Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 372.1 | ||
Root | \(-0.309017 - 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.372 |
Dual form | 847.2.f.l.148.1 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.118034 | + | 0.363271i | −0.0834626 | + | 0.256872i | −0.984076 | − | 0.177750i | \(-0.943118\pi\) |
0.900613 | + | 0.434622i | \(0.143118\pi\) | |||||||
\(3\) | 1.30902 | − | 0.951057i | 0.755761 | − | 0.549093i | −0.141846 | − | 0.989889i | \(-0.545304\pi\) |
0.897607 | + | 0.440796i | \(0.145304\pi\) | |||||||
\(4\) | 1.50000 | + | 1.08981i | 0.750000 | + | 0.544907i | ||||
\(5\) | 0.309017 | + | 0.951057i | 0.138197 | + | 0.425325i | 0.996074 | − | 0.0885298i | \(-0.0282169\pi\) |
−0.857877 | + | 0.513855i | \(0.828217\pi\) | |||||||
\(6\) | 0.190983 | + | 0.587785i | 0.0779685 | + | 0.239962i | ||||
\(7\) | −0.809017 | − | 0.587785i | −0.305780 | − | 0.222162i | ||||
\(8\) | −1.19098 | + | 0.865300i | −0.421076 | + | 0.305930i | ||||
\(9\) | −0.118034 | + | 0.363271i | −0.0393447 | + | 0.121090i | ||||
\(10\) | −0.381966 | −0.120788 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.00000 | 0.866025 | ||||||||
\(13\) | −0.381966 | + | 1.17557i | −0.105938 | + | 0.326045i | −0.989950 | − | 0.141421i | \(-0.954833\pi\) |
0.884011 | + | 0.467466i | \(0.154833\pi\) | |||||||
\(14\) | 0.309017 | − | 0.224514i | 0.0825883 | − | 0.0600039i | ||||
\(15\) | 1.30902 | + | 0.951057i | 0.337987 | + | 0.245562i | ||||
\(16\) | 0.972136 | + | 2.99193i | 0.243034 | + | 0.747982i | ||||
\(17\) | 0.954915 | + | 2.93893i | 0.231601 | + | 0.712794i | 0.997554 | + | 0.0698980i | \(0.0222674\pi\) |
−0.765953 | + | 0.642896i | \(0.777733\pi\) | |||||||
\(18\) | −0.118034 | − | 0.0857567i | −0.0278209 | − | 0.0202131i | ||||
\(19\) | 1.42705 | − | 1.03681i | 0.327388 | − | 0.237861i | −0.411934 | − | 0.911214i | \(-0.635146\pi\) |
0.739321 | + | 0.673353i | \(0.235146\pi\) | |||||||
\(20\) | −0.572949 | + | 1.76336i | −0.128115 | + | 0.394298i | ||||
\(21\) | −1.61803 | −0.353084 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.09017 | 1.06137 | 0.530687 | − | 0.847568i | \(-0.321934\pi\) | ||||
0.530687 | + | 0.847568i | \(0.321934\pi\) | |||||||
\(24\) | −0.736068 | + | 2.26538i | −0.150249 | + | 0.462420i | ||||
\(25\) | 3.23607 | − | 2.35114i | 0.647214 | − | 0.470228i | ||||
\(26\) | −0.381966 | − | 0.277515i | −0.0749097 | − | 0.0544251i | ||||
\(27\) | 1.69098 | + | 5.20431i | 0.325430 | + | 1.00157i | ||||
\(28\) | −0.572949 | − | 1.76336i | −0.108277 | − | 0.333243i | ||||
\(29\) | 3.73607 | + | 2.71441i | 0.693770 | + | 0.504054i | 0.877897 | − | 0.478849i | \(-0.158946\pi\) |
−0.184127 | + | 0.982902i | \(0.558946\pi\) | |||||||
\(30\) | −0.500000 | + | 0.363271i | −0.0912871 | + | 0.0663240i | ||||
\(31\) | −1.30902 | + | 4.02874i | −0.235106 | + | 0.723583i | 0.762001 | + | 0.647576i | \(0.224217\pi\) |
−0.997107 | + | 0.0760071i | \(0.975783\pi\) | |||||||
\(32\) | −4.14590 | −0.732898 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.18034 | −0.202427 | ||||||||
\(35\) | 0.309017 | − | 0.951057i | 0.0522334 | − | 0.160758i | ||||
\(36\) | −0.572949 | + | 0.416272i | −0.0954915 | + | 0.0693786i | ||||
\(37\) | −5.23607 | − | 3.80423i | −0.860804 | − | 0.625411i | 0.0672994 | − | 0.997733i | \(-0.478562\pi\) |
−0.928104 | + | 0.372322i | \(0.878562\pi\) | |||||||
\(38\) | 0.208204 | + | 0.640786i | 0.0337751 | + | 0.103949i | ||||
\(39\) | 0.618034 | + | 1.90211i | 0.0989646 | + | 0.304582i | ||||
\(40\) | −1.19098 | − | 0.865300i | −0.188311 | − | 0.136816i | ||||
\(41\) | 9.04508 | − | 6.57164i | 1.41260 | − | 1.02632i | 0.419668 | − | 0.907678i | \(-0.362147\pi\) |
0.992937 | − | 0.118640i | \(-0.0378533\pi\) | |||||||
\(42\) | 0.190983 | − | 0.587785i | 0.0294693 | − | 0.0906972i | ||||
\(43\) | −12.5623 | −1.91573 | −0.957867 | − | 0.287213i | \(-0.907271\pi\) | ||||
−0.957867 | + | 0.287213i | \(0.907271\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.381966 | −0.0569401 | ||||||||
\(46\) | −0.600813 | + | 1.84911i | −0.0885851 | + | 0.272637i | ||||
\(47\) | 5.35410 | − | 3.88998i | 0.780976 | − | 0.567412i | −0.124296 | − | 0.992245i | \(-0.539667\pi\) |
0.905272 | + | 0.424833i | \(0.139667\pi\) | |||||||
\(48\) | 4.11803 | + | 2.99193i | 0.594387 | + | 0.431847i | ||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | 0.472136 | + | 1.45309i | 0.0667701 | + | 0.205497i | ||||
\(51\) | 4.04508 | + | 2.93893i | 0.566425 | + | 0.411532i | ||||
\(52\) | −1.85410 | + | 1.34708i | −0.257118 | + | 0.186807i | ||||
\(53\) | −0.736068 | + | 2.26538i | −0.101107 | + | 0.311174i | −0.988797 | − | 0.149267i | \(-0.952309\pi\) |
0.887690 | + | 0.460441i | \(0.152309\pi\) | |||||||
\(54\) | −2.09017 | −0.284436 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.47214 | 0.196722 | ||||||||
\(57\) | 0.881966 | − | 2.71441i | 0.116819 | − | 0.359533i | ||||
\(58\) | −1.42705 | + | 1.03681i | −0.187381 | + | 0.136140i | ||||
\(59\) | −8.97214 | − | 6.51864i | −1.16807 | − | 0.848654i | −0.177296 | − | 0.984158i | \(-0.556735\pi\) |
−0.990777 | + | 0.135503i | \(0.956735\pi\) | |||||||
\(60\) | 0.927051 | + | 2.85317i | 0.119682 | + | 0.368343i | ||||
\(61\) | −2.35410 | − | 7.24518i | −0.301412 | − | 0.927650i | −0.980992 | − | 0.194049i | \(-0.937838\pi\) |
0.679580 | − | 0.733601i | \(-0.262162\pi\) | |||||||
\(62\) | −1.30902 | − | 0.951057i | −0.166245 | − | 0.120784i | ||||
\(63\) | 0.309017 | − | 0.224514i | 0.0389325 | − | 0.0282861i | ||||
\(64\) | −1.45492 | + | 4.47777i | −0.181864 | + | 0.559721i | ||||
\(65\) | −1.23607 | −0.153315 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.32624 | −1.01721 | −0.508606 | − | 0.860999i | \(-0.669839\pi\) | ||||
−0.508606 | + | 0.860999i | \(0.669839\pi\) | |||||||
\(68\) | −1.77051 | + | 5.44907i | −0.214706 | + | 0.660797i | ||||
\(69\) | 6.66312 | − | 4.84104i | 0.802145 | − | 0.582793i | ||||
\(70\) | 0.309017 | + | 0.224514i | 0.0369346 | + | 0.0268346i | ||||
\(71\) | −4.97214 | − | 15.3027i | −0.590084 | − | 1.81609i | −0.577816 | − | 0.816167i | \(-0.696095\pi\) |
−0.0122679 | − | 0.999925i | \(-0.503905\pi\) | |||||||
\(72\) | −0.173762 | − | 0.534785i | −0.0204781 | − | 0.0630250i | ||||
\(73\) | 11.5172 | + | 8.36775i | 1.34799 | + | 0.979371i | 0.999109 | + | 0.0422036i | \(0.0134378\pi\) |
0.348880 | + | 0.937168i | \(0.386562\pi\) | |||||||
\(74\) | 2.00000 | − | 1.45309i | 0.232495 | − | 0.168918i | ||||
\(75\) | 2.00000 | − | 6.15537i | 0.230940 | − | 0.710761i | ||||
\(76\) | 3.27051 | 0.375153 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.763932 | −0.0864983 | ||||||||
\(79\) | 1.97214 | − | 6.06961i | 0.221883 | − | 0.682885i | −0.776710 | − | 0.629858i | \(-0.783113\pi\) |
0.998593 | − | 0.0530267i | \(-0.0168868\pi\) | |||||||
\(80\) | −2.54508 | + | 1.84911i | −0.284549 | + | 0.206737i | ||||
\(81\) | 6.23607 | + | 4.53077i | 0.692896 | + | 0.503419i | ||||
\(82\) | 1.31966 | + | 4.06150i | 0.145732 | + | 0.448517i | ||||
\(83\) | 0.836881 | + | 2.57565i | 0.0918596 | + | 0.282715i | 0.986423 | − | 0.164227i | \(-0.0525130\pi\) |
−0.894563 | + | 0.446942i | \(0.852513\pi\) | |||||||
\(84\) | −2.42705 | − | 1.76336i | −0.264813 | − | 0.192398i | ||||
\(85\) | −2.50000 | + | 1.81636i | −0.271163 | + | 0.197012i | ||||
\(86\) | 1.48278 | − | 4.56352i | 0.159892 | − | 0.492098i | ||||
\(87\) | 7.47214 | 0.801097 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.85410 | 0.726533 | 0.363267 | − | 0.931685i | \(-0.381661\pi\) | ||||
0.363267 | + | 0.931685i | \(0.381661\pi\) | |||||||
\(90\) | 0.0450850 | − | 0.138757i | 0.00475237 | − | 0.0146263i | ||||
\(91\) | 1.00000 | − | 0.726543i | 0.104828 | − | 0.0761624i | ||||
\(92\) | 7.63525 | + | 5.54734i | 0.796030 | + | 0.578350i | ||||
\(93\) | 2.11803 | + | 6.51864i | 0.219630 | + | 0.675951i | ||||
\(94\) | 0.781153 | + | 2.40414i | 0.0805698 | + | 0.247968i | ||||
\(95\) | 1.42705 | + | 1.03681i | 0.146412 | + | 0.106375i | ||||
\(96\) | −5.42705 | + | 3.94298i | −0.553896 | + | 0.402429i | ||||
\(97\) | 2.16312 | − | 6.65740i | 0.219631 | − | 0.675956i | −0.779161 | − | 0.626824i | \(-0.784354\pi\) |
0.998792 | − | 0.0491321i | \(-0.0156455\pi\) | |||||||
\(98\) | −0.381966 | −0.0385844 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.41641 | 0.741641 | ||||||||
\(101\) | −4.57295 | + | 14.0741i | −0.455025 | + | 1.40042i | 0.416080 | + | 0.909328i | \(0.363404\pi\) |
−0.871105 | + | 0.491096i | \(0.836596\pi\) | |||||||
\(102\) | −1.54508 | + | 1.12257i | −0.152986 | + | 0.111151i | ||||
\(103\) | −7.16312 | − | 5.20431i | −0.705803 | − | 0.512796i | 0.176014 | − | 0.984388i | \(-0.443680\pi\) |
−0.881817 | + | 0.471592i | \(0.843680\pi\) | |||||||
\(104\) | −0.562306 | − | 1.73060i | −0.0551386 | − | 0.169699i | ||||
\(105\) | −0.500000 | − | 1.53884i | −0.0487950 | − | 0.150176i | ||||
\(106\) | −0.736068 | − | 0.534785i | −0.0714932 | − | 0.0519429i | ||||
\(107\) | −2.19098 | + | 1.59184i | −0.211810 | + | 0.153889i | −0.688632 | − | 0.725111i | \(-0.741789\pi\) |
0.476822 | + | 0.879000i | \(0.341789\pi\) | |||||||
\(108\) | −3.13525 | + | 9.64932i | −0.301690 | + | 0.928506i | ||||
\(109\) | −1.52786 | −0.146343 | −0.0731714 | − | 0.997319i | \(-0.523312\pi\) | ||||
−0.0731714 | + | 0.997319i | \(0.523312\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.4721 | −0.993971 | ||||||||
\(112\) | 0.972136 | − | 2.99193i | 0.0918582 | − | 0.282711i | ||||
\(113\) | −0.118034 | + | 0.0857567i | −0.0111037 | + | 0.00806731i | −0.593323 | − | 0.804964i | \(-0.702184\pi\) |
0.582220 | + | 0.813032i | \(0.302184\pi\) | |||||||
\(114\) | 0.881966 | + | 0.640786i | 0.0826037 | + | 0.0600151i | ||||
\(115\) | 1.57295 | + | 4.84104i | 0.146678 | + | 0.451429i | ||||
\(116\) | 2.64590 | + | 8.14324i | 0.245665 | + | 0.756081i | ||||
\(117\) | −0.381966 | − | 0.277515i | −0.0353128 | − | 0.0256562i | ||||
\(118\) | 3.42705 | − | 2.48990i | 0.315486 | − | 0.229214i | ||||
\(119\) | 0.954915 | − | 2.93893i | 0.0875369 | − | 0.269411i | ||||
\(120\) | −2.38197 | −0.217443 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2.90983 | 0.263444 | ||||||||
\(123\) | 5.59017 | − | 17.2048i | 0.504049 | − | 1.55130i | ||||
\(124\) | −6.35410 | + | 4.61653i | −0.570615 | + | 0.414576i | ||||
\(125\) | 7.28115 | + | 5.29007i | 0.651246 | + | 0.473158i | ||||
\(126\) | 0.0450850 | + | 0.138757i | 0.00401649 | + | 0.0123615i | ||||
\(127\) | 0.909830 | + | 2.80017i | 0.0807344 | + | 0.248475i | 0.983274 | − | 0.182132i | \(-0.0582997\pi\) |
−0.902540 | + | 0.430606i | \(0.858300\pi\) | |||||||
\(128\) | −8.16312 | − | 5.93085i | −0.721525 | − | 0.524218i | ||||
\(129\) | −16.4443 | + | 11.9475i | −1.44784 | + | 1.05192i | ||||
\(130\) | 0.145898 | − | 0.449028i | 0.0127961 | − | 0.0393824i | ||||
\(131\) | 18.9443 | 1.65517 | 0.827584 | − | 0.561341i | \(-0.189715\pi\) | ||||
0.827584 | + | 0.561341i | \(0.189715\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.76393 | −0.152952 | ||||||||
\(134\) | 0.982779 | − | 3.02468i | 0.0848992 | − | 0.261293i | ||||
\(135\) | −4.42705 | + | 3.21644i | −0.381020 | + | 0.276827i | ||||
\(136\) | −3.68034 | − | 2.67392i | −0.315587 | − | 0.229287i | ||||
\(137\) | −4.73607 | − | 14.5761i | −0.404630 | − | 1.24532i | −0.921204 | − | 0.389080i | \(-0.872793\pi\) |
0.516575 | − | 0.856242i | \(-0.327207\pi\) | |||||||
\(138\) | 0.972136 | + | 2.99193i | 0.0827537 | + | 0.254690i | ||||
\(139\) | −9.66312 | − | 7.02067i | −0.819615 | − | 0.595485i | 0.0969872 | − | 0.995286i | \(-0.469079\pi\) |
−0.916602 | + | 0.399800i | \(0.869079\pi\) | |||||||
\(140\) | 1.50000 | − | 1.08981i | 0.126773 | − | 0.0921061i | ||||
\(141\) | 3.30902 | − | 10.1841i | 0.278670 | − | 0.857657i | ||||
\(142\) | 6.14590 | 0.515752 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.20163 | −0.100136 | ||||||||
\(145\) | −1.42705 | + | 4.39201i | −0.118510 | + | 0.364737i | ||||
\(146\) | −4.39919 | + | 3.19620i | −0.364079 | + | 0.264519i | ||||
\(147\) | 1.30902 | + | 0.951057i | 0.107966 | + | 0.0784418i | ||||
\(148\) | −3.70820 | − | 11.4127i | −0.304812 | − | 0.938116i | ||||
\(149\) | −2.73607 | − | 8.42075i | −0.224147 | − | 0.689855i | −0.998377 | − | 0.0569500i | \(-0.981862\pi\) |
0.774230 | − | 0.632905i | \(-0.218138\pi\) | |||||||
\(150\) | 2.00000 | + | 1.45309i | 0.163299 | + | 0.118644i | ||||
\(151\) | −0.0450850 | + | 0.0327561i | −0.00366896 | + | 0.00266566i | −0.589618 | − | 0.807682i | \(-0.700722\pi\) |
0.585949 | + | 0.810348i | \(0.300722\pi\) | |||||||
\(152\) | −0.802439 | + | 2.46965i | −0.0650864 | + | 0.200315i | ||||
\(153\) | −1.18034 | −0.0954248 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.23607 | −0.340249 | ||||||||
\(156\) | −1.14590 | + | 3.52671i | −0.0917453 | + | 0.282363i | ||||
\(157\) | −16.0902 | + | 11.6902i | −1.28414 | + | 0.932979i | −0.999670 | − | 0.0257072i | \(-0.991816\pi\) |
−0.284466 | + | 0.958686i | \(0.591816\pi\) | |||||||
\(158\) | 1.97214 | + | 1.43284i | 0.156895 | + | 0.113991i | ||||
\(159\) | 1.19098 | + | 3.66547i | 0.0944511 | + | 0.290691i | ||||
\(160\) | −1.28115 | − | 3.94298i | −0.101284 | − | 0.311720i | ||||
\(161\) | −4.11803 | − | 2.99193i | −0.324547 | − | 0.235797i | ||||
\(162\) | −2.38197 | + | 1.73060i | −0.187145 | + | 0.135969i | ||||
\(163\) | −2.69098 | + | 8.28199i | −0.210774 | + | 0.648696i | 0.788653 | + | 0.614839i | \(0.210779\pi\) |
−0.999427 | + | 0.0338568i | \(0.989221\pi\) | |||||||
\(164\) | 20.7295 | 1.61870 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.03444 | −0.0802883 | ||||||||
\(167\) | 2.00000 | − | 6.15537i | 0.154765 | − | 0.476317i | −0.843372 | − | 0.537330i | \(-0.819433\pi\) |
0.998137 | + | 0.0610130i | \(0.0194331\pi\) | |||||||
\(168\) | 1.92705 | − | 1.40008i | 0.148675 | − | 0.108019i | ||||
\(169\) | 9.28115 | + | 6.74315i | 0.713935 | + | 0.518704i | ||||
\(170\) | −0.364745 | − | 1.12257i | −0.0279747 | − | 0.0860972i | ||||
\(171\) | 0.208204 | + | 0.640786i | 0.0159218 | + | 0.0490021i | ||||
\(172\) | −18.8435 | − | 13.6906i | −1.43680 | − | 1.04390i | ||||
\(173\) | 12.4443 | − | 9.04129i | 0.946120 | − | 0.687397i | −0.00376565 | − | 0.999993i | \(-0.501199\pi\) |
0.949886 | + | 0.312596i | \(0.101199\pi\) | |||||||
\(174\) | −0.881966 | + | 2.71441i | −0.0668617 | + | 0.205779i | ||||
\(175\) | −4.00000 | −0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.9443 | −1.34877 | ||||||||
\(178\) | −0.809017 | + | 2.48990i | −0.0606384 | + | 0.186626i | ||||
\(179\) | 3.04508 | − | 2.21238i | 0.227600 | − | 0.165361i | −0.468141 | − | 0.883654i | \(-0.655076\pi\) |
0.695741 | + | 0.718293i | \(0.255076\pi\) | |||||||
\(180\) | −0.572949 | − | 0.416272i | −0.0427051 | − | 0.0310271i | ||||
\(181\) | −2.29180 | − | 7.05342i | −0.170348 | − | 0.524277i | 0.829043 | − | 0.559185i | \(-0.188886\pi\) |
−0.999391 | + | 0.0349086i | \(0.988886\pi\) | |||||||
\(182\) | 0.145898 | + | 0.449028i | 0.0108147 | + | 0.0332842i | ||||
\(183\) | −9.97214 | − | 7.24518i | −0.737162 | − | 0.535579i | ||||
\(184\) | −6.06231 | + | 4.40452i | −0.446919 | + | 0.324706i | ||||
\(185\) | 2.00000 | − | 6.15537i | 0.147043 | − | 0.452552i | ||||
\(186\) | −2.61803 | −0.191964 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.2705 | 0.894919 | ||||||||
\(189\) | 1.69098 | − | 5.20431i | 0.123001 | − | 0.378558i | ||||
\(190\) | −0.545085 | + | 0.396027i | −0.0395446 | + | 0.0287308i | ||||
\(191\) | −12.7533 | − | 9.26581i | −0.922796 | − | 0.670450i | 0.0214227 | − | 0.999771i | \(-0.493180\pi\) |
−0.944218 | + | 0.329320i | \(0.893180\pi\) | |||||||
\(192\) | 2.35410 | + | 7.24518i | 0.169893 | + | 0.522876i | ||||
\(193\) | −4.73607 | − | 14.5761i | −0.340910 | − | 1.04921i | −0.963737 | − | 0.266853i | \(-0.914016\pi\) |
0.622828 | − | 0.782359i | \(-0.285984\pi\) | |||||||
\(194\) | 2.16312 | + | 1.57160i | 0.155303 | + | 0.112834i | ||||
\(195\) | −1.61803 | + | 1.17557i | −0.115870 | + | 0.0841844i | ||||
\(196\) | −0.572949 | + | 1.76336i | −0.0409249 | + | 0.125954i | ||||
\(197\) | −4.29180 | −0.305778 | −0.152889 | − | 0.988243i | \(-0.548858\pi\) | ||||
−0.152889 | + | 0.988243i | \(0.548858\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.23607 | −0.583839 | −0.291920 | − | 0.956443i | \(-0.594294\pi\) | ||||
−0.291920 | + | 0.956443i | \(0.594294\pi\) | |||||||
\(200\) | −1.81966 | + | 5.60034i | −0.128669 | + | 0.396004i | ||||
\(201\) | −10.8992 | + | 7.91872i | −0.768769 | + | 0.558544i | ||||
\(202\) | −4.57295 | − | 3.32244i | −0.321752 | − | 0.233766i | ||||
\(203\) | −1.42705 | − | 4.39201i | −0.100159 | − | 0.308259i | ||||
\(204\) | 2.86475 | + | 8.81678i | 0.200572 | + | 0.617298i | ||||
\(205\) | 9.04508 | + | 6.57164i | 0.631736 | + | 0.458983i | ||||
\(206\) | 2.73607 | − | 1.98787i | 0.190631 | − | 0.138501i | ||||
\(207\) | −0.600813 | + | 1.84911i | −0.0417594 | + | 0.128522i | ||||
\(208\) | −3.88854 | −0.269622 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.618034 | 0.0426484 | ||||||||
\(211\) | 4.82624 | − | 14.8536i | 0.332252 | − | 1.02257i | −0.635808 | − | 0.771847i | \(-0.719333\pi\) |
0.968060 | − | 0.250719i | \(-0.0806670\pi\) | |||||||
\(212\) | −3.57295 | + | 2.59590i | −0.245391 | + | 0.178287i | ||||
\(213\) | −21.0623 | − | 15.3027i | −1.44317 | − | 1.04852i | ||||
\(214\) | −0.319660 | − | 0.983813i | −0.0218515 | − | 0.0672520i | ||||
\(215\) | −3.88197 | − | 11.9475i | −0.264748 | − | 0.814810i | ||||
\(216\) | −6.51722 | − | 4.73504i | −0.443441 | − | 0.322179i | ||||
\(217\) | 3.42705 | − | 2.48990i | 0.232643 | − | 0.169025i | ||||
\(218\) | 0.180340 | − | 0.555029i | 0.0122142 | − | 0.0375913i | ||||
\(219\) | 23.0344 | 1.55652 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.81966 | −0.256938 | ||||||||
\(222\) | 1.23607 | − | 3.80423i | 0.0829595 | − | 0.255323i | ||||
\(223\) | −1.64590 | + | 1.19581i | −0.110217 | + | 0.0800777i | −0.641529 | − | 0.767099i | \(-0.721699\pi\) |
0.531311 | + | 0.847177i | \(0.321699\pi\) | |||||||
\(224\) | 3.35410 | + | 2.43690i | 0.224105 | + | 0.162822i | ||||
\(225\) | 0.472136 | + | 1.45309i | 0.0314757 | + | 0.0968723i | ||||
\(226\) | −0.0172209 | − | 0.0530006i | −0.00114552 | − | 0.00352555i | ||||
\(227\) | 12.9721 | + | 9.42481i | 0.860991 | + | 0.625547i | 0.928154 | − | 0.372195i | \(-0.121395\pi\) |
−0.0671635 | + | 0.997742i | \(0.521395\pi\) | |||||||
\(228\) | 4.28115 | − | 3.11044i | 0.283526 | − | 0.205994i | ||||
\(229\) | 2.09017 | − | 6.43288i | 0.138122 | − | 0.425097i | −0.857940 | − | 0.513749i | \(-0.828256\pi\) |
0.996063 | + | 0.0886526i | \(0.0282561\pi\) | |||||||
\(230\) | −1.94427 | −0.128201 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.79837 | −0.446335 | ||||||||
\(233\) | −9.09017 | + | 27.9767i | −0.595517 | + | 1.83281i | −0.0433803 | + | 0.999059i | \(0.513813\pi\) |
−0.552137 | + | 0.833754i | \(0.686187\pi\) | |||||||
\(234\) | 0.145898 | − | 0.106001i | 0.00953765 | − | 0.00692951i | ||||
\(235\) | 5.35410 | + | 3.88998i | 0.349263 | + | 0.253754i | ||||
\(236\) | −6.35410 | − | 19.5559i | −0.413617 | − | 1.27298i | ||||
\(237\) | −3.19098 | − | 9.82084i | −0.207277 | − | 0.637932i | ||||
\(238\) | 0.954915 | + | 0.693786i | 0.0618979 | + | 0.0449715i | ||||
\(239\) | 13.8262 | − | 10.0453i | 0.894345 | − | 0.649780i | −0.0426623 | − | 0.999090i | \(-0.513584\pi\) |
0.937007 | + | 0.349310i | \(0.113584\pi\) | |||||||
\(240\) | −1.57295 | + | 4.84104i | −0.101533 | + | 0.312488i | ||||
\(241\) | 16.2705 | 1.04808 | 0.524038 | − | 0.851695i | \(-0.324425\pi\) | ||||
0.524038 | + | 0.851695i | \(0.324425\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | 4.36475 | − | 13.4333i | 0.279424 | − | 0.859979i | ||||
\(245\) | −0.809017 | + | 0.587785i | −0.0516862 | + | 0.0375522i | ||||
\(246\) | 5.59017 | + | 4.06150i | 0.356416 | + | 0.258952i | ||||
\(247\) | 0.673762 | + | 2.07363i | 0.0428705 | + | 0.131942i | ||||
\(248\) | −1.92705 | − | 5.93085i | −0.122368 | − | 0.376610i | ||||
\(249\) | 3.54508 | + | 2.57565i | 0.224661 | + | 0.163226i | ||||
\(250\) | −2.78115 | + | 2.02063i | −0.175896 | + | 0.127796i | ||||
\(251\) | 7.10739 | − | 21.8743i | 0.448615 | − | 1.38069i | −0.429856 | − | 0.902897i | \(-0.641436\pi\) |
0.878471 | − | 0.477796i | \(-0.158564\pi\) | |||||||
\(252\) | 0.708204 | 0.0446127 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.12461 | −0.0705644 | ||||||||
\(255\) | −1.54508 | + | 4.75528i | −0.0967570 | + | 0.297787i | ||||
\(256\) | −4.50000 | + | 3.26944i | −0.281250 | + | 0.204340i | ||||
\(257\) | 6.92705 | + | 5.03280i | 0.432098 | + | 0.313937i | 0.782487 | − | 0.622667i | \(-0.213951\pi\) |
−0.350390 | + | 0.936604i | \(0.613951\pi\) | |||||||
\(258\) | −2.39919 | − | 7.38394i | −0.149367 | − | 0.459704i | ||||
\(259\) | 2.00000 | + | 6.15537i | 0.124274 | + | 0.382476i | ||||
\(260\) | −1.85410 | − | 1.34708i | −0.114987 | − | 0.0835426i | ||||
\(261\) | −1.42705 | + | 1.03681i | −0.0883322 | + | 0.0641771i | ||||
\(262\) | −2.23607 | + | 6.88191i | −0.138145 | + | 0.425166i | ||||
\(263\) | −17.1246 | −1.05595 | −0.527974 | − | 0.849260i | \(-0.677048\pi\) | ||||
−0.527974 | + | 0.849260i | \(0.677048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.38197 | −0.146323 | ||||||||
\(266\) | 0.208204 | − | 0.640786i | 0.0127658 | − | 0.0392891i | ||||
\(267\) | 8.97214 | − | 6.51864i | 0.549086 | − | 0.398934i | ||||
\(268\) | −12.4894 | − | 9.07405i | −0.762909 | − | 0.554286i | ||||
\(269\) | 5.20820 | + | 16.0292i | 0.317550 | + | 0.977318i | 0.974692 | + | 0.223551i | \(0.0717650\pi\) |
−0.657142 | + | 0.753766i | \(0.728235\pi\) | |||||||
\(270\) | −0.645898 | − | 1.98787i | −0.0393081 | − | 0.120978i | ||||
\(271\) | 3.88197 | + | 2.82041i | 0.235813 | + | 0.171328i | 0.699416 | − | 0.714715i | \(-0.253444\pi\) |
−0.463603 | + | 0.886043i | \(0.653444\pi\) | |||||||
\(272\) | −7.86475 | + | 5.71407i | −0.476870 | + | 0.346466i | ||||
\(273\) | 0.618034 | − | 1.90211i | 0.0374051 | − | 0.115121i | ||||
\(274\) | 5.85410 | 0.353659 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.2705 | 0.919177 | ||||||||
\(277\) | 7.11803 | − | 21.9071i | 0.427681 | − | 1.31627i | −0.472722 | − | 0.881211i | \(-0.656729\pi\) |
0.900403 | − | 0.435056i | \(-0.143271\pi\) | |||||||
\(278\) | 3.69098 | − | 2.68166i | 0.221370 | − | 0.160835i | ||||
\(279\) | −1.30902 | − | 0.951057i | −0.0783688 | − | 0.0569383i | ||||
\(280\) | 0.454915 | + | 1.40008i | 0.0271864 | + | 0.0836711i | ||||
\(281\) | −7.78115 | − | 23.9479i | −0.464185 | − | 1.42861i | −0.860005 | − | 0.510286i | \(-0.829540\pi\) |
0.395820 | − | 0.918328i | \(-0.370460\pi\) | |||||||
\(282\) | 3.30902 | + | 2.40414i | 0.197049 | + | 0.143165i | ||||
\(283\) | −9.66312 | + | 7.02067i | −0.574413 | + | 0.417335i | −0.836706 | − | 0.547653i | \(-0.815521\pi\) |
0.262293 | + | 0.964988i | \(0.415521\pi\) | |||||||
\(284\) | 9.21885 | − | 28.3727i | 0.547038 | − | 1.68361i | ||||
\(285\) | 2.85410 | 0.169062 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.1803 | −0.659955 | ||||||||
\(288\) | 0.489357 | − | 1.50609i | 0.0288356 | − | 0.0887469i | ||||
\(289\) | 6.02786 | − | 4.37950i | 0.354580 | − | 0.257618i | ||||
\(290\) | −1.42705 | − | 1.03681i | −0.0837993 | − | 0.0608838i | ||||
\(291\) | −3.50000 | − | 10.7719i | −0.205174 | − | 0.631460i | ||||
\(292\) | 8.15654 | + | 25.1033i | 0.477325 | + | 1.46906i | ||||
\(293\) | 8.89919 | + | 6.46564i | 0.519896 | + | 0.377727i | 0.816565 | − | 0.577254i | \(-0.195876\pi\) |
−0.296669 | + | 0.954980i | \(0.595876\pi\) | |||||||
\(294\) | −0.500000 | + | 0.363271i | −0.0291606 | + | 0.0211864i | ||||
\(295\) | 3.42705 | − | 10.5474i | 0.199531 | − | 0.614092i | ||||
\(296\) | 9.52786 | 0.553796 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.38197 | 0.195912 | ||||||||
\(299\) | −1.94427 | + | 5.98385i | −0.112440 | + | 0.346055i | ||||
\(300\) | 9.70820 | − | 7.05342i | 0.560503 | − | 0.407230i | ||||
\(301\) | 10.1631 | + | 7.38394i | 0.585792 | + | 0.425603i | ||||
\(302\) | −0.00657781 | − | 0.0202444i | −0.000378510 | − | 0.00116494i | ||||
\(303\) | 7.39919 | + | 22.7724i | 0.425072 | + | 1.30824i | ||||
\(304\) | 4.48936 | + | 3.26171i | 0.257482 | + | 0.187072i | ||||
\(305\) | 6.16312 | − | 4.47777i | 0.352899 | − | 0.256396i | ||||
\(306\) | 0.139320 | − | 0.428784i | 0.00796441 | − | 0.0245119i | ||||
\(307\) | −23.1803 | −1.32297 | −0.661486 | − | 0.749958i | \(-0.730074\pi\) | ||||
−0.661486 | + | 0.749958i | \(0.730074\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.3262 | −0.814991 | ||||||||
\(310\) | 0.500000 | − | 1.53884i | 0.0283981 | − | 0.0874003i | ||||
\(311\) | −7.28115 | + | 5.29007i | −0.412876 | + | 0.299972i | −0.774765 | − | 0.632249i | \(-0.782132\pi\) |
0.361889 | + | 0.932221i | \(0.382132\pi\) | |||||||
\(312\) | −2.38197 | − | 1.73060i | −0.134852 | − | 0.0979759i | ||||
\(313\) | 5.66312 | + | 17.4293i | 0.320098 | + | 0.985162i | 0.973605 | + | 0.228241i | \(0.0732973\pi\) |
−0.653506 | + | 0.756921i | \(0.726703\pi\) | |||||||
\(314\) | −2.34752 | − | 7.22494i | −0.132478 | − | 0.407727i | ||||
\(315\) | 0.309017 | + | 0.224514i | 0.0174111 | + | 0.0126499i | ||||
\(316\) | 9.57295 | − | 6.95515i | 0.538520 | − | 0.391258i | ||||
\(317\) | −1.37132 | + | 4.22050i | −0.0770212 | + | 0.237047i | −0.982153 | − | 0.188085i | \(-0.939772\pi\) |
0.905132 | + | 0.425131i | \(0.139772\pi\) | |||||||
\(318\) | −1.47214 | −0.0825533 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −4.70820 | −0.263197 | ||||||||
\(321\) | −1.35410 | + | 4.16750i | −0.0755786 | + | 0.232607i | ||||
\(322\) | 1.57295 | − | 1.14281i | 0.0876570 | − | 0.0636866i | ||||
\(323\) | 4.40983 | + | 3.20393i | 0.245370 | + | 0.178271i | ||||
\(324\) | 4.41641 | + | 13.5923i | 0.245356 | + | 0.755128i | ||||
\(325\) | 1.52786 | + | 4.70228i | 0.0847506 | + | 0.260836i | ||||
\(326\) | −2.69098 | − | 1.95511i | −0.149040 | − | 0.108284i | ||||
\(327\) | −2.00000 | + | 1.45309i | −0.110600 | + | 0.0803558i | ||||
\(328\) | −5.08610 | + | 15.6534i | −0.280833 | + | 0.864316i | ||||
\(329\) | −6.61803 | −0.364864 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.18034 | 0.339702 | 0.169851 | − | 0.985470i | \(-0.445671\pi\) | ||||
0.169851 | + | 0.985470i | \(0.445671\pi\) | |||||||
\(332\) | −1.55166 | + | 4.77553i | −0.0851586 | + | 0.262091i | ||||
\(333\) | 2.00000 | − | 1.45309i | 0.109599 | − | 0.0796286i | ||||
\(334\) | 2.00000 | + | 1.45309i | 0.109435 | + | 0.0795093i | ||||
\(335\) | −2.57295 | − | 7.91872i | −0.140575 | − | 0.432646i | ||||
\(336\) | −1.57295 | − | 4.84104i | −0.0858114 | − | 0.264100i | ||||
\(337\) | −20.9894 | − | 15.2497i | −1.14336 | − | 0.830702i | −0.155779 | − | 0.987792i | \(-0.549789\pi\) |
−0.987584 | + | 0.157090i | \(0.949789\pi\) | |||||||
\(338\) | −3.54508 | + | 2.57565i | −0.192827 | + | 0.140097i | ||||
\(339\) | −0.0729490 | + | 0.224514i | −0.00396205 | + | 0.0121939i | ||||
\(340\) | −5.72949 | −0.310725 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.257354 | −0.0139161 | ||||||||
\(343\) | 0.309017 | − | 0.951057i | 0.0166853 | − | 0.0513522i | ||||
\(344\) | 14.9615 | − | 10.8702i | 0.806670 | − | 0.586080i | ||||
\(345\) | 6.66312 | + | 4.84104i | 0.358730 | + | 0.260633i | ||||
\(346\) | 1.81559 | + | 5.58783i | 0.0976070 | + | 0.300403i | ||||
\(347\) | 0.725425 | + | 2.23263i | 0.0389428 | + | 0.119854i | 0.968638 | − | 0.248476i | \(-0.0799297\pi\) |
−0.929695 | + | 0.368330i | \(0.879930\pi\) | |||||||
\(348\) | 11.2082 | + | 8.14324i | 0.600823 | + | 0.436523i | ||||
\(349\) | −26.5344 | + | 19.2784i | −1.42036 | + | 1.03195i | −0.428643 | + | 0.903474i | \(0.641008\pi\) |
−0.991713 | + | 0.128475i | \(0.958992\pi\) | |||||||
\(350\) | 0.472136 | − | 1.45309i | 0.0252367 | − | 0.0776707i | ||||
\(351\) | −6.76393 | −0.361032 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.0902 | 1.28219 | 0.641095 | − | 0.767461i | \(-0.278480\pi\) | ||||
0.641095 | + | 0.767461i | \(0.278480\pi\) | |||||||
\(354\) | 2.11803 | − | 6.51864i | 0.112572 | − | 0.346462i | ||||
\(355\) | 13.0172 | − | 9.45756i | 0.690882 | − | 0.501955i | ||||
\(356\) | 10.2812 | + | 7.46969i | 0.544900 | + | 0.395893i | ||||
\(357\) | −1.54508 | − | 4.75528i | −0.0817746 | − | 0.251676i | ||||
\(358\) | 0.444272 | + | 1.36733i | 0.0234805 | + | 0.0722655i | ||||
\(359\) | 12.6353 | + | 9.18005i | 0.666863 | + | 0.484505i | 0.868974 | − | 0.494858i | \(-0.164780\pi\) |
−0.202110 | + | 0.979363i | \(0.564780\pi\) | |||||||
\(360\) | 0.454915 | − | 0.330515i | 0.0239761 | − | 0.0174197i | ||||
\(361\) | −4.90983 | + | 15.1109i | −0.258412 | + | 0.795311i | ||||
\(362\) | 2.83282 | 0.148889 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.29180 | 0.120123 | ||||||||
\(365\) | −4.39919 | + | 13.5393i | −0.230264 | + | 0.708680i | ||||
\(366\) | 3.80902 | − | 2.76741i | 0.199101 | − | 0.144655i | ||||
\(367\) | −26.5623 | − | 19.2986i | −1.38654 | − | 1.00738i | −0.996235 | − | 0.0866960i | \(-0.972369\pi\) |
−0.390306 | − | 0.920685i | \(-0.627631\pi\) | |||||||
\(368\) | 4.94834 | + | 15.2294i | 0.257950 | + | 0.793888i | ||||
\(369\) | 1.31966 | + | 4.06150i | 0.0686988 | + | 0.211433i | ||||
\(370\) | 2.00000 | + | 1.45309i | 0.103975 | + | 0.0755423i | ||||
\(371\) | 1.92705 | − | 1.40008i | 0.100048 | − | 0.0726888i | ||||
\(372\) | −3.92705 | + | 12.0862i | −0.203608 | + | 0.626641i | ||||
\(373\) | −15.4377 | −0.799334 | −0.399667 | − | 0.916661i | \(-0.630874\pi\) | ||||
−0.399667 | + | 0.916661i | \(0.630874\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.5623 | 0.751994 | ||||||||
\(376\) | −3.01064 | + | 9.26581i | −0.155262 | + | 0.477847i | ||||
\(377\) | −4.61803 | + | 3.35520i | −0.237841 | + | 0.172801i | ||||
\(378\) | 1.69098 | + | 1.22857i | 0.0869748 | + | 0.0631909i | ||||
\(379\) | 9.90983 | + | 30.4993i | 0.509034 | + | 1.56664i | 0.793882 | + | 0.608072i | \(0.208057\pi\) |
−0.284848 | + | 0.958573i | \(0.591943\pi\) | |||||||
\(380\) | 1.01064 | + | 3.11044i | 0.0518449 | + | 0.159562i | ||||
\(381\) | 3.85410 | + | 2.80017i | 0.197452 | + | 0.143457i | ||||
\(382\) | 4.87132 | − | 3.53922i | 0.249239 | − | 0.181082i | ||||
\(383\) | −10.6910 | + | 32.9035i | −0.546284 | + | 1.68129i | 0.171634 | + | 0.985161i | \(0.445095\pi\) |
−0.717918 | + | 0.696128i | \(0.754905\pi\) | |||||||
\(384\) | −16.3262 | −0.833145 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.85410 | 0.297966 | ||||||||
\(387\) | 1.48278 | − | 4.56352i | 0.0753739 | − | 0.231977i | ||||
\(388\) | 10.5000 | − | 7.62870i | 0.533057 | − | 0.387288i | ||||
\(389\) | 27.6525 | + | 20.0907i | 1.40204 | + | 1.01864i | 0.994421 | + | 0.105485i | \(0.0336396\pi\) |
0.407615 | + | 0.913154i | \(0.366360\pi\) | |||||||
\(390\) | −0.236068 | − | 0.726543i | −0.0119538 | − | 0.0367899i | ||||
\(391\) | 4.86068 | + | 14.9596i | 0.245815 | + | 0.756541i | ||||
\(392\) | −1.19098 | − | 0.865300i | −0.0601537 | − | 0.0437042i | ||||
\(393\) | 24.7984 | − | 18.0171i | 1.25091 | − | 0.908841i | ||||
\(394\) | 0.506578 | − | 1.55909i | 0.0255210 | − | 0.0785456i | ||||
\(395\) | 6.38197 | 0.321112 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.819660 | −0.0411376 | −0.0205688 | − | 0.999788i | \(-0.506548\pi\) | ||||
−0.0205688 | + | 0.999788i | \(0.506548\pi\) | |||||||
\(398\) | 0.972136 | − | 2.99193i | 0.0487288 | − | 0.149972i | ||||
\(399\) | −2.30902 | + | 1.67760i | −0.115595 | + | 0.0839850i | ||||
\(400\) | 10.1803 | + | 7.39645i | 0.509017 | + | 0.369822i | ||||
\(401\) | −5.41641 | − | 16.6700i | −0.270483 | − | 0.832460i | −0.990379 | − | 0.138379i | \(-0.955811\pi\) |
0.719897 | − | 0.694081i | \(-0.244189\pi\) | |||||||
\(402\) | −1.59017 | − | 4.89404i | −0.0793105 | − | 0.244093i | ||||
\(403\) | −4.23607 | − | 3.07768i | −0.211014 | − | 0.153310i | ||||
\(404\) | −22.1976 | + | 16.1275i | −1.10437 | + | 0.802372i | ||||
\(405\) | −2.38197 | + | 7.33094i | −0.118361 | + | 0.364277i | ||||
\(406\) | 1.76393 | 0.0875425 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.36068 | −0.364408 | ||||||||
\(409\) | −5.47214 | + | 16.8415i | −0.270580 | + | 0.832759i | 0.719775 | + | 0.694207i | \(0.244245\pi\) |
−0.990355 | + | 0.138552i | \(0.955755\pi\) | |||||||
\(410\) | −3.45492 | + | 2.51014i | −0.170626 | + | 0.123967i | ||||
\(411\) | −20.0623 | − | 14.5761i | −0.989601 | − | 0.718987i | ||||
\(412\) | −5.07295 | − | 15.6129i | −0.249926 | − | 0.769194i | ||||
\(413\) | 3.42705 | + | 10.5474i | 0.168634 | + | 0.519003i | ||||
\(414\) | −0.600813 | − | 0.436516i | −0.0295284 | − | 0.0214536i | ||||
\(415\) | −2.19098 | + | 1.59184i | −0.107551 | + | 0.0781405i | ||||
\(416\) | 1.58359 | − | 4.87380i | 0.0776420 | − | 0.238957i | ||||
\(417\) | −19.3262 | −0.946410 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.8885 | 1.46015 | 0.730075 | − | 0.683367i | \(-0.239485\pi\) | ||||
0.730075 | + | 0.683367i | \(0.239485\pi\) | |||||||
\(420\) | 0.927051 | − | 2.85317i | 0.0452355 | − | 0.139220i | ||||
\(421\) | −0.618034 | + | 0.449028i | −0.0301211 | + | 0.0218843i | −0.602744 | − | 0.797935i | \(-0.705926\pi\) |
0.572623 | + | 0.819819i | \(0.305926\pi\) | |||||||
\(422\) | 4.82624 | + | 3.50647i | 0.234938 | + | 0.170692i | ||||
\(423\) | 0.781153 | + | 2.40414i | 0.0379810 | + | 0.116893i | ||||
\(424\) | −1.08359 | − | 3.33495i | −0.0526239 | − | 0.161960i | ||||
\(425\) | 10.0000 | + | 7.26543i | 0.485071 | + | 0.352425i | ||||
\(426\) | 8.04508 | − | 5.84510i | 0.389786 | − | 0.283196i | ||||
\(427\) | −2.35410 | + | 7.24518i | −0.113923 | + | 0.350619i | ||||
\(428\) | −5.02129 | −0.242713 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.79837 | 0.231398 | ||||||||
\(431\) | −4.28115 | + | 13.1760i | −0.206216 | + | 0.634667i | 0.793445 | + | 0.608641i | \(0.208285\pi\) |
−0.999661 | + | 0.0260258i | \(0.991715\pi\) | |||||||
\(432\) | −13.9271 | + | 10.1186i | −0.670066 | + | 0.486831i | ||||
\(433\) | 7.25329 | + | 5.26982i | 0.348571 | + | 0.253252i | 0.748269 | − | 0.663395i | \(-0.230885\pi\) |
−0.399698 | + | 0.916647i | \(0.630885\pi\) | |||||||
\(434\) | 0.500000 | + | 1.53884i | 0.0240008 | + | 0.0738668i | ||||
\(435\) | 2.30902 | + | 7.10642i | 0.110709 | + | 0.340727i | ||||
\(436\) | −2.29180 | − | 1.66509i | −0.109757 | − | 0.0797432i | ||||
\(437\) | 7.26393 | − | 5.27756i | 0.347481 | − | 0.252460i | ||||
\(438\) | −2.71885 | + | 8.36775i | −0.129912 | + | 0.399827i | ||||
\(439\) | 3.38197 | 0.161412 | 0.0807062 | − | 0.996738i | \(-0.474282\pi\) | ||||
0.0807062 | + | 0.996738i | \(0.474282\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | 0.450850 | − | 1.38757i | 0.0214447 | − | 0.0660001i | ||||
\(443\) | −2.50000 | + | 1.81636i | −0.118779 | + | 0.0862977i | −0.645589 | − | 0.763685i | \(-0.723388\pi\) |
0.526810 | + | 0.849983i | \(0.323388\pi\) | |||||||
\(444\) | −15.7082 | − | 11.4127i | −0.745478 | − | 0.541622i | ||||
\(445\) | 2.11803 | + | 6.51864i | 0.100404 | + | 0.309013i | ||||
\(446\) | −0.240133 | − | 0.739054i | −0.0113706 | − | 0.0349952i | ||||
\(447\) | −11.5902 | − | 8.42075i | −0.548196 | − | 0.398288i | ||||
\(448\) | 3.80902 | − | 2.76741i | 0.179959 | − | 0.130748i | ||||
\(449\) | 3.80902 | − | 11.7229i | 0.179759 | − | 0.553240i | −0.820060 | − | 0.572277i | \(-0.806060\pi\) |
0.999819 | + | 0.0190372i | \(0.00606009\pi\) | |||||||
\(450\) | −0.583592 | −0.0275108 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.270510 | −0.0127237 | ||||||||
\(453\) | −0.0278640 | + | 0.0857567i | −0.00130917 | + | 0.00402920i | ||||
\(454\) | −4.95492 | + | 3.59996i | −0.232546 | + | 0.168954i | ||||
\(455\) | 1.00000 | + | 0.726543i | 0.0468807 | + | 0.0340608i | ||||
\(456\) | 1.29837 | + | 3.99598i | 0.0608019 | + | 0.187129i | ||||
\(457\) | −0.0450850 | − | 0.138757i | −0.00210899 | − | 0.00649079i | 0.949996 | − | 0.312261i | \(-0.101086\pi\) |
−0.952105 | + | 0.305770i | \(0.901086\pi\) | |||||||
\(458\) | 2.09017 | + | 1.51860i | 0.0976672 | + | 0.0709594i | ||||
\(459\) | −13.6803 | + | 9.93935i | −0.638544 | + | 0.463929i | ||||
\(460\) | −2.91641 | + | 8.97578i | −0.135978 | + | 0.418498i | ||||
\(461\) | −18.5066 | −0.861937 | −0.430969 | − | 0.902367i | \(-0.641828\pi\) | ||||
−0.430969 | + | 0.902367i | \(0.641828\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.2361 | 1.03340 | 0.516699 | − | 0.856167i | \(-0.327161\pi\) | ||||
0.516699 | + | 0.856167i | \(0.327161\pi\) | |||||||
\(464\) | −4.48936 | + | 13.8168i | −0.208413 | + | 0.641430i | ||||
\(465\) | −5.54508 | + | 4.02874i | −0.257147 | + | 0.186828i | ||||
\(466\) | −9.09017 | − | 6.60440i | −0.421094 | − | 0.305943i | ||||
\(467\) | −1.39261 | − | 4.28601i | −0.0644423 | − | 0.198333i | 0.913651 | − | 0.406499i | \(-0.133251\pi\) |
−0.978093 | + | 0.208166i | \(0.933251\pi\) | |||||||
\(468\) | −0.270510 | − | 0.832544i | −0.0125043 | − | 0.0384843i | ||||
\(469\) | 6.73607 | + | 4.89404i | 0.311043 | + | 0.225986i | ||||
\(470\) | −2.04508 | + | 1.48584i | −0.0943327 | + | 0.0685367i | ||||
\(471\) | −9.94427 | + | 30.6053i | −0.458208 | + | 1.41022i | ||||
\(472\) | 16.3262 | 0.751476 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.94427 | 0.181166 | ||||||||
\(475\) | 2.18034 | − | 6.71040i | 0.100041 | − | 0.307894i | ||||
\(476\) | 4.63525 | − | 3.36771i | 0.212457 | − | 0.154359i | ||||
\(477\) | −0.736068 | − | 0.534785i | −0.0337022 | − | 0.0244861i | ||||
\(478\) | 2.01722 | + | 6.20837i | 0.0922655 | + | 0.283964i | ||||
\(479\) | 6.72542 | + | 20.6987i | 0.307293 | + | 0.945749i | 0.978812 | + | 0.204762i | \(0.0656420\pi\) |
−0.671519 | + | 0.740987i | \(0.734358\pi\) | |||||||
\(480\) | −5.42705 | − | 3.94298i | −0.247710 | − | 0.179972i | ||||
\(481\) | 6.47214 | − | 4.70228i | 0.295104 | − | 0.214406i | ||||
\(482\) | −1.92047 | + | 5.91061i | −0.0874752 | + | 0.269221i | ||||
\(483\) | −8.23607 | −0.374754 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.00000 | 0.317854 | ||||||||
\(486\) | 0.465558 | − | 1.43284i | 0.0211181 | − | 0.0649950i | ||||
\(487\) | 26.3713 | − | 19.1599i | 1.19500 | − | 0.868217i | 0.201215 | − | 0.979547i | \(-0.435511\pi\) |
0.993784 | + | 0.111330i | \(0.0355110\pi\) | |||||||
\(488\) | 9.07295 | + | 6.59188i | 0.410713 | + | 0.298401i | ||||
\(489\) | 4.35410 | + | 13.4005i | 0.196899 | + | 0.605994i | ||||
\(490\) | −0.118034 | − | 0.363271i | −0.00533223 | − | 0.0164109i | ||||
\(491\) | −17.9164 | − | 13.0170i | −0.808556 | − | 0.587450i | 0.104855 | − | 0.994487i | \(-0.466562\pi\) |
−0.913412 | + | 0.407037i | \(0.866562\pi\) | |||||||
\(492\) | 27.1353 | − | 19.7149i | 1.22335 | − | 0.888817i | ||||
\(493\) | −4.40983 | + | 13.5721i | −0.198609 | + | 0.611255i | ||||
\(494\) | −0.832816 | −0.0374702 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.3262 | −0.598366 | ||||||||
\(497\) | −4.97214 | + | 15.3027i | −0.223031 | + | 0.686418i | ||||
\(498\) | −1.35410 | + | 0.983813i | −0.0606788 | + | 0.0440857i | ||||
\(499\) | 8.16312 | + | 5.93085i | 0.365431 | + | 0.265501i | 0.755314 | − | 0.655363i | \(-0.227484\pi\) |
−0.389883 | + | 0.920865i | \(0.627484\pi\) | |||||||
\(500\) | 5.15654 | + | 15.8702i | 0.230608 | + | 0.709737i | ||||
\(501\) | −3.23607 | − | 9.95959i | −0.144577 | − | 0.444962i | ||||
\(502\) | 7.10739 | + | 5.16382i | 0.317218 | + | 0.230473i | ||||
\(503\) | 28.1803 | − | 20.4742i | 1.25650 | − | 0.912900i | 0.257919 | − | 0.966167i | \(-0.416963\pi\) |
0.998580 | + | 0.0532664i | \(0.0169633\pi\) | |||||||
\(504\) | −0.173762 | + | 0.534785i | −0.00773998 | + | 0.0238212i | ||||
\(505\) | −14.7984 | −0.658519 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.5623 | 0.824381 | ||||||||
\(508\) | −1.68692 | + | 5.19180i | −0.0748449 | + | 0.230349i | ||||
\(509\) | 8.69098 | − | 6.31437i | 0.385221 | − | 0.279879i | −0.378273 | − | 0.925694i | \(-0.623482\pi\) |
0.763494 | + | 0.645814i | \(0.223482\pi\) | |||||||
\(510\) | −1.54508 | − | 1.12257i | −0.0684175 | − | 0.0497082i | ||||
\(511\) | −4.39919 | − | 13.5393i | −0.194609 | − | 0.598944i | ||||
\(512\) | −6.89261 | − | 21.2133i | −0.304613 | − | 0.937503i | ||||
\(513\) | 7.80902 | + | 5.67358i | 0.344777 | + | 0.250495i | ||||
\(514\) | −2.64590 | + | 1.92236i | −0.116706 | + | 0.0847916i | ||||
\(515\) | 2.73607 | − | 8.42075i | 0.120566 | − | 0.371063i | ||||
\(516\) | −37.6869 | −1.65907 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.47214 | −0.108619 | ||||||||
\(519\) | 7.69098 | − | 23.6704i | 0.337597 | − | 1.03902i | ||||
\(520\) | 1.47214 | − | 1.06957i | 0.0645574 | − | 0.0469037i | ||||
\(521\) | 9.89919 | + | 7.19218i | 0.433691 | + | 0.315095i | 0.783123 | − | 0.621867i | \(-0.213625\pi\) |
−0.349432 | + | 0.936962i | \(0.613625\pi\) | |||||||
\(522\) | −0.208204 | − | 0.640786i | −0.00911284 | − | 0.0280464i | ||||
\(523\) | 5.11803 | + | 15.7517i | 0.223796 | + | 0.688773i | 0.998412 | + | 0.0563409i | \(0.0179434\pi\) |
−0.774616 | + | 0.632432i | \(0.782057\pi\) | |||||||
\(524\) | 28.4164 | + | 20.6457i | 1.24138 | + | 0.901913i | ||||
\(525\) | −5.23607 | + | 3.80423i | −0.228521 | + | 0.166030i | ||||
\(526\) | 2.02129 | − | 6.22088i | 0.0881323 | − | 0.271243i | ||||
\(527\) | −13.0902 | −0.570217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.90983 | 0.126514 | ||||||||
\(530\) | 0.281153 | − | 0.865300i | 0.0122125 | − | 0.0375862i | ||||
\(531\) | 3.42705 | − | 2.48990i | 0.148721 | − | 0.108052i | ||||
\(532\) | −2.64590 | − | 1.92236i | −0.114714 | − | 0.0833448i | ||||
\(533\) | 4.27051 | + | 13.1433i | 0.184976 | + | 0.569299i | ||||
\(534\) | 1.30902 | + | 4.02874i | 0.0566467 | + | 0.174341i | ||||
\(535\) | −2.19098 | − | 1.59184i | −0.0947245 | − | 0.0688213i | ||||
\(536\) | 9.91641 | − | 7.20469i | 0.428324 | − | 0.311195i | ||||
\(537\) | 1.88197 | − | 5.79210i | 0.0812128 | − | 0.249947i | ||||
\(538\) | −6.43769 | −0.277549 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10.1459 | −0.436610 | ||||||||
\(541\) | 0.218847 | − | 0.673542i | 0.00940897 | − | 0.0289578i | −0.946242 | − | 0.323460i | \(-0.895154\pi\) |
0.955651 | + | 0.294502i | \(0.0951539\pi\) | |||||||
\(542\) | −1.48278 | + | 1.07730i | −0.0636908 | + | 0.0462741i | ||||
\(543\) | −9.70820 | − | 7.05342i | −0.416619 | − | 0.302691i | ||||
\(544\) | −3.95898 | − | 12.1845i | −0.169740 | − | 0.522406i | ||||
\(545\) | −0.472136 | − | 1.45309i | −0.0202241 | − | 0.0622433i | ||||
\(546\) | 0.618034 | + | 0.449028i | 0.0264494 | + | 0.0192166i | ||||
\(547\) | 1.39919 | − | 1.01657i | 0.0598249 | − | 0.0434653i | −0.557471 | − | 0.830196i | \(-0.688228\pi\) |
0.617296 | + | 0.786731i | \(0.288228\pi\) | |||||||
\(548\) | 8.78115 | − | 27.0256i | 0.375112 | − | 1.15448i | ||||
\(549\) | 2.90983 | 0.124189 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.14590 | 0.347027 | ||||||||
\(552\) | −3.74671 | + | 11.5312i | −0.159471 | + | 0.490800i | ||||
\(553\) | −5.16312 | + | 3.75123i | −0.219558 | + | 0.159518i | ||||
\(554\) | 7.11803 | + | 5.17155i | 0.302416 | + | 0.219718i | ||||
\(555\) | −3.23607 | − | 9.95959i | −0.137363 | − | 0.422761i | ||||
\(556\) | −6.84346 | − | 21.0620i | −0.290227 | − | 0.893228i | ||||
\(557\) | 7.89919 | + | 5.73910i | 0.334699 | + | 0.243173i | 0.742422 | − | 0.669933i | \(-0.233677\pi\) |
−0.407723 | + | 0.913106i | \(0.633677\pi\) | |||||||
\(558\) | 0.500000 | − | 0.363271i | 0.0211667 | − | 0.0153785i | ||||
\(559\) | 4.79837 | − | 14.7679i | 0.202950 | − | 0.624615i | ||||
\(560\) | 3.14590 | 0.132938 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.61803 | 0.405712 | ||||||||
\(563\) | −9.88197 | + | 30.4136i | −0.416475 | + | 1.28178i | 0.494450 | + | 0.869206i | \(0.335370\pi\) |
−0.910925 | + | 0.412573i | \(0.864630\pi\) | |||||||
\(564\) | 16.0623 | − | 11.6699i | 0.676345 | − | 0.491393i | ||||
\(565\) | −0.118034 | − | 0.0857567i | −0.00496573 | − | 0.00360781i | ||||
\(566\) | −1.40983 | − | 4.33901i | −0.0592596 | − | 0.182382i | ||||
\(567\) | −2.38197 | − | 7.33094i | −0.100033 | − | 0.307870i | ||||
\(568\) | 19.1631 | + | 13.9228i | 0.804067 | + | 0.584189i | ||||
\(569\) | −30.1803 | + | 21.9273i | −1.26523 | + | 0.919240i | −0.999002 | − | 0.0446710i | \(-0.985776\pi\) |
−0.266224 | + | 0.963911i | \(0.585776\pi\) | |||||||
\(570\) | −0.336881 | + | 1.03681i | −0.0141104 | + | 0.0434273i | ||||
\(571\) | 34.3050 | 1.43562 | 0.717809 | − | 0.696240i | \(-0.245145\pi\) | ||||
0.717809 | + | 0.696240i | \(0.245145\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.5066 | −1.06555 | ||||||||
\(574\) | 1.31966 | − | 4.06150i | 0.0550815 | − | 0.169524i | ||||
\(575\) | 16.4721 | − | 11.9677i | 0.686936 | − | 0.499088i | ||||
\(576\) | −1.45492 | − | 1.05706i | −0.0606215 | − | 0.0440441i | ||||
\(577\) | 2.98278 | + | 9.18005i | 0.124175 | + | 0.382170i | 0.993750 | − | 0.111630i | \(-0.0356072\pi\) |
−0.869575 | + | 0.493801i | \(0.835607\pi\) | |||||||
\(578\) | 0.879454 | + | 2.70668i | 0.0365804 | + | 0.112583i | ||||
\(579\) | −20.0623 | − | 14.5761i | −0.833761 | − | 0.605763i | ||||
\(580\) | −6.92705 | + | 5.03280i | −0.287630 | + | 0.208976i | ||||
\(581\) | 0.836881 | − | 2.57565i | 0.0347197 | − | 0.106856i | ||||
\(582\) | 4.32624 | 0.179328 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −20.9574 | −0.867225 | ||||||||
\(585\) | 0.145898 | − | 0.449028i | 0.00603214 | − | 0.0185650i | ||||
\(586\) | −3.39919 | + | 2.46965i | −0.140419 | + | 0.102020i | ||||
\(587\) | −0.809017 | − | 0.587785i | −0.0333917 | − | 0.0242605i | 0.570964 | − | 0.820975i | \(-0.306569\pi\) |
−0.604356 | + | 0.796714i | \(0.706569\pi\) | |||||||
\(588\) | 0.927051 | + | 2.85317i | 0.0382309 | + | 0.117663i | ||||
\(589\) | 2.30902 | + | 7.10642i | 0.0951414 | + | 0.292815i | ||||
\(590\) | 3.42705 | + | 2.48990i | 0.141089 | + | 0.102507i | ||||
\(591\) | −5.61803 | + | 4.08174i | −0.231095 | + | 0.167900i | ||||
\(592\) | 6.29180 | − | 19.3642i | 0.258591 | − | 0.795862i | ||||
\(593\) | 11.1246 | 0.456833 | 0.228417 | − | 0.973564i | \(-0.426645\pi\) | ||||
0.228417 | + | 0.973564i | \(0.426645\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.09017 | 0.126685 | ||||||||
\(596\) | 5.07295 | − | 15.6129i | 0.207796 | − | 0.639531i | ||||
\(597\) | −10.7812 | + | 7.83297i | −0.441243 | + | 0.320582i | ||||
\(598\) | −1.94427 | − | 1.41260i | −0.0795072 | − | 0.0577654i | ||||
\(599\) | −4.94427 | − | 15.2169i | −0.202017 | − | 0.621746i | −0.999823 | − | 0.0188306i | \(-0.994006\pi\) |
0.797805 | − | 0.602915i | \(-0.205994\pi\) | |||||||
\(600\) | 2.94427 | + | 9.06154i | 0.120199 | + | 0.369936i | ||||
\(601\) | −11.0902 | − | 8.05748i | −0.452377 | − | 0.328671i | 0.338156 | − | 0.941090i | \(-0.390197\pi\) |
−0.790534 | + | 0.612419i | \(0.790197\pi\) | |||||||
\(602\) | −3.88197 | + | 2.82041i | −0.158217 | + | 0.114951i | ||||
\(603\) | 0.982779 | − | 3.02468i | 0.0400219 | − | 0.123175i | ||||
\(604\) | −0.103326 | −0.00420426 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.14590 | −0.371527 | ||||||||
\(607\) | 6.24265 | − | 19.2129i | 0.253381 | − | 0.779827i | −0.740763 | − | 0.671766i | \(-0.765536\pi\) |
0.994144 | − | 0.108061i | \(-0.0344641\pi\) | |||||||
\(608\) | −5.91641 | + | 4.29852i | −0.239942 | + | 0.174328i | ||||
\(609\) | −6.04508 | − | 4.39201i | −0.244959 | − | 0.177973i | ||||
\(610\) | 0.899187 | + | 2.76741i | 0.0364070 | + | 0.112049i | ||||
\(611\) | 2.52786 | + | 7.77997i | 0.102266 | + | 0.314744i | ||||
\(612\) | −1.77051 | − | 1.28635i | −0.0715686 | − | 0.0519976i | ||||
\(613\) | 0.718847 | − | 0.522273i | 0.0290340 | − | 0.0210944i | −0.573174 | − | 0.819434i | \(-0.694288\pi\) |
0.602208 | + | 0.798340i | \(0.294288\pi\) | |||||||
\(614\) | 2.73607 | − | 8.42075i | 0.110419 | − | 0.339834i | ||||
\(615\) | 18.0902 | 0.729466 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.41641 | 0.379090 | 0.189545 | − | 0.981872i | \(-0.439299\pi\) | ||||
0.189545 | + | 0.981872i | \(0.439299\pi\) | |||||||
\(618\) | 1.69098 | − | 5.20431i | 0.0680213 | − | 0.209348i | ||||
\(619\) | 32.1246 | − | 23.3399i | 1.29120 | − | 0.938110i | 0.291368 | − | 0.956611i | \(-0.405889\pi\) |
0.999829 | + | 0.0185013i | \(0.00588948\pi\) | |||||||
\(620\) | −6.35410 | − | 4.61653i | −0.255187 | − | 0.185404i | ||||
\(621\) | 8.60739 | + | 26.4908i | 0.345403 | + | 1.06304i | ||||
\(622\) | −1.06231 | − | 3.26944i | −0.0425946 | − | 0.131093i | ||||
\(623\) | −5.54508 | − | 4.02874i | −0.222159 | − | 0.161408i | ||||
\(624\) | −5.09017 | + | 3.69822i | −0.203770 | + | 0.148047i | ||||
\(625\) | 3.39919 | − | 10.4616i | 0.135967 | − | 0.418465i | ||||
\(626\) | −7.00000 | −0.279776 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36.8754 | −1.47149 | ||||||||
\(629\) | 6.18034 | − | 19.0211i | 0.246426 | − | 0.758422i | ||||
\(630\) | −0.118034 | + | 0.0857567i | −0.00470259 | + | 0.00341663i | ||||
\(631\) | −14.4271 | − | 10.4819i | −0.574332 | − | 0.417277i | 0.262344 | − | 0.964974i | \(-0.415504\pi\) |
−0.836676 | + | 0.547698i | \(0.815504\pi\) | |||||||
\(632\) | 2.90325 | + | 8.93529i | 0.115485 | + | 0.355427i | ||||
\(633\) | −7.80902 | − | 24.0337i | −0.310381 | − | 0.955253i | ||||
\(634\) | −1.37132 | − | 0.996324i | −0.0544622 | − | 0.0395691i | ||||
\(635\) | −2.38197 | + | 1.73060i | −0.0945254 | + | 0.0686768i | ||||
\(636\) | −2.20820 | + | 6.79615i | −0.0875610 | + | 0.269485i | ||||
\(637\) | −1.23607 | −0.0489748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.14590 | 0.243128 | ||||||||
\(640\) | 3.11803 | − | 9.59632i | 0.123251 | − | 0.379328i | ||||
\(641\) | −25.6074 | + | 18.6049i | −1.01143 | + | 0.734848i | −0.964509 | − | 0.264051i | \(-0.914941\pi\) |
−0.0469224 | + | 0.998899i | \(0.514941\pi\) | |||||||
\(642\) | −1.35410 | − | 0.983813i | −0.0534421 | − | 0.0388280i | ||||
\(643\) | 0.489357 | + | 1.50609i | 0.0192984 | + | 0.0593942i | 0.960242 | − | 0.279169i | \(-0.0900590\pi\) |
−0.940944 | + | 0.338563i | \(0.890059\pi\) | |||||||
\(644\) | −2.91641 | − | 8.97578i | −0.114923 | − | 0.353695i | ||||
\(645\) | −16.4443 | − | 11.9475i | −0.647493 | − | 0.470431i | ||||
\(646\) | −1.68441 | + | 1.22379i | −0.0662720 | + | 0.0481495i | ||||
\(647\) | 1.90983 | − | 5.87785i | 0.0750832 | − | 0.231082i | −0.906470 | − | 0.422269i | \(-0.861234\pi\) |
0.981554 | + | 0.191187i | \(0.0612337\pi\) | |||||||
\(648\) | −11.3475 | −0.445773 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.88854 | −0.0740748 | ||||||||
\(651\) | 2.11803 | − | 6.51864i | 0.0830123 | − | 0.255486i | ||||
\(652\) | −13.0623 | + | 9.49032i | −0.511559 | + | 0.371670i | ||||
\(653\) | −14.7533 | − | 10.7189i | −0.577341 | − | 0.419463i | 0.260424 | − | 0.965494i | \(-0.416138\pi\) |
−0.837764 | + | 0.546032i | \(0.816138\pi\) | |||||||
\(654\) | −0.291796 | − | 0.898056i | −0.0114101 | − | 0.0351168i | ||||
\(655\) | 5.85410 | + | 18.0171i | 0.228739 | + | 0.703985i | ||||
\(656\) | 28.4549 | + | 20.6737i | 1.11098 | + | 0.807173i | ||||
\(657\) | −4.39919 | + | 3.19620i | −0.171629 | + | 0.124695i | ||||
\(658\) | 0.781153 | − | 2.40414i | 0.0304525 | − | 0.0937232i | ||||
\(659\) | 31.4721 | 1.22598 | 0.612990 | − | 0.790091i | \(-0.289967\pi\) | ||||
0.612990 | + | 0.790091i | \(0.289967\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.5623 | −1.34432 | −0.672159 | − | 0.740407i | \(-0.734633\pi\) | ||||
−0.672159 | + | 0.740407i | \(0.734633\pi\) | |||||||
\(662\) | −0.729490 | + | 2.24514i | −0.0283524 | + | 0.0872598i | ||||
\(663\) | −5.00000 | + | 3.63271i | −0.194184 | + | 0.141083i | ||||
\(664\) | −3.22542 | − | 2.34341i | −0.125171 | − | 0.0909419i | ||||
\(665\) | −0.545085 | − | 1.67760i | −0.0211375 | − | 0.0650545i | ||||
\(666\) | 0.291796 | + | 0.898056i | 0.0113069 | + | 0.0347990i | ||||
\(667\) | 19.0172 | + | 13.8168i | 0.736350 | + | 0.534989i | ||||
\(668\) | 9.70820 | − | 7.05342i | 0.375622 | − | 0.272905i | ||||
\(669\) | −1.01722 | + | 3.13068i | −0.0393280 | + | 0.121039i | ||||
\(670\) | 3.18034 | 0.122867 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 6.70820 | 0.258775 | ||||||||
\(673\) | −2.03444 | + | 6.26137i | −0.0784220 | + | 0.241358i | −0.982580 | − | 0.185840i | \(-0.940499\pi\) |
0.904158 | + | 0.427198i | \(0.140499\pi\) | |||||||
\(674\) | 8.01722 | − | 5.82485i | 0.308812 | − | 0.224365i | ||||
\(675\) | 17.7082 | + | 12.8658i | 0.681589 | + | 0.495203i | ||||
\(676\) | 6.57295 | + | 20.2295i | 0.252806 | + | 0.778056i | ||||
\(677\) | −11.2082 | − | 34.4953i | −0.430766 | − | 1.32576i | −0.897363 | − | 0.441292i | \(-0.854520\pi\) |
0.466597 | − | 0.884470i | \(-0.345480\pi\) | |||||||
\(678\) | −0.0729490 | − | 0.0530006i | −0.00280159 | − | 0.00203547i | ||||
\(679\) | −5.66312 | + | 4.11450i | −0.217331 | + | 0.157900i | ||||
\(680\) | 1.40576 | − | 4.32650i | 0.0539086 | − | 0.165914i | ||||
\(681\) | 25.9443 | 0.994187 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.493422 | 0.0188803 | 0.00944014 | − | 0.999955i | \(-0.496995\pi\) | ||||
0.00944014 | + | 0.999955i | \(0.496995\pi\) | |||||||
\(684\) | −0.386031 | + | 1.18808i | −0.0147603 | + | 0.0454275i | ||||
\(685\) | 12.3992 | − | 9.00854i | 0.473749 | − | 0.344198i | ||||
\(686\) | 0.309017 | + | 0.224514i | 0.0117983 | + | 0.00857198i | ||||
\(687\) | −3.38197 | − | 10.4086i | −0.129030 | − | 0.397114i | ||||
\(688\) | −12.2123 | − | 37.5855i | −0.465588 | − | 1.43293i | ||||
\(689\) | −2.38197 | − | 1.73060i | −0.0907457 | − | 0.0659306i | ||||
\(690\) | −2.54508 | + | 1.84911i | −0.0968897 | + | 0.0703945i | ||||
\(691\) | 5.72949 | − | 17.6336i | 0.217960 | − | 0.670812i | −0.780970 | − | 0.624568i | \(-0.785275\pi\) |
0.998930 | − | 0.0462437i | \(-0.0147251\pi\) | |||||||
\(692\) | 28.5197 | 1.08416 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.896674 | −0.0340373 | ||||||||
\(695\) | 3.69098 | − | 11.3597i | 0.140007 | − | 0.430897i | ||||
\(696\) | −8.89919 | + | 6.46564i | −0.337323 | + | 0.245079i | ||||
\(697\) | 27.9508 | + | 20.3075i | 1.05871 | + | 0.769201i | ||||
\(698\) | −3.87132 | − | 11.9147i | −0.146532 | − | 0.450978i | ||||
\(699\) | 14.7082 | + | 45.2672i | 0.556315 | + | 1.71216i | ||||
\(700\) | −6.00000 | − | 4.35926i | −0.226779 | − | 0.164764i | ||||
\(701\) | −14.9721 | + | 10.8779i | −0.565490 | + | 0.410852i | −0.833464 | − | 0.552574i | \(-0.813646\pi\) |
0.267974 | + | 0.963426i | \(0.413646\pi\) | |||||||
\(702\) | 0.798374 | − | 2.45714i | 0.0301327 | − | 0.0927389i | ||||
\(703\) | −11.4164 | −0.430578 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.7082 | 0.403294 | ||||||||
\(706\) | −2.84346 | + | 8.75127i | −0.107015 | + | 0.329358i | ||||
\(707\) | 11.9721 | − | 8.69827i | 0.450259 | − | 0.327132i | ||||
\(708\) | −26.9164 | − | 19.5559i | −1.01158 | − | 0.734956i | ||||
\(709\) | −2.17376 | − | 6.69015i | −0.0816373 | − | 0.251254i | 0.901904 | − | 0.431936i | \(-0.142169\pi\) |
−0.983542 | + | 0.180682i | \(0.942169\pi\) | |||||||
\(710\) | 1.89919 | + | 5.84510i | 0.0712752 | + | 0.219363i | ||||
\(711\) | 1.97214 | + | 1.43284i | 0.0739609 | + | 0.0537357i | ||||
\(712\) | −8.16312 | + | 5.93085i | −0.305926 | + | 0.222268i | ||||
\(713\) | −6.66312 | + | 20.5070i | −0.249536 | + | 0.767992i | ||||
\(714\) | 1.90983 | 0.0714736 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.97871 | 0.260807 | ||||||||
\(717\) | 8.54508 | − | 26.2991i | 0.319122 | − | 0.982157i | ||||
\(718\) | −4.82624 | + | 3.50647i | −0.180114 | + | 0.130860i | ||||
\(719\) | 2.33688 | + | 1.69784i | 0.0871510 | + | 0.0633189i | 0.630507 | − | 0.776183i | \(-0.282847\pi\) |
−0.543357 | + | 0.839502i | \(0.682847\pi\) | |||||||
\(720\) | −0.371323 | − | 1.14281i | −0.0138384 | − | 0.0425902i | ||||
\(721\) | 2.73607 | + | 8.42075i | 0.101896 | + | 0.313605i | ||||
\(722\) | −4.90983 | − | 3.56720i | −0.182725 | − | 0.132757i | ||||
\(723\) | 21.2984 | − | 15.4742i | 0.792095 | − | 0.575491i | ||||
\(724\) | 4.24922 | − | 13.0778i | 0.157921 | − | 0.486031i | ||||
\(725\) | 18.4721 | 0.686038 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.4508 | −0.461776 | −0.230888 | − | 0.972980i | \(-0.574163\pi\) | ||||
−0.230888 | + | 0.972980i | \(0.574163\pi\) | |||||||
\(728\) | −0.562306 | + | 1.73060i | −0.0208404 | + | 0.0641403i | ||||
\(729\) | −23.8713 | + | 17.3435i | −0.884123 | + | 0.642353i | ||||
\(730\) | −4.39919 | − | 3.19620i | −0.162821 | − | 0.118297i | ||||
\(731\) | −11.9959 | − | 36.9197i | −0.443686 | − | 1.36552i | ||||
\(732\) | −7.06231 | − | 21.7355i | −0.261030 | − | 0.803369i | ||||
\(733\) | −42.8328 | − | 31.1199i | −1.58207 | − | 1.14944i | −0.914278 | − | 0.405087i | \(-0.867241\pi\) |
−0.667788 | − | 0.744352i | \(-0.732759\pi\) | |||||||
\(734\) | 10.1459 | − | 7.37143i | 0.374492 | − | 0.272084i | ||||
\(735\) | −0.500000 | + | 1.53884i | −0.0184428 | + | 0.0567610i | ||||
\(736\) | −21.1033 | −0.777879 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.63119 | −0.0600449 | ||||||||
\(739\) | −3.51722 | + | 10.8249i | −0.129383 | + | 0.398200i | −0.994674 | − | 0.103070i | \(-0.967134\pi\) |
0.865291 | + | 0.501270i | \(0.167134\pi\) | |||||||
\(740\) | 9.70820 | − | 7.05342i | 0.356881 | − | 0.259289i | ||||
\(741\) | 2.85410 | + | 2.07363i | 0.104848 | + | 0.0761766i | ||||
\(742\) | 0.281153 | + | 0.865300i | 0.0103214 | + | 0.0317662i | ||||
\(743\) | −4.60739 | − | 14.1801i | −0.169029 | − | 0.520217i | 0.830282 | − | 0.557344i | \(-0.188179\pi\) |
−0.999311 | + | 0.0371268i | \(0.988179\pi\) | |||||||
\(744\) | −8.16312 | − | 5.93085i | −0.299274 | − | 0.217436i | ||||
\(745\) | 7.16312 | − | 5.20431i | 0.262436 | − | 0.190671i | ||||
\(746\) | 1.82217 | − | 5.60807i | 0.0667145 | − | 0.205326i | ||||
\(747\) | −1.03444 | −0.0378482 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.70820 | 0.0989556 | ||||||||
\(750\) | −1.71885 | + | 5.29007i | −0.0627634 | + | 0.193166i | ||||
\(751\) | −33.4164 | + | 24.2784i | −1.21938 | + | 0.885933i | −0.996049 | − | 0.0888092i | \(-0.971694\pi\) |
−0.223333 | + | 0.974742i | \(0.571694\pi\) | |||||||
\(752\) | 16.8435 | + | 12.2375i | 0.614218 | + | 0.446255i | ||||
\(753\) | −11.5000 | − | 35.3934i | −0.419083 | − | 1.28981i | ||||
\(754\) | −0.673762 | − | 2.07363i | −0.0245370 | − | 0.0755170i | ||||
\(755\) | −0.0450850 | − | 0.0327561i | −0.00164081 | − | 0.00119212i | ||||
\(756\) | 8.20820 | − | 5.96361i | 0.298529 | − | 0.216894i | ||||
\(757\) | −4.56231 | + | 14.0413i | −0.165820 | + | 0.510341i | −0.999096 | − | 0.0425164i | \(-0.986463\pi\) |
0.833276 | + | 0.552857i | \(0.186463\pi\) | |||||||
\(758\) | −12.2492 | −0.444912 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.59675 | −0.0941939 | ||||||||
\(761\) | 4.72949 | − | 14.5559i | 0.171444 | − | 0.527650i | −0.828009 | − | 0.560714i | \(-0.810527\pi\) |
0.999453 | + | 0.0330643i | \(0.0105266\pi\) | |||||||
\(762\) | −1.47214 | + | 1.06957i | −0.0533299 | + | 0.0387464i | ||||
\(763\) | 1.23607 | + | 0.898056i | 0.0447487 | + | 0.0325118i | ||||
\(764\) | −9.03193 | − | 27.7974i | −0.326764 | − | 1.00568i | ||||
\(765\) | −0.364745 | − | 1.12257i | −0.0131874 | − | 0.0405866i | ||||
\(766\) | −10.6910 | − | 7.76745i | −0.386281 | − | 0.280650i | ||||
\(767\) | 11.0902 | − | 8.05748i | 0.400443 | − | 0.290939i | ||||
\(768\) | −2.78115 | + | 8.55951i | −0.100356 | + | 0.308865i | ||||
\(769\) | 48.5623 | 1.75120 | 0.875601 | − | 0.483035i | \(-0.160466\pi\) | ||||
0.875601 | + | 0.483035i | \(0.160466\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.8541 | 0.498943 | ||||||||
\(772\) | 8.78115 | − | 27.0256i | 0.316041 | − | 0.972673i | ||||
\(773\) | −32.5517 | + | 23.6502i | −1.17080 | + | 0.850637i | −0.991105 | − | 0.133085i | \(-0.957512\pi\) |
−0.179697 | + | 0.983722i | \(0.557512\pi\) | |||||||
\(774\) | 1.48278 | + | 1.07730i | 0.0532974 | + | 0.0387228i | ||||
\(775\) | 5.23607 | + | 16.1150i | 0.188085 | + | 0.578866i | ||||
\(776\) | 3.18441 | + | 9.80059i | 0.114313 | + | 0.351821i | ||||
\(777\) | 8.47214 | + | 6.15537i | 0.303936 | + | 0.220823i | ||||
\(778\) | −10.5623 | + | 7.67396i | −0.378677 | + | 0.275125i | ||||
\(779\) | 6.09424 | − | 18.7561i | 0.218349 | − | 0.672008i | ||||
\(780\) | −3.70820 | −0.132775 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −6.00813 | −0.214850 | ||||||||
\(783\) | −7.80902 | + | 24.0337i | −0.279072 | + | 0.858894i | ||||
\(784\) | −2.54508 | + | 1.84911i | −0.0908959 | + | 0.0660397i | ||||
\(785\) | −16.0902 | − | 11.6902i | −0.574283 | − | 0.417241i | ||||
\(786\) | 3.61803 | + | 11.1352i | 0.129051 | + | 0.397178i | ||||
\(787\) | 6.35410 | + | 19.5559i | 0.226499 | + | 0.697093i | 0.998136 | + | 0.0610295i | \(0.0194384\pi\) |
−0.771637 | + | 0.636064i | \(0.780562\pi\) | |||||||
\(788\) | −6.43769 | − | 4.67726i | −0.229333 | − | 0.166620i | ||||
\(789\) | −22.4164 | + | 16.2865i | −0.798045 | + | 0.579814i | ||||
\(790\) | −0.753289 | + | 2.31838i | −0.0268008 | + | 0.0824844i | ||||
\(791\) | 0.145898 | 0.00518754 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.41641 | 0.334386 | ||||||||
\(794\) | 0.0967478 | − | 0.297759i | 0.00343345 | − | 0.0105671i | ||||
\(795\) | −3.11803 | + | 2.26538i | −0.110585 | + | 0.0803449i | ||||
\(796\) | −12.3541 | − | 8.97578i | −0.437880 | − | 0.318138i | ||||
\(797\) | 9.96149 | + | 30.6583i | 0.352854 | + | 1.08597i | 0.957243 | + | 0.289284i | \(0.0934173\pi\) |
−0.604389 | + | 0.796689i | \(0.706583\pi\) | |||||||
\(798\) | −0.336881 | − | 1.03681i | −0.0119255 | − | 0.0367028i | ||||
\(799\) | 16.5451 | + | 12.0207i | 0.585323 | + | 0.425262i | ||||
\(800\) | −13.4164 | + | 9.74759i | −0.474342 | + | 0.344629i | ||||
\(801\) | −0.809017 | + | 2.48990i | −0.0285852 | + | 0.0879762i | ||||
\(802\) | 6.69505 | 0.236410 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −24.9787 | −0.880931 | ||||||||
\(805\) | 1.57295 | − | 4.84104i | 0.0554392 | − | 0.170624i | ||||
\(806\) | 1.61803 | − | 1.17557i | 0.0569928 | − | 0.0414077i | ||||
\(807\) | 22.0623 | + | 16.0292i | 0.776630 | + | 0.564255i | ||||
\(808\) | −6.73200 | − | 20.7190i | −0.236831 | − | 0.728891i | ||||
\(809\) | 10.0451 | + | 30.9156i | 0.353166 | + | 1.08693i | 0.957065 | + | 0.289873i | \(0.0936132\pi\) |
−0.603899 | + | 0.797061i | \(0.706387\pi\) | |||||||
\(810\) | −2.38197 | − | 1.73060i | −0.0836938 | − | 0.0608071i | ||||
\(811\) | −0.944272 | + | 0.686054i | −0.0331579 | + | 0.0240906i | −0.604241 | − | 0.796802i | \(-0.706523\pi\) |
0.571083 | + | 0.820892i | \(0.306523\pi\) | |||||||
\(812\) | 2.64590 | − | 8.14324i | 0.0928528 | − | 0.285772i | ||||
\(813\) | 7.76393 | 0.272293 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.70820 | −0.305035 | ||||||||
\(816\) | −4.86068 | + | 14.9596i | −0.170158 | + | 0.523692i | ||||
\(817\) | −17.9271 | + | 13.0248i | −0.627188 | + | 0.455679i | ||||
\(818\) | −5.47214 | − | 3.97574i | −0.191329 | − | 0.139008i | ||||
\(819\) | 0.145898 | + | 0.449028i | 0.00509809 | + | 0.0156903i | ||||
\(820\) | 6.40576 | + | 19.7149i | 0.223699 | + | 0.688475i | ||||
\(821\) | −45.8435 | − | 33.3072i | −1.59995 | − | 1.16243i | −0.887613 | − | 0.460590i | \(-0.847638\pi\) |
−0.712335 | − | 0.701840i | \(-0.752362\pi\) | |||||||
\(822\) | 7.66312 | − | 5.56758i | 0.267282 | − | 0.194192i | ||||
\(823\) | −9.85410 | + | 30.3278i | −0.343492 | + | 1.05716i | 0.618894 | + | 0.785475i | \(0.287581\pi\) |
−0.962386 | + | 0.271686i | \(0.912419\pi\) | |||||||
\(824\) | 13.0344 | 0.454076 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.23607 | −0.147392 | ||||||||
\(827\) | −6.05573 | + | 18.6376i | −0.210578 | + | 0.648093i | 0.788860 | + | 0.614573i | \(0.210672\pi\) |
−0.999438 | + | 0.0335201i | \(0.989328\pi\) | |||||||
\(828\) | −2.91641 | + | 2.11889i | −0.101352 | + | 0.0736367i | ||||
\(829\) | 38.8156 | + | 28.2012i | 1.34812 | + | 0.979467i | 0.999103 | + | 0.0423517i | \(0.0134850\pi\) |
0.349019 | + | 0.937116i | \(0.386515\pi\) | |||||||
\(830\) | −0.319660 | − | 0.983813i | −0.0110956 | − | 0.0341486i | ||||
\(831\) | −11.5172 | − | 35.4464i | −0.399528 | − | 1.22962i | ||||
\(832\) | −4.70820 | − | 3.42071i | −0.163228 | − | 0.118592i | ||||
\(833\) | −2.50000 | + | 1.81636i | −0.0866199 | + | 0.0629330i | ||||
\(834\) | 2.28115 | − | 7.02067i | 0.0789899 | − | 0.243106i | ||||
\(835\) | 6.47214 | 0.223978 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.1803 | −0.801230 | ||||||||
\(838\) | −3.52786 | + | 10.8576i | −0.121868 | + | 0.375071i | ||||
\(839\) | −24.7533 | + | 17.9843i | −0.854578 | + | 0.620888i | −0.926405 | − | 0.376530i | \(-0.877117\pi\) |
0.0718262 | + | 0.997417i | \(0.477117\pi\) | |||||||
\(840\) | 1.92705 | + | 1.40008i | 0.0664896 | + | 0.0483075i | ||||
\(841\) | −2.37132 | − | 7.29818i | −0.0817698 | − | 0.251661i | ||||
\(842\) | −0.0901699 | − | 0.277515i | −0.00310746 | − | 0.00956378i | ||||
\(843\) | −32.9615 | − | 23.9479i | −1.13525 | − | 0.824810i | ||||
\(844\) | 23.4271 | − | 17.0207i | 0.806392 | − | 0.585878i | ||||
\(845\) | −3.54508 | + | 10.9106i | −0.121955 | + | 0.375338i | ||||
\(846\) | −0.965558 | −0.0331966 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.49342 | −0.257325 | ||||||||
\(849\) | −5.97214 | + | 18.3803i | −0.204963 | + | 0.630812i | ||||
\(850\) | −3.81966 | + | 2.77515i | −0.131013 | + | 0.0951867i | ||||
\(851\) | −26.6525 | − | 19.3642i | −0.913635 | − | 0.663795i | ||||
\(852\) | −14.9164 | − | 45.9080i | −0.511028 | − | 1.57278i | ||||
\(853\) | −10.7877 | − | 33.2012i | −0.369365 | − | 1.13679i | −0.947202 | − | 0.320636i | \(-0.896103\pi\) |
0.577838 | − | 0.816152i | \(-0.303897\pi\) | |||||||
\(854\) | −2.35410 | − | 1.71036i | −0.0805557 | − | 0.0585271i | ||||
\(855\) | −0.545085 | + | 0.396027i | −0.0186415 | + | 0.0135439i | ||||
\(856\) | 1.23200 | − | 3.79171i | 0.0421090 | − | 0.129598i | ||||
\(857\) | −15.0902 | −0.515470 | −0.257735 | − | 0.966216i | \(-0.582976\pi\) | ||||
−0.257735 | + | 0.966216i | \(0.582976\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.5623 | 0.735696 | 0.367848 | − | 0.929886i | \(-0.380095\pi\) | ||||
0.367848 | + | 0.929886i | \(0.380095\pi\) | |||||||
\(860\) | 7.19756 | − | 22.1518i | 0.245435 | − | 0.755371i | ||||
\(861\) | −14.6353 | + | 10.6331i | −0.498768 | + | 0.362376i | ||||
\(862\) | −4.28115 | − | 3.11044i | −0.145817 | − | 0.105942i | ||||
\(863\) | −14.8156 | − | 45.5977i | −0.504329 | − | 1.55216i | −0.801896 | − | 0.597463i | \(-0.796175\pi\) |
0.297567 | − | 0.954701i | \(-0.403825\pi\) | |||||||
\(864\) | −7.01064 | − | 21.5765i | −0.238507 | − | 0.734049i | ||||
\(865\) | 12.4443 | + | 9.04129i | 0.423118 | + | 0.307413i | ||||
\(866\) | −2.77051 | + | 2.01289i | −0.0941458 | + | 0.0684009i | ||||
\(867\) | 3.72542 | − | 11.4657i | 0.126522 | − | 0.389395i | ||||
\(868\) | 7.85410 | 0.266586 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.85410 | −0.0967631 | ||||||||
\(871\) | 3.18034 | − | 9.78808i | 0.107762 | − | 0.331656i | ||||
\(872\) | 1.81966 | − | 1.32206i | 0.0616215 | − | 0.0447706i | ||||
\(873\) | 2.16312 | + | 1.57160i | 0.0732105 | + | 0.0531905i | ||||
\(874\) | 1.05979 | + | 3.26171i | 0.0358480 | + | 0.110329i | ||||
\(875\) | −2.78115 | − | 8.55951i | −0.0940201 | − | 0.289364i | ||||
\(876\) | 34.5517 | + | 25.1033i | 1.16739 | + | 0.848160i | ||||
\(877\) | −10.5172 | + | 7.64121i | −0.355141 | + | 0.258025i | −0.751023 | − | 0.660276i | \(-0.770439\pi\) |
0.395881 | + | 0.918302i | \(0.370439\pi\) | |||||||
\(878\) | −0.399187 | + | 1.22857i | −0.0134719 | + | 0.0414623i | ||||
\(879\) | 17.7984 | 0.600324 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.1459 | 0.476587 | 0.238294 | − | 0.971193i | \(-0.423412\pi\) | ||||
0.238294 | + | 0.971193i | \(0.423412\pi\) | |||||||
\(882\) | 0.0450850 | − | 0.138757i | 0.00151809 | − | 0.00467220i | ||||
\(883\) | −25.5902 | + | 18.5923i | −0.861178 | + | 0.625682i | −0.928205 | − | 0.372069i | \(-0.878649\pi\) |
0.0670273 | + | 0.997751i | \(0.478649\pi\) | |||||||
\(884\) | −5.72949 | − | 4.16272i | −0.192704 | − | 0.140007i | ||||
\(885\) | −5.54508 | − | 17.0660i | −0.186396 | − | 0.573668i | ||||
\(886\) | −0.364745 | − | 1.12257i | −0.0122539 | − | 0.0377135i | ||||
\(887\) | −46.2877 | − | 33.6300i | −1.55419 | − | 1.12919i | −0.940578 | − | 0.339577i | \(-0.889716\pi\) |
−0.613612 | − | 0.789608i | \(-0.710284\pi\) | |||||||
\(888\) | 12.4721 | − | 9.06154i | 0.418537 | − | 0.304085i | ||||
\(889\) | 0.909830 | − | 2.80017i | 0.0305147 | − | 0.0939147i | ||||
\(890\) | −2.61803 | −0.0877567 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.77206 | −0.126298 | ||||||||
\(893\) | 3.60739 | − | 11.1024i | 0.120717 | − | 0.371528i | ||||
\(894\) | 4.42705 | − | 3.21644i | 0.148063 | − | 0.107574i | ||||
\(895\) | 3.04508 | + | 2.21238i | 0.101786 | + | 0.0739518i | ||||
\(896\) | 3.11803 | + | 9.59632i | 0.104166 | + | 0.320591i | ||||
\(897\) | 3.14590 | + | 9.68208i | 0.105038 | + | 0.323275i | ||||
\(898\) | 3.80902 | + | 2.76741i | 0.127109 | + | 0.0923498i | ||||
\(899\) | −15.8262 | + | 11.4984i | −0.527835 | + | 0.383494i | ||||
\(900\) | −0.875388 | + | 2.69417i | −0.0291796 | + | 0.0898056i | ||||
\(901\) | −7.36068 | −0.245220 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.3262 | 0.676415 | ||||||||
\(904\) | 0.0663712 | − | 0.204270i | 0.00220747 | − | 0.00679390i | ||||
\(905\) | 6.00000 | − | 4.35926i | 0.199447 | − | 0.144907i | ||||
\(906\) | −0.0278640 | − | 0.0202444i | −0.000925721 | − | 0.000672576i | ||||
\(907\) | −4.87132 | − | 14.9924i | −0.161750 | − | 0.497814i | 0.837032 | − | 0.547153i | \(-0.184289\pi\) |
−0.998782 | + | 0.0493391i | \(0.984289\pi\) | |||||||
\(908\) | 9.18692 | + | 28.2744i | 0.304879 | + | 0.938320i | ||||
\(909\) | −4.57295 | − | 3.32244i | −0.151675 | − | 0.110198i | ||||
\(910\) | −0.381966 | + | 0.277515i | −0.0126620 | + | 0.00919952i | ||||
\(911\) | −13.9615 | + | 42.9691i | −0.462565 | + | 1.42363i | 0.399454 | + | 0.916753i | \(0.369200\pi\) |
−0.862019 | + | 0.506875i | \(0.830800\pi\) | |||||||
\(912\) | 8.97871 | 0.297315 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.0557281 | 0.00184332 | ||||||||
\(915\) | 3.80902 | − | 11.7229i | 0.125922 | − | 0.387549i | ||||
\(916\) | 10.1459 | − | 7.37143i | 0.335230 | − | 0.243559i | ||||
\(917\) | −15.3262 | − | 11.1352i | −0.506117 | − | 0.367715i | ||||
\(918\) | −1.99593 | − | 6.14286i | −0.0658757 | − | 0.202744i | ||||
\(919\) | −4.60081 | − | 14.1598i | −0.151767 | − | 0.467090i | 0.846052 | − | 0.533100i | \(-0.178973\pi\) |
−0.997819 | + | 0.0660099i | \(0.978973\pi\) | |||||||
\(920\) | −6.06231 | − | 4.40452i | −0.199868 | − | 0.145213i | ||||
\(921\) | −30.3435 | + | 22.0458i | −0.999851 | + | 0.726434i | ||||
\(922\) | 2.18441 | − | 6.72291i | 0.0719396 | − | 0.221407i | ||||
\(923\) | 19.8885 | 0.654639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.8885 | −0.851210 | ||||||||
\(926\) | −2.62461 | + | 8.07772i | −0.0862501 | + | 0.265450i | ||||
\(927\) | 2.73607 | − | 1.98787i | 0.0898643 | − | 0.0652902i | ||||
\(928\) | −15.4894 | − | 11.2537i | −0.508463 | − | 0.369420i | ||||
\(929\) | 7.41641 | + | 22.8254i | 0.243324 | + | 0.748876i | 0.995908 | + | 0.0903783i | \(0.0288076\pi\) |
−0.752583 | + | 0.658497i | \(0.771192\pi\) | |||||||
\(930\) | −0.809017 | − | 2.48990i | −0.0265287 | − | 0.0816470i | ||||
\(931\) | 1.42705 | + | 1.03681i | 0.0467697 | + | 0.0339802i | ||||
\(932\) | −44.1246 | + | 32.0584i | −1.44535 | + | 1.05011i | ||||
\(933\) | −4.50000 | + | 13.8496i | −0.147323 | + | 0.453415i | ||||
\(934\) | 1.72136 | 0.0563246 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.695048 | 0.0227184 | ||||||||
\(937\) | −15.9828 | + | 49.1899i | −0.522135 | + | 1.60697i | 0.247779 | + | 0.968817i | \(0.420299\pi\) |
−0.769913 | + | 0.638148i | \(0.779701\pi\) | |||||||
\(938\) | −2.57295 | + | 1.86936i | −0.0840098 | + | 0.0610367i | ||||
\(939\) | 23.9894 | + | 17.4293i | 0.782863 | + | 0.568783i | ||||
\(940\) | 3.79180 | + | 11.6699i | 0.123675 | + | 0.380632i | ||||
\(941\) | 8.36475 | + | 25.7440i | 0.272683 | + | 0.839232i | 0.989823 | + | 0.142303i | \(0.0454507\pi\) |
−0.717140 | + | 0.696929i | \(0.754549\pi\) | |||||||
\(942\) | −9.94427 | − | 7.22494i | −0.324002 | − | 0.235401i | ||||
\(943\) | 46.0410 | − | 33.4508i | 1.49930 | − | 1.08931i | ||||
\(944\) | 10.7812 | − | 33.1810i | 0.350897 | − | 1.07995i | ||||
\(945\) | 5.47214 | 0.178009 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.29180 | 0.204456 | 0.102228 | − | 0.994761i | \(-0.467403\pi\) | ||||
0.102228 | + | 0.994761i | \(0.467403\pi\) | |||||||
\(948\) | 5.91641 | − | 18.2088i | 0.192156 | − | 0.591395i | ||||
\(949\) | −14.2361 | + | 10.3431i | −0.462122 | + | 0.335752i | ||||
\(950\) | 2.18034 | + | 1.58411i | 0.0707396 | + | 0.0513953i | ||||
\(951\) | 2.21885 | + | 6.82891i | 0.0719510 | + | 0.221443i | ||||
\(952\) | 1.40576 | + | 4.32650i | 0.0455611 | + | 0.140223i | ||||
\(953\) | 5.04508 | + | 3.66547i | 0.163426 | + | 0.118736i | 0.666493 | − | 0.745512i | \(-0.267795\pi\) |
−0.503066 | + | 0.864248i | \(0.667795\pi\) | |||||||
\(954\) | 0.281153 | − | 0.204270i | 0.00910266 | − | 0.00661347i | ||||
\(955\) | 4.87132 | − | 14.9924i | 0.157632 | − | 0.485142i | ||||
\(956\) | 31.6869 | 1.02483 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.31308 | −0.268583 | ||||||||
\(959\) | −4.73607 | + | 14.5761i | −0.152936 | + | 0.470687i | ||||
\(960\) | −6.16312 | + | 4.47777i | −0.198914 | + | 0.144519i | ||||
\(961\) | 10.5623 | + | 7.67396i | 0.340720 | + | 0.247547i | ||||
\(962\) | 0.944272 | + | 2.90617i | 0.0304445 | + | 0.0936987i | ||||
\(963\) | −0.319660 | − | 0.983813i | −0.0103009 | − | 0.0317029i | ||||
\(964\) | 24.4058 | + | 17.7318i | 0.786057 | + | 0.571104i | ||||
\(965\) | 12.3992 | − | 9.00854i | 0.399144 | − | 0.289995i | ||||
\(966\) | 0.972136 | − | 2.99193i | 0.0312780 | − | 0.0962637i | ||||
\(967\) | 27.4508 | 0.882760 | 0.441380 | − | 0.897320i | \(-0.354489\pi\) | ||||
0.441380 | + | 0.897320i | \(0.354489\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.81966 | 0.283328 | ||||||||
\(970\) | −0.826238 | + | 2.54290i | −0.0265289 | + | 0.0816476i | ||||
\(971\) | 22.8541 | − | 16.6045i | 0.733423 | − | 0.532863i | −0.157221 | − | 0.987563i | \(-0.550254\pi\) |
0.890644 | + | 0.454700i | \(0.150254\pi\) | |||||||
\(972\) | −5.91641 | − | 4.29852i | −0.189769 | − | 0.137875i | ||||
\(973\) | 3.69098 | + | 11.3597i | 0.118327 | + | 0.364175i | ||||
\(974\) | 3.84752 | + | 11.8415i | 0.123283 | + | 0.379425i | ||||
\(975\) | 6.47214 | + | 4.70228i | 0.207274 | + | 0.150594i | ||||
\(976\) | 19.3885 | − | 14.0866i | 0.620612 | − | 0.450901i | ||||
\(977\) | −3.34346 | + | 10.2901i | −0.106967 | + | 0.329210i | −0.990187 | − | 0.139749i | \(-0.955371\pi\) |
0.883220 | + | 0.468958i | \(0.155371\pi\) | |||||||
\(978\) | −5.38197 | −0.172096 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.85410 | −0.0592271 | ||||||||
\(981\) | 0.180340 | − | 0.555029i | 0.00575781 | − | 0.0177207i | ||||
\(982\) | 6.84346 | − | 4.97206i | 0.218384 | − | 0.158665i | ||||
\(983\) | 10.0172 | + | 7.27794i | 0.319500 | + | 0.232130i | 0.735962 | − | 0.677023i | \(-0.236730\pi\) |
−0.416462 | + | 0.909153i | \(0.636730\pi\) | |||||||
\(984\) | 8.22949 | + | 25.3278i | 0.262347 | + | 0.807420i | ||||
\(985\) | −1.32624 | − | 4.08174i | −0.0422575 | − | 0.130055i | ||||
\(986\) | −4.40983 | − | 3.20393i | −0.140438 | − | 0.102034i | ||||
\(987\) | −8.66312 | + | 6.29412i | −0.275750 | + | 0.200344i | ||||
\(988\) | −1.24922 | + | 3.84471i | −0.0397431 | + | 0.122317i | ||||
\(989\) | −63.9443 | −2.03331 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.729490 | −0.0231730 | −0.0115865 | − | 0.999933i | \(-0.503688\pi\) | ||||
−0.0115865 | + | 0.999933i | \(0.503688\pi\) | |||||||
\(992\) | 5.42705 | − | 16.7027i | 0.172309 | − | 0.530313i | ||||
\(993\) | 8.09017 | − | 5.87785i | 0.256734 | − | 0.186528i | ||||
\(994\) | −4.97214 | − | 3.61247i | −0.157707 | − | 0.114581i | ||||
\(995\) | −2.54508 | − | 7.83297i | −0.0806846 | − | 0.248322i | ||||
\(996\) | 2.51064 | + | 7.72696i | 0.0795528 | + | 0.244838i | ||||
\(997\) | 45.1976 | + | 32.8380i | 1.43142 | + | 1.03999i | 0.989750 | + | 0.142811i | \(0.0456142\pi\) |
0.441671 | + | 0.897177i | \(0.354386\pi\) | |||||||
\(998\) | −3.11803 | + | 2.26538i | −0.0986996 | + | 0.0717095i | ||||
\(999\) | 10.9443 | − | 33.6830i | 0.346261 | − | 1.06568i |
(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 | 847.2.f.l.372.1 | 4 | ||
11.2 | odd | 10 | 847.2.f.j.729.1 | 4 | |||
11.3 | even | 5 | 847.2.f.d.323.1 | 4 | |||
11.4 | even | 5 | 847.2.a.d.1.2 | ✓ | 2 | ||
11.5 | even | 5 | inner | 847.2.f.l.148.1 | 4 | ||
11.6 | odd | 10 | 847.2.f.c.148.1 | 4 | |||
11.7 | odd | 10 | 847.2.a.h.1.1 | yes | 2 | ||
11.8 | odd | 10 | 847.2.f.j.323.1 | 4 | |||
11.9 | even | 5 | 847.2.f.d.729.1 | 4 | |||
11.10 | odd | 2 | 847.2.f.c.372.1 | 4 | |||
33.26 | odd | 10 | 7623.2.a.bx.1.1 | 2 | |||
33.29 | even | 10 | 7623.2.a.t.1.2 | 2 | |||
77.48 | odd | 10 | 5929.2.a.i.1.2 | 2 | |||
77.62 | even | 10 | 5929.2.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.d.1.2 | ✓ | 2 | 11.4 | even | 5 | ||
847.2.a.h.1.1 | yes | 2 | 11.7 | odd | 10 | ||
847.2.f.c.148.1 | 4 | 11.6 | odd | 10 | |||
847.2.f.c.372.1 | 4 | 11.10 | odd | 2 | |||
847.2.f.d.323.1 | 4 | 11.3 | even | 5 | |||
847.2.f.d.729.1 | 4 | 11.9 | even | 5 | |||
847.2.f.j.323.1 | 4 | 11.8 | odd | 10 | |||
847.2.f.j.729.1 | 4 | 11.2 | odd | 10 | |||
847.2.f.l.148.1 | 4 | 11.5 | even | 5 | inner | ||
847.2.f.l.372.1 | 4 | 1.1 | even | 1 | trivial | ||
5929.2.a.i.1.2 | 2 | 77.48 | odd | 10 | |||
5929.2.a.s.1.1 | 2 | 77.62 | even | 10 | |||
7623.2.a.t.1.2 | 2 | 33.29 | even | 10 | |||
7623.2.a.bx.1.1 | 2 | 33.26 | odd | 10 |