Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(199,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.da (of order \(18\), degree \(6\), 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: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 244.7 | ||
Character | \(\chi\) | \(=\) | 855.244 |
Dual form | 855.2.da.b.424.7 |
$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.14717 | − | 1.36714i | 0.811171 | − | 0.966716i | −0.188712 | − | 0.982033i | \(-0.560431\pi\) |
0.999883 | + | 0.0153165i | \(0.00487559\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.205786 | − | 1.16707i | −0.102893 | − | 0.583536i | ||||
\(5\) | 2.08176 | − | 0.816246i | 0.930993 | − | 0.365036i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.67118 | − | 2.11955i | 1.38757 | − | 0.801116i | 0.394532 | − | 0.918882i | \(-0.370907\pi\) |
0.993041 | + | 0.117766i | \(0.0375732\pi\) | |||||||
\(8\) | 1.25953 | + | 0.727188i | 0.445310 | + | 0.257100i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.27221 | − | 3.78244i | 0.402308 | − | 1.19611i | ||||
\(11\) | −0.245445 | + | 0.425123i | −0.0740043 | + | 0.128179i | −0.900653 | − | 0.434539i | \(-0.856911\pi\) |
0.826649 | + | 0.562719i | \(0.190245\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.42349 | + | 3.91099i | −0.394804 | + | 1.08471i | 0.569977 | + | 0.821661i | \(0.306952\pi\) |
−0.964781 | + | 0.263054i | \(0.915270\pi\) | |||||||
\(14\) | 1.31373 | − | 7.45051i | 0.351108 | − | 1.99123i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.66628 | − | 1.69839i | 1.16657 | − | 0.424596i | ||||
\(17\) | −1.30884 | + | 1.55982i | −0.317440 | + | 0.378311i | −0.901044 | − | 0.433728i | \(-0.857198\pi\) |
0.583603 | + | 0.812039i | \(0.301642\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.86816 | + | 3.93827i | −0.428586 | + | 0.903501i | ||||
\(20\) | −1.38102 | − | 2.26160i | −0.308805 | − | 0.505709i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.299637 | + | 0.823245i | 0.0638828 | + | 0.175517i | ||||
\(23\) | −4.32847 | + | 0.763227i | −0.902549 | + | 0.159144i | −0.605618 | − | 0.795755i | \(-0.707074\pi\) |
−0.296931 | + | 0.954899i | \(0.595963\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.66748 | − | 3.39846i | 0.733497 | − | 0.679693i | ||||
\(26\) | 3.71391 | + | 6.43268i | 0.728358 | + | 1.26155i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.22915 | − | 3.84835i | −0.610252 | − | 0.727270i | ||||
\(29\) | −2.49937 | + | 2.09722i | −0.464122 | + | 0.389445i | −0.844645 | − | 0.535327i | \(-0.820188\pi\) |
0.380523 | + | 0.924772i | \(0.375744\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.04416 | − | 3.54059i | −0.367143 | − | 0.635909i | 0.621975 | − | 0.783037i | \(-0.286331\pi\) |
−0.989118 | + | 0.147128i | \(0.952997\pi\) | |||||||
\(32\) | 2.03622 | − | 5.59447i | 0.359956 | − | 0.988972i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.631029 | + | 3.57874i | 0.108221 | + | 0.613750i | ||||
\(35\) | 5.91244 | − | 7.40900i | 0.999385 | − | 1.25235i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.14440i | − | 0.352538i | −0.984342 | − | 0.176269i | \(-0.943597\pi\) | ||
0.984342 | − | 0.176269i | \(-0.0564028\pi\) | |||||||
\(38\) | 3.24108 | + | 7.07191i | 0.525772 | + | 1.14721i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.21560 | + | 0.485750i | 0.508431 | + | 0.0768038i | ||||
\(41\) | 4.10271 | − | 1.49327i | 0.640736 | − | 0.233209i | −0.00116142 | − | 0.999999i | \(-0.500370\pi\) |
0.641897 | + | 0.766790i | \(0.278147\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.4627 | − | 1.84485i | −1.59554 | − | 0.281337i | −0.695956 | − | 0.718085i | \(-0.745019\pi\) |
−0.899584 | + | 0.436748i | \(0.856130\pi\) | |||||||
\(44\) | 0.546658 | + | 0.198967i | 0.0824118 | + | 0.0299955i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.92205 | + | 6.79319i | −0.578275 | + | 1.00160i | ||||
\(47\) | −1.68502 | − | 2.00812i | −0.245785 | − | 0.292915i | 0.629021 | − | 0.777388i | \(-0.283456\pi\) |
−0.874806 | + | 0.484473i | \(0.839011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.48502 | − | 9.50033i | 0.783574 | − | 1.35719i | ||||
\(50\) | −0.438963 | − | 8.91259i | −0.0620788 | − | 1.26043i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.85735 | + | 0.856482i | 0.673593 | + | 0.118773i | ||||
\(53\) | −11.2604 | + | 1.98551i | −1.54673 | + | 0.272730i | −0.880874 | − | 0.473350i | \(-0.843045\pi\) |
−0.665856 | + | 0.746080i | \(0.731934\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.163953 | + | 1.08535i | −0.0221074 | + | 0.146348i | ||||
\(56\) | 6.16526 | 0.823867 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.82287i | 0.764581i | ||||||||
\(59\) | −0.415431 | − | 0.348588i | −0.0540845 | − | 0.0453823i | 0.615345 | − | 0.788258i | \(-0.289017\pi\) |
−0.669429 | + | 0.742876i | \(0.733461\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.36895 | − | 13.4350i | −0.303313 | − | 1.72018i | −0.631339 | − | 0.775507i | \(-0.717494\pi\) |
0.328026 | − | 0.944669i | \(-0.393617\pi\) | |||||||
\(62\) | −7.18550 | − | 1.26700i | −0.912559 | − | 0.160909i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.346803 | − | 0.600680i | −0.0433503 | − | 0.0750850i | ||||
\(65\) | 0.228974 | + | 9.30368i | 0.0284007 | + | 1.15398i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.60042 | − | 5.48257i | −0.562031 | − | 0.669802i | 0.407944 | − | 0.913007i | \(-0.366246\pi\) |
−0.969975 | + | 0.243205i | \(0.921801\pi\) | |||||||
\(68\) | 2.08976 | + | 1.20652i | 0.253421 | + | 0.146312i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.34658 | − | 16.5825i | −0.399993 | − | 1.98199i | ||||
\(71\) | −1.04859 | + | 5.94684i | −0.124444 | + | 0.705760i | 0.857192 | + | 0.514997i | \(0.172207\pi\) |
−0.981636 | + | 0.190762i | \(0.938904\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.702575 | + | 1.93031i | 0.0822302 | + | 0.225925i | 0.973993 | − | 0.226577i | \(-0.0727535\pi\) |
−0.891763 | + | 0.452503i | \(0.850531\pi\) | |||||||
\(74\) | −2.93170 | − | 2.45999i | −0.340804 | − | 0.285968i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.98069 | + | 1.36984i | 0.571324 | + | 0.157131i | ||||
\(77\) | 2.08093i | 0.237144i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.01823 | − | 1.82649i | 0.564595 | − | 0.205496i | −0.0439240 | − | 0.999035i | \(-0.513986\pi\) |
0.608519 | + | 0.793539i | \(0.291764\pi\) | |||||||
\(80\) | 8.32778 | − | 7.34447i | 0.931075 | − | 0.821137i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.66500 | − | 7.32202i | 0.294300 | − | 0.808582i | ||||
\(83\) | 7.02847 | − | 4.05789i | 0.771475 | − | 0.445411i | −0.0619255 | − | 0.998081i | \(-0.519724\pi\) |
0.833401 | + | 0.552669i | \(0.186391\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.45150 | + | 4.31550i | −0.157438 | + | 0.468082i | ||||
\(86\) | −14.5246 | + | 12.1876i | −1.56623 | + | 1.31422i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.618288 | + | 0.356969i | −0.0659097 | + | 0.0380530i | ||||
\(89\) | 4.07920 | + | 1.48471i | 0.432394 | + | 0.157379i | 0.549042 | − | 0.835795i | \(-0.314993\pi\) |
−0.116648 | + | 0.993173i | \(0.537215\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.06370 | + | 17.3751i | 0.321163 | + | 1.82141i | ||||
\(92\) | 1.78148 | + | 4.89458i | 0.185732 | + | 0.510296i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.67839 | −0.482539 | ||||||||
\(95\) | −0.674475 | + | 9.72343i | −0.0691997 | + | 0.997603i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.62962 | + | 4.32562i | −0.368533 | + | 0.439200i | −0.918160 | − | 0.396210i | \(-0.870325\pi\) |
0.549627 | + | 0.835410i | \(0.314770\pi\) | |||||||
\(98\) | −6.69607 | − | 18.3973i | −0.676405 | − | 1.85841i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.72097 | − | 3.58086i | −0.472097 | − | 0.358086i | ||||
\(101\) | −3.10176 | − | 1.12895i | −0.308637 | − | 0.112335i | 0.183058 | − | 0.983102i | \(-0.441400\pi\) |
−0.491695 | + | 0.870767i | \(0.663622\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.95805 | − | 1.70783i | −0.291466 | − | 0.168278i | 0.347137 | − | 0.937814i | \(-0.387154\pi\) |
−0.638603 | + | 0.769537i | \(0.720487\pi\) | |||||||
\(104\) | −4.63695 | + | 3.89086i | −0.454690 | + | 0.381530i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.2031 | + | 17.6722i | −0.991010 | + | 1.71648i | ||||
\(107\) | 1.51772 | − | 0.876258i | 0.146724 | − | 0.0847110i | −0.424841 | − | 0.905268i | \(-0.639670\pi\) |
0.571565 | + | 0.820557i | \(0.306337\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.611108 | − | 3.46576i | 0.0585335 | − | 0.331960i | −0.941453 | − | 0.337144i | \(-0.890539\pi\) |
0.999987 | + | 0.00518405i | \(0.00165014\pi\) | |||||||
\(110\) | 1.29574 | + | 1.46923i | 0.123544 | + | 0.140085i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 13.5309 | − | 16.1255i | 1.27855 | − | 1.52372i | ||||
\(113\) | 13.2583i | 1.24723i | 0.781731 | + | 0.623616i | \(0.214337\pi\) | ||||
−0.781731 | + | 0.623616i | \(0.785663\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.38788 | + | 5.12196i | −0.782174 | + | 0.477625i | ||||
\(116\) | 2.96195 | + | 2.48537i | 0.275010 | + | 0.230761i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.953138 | + | 0.168064i | −0.0877435 | + | 0.0154715i | ||||
\(119\) | −1.49887 | + | 8.50051i | −0.137401 | + | 0.779241i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.37951 | + | 9.31759i | 0.489047 | + | 0.847054i | ||||
\(122\) | −21.0852 | − | 12.1735i | −1.90896 | − | 1.10214i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.71147 | + | 3.11429i | −0.333300 | + | 0.279672i | ||||
\(125\) | 4.86085 | − | 10.0684i | 0.434768 | − | 0.900543i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.77480 | + | 18.6136i | −0.601166 | + | 1.65169i | 0.147749 | + | 0.989025i | \(0.452797\pi\) |
−0.748915 | + | 0.662666i | \(0.769425\pi\) | |||||||
\(128\) | 10.5071 | + | 1.85268i | 0.928702 | + | 0.163755i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.9821 | + | 10.3599i | 1.13861 | + | 0.908620i | ||||
\(131\) | 2.62756 | + | 2.20479i | 0.229571 | + | 0.192633i | 0.750316 | − | 0.661079i | \(-0.229901\pi\) |
−0.520745 | + | 0.853712i | \(0.674346\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.48902 | + | 18.4178i | 0.129115 | + | 1.59702i | ||||
\(134\) | −12.7729 | −1.10341 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.78280 | + | 1.01286i | −0.238623 | + | 0.0868517i | ||||
\(137\) | 0.599055 | − | 0.105629i | 0.0511807 | − | 0.00902454i | −0.147999 | − | 0.988987i | \(-0.547283\pi\) |
0.199180 | + | 0.979963i | \(0.436172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.94791 | − | 2.89280i | −0.674133 | − | 0.245364i | −0.0178066 | − | 0.999841i | \(-0.505668\pi\) |
−0.656326 | + | 0.754477i | \(0.727891\pi\) | |||||||
\(140\) | −9.86354 | − | 5.37558i | −0.833621 | − | 0.454319i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.92727 | + | 8.25560i | 0.581324 | + | 0.692794i | ||||
\(143\) | −1.31327 | − | 1.56509i | −0.109821 | − | 0.130879i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.49126 | + | 6.40603i | −0.289933 | + | 0.531992i | ||||
\(146\) | 3.44498 | + | 1.25387i | 0.285109 | + | 0.103771i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.50267 | + | 0.441289i | −0.205719 | + | 0.0362737i | ||||
\(149\) | 4.35768 | − | 1.58607i | 0.356995 | − | 0.129936i | −0.157295 | − | 0.987552i | \(-0.550277\pi\) |
0.514291 | + | 0.857616i | \(0.328055\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.2109 | 1.15646 | 0.578232 | − | 0.815872i | \(-0.303743\pi\) | ||||
0.578232 | + | 0.815872i | \(0.303743\pi\) | |||||||
\(152\) | −5.21686 | + | 3.60185i | −0.423143 | + | 0.292149i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.84493 | + | 2.38718i | 0.229251 | + | 0.192365i | ||||
\(155\) | −7.14546 | − | 5.70214i | −0.573937 | − | 0.458007i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5651 | + | 1.86291i | 0.843186 | + | 0.148676i | 0.578525 | − | 0.815665i | \(-0.303629\pi\) |
0.264662 | + | 0.964341i | \(0.414740\pi\) | |||||||
\(158\) | 3.25969 | − | 8.95593i | 0.259327 | − | 0.712496i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.327535 | − | 13.3084i | −0.0258939 | − | 1.05212i | ||||
\(161\) | −14.2729 | + | 11.9764i | −1.12486 | + | 0.943870i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.6675 | − | 8.46831i | −1.14885 | − | 0.663289i | −0.200244 | − | 0.979746i | \(-0.564173\pi\) |
−0.948607 | + | 0.316457i | \(0.897507\pi\) | |||||||
\(164\) | −2.58703 | − | 4.48087i | −0.202013 | − | 0.349897i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.51513 | − | 14.2640i | 0.195212 | − | 1.10710i | ||||
\(167\) | 16.0097 | − | 2.82295i | 1.23887 | − | 0.218446i | 0.484439 | − | 0.874825i | \(-0.339024\pi\) |
0.754432 | + | 0.656379i | \(0.227913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.31099 | − | 2.77825i | −0.254692 | − | 0.213712i | ||||
\(170\) | 4.23479 | + | 6.93503i | 0.324794 | + | 0.531892i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.5903i | 0.960003i | ||||||||
\(173\) | −5.52227 | + | 6.58118i | −0.419850 | + | 0.500358i | −0.933966 | − | 0.357363i | \(-0.883676\pi\) |
0.514115 | + | 0.857721i | \(0.328120\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.26075 | − | 20.2498i | 0.473268 | − | 1.53074i | ||||
\(176\) | −0.423290 | + | 2.40060i | −0.0319067 | + | 0.180952i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.70934 | − | 3.87364i | 0.502886 | − | 0.290342i | ||||
\(179\) | 11.7638 | − | 20.3755i | 0.879267 | − | 1.52293i | 0.0271196 | − | 0.999632i | \(-0.491367\pi\) |
0.852147 | − | 0.523302i | \(-0.175300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.7266 | + | 10.6789i | −0.945964 | + | 0.793758i | −0.978613 | − | 0.205709i | \(-0.934050\pi\) |
0.0326493 | + | 0.999467i | \(0.489606\pi\) | |||||||
\(182\) | 27.2688 | + | 15.7437i | 2.02130 | + | 1.16700i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.00684 | − | 2.18631i | −0.442830 | − | 0.161177i | ||||
\(185\) | −1.75036 | − | 4.46414i | −0.128689 | − | 0.328210i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.341865 | − | 0.939266i | −0.0249996 | − | 0.0686859i | ||||
\(188\) | −1.99687 | + | 2.37978i | −0.145637 | + | 0.173563i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.5196 | + | 12.0765i | 0.908266 | + | 0.876123i | ||||
\(191\) | 12.8109 | 0.926965 | 0.463482 | − | 0.886106i | \(-0.346600\pi\) | ||||
0.463482 | + | 0.886106i | \(0.346600\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.29702 | + | 9.05848i | 0.237324 | + | 0.652043i | 0.999986 | + | 0.00524597i | \(0.00166985\pi\) |
−0.762662 | + | 0.646797i | \(0.776108\pi\) | |||||||
\(194\) | 1.74994 | + | 9.92443i | 0.125639 | + | 0.712533i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.2163 | − | 4.44638i | −0.872594 | − | 0.317598i | ||||
\(197\) | −2.68677 | + | 1.55121i | −0.191424 | + | 0.110519i | −0.592649 | − | 0.805461i | \(-0.701918\pi\) |
0.401225 | + | 0.915980i | \(0.368585\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.401629 | + | 0.337007i | −0.0284708 | + | 0.0238898i | −0.656912 | − | 0.753967i | \(-0.728138\pi\) |
0.628441 | + | 0.777857i | \(0.283693\pi\) | |||||||
\(200\) | 7.09061 | − | 1.61351i | 0.501382 | − | 0.114092i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.10168 | + | 2.94545i | −0.358953 | + | 0.207241i | ||||
\(203\) | −4.73046 | + | 12.9968i | −0.332013 | + | 0.912199i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.32201 | − | 6.45745i | 0.511391 | − | 0.451008i | ||||
\(206\) | −5.72824 | + | 2.08491i | −0.399105 | + | 0.145262i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.6674i | 1.43303i | ||||||||
\(209\) | −1.21572 | − | 1.76083i | −0.0840929 | − | 0.121799i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.6037 | − | 12.2539i | −1.00536 | − | 0.843596i | −0.0176404 | − | 0.999844i | \(-0.505615\pi\) |
−0.987718 | + | 0.156249i | \(0.950060\pi\) | |||||||
\(212\) | 4.63446 | + | 12.7331i | 0.318296 | + | 0.874512i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.543115 | − | 3.08016i | 0.0371266 | − | 0.210555i | ||||
\(215\) | −23.2866 | + | 4.69956i | −1.58813 | + | 0.320508i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.0090 | − | 8.66543i | −1.01887 | − | 0.588248i | ||||
\(218\) | −4.03715 | − | 4.81129i | −0.273430 | − | 0.325862i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.30042 | − | 0.0320048i | 0.0876743 | − | 0.00215776i | ||||
\(221\) | −4.23731 | − | 7.33924i | −0.285033 | − | 0.493691i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.11478 | + | 0.549220i | 0.208581 | + | 0.0367785i | 0.276962 | − | 0.960881i | \(-0.410672\pi\) |
−0.0683812 | + | 0.997659i | \(0.521783\pi\) | |||||||
\(224\) | −4.38246 | − | 24.8542i | −0.292815 | − | 1.66064i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.1259 | + | 15.2095i | 1.20572 | + | 1.01172i | ||||
\(227\) | 9.04654i | 0.600440i | 0.953870 | + | 0.300220i | \(0.0970600\pi\) | ||||
−0.953870 | + | 0.300220i | \(0.902940\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.8920 | 1.18234 | 0.591168 | − | 0.806549i | \(-0.298667\pi\) | ||||
0.591168 | + | 0.806549i | \(0.298667\pi\) | |||||||
\(230\) | −2.61987 | + | 17.3432i | −0.172749 | + | 1.14358i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.67310 | + | 0.823994i | −0.306804 | + | 0.0540979i | ||||
\(233\) | 6.34541 | + | 1.11887i | 0.415701 | + | 0.0732994i | 0.377587 | − | 0.925974i | \(-0.376754\pi\) |
0.0381142 | + | 0.999273i | \(0.487865\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.14693 | − | 2.80505i | −0.335749 | − | 0.182981i | ||||
\(236\) | −0.321337 | + | 0.556572i | −0.0209173 | + | 0.0362298i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.90196 | + | 11.8007i | 0.641849 | + | 0.764926i | ||||
\(239\) | 6.73708 | − | 11.6690i | 0.435785 | − | 0.754802i | −0.561574 | − | 0.827426i | \(-0.689804\pi\) |
0.997359 | + | 0.0726241i | \(0.0231374\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5716 | + | 6.03157i | 1.06747 | + | 0.388528i | 0.815231 | − | 0.579137i | \(-0.196610\pi\) |
0.252241 | + | 0.967664i | \(0.418832\pi\) | |||||||
\(242\) | 18.9097 | + | 3.33429i | 1.21556 | + | 0.214336i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −15.1921 | + | 5.52948i | −0.972576 | + | 0.353989i | ||||
\(245\) | 3.66390 | − | 24.2546i | 0.234078 | − | 1.54957i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.7433 | − | 12.9124i | −0.810834 | − | 0.821599i | ||||
\(248\) | − | 5.94596i | − | 0.377569i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.18869 | − | 18.1956i | −0.517898 | − | 1.15079i | ||||
\(251\) | −3.07923 | − | 17.4632i | −0.194360 | − | 1.10227i | −0.913328 | − | 0.407225i | \(-0.866496\pi\) |
0.718968 | − | 0.695043i | \(-0.244615\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.737936 | − | 2.02746i | 0.0463936 | − | 0.127465i | ||||
\(254\) | 17.6756 | + | 30.6151i | 1.10907 | + | 1.92096i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.6489 | − | 13.1310i | 0.978058 | − | 0.820688i | ||||
\(257\) | −17.8358 | − | 21.2558i | −1.11256 | − | 1.32590i | −0.940105 | − | 0.340885i | \(-0.889273\pi\) |
−0.172459 | − | 0.985017i | \(-0.555171\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.54518 | − | 7.87248i | −0.282424 | − | 0.489172i | ||||
\(260\) | 10.8110 | − | 2.18180i | 0.670467 | − | 0.135310i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.02852 | − | 1.06299i | 0.372443 | − | 0.0656718i | ||||
\(263\) | 1.90174 | + | 5.22499i | 0.117266 | + | 0.322187i | 0.984415 | − | 0.175864i | \(-0.0562718\pi\) |
−0.867148 | + | 0.498050i | \(0.834050\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.8208 | + | 13.3246i | −1.34044 | + | 0.818523i | ||||
\(266\) | 26.8879 | + | 19.0926i | 1.64860 | + | 1.17064i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.45185 | + | 6.49727i | −0.333025 | + | 0.396884i | ||||
\(269\) | 4.34856 | − | 1.58275i | 0.265137 | − | 0.0965019i | −0.206031 | − | 0.978545i | \(-0.566055\pi\) |
0.471168 | + | 0.882044i | \(0.343833\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.32118 | + | 7.49279i | −0.0802561 | + | 0.455155i | 0.918024 | + | 0.396525i | \(0.129784\pi\) |
−0.998280 | + | 0.0586294i | \(0.981327\pi\) | |||||||
\(272\) | −3.45824 | + | 9.50144i | −0.209687 | + | 0.576110i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.542806 | − | 0.940168i | 0.0327921 | − | 0.0567976i | ||||
\(275\) | 0.544600 | + | 2.39327i | 0.0328406 | + | 0.144319i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.52588 | + | 3.76772i | 0.392102 | + | 0.226380i | 0.683071 | − | 0.730352i | \(-0.260644\pi\) |
−0.290968 | + | 0.956733i | \(0.593977\pi\) | |||||||
\(278\) | −13.0725 | + | 7.54740i | −0.784035 | + | 0.452663i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.8346 | − | 5.03237i | 0.767015 | − | 0.300742i | ||||
\(281\) | 3.16993 | + | 17.9776i | 0.189102 | + | 1.07245i | 0.920570 | + | 0.390577i | \(0.127724\pi\) |
−0.731468 | + | 0.681876i | \(0.761164\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.8836 | − | 23.6963i | 1.18196 | − | 1.40860i | 0.289671 | − | 0.957126i | \(-0.406454\pi\) |
0.892284 | − | 0.451474i | \(-0.149102\pi\) | |||||||
\(284\) | 7.15618 | 0.424641 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.64624 | −0.215607 | ||||||||
\(287\) | 11.8967 | − | 14.1780i | 0.702241 | − | 0.836898i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.23206 | + | 12.6586i | 0.131298 | + | 0.744625i | ||||
\(290\) | 4.75290 | + | 12.1218i | 0.279100 | + | 0.711819i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.10823 | − | 1.21719i | 0.123375 | − | 0.0712305i | ||||
\(293\) | 18.9653 | + | 10.9496i | 1.10796 | + | 0.639683i | 0.938301 | − | 0.345820i | \(-0.112399\pi\) |
0.169662 | + | 0.985502i | \(0.445732\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.14936 | − | 0.386584i | −0.0669184 | − | 0.0225078i | ||||
\(296\) | 1.55938 | − | 2.70093i | 0.0906373 | − | 0.156988i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.83062 | − | 7.77706i | 0.163973 | − | 0.450513i | ||||
\(299\) | 3.17654 | − | 18.0151i | 0.183704 | − | 1.04184i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.3205 | + | 15.4034i | −2.43931 | + | 0.887837i | ||||
\(302\) | 16.3023 | − | 19.4283i | 0.938090 | − | 1.11797i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.02866 | + | 21.5499i | −0.116352 | + | 1.23597i | ||||
\(305\) | −15.8979 | − | 26.0349i | −0.910309 | − | 1.49075i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.86587 | − | 5.12643i | −0.106491 | − | 0.292581i | 0.874990 | − | 0.484141i | \(-0.160868\pi\) |
−0.981481 | + | 0.191560i | \(0.938645\pi\) | |||||||
\(308\) | 2.42860 | − | 0.428228i | 0.138382 | − | 0.0244005i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.9927 | + | 3.22755i | −0.908324 | + | 0.183312i | ||||
\(311\) | 3.34861 | + | 5.79996i | 0.189882 | + | 0.328885i | 0.945211 | − | 0.326461i | \(-0.105856\pi\) |
−0.755329 | + | 0.655346i | \(0.772523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.94576 | + | 3.51062i | 0.166504 | + | 0.198432i | 0.842844 | − | 0.538157i | \(-0.180879\pi\) |
−0.676340 | + | 0.736590i | \(0.736435\pi\) | |||||||
\(314\) | 14.6668 | − | 12.3069i | 0.827696 | − | 0.694520i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.16433 | − | 5.48078i | −0.178007 | − | 0.308318i | ||||
\(317\) | −9.46690 | + | 26.0101i | −0.531714 | + | 1.46087i | 0.325316 | + | 0.945605i | \(0.394529\pi\) |
−0.857030 | + | 0.515267i | \(0.827693\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.278119 | − | 1.57729i | −0.0155717 | − | 0.0883115i | ||||
\(320\) | −1.21226 | − | 0.967398i | −0.0677676 | − | 0.0540792i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 33.2520i | 1.85306i | ||||||||
\(323\) | −3.69785 | − | 8.06856i | −0.205754 | − | 0.448946i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.07077 | + | 19.1812i | 0.447686 | + | 1.06398i | ||||
\(326\) | −28.4035 | + | 10.3380i | −1.57313 | + | 0.572571i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.25336 | + | 1.10264i | 0.345284 | + | 0.0608829i | ||||
\(329\) | −10.4423 | − | 3.80069i | −0.575703 | − | 0.209539i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.06509 | − | 12.2371i | 0.388332 | − | 0.672611i | −0.603893 | − | 0.797065i | \(-0.706385\pi\) |
0.992225 | + | 0.124454i | \(0.0397179\pi\) | |||||||
\(332\) | −6.18222 | − | 7.36768i | −0.339293 | − | 0.404354i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.5065 | − | 25.1260i | 0.793761 | − | 1.37483i | ||||
\(335\) | −14.0521 | − | 7.65834i | −0.767749 | − | 0.418420i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.7696 | − | 2.60428i | −0.804550 | − | 0.141864i | −0.243775 | − | 0.969832i | \(-0.578386\pi\) |
−0.560775 | + | 0.827968i | \(0.689497\pi\) | |||||||
\(338\) | −7.59654 | + | 1.33947i | −0.413197 | + | 0.0728578i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.33521 | + | 0.805938i | 0.289342 | + | 0.0437081i | ||||
\(341\) | 2.00692 | 0.108681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.8294i | − | 0.908703i | ||||||
\(344\) | −11.8364 | − | 9.93195i | −0.638178 | − | 0.535495i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.66244 | + | 15.0995i | 0.143134 | + | 0.811752i | ||||
\(347\) | −20.5956 | − | 3.63155i | −1.10563 | − | 0.194952i | −0.409106 | − | 0.912487i | \(-0.634159\pi\) |
−0.696522 | + | 0.717535i | \(0.745270\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.56527 | − | 2.71113i | −0.0837872 | − | 0.145124i | 0.821087 | − | 0.570804i | \(-0.193368\pi\) |
−0.904874 | + | 0.425680i | \(0.860035\pi\) | |||||||
\(350\) | −20.5022 | − | 31.7893i | −1.09589 | − | 1.69921i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.87856 | + | 2.23878i | 0.100127 | + | 0.119327i | ||||
\(353\) | 6.96750 | + | 4.02269i | 0.370843 | + | 0.214106i | 0.673827 | − | 0.738890i | \(-0.264650\pi\) |
−0.302984 | + | 0.952996i | \(0.597983\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.67117 | + | 13.2358i | 0.141771 | + | 0.702484i | ||||
\(356\) | 0.893318 | − | 5.06626i | 0.0473457 | − | 0.268511i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.3611 | − | 39.4569i | −0.759010 | − | 2.08536i | ||||
\(359\) | 23.4289 | + | 19.6592i | 1.23653 | + | 1.03757i | 0.997787 | + | 0.0664886i | \(0.0211796\pi\) |
0.238742 | + | 0.971083i | \(0.423265\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.0199 | − | 14.7147i | −0.632628 | − | 0.774456i | ||||
\(362\) | 29.6497i | 1.55835i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 19.6475 | − | 7.15112i | 1.02981 | − | 0.374821i | ||||
\(365\) | 3.03820 | + | 3.44497i | 0.159027 | + | 0.180318i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.40370 | − | 9.35159i | 0.177672 | − | 0.488149i | −0.818606 | − | 0.574356i | \(-0.805252\pi\) |
0.996277 | + | 0.0862072i | \(0.0274747\pi\) | |||||||
\(368\) | −18.9016 | + | 10.9128i | −0.985314 | + | 0.568871i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.11108 | − | 2.72813i | −0.421675 | − | 0.141829i | ||||
\(371\) | −37.1304 | + | 31.1561i | −1.92771 | + | 1.61754i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.03335 | + | 4.63806i | −0.415951 | + | 0.240149i | −0.693343 | − | 0.720607i | \(-0.743863\pi\) |
0.277392 | + | 0.960757i | \(0.410530\pi\) | |||||||
\(374\) | −1.67629 | − | 0.610119i | −0.0866788 | − | 0.0315485i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.662039 | − | 3.75461i | −0.0341420 | − | 0.193629i | ||||
\(377\) | −4.64441 | − | 12.7604i | −0.239199 | − | 0.657195i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.1472 | 1.08626 | 0.543129 | − | 0.839649i | \(-0.317239\pi\) | ||||
0.543129 | + | 0.839649i | \(0.317239\pi\) | |||||||
\(380\) | 11.4867 | − | 1.21379i | 0.589258 | − | 0.0622660i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.6963 | − | 17.5143i | 0.751927 | − | 0.896112i | ||||
\(383\) | −5.18165 | − | 14.2365i | −0.264770 | − | 0.727450i | −0.998830 | − | 0.0483649i | \(-0.984599\pi\) |
0.734060 | − | 0.679085i | \(-0.237623\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.69855 | + | 4.33201i | 0.0865663 | + | 0.220780i | ||||
\(386\) | 16.1665 | + | 5.88411i | 0.822851 | + | 0.299493i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.79524 | + | 3.34588i | 0.294209 | + | 0.169861i | ||||
\(389\) | −24.0908 | + | 20.2146i | −1.22145 | + | 1.02492i | −0.222706 | + | 0.974886i | \(0.571489\pi\) |
−0.998747 | + | 0.0500353i | \(0.984067\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.47479 | − | 7.75056i | 0.226300 | − | 0.391963i | ||||
\(392\) | 13.8171 | − | 7.97728i | 0.697866 | − | 0.402913i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.961457 | + | 5.45269i | −0.0484375 | + | 0.274703i | ||||
\(395\) | 8.95592 | − | 7.89843i | 0.450621 | − | 0.397413i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.03294 | + | 7.18978i | −0.302784 | + | 0.360844i | −0.895887 | − | 0.444283i | \(-0.853459\pi\) |
0.593102 | + | 0.805127i | \(0.297903\pi\) | |||||||
\(398\) | 0.935689i | 0.0469019i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.3416 | − | 22.0870i | 0.567079 | − | 1.10435i | ||||
\(401\) | −4.71921 | − | 3.95989i | −0.235666 | − | 0.197747i | 0.517305 | − | 0.855801i | \(-0.326935\pi\) |
−0.752971 | + | 0.658054i | \(0.771380\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.7571 | − | 2.95473i | 0.834730 | − | 0.147185i | ||||
\(404\) | −0.679265 | + | 3.85230i | −0.0337947 | + | 0.191659i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.3419 | + | 21.3768i | 0.612518 | + | 1.06091i | ||||
\(407\) | 0.911634 | + | 0.526332i | 0.0451880 | + | 0.0260893i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.75027 | + | 1.46865i | −0.0865454 | + | 0.0726202i | −0.685034 | − | 0.728511i | \(-0.740213\pi\) |
0.598489 | + | 0.801131i | \(0.295768\pi\) | |||||||
\(410\) | −0.428677 | − | 17.4180i | −0.0211708 | − | 0.860215i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.38444 | + | 3.80371i | −0.0682064 | + | 0.187395i | ||||
\(413\) | −2.26397 | − | 0.399199i | −0.111403 | − | 0.0196433i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.3194 | − | 14.1845i | 0.555647 | − | 0.696291i | ||||
\(416\) | 18.9814 | + | 15.9273i | 0.930640 | + | 0.780900i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.80193 | − | 0.357906i | −0.185959 | − | 0.0175057i | ||||
\(419\) | −22.6494 | −1.10649 | −0.553247 | − | 0.833017i | \(-0.686611\pi\) | ||||
−0.553247 | + | 0.833017i | \(0.686611\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.6100 | − | 7.86540i | 1.05321 | − | 0.383336i | 0.243335 | − | 0.969942i | \(-0.421759\pi\) |
0.809872 | + | 0.586606i | \(0.199536\pi\) | |||||||
\(422\) | −33.5058 | + | 5.90797i | −1.63103 | + | 0.287595i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.6266 | − | 5.68761i | −0.758893 | − | 0.276215i | ||||
\(425\) | 0.500827 | + | 10.1686i | 0.0242937 | + | 0.493252i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −37.1730 | − | 44.3011i | −1.79893 | − | 2.14388i | ||||
\(428\) | −1.33498 | − | 1.59097i | −0.0645289 | − | 0.0769025i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20.2887 | + | 37.2273i | −0.978409 | + | 1.79526i | ||||
\(431\) | 24.0861 | + | 8.76663i | 1.16019 | + | 0.422274i | 0.849164 | − | 0.528129i | \(-0.177106\pi\) |
0.311023 | + | 0.950402i | \(0.399328\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.32740 | − | 0.410383i | 0.111847 | − | 0.0197217i | −0.117444 | − | 0.993079i | \(-0.537470\pi\) |
0.229292 | + | 0.973358i | \(0.426359\pi\) | |||||||
\(434\) | −29.0647 | + | 10.5787i | −1.39515 | + | 0.507793i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.17056 | −0.199734 | ||||||||
\(437\) | 5.08050 | − | 18.4725i | 0.243033 | − | 0.883661i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.83879 | + | 4.06022i | 0.230943 | + | 0.193784i | 0.750914 | − | 0.660400i | \(-0.229613\pi\) |
−0.519972 | + | 0.854183i | \(0.674058\pi\) | |||||||
\(440\) | −0.995755 | + | 1.24780i | −0.0474708 | + | 0.0594865i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.8947 | − | 2.62634i | −0.708469 | − | 0.124922i | ||||
\(443\) | 10.7821 | − | 29.6234i | 0.512271 | − | 1.40745i | −0.366594 | − | 0.930381i | \(-0.619476\pi\) |
0.878865 | − | 0.477071i | \(-0.158302\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.70382 | − | 0.238822i | 0.460005 | − | 0.0113212i | ||||
\(446\) | 4.32404 | − | 3.62830i | 0.204749 | − | 0.171805i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.54635 | − | 1.47013i | −0.120304 | − | 0.0694573i | ||||
\(449\) | 7.54142 | + | 13.0621i | 0.355902 | + | 0.616440i | 0.987272 | − | 0.159042i | \(-0.0508405\pi\) |
−0.631370 | + | 0.775482i | \(0.717507\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.372168 | + | 2.11067i | −0.0175247 | + | 0.0993876i | ||||
\(452\) | 15.4734 | − | 2.72837i | 0.727805 | − | 0.128332i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.3679 | + | 10.3779i | 0.580455 | + | 0.487059i | ||||
\(455\) | 20.5603 | + | 33.6701i | 0.963880 | + | 1.57848i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.1347i | 0.941861i | 0.882170 | + | 0.470930i | \(0.156082\pi\) | ||||
−0.882170 | + | 0.470930i | \(0.843918\pi\) | |||||||
\(458\) | 20.5251 | − | 24.4609i | 0.959076 | − | 1.14298i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.70381 | + | 8.73524i | 0.359192 | + | 0.407283i | ||||
\(461\) | 1.29974 | − | 7.37118i | 0.0605348 | − | 0.343310i | −0.939465 | − | 0.342645i | \(-0.888677\pi\) |
1.00000 | 0.000665051i | \(-0.000211692\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.7038 | − | 10.7986i | 0.869239 | − | 0.501855i | 0.00214362 | − | 0.999998i | \(-0.499318\pi\) |
0.867095 | + | 0.498142i | \(0.165984\pi\) | |||||||
\(464\) | −8.10087 | + | 14.0311i | −0.376074 | + | 0.651379i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.80891 | − | 7.39155i | 0.408065 | − | 0.342407i | ||||
\(467\) | −23.4263 | − | 13.5252i | −1.08404 | − | 0.625870i | −0.152056 | − | 0.988372i | \(-0.548589\pi\) |
−0.931983 | + | 0.362501i | \(0.881923\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.5096 | − | 10.3766i | −1.31645 | − | 0.479148i | ||||
\(470\) | −9.73930 | + | 3.81872i | −0.449241 | + | 0.176144i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.269757 | − | 0.741151i | −0.0124166 | − | 0.0341143i | ||||
\(473\) | 3.35229 | − | 3.99510i | 0.154138 | − | 0.183695i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.53262 | + | 20.7924i | 0.299737 | + | 0.954022i | ||||
\(476\) | 10.2292 | 0.468853 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.22457 | − | 22.5968i | −0.376183 | − | 1.03355i | ||||
\(479\) | −6.60791 | − | 37.4753i | −0.301923 | − | 1.71229i | −0.637646 | − | 0.770329i | \(-0.720092\pi\) |
0.335723 | − | 0.941961i | \(-0.391019\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.38675 | + | 3.05253i | 0.382403 | + | 0.139183i | ||||
\(482\) | 27.2565 | − | 15.7365i | 1.24150 | − | 0.716779i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.76728 | − | 8.19572i | 0.443967 | − | 0.372533i | ||||
\(485\) | −4.02525 | + | 11.9676i | −0.182777 | + | 0.543420i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.8788 | + | 9.16764i | −0.719538 | + | 0.415426i | −0.814583 | − | 0.580047i | \(-0.803034\pi\) |
0.0950445 | + | 0.995473i | \(0.469701\pi\) | |||||||
\(488\) | 6.78601 | − | 18.6444i | 0.307188 | − | 0.843993i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −28.9564 | − | 32.8332i | −1.30811 | − | 1.48325i | ||||
\(491\) | −14.1588 | + | 5.15338i | −0.638978 | + | 0.232569i | −0.641134 | − | 0.767429i | \(-0.721536\pi\) |
0.00215650 | + | 0.999998i | \(0.499314\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6.64350i | − | 0.299208i | ||||||
\(494\) | −32.2718 | + | 2.60909i | −1.45198 | + | 0.117388i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.5519 | − | 13.0496i | −0.698302 | − | 0.585945i | ||||
\(497\) | 8.75509 | + | 24.0544i | 0.392720 | + | 1.07899i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.99606 | + | 34.0053i | −0.268420 | + | 1.52229i | 0.490695 | + | 0.871332i | \(0.336743\pi\) |
−0.759115 | + | 0.650956i | \(0.774368\pi\) | |||||||
\(500\) | −12.7508 | − | 3.60103i | −0.570234 | − | 0.161043i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −27.4071 | − | 15.8235i | −1.22324 | − | 0.706237i | ||||
\(503\) | −19.8431 | − | 23.6481i | −0.884760 | − | 1.05442i | −0.998146 | − | 0.0608649i | \(-0.980614\pi\) |
0.113386 | − | 0.993551i | \(-0.463830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.37863 | + | 0.181596i | −0.328345 | + | 0.00808093i | ||||
\(506\) | −1.92529 | − | 3.33471i | −0.0855897 | − | 0.148246i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 23.1176 | + | 4.07626i | 1.02568 | + | 0.180855i | ||||
\(509\) | 1.76734 | + | 10.0231i | 0.0783358 | + | 0.444264i | 0.998597 | + | 0.0529589i | \(0.0168652\pi\) |
−0.920261 | + | 0.391305i | \(0.872024\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.67067 | + | 5.59735i | 0.295093 | + | 0.247612i | ||||
\(512\) | − | 15.1195i | − | 0.668194i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −49.5204 | −2.18425 | ||||||||
\(515\) | −7.55198 | − | 1.14080i | −0.332780 | − | 0.0502699i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.26728 | − | 0.223455i | 0.0557348 | − | 0.00982754i | ||||
\(518\) | −15.9769 | − | 2.81716i | −0.701984 | − | 0.123779i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.47713 | + | 11.8847i | −0.284041 | + | 0.521180i | ||||
\(521\) | 8.27116 | − | 14.3261i | 0.362366 | − | 0.627636i | −0.625984 | − | 0.779836i | \(-0.715302\pi\) |
0.988350 | + | 0.152200i | \(0.0486357\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.14102 | + | 6.12683i | 0.224801 | + | 0.267908i | 0.866642 | − | 0.498930i | \(-0.166274\pi\) |
−0.641841 | + | 0.766838i | \(0.721829\pi\) | |||||||
\(524\) | 2.03243 | − | 3.52027i | 0.0887871 | − | 0.153784i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.32492 | + | 3.39399i | 0.406586 | + | 0.147985i | ||||
\(527\) | 8.19816 | + | 1.44556i | 0.357117 | + | 0.0629694i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.45976 | + | 1.25925i | −0.150424 | + | 0.0547500i | ||||
\(530\) | −6.81549 | + | 45.1177i | −0.296046 | + | 1.95979i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 21.1884 | − | 5.52792i | 0.918635 | − | 0.239666i | ||||
\(533\) | 18.1713i | 0.787088i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.44430 | − | 3.06300i | 0.105676 | − | 0.132425i | ||||
\(536\) | −1.80749 | − | 10.2508i | −0.0780719 | − | 0.442768i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.82470 | − | 7.76079i | 0.121781 | − | 0.334591i | ||||
\(539\) | 2.69254 | + | 4.66361i | 0.115976 | + | 0.200876i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.98380 | − | 3.34280i | 0.171277 | − | 0.143718i | −0.553120 | − | 0.833102i | \(-0.686563\pi\) |
0.724397 | + | 0.689383i | \(0.242118\pi\) | |||||||
\(542\) | 8.72810 | + | 10.4017i | 0.374904 | + | 0.446793i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.06125 | + | 10.4984i | 0.259874 | + | 0.450115i | ||||
\(545\) | −1.55674 | − | 7.71372i | −0.0666832 | − | 0.330419i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.8663 | + | 1.91602i | −0.464610 | + | 0.0819233i | −0.401053 | − | 0.916055i | \(-0.631356\pi\) |
−0.0635572 | + | 0.997978i | \(0.520245\pi\) | |||||||
\(548\) | −0.246555 | − | 0.677403i | −0.0105323 | − | 0.0289372i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.89668 | + | 2.00093i | 0.166155 | + | 0.0853201i | ||||
\(551\) | −3.59020 | − | 13.7612i | −0.152948 | − | 0.586245i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.5515 | − | 17.3418i | 0.618792 | − | 0.737447i | ||||
\(554\) | 12.6373 | − | 4.59960i | 0.536907 | − | 0.195418i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.74054 | + | 9.87109i | −0.0738153 | + | 0.418628i | ||||
\(557\) | 7.27877 | − | 19.9983i | 0.308411 | − | 0.847353i | −0.684555 | − | 0.728961i | \(-0.740004\pi\) |
0.992967 | − | 0.118393i | \(-0.0377741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.1086 | − | 38.2933i | 0.935095 | − | 1.61963i | ||||
\(560\) | 15.0058 | − | 44.6140i | 0.634109 | − | 1.88529i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.2144 | + | 16.2896i | 1.19015 | + | 0.687134i | ||||
\(563\) | 12.7368 | − | 7.35358i | 0.536791 | − | 0.309917i | −0.206986 | − | 0.978344i | \(-0.566366\pi\) |
0.743778 | + | 0.668427i | \(0.233032\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.8220 | + | 27.6006i | 0.455285 | + | 1.16116i | ||||
\(566\) | −9.58644 | − | 54.3674i | −0.402948 | − | 2.28523i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.64519 | + | 6.72768i | −0.236867 | + | 0.282287i | ||||
\(569\) | 40.6551 | 1.70435 | 0.852174 | − | 0.523258i | \(-0.175284\pi\) | ||||
0.852174 | + | 0.523258i | \(0.175284\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.3240 | −1.01793 | −0.508964 | − | 0.860788i | \(-0.669972\pi\) | ||||
−0.508964 | + | 0.860788i | \(0.669972\pi\) | |||||||
\(572\) | −1.55632 | + | 1.85475i | −0.0650730 | + | 0.0775510i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.73575 | − | 32.5290i | −0.239405 | − | 1.35774i | ||||
\(575\) | −13.2808 | + | 17.5093i | −0.553848 | + | 0.730188i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.1743 | − | 16.8438i | 1.21454 | − | 0.701216i | 0.250796 | − | 0.968040i | \(-0.419308\pi\) |
0.963745 | + | 0.266824i | \(0.0859742\pi\) | |||||||
\(578\) | 19.8667 | + | 11.4700i | 0.826346 | + | 0.477091i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.19476 | + | 2.75628i | 0.340269 | + | 0.114448i | ||||
\(581\) | 17.2018 | − | 29.7945i | 0.713652 | − | 1.23608i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.91971 | − | 5.27437i | 0.0795064 | − | 0.218442i | ||||
\(584\) | −0.518785 | + | 2.94218i | −0.0214675 | + | 0.121748i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.7261 | − | 13.3672i | 1.51714 | − | 0.552194i | ||||
\(587\) | −1.44613 | + | 1.72343i | −0.0596880 | + | 0.0711334i | −0.795062 | − | 0.606528i | \(-0.792562\pi\) |
0.735374 | + | 0.677661i | \(0.237006\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.7626 | − | 1.43606i | 0.731897 | − | 0.0591718i | ||||
\(590\) | −1.84703 | + | 1.12787i | −0.0760409 | + | 0.0464335i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.64202 | − | 10.0064i | −0.149686 | − | 0.411259i | ||||
\(593\) | 30.9103 | − | 5.45032i | 1.26933 | − | 0.223818i | 0.501888 | − | 0.864932i | \(-0.332639\pi\) |
0.767445 | + | 0.641115i | \(0.221528\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.81822 | + | 18.9195i | 0.156532 | + | 0.775624i | ||||
\(596\) | −2.74781 | − | 4.75934i | −0.112555 | − | 0.194950i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −20.9852 | − | 25.0091i | −0.858147 | − | 1.02270i | ||||
\(599\) | 7.97210 | − | 6.68939i | 0.325731 | − | 0.273321i | −0.465227 | − | 0.885192i | \(-0.654027\pi\) |
0.790958 | + | 0.611871i | \(0.209583\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.647959 | + | 1.12230i | 0.0264308 | + | 0.0457795i | 0.878938 | − | 0.476936i | \(-0.158253\pi\) |
−0.852507 | + | 0.522715i | \(0.824919\pi\) | |||||||
\(602\) | −27.4901 | + | 75.5285i | −1.12041 | + | 3.07831i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.92440 | − | 16.5851i | −0.118992 | − | 0.674839i | ||||
\(605\) | 18.8043 | + | 15.0060i | 0.764505 | + | 0.610081i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.50902i | 0.223604i | 0.993730 | + | 0.111802i | \(0.0356623\pi\) | ||||
−0.993730 | + | 0.111802i | \(0.964338\pi\) | |||||||
\(608\) | 18.2285 | + | 18.4706i | 0.739265 | + | 0.749080i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −53.8309 | − | 8.13172i | −2.17955 | − | 0.329244i | ||||
\(611\) | 10.2524 | − | 3.73155i | 0.414766 | − | 0.150962i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.0547 | + | 7.06273i | 1.61780 | + | 0.285261i | 0.907945 | − | 0.419090i | \(-0.137651\pi\) |
0.709851 | + | 0.704351i | \(0.248762\pi\) | |||||||
\(614\) | −9.14903 | − | 3.32997i | −0.369225 | − | 0.134387i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.51323 | + | 2.62099i | −0.0609697 | + | 0.105603i | ||||
\(617\) | −19.6085 | − | 23.3684i | −0.789407 | − | 0.940778i | 0.209911 | − | 0.977721i | \(-0.432683\pi\) |
−0.999317 | + | 0.0369423i | \(0.988238\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.90205 | − | 5.02651i | 0.116643 | − | 0.202032i | −0.801792 | − | 0.597603i | \(-0.796120\pi\) |
0.918436 | + | 0.395571i | \(0.129453\pi\) | |||||||
\(620\) | −5.18438 | + | 9.51270i | −0.208210 | + | 0.382039i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.7708 | + | 2.07551i | 0.471966 | + | 0.0832203i | ||||
\(623\) | 18.1224 | − | 3.19546i | 0.726058 | − | 0.128024i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.90087 | − | 24.9276i | 0.0760349 | − | 0.997105i | ||||
\(626\) | 8.17881 | 0.326891 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 12.7136i | − | 0.507328i | ||||||
\(629\) | 3.34487 | + | 2.80668i | 0.133369 | + | 0.111910i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.05716 | − | 23.0093i | −0.161513 | − | 0.915985i | −0.952587 | − | 0.304265i | \(-0.901589\pi\) |
0.791074 | − | 0.611720i | \(-0.209522\pi\) | |||||||
\(632\) | 7.64880 | + | 1.34869i | 0.304253 | + | 0.0536480i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.6994 | + | 42.7806i | 0.980937 | + | 1.69903i | ||||
\(635\) | 1.08976 | + | 44.2791i | 0.0432457 | + | 1.75716i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.3479 | + | 34.9755i | 1.16281 | + | 1.38578i | ||||
\(638\) | −2.47544 | − | 1.42919i | −0.0980034 | − | 0.0565823i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 23.3855 | − | 4.71951i | 0.924392 | − | 0.186555i | ||||
\(641\) | −3.18574 | + | 18.0672i | −0.125829 | + | 0.713612i | 0.854983 | + | 0.518656i | \(0.173568\pi\) |
−0.980812 | + | 0.194956i | \(0.937544\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.39128 | + | 14.8124i | 0.212611 | + | 0.584144i | 0.999455 | − | 0.0330077i | \(-0.0105086\pi\) |
−0.786844 | + | 0.617152i | \(0.788286\pi\) | |||||||
\(644\) | 16.9145 | + | 14.1929i | 0.666523 | + | 0.559279i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.2729 | − | 4.20051i | −0.600905 | − | 0.165267i | ||||
\(647\) | 25.0443i | 0.984592i | 0.870428 | + | 0.492296i | \(0.163842\pi\) | ||||
−0.870428 | + | 0.492296i | \(0.836158\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.250158 | − | 0.0910500i | 0.00981955 | − | 0.00357402i | ||||
\(650\) | 35.4819 | + | 10.9702i | 1.39172 | + | 0.430285i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.86475 | + | 18.8608i | −0.268844 | + | 0.738644i | ||||
\(653\) | 2.58813 | − | 1.49426i | 0.101282 | − | 0.0584749i | −0.448504 | − | 0.893781i | \(-0.648043\pi\) |
0.549785 | + | 0.835306i | \(0.314710\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.26962 | + | 2.44511i | 0.284047 | + | 0.0955383i | ||||
\(656\) | 16.6082 | − | 13.9360i | 0.648443 | − | 0.544108i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −17.1752 | + | 9.91610i | −0.669559 | + | 0.386570i | ||||
\(659\) | 33.6123 | + | 12.2339i | 1.30935 | + | 0.476564i | 0.900031 | − | 0.435827i | \(-0.143544\pi\) |
0.409320 | + | 0.912391i | \(0.365766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.559402 | + | 3.17253i | 0.0217582 | + | 0.123397i | 0.993752 | − | 0.111609i | \(-0.0356003\pi\) |
−0.971994 | + | 0.235006i | \(0.924489\pi\) | |||||||
\(662\) | −8.62500 | − | 23.6970i | −0.335220 | − | 0.921010i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.8034 | 0.458061 | ||||||||
\(665\) | 18.1332 | + | 37.1260i | 0.703176 | + | 1.43968i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.21782 | − | 10.9854i | 0.356915 | − | 0.425355i | ||||
\(668\) | −6.58918 | − | 18.1036i | −0.254943 | − | 0.700450i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −26.5902 | + | 10.4258i | −1.02727 | + | 0.402786i | ||||
\(671\) | 6.29297 | + | 2.29045i | 0.242937 | + | 0.0884220i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.554001 | − | 0.319853i | −0.0213552 | − | 0.0123294i | 0.489284 | − | 0.872124i | \(-0.337258\pi\) |
−0.510640 | + | 0.859795i | \(0.670591\pi\) | |||||||
\(674\) | −20.5036 | + | 17.2046i | −0.789770 | + | 0.662696i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.56107 | + | 4.43590i | −0.0985025 | + | 0.170611i | ||||
\(677\) | −22.3439 | + | 12.9002i | −0.858744 | + | 0.495796i | −0.863592 | − | 0.504192i | \(-0.831790\pi\) |
0.00484733 | + | 0.999988i | \(0.498457\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.15661 | + | 23.5733i | −0.159516 | + | 0.904660i | ||||
\(680\) | −4.96639 | + | 4.37998i | −0.190452 | + | 0.167964i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.30227 | − | 2.74374i | 0.0881585 | − | 0.105063i | ||||
\(683\) | 5.33696i | 0.204213i | 0.994773 | + | 0.102107i | \(0.0325583\pi\) | ||||
−0.994773 | + | 0.102107i | \(0.967442\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.16087 | − | 0.708872i | 0.0443546 | − | 0.0270846i | ||||
\(686\) | −23.0082 | − | 19.3062i | −0.878458 | − | 0.737114i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −51.9549 | + | 9.16105i | −1.98076 | + | 0.349262i | ||||
\(689\) | 8.26367 | − | 46.8656i | 0.314821 | − | 1.78544i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.62534 | − | 11.4754i | −0.252040 | − | 0.436545i | 0.712048 | − | 0.702131i | \(-0.247768\pi\) |
−0.964087 | + | 0.265586i | \(0.914435\pi\) | |||||||
\(692\) | 8.81712 | + | 5.09057i | 0.335177 | + | 0.193514i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.5915 | + | 23.9911i | −1.08532 | + | 0.910689i | ||||
\(695\) | −18.9069 | + | 0.465320i | −0.717180 | + | 0.0176506i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.04058 | + | 8.35392i | −0.115170 | + | 0.316427i | ||||
\(698\) | −5.50214 | − | 0.970176i | −0.208259 | − | 0.0367217i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −24.9214 | − | 3.13961i | −0.941939 | − | 0.118666i | ||||
\(701\) | −31.3081 | − | 26.2706i | −1.18249 | − | 0.992228i | −0.999959 | − | 0.00902862i | \(-0.997126\pi\) |
−0.182533 | − | 0.983200i | \(-0.558429\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.44523 | + | 4.00609i | 0.318518 | + | 0.151093i | ||||
\(704\) | 0.340484 | 0.0128325 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.4925 | − | 4.91087i | 0.507797 | − | 0.184823i | ||||
\(707\) | −13.7800 | + | 2.42978i | −0.518249 | + | 0.0913813i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.91375 | + | 2.51640i | 0.259651 | + | 0.0945053i | 0.468566 | − | 0.883429i | \(-0.344771\pi\) |
−0.208915 | + | 0.977934i | \(0.566993\pi\) | |||||||
\(710\) | 21.1595 | + | 11.5319i | 0.794104 | + | 0.432783i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.05820 | + | 4.83637i | 0.152087 | + | 0.181251i | ||||
\(713\) | 11.5504 | + | 13.7652i | 0.432565 | + | 0.515511i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.01141 | − | 2.18620i | −0.150018 | − | 0.0817592i | ||||
\(716\) | −26.2005 | − | 9.53620i | −0.979158 | − | 0.356384i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 53.7538 | − | 9.47825i | 2.00607 | − | 0.353725i | ||||
\(719\) | 30.0323 | − | 10.9309i | 1.12002 | − | 0.407653i | 0.285358 | − | 0.958421i | \(-0.407887\pi\) |
0.834658 | + | 0.550768i | \(0.185665\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4794 | −0.539240 | ||||||||
\(722\) | −33.9059 | − | 0.447227i | −1.26185 | − | 0.0166441i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.0820 | + | 12.6553i | 0.560520 | + | 0.470332i | ||||
\(725\) | −2.03907 | + | 16.1856i | −0.0757292 | + | 0.601117i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.9418 | − | 5.10323i | −1.07339 | − | 0.189268i | −0.391101 | − | 0.920348i | \(-0.627906\pi\) |
−0.682292 | + | 0.731079i | \(0.739017\pi\) | |||||||
\(728\) | −8.77615 | + | 24.1123i | −0.325266 | + | 0.893661i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.19510 | − | 0.201691i | 0.303314 | − | 0.00746490i | ||||
\(731\) | 16.5716 | − | 13.9052i | 0.612922 | − | 0.514302i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.0187 | − | 25.4142i | −1.62587 | − | 0.938696i | −0.985307 | − | 0.170790i | \(-0.945368\pi\) |
−0.640562 | − | 0.767906i | \(-0.721299\pi\) | |||||||
\(734\) | −8.88034 | − | 15.3812i | −0.327779 | − | 0.567730i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.54388 | + | 25.7696i | −0.167490 | + | 0.949880i | ||||
\(737\) | 3.45991 | − | 0.610076i | 0.127448 | − | 0.0224724i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.2796 | − | 9.46473i | −0.414928 | − | 0.348166i | 0.411302 | − | 0.911499i | \(-0.365074\pi\) |
−0.826230 | + | 0.563334i | \(0.809519\pi\) | |||||||
\(740\) | −4.84978 | + | 2.96146i | −0.178281 | + | 0.108865i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 86.5039i | 3.17566i | ||||||||
\(743\) | −22.2770 | + | 26.5487i | −0.817263 | + | 0.973976i | −0.999958 | − | 0.00919385i | \(-0.997073\pi\) |
0.182695 | + | 0.983170i | \(0.441518\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.77705 | − | 6.85876i | 0.284929 | − | 0.251286i | ||||
\(746\) | −2.87472 | + | 16.3034i | −0.105251 | + | 0.596909i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.02584 | + | 0.592270i | −0.0375085 | + | 0.0216555i | ||||
\(749\) | 3.71455 | − | 6.43379i | 0.135727 | − | 0.235086i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.40060 | + | 5.37074i | −0.233561 | + | 0.195981i | −0.752055 | − | 0.659100i | \(-0.770937\pi\) |
0.518494 | + | 0.855081i | \(0.326493\pi\) | |||||||
\(752\) | −11.2733 | − | 6.50865i | −0.411095 | − | 0.237346i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −22.7732 | − | 8.28878i | −0.829352 | − | 0.301859i | ||||
\(755\) | 29.5837 | − | 11.5996i | 1.07666 | − | 0.422152i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.74412 | − | 13.0344i | −0.172428 | − | 0.473742i | 0.823134 | − | 0.567847i | \(-0.192223\pi\) |
−0.995562 | + | 0.0941046i | \(0.970001\pi\) | |||||||
\(758\) | 24.2594 | − | 28.9112i | 0.881142 | − | 1.05010i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.92028 | + | 11.7564i | −0.287299 | + | 0.426451i | ||||
\(761\) | −44.3970 | −1.60939 | −0.804696 | − | 0.593687i | \(-0.797672\pi\) | ||||
−0.804696 | + | 0.593687i | \(0.797672\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.10239 | − | 14.0187i | −0.184719 | − | 0.507511i | ||||
\(764\) | −2.63631 | − | 14.9513i | −0.0953784 | − | 0.540918i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.4075 | − | 9.24758i | −0.918011 | − | 0.334129i | ||||
\(767\) | 1.95468 | − | 1.12854i | 0.0705796 | − | 0.0407491i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.5549 | + | 12.2130i | −0.524863 | + | 0.440412i | −0.866323 | − | 0.499484i | \(-0.833523\pi\) |
0.341460 | + | 0.939896i | \(0.389079\pi\) | |||||||
\(770\) | 7.87101 | + | 2.64738i | 0.283651 | + | 0.0954051i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.89342 | − | 5.71197i | 0.356072 | − | 0.205578i | ||||
\(773\) | −0.638682 | + | 1.75476i | −0.0229718 | + | 0.0631144i | −0.950648 | − | 0.310270i | \(-0.899581\pi\) |
0.927677 | + | 0.373384i | \(0.121803\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.5295 | − | 6.03806i | −0.701521 | − | 0.216893i | ||||
\(776\) | −7.71714 | + | 2.80881i | −0.277029 | + | 0.100830i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 56.1252i | 2.01218i | ||||||||
\(779\) | −1.78365 | + | 18.9473i | −0.0639060 | + | 0.678856i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.27077 | − | 1.90540i | −0.0812544 | − | 0.0681805i | ||||
\(782\) | −5.46279 | − | 15.0089i | −0.195349 | − | 0.536717i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.45938 | − | 53.6468i | 0.337835 | − | 1.91596i | ||||
\(785\) | 23.5146 | − | 4.74558i | 0.839273 | − | 0.169377i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.2314 | − | 6.48445i | −0.400356 | − | 0.231146i | 0.286282 | − | 0.958146i | \(-0.407581\pi\) |
−0.686638 | + | 0.727000i | \(0.740914\pi\) | |||||||
\(788\) | 2.36327 | + | 2.81644i | 0.0841881 | + | 0.100331i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.524336 | − | 21.3049i | −0.0186550 | − | 0.757993i | ||||
\(791\) | 28.1016 | + | 48.6734i | 0.999178 | + | 1.73063i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.9164 | + | 9.85957i | 1.98565 | + | 0.350124i | ||||
\(794\) | 2.90865 | + | 16.4958i | 0.103224 | + | 0.585413i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.475962 | + | 0.399379i | 0.0168700 | + | 0.0141556i | ||||
\(797\) | 29.9226i | 1.05991i | 0.848025 | + | 0.529956i | \(0.177791\pi\) | ||||
−0.848025 | + | 0.529956i | \(0.822209\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.33772 | 0.188835 | ||||||||
\(800\) | −11.5448 | − | 27.4376i | −0.408170 | − | 0.970067i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.8275 | + | 1.90918i | −0.382331 | + | 0.0674153i | ||||
\(803\) | −0.993061 | − | 0.175103i | −0.0350444 | − | 0.00617927i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.9371 | + | 36.5822i | −0.702691 | + | 1.28935i | ||||
\(806\) | 15.1837 | − | 26.2989i | 0.534822 | − | 0.926339i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.08579 | − | 3.67750i | −0.108558 | − | 0.129374i | ||||
\(809\) | −21.2289 | + | 36.7696i | −0.746369 | + | 1.29275i | 0.203183 | + | 0.979141i | \(0.434871\pi\) |
−0.949552 | + | 0.313608i | \(0.898462\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.2727 | + | 10.6544i | 1.02790 | + | 0.374126i | 0.800282 | − | 0.599623i | \(-0.204683\pi\) |
0.227621 | + | 0.973750i | \(0.426905\pi\) | |||||||
\(812\) | 16.1417 | + | 2.84622i | 0.566463 | + | 0.0998828i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.76537 | − | 0.642542i | 0.0618762 | − | 0.0225211i | ||||
\(815\) | −37.4466 | − | 5.65669i | −1.31170 | − | 0.198145i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.8114 | − | 37.7583i | 0.938014 | − | 1.32099i | ||||
\(818\) | 4.07767i | 0.142572i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.04308 | − | 7.21646i | −0.315798 | − | 0.252010i | ||||
\(821\) | 1.07790 | + | 6.11310i | 0.0376191 | + | 0.213349i | 0.997823 | − | 0.0659521i | \(-0.0210085\pi\) |
−0.960204 | + | 0.279301i | \(0.909897\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.3025 | + | 33.8009i | −0.428839 | + | 1.17823i | 0.517679 | + | 0.855575i | \(0.326796\pi\) |
−0.946518 | + | 0.322651i | \(0.895426\pi\) | |||||||
\(824\) | −2.48383 | − | 4.30212i | −0.0865283 | − | 0.149871i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.14292 | + | 2.63722i | −0.109356 | + | 0.0917606i | ||||
\(827\) | 9.88848 | + | 11.7846i | 0.343856 | + | 0.409792i | 0.910062 | − | 0.414472i | \(-0.136034\pi\) |
−0.566206 | + | 0.824264i | \(0.691589\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.0970 | − | 20.9527i | −0.420148 | − | 0.727717i | 0.575806 | − | 0.817586i | \(-0.304688\pi\) |
−0.995954 | + | 0.0898693i | \(0.971355\pi\) | |||||||
\(830\) | −6.40704 | − | 31.7473i | −0.222392 | − | 1.10196i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.84293 | − | 0.501284i | 0.0985607 | − | 0.0173789i | ||||
\(833\) | 7.63975 | + | 20.9900i | 0.264702 | + | 0.727262i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31.0243 | − | 18.9446i | 1.07364 | − | 0.655605i | ||||
\(836\) | −1.80483 | + | 1.78118i | −0.0624215 | + | 0.0616035i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.9827 | + | 30.9649i | −0.897556 | + | 1.06967i | ||||
\(839\) | −11.6771 | + | 4.25013i | −0.403139 | + | 0.146731i | −0.535628 | − | 0.844454i | \(-0.679925\pi\) |
0.132489 | + | 0.991184i | \(0.457703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.18727 | + | 18.0759i | −0.109906 | + | 0.623308i | ||||
\(842\) | 14.0372 | − | 38.5669i | 0.483754 | − | 1.32910i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.2960 | + | 19.5652i | −0.388824 | + | 0.673463i | ||||
\(845\) | −9.16044 | − | 3.08108i | −0.315129 | − | 0.105992i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.4983 | + | 22.8043i | 1.35718 | + | 0.783566i | ||||
\(848\) | −49.1718 | + | 28.3894i | −1.68857 | + | 0.974895i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 14.4765 | + | 10.9805i | 0.496541 | + | 0.376627i | ||||
\(851\) | 1.63667 | + | 9.28199i | 0.0561042 | + | 0.318182i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.8823 | + | 17.7360i | −0.509560 | + | 0.607270i | −0.958079 | − | 0.286503i | \(-0.907507\pi\) |
0.448519 | + | 0.893773i | \(0.351951\pi\) | |||||||
\(854\) | −103.210 | −3.53176 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.54882 | 0.0871167 | ||||||||
\(857\) | 1.82726 | − | 2.17765i | 0.0624181 | − | 0.0743870i | −0.733932 | − | 0.679223i | \(-0.762317\pi\) |
0.796350 | + | 0.604836i | \(0.206761\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.49254 | + | 25.4785i | 0.153284 | + | 0.869314i | 0.960338 | + | 0.278838i | \(0.0899492\pi\) |
−0.807055 | + | 0.590477i | \(0.798940\pi\) | |||||||
\(860\) | 10.2768 | + | 26.2101i | 0.350436 | + | 0.893756i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 39.6161 | − | 22.8724i | 1.34933 | − | 0.779036i | ||||
\(863\) | −32.9118 | − | 19.0016i | −1.12033 | − | 0.646823i | −0.178844 | − | 0.983877i | \(-0.557236\pi\) |
−0.941485 | + | 0.337055i | \(0.890569\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.12419 | + | 18.2080i | −0.208229 | + | 0.619090i | ||||
\(866\) | 2.10886 | − | 3.65266i | 0.0716621 | − | 0.124122i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.02455 | + | 19.2998i | −0.238429 | + | 0.655077i | ||||
\(869\) | −0.455217 | + | 2.58167i | −0.0154422 | + | 0.0875770i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.9909 | − | 10.1879i | 0.948437 | − | 0.345203i | ||||
\(872\) | 3.28997 | − | 3.92083i | 0.111412 | − | 0.132776i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −19.4264 | − | 28.1369i | −0.657108 | − | 0.951744i | ||||
\(875\) | −3.49542 | − | 47.2656i | −0.118167 | − | 1.59787i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.7912 | + | 46.1335i | 0.567000 | + | 1.55782i | 0.809164 | + | 0.587583i | \(0.199921\pi\) |
−0.242164 | + | 0.970235i | \(0.577857\pi\) | |||||||
\(878\) | 11.1018 | − | 1.95755i | 0.374668 | − | 0.0660641i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.07829 | + | 5.34299i | 0.0363491 | + | 0.180112i | ||||
\(881\) | −27.8747 | − | 48.2804i | −0.939123 | − | 1.62661i | −0.767112 | − | 0.641514i | \(-0.778307\pi\) |
−0.172011 | − | 0.985095i | \(-0.555027\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.6931 | − | 12.7435i | −0.359851 | − | 0.428853i | 0.555496 | − | 0.831519i | \(-0.312528\pi\) |
−0.915347 | + | 0.402666i | \(0.868084\pi\) | |||||||
\(884\) | −7.69345 | + | 6.45557i | −0.258759 | + | 0.217124i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.1307 | − | 48.7237i | −0.945068 | − | 1.63691i | ||||
\(887\) | 14.8397 | − | 40.7717i | 0.498267 | − | 1.36898i | −0.394680 | − | 0.918818i | \(-0.629145\pi\) |
0.892948 | − | 0.450160i | \(-0.148633\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.5811 | + | 82.6934i | 0.489034 | + | 2.77345i | ||||
\(890\) | 10.8054 | − | 13.5405i | 0.362198 | − | 0.453878i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 3.74820i | − | 0.125499i | ||||||
\(893\) | 11.0564 | − | 2.88455i | 0.369989 | − | 0.0965276i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.85802 | − | 52.0191i | 0.262665 | − | 1.73881i | ||||
\(896\) | 42.5001 | − | 15.4688i | 1.41983 | − | 0.516776i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.5091 | + | 4.67426i | 0.884619 | + | 0.155982i | ||||
\(899\) | 12.5345 | + | 4.56220i | 0.418051 | + | 0.152158i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.6410 | − | 20.1628i | 0.387818 | − | 0.671721i | ||||
\(902\) | 2.45865 | + | 2.93010i | 0.0818640 | + | 0.0975617i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.64125 | + | 16.6991i | −0.320663 | + | 0.555405i | ||||
\(905\) | −17.7772 | + | 32.6191i | −0.590935 | + | 1.08429i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.5350 | − | 3.44455i | −0.648649 | − | 0.114374i | −0.160363 | − | 0.987058i | \(-0.551267\pi\) |
−0.488286 | + | 0.872684i | \(0.662378\pi\) | |||||||
\(908\) | 10.5580 | − | 1.86165i | 0.350378 | − | 0.0617812i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 69.6180 | + | 10.5165i | 2.30781 | + | 0.348619i | ||||
\(911\) | −15.4076 | −0.510478 | −0.255239 | − | 0.966878i | \(-0.582154\pi\) | ||||
−0.255239 | + | 0.966878i | \(0.582154\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.98395i | 0.131849i | ||||||||
\(914\) | 27.5270 | + | 23.0979i | 0.910512 | + | 0.764010i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.68193 | − | 20.8812i | −0.121654 | − | 0.689936i | ||||
\(917\) | 14.3194 | + | 2.52490i | 0.472869 | + | 0.0833795i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.62805 | − | 11.4801i | −0.218639 | − | 0.378694i | 0.735753 | − | 0.677250i | \(-0.236828\pi\) |
−0.954392 | + | 0.298556i | \(0.903495\pi\) | |||||||
\(920\) | −14.2894 | + | 0.351678i | −0.471107 | + | 0.0115945i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.58644 | − | 10.2329i | −0.282779 | − | 0.337003i | ||||
\(923\) | −21.7654 | − | 12.5663i | −0.716417 | − | 0.413624i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.28768 | − | 7.86456i | −0.239617 | − | 0.258585i | ||||
\(926\) | 6.69313 | − | 37.9586i | 0.219950 | − | 1.24740i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.64358 | + | 18.2531i | 0.218086 | + | 0.599187i | ||||
\(929\) | 23.9018 | + | 20.0560i | 0.784193 | + | 0.658016i | 0.944301 | − | 0.329083i | \(-0.106740\pi\) |
−0.160108 | + | 0.987100i | \(0.551184\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.1680 | + | 39.3496i | 0.890394 | + | 1.28963i | ||||
\(932\) | − | 7.63580i | − | 0.250119i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −45.3648 | + | 16.5114i | −1.48438 | + | 0.540270i | ||||
\(935\) | −1.47835 | − | 1.67628i | −0.0483474 | − | 0.0548204i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.54711 | − | 15.2405i | 0.181216 | − | 0.497887i | −0.815510 | − | 0.578743i | \(-0.803543\pi\) |
0.996726 | + | 0.0808564i | \(0.0257655\pi\) | |||||||
\(938\) | −46.8916 | + | 27.0729i | −1.53107 | + | 0.883961i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.21453 | + | 6.58408i | −0.0722300 | + | 0.214749i | ||||
\(941\) | −26.9454 | + | 22.6099i | −0.878396 | + | 0.737062i | −0.965849 | − | 0.259107i | \(-0.916572\pi\) |
0.0874525 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.6188 | + | 9.59486i | −0.541182 | + | 0.312452i | ||||
\(944\) | −2.53055 | − | 0.921045i | −0.0823624 | − | 0.0299775i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.61623 | − | 9.16612i | −0.0525483 | − | 0.298016i | ||||
\(947\) | 7.61965 | + | 20.9348i | 0.247605 | + | 0.680290i | 0.999773 | + | 0.0213182i | \(0.00678632\pi\) |
−0.752167 | + | 0.658972i | \(0.770991\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.54953 | −0.277530 | ||||||||
\(950\) | 35.9202 | + | 14.9214i | 1.16541 | + | 0.484114i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.06934 | + | 9.61666i | −0.261529 | + | 0.311678i | ||||
\(953\) | −1.45699 | − | 4.00305i | −0.0471966 | − | 0.129672i | 0.913855 | − | 0.406041i | \(-0.133091\pi\) |
−0.961052 | + | 0.276369i | \(0.910869\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.6693 | − | 10.4569i | 0.862998 | − | 0.338376i | ||||
\(956\) | −15.0049 | − | 5.46135i | −0.485294 | − | 0.176633i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −58.8145 | − | 33.9566i | −1.90021 | − | 1.09709i | ||||
\(959\) | 1.97535 | − | 1.65751i | 0.0637873 | − | 0.0535239i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.14280 | − | 12.3717i | 0.230413 | − | 0.399087i | ||||
\(962\) | 13.7943 | − | 7.96412i | 0.444745 | − | 0.256773i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.62907 | − | 20.5815i | 0.116885 | − | 0.662885i | ||||
\(965\) | 14.2576 | + | 16.1664i | 0.458967 | + | 0.520416i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.783596 | + | 0.933854i | −0.0251988 | + | 0.0300307i | −0.778497 | − | 0.627649i | \(-0.784017\pi\) |
0.753298 | + | 0.657679i | \(0.228462\pi\) | |||||||
\(968\) | 15.6477i | 0.502935i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.7438 | + | 19.2319i | 0.377069 | + | 0.617500i | ||||
\(971\) | 3.32466 | + | 2.78972i | 0.106693 | + | 0.0895264i | 0.694574 | − | 0.719421i | \(-0.255593\pi\) |
−0.587880 | + | 0.808948i | \(0.700037\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.3096 | + | 6.22604i | −1.13197 | + | 0.199598i | ||||
\(974\) | −5.68222 | + | 32.2255i | −0.182070 | + | 1.03257i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −33.8720 | − | 58.6680i | −1.08422 | − | 1.87792i | ||||
\(977\) | −18.6429 | − | 10.7635i | −0.596440 | − | 0.344355i | 0.171200 | − | 0.985236i | \(-0.445236\pi\) |
−0.767640 | + | 0.640882i | \(0.778569\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.63240 | + | 1.36975i | −0.0521718 | + | 0.0437773i | ||||
\(980\) | −29.0608 | + | 0.715219i | −0.928314 | + | 0.0228468i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.19713 | + | 25.2689i | −0.293492 | + | 0.806363i | ||||
\(983\) | −14.3780 | − | 2.53522i | −0.458586 | − | 0.0808611i | −0.0604172 | − | 0.998173i | \(-0.519243\pi\) |
−0.398169 | + | 0.917312i | \(0.630354\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.32705 | + | 5.42231i | −0.137871 | + | 0.172769i | ||||
\(986\) | −9.08261 | − | 7.62121i | −0.289249 | − | 0.242709i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.4474 | + | 17.5295i | −0.396004 | + | 0.557688i | ||||
\(989\) | 46.6954 | 1.48483 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.0031 | + | 10.9202i | −0.953080 | + | 0.346893i | −0.771318 | − | 0.636450i | \(-0.780402\pi\) |
−0.181762 | + | 0.983343i | \(0.558180\pi\) | |||||||
\(992\) | −23.9701 | + | 4.22658i | −0.761052 | + | 0.134194i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 42.9294 | + | 15.6250i | 1.36164 | + | 0.495596i | ||||
\(995\) | −0.561017 | + | 1.02940i | −0.0177854 | + | 0.0326341i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.4698 | − | 42.2712i | −1.12334 | − | 1.33874i | −0.934182 | − | 0.356797i | \(-0.883869\pi\) |
−0.189157 | − | 0.981947i | \(-0.560576\pi\) | |||||||
\(998\) | 39.6117 | + | 47.2073i | 1.25389 | + | 1.49432i | ||||
\(999\) | 0 | 0 |
(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 | 855.2.da.b.244.7 | 48 | ||
3.2 | odd | 2 | 95.2.p.a.54.2 | yes | 48 | ||
5.4 | even | 2 | inner | 855.2.da.b.244.2 | 48 | ||
15.2 | even | 4 | 475.2.l.f.301.2 | 48 | |||
15.8 | even | 4 | 475.2.l.f.301.7 | 48 | |||
15.14 | odd | 2 | 95.2.p.a.54.7 | yes | 48 | ||
19.6 | even | 9 | inner | 855.2.da.b.424.2 | 48 | ||
57.5 | odd | 18 | 1805.2.b.k.1084.20 | 24 | |||
57.14 | even | 18 | 1805.2.b.l.1084.5 | 24 | |||
57.44 | odd | 18 | 95.2.p.a.44.7 | yes | 48 | ||
95.44 | even | 18 | inner | 855.2.da.b.424.7 | 48 | ||
285.14 | even | 18 | 1805.2.b.l.1084.20 | 24 | |||
285.44 | odd | 18 | 95.2.p.a.44.2 | ✓ | 48 | ||
285.62 | even | 36 | 9025.2.a.cu.1.5 | 24 | |||
285.119 | odd | 18 | 1805.2.b.k.1084.5 | 24 | |||
285.128 | odd | 36 | 9025.2.a.ct.1.5 | 24 | |||
285.158 | even | 36 | 475.2.l.f.101.7 | 48 | |||
285.233 | even | 36 | 9025.2.a.cu.1.20 | 24 | |||
285.242 | odd | 36 | 9025.2.a.ct.1.20 | 24 | |||
285.272 | even | 36 | 475.2.l.f.101.2 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.44.2 | ✓ | 48 | 285.44 | odd | 18 | ||
95.2.p.a.44.7 | yes | 48 | 57.44 | odd | 18 | ||
95.2.p.a.54.2 | yes | 48 | 3.2 | odd | 2 | ||
95.2.p.a.54.7 | yes | 48 | 15.14 | odd | 2 | ||
475.2.l.f.101.2 | 48 | 285.272 | even | 36 | |||
475.2.l.f.101.7 | 48 | 285.158 | even | 36 | |||
475.2.l.f.301.2 | 48 | 15.2 | even | 4 | |||
475.2.l.f.301.7 | 48 | 15.8 | even | 4 | |||
855.2.da.b.244.2 | 48 | 5.4 | even | 2 | inner | ||
855.2.da.b.244.7 | 48 | 1.1 | even | 1 | trivial | ||
855.2.da.b.424.2 | 48 | 19.6 | even | 9 | inner | ||
855.2.da.b.424.7 | 48 | 95.44 | even | 18 | inner | ||
1805.2.b.k.1084.5 | 24 | 285.119 | odd | 18 | |||
1805.2.b.k.1084.20 | 24 | 57.5 | odd | 18 | |||
1805.2.b.l.1084.5 | 24 | 57.14 | even | 18 | |||
1805.2.b.l.1084.20 | 24 | 285.14 | even | 18 | |||
9025.2.a.ct.1.5 | 24 | 285.128 | odd | 36 | |||
9025.2.a.ct.1.20 | 24 | 285.242 | odd | 36 | |||
9025.2.a.cu.1.5 | 24 | 285.62 | even | 36 | |||
9025.2.a.cu.1.20 | 24 | 285.233 | even | 36 |