Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(481,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.n (of order \(5\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 901.1 | ||
Root | \(1.69513 + 1.23158i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.901 |
Dual form | 930.2.n.a.481.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | − | 0.587785i | −0.572061 | − | 0.415627i | ||||
\(3\) | 0.809017 | − | 0.587785i | 0.467086 | − | 0.339358i | ||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.518200 | − | 1.59485i | −0.195861 | − | 0.602798i | −0.999965 | − | 0.00831018i | \(-0.997355\pi\) |
0.804104 | − | 0.594488i | \(-0.202645\pi\) | |||||||
\(8\) | 0.309017 | − | 0.951057i | 0.109254 | − | 0.336249i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | −0.809017 | − | 0.587785i | −0.255834 | − | 0.185874i | ||||
\(11\) | −1.18976 | − | 3.66171i | −0.358726 | − | 1.10405i | −0.953817 | − | 0.300387i | \(-0.902884\pi\) |
0.595091 | − | 0.803658i | \(-0.297116\pi\) | |||||||
\(12\) | 0.809017 | + | 0.587785i | 0.233543 | + | 0.169679i | ||||
\(13\) | −2.15163 | + | 1.56325i | −0.596754 | + | 0.433567i | −0.844725 | − | 0.535200i | \(-0.820236\pi\) |
0.247971 | + | 0.968767i | \(0.420236\pi\) | |||||||
\(14\) | −0.518200 | + | 1.59485i | −0.138495 | + | 0.426243i | ||||
\(15\) | 0.809017 | − | 0.587785i | 0.208887 | − | 0.151765i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | 0.938299 | − | 2.88779i | 0.227571 | − | 0.700391i | −0.770450 | − | 0.637501i | \(-0.779968\pi\) |
0.998020 | − | 0.0628903i | \(-0.0200318\pi\) | |||||||
\(18\) | −0.809017 | + | 0.587785i | −0.190687 | + | 0.138542i | ||||
\(19\) | −3.05850 | − | 2.22213i | −0.701668 | − | 0.509792i | 0.178807 | − | 0.983884i | \(-0.442776\pi\) |
−0.880475 | + | 0.474093i | \(0.842776\pi\) | |||||||
\(20\) | 0.309017 | + | 0.951057i | 0.0690983 | + | 0.212663i | ||||
\(21\) | −1.35666 | − | 0.985674i | −0.296048 | − | 0.215092i | ||||
\(22\) | −1.18976 | + | 3.66171i | −0.253658 | + | 0.780678i | ||||
\(23\) | −0.770884 | + | 2.37254i | −0.160740 | + | 0.494708i | −0.998697 | − | 0.0510286i | \(-0.983750\pi\) |
0.837957 | + | 0.545736i | \(0.183750\pi\) | |||||||
\(24\) | −0.309017 | − | 0.951057i | −0.0630778 | − | 0.194134i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.65956 | 0.521582 | ||||||||
\(27\) | −0.309017 | − | 0.951057i | −0.0594703 | − | 0.183031i | ||||
\(28\) | 1.35666 | − | 0.985674i | 0.256385 | − | 0.186275i | ||||
\(29\) | −5.53991 | − | 4.02498i | −1.02873 | − | 0.747419i | −0.0606796 | − | 0.998157i | \(-0.519327\pi\) |
−0.968055 | + | 0.250738i | \(0.919327\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 5.52783 | − | 0.665657i | 0.992828 | − | 0.119556i | ||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.11483 | − | 2.26306i | −0.542223 | − | 0.393948i | ||||
\(34\) | −2.45650 | + | 1.78475i | −0.421286 | + | 0.306082i | ||||
\(35\) | −0.518200 | − | 1.59485i | −0.0875917 | − | 0.269580i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.39855 | −0.887516 | −0.443758 | − | 0.896147i | \(-0.646355\pi\) | ||||
−0.443758 | + | 0.896147i | \(0.646355\pi\) | |||||||
\(38\) | 1.16824 | + | 3.59548i | 0.189514 | + | 0.583264i | ||||
\(39\) | −0.821848 | + | 2.52939i | −0.131601 | + | 0.405026i | ||||
\(40\) | 0.309017 | − | 0.951057i | 0.0488599 | − | 0.150375i | ||||
\(41\) | 8.86495 | + | 6.44077i | 1.38447 | + | 1.00588i | 0.996446 | + | 0.0842308i | \(0.0268433\pi\) |
0.388027 | + | 0.921648i | \(0.373157\pi\) | |||||||
\(42\) | 0.518200 | + | 1.59485i | 0.0799599 | + | 0.246091i | ||||
\(43\) | −9.64452 | − | 7.00716i | −1.47078 | − | 1.06858i | −0.980388 | − | 0.197077i | \(-0.936855\pi\) |
−0.490388 | − | 0.871504i | \(-0.663145\pi\) | |||||||
\(44\) | 3.11483 | − | 2.26306i | 0.469579 | − | 0.341169i | ||||
\(45\) | 0.309017 | − | 0.951057i | 0.0460655 | − | 0.141775i | ||||
\(46\) | 2.01820 | − | 1.46631i | 0.297567 | − | 0.216195i | ||||
\(47\) | 6.53518 | − | 4.74808i | 0.953253 | − | 0.692579i | 0.00167932 | − | 0.999999i | \(-0.499465\pi\) |
0.951574 | + | 0.307419i | \(0.0994655\pi\) | |||||||
\(48\) | −0.309017 | + | 0.951057i | −0.0446028 | + | 0.137273i | ||||
\(49\) | 3.38809 | − | 2.46159i | 0.484013 | − | 0.351656i | ||||
\(50\) | −0.809017 | − | 0.587785i | −0.114412 | − | 0.0831254i | ||||
\(51\) | −0.938299 | − | 2.88779i | −0.131388 | − | 0.404371i | ||||
\(52\) | −2.15163 | − | 1.56325i | −0.298377 | − | 0.216784i | ||||
\(53\) | 0.156995 | − | 0.483181i | 0.0215649 | − | 0.0663700i | −0.939695 | − | 0.342014i | \(-0.888891\pi\) |
0.961260 | + | 0.275644i | \(0.0888910\pi\) | |||||||
\(54\) | −0.309017 | + | 0.951057i | −0.0420519 | + | 0.129422i | ||||
\(55\) | −1.18976 | − | 3.66171i | −0.160427 | − | 0.493744i | ||||
\(56\) | −1.67693 | −0.224089 | ||||||||
\(57\) | −3.78051 | −0.500741 | ||||||||
\(58\) | 2.11606 | + | 6.51255i | 0.277852 | + | 0.855140i | ||||
\(59\) | 11.4148 | − | 8.29332i | 1.48608 | − | 1.07970i | 0.510541 | − | 0.859853i | \(-0.329445\pi\) |
0.975535 | − | 0.219844i | \(-0.0705550\pi\) | |||||||
\(60\) | 0.809017 | + | 0.587785i | 0.104444 | + | 0.0758827i | ||||
\(61\) | −4.85410 | −0.621504 | −0.310752 | − | 0.950491i | \(-0.600581\pi\) | ||||
−0.310752 | + | 0.950491i | \(0.600581\pi\) | |||||||
\(62\) | −4.86337 | − | 2.71065i | −0.617649 | − | 0.344253i | ||||
\(63\) | −1.67693 | −0.211273 | ||||||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | −2.15163 | + | 1.56325i | −0.266876 | + | 0.193897i | ||||
\(66\) | 1.18976 | + | 3.66171i | 0.146449 | + | 0.450725i | ||||
\(67\) | −13.9109 | −1.69949 | −0.849745 | − | 0.527194i | \(-0.823244\pi\) | ||||
−0.849745 | + | 0.527194i | \(0.823244\pi\) | |||||||
\(68\) | 3.03640 | 0.368217 | ||||||||
\(69\) | 0.770884 | + | 2.37254i | 0.0928035 | + | 0.285620i | ||||
\(70\) | −0.518200 | + | 1.59485i | −0.0619367 | + | 0.190622i | ||||
\(71\) | 2.38082 | − | 7.32740i | 0.282551 | − | 0.869602i | −0.704571 | − | 0.709633i | \(-0.748861\pi\) |
0.987122 | − | 0.159969i | \(-0.0511393\pi\) | |||||||
\(72\) | −0.809017 | − | 0.587785i | −0.0953436 | − | 0.0692712i | ||||
\(73\) | 5.01990 | + | 15.4497i | 0.587535 | + | 1.80825i | 0.588844 | + | 0.808247i | \(0.299583\pi\) |
−0.00130879 | + | 0.999999i | \(0.500417\pi\) | |||||||
\(74\) | 4.36752 | + | 3.17319i | 0.507714 | + | 0.368875i | ||||
\(75\) | 0.809017 | − | 0.587785i | 0.0934172 | − | 0.0678716i | ||||
\(76\) | 1.16824 | − | 3.59548i | 0.134007 | − | 0.412430i | ||||
\(77\) | −5.22335 | + | 3.79499i | −0.595256 | + | 0.432479i | ||||
\(78\) | 2.15163 | − | 1.56325i | 0.243624 | − | 0.177003i | ||||
\(79\) | −0.834903 | + | 2.56957i | −0.0939339 | + | 0.289099i | −0.986974 | − | 0.160878i | \(-0.948568\pi\) |
0.893040 | + | 0.449976i | \(0.148568\pi\) | |||||||
\(80\) | −0.809017 | + | 0.587785i | −0.0904508 | + | 0.0657164i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −3.38611 | − | 10.4214i | −0.373933 | − | 1.15085i | ||||
\(83\) | 1.81439 | + | 1.31823i | 0.199155 | + | 0.144694i | 0.682893 | − | 0.730518i | \(-0.260721\pi\) |
−0.483739 | + | 0.875213i | \(0.660721\pi\) | |||||||
\(84\) | 0.518200 | − | 1.59485i | 0.0565402 | − | 0.174013i | ||||
\(85\) | 0.938299 | − | 2.88779i | 0.101773 | − | 0.313224i | ||||
\(86\) | 3.68388 | + | 11.3378i | 0.397243 | + | 1.22259i | ||||
\(87\) | −6.84770 | −0.734150 | ||||||||
\(88\) | −3.85015 | −0.410427 | ||||||||
\(89\) | −2.33749 | − | 7.19404i | −0.247773 | − | 0.762567i | −0.995168 | − | 0.0981869i | \(-0.968696\pi\) |
0.747395 | − | 0.664380i | \(-0.231304\pi\) | |||||||
\(90\) | −0.809017 | + | 0.587785i | −0.0852779 | + | 0.0619580i | ||||
\(91\) | 3.60813 | + | 2.62146i | 0.378234 | + | 0.274803i | ||||
\(92\) | −2.49463 | −0.260083 | ||||||||
\(93\) | 4.08084 | − | 3.78770i | 0.423164 | − | 0.392767i | ||||
\(94\) | −8.07792 | −0.833174 | ||||||||
\(95\) | −3.05850 | − | 2.22213i | −0.313795 | − | 0.227986i | ||||
\(96\) | 0.809017 | − | 0.587785i | 0.0825700 | − | 0.0599906i | ||||
\(97\) | −4.26883 | − | 13.1381i | −0.433434 | − | 1.33397i | −0.894683 | − | 0.446703i | \(-0.852598\pi\) |
0.461248 | − | 0.887271i | \(-0.347402\pi\) | |||||||
\(98\) | −4.18791 | −0.423043 | ||||||||
\(99\) | −3.85015 | −0.386954 | ||||||||
\(100\) | 0.309017 | + | 0.951057i | 0.0309017 | + | 0.0951057i | ||||
\(101\) | −3.16651 | + | 9.74551i | −0.315079 | + | 0.969715i | 0.660642 | + | 0.750701i | \(0.270284\pi\) |
−0.975722 | + | 0.219014i | \(0.929716\pi\) | |||||||
\(102\) | −0.938299 | + | 2.88779i | −0.0929054 | + | 0.285934i | ||||
\(103\) | 9.11764 | + | 6.62435i | 0.898388 | + | 0.652717i | 0.938051 | − | 0.346496i | \(-0.112629\pi\) |
−0.0396637 | + | 0.999213i | \(0.512629\pi\) | |||||||
\(104\) | 0.821848 | + | 2.52939i | 0.0805889 | + | 0.248027i | ||||
\(105\) | −1.35666 | − | 0.985674i | −0.132397 | − | 0.0961919i | ||||
\(106\) | −0.411018 | + | 0.298622i | −0.0399216 | + | 0.0290048i | ||||
\(107\) | 0.810823 | − | 2.49546i | 0.0783852 | − | 0.241245i | −0.904184 | − | 0.427144i | \(-0.859520\pi\) |
0.982569 | + | 0.185899i | \(0.0595197\pi\) | |||||||
\(108\) | 0.809017 | − | 0.587785i | 0.0778477 | − | 0.0565597i | ||||
\(109\) | −8.79003 | + | 6.38633i | −0.841932 | + | 0.611699i | −0.922910 | − | 0.385017i | \(-0.874196\pi\) |
0.0809777 | + | 0.996716i | \(0.474196\pi\) | |||||||
\(110\) | −1.18976 | + | 3.66171i | −0.113439 | + | 0.349130i | ||||
\(111\) | −4.36752 | + | 3.17319i | −0.414546 | + | 0.301186i | ||||
\(112\) | 1.35666 | + | 0.985674i | 0.128193 | + | 0.0931374i | ||||
\(113\) | −2.48997 | − | 7.66335i | −0.234237 | − | 0.720908i | −0.997222 | − | 0.0744910i | \(-0.976267\pi\) |
0.762985 | − | 0.646417i | \(-0.223733\pi\) | |||||||
\(114\) | 3.05850 | + | 2.22213i | 0.286455 | + | 0.208122i | ||||
\(115\) | −0.770884 | + | 2.37254i | −0.0718853 | + | 0.221240i | ||||
\(116\) | 2.11606 | − | 6.51255i | 0.196471 | − | 0.604675i | ||||
\(117\) | 0.821848 | + | 2.52939i | 0.0759799 | + | 0.233842i | ||||
\(118\) | −14.1094 | −1.29888 | ||||||||
\(119\) | −5.09183 | −0.466767 | ||||||||
\(120\) | −0.309017 | − | 0.951057i | −0.0282093 | − | 0.0868192i | ||||
\(121\) | −3.09337 | + | 2.24747i | −0.281216 | + | 0.204315i | ||||
\(122\) | 3.92705 | + | 2.85317i | 0.355538 | + | 0.258314i | ||||
\(123\) | 10.9577 | 0.988021 | ||||||||
\(124\) | 2.34127 | + | 5.05158i | 0.210252 | + | 0.453645i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.35666 | + | 0.985674i | 0.120861 | + | 0.0878108i | ||||
\(127\) | −16.2381 | + | 11.7977i | −1.44090 | + | 1.04688i | −0.453049 | + | 0.891485i | \(0.649664\pi\) |
−0.987853 | + | 0.155391i | \(0.950336\pi\) | |||||||
\(128\) | 0.309017 | + | 0.951057i | 0.0273135 | + | 0.0840623i | ||||
\(129\) | −11.9213 | −1.04961 | ||||||||
\(130\) | 2.65956 | 0.233259 | ||||||||
\(131\) | 1.29057 | + | 3.97198i | 0.112758 | + | 0.347033i | 0.991473 | − | 0.130314i | \(-0.0415985\pi\) |
−0.878715 | + | 0.477347i | \(0.841598\pi\) | |||||||
\(132\) | 1.18976 | − | 3.66171i | 0.103555 | − | 0.318711i | ||||
\(133\) | −1.95906 | + | 6.02937i | −0.169872 | + | 0.522813i | ||||
\(134\) | 11.2542 | + | 8.17664i | 0.972213 | + | 0.706354i | ||||
\(135\) | −0.309017 | − | 0.951057i | −0.0265959 | − | 0.0818539i | ||||
\(136\) | −2.45650 | − | 1.78475i | −0.210643 | − | 0.153041i | ||||
\(137\) | 9.13623 | − | 6.63786i | 0.780561 | − | 0.567111i | −0.124586 | − | 0.992209i | \(-0.539760\pi\) |
0.905147 | + | 0.425098i | \(0.139760\pi\) | |||||||
\(138\) | 0.770884 | − | 2.37254i | 0.0656220 | − | 0.201964i | ||||
\(139\) | 14.7530 | − | 10.7186i | 1.25133 | − | 0.909144i | 0.253031 | − | 0.967458i | \(-0.418573\pi\) |
0.998298 | + | 0.0583142i | \(0.0185725\pi\) | |||||||
\(140\) | 1.35666 | − | 0.985674i | 0.114659 | − | 0.0833047i | ||||
\(141\) | 2.49622 | − | 7.68256i | 0.210219 | − | 0.646988i | ||||
\(142\) | −6.23306 | + | 4.52858i | −0.523066 | + | 0.380030i | ||||
\(143\) | 8.28408 | + | 6.01873i | 0.692749 | + | 0.503312i | ||||
\(144\) | 0.309017 | + | 0.951057i | 0.0257514 | + | 0.0792547i | ||||
\(145\) | −5.53991 | − | 4.02498i | −0.460064 | − | 0.334256i | ||||
\(146\) | 5.01990 | − | 15.4497i | 0.415450 | − | 1.27862i | ||||
\(147\) | 1.29414 | − | 3.98294i | 0.106738 | − | 0.328507i | ||||
\(148\) | −1.66824 | − | 5.13432i | −0.137129 | − | 0.422039i | ||||
\(149\) | 18.1675 | 1.48834 | 0.744171 | − | 0.667989i | \(-0.232845\pi\) | ||||
0.744171 | + | 0.667989i | \(0.232845\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 1.95440 | + | 6.01504i | 0.159047 | + | 0.489497i | 0.998548 | − | 0.0538610i | \(-0.0171528\pi\) |
−0.839501 | + | 0.543358i | \(0.817153\pi\) | |||||||
\(152\) | −3.05850 | + | 2.22213i | −0.248077 | + | 0.180239i | ||||
\(153\) | −2.45650 | − | 1.78475i | −0.198596 | − | 0.144289i | ||||
\(154\) | 6.45642 | 0.520273 | ||||||||
\(155\) | 5.52783 | − | 0.665657i | 0.444006 | − | 0.0534668i | ||||
\(156\) | −2.65956 | −0.212935 | ||||||||
\(157\) | −4.27222 | − | 3.10395i | −0.340961 | − | 0.247722i | 0.404106 | − | 0.914712i | \(-0.367583\pi\) |
−0.745067 | + | 0.666990i | \(0.767583\pi\) | |||||||
\(158\) | 2.18580 | − | 1.58808i | 0.173893 | − | 0.126341i | ||||
\(159\) | −0.156995 | − | 0.483181i | −0.0124505 | − | 0.0383188i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 4.18332 | 0.329692 | ||||||||
\(162\) | 0.309017 | + | 0.951057i | 0.0242787 | + | 0.0747221i | ||||
\(163\) | 4.61898 | − | 14.2158i | 0.361786 | − | 1.11346i | −0.590183 | − | 0.807270i | \(-0.700944\pi\) |
0.951969 | − | 0.306194i | \(-0.0990557\pi\) | |||||||
\(164\) | −3.38611 | + | 10.4214i | −0.264411 | + | 0.813773i | ||||
\(165\) | −3.11483 | − | 2.26306i | −0.242489 | − | 0.176179i | ||||
\(166\) | −0.693033 | − | 2.13294i | −0.0537898 | − | 0.165548i | ||||
\(167\) | −1.98402 | − | 1.44148i | −0.153528 | − | 0.111545i | 0.508369 | − | 0.861139i | \(-0.330249\pi\) |
−0.661897 | + | 0.749594i | \(0.730249\pi\) | |||||||
\(168\) | −1.35666 | + | 0.985674i | −0.104669 | + | 0.0760464i | ||||
\(169\) | −1.83147 | + | 5.63668i | −0.140882 | + | 0.433591i | ||||
\(170\) | −2.45650 | + | 1.78475i | −0.188405 | + | 0.136884i | ||||
\(171\) | −3.05850 | + | 2.22213i | −0.233889 | + | 0.169931i | ||||
\(172\) | 3.68388 | − | 11.3378i | 0.280893 | − | 0.864501i | ||||
\(173\) | −0.00972012 | + | 0.00706208i | −0.000739007 | + | 0.000536920i | −0.588155 | − | 0.808748i | \(-0.700145\pi\) |
0.587416 | + | 0.809285i | \(0.300145\pi\) | |||||||
\(174\) | 5.53991 | + | 4.02498i | 0.419979 | + | 0.305133i | ||||
\(175\) | −0.518200 | − | 1.59485i | −0.0391722 | − | 0.120560i | ||||
\(176\) | 3.11483 | + | 2.26306i | 0.234789 | + | 0.170584i | ||||
\(177\) | 4.36005 | − | 13.4189i | 0.327722 | − | 1.00862i | ||||
\(178\) | −2.33749 | + | 7.19404i | −0.175202 | + | 0.539216i | ||||
\(179\) | 4.36069 | + | 13.4208i | 0.325933 | + | 1.00312i | 0.971017 | + | 0.239008i | \(0.0768224\pi\) |
−0.645084 | + | 0.764112i | \(0.723178\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 14.9596 | 1.11194 | 0.555968 | − | 0.831204i | \(-0.312348\pi\) | ||||
0.555968 | + | 0.831204i | \(0.312348\pi\) | |||||||
\(182\) | −1.37818 | − | 4.24161i | −0.102158 | − | 0.314409i | ||||
\(183\) | −3.92705 | + | 2.85317i | −0.290296 | + | 0.210912i | ||||
\(184\) | 2.01820 | + | 1.46631i | 0.148784 | + | 0.108098i | ||||
\(185\) | −5.39855 | −0.396909 | ||||||||
\(186\) | −5.52783 | + | 0.665657i | −0.405320 | + | 0.0488083i | ||||
\(187\) | −11.6906 | −0.854900 | ||||||||
\(188\) | 6.53518 | + | 4.74808i | 0.476627 | + | 0.346290i | ||||
\(189\) | −1.35666 | + | 0.985674i | −0.0986828 | + | 0.0716972i | ||||
\(190\) | 1.16824 | + | 3.59548i | 0.0847533 | + | 0.260844i | ||||
\(191\) | 4.48476 | 0.324506 | 0.162253 | − | 0.986749i | \(-0.448124\pi\) | ||||
0.162253 | + | 0.986749i | \(0.448124\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 5.55057 | + | 17.0829i | 0.399539 | + | 1.22965i | 0.925370 | + | 0.379065i | \(0.123754\pi\) |
−0.525831 | + | 0.850589i | \(0.676246\pi\) | |||||||
\(194\) | −4.26883 | + | 13.1381i | −0.306484 | + | 0.943262i | ||||
\(195\) | −0.821848 | + | 2.52939i | −0.0588538 | + | 0.181133i | ||||
\(196\) | 3.38809 | + | 2.46159i | 0.242006 | + | 0.175828i | ||||
\(197\) | 1.20550 | + | 3.71016i | 0.0858886 | + | 0.264338i | 0.984772 | − | 0.173849i | \(-0.0556206\pi\) |
−0.898884 | + | 0.438187i | \(0.855621\pi\) | |||||||
\(198\) | 3.11483 | + | 2.26306i | 0.221362 | + | 0.160829i | ||||
\(199\) | 19.9327 | − | 14.4819i | 1.41299 | − | 1.02660i | 0.420112 | − | 0.907472i | \(-0.361991\pi\) |
0.992879 | − | 0.119126i | \(-0.0380091\pi\) | |||||||
\(200\) | 0.309017 | − | 0.951057i | 0.0218508 | − | 0.0672499i | ||||
\(201\) | −11.2542 | + | 8.17664i | −0.793808 | + | 0.576736i | ||||
\(202\) | 8.29003 | − | 6.02306i | 0.583284 | − | 0.423781i | ||||
\(203\) | −3.54847 | + | 10.9211i | −0.249054 | + | 0.766510i | ||||
\(204\) | 2.45650 | − | 1.78475i | 0.171989 | − | 0.124958i | ||||
\(205\) | 8.86495 | + | 6.44077i | 0.619155 | + | 0.449843i | ||||
\(206\) | −3.48263 | − | 10.7184i | −0.242646 | − | 0.746788i | ||||
\(207\) | 2.01820 | + | 1.46631i | 0.140275 | + | 0.101915i | ||||
\(208\) | 0.821848 | − | 2.52939i | 0.0569849 | − | 0.175382i | ||||
\(209\) | −4.49791 | + | 13.8431i | −0.311127 | + | 0.957549i | ||||
\(210\) | 0.518200 | + | 1.59485i | 0.0357592 | + | 0.110055i | ||||
\(211\) | 19.8006 | 1.36313 | 0.681566 | − | 0.731757i | \(-0.261299\pi\) | ||||
0.681566 | + | 0.731757i | \(0.261299\pi\) | |||||||
\(212\) | 0.508047 | 0.0348928 | ||||||||
\(213\) | −2.38082 | − | 7.32740i | −0.163131 | − | 0.502065i | ||||
\(214\) | −2.12276 | + | 1.54228i | −0.145109 | + | 0.105428i | ||||
\(215\) | −9.64452 | − | 7.00716i | −0.657751 | − | 0.477884i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −3.92614 | − | 8.47114i | −0.266524 | − | 0.575058i | ||||
\(218\) | 10.8651 | 0.735875 | ||||||||
\(219\) | 13.1423 | + | 9.54842i | 0.888072 | + | 0.645222i | ||||
\(220\) | 3.11483 | − | 2.26306i | 0.210002 | − | 0.152575i | ||||
\(221\) | 2.49546 | + | 7.68023i | 0.167863 | + | 0.516628i | ||||
\(222\) | 5.39855 | 0.362327 | ||||||||
\(223\) | 18.5384 | 1.24142 | 0.620712 | − | 0.784038i | \(-0.286844\pi\) | ||||
0.620712 | + | 0.784038i | \(0.286844\pi\) | |||||||
\(224\) | −0.518200 | − | 1.59485i | −0.0346237 | − | 0.106561i | ||||
\(225\) | 0.309017 | − | 0.951057i | 0.0206011 | − | 0.0634038i | ||||
\(226\) | −2.48997 | + | 7.66335i | −0.165631 | + | 0.509759i | ||||
\(227\) | 0.436960 | + | 0.317470i | 0.0290020 | + | 0.0210712i | 0.602192 | − | 0.798351i | \(-0.294294\pi\) |
−0.573190 | + | 0.819423i | \(0.694294\pi\) | |||||||
\(228\) | −1.16824 | − | 3.59548i | −0.0773688 | − | 0.238117i | ||||
\(229\) | −6.22719 | − | 4.52432i | −0.411505 | − | 0.298976i | 0.362706 | − | 0.931904i | \(-0.381853\pi\) |
−0.774211 | + | 0.632928i | \(0.781853\pi\) | |||||||
\(230\) | 2.01820 | − | 1.46631i | 0.133076 | − | 0.0966855i | ||||
\(231\) | −1.99514 | + | 6.14042i | −0.131271 | + | 0.404010i | ||||
\(232\) | −5.53991 | + | 4.02498i | −0.363713 | + | 0.264253i | ||||
\(233\) | −3.48101 | + | 2.52910i | −0.228049 | + | 0.165687i | −0.695942 | − | 0.718098i | \(-0.745013\pi\) |
0.467894 | + | 0.883785i | \(0.345013\pi\) | |||||||
\(234\) | 0.821848 | − | 2.52939i | 0.0537259 | − | 0.165351i | ||||
\(235\) | 6.53518 | − | 4.74808i | 0.426308 | − | 0.309731i | ||||
\(236\) | 11.4148 | + | 8.29332i | 0.743038 | + | 0.539849i | ||||
\(237\) | 0.834903 | + | 2.56957i | 0.0542328 | + | 0.166911i | ||||
\(238\) | 4.11937 | + | 2.99290i | 0.267019 | + | 0.194001i | ||||
\(239\) | −5.96688 | + | 18.3642i | −0.385966 | + | 1.18788i | 0.549812 | + | 0.835289i | \(0.314699\pi\) |
−0.935777 | + | 0.352592i | \(0.885301\pi\) | |||||||
\(240\) | −0.309017 | + | 0.951057i | −0.0199470 | + | 0.0613904i | ||||
\(241\) | 4.26049 | + | 13.1124i | 0.274442 | + | 0.844646i | 0.989366 | + | 0.145444i | \(0.0464611\pi\) |
−0.714924 | + | 0.699202i | \(0.753539\pi\) | |||||||
\(242\) | 3.82362 | 0.245791 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.50000 | − | 4.61653i | −0.0960277 | − | 0.295543i | ||||
\(245\) | 3.38809 | − | 2.46159i | 0.216457 | − | 0.157265i | ||||
\(246\) | −8.86495 | − | 6.44077i | −0.565209 | − | 0.410648i | ||||
\(247\) | 10.0545 | 0.639752 | ||||||||
\(248\) | 1.07512 | − | 5.46298i | 0.0682699 | − | 0.346899i | ||||
\(249\) | 2.24270 | 0.142126 | ||||||||
\(250\) | −0.809017 | − | 0.587785i | −0.0511667 | − | 0.0371748i | ||||
\(251\) | 2.08725 | − | 1.51647i | 0.131746 | − | 0.0957190i | −0.519961 | − | 0.854190i | \(-0.674053\pi\) |
0.651707 | + | 0.758471i | \(0.274053\pi\) | |||||||
\(252\) | −0.518200 | − | 1.59485i | −0.0326435 | − | 0.100466i | ||||
\(253\) | 9.60469 | 0.603842 | ||||||||
\(254\) | 20.0715 | 1.25939 | ||||||||
\(255\) | −0.938299 | − | 2.88779i | −0.0587586 | − | 0.180840i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | −1.22655 | + | 3.77495i | −0.0765104 | + | 0.235475i | −0.981996 | − | 0.188903i | \(-0.939507\pi\) |
0.905485 | + | 0.424377i | \(0.139507\pi\) | |||||||
\(258\) | 9.64452 | + | 7.00716i | 0.600442 | + | 0.436247i | ||||
\(259\) | 2.79752 | + | 8.60990i | 0.173830 | + | 0.534993i | ||||
\(260\) | −2.15163 | − | 1.56325i | −0.133438 | − | 0.0969486i | ||||
\(261\) | −5.53991 | + | 4.02498i | −0.342912 | + | 0.249140i | ||||
\(262\) | 1.29057 | − | 3.97198i | 0.0797319 | − | 0.245390i | ||||
\(263\) | 24.5731 | − | 17.8534i | 1.51524 | − | 1.10089i | 0.551456 | − | 0.834204i | \(-0.314072\pi\) |
0.963784 | − | 0.266682i | \(-0.0859275\pi\) | |||||||
\(264\) | −3.11483 | + | 2.26306i | −0.191705 | + | 0.139282i | ||||
\(265\) | 0.156995 | − | 0.483181i | 0.00964413 | − | 0.0296816i | ||||
\(266\) | 5.12889 | − | 3.72635i | 0.314472 | − | 0.228477i | ||||
\(267\) | −6.11962 | − | 4.44616i | −0.374515 | − | 0.272101i | ||||
\(268\) | −4.29871 | − | 13.2301i | −0.262586 | − | 0.808156i | ||||
\(269\) | 6.74787 | + | 4.90261i | 0.411425 | + | 0.298917i | 0.774178 | − | 0.632968i | \(-0.218163\pi\) |
−0.362754 | + | 0.931885i | \(0.618163\pi\) | |||||||
\(270\) | −0.309017 | + | 0.951057i | −0.0188062 | + | 0.0578795i | ||||
\(271\) | −0.491953 | + | 1.51408i | −0.0298840 | + | 0.0919736i | −0.964886 | − | 0.262669i | \(-0.915397\pi\) |
0.935002 | + | 0.354642i | \(0.115397\pi\) | |||||||
\(272\) | 0.938299 | + | 2.88779i | 0.0568927 | + | 0.175098i | ||||
\(273\) | 4.45989 | 0.269925 | ||||||||
\(274\) | −11.2930 | −0.682235 | ||||||||
\(275\) | −1.18976 | − | 3.66171i | −0.0717452 | − | 0.220809i | ||||
\(276\) | −2.01820 | + | 1.46631i | −0.121481 | + | 0.0882614i | ||||
\(277\) | 2.59899 | + | 1.88828i | 0.156158 | + | 0.113456i | 0.663120 | − | 0.748513i | \(-0.269232\pi\) |
−0.506962 | + | 0.861968i | \(0.669232\pi\) | |||||||
\(278\) | −18.2357 | −1.09370 | ||||||||
\(279\) | 1.07512 | − | 5.46298i | 0.0643655 | − | 0.327060i | ||||
\(280\) | −1.67693 | −0.100216 | ||||||||
\(281\) | −6.07670 | − | 4.41498i | −0.362505 | − | 0.263376i | 0.391591 | − | 0.920139i | \(-0.371925\pi\) |
−0.754096 | + | 0.656764i | \(0.771925\pi\) | |||||||
\(282\) | −6.53518 | + | 4.74808i | −0.389164 | + | 0.282744i | ||||
\(283\) | 1.94344 | + | 5.98131i | 0.115526 | + | 0.355552i | 0.992056 | − | 0.125794i | \(-0.0401480\pi\) |
−0.876531 | + | 0.481346i | \(0.840148\pi\) | |||||||
\(284\) | 7.70448 | 0.457177 | ||||||||
\(285\) | −3.78051 | −0.223938 | ||||||||
\(286\) | −3.16424 | − | 9.73851i | −0.187105 | − | 0.575850i | ||||
\(287\) | 5.67827 | − | 17.4759i | 0.335178 | − | 1.03157i | ||||
\(288\) | 0.309017 | − | 0.951057i | 0.0182090 | − | 0.0560415i | ||||
\(289\) | 6.29438 | + | 4.57313i | 0.370258 | + | 0.269008i | ||||
\(290\) | 2.11606 | + | 6.51255i | 0.124259 | + | 0.382430i | ||||
\(291\) | −11.1760 | − | 8.11980i | −0.655146 | − | 0.475991i | ||||
\(292\) | −13.1423 | + | 9.54842i | −0.769093 | + | 0.558779i | ||||
\(293\) | −8.12230 | + | 24.9979i | −0.474510 | + | 1.46039i | 0.372108 | + | 0.928189i | \(0.378635\pi\) |
−0.846618 | + | 0.532201i | \(0.821365\pi\) | |||||||
\(294\) | −3.38809 | + | 2.46159i | −0.197597 | + | 0.143563i | ||||
\(295\) | 11.4148 | − | 8.29332i | 0.664594 | − | 0.482855i | ||||
\(296\) | −1.66824 | + | 5.13432i | −0.0969647 | + | 0.298427i | ||||
\(297\) | −3.11483 | + | 2.26306i | −0.180741 | + | 0.131316i | ||||
\(298\) | −14.6978 | − | 10.6786i | −0.851423 | − | 0.618595i | ||||
\(299\) | −2.05021 | − | 6.30989i | −0.118567 | − | 0.364911i | ||||
\(300\) | 0.809017 | + | 0.587785i | 0.0467086 | + | 0.0339358i | ||||
\(301\) | −6.17761 | + | 19.0127i | −0.356071 | + | 1.09587i | ||||
\(302\) | 1.95440 | − | 6.01504i | 0.112463 | − | 0.346126i | ||||
\(303\) | 3.16651 | + | 9.74551i | 0.181911 | + | 0.559865i | ||||
\(304\) | 3.78051 | 0.216827 | ||||||||
\(305\) | −4.85410 | −0.277945 | ||||||||
\(306\) | 0.938299 | + | 2.88779i | 0.0536390 | + | 0.165084i | ||||
\(307\) | 9.55441 | − | 6.94169i | 0.545299 | − | 0.396183i | −0.280750 | − | 0.959781i | \(-0.590583\pi\) |
0.826049 | + | 0.563598i | \(0.190583\pi\) | |||||||
\(308\) | −5.22335 | − | 3.79499i | −0.297628 | − | 0.216240i | ||||
\(309\) | 11.2700 | 0.641129 | ||||||||
\(310\) | −4.86337 | − | 2.71065i | −0.276221 | − | 0.153955i | ||||
\(311\) | −5.82094 | −0.330075 | −0.165038 | − | 0.986287i | \(-0.552775\pi\) | ||||
−0.165038 | + | 0.986287i | \(0.552775\pi\) | |||||||
\(312\) | 2.15163 | + | 1.56325i | 0.121812 | + | 0.0885015i | ||||
\(313\) | 8.82969 | − | 6.41514i | 0.499084 | − | 0.362605i | −0.309583 | − | 0.950872i | \(-0.600190\pi\) |
0.808667 | + | 0.588267i | \(0.200190\pi\) | |||||||
\(314\) | 1.63184 | + | 5.02230i | 0.0920903 | + | 0.283425i | ||||
\(315\) | −1.67693 | −0.0944842 | ||||||||
\(316\) | −2.70180 | −0.151988 | ||||||||
\(317\) | 0.410981 | + | 1.26487i | 0.0230830 | + | 0.0710421i | 0.961934 | − | 0.273280i | \(-0.0881087\pi\) |
−0.938851 | + | 0.344322i | \(0.888109\pi\) | |||||||
\(318\) | −0.156995 | + | 0.483181i | −0.00880385 | + | 0.0270955i | ||||
\(319\) | −8.14712 | + | 25.0743i | −0.456151 | + | 1.40389i | ||||
\(320\) | −0.809017 | − | 0.587785i | −0.0452254 | − | 0.0328582i | ||||
\(321\) | −0.810823 | − | 2.49546i | −0.0452557 | − | 0.139283i | ||||
\(322\) | −3.38438 | − | 2.45889i | −0.188604 | − | 0.137029i | ||||
\(323\) | −9.28683 | + | 6.74727i | −0.516733 | + | 0.375428i | ||||
\(324\) | 0.309017 | − | 0.951057i | 0.0171676 | − | 0.0528365i | ||||
\(325\) | −2.15163 | + | 1.56325i | −0.119351 | + | 0.0867134i | ||||
\(326\) | −12.0926 | + | 8.78582i | −0.669749 | + | 0.486601i | ||||
\(327\) | −3.35749 | + | 10.3333i | −0.185670 | + | 0.571433i | ||||
\(328\) | 8.86495 | − | 6.44077i | 0.489485 | − | 0.355632i | ||||
\(329\) | −10.9590 | − | 7.96220i | −0.604191 | − | 0.438970i | ||||
\(330\) | 1.18976 | + | 3.66171i | 0.0654941 | + | 0.201570i | ||||
\(331\) | 22.3438 | + | 16.2337i | 1.22813 | + | 0.892286i | 0.996748 | − | 0.0805780i | \(-0.0256766\pi\) |
0.231378 | + | 0.972864i | \(0.425677\pi\) | |||||||
\(332\) | −0.693033 | + | 2.13294i | −0.0380352 | + | 0.117060i | ||||
\(333\) | −1.66824 | + | 5.13432i | −0.0914192 | + | 0.281359i | ||||
\(334\) | 0.757829 | + | 2.33236i | 0.0414666 | + | 0.127621i | ||||
\(335\) | −13.9109 | −0.760035 | ||||||||
\(336\) | 1.67693 | 0.0914840 | ||||||||
\(337\) | 3.09944 | + | 9.53909i | 0.168837 | + | 0.519628i | 0.999299 | − | 0.0374487i | \(-0.0119231\pi\) |
−0.830461 | + | 0.557076i | \(0.811923\pi\) | |||||||
\(338\) | 4.79485 | − | 3.48366i | 0.260805 | − | 0.189486i | ||||
\(339\) | −6.51884 | − | 4.73621i | −0.354055 | − | 0.257236i | ||||
\(340\) | 3.03640 | 0.164672 | ||||||||
\(341\) | −9.01423 | − | 19.4493i | −0.488148 | − | 1.05324i | ||||
\(342\) | 3.78051 | 0.204427 | ||||||||
\(343\) | −15.1782 | − | 11.0276i | −0.819548 | − | 0.595436i | ||||
\(344\) | −9.64452 | + | 7.00716i | −0.519998 | + | 0.377801i | ||||
\(345\) | 0.770884 | + | 2.37254i | 0.0415030 | + | 0.127733i | ||||
\(346\) | 0.0120147 | 0.000645916 | ||||||||
\(347\) | −35.1983 | −1.88954 | −0.944772 | − | 0.327727i | \(-0.893717\pi\) | ||||
−0.944772 | + | 0.327727i | \(0.893717\pi\) | |||||||
\(348\) | −2.11606 | − | 6.51255i | −0.113432 | − | 0.349109i | ||||
\(349\) | 2.39739 | − | 7.37842i | 0.128330 | − | 0.394958i | −0.866163 | − | 0.499761i | \(-0.833421\pi\) |
0.994493 | + | 0.104803i | \(0.0334212\pi\) | |||||||
\(350\) | −0.518200 | + | 1.59485i | −0.0276989 | + | 0.0852485i | ||||
\(351\) | 2.15163 | + | 1.56325i | 0.114845 | + | 0.0834400i | ||||
\(352\) | −1.18976 | − | 3.66171i | −0.0634144 | − | 0.195170i | ||||
\(353\) | −1.86663 | − | 1.35618i | −0.0993506 | − | 0.0721824i | 0.537001 | − | 0.843582i | \(-0.319557\pi\) |
−0.636351 | + | 0.771399i | \(0.719557\pi\) | |||||||
\(354\) | −11.4148 | + | 8.29332i | −0.606688 | + | 0.440785i | ||||
\(355\) | 2.38082 | − | 7.32740i | 0.126361 | − | 0.388898i | ||||
\(356\) | 6.11962 | − | 4.44616i | 0.324339 | − | 0.235646i | ||||
\(357\) | −4.11937 | + | 2.99290i | −0.218020 | + | 0.158401i | ||||
\(358\) | 4.36069 | − | 13.4208i | 0.230470 | − | 0.709313i | ||||
\(359\) | 18.0116 | − | 13.0862i | 0.950618 | − | 0.690665i | −0.000334704 | − | 1.00000i | \(-0.500107\pi\) |
0.950953 | + | 0.309335i | \(0.100107\pi\) | |||||||
\(360\) | −0.809017 | − | 0.587785i | −0.0426389 | − | 0.0309790i | ||||
\(361\) | −1.45476 | − | 4.47730i | −0.0765665 | − | 0.235648i | ||||
\(362\) | −12.1026 | − | 8.79302i | −0.636096 | − | 0.462151i | ||||
\(363\) | −1.18156 | + | 3.63648i | −0.0620160 | + | 0.190865i | ||||
\(364\) | −1.37818 | + | 4.24161i | −0.0722363 | + | 0.222321i | ||||
\(365\) | 5.01990 | + | 15.4497i | 0.262754 | + | 0.808672i | ||||
\(366\) | 4.85410 | 0.253728 | ||||||||
\(367\) | −23.3763 | −1.22023 | −0.610116 | − | 0.792312i | \(-0.708877\pi\) | ||||
−0.610116 | + | 0.792312i | \(0.708877\pi\) | |||||||
\(368\) | −0.770884 | − | 2.37254i | −0.0401851 | − | 0.123677i | ||||
\(369\) | 8.86495 | − | 6.44077i | 0.461491 | − | 0.335293i | ||||
\(370\) | 4.36752 | + | 3.17319i | 0.227056 | + | 0.164966i | ||||
\(371\) | −0.851958 | −0.0442315 | ||||||||
\(372\) | 4.86337 | + | 2.71065i | 0.252154 | + | 0.140541i | ||||
\(373\) | 19.6859 | 1.01930 | 0.509650 | − | 0.860382i | \(-0.329775\pi\) | ||||
0.509650 | + | 0.860382i | \(0.329775\pi\) | |||||||
\(374\) | 9.45788 | + | 6.87155i | 0.489055 | + | 0.355319i | ||||
\(375\) | 0.809017 | − | 0.587785i | 0.0417775 | − | 0.0303531i | ||||
\(376\) | −2.49622 | − | 7.68256i | −0.128732 | − | 0.396198i | ||||
\(377\) | 18.2118 | 0.937958 | ||||||||
\(378\) | 1.67693 | 0.0862519 | ||||||||
\(379\) | −2.65648 | − | 8.17582i | −0.136454 | − | 0.419963i | 0.859359 | − | 0.511373i | \(-0.170863\pi\) |
−0.995813 | + | 0.0914093i | \(0.970863\pi\) | |||||||
\(380\) | 1.16824 | − | 3.59548i | 0.0599296 | − | 0.184444i | ||||
\(381\) | −6.20242 | + | 19.0891i | −0.317760 | + | 0.977963i | ||||
\(382\) | −3.62825 | − | 2.63608i | −0.185637 | − | 0.134873i | ||||
\(383\) | 4.54596 | + | 13.9910i | 0.232288 | + | 0.714908i | 0.997470 | + | 0.0710937i | \(0.0226489\pi\) |
−0.765182 | + | 0.643814i | \(0.777351\pi\) | |||||||
\(384\) | 0.809017 | + | 0.587785i | 0.0412850 | + | 0.0299953i | ||||
\(385\) | −5.22335 | + | 3.79499i | −0.266207 | + | 0.193411i | ||||
\(386\) | 5.55057 | − | 17.0829i | 0.282517 | − | 0.869497i | ||||
\(387\) | −9.64452 | + | 7.00716i | −0.490259 | + | 0.356194i | ||||
\(388\) | 11.1760 | − | 8.11980i | 0.567373 | − | 0.412221i | ||||
\(389\) | 11.5687 | − | 35.6049i | 0.586558 | − | 1.80524i | −0.00636558 | − | 0.999980i | \(-0.502026\pi\) |
0.592923 | − | 0.805259i | \(-0.297974\pi\) | |||||||
\(390\) | 2.15163 | − | 1.56325i | 0.108952 | − | 0.0791582i | ||||
\(391\) | 6.12806 | + | 4.45230i | 0.309909 | + | 0.225162i | ||||
\(392\) | −1.29414 | − | 3.98294i | −0.0653637 | − | 0.201169i | ||||
\(393\) | 3.37876 | + | 2.45482i | 0.170436 | + | 0.123829i | ||||
\(394\) | 1.20550 | − | 3.71016i | 0.0607324 | − | 0.186915i | ||||
\(395\) | −0.834903 | + | 2.56957i | −0.0420085 | + | 0.129289i | ||||
\(396\) | −1.18976 | − | 3.66171i | −0.0597877 | − | 0.184008i | ||||
\(397\) | −15.1170 | −0.758700 | −0.379350 | − | 0.925253i | \(-0.623852\pi\) | ||||
−0.379350 | + | 0.925253i | \(0.623852\pi\) | |||||||
\(398\) | −24.6382 | −1.23500 | ||||||||
\(399\) | 1.95906 | + | 6.02937i | 0.0980757 | + | 0.301846i | ||||
\(400\) | −0.809017 | + | 0.587785i | −0.0404508 | + | 0.0293893i | ||||
\(401\) | −28.4912 | − | 20.7001i | −1.42278 | − | 1.03371i | −0.991304 | − | 0.131592i | \(-0.957991\pi\) |
−0.431481 | − | 0.902122i | \(-0.642009\pi\) | |||||||
\(402\) | 13.9109 | 0.693814 | ||||||||
\(403\) | −10.8532 | + | 10.0736i | −0.540638 | + | 0.501803i | ||||
\(404\) | −10.2470 | −0.509809 | ||||||||
\(405\) | −0.809017 | − | 0.587785i | −0.0402004 | − | 0.0292073i | ||||
\(406\) | 9.29003 | − | 6.74960i | 0.461056 | − | 0.334977i | ||||
\(407\) | 6.42298 | + | 19.7679i | 0.318375 | + | 0.979858i | ||||
\(408\) | −3.03640 | −0.150324 | ||||||||
\(409\) | −24.0640 | −1.18989 | −0.594943 | − | 0.803768i | \(-0.702825\pi\) | ||||
−0.594943 | + | 0.803768i | \(0.702825\pi\) | |||||||
\(410\) | −3.38611 | − | 10.4214i | −0.167228 | − | 0.514675i | ||||
\(411\) | 3.48973 | − | 10.7403i | 0.172136 | − | 0.529779i | ||||
\(412\) | −3.48263 | + | 10.7184i | −0.171577 | + | 0.528059i | ||||
\(413\) | −19.1418 | − | 13.9073i | −0.941904 | − | 0.684333i | ||||
\(414\) | −0.770884 | − | 2.37254i | −0.0378869 | − | 0.116604i | ||||
\(415\) | 1.81439 | + | 1.31823i | 0.0890647 | + | 0.0647093i | ||||
\(416\) | −2.15163 | + | 1.56325i | −0.105492 | + | 0.0766446i | ||||
\(417\) | 5.63513 | − | 17.3431i | 0.275953 | − | 0.849297i | ||||
\(418\) | 11.7757 | − | 8.55552i | 0.575967 | − | 0.418464i | ||||
\(419\) | 4.70854 | − | 3.42096i | 0.230027 | − | 0.167125i | −0.466801 | − | 0.884362i | \(-0.654594\pi\) |
0.696829 | + | 0.717237i | \(0.254594\pi\) | |||||||
\(420\) | 0.518200 | − | 1.59485i | 0.0252855 | − | 0.0778209i | ||||
\(421\) | −25.3582 | + | 18.4238i | −1.23588 | + | 0.897922i | −0.997317 | − | 0.0732041i | \(-0.976678\pi\) |
−0.238567 | + | 0.971126i | \(0.576678\pi\) | |||||||
\(422\) | −16.0191 | − | 11.6385i | −0.779795 | − | 0.566554i | ||||
\(423\) | −2.49622 | − | 7.68256i | −0.121370 | − | 0.373539i | ||||
\(424\) | −0.411018 | − | 0.298622i | −0.0199608 | − | 0.0145024i | ||||
\(425\) | 0.938299 | − | 2.88779i | 0.0455142 | − | 0.140078i | ||||
\(426\) | −2.38082 | + | 7.32740i | −0.115351 | + | 0.355013i | ||||
\(427\) | 2.51539 | + | 7.74158i | 0.121728 | + | 0.374642i | ||||
\(428\) | 2.62388 | 0.126830 | ||||||||
\(429\) | 10.2397 | 0.494376 | ||||||||
\(430\) | 3.68388 | + | 11.3378i | 0.177652 | + | 0.546758i | ||||
\(431\) | 18.7422 | − | 13.6170i | 0.902778 | − | 0.655907i | −0.0364001 | − | 0.999337i | \(-0.511589\pi\) |
0.939178 | + | 0.343431i | \(0.111589\pi\) | |||||||
\(432\) | 0.809017 | + | 0.587785i | 0.0389238 | + | 0.0282798i | ||||
\(433\) | 1.83752 | 0.0883056 | 0.0441528 | − | 0.999025i | \(-0.485941\pi\) | ||||
0.0441528 | + | 0.999025i | \(0.485941\pi\) | |||||||
\(434\) | −1.80289 | + | 9.16103i | −0.0865416 | + | 0.439743i | ||||
\(435\) | −6.84770 | −0.328322 | ||||||||
\(436\) | −8.79003 | − | 6.38633i | −0.420966 | − | 0.305850i | ||||
\(437\) | 7.62983 | − | 5.54340i | 0.364984 | − | 0.265177i | ||||
\(438\) | −5.01990 | − | 15.4497i | −0.239860 | − | 0.738213i | ||||
\(439\) | 1.91593 | 0.0914424 | 0.0457212 | − | 0.998954i | \(-0.485441\pi\) | ||||
0.0457212 | + | 0.998954i | \(0.485441\pi\) | |||||||
\(440\) | −3.85015 | −0.183548 | ||||||||
\(441\) | −1.29414 | − | 3.98294i | −0.0616255 | − | 0.189664i | ||||
\(442\) | 2.49546 | − | 7.68023i | 0.118697 | − | 0.365312i | ||||
\(443\) | −0.106391 | + | 0.327438i | −0.00505479 | + | 0.0155570i | −0.953552 | − | 0.301228i | \(-0.902603\pi\) |
0.948497 | + | 0.316785i | \(0.102603\pi\) | |||||||
\(444\) | −4.36752 | − | 3.17319i | −0.207273 | − | 0.150593i | ||||
\(445\) | −2.33749 | − | 7.19404i | −0.110807 | − | 0.341030i | ||||
\(446\) | −14.9979 | − | 10.8966i | −0.710171 | − | 0.515969i | ||||
\(447\) | 14.6978 | − | 10.6786i | 0.695184 | − | 0.505081i | ||||
\(448\) | −0.518200 | + | 1.59485i | −0.0244826 | + | 0.0753498i | ||||
\(449\) | −22.5681 | + | 16.3967i | −1.06505 | + | 0.773807i | −0.975017 | − | 0.222132i | \(-0.928698\pi\) |
−0.0900368 | + | 0.995938i | \(0.528698\pi\) | |||||||
\(450\) | −0.809017 | + | 0.587785i | −0.0381374 | + | 0.0277085i | ||||
\(451\) | 13.0370 | − | 40.1238i | 0.613889 | − | 1.88936i | ||||
\(452\) | 6.51884 | − | 4.73621i | 0.306620 | − | 0.222773i | ||||
\(453\) | 5.11669 | + | 3.71750i | 0.240403 | + | 0.174663i | ||||
\(454\) | −0.166904 | − | 0.513677i | −0.00783318 | − | 0.0241080i | ||||
\(455\) | 3.60813 | + | 2.62146i | 0.169152 | + | 0.122896i | ||||
\(456\) | −1.16824 | + | 3.59548i | −0.0547080 | + | 0.168374i | ||||
\(457\) | −9.40918 | + | 28.9585i | −0.440143 | + | 1.35462i | 0.447581 | + | 0.894243i | \(0.352286\pi\) |
−0.887724 | + | 0.460377i | \(0.847714\pi\) | |||||||
\(458\) | 2.37858 | + | 7.32051i | 0.111144 | + | 0.342065i | ||||
\(459\) | −3.03640 | −0.141727 | ||||||||
\(460\) | −2.49463 | −0.116313 | ||||||||
\(461\) | −2.13875 | − | 6.58240i | −0.0996116 | − | 0.306573i | 0.888816 | − | 0.458263i | \(-0.151528\pi\) |
−0.988428 | + | 0.151690i | \(0.951528\pi\) | |||||||
\(462\) | 5.22335 | − | 3.79499i | 0.243012 | − | 0.176559i | ||||
\(463\) | −3.39270 | − | 2.46494i | −0.157672 | − | 0.114556i | 0.506152 | − | 0.862444i | \(-0.331068\pi\) |
−0.663824 | + | 0.747889i | \(0.731068\pi\) | |||||||
\(464\) | 6.84770 | 0.317896 | ||||||||
\(465\) | 4.08084 | − | 3.78770i | 0.189245 | − | 0.175651i | ||||
\(466\) | 4.30277 | 0.199322 | ||||||||
\(467\) | 16.8293 | + | 12.2272i | 0.778769 | + | 0.565809i | 0.904609 | − | 0.426241i | \(-0.140163\pi\) |
−0.125840 | + | 0.992051i | \(0.540163\pi\) | |||||||
\(468\) | −2.15163 | + | 1.56325i | −0.0994590 | + | 0.0722612i | ||||
\(469\) | 7.20864 | + | 22.1859i | 0.332864 | + | 1.02445i | ||||
\(470\) | −8.07792 | −0.372607 | ||||||||
\(471\) | −5.28076 | −0.243324 | ||||||||
\(472\) | −4.36005 | − | 13.4189i | −0.200688 | − | 0.617653i | ||||
\(473\) | −14.1835 | + | 43.6522i | −0.652157 | + | 2.00713i | ||||
\(474\) | 0.834903 | − | 2.56957i | 0.0383483 | − | 0.118024i | ||||
\(475\) | −3.05850 | − | 2.22213i | −0.140334 | − | 0.101958i | ||||
\(476\) | −1.57346 | − | 4.84261i | −0.0721194 | − | 0.221961i | ||||
\(477\) | −0.411018 | − | 0.298622i | −0.0188192 | − | 0.0136730i | ||||
\(478\) | 15.6215 | − | 11.3497i | 0.714511 | − | 0.519123i | ||||
\(479\) | 0.0796188 | − | 0.245042i | 0.00363788 | − | 0.0111962i | −0.949221 | − | 0.314610i | \(-0.898126\pi\) |
0.952859 | + | 0.303414i | \(0.0981264\pi\) | |||||||
\(480\) | 0.809017 | − | 0.587785i | 0.0369264 | − | 0.0268286i | ||||
\(481\) | 11.6157 | − | 8.43927i | 0.529629 | − | 0.384798i | ||||
\(482\) | 4.26049 | − | 13.1124i | 0.194060 | − | 0.597255i | ||||
\(483\) | 3.38438 | − | 2.45889i | 0.153994 | − | 0.111884i | ||||
\(484\) | −3.09337 | − | 2.24747i | −0.140608 | − | 0.102158i | ||||
\(485\) | −4.26883 | − | 13.1381i | −0.193838 | − | 0.596571i | ||||
\(486\) | 0.809017 | + | 0.587785i | 0.0366978 | + | 0.0266625i | ||||
\(487\) | −0.0931990 | + | 0.286837i | −0.00422325 | + | 0.0129978i | −0.953146 | − | 0.302511i | \(-0.902175\pi\) |
0.948923 | + | 0.315509i | \(0.102175\pi\) | |||||||
\(488\) | −1.50000 | + | 4.61653i | −0.0679018 | + | 0.208980i | ||||
\(489\) | −4.61898 | − | 14.2158i | −0.208877 | − | 0.642859i | ||||
\(490\) | −4.18791 | −0.189190 | ||||||||
\(491\) | −19.6973 | −0.888926 | −0.444463 | − | 0.895797i | \(-0.646606\pi\) | ||||
−0.444463 | + | 0.895797i | \(0.646606\pi\) | |||||||
\(492\) | 3.38611 | + | 10.4214i | 0.152658 | + | 0.469832i | ||||
\(493\) | −16.8214 | + | 12.2214i | −0.757596 | + | 0.550426i | ||||
\(494\) | −8.13426 | − | 5.90988i | −0.365977 | − | 0.265898i | ||||
\(495\) | −3.85015 | −0.173051 | ||||||||
\(496\) | −4.08084 | + | 3.78770i | −0.183235 | + | 0.170073i | ||||
\(497\) | −12.9199 | −0.579535 | ||||||||
\(498\) | −1.81439 | − | 1.31823i | −0.0813045 | − | 0.0590712i | ||||
\(499\) | 9.65864 | − | 7.01741i | 0.432380 | − | 0.314143i | −0.350220 | − | 0.936668i | \(-0.613893\pi\) |
0.782600 | + | 0.622525i | \(0.213893\pi\) | |||||||
\(500\) | 0.309017 | + | 0.951057i | 0.0138197 | + | 0.0425325i | ||||
\(501\) | −2.45239 | −0.109565 | ||||||||
\(502\) | −2.57998 | −0.115150 | ||||||||
\(503\) | −3.70335 | − | 11.3977i | −0.165124 | − | 0.508200i | 0.833921 | − | 0.551883i | \(-0.186091\pi\) |
−0.999045 | + | 0.0436836i | \(0.986091\pi\) | |||||||
\(504\) | −0.518200 | + | 1.59485i | −0.0230824 | + | 0.0710405i | ||||
\(505\) | −3.16651 | + | 9.74551i | −0.140908 | + | 0.433670i | ||||
\(506\) | −7.77036 | − | 5.64550i | −0.345435 | − | 0.250973i | ||||
\(507\) | 1.83147 | + | 5.63668i | 0.0813384 | + | 0.250334i | ||||
\(508\) | −16.2381 | − | 11.7977i | −0.720451 | − | 0.523438i | ||||
\(509\) | 4.33251 | − | 3.14775i | 0.192035 | − | 0.139522i | −0.487613 | − | 0.873060i | \(-0.662132\pi\) |
0.679648 | + | 0.733538i | \(0.262132\pi\) | |||||||
\(510\) | −0.938299 | + | 2.88779i | −0.0415486 | + | 0.127873i | ||||
\(511\) | 22.0386 | − | 16.0120i | 0.974932 | − | 0.708330i | ||||
\(512\) | −0.809017 | + | 0.587785i | −0.0357538 | + | 0.0259767i | ||||
\(513\) | −1.16824 | + | 3.59548i | −0.0515792 | + | 0.158744i | ||||
\(514\) | 3.21116 | − | 2.33305i | 0.141638 | − | 0.102906i | ||||
\(515\) | 9.11764 | + | 6.62435i | 0.401771 | + | 0.291904i | ||||
\(516\) | −3.68388 | − | 11.3378i | −0.162174 | − | 0.499120i | ||||
\(517\) | −25.1614 | − | 18.2808i | −1.10660 | − | 0.803989i | ||||
\(518\) | 2.79752 | − | 8.60990i | 0.122916 | − | 0.378297i | ||||
\(519\) | −0.00371276 | + | 0.0114267i | −0.000162972 | + | 0.000501576i | ||||
\(520\) | 0.821848 | + | 2.52939i | 0.0360404 | + | 0.110921i | ||||
\(521\) | −37.8297 | −1.65735 | −0.828674 | − | 0.559732i | \(-0.810904\pi\) | ||||
−0.828674 | + | 0.559732i | \(0.810904\pi\) | |||||||
\(522\) | 6.84770 | 0.299716 | ||||||||
\(523\) | −5.85544 | − | 18.0212i | −0.256041 | − | 0.788012i | −0.993623 | − | 0.112755i | \(-0.964033\pi\) |
0.737582 | − | 0.675257i | \(-0.235967\pi\) | |||||||
\(524\) | −3.37876 | + | 2.45482i | −0.147602 | + | 0.107239i | ||||
\(525\) | −1.35666 | − | 0.985674i | −0.0592097 | − | 0.0430183i | ||||
\(526\) | −30.3740 | −1.32437 | ||||||||
\(527\) | 3.26448 | − | 16.5878i | 0.142203 | − | 0.722575i | ||||
\(528\) | 3.85015 | 0.167556 | ||||||||
\(529\) | 13.5727 | + | 9.86116i | 0.590119 | + | 0.428746i | ||||
\(530\) | −0.411018 | + | 0.298622i | −0.0178535 | + | 0.0129713i | ||||
\(531\) | −4.36005 | − | 13.4189i | −0.189210 | − | 0.582329i | ||||
\(532\) | −6.33965 | −0.274859 | ||||||||
\(533\) | −29.1426 | −1.26231 | ||||||||
\(534\) | 2.33749 | + | 7.19404i | 0.101153 | + | 0.311317i | ||||
\(535\) | 0.810823 | − | 2.49546i | 0.0350549 | − | 0.107888i | ||||
\(536\) | −4.29871 | + | 13.2301i | −0.185676 | + | 0.571452i | ||||
\(537\) | 11.4164 | + | 8.29453i | 0.492656 | + | 0.357935i | ||||
\(538\) | −2.57746 | − | 7.93259i | −0.111122 | − | 0.341998i | ||||
\(539\) | −13.0446 | − | 9.47748i | −0.561872 | − | 0.408224i | ||||
\(540\) | 0.809017 | − | 0.587785i | 0.0348145 | − | 0.0252942i | ||||
\(541\) | −12.8537 | + | 39.5595i | −0.552622 | + | 1.70079i | 0.149521 | + | 0.988759i | \(0.452227\pi\) |
−0.702143 | + | 0.712036i | \(0.747773\pi\) | |||||||
\(542\) | 1.28795 | − | 0.935751i | 0.0553222 | − | 0.0401939i | ||||
\(543\) | 12.1026 | − | 8.79302i | 0.519370 | − | 0.377345i | ||||
\(544\) | 0.938299 | − | 2.88779i | 0.0402292 | − | 0.123813i | ||||
\(545\) | −8.79003 | + | 6.38633i | −0.376523 | + | 0.273560i | ||||
\(546\) | −3.60813 | − | 2.62146i | −0.154414 | − | 0.112188i | ||||
\(547\) | −9.05243 | − | 27.8605i | −0.387054 | − | 1.19123i | −0.934979 | − | 0.354702i | \(-0.884582\pi\) |
0.547925 | − | 0.836527i | \(-0.315418\pi\) | |||||||
\(548\) | 9.13623 | + | 6.63786i | 0.390281 | + | 0.283555i | ||||
\(549\) | −1.50000 | + | 4.61653i | −0.0640184 | + | 0.197028i | ||||
\(550\) | −1.18976 | + | 3.66171i | −0.0507315 | + | 0.156136i | ||||
\(551\) | 7.99978 | + | 24.6208i | 0.340802 | + | 1.04888i | ||||
\(552\) | 2.49463 | 0.106179 | ||||||||
\(553\) | 4.53073 | 0.192666 | ||||||||
\(554\) | −0.992725 | − | 3.05529i | −0.0421769 | − | 0.129807i | ||||
\(555\) | −4.36752 | + | 3.17319i | −0.185391 | + | 0.134694i | ||||
\(556\) | 14.7530 | + | 10.7186i | 0.625665 | + | 0.454572i | ||||
\(557\) | 10.3856 | 0.440052 | 0.220026 | − | 0.975494i | \(-0.429386\pi\) | ||||
0.220026 | + | 0.975494i | \(0.429386\pi\) | |||||||
\(558\) | −4.08084 | + | 3.78770i | −0.172756 | + | 0.160346i | ||||
\(559\) | 31.7053 | 1.34099 | ||||||||
\(560\) | 1.35666 | + | 0.985674i | 0.0573295 | + | 0.0416523i | ||||
\(561\) | −9.45788 | + | 6.87155i | −0.399312 | + | 0.290117i | ||||
\(562\) | 2.32109 | + | 7.14359i | 0.0979094 | + | 0.301334i | ||||
\(563\) | −20.7504 | −0.874527 | −0.437264 | − | 0.899333i | \(-0.644052\pi\) | ||||
−0.437264 | + | 0.899333i | \(0.644052\pi\) | |||||||
\(564\) | 8.07792 | 0.340142 | ||||||||
\(565\) | −2.48997 | − | 7.66335i | −0.104754 | − | 0.322400i | ||||
\(566\) | 1.94344 | − | 5.98131i | 0.0816891 | − | 0.251413i | ||||
\(567\) | −0.518200 | + | 1.59485i | −0.0217623 | + | 0.0669776i | ||||
\(568\) | −6.23306 | − | 4.52858i | −0.261533 | − | 0.190015i | ||||
\(569\) | −11.0575 | − | 34.0315i | −0.463555 | − | 1.42668i | −0.860791 | − | 0.508959i | \(-0.830031\pi\) |
0.397236 | − | 0.917717i | \(-0.369969\pi\) | |||||||
\(570\) | 3.05850 | + | 2.22213i | 0.128106 | + | 0.0930748i | ||||
\(571\) | 23.3830 | − | 16.9887i | 0.978548 | − | 0.710957i | 0.0211646 | − | 0.999776i | \(-0.493263\pi\) |
0.957384 | + | 0.288819i | \(0.0932626\pi\) | |||||||
\(572\) | −3.16424 | + | 9.73851i | −0.132303 | + | 0.407188i | ||||
\(573\) | 3.62825 | − | 2.63608i | 0.151572 | − | 0.110124i | ||||
\(574\) | −14.8659 | + | 10.8007i | −0.620491 | + | 0.450813i | ||||
\(575\) | −0.770884 | + | 2.37254i | −0.0321481 | + | 0.0989416i | ||||
\(576\) | −0.809017 | + | 0.587785i | −0.0337090 | + | 0.0244911i | ||||
\(577\) | 2.10462 | + | 1.52910i | 0.0876164 | + | 0.0636571i | 0.630731 | − | 0.776001i | \(-0.282755\pi\) |
−0.543115 | + | 0.839659i | \(0.682755\pi\) | |||||||
\(578\) | −2.40424 | − | 7.39949i | −0.100003 | − | 0.307778i | ||||
\(579\) | 14.5316 | + | 10.5578i | 0.603912 | + | 0.438768i | ||||
\(580\) | 2.11606 | − | 6.51255i | 0.0878644 | − | 0.270419i | ||||
\(581\) | 1.16217 | − | 3.57678i | 0.0482148 | − | 0.148390i | ||||
\(582\) | 4.26883 | + | 13.1381i | 0.176949 | + | 0.544592i | ||||
\(583\) | −1.95605 | −0.0810115 | ||||||||
\(584\) | 16.2447 | 0.672212 | ||||||||
\(585\) | 0.821848 | + | 2.52939i | 0.0339792 | + | 0.104577i | ||||
\(586\) | 21.2644 | − | 15.4495i | 0.878426 | − | 0.638214i | ||||
\(587\) | 25.5508 | + | 18.5638i | 1.05460 | + | 0.766208i | 0.973081 | − | 0.230464i | \(-0.0740243\pi\) |
0.0815144 | + | 0.996672i | \(0.474024\pi\) | |||||||
\(588\) | 4.18791 | 0.172706 | ||||||||
\(589\) | −18.3860 | − | 10.2476i | −0.757584 | − | 0.422247i | ||||
\(590\) | −14.1094 | −0.580876 | ||||||||
\(591\) | 3.15605 | + | 2.29301i | 0.129823 | + | 0.0943216i | ||||
\(592\) | 4.36752 | − | 3.17319i | 0.179504 | − | 0.130417i | ||||
\(593\) | −8.66800 | − | 26.6774i | −0.355952 | − | 1.09551i | −0.955455 | − | 0.295136i | \(-0.904635\pi\) |
0.599503 | − | 0.800372i | \(-0.295365\pi\) | |||||||
\(594\) | 3.85015 | 0.157973 | ||||||||
\(595\) | −5.09183 | −0.208744 | ||||||||
\(596\) | 5.61408 | + | 17.2784i | 0.229962 | + | 0.707749i | ||||
\(597\) | 7.61361 | − | 23.4323i | 0.311604 | − | 0.959019i | ||||
\(598\) | −2.05021 | + | 6.30989i | −0.0838393 | + | 0.258031i | ||||
\(599\) | −13.7497 | − | 9.98976i | −0.561799 | − | 0.408171i | 0.270318 | − | 0.962771i | \(-0.412871\pi\) |
−0.832117 | + | 0.554600i | \(0.812871\pi\) | |||||||
\(600\) | −0.309017 | − | 0.951057i | −0.0126156 | − | 0.0388267i | ||||
\(601\) | −17.3201 | − | 12.5838i | −0.706500 | − | 0.513302i | 0.175543 | − | 0.984472i | \(-0.443832\pi\) |
−0.882043 | + | 0.471170i | \(0.843832\pi\) | |||||||
\(602\) | 16.1732 | − | 11.7505i | 0.659170 | − | 0.478915i | ||||
\(603\) | −4.29871 | + | 13.2301i | −0.175057 | + | 0.538770i | ||||
\(604\) | −5.11669 | + | 3.71750i | −0.208195 | + | 0.151263i | ||||
\(605\) | −3.09337 | + | 2.24747i | −0.125763 | + | 0.0913725i | ||||
\(606\) | 3.16651 | − | 9.74551i | 0.128631 | − | 0.395884i | ||||
\(607\) | 37.5690 | − | 27.2955i | 1.52488 | − | 1.10789i | 0.565875 | − | 0.824491i | \(-0.308538\pi\) |
0.959002 | − | 0.283398i | \(-0.0914617\pi\) | |||||||
\(608\) | −3.05850 | − | 2.22213i | −0.124039 | − | 0.0901193i | ||||
\(609\) | 3.54847 | + | 10.9211i | 0.143791 | + | 0.442545i | ||||
\(610\) | 3.92705 | + | 2.85317i | 0.159002 | + | 0.115521i | ||||
\(611\) | −6.63883 | + | 20.4322i | −0.268578 | + | 0.826599i | ||||
\(612\) | 0.938299 | − | 2.88779i | 0.0379285 | − | 0.116732i | ||||
\(613\) | 2.30955 | + | 7.10806i | 0.0932818 | + | 0.287092i | 0.986802 | − | 0.161931i | \(-0.0517722\pi\) |
−0.893520 | + | 0.449023i | \(0.851772\pi\) | |||||||
\(614\) | −11.8099 | −0.476609 | ||||||||
\(615\) | 10.9577 | 0.441857 | ||||||||
\(616\) | 1.99514 | + | 6.14042i | 0.0803866 | + | 0.247405i | ||||
\(617\) | 18.3053 | − | 13.2996i | 0.736942 | − | 0.535420i | −0.154810 | − | 0.987944i | \(-0.549476\pi\) |
0.891752 | + | 0.452524i | \(0.149476\pi\) | |||||||
\(618\) | −9.11764 | − | 6.62435i | −0.366765 | − | 0.266471i | ||||
\(619\) | −33.2346 | −1.33581 | −0.667906 | − | 0.744246i | \(-0.732809\pi\) | ||||
−0.667906 | + | 0.744246i | \(0.732809\pi\) | |||||||
\(620\) | 2.34127 | + | 5.05158i | 0.0940277 | + | 0.202876i | ||||
\(621\) | 2.49463 | 0.100106 | ||||||||
\(622\) | 4.70924 | + | 3.42146i | 0.188823 | + | 0.137188i | ||||
\(623\) | −10.2622 | + | 7.45590i | −0.411145 | + | 0.298714i | ||||
\(624\) | −0.821848 | − | 2.52939i | −0.0329003 | − | 0.101257i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.9141 | −0.436215 | ||||||||
\(627\) | 4.49791 | + | 13.8431i | 0.179629 | + | 0.552841i | ||||
\(628\) | 1.63184 | − | 5.02230i | 0.0651177 | − | 0.200412i | ||||
\(629\) | −5.06545 | + | 15.5899i | −0.201973 | + | 0.621608i | ||||
\(630\) | 1.35666 | + | 0.985674i | 0.0540508 | + | 0.0392702i | ||||
\(631\) | 1.31727 | + | 4.05414i | 0.0524397 | + | 0.161393i | 0.973847 | − | 0.227206i | \(-0.0729591\pi\) |
−0.921407 | + | 0.388599i | \(0.872959\pi\) | |||||||
\(632\) | 2.18580 | + | 1.58808i | 0.0869466 | + | 0.0631704i | ||||
\(633\) | 16.0191 | − | 11.6385i | 0.636700 | − | 0.462590i | ||||
\(634\) | 0.410981 | − | 1.26487i | 0.0163221 | − | 0.0502344i | ||||
\(635\) | −16.2381 | + | 11.7977i | −0.644391 | + | 0.468178i | ||||
\(636\) | 0.411018 | − | 0.298622i | 0.0162979 | − | 0.0118411i | ||||
\(637\) | −3.44183 | + | 10.5929i | −0.136370 | + | 0.419704i | ||||
\(638\) | 21.3294 | − | 15.4967i | 0.844441 | − | 0.613522i | ||||
\(639\) | −6.23306 | − | 4.52858i | −0.246576 | − | 0.179148i | ||||
\(640\) | 0.309017 | + | 0.951057i | 0.0122150 | + | 0.0375938i | ||||
\(641\) | −17.8198 | − | 12.9469i | −0.703841 | − | 0.511371i | 0.177340 | − | 0.984150i | \(-0.443251\pi\) |
−0.881181 | + | 0.472779i | \(0.843251\pi\) | |||||||
\(642\) | −0.810823 | + | 2.49546i | −0.0320006 | + | 0.0984879i | ||||
\(643\) | −4.87472 | + | 15.0028i | −0.192240 | + | 0.591654i | 0.807758 | + | 0.589515i | \(0.200681\pi\) |
−0.999998 | + | 0.00213956i | \(0.999319\pi\) | |||||||
\(644\) | 1.29272 | + | 3.97857i | 0.0509402 | + | 0.156778i | ||||
\(645\) | −11.9213 | −0.469400 | ||||||||
\(646\) | 11.4791 | 0.451641 | ||||||||
\(647\) | 0.0213451 | + | 0.0656935i | 0.000839163 | + | 0.00258268i | 0.951475 | − | 0.307725i | \(-0.0995678\pi\) |
−0.950636 | + | 0.310308i | \(0.899568\pi\) | |||||||
\(648\) | −0.809017 | + | 0.587785i | −0.0317812 | + | 0.0230904i | ||||
\(649\) | −43.9485 | − | 31.9305i | −1.72513 | − | 1.25338i | ||||
\(650\) | 2.65956 | 0.104316 | ||||||||
\(651\) | −8.15553 | − | 4.54557i | −0.319640 | − | 0.178155i | ||||
\(652\) | 14.9473 | 0.585383 | ||||||||
\(653\) | 16.7612 | + | 12.1777i | 0.655916 | + | 0.476551i | 0.865281 | − | 0.501287i | \(-0.167140\pi\) |
−0.209365 | + | 0.977838i | \(0.567140\pi\) | |||||||
\(654\) | 8.79003 | − | 6.38633i | 0.343717 | − | 0.249725i | ||||
\(655\) | 1.29057 | + | 3.97198i | 0.0504269 | + | 0.155198i | ||||
\(656\) | −10.9577 | −0.427826 | ||||||||
\(657\) | 16.2447 | 0.633768 | ||||||||
\(658\) | 4.18598 | + | 12.8831i | 0.163186 | + | 0.502236i | ||||
\(659\) | −0.359759 | + | 1.10722i | −0.0140142 | + | 0.0431313i | −0.957819 | − | 0.287372i | \(-0.907218\pi\) |
0.943805 | + | 0.330503i | \(0.107218\pi\) | |||||||
\(660\) | 1.18976 | − | 3.66171i | 0.0463114 | − | 0.142532i | ||||
\(661\) | 24.3789 | + | 17.7123i | 0.948229 | + | 0.688928i | 0.950387 | − | 0.311069i | \(-0.100687\pi\) |
−0.00215856 | + | 0.999998i | \(0.500687\pi\) | |||||||
\(662\) | −8.53457 | − | 26.2667i | −0.331706 | − | 1.02088i | ||||
\(663\) | 6.53320 | + | 4.74665i | 0.253728 | + | 0.184344i | ||||
\(664\) | 1.81439 | − | 1.31823i | 0.0704118 | − | 0.0511572i | ||||
\(665\) | −1.95906 | + | 6.02937i | −0.0759691 | + | 0.233809i | ||||
\(666\) | 4.36752 | − | 3.17319i | 0.169238 | − | 0.122958i | ||||
\(667\) | 13.8200 | − | 10.0408i | 0.535113 | − | 0.388783i | ||||
\(668\) | 0.757829 | − | 2.33236i | 0.0293213 | − | 0.0902417i | ||||
\(669\) | 14.9979 | − | 10.8966i | 0.579852 | − | 0.421287i | ||||
\(670\) | 11.2542 | + | 8.17664i | 0.434787 | + | 0.315891i | ||||
\(671\) | 5.77522 | + | 17.7743i | 0.222950 | + | 0.686169i | ||||
\(672\) | −1.35666 | − | 0.985674i | −0.0523344 | − | 0.0380232i | ||||
\(673\) | −7.90452 | + | 24.3276i | −0.304697 | + | 0.937761i | 0.675093 | + | 0.737732i | \(0.264103\pi\) |
−0.979790 | + | 0.200028i | \(0.935897\pi\) | |||||||
\(674\) | 3.09944 | − | 9.53909i | 0.119386 | − | 0.367432i | ||||
\(675\) | −0.309017 | − | 0.951057i | −0.0118941 | − | 0.0366062i | ||||
\(676\) | −5.92676 | −0.227952 | ||||||||
\(677\) | 41.2455 | 1.58519 | 0.792597 | − | 0.609746i | \(-0.208729\pi\) | ||||
0.792597 | + | 0.609746i | \(0.208729\pi\) | |||||||
\(678\) | 2.48997 | + | 7.66335i | 0.0956269 | + | 0.294309i | ||||
\(679\) | −18.7413 | + | 13.6163i | −0.719224 | + | 0.522547i | ||||
\(680\) | −2.45650 | − | 1.78475i | −0.0942024 | − | 0.0684421i | ||||
\(681\) | 0.540112 | 0.0206971 | ||||||||
\(682\) | −4.13935 | + | 21.0333i | −0.158504 | + | 0.805405i | ||||
\(683\) | −7.77607 | −0.297543 | −0.148771 | − | 0.988872i | \(-0.547532\pi\) | ||||
−0.148771 | + | 0.988872i | \(0.547532\pi\) | |||||||
\(684\) | −3.05850 | − | 2.22213i | −0.116945 | − | 0.0849653i | ||||
\(685\) | 9.13623 | − | 6.63786i | 0.349078 | − | 0.253620i | ||||
\(686\) | 5.79757 | + | 17.8431i | 0.221352 | + | 0.681252i | ||||
\(687\) | −7.69723 | −0.293668 | ||||||||
\(688\) | 11.9213 | 0.454495 | ||||||||
\(689\) | 0.417537 | + | 1.28505i | 0.0159069 | + | 0.0489564i | ||||
\(690\) | 0.770884 | − | 2.37254i | 0.0293470 | − | 0.0903209i | ||||
\(691\) | −1.16438 | + | 3.58358i | −0.0442950 | + | 0.136326i | −0.970758 | − | 0.240059i | \(-0.922833\pi\) |
0.926463 | + | 0.376385i | \(0.122833\pi\) | |||||||
\(692\) | −0.00972012 | − | 0.00706208i | −0.000369504 | − | 0.000268460i | ||||
\(693\) | 1.99514 | + | 6.14042i | 0.0757892 | + | 0.233255i | ||||
\(694\) | 28.4760 | + | 20.6891i | 1.08094 | + | 0.785346i | ||||
\(695\) | 14.7530 | − | 10.7186i | 0.559611 | − | 0.406582i | ||||
\(696\) | −2.11606 | + | 6.51255i | −0.0802089 | + | 0.246858i | ||||
\(697\) | 26.9175 | − | 19.5567i | 1.01957 | − | 0.740764i | ||||
\(698\) | −6.27646 | + | 4.56011i | −0.237567 | + | 0.172603i | ||||
\(699\) | −1.32963 | + | 4.09217i | −0.0502911 | + | 0.154780i | ||||
\(700\) | 1.35666 | − | 0.985674i | 0.0512771 | − | 0.0372550i | ||||
\(701\) | 5.89836 | + | 4.28541i | 0.222778 | + | 0.161858i | 0.693576 | − | 0.720383i | \(-0.256034\pi\) |
−0.470798 | + | 0.882241i | \(0.656034\pi\) | |||||||
\(702\) | −0.821848 | − | 2.52939i | −0.0310187 | − | 0.0954656i | ||||
\(703\) | 16.5115 | + | 11.9963i | 0.622741 | + | 0.452448i | ||||
\(704\) | −1.18976 | + | 3.66171i | −0.0448408 | + | 0.138006i | ||||
\(705\) | 2.49622 | − | 7.68256i | 0.0940129 | − | 0.289342i | ||||
\(706\) | 0.712989 | + | 2.19435i | 0.0268337 | + | 0.0825856i | ||||
\(707\) | 17.1836 | 0.646254 | ||||||||
\(708\) | 14.1094 | 0.530265 | ||||||||
\(709\) | 2.35152 | + | 7.23723i | 0.0883131 | + | 0.271800i | 0.985453 | − | 0.169946i | \(-0.0543593\pi\) |
−0.897140 | + | 0.441746i | \(0.854359\pi\) | |||||||
\(710\) | −6.23306 | + | 4.52858i | −0.233922 | + | 0.169955i | ||||
\(711\) | 2.18580 | + | 1.58808i | 0.0819740 | + | 0.0595576i | ||||
\(712\) | −7.56426 | −0.283483 | ||||||||
\(713\) | −2.68202 | + | 13.6281i | −0.100442 | + | 0.510377i | ||||
\(714\) | 5.09183 | 0.190557 | ||||||||
\(715\) | 8.28408 | + | 6.01873i | 0.309807 | + | 0.225088i | ||||
\(716\) | −11.4164 | + | 8.29453i | −0.426652 | + | 0.309981i | ||||
\(717\) | 5.96688 | + | 18.3642i | 0.222837 | + | 0.685823i | ||||
\(718\) | −22.2636 | −0.830871 | ||||||||
\(719\) | 9.19960 | 0.343087 | 0.171544 | − | 0.985177i | \(-0.445125\pi\) | ||||
0.171544 | + | 0.985177i | \(0.445125\pi\) | |||||||
\(720\) | 0.309017 | + | 0.951057i | 0.0115164 | + | 0.0354438i | ||||
\(721\) | 5.84012 | − | 17.9740i | 0.217497 | − | 0.669388i | ||||
\(722\) | −1.45476 | + | 4.47730i | −0.0541407 | + | 0.166628i | ||||
\(723\) | 11.1541 | + | 8.10393i | 0.414825 | + | 0.301388i | ||||
\(724\) | 4.62276 | + | 14.2274i | 0.171804 | + | 0.528757i | ||||
\(725\) | −5.53991 | − | 4.02498i | −0.205747 | − | 0.149484i | ||||
\(726\) | 3.09337 | − | 2.24747i | 0.114806 | − | 0.0834113i | ||||
\(727\) | −14.9230 | + | 45.9284i | −0.553465 | + | 1.70339i | 0.146498 | + | 0.989211i | \(0.453200\pi\) |
−0.699963 | + | 0.714179i | \(0.746800\pi\) | |||||||
\(728\) | 3.60813 | − | 2.62146i | 0.133726 | − | 0.0971576i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 5.01990 | − | 15.4497i | 0.185795 | − | 0.571818i | ||||
\(731\) | −29.2846 | + | 21.2765i | −1.08313 | + | 0.786941i | ||||
\(732\) | −3.92705 | − | 2.85317i | −0.145148 | − | 0.105456i | ||||
\(733\) | 3.37368 | + | 10.3831i | 0.124610 | + | 0.383509i | 0.993830 | − | 0.110916i | \(-0.0353785\pi\) |
−0.869220 | + | 0.494425i | \(0.835379\pi\) | |||||||
\(734\) | 18.9118 | + | 13.7402i | 0.698048 | + | 0.507161i | ||||
\(735\) | 1.29414 | − | 3.98294i | 0.0477349 | − | 0.146913i | ||||
\(736\) | −0.770884 | + | 2.37254i | −0.0284151 | + | 0.0874528i | ||||
\(737\) | 16.5507 | + | 50.9377i | 0.609652 | + | 1.87632i | ||||
\(738\) | −10.9577 | −0.403358 | ||||||||
\(739\) | 13.3199 | 0.489979 | 0.244990 | − | 0.969526i | \(-0.421215\pi\) | ||||
0.244990 | + | 0.969526i | \(0.421215\pi\) | |||||||
\(740\) | −1.66824 | − | 5.13432i | −0.0613258 | − | 0.188742i | ||||
\(741\) | 8.13426 | − | 5.90988i | 0.298819 | − | 0.217105i | ||||
\(742\) | 0.689249 | + | 0.500768i | 0.0253031 | + | 0.0183838i | ||||
\(743\) | 4.08463 | 0.149851 | 0.0749253 | − | 0.997189i | \(-0.476128\pi\) | ||||
0.0749253 | + | 0.997189i | \(0.476128\pi\) | |||||||
\(744\) | −2.34127 | − | 5.05158i | −0.0858351 | − | 0.185200i | ||||
\(745\) | 18.1675 | 0.665607 | ||||||||
\(746\) | −15.9263 | − | 11.5711i | −0.583102 | − | 0.423648i | ||||
\(747\) | 1.81439 | − | 1.31823i | 0.0663849 | − | 0.0482314i | ||||
\(748\) | −3.61259 | − | 11.1184i | −0.132089 | − | 0.406529i | ||||
\(749\) | −4.40006 | −0.160775 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 4.70543 | + | 14.4818i | 0.171704 | + | 0.528450i | 0.999468 | − | 0.0326270i | \(-0.0103873\pi\) |
−0.827764 | + | 0.561077i | \(0.810387\pi\) | |||||||
\(752\) | −2.49622 | + | 7.68256i | −0.0910276 | + | 0.280154i | ||||
\(753\) | 0.797258 | − | 2.45371i | 0.0290537 | − | 0.0894180i | ||||
\(754\) | −14.7337 | − | 10.7047i | −0.536570 | − | 0.389841i | ||||
\(755\) | 1.95440 | + | 6.01504i | 0.0711280 | + | 0.218910i | ||||
\(756\) | −1.35666 | − | 0.985674i | −0.0493414 | − | 0.0358486i | ||||
\(757\) | −9.45844 | + | 6.87196i | −0.343773 | + | 0.249766i | −0.746252 | − | 0.665664i | \(-0.768149\pi\) |
0.402479 | + | 0.915429i | \(0.368149\pi\) | |||||||
\(758\) | −2.65648 | + | 8.17582i | −0.0964878 | + | 0.296959i | ||||
\(759\) | 7.77036 | − | 5.64550i | 0.282046 | − | 0.204919i | ||||
\(760\) | −3.05850 | + | 2.22213i | −0.110943 | + | 0.0806051i | ||||
\(761\) | −2.64940 | + | 8.15403i | −0.0960408 | + | 0.295583i | −0.987524 | − | 0.157471i | \(-0.949666\pi\) |
0.891483 | + | 0.453055i | \(0.149666\pi\) | |||||||
\(762\) | 16.2381 | − | 11.7977i | 0.588246 | − | 0.427386i | ||||
\(763\) | 14.7403 | + | 10.7094i | 0.533633 | + | 0.387707i | ||||
\(764\) | 1.38587 | + | 4.26526i | 0.0501389 | + | 0.154312i | ||||
\(765\) | −2.45650 | − | 1.78475i | −0.0888149 | − | 0.0645278i | ||||
\(766\) | 4.54596 | − | 13.9910i | 0.164252 | − | 0.505516i | ||||
\(767\) | −11.5958 | + | 35.6882i | −0.418700 | + | 1.28863i | ||||
\(768\) | −0.309017 | − | 0.951057i | −0.0111507 | − | 0.0343183i | ||||
\(769\) | 8.29383 | 0.299083 | 0.149542 | − | 0.988755i | \(-0.452220\pi\) | ||||
0.149542 | + | 0.988755i | \(0.452220\pi\) | |||||||
\(770\) | 6.45642 | 0.232673 | ||||||||
\(771\) | 1.22655 | + | 3.77495i | 0.0441733 | + | 0.135951i | ||||
\(772\) | −14.5316 | + | 10.5578i | −0.523003 | + | 0.379984i | ||||
\(773\) | −6.06240 | − | 4.40459i | −0.218049 | − | 0.158422i | 0.473399 | − | 0.880848i | \(-0.343027\pi\) |
−0.691448 | + | 0.722426i | \(0.743027\pi\) | |||||||
\(774\) | 11.9213 | 0.428502 | ||||||||
\(775\) | 5.52783 | − | 0.665657i | 0.198566 | − | 0.0239111i | ||||
\(776\) | −13.8142 | −0.495902 | ||||||||
\(777\) | 7.32402 | + | 5.32121i | 0.262748 | + | 0.190897i | ||||
\(778\) | −30.2873 | + | 22.0050i | −1.08585 | + | 0.788918i | ||||
\(779\) | −12.8012 | − | 39.3982i | −0.458652 | − | 1.41159i | ||||
\(780\) | −2.65956 | −0.0952274 | ||||||||
\(781\) | −29.6634 | −1.06144 | ||||||||
\(782\) | −2.34071 | − | 7.20397i | −0.0837036 | − | 0.257613i | ||||
\(783\) | −2.11606 | + | 6.51255i | −0.0756217 | + | 0.232740i | ||||
\(784\) | −1.29414 | + | 3.98294i | −0.0462191 | + | 0.142248i | ||||
\(785\) | −4.27222 | − | 3.10395i | −0.152482 | − | 0.110785i | ||||
\(786\) | −1.29057 | − | 3.97198i | −0.0460332 | − | 0.141676i | ||||
\(787\) | −43.8205 | − | 31.8375i | −1.56203 | − | 1.13488i | −0.934318 | − | 0.356441i | \(-0.883990\pi\) |
−0.627716 | − | 0.778443i | \(-0.716010\pi\) | |||||||
\(788\) | −3.15605 | + | 2.29301i | −0.112430 | + | 0.0816849i | ||||
\(789\) | 9.38608 | − | 28.8874i | 0.334153 | − | 1.02842i | ||||
\(790\) | 2.18580 | − | 1.58808i | 0.0777674 | − | 0.0565013i | ||||
\(791\) | −10.9316 | + | 7.94229i | −0.388684 | + | 0.282395i | ||||
\(792\) | −1.18976 | + | 3.66171i | −0.0422763 | + | 0.130113i | ||||
\(793\) | 10.4442 | − | 7.58817i | 0.370885 | − | 0.269464i | ||||
\(794\) | 12.2299 | + | 8.88555i | 0.434023 | + | 0.315336i | ||||
\(795\) | −0.156995 | − | 0.483181i | −0.00556804 | − | 0.0171367i | ||||
\(796\) | 19.9327 | + | 14.4819i | 0.706495 | + | 0.513299i | ||||
\(797\) | −8.99329 | + | 27.6785i | −0.318559 | + | 0.980423i | 0.655706 | + | 0.755016i | \(0.272371\pi\) |
−0.974265 | + | 0.225407i | \(0.927629\pi\) | |||||||
\(798\) | 1.95906 | − | 6.02937i | 0.0693500 | − | 0.213437i | ||||
\(799\) | −7.57951 | − | 23.3273i | −0.268144 | − | 0.825261i | ||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −7.56426 | −0.267270 | ||||||||
\(802\) | 10.8827 | + | 33.4935i | 0.384281 | + | 1.18270i | ||||
\(803\) | 50.5996 | − | 36.7628i | 1.78562 | − | 1.29733i | ||||
\(804\) | −11.2542 | − | 8.17664i | −0.396904 | − | 0.288368i | ||||
\(805\) | 4.18332 | 0.147443 | ||||||||
\(806\) | 14.7016 | − | 1.77035i | 0.517841 | − | 0.0623580i | ||||
\(807\) | 8.34082 | 0.293611 | ||||||||
\(808\) | 8.29003 | + | 6.02306i | 0.291642 | + | 0.211890i | ||||
\(809\) | −1.61157 | + | 1.17087i | −0.0566598 | + | 0.0411658i | −0.615755 | − | 0.787938i | \(-0.711149\pi\) |
0.559095 | + | 0.829104i | \(0.311149\pi\) | |||||||
\(810\) | 0.309017 | + | 0.951057i | 0.0108578 | + | 0.0334167i | ||||
\(811\) | 34.0879 | 1.19699 | 0.598494 | − | 0.801127i | \(-0.295766\pi\) | ||||
0.598494 | + | 0.801127i | \(0.295766\pi\) | |||||||
\(812\) | −11.4831 | −0.402978 | ||||||||
\(813\) | 0.491953 | + | 1.51408i | 0.0172536 | + | 0.0531010i | ||||
\(814\) | 6.42298 | − | 19.7679i | 0.225125 | − | 0.692864i | ||||
\(815\) | 4.61898 | − | 14.2158i | 0.161796 | − | 0.497956i | ||||
\(816\) | 2.45650 | + | 1.78475i | 0.0859946 | + | 0.0624788i | ||||
\(817\) | 13.9270 | + | 42.8628i | 0.487243 | + | 1.49958i | ||||
\(818\) | 19.4681 | + | 14.1444i | 0.680688 | + | 0.494549i | ||||
\(819\) | 3.60813 | − | 2.62146i | 0.126078 | − | 0.0916011i | ||||
\(820\) | −3.38611 | + | 10.4214i | −0.118248 | + | 0.363930i | ||||
\(821\) | 43.1311 | − | 31.3366i | 1.50529 | − | 1.09365i | 0.537071 | − | 0.843537i | \(-0.319531\pi\) |
0.968216 | − | 0.250117i | \(-0.0804691\pi\) | |||||||
\(822\) | −9.13623 | + | 6.63786i | −0.318663 | + | 0.231522i | ||||
\(823\) | 0.915264 | − | 2.81689i | 0.0319041 | − | 0.0981907i | −0.933836 | − | 0.357700i | \(-0.883561\pi\) |
0.965741 | + | 0.259510i | \(0.0835609\pi\) | |||||||
\(824\) | 9.11764 | − | 6.62435i | 0.317628 | − | 0.230770i | ||||
\(825\) | −3.11483 | − | 2.26306i | −0.108445 | − | 0.0787896i | ||||
\(826\) | 7.31150 | + | 22.5025i | 0.254400 | + | 0.782962i | ||||
\(827\) | −25.4036 | − | 18.4568i | −0.883371 | − | 0.641807i | 0.0507701 | − | 0.998710i | \(-0.483832\pi\) |
−0.934141 | + | 0.356904i | \(0.883832\pi\) | |||||||
\(828\) | −0.770884 | + | 2.37254i | −0.0267901 | + | 0.0824513i | ||||
\(829\) | 0.198051 | − | 0.609539i | 0.00687860 | − | 0.0211702i | −0.947558 | − | 0.319583i | \(-0.896457\pi\) |
0.954437 | + | 0.298413i | \(0.0964572\pi\) | |||||||
\(830\) | −0.693033 | − | 2.13294i | −0.0240555 | − | 0.0740353i | ||||
\(831\) | 3.21253 | 0.111441 | ||||||||
\(832\) | 2.65956 | 0.0922036 | ||||||||
\(833\) | −3.92951 | − | 12.0938i | −0.136149 | − | 0.419025i | ||||
\(834\) | −14.7530 | + | 10.7186i | −0.510853 | + | 0.371156i | ||||
\(835\) | −1.98402 | − | 1.44148i | −0.0686599 | − | 0.0498844i | ||||
\(836\) | −14.5555 | −0.503413 | ||||||||
\(837\) | −2.34127 | − | 5.05158i | −0.0809262 | − | 0.174608i | ||||
\(838\) | −5.82008 | −0.201051 | ||||||||
\(839\) | −34.6574 | − | 25.1801i | −1.19651 | − | 0.869313i | −0.202570 | − | 0.979268i | \(-0.564929\pi\) |
−0.993937 | + | 0.109954i | \(0.964929\pi\) | |||||||
\(840\) | −1.35666 | + | 0.985674i | −0.0468094 | + | 0.0340090i | ||||
\(841\) | 5.52862 | + | 17.0153i | 0.190642 | + | 0.586736i | ||||
\(842\) | 31.3445 | 1.08020 | ||||||||
\(843\) | −7.51121 | −0.258700 | ||||||||
\(844\) | 6.11873 | + | 18.8315i | 0.210616 | + | 0.648208i | ||||
\(845\) | −1.83147 | + | 5.63668i | −0.0630044 | + | 0.193908i | ||||
\(846\) | −2.49622 | + | 7.68256i | −0.0858216 | + | 0.264132i | ||||
\(847\) | 5.18736 | + | 3.76884i | 0.178240 | + | 0.129499i | ||||
\(848\) | 0.156995 | + | 0.483181i | 0.00539123 | + | 0.0165925i | ||||
\(849\) | 5.08800 | + | 3.69665i | 0.174620 | + | 0.126869i | ||||
\(850\) | −2.45650 | + | 1.78475i | −0.0842572 | + | 0.0612164i | ||||
\(851\) | 4.16165 | − | 12.8082i | 0.142660 | − | 0.439061i | ||||
\(852\) | 6.23306 | − | 4.52858i | 0.213541 | − | 0.155147i | ||||
\(853\) | −19.6781 | + | 14.2969i | −0.673764 | + | 0.489518i | −0.871283 | − | 0.490781i | \(-0.836712\pi\) |
0.197519 | + | 0.980299i | \(0.436712\pi\) | |||||||
\(854\) | 2.51539 | − | 7.74158i | 0.0860750 | − | 0.264912i | ||||
\(855\) | −3.05850 | + | 2.22213i | −0.104598 | + | 0.0759953i | ||||
\(856\) | −2.12276 | − | 1.54228i | −0.0725545 | − | 0.0527140i | ||||
\(857\) | −15.3801 | − | 47.3350i | −0.525373 | − | 1.61693i | −0.763577 | − | 0.645716i | \(-0.776559\pi\) |
0.238205 | − | 0.971215i | \(-0.423441\pi\) | |||||||
\(858\) | −8.28408 | − | 6.01873i | −0.282814 | − | 0.205476i | ||||
\(859\) | 4.83321 | − | 14.8751i | 0.164907 | − | 0.507532i | −0.834122 | − | 0.551579i | \(-0.814025\pi\) |
0.999029 | + | 0.0440476i | \(0.0140253\pi\) | |||||||
\(860\) | 3.68388 | − | 11.3378i | 0.125619 | − | 0.386616i | ||||
\(861\) | −5.67827 | − | 17.4759i | −0.193515 | − | 0.595578i | ||||
\(862\) | −23.1666 | −0.789057 | ||||||||
\(863\) | 15.4301 | 0.525248 | 0.262624 | − | 0.964898i | \(-0.415412\pi\) | ||||
0.262624 | + | 0.964898i | \(0.415412\pi\) | |||||||
\(864\) | −0.309017 | − | 0.951057i | −0.0105130 | − | 0.0323556i | ||||
\(865\) | −0.00972012 | + | 0.00706208i | −0.000330494 | + | 0.000240118i | ||||
\(866\) | −1.48659 | − | 1.08007i | −0.0505162 | − | 0.0367022i | ||||
\(867\) | 7.78028 | 0.264232 | ||||||||
\(868\) | 6.84329 | − | 6.35171i | 0.232276 | − | 0.215591i | ||||
\(869\) | 10.4023 | 0.352875 | ||||||||
\(870\) | 5.53991 | + | 4.02498i | 0.187820 | + | 0.136459i | ||||
\(871\) | 29.9311 | − | 21.7462i | 1.01418 | − | 0.736843i | ||||
\(872\) | 3.35749 | + | 10.3333i | 0.113699 | + | 0.349930i | ||||
\(873\) | −13.8142 | −0.467541 | ||||||||
\(874\) | −9.43099 | −0.319008 | ||||||||
\(875\) | −0.518200 | − | 1.59485i | −0.0175183 | − | 0.0539159i | ||||
\(876\) | −5.01990 | + | 15.4497i | −0.169607 | + | 0.521996i | ||||
\(877\) | 2.43988 | − | 7.50919i | 0.0823890 | − | 0.253567i | −0.901374 | − | 0.433042i | \(-0.857440\pi\) |
0.983762 | + | 0.179475i | \(0.0574400\pi\) | |||||||
\(878\) | −1.55002 | − | 1.12616i | −0.0523107 | − | 0.0380059i | ||||
\(879\) | 8.12230 | + | 24.9979i | 0.273958 | + | 0.843157i | ||||
\(880\) | 3.11483 | + | 2.26306i | 0.105001 | + | 0.0762877i | ||||
\(881\) | 20.8035 | − | 15.1146i | 0.700888 | − | 0.509225i | −0.179334 | − | 0.983788i | \(-0.557394\pi\) |
0.880221 | + | 0.474564i | \(0.157394\pi\) | |||||||
\(882\) | −1.29414 | + | 3.98294i | −0.0435758 | + | 0.134113i | ||||
\(883\) | 25.6154 | − | 18.6107i | 0.862026 | − | 0.626299i | −0.0664093 | − | 0.997792i | \(-0.521154\pi\) |
0.928435 | + | 0.371494i | \(0.121154\pi\) | |||||||
\(884\) | −6.53320 | + | 4.74665i | −0.219735 | + | 0.159647i | ||||
\(885\) | 4.36005 | − | 13.4189i | 0.146562 | − | 0.451070i | ||||
\(886\) | 0.278535 | − | 0.202368i | 0.00935758 | − | 0.00679868i | ||||
\(887\) | 41.7064 | + | 30.3014i | 1.40036 | + | 1.01742i | 0.994637 | + | 0.103428i | \(0.0329810\pi\) |
0.405725 | + | 0.913995i | \(0.367019\pi\) | |||||||
\(888\) | 1.66824 | + | 5.13432i | 0.0559826 | + | 0.172297i | ||||
\(889\) | 27.2302 | + | 19.7839i | 0.913272 | + | 0.663531i | ||||
\(890\) | −2.33749 | + | 7.19404i | −0.0783527 | + | 0.241145i | ||||
\(891\) | −1.18976 | + | 3.66171i | −0.0398585 | + | 0.122672i | ||||
\(892\) | 5.72869 | + | 17.6311i | 0.191811 | + | 0.590332i | ||||
\(893\) | −30.5387 | −1.02194 | ||||||||
\(894\) | −18.1675 | −0.607613 | ||||||||
\(895\) | 4.36069 | + | 13.4208i | 0.145762 | + | 0.448609i | ||||
\(896\) | 1.35666 | − | 0.985674i | 0.0453230 | − | 0.0329291i | ||||
\(897\) | −5.36752 | − | 3.89973i | −0.179216 | − | 0.130208i | ||||
\(898\) | 27.8957 | 0.930891 | ||||||||
\(899\) | −33.3029 | − | 18.5617i | −1.11071 | − | 0.619068i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −1.24802 | − | 0.906737i | −0.0415774 | − | 0.0302078i | ||||
\(902\) | −34.1314 | + | 24.7979i | −1.13645 | + | 0.825679i | ||||
\(903\) | 6.17761 | + | 19.0127i | 0.205578 | + | 0.632704i | ||||
\(904\) | −8.05773 | −0.267996 | ||||||||
\(905\) | 14.9596 | 0.497273 | ||||||||
\(906\) | −1.95440 | − | 6.01504i | −0.0649307 | − | 0.199836i | ||||
\(907\) | 5.44586 | − | 16.7606i | 0.180827 | − | 0.556528i | −0.819025 | − | 0.573758i | \(-0.805485\pi\) |
0.999852 | + | 0.0172304i | \(0.00548487\pi\) | |||||||
\(908\) | −0.166904 | + | 0.513677i | −0.00553889 | + | 0.0170470i | ||||
\(909\) | 8.29003 | + | 6.02306i | 0.274963 | + | 0.199772i | ||||
\(910\) | −1.37818 | − | 4.24161i | −0.0456863 | − | 0.140608i | ||||
\(911\) | 29.9655 | + | 21.7712i | 0.992801 | + | 0.721312i | 0.960533 | − | 0.278167i | \(-0.0897269\pi\) |
0.0322684 | + | 0.999479i | \(0.489727\pi\) | |||||||
\(912\) | 3.05850 | − | 2.22213i | 0.101277 | − | 0.0735821i | ||||
\(913\) | 2.66828 | − | 8.21212i | 0.0883072 | − | 0.271781i | ||||
\(914\) | 24.6335 | − | 17.8973i | 0.814805 | − | 0.591991i | ||||
\(915\) | −3.92705 | + | 2.85317i | −0.129824 | + | 0.0943229i | ||||
\(916\) | 2.37858 | − | 7.32051i | 0.0785904 | − | 0.241876i | ||||
\(917\) | 5.66595 | − | 4.11655i | 0.187106 | − | 0.135941i | ||||
\(918\) | 2.45650 | + | 1.78475i | 0.0810765 | + | 0.0589055i | ||||
\(919\) | −17.3587 | − | 53.4246i | −0.572611 | − | 1.76232i | −0.644173 | − | 0.764880i | \(-0.722798\pi\) |
0.0715615 | − | 0.997436i | \(-0.477202\pi\) | |||||||
\(920\) | 2.01820 | + | 1.46631i | 0.0665381 | + | 0.0483427i | ||||
\(921\) | 3.64946 | − | 11.2319i | 0.120254 | − | 0.370103i | ||||
\(922\) | −2.13875 | + | 6.58240i | −0.0704360 | + | 0.216780i | ||||
\(923\) | 6.33191 | + | 19.4876i | 0.208417 | + | 0.641443i | ||||
\(924\) | −6.45642 | −0.212401 | ||||||||
\(925\) | −5.39855 | −0.177503 | ||||||||
\(926\) | 1.29590 | + | 3.98836i | 0.0425858 | + | 0.131066i | ||||
\(927\) | 9.11764 | − | 6.62435i | 0.299463 | − | 0.217572i | ||||
\(928\) | −5.53991 | − | 4.02498i | −0.181856 | − | 0.132126i | ||||
\(929\) | −4.75181 | −0.155902 | −0.0779508 | − | 0.996957i | \(-0.524838\pi\) | ||||
−0.0779508 | + | 0.996957i | \(0.524838\pi\) | |||||||
\(930\) | −5.52783 | + | 0.665657i | −0.181265 | + | 0.0218277i | ||||
\(931\) | −15.8324 | −0.518888 | ||||||||
\(932\) | −3.48101 | − | 2.52910i | −0.114024 | − | 0.0828435i | ||||
\(933\) | −4.70924 | + | 3.42146i | −0.154174 | + | 0.112014i | ||||
\(934\) | −6.42824 | − | 19.7841i | −0.210338 | − | 0.647355i | ||||
\(935\) | −11.6906 | −0.382323 | ||||||||
\(936\) | 2.65956 | 0.0869303 | ||||||||
\(937\) | −3.59463 | − | 11.0631i | −0.117432 | − | 0.361417i | 0.875015 | − | 0.484096i | \(-0.160851\pi\) |
−0.992446 | + | 0.122679i | \(0.960851\pi\) | |||||||
\(938\) | 7.20864 | − | 22.1859i | 0.235370 | − | 0.724395i | ||||
\(939\) | 3.37264 | − | 10.3799i | 0.110062 | − | 0.338736i | ||||
\(940\) | 6.53518 | + | 4.74808i | 0.213154 | + | 0.154865i | ||||
\(941\) | 17.4503 | + | 53.7066i | 0.568865 | + | 1.75079i | 0.656179 | + | 0.754605i | \(0.272172\pi\) |
−0.0873139 | + | 0.996181i | \(0.527828\pi\) | |||||||
\(942\) | 4.27222 | + | 3.10395i | 0.139197 | + | 0.101132i | ||||
\(943\) | −22.1148 | + | 16.0673i | −0.720157 | + | 0.523225i | ||||
\(944\) | −4.36005 | + | 13.4189i | −0.141908 | + | 0.436747i | ||||
\(945\) | −1.35666 | + | 0.985674i | −0.0441323 | + | 0.0320640i | ||||
\(946\) | 37.1328 | − | 26.9786i | 1.20729 | − | 0.877149i | ||||
\(947\) | −5.66830 | + | 17.4452i | −0.184195 | + | 0.566894i | −0.999934 | − | 0.0115269i | \(-0.996331\pi\) |
0.815739 | + | 0.578421i | \(0.196331\pi\) | |||||||
\(948\) | −2.18580 | + | 1.58808i | −0.0709916 | + | 0.0515784i | ||||
\(949\) | −34.9526 | − | 25.3946i | −1.13461 | − | 0.824342i | ||||
\(950\) | 1.16824 | + | 3.59548i | 0.0379028 | + | 0.116653i | ||||
\(951\) | 1.07596 | + | 0.781732i | 0.0348904 | + | 0.0253494i | ||||
\(952\) | −1.57346 | + | 4.84261i | −0.0509962 | + | 0.156950i | ||||
\(953\) | 7.77814 | − | 23.9387i | 0.251959 | − | 0.775449i | −0.742455 | − | 0.669896i | \(-0.766339\pi\) |
0.994414 | − | 0.105553i | \(-0.0336613\pi\) | |||||||
\(954\) | 0.156995 | + | 0.483181i | 0.00508290 | + | 0.0156436i | ||||
\(955\) | 4.48476 | 0.145123 | ||||||||
\(956\) | −19.3092 | −0.624506 | ||||||||
\(957\) | 8.14712 | + | 25.0743i | 0.263359 | + | 0.810536i | ||||
\(958\) | −0.208445 | + | 0.151444i | −0.00673455 | + | 0.00489293i | ||||
\(959\) | −15.3208 | − | 11.1312i | −0.494735 | − | 0.359446i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 30.1138 | − | 7.35928i | 0.971413 | − | 0.237396i | ||||
\(962\) | −14.3577 | −0.462912 | ||||||||
\(963\) | −2.12276 | − | 1.54228i | −0.0684051 | − | 0.0496992i | ||||
\(964\) | −11.1541 | + | 8.10393i | −0.359249 | + | 0.261010i | ||||
\(965\) | 5.55057 | + | 17.0829i | 0.178679 | + | 0.549918i | ||||
\(966\) | −4.18332 | −0.134596 | ||||||||
\(967\) | −55.8047 | −1.79456 | −0.897280 | − | 0.441462i | \(-0.854460\pi\) | ||||
−0.897280 | + | 0.441462i | \(0.854460\pi\) | |||||||
\(968\) | 1.18156 | + | 3.63648i | 0.0379769 | + | 0.116881i | ||||
\(969\) | −3.54725 | + | 10.9173i | −0.113954 | + | 0.350715i | ||||
\(970\) | −4.26883 | + | 13.1381i | −0.137064 | + | 0.421840i | ||||
\(971\) | −32.0844 | − | 23.3107i | −1.02964 | − | 0.748075i | −0.0614008 | − | 0.998113i | \(-0.519557\pi\) |
−0.968236 | + | 0.250038i | \(0.919557\pi\) | |||||||
\(972\) | −0.309017 | − | 0.951057i | −0.00991172 | − | 0.0305052i | ||||
\(973\) | −24.7397 | − | 17.9744i | −0.793117 | − | 0.576233i | ||||
\(974\) | 0.243998 | − | 0.177275i | 0.00781821 | − | 0.00568026i | ||||
\(975\) | −0.821848 | + | 2.52939i | −0.0263202 | + | 0.0810053i | ||||
\(976\) | 3.92705 | − | 2.85317i | 0.125702 | − | 0.0913277i | ||||
\(977\) | 25.5526 | − | 18.5650i | 0.817500 | − | 0.593948i | −0.0984954 | − | 0.995138i | \(-0.531403\pi\) |
0.915995 | + | 0.401189i | \(0.131403\pi\) | |||||||
\(978\) | −4.61898 | + | 14.2158i | −0.147699 | + | 0.454570i | ||||
\(979\) | −23.5614 | + | 17.1184i | −0.753026 | + | 0.547105i | ||||
\(980\) | 3.38809 | + | 2.46159i | 0.108229 | + | 0.0786327i | ||||
\(981\) | 3.35749 | + | 10.3333i | 0.107196 | + | 0.329917i | ||||
\(982\) | 15.9354 | + | 11.5778i | 0.508520 | + | 0.369462i | ||||
\(983\) | −14.4709 | + | 44.5370i | −0.461551 | + | 1.42051i | 0.401718 | + | 0.915764i | \(0.368413\pi\) |
−0.863269 | + | 0.504745i | \(0.831587\pi\) | |||||||
\(984\) | 3.38611 | − | 10.4214i | 0.107945 | − | 0.332221i | ||||
\(985\) | 1.20550 | + | 3.71016i | 0.0384106 | + | 0.118216i | ||||
\(986\) | 20.7923 | 0.662163 | ||||||||
\(987\) | −13.5461 | −0.431177 | ||||||||
\(988\) | 3.10701 | + | 9.56239i | 0.0988471 | + | 0.304220i | ||||
\(989\) | 24.0595 | − | 17.4803i | 0.765049 | − | 0.555840i | ||||
\(990\) | 3.11483 | + | 2.26306i | 0.0989959 | + | 0.0719247i | ||||
\(991\) | 17.6127 | 0.559487 | 0.279743 | − | 0.960075i | \(-0.409751\pi\) | ||||
0.279743 | + | 0.960075i | \(0.409751\pi\) | |||||||
\(992\) | 5.52783 | − | 0.665657i | 0.175509 | − | 0.0211346i | ||||
\(993\) | 27.6185 | 0.876445 | ||||||||
\(994\) | 10.4524 | + | 7.59411i | 0.331530 | + | 0.240870i | ||||
\(995\) | 19.9327 | − | 14.4819i | 0.631909 | − | 0.459109i | ||||
\(996\) | 0.693033 | + | 2.13294i | 0.0219596 | + | 0.0675847i | ||||
\(997\) | 36.2796 | 1.14899 | 0.574494 | − | 0.818509i | \(-0.305199\pi\) | ||||
0.574494 | + | 0.818509i | \(0.305199\pi\) | |||||||
\(998\) | −11.9387 | −0.377914 | ||||||||
\(999\) | 1.66824 | + | 5.13432i | 0.0527809 | + | 0.162443i |
(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 | 930.2.n.a.901.1 | yes | 8 | |
31.16 | even | 5 | inner | 930.2.n.a.481.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.n.a.481.1 | ✓ | 8 | 31.16 | even | 5 | inner | |
930.2.n.a.901.1 | yes | 8 | 1.1 | even | 1 | trivial |