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 | 157.1 | ||
Root | \(1.97578 + 1.04705i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.157 |
Dual form | 350.2.o.d.243.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 | \(-0.707118\pi\) |
−0.126739 | + | 0.991936i | \(0.540451\pi\) | |||||||
\(4\) | −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 | −0.127473 | − | 0.991842i | \(-0.540687\pi\) |
0.922697 | − | 0.385526i | \(-0.125980\pi\) | |||||||
\(12\) | 1.26867 | + | 0.339939i | 0.366234 | + | 0.0981320i | ||||
\(13\) | −0.296014 | − | 0.296014i | −0.0820995 | − | 0.0820995i | 0.664865 | − | 0.746964i | \(-0.268489\pi\) |
−0.746964 | + | 0.664865i | \(0.768489\pi\) | |||||||
\(14\) | −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 | −0.985289 | − | 0.170896i | \(-0.945334\pi\) |
0.767838 | − | 0.640644i | \(-0.221333\pi\) | |||||||
\(18\) | −0.329973 | − | 1.23148i | −0.0777753 | − | 0.290262i | ||||
\(19\) | −2.83616 | − | 4.91238i | −0.650660 | − | 1.12698i | −0.982963 | − | 0.183804i | \(-0.941159\pi\) |
0.332303 | − | 0.943173i | \(-0.392174\pi\) | |||||||
\(20\) | 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 | \(-0.517924\pi\) |
−0.547948 | + | 0.836512i | \(0.684591\pi\) | |||||||
\(24\) | −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 | \(0.0677439\pi\) | ||||
−0.977438 | + | 0.211221i | \(0.932256\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | − | 1.73205i | −0.538816 | − | 0.311086i | 0.205783 | − | 0.978598i | \(-0.434026\pi\) |
−0.744599 | + | 0.667512i | \(0.767359\pi\) | |||||||
\(32\) | −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 | −0.758180 | − | 0.652045i | \(-0.773911\pi\) |
0.982626 | − | 0.185597i | \(-0.0594220\pi\) | |||||||
\(38\) | 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 | \(0.132990\pi\) | ||||
−0.913984 | + | 0.405751i | \(0.867010\pi\) | |||||||
\(42\) | 1.16213 | + | 3.27491i | 0.179320 | + | 0.505330i | ||||
\(43\) | 5.85125 | − | 5.85125i | 0.892307 | − | 0.892307i | −0.102433 | − | 0.994740i | \(-0.532663\pi\) |
0.994740 | + | 0.102433i | \(0.0326626\pi\) | |||||||
\(44\) | −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 | \(-0.787659\pi\) |
−0.989723 | + | 0.142999i | \(0.954325\pi\) | |||||||
\(48\) | −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 | 0.887526 | + | 0.460758i | \(0.152422\pi\) |
−0.538241 | + | 0.842791i | \(0.680911\pi\) | |||||||
\(54\) | 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 | 0.299552 | + | 0.954080i | \(0.403163\pi\) |
−0.976034 | + | 0.217620i | \(0.930171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4124 | + | 7.16629i | −1.58924 | + | 0.917549i | −0.595810 | + | 0.803126i | \(0.703169\pi\) |
−0.993432 | + | 0.114424i | \(0.963498\pi\) | |||||||
\(62\) | 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 | \(-0.656403\pi\) |
0.0322373 | + | 0.999480i | \(0.489737\pi\) | |||||||
\(68\) | −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 | \(-0.772212\pi\) |
−0.325539 | + | 0.945529i | \(0.605546\pi\) | |||||||
\(74\) | 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 | 0.0737937 | − | 0.997274i | \(-0.476489\pi\) |
0.900561 | + | 0.434730i | \(0.143156\pi\) | |||||||
\(80\) | 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 | −0.992822 | − | 0.119602i | \(-0.961838\pi\) |
−0.119602 | − | 0.992822i | \(-0.538162\pi\) | |||||||
\(84\) | −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 | 0.951348 | − | 0.308120i | \(-0.0996998\pi\) |
−0.742513 | + | 0.669831i | \(0.766366\pi\) | |||||||
\(90\) | 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 | 0.514588 | − | 0.857438i | \(-0.327945\pi\) |
0.857438 | − | 0.514588i | \(-0.172055\pi\) | |||||||
\(98\) | 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 | 0.660070 | − | 0.751204i | \(-0.270526\pi\) |
−0.320526 | + | 0.947240i | \(0.603860\pi\) | |||||||
\(102\) | −4.39480 | + | 1.17758i | −0.435150 | + | 0.116598i | ||||
\(103\) | 1.23651 | − | 4.61474i | 0.121837 | − | 0.454703i | −0.877870 | − | 0.478899i | \(-0.841036\pi\) |
0.999707 | + | 0.0241959i | \(0.00770256\pi\) | |||||||
\(104\) | −0.418627 | −0.0410497 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.82475 | −0.954264 | ||||||||
\(107\) | −1.76638 | + | 6.59220i | −0.170762 | + | 0.637292i | 0.826473 | + | 0.562977i | \(0.190344\pi\) |
−0.997235 | + | 0.0743157i | \(0.976323\pi\) | |||||||
\(108\) | −5.42346 | + | 1.45321i | −0.521873 | + | 0.139835i | ||||
\(109\) | −7.64246 | − | 4.41238i | −0.732015 | − | 0.422629i | 0.0871440 | − | 0.996196i | \(-0.472226\pi\) |
−0.819159 | + | 0.573567i | \(0.805559\pi\) | |||||||
\(110\) | 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 | \(-0.658930\pi\) |
0.877920 | + | 0.478806i | \(0.158930\pi\) | |||||||
\(114\) | −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 | 0.996139 | + | 0.0877853i | \(0.0279789\pi\) |
0.0877853 | + | 0.996139i | \(0.472021\pi\) | |||||||
\(128\) | 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 | −0.112794 | − | 0.993618i | \(-0.535980\pi\) |
0.804102 | + | 0.594492i | \(0.202647\pi\) | |||||||
\(132\) | 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 | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(138\) | −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 | 0.0294908 | − | 0.999565i | \(-0.490611\pi\) |
0.880394 | + | 0.474243i | \(0.157278\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | + | 1.73205i | −0.0813788 | + | 0.140952i | −0.903842 | − | 0.427865i | \(-0.859266\pi\) |
0.822464 | + | 0.568818i | \(0.192599\pi\) | |||||||
\(152\) | −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 | 0.989137 | + | 0.146994i | \(0.0469599\pi\) |
−0.783121 | + | 0.621869i | \(0.786373\pi\) | |||||||
\(158\) | 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 | \(-0.260936\pi\) |
0.225486 | + | 0.974246i | \(0.427603\pi\) | |||||||
\(164\) | 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 | \(-0.728652\pi\) |
0.752904 | + | 0.658130i | \(0.228652\pi\) | |||||||
\(168\) | 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 | \(-0.974091\pi\) |
0.903811 | + | 0.427932i | \(0.140758\pi\) | |||||||
\(174\) | 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 | 0.147100 | − | 0.989122i | \(-0.453006\pi\) |
−0.783054 | + | 0.621953i | \(0.786339\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.2608i | − | 1.58030i | −0.612913 | − | 0.790151i | \(-0.710002\pi\) | ||
0.612913 | − | 0.790151i | \(-0.289998\pi\) | |||||||
\(182\) | −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 | 0.653142 | − | 0.757236i | \(-0.273451\pi\) |
−0.982356 | + | 0.187019i | \(0.940117\pi\) | |||||||
\(192\) | 0.339939 | + | 1.26867i | 0.0245330 | + | 0.0915584i | ||||
\(193\) | 2.73050 | + | 10.1904i | 0.196546 | + | 0.733518i | 0.991861 | + | 0.127323i | \(0.0406384\pi\) |
−0.795316 | + | 0.606195i | \(0.792695\pi\) | |||||||
\(194\) | 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 | \(-0.0593645\pi\) |
−0.185420 | + | 0.982659i | \(0.559365\pi\) | |||||||
\(198\) | −6.49593 | − | 1.74058i | −0.461646 | − | 0.123698i | ||||
\(199\) | 9.13642 | − | 15.8248i | 0.647664 | − | 1.12179i | −0.336015 | − | 0.941857i | \(-0.609079\pi\) |
0.983679 | − | 0.179930i | \(-0.0575873\pi\) | |||||||
\(200\) | 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 | \(-0.344285\pi\) |
−0.882713 | + | 0.469913i | \(0.844285\pi\) | |||||||
\(224\) | 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 | \(-0.120007\pi\) |
−0.989276 | + | 0.146060i | \(0.953341\pi\) | |||||||
\(228\) | −1.92824 | − | 7.19631i | −0.127701 | − | 0.476587i | ||||
\(229\) | −6.92820 | − | 12.0000i | −0.457829 | − | 0.792982i | 0.541017 | − | 0.841011i | \(-0.318039\pi\) |
−0.998846 | + | 0.0480291i | \(0.984706\pi\) | |||||||
\(230\) | 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 | \(-0.734216\pi\) |
−0.951910 | + | 0.306379i | \(0.900883\pi\) | |||||||
\(234\) | −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 | \(0.0470107\pi\) | ||||
−0.989114 | + | 0.147152i | \(0.952989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.91238 | + | 4.56821i | 0.509681 | + | 0.294264i | 0.732702 | − | 0.680549i | \(-0.238259\pi\) |
−0.223022 | + | 0.974814i | \(0.571592\pi\) | |||||||
\(242\) | 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 | \(0.211378\pi\) | ||||
−0.787495 | + | 0.616321i | \(0.788622\pi\) | |||||||
\(252\) | −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 | \(-0.223643\pi\) |
0.337823 | + | 0.941210i | \(0.390310\pi\) | |||||||
\(258\) | −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 | −0.936806 | − | 0.349850i | \(-0.886233\pi\) |
0.636373 | − | 0.771382i | \(-0.280434\pi\) | |||||||
\(264\) | 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 | −0.947454 | − | 0.319891i | \(-0.896354\pi\) |
0.750761 | + | 0.660574i | \(0.229687\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.82475 | + | 3.94027i | −0.414574 | + | 0.239354i | −0.692753 | − | 0.721175i | \(-0.743602\pi\) |
0.278179 | + | 0.960529i | \(0.410269\pi\) | |||||||
\(272\) | 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 | \(-0.733203\pi\) |
−0.207511 | + | 0.978233i | \(0.566536\pi\) | |||||||
\(278\) | 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 | \(-0.516202\pi\) |
0.455291 | + | 0.890343i | \(0.349535\pi\) | |||||||
\(284\) | 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 | \(-0.205974\pi\) |
−0.602864 | + | 0.797844i | \(0.705974\pi\) | |||||||
\(294\) | −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 | \(-0.721777\pi\) |
0.766943 | + | 0.641715i | \(0.221777\pi\) | |||||||
\(308\) | 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 | 0.977638 | − | 0.210296i | \(-0.0674426\pi\) |
0.306698 | + | 0.951807i | \(0.400776\pi\) | |||||||
\(312\) | 0.531099 | − | 0.142308i | 0.0300676 | − | 0.00805658i | ||||
\(313\) | 5.16276 | − | 19.2677i | 0.291816 | − | 1.08907i | −0.651897 | − | 0.758308i | \(-0.726026\pi\) |
0.943713 | − | 0.330765i | \(-0.107307\pi\) | |||||||
\(314\) | −9.97368 | −0.562847 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | −4.65874 | + | 17.3867i | −0.261661 | + | 0.976532i | 0.702601 | + | 0.711584i | \(0.252022\pi\) |
−0.964262 | + | 0.264949i | \(0.914645\pi\) | |||||||
\(318\) | 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 | 0.768607 | − | 0.639721i | \(-0.220950\pi\) |
−0.938318 | + | 0.345773i | \(0.887617\pi\) | |||||||
\(332\) | 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 | −0.815281 | − | 0.579065i | \(-0.803418\pi\) |
−0.579065 | − | 0.815281i | \(-0.696582\pi\) | |||||||
\(338\) | 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 | \(-0.538973\pi\) |
0.390487 | + | 0.920608i | \(0.372306\pi\) | |||||||
\(348\) | −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 | \(-0.591401\pi\) |
0.234255 | + | 0.972175i | \(0.424735\pi\) | |||||||
\(354\) | 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 | −0.778378 | − | 0.627796i | \(-0.783957\pi\) |
0.154499 | + | 0.987993i | \(0.450624\pi\) | |||||||
\(360\) | 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 | \(-0.0329994\pi\) |
−0.913118 | + | 0.407695i | \(0.866333\pi\) | |||||||
\(368\) | −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 | \(-0.218235\pi\) |
0.353765 | + | 0.935334i | \(0.384901\pi\) | |||||||
\(374\) | 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 | \(0.230829\pi\) | ||||
−0.748385 | + | 0.663264i | \(0.769171\pi\) | |||||||
\(380\) | 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 | 0.677220 | + | 0.735781i | \(0.263185\pi\) |
−0.954380 | + | 0.298595i | \(0.903482\pi\) | |||||||
\(384\) | −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 | 0.566506 | − | 0.824058i | \(-0.308295\pi\) |
−0.430402 | + | 0.902637i | \(0.641628\pi\) | |||||||
\(390\) | 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 | \(-0.430046\pi\) |
−0.299179 | + | 0.954197i | \(0.596713\pi\) | |||||||
\(398\) | 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 | 0.998506 | − | 0.0546470i | \(-0.0174034\pi\) |
−0.546579 | + | 0.837408i | \(0.684070\pi\) | |||||||
\(402\) | 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 | −0.997688 | − | 0.0679538i | \(-0.978353\pi\) |
0.557694 | + | 0.830047i | \(0.311686\pi\) | |||||||
\(410\) | 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 | −0.0642636 | − | 0.997933i | \(-0.520470\pi\) |
0.896367 | − | 0.443313i | \(-0.146197\pi\) | |||||||
\(432\) | 5.42346 | + | 1.45321i | 0.260936 | + | 0.0699177i | ||||
\(433\) | −7.94050 | − | 7.94050i | −0.381596 | − | 0.381596i | 0.490081 | − | 0.871677i | \(-0.336967\pi\) |
−0.871677 | + | 0.490081i | \(0.836967\pi\) | |||||||
\(434\) | −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 | 0.503992 | − | 0.863708i | \(-0.331864\pi\) |
−0.999989 | + | 0.00461537i | \(0.998531\pi\) | |||||||
\(440\) | 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 | \(-0.502196\pi\) |
−0.505962 | + | 0.862556i | \(0.668862\pi\) | |||||||
\(444\) | 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 | \(-0.822288\pi\) | ||
0.848157 | − | 0.529744i | \(-0.177712\pi\) | |||||||
\(450\) | 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 | −0.359844 | − | 0.933013i | \(-0.617170\pi\) |
0.778140 | − | 0.628091i | \(-0.216163\pi\) | |||||||
\(458\) | 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 | \(-0.880373\pi\) | ||
0.930208 | − | 0.367034i | \(-0.119627\pi\) | |||||||
\(462\) | 18.0255 | + | 3.32861i | 0.838624 | + | 0.154861i | ||||
\(463\) | −22.3091 | + | 22.3091i | −1.03679 | + | 1.03679i | −0.0374951 | + | 0.999297i | \(0.511938\pi\) |
−0.999297 | + | 0.0374951i | \(0.988062\pi\) | |||||||
\(464\) | −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 | \(-0.316478\pi\) |
0.0529290 | + | 0.998598i | \(0.483144\pi\) | |||||||
\(468\) | −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 | −0.941892 | − | 0.335915i | \(-0.890955\pi\) |
0.761857 | + | 0.647745i | \(0.224288\pi\) | |||||||
\(480\) | 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 | \(-0.517232\pi\) |
0.452406 | + | 0.891812i | \(0.350566\pi\) | |||||||
\(488\) | −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 | −0.575529 | − | 0.817781i | \(-0.695204\pi\) |
0.420455 | + | 0.907314i | \(0.361871\pi\) | |||||||
\(500\) | 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 | \(-0.0928148\pi\) |
−0.287472 | + | 0.957789i | \(0.592815\pi\) | |||||||
\(504\) | −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 | 0.849762 | − | 0.527167i | \(-0.176746\pi\) |
−0.881421 | + | 0.472332i | \(0.843412\pi\) | |||||||
\(510\) | 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 | −0.120125 | − | 0.992759i | \(-0.538330\pi\) |
−0.919817 | + | 0.392348i | \(0.871663\pi\) | |||||||
\(522\) | 2.80150 | − | 0.750661i | 0.122619 | − | 0.0328555i | ||||
\(523\) | 8.28588 | − | 30.9233i | 0.362316 | − | 1.35218i | −0.508707 | − | 0.860940i | \(-0.669876\pi\) |
0.871023 | − | 0.491242i | \(-0.163457\pi\) | |||||||
\(524\) | −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 | 0.947632 | − | 0.319365i | \(-0.103470\pi\) |
−0.750394 | + | 0.660990i | \(0.770136\pi\) | |||||||
\(542\) | −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 | \(-0.161596\pi\) |
−0.486141 | + | 0.873881i | \(0.661596\pi\) | |||||||
\(548\) | 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 | \(-0.723913\pi\) |
−0.178877 | + | 0.983871i | \(0.557246\pi\) | |||||||
\(558\) | −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 | \(-0.626745\pi\) |
0.125088 | + | 0.992146i | \(0.460079\pi\) | |||||||
\(564\) | −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 | −0.667630 | − | 0.744494i | \(-0.732691\pi\) |
0.310935 | + | 0.950431i | \(0.399358\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.8248 | − | 25.6772i | 0.620397 | − | 1.07456i | −0.369015 | − | 0.929423i | \(-0.620305\pi\) |
0.989412 | − | 0.145135i | \(-0.0463617\pi\) | |||||||
\(572\) | 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 | 0.974871 | + | 0.222768i | \(0.0715092\pi\) |
−0.732880 | + | 0.680358i | \(0.761824\pi\) | |||||||
\(578\) | 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 | \(-0.818802\pi\) |
0.539001 | + | 0.842305i | \(0.318802\pi\) | |||||||
\(588\) | 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 | −0.533098 | − | 0.846054i | \(-0.678972\pi\) |
0.884703 | − | 0.466155i | \(-0.154361\pi\) | |||||||
\(594\) | 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 | 0.550435 | − | 0.834878i | \(-0.314462\pi\) |
−0.447808 | + | 0.894130i | \(0.647795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.92820i | − | 0.282607i | −0.989966 | − | 0.141304i | \(-0.954871\pi\) | ||
0.989966 | − | 0.141304i | \(-0.0451294\pi\) | |||||||
\(602\) | −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 | \(-0.270827\pi\) |
0.195109 | + | 0.980782i | \(0.437494\pi\) | |||||||
\(608\) | 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 | −0.999593 | − | 0.0285247i | \(-0.990919\pi\) |
0.851411 | − | 0.524500i | \(-0.175748\pi\) | |||||||
\(614\) | 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 | \(-0.469858\pi\) |
−0.995520 | + | 0.0945520i | \(0.969858\pi\) | |||||||
\(618\) | −6.06110 | − | 1.62407i | −0.243813 | − | 0.0653296i | ||||
\(619\) | −1.10411 | + | 1.91238i | −0.0443780 | + | 0.0768649i | −0.887361 | − | 0.461075i | \(-0.847464\pi\) |
0.842983 | + | 0.537940i | \(0.180797\pi\) | |||||||
\(620\) | 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 | −0.466029 | − | 0.884769i | \(-0.654316\pi\) |
0.999247 | − | 0.0387913i | \(-0.0123508\pi\) | |||||||
\(642\) | 8.65836 | + | 2.32000i | 0.341718 | + | 0.0915631i | ||||
\(643\) | 4.98036 | + | 4.98036i | 0.196406 | + | 0.196406i | 0.798457 | − | 0.602051i | \(-0.205650\pi\) |
−0.602051 | + | 0.798457i | \(0.705650\pi\) | |||||||
\(644\) | −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 | \(-0.115903\pi\) |
−0.987310 | + | 0.158805i | \(0.949236\pi\) | |||||||
\(648\) | 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 | \(-0.221004\pi\) |
0.345615 | + | 0.938376i | \(0.387670\pi\) | |||||||
\(654\) | −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 | \(-0.895529\pi\) | ||
0.946622 | − | 0.322345i | \(-0.104471\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.58762 | − | 4.95807i | −0.334020 | − | 0.192846i | 0.323605 | − | 0.946192i | \(-0.395105\pi\) |
−0.657624 | + | 0.753346i | \(0.728439\pi\) | |||||||
\(662\) | 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 | \(-0.635921\pi\) |
0.910209 | + | 0.414150i | \(0.135921\pi\) | |||||||
\(674\) | 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 | \(-0.214499\pi\) |
0.364716 | + | 0.931119i | \(0.381166\pi\) | |||||||
\(678\) | −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 | 0.932712 | + | 0.360622i | \(0.117436\pi\) |
−0.627441 | + | 0.778664i | \(0.715898\pi\) | |||||||
\(684\) | −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 | 0.361325 | − | 0.932440i | \(-0.382324\pi\) |
0.988179 | + | 0.153303i | \(0.0489911\pi\) | |||||||
\(692\) | 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 | −0.698714 | − | 0.715401i | \(-0.746244\pi\) |
0.270199 | + | 0.962805i | \(0.412911\pi\) | |||||||
\(710\) | 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 | 0.957602 | + | 0.288095i | \(0.0930220\pi\) |
−0.229303 | + | 0.973355i | \(0.573645\pi\) | |||||||
\(720\) | 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 | \(-0.739095\pi\) |
0.730913 | + | 0.682471i | \(0.239095\pi\) | |||||||
\(728\) | 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 | −0.633416 | − | 0.773811i | \(-0.718348\pi\) |
0.935460 | − | 0.353432i | \(-0.114985\pi\) | |||||||
\(734\) | −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 | 0.432017 | − | 0.901865i | \(-0.357802\pi\) |
−0.565029 | + | 0.825071i | \(0.691135\pi\) | |||||||
\(740\) | 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 | \(-0.838727\pi\) |
0.485254 | + | 0.874373i | \(0.338727\pi\) | |||||||
\(744\) | 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 | 0.956963 | + | 0.290209i | \(0.0937250\pi\) |
−0.227153 | + | 0.973859i | \(0.572942\pi\) | |||||||
\(752\) | −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 | \(-0.215223\pi\) |
−0.625790 | + | 0.779992i | \(0.715223\pi\) | |||||||
\(758\) | −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 | −0.598828 | + | 0.800878i | \(0.704367\pi\) |
−0.992994 | + | 0.118161i | \(0.962300\pi\) | |||||||
\(762\) | 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 | \(-0.378345\pi\) |
0.786912 | + | 0.617066i | \(0.211679\pi\) | |||||||
\(774\) | −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 | 0.942722 | + | 0.333578i | \(0.108256\pi\) |
−0.649632 | + | 0.760249i | \(0.725077\pi\) | |||||||
\(788\) | −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 | \(-0.828922\pi\) |
0.511952 | + | 0.859014i | \(0.328922\pi\) | |||||||
\(798\) | 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 | 0.404256 | − | 0.914646i | \(-0.367530\pi\) |
−0.589978 | + | 0.807419i | \(0.700864\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.0170i | 0.597547i | 0.954324 | + | 0.298773i | \(0.0965774\pi\) | ||||
−0.954324 | + | 0.298773i | \(0.903423\pi\) | |||||||
\(812\) | −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 | −0.888979 | − | 0.457948i | \(-0.848584\pi\) |
0.0478946 | − | 0.998852i | \(-0.484749\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.87220 | − | 18.1833i | −0.169834 | − | 0.633830i | −0.997374 | − | 0.0724232i | \(-0.976927\pi\) |
0.827540 | − | 0.561407i | \(-0.189740\pi\) | |||||||
\(824\) | −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 | \(-0.402258\pi\) |
−0.953225 | + | 0.302262i | \(0.902258\pi\) | |||||||
\(828\) | −3.69443 | − | 0.989919i | −0.128390 | − | 0.0344020i | ||||
\(829\) | −5.67232 | + | 9.82475i | −0.197008 | + | 0.341228i | −0.947557 | − | 0.319587i | \(-0.896456\pi\) |
0.750549 | + | 0.660815i | \(0.229789\pi\) | |||||||
\(830\) | 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 | \(-0.450800\pi\) |
−0.988078 | + | 0.153952i | \(0.950800\pi\) | |||||||
\(854\) | 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 | 0.999942 | + | 0.0107567i | \(0.00342404\pi\) |
−0.860597 | + | 0.509287i | \(0.829909\pi\) | |||||||
\(858\) | 0.750661 | + | 2.80150i | 0.0256271 | + | 0.0956418i | ||||
\(859\) | −1.25588 | − | 2.17525i | −0.0428501 | − | 0.0742185i | 0.843805 | − | 0.536650i | \(-0.180310\pi\) |
−0.886655 | + | 0.462431i | \(0.846977\pi\) | |||||||
\(860\) | 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 | \(-0.647719\pi\) |
−0.834746 | + | 0.550635i | \(0.814385\pi\) | |||||||
\(864\) | −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 | \(-0.839738\pi\) |
0.999798 | + | 0.0201202i | \(0.00640488\pi\) | |||||||
\(878\) | 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 | \(-0.822906\pi\) | ||
0.849184 | − | 0.528097i | \(-0.177094\pi\) | |||||||
\(882\) | −7.22688 | − | 5.23617i | −0.243342 | − | 0.176311i | ||||
\(883\) | −6.43444 | + | 6.43444i | −0.216536 | + | 0.216536i | −0.807037 | − | 0.590501i | \(-0.798930\pi\) |
0.590501 | + | 0.807037i | \(0.298930\pi\) | |||||||
\(884\) | 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 | \(-0.538311\pi\) |
−0.600363 | + | 0.799727i | \(0.704977\pi\) | |||||||
\(888\) | 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 | \(-0.736779\pi\) |
−0.218486 | + | 0.975840i | \(0.570112\pi\) | |||||||
\(908\) | −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 | −0.896568 | − | 0.442906i | \(-0.853947\pi\) |
−0.0647157 | + | 0.997904i | \(0.520614\pi\) | |||||||
\(920\) | 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 | 0.953123 | − | 0.302584i | \(-0.0978492\pi\) |
−0.738607 | + | 0.674137i | \(0.764516\pi\) | |||||||
\(930\) | 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 | 0.262781 | − | 0.964856i | \(-0.415360\pi\) |
0.964856 | − | 0.262781i | \(-0.0846397\pi\) | |||||||
\(938\) | 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 | 0.427410 | − | 0.904058i | \(-0.359426\pi\) |
−0.569232 | + | 0.822177i | \(0.692759\pi\) | |||||||
\(942\) | 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 | −0.840472 | − | 0.541855i | \(-0.817722\pi\) |
0.998798 | − | 0.0490237i | \(-0.0156110\pi\) | |||||||
\(948\) | 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 | \(-0.530377\pi\) |
0.995450 | + | 0.0952888i | \(0.0303775\pi\) | |||||||
\(954\) | 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 | \(-0.398218\pi\) |
−0.949311 | + | 0.314337i | \(0.898218\pi\) | |||||||
\(968\) | −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 | 0.352689 | − | 0.935741i | \(-0.385267\pi\) |
0.986720 | + | 0.162433i | \(0.0519342\pi\) | |||||||
\(972\) | 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 | \(-0.481556\pi\) |
0.549313 | + | 0.835617i | \(0.314890\pi\) | |||||||
\(978\) | 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 | \(-0.395978\pi\) |
0.751539 | + | 0.659688i | \(0.229312\pi\) | |||||||
\(984\) | −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 | −0.641286 | − | 0.767302i | \(-0.721599\pi\) |
0.985146 | + | 0.171719i | \(0.0549322\pi\) | |||||||
\(992\) | 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 | −0.971492 | − | 0.237071i | \(-0.923813\pi\) |
0.722802 | − | 0.691055i | \(-0.242854\pi\) | |||||||
\(998\) | −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.157.1 | yes | 16 | |
5.2 | odd | 4 | inner | 350.2.o.d.143.2 | ✓ | 16 | |
5.3 | odd | 4 | inner | 350.2.o.d.143.3 | yes | 16 | |
5.4 | even | 2 | inner | 350.2.o.d.157.4 | yes | 16 | |
7.5 | odd | 6 | inner | 350.2.o.d.257.3 | yes | 16 | |
35.12 | even | 12 | inner | 350.2.o.d.243.4 | yes | 16 | |
35.19 | odd | 6 | inner | 350.2.o.d.257.2 | yes | 16 | |
35.33 | even | 12 | inner | 350.2.o.d.243.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.2.o.d.143.2 | ✓ | 16 | 5.2 | odd | 4 | inner | |
350.2.o.d.143.3 | yes | 16 | 5.3 | odd | 4 | inner | |
350.2.o.d.157.1 | yes | 16 | 1.1 | even | 1 | trivial | |
350.2.o.d.157.4 | yes | 16 | 5.4 | even | 2 | inner | |
350.2.o.d.243.1 | yes | 16 | 35.33 | even | 12 | inner | |
350.2.o.d.243.4 | yes | 16 | 35.12 | even | 12 | inner | |
350.2.o.d.257.2 | yes | 16 | 35.19 | odd | 6 | inner | |
350.2.o.d.257.3 | yes | 16 | 7.5 | odd | 6 | inner |