Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(143,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.o (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.79476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 16.0.478584585616890104119296.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 31x^{12} + 336x^{8} - 19375x^{4} + 390625 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 243.4 | ||
Root | \(-1.97578 + 1.04705i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.243 |
Dual form | 350.2.o.d.157.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | + | 0.965926i | 0.183013 | + | 0.683013i | ||||
\(3\) | 1.26867 | + | 0.339939i | 0.732467 | + | 0.196264i | 0.605728 | − | 0.795672i | \(-0.292882\pi\) |
0.126739 | + | 0.991936i | \(0.459549\pi\) | |||||||
\(4\) | −0.866025 | + | 0.500000i | −0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.31342i | 0.536203i | ||||||||
\(7\) | 2.49342 | + | 0.884806i | 0.942422 | + | 0.334425i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −1.10411 | − | 0.637459i | −0.368037 | − | 0.212486i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.63746 | + | 4.56821i | 0.795224 | + | 1.37737i | 0.922697 | + | 0.385526i | \(0.125980\pi\) |
−0.127473 | + | 0.991842i | \(0.540687\pi\) | |||||||
\(12\) | −1.26867 | + | 0.339939i | −0.366234 | + | 0.0981320i | ||||
\(13\) | 0.296014 | − | 0.296014i | 0.0820995 | − | 0.0820995i | −0.664865 | − | 0.746964i | \(-0.731511\pi\) |
0.746964 | + | 0.664865i | \(0.231511\pi\) | |||||||
\(14\) | −0.209313 | + | 2.63746i | −0.0559414 | + | 0.704890i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 0.896575 | − | 3.34607i | 0.217451 | − | 0.811540i | −0.767838 | − | 0.640644i | \(-0.778667\pi\) |
0.985289 | − | 0.170896i | \(-0.0546661\pi\) | |||||||
\(18\) | 0.329973 | − | 1.23148i | 0.0777753 | − | 0.290262i | ||||
\(19\) | −2.83616 | + | 4.91238i | −0.650660 | + | 1.12698i | 0.332303 | + | 0.943173i | \(0.392174\pi\) |
−0.982963 | + | 0.183804i | \(0.941159\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.86254 | + | 1.97014i | 0.624658 | + | 0.429919i | ||||
\(22\) | −3.72993 | + | 3.72993i | −0.795224 | + | 0.795224i | ||||
\(23\) | 2.89778 | − | 0.776457i | 0.604228 | − | 0.161903i | 0.0562805 | − | 0.998415i | \(-0.482076\pi\) |
0.547948 | + | 0.836512i | \(0.315409\pi\) | |||||||
\(24\) | −0.656712 | − | 1.13746i | −0.134051 | − | 0.232183i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.362541 | + | 0.209313i | 0.0711002 | + | 0.0410497i | ||||
\(27\) | −3.97025 | − | 3.97025i | −0.764075 | − | 0.764075i | ||||
\(28\) | −2.60176 | + | 0.480443i | −0.491687 | + | 0.0907953i | ||||
\(29\) | − | 2.27492i | − | 0.422442i | −0.977438 | − | 0.211221i | \(-0.932256\pi\) | ||
0.977438 | − | 0.211221i | \(-0.0677439\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | + | 1.73205i | −0.538816 | + | 0.311086i | −0.744599 | − | 0.667512i | \(-0.767359\pi\) |
0.205783 | + | 0.978598i | \(0.434026\pi\) | |||||||
\(32\) | 0.965926 | + | 0.258819i | 0.170753 | + | 0.0457532i | ||||
\(33\) | 1.79315 | + | 6.69213i | 0.312148 | + | 1.16495i | ||||
\(34\) | 3.46410 | 0.594089 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.27492 | 0.212486 | ||||||||
\(37\) | −1.36525 | − | 5.09518i | −0.224446 | − | 0.837642i | −0.982626 | − | 0.185597i | \(-0.940578\pi\) |
0.758180 | − | 0.652045i | \(-0.226089\pi\) | |||||||
\(38\) | −5.47904 | − | 1.46811i | −0.888818 | − | 0.238158i | ||||
\(39\) | 0.476171 | − | 0.274917i | 0.0762483 | − | 0.0440220i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.19615i | − | 0.811503i | −0.913984 | − | 0.405751i | \(-0.867010\pi\) | ||
0.913984 | − | 0.405751i | \(-0.132990\pi\) | |||||||
\(42\) | −1.16213 | + | 3.27491i | −0.179320 | + | 0.505330i | ||||
\(43\) | −5.85125 | − | 5.85125i | −0.892307 | − | 0.892307i | 0.102433 | − | 0.994740i | \(-0.467337\pi\) |
−0.994740 | + | 0.102433i | \(0.967337\pi\) | |||||||
\(44\) | −4.56821 | − | 2.63746i | −0.688684 | − | 0.397612i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.50000 | + | 2.59808i | 0.221163 | + | 0.383065i | ||||
\(47\) | 12.1712 | − | 3.26126i | 1.77535 | − | 0.475703i | 0.785625 | − | 0.618702i | \(-0.212341\pi\) |
0.989723 | + | 0.142999i | \(0.0456747\pi\) | |||||||
\(48\) | 0.928731 | − | 0.928731i | 0.134051 | − | 0.134051i | ||||
\(49\) | 5.43424 | + | 4.41238i | 0.776320 | + | 0.630339i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.27492 | − | 3.94027i | 0.318552 | − | 0.551748i | ||||
\(52\) | −0.108349 | + | 0.404362i | −0.0150252 | + | 0.0560750i | ||||
\(53\) | −2.54283 | + | 9.48998i | −0.349285 | + | 1.30355i | 0.538241 | + | 0.842791i | \(0.319089\pi\) |
−0.887526 | + | 0.460758i | \(0.847578\pi\) | |||||||
\(54\) | 2.80739 | − | 4.86254i | 0.382037 | − | 0.661708i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.13746 | − | 2.38876i | −0.151999 | − | 0.319212i | ||||
\(57\) | −5.26806 | + | 5.26806i | −0.697772 | + | 0.697772i | ||||
\(58\) | 2.19740 | − | 0.588792i | 0.288533 | − | 0.0773122i | ||||
\(59\) | −5.19615 | − | 9.00000i | −0.676481 | − | 1.17170i | −0.976034 | − | 0.217620i | \(-0.930171\pi\) |
0.299552 | − | 0.954080i | \(-0.403163\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4124 | − | 7.16629i | −1.58924 | − | 0.917549i | −0.993432 | − | 0.114424i | \(-0.963498\pi\) |
−0.595810 | − | 0.803126i | \(-0.703169\pi\) | |||||||
\(62\) | −2.44949 | − | 2.44949i | −0.311086 | − | 0.311086i | ||||
\(63\) | −2.18898 | − | 2.56637i | −0.275785 | − | 0.323333i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.00000 | + | 3.46410i | −0.738549 | + | 0.426401i | ||||
\(67\) | 3.59815 | + | 0.964122i | 0.439584 | + | 0.117786i | 0.471822 | − | 0.881694i | \(-0.343597\pi\) |
−0.0322373 | + | 0.999480i | \(0.510263\pi\) | |||||||
\(68\) | 0.896575 | + | 3.34607i | 0.108726 | + | 0.405770i | ||||
\(69\) | 3.94027 | 0.474353 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0.329973 | + | 1.23148i | 0.0388877 | + | 0.145131i | ||||
\(73\) | 9.22947 | + | 2.47303i | 1.08023 | + | 0.289446i | 0.754689 | − | 0.656083i | \(-0.227788\pi\) |
0.325539 | + | 0.945529i | \(0.394454\pi\) | |||||||
\(74\) | 4.56821 | − | 2.63746i | 0.531044 | − | 0.306598i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 5.67232i | − | 0.650660i | ||||||
\(77\) | 2.53430 | + | 13.7241i | 0.288810 | + | 1.56400i | ||||
\(78\) | 0.388792 | + | 0.388792i | 0.0440220 | + | 0.0440220i | ||||
\(79\) | 8.66025 | + | 5.00000i | 0.974355 | + | 0.562544i | 0.900561 | − | 0.434730i | \(-0.143156\pi\) |
0.0737937 | + | 0.997274i | \(0.476489\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.77492 | − | 3.07425i | −0.197213 | − | 0.341583i | ||||
\(82\) | 5.01910 | − | 1.34486i | 0.554267 | − | 0.148515i | ||||
\(83\) | 10.1347 | − | 10.1347i | 1.11242 | − | 1.11242i | 0.119602 | − | 0.992822i | \(-0.461838\pi\) |
0.992822 | − | 0.119602i | \(-0.0381618\pi\) | |||||||
\(84\) | −3.46410 | − | 0.274917i | −0.377964 | − | 0.0299959i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.13746 | − | 7.16629i | 0.446154 | − | 0.772761i | ||||
\(87\) | 0.773333 | − | 2.88612i | 0.0829100 | − | 0.309425i | ||||
\(88\) | 1.36525 | − | 5.09518i | 0.145536 | − | 0.543148i | ||||
\(89\) | 1.97014 | − | 3.41238i | 0.208834 | − | 0.361711i | −0.742513 | − | 0.669831i | \(-0.766366\pi\) |
0.951348 | + | 0.308120i | \(0.0996998\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | − | 0.476171i | 0.104828 | − | 0.0499162i | ||||
\(92\) | −2.12132 | + | 2.12132i | −0.221163 | + | 0.221163i | ||||
\(93\) | −4.39480 | + | 1.17758i | −0.455720 | + | 0.122110i | ||||
\(94\) | 6.30026 | + | 10.9124i | 0.649823 | + | 1.12553i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.13746 | + | 0.656712i | 0.116091 | + | 0.0670254i | ||||
\(97\) | −13.5129 | − | 13.5129i | −1.37203 | − | 1.37203i | −0.857438 | − | 0.514588i | \(-0.827945\pi\) |
−0.514588 | − | 0.857438i | \(-0.672055\pi\) | |||||||
\(98\) | −2.85554 | + | 6.39108i | −0.288453 | + | 0.645596i | ||||
\(99\) | − | 6.72508i | − | 0.675896i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.41238 | − | 1.97014i | 0.339544 | − | 0.196036i | −0.320526 | − | 0.947240i | \(-0.603860\pi\) |
0.660070 | + | 0.751204i | \(0.270526\pi\) | |||||||
\(102\) | 4.39480 | + | 1.17758i | 0.435150 | + | 0.116598i | ||||
\(103\) | −1.23651 | − | 4.61474i | −0.121837 | − | 0.454703i | 0.877870 | − | 0.478899i | \(-0.158964\pi\) |
−0.999707 | + | 0.0241959i | \(0.992297\pi\) | |||||||
\(104\) | −0.418627 | −0.0410497 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.82475 | −0.954264 | ||||||||
\(107\) | 1.76638 | + | 6.59220i | 0.170762 | + | 0.637292i | 0.997235 | + | 0.0743157i | \(0.0236773\pi\) |
−0.826473 | + | 0.562977i | \(0.809656\pi\) | |||||||
\(108\) | 5.42346 | + | 1.45321i | 0.521873 | + | 0.139835i | ||||
\(109\) | −7.64246 | + | 4.41238i | −0.732015 | + | 0.422629i | −0.819159 | − | 0.573567i | \(-0.805559\pi\) |
0.0871440 | + | 0.996196i | \(0.472226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 6.92820i | − | 0.657596i | ||||||
\(112\) | 2.01297 | − | 1.71696i | 0.190208 | − | 0.162237i | ||||
\(113\) | −4.24264 | − | 4.24264i | −0.399114 | − | 0.399114i | 0.478806 | − | 0.877920i | \(-0.341070\pi\) |
−0.877920 | + | 0.478806i | \(0.841070\pi\) | |||||||
\(114\) | −6.45203 | − | 3.72508i | −0.604288 | − | 0.348886i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.13746 | + | 1.97014i | 0.105610 | + | 0.182923i | ||||
\(117\) | −0.515529 | + | 0.138135i | −0.0476606 | + | 0.0127706i | ||||
\(118\) | 7.34847 | − | 7.34847i | 0.676481 | − | 0.676481i | ||||
\(119\) | 5.19615 | − | 7.54983i | 0.476331 | − | 0.692092i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.41238 | + | 14.5707i | −0.764761 | + | 1.32461i | ||||
\(122\) | 3.70954 | − | 13.8442i | 0.335846 | − | 1.25340i | ||||
\(123\) | 1.76638 | − | 6.59220i | 0.159269 | − | 0.594399i | ||||
\(124\) | 1.73205 | − | 3.00000i | 0.155543 | − | 0.269408i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.91238 | − | 2.77862i | 0.170368 | − | 0.247539i | ||||
\(127\) | −12.2152 | + | 12.2152i | −1.08392 | + | 1.08392i | −0.0877853 | + | 0.996139i | \(0.527979\pi\) |
−0.996139 | + | 0.0877853i | \(0.972021\pi\) | |||||||
\(128\) | −0.965926 | + | 0.258819i | −0.0853766 | + | 0.0228766i | ||||
\(129\) | −5.43424 | − | 9.41238i | −0.478458 | − | 0.828713i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.91238 | + | 4.56821i | 0.691307 | + | 0.399127i | 0.804102 | − | 0.594492i | \(-0.202647\pi\) |
−0.112794 | + | 0.993618i | \(0.535980\pi\) | |||||||
\(132\) | −4.89898 | − | 4.89898i | −0.426401 | − | 0.426401i | ||||
\(133\) | −11.4182 | + | 9.73914i | −0.990086 | + | 0.844491i | ||||
\(134\) | 3.72508i | 0.321798i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | + | 1.73205i | −0.257248 | + | 0.148522i | ||||
\(137\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(138\) | 1.01982 | + | 3.80601i | 0.0868126 | + | 0.323989i | ||||
\(139\) | −4.41644 | −0.374598 | −0.187299 | − | 0.982303i | \(-0.559973\pi\) | ||||
−0.187299 | + | 0.982303i | \(0.559973\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.5498 | 1.39375 | ||||||||
\(142\) | −1.55291 | − | 5.79555i | −0.130318 | − | 0.486352i | ||||
\(143\) | 2.13298 | + | 0.571530i | 0.178369 | + | 0.0477937i | ||||
\(144\) | −1.10411 | + | 0.637459i | −0.0920092 | + | 0.0531216i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.55505i | 0.790782i | ||||||||
\(147\) | 5.39432 | + | 7.44516i | 0.444916 | + | 0.614066i | ||||
\(148\) | 3.72993 | + | 3.72993i | 0.306598 | + | 0.306598i | ||||
\(149\) | 11.1066 | + | 6.41238i | 0.909885 | + | 0.525322i | 0.880394 | − | 0.474243i | \(-0.157278\pi\) |
0.0294908 | + | 0.999565i | \(0.490611\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | − | 1.73205i | −0.0813788 | − | 0.140952i | 0.822464 | − | 0.568818i | \(-0.192599\pi\) |
−0.903842 | + | 0.427865i | \(0.859266\pi\) | |||||||
\(152\) | 5.47904 | − | 1.46811i | 0.444409 | − | 0.119079i | ||||
\(153\) | −3.12290 | + | 3.12290i | −0.252471 | + | 0.252471i | ||||
\(154\) | −12.6005 | + | 6.00000i | −1.01538 | + | 0.483494i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.274917 | + | 0.476171i | −0.0220110 | + | 0.0381242i | ||||
\(157\) | −2.58138 | + | 9.63383i | −0.206016 | + | 0.768864i | 0.783121 | + | 0.621869i | \(0.213627\pi\) |
−0.989137 | + | 0.146994i | \(0.953040\pi\) | |||||||
\(158\) | −2.58819 | + | 9.65926i | −0.205905 | + | 0.768449i | ||||
\(159\) | −6.45203 | + | 11.1752i | −0.511679 | + | 0.886255i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.91238 | + | 0.627940i | 0.623583 | + | 0.0494886i | ||||
\(162\) | 2.51011 | − | 2.51011i | 0.197213 | − | 0.197213i | ||||
\(163\) | −11.5911 | + | 3.10583i | −0.907886 | + | 0.243267i | −0.682400 | − | 0.730979i | \(-0.739064\pi\) |
−0.225486 | + | 0.974246i | \(0.572397\pi\) | |||||||
\(164\) | 2.59808 | + | 4.50000i | 0.202876 | + | 0.351391i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.4124 | + | 7.16629i | 0.963387 | + | 0.556212i | ||||
\(167\) | −1.22474 | − | 1.22474i | −0.0947736 | − | 0.0947736i | 0.658130 | − | 0.752904i | \(-0.271348\pi\) |
−0.752904 | + | 0.658130i | \(0.771348\pi\) | |||||||
\(168\) | −0.631026 | − | 3.41722i | −0.0486847 | − | 0.263644i | ||||
\(169\) | 12.8248i | 0.986519i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.26287 | − | 3.61587i | 0.478934 | − | 0.276513i | ||||
\(172\) | 7.99296 | + | 2.14171i | 0.609457 | + | 0.163304i | ||||
\(173\) | 1.22162 | + | 4.55915i | 0.0928781 | + | 0.346626i | 0.996689 | − | 0.0813058i | \(-0.0259090\pi\) |
−0.903811 | + | 0.427932i | \(0.859242\pi\) | |||||||
\(174\) | 2.98793 | 0.226514 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.27492 | 0.397612 | ||||||||
\(177\) | −3.53275 | − | 13.1844i | −0.265538 | − | 0.991001i | ||||
\(178\) | 3.80601 | + | 1.01982i | 0.285273 | + | 0.0764386i | ||||
\(179\) | −8.50848 | + | 4.91238i | −0.635954 | + | 0.367168i | −0.783054 | − | 0.621953i | \(-0.786339\pi\) |
0.147100 | + | 0.989122i | \(0.453006\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.2608i | 1.58030i | 0.612913 | + | 0.790151i | \(0.289998\pi\) | ||||
−0.612913 | + | 0.790151i | \(0.710002\pi\) | |||||||
\(182\) | 0.718765 | + | 0.842684i | 0.0532784 | + | 0.0624639i | ||||
\(183\) | −13.3111 | − | 13.3111i | −0.983986 | − | 0.983986i | ||||
\(184\) | −2.59808 | − | 1.50000i | −0.191533 | − | 0.110581i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.27492 | − | 3.94027i | −0.166805 | − | 0.288915i | ||||
\(187\) | 17.6502 | − | 4.72936i | 1.29071 | − | 0.345845i | ||||
\(188\) | −8.90992 | + | 8.90992i | −0.649823 | + | 0.649823i | ||||
\(189\) | −6.38658 | − | 13.4124i | −0.464555 | − | 0.975607i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.54983 | + | 7.88054i | −0.329214 | + | 0.570216i | −0.982356 | − | 0.187019i | \(-0.940117\pi\) |
0.653142 | + | 0.757236i | \(0.273451\pi\) | |||||||
\(192\) | −0.339939 | + | 1.26867i | −0.0245330 | + | 0.0915584i | ||||
\(193\) | −2.73050 | + | 10.1904i | −0.196546 | + | 0.733518i | 0.795316 | + | 0.606195i | \(0.207305\pi\) |
−0.991861 | + | 0.127323i | \(0.959362\pi\) | |||||||
\(194\) | 9.55505 | − | 16.5498i | 0.686013 | − | 1.18821i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.91238 | − | 1.10411i | −0.493741 | − | 0.0788650i | ||||
\(197\) | −11.1898 | + | 11.1898i | −0.797239 | + | 0.797239i | −0.982659 | − | 0.185420i | \(-0.940635\pi\) |
0.185420 | + | 0.982659i | \(0.440635\pi\) | |||||||
\(198\) | 6.49593 | − | 1.74058i | 0.461646 | − | 0.123698i | ||||
\(199\) | 9.13642 | + | 15.8248i | 0.647664 | + | 1.12179i | 0.983679 | + | 0.179930i | \(0.0575873\pi\) |
−0.336015 | + | 0.941857i | \(0.609079\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.23713 | + | 2.44631i | 0.298864 | + | 0.172549i | ||||
\(202\) | 2.78619 | + | 2.78619i | 0.196036 | + | 0.196036i | ||||
\(203\) | 2.01286 | − | 5.67231i | 0.141275 | − | 0.398118i | ||||
\(204\) | 4.54983i | 0.318552i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.13746 | − | 2.38876i | 0.288270 | − | 0.166433i | ||||
\(207\) | −3.69443 | − | 0.989919i | −0.256780 | − | 0.0688041i | ||||
\(208\) | −0.108349 | − | 0.404362i | −0.00751262 | − | 0.0280375i | ||||
\(209\) | −29.9210 | −2.06968 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.82475 | −0.400992 | −0.200496 | − | 0.979694i | \(-0.564255\pi\) | ||||
−0.200496 | + | 0.979694i | \(0.564255\pi\) | |||||||
\(212\) | −2.54283 | − | 9.48998i | −0.174642 | − | 0.651775i | ||||
\(213\) | −7.61202 | − | 2.03963i | −0.521567 | − | 0.139753i | ||||
\(214\) | −5.91041 | + | 3.41238i | −0.404027 | + | 0.233265i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.61478i | 0.382037i | ||||||||
\(217\) | −9.01277 | + | 1.66430i | −0.611827 | + | 0.112980i | ||||
\(218\) | −6.24004 | − | 6.24004i | −0.422629 | − | 0.422629i | ||||
\(219\) | 10.8685 | + | 6.27492i | 0.734424 | + | 0.424020i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.725083 | − | 1.25588i | −0.0487743 | − | 0.0844796i | ||||
\(222\) | 6.69213 | − | 1.79315i | 0.449146 | − | 0.120348i | ||||
\(223\) | 6.16441 | − | 6.16441i | 0.412800 | − | 0.412800i | −0.469913 | − | 0.882713i | \(-0.655715\pi\) |
0.882713 | + | 0.469913i | \(0.155715\pi\) | |||||||
\(224\) | 2.17945 | + | 1.50000i | 0.145621 | + | 0.100223i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | − | 5.19615i | 0.199557 | − | 0.345643i | ||||
\(227\) | 0.896575 | − | 3.34607i | 0.0595078 | − | 0.222086i | −0.929768 | − | 0.368146i | \(-0.879993\pi\) |
0.989276 | + | 0.146060i | \(0.0466593\pi\) | |||||||
\(228\) | 1.92824 | − | 7.19631i | 0.127701 | − | 0.476587i | ||||
\(229\) | −6.92820 | + | 12.0000i | −0.457829 | + | 0.792982i | −0.998846 | − | 0.0480291i | \(-0.984706\pi\) |
0.541017 | + | 0.841011i | \(0.318039\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.45017 | + | 18.2728i | −0.0954139 | + | 1.20227i | ||||
\(232\) | −1.60861 | + | 1.60861i | −0.105610 | + | 0.105610i | ||||
\(233\) | 24.7755 | − | 6.63858i | 1.62310 | − | 0.434908i | 0.671188 | − | 0.741287i | \(-0.265784\pi\) |
0.951910 | + | 0.306379i | \(0.0991174\pi\) | |||||||
\(234\) | −0.266857 | − | 0.462210i | −0.0174450 | − | 0.0302156i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.00000 | + | 5.19615i | 0.585850 | + | 0.338241i | ||||
\(237\) | 9.28731 | + | 9.28731i | 0.603276 | + | 0.603276i | ||||
\(238\) | 8.63744 | + | 3.06506i | 0.559882 | + | 0.198678i | ||||
\(239\) | − | 4.54983i | − | 0.294304i | −0.989114 | − | 0.147152i | \(-0.952989\pi\) | ||
0.989114 | − | 0.147152i | \(-0.0470107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.91238 | − | 4.56821i | 0.509681 | − | 0.294264i | −0.223022 | − | 0.974814i | \(-0.571592\pi\) |
0.732702 | + | 0.680549i | \(0.238259\pi\) | |||||||
\(242\) | −16.2515 | − | 4.35457i | −1.04468 | − | 0.279922i | ||||
\(243\) | 3.15291 | + | 11.7668i | 0.202259 | + | 0.754841i | ||||
\(244\) | 14.3326 | 0.917549 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.82475 | 0.435130 | ||||||||
\(247\) | 0.614588 | + | 2.29367i | 0.0391053 | + | 0.145943i | ||||
\(248\) | 3.34607 | + | 0.896575i | 0.212475 | + | 0.0569326i | ||||
\(249\) | 16.3027 | − | 9.41238i | 1.03314 | − | 0.596485i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 19.5287i | − | 1.23264i | −0.787495 | − | 0.616321i | \(-0.788622\pi\) | ||
0.787495 | − | 0.616321i | \(-0.211378\pi\) | |||||||
\(252\) | 3.17890 | + | 1.12805i | 0.200252 | + | 0.0710607i | ||||
\(253\) | 11.1898 | + | 11.1898i | 0.703496 | + | 0.703496i | ||||
\(254\) | −14.9605 | − | 8.63746i | −0.938706 | − | 0.541962i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −17.6502 | + | 4.72936i | −1.10099 | + | 0.295009i | −0.763168 | − | 0.646200i | \(-0.776357\pi\) |
−0.337823 | + | 0.941210i | \(0.609690\pi\) | |||||||
\(258\) | 7.68517 | − | 7.68517i | 0.478458 | − | 0.478458i | ||||
\(259\) | 1.10411 | − | 13.9124i | 0.0686061 | − | 0.864473i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.45017 | + | 2.51176i | −0.0897630 | + | 0.155474i | ||||
\(262\) | −2.36468 | + | 8.82511i | −0.146090 | + | 0.545217i | ||||
\(263\) | 4.87220 | − | 18.1833i | 0.300433 | − | 1.12123i | −0.636373 | − | 0.771382i | \(-0.719566\pi\) |
0.936806 | − | 0.349850i | \(-0.113767\pi\) | |||||||
\(264\) | 3.46410 | − | 6.00000i | 0.213201 | − | 0.369274i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.3625 | − | 8.50848i | −0.757996 | − | 0.521689i | ||||
\(267\) | 3.65945 | − | 3.65945i | 0.223955 | − | 0.223955i | ||||
\(268\) | −3.59815 | + | 0.964122i | −0.219792 | + | 0.0588931i | ||||
\(269\) | −3.22602 | − | 5.58762i | −0.196694 | − | 0.340683i | 0.750761 | − | 0.660574i | \(-0.229687\pi\) |
−0.947454 | + | 0.319891i | \(0.896354\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.82475 | − | 3.94027i | −0.414574 | − | 0.239354i | 0.278179 | − | 0.960529i | \(-0.410269\pi\) |
−0.692753 | + | 0.721175i | \(0.743602\pi\) | |||||||
\(272\) | −2.44949 | − | 2.44949i | −0.148522 | − | 0.148522i | ||||
\(273\) | 1.43054 | − | 0.264164i | 0.0865802 | − | 0.0159879i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.41238 | + | 1.97014i | −0.205401 | + | 0.118588i | ||||
\(277\) | 14.5852 | + | 3.90808i | 0.876337 | + | 0.234814i | 0.668826 | − | 0.743419i | \(-0.266797\pi\) |
0.207511 | + | 0.978233i | \(0.433464\pi\) | |||||||
\(278\) | −1.14306 | − | 4.26596i | −0.0685562 | − | 0.255855i | ||||
\(279\) | 4.41644 | 0.264406 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.37459 | −0.499586 | −0.249793 | − | 0.968299i | \(-0.580363\pi\) | ||||
−0.249793 | + | 0.968299i | \(0.580363\pi\) | |||||||
\(282\) | 4.28341 | + | 15.9859i | 0.255073 | + | 0.951947i | ||||
\(283\) | −6.80330 | − | 1.82294i | −0.404414 | − | 0.108362i | 0.0508774 | − | 0.998705i | \(-0.483798\pi\) |
−0.455291 | + | 0.890343i | \(0.650465\pi\) | |||||||
\(284\) | 5.19615 | − | 3.00000i | 0.308335 | − | 0.178017i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.20822i | 0.130575i | ||||||||
\(287\) | 4.59759 | − | 12.9562i | 0.271387 | − | 0.764778i | ||||
\(288\) | −0.901503 | − | 0.901503i | −0.0531216 | − | 0.0531216i | ||||
\(289\) | 4.33013 | + | 2.50000i | 0.254713 | + | 0.147059i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.5498 | − | 21.7370i | −0.735684 | − | 1.27424i | ||||
\(292\) | −9.22947 | + | 2.47303i | −0.540114 | + | 0.144723i | ||||
\(293\) | −3.33753 | + | 3.33753i | −0.194981 | + | 0.194981i | −0.797844 | − | 0.602864i | \(-0.794026\pi\) |
0.602864 | + | 0.797844i | \(0.294026\pi\) | |||||||
\(294\) | −5.79532 | + | 7.13746i | −0.337990 | + | 0.416265i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.63746 | + | 4.56821i | −0.153299 | + | 0.265522i | ||||
\(297\) | 7.66557 | − | 28.6083i | 0.444802 | − | 1.66002i | ||||
\(298\) | −3.31929 | + | 12.3878i | −0.192281 | + | 0.717604i | ||||
\(299\) | 0.627940 | − | 1.08762i | 0.0363147 | − | 0.0628989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.41238 | − | 19.7668i | −0.542520 | − | 1.13934i | ||||
\(302\) | 1.41421 | − | 1.41421i | 0.0813788 | − | 0.0813788i | ||||
\(303\) | 4.99891 | − | 1.33945i | 0.287180 | − | 0.0769496i | ||||
\(304\) | 2.83616 | + | 4.91238i | 0.162665 | + | 0.281744i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.82475 | − | 2.20822i | −0.218646 | − | 0.126236i | ||||
\(307\) | −2.19417 | − | 2.19417i | −0.125228 | − | 0.125228i | 0.641715 | − | 0.766943i | \(-0.278223\pi\) |
−0.766943 | + | 0.641715i | \(0.778223\pi\) | |||||||
\(308\) | −9.05681 | − | 10.6183i | −0.516060 | − | 0.605031i | ||||
\(309\) | − | 6.27492i | − | 0.356968i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.6495 | − | 13.0767i | 1.28434 | − | 0.741511i | 0.306698 | − | 0.951807i | \(-0.400776\pi\) |
0.977638 | + | 0.210296i | \(0.0674426\pi\) | |||||||
\(312\) | −0.531099 | − | 0.142308i | −0.0300676 | − | 0.00805658i | ||||
\(313\) | −5.16276 | − | 19.2677i | −0.291816 | − | 1.08907i | −0.943713 | − | 0.330765i | \(-0.892693\pi\) |
0.651897 | − | 0.758308i | \(-0.273974\pi\) | |||||||
\(314\) | −9.97368 | −0.562847 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | 4.65874 | + | 17.3867i | 0.261661 | + | 0.976532i | 0.964262 | + | 0.264949i | \(0.0853551\pi\) |
−0.702601 | + | 0.711584i | \(0.747978\pi\) | |||||||
\(318\) | −12.4644 | − | 3.33982i | −0.698967 | − | 0.187288i | ||||
\(319\) | 10.3923 | − | 6.00000i | 0.581857 | − | 0.335936i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.96379i | 0.500310i | ||||||||
\(322\) | 1.44133 | + | 7.80529i | 0.0803222 | + | 0.434972i | ||||
\(323\) | 13.8943 | + | 13.8943i | 0.773099 | + | 0.773099i | ||||
\(324\) | 3.07425 | + | 1.77492i | 0.170791 | + | 0.0986065i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.00000 | − | 10.3923i | −0.332309 | − | 0.575577i | ||||
\(327\) | −11.1957 | + | 2.99988i | −0.619124 | + | 0.165894i | ||||
\(328\) | −3.67423 | + | 3.67423i | −0.202876 | + | 0.202876i | ||||
\(329\) | 33.2334 | + | 2.63746i | 1.83221 | + | 0.145408i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.08762 | + | 5.34792i | −0.169711 | + | 0.293948i | −0.938318 | − | 0.345773i | \(-0.887617\pi\) |
0.768607 | + | 0.639721i | \(0.220950\pi\) | |||||||
\(332\) | −3.70954 | + | 13.8442i | −0.203588 | + | 0.759800i | ||||
\(333\) | −1.74058 | + | 6.49593i | −0.0953832 | + | 0.355975i | ||||
\(334\) | 0.866025 | − | 1.50000i | 0.0473868 | − | 0.0820763i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.13746 | − | 1.49397i | 0.171162 | − | 0.0815025i | ||||
\(337\) | 25.5968 | − | 25.5968i | 1.39435 | − | 1.39435i | 0.579065 | − | 0.815281i | \(-0.303418\pi\) |
0.815281 | − | 0.579065i | \(-0.196582\pi\) | |||||||
\(338\) | −12.3878 | + | 3.31929i | −0.673805 | + | 0.180546i | ||||
\(339\) | −3.94027 | − | 6.82475i | −0.214006 | − | 0.370670i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.8248 | − | 9.13642i | −0.856958 | − | 0.494765i | ||||
\(342\) | 5.11361 | + | 5.11361i | 0.276513 | + | 0.276513i | ||||
\(343\) | 9.64572 | + | 15.8101i | 0.520820 | + | 0.853667i | ||||
\(344\) | 8.27492i | 0.446154i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.08762 | + | 2.35999i | −0.219752 | + | 0.126874i | ||||
\(347\) | −4.99891 | − | 1.33945i | −0.268355 | − | 0.0719056i | 0.122132 | − | 0.992514i | \(-0.461027\pi\) |
−0.390487 | + | 0.920608i | \(0.627694\pi\) | |||||||
\(348\) | 0.773333 | + | 2.88612i | 0.0414550 | + | 0.154712i | ||||
\(349\) | 3.94027 | 0.210918 | 0.105459 | − | 0.994424i | \(-0.466369\pi\) | ||||
0.105459 | + | 0.994424i | \(0.466369\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.35050 | −0.125460 | ||||||||
\(352\) | 1.36525 | + | 5.09518i | 0.0727680 | + | 0.271574i | ||||
\(353\) | 0.919891 | + | 0.246484i | 0.0489609 | + | 0.0131190i | 0.283216 | − | 0.959056i | \(-0.408599\pi\) |
−0.234255 | + | 0.972175i | \(0.575265\pi\) | |||||||
\(354\) | 11.8208 | − | 6.82475i | 0.628269 | − | 0.362731i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.94027i | 0.208834i | ||||||||
\(357\) | 9.15869 | − | 7.81187i | 0.484729 | − | 0.413448i | ||||
\(358\) | −6.94715 | − | 6.94715i | −0.367168 | − | 0.367168i | ||||
\(359\) | −11.8208 | − | 6.82475i | −0.623879 | − | 0.360197i | 0.154499 | − | 0.987993i | \(-0.450624\pi\) |
−0.778378 | + | 0.627796i | \(0.783957\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.58762 | − | 11.4101i | −0.346717 | − | 0.600532i | ||||
\(362\) | −20.5363 | + | 5.50269i | −1.07937 | + | 0.289215i | ||||
\(363\) | −15.6257 | + | 15.6257i | −0.820135 | + | 0.820135i | ||||
\(364\) | −0.627940 | + | 0.912376i | −0.0329130 | + | 0.0478215i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.41238 | − | 16.3027i | 0.491993 | − | 0.852156i | ||||
\(367\) | −1.56156 | + | 5.82782i | −0.0815128 | + | 0.304210i | −0.994631 | − | 0.103485i | \(-0.967001\pi\) |
0.913118 | + | 0.407695i | \(0.133667\pi\) | |||||||
\(368\) | 0.776457 | − | 2.89778i | 0.0404756 | − | 0.151057i | ||||
\(369\) | −3.31233 | + | 5.73713i | −0.172433 | + | 0.298663i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.7371 | + | 21.4125i | −0.765114 | + | 1.11168i | ||||
\(372\) | 3.21722 | − | 3.21722i | 0.166805 | − | 0.166805i | ||||
\(373\) | −21.7815 | + | 5.83633i | −1.12780 | + | 0.302194i | −0.774037 | − | 0.633141i | \(-0.781765\pi\) |
−0.353765 | + | 0.935334i | \(0.615099\pi\) | |||||||
\(374\) | 9.13642 | + | 15.8248i | 0.472433 | + | 0.818278i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.9124 | − | 6.30026i | −0.562763 | − | 0.324911i | ||||
\(377\) | −0.673407 | − | 0.673407i | −0.0346822 | − | 0.0346822i | ||||
\(378\) | 11.3024 | − | 9.64034i | 0.581332 | − | 0.495846i | ||||
\(379\) | − | 25.8248i | − | 1.32653i | −0.748385 | − | 0.663264i | \(-0.769171\pi\) | ||
0.748385 | − | 0.663264i | \(-0.230829\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.6495 | + | 11.3446i | −1.00667 | + | 0.581204i | ||||
\(382\) | −8.78961 | − | 2.35517i | −0.449715 | − | 0.120501i | ||||
\(383\) | 5.42413 | + | 20.2431i | 0.277160 | + | 1.03438i | 0.954380 | + | 0.298595i | \(0.0965180\pi\) |
−0.677220 | + | 0.735781i | \(0.736815\pi\) | |||||||
\(384\) | −1.31342 | −0.0670254 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.5498 | −0.536972 | ||||||||
\(387\) | 2.73050 | + | 10.1904i | 0.138799 | + | 0.518005i | ||||
\(388\) | 18.4589 | + | 4.94606i | 0.937111 | + | 0.251098i | ||||
\(389\) | 2.68439 | − | 1.54983i | 0.136104 | − | 0.0785797i | −0.430402 | − | 0.902637i | \(-0.641628\pi\) |
0.566506 | + | 0.824058i | \(0.308295\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.3923i | − | 0.525561i | ||||||
\(392\) | −0.722565 | − | 6.96261i | −0.0364951 | − | 0.351665i | ||||
\(393\) | 8.48528 | + | 8.48528i | 0.428026 | + | 0.428026i | ||||
\(394\) | −13.7046 | − | 7.91238i | −0.690430 | − | 0.398620i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.36254 | + | 5.82409i | 0.168974 | + | 0.292672i | ||||
\(397\) | 1.61745 | − | 0.433394i | 0.0811775 | − | 0.0217514i | −0.218002 | − | 0.975948i | \(-0.569954\pi\) |
0.299179 | + | 0.954197i | \(0.403287\pi\) | |||||||
\(398\) | −12.9209 | + | 12.9209i | −0.647664 | + | 0.647664i | ||||
\(399\) | −17.7967 | + | 8.47425i | −0.890948 | + | 0.424243i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.04983 | − | 15.6748i | 0.451927 | − | 0.782761i | −0.546579 | − | 0.837408i | \(-0.684070\pi\) |
0.998506 | + | 0.0546470i | \(0.0174034\pi\) | |||||||
\(402\) | −1.26630 | + | 4.72590i | −0.0631574 | + | 0.235707i | ||||
\(403\) | −0.375330 | + | 1.40075i | −0.0186965 | + | 0.0697764i | ||||
\(404\) | −1.97014 | + | 3.41238i | −0.0980179 | + | 0.169772i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | + | 0.476171i | 0.297775 | + | 0.0236319i | ||||
\(407\) | 19.6751 | − | 19.6751i | 0.975257 | − | 0.975257i | ||||
\(408\) | −4.39480 | + | 1.17758i | −0.217575 | + | 0.0582991i | ||||
\(409\) | −8.89834 | − | 15.4124i | −0.439995 | − | 0.762093i | 0.557694 | − | 0.830047i | \(-0.311686\pi\) |
−0.997688 | + | 0.0679538i | \(0.978353\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.37822 | + | 3.37822i | 0.166433 | + | 0.166433i | ||||
\(413\) | −4.99291 | − | 27.0383i | −0.245685 | − | 1.33047i | ||||
\(414\) | − | 3.82475i | − | 0.187976i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.362541 | − | 0.209313i | 0.0177751 | − | 0.0102624i | ||||
\(417\) | −5.60301 | − | 1.50132i | −0.274381 | − | 0.0735200i | ||||
\(418\) | −7.74413 | − | 28.9015i | −0.378778 | − | 1.41362i | ||||
\(419\) | 27.4093 | 1.33903 | 0.669515 | − | 0.742798i | \(-0.266502\pi\) | ||||
0.669515 | + | 0.742798i | \(0.266502\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.8248 | 1.69725 | 0.848627 | − | 0.528991i | \(-0.177430\pi\) | ||||
0.848627 | + | 0.528991i | \(0.177430\pi\) | |||||||
\(422\) | −1.50756 | − | 5.62628i | −0.0733867 | − | 0.273883i | ||||
\(423\) | −15.5172 | − | 4.15783i | −0.754474 | − | 0.202161i | ||||
\(424\) | 8.50848 | − | 4.91238i | 0.413209 | − | 0.238566i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 7.88054i | − | 0.381814i | ||||||
\(427\) | −24.6084 | − | 28.8511i | −1.19089 | − | 1.39620i | ||||
\(428\) | −4.82583 | − | 4.82583i | −0.233265 | − | 0.233265i | ||||
\(429\) | 2.51176 | + | 1.45017i | 0.121269 | + | 0.0700147i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.2749 | + | 29.9210i | 0.832103 | + | 1.44125i | 0.896367 | + | 0.443313i | \(0.146197\pi\) |
−0.0642636 | + | 0.997933i | \(0.520470\pi\) | |||||||
\(432\) | −5.42346 | + | 1.45321i | −0.260936 | + | 0.0699177i | ||||
\(433\) | 7.94050 | − | 7.94050i | 0.381596 | − | 0.381596i | −0.490081 | − | 0.871677i | \(-0.663033\pi\) |
0.871677 | + | 0.490081i | \(0.163033\pi\) | |||||||
\(434\) | −3.94027 | − | 8.27492i | −0.189139 | − | 0.397209i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.41238 | − | 7.64246i | 0.211314 | − | 0.366007i | ||||
\(437\) | −4.40432 | + | 16.4371i | −0.210687 | + | 0.786295i | ||||
\(438\) | −3.24814 | + | 12.1222i | −0.155202 | + | 0.579222i | ||||
\(439\) | −10.3923 | + | 18.0000i | −0.495998 | + | 0.859093i | −0.999989 | − | 0.00461537i | \(-0.998531\pi\) |
0.503992 | + | 0.863708i | \(0.331864\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.18729 | − | 8.33585i | −0.151776 | − | 0.396945i | ||||
\(442\) | 1.02542 | − | 1.02542i | 0.0487743 | − | 0.0487743i | ||||
\(443\) | 10.7945 | − | 2.89237i | 0.512860 | − | 0.137421i | 0.00689820 | − | 0.999976i | \(-0.497804\pi\) |
0.505962 | + | 0.862556i | \(0.331138\pi\) | |||||||
\(444\) | 3.46410 | + | 6.00000i | 0.164399 | + | 0.284747i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.54983 | + | 4.35890i | 0.357495 | + | 0.206400i | ||||
\(447\) | 11.9107 | + | 11.9107i | 0.563359 | + | 0.563359i | ||||
\(448\) | −0.884806 | + | 2.49342i | −0.0418031 | + | 0.117803i | ||||
\(449\) | 22.4502i | 1.05949i | 0.848157 | + | 0.529744i | \(0.177712\pi\) | ||||
−0.848157 | + | 0.529744i | \(0.822288\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.7371 | − | 13.7046i | 1.11774 | − | 0.645326i | ||||
\(452\) | 5.79555 | + | 1.55291i | 0.272600 | + | 0.0730429i | ||||
\(453\) | −0.679878 | − | 2.53734i | −0.0319435 | − | 0.119215i | ||||
\(454\) | 3.46410 | 0.162578 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.45017 | 0.348886 | ||||||||
\(457\) | −8.94216 | − | 33.3726i | −0.418296 | − | 1.56110i | −0.778140 | − | 0.628091i | \(-0.783837\pi\) |
0.359844 | − | 0.933013i | \(-0.382830\pi\) | |||||||
\(458\) | −13.3843 | − | 3.58630i | −0.625405 | − | 0.167577i | ||||
\(459\) | −16.8443 | + | 9.72508i | −0.786226 | + | 0.453928i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.7611i | 0.734067i | 0.930208 | + | 0.367034i | \(0.119627\pi\) | ||||
−0.930208 | + | 0.367034i | \(0.880373\pi\) | |||||||
\(462\) | −18.0255 | + | 3.32861i | −0.838624 | + | 0.154861i | ||||
\(463\) | 22.3091 | + | 22.3091i | 1.03679 | + | 1.03679i | 0.999297 | + | 0.0374951i | \(0.0119379\pi\) |
0.0374951 | + | 0.999297i | \(0.488062\pi\) | |||||||
\(464\) | −1.97014 | − | 1.13746i | −0.0914613 | − | 0.0528052i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.8248 | + | 22.2131i | 0.594095 | + | 1.02900i | ||||
\(467\) | −12.9243 | + | 3.46306i | −0.598066 | + | 0.160251i | −0.545137 | − | 0.838347i | \(-0.683522\pi\) |
−0.0529290 | + | 0.998598i | \(0.516856\pi\) | |||||||
\(468\) | 0.377393 | − | 0.377393i | 0.0174450 | − | 0.0174450i | ||||
\(469\) | 8.11863 | + | 5.58762i | 0.374883 | + | 0.258013i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.54983 | + | 11.3446i | −0.301800 | + | 0.522734i | ||||
\(472\) | −2.68973 | + | 10.0382i | −0.123805 | + | 0.462045i | ||||
\(473\) | 11.2973 | − | 42.1622i | 0.519451 | − | 1.93862i | ||||
\(474\) | −6.56712 | + | 11.3746i | −0.301638 | + | 0.522452i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.725083 | + | 9.13642i | −0.0332341 | + | 0.418767i | ||||
\(477\) | 8.85704 | − | 8.85704i | 0.405536 | − | 0.405536i | ||||
\(478\) | 4.39480 | − | 1.17758i | 0.201014 | − | 0.0538614i | ||||
\(479\) | −3.94027 | − | 6.82475i | −0.180036 | − | 0.311831i | 0.761857 | − | 0.647745i | \(-0.224288\pi\) |
−0.941892 | + | 0.335915i | \(0.890955\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.91238 | − | 1.10411i | −0.0871968 | − | 0.0503431i | ||||
\(482\) | 6.46043 | + | 6.46043i | 0.294264 | + | 0.294264i | ||||
\(483\) | 9.82473 | + | 3.48638i | 0.447041 | + | 0.158636i | ||||
\(484\) | − | 16.8248i | − | 0.764761i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10.5498 | + | 6.09095i | −0.478550 | + | 0.276291i | ||||
\(487\) | −8.78961 | − | 2.35517i | −0.398295 | − | 0.106723i | 0.0541110 | − | 0.998535i | \(-0.482768\pi\) |
−0.452406 | + | 0.891812i | \(0.649434\pi\) | |||||||
\(488\) | 3.70954 | + | 13.8442i | 0.167923 | + | 0.626698i | ||||
\(489\) | −15.7611 | −0.712741 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.4502 | −0.877774 | −0.438887 | − | 0.898542i | \(-0.644627\pi\) | ||||
−0.438887 | + | 0.898542i | \(0.644627\pi\) | |||||||
\(492\) | 1.76638 | + | 6.59220i | 0.0796344 | + | 0.297200i | ||||
\(493\) | −7.61202 | − | 2.03963i | −0.342828 | − | 0.0918605i | ||||
\(494\) | −2.05645 | + | 1.18729i | −0.0925241 | + | 0.0534188i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.46410i | 0.155543i | ||||||||
\(497\) | −14.9605 | − | 5.30883i | −0.671070 | − | 0.238134i | ||||
\(498\) | 13.3111 | + | 13.3111i | 0.596485 | + | 0.596485i | ||||
\(499\) | −3.46410 | − | 2.00000i | −0.155074 | − | 0.0895323i | 0.420455 | − | 0.907314i | \(-0.361871\pi\) |
−0.575529 | + | 0.817781i | \(0.695204\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.13746 | − | 1.97014i | −0.0508179 | − | 0.0880192i | ||||
\(502\) | 18.8633 | − | 5.05441i | 0.841910 | − | 0.225589i | ||||
\(503\) | −15.0336 | + | 15.0336i | −0.670317 | + | 0.670317i | −0.957789 | − | 0.287472i | \(-0.907185\pi\) |
0.287472 | + | 0.957789i | \(0.407185\pi\) | |||||||
\(504\) | −0.266857 | + | 3.36254i | −0.0118868 | + | 0.149779i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.91238 | + | 13.7046i | −0.351748 | + | 0.609245i | ||||
\(507\) | −4.35964 | + | 16.2704i | −0.193618 | + | 0.722593i | ||||
\(508\) | 4.47108 | − | 16.6863i | 0.198372 | − | 0.740334i | ||||
\(509\) | −0.714256 | + | 1.23713i | −0.0316588 | + | 0.0548347i | −0.881421 | − | 0.472332i | \(-0.843412\pi\) |
0.849762 | + | 0.527167i | \(0.176746\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.8248 | + | 14.3326i | 0.921233 | + | 0.634036i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 30.7636 | − | 8.24309i | 1.35825 | − | 0.363941i | ||||
\(514\) | −9.13642 | − | 15.8248i | −0.402990 | − | 0.698000i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.41238 | + | 5.43424i | 0.414357 | + | 0.239229i | ||||
\(517\) | 46.9991 | + | 46.9991i | 2.06702 | + | 2.06702i | ||||
\(518\) | 13.7241 | − | 2.53430i | 0.603002 | − | 0.111351i | ||||
\(519\) | 6.19934i | 0.272121i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.7371 | + | 13.7046i | −1.03994 | + | 0.600411i | −0.919817 | − | 0.392348i | \(-0.871663\pi\) |
−0.120125 | + | 0.992759i | \(0.538330\pi\) | |||||||
\(522\) | −2.80150 | − | 0.750661i | −0.122619 | − | 0.0328555i | ||||
\(523\) | −8.28588 | − | 30.9233i | −0.362316 | − | 1.35218i | −0.871023 | − | 0.491242i | \(-0.836543\pi\) |
0.508707 | − | 0.860940i | \(-0.330124\pi\) | |||||||
\(524\) | −9.13642 | −0.399127 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.8248 | 0.820798 | ||||||||
\(527\) | 3.10583 | + | 11.5911i | 0.135292 | + | 0.504917i | ||||
\(528\) | 6.69213 | + | 1.79315i | 0.291238 | + | 0.0780369i | ||||
\(529\) | −12.1244 | + | 7.00000i | −0.527146 | + | 0.304348i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.2493i | 0.574972i | ||||||||
\(532\) | 5.01890 | − | 14.1435i | 0.217597 | − | 0.613197i | ||||
\(533\) | −1.53813 | − | 1.53813i | −0.0666239 | − | 0.0666239i | ||||
\(534\) | 4.48190 | + | 2.58762i | 0.193951 | + | 0.111977i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.86254 | − | 3.22602i | −0.0804495 | − | 0.139343i | ||||
\(537\) | −12.4644 | + | 3.33982i | −0.537877 | + | 0.144124i | ||||
\(538\) | 4.56228 | − | 4.56228i | 0.196694 | − | 0.196694i | ||||
\(539\) | −5.82409 | + | 36.4622i | −0.250861 | + | 1.57054i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.58762 | − | 7.94600i | 0.197237 | − | 0.341625i | −0.750394 | − | 0.660990i | \(-0.770136\pi\) |
0.947632 | + | 0.319365i | \(0.103470\pi\) | |||||||
\(542\) | 2.03963 | − | 7.61202i | 0.0876098 | − | 0.326964i | ||||
\(543\) | −7.22737 | + | 26.9729i | −0.310156 | + | 1.15752i | ||||
\(544\) | 1.73205 | − | 3.00000i | 0.0742611 | − | 0.128624i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.625414 | + | 1.31342i | 0.0267652 | + | 0.0562094i | ||||
\(547\) | −9.06847 | + | 9.06847i | −0.387740 | + | 0.387740i | −0.873881 | − | 0.486141i | \(-0.838404\pi\) |
0.486141 | + | 0.873881i | \(0.338404\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.13642 | + | 15.8248i | 0.389933 | + | 0.675384i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.1752 | + | 6.45203i | 0.476082 | + | 0.274866i | ||||
\(552\) | −2.78619 | − | 2.78619i | −0.118588 | − | 0.118588i | ||||
\(553\) | 17.1696 | + | 20.1297i | 0.730125 | + | 0.856003i | ||||
\(554\) | 15.0997i | 0.641523i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.82475 | − | 2.20822i | 0.162206 | − | 0.0936494i | ||||
\(557\) | 19.4878 | + | 5.22174i | 0.825724 | + | 0.221252i | 0.646848 | − | 0.762619i | \(-0.276087\pi\) |
0.178877 | + | 0.983871i | \(0.442754\pi\) | |||||||
\(558\) | 1.14306 | + | 4.26596i | 0.0483896 | + | 0.180592i | ||||
\(559\) | −3.46410 | −0.146516 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | −2.16750 | − | 8.08923i | −0.0914306 | − | 0.341224i | ||||
\(563\) | 6.23218 | + | 1.66991i | 0.262655 | + | 0.0703783i | 0.387743 | − | 0.921767i | \(-0.373255\pi\) |
−0.125088 | + | 0.992146i | \(0.539921\pi\) | |||||||
\(564\) | −14.3326 | + | 8.27492i | −0.603510 | + | 0.348437i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 7.04329i | − | 0.296052i | ||||||
\(567\) | −1.70549 | − | 9.23583i | −0.0716240 | − | 0.387868i | ||||
\(568\) | 4.24264 | + | 4.24264i | 0.178017 | + | 0.178017i | ||||
\(569\) | −8.50848 | − | 4.91238i | −0.356694 | − | 0.205938i | 0.310935 | − | 0.950431i | \(-0.399358\pi\) |
−0.667630 | + | 0.744494i | \(0.732691\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.8248 | + | 25.6772i | 0.620397 | + | 1.07456i | 0.989412 | + | 0.145135i | \(0.0463617\pi\) |
−0.369015 | + | 0.929423i | \(0.620305\pi\) | |||||||
\(572\) | −2.13298 | + | 0.571530i | −0.0891843 | + | 0.0238969i | ||||
\(573\) | −8.45115 | + | 8.45115i | −0.353052 | + | 0.353052i | ||||
\(574\) | 13.7046 | + | 1.08762i | 0.572020 | + | 0.0453966i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.637459 | − | 1.10411i | 0.0265608 | − | 0.0460046i | ||||
\(577\) | −5.81285 | + | 21.6938i | −0.241992 | + | 0.903126i | 0.732880 | + | 0.680358i | \(0.238176\pi\) |
−0.974871 | + | 0.222768i | \(0.928491\pi\) | |||||||
\(578\) | −1.29410 | + | 4.82963i | −0.0538273 | + | 0.200886i | ||||
\(579\) | −6.92820 | + | 12.0000i | −0.287926 | + | 0.498703i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34.2371 | − | 16.3027i | 1.42040 | − | 0.676351i | ||||
\(582\) | 17.7481 | − | 17.7481i | 0.735684 | − | 0.735684i | ||||
\(583\) | −50.0589 | + | 13.4132i | −2.07323 | + | 0.555519i | ||||
\(584\) | −4.77753 | − | 8.27492i | −0.197695 | − | 0.342419i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.08762 | − | 2.35999i | −0.168858 | − | 0.0974903i | ||||
\(587\) | 7.34847 | + | 7.34847i | 0.303304 | + | 0.303304i | 0.842305 | − | 0.539001i | \(-0.181198\pi\) |
−0.539001 | + | 0.842305i | \(0.681198\pi\) | |||||||
\(588\) | −8.39419 | − | 3.75054i | −0.346171 | − | 0.154670i | ||||
\(589\) | − | 19.6495i | − | 0.809644i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0000 | + | 10.3923i | −0.740421 | + | 0.427482i | ||||
\(592\) | −5.09518 | − | 1.36525i | −0.209411 | − | 0.0561114i | ||||
\(593\) | −8.56215 | − | 31.9544i | −0.351605 | − | 1.31221i | −0.884703 | − | 0.466155i | \(-0.845639\pi\) |
0.533098 | − | 0.846054i | \(-0.321028\pi\) | |||||||
\(594\) | 29.6175 | 1.21522 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.8248 | −0.525322 | ||||||||
\(597\) | 6.21166 | + | 23.1822i | 0.254226 | + | 0.948785i | ||||
\(598\) | 1.21309 | + | 0.325046i | 0.0496068 | + | 0.0132921i | ||||
\(599\) | 2.51176 | − | 1.45017i | 0.102628 | − | 0.0592522i | −0.447808 | − | 0.894130i | \(-0.647795\pi\) |
0.550435 | + | 0.834878i | \(0.314462\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.92820i | 0.282607i | 0.989966 | + | 0.141304i | \(0.0451294\pi\) | ||||
−0.989966 | + | 0.141304i | \(0.954871\pi\) | |||||||
\(602\) | 16.6572 | − | 14.2077i | 0.678896 | − | 0.579062i | ||||
\(603\) | −3.35817 | − | 3.35817i | −0.136755 | − | 0.136755i | ||||
\(604\) | 1.73205 | + | 1.00000i | 0.0704761 | + | 0.0406894i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.58762 | + | 4.48190i | 0.105115 | + | 0.182065i | ||||
\(607\) | −21.0519 | + | 5.64083i | −0.854469 | + | 0.228954i | −0.659360 | − | 0.751827i | \(-0.729173\pi\) |
−0.195109 | + | 0.980782i | \(0.562506\pi\) | |||||||
\(608\) | −4.01094 | + | 4.01094i | −0.162665 | + | 0.162665i | ||||
\(609\) | 4.48190 | − | 6.51204i | 0.181616 | − | 0.263881i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.63746 | − | 4.56821i | 0.106700 | − | 0.184810i | ||||
\(612\) | 1.14306 | − | 4.26596i | 0.0462054 | − | 0.172441i | ||||
\(613\) | 3.66882 | − | 13.6922i | 0.148182 | − | 0.553024i | −0.851411 | − | 0.524500i | \(-0.824252\pi\) |
0.999593 | − | 0.0285247i | \(-0.00908092\pi\) | |||||||
\(614\) | 1.55151 | − | 2.68729i | 0.0626138 | − | 0.108450i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.91238 | − | 11.4964i | 0.318799 | − | 0.463204i | ||||
\(617\) | 22.3796 | − | 22.3796i | 0.900968 | − | 0.900968i | −0.0945520 | − | 0.995520i | \(-0.530142\pi\) |
0.995520 | + | 0.0945520i | \(0.0301419\pi\) | |||||||
\(618\) | 6.06110 | − | 1.62407i | 0.243813 | − | 0.0653296i | ||||
\(619\) | −1.10411 | − | 1.91238i | −0.0443780 | − | 0.0768649i | 0.842983 | − | 0.537940i | \(-0.180797\pi\) |
−0.887361 | + | 0.461075i | \(0.847464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.5876 | − | 8.42217i | −0.585381 | − | 0.337970i | ||||
\(622\) | 18.4932 | + | 18.4932i | 0.741511 | + | 0.741511i | ||||
\(623\) | 7.93166 | − | 6.76528i | 0.317775 | − | 0.271045i | ||||
\(624\) | − | 0.549834i | − | 0.0220110i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.2749 | − | 9.97368i | 0.690445 | − | 0.398628i | ||||
\(627\) | −37.9599 | − | 10.1713i | −1.51597 | − | 0.406204i | ||||
\(628\) | −2.58138 | − | 9.63383i | −0.103008 | − | 0.384432i | ||||
\(629\) | −18.2728 | −0.728586 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.6495 | −1.41918 | −0.709592 | − | 0.704613i | \(-0.751121\pi\) | ||||
−0.709592 | + | 0.704613i | \(0.751121\pi\) | |||||||
\(632\) | −2.58819 | − | 9.65926i | −0.102953 | − | 0.384225i | ||||
\(633\) | −7.38969 | − | 1.98006i | −0.293714 | − | 0.0787004i | ||||
\(634\) | −15.5885 | + | 9.00000i | −0.619097 | + | 0.357436i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 12.9041i | − | 0.511679i | ||||||
\(637\) | 2.91473 | − | 0.302485i | 0.115486 | − | 0.0119849i | ||||
\(638\) | 8.48528 | + | 8.48528i | 0.335936 | + | 0.335936i | ||||
\(639\) | 6.62466 | + | 3.82475i | 0.262068 | + | 0.151305i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.5000 | + | 23.3827i | 0.533218 | + | 0.923561i | 0.999247 | + | 0.0387913i | \(0.0123508\pi\) |
−0.466029 | + | 0.884769i | \(0.654316\pi\) | |||||||
\(642\) | −8.65836 | + | 2.32000i | −0.341718 | + | 0.0915631i | ||||
\(643\) | −4.98036 | + | 4.98036i | −0.196406 | + | 0.196406i | −0.798457 | − | 0.602051i | \(-0.794350\pi\) |
0.602051 | + | 0.798457i | \(0.294350\pi\) | |||||||
\(644\) | −7.16629 | + | 3.41238i | −0.282391 | + | 0.134466i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.82475 | + | 17.0170i | −0.386550 | + | 0.669524i | ||||
\(647\) | 1.34486 | − | 5.01910i | 0.0528720 | − | 0.197321i | −0.934438 | − | 0.356126i | \(-0.884097\pi\) |
0.987310 | + | 0.158805i | \(0.0507641\pi\) | |||||||
\(648\) | −0.918765 | + | 3.42888i | −0.0360925 | + | 0.134699i | ||||
\(649\) | 27.4093 | − | 47.4743i | 1.07591 | − | 1.86353i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | − | 0.952341i | −0.470317 | − | 0.0373252i | ||||
\(652\) | 8.48528 | − | 8.48528i | 0.332309 | − | 0.332309i | ||||
\(653\) | −28.4699 | + | 7.62850i | −1.11412 | + | 0.298526i | −0.768500 | − | 0.639850i | \(-0.778996\pi\) |
−0.345615 | + | 0.938376i | \(0.612330\pi\) | |||||||
\(654\) | −5.79532 | − | 10.0378i | −0.226615 | − | 0.392509i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.50000 | − | 2.59808i | −0.175695 | − | 0.101438i | ||||
\(657\) | −8.61390 | − | 8.61390i | −0.336060 | − | 0.336060i | ||||
\(658\) | 6.05384 | + | 32.7836i | 0.236003 | + | 1.27804i | ||||
\(659\) | 16.5498i | 0.644690i | 0.946622 | + | 0.322345i | \(0.104471\pi\) | ||||
−0.946622 | + | 0.322345i | \(0.895529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.58762 | + | 4.95807i | −0.334020 | + | 0.192846i | −0.657624 | − | 0.753346i | \(-0.728439\pi\) |
0.323605 | + | 0.946192i | \(0.395105\pi\) | |||||||
\(662\) | −5.96483 | − | 1.59827i | −0.231830 | − | 0.0621186i | ||||
\(663\) | −0.492968 | − | 1.83978i | −0.0191453 | − | 0.0714512i | ||||
\(664\) | −14.3326 | −0.556212 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.72508 | −0.260592 | ||||||||
\(667\) | −1.76638 | − | 6.59220i | −0.0683943 | − | 0.255251i | ||||
\(668\) | 1.67303 | + | 0.448288i | 0.0647316 | + | 0.0173448i | ||||
\(669\) | 9.91613 | − | 5.72508i | 0.383380 | − | 0.221344i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 75.6032i | − | 2.91863i | ||||||
\(672\) | 2.25509 | + | 2.64389i | 0.0869921 | + | 0.101990i | ||||
\(673\) | −12.8689 | − | 12.8689i | −0.496059 | − | 0.496059i | 0.414150 | − | 0.910209i | \(-0.364079\pi\) |
−0.910209 | + | 0.414150i | \(0.864079\pi\) | |||||||
\(674\) | 31.3495 | + | 18.0997i | 1.20754 | + | 0.697173i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.41238 | − | 11.1066i | −0.246630 | − | 0.427175i | ||||
\(677\) | −29.8214 | + | 7.99062i | −1.14613 | + | 0.307104i | −0.781413 | − | 0.624014i | \(-0.785501\pi\) |
−0.364716 | + | 0.931119i | \(0.618834\pi\) | |||||||
\(678\) | 5.57239 | − | 5.57239i | 0.214006 | − | 0.214006i | ||||
\(679\) | −21.7370 | − | 45.6495i | −0.834188 | − | 1.75187i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.27492 | − | 3.94027i | 0.0871750 | − | 0.150992i | ||||
\(682\) | 4.72936 | − | 17.6502i | 0.181097 | − | 0.675862i | ||||
\(683\) | −7.97803 | + | 29.7744i | −0.305271 | + | 1.13929i | 0.627441 | + | 0.778664i | \(0.284102\pi\) |
−0.932712 | + | 0.360622i | \(0.882564\pi\) | |||||||
\(684\) | −3.61587 | + | 6.26287i | −0.138256 | + | 0.239467i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.7749 | + | 13.4090i | −0.487749 | + | 0.511958i | ||||
\(687\) | −12.8689 | + | 12.8689i | −0.490978 | + | 0.490978i | ||||
\(688\) | −7.99296 | + | 2.14171i | −0.304729 | + | 0.0816518i | ||||
\(689\) | 2.05645 | + | 3.56188i | 0.0783446 | + | 0.135697i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.4743 | + | 20.4811i | 1.34950 | + | 0.779137i | 0.988179 | − | 0.153303i | \(-0.0489911\pi\) |
0.361325 | + | 0.932440i | \(0.382324\pi\) | |||||||
\(692\) | −3.33753 | − | 3.33753i | −0.126874 | − | 0.126874i | ||||
\(693\) | 5.95039 | − | 16.7684i | 0.226037 | − | 0.636980i | ||||
\(694\) | − | 5.17525i | − | 0.196450i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.58762 | + | 1.49397i | −0.0980836 | + | 0.0566286i | ||||
\(697\) | −17.3867 | − | 4.65874i | −0.658567 | − | 0.176462i | ||||
\(698\) | 1.01982 | + | 3.80601i | 0.0386007 | + | 0.144060i | ||||
\(699\) | 33.6887 | 1.27422 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.27492 | −0.312539 | −0.156270 | − | 0.987714i | \(-0.549947\pi\) | ||||
−0.156270 | + | 0.987714i | \(0.549947\pi\) | |||||||
\(702\) | −0.608353 | − | 2.27041i | −0.0229608 | − | 0.0856909i | ||||
\(703\) | 28.9015 | + | 7.74413i | 1.09004 | + | 0.292076i | ||||
\(704\) | −4.56821 | + | 2.63746i | −0.172171 | + | 0.0994030i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.952341i | 0.0358418i | ||||||||
\(707\) | 10.2517 | − | 1.89308i | 0.385553 | − | 0.0711965i | ||||
\(708\) | 9.65166 | + | 9.65166i | 0.362731 | + | 0.362731i | ||||
\(709\) | −11.4101 | − | 6.58762i | −0.428515 | − | 0.247403i | 0.270199 | − | 0.962805i | \(-0.412911\pi\) |
−0.698714 | + | 0.715401i | \(0.746244\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.37459 | − | 11.0411i | −0.239066 | − | 0.414074i | ||||
\(712\) | −3.80601 | + | 1.01982i | −0.142636 | + | 0.0382193i | ||||
\(713\) | −7.34847 | + | 7.34847i | −0.275202 | + | 0.275202i | ||||
\(714\) | 9.91613 | + | 6.82475i | 0.371102 | + | 0.255410i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.91238 | − | 8.50848i | 0.183584 | − | 0.317977i | ||||
\(717\) | 1.54667 | − | 5.77224i | 0.0577613 | − | 0.215568i | ||||
\(718\) | 3.53275 | − | 13.1844i | 0.131841 | − | 0.492038i | ||||
\(719\) | 19.5287 | − | 33.8248i | 0.728299 | − | 1.26145i | −0.229303 | − | 0.973355i | \(-0.573645\pi\) |
0.957602 | − | 0.288095i | \(-0.0930220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.00000 | − | 12.6005i | 0.0372419 | − | 0.469268i | ||||
\(722\) | 9.31631 | − | 9.31631i | 0.346717 | − | 0.346717i | ||||
\(723\) | 11.5911 | − | 3.10583i | 0.431078 | − | 0.115507i | ||||
\(724\) | −10.6304 | − | 18.4124i | −0.395075 | − | 0.684291i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −19.1375 | − | 11.0490i | −0.710258 | − | 0.410067i | ||||
\(727\) | −1.30612 | − | 1.30612i | −0.0484415 | − | 0.0484415i | 0.682471 | − | 0.730913i | \(-0.260905\pi\) |
−0.730913 | + | 0.682471i | \(0.760905\pi\) | |||||||
\(728\) | −1.04381 | − | 0.370403i | −0.0386862 | − | 0.0137281i | ||||
\(729\) | 26.6495i | 0.987019i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.8248 | + | 14.3326i | −0.918177 | + | 0.530110i | ||||
\(732\) | 18.1833 | + | 4.87220i | 0.672075 | + | 0.180082i | ||||
\(733\) | −8.17753 | − | 30.5189i | −0.302044 | − | 1.12724i | −0.935460 | − | 0.353432i | \(-0.885015\pi\) |
0.633416 | − | 0.773811i | \(-0.281652\pi\) | |||||||
\(734\) | −6.03341 | −0.222697 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | 5.08567 | + | 18.9800i | 0.187333 | + | 0.699136i | ||||
\(738\) | −6.39893 | − | 1.71459i | −0.235548 | − | 0.0631149i | ||||
\(739\) | −3.61587 | + | 2.08762i | −0.133012 | + | 0.0767945i | −0.565029 | − | 0.825071i | \(-0.691135\pi\) |
0.432017 | + | 0.901865i | \(0.357802\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.11884i | 0.114573i | ||||||||
\(742\) | −24.4972 | − | 8.69300i | −0.899320 | − | 0.319130i | ||||
\(743\) | 10.6066 | + | 10.6066i | 0.389118 | + | 0.389118i | 0.874373 | − | 0.485254i | \(-0.161273\pi\) |
−0.485254 | + | 0.874373i | \(0.661273\pi\) | |||||||
\(744\) | 3.94027 | + | 2.27492i | 0.144457 | + | 0.0834025i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.2749 | − | 19.5287i | −0.412804 | − | 0.714998i | ||||
\(747\) | −17.6502 | + | 4.72936i | −0.645788 | + | 0.173038i | ||||
\(748\) | −12.9209 | + | 12.9209i | −0.472433 | + | 0.472433i | ||||
\(749\) | −1.42851 | + | 18.0000i | −0.0521967 | + | 0.657706i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0000 | − | 34.6410i | 0.729810 | − | 1.26407i | −0.227153 | − | 0.973859i | \(-0.572942\pi\) |
0.956963 | − | 0.290209i | \(-0.0937250\pi\) | |||||||
\(752\) | 3.26126 | − | 12.1712i | 0.118926 | − | 0.443837i | ||||
\(753\) | 6.63858 | − | 24.7755i | 0.241923 | − | 0.902870i | ||||
\(754\) | 0.476171 | − | 0.824752i | 0.0173411 | − | 0.0300357i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12.2371 | + | 8.42217i | 0.445060 | + | 0.306311i | ||||
\(757\) | −4.24264 | + | 4.24264i | −0.154201 | + | 0.154201i | −0.779992 | − | 0.625790i | \(-0.784777\pi\) |
0.625790 | + | 0.779992i | \(0.284777\pi\) | |||||||
\(758\) | 24.9448 | − | 6.68394i | 0.906036 | − | 0.242772i | ||||
\(759\) | 10.3923 | + | 18.0000i | 0.377217 | + | 0.653359i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.9124 | − | 25.3528i | −1.59182 | − | 0.919039i | −0.992994 | − | 0.118161i | \(-0.962300\pi\) |
−0.598828 | − | 0.800878i | \(-0.704367\pi\) | |||||||
\(762\) | −16.0438 | − | 16.0438i | −0.581204 | − | 0.581204i | ||||
\(763\) | −22.9599 | + | 4.23979i | −0.831205 | + | 0.153491i | ||||
\(764\) | − | 9.09967i | − | 0.329214i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.1495 | + | 10.4786i | −0.655768 | + | 0.378608i | ||||
\(767\) | −4.20226 | − | 1.12599i | −0.151735 | − | 0.0406572i | ||||
\(768\) | −0.339939 | − | 1.26867i | −0.0122665 | − | 0.0457792i | ||||
\(769\) | 17.9693 | 0.647990 | 0.323995 | − | 0.946059i | \(-0.394974\pi\) | ||||
0.323995 | + | 0.946059i | \(0.394974\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0000 | −0.864339 | ||||||||
\(772\) | −2.73050 | − | 10.1904i | −0.0982728 | − | 0.366759i | ||||
\(773\) | −32.2476 | − | 8.64071i | −1.15986 | − | 0.310785i | −0.372953 | − | 0.927850i | \(-0.621655\pi\) |
−0.786912 | + | 0.617066i | \(0.788321\pi\) | |||||||
\(774\) | −9.13642 | + | 5.27492i | −0.328402 | + | 0.189603i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 19.1101i | 0.686013i | ||||||||
\(777\) | 6.13011 | − | 17.2749i | 0.219917 | − | 0.619733i | ||||
\(778\) | 2.19180 | + | 2.19180i | 0.0785797 | + | 0.0785797i | ||||
\(779\) | 25.5255 | + | 14.7371i | 0.914544 | + | 0.528012i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.8248 | − | 27.4093i | −0.566254 | − | 0.980781i | ||||
\(782\) | 10.0382 | − | 2.68973i | 0.358965 | − | 0.0961844i | ||||
\(783\) | −9.03199 | + | 9.03199i | −0.322777 | + | 0.322777i | ||||
\(784\) | 6.53835 | − | 2.50000i | 0.233512 | − | 0.0892857i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.00000 | + | 10.3923i | −0.214013 | + | 0.370681i | ||||
\(787\) | −8.22221 | + | 30.6857i | −0.293090 | + | 1.09383i | 0.649632 | + | 0.760249i | \(0.274923\pi\) |
−0.942722 | + | 0.333578i | \(0.891744\pi\) | |||||||
\(788\) | 4.09575 | − | 15.2855i | 0.145905 | − | 0.544525i | ||||
\(789\) | 12.3624 | − | 21.4124i | 0.440115 | − | 0.762301i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.82475 | − | 14.3326i | −0.242660 | − | 0.509608i | ||||
\(792\) | −4.75535 | + | 4.75535i | −0.168974 | + | 0.168974i | ||||
\(793\) | −5.79555 | + | 1.55291i | −0.205806 | + | 0.0551456i | ||||
\(794\) | 0.837253 | + | 1.45017i | 0.0297130 | + | 0.0514645i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.8248 | − | 9.13642i | −0.560893 | − | 0.323832i | ||||
\(797\) | 9.79796 | + | 9.79796i | 0.347062 | + | 0.347062i | 0.859014 | − | 0.511952i | \(-0.171078\pi\) |
−0.511952 | + | 0.859014i | \(0.671078\pi\) | |||||||
\(798\) | −12.7916 | − | 14.9970i | −0.452818 | − | 0.530887i | ||||
\(799\) | − | 43.6495i | − | 1.54421i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.35050 | + | 2.51176i | −0.153717 | + | 0.0887487i | ||||
\(802\) | 17.4829 | + | 4.68454i | 0.617344 | + | 0.165417i | ||||
\(803\) | 13.0450 | + | 48.6847i | 0.460349 | + | 1.71805i | ||||
\(804\) | −4.89261 | −0.172549 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.45017 | −0.0510799 | ||||||||
\(807\) | −2.19330 | − | 8.18550i | −0.0772078 | − | 0.288143i | ||||
\(808\) | −3.80601 | − | 1.01982i | −0.133895 | − | 0.0358771i | ||||
\(809\) | −5.28247 | + | 3.04983i | −0.185722 | + | 0.107226i | −0.589978 | − | 0.807419i | \(-0.700864\pi\) |
0.404256 | + | 0.914646i | \(0.367530\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17.0170i | − | 0.597547i | −0.954324 | − | 0.298773i | \(-0.903423\pi\) | ||
0.954324 | − | 0.298773i | \(-0.0965774\pi\) | |||||||
\(812\) | 1.09297 | + | 5.91880i | 0.0383557 | + | 0.207709i | ||||
\(813\) | −7.31891 | − | 7.31891i | −0.256685 | − | 0.256685i | ||||
\(814\) | 24.0969 | + | 13.9124i | 0.844597 | + | 0.487629i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.27492 | − | 3.94027i | −0.0796380 | − | 0.137937i | ||||
\(817\) | 45.3386 | − | 12.1484i | 1.58620 | − | 0.425020i | ||||
\(818\) | 12.5842 | − | 12.5842i | 0.439995 | − | 0.439995i | ||||
\(819\) | −1.40765 | − | 0.111714i | −0.0491873 | − | 0.00390359i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.0997 | + | 41.7419i | −0.841084 | + | 1.45680i | 0.0478946 | + | 0.998852i | \(0.484749\pi\) |
−0.888979 | + | 0.457948i | \(0.848584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.87220 | − | 18.1833i | 0.169834 | − | 0.633830i | −0.827540 | − | 0.561407i | \(-0.810260\pi\) |
0.997374 | − | 0.0724232i | \(-0.0230732\pi\) | |||||||
\(824\) | −2.38876 | + | 4.13746i | −0.0832165 | + | 0.144135i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.8248 | − | 11.8208i | 0.863764 | − | 0.411299i | ||||
\(827\) | 18.7201 | − | 18.7201i | 0.650963 | − | 0.650963i | −0.302262 | − | 0.953225i | \(-0.597742\pi\) |
0.953225 | + | 0.302262i | \(0.0977418\pi\) | |||||||
\(828\) | 3.69443 | − | 0.989919i | 0.128390 | − | 0.0344020i | ||||
\(829\) | −5.67232 | − | 9.82475i | −0.197008 | − | 0.341228i | 0.750549 | − | 0.660815i | \(-0.229789\pi\) |
−0.947557 | + | 0.319587i | \(0.896456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.1752 | + | 9.91613i | 0.595803 | + | 0.343987i | ||||
\(832\) | 0.296014 | + | 0.296014i | 0.0102624 | + | 0.0102624i | ||||
\(833\) | 19.6363 | − | 14.2273i | 0.680358 | − | 0.492946i | ||||
\(834\) | − | 5.80066i | − | 0.200861i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 25.9124 | − | 14.9605i | 0.896198 | − | 0.517420i | ||||
\(837\) | 18.7874 | + | 5.03407i | 0.649388 | + | 0.174003i | ||||
\(838\) | 7.09404 | + | 26.4753i | 0.245060 | + | 0.914575i | ||||
\(839\) | 2.51176 | 0.0867156 | 0.0433578 | − | 0.999060i | \(-0.486194\pi\) | ||||
0.0433578 | + | 0.999060i | \(0.486194\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.8248 | 0.821543 | ||||||||
\(842\) | 9.01331 | + | 33.6381i | 0.310619 | + | 1.15925i | ||||
\(843\) | −10.6246 | − | 2.84685i | −0.365930 | − | 0.0980507i | ||||
\(844\) | 5.04438 | − | 2.91238i | 0.173635 | − | 0.100248i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 16.0646i | − | 0.552313i | ||||||
\(847\) | −33.8678 | + | 28.8874i | −1.16371 | + | 0.992583i | ||||
\(848\) | 6.94715 | + | 6.94715i | 0.238566 | + | 0.238566i | ||||
\(849\) | −8.01145 | − | 4.62541i | −0.274952 | − | 0.158744i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.91238 | − | 13.7046i | −0.271233 | − | 0.469789i | ||||
\(852\) | 7.61202 | − | 2.03963i | 0.260784 | − | 0.0698767i | ||||
\(853\) | 24.3616 | − | 24.3616i | 0.834127 | − | 0.834127i | −0.153952 | − | 0.988078i | \(-0.549200\pi\) |
0.988078 | + | 0.153952i | \(0.0492000\pi\) | |||||||
\(854\) | 21.4989 | − | 31.2371i | 0.735676 | − | 1.06891i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.41238 | − | 5.91041i | 0.116633 | − | 0.202014i | ||||
\(857\) | −4.07927 | + | 15.2240i | −0.139345 | + | 0.520043i | 0.860597 | + | 0.509287i | \(0.170091\pi\) |
−0.999942 | + | 0.0107567i | \(0.996576\pi\) | |||||||
\(858\) | −0.750661 | + | 2.80150i | −0.0256271 | + | 0.0956418i | ||||
\(859\) | −1.25588 | + | 2.17525i | −0.0428501 | + | 0.0742185i | −0.886655 | − | 0.462431i | \(-0.846977\pi\) |
0.843805 | + | 0.536650i | \(0.180310\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.2371 | − | 14.8742i | 0.348880 | − | 0.506911i | ||||
\(862\) | −24.4304 | + | 24.4304i | −0.832103 | + | 0.832103i | ||||
\(863\) | 37.6711 | − | 10.0939i | 1.28234 | − | 0.343602i | 0.447593 | − | 0.894237i | \(-0.352281\pi\) |
0.834746 | + | 0.550635i | \(0.185615\pi\) | |||||||
\(864\) | −2.80739 | − | 4.86254i | −0.0955093 | − | 0.165427i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.72508 | + | 5.61478i | 0.330472 | + | 0.190798i | ||||
\(867\) | 4.64366 | + | 4.64366i | 0.157707 | + | 0.157707i | ||||
\(868\) | 6.97314 | − | 5.94772i | 0.236684 | − | 0.201879i | ||||
\(869\) | 52.7492i | 1.78939i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.35050 | − | 0.779710i | 0.0457598 | − | 0.0264195i | ||||
\(872\) | 8.52406 | + | 2.28401i | 0.288661 | + | 0.0773465i | ||||
\(873\) | 6.30582 | + | 23.5336i | 0.213420 | + | 0.796492i | ||||
\(874\) | −17.0170 | −0.575608 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.5498 | −0.424020 | ||||||||
\(877\) | −3.66882 | − | 13.6922i | −0.123887 | − | 0.462354i | 0.875910 | − | 0.482474i | \(-0.160262\pi\) |
−0.999798 | + | 0.0201202i | \(0.993595\pi\) | |||||||
\(878\) | −20.0764 | − | 5.37945i | −0.677545 | − | 0.181548i | ||||
\(879\) | −5.36878 | + | 3.09967i | −0.181085 | + | 0.104549i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.3495i | 1.05619i | 0.849184 | + | 0.528097i | \(0.177094\pi\) | ||||
−0.849184 | + | 0.528097i | \(0.822906\pi\) | |||||||
\(882\) | 7.22688 | − | 5.23617i | 0.243342 | − | 0.176311i | ||||
\(883\) | 6.43444 | + | 6.43444i | 0.216536 | + | 0.216536i | 0.807037 | − | 0.590501i | \(-0.201070\pi\) |
−0.590501 | + | 0.807037i | \(0.701070\pi\) | |||||||
\(884\) | 1.25588 | + | 0.725083i | 0.0422398 | + | 0.0243872i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.58762 | + | 9.67805i | 0.187720 | + | 0.325140i | ||||
\(887\) | 21.4562 | − | 5.74918i | 0.720430 | − | 0.193039i | 0.120066 | − | 0.992766i | \(-0.461689\pi\) |
0.600363 | + | 0.799727i | \(0.295023\pi\) | |||||||
\(888\) | −4.89898 | + | 4.89898i | −0.164399 | + | 0.164399i | ||||
\(889\) | −41.2657 | + | 19.6495i | −1.38401 | + | 0.659023i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.36254 | − | 16.2164i | 0.313657 | − | 0.543270i | ||||
\(892\) | −2.25633 | + | 8.42075i | −0.0755476 | + | 0.281947i | ||||
\(893\) | −18.4989 | + | 69.0388i | −0.619042 | + | 2.31030i | ||||
\(894\) | −8.42217 | + | 14.5876i | −0.281679 | + | 0.487883i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.63746 | − | 0.209313i | −0.0881113 | − | 0.00699267i | ||||
\(897\) | 1.16637 | − | 1.16637i | 0.0389441 | − | 0.0389441i | ||||
\(898\) | −21.6852 | + | 5.81053i | −0.723644 | + | 0.193900i | ||||
\(899\) | 3.94027 | + | 6.82475i | 0.131415 | + | 0.227618i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.4743 | + | 17.0170i | 0.981930 | + | 0.566917i | ||||
\(902\) | 19.3813 | + | 19.3813i | 0.645326 | + | 0.645326i | ||||
\(903\) | −5.22169 | − | 28.2772i | −0.173767 | − | 0.941006i | ||||
\(904\) | 6.00000i | 0.199557i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.27492 | − | 1.31342i | 0.0755791 | − | 0.0436356i | ||||
\(907\) | 26.9729 | + | 7.22737i | 0.895621 | + | 0.239981i | 0.677135 | − | 0.735859i | \(-0.263221\pi\) |
0.218486 | + | 0.975840i | \(0.429888\pi\) | |||||||
\(908\) | 0.896575 | + | 3.34607i | 0.0297539 | + | 0.111043i | ||||
\(909\) | −5.02352 | −0.166620 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.6495 | −0.651017 | −0.325509 | − | 0.945539i | \(-0.605535\pi\) | ||||
−0.325509 | + | 0.945539i | \(0.605535\pi\) | |||||||
\(912\) | 1.92824 | + | 7.19631i | 0.0638506 | + | 0.238294i | ||||
\(913\) | 73.0270 | + | 19.5675i | 2.41684 | + | 0.647591i | ||||
\(914\) | 29.9210 | − | 17.2749i | 0.989700 | − | 0.571403i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 13.8564i | − | 0.457829i | ||||||
\(917\) | 15.6869 | + | 18.3914i | 0.518026 | + | 0.607336i | ||||
\(918\) | −13.7533 | − | 13.7533i | −0.453928 | − | 0.453928i | ||||
\(919\) | −29.1413 | − | 16.8248i | −0.961284 | − | 0.554997i | −0.0647157 | − | 0.997904i | \(-0.520614\pi\) |
−0.896568 | + | 0.442906i | \(0.853947\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.03779 | − | 3.52956i | −0.0671475 | − | 0.116303i | ||||
\(922\) | −15.2240 | + | 4.07927i | −0.501377 | + | 0.134344i | ||||
\(923\) | −1.77608 | + | 1.77608i | −0.0584605 | + | 0.0584605i | ||||
\(924\) | −7.88054 | − | 16.5498i | −0.259251 | − | 0.544450i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.7749 | + | 27.3230i | −0.518396 | + | 0.897888i | ||||
\(927\) | −1.57645 | + | 5.88341i | −0.0517775 | + | 0.193236i | ||||
\(928\) | 0.588792 | − | 2.19740i | 0.0193280 | − | 0.0721332i | ||||
\(929\) | 6.53835 | − | 11.3248i | 0.214516 | − | 0.371553i | −0.738607 | − | 0.674137i | \(-0.764516\pi\) |
0.953123 | + | 0.302584i | \(0.0978492\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.0876 | + | 14.1808i | −1.21550 | + | 0.464757i | ||||
\(932\) | −18.1369 | + | 18.1369i | −0.594095 | + | 0.594095i | ||||
\(933\) | 33.1800 | − | 8.89056i | 1.08627 | − | 0.291064i | ||||
\(934\) | −6.69012 | − | 11.5876i | −0.218907 | − | 0.379159i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.462210 | + | 0.266857i | 0.0151078 | + | 0.00872250i | ||||
\(937\) | −37.5785 | − | 37.5785i | −1.22764 | − | 1.22764i | −0.964856 | − | 0.262781i | \(-0.915360\pi\) |
−0.262781 | − | 0.964856i | \(-0.584640\pi\) | |||||||
\(938\) | −3.29597 | + | 9.28818i | −0.107617 | + | 0.303270i | ||||
\(939\) | − | 26.1993i | − | 0.854983i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.35050 | + | 2.51176i | −0.141822 | + | 0.0818811i | −0.569232 | − | 0.822177i | \(-0.692759\pi\) |
0.427410 | + | 0.904058i | \(0.359426\pi\) | |||||||
\(942\) | −12.6533 | − | 3.39044i | −0.412267 | − | 0.110467i | ||||
\(943\) | −4.03459 | − | 15.0573i | −0.131384 | − | 0.490333i | ||||
\(944\) | −10.3923 | −0.338241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 43.6495 | 1.41917 | ||||||||
\(947\) | −4.87220 | − | 18.1833i | −0.158325 | − | 0.590878i | −0.998798 | − | 0.0490237i | \(-0.984389\pi\) |
0.840472 | − | 0.541855i | \(-0.182278\pi\) | |||||||
\(948\) | −12.6867 | − | 3.39939i | −0.412045 | − | 0.110407i | ||||
\(949\) | 3.46410 | − | 2.00000i | 0.112449 | − | 0.0649227i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.6416i | 0.766632i | ||||||||
\(952\) | −9.01277 | + | 1.66430i | −0.292106 | + | 0.0539404i | ||||
\(953\) | −27.7886 | − | 27.7886i | −0.900161 | − | 0.900161i | 0.0952888 | − | 0.995450i | \(-0.469623\pi\) |
−0.995450 | + | 0.0952888i | \(0.969623\pi\) | |||||||
\(954\) | 10.8476 | + | 6.26287i | 0.351204 | + | 0.202768i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.27492 | + | 3.94027i | 0.0735761 | + | 0.127438i | ||||
\(957\) | 15.2240 | − | 4.07927i | 0.492123 | − | 0.131864i | ||||
\(958\) | 5.57239 | − | 5.57239i | 0.180036 | − | 0.180036i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.50000 | + | 16.4545i | −0.306452 | + | 0.530790i | ||||
\(962\) | 0.571530 | − | 2.13298i | 0.0184269 | − | 0.0687700i | ||||
\(963\) | 2.25198 | − | 8.40451i | 0.0725691 | − | 0.270832i | ||||
\(964\) | −4.56821 | + | 7.91238i | −0.147132 | + | 0.254840i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.824752 | + | 10.3923i | −0.0265359 | + | 0.334367i | ||||
\(967\) | 19.7455 | − | 19.7455i | 0.634974 | − | 0.634974i | −0.314337 | − | 0.949311i | \(-0.601782\pi\) |
0.949311 | + | 0.314337i | \(0.101782\pi\) | |||||||
\(968\) | 16.2515 | − | 4.35457i | 0.522342 | − | 0.139961i | ||||
\(969\) | 12.9041 | + | 22.3505i | 0.414538 | + | 0.718001i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.7371 | + | 24.0969i | 1.33941 | + | 0.773308i | 0.986720 | − | 0.162433i | \(-0.0519342\pi\) |
0.352689 | + | 0.935741i | \(0.385267\pi\) | |||||||
\(972\) | −8.61390 | − | 8.61390i | −0.276291 | − | 0.276291i | ||||
\(973\) | −11.0120 | − | 3.90769i | −0.353029 | − | 0.125275i | ||||
\(974\) | − | 9.09967i | − | 0.291572i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.4124 | + | 7.16629i | −0.397310 | + | 0.229387i | ||||
\(977\) | −18.9800 | − | 5.08567i | −0.607223 | − | 0.162705i | −0.0579102 | − | 0.998322i | \(-0.518444\pi\) |
−0.549313 | + | 0.835617i | \(0.685110\pi\) | |||||||
\(978\) | −4.07927 | − | 15.2240i | −0.130441 | − | 0.486811i | ||||
\(979\) | 20.7846 | 0.664279 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.2508 | 0.359211 | ||||||||
\(982\) | −5.03407 | − | 18.7874i | −0.160644 | − | 0.599531i | ||||
\(983\) | −33.6274 | − | 9.01044i | −1.07255 | − | 0.287388i | −0.321008 | − | 0.947076i | \(-0.604022\pi\) |
−0.751539 | + | 0.659688i | \(0.770688\pi\) | |||||||
\(984\) | −5.91041 | + | 3.41238i | −0.188417 | + | 0.108783i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 7.88054i | − | 0.250968i | ||||||
\(987\) | 41.2656 | + | 14.6434i | 1.31350 | + | 0.466104i | ||||
\(988\) | −1.67909 | − | 1.67909i | −0.0534188 | − | 0.0534188i | ||||
\(989\) | −21.4989 | − | 12.4124i | −0.683624 | − | 0.394691i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.8248 | + | 18.7490i | 0.343860 | + | 0.595582i | 0.985146 | − | 0.171719i | \(-0.0549322\pi\) |
−0.641286 | + | 0.767302i | \(0.721599\pi\) | |||||||
\(992\) | −3.34607 | + | 0.896575i | −0.106238 | + | 0.0284663i | ||||
\(993\) | −5.73514 | + | 5.73514i | −0.181999 | + | 0.181999i | ||||
\(994\) | 1.25588 | − | 15.8248i | 0.0398341 | − | 0.501931i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.41238 | + | 16.3027i | −0.298243 | + | 0.516571i | ||||
\(997\) | 7.85248 | − | 29.3059i | 0.248691 | − | 0.928126i | −0.722802 | − | 0.691055i | \(-0.757146\pi\) |
0.971492 | − | 0.237071i | \(-0.0761873\pi\) | |||||||
\(998\) | 1.03528 | − | 3.86370i | 0.0327711 | − | 0.122303i | ||||
\(999\) | −14.8087 | + | 25.6495i | −0.468528 | + | 0.811514i |
(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 | 350.2.o.d.243.4 | yes | 16 | |
5.2 | odd | 4 | inner | 350.2.o.d.257.2 | yes | 16 | |
5.3 | odd | 4 | inner | 350.2.o.d.257.3 | yes | 16 | |
5.4 | even | 2 | inner | 350.2.o.d.243.1 | yes | 16 | |
7.3 | odd | 6 | inner | 350.2.o.d.143.2 | ✓ | 16 | |
35.3 | even | 12 | inner | 350.2.o.d.157.1 | yes | 16 | |
35.17 | even | 12 | inner | 350.2.o.d.157.4 | yes | 16 | |
35.24 | odd | 6 | inner | 350.2.o.d.143.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.2.o.d.143.2 | ✓ | 16 | 7.3 | odd | 6 | inner | |
350.2.o.d.143.3 | yes | 16 | 35.24 | odd | 6 | inner | |
350.2.o.d.157.1 | yes | 16 | 35.3 | even | 12 | inner | |
350.2.o.d.157.4 | yes | 16 | 35.17 | even | 12 | inner | |
350.2.o.d.243.1 | yes | 16 | 5.4 | even | 2 | inner | |
350.2.o.d.243.4 | yes | 16 | 1.1 | even | 1 | trivial | |
350.2.o.d.257.2 | yes | 16 | 5.2 | odd | 4 | inner | |
350.2.o.d.257.3 | yes | 16 | 5.3 | odd | 4 | inner |