Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,2,Mod(29,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.29");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.u (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.78864900528\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 141.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.141 |
Dual form | 224.2.u.a.197.1 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.707107 | − | 0.707107i | ||||
\(3\) | −1.00000 | + | 2.41421i | −0.577350 | + | 1.39385i | 0.317832 | + | 0.948147i | \(0.397045\pi\) |
−0.895182 | + | 0.445700i | \(0.852955\pi\) | |||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | −3.41421 | + | 1.41421i | −1.52688 | + | 0.632456i | −0.978956 | − | 0.204071i | \(-0.934583\pi\) |
−0.547927 | + | 0.836526i | \(0.684583\pi\) | |||||||
\(6\) | 3.41421 | − | 1.41421i | 1.39385 | − | 0.577350i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | −2.70711 | − | 2.70711i | −0.902369 | − | 0.902369i | ||||
\(10\) | 4.82843 | + | 2.00000i | 1.52688 | + | 0.632456i | ||||
\(11\) | −2.29289 | − | 5.53553i | −0.691333 | − | 1.66903i | −0.742077 | − | 0.670315i | \(-0.766159\pi\) |
0.0507438 | − | 0.998712i | \(-0.483841\pi\) | |||||||
\(12\) | −4.82843 | − | 2.00000i | −1.39385 | − | 0.577350i | ||||
\(13\) | 1.41421 | + | 0.585786i | 0.392232 | + | 0.162468i | 0.570078 | − | 0.821590i | \(-0.306913\pi\) |
−0.177846 | + | 0.984058i | \(0.556913\pi\) | |||||||
\(14\) | −1.41421 | −0.377964 | ||||||||
\(15\) | − | 9.65685i | − | 2.49339i | ||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 5.41421i | 1.27614i | ||||||||
\(19\) | 0.414214 | + | 0.171573i | 0.0950271 | + | 0.0393615i | 0.429691 | − | 0.902976i | \(-0.358623\pi\) |
−0.334663 | + | 0.942338i | \(0.608623\pi\) | |||||||
\(20\) | −2.82843 | − | 6.82843i | −0.632456 | − | 1.52688i | ||||
\(21\) | 1.00000 | + | 2.41421i | 0.218218 | + | 0.526825i | ||||
\(22\) | −3.24264 | + | 7.82843i | −0.691333 | + | 1.66903i | ||||
\(23\) | −1.00000 | − | 1.00000i | −0.208514 | − | 0.208514i | 0.595121 | − | 0.803636i | \(-0.297104\pi\) |
−0.803636 | + | 0.595121i | \(0.797104\pi\) | |||||||
\(24\) | 2.82843 | + | 6.82843i | 0.577350 | + | 1.39385i | ||||
\(25\) | 6.12132 | − | 6.12132i | 1.22426 | − | 1.22426i | ||||
\(26\) | −0.828427 | − | 2.00000i | −0.162468 | − | 0.392232i | ||||
\(27\) | 2.00000 | − | 0.828427i | 0.384900 | − | 0.159431i | ||||
\(28\) | 1.41421 | + | 1.41421i | 0.267261 | + | 0.267261i | ||||
\(29\) | −3.29289 | + | 7.94975i | −0.611475 | + | 1.47623i | 0.249905 | + | 0.968270i | \(0.419601\pi\) |
−0.861380 | + | 0.507961i | \(0.830399\pi\) | |||||||
\(30\) | −9.65685 | + | 9.65685i | −1.76309 | + | 1.76309i | ||||
\(31\) | −8.82843 | −1.58563 | −0.792816 | − | 0.609461i | \(-0.791386\pi\) | ||||
−0.792816 | + | 0.609461i | \(0.791386\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.707107 | + | 0.707107i | ||||
\(33\) | 15.6569 | 2.72551 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.41421 | + | 3.41421i | −0.239046 | + | 0.577107i | ||||
\(36\) | 5.41421 | − | 5.41421i | 0.902369 | − | 0.902369i | ||||
\(37\) | −4.70711 | + | 1.94975i | −0.773844 | + | 0.320537i | −0.734428 | − | 0.678686i | \(-0.762550\pi\) |
−0.0394154 | + | 0.999223i | \(0.512550\pi\) | |||||||
\(38\) | −0.242641 | − | 0.585786i | −0.0393615 | − | 0.0950271i | ||||
\(39\) | −2.82843 | + | 2.82843i | −0.452911 | + | 0.452911i | ||||
\(40\) | −4.00000 | + | 9.65685i | −0.632456 | + | 1.52688i | ||||
\(41\) | −3.41421 | − | 3.41421i | −0.533211 | − | 0.533211i | 0.388316 | − | 0.921526i | \(-0.373057\pi\) |
−0.921526 | + | 0.388316i | \(0.873057\pi\) | |||||||
\(42\) | 1.41421 | − | 3.41421i | 0.218218 | − | 0.526825i | ||||
\(43\) | −1.87868 | − | 4.53553i | −0.286496 | − | 0.691662i | 0.713463 | − | 0.700693i | \(-0.247126\pi\) |
−0.999959 | + | 0.00903020i | \(0.997126\pi\) | |||||||
\(44\) | 11.0711 | − | 4.58579i | 1.66903 | − | 0.691333i | ||||
\(45\) | 13.0711 | + | 5.41421i | 1.94852 | + | 0.807103i | ||||
\(46\) | 2.00000i | 0.294884i | ||||||||
\(47\) | − | 8.82843i | − | 1.28776i | −0.765127 | − | 0.643879i | \(-0.777324\pi\) | ||
0.765127 | − | 0.643879i | \(-0.222676\pi\) | |||||||
\(48\) | 4.00000 | − | 9.65685i | 0.577350 | − | 1.39385i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −12.2426 | −1.73137 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.17157 | + | 2.82843i | −0.162468 | + | 0.392232i | ||||
\(53\) | 0.0502525 | + | 0.121320i | 0.00690272 | + | 0.0166646i | 0.927293 | − | 0.374336i | \(-0.122129\pi\) |
−0.920391 | + | 0.391000i | \(0.872129\pi\) | |||||||
\(54\) | −2.82843 | − | 1.17157i | −0.384900 | − | 0.159431i | ||||
\(55\) | 15.6569 | + | 15.6569i | 2.11117 | + | 2.11117i | ||||
\(56\) | − | 2.82843i | − | 0.377964i | ||||||
\(57\) | −0.828427 | + | 0.828427i | −0.109728 | + | 0.109728i | ||||
\(58\) | 11.2426 | − | 4.65685i | 1.47623 | − | 0.611475i | ||||
\(59\) | −5.00000 | + | 2.07107i | −0.650945 | + | 0.269630i | −0.683622 | − | 0.729836i | \(-0.739596\pi\) |
0.0326779 | + | 0.999466i | \(0.489596\pi\) | |||||||
\(60\) | 19.3137 | 2.49339 | ||||||||
\(61\) | −1.17157 | + | 2.82843i | −0.150005 | + | 0.362143i | −0.980964 | − | 0.194190i | \(-0.937792\pi\) |
0.830959 | + | 0.556333i | \(0.187792\pi\) | |||||||
\(62\) | 8.82843 | + | 8.82843i | 1.12121 | + | 1.12121i | ||||
\(63\) | −3.82843 | −0.482336 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | −5.65685 | −0.701646 | ||||||||
\(66\) | −15.6569 | − | 15.6569i | −1.92723 | − | 1.92723i | ||||
\(67\) | 4.70711 | − | 11.3640i | 0.575065 | − | 1.38833i | −0.322131 | − | 0.946695i | \(-0.604399\pi\) |
0.897195 | − | 0.441634i | \(-0.145601\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.41421 | − | 1.41421i | 0.411023 | − | 0.170251i | ||||
\(70\) | 4.82843 | − | 2.00000i | 0.577107 | − | 0.239046i | ||||
\(71\) | −4.24264 | + | 4.24264i | −0.503509 | + | 0.503509i | −0.912526 | − | 0.409018i | \(-0.865871\pi\) |
0.409018 | + | 0.912526i | \(0.365871\pi\) | |||||||
\(72\) | −10.8284 | −1.27614 | ||||||||
\(73\) | 3.17157 | + | 3.17157i | 0.371205 | + | 0.371205i | 0.867916 | − | 0.496711i | \(-0.165459\pi\) |
−0.496711 | + | 0.867916i | \(0.665459\pi\) | |||||||
\(74\) | 6.65685 | + | 2.75736i | 0.773844 | + | 0.320537i | ||||
\(75\) | 8.65685 | + | 20.8995i | 0.999607 | + | 2.41327i | ||||
\(76\) | −0.343146 | + | 0.828427i | −0.0393615 | + | 0.0950271i | ||||
\(77\) | −5.53553 | − | 2.29289i | −0.630833 | − | 0.261299i | ||||
\(78\) | 5.65685 | 0.640513 | ||||||||
\(79\) | 9.89949i | 1.11378i | 0.830586 | + | 0.556890i | \(0.188006\pi\) | ||||
−0.830586 | + | 0.556890i | \(0.811994\pi\) | |||||||
\(80\) | 13.6569 | − | 5.65685i | 1.52688 | − | 0.632456i | ||||
\(81\) | − | 5.82843i | − | 0.647603i | ||||||
\(82\) | 6.82843i | 0.754074i | ||||||||
\(83\) | 3.24264 | + | 1.34315i | 0.355926 | + | 0.147429i | 0.553480 | − | 0.832863i | \(-0.313300\pi\) |
−0.197554 | + | 0.980292i | \(0.563300\pi\) | |||||||
\(84\) | −4.82843 | + | 2.00000i | −0.526825 | + | 0.218218i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.65685 | + | 6.41421i | −0.286496 | + | 0.691662i | ||||
\(87\) | −15.8995 | − | 15.8995i | −1.70460 | − | 1.70460i | ||||
\(88\) | −15.6569 | − | 6.48528i | −1.66903 | − | 0.691333i | ||||
\(89\) | −5.17157 | + | 5.17157i | −0.548186 | + | 0.548186i | −0.925916 | − | 0.377730i | \(-0.876705\pi\) |
0.377730 | + | 0.925916i | \(0.376705\pi\) | |||||||
\(90\) | −7.65685 | − | 18.4853i | −0.807103 | − | 1.94852i | ||||
\(91\) | 1.41421 | − | 0.585786i | 0.148250 | − | 0.0614071i | ||||
\(92\) | 2.00000 | − | 2.00000i | 0.208514 | − | 0.208514i | ||||
\(93\) | 8.82843 | − | 21.3137i | 0.915465 | − | 2.21013i | ||||
\(94\) | −8.82843 | + | 8.82843i | −0.910583 | + | 0.910583i | ||||
\(95\) | −1.65685 | −0.169990 | ||||||||
\(96\) | −13.6569 | + | 5.65685i | −1.39385 | + | 0.577350i | ||||
\(97\) | 1.17157 | 0.118955 | 0.0594776 | − | 0.998230i | \(-0.481057\pi\) | ||||
0.0594776 | + | 0.998230i | \(0.481057\pi\) | |||||||
\(98\) | −1.00000 | + | 1.00000i | −0.101015 | + | 0.101015i | ||||
\(99\) | −8.77817 | + | 21.1924i | −0.882240 | + | 2.12992i | ||||
\(100\) | 12.2426 | + | 12.2426i | 1.22426 | + | 1.22426i | ||||
\(101\) | −3.41421 | + | 1.41421i | −0.339727 | + | 0.140720i | −0.546023 | − | 0.837770i | \(-0.683859\pi\) |
0.206296 | + | 0.978490i | \(0.433859\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.2426 | + | 10.2426i | −1.00924 | + | 1.00924i | −0.00928044 | + | 0.999957i | \(0.502954\pi\) |
−0.999957 | + | 0.00928044i | \(0.997046\pi\) | |||||||
\(104\) | 4.00000 | − | 1.65685i | 0.392232 | − | 0.162468i | ||||
\(105\) | −6.82843 | − | 6.82843i | −0.666386 | − | 0.666386i | ||||
\(106\) | 0.0710678 | − | 0.171573i | 0.00690272 | − | 0.0166646i | ||||
\(107\) | −2.36396 | − | 5.70711i | −0.228533 | − | 0.551727i | 0.767466 | − | 0.641089i | \(-0.221517\pi\) |
−0.995999 | + | 0.0893623i | \(0.971517\pi\) | |||||||
\(108\) | 1.65685 | + | 4.00000i | 0.159431 | + | 0.384900i | ||||
\(109\) | −8.53553 | − | 3.53553i | −0.817556 | − | 0.338643i | −0.0655916 | − | 0.997847i | \(-0.520893\pi\) |
−0.751964 | + | 0.659204i | \(0.770893\pi\) | |||||||
\(110\) | − | 31.3137i | − | 2.98564i | ||||||
\(111\) | − | 13.3137i | − | 1.26368i | ||||||
\(112\) | −2.82843 | + | 2.82843i | −0.267261 | + | 0.267261i | ||||
\(113\) | 17.4142i | 1.63819i | 0.573657 | + | 0.819096i | \(0.305524\pi\) | ||||
−0.573657 | + | 0.819096i | \(0.694476\pi\) | |||||||
\(114\) | 1.65685 | 0.155179 | ||||||||
\(115\) | 4.82843 | + | 2.00000i | 0.450253 | + | 0.186501i | ||||
\(116\) | −15.8995 | − | 6.58579i | −1.47623 | − | 0.611475i | ||||
\(117\) | −2.24264 | − | 5.41421i | −0.207332 | − | 0.500544i | ||||
\(118\) | 7.07107 | + | 2.92893i | 0.650945 | + | 0.269630i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −19.3137 | − | 19.3137i | −1.76309 | − | 1.76309i | ||||
\(121\) | −17.6066 | + | 17.6066i | −1.60060 | + | 1.60060i | ||||
\(122\) | 4.00000 | − | 1.65685i | 0.362143 | − | 0.150005i | ||||
\(123\) | 11.6569 | − | 4.82843i | 1.05106 | − | 0.435365i | ||||
\(124\) | − | 17.6569i | − | 1.58563i | ||||||
\(125\) | −5.17157 | + | 12.4853i | −0.462560 | + | 1.11672i | ||||
\(126\) | 3.82843 | + | 3.82843i | 0.341063 | + | 0.341063i | ||||
\(127\) | 14.9706 | 1.32842 | 0.664211 | − | 0.747545i | \(-0.268768\pi\) | ||||
0.664211 | + | 0.747545i | \(0.268768\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.707107 | + | 0.707107i | ||||
\(129\) | 12.8284 | 1.12948 | ||||||||
\(130\) | 5.65685 | + | 5.65685i | 0.496139 | + | 0.496139i | ||||
\(131\) | 2.41421 | − | 5.82843i | 0.210931 | − | 0.509232i | −0.782636 | − | 0.622480i | \(-0.786125\pi\) |
0.993567 | + | 0.113248i | \(0.0361253\pi\) | |||||||
\(132\) | 31.3137i | 2.72551i | ||||||||
\(133\) | 0.414214 | − | 0.171573i | 0.0359169 | − | 0.0148773i | ||||
\(134\) | −16.0711 | + | 6.65685i | −1.38833 | + | 0.575065i | ||||
\(135\) | −5.65685 | + | 5.65685i | −0.486864 | + | 0.486864i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.1421 | + | 15.1421i | 1.29368 | + | 1.29368i | 0.932494 | + | 0.361186i | \(0.117628\pi\) |
0.361186 | + | 0.932494i | \(0.382372\pi\) | |||||||
\(138\) | −4.82843 | − | 2.00000i | −0.411023 | − | 0.170251i | ||||
\(139\) | 3.24264 | + | 7.82843i | 0.275037 | + | 0.663999i | 0.999684 | − | 0.0251215i | \(-0.00799727\pi\) |
−0.724647 | + | 0.689120i | \(0.757997\pi\) | |||||||
\(140\) | −6.82843 | − | 2.82843i | −0.577107 | − | 0.239046i | ||||
\(141\) | 21.3137 | + | 8.82843i | 1.79494 | + | 0.743488i | ||||
\(142\) | 8.48528 | 0.712069 | ||||||||
\(143\) | − | 9.17157i | − | 0.766965i | ||||||
\(144\) | 10.8284 | + | 10.8284i | 0.902369 | + | 0.902369i | ||||
\(145\) | − | 31.7990i | − | 2.64076i | ||||||
\(146\) | − | 6.34315i | − | 0.524962i | ||||||
\(147\) | 2.41421 | + | 1.00000i | 0.199121 | + | 0.0824786i | ||||
\(148\) | −3.89949 | − | 9.41421i | −0.320537 | − | 0.773844i | ||||
\(149\) | −0.0502525 | − | 0.121320i | −0.00411685 | − | 0.00993895i | 0.921808 | − | 0.387647i | \(-0.126712\pi\) |
−0.925925 | + | 0.377708i | \(0.876712\pi\) | |||||||
\(150\) | 12.2426 | − | 29.5563i | 0.999607 | − | 2.41327i | ||||
\(151\) | −3.00000 | − | 3.00000i | −0.244137 | − | 0.244137i | 0.574422 | − | 0.818559i | \(-0.305227\pi\) |
−0.818559 | + | 0.574422i | \(0.805227\pi\) | |||||||
\(152\) | 1.17157 | − | 0.485281i | 0.0950271 | − | 0.0393615i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.24264 | + | 7.82843i | 0.261299 | + | 0.630833i | ||||
\(155\) | 30.1421 | − | 12.4853i | 2.42107 | − | 1.00284i | ||||
\(156\) | −5.65685 | − | 5.65685i | −0.452911 | − | 0.452911i | ||||
\(157\) | −2.48528 | + | 6.00000i | −0.198347 | + | 0.478852i | −0.991490 | − | 0.130183i | \(-0.958443\pi\) |
0.793143 | + | 0.609036i | \(0.208443\pi\) | |||||||
\(158\) | 9.89949 | − | 9.89949i | 0.787562 | − | 0.787562i | ||||
\(159\) | −0.343146 | −0.0272132 | ||||||||
\(160\) | −19.3137 | − | 8.00000i | −1.52688 | − | 0.632456i | ||||
\(161\) | −1.41421 | −0.111456 | ||||||||
\(162\) | −5.82843 | + | 5.82843i | −0.457924 | + | 0.457924i | ||||
\(163\) | 2.05025 | − | 4.94975i | 0.160588 | − | 0.387694i | −0.823020 | − | 0.568012i | \(-0.807713\pi\) |
0.983608 | + | 0.180318i | \(0.0577127\pi\) | |||||||
\(164\) | 6.82843 | − | 6.82843i | 0.533211 | − | 0.533211i | ||||
\(165\) | −53.4558 | + | 22.1421i | −4.16153 | + | 1.72376i | ||||
\(166\) | −1.89949 | − | 4.58579i | −0.147429 | − | 0.355926i | ||||
\(167\) | 5.75736 | − | 5.75736i | 0.445518 | − | 0.445518i | −0.448344 | − | 0.893861i | \(-0.647986\pi\) |
0.893861 | + | 0.448344i | \(0.147986\pi\) | |||||||
\(168\) | 6.82843 | + | 2.82843i | 0.526825 | + | 0.218218i | ||||
\(169\) | −7.53553 | − | 7.53553i | −0.579656 | − | 0.579656i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.656854 | − | 1.58579i | −0.0502309 | − | 0.121268i | ||||
\(172\) | 9.07107 | − | 3.75736i | 0.691662 | − | 0.286496i | ||||
\(173\) | 4.24264 | + | 1.75736i | 0.322562 | + | 0.133610i | 0.538088 | − | 0.842888i | \(-0.319147\pi\) |
−0.215526 | + | 0.976498i | \(0.569147\pi\) | |||||||
\(174\) | 31.7990i | 2.41068i | ||||||||
\(175\) | − | 8.65685i | − | 0.654397i | ||||||
\(176\) | 9.17157 | + | 22.1421i | 0.691333 | + | 1.66903i | ||||
\(177\) | − | 14.1421i | − | 1.06299i | ||||||
\(178\) | 10.3431 | 0.775252 | ||||||||
\(179\) | −10.5355 | − | 4.36396i | −0.787463 | − | 0.326178i | −0.0475398 | − | 0.998869i | \(-0.515138\pi\) |
−0.739923 | + | 0.672692i | \(0.765138\pi\) | |||||||
\(180\) | −10.8284 | + | 26.1421i | −0.807103 | + | 1.94852i | ||||
\(181\) | −5.41421 | − | 13.0711i | −0.402435 | − | 0.971565i | −0.987073 | − | 0.160270i | \(-0.948763\pi\) |
0.584638 | − | 0.811294i | \(-0.301237\pi\) | |||||||
\(182\) | −2.00000 | − | 0.828427i | −0.148250 | − | 0.0614071i | ||||
\(183\) | −5.65685 | − | 5.65685i | −0.418167 | − | 0.418167i | ||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | 13.3137 | − | 13.3137i | 0.978843 | − | 0.978843i | ||||
\(186\) | −30.1421 | + | 12.4853i | −2.21013 | + | 0.915465i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 17.6569 | 1.28776 | ||||||||
\(189\) | 0.828427 | − | 2.00000i | 0.0602592 | − | 0.145479i | ||||
\(190\) | 1.65685 | + | 1.65685i | 0.120201 | + | 0.120201i | ||||
\(191\) | 3.07107 | 0.222215 | 0.111107 | − | 0.993808i | \(-0.464560\pi\) | ||||
0.111107 | + | 0.993808i | \(0.464560\pi\) | |||||||
\(192\) | 19.3137 | + | 8.00000i | 1.39385 | + | 0.577350i | ||||
\(193\) | 1.41421 | 0.101797 | 0.0508987 | − | 0.998704i | \(-0.483791\pi\) | ||||
0.0508987 | + | 0.998704i | \(0.483791\pi\) | |||||||
\(194\) | −1.17157 | − | 1.17157i | −0.0841140 | − | 0.0841140i | ||||
\(195\) | 5.65685 | − | 13.6569i | 0.405096 | − | 0.977988i | ||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 12.6066 | − | 5.22183i | 0.898183 | − | 0.372040i | 0.114662 | − | 0.993405i | \(-0.463422\pi\) |
0.783521 | + | 0.621365i | \(0.213422\pi\) | |||||||
\(198\) | 29.9706 | − | 12.4142i | 2.12992 | − | 0.882240i | ||||
\(199\) | 0.928932 | − | 0.928932i | 0.0658503 | − | 0.0658503i | −0.673415 | − | 0.739265i | \(-0.735173\pi\) |
0.739265 | + | 0.673415i | \(0.235173\pi\) | |||||||
\(200\) | − | 24.4853i | − | 1.73137i | ||||||
\(201\) | 22.7279 | + | 22.7279i | 1.60310 | + | 1.60310i | ||||
\(202\) | 4.82843 | + | 2.00000i | 0.339727 | + | 0.140720i | ||||
\(203\) | 3.29289 | + | 7.94975i | 0.231116 | + | 0.557963i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.4853 | + | 6.82843i | 1.15138 | + | 0.476918i | ||||
\(206\) | 20.4853 | 1.42728 | ||||||||
\(207\) | 5.41421i | 0.376314i | ||||||||
\(208\) | −5.65685 | − | 2.34315i | −0.392232 | − | 0.162468i | ||||
\(209\) | − | 2.68629i | − | 0.185815i | ||||||
\(210\) | 13.6569i | 0.942412i | ||||||||
\(211\) | −4.12132 | − | 1.70711i | −0.283723 | − | 0.117522i | 0.236283 | − | 0.971684i | \(-0.424071\pi\) |
−0.520007 | + | 0.854162i | \(0.674071\pi\) | |||||||
\(212\) | −0.242641 | + | 0.100505i | −0.0166646 | + | 0.00690272i | ||||
\(213\) | −6.00000 | − | 14.4853i | −0.411113 | − | 0.992515i | ||||
\(214\) | −3.34315 | + | 8.07107i | −0.228533 | + | 0.551727i | ||||
\(215\) | 12.8284 | + | 12.8284i | 0.874891 | + | 0.874891i | ||||
\(216\) | 2.34315 | − | 5.65685i | 0.159431 | − | 0.384900i | ||||
\(217\) | −6.24264 | + | 6.24264i | −0.423778 | + | 0.423778i | ||||
\(218\) | 5.00000 | + | 12.0711i | 0.338643 | + | 0.817556i | ||||
\(219\) | −10.8284 | + | 4.48528i | −0.731717 | + | 0.303087i | ||||
\(220\) | −31.3137 | + | 31.3137i | −2.11117 | + | 2.11117i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −13.3137 | + | 13.3137i | −0.893558 | + | 0.893558i | ||||
\(223\) | −23.3137 | −1.56120 | −0.780601 | − | 0.625030i | \(-0.785087\pi\) | ||||
−0.780601 | + | 0.625030i | \(0.785087\pi\) | |||||||
\(224\) | 5.65685 | 0.377964 | ||||||||
\(225\) | −33.1421 | −2.20948 | ||||||||
\(226\) | 17.4142 | − | 17.4142i | 1.15838 | − | 1.15838i | ||||
\(227\) | −11.0000 | + | 26.5563i | −0.730096 | + | 1.76261i | −0.0878156 | + | 0.996137i | \(0.527989\pi\) |
−0.642280 | + | 0.766470i | \(0.722011\pi\) | |||||||
\(228\) | −1.65685 | − | 1.65685i | −0.109728 | − | 0.109728i | ||||
\(229\) | 8.00000 | − | 3.31371i | 0.528655 | − | 0.218976i | −0.102359 | − | 0.994748i | \(-0.532639\pi\) |
0.631014 | + | 0.775771i | \(0.282639\pi\) | |||||||
\(230\) | −2.82843 | − | 6.82843i | −0.186501 | − | 0.450253i | ||||
\(231\) | 11.0711 | − | 11.0711i | 0.728423 | − | 0.728423i | ||||
\(232\) | 9.31371 | + | 22.4853i | 0.611475 | + | 1.47623i | ||||
\(233\) | −1.82843 | − | 1.82843i | −0.119784 | − | 0.119784i | 0.644674 | − | 0.764458i | \(-0.276993\pi\) |
−0.764458 | + | 0.644674i | \(0.776993\pi\) | |||||||
\(234\) | −3.17157 | + | 7.65685i | −0.207332 | + | 0.500544i | ||||
\(235\) | 12.4853 | + | 30.1421i | 0.814450 | + | 1.96626i | ||||
\(236\) | −4.14214 | − | 10.0000i | −0.269630 | − | 0.650945i | ||||
\(237\) | −23.8995 | − | 9.89949i | −1.55244 | − | 0.643041i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000i | 0.388108i | 0.980991 | + | 0.194054i | \(0.0621637\pi\) | ||||
−0.980991 | + | 0.194054i | \(0.937836\pi\) | |||||||
\(240\) | 38.6274i | 2.49339i | ||||||||
\(241\) | − | 23.7990i | − | 1.53303i | −0.642228 | − | 0.766514i | \(-0.721990\pi\) | ||
0.642228 | − | 0.766514i | \(-0.278010\pi\) | |||||||
\(242\) | 35.2132 | 2.26359 | ||||||||
\(243\) | 20.0711 | + | 8.31371i | 1.28756 | + | 0.533325i | ||||
\(244\) | −5.65685 | − | 2.34315i | −0.362143 | − | 0.150005i | ||||
\(245\) | 1.41421 | + | 3.41421i | 0.0903508 | + | 0.218126i | ||||
\(246\) | −16.4853 | − | 6.82843i | −1.05106 | − | 0.435365i | ||||
\(247\) | 0.485281 | + | 0.485281i | 0.0308777 | + | 0.0308777i | ||||
\(248\) | −17.6569 | + | 17.6569i | −1.12121 | + | 1.12121i | ||||
\(249\) | −6.48528 | + | 6.48528i | −0.410988 | + | 0.410988i | ||||
\(250\) | 17.6569 | − | 7.31371i | 1.11672 | − | 0.462560i | ||||
\(251\) | 2.65685 | − | 1.10051i | 0.167699 | − | 0.0694633i | −0.297255 | − | 0.954798i | \(-0.596071\pi\) |
0.464954 | + | 0.885335i | \(0.346071\pi\) | |||||||
\(252\) | − | 7.65685i | − | 0.482336i | ||||||
\(253\) | −3.24264 | + | 7.82843i | −0.203863 | + | 0.492169i | ||||
\(254\) | −14.9706 | − | 14.9706i | −0.939337 | − | 0.939337i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −28.1421 | −1.75546 | −0.877729 | − | 0.479157i | \(-0.840942\pi\) | ||||
−0.877729 | + | 0.479157i | \(0.840942\pi\) | |||||||
\(258\) | −12.8284 | − | 12.8284i | −0.798663 | − | 0.798663i | ||||
\(259\) | −1.94975 | + | 4.70711i | −0.121151 | + | 0.292485i | ||||
\(260\) | − | 11.3137i | − | 0.701646i | ||||||
\(261\) | 30.4350 | − | 12.6066i | 1.88388 | − | 0.780329i | ||||
\(262\) | −8.24264 | + | 3.41421i | −0.509232 | + | 0.210931i | ||||
\(263\) | −9.65685 | + | 9.65685i | −0.595467 | + | 0.595467i | −0.939103 | − | 0.343636i | \(-0.888341\pi\) |
0.343636 | + | 0.939103i | \(0.388341\pi\) | |||||||
\(264\) | 31.3137 | − | 31.3137i | 1.92723 | − | 1.92723i | ||||
\(265\) | −0.343146 | − | 0.343146i | −0.0210793 | − | 0.0210793i | ||||
\(266\) | −0.585786 | − | 0.242641i | −0.0359169 | − | 0.0148773i | ||||
\(267\) | −7.31371 | − | 17.6569i | −0.447592 | − | 1.08058i | ||||
\(268\) | 22.7279 | + | 9.41421i | 1.38833 | + | 0.575065i | ||||
\(269\) | −14.2426 | − | 5.89949i | −0.868389 | − | 0.359699i | −0.0964064 | − | 0.995342i | \(-0.530735\pi\) |
−0.771983 | + | 0.635644i | \(0.780735\pi\) | |||||||
\(270\) | 11.3137 | 0.688530 | ||||||||
\(271\) | 11.5147i | 0.699469i | 0.936849 | + | 0.349735i | \(0.113728\pi\) | ||||
−0.936849 | + | 0.349735i | \(0.886272\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.00000i | 0.242091i | ||||||||
\(274\) | − | 30.2843i | − | 1.82954i | ||||||
\(275\) | −47.9203 | − | 19.8492i | −2.88970 | − | 1.19695i | ||||
\(276\) | 2.82843 | + | 6.82843i | 0.170251 | + | 0.411023i | ||||
\(277\) | −8.36396 | − | 20.1924i | −0.502542 | − | 1.21324i | −0.948095 | − | 0.317988i | \(-0.896993\pi\) |
0.445553 | − | 0.895255i | \(-0.353007\pi\) | |||||||
\(278\) | 4.58579 | − | 11.0711i | 0.275037 | − | 0.663999i | ||||
\(279\) | 23.8995 | + | 23.8995i | 1.43083 | + | 1.43083i | ||||
\(280\) | 4.00000 | + | 9.65685i | 0.239046 | + | 0.577107i | ||||
\(281\) | −1.34315 | + | 1.34315i | −0.0801254 | + | 0.0801254i | −0.746034 | − | 0.665908i | \(-0.768044\pi\) |
0.665908 | + | 0.746034i | \(0.268044\pi\) | |||||||
\(282\) | −12.4853 | − | 30.1421i | −0.743488 | − | 1.79494i | ||||
\(283\) | 12.8995 | − | 5.34315i | 0.766795 | − | 0.317617i | 0.0352218 | − | 0.999380i | \(-0.488786\pi\) |
0.731574 | + | 0.681762i | \(0.238786\pi\) | |||||||
\(284\) | −8.48528 | − | 8.48528i | −0.503509 | − | 0.503509i | ||||
\(285\) | 1.65685 | − | 4.00000i | 0.0981436 | − | 0.236940i | ||||
\(286\) | −9.17157 | + | 9.17157i | −0.542326 | + | 0.542326i | ||||
\(287\) | −4.82843 | −0.285013 | ||||||||
\(288\) | − | 21.6569i | − | 1.27614i | ||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | −31.7990 | + | 31.7990i | −1.86730 | + | 1.86730i | ||||
\(291\) | −1.17157 | + | 2.82843i | −0.0686788 | + | 0.165805i | ||||
\(292\) | −6.34315 | + | 6.34315i | −0.371205 | + | 0.371205i | ||||
\(293\) | 14.8284 | − | 6.14214i | 0.866286 | − | 0.358827i | 0.0951233 | − | 0.995466i | \(-0.469675\pi\) |
0.771163 | + | 0.636638i | \(0.219675\pi\) | |||||||
\(294\) | −1.41421 | − | 3.41421i | −0.0824786 | − | 0.199121i | ||||
\(295\) | 14.1421 | − | 14.1421i | 0.823387 | − | 0.823387i | ||||
\(296\) | −5.51472 | + | 13.3137i | −0.320537 | + | 0.773844i | ||||
\(297\) | −9.17157 | − | 9.17157i | −0.532189 | − | 0.532189i | ||||
\(298\) | −0.0710678 | + | 0.171573i | −0.00411685 | + | 0.00993895i | ||||
\(299\) | −0.828427 | − | 2.00000i | −0.0479092 | − | 0.115663i | ||||
\(300\) | −41.7990 | + | 17.3137i | −2.41327 | + | 0.999607i | ||||
\(301\) | −4.53553 | − | 1.87868i | −0.261424 | − | 0.108285i | ||||
\(302\) | 6.00000i | 0.345261i | ||||||||
\(303\) | − | 9.65685i | − | 0.554772i | ||||||
\(304\) | −1.65685 | − | 0.686292i | −0.0950271 | − | 0.0393615i | ||||
\(305\) | − | 11.3137i | − | 0.647821i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.1421 | − | 12.0711i | −1.66323 | − | 0.688932i | −0.664912 | − | 0.746921i | \(-0.731531\pi\) |
−0.998317 | + | 0.0579892i | \(0.981531\pi\) | |||||||
\(308\) | 4.58579 | − | 11.0711i | 0.261299 | − | 0.630833i | ||||
\(309\) | −14.4853 | − | 34.9706i | −0.824039 | − | 1.98941i | ||||
\(310\) | −42.6274 | − | 17.6569i | −2.42107 | − | 1.00284i | ||||
\(311\) | 19.3137 | + | 19.3137i | 1.09518 | + | 1.09518i | 0.994966 | + | 0.100214i | \(0.0319528\pi\) |
0.100214 | + | 0.994966i | \(0.468047\pi\) | |||||||
\(312\) | 11.3137i | 0.640513i | ||||||||
\(313\) | −4.92893 | + | 4.92893i | −0.278600 | + | 0.278600i | −0.832550 | − | 0.553950i | \(-0.813120\pi\) |
0.553950 | + | 0.832550i | \(0.313120\pi\) | |||||||
\(314\) | 8.48528 | − | 3.51472i | 0.478852 | − | 0.198347i | ||||
\(315\) | 13.0711 | − | 5.41421i | 0.736471 | − | 0.305056i | ||||
\(316\) | −19.7990 | −1.11378 | ||||||||
\(317\) | 4.36396 | − | 10.5355i | 0.245104 | − | 0.591735i | −0.752671 | − | 0.658397i | \(-0.771235\pi\) |
0.997776 | + | 0.0666621i | \(0.0212350\pi\) | |||||||
\(318\) | 0.343146 | + | 0.343146i | 0.0192427 | + | 0.0192427i | ||||
\(319\) | 51.5563 | 2.88660 | ||||||||
\(320\) | 11.3137 | + | 27.3137i | 0.632456 | + | 1.52688i | ||||
\(321\) | 16.1421 | 0.900966 | ||||||||
\(322\) | 1.41421 | + | 1.41421i | 0.0788110 | + | 0.0788110i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 11.6569 | 0.647603 | ||||||||
\(325\) | 12.2426 | − | 5.07107i | 0.679100 | − | 0.281292i | ||||
\(326\) | −7.00000 | + | 2.89949i | −0.387694 | + | 0.160588i | ||||
\(327\) | 17.0711 | − | 17.0711i | 0.944032 | − | 0.944032i | ||||
\(328\) | −13.6569 | −0.754074 | ||||||||
\(329\) | −6.24264 | − | 6.24264i | −0.344168 | − | 0.344168i | ||||
\(330\) | 75.5980 | + | 31.3137i | 4.16153 | + | 1.72376i | ||||
\(331\) | 5.12132 | + | 12.3640i | 0.281493 | + | 0.679585i | 0.999871 | − | 0.0160685i | \(-0.00511500\pi\) |
−0.718378 | + | 0.695653i | \(0.755115\pi\) | |||||||
\(332\) | −2.68629 | + | 6.48528i | −0.147429 | + | 0.355926i | ||||
\(333\) | 18.0208 | + | 7.46447i | 0.987535 | + | 0.409050i | ||||
\(334\) | −11.5147 | −0.630057 | ||||||||
\(335\) | 45.4558i | 2.48352i | ||||||||
\(336\) | −4.00000 | − | 9.65685i | −0.218218 | − | 0.526825i | ||||
\(337\) | − | 7.27208i | − | 0.396135i | −0.980188 | − | 0.198068i | \(-0.936533\pi\) | ||
0.980188 | − | 0.198068i | \(-0.0634666\pi\) | |||||||
\(338\) | 15.0711i | 0.819758i | ||||||||
\(339\) | −42.0416 | − | 17.4142i | −2.28339 | − | 0.945810i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.2426 | + | 48.8701i | 1.09620 | + | 2.64646i | ||||
\(342\) | −0.928932 | + | 2.24264i | −0.0502309 | + | 0.121268i | ||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | −12.8284 | − | 5.31371i | −0.691662 | − | 0.286496i | ||||
\(345\) | −9.65685 | + | 9.65685i | −0.519908 | + | 0.519908i | ||||
\(346\) | −2.48528 | − | 6.00000i | −0.133610 | − | 0.322562i | ||||
\(347\) | −2.12132 | + | 0.878680i | −0.113878 | + | 0.0471700i | −0.438895 | − | 0.898538i | \(-0.644630\pi\) |
0.325017 | + | 0.945708i | \(0.394630\pi\) | |||||||
\(348\) | 31.7990 | − | 31.7990i | 1.70460 | − | 1.70460i | ||||
\(349\) | −3.31371 | + | 8.00000i | −0.177379 | + | 0.428230i | −0.987415 | − | 0.158149i | \(-0.949447\pi\) |
0.810036 | + | 0.586380i | \(0.199447\pi\) | |||||||
\(350\) | −8.65685 | + | 8.65685i | −0.462728 | + | 0.462728i | ||||
\(351\) | 3.31371 | 0.176873 | ||||||||
\(352\) | 12.9706 | − | 31.3137i | 0.691333 | − | 1.66903i | ||||
\(353\) | 27.4558 | 1.46133 | 0.730664 | − | 0.682738i | \(-0.239211\pi\) | ||||
0.730664 | + | 0.682738i | \(0.239211\pi\) | |||||||
\(354\) | −14.1421 | + | 14.1421i | −0.751646 | + | 0.751646i | ||||
\(355\) | 8.48528 | − | 20.4853i | 0.450352 | − | 1.08725i | ||||
\(356\) | −10.3431 | − | 10.3431i | −0.548186 | − | 0.548186i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.17157 | + | 14.8995i | 0.326178 | + | 0.787463i | ||||
\(359\) | 11.9706 | − | 11.9706i | 0.631782 | − | 0.631782i | −0.316733 | − | 0.948515i | \(-0.602586\pi\) |
0.948515 | + | 0.316733i | \(0.102586\pi\) | |||||||
\(360\) | 36.9706 | − | 15.3137i | 1.94852 | − | 0.807103i | ||||
\(361\) | −13.2929 | − | 13.2929i | −0.699626 | − | 0.699626i | ||||
\(362\) | −7.65685 | + | 18.4853i | −0.402435 | + | 0.971565i | ||||
\(363\) | −24.8995 | − | 60.1127i | −1.30688 | − | 3.15510i | ||||
\(364\) | 1.17157 | + | 2.82843i | 0.0614071 | + | 0.148250i | ||||
\(365\) | −15.3137 | − | 6.34315i | −0.801556 | − | 0.332015i | ||||
\(366\) | 11.3137i | 0.591377i | ||||||||
\(367\) | 12.4853i | 0.651726i | 0.945417 | + | 0.325863i | \(0.105655\pi\) | ||||
−0.945417 | + | 0.325863i | \(0.894345\pi\) | |||||||
\(368\) | 4.00000 | + | 4.00000i | 0.208514 | + | 0.208514i | ||||
\(369\) | 18.4853i | 0.962305i | ||||||||
\(370\) | −26.6274 | −1.38429 | ||||||||
\(371\) | 0.121320 | + | 0.0502525i | 0.00629864 | + | 0.00260898i | ||||
\(372\) | 42.6274 | + | 17.6569i | 2.21013 | + | 0.915465i | ||||
\(373\) | 7.39340 | + | 17.8492i | 0.382816 | + | 0.924199i | 0.991419 | + | 0.130724i | \(0.0417302\pi\) |
−0.608603 | + | 0.793475i | \(0.708270\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −24.9706 | − | 24.9706i | −1.28947 | − | 1.28947i | ||||
\(376\) | −17.6569 | − | 17.6569i | −0.910583 | − | 0.910583i | ||||
\(377\) | −9.31371 | + | 9.31371i | −0.479680 | + | 0.479680i | ||||
\(378\) | −2.82843 | + | 1.17157i | −0.145479 | + | 0.0602592i | ||||
\(379\) | −19.2635 | + | 7.97918i | −0.989497 | + | 0.409863i | −0.817935 | − | 0.575310i | \(-0.804881\pi\) |
−0.171562 | + | 0.985173i | \(0.554881\pi\) | |||||||
\(380\) | − | 3.31371i | − | 0.169990i | ||||||
\(381\) | −14.9706 | + | 36.1421i | −0.766965 | + | 1.85162i | ||||
\(382\) | −3.07107 | − | 3.07107i | −0.157129 | − | 0.157129i | ||||
\(383\) | −12.8284 | −0.655502 | −0.327751 | − | 0.944764i | \(-0.606291\pi\) | ||||
−0.327751 | + | 0.944764i | \(0.606291\pi\) | |||||||
\(384\) | −11.3137 | − | 27.3137i | −0.577350 | − | 1.39385i | ||||
\(385\) | 22.1421 | 1.12847 | ||||||||
\(386\) | −1.41421 | − | 1.41421i | −0.0719816 | − | 0.0719816i | ||||
\(387\) | −7.19239 | + | 17.3640i | −0.365610 | + | 0.882660i | ||||
\(388\) | 2.34315i | 0.118955i | ||||||||
\(389\) | 12.0208 | − | 4.97918i | 0.609480 | − | 0.252455i | −0.0565264 | − | 0.998401i | \(-0.518003\pi\) |
0.666006 | + | 0.745946i | \(0.268003\pi\) | |||||||
\(390\) | −19.3137 | + | 8.00000i | −0.977988 | + | 0.405096i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.00000 | − | 2.00000i | −0.101015 | − | 0.101015i | ||||
\(393\) | 11.6569 | + | 11.6569i | 0.588011 | + | 0.588011i | ||||
\(394\) | −17.8284 | − | 7.38478i | −0.898183 | − | 0.372040i | ||||
\(395\) | −14.0000 | − | 33.7990i | −0.704416 | − | 1.70061i | ||||
\(396\) | −42.3848 | − | 17.5563i | −2.12992 | − | 0.882240i | ||||
\(397\) | −1.65685 | − | 0.686292i | −0.0831551 | − | 0.0344440i | 0.340718 | − | 0.940165i | \(-0.389330\pi\) |
−0.423873 | + | 0.905722i | \(0.639330\pi\) | |||||||
\(398\) | −1.85786 | −0.0931263 | ||||||||
\(399\) | 1.17157i | 0.0586520i | ||||||||
\(400\) | −24.4853 | + | 24.4853i | −1.22426 | + | 1.22426i | ||||
\(401\) | 32.2426i | 1.61012i | 0.593193 | + | 0.805060i | \(0.297867\pi\) | ||||
−0.593193 | + | 0.805060i | \(0.702133\pi\) | |||||||
\(402\) | − | 45.4558i | − | 2.26713i | ||||||
\(403\) | −12.4853 | − | 5.17157i | −0.621936 | − | 0.257614i | ||||
\(404\) | −2.82843 | − | 6.82843i | −0.140720 | − | 0.339727i | ||||
\(405\) | 8.24264 | + | 19.8995i | 0.409580 | + | 0.988814i | ||||
\(406\) | 4.65685 | − | 11.2426i | 0.231116 | − | 0.557963i | ||||
\(407\) | 21.5858 | + | 21.5858i | 1.06997 | + | 1.06997i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.7574 | − | 15.7574i | 0.779151 | − | 0.779151i | −0.200535 | − | 0.979686i | \(-0.564268\pi\) |
0.979686 | + | 0.200535i | \(0.0642681\pi\) | |||||||
\(410\) | −9.65685 | − | 23.3137i | −0.476918 | − | 1.15138i | ||||
\(411\) | −51.6985 | + | 21.4142i | −2.55010 | + | 1.05629i | ||||
\(412\) | −20.4853 | − | 20.4853i | −1.00924 | − | 1.00924i | ||||
\(413\) | −2.07107 | + | 5.00000i | −0.101911 | + | 0.246034i | ||||
\(414\) | 5.41421 | − | 5.41421i | 0.266094 | − | 0.266094i | ||||
\(415\) | −12.9706 | −0.636700 | ||||||||
\(416\) | 3.31371 | + | 8.00000i | 0.162468 | + | 0.392232i | ||||
\(417\) | −22.1421 | −1.08431 | ||||||||
\(418\) | −2.68629 | + | 2.68629i | −0.131391 | + | 0.131391i | ||||
\(419\) | 1.24264 | − | 3.00000i | 0.0607070 | − | 0.146560i | −0.890615 | − | 0.454758i | \(-0.849726\pi\) |
0.951322 | + | 0.308198i | \(0.0997259\pi\) | |||||||
\(420\) | 13.6569 | − | 13.6569i | 0.666386 | − | 0.666386i | ||||
\(421\) | 23.6066 | − | 9.77817i | 1.15052 | − | 0.476559i | 0.275809 | − | 0.961212i | \(-0.411054\pi\) |
0.874706 | + | 0.484653i | \(0.161054\pi\) | |||||||
\(422\) | 2.41421 | + | 5.82843i | 0.117522 | + | 0.283723i | ||||
\(423\) | −23.8995 | + | 23.8995i | −1.16203 | + | 1.16203i | ||||
\(424\) | 0.343146 | + | 0.142136i | 0.0166646 | + | 0.00690272i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.48528 | + | 20.4853i | −0.411113 | + | 0.992515i | ||||
\(427\) | 1.17157 | + | 2.82843i | 0.0566964 | + | 0.136877i | ||||
\(428\) | 11.4142 | − | 4.72792i | 0.551727 | − | 0.228533i | ||||
\(429\) | 22.1421 | + | 9.17157i | 1.06903 | + | 0.442808i | ||||
\(430\) | − | 25.6569i | − | 1.23728i | ||||||
\(431\) | 21.6569i | 1.04317i | 0.853198 | + | 0.521587i | \(0.174660\pi\) | ||||
−0.853198 | + | 0.521587i | \(0.825340\pi\) | |||||||
\(432\) | −8.00000 | + | 3.31371i | −0.384900 | + | 0.159431i | ||||
\(433\) | 24.2843i | 1.16703i | 0.812103 | + | 0.583514i | \(0.198323\pi\) | ||||
−0.812103 | + | 0.583514i | \(0.801677\pi\) | |||||||
\(434\) | 12.4853 | 0.599313 | ||||||||
\(435\) | 76.7696 | + | 31.7990i | 3.68082 | + | 1.52464i | ||||
\(436\) | 7.07107 | − | 17.0711i | 0.338643 | − | 0.817556i | ||||
\(437\) | −0.242641 | − | 0.585786i | −0.0116071 | − | 0.0280220i | ||||
\(438\) | 15.3137 | + | 6.34315i | 0.731717 | + | 0.303087i | ||||
\(439\) | −18.0000 | − | 18.0000i | −0.859093 | − | 0.859093i | 0.132138 | − | 0.991231i | \(-0.457816\pi\) |
−0.991231 | + | 0.132138i | \(0.957816\pi\) | |||||||
\(440\) | 62.6274 | 2.98564 | ||||||||
\(441\) | −2.70711 | + | 2.70711i | −0.128910 | + | 0.128910i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.1924 | − | 5.87868i | 0.674301 | − | 0.279304i | −0.0191415 | − | 0.999817i | \(-0.506093\pi\) |
0.693442 | + | 0.720512i | \(0.256093\pi\) | |||||||
\(444\) | 26.6274 | 1.26368 | ||||||||
\(445\) | 10.3431 | − | 24.9706i | 0.490312 | − | 1.18372i | ||||
\(446\) | 23.3137 | + | 23.3137i | 1.10394 | + | 1.10394i | ||||
\(447\) | 0.343146 | 0.0162302 | ||||||||
\(448\) | −5.65685 | − | 5.65685i | −0.267261 | − | 0.267261i | ||||
\(449\) | −33.4558 | −1.57888 | −0.789439 | − | 0.613828i | \(-0.789629\pi\) | ||||
−0.789439 | + | 0.613828i | \(0.789629\pi\) | |||||||
\(450\) | 33.1421 | + | 33.1421i | 1.56234 | + | 1.56234i | ||||
\(451\) | −11.0711 | + | 26.7279i | −0.521316 | + | 1.25857i | ||||
\(452\) | −34.8284 | −1.63819 | ||||||||
\(453\) | 10.2426 | − | 4.24264i | 0.481241 | − | 0.199337i | ||||
\(454\) | 37.5563 | − | 15.5563i | 1.76261 | − | 0.730096i | ||||
\(455\) | −4.00000 | + | 4.00000i | −0.187523 | + | 0.187523i | ||||
\(456\) | 3.31371i | 0.155179i | ||||||||
\(457\) | 8.00000 | + | 8.00000i | 0.374224 | + | 0.374224i | 0.869013 | − | 0.494789i | \(-0.164755\pi\) |
−0.494789 | + | 0.869013i | \(0.664755\pi\) | |||||||
\(458\) | −11.3137 | − | 4.68629i | −0.528655 | − | 0.218976i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.00000 | + | 9.65685i | −0.186501 | + | 0.450253i | ||||
\(461\) | −8.48528 | − | 3.51472i | −0.395199 | − | 0.163697i | 0.176229 | − | 0.984349i | \(-0.443610\pi\) |
−0.571428 | + | 0.820652i | \(0.693610\pi\) | |||||||
\(462\) | −22.1421 | −1.03015 | ||||||||
\(463\) | − | 28.0416i | − | 1.30321i | −0.758561 | − | 0.651603i | \(-0.774097\pi\) | ||
0.758561 | − | 0.651603i | \(-0.225903\pi\) | |||||||
\(464\) | 13.1716 | − | 31.7990i | 0.611475 | − | 1.47623i | ||||
\(465\) | 85.2548i | 3.95360i | ||||||||
\(466\) | 3.65685i | 0.169401i | ||||||||
\(467\) | 3.34315 | + | 1.38478i | 0.154702 | + | 0.0640798i | 0.458691 | − | 0.888596i | \(-0.348318\pi\) |
−0.303989 | + | 0.952676i | \(0.598318\pi\) | |||||||
\(468\) | 10.8284 | − | 4.48528i | 0.500544 | − | 0.207332i | ||||
\(469\) | −4.70711 | − | 11.3640i | −0.217354 | − | 0.524739i | ||||
\(470\) | 17.6569 | − | 42.6274i | 0.814450 | − | 1.96626i | ||||
\(471\) | −12.0000 | − | 12.0000i | −0.552931 | − | 0.552931i | ||||
\(472\) | −5.85786 | + | 14.1421i | −0.269630 | + | 0.650945i | ||||
\(473\) | −20.7990 | + | 20.7990i | −0.956339 | + | 0.956339i | ||||
\(474\) | 14.0000 | + | 33.7990i | 0.643041 | + | 1.55244i | ||||
\(475\) | 3.58579 | − | 1.48528i | 0.164527 | − | 0.0681494i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.192388 | − | 0.464466i | 0.00880885 | − | 0.0212664i | ||||
\(478\) | 6.00000 | − | 6.00000i | 0.274434 | − | 0.274434i | ||||
\(479\) | −29.3137 | −1.33938 | −0.669689 | − | 0.742642i | \(-0.733572\pi\) | ||||
−0.669689 | + | 0.742642i | \(0.733572\pi\) | |||||||
\(480\) | 38.6274 | − | 38.6274i | 1.76309 | − | 1.76309i | ||||
\(481\) | −7.79899 | −0.355603 | ||||||||
\(482\) | −23.7990 | + | 23.7990i | −1.08401 | + | 1.08401i | ||||
\(483\) | 1.41421 | − | 3.41421i | 0.0643489 | − | 0.155352i | ||||
\(484\) | −35.2132 | − | 35.2132i | −1.60060 | − | 1.60060i | ||||
\(485\) | −4.00000 | + | 1.65685i | −0.181631 | + | 0.0752339i | ||||
\(486\) | −11.7574 | − | 28.3848i | −0.533325 | − | 1.28756i | ||||
\(487\) | −0.857864 | + | 0.857864i | −0.0388735 | + | 0.0388735i | −0.726276 | − | 0.687403i | \(-0.758751\pi\) |
0.687403 | + | 0.726276i | \(0.258751\pi\) | |||||||
\(488\) | 3.31371 | + | 8.00000i | 0.150005 | + | 0.362143i | ||||
\(489\) | 9.89949 | + | 9.89949i | 0.447671 | + | 0.447671i | ||||
\(490\) | 2.00000 | − | 4.82843i | 0.0903508 | − | 0.218126i | ||||
\(491\) | 6.46447 | + | 15.6066i | 0.291737 | + | 0.704316i | 0.999999 | − | 0.00163420i | \(-0.000520184\pi\) |
−0.708261 | + | 0.705950i | \(0.750520\pi\) | |||||||
\(492\) | 9.65685 | + | 23.3137i | 0.435365 | + | 1.05106i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | − | 0.970563i | − | 0.0436677i | ||||||
\(495\) | − | 84.7696i | − | 3.81011i | ||||||
\(496\) | 35.3137 | 1.58563 | ||||||||
\(497\) | 6.00000i | 0.269137i | ||||||||
\(498\) | 12.9706 | 0.581225 | ||||||||
\(499\) | 14.5355 | + | 6.02082i | 0.650700 | + | 0.269529i | 0.683519 | − | 0.729933i | \(-0.260449\pi\) |
−0.0328193 | + | 0.999461i | \(0.510449\pi\) | |||||||
\(500\) | −24.9706 | − | 10.3431i | −1.11672 | − | 0.462560i | ||||
\(501\) | 8.14214 | + | 19.6569i | 0.363764 | + | 0.878203i | ||||
\(502\) | −3.75736 | − | 1.55635i | −0.167699 | − | 0.0694633i | ||||
\(503\) | 5.17157 | + | 5.17157i | 0.230589 | + | 0.230589i | 0.812939 | − | 0.582349i | \(-0.197866\pi\) |
−0.582349 | + | 0.812939i | \(0.697866\pi\) | |||||||
\(504\) | −7.65685 | + | 7.65685i | −0.341063 | + | 0.341063i | ||||
\(505\) | 9.65685 | − | 9.65685i | 0.429724 | − | 0.429724i | ||||
\(506\) | 11.0711 | − | 4.58579i | 0.492169 | − | 0.203863i | ||||
\(507\) | 25.7279 | − | 10.6569i | 1.14262 | − | 0.473288i | ||||
\(508\) | 29.9411i | 1.32842i | ||||||||
\(509\) | 3.31371 | − | 8.00000i | 0.146878 | − | 0.354594i | −0.833269 | − | 0.552868i | \(-0.813534\pi\) |
0.980147 | + | 0.198274i | \(0.0635335\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.48528 | 0.198417 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | 0.970563 | 0.0428514 | ||||||||
\(514\) | 28.1421 | + | 28.1421i | 1.24130 | + | 1.24130i | ||||
\(515\) | 20.4853 | − | 49.4558i | 0.902689 | − | 2.17928i | ||||
\(516\) | 25.6569i | 1.12948i | ||||||||
\(517\) | −48.8701 | + | 20.2426i | −2.14930 | + | 0.890270i | ||||
\(518\) | 6.65685 | − | 2.75736i | 0.292485 | − | 0.121151i | ||||
\(519\) | −8.48528 | + | 8.48528i | −0.372463 | + | 0.372463i | ||||
\(520\) | −11.3137 | + | 11.3137i | −0.496139 | + | 0.496139i | ||||
\(521\) | −16.7279 | − | 16.7279i | −0.732864 | − | 0.732864i | 0.238323 | − | 0.971186i | \(-0.423402\pi\) |
−0.971186 | + | 0.238323i | \(0.923402\pi\) | |||||||
\(522\) | −43.0416 | − | 17.8284i | −1.88388 | − | 0.780329i | ||||
\(523\) | −1.00000 | − | 2.41421i | −0.0437269 | − | 0.105566i | 0.900507 | − | 0.434841i | \(-0.143196\pi\) |
−0.944234 | + | 0.329275i | \(0.893196\pi\) | |||||||
\(524\) | 11.6569 | + | 4.82843i | 0.509232 | + | 0.210931i | ||||
\(525\) | 20.8995 | + | 8.65685i | 0.912129 | + | 0.377816i | ||||
\(526\) | 19.3137 | 0.842118 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −62.6274 | −2.72551 | ||||||||
\(529\) | − | 21.0000i | − | 0.913043i | ||||||
\(530\) | 0.686292i | 0.0298106i | ||||||||
\(531\) | 19.1421 | + | 7.92893i | 0.830698 | + | 0.344086i | ||||
\(532\) | 0.343146 | + | 0.828427i | 0.0148773 | + | 0.0359169i | ||||
\(533\) | −2.82843 | − | 6.82843i | −0.122513 | − | 0.295772i | ||||
\(534\) | −10.3431 | + | 24.9706i | −0.447592 | + | 1.08058i | ||||
\(535\) | 16.1421 | + | 16.1421i | 0.697885 | + | 0.697885i | ||||
\(536\) | −13.3137 | − | 32.1421i | −0.575065 | − | 1.38833i | ||||
\(537\) | 21.0711 | − | 21.0711i | 0.909284 | − | 0.909284i | ||||
\(538\) | 8.34315 | + | 20.1421i | 0.359699 | + | 0.868389i | ||||
\(539\) | −5.53553 | + | 2.29289i | −0.238432 | + | 0.0987619i | ||||
\(540\) | −11.3137 | − | 11.3137i | −0.486864 | − | 0.486864i | ||||
\(541\) | 4.87868 | − | 11.7782i | 0.209751 | − | 0.506383i | −0.783633 | − | 0.621224i | \(-0.786636\pi\) |
0.993384 | + | 0.114841i | \(0.0366357\pi\) | |||||||
\(542\) | 11.5147 | − | 11.5147i | 0.494600 | − | 0.494600i | ||||
\(543\) | 36.9706 | 1.58656 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 34.1421 | 1.46249 | ||||||||
\(546\) | 4.00000 | − | 4.00000i | 0.171184 | − | 0.171184i | ||||
\(547\) | −6.77817 | + | 16.3640i | −0.289814 | + | 0.699672i | −0.999991 | − | 0.00435101i | \(-0.998615\pi\) |
0.710177 | + | 0.704023i | \(0.248615\pi\) | |||||||
\(548\) | −30.2843 | + | 30.2843i | −1.29368 | + | 1.29368i | ||||
\(549\) | 10.8284 | − | 4.48528i | 0.462146 | − | 0.191427i | ||||
\(550\) | 28.0711 | + | 67.7696i | 1.19695 | + | 2.88970i | ||||
\(551\) | −2.72792 | + | 2.72792i | −0.116213 | + | 0.116213i | ||||
\(552\) | 4.00000 | − | 9.65685i | 0.170251 | − | 0.411023i | ||||
\(553\) | 7.00000 | + | 7.00000i | 0.297670 | + | 0.297670i | ||||
\(554\) | −11.8284 | + | 28.5563i | −0.502542 | + | 1.21324i | ||||
\(555\) | 18.8284 | + | 45.4558i | 0.799222 | + | 1.92949i | ||||
\(556\) | −15.6569 | + | 6.48528i | −0.663999 | + | 0.275037i | ||||
\(557\) | 20.1924 | + | 8.36396i | 0.855579 | + | 0.354392i | 0.766977 | − | 0.641675i | \(-0.221760\pi\) |
0.0886020 | + | 0.996067i | \(0.471760\pi\) | |||||||
\(558\) | − | 47.7990i | − | 2.02349i | ||||||
\(559\) | − | 7.51472i | − | 0.317839i | ||||||
\(560\) | 5.65685 | − | 13.6569i | 0.239046 | − | 0.577107i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.68629 | 0.113314 | ||||||||
\(563\) | 14.3137 | + | 5.92893i | 0.603251 | + | 0.249875i | 0.663340 | − | 0.748318i | \(-0.269138\pi\) |
−0.0600889 | + | 0.998193i | \(0.519138\pi\) | |||||||
\(564\) | −17.6569 | + | 42.6274i | −0.743488 | + | 1.79494i | ||||
\(565\) | −24.6274 | − | 59.4558i | −1.03608 | − | 2.50133i | ||||
\(566\) | −18.2426 | − | 7.55635i | −0.766795 | − | 0.317617i | ||||
\(567\) | −4.12132 | − | 4.12132i | −0.173079 | − | 0.173079i | ||||
\(568\) | 16.9706i | 0.712069i | ||||||||
\(569\) | 19.7990 | − | 19.7990i | 0.830017 | − | 0.830017i | −0.157502 | − | 0.987519i | \(-0.550344\pi\) |
0.987519 | + | 0.157502i | \(0.0503440\pi\) | |||||||
\(570\) | −5.65685 | + | 2.34315i | −0.236940 | + | 0.0981436i | ||||
\(571\) | −7.87868 | + | 3.26346i | −0.329712 | + | 0.136571i | −0.541398 | − | 0.840766i | \(-0.682105\pi\) |
0.211685 | + | 0.977338i | \(0.432105\pi\) | |||||||
\(572\) | 18.3431 | 0.766965 | ||||||||
\(573\) | −3.07107 | + | 7.41421i | −0.128296 | + | 0.309733i | ||||
\(574\) | 4.82843 | + | 4.82843i | 0.201535 | + | 0.201535i | ||||
\(575\) | −12.2426 | −0.510553 | ||||||||
\(576\) | −21.6569 | + | 21.6569i | −0.902369 | + | 0.902369i | ||||
\(577\) | 4.14214 | 0.172439 | 0.0862197 | − | 0.996276i | \(-0.472521\pi\) | ||||
0.0862197 | + | 0.996276i | \(0.472521\pi\) | |||||||
\(578\) | −17.0000 | − | 17.0000i | −0.707107 | − | 0.707107i | ||||
\(579\) | −1.41421 | + | 3.41421i | −0.0587727 | + | 0.141890i | ||||
\(580\) | 63.5980 | 2.64076 | ||||||||
\(581\) | 3.24264 | − | 1.34315i | 0.134527 | − | 0.0557231i | ||||
\(582\) | 4.00000 | − | 1.65685i | 0.165805 | − | 0.0686788i | ||||
\(583\) | 0.556349 | − | 0.556349i | 0.0230416 | − | 0.0230416i | ||||
\(584\) | 12.6863 | 0.524962 | ||||||||
\(585\) | 15.3137 | + | 15.3137i | 0.633144 | + | 0.633144i | ||||
\(586\) | −20.9706 | − | 8.68629i | −0.866286 | − | 0.358827i | ||||
\(587\) | −14.7574 | − | 35.6274i | −0.609101 | − | 1.47050i | −0.863979 | − | 0.503528i | \(-0.832035\pi\) |
0.254878 | − | 0.966973i | \(-0.417965\pi\) | |||||||
\(588\) | −2.00000 | + | 4.82843i | −0.0824786 | + | 0.199121i | ||||
\(589\) | −3.65685 | − | 1.51472i | −0.150678 | − | 0.0624129i | ||||
\(590\) | −28.2843 | −1.16445 | ||||||||
\(591\) | 35.6569i | 1.46673i | ||||||||
\(592\) | 18.8284 | − | 7.79899i | 0.773844 | − | 0.320537i | ||||
\(593\) | − | 23.1716i | − | 0.951542i | −0.879569 | − | 0.475771i | \(-0.842169\pi\) | ||
0.879569 | − | 0.475771i | \(-0.157831\pi\) | |||||||
\(594\) | 18.3431i | 0.752628i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.242641 | − | 0.100505i | 0.00993895 | − | 0.00411685i | ||||
\(597\) | 1.31371 | + | 3.17157i | 0.0537665 | + | 0.129804i | ||||
\(598\) | −1.17157 | + | 2.82843i | −0.0479092 | + | 0.115663i | ||||
\(599\) | −19.3137 | − | 19.3137i | −0.789137 | − | 0.789137i | 0.192216 | − | 0.981353i | \(-0.438433\pi\) |
−0.981353 | + | 0.192216i | \(0.938433\pi\) | |||||||
\(600\) | 59.1127 | + | 24.4853i | 2.41327 | + | 0.999607i | ||||
\(601\) | 1.31371 | − | 1.31371i | 0.0535873 | − | 0.0535873i | −0.679805 | − | 0.733393i | \(-0.737936\pi\) |
0.733393 | + | 0.679805i | \(0.237936\pi\) | |||||||
\(602\) | 2.65685 | + | 6.41421i | 0.108285 | + | 0.261424i | ||||
\(603\) | −43.5061 | + | 18.0208i | −1.77171 | + | 0.733864i | ||||
\(604\) | 6.00000 | − | 6.00000i | 0.244137 | − | 0.244137i | ||||
\(605\) | 35.2132 | − | 85.0122i | 1.43162 | − | 3.45624i | ||||
\(606\) | −9.65685 | + | 9.65685i | −0.392283 | + | 0.392283i | ||||
\(607\) | −26.3431 | −1.06924 | −0.534618 | − | 0.845094i | \(-0.679544\pi\) | ||||
−0.534618 | + | 0.845094i | \(0.679544\pi\) | |||||||
\(608\) | 0.970563 | + | 2.34315i | 0.0393615 | + | 0.0950271i | ||||
\(609\) | −22.4853 | −0.911150 | ||||||||
\(610\) | −11.3137 | + | 11.3137i | −0.458079 | + | 0.458079i | ||||
\(611\) | 5.17157 | − | 12.4853i | 0.209219 | − | 0.505100i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.7487 | + | 13.9792i | −1.36310 | + | 0.564614i | −0.939908 | − | 0.341427i | \(-0.889090\pi\) |
−0.423190 | + | 0.906041i | \(0.639090\pi\) | |||||||
\(614\) | 17.0711 | + | 41.2132i | 0.688932 | + | 1.66323i | ||||
\(615\) | −32.9706 | + | 32.9706i | −1.32950 | + | 1.32950i | ||||
\(616\) | −15.6569 | + | 6.48528i | −0.630833 | + | 0.261299i | ||||
\(617\) | −6.97056 | − | 6.97056i | −0.280624 | − | 0.280624i | 0.552734 | − | 0.833358i | \(-0.313585\pi\) |
−0.833358 | + | 0.552734i | \(0.813585\pi\) | |||||||
\(618\) | −20.4853 | + | 49.4558i | −0.824039 | + | 1.98941i | ||||
\(619\) | 2.89949 | + | 7.00000i | 0.116541 | + | 0.281354i | 0.971377 | − | 0.237544i | \(-0.0763425\pi\) |
−0.854836 | + | 0.518898i | \(0.826342\pi\) | |||||||
\(620\) | 24.9706 | + | 60.2843i | 1.00284 | + | 2.42107i | ||||
\(621\) | −2.82843 | − | 1.17157i | −0.113501 | − | 0.0470136i | ||||
\(622\) | − | 38.6274i | − | 1.54882i | ||||||
\(623\) | 7.31371i | 0.293018i | ||||||||
\(624\) | 11.3137 | − | 11.3137i | 0.452911 | − | 0.452911i | ||||
\(625\) | − | 6.65685i | − | 0.266274i | ||||||
\(626\) | 9.85786 | 0.394000 | ||||||||
\(627\) | 6.48528 | + | 2.68629i | 0.258997 | + | 0.107280i | ||||
\(628\) | −12.0000 | − | 4.97056i | −0.478852 | − | 0.198347i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −18.4853 | − | 7.65685i | −0.736471 | − | 0.305056i | ||||
\(631\) | −11.7574 | − | 11.7574i | −0.468053 | − | 0.468053i | 0.433230 | − | 0.901283i | \(-0.357374\pi\) |
−0.901283 | + | 0.433230i | \(0.857374\pi\) | |||||||
\(632\) | 19.7990 | + | 19.7990i | 0.787562 | + | 0.787562i | ||||
\(633\) | 8.24264 | − | 8.24264i | 0.327616 | − | 0.327616i | ||||
\(634\) | −14.8995 | + | 6.17157i | −0.591735 | + | 0.245104i | ||||
\(635\) | −51.1127 | + | 21.1716i | −2.02835 | + | 0.840168i | ||||
\(636\) | − | 0.686292i | − | 0.0272132i | ||||||
\(637\) | 0.585786 | − | 1.41421i | 0.0232097 | − | 0.0560332i | ||||
\(638\) | −51.5563 | − | 51.5563i | −2.04114 | − | 2.04114i | ||||
\(639\) | 22.9706 | 0.908701 | ||||||||
\(640\) | 16.0000 | − | 38.6274i | 0.632456 | − | 1.52688i | ||||
\(641\) | 38.1838 | 1.50817 | 0.754084 | − | 0.656778i | \(-0.228081\pi\) | ||||
0.754084 | + | 0.656778i | \(0.228081\pi\) | |||||||
\(642\) | −16.1421 | − | 16.1421i | −0.637079 | − | 0.637079i | ||||
\(643\) | 12.5563 | − | 30.3137i | 0.495174 | − | 1.19546i | −0.456881 | − | 0.889528i | \(-0.651033\pi\) |
0.952055 | − | 0.305928i | \(-0.0989667\pi\) | |||||||
\(644\) | − | 2.82843i | − | 0.111456i | ||||||
\(645\) | −43.7990 | + | 18.1421i | −1.72458 | + | 0.714346i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.5563 | − | 19.5563i | 0.768839 | − | 0.768839i | −0.209063 | − | 0.977902i | \(-0.567041\pi\) |
0.977902 | + | 0.209063i | \(0.0670413\pi\) | |||||||
\(648\) | −11.6569 | − | 11.6569i | −0.457924 | − | 0.457924i | ||||
\(649\) | 22.9289 | + | 22.9289i | 0.900039 | + | 0.900039i | ||||
\(650\) | −17.3137 | − | 7.17157i | −0.679100 | − | 0.281292i | ||||
\(651\) | −8.82843 | − | 21.3137i | −0.346013 | − | 0.835350i | ||||
\(652\) | 9.89949 | + | 4.10051i | 0.387694 | + | 0.160588i | ||||
\(653\) | −8.77817 | − | 3.63604i | −0.343517 | − | 0.142289i | 0.204254 | − | 0.978918i | \(-0.434523\pi\) |
−0.547770 | + | 0.836629i | \(0.684523\pi\) | |||||||
\(654\) | −34.1421 | −1.33506 | ||||||||
\(655\) | 23.3137i | 0.910942i | ||||||||
\(656\) | 13.6569 | + | 13.6569i | 0.533211 | + | 0.533211i | ||||
\(657\) | − | 17.1716i | − | 0.669927i | ||||||
\(658\) | 12.4853i | 0.486727i | ||||||||
\(659\) | −25.4350 | − | 10.5355i | −0.990808 | − | 0.410406i | −0.172390 | − | 0.985029i | \(-0.555149\pi\) |
−0.818418 | + | 0.574623i | \(0.805149\pi\) | |||||||
\(660\) | −44.2843 | − | 106.912i | −1.72376 | − | 4.16153i | ||||
\(661\) | 12.8701 | + | 31.0711i | 0.500587 | + | 1.20852i | 0.949165 | + | 0.314780i | \(0.101931\pi\) |
−0.448577 | + | 0.893744i | \(0.648069\pi\) | |||||||
\(662\) | 7.24264 | − | 17.4853i | 0.281493 | − | 0.679585i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.17157 | − | 3.79899i | 0.355926 | − | 0.147429i | ||||
\(665\) | −1.17157 | + | 1.17157i | −0.0454316 | + | 0.0454316i | ||||
\(666\) | −10.5563 | − | 25.4853i | −0.409050 | − | 0.987535i | ||||
\(667\) | 11.2426 | − | 4.65685i | 0.435317 | − | 0.180314i | ||||
\(668\) | 11.5147 | + | 11.5147i | 0.445518 | + | 0.445518i | ||||
\(669\) | 23.3137 | − | 56.2843i | 0.901360 | − | 2.17608i | ||||
\(670\) | 45.4558 | − | 45.4558i | 1.75611 | − | 1.75611i | ||||
\(671\) | 18.3431 | 0.708129 | ||||||||
\(672\) | −5.65685 | + | 13.6569i | −0.218218 | + | 0.526825i | ||||
\(673\) | 25.4558 | 0.981251 | 0.490625 | − | 0.871371i | \(-0.336768\pi\) | ||||
0.490625 | + | 0.871371i | \(0.336768\pi\) | |||||||
\(674\) | −7.27208 | + | 7.27208i | −0.280110 | + | 0.280110i | ||||
\(675\) | 7.17157 | − | 17.3137i | 0.276034 | − | 0.666405i | ||||
\(676\) | 15.0711 | − | 15.0711i | 0.579656 | − | 0.579656i | ||||
\(677\) | 44.6274 | − | 18.4853i | 1.71517 | − | 0.710447i | 0.715238 | − | 0.698881i | \(-0.246318\pi\) |
0.999933 | − | 0.0115660i | \(-0.00368164\pi\) | |||||||
\(678\) | 24.6274 | + | 59.4558i | 0.945810 | + | 2.28339i | ||||
\(679\) | 0.828427 | − | 0.828427i | 0.0317921 | − | 0.0317921i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −53.1127 | − | 53.1127i | −2.03528 | − | 2.03528i | ||||
\(682\) | 28.6274 | − | 69.1127i | 1.09620 | − | 2.64646i | ||||
\(683\) | −3.63604 | − | 8.77817i | −0.139129 | − | 0.335888i | 0.838922 | − | 0.544251i | \(-0.183186\pi\) |
−0.978051 | + | 0.208364i | \(0.933186\pi\) | |||||||
\(684\) | 3.17157 | − | 1.31371i | 0.121268 | − | 0.0502309i | ||||
\(685\) | −73.1127 | − | 30.2843i | −2.79349 | − | 1.15710i | ||||
\(686\) | 1.41421i | 0.0539949i | ||||||||
\(687\) | 22.6274i | 0.863290i | ||||||||
\(688\) | 7.51472 | + | 18.1421i | 0.286496 | + | 0.691662i | ||||
\(689\) | 0.201010i | 0.00765788i | ||||||||
\(690\) | 19.3137 | 0.735260 | ||||||||
\(691\) | −2.89949 | − | 1.20101i | −0.110302 | − | 0.0456886i | 0.326850 | − | 0.945076i | \(-0.394013\pi\) |
−0.437152 | + | 0.899388i | \(0.644013\pi\) | |||||||
\(692\) | −3.51472 | + | 8.48528i | −0.133610 | + | 0.322562i | ||||
\(693\) | 8.77817 | + | 21.1924i | 0.333455 | + | 0.805032i | ||||
\(694\) | 3.00000 | + | 1.24264i | 0.113878 | + | 0.0471700i | ||||
\(695\) | −22.1421 | − | 22.1421i | −0.839899 | − | 0.839899i | ||||
\(696\) | −63.5980 | −2.41068 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 11.3137 | − | 4.68629i | 0.428230 | − | 0.177379i | ||||
\(699\) | 6.24264 | − | 2.58579i | 0.236118 | − | 0.0978034i | ||||
\(700\) | 17.3137 | 0.654397 | ||||||||
\(701\) | −3.22183 | + | 7.77817i | −0.121687 | + | 0.293778i | −0.972971 | − | 0.230927i | \(-0.925824\pi\) |
0.851284 | + | 0.524704i | \(0.175824\pi\) | |||||||
\(702\) | −3.31371 | − | 3.31371i | −0.125068 | − | 0.125068i | ||||
\(703\) | −2.28427 | −0.0861529 | ||||||||
\(704\) | −44.2843 | + | 18.3431i | −1.66903 | + | 0.691333i | ||||
\(705\) | −85.2548 | −3.21088 | ||||||||
\(706\) | −27.4558 | − | 27.4558i | −1.03331 | − | 1.03331i | ||||
\(707\) | −1.41421 | + | 3.41421i | −0.0531870 | + | 0.128405i | ||||
\(708\) | 28.2843 | 1.06299 | ||||||||
\(709\) | −9.46447 | + | 3.92031i | −0.355445 | + | 0.147230i | −0.553259 | − | 0.833009i | \(-0.686616\pi\) |
0.197813 | + | 0.980240i | \(0.436616\pi\) | |||||||
\(710\) | −28.9706 | + | 12.0000i | −1.08725 | + | 0.450352i | ||||
\(711\) | 26.7990 | − | 26.7990i | 1.00504 | − | 1.00504i | ||||
\(712\) | 20.6863i | 0.775252i | ||||||||
\(713\) | 8.82843 | + | 8.82843i | 0.330627 | + | 0.330627i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.9706 | + | 31.3137i | 0.485072 | + | 1.17107i | ||||
\(716\) | 8.72792 | − | 21.0711i | 0.326178 | − | 0.787463i | ||||
\(717\) | −14.4853 | − | 6.00000i | −0.540963 | − | 0.224074i | ||||
\(718\) | −23.9411 | −0.893475 | ||||||||
\(719\) | − | 10.6863i | − | 0.398531i | −0.979945 | − | 0.199266i | \(-0.936144\pi\) | ||
0.979945 | − | 0.199266i | \(-0.0638557\pi\) | |||||||
\(720\) | −52.2843 | − | 21.6569i | −1.94852 | − | 0.807103i | ||||
\(721\) | 14.4853i | 0.539460i | ||||||||
\(722\) | 26.5858i | 0.989421i | ||||||||
\(723\) | 57.4558 | + | 23.7990i | 2.13681 | + | 0.885094i | ||||
\(724\) | 26.1421 | − | 10.8284i | 0.971565 | − | 0.402435i | ||||
\(725\) | 28.5061 | + | 68.8198i | 1.05869 | + | 2.55590i | ||||
\(726\) | −35.2132 | + | 85.0122i | −1.30688 | + | 3.15510i | ||||
\(727\) | −23.2132 | − | 23.2132i | −0.860930 | − | 0.860930i | 0.130516 | − | 0.991446i | \(-0.458337\pi\) |
−0.991446 | + | 0.130516i | \(0.958337\pi\) | |||||||
\(728\) | 1.65685 | − | 4.00000i | 0.0614071 | − | 0.148250i | ||||
\(729\) | −27.7782 | + | 27.7782i | −1.02882 | + | 1.02882i | ||||
\(730\) | 8.97056 | + | 21.6569i | 0.332015 | + | 0.801556i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 11.3137 | − | 11.3137i | 0.418167 | − | 0.418167i | ||||
\(733\) | −3.85786 | + | 9.31371i | −0.142493 | + | 0.344010i | −0.978973 | − | 0.203988i | \(-0.934610\pi\) |
0.836480 | + | 0.547998i | \(0.184610\pi\) | |||||||
\(734\) | 12.4853 | − | 12.4853i | 0.460840 | − | 0.460840i | ||||
\(735\) | −9.65685 | −0.356198 | ||||||||
\(736\) | − | 8.00000i | − | 0.294884i | ||||||
\(737\) | −73.6985 | −2.71472 | ||||||||
\(738\) | 18.4853 | − | 18.4853i | 0.680453 | − | 0.680453i | ||||
\(739\) | −16.1924 | + | 39.0919i | −0.595647 | + | 1.43802i | 0.282331 | + | 0.959317i | \(0.408892\pi\) |
−0.877978 | + | 0.478701i | \(0.841108\pi\) | |||||||
\(740\) | 26.6274 | + | 26.6274i | 0.978843 | + | 0.978843i | ||||
\(741\) | −1.65685 | + | 0.686292i | −0.0608661 | + | 0.0252115i | ||||
\(742\) | −0.0710678 | − | 0.171573i | −0.00260898 | − | 0.00629864i | ||||
\(743\) | −1.48528 | + | 1.48528i | −0.0544897 | + | 0.0544897i | −0.733827 | − | 0.679337i | \(-0.762268\pi\) |
0.679337 | + | 0.733827i | \(0.262268\pi\) | |||||||
\(744\) | −24.9706 | − | 60.2843i | −0.915465 | − | 2.21013i | ||||
\(745\) | 0.343146 | + | 0.343146i | 0.0125719 | + | 0.0125719i | ||||
\(746\) | 10.4558 | − | 25.2426i | 0.382816 | − | 0.924199i | ||||
\(747\) | −5.14214 | − | 12.4142i | −0.188141 | − | 0.454212i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.70711 | − | 2.36396i | −0.208533 | − | 0.0863773i | ||||
\(750\) | 49.9411i | 1.82359i | ||||||||
\(751\) | − | 26.2843i | − | 0.959127i | −0.877507 | − | 0.479563i | \(-0.840795\pi\) | ||
0.877507 | − | 0.479563i | \(-0.159205\pi\) | |||||||
\(752\) | 35.3137i | 1.28776i | ||||||||
\(753\) | 7.51472i | 0.273852i | ||||||||
\(754\) | 18.6274 | 0.678371 | ||||||||
\(755\) | 14.4853 | + | 6.00000i | 0.527173 | + | 0.218362i | ||||
\(756\) | 4.00000 | + | 1.65685i | 0.145479 | + | 0.0602592i | ||||
\(757\) | 3.46447 | + | 8.36396i | 0.125918 | + | 0.303993i | 0.974250 | − | 0.225472i | \(-0.0723925\pi\) |
−0.848331 | + | 0.529466i | \(0.822392\pi\) | |||||||
\(758\) | 27.2426 | + | 11.2843i | 0.989497 | + | 0.409863i | ||||
\(759\) | −15.6569 | − | 15.6569i | −0.568308 | − | 0.568308i | ||||
\(760\) | −3.31371 | + | 3.31371i | −0.120201 | + | 0.120201i | ||||
\(761\) | −7.41421 | + | 7.41421i | −0.268765 | + | 0.268765i | −0.828602 | − | 0.559837i | \(-0.810864\pi\) |
0.559837 | + | 0.828602i | \(0.310864\pi\) | |||||||
\(762\) | 51.1127 | − | 21.1716i | 1.85162 | − | 0.766965i | ||||
\(763\) | −8.53553 | + | 3.53553i | −0.309007 | + | 0.127995i | ||||
\(764\) | 6.14214i | 0.222215i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.8284 | + | 12.8284i | 0.463510 | + | 0.463510i | ||||
\(767\) | −8.28427 | −0.299128 | ||||||||
\(768\) | −16.0000 | + | 38.6274i | −0.577350 | + | 1.39385i | ||||
\(769\) | 45.9411 | 1.65668 | 0.828340 | − | 0.560226i | \(-0.189286\pi\) | ||||
0.828340 | + | 0.560226i | \(0.189286\pi\) | |||||||
\(770\) | −22.1421 | − | 22.1421i | −0.797947 | − | 0.797947i | ||||
\(771\) | 28.1421 | − | 67.9411i | 1.01351 | − | 2.44684i | ||||
\(772\) | 2.82843i | 0.101797i | ||||||||
\(773\) | −0.828427 | + | 0.343146i | −0.0297965 | + | 0.0123421i | −0.397532 | − | 0.917588i | \(-0.630133\pi\) |
0.367735 | + | 0.929930i | \(0.380133\pi\) | |||||||
\(774\) | 24.5563 | − | 10.1716i | 0.882660 | − | 0.365610i | ||||
\(775\) | −54.0416 | + | 54.0416i | −1.94123 | + | 1.94123i | ||||
\(776\) | 2.34315 | − | 2.34315i | 0.0841140 | − | 0.0841140i | ||||
\(777\) | −9.41421 | − | 9.41421i | −0.337733 | − | 0.337733i | ||||
\(778\) | −17.0000 | − | 7.04163i | −0.609480 | − | 0.252455i | ||||
\(779\) | −0.828427 | − | 2.00000i | −0.0296815 | − | 0.0716574i | ||||
\(780\) | 27.3137 | + | 11.3137i | 0.977988 | + | 0.405096i | ||||
\(781\) | 33.2132 | + | 13.7574i | 1.18846 | + | 0.492277i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.6274i | 0.665690i | ||||||||
\(784\) | 4.00000i | 0.142857i | ||||||||
\(785\) | − | 24.0000i | − | 0.856597i | ||||||
\(786\) | − | 23.3137i | − | 0.831572i | ||||||
\(787\) | 5.24264 | + | 2.17157i | 0.186880 | + | 0.0774082i | 0.474161 | − | 0.880438i | \(-0.342751\pi\) |
−0.287281 | + | 0.957846i | \(0.592751\pi\) | |||||||
\(788\) | 10.4437 | + | 25.2132i | 0.372040 | + | 0.898183i | ||||
\(789\) | −13.6569 | − | 32.9706i | −0.486197 | − | 1.17378i | ||||
\(790\) | −19.7990 | + | 47.7990i | −0.704416 | + | 1.70061i | ||||
\(791\) | 12.3137 | + | 12.3137i | 0.437825 | + | 0.437825i | ||||
\(792\) | 24.8284 | + | 59.9411i | 0.882240 | + | 2.12992i | ||||
\(793\) | −3.31371 | + | 3.31371i | −0.117673 | + | 0.117673i | ||||
\(794\) | 0.970563 | + | 2.34315i | 0.0344440 | + | 0.0831551i | ||||
\(795\) | 1.17157 | − | 0.485281i | 0.0415514 | − | 0.0172112i | ||||
\(796\) | 1.85786 | + | 1.85786i | 0.0658503 | + | 0.0658503i | ||||
\(797\) | −19.5563 | + | 47.2132i | −0.692721 | + | 1.67238i | 0.0465029 | + | 0.998918i | \(0.485192\pi\) |
−0.739224 | + | 0.673459i | \(0.764808\pi\) | |||||||
\(798\) | 1.17157 | − | 1.17157i | 0.0414732 | − | 0.0414732i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 48.9706 | 1.73137 | ||||||||
\(801\) | 28.0000 | 0.989331 | ||||||||
\(802\) | 32.2426 | − | 32.2426i | 1.13853 | − | 1.13853i | ||||
\(803\) | 10.2843 | − | 24.8284i | 0.362924 | − | 0.876176i | ||||
\(804\) | −45.4558 | + | 45.4558i | −1.60310 | + | 1.60310i | ||||
\(805\) | 4.82843 | − | 2.00000i | 0.170180 | − | 0.0704907i | ||||
\(806\) | 7.31371 | + | 17.6569i | 0.257614 | + | 0.621936i | ||||
\(807\) | 28.4853 | − | 28.4853i | 1.00273 | − | 1.00273i | ||||
\(808\) | −4.00000 | + | 9.65685i | −0.140720 | + | 0.339727i | ||||
\(809\) | −25.4558 | − | 25.4558i | −0.894980 | − | 0.894980i | 0.100007 | − | 0.994987i | \(-0.468114\pi\) |
−0.994987 | + | 0.100007i | \(0.968114\pi\) | |||||||
\(810\) | 11.6569 | − | 28.1421i | 0.409580 | − | 0.988814i | ||||
\(811\) | 19.3848 | + | 46.7990i | 0.680692 | + | 1.64333i | 0.762739 | + | 0.646706i | \(0.223854\pi\) |
−0.0820475 | + | 0.996628i | \(0.526146\pi\) | |||||||
\(812\) | −15.8995 | + | 6.58579i | −0.557963 | + | 0.231116i | ||||
\(813\) | −27.7990 | − | 11.5147i | −0.974953 | − | 0.403839i | ||||
\(814\) | − | 43.1716i | − | 1.51316i | ||||||
\(815\) | 19.7990i | 0.693528i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.20101i | − | 0.0770036i | ||||||
\(818\) | −31.5147 | −1.10189 | ||||||||
\(819\) | −5.41421 | − | 2.24264i | −0.189188 | − | 0.0783642i | ||||
\(820\) | −13.6569 | + | 32.9706i | −0.476918 | + | 1.15138i | ||||
\(821\) | 8.60660 | + | 20.7782i | 0.300372 | + | 0.725163i | 0.999944 | + | 0.0106005i | \(0.00337432\pi\) |
−0.699571 | + | 0.714563i | \(0.746626\pi\) | |||||||
\(822\) | 73.1127 | + | 30.2843i | 2.55010 | + | 1.05629i | ||||
\(823\) | 27.1127 | + | 27.1127i | 0.945089 | + | 0.945089i | 0.998569 | − | 0.0534797i | \(-0.0170312\pi\) |
−0.0534797 | + | 0.998569i | \(0.517031\pi\) | |||||||
\(824\) | 40.9706i | 1.42728i | ||||||||
\(825\) | 95.8406 | − | 95.8406i | 3.33674 | − | 3.33674i | ||||
\(826\) | 7.07107 | − | 2.92893i | 0.246034 | − | 0.101911i | ||||
\(827\) | 4.53553 | − | 1.87868i | 0.157716 | − | 0.0653281i | −0.302429 | − | 0.953172i | \(-0.597797\pi\) |
0.460145 | + | 0.887844i | \(0.347797\pi\) | |||||||
\(828\) | −10.8284 | −0.376314 | ||||||||
\(829\) | −11.0711 | + | 26.7279i | −0.384514 | + | 0.928299i | 0.606566 | + | 0.795033i | \(0.292547\pi\) |
−0.991080 | + | 0.133266i | \(0.957453\pi\) | |||||||
\(830\) | 12.9706 | + | 12.9706i | 0.450215 | + | 0.450215i | ||||
\(831\) | 57.1127 | 1.98122 | ||||||||
\(832\) | 4.68629 | − | 11.3137i | 0.162468 | − | 0.392232i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 22.1421 | + | 22.1421i | 0.766719 | + | 0.766719i | ||||
\(835\) | −11.5147 | + | 27.7990i | −0.398483 | + | 0.962024i | ||||
\(836\) | 5.37258 | 0.185815 | ||||||||
\(837\) | −17.6569 | + | 7.31371i | −0.610310 | + | 0.252799i | ||||
\(838\) | −4.24264 | + | 1.75736i | −0.146560 | + | 0.0607070i | ||||
\(839\) | 28.5858 | − | 28.5858i | 0.986891 | − | 0.986891i | −0.0130242 | − | 0.999915i | \(-0.504146\pi\) |
0.999915 | + | 0.0130242i | \(0.00414586\pi\) | |||||||
\(840\) | −27.3137 | −0.942412 | ||||||||
\(841\) | −31.8492 | − | 31.8492i | −1.09825 | − | 1.09825i | ||||
\(842\) | −33.3848 | − | 13.8284i | −1.15052 | − | 0.476559i | ||||
\(843\) | −1.89949 | − | 4.58579i | −0.0654221 | − | 0.157943i | ||||
\(844\) | 3.41421 | − | 8.24264i | 0.117522 | − | 0.283723i | ||||
\(845\) | 36.3848 | + | 15.0711i | 1.25167 | + | 0.518460i | ||||
\(846\) | 47.7990 | 1.64336 | ||||||||
\(847\) | 24.8995i | 0.855557i | ||||||||
\(848\) | −0.201010 | − | 0.485281i | −0.00690272 | − | 0.0166646i | ||||
\(849\) | 36.4853i | 1.25217i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.65685 | + | 2.75736i | 0.228194 | + | 0.0945211i | ||||
\(852\) | 28.9706 | − | 12.0000i | 0.992515 | − | 0.411113i | ||||
\(853\) | −20.6863 | − | 49.9411i | −0.708285 | − | 1.70995i | −0.704242 | − | 0.709960i | \(-0.748713\pi\) |
−0.00404287 | − | 0.999992i | \(-0.501287\pi\) | |||||||
\(854\) | 1.65685 | − | 4.00000i | 0.0566964 | − | 0.136877i | ||||
\(855\) | 4.48528 | + | 4.48528i | 0.153393 | + | 0.153393i | ||||
\(856\) | −16.1421 | − | 6.68629i | −0.551727 | − | 0.228533i | ||||
\(857\) | −32.3848 | + | 32.3848i | −1.10624 | + | 1.10624i | −0.112603 | + | 0.993640i | \(0.535919\pi\) |
−0.993640 | + | 0.112603i | \(0.964081\pi\) | |||||||
\(858\) | −12.9706 | − | 31.3137i | −0.442808 | − | 1.06903i | ||||
\(859\) | 13.5858 | − | 5.62742i | 0.463541 | − | 0.192005i | −0.138675 | − | 0.990338i | \(-0.544284\pi\) |
0.602216 | + | 0.798333i | \(0.294284\pi\) | |||||||
\(860\) | −25.6569 | + | 25.6569i | −0.874891 | + | 0.874891i | ||||
\(861\) | 4.82843 | − | 11.6569i | 0.164552 | − | 0.397265i | ||||
\(862\) | 21.6569 | − | 21.6569i | 0.737635 | − | 0.737635i | ||||
\(863\) | −29.6985 | −1.01095 | −0.505474 | − | 0.862842i | \(-0.668682\pi\) | ||||
−0.505474 | + | 0.862842i | \(0.668682\pi\) | |||||||
\(864\) | 11.3137 | + | 4.68629i | 0.384900 | + | 0.159431i | ||||
\(865\) | −16.9706 | −0.577016 | ||||||||
\(866\) | 24.2843 | − | 24.2843i | 0.825213 | − | 0.825213i | ||||
\(867\) | −17.0000 | + | 41.0416i | −0.577350 | + | 1.39385i | ||||
\(868\) | −12.4853 | − | 12.4853i | −0.423778 | − | 0.423778i | ||||
\(869\) | 54.7990 | − | 22.6985i | 1.85893 | − | 0.769993i | ||||
\(870\) | −44.9706 | − | 108.569i | −1.52464 | − | 3.68082i | ||||
\(871\) | 13.3137 | − | 13.3137i | 0.451118 | − | 0.451118i | ||||
\(872\) | −24.1421 | + | 10.0000i | −0.817556 | + | 0.338643i | ||||
\(873\) | −3.17157 | − | 3.17157i | −0.107341 | − | 0.107341i | ||||
\(874\) | −0.343146 | + | 0.828427i | −0.0116071 | + | 0.0280220i | ||||
\(875\) | 5.17157 | + | 12.4853i | 0.174831 | + | 0.422080i | ||||
\(876\) | −8.97056 | − | 21.6569i | −0.303087 | − | 0.731717i | ||||
\(877\) | −3.19239 | − | 1.32233i | −0.107799 | − | 0.0446519i | 0.328132 | − | 0.944632i | \(-0.393581\pi\) |
−0.435931 | + | 0.899980i | \(0.643581\pi\) | |||||||
\(878\) | 36.0000i | 1.21494i | ||||||||
\(879\) | 41.9411i | 1.41464i | ||||||||
\(880\) | −62.6274 | − | 62.6274i | −2.11117 | − | 2.11117i | ||||
\(881\) | − | 23.4558i | − | 0.790247i | −0.918628 | − | 0.395124i | \(-0.870702\pi\) | ||
0.918628 | − | 0.395124i | \(-0.129298\pi\) | |||||||
\(882\) | 5.41421 | 0.182306 | ||||||||
\(883\) | −31.3345 | − | 12.9792i | −1.05449 | − | 0.436784i | −0.212998 | − | 0.977053i | \(-0.568323\pi\) |
−0.841493 | + | 0.540268i | \(0.818323\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.0000 | + | 48.2843i | 0.672293 | + | 1.62306i | ||||
\(886\) | −20.0711 | − | 8.31371i | −0.674301 | − | 0.279304i | ||||
\(887\) | 15.2721 | + | 15.2721i | 0.512786 | + | 0.512786i | 0.915379 | − | 0.402593i | \(-0.131891\pi\) |
−0.402593 | + | 0.915379i | \(0.631891\pi\) | |||||||
\(888\) | −26.6274 | − | 26.6274i | −0.893558 | − | 0.893558i | ||||
\(889\) | 10.5858 | − | 10.5858i | 0.355036 | − | 0.355036i | ||||
\(890\) | −35.3137 | + | 14.6274i | −1.18372 | + | 0.490312i | ||||
\(891\) | −32.2635 | + | 13.3640i | −1.08087 | + | 0.447710i | ||||
\(892\) | − | 46.6274i | − | 1.56120i | ||||||
\(893\) | 1.51472 | − | 3.65685i | 0.0506881 | − | 0.122372i | ||||
\(894\) | −0.343146 | − | 0.343146i | −0.0114765 | − | 0.0114765i | ||||
\(895\) | 42.1421 | 1.40866 | ||||||||
\(896\) | 11.3137i | 0.377964i | ||||||||
\(897\) | 5.65685 | 0.188877 | ||||||||
\(898\) | 33.4558 | + | 33.4558i | 1.11644 | + | 1.11644i | ||||
\(899\) | 29.0711 | − | 70.1838i | 0.969574 | − | 2.34076i | ||||
\(900\) | − | 66.2843i | − | 2.20948i | ||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 37.7990 | − | 15.6569i | 1.25857 | − | 0.521316i | ||||
\(903\) | 9.07107 | − | 9.07107i | 0.301866 | − | 0.301866i | ||||
\(904\) | 34.8284 | + | 34.8284i | 1.15838 | + | 1.15838i | ||||
\(905\) | 36.9706 | + | 36.9706i | 1.22894 | + | 1.22894i | ||||
\(906\) | −14.4853 | − | 6.00000i | −0.481241 | − | 0.199337i | ||||
\(907\) | 6.77817 | + | 16.3640i | 0.225066 | + | 0.543356i | 0.995564 | − | 0.0940854i | \(-0.0299927\pi\) |
−0.770499 | + | 0.637442i | \(0.779993\pi\) | |||||||
\(908\) | −53.1127 | − | 22.0000i | −1.76261 | − | 0.730096i | ||||
\(909\) | 13.0711 | + | 5.41421i | 0.433540 | + | 0.179578i | ||||
\(910\) | 8.00000 | 0.265197 | ||||||||
\(911\) | − | 41.3137i | − | 1.36878i | −0.729114 | − | 0.684392i | \(-0.760068\pi\) | ||
0.729114 | − | 0.684392i | \(-0.239932\pi\) | |||||||
\(912\) | 3.31371 | − | 3.31371i | 0.109728 | − | 0.109728i | ||||
\(913\) | − | 21.0294i | − | 0.695973i | ||||||
\(914\) | − | 16.0000i | − | 0.529233i | ||||||
\(915\) | 27.3137 | + | 11.3137i | 0.902963 | + | 0.374020i | ||||
\(916\) | 6.62742 | + | 16.0000i | 0.218976 | + | 0.528655i | ||||
\(917\) | −2.41421 | − | 5.82843i | −0.0797244 | − | 0.192472i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.0711 | − | 23.0711i | −0.761044 | − | 0.761044i | 0.215467 | − | 0.976511i | \(-0.430873\pi\) |
−0.976511 | + | 0.215467i | \(0.930873\pi\) | |||||||
\(920\) | 13.6569 | − | 5.65685i | 0.450253 | − | 0.186501i | ||||
\(921\) | 58.2843 | − | 58.2843i | 1.92053 | − | 1.92053i | ||||
\(922\) | 4.97056 | + | 12.0000i | 0.163697 | + | 0.395199i | ||||
\(923\) | −8.48528 | + | 3.51472i | −0.279296 | + | 0.115688i | ||||
\(924\) | 22.1421 | + | 22.1421i | 0.728423 | + | 0.728423i | ||||
\(925\) | −16.8787 | + | 40.7487i | −0.554968 | + | 1.33981i | ||||
\(926\) | −28.0416 | + | 28.0416i | −0.921505 | + | 0.921505i | ||||
\(927\) | 55.4558 | 1.82141 | ||||||||
\(928\) | −44.9706 | + | 18.6274i | −1.47623 | + | 0.611475i | ||||
\(929\) | −25.9411 | −0.851101 | −0.425550 | − | 0.904935i | \(-0.639919\pi\) | ||||
−0.425550 | + | 0.904935i | \(0.639919\pi\) | |||||||
\(930\) | 85.2548 | − | 85.2548i | 2.79562 | − | 2.79562i | ||||
\(931\) | 0.171573 | − | 0.414214i | 0.00562307 | − | 0.0135753i | ||||
\(932\) | 3.65685 | − | 3.65685i | 0.119784 | − | 0.119784i | ||||
\(933\) | −65.9411 | + | 27.3137i | −2.15882 | + | 0.894211i | ||||
\(934\) | −1.95837 | − | 4.72792i | −0.0640798 | − | 0.154702i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15.3137 | − | 6.34315i | −0.500544 | − | 0.207332i | ||||
\(937\) | −8.14214 | − | 8.14214i | −0.265992 | − | 0.265992i | 0.561491 | − | 0.827483i | \(-0.310228\pi\) |
−0.827483 | + | 0.561491i | \(0.810228\pi\) | |||||||
\(938\) | −6.65685 | + | 16.0711i | −0.217354 | + | 0.524739i | ||||
\(939\) | −6.97056 | − | 16.8284i | −0.227476 | − | 0.549175i | ||||
\(940\) | −60.2843 | + | 24.9706i | −1.96626 | + | 0.814450i | ||||
\(941\) | −32.9706 | − | 13.6569i | −1.07481 | − | 0.445201i | −0.226124 | − | 0.974099i | \(-0.572605\pi\) |
−0.848686 | + | 0.528898i | \(0.822605\pi\) | |||||||
\(942\) | 24.0000i | 0.781962i | ||||||||
\(943\) | 6.82843i | 0.222364i | ||||||||
\(944\) | 20.0000 | − | 8.28427i | 0.650945 | − | 0.269630i | ||||
\(945\) | 8.00000i | 0.260240i | ||||||||
\(946\) | 41.5980 | 1.35247 | ||||||||
\(947\) | 38.7487 | + | 16.0503i | 1.25916 | + | 0.521563i | 0.909653 | − | 0.415369i | \(-0.136347\pi\) |
0.349512 | + | 0.936932i | \(0.386347\pi\) | |||||||
\(948\) | 19.7990 | − | 47.7990i | 0.643041 | − | 1.55244i | ||||
\(949\) | 2.62742 | + | 6.34315i | 0.0852896 | + | 0.205907i | ||||
\(950\) | −5.07107 | − | 2.10051i | −0.164527 | − | 0.0681494i | ||||
\(951\) | 21.0711 | + | 21.0711i | 0.683276 | + | 0.683276i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.9706 | − | 27.9706i | 0.906055 | − | 0.906055i | −0.0898958 | − | 0.995951i | \(-0.528653\pi\) |
0.995951 | + | 0.0898958i | \(0.0286534\pi\) | |||||||
\(954\) | −0.656854 | + | 0.272078i | −0.0212664 | + | 0.00880885i | ||||
\(955\) | −10.4853 | + | 4.34315i | −0.339296 | + | 0.140541i | ||||
\(956\) | −12.0000 | −0.388108 | ||||||||
\(957\) | −51.5563 | + | 124.468i | −1.66658 | + | 4.02348i | ||||
\(958\) | 29.3137 | + | 29.3137i | 0.947083 | + | 0.947083i | ||||
\(959\) | 21.4142 | 0.691501 | ||||||||
\(960\) | −77.2548 | −2.49339 | ||||||||
\(961\) | 46.9411 | 1.51423 | ||||||||
\(962\) | 7.79899 | + | 7.79899i | 0.251450 | + | 0.251450i | ||||
\(963\) | −9.05025 | + | 21.8492i | −0.291640 | + | 0.704082i | ||||
\(964\) | 47.5980 | 1.53303 | ||||||||
\(965\) | −4.82843 | + | 2.00000i | −0.155433 | + | 0.0643823i | ||||
\(966\) | −4.82843 | + | 2.00000i | −0.155352 | + | 0.0643489i | ||||
\(967\) | 18.6569 | − | 18.6569i | 0.599964 | − | 0.599964i | −0.340339 | − | 0.940303i | \(-0.610542\pi\) |
0.940303 | + | 0.340339i | \(0.110542\pi\) | |||||||
\(968\) | 70.4264i | 2.26359i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.65685 | + | 2.34315i | 0.181631 | + | 0.0752339i | ||||
\(971\) | 4.55635 | + | 11.0000i | 0.146220 | + | 0.353007i | 0.979973 | − | 0.199131i | \(-0.0638121\pi\) |
−0.833753 | + | 0.552138i | \(0.813812\pi\) | |||||||
\(972\) | −16.6274 | + | 40.1421i | −0.533325 | + | 1.28756i | ||||
\(973\) | 7.82843 | + | 3.24264i | 0.250968 | + | 0.103954i | ||||
\(974\) | 1.71573 | 0.0549755 | ||||||||
\(975\) | 34.6274i | 1.10896i | ||||||||
\(976\) | 4.68629 | − | 11.3137i | 0.150005 | − | 0.362143i | ||||
\(977\) | 58.8284i | 1.88209i | 0.338284 | + | 0.941044i | \(0.390154\pi\) | ||||
−0.338284 | + | 0.941044i | \(0.609846\pi\) | |||||||
\(978\) | − | 19.7990i | − | 0.633102i | ||||||
\(979\) | 40.4853 | + | 16.7696i | 1.29392 | + | 0.535957i | ||||
\(980\) | −6.82843 | + | 2.82843i | −0.218126 | + | 0.0903508i | ||||
\(981\) | 13.5355 | + | 32.6777i | 0.432156 | + | 1.04332i | ||||
\(982\) | 9.14214 | − | 22.0711i | 0.291737 | − | 0.704316i | ||||
\(983\) | −3.41421 | − | 3.41421i | −0.108897 | − | 0.108897i | 0.650559 | − | 0.759456i | \(-0.274535\pi\) |
−0.759456 | + | 0.650559i | \(0.774535\pi\) | |||||||
\(984\) | 13.6569 | − | 32.9706i | 0.435365 | − | 1.05106i | ||||
\(985\) | −35.6569 | + | 35.6569i | −1.13612 | + | 1.13612i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.3137 | − | 8.82843i | 0.678423 | − | 0.281012i | ||||
\(988\) | −0.970563 | + | 0.970563i | −0.0308777 | + | 0.0308777i | ||||
\(989\) | −2.65685 | + | 6.41421i | −0.0844831 | + | 0.203960i | ||||
\(990\) | −84.7696 | + | 84.7696i | −2.69415 | + | 2.69415i | ||||
\(991\) | −26.1838 | −0.831755 | −0.415877 | − | 0.909421i | \(-0.636525\pi\) | ||||
−0.415877 | + | 0.909421i | \(0.636525\pi\) | |||||||
\(992\) | −35.3137 | − | 35.3137i | −1.12121 | − | 1.12121i | ||||
\(993\) | −34.9706 | −1.10976 | ||||||||
\(994\) | 6.00000 | − | 6.00000i | 0.190308 | − | 0.190308i | ||||
\(995\) | −1.85786 | + | 4.48528i | −0.0588983 | + | 0.142193i | ||||
\(996\) | −12.9706 | − | 12.9706i | −0.410988 | − | 0.410988i | ||||
\(997\) | 10.7279 | − | 4.44365i | 0.339757 | − | 0.140732i | −0.206280 | − | 0.978493i | \(-0.566136\pi\) |
0.546037 | + | 0.837761i | \(0.316136\pi\) | |||||||
\(998\) | −8.51472 | − | 20.5563i | −0.269529 | − | 0.650700i | ||||
\(999\) | −7.79899 | + | 7.79899i | −0.246749 | + | 0.246749i |
(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 | 224.2.u.a.141.1 | ✓ | 4 | |
4.3 | odd | 2 | 896.2.u.a.785.1 | 4 | |||
32.5 | even | 8 | inner | 224.2.u.a.197.1 | yes | 4 | |
32.27 | odd | 8 | 896.2.u.a.113.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.u.a.141.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
224.2.u.a.197.1 | yes | 4 | 32.5 | even | 8 | inner | |
896.2.u.a.113.1 | 4 | 32.27 | odd | 8 | |||
896.2.u.a.785.1 | 4 | 4.3 | odd | 2 |