Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(16,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.l (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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.8 | ||
Root | \(0.904928 + 1.56738i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.16 |
Dual form | 273.2.l.c.256.8 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.80986 | 1.27976 | 0.639881 | − | 0.768474i | \(-0.278984\pi\) | ||||
0.639881 | + | 0.768474i | \(0.278984\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 1.27558 | 0.637789 | ||||||||
\(5\) | 1.98776 | − | 3.44291i | 0.888954 | − | 1.53971i | 0.0478412 | − | 0.998855i | \(-0.484766\pi\) |
0.841113 | − | 0.540859i | \(-0.181901\pi\) | |||||||
\(6\) | −0.904928 | + | 1.56738i | −0.369435 | + | 0.639881i | ||||
\(7\) | 1.70815 | + | 2.02045i | 0.645621 | + | 0.763658i | ||||
\(8\) | −1.31110 | −0.463543 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 3.59756 | − | 6.23116i | 1.13765 | − | 1.97047i | ||||
\(11\) | 0.143327 | − | 0.248250i | 0.0432148 | − | 0.0748502i | −0.843609 | − | 0.536958i | \(-0.819573\pi\) |
0.886824 | + | 0.462108i | \(0.152907\pi\) | |||||||
\(12\) | −0.637789 | + | 1.10468i | −0.184114 | + | 0.318895i | ||||
\(13\) | 3.60075 | + | 0.185985i | 0.998669 | + | 0.0515830i | ||||
\(14\) | 3.09151 | + | 3.65672i | 0.826240 | + | 0.977300i | ||||
\(15\) | 1.98776 | + | 3.44291i | 0.513238 | + | 0.888954i | ||||
\(16\) | −4.92406 | −1.23101 | ||||||||
\(17\) | −4.60182 | −1.11611 | −0.558053 | − | 0.829805i | \(-0.688452\pi\) | ||||
−0.558053 | + | 0.829805i | \(0.688452\pi\) | |||||||
\(18\) | −0.904928 | − | 1.56738i | −0.213294 | − | 0.369435i | ||||
\(19\) | 3.48374 | + | 6.03402i | 0.799225 | + | 1.38430i | 0.920121 | + | 0.391634i | \(0.128090\pi\) |
−0.120896 | + | 0.992665i | \(0.538577\pi\) | |||||||
\(20\) | 2.53555 | − | 4.39170i | 0.566965 | − | 0.982013i | ||||
\(21\) | −2.60384 | + | 0.469078i | −0.568204 | + | 0.102361i | ||||
\(22\) | 0.259402 | − | 0.449297i | 0.0553046 | − | 0.0957904i | ||||
\(23\) | −7.23857 | −1.50935 | −0.754673 | − | 0.656101i | \(-0.772205\pi\) | ||||
−0.754673 | + | 0.656101i | \(0.772205\pi\) | |||||||
\(24\) | 0.655549 | − | 1.13544i | 0.133813 | − | 0.231772i | ||||
\(25\) | −5.40240 | − | 9.35723i | −1.08048 | − | 1.87145i | ||||
\(26\) | 6.51684 | + | 0.336606i | 1.27806 | + | 0.0660139i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.17888 | + | 2.57724i | 0.411770 | + | 0.487053i | ||||
\(29\) | 0.421754 | + | 0.730500i | 0.0783178 | + | 0.135650i | 0.902524 | − | 0.430639i | \(-0.141712\pi\) |
−0.824206 | + | 0.566289i | \(0.808378\pi\) | |||||||
\(30\) | 3.59756 | + | 6.23116i | 0.656822 | + | 1.13765i | ||||
\(31\) | −0.212854 | − | 0.368675i | −0.0382298 | − | 0.0662159i | 0.846277 | − | 0.532742i | \(-0.178839\pi\) |
−0.884507 | + | 0.466527i | \(0.845505\pi\) | |||||||
\(32\) | −6.28963 | −1.11186 | ||||||||
\(33\) | 0.143327 | + | 0.248250i | 0.0249501 | + | 0.0432148i | ||||
\(34\) | −8.32864 | −1.42835 | ||||||||
\(35\) | 10.3516 | − | 1.86483i | 1.74974 | − | 0.315214i | ||||
\(36\) | −0.637789 | − | 1.10468i | −0.106298 | − | 0.184114i | ||||
\(37\) | −4.36416 | −0.717464 | −0.358732 | − | 0.933441i | \(-0.616791\pi\) | ||||
−0.358732 | + | 0.933441i | \(0.616791\pi\) | |||||||
\(38\) | 6.30507 | + | 10.9207i | 1.02282 | + | 1.77157i | ||||
\(39\) | −1.96144 | + | 3.02535i | −0.314082 | + | 0.484444i | ||||
\(40\) | −2.60615 | + | 4.51399i | −0.412069 | + | 0.713724i | ||||
\(41\) | −0.509885 | − | 0.883147i | −0.0796307 | − | 0.137924i | 0.823460 | − | 0.567374i | \(-0.192041\pi\) |
−0.903091 | + | 0.429450i | \(0.858707\pi\) | |||||||
\(42\) | −4.71257 | + | 0.848963i | −0.727165 | + | 0.130998i | ||||
\(43\) | 0.585291 | − | 1.01375i | 0.0892560 | − | 0.154596i | −0.817941 | − | 0.575302i | \(-0.804884\pi\) |
0.907197 | + | 0.420706i | \(0.138218\pi\) | |||||||
\(44\) | 0.182825 | − | 0.316662i | 0.0275619 | − | 0.0477386i | ||||
\(45\) | −3.97552 | −0.592636 | ||||||||
\(46\) | −13.1008 | −1.93160 | ||||||||
\(47\) | 2.71264 | − | 4.69843i | 0.395680 | − | 0.685337i | −0.597508 | − | 0.801863i | \(-0.703842\pi\) |
0.993188 | + | 0.116526i | \(0.0371758\pi\) | |||||||
\(48\) | 2.46203 | − | 4.26436i | 0.355363 | − | 0.615507i | ||||
\(49\) | −1.16444 | + | 6.90247i | −0.166348 | + | 0.986067i | ||||
\(50\) | −9.77756 | − | 16.9352i | −1.38276 | − | 2.39500i | ||||
\(51\) | 2.30091 | − | 3.98530i | 0.322192 | − | 0.558053i | ||||
\(52\) | 4.59304 | + | 0.237238i | 0.636940 | + | 0.0328991i | ||||
\(53\) | −0.574226 | − | 0.994589i | −0.0788760 | − | 0.136617i | 0.823889 | − | 0.566751i | \(-0.191800\pi\) |
−0.902765 | + | 0.430134i | \(0.858466\pi\) | |||||||
\(54\) | 1.80986 | 0.246290 | ||||||||
\(55\) | −0.569801 | − | 0.986924i | −0.0768319 | − | 0.133077i | ||||
\(56\) | −2.23956 | − | 2.64901i | −0.299273 | − | 0.353989i | ||||
\(57\) | −6.96749 | −0.922866 | ||||||||
\(58\) | 0.763315 | + | 1.32210i | 0.100228 | + | 0.173600i | ||||
\(59\) | −4.85854 | −0.632528 | −0.316264 | − | 0.948671i | \(-0.602429\pi\) | ||||
−0.316264 | + | 0.948671i | \(0.602429\pi\) | |||||||
\(60\) | 2.53555 | + | 4.39170i | 0.327338 | + | 0.566965i | ||||
\(61\) | −4.08424 | − | 7.07411i | −0.522933 | − | 0.905747i | −0.999644 | − | 0.0266869i | \(-0.991504\pi\) |
0.476710 | − | 0.879060i | \(-0.341829\pi\) | |||||||
\(62\) | −0.385236 | − | 0.667248i | −0.0489250 | − | 0.0847406i | ||||
\(63\) | 0.895685 | − | 2.48953i | 0.112846 | − | 0.313651i | ||||
\(64\) | −1.53522 | −0.191902 | ||||||||
\(65\) | 7.79777 | − | 12.0274i | 0.967194 | − | 1.49181i | ||||
\(66\) | 0.259402 | + | 0.449297i | 0.0319301 | + | 0.0553046i | ||||
\(67\) | −0.786937 | + | 1.36302i | −0.0961397 | + | 0.166519i | −0.910084 | − | 0.414425i | \(-0.863983\pi\) |
0.813944 | + | 0.580943i | \(0.197316\pi\) | |||||||
\(68\) | −5.86999 | −0.711841 | ||||||||
\(69\) | 3.61929 | − | 6.26879i | 0.435711 | − | 0.754673i | ||||
\(70\) | 18.7349 | − | 3.37507i | 2.23925 | − | 0.403399i | ||||
\(71\) | −3.22369 | + | 5.58359i | −0.382581 | + | 0.662650i | −0.991430 | − | 0.130636i | \(-0.958298\pi\) |
0.608849 | + | 0.793286i | \(0.291631\pi\) | |||||||
\(72\) | 0.655549 | + | 1.13544i | 0.0772572 | + | 0.133813i | ||||
\(73\) | 8.24845 | + | 14.2867i | 0.965408 | + | 1.67214i | 0.708515 | + | 0.705696i | \(0.249365\pi\) |
0.256893 | + | 0.966440i | \(0.417301\pi\) | |||||||
\(74\) | −7.89851 | −0.918183 | ||||||||
\(75\) | 10.8048 | 1.24763 | ||||||||
\(76\) | 4.44379 | + | 7.69686i | 0.509737 | + | 0.882891i | ||||
\(77\) | 0.746401 | − | 0.134463i | 0.0850603 | − | 0.0153235i | ||||
\(78\) | −3.54993 | + | 5.47545i | −0.401950 | + | 0.619972i | ||||
\(79\) | −3.84412 | + | 6.65821i | −0.432497 | + | 0.749107i | −0.997088 | − | 0.0762639i | \(-0.975701\pi\) |
0.564590 | + | 0.825371i | \(0.309034\pi\) | |||||||
\(80\) | −9.78785 | + | 16.9531i | −1.09432 | + | 1.89541i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −0.922819 | − | 1.59837i | −0.101908 | − | 0.176510i | ||||
\(83\) | 13.3888 | 1.46961 | 0.734805 | − | 0.678279i | \(-0.237274\pi\) | ||||
0.734805 | + | 0.678279i | \(0.237274\pi\) | |||||||
\(84\) | −3.32140 | + | 0.598345i | −0.362394 | + | 0.0652848i | ||||
\(85\) | −9.14733 | + | 15.8436i | −0.992168 | + | 1.71848i | ||||
\(86\) | 1.05929 | − | 1.83475i | 0.114226 | − | 0.197846i | ||||
\(87\) | −0.843509 | −0.0904336 | ||||||||
\(88\) | −0.187916 | + | 0.325480i | −0.0200319 | + | 0.0346963i | ||||
\(89\) | −2.21571 | −0.234865 | −0.117433 | − | 0.993081i | \(-0.537466\pi\) | ||||
−0.117433 | + | 0.993081i | \(0.537466\pi\) | |||||||
\(90\) | −7.19513 | −0.758433 | ||||||||
\(91\) | 5.77486 | + | 7.59283i | 0.605369 | + | 0.795945i | ||||
\(92\) | −9.23336 | −0.962645 | ||||||||
\(93\) | 0.425709 | 0.0441439 | ||||||||
\(94\) | 4.90949 | − | 8.50349i | 0.506375 | − | 0.877068i | ||||
\(95\) | 27.6994 | 2.84190 | ||||||||
\(96\) | 3.14482 | − | 5.44698i | 0.320967 | − | 0.555930i | ||||
\(97\) | 9.52241 | − | 16.4933i | 0.966854 | − | 1.67464i | 0.262306 | − | 0.964985i | \(-0.415517\pi\) |
0.704549 | − | 0.709656i | \(-0.251150\pi\) | |||||||
\(98\) | −2.10746 | + | 12.4925i | −0.212886 | + | 1.26193i | ||||
\(99\) | −0.286654 | −0.0288098 | ||||||||
\(100\) | −6.89118 | − | 11.9359i | −0.689118 | − | 1.19359i | ||||
\(101\) | 4.54427 | − | 7.87091i | 0.452172 | − | 0.783185i | −0.546348 | − | 0.837558i | \(-0.683983\pi\) |
0.998521 | + | 0.0543727i | \(0.0173159\pi\) | |||||||
\(102\) | 4.16432 | − | 7.21281i | 0.412329 | − | 0.714175i | ||||
\(103\) | 2.34421 | − | 4.06029i | 0.230982 | − | 0.400072i | −0.727116 | − | 0.686515i | \(-0.759140\pi\) |
0.958097 | + | 0.286443i | \(0.0924729\pi\) | |||||||
\(104\) | −4.72094 | − | 0.243845i | −0.462926 | − | 0.0239109i | ||||
\(105\) | −3.56082 | + | 9.89718i | −0.347500 | + | 0.965866i | ||||
\(106\) | −1.03927 | − | 1.80006i | −0.100943 | − | 0.174838i | ||||
\(107\) | 14.5056 | 1.40231 | 0.701154 | − | 0.713010i | \(-0.252669\pi\) | ||||
0.701154 | + | 0.713010i | \(0.252669\pi\) | |||||||
\(108\) | 1.27558 | 0.122743 | ||||||||
\(109\) | 2.09694 | + | 3.63200i | 0.200850 | + | 0.347883i | 0.948803 | − | 0.315870i | \(-0.102296\pi\) |
−0.747952 | + | 0.663752i | \(0.768963\pi\) | |||||||
\(110\) | −1.03126 | − | 1.78619i | −0.0983265 | − | 0.170307i | ||||
\(111\) | 2.18208 | − | 3.77948i | 0.207114 | − | 0.358732i | ||||
\(112\) | −8.41104 | − | 9.94881i | −0.794768 | − | 0.940074i | ||||
\(113\) | 4.12305 | − | 7.14133i | 0.387864 | − | 0.671800i | −0.604298 | − | 0.796758i | \(-0.706546\pi\) |
0.992162 | + | 0.124958i | \(0.0398797\pi\) | |||||||
\(114\) | −12.6101 | −1.18105 | ||||||||
\(115\) | −14.3886 | + | 24.9217i | −1.34174 | + | 2.32396i | ||||
\(116\) | 0.537981 | + | 0.931810i | 0.0499503 | + | 0.0865164i | ||||
\(117\) | −1.63931 | − | 3.21133i | −0.151554 | − | 0.296888i | ||||
\(118\) | −8.79326 | −0.809485 | ||||||||
\(119\) | −7.86061 | − | 9.29776i | −0.720581 | − | 0.852324i | ||||
\(120\) | −2.60615 | − | 4.51399i | −0.237908 | − | 0.412069i | ||||
\(121\) | 5.45891 | + | 9.45512i | 0.496265 | + | 0.859556i | ||||
\(122\) | −7.39189 | − | 12.8031i | −0.669230 | − | 1.15914i | ||||
\(123\) | 1.01977 | 0.0919496 | ||||||||
\(124\) | −0.271512 | − | 0.470273i | −0.0243825 | − | 0.0422318i | ||||
\(125\) | −23.0771 | −2.06408 | ||||||||
\(126\) | 1.62106 | − | 4.50569i | 0.144416 | − | 0.401398i | ||||
\(127\) | −3.92173 | − | 6.79263i | −0.347997 | − | 0.602748i | 0.637897 | − | 0.770122i | \(-0.279805\pi\) |
−0.985894 | + | 0.167374i | \(0.946471\pi\) | |||||||
\(128\) | 9.80074 | 0.866272 | ||||||||
\(129\) | 0.585291 | + | 1.01375i | 0.0515320 | + | 0.0892560i | ||||
\(130\) | 14.1128 | − | 21.7678i | 1.23778 | − | 1.90916i | ||||
\(131\) | −4.04277 | + | 7.00228i | −0.353218 | + | 0.611792i | −0.986811 | − | 0.161874i | \(-0.948246\pi\) |
0.633593 | + | 0.773666i | \(0.281579\pi\) | |||||||
\(132\) | 0.182825 | + | 0.316662i | 0.0159129 | + | 0.0275619i | ||||
\(133\) | −6.24067 | + | 17.3457i | −0.541135 | + | 1.50407i | ||||
\(134\) | −1.42424 | + | 2.46686i | −0.123036 | + | 0.213104i | ||||
\(135\) | 1.98776 | − | 3.44291i | 0.171079 | − | 0.296318i | ||||
\(136\) | 6.03345 | 0.517364 | ||||||||
\(137\) | 1.50968 | 0.128981 | 0.0644904 | − | 0.997918i | \(-0.479458\pi\) | ||||
0.0644904 | + | 0.997918i | \(0.479458\pi\) | |||||||
\(138\) | 6.55039 | − | 11.3456i | 0.557606 | − | 0.965802i | ||||
\(139\) | 2.02132 | − | 3.50104i | 0.171446 | − | 0.296954i | −0.767479 | − | 0.641074i | \(-0.778489\pi\) |
0.938926 | + | 0.344120i | \(0.111823\pi\) | |||||||
\(140\) | 13.2043 | − | 2.37874i | 1.11597 | − | 0.201040i | ||||
\(141\) | 2.71264 | + | 4.69843i | 0.228446 | + | 0.395680i | ||||
\(142\) | −5.83441 | + | 10.1055i | −0.489613 | + | 0.848034i | ||||
\(143\) | 0.562256 | − | 0.867230i | 0.0470182 | − | 0.0725214i | ||||
\(144\) | 2.46203 | + | 4.26436i | 0.205169 | + | 0.355363i | ||||
\(145\) | 3.35339 | 0.278484 | ||||||||
\(146\) | 14.9285 | + | 25.8569i | 1.23549 | + | 2.13993i | ||||
\(147\) | −5.39550 | − | 4.45967i | −0.445013 | − | 0.367827i | ||||
\(148\) | −5.56683 | −0.457591 | ||||||||
\(149\) | 9.59737 | + | 16.6231i | 0.786247 | + | 1.36182i | 0.928251 | + | 0.371954i | \(0.121312\pi\) |
−0.142004 | + | 0.989866i | \(0.545355\pi\) | |||||||
\(150\) | 19.5551 | 1.59667 | ||||||||
\(151\) | −9.47334 | − | 16.4083i | −0.770929 | − | 1.33529i | −0.937054 | − | 0.349184i | \(-0.886459\pi\) |
0.166125 | − | 0.986105i | \(-0.446874\pi\) | |||||||
\(152\) | −4.56753 | − | 7.91120i | −0.370476 | − | 0.641683i | ||||
\(153\) | 2.30091 | + | 3.98530i | 0.186018 | + | 0.322192i | ||||
\(154\) | 1.35088 | − | 0.243359i | 0.108857 | − | 0.0196104i | ||||
\(155\) | −1.69242 | −0.135938 | ||||||||
\(156\) | −2.50197 | + | 3.85907i | −0.200318 | + | 0.308973i | ||||
\(157\) | −9.31770 | − | 16.1387i | −0.743633 | − | 1.28801i | −0.950831 | − | 0.309711i | \(-0.899768\pi\) |
0.207197 | − | 0.978299i | \(-0.433566\pi\) | |||||||
\(158\) | −6.95730 | + | 12.0504i | −0.553493 | + | 0.958679i | ||||
\(159\) | 1.14845 | 0.0910782 | ||||||||
\(160\) | −12.5023 | + | 21.6546i | −0.988394 | + | 1.71195i | ||||
\(161\) | −12.3646 | − | 14.6252i | −0.974465 | − | 1.15262i | ||||
\(162\) | −0.904928 | + | 1.56738i | −0.0710979 | + | 0.123145i | ||||
\(163\) | −5.35262 | − | 9.27102i | −0.419250 | − | 0.726162i | 0.576614 | − | 0.817016i | \(-0.304374\pi\) |
−0.995864 | + | 0.0908544i | \(0.971040\pi\) | |||||||
\(164\) | −0.650398 | − | 1.12652i | −0.0507876 | − | 0.0879667i | ||||
\(165\) | 1.13960 | 0.0887179 | ||||||||
\(166\) | 24.2318 | 1.88075 | ||||||||
\(167\) | 0.0240620 | + | 0.0416766i | 0.00186197 | + | 0.00322503i | 0.866955 | − | 0.498387i | \(-0.166074\pi\) |
−0.865093 | + | 0.501612i | \(0.832741\pi\) | |||||||
\(168\) | 3.41389 | − | 0.615007i | 0.263387 | − | 0.0474489i | ||||
\(169\) | 12.9308 | + | 1.33937i | 0.994678 | + | 0.103029i | ||||
\(170\) | −16.5554 | + | 28.6747i | −1.26974 | + | 2.19925i | ||||
\(171\) | 3.48374 | − | 6.03402i | 0.266408 | − | 0.461433i | ||||
\(172\) | 0.746584 | − | 1.29312i | 0.0569265 | − | 0.0985996i | ||||
\(173\) | 7.01486 | + | 12.1501i | 0.533330 | + | 0.923755i | 0.999242 | + | 0.0389240i | \(0.0123930\pi\) |
−0.465912 | + | 0.884831i | \(0.654274\pi\) | |||||||
\(174\) | −1.52663 | −0.115733 | ||||||||
\(175\) | 9.67770 | − | 26.8988i | 0.731565 | − | 2.03336i | ||||
\(176\) | −0.705751 | + | 1.22240i | −0.0531980 | + | 0.0921416i | ||||
\(177\) | 2.42927 | − | 4.20762i | 0.182595 | − | 0.316264i | ||||
\(178\) | −4.01012 | −0.300571 | ||||||||
\(179\) | −2.34931 | + | 4.06913i | −0.175596 | + | 0.304141i | −0.940367 | − | 0.340161i | \(-0.889519\pi\) |
0.764771 | + | 0.644302i | \(0.222852\pi\) | |||||||
\(180\) | −5.07109 | −0.377977 | ||||||||
\(181\) | −22.0382 | −1.63809 | −0.819044 | − | 0.573730i | \(-0.805496\pi\) | ||||
−0.819044 | + | 0.573730i | \(0.805496\pi\) | |||||||
\(182\) | 10.4517 | + | 13.7419i | 0.774728 | + | 1.01862i | ||||
\(183\) | 8.16848 | 0.603832 | ||||||||
\(184\) | 9.49048 | 0.699648 | ||||||||
\(185\) | −8.67492 | + | 15.0254i | −0.637793 | + | 1.10469i | ||||
\(186\) | 0.770472 | 0.0564937 | ||||||||
\(187\) | −0.659567 | + | 1.14240i | −0.0482323 | + | 0.0835408i | ||||
\(188\) | 3.46019 | − | 5.99322i | 0.252360 | − | 0.437101i | ||||
\(189\) | 1.70815 | + | 2.02045i | 0.124250 | + | 0.146966i | ||||
\(190\) | 50.1319 | 3.63695 | ||||||||
\(191\) | −5.54871 | − | 9.61065i | −0.401491 | − | 0.695402i | 0.592415 | − | 0.805633i | \(-0.298174\pi\) |
−0.993906 | + | 0.110230i | \(0.964841\pi\) | |||||||
\(192\) | 0.767610 | − | 1.32954i | 0.0553975 | − | 0.0959512i | ||||
\(193\) | 0.243115 | − | 0.421088i | 0.0174998 | − | 0.0303106i | −0.857143 | − | 0.515079i | \(-0.827763\pi\) |
0.874643 | + | 0.484768i | \(0.161096\pi\) | |||||||
\(194\) | 17.2342 | − | 29.8505i | 1.23734 | − | 2.14314i | ||||
\(195\) | 6.51711 | + | 12.7667i | 0.466700 | + | 0.914245i | ||||
\(196\) | −1.48533 | + | 8.80464i | −0.106095 | + | 0.628903i | ||||
\(197\) | −8.53814 | − | 14.7885i | −0.608317 | − | 1.05364i | −0.991518 | − | 0.129971i | \(-0.958511\pi\) |
0.383200 | − | 0.923665i | \(-0.374822\pi\) | |||||||
\(198\) | −0.518803 | −0.0368697 | ||||||||
\(199\) | 23.1698 | 1.64246 | 0.821230 | − | 0.570597i | \(-0.193288\pi\) | ||||
0.821230 | + | 0.570597i | \(0.193288\pi\) | |||||||
\(200\) | 7.08308 | + | 12.2683i | 0.500849 | + | 0.867497i | ||||
\(201\) | −0.786937 | − | 1.36302i | −0.0555063 | − | 0.0961397i | ||||
\(202\) | 8.22448 | − | 14.2452i | 0.578673 | − | 1.00229i | ||||
\(203\) | −0.755518 | + | 2.09994i | −0.0530270 | + | 0.147387i | ||||
\(204\) | 2.93499 | − | 5.08356i | 0.205491 | − | 0.355920i | ||||
\(205\) | −4.05412 | −0.283152 | ||||||||
\(206\) | 4.24268 | − | 7.34853i | 0.295601 | − | 0.511997i | ||||
\(207\) | 3.61929 | + | 6.26879i | 0.251558 | + | 0.435711i | ||||
\(208\) | −17.7303 | − | 0.915801i | −1.22938 | − | 0.0634994i | ||||
\(209\) | 1.99726 | 0.138153 | ||||||||
\(210\) | −6.44457 | + | 17.9125i | −0.444717 | + | 1.23608i | ||||
\(211\) | 1.40788 | + | 2.43852i | 0.0969224 | + | 0.167874i | 0.910409 | − | 0.413709i | \(-0.135767\pi\) |
−0.813487 | + | 0.581583i | \(0.802433\pi\) | |||||||
\(212\) | −0.732470 | − | 1.26868i | −0.0503063 | − | 0.0871330i | ||||
\(213\) | −3.22369 | − | 5.58359i | −0.220883 | − | 0.382581i | ||||
\(214\) | 26.2530 | 1.79462 | ||||||||
\(215\) | −2.32684 | − | 4.03020i | −0.158689 | − | 0.274857i | ||||
\(216\) | −1.31110 | −0.0892090 | ||||||||
\(217\) | 0.381301 | − | 1.05981i | 0.0258844 | − | 0.0719449i | ||||
\(218\) | 3.79515 | + | 6.57340i | 0.257040 | + | 0.445207i | ||||
\(219\) | −16.4969 | −1.11476 | ||||||||
\(220\) | −0.726825 | − | 1.25890i | −0.0490026 | − | 0.0848749i | ||||
\(221\) | −16.5700 | − | 0.855871i | −1.11462 | − | 0.0575721i | ||||
\(222\) | 3.94925 | − | 6.84031i | 0.265057 | − | 0.459092i | ||||
\(223\) | −8.16232 | − | 14.1375i | −0.546589 | − | 0.946720i | −0.998505 | − | 0.0546597i | \(-0.982593\pi\) |
0.451916 | − | 0.892061i | \(-0.350741\pi\) | |||||||
\(224\) | −10.7437 | − | 12.7079i | −0.717840 | − | 0.849082i | ||||
\(225\) | −5.40240 | + | 9.35723i | −0.360160 | + | 0.623815i | ||||
\(226\) | 7.46213 | − | 12.9248i | 0.496373 | − | 0.859744i | ||||
\(227\) | −6.20577 | −0.411892 | −0.205946 | − | 0.978563i | \(-0.566027\pi\) | ||||
−0.205946 | + | 0.978563i | \(0.566027\pi\) | |||||||
\(228\) | −8.88757 | −0.588594 | ||||||||
\(229\) | 0.261463 | − | 0.452867i | 0.0172779 | − | 0.0299263i | −0.857257 | − | 0.514889i | \(-0.827833\pi\) |
0.874535 | + | 0.484962i | \(0.161167\pi\) | |||||||
\(230\) | −26.0412 | + | 45.1047i | −1.71711 | + | 2.97412i | ||||
\(231\) | −0.256752 | + | 0.713634i | −0.0168930 | + | 0.0469537i | ||||
\(232\) | −0.552962 | − | 0.957758i | −0.0363037 | − | 0.0628799i | ||||
\(233\) | −6.48273 | + | 11.2284i | −0.424697 | + | 0.735598i | −0.996392 | − | 0.0848689i | \(-0.972953\pi\) |
0.571695 | + | 0.820466i | \(0.306286\pi\) | |||||||
\(234\) | −2.96691 | − | 5.81205i | −0.193953 | − | 0.379946i | ||||
\(235\) | −10.7842 | − | 18.6787i | −0.703482 | − | 1.21847i | ||||
\(236\) | −6.19745 | −0.403419 | ||||||||
\(237\) | −3.84412 | − | 6.65821i | −0.249702 | − | 0.432497i | ||||
\(238\) | −14.2266 | − | 16.8276i | −0.922172 | − | 1.09077i | ||||
\(239\) | −4.79605 | −0.310231 | −0.155116 | − | 0.987896i | \(-0.549575\pi\) | ||||
−0.155116 | + | 0.987896i | \(0.549575\pi\) | |||||||
\(240\) | −9.78785 | − | 16.9531i | −0.631803 | − | 1.09432i | ||||
\(241\) | 10.4195 | 0.671179 | 0.335589 | − | 0.942008i | \(-0.391065\pi\) | ||||
0.335589 | + | 0.942008i | \(0.391065\pi\) | |||||||
\(242\) | 9.87985 | + | 17.1124i | 0.635101 | + | 1.10003i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −5.20977 | − | 9.02358i | −0.333521 | − | 0.577676i | ||||
\(245\) | 21.4499 | + | 17.7295i | 1.37039 | + | 1.13270i | ||||
\(246\) | 1.84564 | 0.117674 | ||||||||
\(247\) | 11.4219 | + | 22.3749i | 0.726755 | + | 1.42368i | ||||
\(248\) | 0.279073 | + | 0.483369i | 0.0177212 | + | 0.0306940i | ||||
\(249\) | −6.69439 | + | 11.5950i | −0.424240 | + | 0.734805i | ||||
\(250\) | −41.7663 | −2.64153 | ||||||||
\(251\) | −5.10645 | + | 8.84463i | −0.322316 | + | 0.558268i | −0.980966 | − | 0.194182i | \(-0.937795\pi\) |
0.658649 | + | 0.752450i | \(0.271128\pi\) | |||||||
\(252\) | 1.14252 | − | 3.17559i | 0.0719718 | − | 0.200043i | ||||
\(253\) | −1.03748 | + | 1.79698i | −0.0652261 | + | 0.112975i | ||||
\(254\) | −7.09776 | − | 12.2937i | −0.445353 | − | 0.771374i | ||||
\(255\) | −9.14733 | − | 15.8436i | −0.572828 | − | 0.992168i | ||||
\(256\) | 20.8084 | 1.30052 | ||||||||
\(257\) | −6.36280 | −0.396901 | −0.198450 | − | 0.980111i | \(-0.563591\pi\) | ||||
−0.198450 | + | 0.980111i | \(0.563591\pi\) | |||||||
\(258\) | 1.05929 | + | 1.83475i | 0.0659486 | + | 0.114226i | ||||
\(259\) | −7.45466 | − | 8.81758i | −0.463210 | − | 0.547898i | ||||
\(260\) | 9.94666 | − | 15.3418i | 0.616866 | − | 0.951460i | ||||
\(261\) | 0.421754 | − | 0.730500i | 0.0261059 | − | 0.0452168i | ||||
\(262\) | −7.31683 | + | 12.6731i | −0.452035 | + | 0.782948i | ||||
\(263\) | 8.50677 | − | 14.7342i | 0.524550 | − | 0.908547i | −0.475041 | − | 0.879963i | \(-0.657567\pi\) |
0.999591 | − | 0.0285838i | \(-0.00909974\pi\) | |||||||
\(264\) | −0.187916 | − | 0.325480i | −0.0115654 | − | 0.0200319i | ||||
\(265\) | −4.56570 | −0.280469 | ||||||||
\(266\) | −11.2947 | + | 31.3933i | −0.692524 | + | 1.92485i | ||||
\(267\) | 1.10786 | − | 1.91886i | 0.0677997 | − | 0.117433i | ||||
\(268\) | −1.00380 | + | 1.73863i | −0.0613168 | + | 0.106204i | ||||
\(269\) | −9.06039 | −0.552422 | −0.276211 | − | 0.961097i | \(-0.589079\pi\) | ||||
−0.276211 | + | 0.961097i | \(0.589079\pi\) | |||||||
\(270\) | 3.59756 | − | 6.23116i | 0.218941 | − | 0.379216i | ||||
\(271\) | 2.22796 | 0.135339 | 0.0676696 | − | 0.997708i | \(-0.478444\pi\) | ||||
0.0676696 | + | 0.997708i | \(0.478444\pi\) | |||||||
\(272\) | 22.6596 | 1.37394 | ||||||||
\(273\) | −9.46301 | + | 1.20476i | −0.572727 | + | 0.0729153i | ||||
\(274\) | 2.73231 | 0.165065 | ||||||||
\(275\) | −3.09724 | −0.186771 | ||||||||
\(276\) | 4.61668 | − | 7.99633i | 0.277892 | − | 0.481322i | ||||
\(277\) | −7.80754 | −0.469110 | −0.234555 | − | 0.972103i | \(-0.575363\pi\) | ||||
−0.234555 | + | 0.972103i | \(0.575363\pi\) | |||||||
\(278\) | 3.65830 | − | 6.33637i | 0.219411 | − | 0.380030i | ||||
\(279\) | −0.212854 | + | 0.368675i | −0.0127433 | + | 0.0220720i | ||||
\(280\) | −13.5720 | + | 2.44498i | −0.811082 | + | 0.146115i | ||||
\(281\) | −12.7531 | −0.760789 | −0.380394 | − | 0.924824i | \(-0.624212\pi\) | ||||
−0.380394 | + | 0.924824i | \(0.624212\pi\) | |||||||
\(282\) | 4.90949 | + | 8.50349i | 0.292356 | + | 0.506375i | ||||
\(283\) | −8.17193 | + | 14.1542i | −0.485771 | + | 0.841380i | −0.999866 | − | 0.0163530i | \(-0.994794\pi\) |
0.514095 | + | 0.857733i | \(0.328128\pi\) | |||||||
\(284\) | −4.11206 | + | 7.12230i | −0.244006 | + | 0.422631i | ||||
\(285\) | −13.8497 | + | 23.9884i | −0.820386 | + | 1.42095i | ||||
\(286\) | 1.01760 | − | 1.56956i | 0.0601721 | − | 0.0928101i | ||||
\(287\) | 0.913393 | − | 2.53875i | 0.0539159 | − | 0.149857i | ||||
\(288\) | 3.14482 | + | 5.44698i | 0.185310 | + | 0.320967i | ||||
\(289\) | 4.17679 | 0.245694 | ||||||||
\(290\) | 6.06915 | 0.356393 | ||||||||
\(291\) | 9.52241 | + | 16.4933i | 0.558214 | + | 0.966854i | ||||
\(292\) | 10.5215 | + | 18.2238i | 0.615727 | + | 1.06647i | ||||
\(293\) | 11.8319 | − | 20.4935i | 0.691227 | − | 1.19724i | −0.280209 | − | 0.959939i | \(-0.590404\pi\) |
0.971436 | − | 0.237302i | \(-0.0762630\pi\) | |||||||
\(294\) | −9.76507 | − | 8.07135i | −0.569511 | − | 0.470731i | ||||
\(295\) | −9.65762 | + | 16.7275i | −0.562288 | + | 0.973912i | ||||
\(296\) | 5.72185 | 0.332576 | ||||||||
\(297\) | 0.143327 | − | 0.248250i | 0.00831669 | − | 0.0144049i | ||||
\(298\) | 17.3699 | + | 30.0855i | 1.00621 | + | 1.74280i | ||||
\(299\) | −26.0643 | − | 1.34627i | −1.50734 | − | 0.0778566i | ||||
\(300\) | 13.7824 | 0.795725 | ||||||||
\(301\) | 3.04800 | − | 0.549094i | 0.175684 | − | 0.0316492i | ||||
\(302\) | −17.1454 | − | 29.6967i | −0.986605 | − | 1.70885i | ||||
\(303\) | 4.54427 | + | 7.87091i | 0.261062 | + | 0.452172i | ||||
\(304\) | −17.1541 | − | 29.7119i | −0.983858 | − | 1.70409i | ||||
\(305\) | −32.4740 | −1.85946 | ||||||||
\(306\) | 4.16432 | + | 7.21281i | 0.238058 | + | 0.412329i | ||||
\(307\) | 8.99691 | 0.513481 | 0.256740 | − | 0.966480i | \(-0.417351\pi\) | ||||
0.256740 | + | 0.966480i | \(0.417351\pi\) | |||||||
\(308\) | 0.952093 | − | 0.171518i | 0.0542505 | − | 0.00977316i | ||||
\(309\) | 2.34421 | + | 4.06029i | 0.133357 | + | 0.230982i | ||||
\(310\) | −3.06303 | −0.173968 | ||||||||
\(311\) | 15.4498 | + | 26.7598i | 0.876077 | + | 1.51741i | 0.855611 | + | 0.517619i | \(0.173181\pi\) |
0.0204655 | + | 0.999791i | \(0.493485\pi\) | |||||||
\(312\) | 2.57165 | − | 3.96653i | 0.145591 | − | 0.224561i | ||||
\(313\) | 3.74574 | − | 6.48782i | 0.211722 | − | 0.366713i | −0.740532 | − | 0.672022i | \(-0.765426\pi\) |
0.952254 | + | 0.305308i | \(0.0987595\pi\) | |||||||
\(314\) | −16.8637 | − | 29.2088i | −0.951673 | − | 1.64835i | ||||
\(315\) | −6.79080 | − | 8.03235i | −0.382618 | − | 0.452572i | ||||
\(316\) | −4.90348 | + | 8.49307i | −0.275842 | + | 0.477773i | ||||
\(317\) | 8.11402 | − | 14.0539i | 0.455729 | − | 0.789346i | −0.543001 | − | 0.839732i | \(-0.682712\pi\) |
0.998730 | + | 0.0503864i | \(0.0160453\pi\) | |||||||
\(318\) | 2.07853 | 0.116558 | ||||||||
\(319\) | 0.241796 | 0.0135379 | ||||||||
\(320\) | −3.05165 | + | 5.28562i | −0.170593 | + | 0.295475i | ||||
\(321\) | −7.25279 | + | 12.5622i | −0.404811 | + | 0.701154i | ||||
\(322\) | −22.3781 | − | 26.4695i | −1.24708 | − | 1.47508i | ||||
\(323\) | −16.0316 | − | 27.7675i | −0.892021 | − | 1.54503i | ||||
\(324\) | −0.637789 | + | 1.10468i | −0.0354327 | + | 0.0613713i | ||||
\(325\) | −17.7124 | − | 34.6978i | −0.982507 | − | 1.92469i | ||||
\(326\) | −9.68748 | − | 16.7792i | −0.536540 | − | 0.929314i | ||||
\(327\) | −4.19387 | −0.231922 | ||||||||
\(328\) | 0.668510 | + | 1.15789i | 0.0369123 | + | 0.0639340i | ||||
\(329\) | 14.1266 | − | 2.54488i | 0.778822 | − | 0.140304i | ||||
\(330\) | 2.06251 | 0.113538 | ||||||||
\(331\) | −2.79217 | − | 4.83618i | −0.153472 | − | 0.265821i | 0.779030 | − | 0.626987i | \(-0.215712\pi\) |
−0.932501 | + | 0.361166i | \(0.882379\pi\) | |||||||
\(332\) | 17.0784 | 0.937301 | ||||||||
\(333\) | 2.18208 | + | 3.77948i | 0.119577 | + | 0.207114i | ||||
\(334\) | 0.0435488 | + | 0.0754287i | 0.00238288 | + | 0.00412727i | ||||
\(335\) | 3.12849 | + | 5.41870i | 0.170928 | + | 0.296055i | ||||
\(336\) | 12.8214 | − | 2.30977i | 0.699467 | − | 0.126008i | ||||
\(337\) | −0.504097 | −0.0274599 | −0.0137299 | − | 0.999906i | \(-0.504371\pi\) | ||||
−0.0137299 | + | 0.999906i | \(0.504371\pi\) | |||||||
\(338\) | 23.4029 | + | 2.42407i | 1.27295 | + | 0.131852i | ||||
\(339\) | 4.12305 | + | 7.14133i | 0.223933 | + | 0.387864i | ||||
\(340\) | −11.6681 | + | 20.2098i | −0.632794 | + | 1.09603i | ||||
\(341\) | −0.122031 | −0.00660836 | ||||||||
\(342\) | 6.30507 | − | 10.9207i | 0.340939 | − | 0.590524i | ||||
\(343\) | −15.9351 | + | 9.43778i | −0.860416 | + | 0.509592i | ||||
\(344\) | −0.767374 | + | 1.32913i | −0.0413740 | + | 0.0716619i | ||||
\(345\) | −14.3886 | − | 24.9217i | −0.774654 | − | 1.34174i | ||||
\(346\) | 12.6959 | + | 21.9899i | 0.682535 | + | 1.18219i | ||||
\(347\) | −12.1334 | −0.651357 | −0.325678 | − | 0.945481i | \(-0.605593\pi\) | ||||
−0.325678 | + | 0.945481i | \(0.605593\pi\) | |||||||
\(348\) | −1.07596 | −0.0576776 | ||||||||
\(349\) | 10.9086 | + | 18.8943i | 0.583924 | + | 1.01139i | 0.995009 | + | 0.0997893i | \(0.0318169\pi\) |
−0.411084 | + | 0.911597i | \(0.634850\pi\) | |||||||
\(350\) | 17.5152 | − | 48.6830i | 0.936229 | − | 2.60222i | ||||
\(351\) | 3.60075 | + | 0.185985i | 0.192194 | + | 0.00992715i | ||||
\(352\) | −0.901476 | + | 1.56140i | −0.0480488 | + | 0.0832230i | ||||
\(353\) | 6.04396 | − | 10.4684i | 0.321688 | − | 0.557179i | −0.659149 | − | 0.752013i | \(-0.729083\pi\) |
0.980836 | + | 0.194833i | \(0.0624166\pi\) | |||||||
\(354\) | 4.39663 | − | 7.61518i | 0.233678 | − | 0.404742i | ||||
\(355\) | 12.8158 | + | 22.1977i | 0.680194 | + | 1.17813i | ||||
\(356\) | −2.82631 | −0.149794 | ||||||||
\(357\) | 11.9824 | − | 2.15861i | 0.634176 | − | 0.114246i | ||||
\(358\) | −4.25192 | + | 7.36454i | −0.224721 | + | 0.389228i | ||||
\(359\) | −7.22027 | + | 12.5059i | −0.381071 | + | 0.660035i | −0.991216 | − | 0.132255i | \(-0.957778\pi\) |
0.610144 | + | 0.792290i | \(0.291111\pi\) | |||||||
\(360\) | 5.21231 | 0.274713 | ||||||||
\(361\) | −14.7729 | + | 25.5875i | −0.777523 | + | 1.34671i | ||||
\(362\) | −39.8860 | −2.09636 | ||||||||
\(363\) | −10.9178 | −0.573037 | ||||||||
\(364\) | 7.36628 | + | 9.68525i | 0.386098 | + | 0.507645i | ||||
\(365\) | 65.5838 | 3.43281 | ||||||||
\(366\) | 14.7838 | 0.772760 | ||||||||
\(367\) | −12.1894 | + | 21.1126i | −0.636280 | + | 1.10207i | 0.349963 | + | 0.936764i | \(0.386194\pi\) |
−0.986242 | + | 0.165305i | \(0.947139\pi\) | |||||||
\(368\) | 35.6431 | 1.85803 | ||||||||
\(369\) | −0.509885 | + | 0.883147i | −0.0265436 | + | 0.0459748i | ||||
\(370\) | −15.7004 | + | 27.1938i | −0.816223 | + | 1.41374i | ||||
\(371\) | 1.02865 | − | 2.85910i | 0.0534049 | − | 0.148437i | ||||
\(372\) | 0.543025 | 0.0281545 | ||||||||
\(373\) | 4.20017 | + | 7.27490i | 0.217476 | + | 0.376680i | 0.954036 | − | 0.299693i | \(-0.0968842\pi\) |
−0.736559 | + | 0.676373i | \(0.763551\pi\) | |||||||
\(374\) | −1.19372 | + | 2.06758i | −0.0617258 | + | 0.106912i | ||||
\(375\) | 11.5386 | − | 19.9854i | 0.595849 | − | 1.03204i | ||||
\(376\) | −3.55654 | + | 6.16011i | −0.183415 | + | 0.317684i | ||||
\(377\) | 1.38277 | + | 2.70879i | 0.0712163 | + | 0.139510i | ||||
\(378\) | 3.09151 | + | 3.65672i | 0.159010 | + | 0.188082i | ||||
\(379\) | −1.82895 | − | 3.16783i | −0.0939467 | − | 0.162720i | 0.815222 | − | 0.579149i | \(-0.196615\pi\) |
−0.909169 | + | 0.416428i | \(0.863282\pi\) | |||||||
\(380\) | 35.3328 | 1.81253 | ||||||||
\(381\) | 7.84345 | 0.401832 | ||||||||
\(382\) | −10.0424 | − | 17.3939i | −0.513812 | − | 0.889949i | ||||
\(383\) | 15.3526 | + | 26.5915i | 0.784481 | + | 1.35876i | 0.929308 | + | 0.369305i | \(0.120404\pi\) |
−0.144827 | + | 0.989457i | \(0.546263\pi\) | |||||||
\(384\) | −4.90037 | + | 8.48769i | −0.250071 | + | 0.433136i | ||||
\(385\) | 1.02072 | − | 2.83707i | 0.0520209 | − | 0.144590i | ||||
\(386\) | 0.440003 | − | 0.762108i | 0.0223956 | − | 0.0387903i | ||||
\(387\) | −1.17058 | −0.0595040 | ||||||||
\(388\) | 12.1466 | − | 21.0385i | 0.616649 | − | 1.06807i | ||||
\(389\) | −9.21889 | − | 15.9676i | −0.467416 | − | 0.809589i | 0.531890 | − | 0.846813i | \(-0.321482\pi\) |
−0.999307 | + | 0.0372241i | \(0.988148\pi\) | |||||||
\(390\) | 11.7950 | + | 23.1060i | 0.597264 | + | 1.17002i | ||||
\(391\) | 33.3106 | 1.68459 | ||||||||
\(392\) | 1.52669 | − | 9.04982i | 0.0771095 | − | 0.457085i | ||||
\(393\) | −4.04277 | − | 7.00228i | −0.203931 | − | 0.353218i | ||||
\(394\) | −15.4528 | − | 26.7650i | −0.778501 | − | 1.34840i | ||||
\(395\) | 15.2824 | + | 26.4699i | 0.768941 | + | 1.33184i | ||||
\(396\) | −0.365650 | −0.0183746 | ||||||||
\(397\) | 1.13032 | + | 1.95777i | 0.0567290 | + | 0.0982576i | 0.892995 | − | 0.450066i | \(-0.148600\pi\) |
−0.836266 | + | 0.548324i | \(0.815266\pi\) | |||||||
\(398\) | 41.9339 | 2.10196 | ||||||||
\(399\) | −11.9015 | − | 14.0775i | −0.595821 | − | 0.704754i | ||||
\(400\) | 26.6017 | + | 46.0755i | 1.33009 | + | 2.30378i | ||||
\(401\) | 28.5217 | 1.42431 | 0.712153 | − | 0.702024i | \(-0.247720\pi\) | ||||
0.712153 | + | 0.702024i | \(0.247720\pi\) | |||||||
\(402\) | −1.42424 | − | 2.46686i | −0.0710348 | − | 0.123036i | ||||
\(403\) | −0.697868 | − | 1.36709i | −0.0347633 | − | 0.0680998i | ||||
\(404\) | 5.79658 | − | 10.0400i | 0.288391 | − | 0.499507i | ||||
\(405\) | 1.98776 | + | 3.44291i | 0.0987727 | + | 0.171079i | ||||
\(406\) | −1.36738 | + | 3.80059i | −0.0678619 | + | 0.188620i | ||||
\(407\) | −0.625503 | + | 1.08340i | −0.0310051 | + | 0.0537023i | ||||
\(408\) | −3.01672 | + | 5.22512i | −0.149350 | + | 0.258682i | ||||
\(409\) | 10.8540 | 0.536695 | 0.268348 | − | 0.963322i | \(-0.413522\pi\) | ||||
0.268348 | + | 0.963322i | \(0.413522\pi\) | |||||||
\(410\) | −7.33738 | −0.362367 | ||||||||
\(411\) | −0.754841 | + | 1.30742i | −0.0372335 | + | 0.0644904i | ||||
\(412\) | 2.99022 | − | 5.17921i | 0.147318 | − | 0.255162i | ||||
\(413\) | −8.29912 | − | 9.81643i | −0.408373 | − | 0.483035i | ||||
\(414\) | 6.55039 | + | 11.3456i | 0.321934 | + | 0.557606i | ||||
\(415\) | 26.6137 | − | 46.0963i | 1.30642 | − | 2.26278i | ||||
\(416\) | −22.6474 | − | 1.16978i | −1.11038 | − | 0.0573531i | ||||
\(417\) | 2.02132 | + | 3.50104i | 0.0989846 | + | 0.171446i | ||||
\(418\) | 3.61475 | 0.176803 | ||||||||
\(419\) | −7.68279 | − | 13.3070i | −0.375329 | − | 0.650089i | 0.615047 | − | 0.788490i | \(-0.289137\pi\) |
−0.990376 | + | 0.138401i | \(0.955804\pi\) | |||||||
\(420\) | −4.54210 | + | 12.6246i | −0.221632 | + | 0.616019i | ||||
\(421\) | −3.33695 | −0.162633 | −0.0813166 | − | 0.996688i | \(-0.525912\pi\) | ||||
−0.0813166 | + | 0.996688i | \(0.525912\pi\) | |||||||
\(422\) | 2.54806 | + | 4.41337i | 0.124038 | + | 0.214839i | ||||
\(423\) | −5.42528 | −0.263786 | ||||||||
\(424\) | 0.752867 | + | 1.30400i | 0.0365625 | + | 0.0633281i | ||||
\(425\) | 24.8609 | + | 43.0603i | 1.20593 | + | 2.08873i | ||||
\(426\) | −5.83441 | − | 10.1055i | −0.282678 | − | 0.489613i | ||||
\(427\) | 7.31639 | − | 20.3357i | 0.354065 | − | 0.984112i | ||||
\(428\) | 18.5030 | 0.894377 | ||||||||
\(429\) | 0.469915 | + | 0.920543i | 0.0226877 | + | 0.0444442i | ||||
\(430\) | −4.21124 | − | 7.29408i | −0.203084 | − | 0.351752i | ||||
\(431\) | 2.13047 | − | 3.69008i | 0.102621 | − | 0.177745i | −0.810143 | − | 0.586233i | \(-0.800610\pi\) |
0.912764 | + | 0.408488i | \(0.133944\pi\) | |||||||
\(432\) | −4.92406 | −0.236909 | ||||||||
\(433\) | −5.56416 | + | 9.63741i | −0.267396 | + | 0.463144i | −0.968189 | − | 0.250221i | \(-0.919497\pi\) |
0.700792 | + | 0.713365i | \(0.252830\pi\) | |||||||
\(434\) | 0.690100 | − | 1.91811i | 0.0331259 | − | 0.0920722i | ||||
\(435\) | −1.67670 | + | 2.90412i | −0.0803914 | + | 0.139242i | ||||
\(436\) | 2.67481 | + | 4.63290i | 0.128100 | + | 0.221876i | ||||
\(437\) | −25.2173 | − | 43.6777i | −1.20631 | − | 2.08939i | ||||
\(438\) | −29.8570 | −1.42662 | ||||||||
\(439\) | 41.0024 | 1.95694 | 0.978470 | − | 0.206389i | \(-0.0661712\pi\) | ||||
0.978470 | + | 0.206389i | \(0.0661712\pi\) | |||||||
\(440\) | 0.747065 | + | 1.29395i | 0.0356149 | + | 0.0616869i | ||||
\(441\) | 6.55993 | − | 2.44280i | 0.312378 | − | 0.116324i | ||||
\(442\) | −29.9894 | − | 1.54900i | −1.42645 | − | 0.0736785i | ||||
\(443\) | −7.92693 | + | 13.7298i | −0.376620 | + | 0.652325i | −0.990568 | − | 0.137022i | \(-0.956247\pi\) |
0.613948 | + | 0.789346i | \(0.289580\pi\) | |||||||
\(444\) | 2.78342 | − | 4.82102i | 0.132095 | − | 0.228795i | ||||
\(445\) | −4.40431 | + | 7.62849i | −0.208784 | + | 0.361625i | ||||
\(446\) | −14.7726 | − | 25.5869i | −0.699504 | − | 1.21158i | ||||
\(447\) | −19.1947 | −0.907880 | ||||||||
\(448\) | −2.62239 | − | 3.10183i | −0.123896 | − | 0.146548i | ||||
\(449\) | −7.54997 | + | 13.0769i | −0.356305 | + | 0.617139i | −0.987340 | − | 0.158616i | \(-0.949297\pi\) |
0.631035 | + | 0.775754i | \(0.282630\pi\) | |||||||
\(450\) | −9.77756 | + | 16.9352i | −0.460919 | + | 0.798335i | ||||
\(451\) | −0.292322 | −0.0137649 | ||||||||
\(452\) | 5.25927 | − | 9.10933i | 0.247375 | − | 0.428467i | ||||
\(453\) | 18.9467 | 0.890192 | ||||||||
\(454\) | −11.2316 | −0.527123 | ||||||||
\(455\) | 37.6204 | − | 4.78954i | 1.76367 | − | 0.224537i | ||||
\(456\) | 9.13506 | 0.427789 | ||||||||
\(457\) | −0.0278479 | −0.00130267 | −0.000651335 | − | 1.00000i | \(-0.500207\pi\) | ||||
−0.000651335 | 1.00000i | \(0.500207\pi\) | ||||||||
\(458\) | 0.473210 | − | 0.819624i | 0.0221116 | − | 0.0382985i | ||||
\(459\) | −4.60182 | −0.214795 | ||||||||
\(460\) | −18.3537 | + | 31.7896i | −0.855747 | + | 1.48220i | ||||
\(461\) | 14.0543 | − | 24.3428i | 0.654575 | − | 1.13376i | −0.327425 | − | 0.944877i | \(-0.606181\pi\) |
0.982000 | − | 0.188880i | \(-0.0604859\pi\) | |||||||
\(462\) | −0.464684 | + | 1.29157i | −0.0216191 | + | 0.0600895i | ||||
\(463\) | −0.266538 | −0.0123871 | −0.00619354 | − | 0.999981i | \(-0.501971\pi\) | ||||
−0.00619354 | + | 0.999981i | \(0.501971\pi\) | |||||||
\(464\) | −2.07674 | − | 3.59702i | −0.0964104 | − | 0.166988i | ||||
\(465\) | 0.846208 | − | 1.46568i | 0.0392420 | − | 0.0679691i | ||||
\(466\) | −11.7328 | + | 20.3218i | −0.543511 | + | 0.941389i | ||||
\(467\) | −18.5400 | + | 32.1123i | −0.857931 | + | 1.48598i | 0.0159687 | + | 0.999872i | \(0.494917\pi\) |
−0.873899 | + | 0.486107i | \(0.838417\pi\) | |||||||
\(468\) | −2.09107 | − | 4.09631i | −0.0966595 | − | 0.189352i | ||||
\(469\) | −4.09811 | + | 0.738270i | −0.189233 | + | 0.0340901i | ||||
\(470\) | −19.5178 | − | 33.8058i | −0.900289 | − | 1.55935i | ||||
\(471\) | 18.6354 | 0.858674 | ||||||||
\(472\) | 6.37002 | 0.293204 | ||||||||
\(473\) | −0.167776 | − | 0.290597i | −0.00771436 | − | 0.0133617i | ||||
\(474\) | −6.95730 | − | 12.0504i | −0.319560 | − | 0.553493i | ||||
\(475\) | 37.6411 | − | 65.1964i | 1.72709 | − | 2.99141i | ||||
\(476\) | −10.0268 | − | 11.8600i | −0.459579 | − | 0.543603i | ||||
\(477\) | −0.574226 | + | 0.994589i | −0.0262920 | + | 0.0455391i | ||||
\(478\) | −8.68017 | −0.397022 | ||||||||
\(479\) | −14.3993 | + | 24.9404i | −0.657922 | + | 1.13955i | 0.323231 | + | 0.946320i | \(0.395231\pi\) |
−0.981153 | + | 0.193234i | \(0.938102\pi\) | |||||||
\(480\) | −12.5023 | − | 21.6546i | −0.570649 | − | 0.988394i | ||||
\(481\) | −15.7143 | − | 0.811669i | −0.716509 | − | 0.0370089i | ||||
\(482\) | 18.8578 | 0.858949 | ||||||||
\(483\) | 18.8481 | − | 3.39545i | 0.857616 | − | 0.154498i | ||||
\(484\) | 6.96327 | + | 12.0607i | 0.316512 | + | 0.548216i | ||||
\(485\) | −37.8566 | − | 65.5695i | −1.71898 | − | 2.97736i | ||||
\(486\) | −0.904928 | − | 1.56738i | −0.0410484 | − | 0.0710979i | ||||
\(487\) | −13.7303 | −0.622181 | −0.311090 | − | 0.950380i | \(-0.600694\pi\) | ||||
−0.311090 | + | 0.950380i | \(0.600694\pi\) | |||||||
\(488\) | 5.35484 | + | 9.27486i | 0.242402 | + | 0.419853i | ||||
\(489\) | 10.7052 | 0.484108 | ||||||||
\(490\) | 38.8213 | + | 32.0879i | 1.75377 | + | 1.44958i | ||||
\(491\) | 13.7632 | + | 23.8386i | 0.621126 | + | 1.07582i | 0.989276 | + | 0.146056i | \(0.0466579\pi\) |
−0.368150 | + | 0.929766i | \(0.620009\pi\) | |||||||
\(492\) | 1.30080 | 0.0586445 | ||||||||
\(493\) | −1.94084 | − | 3.36163i | −0.0874110 | − | 0.151400i | ||||
\(494\) | 20.6719 | + | 40.4954i | 0.930073 | + | 1.82197i | ||||
\(495\) | −0.569801 | + | 0.986924i | −0.0256106 | + | 0.0443589i | ||||
\(496\) | 1.04811 | + | 1.81537i | 0.0470614 | + | 0.0815127i | ||||
\(497\) | −16.7879 | + | 3.02432i | −0.753041 | + | 0.135659i | ||||
\(498\) | −12.1159 | + | 20.9853i | −0.542925 | + | 0.940375i | ||||
\(499\) | 1.94567 | − | 3.37000i | 0.0871001 | − | 0.150862i | −0.819184 | − | 0.573531i | \(-0.805573\pi\) |
0.906284 | + | 0.422669i | \(0.138907\pi\) | |||||||
\(500\) | −29.4367 | −1.31645 | ||||||||
\(501\) | −0.0481240 | −0.00215002 | ||||||||
\(502\) | −9.24194 | + | 16.0075i | −0.412488 | + | 0.714450i | ||||
\(503\) | −1.87991 | + | 3.25610i | −0.0838212 | + | 0.145183i | −0.904888 | − | 0.425649i | \(-0.860046\pi\) |
0.821067 | + | 0.570832i | \(0.193379\pi\) | |||||||
\(504\) | −1.17433 | + | 3.26402i | −0.0523089 | + | 0.145391i | ||||
\(505\) | −18.0659 | − | 31.2910i | −0.803921 | − | 1.39243i | ||||
\(506\) | −1.87770 | + | 3.25227i | −0.0834738 | + | 0.144581i | ||||
\(507\) | −7.62534 | + | 10.5287i | −0.338653 | + | 0.467597i | ||||
\(508\) | −5.00247 | − | 8.66453i | −0.221949 | − | 0.384426i | ||||
\(509\) | −38.5481 | −1.70861 | −0.854307 | − | 0.519769i | \(-0.826018\pi\) | ||||
−0.854307 | + | 0.519769i | \(0.826018\pi\) | |||||||
\(510\) | −16.5554 | − | 28.6747i | −0.733084 | − | 1.26974i | ||||
\(511\) | −14.7760 | + | 41.0695i | −0.653653 | + | 1.81681i | ||||
\(512\) | 18.0587 | 0.798088 | ||||||||
\(513\) | 3.48374 | + | 6.03402i | 0.153811 | + | 0.266408i | ||||
\(514\) | −11.5158 | −0.507938 | ||||||||
\(515\) | −9.31946 | − | 16.1418i | −0.410664 | − | 0.711291i | ||||
\(516\) | 0.746584 | + | 1.29312i | 0.0328665 | + | 0.0569265i | ||||
\(517\) | −0.777591 | − | 1.34683i | −0.0341984 | − | 0.0592334i | ||||
\(518\) | −13.4919 | − | 15.9585i | −0.592798 | − | 0.701178i | ||||
\(519\) | −14.0297 | −0.615837 | ||||||||
\(520\) | −10.2236 | + | 15.7690i | −0.448336 | + | 0.691519i | ||||
\(521\) | −6.92277 | − | 11.9906i | −0.303292 | − | 0.525318i | 0.673587 | − | 0.739108i | \(-0.264753\pi\) |
−0.976880 | + | 0.213790i | \(0.931419\pi\) | |||||||
\(522\) | 0.763315 | − | 1.32210i | 0.0334094 | − | 0.0578667i | ||||
\(523\) | 20.0671 | 0.877472 | 0.438736 | − | 0.898616i | \(-0.355426\pi\) | ||||
0.438736 | + | 0.898616i | \(0.355426\pi\) | |||||||
\(524\) | −5.15687 | + | 8.93196i | −0.225279 | + | 0.390194i | ||||
\(525\) | 18.4562 | + | 21.8306i | 0.805496 | + | 0.952763i | ||||
\(526\) | 15.3960 | − | 26.6667i | 0.671299 | − | 1.16272i | ||||
\(527\) | 0.979519 | + | 1.69658i | 0.0426685 | + | 0.0739040i | ||||
\(528\) | −0.705751 | − | 1.22240i | −0.0307139 | − | 0.0531980i | ||||
\(529\) | 29.3969 | 1.27813 | ||||||||
\(530\) | −8.26326 | −0.358933 | ||||||||
\(531\) | 2.42927 | + | 4.20762i | 0.105421 | + | 0.182595i | ||||
\(532\) | −7.96047 | + | 22.1259i | −0.345130 | + | 0.959278i | ||||
\(533\) | −1.67172 | − | 3.27482i | −0.0724101 | − | 0.141848i | ||||
\(534\) | 2.00506 | − | 3.47287i | 0.0867674 | − | 0.150286i | ||||
\(535\) | 28.8337 | − | 49.9414i | 1.24659 | − | 2.15915i | ||||
\(536\) | 1.03175 | − | 1.78705i | 0.0445649 | − | 0.0771887i | ||||
\(537\) | −2.34931 | − | 4.06913i | −0.101380 | − | 0.175596i | ||||
\(538\) | −16.3980 | −0.706968 | ||||||||
\(539\) | 1.54664 | + | 1.27838i | 0.0666186 | + | 0.0550638i | ||||
\(540\) | 2.53555 | − | 4.39170i | 0.109113 | − | 0.188988i | ||||
\(541\) | −18.9415 | + | 32.8076i | −0.814357 | + | 1.41051i | 0.0954310 | + | 0.995436i | \(0.469577\pi\) |
−0.909788 | + | 0.415072i | \(0.863756\pi\) | |||||||
\(542\) | 4.03229 | 0.173202 | ||||||||
\(543\) | 11.0191 | − | 19.0857i | 0.472876 | − | 0.819044i | ||||
\(544\) | 28.9438 | 1.24096 | ||||||||
\(545\) | 16.6728 | 0.714186 | ||||||||
\(546\) | −17.1267 | + | 2.18044i | −0.732954 | + | 0.0933141i | ||||
\(547\) | 29.3783 | 1.25613 | 0.628063 | − | 0.778162i | \(-0.283848\pi\) | ||||
0.628063 | + | 0.778162i | \(0.283848\pi\) | |||||||
\(548\) | 1.92572 | 0.0822625 | ||||||||
\(549\) | −4.08424 | + | 7.07411i | −0.174311 | + | 0.301916i | ||||
\(550\) | −5.60556 | −0.239022 | ||||||||
\(551\) | −2.93857 | + | 5.08975i | −0.125187 | + | 0.216831i | ||||
\(552\) | −4.74524 | + | 8.21900i | −0.201971 | + | 0.349824i | ||||
\(553\) | −20.0189 | + | 3.60638i | −0.851291 | + | 0.153359i | ||||
\(554\) | −14.1305 | −0.600349 | ||||||||
\(555\) | −8.67492 | − | 15.0254i | −0.368230 | − | 0.637793i | ||||
\(556\) | 2.57836 | − | 4.46584i | 0.109347 | − | 0.189394i | ||||
\(557\) | −0.513038 | + | 0.888609i | −0.0217381 | + | 0.0376516i | −0.876690 | − | 0.481056i | \(-0.840253\pi\) |
0.854952 | + | 0.518708i | \(0.173587\pi\) | |||||||
\(558\) | −0.385236 | + | 0.667248i | −0.0163083 | + | 0.0282469i | ||||
\(559\) | 2.29603 | − | 3.54142i | 0.0971117 | − | 0.149786i | ||||
\(560\) | −50.9720 | + | 9.18253i | −2.15396 | + | 0.388033i | ||||
\(561\) | −0.659567 | − | 1.14240i | −0.0278469 | − | 0.0482323i | ||||
\(562\) | −23.0814 | −0.973628 | ||||||||
\(563\) | −36.2249 | −1.52670 | −0.763348 | − | 0.645988i | \(-0.776446\pi\) | ||||
−0.763348 | + | 0.645988i | \(0.776446\pi\) | |||||||
\(564\) | 3.46019 | + | 5.99322i | 0.145700 | + | 0.252360i | ||||
\(565\) | −16.3913 | − | 28.3905i | −0.689587 | − | 1.19440i | ||||
\(566\) | −14.7900 | + | 25.6171i | −0.621671 | + | 1.07677i | ||||
\(567\) | −2.60384 | + | 0.469078i | −0.109351 | + | 0.0196994i | ||||
\(568\) | 4.22657 | − | 7.32064i | 0.177343 | − | 0.307167i | ||||
\(569\) | 2.83671 | 0.118921 | 0.0594605 | − | 0.998231i | \(-0.481062\pi\) | ||||
0.0594605 | + | 0.998231i | \(0.481062\pi\) | |||||||
\(570\) | −25.0660 | + | 43.4155i | −1.04990 | + | 1.81848i | ||||
\(571\) | 2.29825 | + | 3.98069i | 0.0961789 | + | 0.166587i | 0.910100 | − | 0.414389i | \(-0.136005\pi\) |
−0.813921 | + | 0.580975i | \(0.802671\pi\) | |||||||
\(572\) | 0.717202 | − | 1.10622i | 0.0299877 | − | 0.0462534i | ||||
\(573\) | 11.0974 | 0.463602 | ||||||||
\(574\) | 1.65311 | − | 4.59477i | 0.0689995 | − | 0.191782i | ||||
\(575\) | 39.1057 | + | 67.7330i | 1.63082 | + | 2.82466i | ||||
\(576\) | 0.767610 | + | 1.32954i | 0.0319837 | + | 0.0553975i | ||||
\(577\) | 8.75176 | + | 15.1585i | 0.364341 | + | 0.631056i | 0.988670 | − | 0.150105i | \(-0.0479611\pi\) |
−0.624329 | + | 0.781161i | \(0.714628\pi\) | |||||||
\(578\) | 7.55939 | 0.314429 | ||||||||
\(579\) | 0.243115 | + | 0.421088i | 0.0101035 | + | 0.0174998i | ||||
\(580\) | 4.27751 | 0.177614 | ||||||||
\(581\) | 22.8701 | + | 27.0514i | 0.948810 | + | 1.12228i | ||||
\(582\) | 17.2342 | + | 29.8505i | 0.714380 | + | 1.23734i | ||||
\(583\) | −0.329209 | −0.0136344 | ||||||||
\(584\) | −10.8145 | − | 18.7313i | −0.447509 | − | 0.775108i | ||||
\(585\) | −14.3149 | − | 0.739388i | −0.591847 | − | 0.0305699i | ||||
\(586\) | 21.4140 | − | 37.0902i | 0.884606 | − | 1.53218i | ||||
\(587\) | −0.671155 | − | 1.16247i | −0.0277015 | − | 0.0479805i | 0.851842 | − | 0.523798i | \(-0.175485\pi\) |
−0.879544 | + | 0.475818i | \(0.842152\pi\) | |||||||
\(588\) | −6.88238 | − | 5.68865i | −0.283824 | − | 0.234596i | ||||
\(589\) | 1.48306 | − | 2.56874i | 0.0611084 | − | 0.105843i | ||||
\(590\) | −17.4789 | + | 30.2743i | −0.719595 | + | 1.24638i | ||||
\(591\) | 17.0763 | 0.702424 | ||||||||
\(592\) | 21.4894 | 0.883209 | ||||||||
\(593\) | 22.0843 | − | 38.2512i | 0.906895 | − | 1.57079i | 0.0885427 | − | 0.996072i | \(-0.471779\pi\) |
0.818353 | − | 0.574716i | \(-0.194888\pi\) | |||||||
\(594\) | 0.259402 | − | 0.449297i | 0.0106434 | − | 0.0184349i | ||||
\(595\) | −47.6363 | + | 8.58162i | −1.95290 | + | 0.351812i | ||||
\(596\) | 12.2422 | + | 21.2041i | 0.501460 | + | 0.868554i | ||||
\(597\) | −11.5849 | + | 20.0656i | −0.474138 | + | 0.821230i | ||||
\(598\) | −47.1726 | − | 2.43655i | −1.92903 | − | 0.0996378i | ||||
\(599\) | 8.46583 | + | 14.6632i | 0.345904 | + | 0.599124i | 0.985518 | − | 0.169573i | \(-0.0542388\pi\) |
−0.639613 | + | 0.768697i | \(0.720905\pi\) | |||||||
\(600\) | −14.1662 | −0.578331 | ||||||||
\(601\) | 7.56311 | + | 13.0997i | 0.308506 | + | 0.534348i | 0.978036 | − | 0.208437i | \(-0.0668378\pi\) |
−0.669530 | + | 0.742785i | \(0.733504\pi\) | |||||||
\(602\) | 5.51645 | − | 0.993781i | 0.224834 | − | 0.0405035i | ||||
\(603\) | 1.57387 | 0.0640931 | ||||||||
\(604\) | −12.0840 | − | 20.9301i | −0.491690 | − | 0.851633i | ||||
\(605\) | 43.4041 | 1.76463 | ||||||||
\(606\) | 8.22448 | + | 14.2452i | 0.334097 | + | 0.578673i | ||||
\(607\) | −23.8620 | − | 41.3301i | −0.968527 | − | 1.67754i | −0.699825 | − | 0.714314i | \(-0.746739\pi\) |
−0.268701 | − | 0.963224i | \(-0.586594\pi\) | |||||||
\(608\) | −21.9115 | − | 37.9518i | −0.888628 | − | 1.53915i | ||||
\(609\) | −1.44084 | − | 1.70427i | −0.0583858 | − | 0.0690604i | ||||
\(610\) | −58.7733 | −2.37966 | ||||||||
\(611\) | 10.6414 | − | 16.4134i | 0.430505 | − | 0.664014i | ||||
\(612\) | 2.93499 | + | 5.08356i | 0.118640 | + | 0.205491i | ||||
\(613\) | −11.9854 | + | 20.7593i | −0.484086 | + | 0.838462i | −0.999833 | − | 0.0182791i | \(-0.994181\pi\) |
0.515747 | + | 0.856741i | \(0.327515\pi\) | |||||||
\(614\) | 16.2831 | 0.657133 | ||||||||
\(615\) | 2.02706 | − | 3.51097i | 0.0817390 | − | 0.141576i | ||||
\(616\) | −0.978606 | + | 0.176295i | −0.0394292 | + | 0.00710311i | ||||
\(617\) | −1.41810 | + | 2.45623i | −0.0570907 | + | 0.0988839i | −0.893158 | − | 0.449743i | \(-0.851516\pi\) |
0.836068 | + | 0.548626i | \(0.184849\pi\) | |||||||
\(618\) | 4.24268 | + | 7.34853i | 0.170666 | + | 0.295601i | ||||
\(619\) | 0.658494 | + | 1.14055i | 0.0264671 | + | 0.0458424i | 0.878956 | − | 0.476904i | \(-0.158241\pi\) |
−0.852488 | + | 0.522746i | \(0.824908\pi\) | |||||||
\(620\) | −2.15881 | −0.0866999 | ||||||||
\(621\) | −7.23857 | −0.290474 | ||||||||
\(622\) | 27.9619 | + | 48.4314i | 1.12117 | + | 1.94192i | ||||
\(623\) | −3.78477 | − | 4.47674i | −0.151634 | − | 0.179357i | ||||
\(624\) | 9.65826 | − | 14.8970i | 0.386640 | − | 0.596357i | ||||
\(625\) | −18.8598 | + | 32.6662i | −0.754393 | + | 1.30665i | ||||
\(626\) | 6.77926 | − | 11.7420i | 0.270954 | − | 0.469305i | ||||
\(627\) | −0.998630 | + | 1.72968i | −0.0398814 | + | 0.0690767i | ||||
\(628\) | −11.8855 | − | 20.5862i | −0.474281 | − | 0.821479i | ||||
\(629\) | 20.0831 | 0.800766 | ||||||||
\(630\) | −12.2904 | − | 14.5374i | −0.489660 | − | 0.579184i | ||||
\(631\) | −11.5676 | + | 20.0356i | −0.460497 | + | 0.797604i | −0.998986 | − | 0.0450286i | \(-0.985662\pi\) |
0.538489 | + | 0.842633i | \(0.318995\pi\) | |||||||
\(632\) | 5.04002 | − | 8.72957i | 0.200481 | − | 0.347244i | ||||
\(633\) | −2.81576 | −0.111916 | ||||||||
\(634\) | 14.6852 | − | 25.4355i | 0.583224 | − | 1.01017i | ||||
\(635\) | −31.1818 | −1.23741 | ||||||||
\(636\) | 1.46494 | 0.0580887 | ||||||||
\(637\) | −5.47660 | + | 24.6375i | −0.216991 | + | 0.976174i | ||||
\(638\) | 0.437615 | 0.0173253 | ||||||||
\(639\) | 6.44737 | 0.255054 | ||||||||
\(640\) | 19.4816 | − | 33.7430i | 0.770076 | − | 1.33381i | ||||
\(641\) | −36.6525 | −1.44769 | −0.723843 | − | 0.689965i | \(-0.757626\pi\) | ||||
−0.723843 | + | 0.689965i | \(0.757626\pi\) | |||||||
\(642\) | −13.1265 | + | 22.7358i | −0.518062 | + | 0.897310i | ||||
\(643\) | −1.86917 | + | 3.23749i | −0.0737127 | + | 0.127674i | −0.900526 | − | 0.434803i | \(-0.856818\pi\) |
0.826813 | + | 0.562477i | \(0.190151\pi\) | |||||||
\(644\) | −15.7720 | − | 18.6556i | −0.621503 | − | 0.735132i | ||||
\(645\) | 4.65368 | 0.183238 | ||||||||
\(646\) | −29.0148 | − | 50.2552i | −1.14157 | − | 1.97726i | ||||
\(647\) | 0.763093 | − | 1.32172i | 0.0300003 | − | 0.0519620i | −0.850635 | − | 0.525756i | \(-0.823783\pi\) |
0.880636 | + | 0.473794i | \(0.157116\pi\) | |||||||
\(648\) | 0.655549 | − | 1.13544i | 0.0257524 | − | 0.0446045i | ||||
\(649\) | −0.696361 | + | 1.20613i | −0.0273345 | + | 0.0473448i | ||||
\(650\) | −32.0569 | − | 62.7981i | −1.25737 | − | 2.46314i | ||||
\(651\) | 0.727175 | + | 0.860123i | 0.0285002 | + | 0.0337109i | ||||
\(652\) | −6.82769 | − | 11.8259i | −0.267393 | − | 0.463138i | ||||
\(653\) | 8.95092 | 0.350277 | 0.175138 | − | 0.984544i | \(-0.443963\pi\) | ||||
0.175138 | + | 0.984544i | \(0.443963\pi\) | |||||||
\(654\) | −7.59031 | −0.296804 | ||||||||
\(655\) | 16.0721 | + | 27.8377i | 0.627990 | + | 1.08771i | ||||
\(656\) | 2.51070 | + | 4.34867i | 0.0980265 | + | 0.169787i | ||||
\(657\) | 8.24845 | − | 14.2867i | 0.321803 | − | 0.557379i | ||||
\(658\) | 25.5670 | − | 4.60587i | 0.996707 | − | 0.179555i | ||||
\(659\) | 4.30599 | − | 7.45819i | 0.167737 | − | 0.290530i | −0.769887 | − | 0.638181i | \(-0.779687\pi\) |
0.937624 | + | 0.347651i | \(0.113021\pi\) | |||||||
\(660\) | 1.45365 | 0.0565833 | ||||||||
\(661\) | 20.0392 | − | 34.7088i | 0.779433 | − | 1.35002i | −0.152837 | − | 0.988251i | \(-0.548841\pi\) |
0.932269 | − | 0.361765i | \(-0.117826\pi\) | |||||||
\(662\) | −5.05343 | − | 8.75279i | −0.196407 | − | 0.340187i | ||||
\(663\) | 9.02622 | − | 13.9221i | 0.350549 | − | 0.540691i | ||||
\(664\) | −17.5540 | −0.681228 | ||||||||
\(665\) | 47.3148 | + | 55.9653i | 1.83479 | + | 2.17024i | ||||
\(666\) | 3.94925 | + | 6.84031i | 0.153031 | + | 0.265057i | ||||
\(667\) | −3.05290 | − | 5.28778i | −0.118209 | − | 0.204744i | ||||
\(668\) | 0.0306930 | + | 0.0531618i | 0.00118755 | + | 0.00205689i | ||||
\(669\) | 16.3246 | 0.631147 | ||||||||
\(670\) | 5.66211 | + | 9.80707i | 0.218747 | + | 0.378880i | ||||
\(671\) | −2.34153 | −0.0903938 | ||||||||
\(672\) | 16.3772 | − | 2.95033i | 0.631764 | − | 0.113811i | ||||
\(673\) | −22.0131 | − | 38.1277i | −0.848541 | − | 1.46972i | −0.882510 | − | 0.470294i | \(-0.844148\pi\) |
0.0339689 | − | 0.999423i | \(-0.489185\pi\) | |||||||
\(674\) | −0.912342 | −0.0351421 | ||||||||
\(675\) | −5.40240 | − | 9.35723i | −0.207938 | − | 0.360160i | ||||
\(676\) | 16.4943 | + | 1.70847i | 0.634395 | + | 0.0657105i | ||||
\(677\) | −12.0556 | + | 20.8809i | −0.463334 | + | 0.802518i | −0.999125 | − | 0.0418328i | \(-0.986680\pi\) |
0.535791 | + | 0.844351i | \(0.320014\pi\) | |||||||
\(678\) | 7.46213 | + | 12.9248i | 0.286581 | + | 0.496373i | ||||
\(679\) | 49.5896 | − | 8.93350i | 1.90307 | − | 0.342836i | ||||
\(680\) | 11.9931 | − | 20.7726i | 0.459913 | − | 0.796592i | ||||
\(681\) | 3.10289 | − | 5.37436i | 0.118903 | − | 0.205946i | ||||
\(682\) | −0.220859 | −0.00845713 | ||||||||
\(683\) | −18.5855 | −0.711155 | −0.355578 | − | 0.934647i | \(-0.615716\pi\) | ||||
−0.355578 | + | 0.934647i | \(0.615716\pi\) | |||||||
\(684\) | 4.44379 | − | 7.69686i | 0.169912 | − | 0.294297i | ||||
\(685\) | 3.00089 | − | 5.19769i | 0.114658 | − | 0.198594i | ||||
\(686\) | −28.8403 | + | 17.0810i | −1.10113 | + | 0.652157i | ||||
\(687\) | 0.261463 | + | 0.452867i | 0.00997543 | + | 0.0172779i | ||||
\(688\) | −2.88201 | + | 4.99178i | −0.109875 | + | 0.190310i | ||||
\(689\) | −1.88267 | − | 3.68807i | −0.0717239 | − | 0.140504i | ||||
\(690\) | −26.0412 | − | 45.1047i | −0.991372 | − | 1.71711i | ||||
\(691\) | −22.6374 | −0.861166 | −0.430583 | − | 0.902551i | \(-0.641692\pi\) | ||||
−0.430583 | + | 0.902551i | \(0.641692\pi\) | |||||||
\(692\) | 8.94801 | + | 15.4984i | 0.340152 | + | 0.589161i | ||||
\(693\) | −0.489649 | − | 0.579171i | −0.0186002 | − | 0.0220009i | ||||
\(694\) | −21.9598 | −0.833581 | ||||||||
\(695\) | −8.03582 | − | 13.9185i | −0.304816 | − | 0.527957i | ||||
\(696\) | 1.10592 | 0.0419199 | ||||||||
\(697\) | 2.34640 | + | 4.06409i | 0.0888763 | + | 0.153938i | ||||
\(698\) | 19.7430 | + | 34.1959i | 0.747284 | + | 1.29433i | ||||
\(699\) | −6.48273 | − | 11.2284i | −0.245199 | − | 0.424697i | ||||
\(700\) | 12.3447 | − | 34.3116i | 0.466584 | − | 1.29686i | ||||
\(701\) | 50.1432 | 1.89388 | 0.946941 | − | 0.321407i | \(-0.104156\pi\) | ||||
0.946941 | + | 0.321407i | \(0.104156\pi\) | |||||||
\(702\) | 6.51684 | + | 0.336606i | 0.245962 | + | 0.0127044i | ||||
\(703\) | −15.2036 | − | 26.3335i | −0.573416 | − | 0.993185i | ||||
\(704\) | −0.220039 | + | 0.381118i | −0.00829302 | + | 0.0143639i | ||||
\(705\) | 21.5684 | 0.812311 | ||||||||
\(706\) | 10.9387 | − | 18.9464i | 0.411683 | − | 0.713056i | ||||
\(707\) | 23.6651 | − | 4.26324i | 0.890018 | − | 0.160336i | ||||
\(708\) | 3.09872 | − | 5.36715i | 0.116457 | − | 0.201710i | ||||
\(709\) | 14.8556 | + | 25.7306i | 0.557913 | + | 0.966334i | 0.997670 | + | 0.0682172i | \(0.0217311\pi\) |
−0.439757 | + | 0.898117i | \(0.644936\pi\) | |||||||
\(710\) | 23.1948 | + | 40.1746i | 0.870487 | + | 1.50773i | ||||
\(711\) | 7.68824 | 0.288332 | ||||||||
\(712\) | 2.90502 | 0.108870 | ||||||||
\(713\) | 1.54076 | + | 2.66868i | 0.0577020 | + | 0.0999428i | ||||
\(714\) | 21.6864 | − | 3.90678i | 0.811594 | − | 0.146208i | ||||
\(715\) | −1.86816 | − | 3.65964i | −0.0698651 | − | 0.136863i | ||||
\(716\) | −2.99673 | + | 5.19049i | −0.111993 | + | 0.193978i | ||||
\(717\) | 2.39803 | − | 4.15351i | 0.0895560 | − | 0.155116i | ||||
\(718\) | −13.0677 | + | 22.6338i | −0.487681 | + | 0.844687i | ||||
\(719\) | 14.9346 | + | 25.8675i | 0.556968 | + | 0.964697i | 0.997748 | + | 0.0670813i | \(0.0213687\pi\) |
−0.440780 | + | 0.897615i | \(0.645298\pi\) | |||||||
\(720\) | 19.5757 | 0.729544 | ||||||||
\(721\) | 12.2079 | − | 2.19923i | 0.454645 | − | 0.0819037i | ||||
\(722\) | −26.7369 | + | 46.3096i | −0.995044 | + | 1.72347i | ||||
\(723\) | −5.20975 | + | 9.02355i | −0.193753 | + | 0.335589i | ||||
\(724\) | −28.1115 | −1.04476 | ||||||||
\(725\) | 4.55697 | − | 7.89291i | 0.169242 | − | 0.293135i | ||||
\(726\) | −19.7597 | −0.733351 | ||||||||
\(727\) | 36.0210 | 1.33594 | 0.667972 | − | 0.744186i | \(-0.267163\pi\) | ||||
0.667972 | + | 0.744186i | \(0.267163\pi\) | |||||||
\(728\) | −7.57141 | − | 9.95495i | −0.280615 | − | 0.368955i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 118.697 | 4.39318 | ||||||||
\(731\) | −2.69341 | + | 4.66512i | −0.0996192 | + | 0.172546i | ||||
\(732\) | 10.4195 | 0.385117 | ||||||||
\(733\) | 8.97642 | − | 15.5476i | 0.331552 | − | 0.574265i | −0.651265 | − | 0.758851i | \(-0.725761\pi\) |
0.982816 | + | 0.184586i | \(0.0590945\pi\) | |||||||
\(734\) | −22.0610 | + | 38.2108i | −0.814286 | + | 1.41038i | ||||
\(735\) | −26.0792 | + | 9.71143i | −0.961945 | + | 0.358211i | ||||
\(736\) | 45.5280 | 1.67818 | ||||||||
\(737\) | 0.225579 | + | 0.390714i | 0.00830931 | + | 0.0143921i | ||||
\(738\) | −0.922819 | + | 1.59837i | −0.0339694 | + | 0.0588368i | ||||
\(739\) | −22.2469 | + | 38.5328i | −0.818366 | + | 1.41745i | 0.0885201 | + | 0.996074i | \(0.471786\pi\) |
−0.906886 | + | 0.421377i | \(0.861547\pi\) | |||||||
\(740\) | −11.0655 | + | 19.1661i | −0.406777 | + | 0.704559i | ||||
\(741\) | −25.0882 | − | 1.29585i | −0.921637 | − | 0.0476042i | ||||
\(742\) | 1.86171 | − | 5.17457i | 0.0683456 | − | 0.189964i | ||||
\(743\) | −10.7390 | − | 18.6004i | −0.393975 | − | 0.682384i | 0.598995 | − | 0.800753i | \(-0.295567\pi\) |
−0.992970 | + | 0.118368i | \(0.962234\pi\) | |||||||
\(744\) | −0.558146 | −0.0204626 | ||||||||
\(745\) | 76.3092 | 2.79575 | ||||||||
\(746\) | 7.60169 | + | 13.1665i | 0.278318 | + | 0.482061i | ||||
\(747\) | −6.69439 | − | 11.5950i | −0.244935 | − | 0.424240i | ||||
\(748\) | −0.841329 | + | 1.45722i | −0.0307620 | + | 0.0532814i | ||||
\(749\) | 24.7777 | + | 29.3078i | 0.905359 | + | 1.07088i | ||||
\(750\) | 20.8831 | − | 36.1706i | 0.762544 | − | 1.32077i | ||||
\(751\) | 3.20035 | 0.116783 | 0.0583913 | − | 0.998294i | \(-0.481403\pi\) | ||||
0.0583913 | + | 0.998294i | \(0.481403\pi\) | |||||||
\(752\) | −13.3572 | + | 23.1354i | −0.487087 | + | 0.843660i | ||||
\(753\) | −5.10645 | − | 8.84463i | −0.186089 | − | 0.322316i | ||||
\(754\) | 2.50262 | + | 4.90252i | 0.0911399 | + | 0.178539i | ||||
\(755\) | −75.3230 | −2.74128 | ||||||||
\(756\) | 2.17888 | + | 2.57724i | 0.0792451 | + | 0.0937334i | ||||
\(757\) | −12.8640 | − | 22.2811i | −0.467550 | − | 0.809821i | 0.531762 | − | 0.846894i | \(-0.321530\pi\) |
−0.999313 | + | 0.0370727i | \(0.988197\pi\) | |||||||
\(758\) | −3.31013 | − | 5.73331i | −0.120229 | − | 0.208243i | ||||
\(759\) | −1.03748 | − | 1.79698i | −0.0376583 | − | 0.0652261i | ||||
\(760\) | −36.3167 | −1.31734 | ||||||||
\(761\) | −14.3748 | − | 24.8979i | −0.521087 | − | 0.902548i | −0.999699 | − | 0.0245222i | \(-0.992194\pi\) |
0.478613 | − | 0.878026i | \(-0.341140\pi\) | |||||||
\(762\) | 14.1955 | 0.514249 | ||||||||
\(763\) | −3.75639 | + | 10.4408i | −0.135990 | + | 0.377981i | ||||
\(764\) | −7.07782 | − | 12.2591i | −0.256066 | − | 0.443520i | ||||
\(765\) | 18.2947 | 0.661445 | ||||||||
\(766\) | 27.7860 | + | 48.1268i | 1.00395 | + | 1.73889i | ||||
\(767\) | −17.4944 | − | 0.903616i | −0.631686 | − | 0.0326277i | ||||
\(768\) | −10.4042 | + | 18.0206i | −0.375429 | + | 0.650262i | ||||
\(769\) | 8.98213 | + | 15.5575i | 0.323904 | + | 0.561018i | 0.981290 | − | 0.192536i | \(-0.0616712\pi\) |
−0.657386 | + | 0.753554i | \(0.728338\pi\) | |||||||
\(770\) | 1.84736 | − | 5.13469i | 0.0665744 | − | 0.185041i | ||||
\(771\) | 3.18140 | − | 5.51035i | 0.114575 | − | 0.198450i | ||||
\(772\) | 0.310112 | − | 0.537131i | 0.0111612 | − | 0.0193318i | ||||
\(773\) | 39.6652 | 1.42666 | 0.713329 | − | 0.700829i | \(-0.247187\pi\) | ||||
0.713329 | + | 0.700829i | \(0.247187\pi\) | |||||||
\(774\) | −2.11858 | −0.0761509 | ||||||||
\(775\) | −2.29985 | + | 3.98345i | −0.0826130 | + | 0.143090i | ||||
\(776\) | −12.4848 | + | 21.6243i | −0.448179 | + | 0.776269i | ||||
\(777\) | 11.3636 | − | 2.04713i | 0.407666 | − | 0.0734405i | ||||
\(778\) | −16.6849 | − | 28.8990i | −0.598182 | − | 1.03608i | ||||
\(779\) | 3.55262 | − | 6.15331i | 0.127286 | − | 0.220465i | ||||
\(780\) | 8.31308 | + | 16.2850i | 0.297656 | + | 0.583096i | ||||
\(781\) | 0.924084 | + | 1.60056i | 0.0330663 | + | 0.0572725i | ||||
\(782\) | 60.2875 | 2.15587 | ||||||||
\(783\) | 0.421754 | + | 0.730500i | 0.0150723 | + | 0.0261059i | ||||
\(784\) | 5.73375 | − | 33.9882i | 0.204777 | − | 1.21386i | ||||
\(785\) | −74.0855 | −2.64422 | ||||||||
\(786\) | −7.31683 | − | 12.6731i | −0.260983 | − | 0.452035i | ||||
\(787\) | −39.5666 | −1.41040 | −0.705199 | − | 0.709010i | \(-0.749142\pi\) | ||||
−0.705199 | + | 0.709010i | \(0.749142\pi\) | |||||||
\(788\) | −10.8911 | − | 18.8639i | −0.387978 | − | 0.671998i | ||||
\(789\) | 8.50677 | + | 14.7342i | 0.302849 | + | 0.524550i | ||||
\(790\) | 27.6589 | + | 47.9067i | 0.984061 | + | 1.70444i | ||||
\(791\) | 21.4715 | − | 3.86806i | 0.763439 | − | 0.137533i | ||||
\(792\) | 0.375832 | 0.0133546 | ||||||||
\(793\) | −13.3907 | − | 26.2317i | −0.475516 | − | 0.931516i | ||||
\(794\) | 2.04571 | + | 3.54328i | 0.0725996 | + | 0.125746i | ||||
\(795\) | 2.28285 | − | 3.95401i | 0.0809644 | − | 0.140234i | ||||
\(796\) | 29.5548 | 1.04754 | ||||||||
\(797\) | −9.72309 | + | 16.8409i | −0.344409 | + | 0.596535i | −0.985246 | − | 0.171142i | \(-0.945254\pi\) |
0.640837 | + | 0.767677i | \(0.278588\pi\) | |||||||
\(798\) | −21.5400 | − | 25.4782i | −0.762509 | − | 0.901917i | ||||
\(799\) | −12.4831 | + | 21.6214i | −0.441621 | + | 0.764909i | ||||
\(800\) | 33.9791 | + | 58.8536i | 1.20134 | + | 2.08079i | ||||
\(801\) | 1.10786 | + | 1.91886i | 0.0391442 | + | 0.0677997i | ||||
\(802\) | 51.6202 | 1.82277 | ||||||||
\(803\) | 4.72891 | 0.166880 | ||||||||
\(804\) | −1.00380 | − | 1.73863i | −0.0354013 | − | 0.0613168i | ||||
\(805\) | −74.9309 | + | 13.4987i | −2.64097 | + | 0.475767i | ||||
\(806\) | −1.26304 | − | 2.47424i | −0.0444887 | − | 0.0871515i | ||||
\(807\) | 4.53019 | − | 7.84653i | 0.159470 | − | 0.276211i | ||||
\(808\) | −5.95799 | + | 10.3195i | −0.209601 | + | 0.363040i | ||||
\(809\) | 8.65420 | − | 14.9895i | 0.304265 | − | 0.527003i | −0.672832 | − | 0.739795i | \(-0.734922\pi\) |
0.977098 | + | 0.212792i | \(0.0682557\pi\) | |||||||
\(810\) | 3.59756 | + | 6.23116i | 0.126405 | + | 0.218941i | ||||
\(811\) | −2.62646 | −0.0922275 | −0.0461138 | − | 0.998936i | \(-0.514684\pi\) | ||||
−0.0461138 | + | 0.998936i | \(0.514684\pi\) | |||||||
\(812\) | −0.963723 | + | 2.67864i | −0.0338200 | + | 0.0940017i | ||||
\(813\) | −1.11398 | + | 1.92947i | −0.0390690 | + | 0.0676696i | ||||
\(814\) | −1.13207 | + | 1.96080i | −0.0396791 | + | 0.0687262i | ||||
\(815\) | −42.5590 | −1.49078 | ||||||||
\(816\) | −11.3298 | + | 19.6238i | −0.396623 | + | 0.686971i | ||||
\(817\) | 8.15601 | 0.285343 | ||||||||
\(818\) | 19.6442 | 0.686842 | ||||||||
\(819\) | 3.68815 | − | 8.79759i | 0.128875 | − | 0.307413i | ||||
\(820\) | −5.17135 | −0.180591 | ||||||||
\(821\) | −32.3955 | −1.13061 | −0.565305 | − | 0.824882i | \(-0.691242\pi\) | ||||
−0.565305 | + | 0.824882i | \(0.691242\pi\) | |||||||
\(822\) | −1.36615 | + | 2.36625i | −0.0476501 | + | 0.0825323i | ||||
\(823\) | −41.0161 | −1.42973 | −0.714866 | − | 0.699261i | \(-0.753512\pi\) | ||||
−0.714866 | + | 0.699261i | \(0.753512\pi\) | |||||||
\(824\) | −3.07349 | + | 5.32344i | −0.107070 | + | 0.185451i | ||||
\(825\) | 1.54862 | − | 2.68229i | 0.0539161 | − | 0.0933854i | ||||
\(826\) | −15.0202 | − | 17.7663i | −0.522620 | − | 0.618170i | ||||
\(827\) | −44.2260 | −1.53789 | −0.768944 | − | 0.639316i | \(-0.779218\pi\) | ||||
−0.768944 | + | 0.639316i | \(0.779218\pi\) | |||||||
\(828\) | 4.61668 | + | 7.99633i | 0.160441 | + | 0.277892i | ||||
\(829\) | 2.74781 | − | 4.75935i | 0.0954354 | − | 0.165299i | −0.814355 | − | 0.580367i | \(-0.802909\pi\) |
0.909790 | + | 0.415068i | \(0.136242\pi\) | |||||||
\(830\) | 48.1670 | − | 83.4276i | 1.67190 | − | 2.89582i | ||||
\(831\) | 3.90377 | − | 6.76153i | 0.135420 | − | 0.234555i | ||||
\(832\) | −5.52794 | − | 0.285528i | −0.191647 | − | 0.00989890i | ||||
\(833\) | 5.35853 | − | 31.7640i | 0.185662 | − | 1.10056i | ||||
\(834\) | 3.65830 | + | 6.33637i | 0.126677 | + | 0.219411i | ||||
\(835\) | 0.191318 | 0.00662084 | ||||||||
\(836\) | 2.54766 | 0.0881127 | ||||||||
\(837\) | −0.212854 | − | 0.368675i | −0.00735732 | − | 0.0127433i | ||||
\(838\) | −13.9047 | − | 24.0837i | −0.480332 | − | 0.831959i | ||||
\(839\) | −21.4269 | + | 37.1125i | −0.739739 | + | 1.28127i | 0.212873 | + | 0.977080i | \(0.431718\pi\) |
−0.952612 | + | 0.304186i | \(0.901615\pi\) | |||||||
\(840\) | 4.66858 | − | 12.9762i | 0.161081 | − | 0.447721i | ||||
\(841\) | 14.1442 | − | 24.4986i | 0.487733 | − | 0.844778i | ||||
\(842\) | −6.03941 | −0.208132 | ||||||||
\(843\) | 6.37657 | − | 11.0445i | 0.219621 | − | 0.380394i | ||||
\(844\) | 1.79586 | + | 3.11052i | 0.0618160 | + | 0.107069i | ||||
\(845\) | 30.3147 | − | 41.8572i | 1.04286 | − | 1.43993i | ||||
\(846\) | −9.81898 | −0.337584 | ||||||||
\(847\) | −9.77894 | + | 27.1802i | −0.336008 | + | 0.933924i | ||||
\(848\) | 2.82752 | + | 4.89741i | 0.0970975 | + | 0.168178i | ||||
\(849\) | −8.17193 | − | 14.1542i | −0.280460 | − | 0.485771i | ||||
\(850\) | 44.9946 | + | 77.9330i | 1.54330 | + | 2.67308i | ||||
\(851\) | 31.5903 | 1.08290 | ||||||||
\(852\) | −4.11206 | − | 7.12230i | −0.140877 | − | 0.244006i | ||||
\(853\) | −46.0876 | −1.57801 | −0.789004 | − | 0.614388i | \(-0.789403\pi\) | ||||
−0.789004 | + | 0.614388i | \(0.789403\pi\) | |||||||
\(854\) | 13.2416 | − | 36.8046i | 0.453118 | − | 1.25943i | ||||
\(855\) | −13.8497 | − | 23.9884i | −0.473650 | − | 0.820386i | ||||
\(856\) | −19.0183 | −0.650031 | ||||||||
\(857\) | 3.33662 | + | 5.77919i | 0.113977 | + | 0.197413i | 0.917370 | − | 0.398035i | \(-0.130308\pi\) |
−0.803394 | + | 0.595448i | \(0.796974\pi\) | |||||||
\(858\) | 0.850478 | + | 1.66605i | 0.0290348 | + | 0.0568780i | ||||
\(859\) | 8.20940 | − | 14.2191i | 0.280101 | − | 0.485149i | −0.691308 | − | 0.722560i | \(-0.742965\pi\) |
0.971409 | + | 0.237411i | \(0.0762987\pi\) | |||||||
\(860\) | −2.96806 | − | 5.14084i | −0.101210 | − | 0.175301i | ||||
\(861\) | 1.74192 | + | 2.06039i | 0.0593646 | + | 0.0702181i | ||||
\(862\) | 3.85584 | − | 6.67851i | 0.131330 | − | 0.227471i | ||||
\(863\) | 4.92500 | − | 8.53035i | 0.167649 | − | 0.290377i | −0.769944 | − | 0.638112i | \(-0.779716\pi\) |
0.937593 | + | 0.347735i | \(0.113049\pi\) | |||||||
\(864\) | −6.28963 | −0.213978 | ||||||||
\(865\) | 55.7755 | 1.89643 | ||||||||
\(866\) | −10.0703 | + | 17.4423i | −0.342204 | + | 0.592714i | ||||
\(867\) | −2.08840 | + | 3.61721i | −0.0709256 | + | 0.122847i | ||||
\(868\) | 0.486379 | − | 1.35188i | 0.0165088 | − | 0.0458856i | ||||
\(869\) | 1.10193 | + | 1.90861i | 0.0373805 | + | 0.0647450i | ||||
\(870\) | −3.03458 | + | 5.25604i | −0.102882 | + | 0.178196i | ||||
\(871\) | −3.08707 | + | 4.76152i | −0.104601 | + | 0.161338i | ||||
\(872\) | −2.74929 | − | 4.76191i | −0.0931027 | − | 0.161259i | ||||
\(873\) | −19.0448 | −0.644569 | ||||||||
\(874\) | −45.6397 | − | 79.0503i | −1.54379 | − | 2.67392i | ||||
\(875\) | −39.4192 | − | 46.6262i | −1.33261 | − | 1.57625i | ||||
\(876\) | −21.0431 | −0.710980 | ||||||||
\(877\) | −3.02056 | − | 5.23177i | −0.101997 | − | 0.176664i | 0.810510 | − | 0.585724i | \(-0.199190\pi\) |
−0.912507 | + | 0.409060i | \(0.865857\pi\) | |||||||
\(878\) | 74.2085 | 2.50442 | ||||||||
\(879\) | 11.8319 | + | 20.4935i | 0.399080 | + | 0.691227i | ||||
\(880\) | 2.80573 | + | 4.85967i | 0.0945812 | + | 0.163819i | ||||
\(881\) | 15.5861 | + | 26.9959i | 0.525109 | + | 0.909516i | 0.999572 | + | 0.0292404i | \(0.00930885\pi\) |
−0.474463 | + | 0.880275i | \(0.657358\pi\) | |||||||
\(882\) | 11.8725 | − | 4.42112i | 0.399769 | − | 0.148867i | ||||
\(883\) | −18.2205 | −0.613169 | −0.306584 | − | 0.951844i | \(-0.599186\pi\) | ||||
−0.306584 | + | 0.951844i | \(0.599186\pi\) | |||||||
\(884\) | −21.1364 | − | 1.09173i | −0.710893 | − | 0.0367189i | ||||
\(885\) | −9.65762 | − | 16.7275i | −0.324637 | − | 0.562288i | ||||
\(886\) | −14.3466 | + | 24.8490i | −0.481984 | + | 0.834820i | ||||
\(887\) | 7.41684 | 0.249033 | 0.124517 | − | 0.992218i | \(-0.460262\pi\) | ||||
0.124517 | + | 0.992218i | \(0.460262\pi\) | |||||||
\(888\) | −2.86093 | + | 4.95527i | −0.0960064 | + | 0.166288i | ||||
\(889\) | 7.02526 | − | 19.5265i | 0.235620 | − | 0.654898i | ||||
\(890\) | −7.97117 | + | 13.8065i | −0.267194 | + | 0.462794i | ||||
\(891\) | 0.143327 | + | 0.248250i | 0.00480164 | + | 0.00831669i | ||||
\(892\) | −10.4117 | − | 18.0336i | −0.348609 | − | 0.603808i | ||||
\(893\) | 37.8006 | 1.26495 | ||||||||
\(894\) | −34.7397 | −1.16187 | ||||||||
\(895\) | 9.33975 | + | 16.1769i | 0.312194 | + | 0.540735i | ||||
\(896\) | 16.7412 | + | 19.8019i | 0.559283 | + | 0.661535i | ||||
\(897\) | 14.1980 | − | 21.8992i | 0.474059 | − | 0.731193i | ||||
\(898\) | −13.6644 | + | 23.6674i | −0.455986 | + | 0.789790i | ||||
\(899\) | 0.179545 | − | 0.310980i | 0.00598815 | − | 0.0103718i | ||||
\(900\) | −6.89118 | + | 11.9359i | −0.229706 | + | 0.397863i | ||||
\(901\) | 2.64249 | + | 4.57692i | 0.0880341 | + | 0.152479i | ||||
\(902\) | −0.529060 | −0.0176158 | ||||||||
\(903\) | −1.04847 | + | 2.91420i | −0.0348910 | + | 0.0969783i | ||||
\(904\) | −5.40573 | + | 9.36299i | −0.179792 | + | 0.311409i | ||||
\(905\) | −43.8068 | + | 75.8756i | −1.45619 | + | 2.52219i | ||||
\(906\) | 34.2907 | 1.13923 | ||||||||
\(907\) | 8.70718 | − | 15.0813i | 0.289117 | − | 0.500766i | −0.684482 | − | 0.729030i | \(-0.739972\pi\) |
0.973599 | + | 0.228264i | \(0.0733049\pi\) | |||||||
\(908\) | −7.91595 | −0.262700 | ||||||||
\(909\) | −9.08855 | −0.301448 | ||||||||
\(910\) | 68.0876 | − | 8.66839i | 2.25708 | − | 0.287354i | ||||
\(911\) | −40.5753 | −1.34432 | −0.672159 | − | 0.740407i | \(-0.734633\pi\) | ||||
−0.672159 | + | 0.740407i | \(0.734633\pi\) | |||||||
\(912\) | 34.3083 | 1.13606 | ||||||||
\(913\) | 1.91898 | − | 3.32376i | 0.0635088 | − | 0.110001i | ||||
\(914\) | −0.0504007 | −0.00166711 | ||||||||
\(915\) | 16.2370 | − | 28.1233i | 0.536779 | − | 0.929728i | ||||
\(916\) | 0.333516 | − | 0.577667i | 0.0110197 | − | 0.0190867i | ||||
\(917\) | −21.0534 | + | 3.79275i | −0.695245 | + | 0.125247i | ||||
\(918\) | −8.32864 | −0.274886 | ||||||||
\(919\) | 24.2733 | + | 42.0426i | 0.800702 | + | 1.38686i | 0.919154 | + | 0.393898i | \(0.128874\pi\) |
−0.118452 | + | 0.992960i | \(0.537793\pi\) | |||||||
\(920\) | 18.8648 | − | 32.6748i | 0.621955 | − | 1.07726i | ||||
\(921\) | −4.49845 | + | 7.79155i | −0.148229 | + | 0.256740i | ||||
\(922\) | 25.4363 | − | 44.0570i | 0.837700 | − | 1.45094i | ||||
\(923\) | −12.6462 | + | 19.5056i | −0.416253 | + | 0.642033i | ||||
\(924\) | −0.327507 | + | 0.910296i | −0.0107742 | + | 0.0299465i | ||||
\(925\) | 23.5770 | + | 40.8365i | 0.775206 | + | 1.34270i | ||||
\(926\) | −0.482395 | −0.0158525 | ||||||||
\(927\) | −4.68842 | −0.153988 | ||||||||
\(928\) | −2.65268 | − | 4.59458i | −0.0870785 | − | 0.150824i | ||||
\(929\) | 4.06964 | + | 7.04883i | 0.133521 | + | 0.231264i | 0.925031 | − | 0.379891i | \(-0.124038\pi\) |
−0.791511 | + | 0.611155i | \(0.790705\pi\) | |||||||
\(930\) | 1.53151 | − | 2.65266i | 0.0502203 | − | 0.0869842i | ||||
\(931\) | −45.7062 | + | 17.0202i | −1.49796 | + | 0.557815i | ||||
\(932\) | −8.26922 | + | 14.3227i | −0.270867 | + | 0.469156i | ||||
\(933\) | −30.8996 | −1.01161 | ||||||||
\(934\) | −33.5548 | + | 58.1186i | −1.09795 | + | 1.90170i | ||||
\(935\) | 2.62212 | + | 4.54165i | 0.0857526 | + | 0.148528i | ||||
\(936\) | 2.14929 | + | 4.21038i | 0.0702519 | + | 0.137620i | ||||
\(937\) | 30.6536 | 1.00141 | 0.500705 | − | 0.865618i | \(-0.333074\pi\) | ||||
0.500705 | + | 0.865618i | \(0.333074\pi\) | |||||||
\(938\) | −7.41699 | + | 1.33616i | −0.242173 | + | 0.0436272i | ||||
\(939\) | 3.74574 | + | 6.48782i | 0.122238 | + | 0.211722i | ||||
\(940\) | −13.7561 | − | 23.8262i | −0.448673 | − | 0.777125i | ||||
\(941\) | 4.34815 | + | 7.53122i | 0.141746 | + | 0.245511i | 0.928154 | − | 0.372196i | \(-0.121395\pi\) |
−0.786408 | + | 0.617707i | \(0.788062\pi\) | |||||||
\(942\) | 33.7274 | 1.09890 | ||||||||
\(943\) | 3.69084 | + | 6.39272i | 0.120190 | + | 0.208176i | ||||
\(944\) | 23.9237 | 0.778651 | ||||||||
\(945\) | 10.3516 | − | 1.86483i | 0.336738 | − | 0.0606629i | ||||
\(946\) | −0.303651 | − | 0.525938i | −0.00987254 | − | 0.0170997i | ||||
\(947\) | −11.4722 | −0.372796 | −0.186398 | − | 0.982474i | \(-0.559681\pi\) | ||||
−0.186398 | + | 0.982474i | \(0.559681\pi\) | |||||||
\(948\) | −4.90348 | − | 8.49307i | −0.159258 | − | 0.275842i | ||||
\(949\) | 27.0435 | + | 52.9771i | 0.877869 | + | 1.71971i | ||||
\(950\) | 68.1250 | − | 117.996i | 2.21027 | − | 3.82830i | ||||
\(951\) | 8.11402 | + | 14.0539i | 0.263115 | + | 0.455729i | ||||
\(952\) | 10.3060 | + | 12.1903i | 0.334021 | + | 0.395089i | ||||
\(953\) | −23.1731 | + | 40.1370i | −0.750650 | + | 1.30016i | 0.196859 | + | 0.980432i | \(0.436926\pi\) |
−0.947508 | + | 0.319731i | \(0.896407\pi\) | |||||||
\(954\) | −1.03927 | + | 1.80006i | −0.0336475 | + | 0.0582792i | ||||
\(955\) | −44.1181 | −1.42763 | ||||||||
\(956\) | −6.11774 | −0.197862 | ||||||||
\(957\) | −0.120898 | + | 0.209401i | −0.00390807 | + | 0.00676897i | ||||
\(958\) | −26.0607 | + | 45.1384i | −0.841983 | + | 1.45836i | ||||
\(959\) | 2.57876 | + | 3.05024i | 0.0832727 | + | 0.0984972i | ||||
\(960\) | −3.05165 | − | 5.28562i | −0.0984916 | − | 0.170593i | ||||
\(961\) | 15.4094 | − | 26.6898i | 0.497077 | − | 0.860963i | ||||
\(962\) | −28.4406 | − | 1.46900i | −0.916961 | − | 0.0473626i | ||||
\(963\) | −7.25279 | − | 12.5622i | −0.233718 | − | 0.404811i | ||||
\(964\) | 13.2909 | 0.428071 | ||||||||
\(965\) | −0.966511 | − | 1.67405i | −0.0311131 | − | 0.0538894i | ||||
\(966\) | 34.1123 | − | 6.14528i | 1.09754 | − | 0.197721i | ||||
\(967\) | 8.71419 | 0.280229 | 0.140115 | − | 0.990135i | \(-0.455253\pi\) | ||||
0.140115 | + | 0.990135i | \(0.455253\pi\) | |||||||
\(968\) | −7.15718 | − | 12.3966i | −0.230040 | − | 0.398442i | ||||
\(969\) | 32.0632 | 1.03002 | ||||||||
\(970\) | −68.5149 | − | 118.671i | −2.19988 | − | 3.81031i | ||||
\(971\) | −20.0281 | − | 34.6897i | −0.642733 | − | 1.11325i | −0.984820 | − | 0.173578i | \(-0.944467\pi\) |
0.342087 | − | 0.939668i | \(-0.388866\pi\) | |||||||
\(972\) | −0.637789 | − | 1.10468i | −0.0204571 | − | 0.0354327i | ||||
\(973\) | 10.5264 | − | 1.89632i | 0.337461 | − | 0.0607931i | ||||
\(974\) | −24.8499 | −0.796243 | ||||||||
\(975\) | 38.9054 | + | 2.00953i | 1.24597 | + | 0.0643565i | ||||
\(976\) | 20.1110 | + | 34.8333i | 0.643738 | + | 1.11499i | ||||
\(977\) | 21.1533 | − | 36.6387i | 0.676755 | − | 1.17217i | −0.299197 | − | 0.954191i | \(-0.596719\pi\) |
0.975953 | − | 0.217983i | \(-0.0699478\pi\) | |||||||
\(978\) | 19.3750 | 0.619543 | ||||||||
\(979\) | −0.317572 | + | 0.550050i | −0.0101496 | + | 0.0175797i | ||||
\(980\) | 27.3611 | + | 22.6154i | 0.874017 | + | 0.722422i | ||||
\(981\) | 2.09694 | − | 3.63200i | 0.0669500 | − | 0.115961i | ||||
\(982\) | 24.9095 | + | 43.1445i | 0.794893 | + | 1.37680i | ||||
\(983\) | 2.44395 | + | 4.23305i | 0.0779501 | + | 0.135013i | 0.902365 | − | 0.430972i | \(-0.141829\pi\) |
−0.824415 | + | 0.565985i | \(0.808496\pi\) | |||||||
\(984\) | −1.33702 | −0.0426226 | ||||||||
\(985\) | −67.8872 | −2.16307 | ||||||||
\(986\) | −3.51264 | − | 6.08407i | −0.111865 | − | 0.193756i | ||||
\(987\) | −4.85935 | + | 13.5064i | −0.154675 | + | 0.429913i | ||||
\(988\) | 14.5695 | + | 28.5410i | 0.463517 | + | 0.908009i | ||||
\(989\) | −4.23667 | + | 7.33813i | −0.134718 | + | 0.233339i | ||||
\(990\) | −1.03126 | + | 1.78619i | −0.0327755 | + | 0.0567688i | ||||
\(991\) | 9.29795 | − | 16.1045i | 0.295359 | − | 0.511577i | −0.679709 | − | 0.733482i | \(-0.737894\pi\) |
0.975068 | + | 0.221905i | \(0.0712273\pi\) | |||||||
\(992\) | 1.33878 | + | 2.31883i | 0.0425062 | + | 0.0736229i | ||||
\(993\) | 5.58434 | 0.177214 | ||||||||
\(994\) | −30.3837 | + | 5.47358i | −0.963712 | + | 0.173612i | ||||
\(995\) | 46.0560 | − | 79.7713i | 1.46007 | − | 2.52892i | ||||
\(996\) | −8.53922 | + | 14.7904i | −0.270575 | + | 0.468650i | ||||
\(997\) | −25.6363 | −0.811909 | −0.405954 | − | 0.913893i | \(-0.633061\pi\) | ||||
−0.405954 | + | 0.913893i | \(0.633061\pi\) | |||||||
\(998\) | 3.52138 | − | 6.09921i | 0.111467 | − | 0.193067i | ||||
\(999\) | −4.36416 | −0.138076 |
(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 | 273.2.l.c.16.8 | yes | 20 | |
3.2 | odd | 2 | 819.2.s.f.289.3 | 20 | |||
7.4 | even | 3 | 273.2.j.c.172.3 | yes | 20 | ||
13.9 | even | 3 | 273.2.j.c.100.3 | ✓ | 20 | ||
21.11 | odd | 6 | 819.2.n.f.172.8 | 20 | |||
39.35 | odd | 6 | 819.2.n.f.100.8 | 20 | |||
91.74 | even | 3 | inner | 273.2.l.c.256.8 | yes | 20 | |
273.74 | odd | 6 | 819.2.s.f.802.3 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.j.c.100.3 | ✓ | 20 | 13.9 | even | 3 | ||
273.2.j.c.172.3 | yes | 20 | 7.4 | even | 3 | ||
273.2.l.c.16.8 | yes | 20 | 1.1 | even | 1 | trivial | |
273.2.l.c.256.8 | yes | 20 | 91.74 | even | 3 | inner | |
819.2.n.f.100.8 | 20 | 39.35 | odd | 6 | |||
819.2.n.f.172.8 | 20 | 21.11 | odd | 6 | |||
819.2.s.f.289.3 | 20 | 3.2 | odd | 2 | |||
819.2.s.f.802.3 | 20 | 273.74 | odd | 6 |