.613433i | −0.192069 | − | 0.0699072i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.25166 | − | 7.09849i | 0.140822 | − | 0.798642i | −0.829805 | − | 0.558054i | \(-0.811548\pi\) |
0.970627 | − | 0.240589i | \(-0.0773405\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.95648 | − | 4.20647i | 0.884053 | − | 0.467386i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.58744 | − | 14.6741i | 0.284008 | − | 1.61069i | −0.424800 | − | 0.905287i | \(-0.639656\pi\) |
0.708808 | − | 0.705402i | \(-0.249233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.174151 | + | 0.0633858i | 0.0188893 | + | 0.00687516i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.0687 | + | 0.586638i | 1.18669 | + | 0.0628942i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.776563 | − | 1.34505i | 0.0823155 | − | 0.142575i | −0.821929 | − | 0.569590i | \(-0.807102\pi\) |
0.904244 | + | 0.427016i | \(0.140435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.21821 | − | 2.11000i | −0.127703 | − | 0.221189i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.647457 | + | 2.79691i | −0.0671381 | + | 0.290026i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0621565 | + | 0.352507i | 0.00637712 | + | 0.0361665i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.05661 | + | 3.40390i | 0.411887 | + | 0.345614i | 0.825067 | − | 0.565035i | \(-0.191137\pi\) |
−0.413180 | + | 0.910649i | \(0.635582\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.33533 | − | 4.07760i | −0.837732 | − | 0.409814i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.83061 | − | 2.48614i | 0.679671 | − | 0.247380i | 0.0209647 | − | 0.999780i | \(-0.493326\pi\) |
0.658706 | + | 0.752400i | \(0.271104\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.90374 | + | 4.11472i | −0.483179 | + | 0.405436i | −0.851574 | − | 0.524234i | \(-0.824352\pi\) |
0.368395 | + | 0.929669i | \(0.379907\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0860348 | − | 0.0365796i | −0.00839614 | − | 0.00356980i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.54365 | 0.535925 | 0.267963 | − | 0.963429i | \(-0.413650\pi\) | ||||
0.267963 | + | 0.963429i | \(0.413650\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.23137 | −0.596857 | −0.298428 | − | 0.954432i | \(-0.596462\pi\) | ||||
−0.298428 | + | 0.954432i | \(0.596462\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.57722 | − | 4.19758i | 0.529366 | − | 0.398416i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.07301 | + | 7.61316i | −0.853517 | + | 0.716186i | −0.960561 | − | 0.278068i | \(-0.910306\pi\) |
0.107044 | + | 0.994254i | \(0.465861\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.389487 | + | 0.141762i | −0.0363198 | + | 0.0132193i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.11340 | − | 11.5215i | −0.472734 | − | 1.06516i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.884395 | − | 0.742096i | −0.0810724 | − | 0.0680278i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.248809 | − | 1.41107i | −0.0226190 | − | 0.128279i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.81597 | − | 0.554025i | 0.163740 | − | 0.0499547i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.465014 | + | 0.805428i | 0.0415921 | + | 0.0720396i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.76469 | − | 9.98473i | 0.511533 | − | 0.886002i | −0.488377 | − | 0.872633i | \(-0.662411\pi\) |
0.999911 | − | 0.0133693i | \(-0.00425570\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.51604 | + | 10.0209i | −0.573705 | + | 0.882288i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.46830 | − | 3.08221i | −0.739879 | − | 0.269294i | −0.0555383 | − | 0.998457i | \(-0.517688\pi\) |
−0.684340 | + | 0.729163i | \(0.739910\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.387203 | − | 2.19594i | 0.0335747 | − | 0.190412i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.422616 | − | 0.235239i | −0.0363730 | − | 0.0202462i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00047 | − | 11.3452i | 0.170911 | − | 0.969287i | −0.771846 | − | 0.635809i | \(-0.780667\pi\) |
0.942758 | − | 0.333478i | \(-0.108222\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.60108 | + | 0.582746i | 0.135802 | + | 0.0494279i | 0.409027 | − | 0.912522i | \(-0.365868\pi\) |
−0.273225 | + | 0.961950i | \(0.588090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82218 | + | 5.54693i | 0.237670 | + | 0.467136i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.49816 | + | 11.2551i | −0.543403 | + | 0.941202i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.297844 | − | 0.515881i | −0.0247346 | − | 0.0428416i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.43662 | − | 7.87659i | −0.695840 | − | 0.649650i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.75996 | − | 21.3238i | −0.308028 | − | 1.74691i | −0.608897 | − | 0.793249i | \(-0.708388\pi\) |
0.300869 | − | 0.953666i | \(-0.402723\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.63222 | + | 3.04779i | 0.295586 | + | 0.248026i | 0.778504 | − | 0.627640i | \(-0.215979\pi\) |
−0.482918 | + | 0.875665i | \(0.660423\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.14409 | − | 4.30148i | −0.335030 | − | 0.347754i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.144981 | − | 0.0527688i | 0.0116452 | − | 0.00423849i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.160261 | + | 0.134475i | −0.0127902 | + | 0.0107323i | −0.649160 | − | 0.760652i | \(-0.724880\pi\) |
0.636370 | + | 0.771384i | \(0.280435\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.13444 | + | 9.28461i | 0.0899673 | + | 0.736317i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.58202 | 0.203491 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.62384 | −0.440493 | −0.220247 | − | 0.975444i | \(-0.570686\pi\) | ||||
−0.220247 | + | 0.975444i | \(0.570686\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0604821 | + | 0.495002i | 0.00470852 | + | 0.0385358i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.7780 | + | 10.7220i | −0.988791 | + | 0.829695i | −0.985392 | − | 0.170300i | \(-0.945526\pi\) |
−0.00339914 | + | 0.999994i | \(0.501082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.37386 | + | 1.59195i | −0.336451 | + | 0.122458i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.19291 | − | 11.0856i | 0.244168 | − | 0.847738i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.5565 | + | 12.2143i | 1.10671 | + | 0.928639i | 0.997858 | − | 0.0654187i | \(-0.0208383\pi\) |
0.108851 | + | 0.994058i | \(0.465283\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.502587 | − | 2.85031i | −0.0379920 | − | 0.215463i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.0208 | + | 12.1565i | 0.978706 | + | 0.913738i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.11761 | + | 14.0601i | 0.606739 | + | 1.05090i | 0.991774 | + | 0.128001i | \(0.0408560\pi\) |
−0.385035 | + | 0.922902i | \(0.625811\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.49579 | − | 2.59078i | 0.111181 | − | 0.192571i | −0.805066 | − | 0.593186i | \(-0.797870\pi\) |
0.916247 | + | 0.400614i | \(0.131203\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.3647 | + | 20.3716i | 0.766181 | + | 1.50591i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.352512 | − | 0.128304i | −0.0259172 | − | 0.00943308i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.06938 | + | 6.06473i | −0.0782005 | + | 0.443497i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.97271 | + | 2.27747i | 0.143493 | + | 0.165662i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.391371 | − | 2.21958i | 0.0283186 | − | 0.160603i | −0.967369 | − | 0.253371i | \(-0.918461\pi\) |
0.995688 | + | 0.0927685i | \(0.0295716\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.827186 | + | 0.301071i | 0.0595422 | + | 0.0216716i | 0.371620 | − | 0.928385i | \(-0.378803\pi\) |
−0.312077 | + | 0.950057i | \(0.601025\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.369287 | + | 0.567919i | −0.0264452 | + | 0.0406695i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.1383 | + | 17.5600i | −0.722322 | + | 1.25110i | 0.237744 | + | 0.971328i | \(0.423592\pi\) |
−0.960067 | + | 0.279771i | \(0.909741\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.50472 | − | 16.4627i | −0.673772 | − | 1.16701i | −0.976826 | − | 0.214034i | \(-0.931340\pi\) |
0.303054 | − | 0.952973i | \(-0.401994\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.6405 | + | 4.46659i | −1.03266 | + | 0.315049i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.644379 | + | 3.65445i | 0.0452265 | + | 0.256492i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0781625 | − | 0.0655862i | −0.00545911 | − | 0.00458074i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.2836 | + | 1.41202i | 0.923275 | + | 0.0981420i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.1769 | + | 4.06806i | −0.773123 | + | 0.281394i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.3977 | + | 10.4029i | −0.853494 | + | 0.716166i | −0.960556 | − | 0.278086i | \(-0.910300\pi\) |
0.107062 | + | 0.994252i | \(0.465856\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.58448 | + | 1.19253i | −0.108567 | + | 0.0817107i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.642380 | 0.0438100 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.961120 | −0.0652451 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.311575 | − | 0.132473i | −0.0210543 | − | 0.00895168i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.40842 | + | 5.37730i | −0.431077 | + | 0.361716i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.1633 | − | 7.33883i | 1.35023 | − | 0.491444i | 0.437212 | − | 0.899359i | \(-0.355966\pi\) |
0.913020 | + | 0.407914i | \(0.133744\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.02690 | − | 14.9388i | −0.0684602 | − | 0.995917i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.6424 | + | 12.2864i | 0.971848 | + | 0.815477i | 0.982840 | − | 0.184462i | \(-0.0590544\pi\) |
−0.0109918 | + | 0.999940i | \(0.503499\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.90190 | + | 22.1288i | 0.257845 | + | 1.46231i | 0.788663 | + | 0.614826i | \(0.210774\pi\) |
−0.530818 | + | 0.847486i | \(0.678115\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.700605 | − | 3.02650i | 0.0460964 | − | 0.199129i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.84074 | + | 15.3126i | 0.579176 | + | 1.00316i | 0.995574 | + | 0.0939796i | \(0.0299589\pi\) |
−0.416398 | + | 0.909182i | \(0.636708\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.167233 | − | 0.289657i | 0.0109091 | − | 0.0188951i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.4671 | + | 0.660752i | 0.809826 | + | 0.0429204i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.4904 | − | 5.27406i | −0.937303 | − | 0.341151i | −0.172203 | − | 0.985061i | \(-0.555088\pi\) |
−0.765100 | + | 0.643911i | \(0.777311\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.28373 | − | 12.9516i | 0.147108 | − | 0.834289i | −0.818543 | − | 0.574445i | \(-0.805218\pi\) |
0.965651 | − | 0.259844i | \(-0.0836711\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.90345 | + | 12.7956i | 0.571157 | + | 0.820841i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.107711 | + | 0.610862i | −0.00688143 | + | 0.0390265i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.1830 | − | 5.52617i | −0.966073 | − | 0.351622i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 25.7722 | + | 1.36591i | 1.63324 | + | 0.0865612i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.70830 | − | 15.0832i | 0.549663 | − | 0.952045i | −0.448634 | − | 0.893716i | \(-0.648089\pi\) |
0.998297 | − | 0.0583292i | \(-0.0185773\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.88646 | − | 11.9277i | −0.432948 | − | 0.749889i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0723932 | + | 0.312727i | −0.00453344 | + | 0.0195837i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.94270 | + | 11.0176i | 0.121182 | + | 0.687260i | 0.983502 | + | 0.180896i | \(0.0578997\pi\) |
−0.862320 | + | 0.506364i | \(0.830989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.79017 | + | 1.50213i | 0.111236 | + | 0.0933377i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.31662 | + | 19.1533i | 0.0814965 | + | 1.18556i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.4619 | + | 7.08354i | −1.20007 | + | 0.436790i | −0.863249 | − | 0.504779i | \(-0.831574\pi\) |
−0.336821 | + | 0.941569i | \(0.609352\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.385077 | − | 0.323118i | 0.0236551 | − | 0.0198490i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.47562 | + | 1.05256i | 0.151506 | + | 0.0644159i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.2449 | −1.72212 | −0.861060 | − | 0.508504i | \(-0.830199\pi\) | ||||
−0.861060 | + | 0.508504i | \(0.830199\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.2626 | −1.04863 | −0.524316 | − | 0.851524i | \(-0.675679\pi\) | ||||
−0.524316 | + | 0.851524i | \(0.675679\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.37175 | − | 2.53767i | 0.204067 | − | 0.153587i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.8267 | + | 9.92375i | −0.713175 | + | 0.598425i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.85725 | + | 1.76789i | −0.291844 | + | 0.106222i | −0.483793 | − | 0.875182i | \(-0.660741\pi\) |
0.191949 | + | 0.981405i | \(0.438519\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.94464 | − | 0.525604i | −0.296028 | − | 0.0314671i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.52522 | − | 2.11891i | −0.150642 | − | 0.126404i | 0.564352 | − | 0.825534i | \(-0.309126\pi\) |
−0.714994 | + | 0.699131i | \(0.753571\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.58553 | + | 8.99200i | 0.0942501 | + | 0.534519i | 0.994975 | + | 0.100128i | \(0.0319253\pi\) |
−0.900724 | + | 0.434391i | \(0.856964\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.592996 | + | 0.180914i | −0.0351260 | + | 0.0107164i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.317809 | + | 0.550462i | 0.0187597 | + | 0.0324927i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.51799 | − | 11.2895i | 0.383411 | − | 0.664087i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.00004 | + | 7.68945i | −0.293108 | + | 0.450764i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.65598 | + | 0.966697i | 0.155164 | + | 0.0564750i | 0.418434 | − | 0.908247i | \(-0.362579\pi\) |
−0.263271 | + | 0.964722i | \(0.584801\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.166239 | − | 0.942787i | 0.00967880 | − | 0.0548912i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.25947 | − | 15.1872i | 0.305185 | − | 0.881251i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.24888 | − | 18.4253i | 0.187887 | − | 1.06556i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.76036 | − | 1.36866i | −0.216744 | − | 0.0788882i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.70923 | + | 11.2214i | 0.327987 | + | 0.644650i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.614179 | − | 1.06379i | 0.0351678 | − | 0.0609124i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.14723 | + | 5.45116i | 0.179622 | + | 0.311114i | 0.941751 | − | 0.336311i | \(-0.109179\pi\) |
−0.762129 | + | 0.647425i | \(0.775846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.10442 | − | 7.56644i | −0.461045 | − | 0.430440i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.28029 | + | 7.26088i | 0.0725985 | + | 0.411727i | 0.999350 | + | 0.0360515i | \(0.0114780\pi\) |
−0.926751 | + | 0.375675i | \(0.877411\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.27159 | − | 2.74519i | −0.184921 | − | 0.155167i | 0.545628 | − | 0.838028i | \(-0.316291\pi\) |
−0.730549 | + | 0.682860i | \(0.760736\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0448167 | − | 0.155601i | 0.00252513 | − | 0.00876712i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.1738 | + | 5.52279i | −0.852243 | + | 0.310191i | −0.730954 | − | 0.682426i | \(-0.760925\pi\) |
−0.121288 | + | 0.992617i | \(0.538703\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.1632 | − | 12.7235i | 0.848979 | − | 0.712378i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.16455 | + | 9.53101i | 0.0649989 | + | 0.531969i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.65618 | −0.426001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.9723 | −1.16333 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.30902 | − | 10.7134i | −0.0723890 | − | 0.592451i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.59610 | + | 1.33928i | −0.0879956 | + | 0.0738371i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0686 | − | 6.57644i | 0.993142 | − | 0.361474i | 0.206206 | − | 0.978509i | \(-0.433888\pi\) |
0.786936 | + | 0.617035i | \(0.211666\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.38834 | + | 8.70693i | 0.459678 | + | 0.477137i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.630152 | + | 0.528761i | 0.0344289 | + | 0.0288893i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.11615 | − | 29.0152i | −0.278695 | − | 1.58056i | −0.726976 | − | 0.686663i | \(-0.759075\pi\) |
0.448281 | − | 0.893893i | \(-0.352036\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.9950 | − | 13.9996i | −0.814417 | − | 0.760355i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.56339 | + | 4.43993i | 0.138815 | + | 0.240435i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.96154 | − | 6.86159i | 0.213903 | − | 0.370491i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.325545 | − | 0.639851i | −0.0175268 | − | 0.0344484i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.7097 | + | 3.89801i | 0.574927 | + | 0.209256i | 0.613087 | − | 0.790015i | \(-0.289927\pi\) |
−0.0381600 | + | 0.999272i | \(0.512150\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.89021 | − | 27.7338i | 0.261767 | − | 1.48456i | −0.516318 | − | 0.856397i | \(-0.672698\pi\) |
0.778085 | − | 0.628158i | \(-0.216191\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.7343 | − | 11.2116i | 0.999962 | − | 0.598431i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.97573 | − | 28.2188i | 0.264831 | − | 1.50193i | −0.504683 | − | 0.863305i | \(-0.668391\pi\) |
0.769515 | − | 0.638629i | \(-0.220498\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.100148 | + | 0.0364510i | 0.00531532 | + | 0.00193462i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.09007 | − | 1.67640i | 0.0576929 | − | 0.0887245i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.5161 | + | 26.8747i | −0.818909 | + | 1.41839i | 0.0875770 | + | 0.996158i | \(0.472088\pi\) |
−0.906486 | + | 0.422235i | \(0.861246\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.10636 | + | 3.64833i | 0.110861 | + | 0.192017i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.37373 | − | 0.724191i | 0.124589 | − | 0.0380102i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.00315957 | + | 0.0179188i | 0.000165379 | + | 0.000937912i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.4802 | − | 15.5067i | −0.964660 | − | 0.809446i | 0.0170450 | − | 0.999855i | \(-0.494574\pi\) |
−0.981705 | + | 0.190409i | \(0.939019\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.33399 | + | 3.00574i | 0.0694449 | + | 0.156473i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.94260 | + | 1.07102i | −0.152772 | + | 0.0556045i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.64114 | + | 8.08988i | −0.499199 | + | 0.418878i | −0.857309 | − | 0.514801i | \(-0.827866\pi\) |
0.358110 | + | 0.933679i | \(0.383421\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.28706 | + | 0.968677i | −0.0664634 | + | 0.0500223i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.8890 | 1.38486 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.70522 | 0.395790 | 0.197895 | − | 0.980223i | \(-0.436589\pi\) | ||||
0.197895 | + | 0.980223i | \(0.436589\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.3774 | + | 7.81354i | 0.941502 | + | 0.400300i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.6828 | − | 11.4812i | 0.699159 | − | 0.586664i | −0.222376 | − | 0.974961i | \(-0.571381\pi\) |
0.921534 | + | 0.388297i | \(0.126937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.156882 | + | 0.0571005i | −0.00799546 | + | 0.00291011i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.5973 | − | 9.09771i | −0.945356 | − | 0.462463i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.9808 | + | 17.6050i | 1.06377 | + | 0.892607i | 0.994473 | − | 0.104989i | \(-0.0334809\pi\) |
0.0692941 | + | 0.997596i | \(0.477925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.53948 | − | 8.73081i | −0.0778547 | − | 0.441536i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.52020 | − | 15.2067i | 0.177571 | − | 0.767078i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.335472 | − | 0.581055i | −0.0168794 | − | 0.0292361i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.10799 | + | 3.65115i | −0.105797 | + | 0.183246i | −0.914064 | − | 0.405571i | \(-0.867073\pi\) |
0.808266 | + | 0.588817i | \(0.200406\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.85673 | + | 0.204405i | 0.193078 | + | 0.0102331i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.2575 | − | 5.18930i | −0.711985 | − | 0.259141i | −0.0394656 | − | 0.999221i | \(-0.512566\pi\) |
−0.672519 | + | 0.740080i | \(0.734788\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.20935 | + | 6.85857i | −0.0602420 | + | 0.341650i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.315660 | − | 0.776006i | 0.0156853 | − | 0.0385600i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.16460 | − | 12.2760i | 0.107295 | − | 0.608501i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.42559 | − | 1.61078i | −0.218831 | − | 0.0796481i | 0.230278 | − | 0.973125i | \(-0.426036\pi\) |
−0.449109 | + | 0.893477i | \(0.648259\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.9257 | + | 1.05605i | 0.982860 | + | 0.0520912i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.98184 | + | 5.16469i | −0.146727 | + | 0.254138i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.693492 | − | 1.20116i | −0.0340422 | − | 0.0589628i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.665556 | + | 2.87510i | −0.0325924 | + | 0.140794i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.43669 | − | 19.4905i | −0.167894 | − | 0.952171i | −0.946031 | − | 0.324077i | \(-0.894946\pi\) |
0.778137 | − | 0.628094i | \(-0.216165\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.5915 | + | 18.1174i | 1.05231 | + | 0.882989i | 0.993334 | − | 0.115270i | \(-0.0367734\pi\) |
0.0589715 | + | 0.998260i | \(0.481218\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.94379 | + | 6.01731i | −0.434862 | + | 0.292572i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.33836 | + | 3.39889i | −0.452977 | + | 0.164870i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.86180 | + | 4.91863i | −0.283672 | + | 0.238029i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.7156 | − | 8.80769i | −1.00016 | − | 0.425239i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.19681 | 0.250321 | 0.125161 | − | 0.992136i | \(-0.460055\pi\) | ||||
0.125161 | + | 0.992136i | \(0.460055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3285 | 1.21721 | 0.608605 | − | 0.793473i | \(-0.291730\pi\) | ||||
0.608605 | + | 0.793473i | \(0.291730\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.824368 | − | 0.620444i | 0.0395254 | − | 0.0297480i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.1169 | − | 11.0064i | 0.627469 | − | 0.526509i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.7167 | + | 5.35646i | −0.702392 | + | 0.255650i | −0.668432 | − | 0.743773i | \(-0.733034\pi\) |
−0.0339602 | + | 0.999423i | \(0.510812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.7697 | − | 16.1594i | 0.560460 | − | 0.769496i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.9833 | + | 11.7333i | 0.664365 | + | 0.557468i | 0.911391 | − | 0.411541i | \(-0.135009\pi\) |
−0.247027 | + | 0.969009i | \(0.579454\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.0251044 | − | 0.142374i | −0.00119006 | − | 0.00674917i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 35.8714 | − | 10.9439i | 1.69666 | − | 0.517626i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.3608 | − | 24.8737i | −0.677729 | − | 1.17386i | −0.975663 | − | 0.219274i | \(-0.929631\pi\) |
0.297934 | − | 0.954586i | \(-0.403702\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.69525 | − | 2.93626i | 0.0798262 | − | 0.138263i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.47694 | + | 6.88499i | −0.210345 | + | 0.323485i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.213113 | − | 0.0775669i | −0.00999091 | − | 0.00363639i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.14505 | + | 34.8503i | −0.287453 | + | 1.63023i | 0.408936 | + | 0.912563i | \(0.365900\pi\) |
−0.696389 | + | 0.717665i | \(0.745211\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.52484 | − | 8.02840i | 0.304553 | − | 0.374734i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.395350 | − | 2.24214i | 0.0184133 | − | 0.104427i | −0.974216 | − | 0.225617i | \(-0.927560\pi\) |
0.992629 | + | 0.121190i | \(0.0386712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.2664 | + | 6.28446i | 0.802438 | + | 0.292064i | 0.710496 | − | 0.703701i | \(-0.248470\pi\) |
0.0919417 | + | 0.995764i | \(0.470693\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.121180 | + | 0.238176i | 0.00561957 | + | 0.0110451i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.32935 | − | 4.03455i | 0.107789 | − | 0.186697i | −0.807085 | − | 0.590435i | \(-0.798956\pi\) |
0.914874 | + | 0.403738i | \(0.132289\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.56220 | − | 4.43786i | −0.118312 | − | 0.204922i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.264864 | − | 0.247282i | −0.0122043 | − | 0.0113941i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.70665 | + | 21.0215i | 0.170432 | + | 0.966568i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.7033 | − | 12.3375i | −0.674634 | − | 0.566085i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.7244 | + | 3.90082i | −0.719970 | + | 0.178606i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.3210 | + | 4.84844i | −0.608651 | + | 0.221531i | −0.627913 | − | 0.778283i | \(-0.716091\pi\) |
0.0192617 | + | 0.999814i | \(0.493868\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.9717 | − | 10.8846i | 0.591460 | − | 0.496294i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.542402 | + | 4.43917i | 0.0246802 | + | 0.201989i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.492926 | 0.0223826 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.4338 | 0.971258 | 0.485629 | − | 0.874165i | \(-0.338591\pi\) | ||||
0.485629 | + | 0.874165i | \(0.338591\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.18140 | − | 9.66888i | −0.0534246 | − | 0.437242i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.7919 | − | 9.05550i | 0.487033 | − | 0.408669i | −0.365929 | − | 0.930643i | \(-0.619249\pi\) |
0.852961 | + | 0.521974i | \(0.174804\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.9729 | − | 4.35779i | 0.539234 | − | 0.196265i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.838333 | + | 0.207969i | −0.0376803 | + | 0.00934753i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.508585 | − | 0.426753i | −0.0228131 | − | 0.0191425i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.58898 | − | 14.6828i | −0.115899 | − | 0.657294i | −0.986301 | − | 0.164953i | \(-0.947253\pi\) |
0.870403 | − | 0.492340i | \(-0.163858\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.1182 | − | 19.7164i | −0.943494 | − | 0.880864i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.93153 | − | 13.7378i | −0.353650 | − | 0.612539i | 0.633236 | − | 0.773958i | \(-0.281726\pi\) |
−0.986886 | + | 0.161420i | \(0.948393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.338311 | − | 0.585972i | 0.0150546 | − | 0.0260754i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.65580 | − | 7.18540i | −0.162360 | − | 0.319115i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.8807 | − | 11.6036i | −1.41309 | − | 0.514321i | −0.481052 | − | 0.876692i | \(-0.659745\pi\) |
−0.932034 | + | 0.362371i | \(0.881967\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0196825 | − | 0.111625i | 0.000870700 | − | 0.00493799i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.7298 | + | 3.16072i | 0.871093 | + | 0.139549i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.103470 | + | 0.586809i | −0.00455945 | + | 0.0258579i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.4438 | + | 3.80123i | 0.459317 | + | 0.167178i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.9418 | + | 27.5923i | −0.787558 | + | 1.21117i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.3899 | − | 37.0484i | 0.937108 | − | 1.62312i | 0.166277 | − | 0.986079i | \(-0.446825\pi\) |
0.770831 | − | 0.637040i | \(-0.219841\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.38893 | − | 2.40569i | −0.0607335 | − | 0.105193i | 0.834060 | − | 0.551674i | \(-0.186011\pi\) |
−0.894793 | + | 0.446480i | \(0.852677\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.79486 | − | 1.46284i | 0.209265 | − | 0.0638437i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.573049 | + | 3.24992i | 0.0249624 | + | 0.141569i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.43023 | − | 2.03920i | −0.105662 | − | 0.0886609i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.1650 | + | 24.9400i | −0.788292 | + | 1.08230i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.32799 | − | 1.57526i | 0.187466 | − | 0.0682321i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.395296 | − | 0.331693i | 0.0170901 | − | 0.0143403i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.4678 | + | 16.9099i | −0.969557 | + | 0.729717i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.6116 | −0.887803 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.59390 | −0.154514 | −0.0772570 | − | 0.997011i | \(-0.524616\pi\) | ||||
−0.0772570 | + | 0.997011i | \(0.524616\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.76846 | + | 2.02741i | 0.204634 | + | 0.0870047i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.444334 | + | 0.372841i | −0.0190332 | + | 0.0159707i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.1985 | + | 13.5392i | −1.59049 | + | 0.578892i | −0.977452 | − | 0.211158i | \(-0.932276\pi\) |
−0.613042 | + | 0.790051i | \(0.710054\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −32.8468 | + | 22.0991i | −1.40187 | + | 0.943167i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.8514 | + | 15.8182i | 0.803099 | + | 0.673880i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.725786 | + | 4.11614i | 0.0308636 | + | 0.175036i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.146536 | − | 0.633013i | 0.00622011 | − | 0.0268699i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.71731 | + | 9.90267i | 0.242250 | + | 0.419590i | 0.961355 | − | 0.275312i | \(-0.0887812\pi\) |
−0.719105 | + | 0.694902i | \(0.755448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.4983 | + | 25.1119i | −0.613214 | + | 1.06212i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.6515 | − | 0.564526i | −0.449707 | − | 0.0238343i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.6357 | + | 4.96298i | 0.574676 | + | 0.209165i | 0.612976 | − | 0.790101i | \(-0.289972\pi\) |
−0.0383005 | + | 0.999266i | \(0.512194\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.191443 | + | 1.08573i | −0.00805408 | + | 0.0456770i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.50117 | + | 3.87003i | −0.147035 | + | 0.162526i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.225601 | + | 1.27945i | −0.00945767 | + | 0.0536371i | −0.989171 | − | 0.146765i | \(-0.953114\pi\) |
0.979714 | + | 0.200402i | \(0.0642249\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0890 | + | 5.49193i | 0.631453 | + | 0.229830i | 0.637864 | − | 0.770149i | \(-0.279818\pi\) |
−0.00641065 | + | 0.999979i | \(0.502041\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.89825 | + | 0.206606i | 0.162852 | + | 0.00863108i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.1127 | − | 19.2478i | 0.463434 | − | 0.802691i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.23017 | + | 7.32686i | 0.176104 | + | 0.305021i | 0.940543 | − | 0.339675i | \(-0.110317\pi\) |
−0.764439 | + | 0.644696i | \(0.776984\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.343854 | + | 1.48540i | −0.0142901 | + | 0.0617310i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.50035 | + | 8.50893i | 0.0622452 | + | 0.353010i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.7958 | + | 10.7369i | 0.529947 | + | 0.444678i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.05398 | − | 0.515601i | −0.0435767 | − | 0.0213175i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.2764 | + | 6.28811i | −0.713075 | + | 0.259538i | −0.672983 | − | 0.739658i | \(-0.734987\pi\) |
−0.0400919 | + | 0.999196i | \(0.512765\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.88260 | + | 4.09699i | −0.201184 | + | 0.168814i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.3200 | − | 13.7416i | −1.32947 | − | 0.565252i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.5128 | 0.554905 | 0.277452 | − | 0.960739i | \(-0.410510\pi\) | ||||
0.277452 | + | 0.960739i | \(0.410510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.107464 | −0.00440561 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.3070 | − | 19.7994i | 1.07667 | − | 0.810337i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.44772 | + | 7.08848i | −0.345165 | + | 0.289627i | −0.798845 | − | 0.601537i | \(-0.794555\pi\) |
0.453680 | + | 0.891164i | \(0.350111\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.2421 | + | 8.82341i | −0.988856 | + | 0.359914i | −0.785277 | − | 0.619144i | \(-0.787480\pi\) |
−0.203579 | + | 0.979058i | \(0.565257\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.7548 | − | 24.2325i | −0.437968 | − | 0.986824i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.102170 | − | 0.0857306i | −0.00415379 | − | 0.00348545i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.56823 | + | 14.5652i | 0.104241 | + | 0.591182i | 0.991521 | + | 0.129950i | \(0.0414816\pi\) |
−0.887279 | + | 0.461233i | \(0.847407\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.14761 | + | 1.87555i | −0.249114 | + | 0.0760009i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.54882 | + | 13.0749i | 0.305393 | + | 0.528956i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.1370 | + | 31.4141i | −0.732545 | + | 1.26880i | 0.223248 | + | 0.974762i | \(0.428334\pi\) |
−0.955792 | + | 0.294043i | \(0.904999\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.0963404 | − | 0.148160i | 0.00388482 | − | 0.00597438i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.9387 | + | 13.8086i | 1.52736 | + | 0.555912i | 0.962972 | − | 0.269601i | \(-0.0868918\pi\) |
0.564383 | + | 0.825513i | \(0.309114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.19701 | − | 6.78858i | 0.0481119 | − | 0.272856i | −0.951256 | − | 0.308402i | \(-0.900206\pi\) |
0.999368 | + | 0.0355458i | \(0.0113170\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.362848 | + | 23.1347i | 0.0145606 | + | 0.928362i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.156387 | + | 0.886916i | −0.00626552 | + | 0.0355335i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.3703 | − | 8.50608i | −0.934810 | − | 0.340243i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.34200 | − | 18.3615i | −0.373083 | − | 0.733287i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.01193 | − | 6.94887i | 0.159966 | − | 0.277070i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.9095 | + | 25.8241i | 0.593539 | + | 1.02804i | 0.993751 | + | 0.111617i | \(0.0356031\pi\) |
−0.400212 | + | 0.916423i | \(0.631064\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.4897 | − | 19.1296i | −0.814394 | − | 0.760334i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.186358 | − | 1.05689i | −0.00739540 | − | 0.0419414i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.4487 | − | 17.9976i | −0.849830 | − | 0.713092i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.38312 | − | 2.47363i | −0.0942749 | − | 0.0978554i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.2947 | + | 14.6661i | −1.59155 | + | 0.579275i | −0.977673 | − | 0.210131i | \(-0.932611\pi\) |
−0.613872 | + | 0.789406i | \(0.710389\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.9998 | − | 17.6209i | 0.828150 | − | 0.694901i | −0.126715 | − | 0.991939i | \(-0.540443\pi\) |
0.954866 | + | 0.297038i | \(0.0959989\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.134944 | + | 1.10442i | 0.00531343 | + | 0.0434865i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.1623 | 0.635407 | 0.317703 | − | 0.948190i | \(-0.397088\pi\) | ||||
0.317703 | + | 0.948190i | \(0.397088\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.8113 | 1.24870 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.201902 | − | 1.65242i | −0.00791316 | − | 0.0647634i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.7021 | − | 20.7275i | 0.966668 | − | 0.811130i | −0.0153573 | − | 0.999882i | \(-0.504889\pi\) |
0.982025 | + | 0.188752i | \(0.0604441\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.788258 | + | 0.286903i | −0.0307998 | + | 0.0112102i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.162303 | − | 0.563508i | 0.00633206 | − | 0.0219846i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.3103 | − | 17.8814i | −0.830130 | − | 0.696562i | 0.125191 | − | 0.992133i | \(-0.460046\pi\) |
−0.955321 | + | 0.295571i | \(0.904490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.34639 | + | 30.3209i | 0.207950 | + | 1.17934i | 0.892729 | + | 0.450594i | \(0.148788\pi\) |
−0.684779 | + | 0.728751i | \(0.740101\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.5912 | − | 9.88816i | −0.411329 | − | 0.384024i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.103779 | − | 0.179751i | −0.00402439 | − | 0.00697044i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.2479 | + | 24.6781i | −0.551682 | + | 0.955540i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.8531 | + | 33.1243i | 0.651577 | + | 1.28066i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.3557 | + | 13.9603i | 1.48071 | + | 0.538933i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.53753 | + | 25.7336i | −0.174909 | + | 0.991959i | 0.763340 | + | 0.645997i | \(0.223558\pi\) |
−0.938249 | + | 0.345961i | \(0.887553\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.4679 | − | 4.90369i | 0.980262 | − | 0.188743i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.15944 | − | 17.9181i | 0.121427 | − | 0.688648i | −0.861939 | − | 0.507012i | \(-0.830750\pi\) |
0.983366 | − | 0.181635i | \(-0.0581391\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.88549 | − | 1.05023i | −0.110735 | − | 0.0403042i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.0477 | + | 27.7551i | −0.691588 | + | 1.06358i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.7486 | − | 20.3491i | 0.449546 | − | 0.778636i | −0.548811 | − | 0.835947i | \(-0.684919\pi\) |
0.998356 | + | 0.0573104i | \(0.0182525\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.536171 | − | 0.928676i | −0.0204860 | − | 0.0354829i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −37.2256 | + | 11.3570i | −1.42024 | + | 0.433296i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.94021 | + | 22.3460i | 0.150110 | + | 0.851317i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.1180 | + | 28.6284i | 1.29791 | + | 1.08908i | 0.990502 | + | 0.137499i | \(0.0439065\pi\) |
0.307409 | + | 0.951577i | \(0.400538\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.35054 | + | 0.568750i | 0.203250 | + | 0.0216050i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.149034 | − | 0.0542440i | 0.00565318 | − | 0.00205759i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.67184 | − | 1.40284i | 0.0633254 | − | 0.0531363i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.4692 | + | 18.4163i | −0.925512 | + | 0.696567i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.2567 | −0.953934 | −0.476967 | − | 0.878921i | \(-0.658264\pi\) | ||||
−0.476967 | + | 0.878921i | \(0.658264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.4974 | 0.584496 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.533127 | + | 0.226670i | 0.0200787 | + | 0.00853690i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.22888 | + | 2.70935i | −0.121434 | + | 0.101896i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.7382 | − | 5.36425i | 0.553503 | − | 0.201459i | −0.0500991 | − | 0.998744i | \(-0.515954\pi\) |
0.603602 | + | 0.797286i | \(0.293731\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.48295 | + | 21.5731i | 0.0556150 | + | 0.809053i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.65382 | − | 4.74412i | −0.211737 | − | 0.177669i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.210069 | + | 1.19136i | 0.00785615 | + | 0.0445544i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.02352 | − | 26.0207i | 0.224953 | − | 0.971760i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.5804 | − | 46.0385i | −0.991280 | − | 1.71695i | −0.609757 | − | 0.792588i | \(-0.708733\pi\) |
−0.381523 | − | 0.924359i | \(-0.624600\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.85595 | − | 3.21461i | 0.0691194 | − | 0.119718i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.7471 | + | 1.20558i | 0.845972 | + | 0.0448361i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30.0158 | + | 10.9248i | 1.11476 | + | 0.405738i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.0814709 | + | 0.462044i | −0.00302159 | + | 0.0171363i | −0.986281 | − | 0.165073i | \(-0.947214\pi\) |
0.983260 | + | 0.182210i | \(0.0583250\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.1288 | + | 17.9954i | −0.745509 | + | 0.666495i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.38593 | + | 13.5313i | −0.0882469 | + | 0.500473i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.6076 | + | 15.8719i | 1.61068 | + | 0.586241i | 0.981575 | − | 0.191075i | \(-0.0611975\pi\) |
0.629109 | + | 0.777317i | \(0.283420\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.07286 | − | 0.0568611i | −0.0395731 | − | 0.00209735i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.6672 | + | 23.6724i | −0.503439 | + | 0.871983i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.9047 | + | 22.3515i | 0.474706 | + | 0.822214i | 0.999580 | − | 0.0289653i | \(-0.00922124\pi\) |
−0.524875 | + | 0.851179i | \(0.675888\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.31146 | − | 27.2645i | 0.231857 | − | 1.00159i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.02726 | − | 34.1823i | −0.221119 | − | 1.25403i | −0.869967 | − | 0.493110i | \(-0.835860\pi\) |
0.648848 | − | 0.760918i | \(-0.275251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.54397 | − | 1.29555i | −0.0565668 | − | 0.0474652i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.06557 | + | 44.5961i | 0.112163 | + | 1.63169i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.02069 | + | 1.09944i | −0.110374 | + | 0.0401727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.3742 | + | 15.4178i | −0.670485 | + | 0.562604i | −0.913209 | − | 0.407492i | \(-0.866404\pi\) |
0.242724 | + | 0.970095i | \(0.421959\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.7614 | + | 11.8034i | 1.01168 | + | 0.430138i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.441357 | 0.0160626 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.78780 | −0.319398 | −0.159699 | − | 0.987166i | \(-0.551052\pi\) | ||||
−0.159699 | + | 0.987166i | \(0.551052\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.0603 | − | 14.3453i | 0.691843 | − | 0.520701i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5361 | − | 8.84082i | 0.381933 | − | 0.320479i | −0.431528 | − | 0.902100i | \(-0.642025\pi\) |
0.813461 | + | 0.581620i | \(0.197581\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.39542 | − | 1.23583i | 0.122922 | − | 0.0447401i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.552869 | − | 0.0587687i | −0.0199890 | − | 0.00212479i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.1034 | + | 27.7770i | 1.19529 | + | 1.00297i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.44525 | − | 30.8815i | −0.196361 | − | 1.11362i | −0.910468 | − | 0.413580i | \(-0.864278\pi\) |
0.714107 | − | 0.700036i | \(-0.246833\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.5341 | + | 5.65448i | −0.667489 | + | 0.203641i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.0607 | − | 24.3539i | −0.505729 | − | 0.875948i | −0.999978 | − | 0.00662776i | \(-0.997890\pi\) |
0.494249 | − | 0.869320i | \(-0.335443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.13657 | + | 7.16475i | −0.148590 | + | 0.257365i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.20650 | + | 3.39332i | −0.0791576 | + | 0.121735i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.96098 | + | 1.44168i | 0.141917 | + | 0.0516535i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.614960 | + | 3.48761i | −0.0220050 | + | 0.124797i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −32.6531 | + | 6.28714i | −1.16693 | + | 0.224684i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.00338155 | + | 0.0191777i | −0.000120693 | + | 0.000684483i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.0170 | − | 12.3812i | −1.21258 | − | 0.441342i | −0.344979 | − | 0.938610i | \(-0.612114\pi\) |
−0.867597 | + | 0.497269i | \(0.834336\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.2668 | − | 31.9721i | −0.579114 | − | 1.13824i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.43393 | − | 5.94775i | 0.122097 | − | 0.211478i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.7237 | + | 48.0189i | 0.984498 | + | 1.70520i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.636417 | + | 0.594171i | 0.0225714 | + | 0.0210731i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.14000 | − | 29.1504i | −0.182068 | − | 1.03256i | −0.929665 | − | 0.368407i | \(-0.879903\pi\) |
0.747596 | − | 0.664153i | \(-0.231208\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.48028 | + | 4.59850i | 0.193878 | + | 0.162683i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.28958 | + | 4.47736i | −0.0455652 | + | 0.158200i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.568149 | + | 0.206789i | −0.0200495 | + | 0.00729744i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.184113 | − | 0.154489i | 0.00648914 | − | 0.00544504i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.93338 | − | 48.5604i | −0.208865 | − | 1.70941i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.75943 | −0.202491 | −0.101245 | − | 0.994861i | \(-0.532283\pi\) | ||||
−0.101245 | + | 0.994861i | \(0.532283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.4896 | −0.438569 | −0.219284 | − | 0.975661i | \(-0.570372\pi\) | ||||
−0.219284 | + | 0.975661i | \(0.570372\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.62635 | − | 29.6791i | −0.127182 | − | 1.04089i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.401014 | + | 0.336491i | −0.0140469 | + | 0.0117868i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.9373 | + | 9.07644i | −0.872446 | + | 0.317544i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.07123 | + | 5.26384i | 0.177203 | + | 0.183933i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.9911 | + | 27.6828i | 1.15140 | + | 0.966136i | 0.999751 | − | 0.0222995i | \(-0.00709873\pi\) |
0.151644 | + | 0.988435i | \(0.451543\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.78581 | − | 10.1279i | −0.0622496 | − | 0.353035i | −0.999984 | − | 0.00568141i | \(-0.998192\pi\) |
0.937734 | − | 0.347353i | \(-0.112920\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −19.5460 | − | 18.2485i | −0.680504 | − | 0.635331i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.04731 | + | 5.27810i | 0.105965 | + | 0.183538i | 0.914132 | − | 0.405416i | \(-0.132873\pi\) |
−0.808167 | + | 0.588954i | \(0.799540\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.8489 | − | 29.1832i | 0.585188 | − | 1.01358i | −0.409664 | − | 0.912236i | \(-0.634354\pi\) |
0.994852 | − | 0.101339i | \(-0.0323126\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.05984 | − | 7.97952i | −0.140834 | − | 0.276806i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.4673 | − | 4.53774i | −0.431967 | − | 0.157223i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.269620 | + | 1.52909i | −0.00933057 | + | 0.0529163i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.135065 | − | 8.61156i | −0.00466853 | − | 0.297659i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.33250 | − | 41.5847i | 0.253146 | − | 1.43566i | −0.547641 | − | 0.836714i | \(-0.684474\pi\) |
0.800787 | − | 0.598950i | \(-0.204415\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.2328 | − | 4.08841i | −0.387339 | − | 0.140980i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.11250 | − | 4.78664i | 0.107200 | − | 0.164861i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.216631 | + | 0.375216i | −0.00745234 | + | 0.0129078i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.415423 | + | 0.719533i | 0.0142741 | + | 0.0247235i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.1266 | + | 4.61489i | −0.519142 | + | 0.158383i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.11616 | + | 17.6726i | 0.106821 | + | 0.605810i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.3705 | − | 22.9665i | −0.937147 | − | 0.786359i | 0.0399399 | − | 0.999202i | \(-0.487283\pi\) |
−0.977086 | + | 0.212843i | \(0.931728\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.435610 | − | 0.981512i | −0.0148975 | − | 0.0335670i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.43170 | + | 2.70492i | −0.253862 | + | 0.0923983i | −0.465817 | − | 0.884881i | \(-0.654239\pi\) |
0.211954 | + | 0.977280i | \(0.432017\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.2569 | − | 28.7449i | 1.16883 | − | 0.980764i | 0.168841 | − | 0.985643i | \(-0.445998\pi\) |
0.999988 | + | 0.00487963i | \(0.00155324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.879627 | + | 0.662033i | −0.0299776 | + | 0.0225620i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.9170 | 0.780103 | 0.390052 | − | 0.920793i | \(-0.372457\pi\) | ||||
0.390052 | + | 0.920793i | \(0.372457\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.76878 | 0.0601405 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.7788 | + | 8.83457i | 0.705686 | + | 0.300038i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.0789 | − | 14.3309i | 0.579362 | − | 0.486143i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.8926 | + | 12.6999i | −1.18229 | + | 0.430319i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.2706 | − | 6.98108i | −0.482985 | − | 0.236274i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.413118 | − | 0.346647i | −0.0139659 | − | 0.0117188i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.84416 | − | 21.8013i | −0.129808 | − | 0.736178i | −0.978335 | − | 0.207026i | \(-0.933621\pi\) |
0.848527 | − | 0.529152i | \(-0.177490\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.10407 | + | 4.76940i | −0.0372393 | + | 0.160868i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.93202 | − | 8.54251i | −0.166164 | − | 0.287804i | 0.770904 | − | 0.636951i | \(-0.219805\pi\) |
−0.937068 | + | 0.349147i | \(0.886471\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.7865 | − | 41.1995i | 0.800481 | − | 1.38647i | −0.118819 | − | 0.992916i | \(-0.537911\pi\) |
0.919300 | − | 0.393558i | \(-0.128756\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.65582 | + | 0.0877578i | 0.0556598 | + | 0.00294995i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.5517 | + | 4.56846i | 0.421446 | + | 0.153394i | 0.544033 | − | 0.839064i | \(-0.316897\pi\) |
−0.122587 | + | 0.992458i | \(0.539119\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.16091 | + | 6.58387i | −0.0389358 | + | 0.220816i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.2157 | + | 5.85205i | 0.911760 | + | 0.196051i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.39936 | + | 13.6074i | −0.0802914 | + | 0.455355i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.42009 | + | 0.516871i | 0.0474684 | + | 0.0172771i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.3605 | + | 1.71509i | 1.08048 | + | 0.0572652i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.30359 | − | 9.18609i | 0.176885 | − | 0.306373i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.37600 | + | 9.31150i | 0.179100 | + | 0.310211i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.56315 | − | 6.75257i | 0.0520184 | − | 0.224712i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.0483552 | − | 0.274236i | −0.00160738 | − | 0.00911591i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.3135 | − | 23.7578i | −0.940134 | − | 0.788866i | 0.0374746 | − | 0.999298i | \(-0.488069\pi\) |
−0.977609 | + | 0.210431i | \(0.932513\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.0932 | + | 12.1729i | −0.600112 | + | 0.403751i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.4916 | + | 16.5576i | −1.50720 | + | 0.548577i | −0.957914 | − | 0.287056i | \(-0.907323\pi\) |
−0.549288 | + | 0.835633i | \(0.685101\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.3057 | − | 29.6250i | 1.16845 | − | 0.980445i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.95796 | + | 0.832467i | 0.0647280 | + | 0.0275205i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.22558 | 0.172564 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.93459 | −0.294725 | −0.147363 | − | 0.989083i | \(-0.547078\pi\) | ||||
−0.147363 | + | 0.989083i | \(0.547078\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.71086 | + | 6.55604i | −0.287032 | + | 0.216029i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.68526 | + | 3.09230i | −0.121302 | + | 0.101784i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.9024 | − | 6.87992i | 0.621508 | − | 0.226211i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.3062 | − | 15.5231i | 0.371345 | − | 0.509846i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.78330 | − | 4.01366i | −0.156935 | − | 0.131684i | 0.560939 | − | 0.827857i | \(-0.310440\pi\) |
−0.717874 | + | 0.696173i | \(0.754885\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.44973 | − | 25.2357i | −0.145834 | − | 0.827066i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.2144 | + | 3.72644i | −0.399882 | + | 0.121998i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.286617 | + | 0.496435i | 0.00937338 | + | 0.0162352i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.9212 | + | 39.7006i | −0.748802 | + | 1.29696i | 0.199595 | + | 0.979878i | \(0.436037\pi\) |
−0.948397 | + | 0.317085i | \(0.897296\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.03244 | − | 6.20140i | 0.131594 | − | 0.202375i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.09014 | + | 1.48869i | 0.133335 | + | 0.0485298i | 0.407826 | − | 0.913060i | \(-0.366287\pi\) |
−0.274491 | + | 0.961590i | \(0.588509\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.847573 | + | 4.80683i | −0.0276008 | + | 0.156532i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.276934 | + | 0.0443647i | 0.00900865 | + | 0.00144318i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.350202 | + | 1.98610i | −0.0113800 | + | 0.0645395i | −0.989969 | − | 0.141285i | \(-0.954877\pi\) |
0.978589 | + | 0.205825i | \(0.0659877\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.771790 | − | 0.280909i | −0.0250534 | − | 0.00911868i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.6827 | − | 24.9275i | −0.411264 | − | 0.808331i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.8644 | − | 30.9420i | 0.578684 | − | 1.00231i | −0.416947 | − | 0.908931i | \(-0.636900\pi\) |
0.995631 | − | 0.0933786i | \(-0.0297667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.104896 | − | 0.181686i | −0.00339437 | − | 0.00587922i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.0604 | + | 23.3968i | 0.810086 | + | 0.756312i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.15999 | + | 6.57865i | 0.0374581 | + | 0.212436i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6428 | − | 18.1605i | −0.698155 | − | 0.585822i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.1417 | + | 4.00434i | −0.520159 | + | 0.129038i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0769973 | − | 0.0280247i | 0.00247863 | − | 0.000902148i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.531112 | − | 0.445656i | 0.0170794 | − | 0.0143313i | −0.634208 | − | 0.773163i | \(-0.718674\pi\) |
0.651287 | + | 0.758831i | \(0.274229\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.60833 | − | 13.1630i | −0.0516670 | − | 0.422857i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.4942 | −1.52416 | −0.762081 | − | 0.647482i | \(-0.775822\pi\) | ||||
−0.762081 | + | 0.647482i | \(0.775822\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.987988 | −0.0316734 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.40563 | − | 36.0569i | −0.141093 | − | 1.15474i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.65470 | + | 8.10126i | −0.308881 | + | 0.259182i | −0.784029 | − | 0.620724i | \(-0.786839\pi\) |
0.475148 | + | 0.879906i | \(0.342394\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.51423 | − | 1.64305i | 0.144276 | − | 0.0525120i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.1441 | − | 4.50110i | 0.579298 | − | 0.143709i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.84400 | − | 7.42100i | −0.282080 | − | 0.236693i | 0.490759 | − | 0.871295i | \(-0.336720\pi\) |
−0.772839 | + | 0.634602i | \(0.781164\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.327745 | + | 1.85874i | 0.0104428 | + | 0.0592243i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.63787 | − | 2.46277i | −0.0839644 | − | 0.0783908i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.3647 | − | 26.6125i | −0.488569 | − | 0.846227i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.34676 | − | 16.1891i | 0.296910 | − | 0.514263i | −0.678518 | − | 0.734584i | \(-0.737377\pi\) |
0.975427 | + | 0.220322i | \(0.0707107\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.1023 | + | 29.6832i | 0.479257 | + | 0.941969i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.66275 | − | 0.605192i | −0.0527128 | − | 0.0191859i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.583250 | − | 3.30778i | 0.0184717 | − | 0.104758i | −0.974178 | − | 0.225782i | \(-0.927506\pi\) |
0.992650 | + | 0.121023i | \(0.0386175\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.2074 | + | 16.2508i | −0.417863 | + | 0.514154i |
(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 | 432.2.u.c.241.1 | 12 | ||
4.3 | odd | 2 | 27.2.e.a.25.1 | yes | 12 | ||
12.11 | even | 2 | 81.2.e.a.73.2 | 12 | |||
20.3 | even | 4 | 675.2.u.b.349.4 | 24 | |||
20.7 | even | 4 | 675.2.u.b.349.1 | 24 | |||
20.19 | odd | 2 | 675.2.l.c.376.2 | 12 | |||
27.13 | even | 9 | inner | 432.2.u.c.337.1 | 12 | ||
36.7 | odd | 6 | 243.2.e.d.55.2 | 12 | |||
36.11 | even | 6 | 243.2.e.a.55.1 | 12 | |||
36.23 | even | 6 | 243.2.e.b.136.2 | 12 | |||
36.31 | odd | 6 | 243.2.e.c.136.1 | 12 | |||
108.7 | odd | 18 | 729.2.c.e.244.6 | 12 | |||
108.11 | even | 18 | 729.2.a.d.1.6 | 6 | |||
108.23 | even | 18 | 243.2.e.b.109.2 | 12 | |||
108.31 | odd | 18 | 243.2.e.c.109.1 | 12 | |||
108.43 | odd | 18 | 729.2.a.a.1.1 | 6 | |||
108.47 | even | 18 | 729.2.c.b.244.1 | 12 | |||
108.59 | even | 18 | 243.2.e.a.190.1 | 12 | |||
108.67 | odd | 18 | 27.2.e.a.13.1 | ✓ | 12 | ||
108.79 | odd | 18 | 729.2.c.e.487.6 | 12 | |||
108.83 | even | 18 | 729.2.c.b.487.1 | 12 | |||
108.95 | even | 18 | 81.2.e.a.10.2 | 12 | |||
108.103 | odd | 18 | 243.2.e.d.190.2 | 12 | |||
540.67 | even | 36 | 675.2.u.b.499.4 | 24 | |||
540.283 | even | 36 | 675.2.u.b.499.1 | 24 | |||
540.499 | odd | 18 | 675.2.l.c.526.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.13.1 | ✓ | 12 | 108.67 | odd | 18 | ||
27.2.e.a.25.1 | yes | 12 | 4.3 | odd | 2 | ||
81.2.e.a.10.2 | 12 | 108.95 | even | 18 | |||
81.2.e.a.73.2 | 12 | 12.11 | even | 2 | |||
243.2.e.a.55.1 | 12 | 36.11 | even | 6 | |||
243.2.e.a.190.1 | 12 | 108.59 | even | 18 | |||
243.2.e.b.109.2 | 12 | 108.23 | even | 18 | |||
243.2.e.b.136.2 | 12 | 36.23 | even | 6 | |||
243.2.e.c.109.1 | 12 | 108.31 | odd | 18 | |||
243.2.e.c.136.1 | 12 | 36.31 | odd | 6 | |||
243.2.e.d.55.2 | 12 | 36.7 | odd | 6 | |||
243.2.e.d.190.2 | 12 | 108.103 | odd | 18 | |||
432.2.u.c.241.1 | 12 | 1.1 | even | 1 | trivial | ||
432.2.u.c.337.1 | 12 | 27.13 | even | 9 | inner | ||
675.2.l.c.376.2 | 12 | 20.19 | odd | 2 | |||
675.2.l.c.526.2 | 12 | 540.499 | odd | 18 | |||
675.2.u.b.349.1 | 24 | 20.7 | even | 4 | |||
675.2.u.b.349.4 | 24 | 20.3 | even | 4 | |||
675.2.u.b.499.1 | 24 | 540.283 | even | 36 | |||
675.2.u.b.499.4 | 24 | 540.67 | even | 36 | |||
729.2.a.a.1.1 | 6 | 108.43 | odd | 18 | |||
729.2.a.d.1.6 | 6 | 108.11 | even | 18 | |||
729.2.c.b.244.1 | 12 | 108.47 | even | 18 | |||
729.2.c.b.487.1 | 12 | 108.83 | even | 18 | |||
729.2.c.e.244.6 | 12 | 108.7 | odd | 18 | |||
729.2.c.e.487.6 | 12 | 108.79 | odd | 18 |