Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [195,2,Mod(16,195)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(195, base_ring=CyclotomicField(6))
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("195.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 195 = 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 195.i (of order \(3\), degree \(2\), 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: | \(1.55708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 195.16 |
Dual form | 195.2.i.c.61.1 |
$q$-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 \(\left(\mathbb{Z}/195\mathbb{Z}\right)^\times\).
\(n\) | \(106\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | − | 0.633975i | −0.258819 | − | 0.448288i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.732051 | − | 1.26795i | 0.366025 | − | 0.633975i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.366025 | + | 0.633975i | −0.149429 | + | 0.258819i | ||||
\(7\) | 0.866025 | − | 1.50000i | 0.327327 | − | 0.566947i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) |
0.981981 | + | 0.188982i | \(0.0605189\pi\) | |||||||
\(8\) | −2.53590 | −0.896575 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.366025 | − | 0.633975i | −0.115747 | − | 0.200480i | ||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | −1.46410 | −0.422650 | ||||||||
\(13\) | −1.59808 | − | 3.23205i | −0.443227 | − | 0.896410i | ||||
\(14\) | −1.26795 | −0.338874 | ||||||||
\(15\) | −0.500000 | − | 0.866025i | −0.129099 | − | 0.223607i | ||||
\(16\) | −0.535898 | − | 0.928203i | −0.133975 | − | 0.232051i | ||||
\(17\) | −0.366025 | + | 0.633975i | −0.0887742 | + | 0.153761i | −0.906993 | − | 0.421145i | \(-0.861628\pi\) |
0.818219 | + | 0.574907i | \(0.194962\pi\) | |||||||
\(18\) | 0.732051 | 0.172546 | ||||||||
\(19\) | 0.267949 | − | 0.464102i | 0.0614718 | − | 0.106472i | −0.833652 | − | 0.552291i | \(-0.813754\pi\) |
0.895123 | + | 0.445818i | \(0.147087\pi\) | |||||||
\(20\) | 0.732051 | − | 1.26795i | 0.163692 | − | 0.283522i | ||||
\(21\) | −1.73205 | −0.377964 | ||||||||
\(22\) | 0.732051 | − | 1.26795i | 0.156074 | − | 0.270328i | ||||
\(23\) | −1.00000 | − | 1.73205i | −0.208514 | − | 0.361158i | 0.742732 | − | 0.669588i | \(-0.233529\pi\) |
−0.951247 | + | 0.308431i | \(0.900196\pi\) | |||||||
\(24\) | 1.26795 | + | 2.19615i | 0.258819 | + | 0.448288i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.46410 | + | 2.19615i | −0.287134 | + | 0.430701i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.26795 | − | 2.19615i | −0.239620 | − | 0.415034i | ||||
\(29\) | 1.63397 | + | 2.83013i | 0.303421 | + | 0.525541i | 0.976909 | − | 0.213658i | \(-0.0685377\pi\) |
−0.673487 | + | 0.739199i | \(0.735204\pi\) | |||||||
\(30\) | −0.366025 | + | 0.633975i | −0.0668268 | + | 0.115747i | ||||
\(31\) | 4.46410 | 0.801776 | 0.400888 | − | 0.916127i | \(-0.368702\pi\) | ||||
0.400888 | + | 0.916127i | \(0.368702\pi\) | |||||||
\(32\) | −2.92820 | + | 5.07180i | −0.517638 | + | 0.896575i | ||||
\(33\) | 1.00000 | − | 1.73205i | 0.174078 | − | 0.301511i | ||||
\(34\) | 0.535898 | 0.0919058 | ||||||||
\(35\) | 0.866025 | − | 1.50000i | 0.146385 | − | 0.253546i | ||||
\(36\) | 0.732051 | + | 1.26795i | 0.122008 | + | 0.211325i | ||||
\(37\) | 5.19615 | + | 9.00000i | 0.854242 | + | 1.47959i | 0.877346 | + | 0.479858i | \(0.159312\pi\) |
−0.0231041 | + | 0.999733i | \(0.507355\pi\) | |||||||
\(38\) | −0.392305 | −0.0636402 | ||||||||
\(39\) | −2.00000 | + | 3.00000i | −0.320256 | + | 0.480384i | ||||
\(40\) | −2.53590 | −0.400961 | ||||||||
\(41\) | 5.36603 | + | 9.29423i | 0.838032 | + | 1.45151i | 0.891537 | + | 0.452947i | \(0.149627\pi\) |
−0.0535050 | + | 0.998568i | \(0.517039\pi\) | |||||||
\(42\) | 0.633975 | + | 1.09808i | 0.0978244 | + | 0.169437i | ||||
\(43\) | 4.59808 | − | 7.96410i | 0.701200 | − | 1.21451i | −0.266845 | − | 0.963739i | \(-0.585981\pi\) |
0.968045 | − | 0.250775i | \(-0.0806854\pi\) | |||||||
\(44\) | 2.92820 | 0.441443 | ||||||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | −0.732051 | + | 1.26795i | −0.107935 | + | 0.186949i | ||||
\(47\) | 0.196152 | 0.0286118 | 0.0143059 | − | 0.999898i | \(-0.495446\pi\) | ||||
0.0143059 | + | 0.999898i | \(0.495446\pi\) | |||||||
\(48\) | −0.535898 | + | 0.928203i | −0.0773503 | + | 0.133975i | ||||
\(49\) | 2.00000 | + | 3.46410i | 0.285714 | + | 0.494872i | ||||
\(50\) | −0.366025 | − | 0.633975i | −0.0517638 | − | 0.0896575i | ||||
\(51\) | 0.732051 | 0.102508 | ||||||||
\(52\) | −5.26795 | − | 0.339746i | −0.730533 | − | 0.0471143i | ||||
\(53\) | −9.46410 | −1.29999 | −0.649997 | − | 0.759937i | \(-0.725230\pi\) | ||||
−0.649997 | + | 0.759937i | \(0.725230\pi\) | |||||||
\(54\) | −0.366025 | − | 0.633975i | −0.0498097 | − | 0.0862730i | ||||
\(55\) | 1.00000 | + | 1.73205i | 0.134840 | + | 0.233550i | ||||
\(56\) | −2.19615 | + | 3.80385i | −0.293473 | + | 0.508311i | ||||
\(57\) | −0.535898 | −0.0709815 | ||||||||
\(58\) | 1.19615 | − | 2.07180i | 0.157063 | − | 0.272040i | ||||
\(59\) | 5.83013 | − | 10.0981i | 0.759018 | − | 1.31466i | −0.184334 | − | 0.982864i | \(-0.559013\pi\) |
0.943352 | − | 0.331794i | \(-0.107654\pi\) | |||||||
\(60\) | −1.46410 | −0.189015 | ||||||||
\(61\) | −2.69615 | + | 4.66987i | −0.345207 | + | 0.597916i | −0.985391 | − | 0.170305i | \(-0.945525\pi\) |
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | −1.63397 | − | 2.83013i | −0.207515 | − | 0.359426i | ||||
\(63\) | 0.866025 | + | 1.50000i | 0.109109 | + | 0.188982i | ||||
\(64\) | 2.14359 | 0.267949 | ||||||||
\(65\) | −1.59808 | − | 3.23205i | −0.198217 | − | 0.400887i | ||||
\(66\) | −1.46410 | −0.180218 | ||||||||
\(67\) | 4.59808 | + | 7.96410i | 0.561744 | + | 0.972970i | 0.997344 | + | 0.0728295i | \(0.0232029\pi\) |
−0.435600 | + | 0.900140i | \(0.643464\pi\) | |||||||
\(68\) | 0.535898 | + | 0.928203i | 0.0649872 | + | 0.112561i | ||||
\(69\) | −1.00000 | + | 1.73205i | −0.120386 | + | 0.208514i | ||||
\(70\) | −1.26795 | −0.151549 | ||||||||
\(71\) | 2.36603 | − | 4.09808i | 0.280796 | − | 0.486352i | −0.690785 | − | 0.723060i | \(-0.742735\pi\) |
0.971581 | + | 0.236708i | \(0.0760684\pi\) | |||||||
\(72\) | 1.26795 | − | 2.19615i | 0.149429 | − | 0.258819i | ||||
\(73\) | 1.73205 | 0.202721 | 0.101361 | − | 0.994850i | \(-0.467680\pi\) | ||||
0.101361 | + | 0.994850i | \(0.467680\pi\) | |||||||
\(74\) | 3.80385 | − | 6.58846i | 0.442188 | − | 0.765893i | ||||
\(75\) | −0.500000 | − | 0.866025i | −0.0577350 | − | 0.100000i | ||||
\(76\) | −0.392305 | − | 0.679492i | −0.0450005 | − | 0.0779431i | ||||
\(77\) | 3.46410 | 0.394771 | ||||||||
\(78\) | 2.63397 | + | 0.169873i | 0.298239 | + | 0.0192343i | ||||
\(79\) | −11.0000 | −1.23760 | −0.618798 | − | 0.785550i | \(-0.712380\pi\) | ||||
−0.618798 | + | 0.785550i | \(0.712380\pi\) | |||||||
\(80\) | −0.535898 | − | 0.928203i | −0.0599153 | − | 0.103776i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.92820 | − | 6.80385i | 0.433797 | − | 0.751359i | ||||
\(83\) | 2.92820 | 0.321412 | 0.160706 | − | 0.987002i | \(-0.448623\pi\) | ||||
0.160706 | + | 0.987002i | \(0.448623\pi\) | |||||||
\(84\) | −1.26795 | + | 2.19615i | −0.138345 | + | 0.239620i | ||||
\(85\) | −0.366025 | + | 0.633975i | −0.0397010 | + | 0.0687642i | ||||
\(86\) | −6.73205 | −0.725936 | ||||||||
\(87\) | 1.63397 | − | 2.83013i | 0.175180 | − | 0.303421i | ||||
\(88\) | −2.53590 | − | 4.39230i | −0.270328 | − | 0.468221i | ||||
\(89\) | −2.63397 | − | 4.56218i | −0.279201 | − | 0.483590i | 0.691986 | − | 0.721911i | \(-0.256736\pi\) |
−0.971186 | + | 0.238321i | \(0.923403\pi\) | |||||||
\(90\) | 0.732051 | 0.0771649 | ||||||||
\(91\) | −6.23205 | − | 0.401924i | −0.653296 | − | 0.0421331i | ||||
\(92\) | −2.92820 | −0.305286 | ||||||||
\(93\) | −2.23205 | − | 3.86603i | −0.231453 | − | 0.400888i | ||||
\(94\) | −0.0717968 | − | 0.124356i | −0.00740527 | − | 0.0128263i | ||||
\(95\) | 0.267949 | − | 0.464102i | 0.0274910 | − | 0.0476158i | ||||
\(96\) | 5.85641 | 0.597717 | ||||||||
\(97\) | −2.59808 | + | 4.50000i | −0.263795 | + | 0.456906i | −0.967247 | − | 0.253837i | \(-0.918307\pi\) |
0.703452 | + | 0.710742i | \(0.251641\pi\) | |||||||
\(98\) | 1.46410 | − | 2.53590i | 0.147897 | − | 0.256164i | ||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0.732051 | − | 1.26795i | 0.0732051 | − | 0.126795i | ||||
\(101\) | −5.19615 | − | 9.00000i | −0.517036 | − | 0.895533i | −0.999804 | − | 0.0197851i | \(-0.993702\pi\) |
0.482768 | − | 0.875748i | \(-0.339632\pi\) | |||||||
\(102\) | −0.267949 | − | 0.464102i | −0.0265309 | − | 0.0459529i | ||||
\(103\) | 5.73205 | 0.564796 | 0.282398 | − | 0.959297i | \(-0.408870\pi\) | ||||
0.282398 | + | 0.959297i | \(0.408870\pi\) | |||||||
\(104\) | 4.05256 | + | 8.19615i | 0.397386 | + | 0.803699i | ||||
\(105\) | −1.73205 | −0.169031 | ||||||||
\(106\) | 3.46410 | + | 6.00000i | 0.336463 | + | 0.582772i | ||||
\(107\) | −4.09808 | − | 7.09808i | −0.396176 | − | 0.686197i | 0.597075 | − | 0.802186i | \(-0.296330\pi\) |
−0.993251 | + | 0.115989i | \(0.962996\pi\) | |||||||
\(108\) | 0.732051 | − | 1.26795i | 0.0704416 | − | 0.122008i | ||||
\(109\) | −15.3923 | −1.47432 | −0.737158 | − | 0.675721i | \(-0.763833\pi\) | ||||
−0.737158 | + | 0.675721i | \(0.763833\pi\) | |||||||
\(110\) | 0.732051 | − | 1.26795i | 0.0697983 | − | 0.120894i | ||||
\(111\) | 5.19615 | − | 9.00000i | 0.493197 | − | 0.854242i | ||||
\(112\) | −1.85641 | −0.175414 | ||||||||
\(113\) | −9.19615 | + | 15.9282i | −0.865101 | + | 1.49840i | 0.00184536 | + | 0.999998i | \(0.499413\pi\) |
−0.866947 | + | 0.498401i | \(0.833921\pi\) | |||||||
\(114\) | 0.196152 | + | 0.339746i | 0.0183714 | + | 0.0318201i | ||||
\(115\) | −1.00000 | − | 1.73205i | −0.0932505 | − | 0.161515i | ||||
\(116\) | 4.78461 | 0.444240 | ||||||||
\(117\) | 3.59808 | + | 0.232051i | 0.332642 | + | 0.0214531i | ||||
\(118\) | −8.53590 | −0.785793 | ||||||||
\(119\) | 0.633975 | + | 1.09808i | 0.0581164 | + | 0.100660i | ||||
\(120\) | 1.26795 | + | 2.19615i | 0.115747 | + | 0.200480i | ||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 3.94744 | 0.357385 | ||||||||
\(123\) | 5.36603 | − | 9.29423i | 0.483838 | − | 0.838032i | ||||
\(124\) | 3.26795 | − | 5.66025i | 0.293471 | − | 0.508306i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.633975 | − | 1.09808i | 0.0564789 | − | 0.0978244i | ||||
\(127\) | 0.330127 | + | 0.571797i | 0.0292940 | + | 0.0507388i | 0.880301 | − | 0.474416i | \(-0.157341\pi\) |
−0.851007 | + | 0.525155i | \(0.824007\pi\) | |||||||
\(128\) | 5.07180 | + | 8.78461i | 0.448288 | + | 0.776457i | ||||
\(129\) | −9.19615 | −0.809676 | ||||||||
\(130\) | −1.46410 | + | 2.19615i | −0.128410 | + | 0.192615i | ||||
\(131\) | −2.19615 | −0.191879 | −0.0959394 | − | 0.995387i | \(-0.530585\pi\) | ||||
−0.0959394 | + | 0.995387i | \(0.530585\pi\) | |||||||
\(132\) | −1.46410 | − | 2.53590i | −0.127434 | − | 0.220722i | ||||
\(133\) | −0.464102 | − | 0.803848i | −0.0402427 | − | 0.0697024i | ||||
\(134\) | 3.36603 | − | 5.83013i | 0.290780 | − | 0.503646i | ||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0.928203 | − | 1.60770i | 0.0795928 | − | 0.137859i | ||||
\(137\) | 5.83013 | − | 10.0981i | 0.498101 | − | 0.862737i | −0.501896 | − | 0.864928i | \(-0.667364\pi\) |
0.999998 | + | 0.00219097i | \(0.000697407\pi\) | |||||||
\(138\) | 1.46410 | 0.124633 | ||||||||
\(139\) | −9.96410 | + | 17.2583i | −0.845144 | + | 1.46383i | 0.0403520 | + | 0.999186i | \(0.487152\pi\) |
−0.885496 | + | 0.464647i | \(0.846181\pi\) | |||||||
\(140\) | −1.26795 | − | 2.19615i | −0.107161 | − | 0.185609i | ||||
\(141\) | −0.0980762 | − | 0.169873i | −0.00825951 | − | 0.0143059i | ||||
\(142\) | −3.46410 | −0.290701 | ||||||||
\(143\) | 4.00000 | − | 6.00000i | 0.334497 | − | 0.501745i | ||||
\(144\) | 1.07180 | 0.0893164 | ||||||||
\(145\) | 1.63397 | + | 2.83013i | 0.135694 | + | 0.235029i | ||||
\(146\) | −0.633975 | − | 1.09808i | −0.0524681 | − | 0.0908774i | ||||
\(147\) | 2.00000 | − | 3.46410i | 0.164957 | − | 0.285714i | ||||
\(148\) | 15.2154 | 1.25070 | ||||||||
\(149\) | 2.92820 | − | 5.07180i | 0.239888 | − | 0.415498i | −0.720794 | − | 0.693149i | \(-0.756223\pi\) |
0.960682 | + | 0.277651i | \(0.0895560\pi\) | |||||||
\(150\) | −0.366025 | + | 0.633975i | −0.0298858 | + | 0.0517638i | ||||
\(151\) | −0.928203 | −0.0755361 | −0.0377681 | − | 0.999287i | \(-0.512025\pi\) | ||||
−0.0377681 | + | 0.999287i | \(0.512025\pi\) | |||||||
\(152\) | −0.679492 | + | 1.17691i | −0.0551141 | + | 0.0954604i | ||||
\(153\) | −0.366025 | − | 0.633975i | −0.0295914 | − | 0.0512538i | ||||
\(154\) | −1.26795 | − | 2.19615i | −0.102174 | − | 0.176971i | ||||
\(155\) | 4.46410 | 0.358565 | ||||||||
\(156\) | 2.33975 | + | 4.73205i | 0.187330 | + | 0.378867i | ||||
\(157\) | −3.73205 | −0.297850 | −0.148925 | − | 0.988848i | \(-0.547581\pi\) | ||||
−0.148925 | + | 0.988848i | \(0.547581\pi\) | |||||||
\(158\) | 4.02628 | + | 6.97372i | 0.320314 | + | 0.554799i | ||||
\(159\) | 4.73205 | + | 8.19615i | 0.375276 | + | 0.649997i | ||||
\(160\) | −2.92820 | + | 5.07180i | −0.231495 | + | 0.400961i | ||||
\(161\) | −3.46410 | −0.273009 | ||||||||
\(162\) | −0.366025 | + | 0.633975i | −0.0287577 | + | 0.0498097i | ||||
\(163\) | −10.5981 | + | 18.3564i | −0.830105 | + | 1.43778i | 0.0678487 | + | 0.997696i | \(0.478386\pi\) |
−0.897954 | + | 0.440089i | \(0.854947\pi\) | |||||||
\(164\) | 15.7128 | 1.22696 | ||||||||
\(165\) | 1.00000 | − | 1.73205i | 0.0778499 | − | 0.134840i | ||||
\(166\) | −1.07180 | − | 1.85641i | −0.0831876 | − | 0.144085i | ||||
\(167\) | 10.9282 | + | 18.9282i | 0.845650 | + | 1.46471i | 0.885056 | + | 0.465485i | \(0.154120\pi\) |
−0.0394060 | + | 0.999223i | \(0.512547\pi\) | |||||||
\(168\) | 4.39230 | 0.338874 | ||||||||
\(169\) | −7.89230 | + | 10.3301i | −0.607100 | + | 0.794625i | ||||
\(170\) | 0.535898 | 0.0411015 | ||||||||
\(171\) | 0.267949 | + | 0.464102i | 0.0204906 | + | 0.0354907i | ||||
\(172\) | −6.73205 | − | 11.6603i | −0.513314 | − | 0.889086i | ||||
\(173\) | −6.09808 | + | 10.5622i | −0.463628 | + | 0.803028i | −0.999138 | − | 0.0415012i | \(-0.986786\pi\) |
0.535510 | + | 0.844529i | \(0.320119\pi\) | |||||||
\(174\) | −2.39230 | −0.181360 | ||||||||
\(175\) | 0.866025 | − | 1.50000i | 0.0654654 | − | 0.113389i | ||||
\(176\) | 1.07180 | − | 1.85641i | 0.0807897 | − | 0.139932i | ||||
\(177\) | −11.6603 | −0.876438 | ||||||||
\(178\) | −1.92820 | + | 3.33975i | −0.144525 | + | 0.250325i | ||||
\(179\) | −8.83013 | − | 15.2942i | −0.659995 | − | 1.14314i | −0.980616 | − | 0.195937i | \(-0.937225\pi\) |
0.320622 | − | 0.947207i | \(-0.396108\pi\) | |||||||
\(180\) | 0.732051 | + | 1.26795i | 0.0545638 | + | 0.0945074i | ||||
\(181\) | 8.39230 | 0.623795 | 0.311898 | − | 0.950116i | \(-0.399035\pi\) | ||||
0.311898 | + | 0.950116i | \(0.399035\pi\) | |||||||
\(182\) | 2.02628 | + | 4.09808i | 0.150198 | + | 0.303770i | ||||
\(183\) | 5.39230 | 0.398611 | ||||||||
\(184\) | 2.53590 | + | 4.39230i | 0.186949 | + | 0.323805i | ||||
\(185\) | 5.19615 | + | 9.00000i | 0.382029 | + | 0.661693i | ||||
\(186\) | −1.63397 | + | 2.83013i | −0.119809 | + | 0.207515i | ||||
\(187\) | −1.46410 | −0.107066 | ||||||||
\(188\) | 0.143594 | − | 0.248711i | 0.0104726 | − | 0.0181391i | ||||
\(189\) | 0.866025 | − | 1.50000i | 0.0629941 | − | 0.109109i | ||||
\(190\) | −0.392305 | −0.0284608 | ||||||||
\(191\) | −11.2942 | + | 19.5622i | −0.817222 | + | 1.41547i | 0.0904999 | + | 0.995896i | \(0.471154\pi\) |
−0.907722 | + | 0.419573i | \(0.862180\pi\) | |||||||
\(192\) | −1.07180 | − | 1.85641i | −0.0773503 | − | 0.133975i | ||||
\(193\) | 9.59808 | + | 16.6244i | 0.690885 | + | 1.19665i | 0.971548 | + | 0.236841i | \(0.0761121\pi\) |
−0.280664 | + | 0.959806i | \(0.590555\pi\) | |||||||
\(194\) | 3.80385 | 0.273100 | ||||||||
\(195\) | −2.00000 | + | 3.00000i | −0.143223 | + | 0.214834i | ||||
\(196\) | 5.85641 | 0.418315 | ||||||||
\(197\) | −8.19615 | − | 14.1962i | −0.583952 | − | 1.01143i | −0.995005 | − | 0.0998228i | \(-0.968172\pi\) |
0.411054 | − | 0.911611i | \(-0.365161\pi\) | |||||||
\(198\) | 0.732051 | + | 1.26795i | 0.0520246 | + | 0.0901092i | ||||
\(199\) | 12.4282 | − | 21.5263i | 0.881012 | − | 1.52596i | 0.0307946 | − | 0.999526i | \(-0.490196\pi\) |
0.850217 | − | 0.526432i | \(-0.176470\pi\) | |||||||
\(200\) | −2.53590 | −0.179315 | ||||||||
\(201\) | 4.59808 | − | 7.96410i | 0.324323 | − | 0.561744i | ||||
\(202\) | −3.80385 | + | 6.58846i | −0.267638 | + | 0.463562i | ||||
\(203\) | 5.66025 | 0.397272 | ||||||||
\(204\) | 0.535898 | − | 0.928203i | 0.0375204 | − | 0.0649872i | ||||
\(205\) | 5.36603 | + | 9.29423i | 0.374779 | + | 0.649137i | ||||
\(206\) | −2.09808 | − | 3.63397i | −0.146180 | − | 0.253191i | ||||
\(207\) | 2.00000 | 0.139010 | ||||||||
\(208\) | −2.14359 | + | 3.21539i | −0.148631 | + | 0.222947i | ||||
\(209\) | 1.07180 | 0.0741377 | ||||||||
\(210\) | 0.633975 | + | 1.09808i | 0.0437484 | + | 0.0757745i | ||||
\(211\) | −11.1603 | − | 19.3301i | −0.768304 | − | 1.33074i | −0.938482 | − | 0.345328i | \(-0.887768\pi\) |
0.170179 | − | 0.985413i | \(-0.445566\pi\) | |||||||
\(212\) | −6.92820 | + | 12.0000i | −0.475831 | + | 0.824163i | ||||
\(213\) | −4.73205 | −0.324235 | ||||||||
\(214\) | −3.00000 | + | 5.19615i | −0.205076 | + | 0.355202i | ||||
\(215\) | 4.59808 | − | 7.96410i | 0.313586 | − | 0.543147i | ||||
\(216\) | −2.53590 | −0.172546 | ||||||||
\(217\) | 3.86603 | − | 6.69615i | 0.262443 | − | 0.454564i | ||||
\(218\) | 5.63397 | + | 9.75833i | 0.381581 | + | 0.660918i | ||||
\(219\) | −0.866025 | − | 1.50000i | −0.0585206 | − | 0.101361i | ||||
\(220\) | 2.92820 | 0.197419 | ||||||||
\(221\) | 2.63397 | + | 0.169873i | 0.177180 | + | 0.0114269i | ||||
\(222\) | −7.60770 | −0.510595 | ||||||||
\(223\) | −0.928203 | − | 1.60770i | −0.0621571 | − | 0.107659i | 0.833272 | − | 0.552863i | \(-0.186465\pi\) |
−0.895429 | + | 0.445204i | \(0.853131\pi\) | |||||||
\(224\) | 5.07180 | + | 8.78461i | 0.338874 | + | 0.586946i | ||||
\(225\) | −0.500000 | + | 0.866025i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | 13.4641 | 0.895619 | ||||||||
\(227\) | 2.36603 | − | 4.09808i | 0.157039 | − | 0.271999i | −0.776761 | − | 0.629796i | \(-0.783139\pi\) |
0.933799 | + | 0.357797i | \(0.116472\pi\) | |||||||
\(228\) | −0.392305 | + | 0.679492i | −0.0259810 | + | 0.0450005i | ||||
\(229\) | 12.7846 | 0.844831 | 0.422415 | − | 0.906402i | \(-0.361182\pi\) | ||||
0.422415 | + | 0.906402i | \(0.361182\pi\) | |||||||
\(230\) | −0.732051 | + | 1.26795i | −0.0482700 | + | 0.0836061i | ||||
\(231\) | −1.73205 | − | 3.00000i | −0.113961 | − | 0.197386i | ||||
\(232\) | −4.14359 | − | 7.17691i | −0.272040 | − | 0.471188i | ||||
\(233\) | −28.2487 | −1.85063 | −0.925317 | − | 0.379194i | \(-0.876201\pi\) | ||||
−0.925317 | + | 0.379194i | \(0.876201\pi\) | |||||||
\(234\) | −1.16987 | − | 2.36603i | −0.0764770 | − | 0.154672i | ||||
\(235\) | 0.196152 | 0.0127956 | ||||||||
\(236\) | −8.53590 | − | 14.7846i | −0.555640 | − | 0.962396i | ||||
\(237\) | 5.50000 | + | 9.52628i | 0.357263 | + | 0.618798i | ||||
\(238\) | 0.464102 | − | 0.803848i | 0.0300832 | − | 0.0521057i | ||||
\(239\) | −13.8564 | −0.896296 | −0.448148 | − | 0.893959i | \(-0.647916\pi\) | ||||
−0.448148 | + | 0.893959i | \(0.647916\pi\) | |||||||
\(240\) | −0.535898 | + | 0.928203i | −0.0345921 | + | 0.0599153i | ||||
\(241\) | −2.00000 | + | 3.46410i | −0.128831 | + | 0.223142i | −0.923224 | − | 0.384262i | \(-0.874456\pi\) |
0.794393 | + | 0.607404i | \(0.207789\pi\) | |||||||
\(242\) | −5.12436 | −0.329406 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 3.94744 | + | 6.83717i | 0.252709 | + | 0.437705i | ||||
\(245\) | 2.00000 | + | 3.46410i | 0.127775 | + | 0.221313i | ||||
\(246\) | −7.85641 | −0.500906 | ||||||||
\(247\) | −1.92820 | − | 0.124356i | −0.122689 | − | 0.00791256i | ||||
\(248\) | −11.3205 | −0.718853 | ||||||||
\(249\) | −1.46410 | − | 2.53590i | −0.0927837 | − | 0.160706i | ||||
\(250\) | −0.366025 | − | 0.633975i | −0.0231495 | − | 0.0400961i | ||||
\(251\) | 3.26795 | − | 5.66025i | 0.206271 | − | 0.357272i | −0.744266 | − | 0.667883i | \(-0.767200\pi\) |
0.950537 | + | 0.310611i | \(0.100534\pi\) | |||||||
\(252\) | 2.53590 | 0.159747 | ||||||||
\(253\) | 2.00000 | − | 3.46410i | 0.125739 | − | 0.217786i | ||||
\(254\) | 0.241670 | − | 0.418584i | 0.0151637 | − | 0.0262643i | ||||
\(255\) | 0.732051 | 0.0458428 | ||||||||
\(256\) | 5.85641 | − | 10.1436i | 0.366025 | − | 0.633975i | ||||
\(257\) | 1.09808 | + | 1.90192i | 0.0684961 | + | 0.118639i | 0.898239 | − | 0.439506i | \(-0.144847\pi\) |
−0.829743 | + | 0.558145i | \(0.811513\pi\) | |||||||
\(258\) | 3.36603 | + | 5.83013i | 0.209560 | + | 0.362968i | ||||
\(259\) | 18.0000 | 1.11847 | ||||||||
\(260\) | −5.26795 | − | 0.339746i | −0.326704 | − | 0.0210702i | ||||
\(261\) | −3.26795 | −0.202281 | ||||||||
\(262\) | 0.803848 | + | 1.39230i | 0.0496619 | + | 0.0860169i | ||||
\(263\) | −1.43782 | − | 2.49038i | −0.0886599 | − | 0.153563i | 0.818285 | − | 0.574813i | \(-0.194925\pi\) |
−0.906945 | + | 0.421249i | \(0.861592\pi\) | |||||||
\(264\) | −2.53590 | + | 4.39230i | −0.156074 | + | 0.270328i | ||||
\(265\) | −9.46410 | −0.581375 | ||||||||
\(266\) | −0.339746 | + | 0.588457i | −0.0208312 | + | 0.0360806i | ||||
\(267\) | −2.63397 | + | 4.56218i | −0.161197 | + | 0.279201i | ||||
\(268\) | 13.4641 | 0.822451 | ||||||||
\(269\) | 14.2942 | − | 24.7583i | 0.871535 | − | 1.50954i | 0.0111254 | − | 0.999938i | \(-0.496459\pi\) |
0.860409 | − | 0.509604i | \(-0.170208\pi\) | |||||||
\(270\) | −0.366025 | − | 0.633975i | −0.0222756 | − | 0.0385825i | ||||
\(271\) | −11.2321 | − | 19.4545i | −0.682298 | − | 1.18178i | −0.974278 | − | 0.225351i | \(-0.927647\pi\) |
0.291979 | − | 0.956425i | \(-0.405686\pi\) | |||||||
\(272\) | 0.784610 | 0.0475740 | ||||||||
\(273\) | 2.76795 | + | 5.59808i | 0.167524 | + | 0.338811i | ||||
\(274\) | −8.53590 | −0.515672 | ||||||||
\(275\) | 1.00000 | + | 1.73205i | 0.0603023 | + | 0.104447i | ||||
\(276\) | 1.46410 | + | 2.53590i | 0.0881286 | + | 0.152643i | ||||
\(277\) | 13.1962 | − | 22.8564i | 0.792880 | − | 1.37331i | −0.131297 | − | 0.991343i | \(-0.541914\pi\) |
0.924177 | − | 0.381965i | \(-0.124753\pi\) | |||||||
\(278\) | 14.5885 | 0.874958 | ||||||||
\(279\) | −2.23205 | + | 3.86603i | −0.133629 | + | 0.231453i | ||||
\(280\) | −2.19615 | + | 3.80385i | −0.131245 | + | 0.227323i | ||||
\(281\) | −11.2679 | −0.672189 | −0.336095 | − | 0.941828i | \(-0.609106\pi\) | ||||
−0.336095 | + | 0.941828i | \(0.609106\pi\) | |||||||
\(282\) | −0.0717968 | + | 0.124356i | −0.00427544 | + | 0.00740527i | ||||
\(283\) | −8.06218 | − | 13.9641i | −0.479247 | − | 0.830080i | 0.520470 | − | 0.853880i | \(-0.325757\pi\) |
−0.999717 | + | 0.0238003i | \(0.992423\pi\) | |||||||
\(284\) | −3.46410 | − | 6.00000i | −0.205557 | − | 0.356034i | ||||
\(285\) | −0.535898 | −0.0317439 | ||||||||
\(286\) | −5.26795 | − | 0.339746i | −0.311500 | − | 0.0200896i | ||||
\(287\) | 18.5885 | 1.09724 | ||||||||
\(288\) | −2.92820 | − | 5.07180i | −0.172546 | − | 0.298858i | ||||
\(289\) | 8.23205 | + | 14.2583i | 0.484238 | + | 0.838725i | ||||
\(290\) | 1.19615 | − | 2.07180i | 0.0702405 | − | 0.121660i | ||||
\(291\) | 5.19615 | 0.304604 | ||||||||
\(292\) | 1.26795 | − | 2.19615i | 0.0742011 | − | 0.128520i | ||||
\(293\) | −4.09808 | + | 7.09808i | −0.239412 | + | 0.414674i | −0.960546 | − | 0.278122i | \(-0.910288\pi\) |
0.721134 | + | 0.692796i | \(0.243621\pi\) | |||||||
\(294\) | −2.92820 | −0.170776 | ||||||||
\(295\) | 5.83013 | − | 10.0981i | 0.339443 | − | 0.587933i | ||||
\(296\) | −13.1769 | − | 22.8231i | −0.765893 | − | 1.32656i | ||||
\(297\) | 1.00000 | + | 1.73205i | 0.0580259 | + | 0.100504i | ||||
\(298\) | −4.28719 | −0.248350 | ||||||||
\(299\) | −4.00000 | + | 6.00000i | −0.231326 | + | 0.346989i | ||||
\(300\) | −1.46410 | −0.0845299 | ||||||||
\(301\) | −7.96410 | − | 13.7942i | −0.459043 | − | 0.795086i | ||||
\(302\) | 0.339746 | + | 0.588457i | 0.0195502 | + | 0.0338619i | ||||
\(303\) | −5.19615 | + | 9.00000i | −0.298511 | + | 0.517036i | ||||
\(304\) | −0.574374 | −0.0329426 | ||||||||
\(305\) | −2.69615 | + | 4.66987i | −0.154381 | + | 0.267396i | ||||
\(306\) | −0.267949 | + | 0.464102i | −0.0153176 | + | 0.0265309i | ||||
\(307\) | −6.66025 | −0.380121 | −0.190060 | − | 0.981772i | \(-0.560868\pi\) | ||||
−0.190060 | + | 0.981772i | \(0.560868\pi\) | |||||||
\(308\) | 2.53590 | − | 4.39230i | 0.144496 | − | 0.250275i | ||||
\(309\) | −2.86603 | − | 4.96410i | −0.163042 | − | 0.282398i | ||||
\(310\) | −1.63397 | − | 2.83013i | −0.0928035 | − | 0.160740i | ||||
\(311\) | 12.5885 | 0.713826 | 0.356913 | − | 0.934138i | \(-0.383829\pi\) | ||||
0.356913 | + | 0.934138i | \(0.383829\pi\) | |||||||
\(312\) | 5.07180 | − | 7.60770i | 0.287134 | − | 0.430701i | ||||
\(313\) | 19.1962 | 1.08503 | 0.542515 | − | 0.840046i | \(-0.317472\pi\) | ||||
0.542515 | + | 0.840046i | \(0.317472\pi\) | |||||||
\(314\) | 1.36603 | + | 2.36603i | 0.0770893 | + | 0.133523i | ||||
\(315\) | 0.866025 | + | 1.50000i | 0.0487950 | + | 0.0845154i | ||||
\(316\) | −8.05256 | + | 13.9474i | −0.452992 | + | 0.784605i | ||||
\(317\) | −28.3923 | −1.59467 | −0.797335 | − | 0.603537i | \(-0.793758\pi\) | ||||
−0.797335 | + | 0.603537i | \(0.793758\pi\) | |||||||
\(318\) | 3.46410 | − | 6.00000i | 0.194257 | − | 0.336463i | ||||
\(319\) | −3.26795 | + | 5.66025i | −0.182970 | + | 0.316913i | ||||
\(320\) | 2.14359 | 0.119831 | ||||||||
\(321\) | −4.09808 | + | 7.09808i | −0.228732 | + | 0.396176i | ||||
\(322\) | 1.26795 | + | 2.19615i | 0.0706600 | + | 0.122387i | ||||
\(323\) | 0.196152 | + | 0.339746i | 0.0109142 | + | 0.0189040i | ||||
\(324\) | −1.46410 | −0.0813390 | ||||||||
\(325\) | −1.59808 | − | 3.23205i | −0.0886453 | − | 0.179282i | ||||
\(326\) | 15.5167 | 0.859388 | ||||||||
\(327\) | 7.69615 | + | 13.3301i | 0.425598 | + | 0.737158i | ||||
\(328\) | −13.6077 | − | 23.5692i | −0.751359 | − | 1.30139i | ||||
\(329\) | 0.169873 | − | 0.294229i | 0.00936540 | − | 0.0162213i | ||||
\(330\) | −1.46410 | −0.0805961 | ||||||||
\(331\) | −11.9641 | + | 20.7224i | −0.657606 | + | 1.13901i | 0.323627 | + | 0.946185i | \(0.395098\pi\) |
−0.981234 | + | 0.192823i | \(0.938236\pi\) | |||||||
\(332\) | 2.14359 | − | 3.71281i | 0.117645 | − | 0.203767i | ||||
\(333\) | −10.3923 | −0.569495 | ||||||||
\(334\) | 8.00000 | − | 13.8564i | 0.437741 | − | 0.758189i | ||||
\(335\) | 4.59808 | + | 7.96410i | 0.251220 | + | 0.435125i | ||||
\(336\) | 0.928203 | + | 1.60770i | 0.0506376 | + | 0.0877070i | ||||
\(337\) | 25.5885 | 1.39389 | 0.696946 | − | 0.717124i | \(-0.254542\pi\) | ||||
0.696946 | + | 0.717124i | \(0.254542\pi\) | |||||||
\(338\) | 9.43782 | + | 1.22243i | 0.513350 | + | 0.0664915i | ||||
\(339\) | 18.3923 | 0.998933 | ||||||||
\(340\) | 0.535898 | + | 0.928203i | 0.0290632 | + | 0.0503389i | ||||
\(341\) | 4.46410 | + | 7.73205i | 0.241745 | + | 0.418714i | ||||
\(342\) | 0.196152 | − | 0.339746i | 0.0106067 | − | 0.0183714i | ||||
\(343\) | 19.0526 | 1.02874 | ||||||||
\(344\) | −11.6603 | + | 20.1962i | −0.628679 | + | 1.08890i | ||||
\(345\) | −1.00000 | + | 1.73205i | −0.0538382 | + | 0.0932505i | ||||
\(346\) | 8.92820 | 0.479983 | ||||||||
\(347\) | 0.732051 | − | 1.26795i | 0.0392985 | − | 0.0680671i | −0.845707 | − | 0.533647i | \(-0.820821\pi\) |
0.885006 | + | 0.465580i | \(0.154154\pi\) | |||||||
\(348\) | −2.39230 | − | 4.14359i | −0.128241 | − | 0.222120i | ||||
\(349\) | −15.4282 | − | 26.7224i | −0.825853 | − | 1.43042i | −0.901266 | − | 0.433267i | \(-0.857361\pi\) |
0.0754130 | − | 0.997152i | \(-0.475972\pi\) | |||||||
\(350\) | −1.26795 | −0.0677747 | ||||||||
\(351\) | −1.59808 | − | 3.23205i | −0.0852990 | − | 0.172514i | ||||
\(352\) | −11.7128 | −0.624295 | ||||||||
\(353\) | 4.80385 | + | 8.32051i | 0.255683 | + | 0.442856i | 0.965081 | − | 0.261952i | \(-0.0843663\pi\) |
−0.709398 | + | 0.704808i | \(0.751033\pi\) | |||||||
\(354\) | 4.26795 | + | 7.39230i | 0.226839 | + | 0.392897i | ||||
\(355\) | 2.36603 | − | 4.09808i | 0.125576 | − | 0.217503i | ||||
\(356\) | −7.71281 | −0.408778 | ||||||||
\(357\) | 0.633975 | − | 1.09808i | 0.0335535 | − | 0.0581164i | ||||
\(358\) | −6.46410 | + | 11.1962i | −0.341638 | + | 0.591735i | ||||
\(359\) | 0.196152 | 0.0103525 | 0.00517626 | − | 0.999987i | \(-0.498352\pi\) | ||||
0.00517626 | + | 0.999987i | \(0.498352\pi\) | |||||||
\(360\) | 1.26795 | − | 2.19615i | 0.0668268 | − | 0.115747i | ||||
\(361\) | 9.35641 | + | 16.2058i | 0.492442 | + | 0.852935i | ||||
\(362\) | −3.07180 | − | 5.32051i | −0.161450 | − | 0.279640i | ||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | −5.07180 | + | 7.60770i | −0.265834 | + | 0.398752i | ||||
\(365\) | 1.73205 | 0.0906597 | ||||||||
\(366\) | −1.97372 | − | 3.41858i | −0.103168 | − | 0.178692i | ||||
\(367\) | −7.52628 | − | 13.0359i | −0.392869 | − | 0.680468i | 0.599958 | − | 0.800031i | \(-0.295184\pi\) |
−0.992827 | + | 0.119563i | \(0.961851\pi\) | |||||||
\(368\) | −1.07180 | + | 1.85641i | −0.0558713 | + | 0.0967719i | ||||
\(369\) | −10.7321 | −0.558688 | ||||||||
\(370\) | 3.80385 | − | 6.58846i | 0.197753 | − | 0.342518i | ||||
\(371\) | −8.19615 | + | 14.1962i | −0.425523 | + | 0.737028i | ||||
\(372\) | −6.53590 | −0.338871 | ||||||||
\(373\) | −3.66987 | + | 6.35641i | −0.190019 | + | 0.329122i | −0.945256 | − | 0.326329i | \(-0.894188\pi\) |
0.755237 | + | 0.655451i | \(0.227522\pi\) | |||||||
\(374\) | 0.535898 | + | 0.928203i | 0.0277106 | + | 0.0479962i | ||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | −0.497423 | −0.0256526 | ||||||||
\(377\) | 6.53590 | − | 9.80385i | 0.336616 | − | 0.504924i | ||||
\(378\) | −1.26795 | −0.0652163 | ||||||||
\(379\) | −3.23205 | − | 5.59808i | −0.166019 | − | 0.287554i | 0.770997 | − | 0.636838i | \(-0.219758\pi\) |
−0.937017 | + | 0.349284i | \(0.886425\pi\) | |||||||
\(380\) | −0.392305 | − | 0.679492i | −0.0201248 | − | 0.0348572i | ||||
\(381\) | 0.330127 | − | 0.571797i | 0.0169129 | − | 0.0292940i | ||||
\(382\) | 16.5359 | 0.846050 | ||||||||
\(383\) | 9.63397 | − | 16.6865i | 0.492273 | − | 0.852642i | −0.507687 | − | 0.861541i | \(-0.669499\pi\) |
0.999960 | + | 0.00889939i | \(0.00283280\pi\) | |||||||
\(384\) | 5.07180 | − | 8.78461i | 0.258819 | − | 0.448288i | ||||
\(385\) | 3.46410 | 0.176547 | ||||||||
\(386\) | 7.02628 | − | 12.1699i | 0.357628 | − | 0.619430i | ||||
\(387\) | 4.59808 | + | 7.96410i | 0.233733 | + | 0.404838i | ||||
\(388\) | 3.80385 | + | 6.58846i | 0.193111 | + | 0.334478i | ||||
\(389\) | −14.5359 | −0.736999 | −0.368500 | − | 0.929628i | \(-0.620128\pi\) | ||||
−0.368500 | + | 0.929628i | \(0.620128\pi\) | |||||||
\(390\) | 2.63397 | + | 0.169873i | 0.133376 | + | 0.00860185i | ||||
\(391\) | 1.46410 | 0.0740428 | ||||||||
\(392\) | −5.07180 | − | 8.78461i | −0.256164 | − | 0.443690i | ||||
\(393\) | 1.09808 | + | 1.90192i | 0.0553906 | + | 0.0959394i | ||||
\(394\) | −6.00000 | + | 10.3923i | −0.302276 | + | 0.523557i | ||||
\(395\) | −11.0000 | −0.553470 | ||||||||
\(396\) | −1.46410 | + | 2.53590i | −0.0735739 | + | 0.127434i | ||||
\(397\) | −4.86603 | + | 8.42820i | −0.244219 | + | 0.422999i | −0.961912 | − | 0.273360i | \(-0.911865\pi\) |
0.717693 | + | 0.696360i | \(0.245198\pi\) | |||||||
\(398\) | −18.1962 | −0.912091 | ||||||||
\(399\) | −0.464102 | + | 0.803848i | −0.0232341 | + | 0.0402427i | ||||
\(400\) | −0.535898 | − | 0.928203i | −0.0267949 | − | 0.0464102i | ||||
\(401\) | 15.1244 | + | 26.1962i | 0.755274 | + | 1.30817i | 0.945238 | + | 0.326382i | \(0.105830\pi\) |
−0.189964 | + | 0.981791i | \(0.560837\pi\) | |||||||
\(402\) | −6.73205 | −0.335764 | ||||||||
\(403\) | −7.13397 | − | 14.4282i | −0.355369 | − | 0.718720i | ||||
\(404\) | −15.2154 | −0.756994 | ||||||||
\(405\) | −0.500000 | − | 0.866025i | −0.0248452 | − | 0.0430331i | ||||
\(406\) | −2.07180 | − | 3.58846i | −0.102822 | − | 0.178092i | ||||
\(407\) | −10.3923 | + | 18.0000i | −0.515127 | + | 0.892227i | ||||
\(408\) | −1.85641 | −0.0919058 | ||||||||
\(409\) | −3.16025 | + | 5.47372i | −0.156265 | + | 0.270658i | −0.933519 | − | 0.358529i | \(-0.883279\pi\) |
0.777254 | + | 0.629187i | \(0.216612\pi\) | |||||||
\(410\) | 3.92820 | − | 6.80385i | 0.194000 | − | 0.336018i | ||||
\(411\) | −11.6603 | −0.575158 | ||||||||
\(412\) | 4.19615 | − | 7.26795i | 0.206730 | − | 0.358066i | ||||
\(413\) | −10.0981 | − | 17.4904i | −0.496894 | − | 0.860645i | ||||
\(414\) | −0.732051 | − | 1.26795i | −0.0359783 | − | 0.0623163i | ||||
\(415\) | 2.92820 | 0.143740 | ||||||||
\(416\) | 21.0718 | + | 1.35898i | 1.03313 | + | 0.0666297i | ||||
\(417\) | 19.9282 | 0.975888 | ||||||||
\(418\) | −0.392305 | − | 0.679492i | −0.0191883 | − | 0.0332350i | ||||
\(419\) | 19.9545 | + | 34.5622i | 0.974840 | + | 1.68847i | 0.680461 | + | 0.732784i | \(0.261780\pi\) |
0.294379 | + | 0.955689i | \(0.404887\pi\) | |||||||
\(420\) | −1.26795 | + | 2.19615i | −0.0618696 | + | 0.107161i | ||||
\(421\) | 12.8564 | 0.626583 | 0.313291 | − | 0.949657i | \(-0.398568\pi\) | ||||
0.313291 | + | 0.949657i | \(0.398568\pi\) | |||||||
\(422\) | −8.16987 | + | 14.1506i | −0.397703 | + | 0.688842i | ||||
\(423\) | −0.0980762 | + | 0.169873i | −0.00476863 | + | 0.00825951i | ||||
\(424\) | 24.0000 | 1.16554 | ||||||||
\(425\) | −0.366025 | + | 0.633975i | −0.0177548 | + | 0.0307523i | ||||
\(426\) | 1.73205 | + | 3.00000i | 0.0839181 | + | 0.145350i | ||||
\(427\) | 4.66987 | + | 8.08846i | 0.225991 | + | 0.391428i | ||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | −7.19615 | − | 0.464102i | −0.347434 | − | 0.0224070i | ||||
\(430\) | −6.73205 | −0.324648 | ||||||||
\(431\) | 10.5359 | + | 18.2487i | 0.507496 | + | 0.879009i | 0.999962 | + | 0.00867780i | \(0.00276226\pi\) |
−0.492466 | + | 0.870332i | \(0.663904\pi\) | |||||||
\(432\) | −0.535898 | − | 0.928203i | −0.0257834 | − | 0.0446582i | ||||
\(433\) | −9.52628 | + | 16.5000i | −0.457804 | + | 0.792939i | −0.998845 | − | 0.0480569i | \(-0.984697\pi\) |
0.541041 | + | 0.840996i | \(0.318030\pi\) | |||||||
\(434\) | −5.66025 | −0.271701 | ||||||||
\(435\) | 1.63397 | − | 2.83013i | 0.0783431 | − | 0.135694i | ||||
\(436\) | −11.2679 | + | 19.5167i | −0.539637 | + | 0.934679i | ||||
\(437\) | −1.07180 | −0.0512710 | ||||||||
\(438\) | −0.633975 | + | 1.09808i | −0.0302925 | + | 0.0524681i | ||||
\(439\) | 9.69615 | + | 16.7942i | 0.462772 | + | 0.801545i | 0.999098 | − | 0.0424662i | \(-0.0135215\pi\) |
−0.536326 | + | 0.844011i | \(0.680188\pi\) | |||||||
\(440\) | −2.53590 | − | 4.39230i | −0.120894 | − | 0.209395i | ||||
\(441\) | −4.00000 | −0.190476 | ||||||||
\(442\) | −0.856406 | − | 1.73205i | −0.0407351 | − | 0.0823853i | ||||
\(443\) | 29.1244 | 1.38374 | 0.691870 | − | 0.722022i | \(-0.256787\pi\) | ||||
0.691870 | + | 0.722022i | \(0.256787\pi\) | |||||||
\(444\) | −7.60770 | − | 13.1769i | −0.361045 | − | 0.625349i | ||||
\(445\) | −2.63397 | − | 4.56218i | −0.124862 | − | 0.216268i | ||||
\(446\) | −0.679492 | + | 1.17691i | −0.0321749 | + | 0.0557285i | ||||
\(447\) | −5.85641 | −0.276999 | ||||||||
\(448\) | 1.85641 | − | 3.21539i | 0.0877070 | − | 0.151913i | ||||
\(449\) | −7.73205 | + | 13.3923i | −0.364898 | + | 0.632022i | −0.988760 | − | 0.149513i | \(-0.952229\pi\) |
0.623862 | + | 0.781535i | \(0.285563\pi\) | |||||||
\(450\) | 0.732051 | 0.0345092 | ||||||||
\(451\) | −10.7321 | + | 18.5885i | −0.505353 | + | 0.875296i | ||||
\(452\) | 13.4641 | + | 23.3205i | 0.633298 | + | 1.09690i | ||||
\(453\) | 0.464102 | + | 0.803848i | 0.0218054 | + | 0.0377681i | ||||
\(454\) | −3.46410 | −0.162578 | ||||||||
\(455\) | −6.23205 | − | 0.401924i | −0.292163 | − | 0.0188425i | ||||
\(456\) | 1.35898 | 0.0636402 | ||||||||
\(457\) | 7.25833 | + | 12.5718i | 0.339530 | + | 0.588084i | 0.984344 | − | 0.176256i | \(-0.0563985\pi\) |
−0.644814 | + | 0.764339i | \(0.723065\pi\) | |||||||
\(458\) | −4.67949 | − | 8.10512i | −0.218658 | − | 0.378727i | ||||
\(459\) | −0.366025 | + | 0.633975i | −0.0170846 | + | 0.0295914i | ||||
\(460\) | −2.92820 | −0.136528 | ||||||||
\(461\) | 5.02628 | − | 8.70577i | 0.234097 | − | 0.405468i | −0.724913 | − | 0.688841i | \(-0.758120\pi\) |
0.959010 | + | 0.283373i | \(0.0914533\pi\) | |||||||
\(462\) | −1.26795 | + | 2.19615i | −0.0589903 | + | 0.102174i | ||||
\(463\) | −1.33975 | −0.0622633 | −0.0311316 | − | 0.999515i | \(-0.509911\pi\) | ||||
−0.0311316 | + | 0.999515i | \(0.509911\pi\) | |||||||
\(464\) | 1.75129 | − | 3.03332i | 0.0813015 | − | 0.140818i | ||||
\(465\) | −2.23205 | − | 3.86603i | −0.103509 | − | 0.179283i | ||||
\(466\) | 10.3397 | + | 17.9090i | 0.478979 | + | 0.829617i | ||||
\(467\) | 10.3397 | 0.478466 | 0.239233 | − | 0.970962i | \(-0.423104\pi\) | ||||
0.239233 | + | 0.970962i | \(0.423104\pi\) | |||||||
\(468\) | 2.92820 | − | 4.39230i | 0.135356 | − | 0.203034i | ||||
\(469\) | 15.9282 | 0.735496 | ||||||||
\(470\) | −0.0717968 | − | 0.124356i | −0.00331174 | − | 0.00573610i | ||||
\(471\) | 1.86603 | + | 3.23205i | 0.0859819 | + | 0.148925i | ||||
\(472\) | −14.7846 | + | 25.6077i | −0.680517 | + | 1.17869i | ||||
\(473\) | 18.3923 | 0.845679 | ||||||||
\(474\) | 4.02628 | − | 6.97372i | 0.184933 | − | 0.320314i | ||||
\(475\) | 0.267949 | − | 0.464102i | 0.0122944 | − | 0.0212944i | ||||
\(476\) | 1.85641 | 0.0850883 | ||||||||
\(477\) | 4.73205 | − | 8.19615i | 0.216666 | − | 0.375276i | ||||
\(478\) | 5.07180 | + | 8.78461i | 0.231979 | + | 0.401799i | ||||
\(479\) | −19.4186 | − | 33.6340i | −0.887258 | − | 1.53678i | −0.843104 | − | 0.537751i | \(-0.819274\pi\) |
−0.0441539 | − | 0.999025i | \(-0.514059\pi\) | |||||||
\(480\) | 5.85641 | 0.267307 | ||||||||
\(481\) | 20.7846 | − | 31.1769i | 0.947697 | − | 1.42154i | ||||
\(482\) | 2.92820 | 0.133376 | ||||||||
\(483\) | 1.73205 | + | 3.00000i | 0.0788110 | + | 0.136505i | ||||
\(484\) | −5.12436 | − | 8.87564i | −0.232925 | − | 0.403438i | ||||
\(485\) | −2.59808 | + | 4.50000i | −0.117973 | + | 0.204334i | ||||
\(486\) | 0.732051 | 0.0332065 | ||||||||
\(487\) | −2.80385 | + | 4.85641i | −0.127054 | + | 0.220065i | −0.922534 | − | 0.385915i | \(-0.873886\pi\) |
0.795480 | + | 0.605980i | \(0.207219\pi\) | |||||||
\(488\) | 6.83717 | − | 11.8423i | 0.309504 | − | 0.536077i | ||||
\(489\) | 21.1962 | 0.958523 | ||||||||
\(490\) | 1.46410 | − | 2.53590i | 0.0661414 | − | 0.114560i | ||||
\(491\) | 9.49038 | + | 16.4378i | 0.428295 | + | 0.741829i | 0.996722 | − | 0.0809052i | \(-0.0257811\pi\) |
−0.568427 | + | 0.822734i | \(0.692448\pi\) | |||||||
\(492\) | −7.85641 | − | 13.6077i | −0.354194 | − | 0.613482i | ||||
\(493\) | −2.39230 | −0.107744 | ||||||||
\(494\) | 0.626933 | + | 1.26795i | 0.0282071 | + | 0.0570477i | ||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | −2.39230 | − | 4.14359i | −0.107418 | − | 0.186053i | ||||
\(497\) | −4.09808 | − | 7.09808i | −0.183824 | − | 0.318392i | ||||
\(498\) | −1.07180 | + | 1.85641i | −0.0480284 | + | 0.0831876i | ||||
\(499\) | −25.3205 | −1.13350 | −0.566751 | − | 0.823889i | \(-0.691800\pi\) | ||||
−0.566751 | + | 0.823889i | \(0.691800\pi\) | |||||||
\(500\) | 0.732051 | − | 1.26795i | 0.0327383 | − | 0.0567044i | ||||
\(501\) | 10.9282 | − | 18.9282i | 0.488236 | − | 0.845650i | ||||
\(502\) | −4.78461 | −0.213548 | ||||||||
\(503\) | 6.46410 | − | 11.1962i | 0.288220 | − | 0.499212i | −0.685165 | − | 0.728388i | \(-0.740270\pi\) |
0.973385 | + | 0.229176i | \(0.0736032\pi\) | |||||||
\(504\) | −2.19615 | − | 3.80385i | −0.0978244 | − | 0.169437i | ||||
\(505\) | −5.19615 | − | 9.00000i | −0.231226 | − | 0.400495i | ||||
\(506\) | −2.92820 | −0.130175 | ||||||||
\(507\) | 12.8923 | + | 1.66987i | 0.572567 | + | 0.0741617i | ||||
\(508\) | 0.966679 | 0.0428894 | ||||||||
\(509\) | 9.00000 | + | 15.5885i | 0.398918 | + | 0.690946i | 0.993593 | − | 0.113020i | \(-0.0360525\pi\) |
−0.594675 | + | 0.803966i | \(0.702719\pi\) | |||||||
\(510\) | −0.267949 | − | 0.464102i | −0.0118650 | − | 0.0205508i | ||||
\(511\) | 1.50000 | − | 2.59808i | 0.0663561 | − | 0.114932i | ||||
\(512\) | 11.7128 | 0.517638 | ||||||||
\(513\) | 0.267949 | − | 0.464102i | 0.0118302 | − | 0.0204906i | ||||
\(514\) | 0.803848 | − | 1.39230i | 0.0354562 | − | 0.0614119i | ||||
\(515\) | 5.73205 | 0.252584 | ||||||||
\(516\) | −6.73205 | + | 11.6603i | −0.296362 | + | 0.513314i | ||||
\(517\) | 0.196152 | + | 0.339746i | 0.00862677 | + | 0.0149420i | ||||
\(518\) | −6.58846 | − | 11.4115i | −0.289480 | − | 0.501394i | ||||
\(519\) | 12.1962 | 0.535352 | ||||||||
\(520\) | 4.05256 | + | 8.19615i | 0.177716 | + | 0.359425i | ||||
\(521\) | 23.8038 | 1.04287 | 0.521433 | − | 0.853292i | \(-0.325398\pi\) | ||||
0.521433 | + | 0.853292i | \(0.325398\pi\) | |||||||
\(522\) | 1.19615 | + | 2.07180i | 0.0523542 | + | 0.0906801i | ||||
\(523\) | −14.5885 | − | 25.2679i | −0.637909 | − | 1.10489i | −0.985891 | − | 0.167389i | \(-0.946466\pi\) |
0.347982 | − | 0.937501i | \(-0.386867\pi\) | |||||||
\(524\) | −1.60770 | + | 2.78461i | −0.0702325 | + | 0.121646i | ||||
\(525\) | −1.73205 | −0.0755929 | ||||||||
\(526\) | −1.05256 | + | 1.82309i | −0.0458937 | + | 0.0794903i | ||||
\(527\) | −1.63397 | + | 2.83013i | −0.0711771 | + | 0.123282i | ||||
\(528\) | −2.14359 | −0.0932879 | ||||||||
\(529\) | 9.50000 | − | 16.4545i | 0.413043 | − | 0.715412i | ||||
\(530\) | 3.46410 | + | 6.00000i | 0.150471 | + | 0.260623i | ||||
\(531\) | 5.83013 | + | 10.0981i | 0.253006 | + | 0.438219i | ||||
\(532\) | −1.35898 | −0.0589194 | ||||||||
\(533\) | 21.4641 | − | 32.1962i | 0.929713 | − | 1.39457i | ||||
\(534\) | 3.85641 | 0.166883 | ||||||||
\(535\) | −4.09808 | − | 7.09808i | −0.177175 | − | 0.306877i | ||||
\(536\) | −11.6603 | − | 20.1962i | −0.503646 | − | 0.872341i | ||||
\(537\) | −8.83013 | + | 15.2942i | −0.381048 | + | 0.659995i | ||||
\(538\) | −20.9282 | −0.902279 | ||||||||
\(539\) | −4.00000 | + | 6.92820i | −0.172292 | + | 0.298419i | ||||
\(540\) | 0.732051 | − | 1.26795i | 0.0315025 | − | 0.0545638i | ||||
\(541\) | 11.2487 | 0.483620 | 0.241810 | − | 0.970324i | \(-0.422259\pi\) | ||||
0.241810 | + | 0.970324i | \(0.422259\pi\) | |||||||
\(542\) | −8.22243 | + | 14.2417i | −0.353184 | + | 0.611732i | ||||
\(543\) | −4.19615 | − | 7.26795i | −0.180074 | − | 0.311898i | ||||
\(544\) | −2.14359 | − | 3.71281i | −0.0919058 | − | 0.159186i | ||||
\(545\) | −15.3923 | −0.659334 | ||||||||
\(546\) | 2.53590 | − | 3.80385i | 0.108526 | − | 0.162790i | ||||
\(547\) | −31.9808 | −1.36740 | −0.683699 | − | 0.729764i | \(-0.739630\pi\) | ||||
−0.683699 | + | 0.729764i | \(0.739630\pi\) | |||||||
\(548\) | −8.53590 | − | 14.7846i | −0.364636 | − | 0.631567i | ||||
\(549\) | −2.69615 | − | 4.66987i | −0.115069 | − | 0.199305i | ||||
\(550\) | 0.732051 | − | 1.26795i | 0.0312148 | − | 0.0540655i | ||||
\(551\) | 1.75129 | 0.0746074 | ||||||||
\(552\) | 2.53590 | − | 4.39230i | 0.107935 | − | 0.186949i | ||||
\(553\) | −9.52628 | + | 16.5000i | −0.405099 | + | 0.701651i | ||||
\(554\) | −19.3205 | −0.820850 | ||||||||
\(555\) | 5.19615 | − | 9.00000i | 0.220564 | − | 0.382029i | ||||
\(556\) | 14.5885 | + | 25.2679i | 0.618688 | + | 1.07160i | ||||
\(557\) | −4.73205 | − | 8.19615i | −0.200503 | − | 0.347282i | 0.748187 | − | 0.663488i | \(-0.230924\pi\) |
−0.948691 | + | 0.316205i | \(0.897591\pi\) | |||||||
\(558\) | 3.26795 | 0.138343 | ||||||||
\(559\) | −33.0885 | − | 2.13397i | −1.39949 | − | 0.0902575i | ||||
\(560\) | −1.85641 | −0.0784475 | ||||||||
\(561\) | 0.732051 | + | 1.26795i | 0.0309072 | + | 0.0535329i | ||||
\(562\) | 4.12436 | + | 7.14359i | 0.173975 | + | 0.301334i | ||||
\(563\) | 17.3923 | − | 30.1244i | 0.732998 | − | 1.26959i | −0.222598 | − | 0.974910i | \(-0.571454\pi\) |
0.955596 | − | 0.294680i | \(-0.0952130\pi\) | |||||||
\(564\) | −0.287187 | −0.0120928 | ||||||||
\(565\) | −9.19615 | + | 15.9282i | −0.386885 | + | 0.670105i | ||||
\(566\) | −5.90192 | + | 10.2224i | −0.248076 | + | 0.429681i | ||||
\(567\) | −1.73205 | −0.0727393 | ||||||||
\(568\) | −6.00000 | + | 10.3923i | −0.251754 | + | 0.436051i | ||||
\(569\) | 9.49038 | + | 16.4378i | 0.397857 | + | 0.689109i | 0.993461 | − | 0.114169i | \(-0.0364205\pi\) |
−0.595604 | + | 0.803278i | \(0.703087\pi\) | |||||||
\(570\) | 0.196152 | + | 0.339746i | 0.00821592 | + | 0.0142304i | ||||
\(571\) | −42.7846 | −1.79048 | −0.895240 | − | 0.445584i | \(-0.852996\pi\) | ||||
−0.895240 | + | 0.445584i | \(0.852996\pi\) | |||||||
\(572\) | −4.67949 | − | 9.46410i | −0.195659 | − | 0.395714i | ||||
\(573\) | 22.5885 | 0.943646 | ||||||||
\(574\) | −6.80385 | − | 11.7846i | −0.283987 | − | 0.491880i | ||||
\(575\) | −1.00000 | − | 1.73205i | −0.0417029 | − | 0.0722315i | ||||
\(576\) | −1.07180 | + | 1.85641i | −0.0446582 | + | 0.0773503i | ||||
\(577\) | −8.53590 | −0.355354 | −0.177677 | − | 0.984089i | \(-0.556858\pi\) | ||||
−0.177677 | + | 0.984089i | \(0.556858\pi\) | |||||||
\(578\) | 6.02628 | − | 10.4378i | 0.250660 | − | 0.434156i | ||||
\(579\) | 9.59808 | − | 16.6244i | 0.398882 | − | 0.690885i | ||||
\(580\) | 4.78461 | 0.198670 | ||||||||
\(581\) | 2.53590 | − | 4.39230i | 0.105207 | − | 0.182224i | ||||
\(582\) | −1.90192 | − | 3.29423i | −0.0788373 | − | 0.136550i | ||||
\(583\) | −9.46410 | − | 16.3923i | −0.391963 | − | 0.678900i | ||||
\(584\) | −4.39230 | −0.181755 | ||||||||
\(585\) | 3.59808 | + | 0.232051i | 0.148762 | + | 0.00959412i | ||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | −14.4904 | − | 25.0981i | −0.598082 | − | 1.03591i | −0.993104 | − | 0.117237i | \(-0.962596\pi\) |
0.395022 | − | 0.918672i | \(-0.370737\pi\) | |||||||
\(588\) | −2.92820 | − | 5.07180i | −0.120757 | − | 0.209157i | ||||
\(589\) | 1.19615 | − | 2.07180i | 0.0492866 | − | 0.0853669i | ||||
\(590\) | −8.53590 | −0.351417 | ||||||||
\(591\) | −8.19615 | + | 14.1962i | −0.337145 | + | 0.583952i | ||||
\(592\) | 5.56922 | − | 9.64617i | 0.228894 | − | 0.396455i | ||||
\(593\) | −15.4641 | −0.635035 | −0.317517 | − | 0.948252i | \(-0.602849\pi\) | ||||
−0.317517 | + | 0.948252i | \(0.602849\pi\) | |||||||
\(594\) | 0.732051 | − | 1.26795i | 0.0300364 | − | 0.0520246i | ||||
\(595\) | 0.633975 | + | 1.09808i | 0.0259904 | + | 0.0450167i | ||||
\(596\) | −4.28719 | − | 7.42563i | −0.175610 | − | 0.304165i | ||||
\(597\) | −24.8564 | −1.01730 | ||||||||
\(598\) | 5.26795 | + | 0.339746i | 0.215422 | + | 0.0138932i | ||||
\(599\) | −18.9808 | −0.775533 | −0.387766 | − | 0.921758i | \(-0.626753\pi\) | ||||
−0.387766 | + | 0.921758i | \(0.626753\pi\) | |||||||
\(600\) | 1.26795 | + | 2.19615i | 0.0517638 | + | 0.0896575i | ||||
\(601\) | 5.26795 | + | 9.12436i | 0.214884 | + | 0.372190i | 0.953237 | − | 0.302225i | \(-0.0977293\pi\) |
−0.738353 | + | 0.674415i | \(0.764396\pi\) | |||||||
\(602\) | −5.83013 | + | 10.0981i | −0.237618 | + | 0.411567i | ||||
\(603\) | −9.19615 | −0.374496 | ||||||||
\(604\) | −0.679492 | + | 1.17691i | −0.0276481 | + | 0.0478880i | ||||
\(605\) | 3.50000 | − | 6.06218i | 0.142295 | − | 0.246463i | ||||
\(606\) | 7.60770 | 0.309041 | ||||||||
\(607\) | −9.19615 | + | 15.9282i | −0.373260 | + | 0.646506i | −0.990065 | − | 0.140610i | \(-0.955094\pi\) |
0.616805 | + | 0.787116i | \(0.288427\pi\) | |||||||
\(608\) | 1.56922 | + | 2.71797i | 0.0636402 | + | 0.110228i | ||||
\(609\) | −2.83013 | − | 4.90192i | −0.114683 | − | 0.198636i | ||||
\(610\) | 3.94744 | 0.159827 | ||||||||
\(611\) | −0.313467 | − | 0.633975i | −0.0126815 | − | 0.0256479i | ||||
\(612\) | −1.07180 | −0.0433248 | ||||||||
\(613\) | −14.1340 | − | 24.4808i | −0.570866 | − | 0.988769i | −0.996477 | − | 0.0838627i | \(-0.973274\pi\) |
0.425611 | − | 0.904906i | \(-0.360059\pi\) | |||||||
\(614\) | 2.43782 | + | 4.22243i | 0.0983825 | + | 0.170403i | ||||
\(615\) | 5.36603 | − | 9.29423i | 0.216379 | − | 0.374779i | ||||
\(616\) | −8.78461 | −0.353942 | ||||||||
\(617\) | 17.0526 | − | 29.5359i | 0.686510 | − | 1.18907i | −0.286449 | − | 0.958095i | \(-0.592475\pi\) |
0.972960 | − | 0.230975i | \(-0.0741916\pi\) | |||||||
\(618\) | −2.09808 | + | 3.63397i | −0.0843970 | + | 0.146180i | ||||
\(619\) | 31.9282 | 1.28330 | 0.641651 | − | 0.766996i | \(-0.278250\pi\) | ||||
0.641651 | + | 0.766996i | \(0.278250\pi\) | |||||||
\(620\) | 3.26795 | − | 5.66025i | 0.131244 | − | 0.227321i | ||||
\(621\) | −1.00000 | − | 1.73205i | −0.0401286 | − | 0.0695048i | ||||
\(622\) | −4.60770 | − | 7.98076i | −0.184752 | − | 0.319999i | ||||
\(623\) | −9.12436 | −0.365560 | ||||||||
\(624\) | 3.85641 | + | 0.248711i | 0.154380 | + | 0.00995642i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.02628 | − | 12.1699i | −0.280827 | − | 0.486406i | ||||
\(627\) | −0.535898 | − | 0.928203i | −0.0214017 | − | 0.0370689i | ||||
\(628\) | −2.73205 | + | 4.73205i | −0.109021 | + | 0.188829i | ||||
\(629\) | −7.60770 | −0.303339 | ||||||||
\(630\) | 0.633975 | − | 1.09808i | 0.0252582 | − | 0.0437484i | ||||
\(631\) | −12.6962 | + | 21.9904i | −0.505426 | + | 0.875423i | 0.494554 | + | 0.869147i | \(0.335331\pi\) |
−0.999980 | + | 0.00627660i | \(0.998002\pi\) | |||||||
\(632\) | 27.8949 | 1.10960 | ||||||||
\(633\) | −11.1603 | + | 19.3301i | −0.443580 | + | 0.768304i | ||||
\(634\) | 10.3923 | + | 18.0000i | 0.412731 | + | 0.714871i | ||||
\(635\) | 0.330127 | + | 0.571797i | 0.0131007 | + | 0.0226911i | ||||
\(636\) | 13.8564 | 0.549442 | ||||||||
\(637\) | 8.00000 | − | 12.0000i | 0.316972 | − | 0.475457i | ||||
\(638\) | 4.78461 | 0.189425 | ||||||||
\(639\) | 2.36603 | + | 4.09808i | 0.0935985 | + | 0.162117i | ||||
\(640\) | 5.07180 | + | 8.78461i | 0.200480 | + | 0.347242i | ||||
\(641\) | 1.73205 | − | 3.00000i | 0.0684119 | − | 0.118493i | −0.829790 | − | 0.558075i | \(-0.811540\pi\) |
0.898202 | + | 0.439582i | \(0.144873\pi\) | |||||||
\(642\) | 6.00000 | 0.236801 | ||||||||
\(643\) | −6.79423 | + | 11.7679i | −0.267938 | + | 0.464083i | −0.968329 | − | 0.249677i | \(-0.919676\pi\) |
0.700391 | + | 0.713759i | \(0.253009\pi\) | |||||||
\(644\) | −2.53590 | + | 4.39230i | −0.0999284 | + | 0.173081i | ||||
\(645\) | −9.19615 | −0.362098 | ||||||||
\(646\) | 0.143594 | − | 0.248711i | 0.00564961 | − | 0.00978542i | ||||
\(647\) | 2.07180 | + | 3.58846i | 0.0814507 | + | 0.141077i | 0.903873 | − | 0.427800i | \(-0.140711\pi\) |
−0.822423 | + | 0.568877i | \(0.807378\pi\) | |||||||
\(648\) | 1.26795 | + | 2.19615i | 0.0498097 | + | 0.0862730i | ||||
\(649\) | 23.3205 | 0.915410 | ||||||||
\(650\) | −1.46410 | + | 2.19615i | −0.0574268 | + | 0.0861402i | ||||
\(651\) | −7.73205 | −0.303043 | ||||||||
\(652\) | 15.5167 | + | 26.8756i | 0.607679 | + | 1.05253i | ||||
\(653\) | −6.75833 | − | 11.7058i | −0.264474 | − | 0.458082i | 0.702952 | − | 0.711238i | \(-0.251865\pi\) |
−0.967426 | + | 0.253155i | \(0.918532\pi\) | |||||||
\(654\) | 5.63397 | − | 9.75833i | 0.220306 | − | 0.381581i | ||||
\(655\) | −2.19615 | −0.0858108 | ||||||||
\(656\) | 5.75129 | − | 9.96152i | 0.224550 | − | 0.388932i | ||||
\(657\) | −0.866025 | + | 1.50000i | −0.0337869 | + | 0.0585206i | ||||
\(658\) | −0.248711 | −0.00969578 | ||||||||
\(659\) | 9.12436 | − | 15.8038i | 0.355434 | − | 0.615630i | −0.631758 | − | 0.775166i | \(-0.717666\pi\) |
0.987192 | + | 0.159535i | \(0.0509996\pi\) | |||||||
\(660\) | −1.46410 | − | 2.53590i | −0.0569901 | − | 0.0987097i | ||||
\(661\) | −18.0885 | − | 31.3301i | −0.703559 | − | 1.21860i | −0.967209 | − | 0.253982i | \(-0.918260\pi\) |
0.263649 | − | 0.964619i | \(-0.415074\pi\) | |||||||
\(662\) | 17.5167 | 0.680804 | ||||||||
\(663\) | −1.16987 | − | 2.36603i | −0.0454341 | − | 0.0918888i | ||||
\(664\) | −7.42563 | −0.288170 | ||||||||
\(665\) | −0.464102 | − | 0.803848i | −0.0179971 | − | 0.0311719i | ||||
\(666\) | 3.80385 | + | 6.58846i | 0.147396 | + | 0.255298i | ||||
\(667\) | 3.26795 | − | 5.66025i | 0.126535 | − | 0.219166i | ||||
\(668\) | 32.0000 | 1.23812 | ||||||||
\(669\) | −0.928203 | + | 1.60770i | −0.0358864 | + | 0.0621571i | ||||
\(670\) | 3.36603 | − | 5.83013i | 0.130041 | − | 0.225237i | ||||
\(671\) | −10.7846 | −0.416335 | ||||||||
\(672\) | 5.07180 | − | 8.78461i | 0.195649 | − | 0.338874i | ||||
\(673\) | 6.47372 | + | 11.2128i | 0.249544 | + | 0.432222i | 0.963399 | − | 0.268071i | \(-0.0863861\pi\) |
−0.713856 | + | 0.700293i | \(0.753053\pi\) | |||||||
\(674\) | −9.36603 | − | 16.2224i | −0.360766 | − | 0.624865i | ||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 7.32051 | + | 17.5692i | 0.281558 | + | 0.675739i | ||||
\(677\) | 50.9282 | 1.95733 | 0.978665 | − | 0.205463i | \(-0.0658700\pi\) | ||||
0.978665 | + | 0.205463i | \(0.0658700\pi\) | |||||||
\(678\) | −6.73205 | − | 11.6603i | −0.258543 | − | 0.447809i | ||||
\(679\) | 4.50000 | + | 7.79423i | 0.172694 | + | 0.299115i | ||||
\(680\) | 0.928203 | − | 1.60770i | 0.0355950 | − | 0.0616523i | ||||
\(681\) | −4.73205 | −0.181333 | ||||||||
\(682\) | 3.26795 | − | 5.66025i | 0.125136 | − | 0.216742i | ||||
\(683\) | −8.29423 | + | 14.3660i | −0.317370 | + | 0.549701i | −0.979938 | − | 0.199301i | \(-0.936133\pi\) |
0.662569 | + | 0.749001i | \(0.269466\pi\) | |||||||
\(684\) | 0.784610 | 0.0300003 | ||||||||
\(685\) | 5.83013 | − | 10.0981i | 0.222758 | − | 0.385828i | ||||
\(686\) | −6.97372 | − | 12.0788i | −0.266258 | − | 0.461172i | ||||
\(687\) | −6.39230 | − | 11.0718i | −0.243882 | − | 0.422415i | ||||
\(688\) | −9.85641 | −0.375772 | ||||||||
\(689\) | 15.1244 | + | 30.5885i | 0.576192 | + | 1.16533i | ||||
\(690\) | 1.46410 | 0.0557374 | ||||||||
\(691\) | 13.9641 | + | 24.1865i | 0.531219 | + | 0.920099i | 0.999336 | + | 0.0364324i | \(0.0115994\pi\) |
−0.468117 | + | 0.883667i | \(0.655067\pi\) | |||||||
\(692\) | 8.92820 | + | 15.4641i | 0.339399 | + | 0.587857i | ||||
\(693\) | −1.73205 | + | 3.00000i | −0.0657952 | + | 0.113961i | ||||
\(694\) | −1.07180 | −0.0406848 | ||||||||
\(695\) | −9.96410 | + | 17.2583i | −0.377960 | + | 0.654646i | ||||
\(696\) | −4.14359 | + | 7.17691i | −0.157063 | + | 0.272040i | ||||
\(697\) | −7.85641 | −0.297583 | ||||||||
\(698\) | −11.2942 | + | 19.5622i | −0.427493 | + | 0.740439i | ||||
\(699\) | 14.1244 | + | 24.4641i | 0.534232 | + | 0.925317i | ||||
\(700\) | −1.26795 | − | 2.19615i | −0.0479240 | − | 0.0830068i | ||||
\(701\) | −37.4641 | −1.41500 | −0.707500 | − | 0.706714i | \(-0.750177\pi\) | ||||
−0.707500 | + | 0.706714i | \(0.750177\pi\) | |||||||
\(702\) | −1.46410 | + | 2.19615i | −0.0552590 | + | 0.0828884i | ||||
\(703\) | 5.56922 | 0.210047 | ||||||||
\(704\) | 2.14359 | + | 3.71281i | 0.0807897 | + | 0.139932i | ||||
\(705\) | −0.0980762 | − | 0.169873i | −0.00369376 | − | 0.00639779i | ||||
\(706\) | 3.51666 | − | 6.09103i | 0.132351 | − | 0.229239i | ||||
\(707\) | −18.0000 | −0.676960 | ||||||||
\(708\) | −8.53590 | + | 14.7846i | −0.320799 | + | 0.555640i | ||||
\(709\) | 18.6244 | − | 32.2583i | 0.699452 | − | 1.21149i | −0.269204 | − | 0.963083i | \(-0.586761\pi\) |
0.968657 | − | 0.248404i | \(-0.0799060\pi\) | |||||||
\(710\) | −3.46410 | −0.130005 | ||||||||
\(711\) | 5.50000 | − | 9.52628i | 0.206266 | − | 0.357263i | ||||
\(712\) | 6.67949 | + | 11.5692i | 0.250325 | + | 0.433575i | ||||
\(713\) | −4.46410 | − | 7.73205i | −0.167182 | − | 0.289568i | ||||
\(714\) | −0.928203 | −0.0347371 | ||||||||
\(715\) | 4.00000 | − | 6.00000i | 0.149592 | − | 0.224387i | ||||
\(716\) | −25.8564 | −0.966299 | ||||||||
\(717\) | 6.92820 | + | 12.0000i | 0.258738 | + | 0.448148i | ||||
\(718\) | −0.0717968 | − | 0.124356i | −0.00267943 | − | 0.00464091i | ||||
\(719\) | −11.8301 | + | 20.4904i | −0.441189 | + | 0.764162i | −0.997778 | − | 0.0666259i | \(-0.978777\pi\) |
0.556589 | + | 0.830788i | \(0.312110\pi\) | |||||||
\(720\) | 1.07180 | 0.0399435 | ||||||||
\(721\) | 4.96410 | − | 8.59808i | 0.184873 | − | 0.320209i | ||||
\(722\) | 6.84936 | − | 11.8634i | 0.254907 | − | 0.441512i | ||||
\(723\) | 4.00000 | 0.148762 | ||||||||
\(724\) | 6.14359 | − | 10.6410i | 0.228325 | − | 0.395470i | ||||
\(725\) | 1.63397 | + | 2.83013i | 0.0606843 | + | 0.105108i | ||||
\(726\) | 2.56218 | + | 4.43782i | 0.0950913 | + | 0.164703i | ||||
\(727\) | −2.66025 | −0.0986634 | −0.0493317 | − | 0.998782i | \(-0.515709\pi\) | ||||
−0.0493317 | + | 0.998782i | \(0.515709\pi\) | |||||||
\(728\) | 15.8038 | + | 1.01924i | 0.585730 | + | 0.0377755i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.633975 | − | 1.09808i | −0.0234645 | − | 0.0406416i | ||||
\(731\) | 3.36603 | + | 5.83013i | 0.124497 | + | 0.215635i | ||||
\(732\) | 3.94744 | − | 6.83717i | 0.145902 | − | 0.252709i | ||||
\(733\) | 13.9808 | 0.516391 | 0.258196 | − | 0.966093i | \(-0.416872\pi\) | ||||
0.258196 | + | 0.966093i | \(0.416872\pi\) | |||||||
\(734\) | −5.50962 | + | 9.54294i | −0.203364 | + | 0.352236i | ||||
\(735\) | 2.00000 | − | 3.46410i | 0.0737711 | − | 0.127775i | ||||
\(736\) | 11.7128 | 0.431740 | ||||||||
\(737\) | −9.19615 | + | 15.9282i | −0.338745 | + | 0.586723i | ||||
\(738\) | 3.92820 | + | 6.80385i | 0.144599 | + | 0.250453i | ||||
\(739\) | −0.535898 | − | 0.928203i | −0.0197133 | − | 0.0341445i | 0.856000 | − | 0.516975i | \(-0.172942\pi\) |
−0.875714 | + | 0.482831i | \(0.839609\pi\) | |||||||
\(740\) | 15.2154 | 0.559329 | ||||||||
\(741\) | 0.856406 | + | 1.73205i | 0.0314609 | + | 0.0636285i | ||||
\(742\) | 12.0000 | 0.440534 | ||||||||
\(743\) | 17.9545 | + | 31.0981i | 0.658686 | + | 1.14088i | 0.980956 | + | 0.194230i | \(0.0622208\pi\) |
−0.322270 | + | 0.946648i | \(0.604446\pi\) | |||||||
\(744\) | 5.66025 | + | 9.80385i | 0.207515 | + | 0.359426i | ||||
\(745\) | 2.92820 | − | 5.07180i | 0.107281 | − | 0.185816i | ||||
\(746\) | 5.37307 | 0.196722 | ||||||||
\(747\) | −1.46410 | + | 2.53590i | −0.0535687 | + | 0.0927837i | ||||
\(748\) | −1.07180 | + | 1.85641i | −0.0391888 | + | 0.0678769i | ||||
\(749\) | −14.1962 | −0.518716 | ||||||||
\(750\) | −0.366025 | + | 0.633975i | −0.0133654 | + | 0.0231495i | ||||
\(751\) | −5.19615 | − | 9.00000i | −0.189610 | − | 0.328415i | 0.755510 | − | 0.655137i | \(-0.227389\pi\) |
−0.945120 | + | 0.326722i | \(0.894056\pi\) | |||||||
\(752\) | −0.105118 | − | 0.182069i | −0.00383325 | − | 0.00663938i | ||||
\(753\) | −6.53590 | −0.238181 | ||||||||
\(754\) | −8.60770 | − | 0.555136i | −0.313474 | − | 0.0202169i | ||||
\(755\) | −0.928203 | −0.0337808 | ||||||||
\(756\) | −1.26795 | − | 2.19615i | −0.0461149 | − | 0.0798733i | ||||
\(757\) | 9.46410 | + | 16.3923i | 0.343979 | + | 0.595788i | 0.985168 | − | 0.171595i | \(-0.0548919\pi\) |
−0.641189 | + | 0.767383i | \(0.721559\pi\) | |||||||
\(758\) | −2.36603 | + | 4.09808i | −0.0859379 | + | 0.148849i | ||||
\(759\) | −4.00000 | −0.145191 | ||||||||
\(760\) | −0.679492 | + | 1.17691i | −0.0246478 | + | 0.0426912i | ||||
\(761\) | 12.5359 | − | 21.7128i | 0.454426 | − | 0.787089i | −0.544229 | − | 0.838937i | \(-0.683178\pi\) |
0.998655 | + | 0.0518478i | \(0.0165111\pi\) | |||||||
\(762\) | −0.483340 | −0.0175095 | ||||||||
\(763\) | −13.3301 | + | 23.0885i | −0.482583 | + | 0.835858i | ||||
\(764\) | 16.5359 | + | 28.6410i | 0.598248 | + | 1.03620i | ||||
\(765\) | −0.366025 | − | 0.633975i | −0.0132337 | − | 0.0229214i | ||||
\(766\) | −14.1051 | −0.509639 | ||||||||
\(767\) | −41.9545 | − | 2.70577i | −1.51489 | − | 0.0976997i | ||||
\(768\) | −11.7128 | −0.422650 | ||||||||
\(769\) | 4.39230 | + | 7.60770i | 0.158391 | + | 0.274341i | 0.934288 | − | 0.356518i | \(-0.116036\pi\) |
−0.775898 | + | 0.630859i | \(0.782703\pi\) | |||||||
\(770\) | −1.26795 | − | 2.19615i | −0.0456937 | − | 0.0791438i | ||||
\(771\) | 1.09808 | − | 1.90192i | 0.0395462 | − | 0.0684961i | ||||
\(772\) | 28.1051 | 1.01153 | ||||||||
\(773\) | −11.1962 | + | 19.3923i | −0.402698 | + | 0.697493i | −0.994050 | − | 0.108920i | \(-0.965261\pi\) |
0.591353 | + | 0.806413i | \(0.298594\pi\) | |||||||
\(774\) | 3.36603 | − | 5.83013i | 0.120989 | − | 0.209560i | ||||
\(775\) | 4.46410 | 0.160355 | ||||||||
\(776\) | 6.58846 | − | 11.4115i | 0.236512 | − | 0.409651i | ||||
\(777\) | −9.00000 | − | 15.5885i | −0.322873 | − | 0.559233i | ||||
\(778\) | 5.32051 | + | 9.21539i | 0.190749 | + | 0.330388i | ||||
\(779\) | 5.75129 | 0.206061 | ||||||||
\(780\) | 2.33975 | + | 4.73205i | 0.0837763 | + | 0.169435i | ||||
\(781\) | 9.46410 | 0.338652 | ||||||||
\(782\) | −0.535898 | − | 0.928203i | −0.0191637 | − | 0.0331925i | ||||
\(783\) | 1.63397 | + | 2.83013i | 0.0583935 | + | 0.101140i | ||||
\(784\) | 2.14359 | − | 3.71281i | 0.0765569 | − | 0.132600i | ||||
\(785\) | −3.73205 | −0.133203 | ||||||||
\(786\) | 0.803848 | − | 1.39230i | 0.0286723 | − | 0.0496619i | ||||
\(787\) | −22.0622 | + | 38.2128i | −0.786432 | + | 1.36214i | 0.141708 | + | 0.989908i | \(0.454740\pi\) |
−0.928140 | + | 0.372231i | \(0.878593\pi\) | |||||||
\(788\) | −24.0000 | −0.854965 | ||||||||
\(789\) | −1.43782 | + | 2.49038i | −0.0511878 | + | 0.0886599i | ||||
\(790\) | 4.02628 | + | 6.97372i | 0.143249 | + | 0.248114i | ||||
\(791\) | 15.9282 | + | 27.5885i | 0.566342 | + | 0.980933i | ||||
\(792\) | 5.07180 | 0.180218 | ||||||||
\(793\) | 19.4019 | + | 1.25129i | 0.688983 | + | 0.0444346i | ||||
\(794\) | 7.12436 | 0.252834 | ||||||||
\(795\) | 4.73205 | + | 8.19615i | 0.167829 | + | 0.290688i | ||||
\(796\) | −18.1962 | − | 31.5167i | −0.644946 | − | 1.11708i | ||||
\(797\) | 3.83013 | − | 6.63397i | 0.135670 | − | 0.234987i | −0.790183 | − | 0.612871i | \(-0.790015\pi\) |
0.925853 | + | 0.377883i | \(0.123348\pi\) | |||||||
\(798\) | 0.679492 | 0.0240538 | ||||||||
\(799\) | −0.0717968 | + | 0.124356i | −0.00253999 | + | 0.00439939i | ||||
\(800\) | −2.92820 | + | 5.07180i | −0.103528 | + | 0.179315i | ||||
\(801\) | 5.26795 | 0.186134 | ||||||||
\(802\) | 11.0718 | − | 19.1769i | 0.390959 | − | 0.677160i | ||||
\(803\) | 1.73205 | + | 3.00000i | 0.0611227 | + | 0.105868i | ||||
\(804\) | −6.73205 | − | 11.6603i | −0.237421 | − | 0.411225i | ||||
\(805\) | −3.46410 | −0.122094 | ||||||||
\(806\) | −6.53590 | + | 9.80385i | −0.230217 | + | 0.345326i | ||||
\(807\) | −28.5885 | −1.00636 | ||||||||
\(808\) | 13.1769 | + | 22.8231i | 0.463562 | + | 0.802913i | ||||
\(809\) | 22.0526 | + | 38.1962i | 0.775327 | + | 1.34291i | 0.934611 | + | 0.355672i | \(0.115748\pi\) |
−0.159284 | + | 0.987233i | \(0.550919\pi\) | |||||||
\(810\) | −0.366025 | + | 0.633975i | −0.0128608 | + | 0.0222756i | ||||
\(811\) | −17.6410 | −0.619460 | −0.309730 | − | 0.950825i | \(-0.600239\pi\) | ||||
−0.309730 | + | 0.950825i | \(0.600239\pi\) | |||||||
\(812\) | 4.14359 | − | 7.17691i | 0.145412 | − | 0.251860i | ||||
\(813\) | −11.2321 | + | 19.4545i | −0.393925 | + | 0.682298i | ||||
\(814\) | 15.2154 | 0.533299 | ||||||||
\(815\) | −10.5981 | + | 18.3564i | −0.371234 | + | 0.642997i | ||||
\(816\) | −0.392305 | − | 0.679492i | −0.0137334 | − | 0.0237870i | ||||
\(817\) | −2.46410 | − | 4.26795i | −0.0862080 | − | 0.149317i | ||||
\(818\) | 4.62693 | 0.161777 | ||||||||
\(819\) | 3.46410 | − | 5.19615i | 0.121046 | − | 0.181568i | ||||
\(820\) | 15.7128 | 0.548715 | ||||||||
\(821\) | −17.0000 | − | 29.4449i | −0.593304 | − | 1.02763i | −0.993784 | − | 0.111327i | \(-0.964490\pi\) |
0.400480 | − | 0.916306i | \(-0.368843\pi\) | |||||||
\(822\) | 4.26795 | + | 7.39230i | 0.148862 | + | 0.257836i | ||||
\(823\) | 6.33975 | − | 10.9808i | 0.220990 | − | 0.382765i | −0.734119 | − | 0.679021i | \(-0.762405\pi\) |
0.955109 | + | 0.296255i | \(0.0957380\pi\) | |||||||
\(824\) | −14.5359 | −0.506382 | ||||||||
\(825\) | 1.00000 | − | 1.73205i | 0.0348155 | − | 0.0603023i | ||||
\(826\) | −7.39230 | + | 12.8038i | −0.257211 | + | 0.445503i | ||||
\(827\) | 11.6603 | 0.405467 | 0.202733 | − | 0.979234i | \(-0.435018\pi\) | ||||
0.202733 | + | 0.979234i | \(0.435018\pi\) | |||||||
\(828\) | 1.46410 | − | 2.53590i | 0.0508810 | − | 0.0881286i | ||||
\(829\) | −23.1603 | − | 40.1147i | −0.804389 | − | 1.39324i | −0.916703 | − | 0.399570i | \(-0.869160\pi\) |
0.112314 | − | 0.993673i | \(-0.464174\pi\) | |||||||
\(830\) | −1.07180 | − | 1.85641i | −0.0372026 | − | 0.0644368i | ||||
\(831\) | −26.3923 | −0.915539 | ||||||||
\(832\) | −3.42563 | − | 6.92820i | −0.118762 | − | 0.240192i | ||||
\(833\) | −2.92820 | −0.101456 | ||||||||
\(834\) | −7.29423 | − | 12.6340i | −0.252578 | − | 0.437479i | ||||
\(835\) | 10.9282 | + | 18.9282i | 0.378186 | + | 0.655037i | ||||
\(836\) | 0.784610 | − | 1.35898i | 0.0271363 | − | 0.0470014i | ||||
\(837\) | 4.46410 | 0.154302 | ||||||||
\(838\) | 14.6077 | − | 25.3013i | 0.504614 | − | 0.874018i | ||||
\(839\) | −19.1962 | + | 33.2487i | −0.662725 | + | 1.14787i | 0.317172 | + | 0.948368i | \(0.397267\pi\) |
−0.979897 | + | 0.199505i | \(0.936067\pi\) | |||||||
\(840\) | 4.39230 | 0.151549 | ||||||||
\(841\) | 9.16025 | − | 15.8660i | 0.315871 | − | 0.547104i | ||||
\(842\) | −4.70577 | − | 8.15064i | −0.162172 | − | 0.280889i | ||||
\(843\) | 5.63397 | + | 9.75833i | 0.194044 | + | 0.336095i | ||||
\(844\) | −32.6795 | −1.12487 | ||||||||
\(845\) | −7.89230 | + | 10.3301i | −0.271504 | + | 0.355367i | ||||
\(846\) | 0.143594 | 0.00493685 | ||||||||
\(847\) | −6.06218 | − | 10.5000i | −0.208299 | − | 0.360784i | ||||
\(848\) | 5.07180 | + | 8.78461i | 0.174166 | + | 0.301665i | ||||
\(849\) | −8.06218 | + | 13.9641i | −0.276693 | + | 0.479247i | ||||
\(850\) | 0.535898 | 0.0183812 | ||||||||
\(851\) | 10.3923 | − | 18.0000i | 0.356244 | − | 0.617032i | ||||
\(852\) | −3.46410 | + | 6.00000i | −0.118678 | + | 0.205557i | ||||
\(853\) | −32.6603 | −1.11827 | −0.559133 | − | 0.829078i | \(-0.688866\pi\) | ||||
−0.559133 | + | 0.829078i | \(0.688866\pi\) | |||||||
\(854\) | 3.41858 | − | 5.92116i | 0.116982 | − | 0.202618i | ||||
\(855\) | 0.267949 | + | 0.464102i | 0.00916367 | + | 0.0158719i | ||||
\(856\) | 10.3923 | + | 18.0000i | 0.355202 | + | 0.615227i | ||||
\(857\) | −47.8038 | −1.63295 | −0.816474 | − | 0.577382i | \(-0.804074\pi\) | ||||
−0.816474 | + | 0.577382i | \(0.804074\pi\) | |||||||
\(858\) | 2.33975 | + | 4.73205i | 0.0798776 | + | 0.161550i | ||||
\(859\) | 11.9282 | 0.406985 | 0.203493 | − | 0.979077i | \(-0.434771\pi\) | ||||
0.203493 | + | 0.979077i | \(0.434771\pi\) | |||||||
\(860\) | −6.73205 | − | 11.6603i | −0.229561 | − | 0.397611i | ||||
\(861\) | −9.29423 | − | 16.0981i | −0.316746 | − | 0.548621i | ||||
\(862\) | 7.71281 | − | 13.3590i | 0.262699 | − | 0.455009i | ||||
\(863\) | 47.9615 | 1.63263 | 0.816315 | − | 0.577607i | \(-0.196014\pi\) | ||||
0.816315 | + | 0.577607i | \(0.196014\pi\) | |||||||
\(864\) | −2.92820 | + | 5.07180i | −0.0996195 | + | 0.172546i | ||||
\(865\) | −6.09808 | + | 10.5622i | −0.207341 | + | 0.359125i | ||||
\(866\) | 13.9474 | 0.473953 | ||||||||
\(867\) | 8.23205 | − | 14.2583i | 0.279575 | − | 0.484238i | ||||
\(868\) | −5.66025 | − | 9.80385i | −0.192122 | − | 0.332764i | ||||
\(869\) | −11.0000 | − | 19.0526i | −0.373149 | − | 0.646314i | ||||
\(870\) | −2.39230 | −0.0811067 | ||||||||
\(871\) | 18.3923 | − | 27.5885i | 0.623199 | − | 0.934799i | ||||
\(872\) | 39.0333 | 1.32184 | ||||||||
\(873\) | −2.59808 | − | 4.50000i | −0.0879316 | − | 0.152302i | ||||
\(874\) | 0.392305 | + | 0.679492i | 0.0132699 | + | 0.0229842i | ||||
\(875\) | 0.866025 | − | 1.50000i | 0.0292770 | − | 0.0507093i | ||||
\(876\) | −2.53590 | −0.0856801 | ||||||||
\(877\) | −2.80385 | + | 4.85641i | −0.0946792 | + | 0.163989i | −0.909475 | − | 0.415759i | \(-0.863516\pi\) |
0.814795 | + | 0.579749i | \(0.196849\pi\) | |||||||
\(878\) | 7.09808 | − | 12.2942i | 0.239548 | − | 0.414910i | ||||
\(879\) | 8.19615 | 0.276449 | ||||||||
\(880\) | 1.07180 | − | 1.85641i | 0.0361303 | − | 0.0625794i | ||||
\(881\) | 7.80385 | + | 13.5167i | 0.262918 | + | 0.455388i | 0.967016 | − | 0.254715i | \(-0.0819817\pi\) |
−0.704098 | + | 0.710103i | \(0.748648\pi\) | |||||||
\(882\) | 1.46410 | + | 2.53590i | 0.0492989 | + | 0.0853881i | ||||
\(883\) | 31.7321 | 1.06787 | 0.533934 | − | 0.845526i | \(-0.320713\pi\) | ||||
0.533934 | + | 0.845526i | \(0.320713\pi\) | |||||||
\(884\) | 2.14359 | − | 3.21539i | 0.0720969 | − | 0.108145i | ||||
\(885\) | −11.6603 | −0.391955 | ||||||||
\(886\) | −10.6603 | − | 18.4641i | −0.358138 | − | 0.620314i | ||||
\(887\) | −18.6340 | − | 32.2750i | −0.625668 | − | 1.08369i | −0.988411 | − | 0.151799i | \(-0.951493\pi\) |
0.362744 | − | 0.931889i | \(-0.381840\pi\) | |||||||
\(888\) | −13.1769 | + | 22.8231i | −0.442188 | + | 0.765893i | ||||
\(889\) | 1.14359 | 0.0383549 | ||||||||
\(890\) | −1.92820 | + | 3.33975i | −0.0646335 | + | 0.111949i | ||||
\(891\) | 1.00000 | − | 1.73205i | 0.0335013 | − | 0.0580259i | ||||
\(892\) | −2.71797 | −0.0910043 | ||||||||
\(893\) | 0.0525589 | − | 0.0910347i | 0.00175882 | − | 0.00304636i | ||||
\(894\) | 2.14359 | + | 3.71281i | 0.0716925 | + | 0.124175i | ||||
\(895\) | −8.83013 | − | 15.2942i | −0.295159 | − | 0.511230i | ||||
\(896\) | 17.5692 | 0.586946 | ||||||||
\(897\) | 7.19615 | + | 0.464102i | 0.240273 | + | 0.0154959i | ||||
\(898\) | 11.3205 | 0.377770 | ||||||||
\(899\) | 7.29423 | + | 12.6340i | 0.243276 | + | 0.421367i | ||||
\(900\) | 0.732051 | + | 1.26795i | 0.0244017 | + | 0.0422650i | ||||
\(901\) | 3.46410 | − | 6.00000i | 0.115406 | − | 0.199889i | ||||
\(902\) | 15.7128 | 0.523179 | ||||||||
\(903\) | −7.96410 | + | 13.7942i | −0.265029 | + | 0.459043i | ||||
\(904\) | 23.3205 | − | 40.3923i | 0.775629 | − | 1.34343i | ||||
\(905\) | 8.39230 | 0.278970 | ||||||||
\(906\) | 0.339746 | − | 0.588457i | 0.0112873 | − | 0.0195502i | ||||
\(907\) | −28.1244 | − | 48.7128i | −0.933854 | − | 1.61748i | −0.776665 | − | 0.629914i | \(-0.783090\pi\) |
−0.157189 | − | 0.987569i | \(-0.550243\pi\) | |||||||
\(908\) | −3.46410 | − | 6.00000i | −0.114960 | − | 0.199117i | ||||
\(909\) | 10.3923 | 0.344691 | ||||||||
\(910\) | 2.02628 | + | 4.09808i | 0.0671705 | + | 0.135850i | ||||
\(911\) | −43.0333 | −1.42576 | −0.712879 | − | 0.701287i | \(-0.752609\pi\) | ||||
−0.712879 | + | 0.701287i | \(0.752609\pi\) | |||||||
\(912\) | 0.287187 | + | 0.497423i | 0.00950971 | + | 0.0164713i | ||||
\(913\) | 2.92820 | + | 5.07180i | 0.0969094 | + | 0.167852i | ||||
\(914\) | 5.31347 | − | 9.20319i | 0.175754 | − | 0.304415i | ||||
\(915\) | 5.39230 | 0.178264 | ||||||||
\(916\) | 9.35898 | − | 16.2102i | 0.309230 | − | 0.535601i | ||||
\(917\) | −1.90192 | + | 3.29423i | −0.0628071 | + | 0.108785i | ||||
\(918\) | 0.535898 | 0.0176873 | ||||||||
\(919\) | −1.92820 | + | 3.33975i | −0.0636056 | + | 0.110168i | −0.896075 | − | 0.443904i | \(-0.853593\pi\) |
0.832469 | + | 0.554072i | \(0.186927\pi\) | |||||||
\(920\) | 2.53590 | + | 4.39230i | 0.0836061 | + | 0.144810i | ||||
\(921\) | 3.33013 | + | 5.76795i | 0.109731 | + | 0.190060i | ||||
\(922\) | −7.35898 | −0.242355 | ||||||||
\(923\) | −17.0263 | − | 1.09808i | −0.560427 | − | 0.0361436i | ||||
\(924\) | −5.07180 | −0.166850 | ||||||||
\(925\) | 5.19615 | + | 9.00000i | 0.170848 | + | 0.295918i | ||||
\(926\) | 0.490381 | + | 0.849365i | 0.0161149 | + | 0.0279119i | ||||
\(927\) | −2.86603 | + | 4.96410i | −0.0941326 | + | 0.163042i | ||||
\(928\) | −19.1384 | −0.628250 | ||||||||
\(929\) | 20.5359 | − | 35.5692i | 0.673761 | − | 1.16699i | −0.303068 | − | 0.952969i | \(-0.598011\pi\) |
0.976829 | − | 0.214019i | \(-0.0686556\pi\) | |||||||
\(930\) | −1.63397 | + | 2.83013i | −0.0535801 | + | 0.0928035i | ||||
\(931\) | 2.14359 | 0.0702534 | ||||||||
\(932\) | −20.6795 | + | 35.8179i | −0.677379 | + | 1.17326i | ||||
\(933\) | −6.29423 | − | 10.9019i | −0.206064 | − | 0.356913i | ||||
\(934\) | −3.78461 | − | 6.55514i | −0.123836 | − | 0.214491i | ||||
\(935\) | −1.46410 | −0.0478812 | ||||||||
\(936\) | −9.12436 | − | 0.588457i | −0.298239 | − | 0.0192343i | ||||
\(937\) | −12.5359 | −0.409530 | −0.204765 | − | 0.978811i | \(-0.565643\pi\) | ||||
−0.204765 | + | 0.978811i | \(0.565643\pi\) | |||||||
\(938\) | −5.83013 | − | 10.0981i | −0.190360 | − | 0.329714i | ||||
\(939\) | −9.59808 | − | 16.6244i | −0.313221 | − | 0.542515i | ||||
\(940\) | 0.143594 | − | 0.248711i | 0.00468350 | − | 0.00811207i | ||||
\(941\) | 41.5167 | 1.35340 | 0.676702 | − | 0.736257i | \(-0.263408\pi\) | ||||
0.676702 | + | 0.736257i | \(0.263408\pi\) | |||||||
\(942\) | 1.36603 | − | 2.36603i | 0.0445075 | − | 0.0770893i | ||||
\(943\) | 10.7321 | − | 18.5885i | 0.349484 | − | 0.605323i | ||||
\(944\) | −12.4974 | −0.406756 | ||||||||
\(945\) | 0.866025 | − | 1.50000i | 0.0281718 | − | 0.0487950i | ||||
\(946\) | −6.73205 | − | 11.6603i | −0.218878 | − | 0.379108i | ||||
\(947\) | 6.16987 | + | 10.6865i | 0.200494 | + | 0.347266i | 0.948688 | − | 0.316215i | \(-0.102412\pi\) |
−0.748194 | + | 0.663480i | \(0.769079\pi\) | |||||||
\(948\) | 16.1051 | 0.523070 | ||||||||
\(949\) | −2.76795 | − | 5.59808i | −0.0898514 | − | 0.181721i | ||||
\(950\) | −0.392305 | −0.0127280 | ||||||||
\(951\) | 14.1962 | + | 24.5885i | 0.460342 | + | 0.797335i | ||||
\(952\) | −1.60770 | − | 2.78461i | −0.0521057 | − | 0.0902497i | ||||
\(953\) | −9.73205 | + | 16.8564i | −0.315252 | + | 0.546033i | −0.979491 | − | 0.201488i | \(-0.935422\pi\) |
0.664239 | + | 0.747520i | \(0.268756\pi\) | |||||||
\(954\) | −6.92820 | −0.224309 | ||||||||
\(955\) | −11.2942 | + | 19.5622i | −0.365473 | + | 0.633017i | ||||
\(956\) | −10.1436 | + | 17.5692i | −0.328067 | + | 0.568229i | ||||
\(957\) | 6.53590 | 0.211276 | ||||||||
\(958\) | −14.2154 | + | 24.6218i | −0.459278 | + | 0.795494i | ||||
\(959\) | −10.0981 | − | 17.4904i | −0.326084 | − | 0.564794i | ||||
\(960\) | −1.07180 | − | 1.85641i | −0.0345921 | − | 0.0599153i | ||||
\(961\) | −11.0718 | −0.357155 | ||||||||
\(962\) | −27.3731 | − | 1.76537i | −0.882543 | − | 0.0569179i | ||||
\(963\) | 8.19615 | 0.264117 | ||||||||
\(964\) | 2.92820 | + | 5.07180i | 0.0943111 | + | 0.163352i | ||||
\(965\) | 9.59808 | + | 16.6244i | 0.308973 | + | 0.535157i | ||||
\(966\) | 1.26795 | − | 2.19615i | 0.0407956 | − | 0.0706600i | ||||
\(967\) | 28.1051 | 0.903800 | 0.451900 | − | 0.892069i | \(-0.350746\pi\) | ||||
0.451900 | + | 0.892069i | \(0.350746\pi\) | |||||||
\(968\) | −8.87564 | + | 15.3731i | −0.285274 | + | 0.494109i | ||||
\(969\) | 0.196152 | − | 0.339746i | 0.00630132 | − | 0.0109142i | ||||
\(970\) | 3.80385 | 0.122134 | ||||||||
\(971\) | 3.80385 | − | 6.58846i | 0.122071 | − | 0.211434i | −0.798513 | − | 0.601977i | \(-0.794380\pi\) |
0.920584 | + | 0.390544i | \(0.127713\pi\) | |||||||
\(972\) | 0.732051 | + | 1.26795i | 0.0234805 | + | 0.0406695i | ||||
\(973\) | 17.2583 | + | 29.8923i | 0.553277 | + | 0.958303i | ||||
\(974\) | 4.10512 | 0.131536 | ||||||||
\(975\) | −2.00000 | + | 3.00000i | −0.0640513 | + | 0.0960769i | ||||
\(976\) | 5.77945 | 0.184996 | ||||||||
\(977\) | −22.7321 | − | 39.3731i | −0.727263 | − | 1.25966i | −0.958036 | − | 0.286648i | \(-0.907459\pi\) |
0.230773 | − | 0.973008i | \(-0.425874\pi\) | |||||||
\(978\) | −7.75833 | − | 13.4378i | −0.248084 | − | 0.429694i | ||||
\(979\) | 5.26795 | − | 9.12436i | 0.168364 | − | 0.291616i | ||||
\(980\) | 5.85641 | 0.187076 | ||||||||
\(981\) | 7.69615 | − | 13.3301i | 0.245719 | − | 0.425598i | ||||
\(982\) | 6.94744 | − | 12.0333i | 0.221702 | − | 0.383999i | ||||
\(983\) | 13.6077 | 0.434018 | 0.217009 | − | 0.976170i | \(-0.430370\pi\) | ||||
0.217009 | + | 0.976170i | \(0.430370\pi\) | |||||||
\(984\) | −13.6077 | + | 23.5692i | −0.433797 | + | 0.751359i | ||||
\(985\) | −8.19615 | − | 14.1962i | −0.261151 | − | 0.452327i | ||||
\(986\) | 0.875644 | + | 1.51666i | 0.0278862 | + | 0.0483003i | ||||
\(987\) | −0.339746 | −0.0108142 | ||||||||
\(988\) | −1.56922 | + | 2.35383i | −0.0499235 | + | 0.0748853i | ||||
\(989\) | −18.3923 | −0.584841 | ||||||||
\(990\) | 0.732051 | + | 1.26795i | 0.0232661 | + | 0.0402981i | ||||
\(991\) | −0.464102 | − | 0.803848i | −0.0147427 | − | 0.0255351i | 0.858560 | − | 0.512713i | \(-0.171360\pi\) |
−0.873303 | + | 0.487178i | \(0.838026\pi\) | |||||||
\(992\) | −13.0718 | + | 22.6410i | −0.415030 | + | 0.718853i | ||||
\(993\) | 23.9282 | 0.759339 | ||||||||
\(994\) | −3.00000 | + | 5.19615i | −0.0951542 | + | 0.164812i | ||||
\(995\) | 12.4282 | − | 21.5263i | 0.394001 | − | 0.682429i | ||||
\(996\) | −4.28719 | −0.135845 | ||||||||
\(997\) | −0.598076 | + | 1.03590i | −0.0189413 | + | 0.0328072i | −0.875341 | − | 0.483507i | \(-0.839363\pi\) |
0.856399 | + | 0.516314i | \(0.172696\pi\) | |||||||
\(998\) | 9.26795 | + | 16.0526i | 0.293372 | + | 0.508135i | ||||
\(999\) | 5.19615 | + | 9.00000i | 0.164399 | + | 0.284747i |
(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 | 195.2.i.c.16.1 | ✓ | 4 | |
3.2 | odd | 2 | 585.2.j.c.406.2 | 4 | |||
5.2 | odd | 4 | 975.2.bb.h.874.1 | 4 | |||
5.3 | odd | 4 | 975.2.bb.a.874.2 | 4 | |||
5.4 | even | 2 | 975.2.i.j.601.2 | 4 | |||
13.3 | even | 3 | 2535.2.a.o.1.2 | 2 | |||
13.9 | even | 3 | inner | 195.2.i.c.61.1 | yes | 4 | |
13.10 | even | 6 | 2535.2.a.r.1.1 | 2 | |||
39.23 | odd | 6 | 7605.2.a.z.1.2 | 2 | |||
39.29 | odd | 6 | 7605.2.a.bj.1.1 | 2 | |||
39.35 | odd | 6 | 585.2.j.c.451.2 | 4 | |||
65.9 | even | 6 | 975.2.i.j.451.2 | 4 | |||
65.22 | odd | 12 | 975.2.bb.a.724.2 | 4 | |||
65.48 | odd | 12 | 975.2.bb.h.724.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.i.c.16.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
195.2.i.c.61.1 | yes | 4 | 13.9 | even | 3 | inner | |
585.2.j.c.406.2 | 4 | 3.2 | odd | 2 | |||
585.2.j.c.451.2 | 4 | 39.35 | odd | 6 | |||
975.2.i.j.451.2 | 4 | 65.9 | even | 6 | |||
975.2.i.j.601.2 | 4 | 5.4 | even | 2 | |||
975.2.bb.a.724.2 | 4 | 65.22 | odd | 12 | |||
975.2.bb.a.874.2 | 4 | 5.3 | odd | 4 | |||
975.2.bb.h.724.1 | 4 | 65.48 | odd | 12 | |||
975.2.bb.h.874.1 | 4 | 5.2 | odd | 4 | |||
2535.2.a.o.1.2 | 2 | 13.3 | even | 3 | |||
2535.2.a.r.1.1 | 2 | 13.10 | even | 6 | |||
7605.2.a.z.1.2 | 2 | 39.23 | odd | 6 | |||
7605.2.a.bj.1.1 | 2 | 39.29 | odd | 6 |