Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,2,Mod(34,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.e (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: | \(0.790518980011\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 34.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.34 |
Dual form | 99.2.e.c.67.1 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(5\) | 1.00000 | + | 1.73205i | 0.447214 | + | 0.774597i | 0.998203 | − | 0.0599153i | \(-0.0190830\pi\) |
−0.550990 | + | 0.834512i | \(0.685750\pi\) | |||||||
\(6\) | −3.00000 | − | 1.73205i | −1.22474 | − | 0.707107i | ||||
\(7\) | −2.00000 | + | 3.46410i | −0.755929 | + | 1.30931i | 0.188982 | + | 0.981981i | \(0.439481\pi\) |
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 4.00000 | 1.26491 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | −3.00000 | + | 1.73205i | −0.866025 | + | 0.500000i | ||||
\(13\) | −2.00000 | − | 3.46410i | −0.554700 | − | 0.960769i | −0.997927 | − | 0.0643593i | \(-0.979500\pi\) |
0.443227 | − | 0.896410i | \(-0.353834\pi\) | |||||||
\(14\) | 4.00000 | + | 6.92820i | 1.06904 | + | 1.85164i | ||||
\(15\) | 3.00000 | − | 1.73205i | 0.774597 | − | 0.447214i | ||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | −3.00000 | + | 5.19615i | −0.707107 | + | 1.22474i | ||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 2.00000 | − | 3.46410i | 0.447214 | − | 0.774597i | ||||
\(21\) | 6.00000 | + | 3.46410i | 1.30931 | + | 0.755929i | ||||
\(22\) | 1.00000 | + | 1.73205i | 0.213201 | + | 0.369274i | ||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | 0.913434 | − | 0.406986i | \(-0.133420\pi\) |
−0.809177 | + | 0.587565i | \(0.800087\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −8.00000 | −1.56893 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 8.00000 | 1.51186 | ||||||||
\(29\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(30\) | − | 6.92820i | − | 1.26491i | ||||||
\(31\) | −0.500000 | − | 0.866025i | −0.0898027 | − | 0.155543i | 0.817625 | − | 0.575751i | \(-0.195290\pi\) |
−0.907428 | + | 0.420208i | \(0.861957\pi\) | |||||||
\(32\) | −4.00000 | − | 6.92820i | −0.707107 | − | 1.22474i | ||||
\(33\) | 1.50000 | + | 0.866025i | 0.261116 | + | 0.150756i | ||||
\(34\) | 4.00000 | − | 6.92820i | 0.685994 | − | 1.18818i | ||||
\(35\) | −8.00000 | −1.35225 | ||||||||
\(36\) | 3.00000 | + | 5.19615i | 0.500000 | + | 0.866025i | ||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | −6.00000 | + | 10.3923i | −0.973329 | + | 1.68585i | ||||
\(39\) | −6.00000 | + | 3.46410i | −0.960769 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | + | 1.73205i | 0.156174 | + | 0.270501i | 0.933486 | − | 0.358614i | \(-0.116751\pi\) |
−0.777312 | + | 0.629115i | \(0.783417\pi\) | |||||||
\(42\) | 12.0000 | − | 6.92820i | 1.85164 | − | 1.06904i | ||||
\(43\) | −6.00000 | + | 10.3923i | −0.914991 | + | 1.58481i | −0.108078 | + | 0.994142i | \(0.534469\pi\) |
−0.806914 | + | 0.590669i | \(0.798864\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | −3.00000 | − | 5.19615i | −0.447214 | − | 0.774597i | ||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | 3.50000 | − | 6.06218i | 0.510527 | − | 0.884260i | −0.489398 | − | 0.872060i | \(-0.662783\pi\) |
0.999926 | − | 0.0121990i | \(-0.00388317\pi\) | |||||||
\(48\) | −6.00000 | − | 3.46410i | −0.866025 | − | 0.500000i | ||||
\(49\) | −4.50000 | − | 7.79423i | −0.642857 | − | 1.11346i | ||||
\(50\) | −1.00000 | − | 1.73205i | −0.141421 | − | 0.244949i | ||||
\(51\) | − | 6.92820i | − | 0.970143i | ||||||
\(52\) | −4.00000 | + | 6.92820i | −0.554700 | + | 0.960769i | ||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 9.00000 | + | 5.19615i | 1.22474 | + | 0.707107i | ||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.3923i | 1.37649i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.50000 | − | 9.52628i | −0.716039 | − | 1.24022i | −0.962557 | − | 0.271078i | \(-0.912620\pi\) |
0.246518 | − | 0.969138i | \(-0.420713\pi\) | |||||||
\(60\) | −6.00000 | − | 3.46410i | −0.774597 | − | 0.447214i | ||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 6.00000 | − | 10.3923i | 0.755929 | − | 1.30931i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 4.00000 | − | 6.92820i | 0.496139 | − | 0.859338i | ||||
\(66\) | 3.00000 | − | 1.73205i | 0.369274 | − | 0.213201i | ||||
\(67\) | 2.00000 | + | 3.46410i | 0.244339 | + | 0.423207i | 0.961946 | − | 0.273241i | \(-0.0880957\pi\) |
−0.717607 | + | 0.696449i | \(0.754762\pi\) | |||||||
\(68\) | −4.00000 | − | 6.92820i | −0.485071 | − | 0.840168i | ||||
\(69\) | 1.50000 | − | 0.866025i | 0.180579 | − | 0.104257i | ||||
\(70\) | −8.00000 | + | 13.8564i | −0.956183 | + | 1.65616i | ||||
\(71\) | 15.0000 | 1.78017 | 0.890086 | − | 0.455792i | \(-0.150644\pi\) | ||||
0.890086 | + | 0.455792i | \(0.150644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.00000 | −0.936329 | −0.468165 | − | 0.883641i | \(-0.655085\pi\) | ||||
−0.468165 | + | 0.883641i | \(0.655085\pi\) | |||||||
\(74\) | 3.00000 | − | 5.19615i | 0.348743 | − | 0.604040i | ||||
\(75\) | −1.50000 | − | 0.866025i | −0.173205 | − | 0.100000i | ||||
\(76\) | 6.00000 | + | 10.3923i | 0.688247 | + | 1.19208i | ||||
\(77\) | −2.00000 | − | 3.46410i | −0.227921 | − | 0.394771i | ||||
\(78\) | 13.8564i | 1.56893i | ||||||||
\(79\) | 5.00000 | − | 8.66025i | 0.562544 | − | 0.974355i | −0.434730 | − | 0.900561i | \(-0.643156\pi\) |
0.997274 | − | 0.0737937i | \(-0.0235106\pi\) | |||||||
\(80\) | 8.00000 | 0.894427 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 4.00000 | 0.441726 | ||||||||
\(83\) | −6.00000 | + | 10.3923i | −0.658586 | + | 1.14070i | 0.322396 | + | 0.946605i | \(0.395512\pi\) |
−0.980982 | + | 0.194099i | \(0.937822\pi\) | |||||||
\(84\) | − | 13.8564i | − | 1.51186i | ||||||
\(85\) | 4.00000 | + | 6.92820i | 0.433861 | + | 0.751469i | ||||
\(86\) | 12.0000 | + | 20.7846i | 1.29399 | + | 2.24126i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | −12.0000 | −1.26491 | ||||||||
\(91\) | 16.0000 | 1.67726 | ||||||||
\(92\) | 1.00000 | − | 1.73205i | 0.104257 | − | 0.180579i | ||||
\(93\) | −1.50000 | + | 0.866025i | −0.155543 | + | 0.0898027i | ||||
\(94\) | −7.00000 | − | 12.1244i | −0.721995 | − | 1.25053i | ||||
\(95\) | −6.00000 | − | 10.3923i | −0.615587 | − | 1.06623i | ||||
\(96\) | −12.0000 | + | 6.92820i | −1.22474 | + | 0.707107i | ||||
\(97\) | −8.50000 | + | 14.7224i | −0.863044 | + | 1.49484i | 0.00593185 | + | 0.999982i | \(0.498112\pi\) |
−0.868976 | + | 0.494854i | \(0.835222\pi\) | |||||||
\(98\) | −18.0000 | −1.81827 | ||||||||
\(99\) | 1.50000 | − | 2.59808i | 0.150756 | − | 0.261116i | ||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | −1.00000 | + | 1.73205i | −0.0995037 | + | 0.172345i | −0.911479 | − | 0.411346i | \(-0.865059\pi\) |
0.811976 | + | 0.583691i | \(0.198392\pi\) | |||||||
\(102\) | −12.0000 | − | 6.92820i | −1.18818 | − | 0.685994i | ||||
\(103\) | 0.500000 | + | 0.866025i | 0.0492665 | + | 0.0853320i | 0.889607 | − | 0.456727i | \(-0.150978\pi\) |
−0.840341 | + | 0.542059i | \(0.817645\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.8564i | 1.35225i | ||||||||
\(106\) | 3.00000 | − | 5.19615i | 0.291386 | − | 0.504695i | ||||
\(107\) | −6.00000 | −0.580042 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(108\) | 9.00000 | − | 5.19615i | 0.866025 | − | 0.500000i | ||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | −2.00000 | + | 3.46410i | −0.190693 | + | 0.330289i | ||||
\(111\) | − | 5.19615i | − | 0.493197i | ||||||
\(112\) | 8.00000 | + | 13.8564i | 0.755929 | + | 1.30931i | ||||
\(113\) | 1.50000 | + | 2.59808i | 0.141108 | + | 0.244406i | 0.927914 | − | 0.372794i | \(-0.121600\pi\) |
−0.786806 | + | 0.617200i | \(0.788267\pi\) | |||||||
\(114\) | 18.0000 | + | 10.3923i | 1.68585 | + | 0.973329i | ||||
\(115\) | −1.00000 | + | 1.73205i | −0.0932505 | + | 0.161515i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.00000 | + | 10.3923i | 0.554700 | + | 0.960769i | ||||
\(118\) | −22.0000 | −2.02526 | ||||||||
\(119\) | −8.00000 | + | 13.8564i | −0.733359 | + | 1.27021i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.00000 | − | 1.73205i | 0.270501 | − | 0.156174i | ||||
\(124\) | −1.00000 | + | 1.73205i | −0.0898027 | + | 0.155543i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | −12.0000 | − | 20.7846i | −1.06904 | − | 1.85164i | ||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.0000 | + | 10.3923i | 1.58481 | + | 0.914991i | ||||
\(130\) | −8.00000 | − | 13.8564i | −0.701646 | − | 1.21529i | ||||
\(131\) | −9.00000 | − | 15.5885i | −0.786334 | − | 1.36197i | −0.928199 | − | 0.372084i | \(-0.878643\pi\) |
0.141865 | − | 0.989886i | \(-0.454690\pi\) | |||||||
\(132\) | − | 3.46410i | − | 0.301511i | ||||||
\(133\) | 12.0000 | − | 20.7846i | 1.04053 | − | 1.80225i | ||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | −9.00000 | + | 5.19615i | −0.774597 | + | 0.447214i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.50000 | − | 6.06218i | 0.299025 | − | 0.517927i | −0.676888 | − | 0.736086i | \(-0.736672\pi\) |
0.975913 | + | 0.218159i | \(0.0700052\pi\) | |||||||
\(138\) | − | 3.46410i | − | 0.294884i | ||||||
\(139\) | −8.00000 | − | 13.8564i | −0.678551 | − | 1.17529i | −0.975417 | − | 0.220366i | \(-0.929275\pi\) |
0.296866 | − | 0.954919i | \(-0.404058\pi\) | |||||||
\(140\) | 8.00000 | + | 13.8564i | 0.676123 | + | 1.17108i | ||||
\(141\) | −10.5000 | − | 6.06218i | −0.884260 | − | 0.510527i | ||||
\(142\) | 15.0000 | − | 25.9808i | 1.25877 | − | 2.18026i | ||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | −6.00000 | + | 10.3923i | −0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.00000 | + | 13.8564i | −0.662085 | + | 1.14676i | ||||
\(147\) | −13.5000 | + | 7.79423i | −1.11346 | + | 0.642857i | ||||
\(148\) | −3.00000 | − | 5.19615i | −0.246598 | − | 0.427121i | ||||
\(149\) | −1.00000 | − | 1.73205i | −0.0819232 | − | 0.141895i | 0.822153 | − | 0.569267i | \(-0.192773\pi\) |
−0.904076 | + | 0.427372i | \(0.859440\pi\) | |||||||
\(150\) | −3.00000 | + | 1.73205i | −0.244949 | + | 0.141421i | ||||
\(151\) | 5.00000 | − | 8.66025i | 0.406894 | − | 0.704761i | −0.587646 | − | 0.809118i | \(-0.699945\pi\) |
0.994540 | + | 0.104357i | \(0.0332784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.0000 | −0.970143 | ||||||||
\(154\) | −8.00000 | −0.644658 | ||||||||
\(155\) | 1.00000 | − | 1.73205i | 0.0803219 | − | 0.139122i | ||||
\(156\) | 12.0000 | + | 6.92820i | 0.960769 | + | 0.554700i | ||||
\(157\) | −7.00000 | − | 12.1244i | −0.558661 | − | 0.967629i | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) |
0.438948 | − | 0.898513i | \(-0.355351\pi\) | |||||||
\(158\) | −10.0000 | − | 17.3205i | −0.795557 | − | 1.37795i | ||||
\(159\) | − | 5.19615i | − | 0.412082i | ||||||
\(160\) | 8.00000 | − | 13.8564i | 0.632456 | − | 1.09545i | ||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 9.00000 | − | 15.5885i | 0.707107 | − | 1.22474i | ||||
\(163\) | 13.0000 | 1.01824 | 0.509119 | − | 0.860696i | \(-0.329971\pi\) | ||||
0.509119 | + | 0.860696i | \(0.329971\pi\) | |||||||
\(164\) | 2.00000 | − | 3.46410i | 0.156174 | − | 0.270501i | ||||
\(165\) | 3.46410i | 0.269680i | ||||||||
\(166\) | 12.0000 | + | 20.7846i | 0.931381 | + | 1.61320i | ||||
\(167\) | 9.00000 | + | 15.5885i | 0.696441 | + | 1.20627i | 0.969693 | + | 0.244328i | \(0.0785675\pi\) |
−0.273252 | + | 0.961943i | \(0.588099\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | 16.0000 | 1.22714 | ||||||||
\(171\) | 18.0000 | 1.37649 | ||||||||
\(172\) | 24.0000 | 1.82998 | ||||||||
\(173\) | −3.00000 | + | 5.19615i | −0.228086 | + | 0.395056i | −0.957241 | − | 0.289292i | \(-0.906580\pi\) |
0.729155 | + | 0.684349i | \(0.239913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | + | 3.46410i | 0.151186 | + | 0.261861i | ||||
\(176\) | 2.00000 | + | 3.46410i | 0.150756 | + | 0.261116i | ||||
\(177\) | −16.5000 | + | 9.52628i | −1.24022 | + | 0.716039i | ||||
\(178\) | 3.00000 | − | 5.19615i | 0.224860 | − | 0.389468i | ||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | −6.00000 | + | 10.3923i | −0.447214 | + | 0.774597i | ||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 16.0000 | − | 27.7128i | 1.18600 | − | 2.05421i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | + | 5.19615i | 0.220564 | + | 0.382029i | ||||
\(186\) | 3.46410i | 0.254000i | ||||||||
\(187\) | −2.00000 | + | 3.46410i | −0.146254 | + | 0.253320i | ||||
\(188\) | −14.0000 | −1.02105 | ||||||||
\(189\) | −18.0000 | − | 10.3923i | −1.30931 | − | 0.755929i | ||||
\(190\) | −24.0000 | −1.74114 | ||||||||
\(191\) | −10.0000 | + | 17.3205i | −0.723575 | + | 1.25327i | 0.235983 | + | 0.971757i | \(0.424169\pi\) |
−0.959558 | + | 0.281511i | \(0.909164\pi\) | |||||||
\(192\) | 13.8564i | 1.00000i | ||||||||
\(193\) | 7.00000 | + | 12.1244i | 0.503871 | + | 0.872730i | 0.999990 | + | 0.00447566i | \(0.00142465\pi\) |
−0.496119 | + | 0.868255i | \(0.665242\pi\) | |||||||
\(194\) | 17.0000 | + | 29.4449i | 1.22053 | + | 2.11402i | ||||
\(195\) | −12.0000 | − | 6.92820i | −0.859338 | − | 0.496139i | ||||
\(196\) | −9.00000 | + | 15.5885i | −0.642857 | + | 1.11346i | ||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | −3.00000 | − | 5.19615i | −0.213201 | − | 0.369274i | ||||
\(199\) | −15.0000 | −1.06332 | −0.531661 | − | 0.846957i | \(-0.678432\pi\) | ||||
−0.531661 | + | 0.846957i | \(0.678432\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00000 | − | 3.46410i | 0.423207 | − | 0.244339i | ||||
\(202\) | 2.00000 | + | 3.46410i | 0.140720 | + | 0.243733i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −12.0000 | + | 6.92820i | −0.840168 | + | 0.485071i | ||||
\(205\) | −2.00000 | + | 3.46410i | −0.139686 | + | 0.241943i | ||||
\(206\) | 2.00000 | 0.139347 | ||||||||
\(207\) | −1.50000 | − | 2.59808i | −0.104257 | − | 0.180579i | ||||
\(208\) | −16.0000 | −1.10940 | ||||||||
\(209\) | 3.00000 | − | 5.19615i | 0.207514 | − | 0.359425i | ||||
\(210\) | 24.0000 | + | 13.8564i | 1.65616 | + | 0.956183i | ||||
\(211\) | 6.00000 | + | 10.3923i | 0.413057 | + | 0.715436i | 0.995222 | − | 0.0976347i | \(-0.0311277\pi\) |
−0.582165 | + | 0.813070i | \(0.697794\pi\) | |||||||
\(212\) | −3.00000 | − | 5.19615i | −0.206041 | − | 0.356873i | ||||
\(213\) | − | 25.9808i | − | 1.78017i | ||||||
\(214\) | −6.00000 | + | 10.3923i | −0.410152 | + | 0.710403i | ||||
\(215\) | −24.0000 | −1.63679 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | 10.0000 | − | 17.3205i | 0.677285 | − | 1.17309i | ||||
\(219\) | 13.8564i | 0.936329i | ||||||||
\(220\) | 2.00000 | + | 3.46410i | 0.134840 | + | 0.233550i | ||||
\(221\) | −8.00000 | − | 13.8564i | −0.538138 | − | 0.932083i | ||||
\(222\) | −9.00000 | − | 5.19615i | −0.604040 | − | 0.348743i | ||||
\(223\) | −3.50000 | + | 6.06218i | −0.234377 | + | 0.405953i | −0.959092 | − | 0.283096i | \(-0.908638\pi\) |
0.724714 | + | 0.689050i | \(0.241972\pi\) | |||||||
\(224\) | 32.0000 | 2.13809 | ||||||||
\(225\) | −1.50000 | + | 2.59808i | −0.100000 | + | 0.173205i | ||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 6.00000 | − | 10.3923i | 0.398234 | − | 0.689761i | −0.595274 | − | 0.803523i | \(-0.702957\pi\) |
0.993508 | + | 0.113761i | \(0.0362899\pi\) | |||||||
\(228\) | 18.0000 | − | 10.3923i | 1.19208 | − | 0.688247i | ||||
\(229\) | −1.50000 | − | 2.59808i | −0.0991228 | − | 0.171686i | 0.812199 | − | 0.583380i | \(-0.198270\pi\) |
−0.911322 | + | 0.411695i | \(0.864937\pi\) | |||||||
\(230\) | 2.00000 | + | 3.46410i | 0.131876 | + | 0.228416i | ||||
\(231\) | −6.00000 | + | 3.46410i | −0.394771 | + | 0.227921i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 24.0000 | 1.56893 | ||||||||
\(235\) | 14.0000 | 0.913259 | ||||||||
\(236\) | −11.0000 | + | 19.0526i | −0.716039 | + | 1.24022i | ||||
\(237\) | −15.0000 | − | 8.66025i | −0.974355 | − | 0.562544i | ||||
\(238\) | 16.0000 | + | 27.7128i | 1.03713 | + | 1.79635i | ||||
\(239\) | 12.0000 | + | 20.7846i | 0.776215 | + | 1.34444i | 0.934109 | + | 0.356988i | \(0.116196\pi\) |
−0.157893 | + | 0.987456i | \(0.550470\pi\) | |||||||
\(240\) | − | 13.8564i | − | 0.894427i | ||||||
\(241\) | −5.00000 | + | 8.66025i | −0.322078 | + | 0.557856i | −0.980917 | − | 0.194429i | \(-0.937715\pi\) |
0.658838 | + | 0.752285i | \(0.271048\pi\) | |||||||
\(242\) | −2.00000 | −0.128565 | ||||||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.00000 | − | 15.5885i | 0.574989 | − | 0.995910i | ||||
\(246\) | − | 6.92820i | − | 0.441726i | ||||||
\(247\) | 12.0000 | + | 20.7846i | 0.763542 | + | 1.32249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.0000 | + | 10.3923i | 1.14070 | + | 0.658586i | ||||
\(250\) | 12.0000 | − | 20.7846i | 0.758947 | − | 1.31453i | ||||
\(251\) | 13.0000 | 0.820553 | 0.410276 | − | 0.911961i | \(-0.365432\pi\) | ||||
0.410276 | + | 0.911961i | \(0.365432\pi\) | |||||||
\(252\) | −24.0000 | −1.51186 | ||||||||
\(253\) | −1.00000 | −0.0628695 | ||||||||
\(254\) | 2.00000 | − | 3.46410i | 0.125491 | − | 0.217357i | ||||
\(255\) | 12.0000 | − | 6.92820i | 0.751469 | − | 0.433861i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 13.0000 | + | 22.5167i | 0.810918 | + | 1.40455i | 0.912222 | + | 0.409695i | \(0.134365\pi\) |
−0.101305 | + | 0.994855i | \(0.532302\pi\) | |||||||
\(258\) | 36.0000 | − | 20.7846i | 2.24126 | − | 1.29399i | ||||
\(259\) | −6.00000 | + | 10.3923i | −0.372822 | + | 0.645746i | ||||
\(260\) | −16.0000 | −0.992278 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −36.0000 | −2.22409 | ||||||||
\(263\) | −1.00000 | + | 1.73205i | −0.0616626 | + | 0.106803i | −0.895209 | − | 0.445647i | \(-0.852974\pi\) |
0.833546 | + | 0.552450i | \(0.186307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.00000 | + | 5.19615i | 0.184289 | + | 0.319197i | ||||
\(266\) | −24.0000 | − | 41.5692i | −1.47153 | − | 2.54877i | ||||
\(267\) | − | 5.19615i | − | 0.317999i | ||||||
\(268\) | 4.00000 | − | 6.92820i | 0.244339 | − | 0.423207i | ||||
\(269\) | −5.00000 | −0.304855 | −0.152428 | − | 0.988315i | \(-0.548709\pi\) | ||||
−0.152428 | + | 0.988315i | \(0.548709\pi\) | |||||||
\(270\) | 20.7846i | 1.26491i | ||||||||
\(271\) | 2.00000 | 0.121491 | 0.0607457 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607457 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(272\) | 8.00000 | − | 13.8564i | 0.485071 | − | 0.840168i | ||||
\(273\) | − | 27.7128i | − | 1.67726i | ||||||
\(274\) | −7.00000 | − | 12.1244i | −0.422885 | − | 0.732459i | ||||
\(275\) | 0.500000 | + | 0.866025i | 0.0301511 | + | 0.0522233i | ||||
\(276\) | −3.00000 | − | 1.73205i | −0.180579 | − | 0.104257i | ||||
\(277\) | 1.00000 | − | 1.73205i | 0.0600842 | − | 0.104069i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(278\) | −32.0000 | −1.91923 | ||||||||
\(279\) | 1.50000 | + | 2.59808i | 0.0898027 | + | 0.155543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | − | 5.19615i | 0.178965 | − | 0.309976i | −0.762561 | − | 0.646916i | \(-0.776058\pi\) |
0.941526 | + | 0.336939i | \(0.109392\pi\) | |||||||
\(282\) | −21.0000 | + | 12.1244i | −1.25053 | + | 0.721995i | ||||
\(283\) | 1.00000 | + | 1.73205i | 0.0594438 | + | 0.102960i | 0.894216 | − | 0.447636i | \(-0.147734\pi\) |
−0.834772 | + | 0.550596i | \(0.814401\pi\) | |||||||
\(284\) | −15.0000 | − | 25.9808i | −0.890086 | − | 1.54167i | ||||
\(285\) | −18.0000 | + | 10.3923i | −1.06623 | + | 0.615587i | ||||
\(286\) | 4.00000 | − | 6.92820i | 0.236525 | − | 0.409673i | ||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 12.0000 | + | 20.7846i | 0.707107 | + | 1.22474i | ||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.5000 | + | 14.7224i | 1.49484 | + | 0.863044i | ||||
\(292\) | 8.00000 | + | 13.8564i | 0.468165 | + | 0.810885i | ||||
\(293\) | 9.00000 | + | 15.5885i | 0.525786 | + | 0.910687i | 0.999549 | + | 0.0300351i | \(0.00956192\pi\) |
−0.473763 | + | 0.880652i | \(0.657105\pi\) | |||||||
\(294\) | 31.1769i | 1.81827i | ||||||||
\(295\) | 11.0000 | − | 19.0526i | 0.640445 | − | 1.10928i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.50000 | − | 2.59808i | −0.261116 | − | 0.150756i | ||||
\(298\) | −4.00000 | −0.231714 | ||||||||
\(299\) | 2.00000 | − | 3.46410i | 0.115663 | − | 0.200334i | ||||
\(300\) | 3.46410i | 0.200000i | ||||||||
\(301\) | −24.0000 | − | 41.5692i | −1.38334 | − | 2.39601i | ||||
\(302\) | −10.0000 | − | 17.3205i | −0.575435 | − | 0.996683i | ||||
\(303\) | 3.00000 | + | 1.73205i | 0.172345 | + | 0.0995037i | ||||
\(304\) | −12.0000 | + | 20.7846i | −0.688247 | + | 1.19208i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12.0000 | + | 20.7846i | −0.685994 | + | 1.18818i | ||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | −4.00000 | + | 6.92820i | −0.227921 | + | 0.394771i | ||||
\(309\) | 1.50000 | − | 0.866025i | 0.0853320 | − | 0.0492665i | ||||
\(310\) | −2.00000 | − | 3.46410i | −0.113592 | − | 0.196748i | ||||
\(311\) | −1.50000 | − | 2.59808i | −0.0850572 | − | 0.147323i | 0.820358 | − | 0.571850i | \(-0.193774\pi\) |
−0.905416 | + | 0.424526i | \(0.860441\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.50000 | + | 9.52628i | −0.310878 | + | 0.538457i | −0.978553 | − | 0.205996i | \(-0.933957\pi\) |
0.667674 | + | 0.744453i | \(0.267290\pi\) | |||||||
\(314\) | −28.0000 | −1.58013 | ||||||||
\(315\) | 24.0000 | 1.35225 | ||||||||
\(316\) | −20.0000 | −1.12509 | ||||||||
\(317\) | −6.50000 | + | 11.2583i | −0.365076 | + | 0.632331i | −0.988788 | − | 0.149323i | \(-0.952290\pi\) |
0.623712 | + | 0.781654i | \(0.285624\pi\) | |||||||
\(318\) | −9.00000 | − | 5.19615i | −0.504695 | − | 0.291386i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −8.00000 | − | 13.8564i | −0.447214 | − | 0.774597i | ||||
\(321\) | 10.3923i | 0.580042i | ||||||||
\(322\) | −4.00000 | + | 6.92820i | −0.222911 | + | 0.386094i | ||||
\(323\) | −24.0000 | −1.33540 | ||||||||
\(324\) | −9.00000 | − | 15.5885i | −0.500000 | − | 0.866025i | ||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 13.0000 | − | 22.5167i | 0.720003 | − | 1.24708i | ||||
\(327\) | − | 17.3205i | − | 0.957826i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.0000 | + | 24.2487i | 0.771845 | + | 1.33687i | ||||
\(330\) | 6.00000 | + | 3.46410i | 0.330289 | + | 0.190693i | ||||
\(331\) | −2.00000 | + | 3.46410i | −0.109930 | + | 0.190404i | −0.915742 | − | 0.401768i | \(-0.868396\pi\) |
0.805812 | + | 0.592172i | \(0.201729\pi\) | |||||||
\(332\) | 24.0000 | 1.31717 | ||||||||
\(333\) | −9.00000 | −0.493197 | ||||||||
\(334\) | 36.0000 | 1.96983 | ||||||||
\(335\) | −4.00000 | + | 6.92820i | −0.218543 | + | 0.378528i | ||||
\(336\) | 24.0000 | − | 13.8564i | 1.30931 | − | 0.755929i | ||||
\(337\) | −16.0000 | − | 27.7128i | −0.871576 | − | 1.50961i | −0.860366 | − | 0.509676i | \(-0.829765\pi\) |
−0.0112091 | − | 0.999937i | \(-0.503568\pi\) | |||||||
\(338\) | 3.00000 | + | 5.19615i | 0.163178 | + | 0.282633i | ||||
\(339\) | 4.50000 | − | 2.59808i | 0.244406 | − | 0.141108i | ||||
\(340\) | 8.00000 | − | 13.8564i | 0.433861 | − | 0.751469i | ||||
\(341\) | 1.00000 | 0.0541530 | ||||||||
\(342\) | 18.0000 | − | 31.1769i | 0.973329 | − | 1.68585i | ||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.00000 | + | 1.73205i | 0.161515 | + | 0.0932505i | ||||
\(346\) | 6.00000 | + | 10.3923i | 0.322562 | + | 0.558694i | ||||
\(347\) | 1.00000 | + | 1.73205i | 0.0536828 | + | 0.0929814i | 0.891618 | − | 0.452788i | \(-0.149571\pi\) |
−0.837935 | + | 0.545770i | \(0.816237\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.00000 | + | 5.19615i | −0.160586 | + | 0.278144i | −0.935079 | − | 0.354439i | \(-0.884672\pi\) |
0.774493 | + | 0.632583i | \(0.218005\pi\) | |||||||
\(350\) | 8.00000 | 0.427618 | ||||||||
\(351\) | 18.0000 | − | 10.3923i | 0.960769 | − | 0.554700i | ||||
\(352\) | 8.00000 | 0.426401 | ||||||||
\(353\) | −1.50000 | + | 2.59808i | −0.0798369 | + | 0.138282i | −0.903179 | − | 0.429263i | \(-0.858773\pi\) |
0.823343 | + | 0.567545i | \(0.192107\pi\) | |||||||
\(354\) | 38.1051i | 2.02526i | ||||||||
\(355\) | 15.0000 | + | 25.9808i | 0.796117 | + | 1.37892i | ||||
\(356\) | −3.00000 | − | 5.19615i | −0.159000 | − | 0.275396i | ||||
\(357\) | 24.0000 | + | 13.8564i | 1.27021 | + | 0.733359i | ||||
\(358\) | −12.0000 | + | 20.7846i | −0.634220 | + | 1.09850i | ||||
\(359\) | 10.0000 | 0.527780 | 0.263890 | − | 0.964553i | \(-0.414994\pi\) | ||||
0.263890 | + | 0.964553i | \(0.414994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | −14.0000 | + | 24.2487i | −0.735824 | + | 1.27448i | ||||
\(363\) | −1.50000 | + | 0.866025i | −0.0787296 | + | 0.0454545i | ||||
\(364\) | −16.0000 | − | 27.7128i | −0.838628 | − | 1.45255i | ||||
\(365\) | −8.00000 | − | 13.8564i | −0.418739 | − | 0.725277i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00000 | − | 6.92820i | 0.208798 | − | 0.361649i | −0.742538 | − | 0.669804i | \(-0.766378\pi\) |
0.951336 | + | 0.308155i | \(0.0997115\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | −3.00000 | − | 5.19615i | −0.156174 | − | 0.270501i | ||||
\(370\) | 12.0000 | 0.623850 | ||||||||
\(371\) | −6.00000 | + | 10.3923i | −0.311504 | + | 0.539542i | ||||
\(372\) | 3.00000 | + | 1.73205i | 0.155543 | + | 0.0898027i | ||||
\(373\) | −11.0000 | − | 19.0526i | −0.569558 | − | 0.986504i | −0.996610 | − | 0.0822766i | \(-0.973781\pi\) |
0.427051 | − | 0.904227i | \(-0.359552\pi\) | |||||||
\(374\) | 4.00000 | + | 6.92820i | 0.206835 | + | 0.358249i | ||||
\(375\) | − | 20.7846i | − | 1.07331i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −36.0000 | + | 20.7846i | −1.85164 | + | 1.06904i | ||||
\(379\) | −29.0000 | −1.48963 | −0.744815 | − | 0.667271i | \(-0.767462\pi\) | ||||
−0.744815 | + | 0.667271i | \(0.767462\pi\) | |||||||
\(380\) | −12.0000 | + | 20.7846i | −0.615587 | + | 1.06623i | ||||
\(381\) | − | 3.46410i | − | 0.177471i | ||||||
\(382\) | 20.0000 | + | 34.6410i | 1.02329 | + | 1.77239i | ||||
\(383\) | −4.00000 | − | 6.92820i | −0.204390 | − | 0.354015i | 0.745548 | − | 0.666452i | \(-0.232188\pi\) |
−0.949938 | + | 0.312437i | \(0.898855\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | − | 6.92820i | 0.203859 | − | 0.353094i | ||||
\(386\) | 28.0000 | 1.42516 | ||||||||
\(387\) | 18.0000 | − | 31.1769i | 0.914991 | − | 1.58481i | ||||
\(388\) | 34.0000 | 1.72609 | ||||||||
\(389\) | −4.50000 | + | 7.79423i | −0.228159 | + | 0.395183i | −0.957263 | − | 0.289220i | \(-0.906604\pi\) |
0.729103 | + | 0.684403i | \(0.239937\pi\) | |||||||
\(390\) | −24.0000 | + | 13.8564i | −1.21529 | + | 0.701646i | ||||
\(391\) | 2.00000 | + | 3.46410i | 0.101144 | + | 0.175187i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.0000 | + | 15.5885i | −1.36197 | + | 0.786334i | ||||
\(394\) | −2.00000 | + | 3.46410i | −0.100759 | + | 0.174519i | ||||
\(395\) | 20.0000 | 1.00631 | ||||||||
\(396\) | −6.00000 | −0.301511 | ||||||||
\(397\) | 25.0000 | 1.25471 | 0.627357 | − | 0.778732i | \(-0.284137\pi\) | ||||
0.627357 | + | 0.778732i | \(0.284137\pi\) | |||||||
\(398\) | −15.0000 | + | 25.9808i | −0.751882 | + | 1.30230i | ||||
\(399\) | −36.0000 | − | 20.7846i | −1.80225 | − | 1.04053i | ||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | −14.5000 | − | 25.1147i | −0.724095 | − | 1.25417i | −0.959345 | − | 0.282235i | \(-0.908924\pi\) |
0.235250 | − | 0.971935i | \(-0.424409\pi\) | |||||||
\(402\) | − | 13.8564i | − | 0.691095i | ||||||
\(403\) | −2.00000 | + | 3.46410i | −0.0996271 | + | 0.172559i | ||||
\(404\) | 4.00000 | 0.199007 | ||||||||
\(405\) | 9.00000 | + | 15.5885i | 0.447214 | + | 0.774597i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.50000 | + | 2.59808i | −0.0743522 | + | 0.128782i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.00000 | − | 15.5885i | −0.445021 | − | 0.770800i | 0.553032 | − | 0.833160i | \(-0.313471\pi\) |
−0.998054 | + | 0.0623602i | \(0.980137\pi\) | |||||||
\(410\) | 4.00000 | + | 6.92820i | 0.197546 | + | 0.342160i | ||||
\(411\) | −10.5000 | − | 6.06218i | −0.517927 | − | 0.299025i | ||||
\(412\) | 1.00000 | − | 1.73205i | 0.0492665 | − | 0.0853320i | ||||
\(413\) | 44.0000 | 2.16510 | ||||||||
\(414\) | −6.00000 | −0.294884 | ||||||||
\(415\) | −24.0000 | −1.17811 | ||||||||
\(416\) | −16.0000 | + | 27.7128i | −0.784465 | + | 1.35873i | ||||
\(417\) | −24.0000 | + | 13.8564i | −1.17529 | + | 0.678551i | ||||
\(418\) | −6.00000 | − | 10.3923i | −0.293470 | − | 0.508304i | ||||
\(419\) | 3.50000 | + | 6.06218i | 0.170986 | + | 0.296157i | 0.938765 | − | 0.344558i | \(-0.111971\pi\) |
−0.767779 | + | 0.640715i | \(0.778638\pi\) | |||||||
\(420\) | 24.0000 | − | 13.8564i | 1.17108 | − | 0.676123i | ||||
\(421\) | −18.5000 | + | 32.0429i | −0.901635 | + | 1.56168i | −0.0762630 | + | 0.997088i | \(0.524299\pi\) |
−0.825372 | + | 0.564590i | \(0.809034\pi\) | |||||||
\(422\) | 24.0000 | 1.16830 | ||||||||
\(423\) | −10.5000 | + | 18.1865i | −0.510527 | + | 0.884260i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | − | 3.46410i | 0.0970143 | − | 0.168034i | ||||
\(426\) | −45.0000 | − | 25.9808i | −2.18026 | − | 1.25877i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.00000 | + | 10.3923i | 0.290021 | + | 0.502331i | ||||
\(429\) | − | 6.92820i | − | 0.334497i | ||||||
\(430\) | −24.0000 | + | 41.5692i | −1.15738 | + | 2.00465i | ||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 18.0000 | + | 10.3923i | 0.866025 | + | 0.500000i | ||||
\(433\) | 13.0000 | 0.624740 | 0.312370 | − | 0.949960i | \(-0.398877\pi\) | ||||
0.312370 | + | 0.949960i | \(0.398877\pi\) | |||||||
\(434\) | 4.00000 | − | 6.92820i | 0.192006 | − | 0.332564i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | − | 17.3205i | −0.478913 | − | 0.829502i | ||||
\(437\) | −3.00000 | − | 5.19615i | −0.143509 | − | 0.248566i | ||||
\(438\) | 24.0000 | + | 13.8564i | 1.14676 | + | 0.662085i | ||||
\(439\) | 10.0000 | − | 17.3205i | 0.477274 | − | 0.826663i | −0.522387 | − | 0.852709i | \(-0.674958\pi\) |
0.999661 | + | 0.0260459i | \(0.00829161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.5000 | + | 23.3827i | 0.642857 | + | 1.11346i | ||||
\(442\) | −32.0000 | −1.52208 | ||||||||
\(443\) | 20.5000 | − | 35.5070i | 0.973984 | − | 1.68699i | 0.290738 | − | 0.956803i | \(-0.406099\pi\) |
0.683247 | − | 0.730188i | \(-0.260567\pi\) | |||||||
\(444\) | −9.00000 | + | 5.19615i | −0.427121 | + | 0.246598i | ||||
\(445\) | 3.00000 | + | 5.19615i | 0.142214 | + | 0.246321i | ||||
\(446\) | 7.00000 | + | 12.1244i | 0.331460 | + | 0.574105i | ||||
\(447\) | −3.00000 | + | 1.73205i | −0.141895 | + | 0.0819232i | ||||
\(448\) | 16.0000 | − | 27.7128i | 0.755929 | − | 1.30931i | ||||
\(449\) | −1.00000 | −0.0471929 | −0.0235965 | − | 0.999722i | \(-0.507512\pi\) | ||||
−0.0235965 | + | 0.999722i | \(0.507512\pi\) | |||||||
\(450\) | 3.00000 | + | 5.19615i | 0.141421 | + | 0.244949i | ||||
\(451\) | −2.00000 | −0.0941763 | ||||||||
\(452\) | 3.00000 | − | 5.19615i | 0.141108 | − | 0.244406i | ||||
\(453\) | −15.0000 | − | 8.66025i | −0.704761 | − | 0.406894i | ||||
\(454\) | −12.0000 | − | 20.7846i | −0.563188 | − | 0.975470i | ||||
\(455\) | 16.0000 | + | 27.7128i | 0.750092 | + | 1.29920i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.00000 | − | 15.5885i | 0.421002 | − | 0.729197i | −0.575036 | − | 0.818128i | \(-0.695012\pi\) |
0.996038 | + | 0.0889312i | \(0.0283451\pi\) | |||||||
\(458\) | −6.00000 | −0.280362 | ||||||||
\(459\) | 20.7846i | 0.970143i | ||||||||
\(460\) | 4.00000 | 0.186501 | ||||||||
\(461\) | 15.0000 | − | 25.9808i | 0.698620 | − | 1.21004i | −0.270326 | − | 0.962769i | \(-0.587131\pi\) |
0.968945 | − | 0.247276i | \(-0.0795353\pi\) | |||||||
\(462\) | 13.8564i | 0.644658i | ||||||||
\(463\) | 17.5000 | + | 30.3109i | 0.813294 | + | 1.40867i | 0.910546 | + | 0.413407i | \(0.135661\pi\) |
−0.0972525 | + | 0.995260i | \(0.531005\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.00000 | − | 1.73205i | −0.139122 | − | 0.0803219i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 12.0000 | − | 20.7846i | 0.554700 | − | 0.960769i | ||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 14.0000 | − | 24.2487i | 0.645772 | − | 1.11851i | ||||
\(471\) | −21.0000 | + | 12.1244i | −0.967629 | + | 0.558661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.00000 | − | 10.3923i | −0.275880 | − | 0.477839i | ||||
\(474\) | −30.0000 | + | 17.3205i | −1.37795 | + | 0.795557i | ||||
\(475\) | −3.00000 | + | 5.19615i | −0.137649 | + | 0.238416i | ||||
\(476\) | 32.0000 | 1.46672 | ||||||||
\(477\) | −9.00000 | −0.412082 | ||||||||
\(478\) | 48.0000 | 2.19547 | ||||||||
\(479\) | 17.0000 | − | 29.4449i | 0.776750 | − | 1.34537i | −0.157056 | − | 0.987590i | \(-0.550200\pi\) |
0.933806 | − | 0.357780i | \(-0.116466\pi\) | |||||||
\(480\) | −24.0000 | − | 13.8564i | −1.09545 | − | 0.632456i | ||||
\(481\) | −6.00000 | − | 10.3923i | −0.273576 | − | 0.473848i | ||||
\(482\) | 10.0000 | + | 17.3205i | 0.455488 | + | 0.788928i | ||||
\(483\) | 6.92820i | 0.315244i | ||||||||
\(484\) | −1.00000 | + | 1.73205i | −0.0454545 | + | 0.0787296i | ||||
\(485\) | −34.0000 | −1.54386 | ||||||||
\(486\) | −27.0000 | − | 15.5885i | −1.22474 | − | 0.707107i | ||||
\(487\) | −19.0000 | −0.860972 | −0.430486 | − | 0.902597i | \(-0.641658\pi\) | ||||
−0.430486 | + | 0.902597i | \(0.641658\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 22.5167i | − | 1.01824i | ||||||
\(490\) | −18.0000 | − | 31.1769i | −0.813157 | − | 1.40843i | ||||
\(491\) | −5.00000 | − | 8.66025i | −0.225647 | − | 0.390832i | 0.730866 | − | 0.682520i | \(-0.239116\pi\) |
−0.956513 | + | 0.291689i | \(0.905783\pi\) | |||||||
\(492\) | −6.00000 | − | 3.46410i | −0.270501 | − | 0.156174i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 48.0000 | 2.15962 | ||||||||
\(495\) | 6.00000 | 0.269680 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −30.0000 | + | 51.9615i | −1.34568 | + | 2.33079i | ||||
\(498\) | 36.0000 | − | 20.7846i | 1.61320 | − | 0.931381i | ||||
\(499\) | 12.5000 | + | 21.6506i | 0.559577 | + | 0.969216i | 0.997532 | + | 0.0702185i | \(0.0223697\pi\) |
−0.437955 | + | 0.898997i | \(0.644297\pi\) | |||||||
\(500\) | −12.0000 | − | 20.7846i | −0.536656 | − | 0.929516i | ||||
\(501\) | 27.0000 | − | 15.5885i | 1.20627 | − | 0.696441i | ||||
\(502\) | 13.0000 | − | 22.5167i | 0.580218 | − | 1.00497i | ||||
\(503\) | 10.0000 | 0.445878 | 0.222939 | − | 0.974832i | \(-0.428435\pi\) | ||||
0.222939 | + | 0.974832i | \(0.428435\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.00000 | −0.177998 | ||||||||
\(506\) | −1.00000 | + | 1.73205i | −0.0444554 | + | 0.0769991i | ||||
\(507\) | 4.50000 | + | 2.59808i | 0.199852 | + | 0.115385i | ||||
\(508\) | −2.00000 | − | 3.46410i | −0.0887357 | − | 0.153695i | ||||
\(509\) | −1.50000 | − | 2.59808i | −0.0664863 | − | 0.115158i | 0.830866 | − | 0.556473i | \(-0.187846\pi\) |
−0.897352 | + | 0.441315i | \(0.854512\pi\) | |||||||
\(510\) | − | 27.7128i | − | 1.22714i | ||||||
\(511\) | 16.0000 | − | 27.7128i | 0.707798 | − | 1.22594i | ||||
\(512\) | −32.0000 | −1.41421 | ||||||||
\(513\) | − | 31.1769i | − | 1.37649i | ||||||
\(514\) | 52.0000 | 2.29362 | ||||||||
\(515\) | −1.00000 | + | 1.73205i | −0.0440653 | + | 0.0763233i | ||||
\(516\) | − | 41.5692i | − | 1.82998i | ||||||
\(517\) | 3.50000 | + | 6.06218i | 0.153930 | + | 0.266614i | ||||
\(518\) | 12.0000 | + | 20.7846i | 0.527250 | + | 0.913223i | ||||
\(519\) | 9.00000 | + | 5.19615i | 0.395056 | + | 0.228086i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.0000 | −1.18289 | −0.591446 | − | 0.806345i | \(-0.701443\pi\) | ||||
−0.591446 | + | 0.806345i | \(0.701443\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.0000 | −1.48672 | −0.743358 | − | 0.668894i | \(-0.766768\pi\) | ||||
−0.743358 | + | 0.668894i | \(0.766768\pi\) | |||||||
\(524\) | −18.0000 | + | 31.1769i | −0.786334 | + | 1.36197i | ||||
\(525\) | 6.00000 | − | 3.46410i | 0.261861 | − | 0.151186i | ||||
\(526\) | 2.00000 | + | 3.46410i | 0.0872041 | + | 0.151042i | ||||
\(527\) | −2.00000 | − | 3.46410i | −0.0871214 | − | 0.150899i | ||||
\(528\) | 6.00000 | − | 3.46410i | 0.261116 | − | 0.150756i | ||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 12.0000 | 0.521247 | ||||||||
\(531\) | 16.5000 | + | 28.5788i | 0.716039 | + | 1.24022i | ||||
\(532\) | −48.0000 | −2.08106 | ||||||||
\(533\) | 4.00000 | − | 6.92820i | 0.173259 | − | 0.300094i | ||||
\(534\) | −9.00000 | − | 5.19615i | −0.389468 | − | 0.224860i | ||||
\(535\) | −6.00000 | − | 10.3923i | −0.259403 | − | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.7846i | 0.896922i | ||||||||
\(538\) | −5.00000 | + | 8.66025i | −0.215565 | + | 0.373370i | ||||
\(539\) | 9.00000 | 0.387657 | ||||||||
\(540\) | 18.0000 | + | 10.3923i | 0.774597 | + | 0.447214i | ||||
\(541\) | 16.0000 | 0.687894 | 0.343947 | − | 0.938989i | \(-0.388236\pi\) | ||||
0.343947 | + | 0.938989i | \(0.388236\pi\) | |||||||
\(542\) | 2.00000 | − | 3.46410i | 0.0859074 | − | 0.148796i | ||||
\(543\) | 24.2487i | 1.04061i | ||||||||
\(544\) | −16.0000 | − | 27.7128i | −0.685994 | − | 1.18818i | ||||
\(545\) | 10.0000 | + | 17.3205i | 0.428353 | + | 0.741929i | ||||
\(546\) | −48.0000 | − | 27.7128i | −2.05421 | − | 1.18600i | ||||
\(547\) | −1.00000 | + | 1.73205i | −0.0427569 | + | 0.0740571i | −0.886612 | − | 0.462514i | \(-0.846947\pi\) |
0.843855 | + | 0.536571i | \(0.180281\pi\) | |||||||
\(548\) | −14.0000 | −0.598050 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.00000 | 0.0852803 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.0000 | + | 34.6410i | 0.850487 | + | 1.47309i | ||||
\(554\) | −2.00000 | − | 3.46410i | −0.0849719 | − | 0.147176i | ||||
\(555\) | 9.00000 | − | 5.19615i | 0.382029 | − | 0.220564i | ||||
\(556\) | −16.0000 | + | 27.7128i | −0.678551 | + | 1.17529i | ||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | 48.0000 | 2.03018 | ||||||||
\(560\) | −16.0000 | + | 27.7128i | −0.676123 | + | 1.17108i | ||||
\(561\) | 6.00000 | + | 3.46410i | 0.253320 | + | 0.146254i | ||||
\(562\) | −6.00000 | − | 10.3923i | −0.253095 | − | 0.438373i | ||||
\(563\) | 1.00000 | + | 1.73205i | 0.0421450 | + | 0.0729972i | 0.886328 | − | 0.463057i | \(-0.153248\pi\) |
−0.844183 | + | 0.536054i | \(0.819914\pi\) | |||||||
\(564\) | 24.2487i | 1.02105i | ||||||||
\(565\) | −3.00000 | + | 5.19615i | −0.126211 | + | 0.218604i | ||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | −18.0000 | + | 31.1769i | −0.755929 | + | 1.30931i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0000 | − | 20.7846i | 0.503066 | − | 0.871336i | −0.496928 | − | 0.867792i | \(-0.665539\pi\) |
0.999994 | − | 0.00354413i | \(-0.00112814\pi\) | |||||||
\(570\) | 41.5692i | 1.74114i | ||||||||
\(571\) | 8.00000 | + | 13.8564i | 0.334790 | + | 0.579873i | 0.983444 | − | 0.181210i | \(-0.0580014\pi\) |
−0.648655 | + | 0.761083i | \(0.724668\pi\) | |||||||
\(572\) | −4.00000 | − | 6.92820i | −0.167248 | − | 0.289683i | ||||
\(573\) | 30.0000 | + | 17.3205i | 1.25327 | + | 0.723575i | ||||
\(574\) | −8.00000 | + | 13.8564i | −0.333914 | + | 0.578355i | ||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 24.0000 | 1.00000 | ||||||||
\(577\) | −6.00000 | −0.249783 | −0.124892 | − | 0.992170i | \(-0.539858\pi\) | ||||
−0.124892 | + | 0.992170i | \(0.539858\pi\) | |||||||
\(578\) | −1.00000 | + | 1.73205i | −0.0415945 | + | 0.0720438i | ||||
\(579\) | 21.0000 | − | 12.1244i | 0.872730 | − | 0.503871i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | − | 41.5692i | −0.995688 | − | 1.72458i | ||||
\(582\) | 51.0000 | − | 29.4449i | 2.11402 | − | 1.22053i | ||||
\(583\) | −1.50000 | + | 2.59808i | −0.0621237 | + | 0.107601i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.0000 | + | 20.7846i | −0.496139 | + | 0.859338i | ||||
\(586\) | 36.0000 | 1.48715 | ||||||||
\(587\) | 8.50000 | − | 14.7224i | 0.350833 | − | 0.607660i | −0.635563 | − | 0.772049i | \(-0.719232\pi\) |
0.986396 | + | 0.164389i | \(0.0525653\pi\) | |||||||
\(588\) | 27.0000 | + | 15.5885i | 1.11346 | + | 0.642857i | ||||
\(589\) | 3.00000 | + | 5.19615i | 0.123613 | + | 0.214104i | ||||
\(590\) | −22.0000 | − | 38.1051i | −0.905726 | − | 1.56876i | ||||
\(591\) | 3.46410i | 0.142494i | ||||||||
\(592\) | 6.00000 | − | 10.3923i | 0.246598 | − | 0.427121i | ||||
\(593\) | −22.0000 | −0.903432 | −0.451716 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(594\) | −9.00000 | + | 5.19615i | −0.369274 | + | 0.213201i | ||||
\(595\) | −32.0000 | −1.31187 | ||||||||
\(596\) | −2.00000 | + | 3.46410i | −0.0819232 | + | 0.141895i | ||||
\(597\) | 25.9808i | 1.06332i | ||||||||
\(598\) | −4.00000 | − | 6.92820i | −0.163572 | − | 0.283315i | ||||
\(599\) | −8.00000 | − | 13.8564i | −0.326871 | − | 0.566157i | 0.655018 | − | 0.755613i | \(-0.272661\pi\) |
−0.981889 | + | 0.189456i | \(0.939328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0000 | + | 22.5167i | −0.530281 | + | 0.918474i | 0.469095 | + | 0.883148i | \(0.344580\pi\) |
−0.999376 | + | 0.0353259i | \(0.988753\pi\) | |||||||
\(602\) | −96.0000 | −3.91267 | ||||||||
\(603\) | −6.00000 | − | 10.3923i | −0.244339 | − | 0.423207i | ||||
\(604\) | −20.0000 | −0.813788 | ||||||||
\(605\) | 1.00000 | − | 1.73205i | 0.0406558 | − | 0.0704179i | ||||
\(606\) | 6.00000 | − | 3.46410i | 0.243733 | − | 0.140720i | ||||
\(607\) | 2.00000 | + | 3.46410i | 0.0811775 | + | 0.140604i | 0.903756 | − | 0.428048i | \(-0.140799\pi\) |
−0.822578 | + | 0.568652i | \(0.807465\pi\) | |||||||
\(608\) | 24.0000 | + | 41.5692i | 0.973329 | + | 1.68585i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.0000 | −1.13276 | ||||||||
\(612\) | 12.0000 | + | 20.7846i | 0.485071 | + | 0.840168i | ||||
\(613\) | 14.0000 | 0.565455 | 0.282727 | − | 0.959200i | \(-0.408761\pi\) | ||||
0.282727 | + | 0.959200i | \(0.408761\pi\) | |||||||
\(614\) | 20.0000 | − | 34.6410i | 0.807134 | − | 1.39800i | ||||
\(615\) | 6.00000 | + | 3.46410i | 0.241943 | + | 0.139686i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.5000 | + | 23.3827i | 0.543490 | + | 0.941351i | 0.998700 | + | 0.0509678i | \(0.0162306\pi\) |
−0.455211 | + | 0.890384i | \(0.650436\pi\) | |||||||
\(618\) | − | 3.46410i | − | 0.139347i | ||||||
\(619\) | 15.5000 | − | 26.8468i | 0.622998 | − | 1.07906i | −0.365927 | − | 0.930644i | \(-0.619248\pi\) |
0.988924 | − | 0.148420i | \(-0.0474187\pi\) | |||||||
\(620\) | −4.00000 | −0.160644 | ||||||||
\(621\) | −4.50000 | + | 2.59808i | −0.180579 | + | 0.104257i | ||||
\(622\) | −6.00000 | −0.240578 | ||||||||
\(623\) | −6.00000 | + | 10.3923i | −0.240385 | + | 0.416359i | ||||
\(624\) | 27.7128i | 1.10940i | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 11.0000 | + | 19.0526i | 0.439648 | + | 0.761493i | ||||
\(627\) | −9.00000 | − | 5.19615i | −0.359425 | − | 0.207514i | ||||
\(628\) | −14.0000 | + | 24.2487i | −0.558661 | + | 0.967629i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 24.0000 | − | 41.5692i | 0.956183 | − | 1.65616i | ||||
\(631\) | −32.0000 | −1.27390 | −0.636950 | − | 0.770905i | \(-0.719804\pi\) | ||||
−0.636950 | + | 0.770905i | \(0.719804\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.0000 | − | 10.3923i | 0.715436 | − | 0.413057i | ||||
\(634\) | 13.0000 | + | 22.5167i | 0.516296 | + | 0.894251i | ||||
\(635\) | 2.00000 | + | 3.46410i | 0.0793676 | + | 0.137469i | ||||
\(636\) | −9.00000 | + | 5.19615i | −0.356873 | + | 0.206041i | ||||
\(637\) | −18.0000 | + | 31.1769i | −0.713186 | + | 1.23527i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −45.0000 | −1.78017 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.5000 | + | 33.7750i | −0.770204 | + | 1.33403i | 0.167247 | + | 0.985915i | \(0.446512\pi\) |
−0.937451 | + | 0.348117i | \(0.886821\pi\) | |||||||
\(642\) | 18.0000 | + | 10.3923i | 0.710403 | + | 0.410152i | ||||
\(643\) | −8.50000 | − | 14.7224i | −0.335207 | − | 0.580596i | 0.648317 | − | 0.761370i | \(-0.275473\pi\) |
−0.983525 | + | 0.180774i | \(0.942140\pi\) | |||||||
\(644\) | 4.00000 | + | 6.92820i | 0.157622 | + | 0.273009i | ||||
\(645\) | 41.5692i | 1.63679i | ||||||||
\(646\) | −24.0000 | + | 41.5692i | −0.944267 | + | 1.63552i | ||||
\(647\) | 17.0000 | 0.668339 | 0.334169 | − | 0.942513i | \(-0.391544\pi\) | ||||
0.334169 | + | 0.942513i | \(0.391544\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.0000 | 0.431788 | ||||||||
\(650\) | −4.00000 | + | 6.92820i | −0.156893 | + | 0.271746i | ||||
\(651\) | − | 6.92820i | − | 0.271538i | ||||||
\(652\) | −13.0000 | − | 22.5167i | −0.509119 | − | 0.881820i | ||||
\(653\) | −9.50000 | − | 16.4545i | −0.371764 | − | 0.643914i | 0.618073 | − | 0.786121i | \(-0.287914\pi\) |
−0.989837 | + | 0.142207i | \(0.954580\pi\) | |||||||
\(654\) | −30.0000 | − | 17.3205i | −1.17309 | − | 0.677285i | ||||
\(655\) | 18.0000 | − | 31.1769i | 0.703318 | − | 1.21818i | ||||
\(656\) | 8.00000 | 0.312348 | ||||||||
\(657\) | 24.0000 | 0.936329 | ||||||||
\(658\) | 56.0000 | 2.18311 | ||||||||
\(659\) | 10.0000 | − | 17.3205i | 0.389545 | − | 0.674711i | −0.602844 | − | 0.797859i | \(-0.705966\pi\) |
0.992388 | + | 0.123148i | \(0.0392990\pi\) | |||||||
\(660\) | 6.00000 | − | 3.46410i | 0.233550 | − | 0.134840i | ||||
\(661\) | −18.5000 | − | 32.0429i | −0.719567 | − | 1.24633i | −0.961172 | − | 0.275951i | \(-0.911007\pi\) |
0.241605 | − | 0.970375i | \(-0.422326\pi\) | |||||||
\(662\) | 4.00000 | + | 6.92820i | 0.155464 | + | 0.269272i | ||||
\(663\) | −24.0000 | + | 13.8564i | −0.932083 | + | 0.538138i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 48.0000 | 1.86136 | ||||||||
\(666\) | −9.00000 | + | 15.5885i | −0.348743 | + | 0.604040i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 18.0000 | − | 31.1769i | 0.696441 | − | 1.20627i | ||||
\(669\) | 10.5000 | + | 6.06218i | 0.405953 | + | 0.234377i | ||||
\(670\) | 8.00000 | + | 13.8564i | 0.309067 | + | 0.535320i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − | 55.4256i | − | 2.13809i | ||||||
\(673\) | −10.0000 | + | 17.3205i | −0.385472 | + | 0.667657i | −0.991835 | − | 0.127532i | \(-0.959295\pi\) |
0.606363 | + | 0.795188i | \(0.292628\pi\) | |||||||
\(674\) | −64.0000 | −2.46519 | ||||||||
\(675\) | 4.50000 | + | 2.59808i | 0.173205 | + | 0.100000i | ||||
\(676\) | 6.00000 | 0.230769 | ||||||||
\(677\) | 15.0000 | − | 25.9808i | 0.576497 | − | 0.998522i | −0.419380 | − | 0.907811i | \(-0.637753\pi\) |
0.995877 | − | 0.0907112i | \(-0.0289140\pi\) | |||||||
\(678\) | − | 10.3923i | − | 0.399114i | ||||||
\(679\) | −34.0000 | − | 58.8897i | −1.30480 | − | 2.25998i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.0000 | − | 10.3923i | −0.689761 | − | 0.398234i | ||||
\(682\) | 1.00000 | − | 1.73205i | 0.0382920 | − | 0.0663237i | ||||
\(683\) | 29.0000 | 1.10965 | 0.554827 | − | 0.831966i | \(-0.312784\pi\) | ||||
0.554827 | + | 0.831966i | \(0.312784\pi\) | |||||||
\(684\) | −18.0000 | − | 31.1769i | −0.688247 | − | 1.19208i | ||||
\(685\) | 14.0000 | 0.534913 | ||||||||
\(686\) | 8.00000 | − | 13.8564i | 0.305441 | − | 0.529040i | ||||
\(687\) | −4.50000 | + | 2.59808i | −0.171686 | + | 0.0991228i | ||||
\(688\) | 24.0000 | + | 41.5692i | 0.914991 | + | 1.58481i | ||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 6.00000 | − | 3.46410i | 0.228416 | − | 0.131876i | ||||
\(691\) | 2.00000 | − | 3.46410i | 0.0760836 | − | 0.131781i | −0.825473 | − | 0.564441i | \(-0.809092\pi\) |
0.901557 | + | 0.432660i | \(0.142425\pi\) | |||||||
\(692\) | 12.0000 | 0.456172 | ||||||||
\(693\) | 6.00000 | + | 10.3923i | 0.227921 | + | 0.394771i | ||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | 16.0000 | − | 27.7128i | 0.606915 | − | 1.05121i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | + | 6.92820i | 0.151511 | + | 0.262424i | ||||
\(698\) | 6.00000 | + | 10.3923i | 0.227103 | + | 0.393355i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.00000 | − | 6.92820i | 0.151186 | − | 0.261861i | ||||
\(701\) | −28.0000 | −1.05755 | −0.528773 | − | 0.848763i | \(-0.677348\pi\) | ||||
−0.528773 | + | 0.848763i | \(0.677348\pi\) | |||||||
\(702\) | − | 41.5692i | − | 1.56893i | ||||||
\(703\) | −18.0000 | −0.678883 | ||||||||
\(704\) | 4.00000 | − | 6.92820i | 0.150756 | − | 0.261116i | ||||
\(705\) | − | 24.2487i | − | 0.913259i | ||||||
\(706\) | 3.00000 | + | 5.19615i | 0.112906 | + | 0.195560i | ||||
\(707\) | −4.00000 | − | 6.92820i | −0.150435 | − | 0.260562i | ||||
\(708\) | 33.0000 | + | 19.0526i | 1.24022 | + | 0.716039i | ||||
\(709\) | −13.0000 | + | 22.5167i | −0.488225 | + | 0.845631i | −0.999908 | − | 0.0135434i | \(-0.995689\pi\) |
0.511683 | + | 0.859174i | \(0.329022\pi\) | |||||||
\(710\) | 60.0000 | 2.25176 | ||||||||
\(711\) | −15.0000 | + | 25.9808i | −0.562544 | + | 0.974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.500000 | − | 0.866025i | 0.0187251 | − | 0.0324329i | ||||
\(714\) | 48.0000 | − | 27.7128i | 1.79635 | − | 1.03713i | ||||
\(715\) | 4.00000 | + | 6.92820i | 0.149592 | + | 0.259100i | ||||
\(716\) | 12.0000 | + | 20.7846i | 0.448461 | + | 0.776757i | ||||
\(717\) | 36.0000 | − | 20.7846i | 1.34444 | − | 0.776215i | ||||
\(718\) | 10.0000 | − | 17.3205i | 0.373197 | − | 0.646396i | ||||
\(719\) | −12.0000 | −0.447524 | −0.223762 | − | 0.974644i | \(-0.571834\pi\) | ||||
−0.223762 | + | 0.974644i | \(0.571834\pi\) | |||||||
\(720\) | −24.0000 | −0.894427 | ||||||||
\(721\) | −4.00000 | −0.148968 | ||||||||
\(722\) | 17.0000 | − | 29.4449i | 0.632674 | − | 1.09582i | ||||
\(723\) | 15.0000 | + | 8.66025i | 0.557856 | + | 0.322078i | ||||
\(724\) | 14.0000 | + | 24.2487i | 0.520306 | + | 0.901196i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.46410i | 0.128565i | ||||||||
\(727\) | −10.5000 | + | 18.1865i | −0.389423 | + | 0.674501i | −0.992372 | − | 0.123279i | \(-0.960659\pi\) |
0.602949 | + | 0.797780i | \(0.293992\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −32.0000 | −1.18437 | ||||||||
\(731\) | −24.0000 | + | 41.5692i | −0.887672 | + | 1.53749i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.00000 | − | 5.19615i | −0.110808 | − | 0.191924i | 0.805289 | − | 0.592883i | \(-0.202010\pi\) |
−0.916096 | + | 0.400959i | \(0.868677\pi\) | |||||||
\(734\) | −8.00000 | − | 13.8564i | −0.295285 | − | 0.511449i | ||||
\(735\) | −27.0000 | − | 15.5885i | −0.995910 | − | 0.574989i | ||||
\(736\) | 4.00000 | − | 6.92820i | 0.147442 | − | 0.255377i | ||||
\(737\) | −4.00000 | −0.147342 | ||||||||
\(738\) | −12.0000 | −0.441726 | ||||||||
\(739\) | −40.0000 | −1.47142 | −0.735712 | − | 0.677295i | \(-0.763152\pi\) | ||||
−0.735712 | + | 0.677295i | \(0.763152\pi\) | |||||||
\(740\) | 6.00000 | − | 10.3923i | 0.220564 | − | 0.382029i | ||||
\(741\) | 36.0000 | − | 20.7846i | 1.32249 | − | 0.763542i | ||||
\(742\) | 12.0000 | + | 20.7846i | 0.440534 | + | 0.763027i | ||||
\(743\) | −5.00000 | − | 8.66025i | −0.183432 | − | 0.317714i | 0.759615 | − | 0.650373i | \(-0.225387\pi\) |
−0.943047 | + | 0.332659i | \(0.892054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00000 | − | 3.46410i | 0.0732743 | − | 0.126915i | ||||
\(746\) | −44.0000 | −1.61095 | ||||||||
\(747\) | 18.0000 | − | 31.1769i | 0.658586 | − | 1.14070i | ||||
\(748\) | 8.00000 | 0.292509 | ||||||||
\(749\) | 12.0000 | − | 20.7846i | 0.438470 | − | 0.759453i | ||||
\(750\) | −36.0000 | − | 20.7846i | −1.31453 | − | 0.758947i | ||||
\(751\) | 2.50000 | + | 4.33013i | 0.0912263 | + | 0.158009i | 0.908027 | − | 0.418911i | \(-0.137588\pi\) |
−0.816801 | + | 0.576919i | \(0.804255\pi\) | |||||||
\(752\) | −14.0000 | − | 24.2487i | −0.510527 | − | 0.884260i | ||||
\(753\) | − | 22.5167i | − | 0.820553i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.0000 | 0.727875 | ||||||||
\(756\) | 41.5692i | 1.51186i | ||||||||
\(757\) | −43.0000 | −1.56286 | −0.781431 | − | 0.623992i | \(-0.785510\pi\) | ||||
−0.781431 | + | 0.623992i | \(0.785510\pi\) | |||||||
\(758\) | −29.0000 | + | 50.2295i | −1.05333 | + | 1.82442i | ||||
\(759\) | 1.73205i | 0.0628695i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | −6.00000 | − | 3.46410i | −0.217357 | − | 0.125491i | ||||
\(763\) | −20.0000 | + | 34.6410i | −0.724049 | + | 1.25409i | ||||
\(764\) | 40.0000 | 1.44715 | ||||||||
\(765\) | −12.0000 | − | 20.7846i | −0.433861 | − | 0.751469i | ||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | −22.0000 | + | 38.1051i | −0.794374 | + | 1.37590i | ||||
\(768\) | −24.0000 | + | 13.8564i | −0.866025 | + | 0.500000i | ||||
\(769\) | 17.0000 | + | 29.4449i | 0.613036 | + | 1.06181i | 0.990726 | + | 0.135877i | \(0.0433852\pi\) |
−0.377690 | + | 0.925932i | \(0.623282\pi\) | |||||||
\(770\) | −8.00000 | − | 13.8564i | −0.288300 | − | 0.499350i | ||||
\(771\) | 39.0000 | − | 22.5167i | 1.40455 | − | 0.810918i | ||||
\(772\) | 14.0000 | − | 24.2487i | 0.503871 | − | 0.872730i | ||||
\(773\) | 42.0000 | 1.51064 | 0.755318 | − | 0.655359i | \(-0.227483\pi\) | ||||
0.755318 | + | 0.655359i | \(0.227483\pi\) | |||||||
\(774\) | −36.0000 | − | 62.3538i | −1.29399 | − | 2.24126i | ||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.0000 | + | 10.3923i | 0.645746 | + | 0.372822i | ||||
\(778\) | 9.00000 | + | 15.5885i | 0.322666 | + | 0.558873i | ||||
\(779\) | −6.00000 | − | 10.3923i | −0.214972 | − | 0.372343i | ||||
\(780\) | 27.7128i | 0.992278i | ||||||||
\(781\) | −7.50000 | + | 12.9904i | −0.268371 | + | 0.464832i | ||||
\(782\) | 8.00000 | 0.286079 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −36.0000 | −1.28571 | ||||||||
\(785\) | 14.0000 | − | 24.2487i | 0.499681 | − | 0.865474i | ||||
\(786\) | 62.3538i | 2.22409i | ||||||||
\(787\) | −2.00000 | − | 3.46410i | −0.0712923 | − | 0.123482i | 0.828176 | − | 0.560469i | \(-0.189379\pi\) |
−0.899468 | + | 0.436987i | \(0.856046\pi\) | |||||||
\(788\) | 2.00000 | + | 3.46410i | 0.0712470 | + | 0.123404i | ||||
\(789\) | 3.00000 | + | 1.73205i | 0.106803 | + | 0.0616626i | ||||
\(790\) | 20.0000 | − | 34.6410i | 0.711568 | − | 1.23247i | ||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 25.0000 | − | 43.3013i | 0.887217 | − | 1.53670i | ||||
\(795\) | 9.00000 | − | 5.19615i | 0.319197 | − | 0.184289i | ||||
\(796\) | 15.0000 | + | 25.9808i | 0.531661 | + | 0.920864i | ||||
\(797\) | 15.5000 | + | 26.8468i | 0.549038 | + | 0.950962i | 0.998341 | + | 0.0575824i | \(0.0183392\pi\) |
−0.449303 | + | 0.893380i | \(0.648327\pi\) | |||||||
\(798\) | −72.0000 | + | 41.5692i | −2.54877 | + | 1.47153i | ||||
\(799\) | 14.0000 | − | 24.2487i | 0.495284 | − | 0.857858i | ||||
\(800\) | −8.00000 | −0.282843 | ||||||||
\(801\) | −9.00000 | −0.317999 | ||||||||
\(802\) | −58.0000 | −2.04805 | ||||||||
\(803\) | 4.00000 | − | 6.92820i | 0.141157 | − | 0.244491i | ||||
\(804\) | −12.0000 | − | 6.92820i | −0.423207 | − | 0.244339i | ||||
\(805\) | −4.00000 | − | 6.92820i | −0.140981 | − | 0.244187i | ||||
\(806\) | 4.00000 | + | 6.92820i | 0.140894 | + | 0.244036i | ||||
\(807\) | 8.66025i | 0.304855i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 36.0000 | 1.26491 | ||||||||
\(811\) | 40.0000 | 1.40459 | 0.702295 | − | 0.711886i | \(-0.252159\pi\) | ||||
0.702295 | + | 0.711886i | \(0.252159\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 3.46410i | − | 0.121491i | ||||||
\(814\) | 3.00000 | + | 5.19615i | 0.105150 | + | 0.182125i | ||||
\(815\) | 13.0000 | + | 22.5167i | 0.455370 | + | 0.788724i | ||||
\(816\) | −24.0000 | − | 13.8564i | −0.840168 | − | 0.485071i | ||||
\(817\) | 36.0000 | − | 62.3538i | 1.25948 | − | 2.18148i | ||||
\(818\) | −36.0000 | −1.25871 | ||||||||
\(819\) | −48.0000 | −1.67726 | ||||||||
\(820\) | 8.00000 | 0.279372 | ||||||||
\(821\) | −26.0000 | + | 45.0333i | −0.907406 | + | 1.57167i | −0.0897520 | + | 0.995964i | \(0.528607\pi\) |
−0.817654 | + | 0.575710i | \(0.804726\pi\) | |||||||
\(822\) | −21.0000 | + | 12.1244i | −0.732459 | + | 0.422885i | ||||
\(823\) | 4.50000 | + | 7.79423i | 0.156860 | + | 0.271690i | 0.933735 | − | 0.357966i | \(-0.116529\pi\) |
−0.776875 | + | 0.629655i | \(0.783196\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.50000 | − | 0.866025i | 0.0522233 | − | 0.0301511i | ||||
\(826\) | 44.0000 | − | 76.2102i | 1.53096 | − | 2.65169i | ||||
\(827\) | −28.0000 | −0.973655 | −0.486828 | − | 0.873498i | \(-0.661846\pi\) | ||||
−0.486828 | + | 0.873498i | \(0.661846\pi\) | |||||||
\(828\) | −3.00000 | + | 5.19615i | −0.104257 | + | 0.180579i | ||||
\(829\) | 34.0000 | 1.18087 | 0.590434 | − | 0.807086i | \(-0.298956\pi\) | ||||
0.590434 | + | 0.807086i | \(0.298956\pi\) | |||||||
\(830\) | −24.0000 | + | 41.5692i | −0.833052 | + | 1.44289i | ||||
\(831\) | −3.00000 | − | 1.73205i | −0.104069 | − | 0.0600842i | ||||
\(832\) | 16.0000 | + | 27.7128i | 0.554700 | + | 0.960769i | ||||
\(833\) | −18.0000 | − | 31.1769i | −0.623663 | − | 1.08022i | ||||
\(834\) | 55.4256i | 1.91923i | ||||||||
\(835\) | −18.0000 | + | 31.1769i | −0.622916 | + | 1.07892i | ||||
\(836\) | −12.0000 | −0.415029 | ||||||||
\(837\) | 4.50000 | − | 2.59808i | 0.155543 | − | 0.0898027i | ||||
\(838\) | 14.0000 | 0.483622 | ||||||||
\(839\) | 2.50000 | − | 4.33013i | 0.0863096 | − | 0.149493i | −0.819639 | − | 0.572880i | \(-0.805826\pi\) |
0.905949 | + | 0.423388i | \(0.139159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5000 | + | 25.1147i | 0.500000 | + | 0.866025i | ||||
\(842\) | 37.0000 | + | 64.0859i | 1.27510 | + | 2.20855i | ||||
\(843\) | −9.00000 | − | 5.19615i | −0.309976 | − | 0.178965i | ||||
\(844\) | 12.0000 | − | 20.7846i | 0.413057 | − | 0.715436i | ||||
\(845\) | −6.00000 | −0.206406 | ||||||||
\(846\) | 21.0000 | + | 36.3731i | 0.721995 | + | 1.25053i | ||||
\(847\) | 4.00000 | 0.137442 | ||||||||
\(848\) | 6.00000 | − | 10.3923i | 0.206041 | − | 0.356873i | ||||
\(849\) | 3.00000 | − | 1.73205i | 0.102960 | − | 0.0594438i | ||||
\(850\) | −4.00000 | − | 6.92820i | −0.137199 | − | 0.237635i | ||||
\(851\) | 1.50000 | + | 2.59808i | 0.0514193 | + | 0.0890609i | ||||
\(852\) | −45.0000 | + | 25.9808i | −1.54167 | + | 0.890086i | ||||
\(853\) | 8.00000 | − | 13.8564i | 0.273915 | − | 0.474434i | −0.695946 | − | 0.718094i | \(-0.745015\pi\) |
0.969861 | + | 0.243660i | \(0.0783480\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.0000 | + | 31.1769i | 0.615587 | + | 1.06623i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.0000 | − | 19.0526i | 0.375753 | − | 0.650823i | −0.614687 | − | 0.788771i | \(-0.710717\pi\) |
0.990439 | + | 0.137948i | \(0.0440508\pi\) | |||||||
\(858\) | −12.0000 | − | 6.92820i | −0.409673 | − | 0.236525i | ||||
\(859\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(860\) | 24.0000 | + | 41.5692i | 0.818393 | + | 1.41750i | ||||
\(861\) | 13.8564i | 0.472225i | ||||||||
\(862\) | 12.0000 | − | 20.7846i | 0.408722 | − | 0.707927i | ||||
\(863\) | 48.0000 | 1.63394 | 0.816970 | − | 0.576681i | \(-0.195652\pi\) | ||||
0.816970 | + | 0.576681i | \(0.195652\pi\) | |||||||
\(864\) | 36.0000 | − | 20.7846i | 1.22474 | − | 0.707107i | ||||
\(865\) | −12.0000 | −0.408012 | ||||||||
\(866\) | 13.0000 | − | 22.5167i | 0.441758 | − | 0.765147i | ||||
\(867\) | 1.73205i | 0.0588235i | ||||||||
\(868\) | −4.00000 | − | 6.92820i | −0.135769 | − | 0.235159i | ||||
\(869\) | 5.00000 | + | 8.66025i | 0.169613 | + | 0.293779i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000 | − | 13.8564i | 0.271070 | − | 0.469506i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 25.5000 | − | 44.1673i | 0.863044 | − | 1.49484i | ||||
\(874\) | −12.0000 | −0.405906 | ||||||||
\(875\) | −24.0000 | + | 41.5692i | −0.811348 | + | 1.40530i | ||||
\(876\) | 24.0000 | − | 13.8564i | 0.810885 | − | 0.468165i | ||||
\(877\) | 9.00000 | + | 15.5885i | 0.303908 | + | 0.526385i | 0.977018 | − | 0.213158i | \(-0.0683750\pi\) |
−0.673109 | + | 0.739543i | \(0.735042\pi\) | |||||||
\(878\) | −20.0000 | − | 34.6410i | −0.674967 | − | 1.16908i | ||||
\(879\) | 27.0000 | − | 15.5885i | 0.910687 | − | 0.525786i | ||||
\(880\) | −4.00000 | + | 6.92820i | −0.134840 | + | 0.233550i | ||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 54.0000 | 1.81827 | ||||||||
\(883\) | −41.0000 | −1.37976 | −0.689880 | − | 0.723924i | \(-0.742337\pi\) | ||||
−0.689880 | + | 0.723924i | \(0.742337\pi\) | |||||||
\(884\) | −16.0000 | + | 27.7128i | −0.538138 | + | 0.932083i | ||||
\(885\) | −33.0000 | − | 19.0526i | −1.10928 | − | 0.640445i | ||||
\(886\) | −41.0000 | − | 71.0141i | −1.37742 | − | 2.38576i | ||||
\(887\) | 26.0000 | + | 45.0333i | 0.872995 | + | 1.51207i | 0.858884 | + | 0.512170i | \(0.171158\pi\) |
0.0141108 | + | 0.999900i | \(0.495508\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | + | 6.92820i | −0.134156 | + | 0.232364i | ||||
\(890\) | 12.0000 | 0.402241 | ||||||||
\(891\) | −4.50000 | + | 7.79423i | −0.150756 | + | 0.261116i | ||||
\(892\) | 14.0000 | 0.468755 | ||||||||
\(893\) | −21.0000 | + | 36.3731i | −0.702738 | + | 1.21718i | ||||
\(894\) | 6.92820i | 0.231714i | ||||||||
\(895\) | −12.0000 | − | 20.7846i | −0.401116 | − | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00000 | − | 3.46410i | −0.200334 | − | 0.115663i | ||||
\(898\) | −1.00000 | + | 1.73205i | −0.0333704 | + | 0.0577993i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 6.00000 | 0.200000 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | −2.00000 | + | 3.46410i | −0.0665927 | + | 0.115342i | ||||
\(903\) | −72.0000 | + | 41.5692i | −2.39601 | + | 1.38334i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.0000 | − | 24.2487i | −0.465376 | − | 0.806054i | ||||
\(906\) | −30.0000 | + | 17.3205i | −0.996683 | + | 0.575435i | ||||
\(907\) | 30.0000 | − | 51.9615i | 0.996134 | − | 1.72535i | 0.421986 | − | 0.906602i | \(-0.361333\pi\) |
0.574148 | − | 0.818752i | \(-0.305333\pi\) | |||||||
\(908\) | −24.0000 | −0.796468 | ||||||||
\(909\) | 3.00000 | − | 5.19615i | 0.0995037 | − | 0.172345i | ||||
\(910\) | 64.0000 | 2.12158 | ||||||||
\(911\) | 28.5000 | − | 49.3634i | 0.944247 | − | 1.63548i | 0.186995 | − | 0.982361i | \(-0.440125\pi\) |
0.757252 | − | 0.653123i | \(-0.226542\pi\) | |||||||
\(912\) | 36.0000 | + | 20.7846i | 1.19208 | + | 0.688247i | ||||
\(913\) | −6.00000 | − | 10.3923i | −0.198571 | − | 0.343935i | ||||
\(914\) | −18.0000 | − | 31.1769i | −0.595387 | − | 1.03124i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.00000 | + | 5.19615i | −0.0991228 | + | 0.171686i | ||||
\(917\) | 72.0000 | 2.37765 | ||||||||
\(918\) | 36.0000 | + | 20.7846i | 1.18818 | + | 0.685994i | ||||
\(919\) | 22.0000 | 0.725713 | 0.362857 | − | 0.931845i | \(-0.381802\pi\) | ||||
0.362857 | + | 0.931845i | \(0.381802\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 34.6410i | − | 1.14146i | ||||||
\(922\) | −30.0000 | − | 51.9615i | −0.987997 | − | 1.71126i | ||||
\(923\) | −30.0000 | − | 51.9615i | −0.987462 | − | 1.71033i | ||||
\(924\) | 12.0000 | + | 6.92820i | 0.394771 | + | 0.227921i | ||||
\(925\) | 1.50000 | − | 2.59808i | 0.0493197 | − | 0.0854242i | ||||
\(926\) | 70.0000 | 2.30034 | ||||||||
\(927\) | −1.50000 | − | 2.59808i | −0.0492665 | − | 0.0853320i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.50000 | − | 2.59808i | 0.0492134 | − | 0.0852401i | −0.840369 | − | 0.542014i | \(-0.817662\pi\) |
0.889583 | + | 0.456774i | \(0.150995\pi\) | |||||||
\(930\) | −6.00000 | + | 3.46410i | −0.196748 | + | 0.113592i | ||||
\(931\) | 27.0000 | + | 46.7654i | 0.884889 | + | 1.53267i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.50000 | + | 2.59808i | −0.147323 | + | 0.0850572i | ||||
\(934\) | −36.0000 | + | 62.3538i | −1.17796 | + | 2.04028i | ||||
\(935\) | −8.00000 | −0.261628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.0000 | −0.522697 | −0.261349 | − | 0.965244i | \(-0.584167\pi\) | ||||
−0.261349 | + | 0.965244i | \(0.584167\pi\) | |||||||
\(938\) | −16.0000 | + | 27.7128i | −0.522419 | + | 0.904855i | ||||
\(939\) | 16.5000 | + | 9.52628i | 0.538457 | + | 0.310878i | ||||
\(940\) | −14.0000 | − | 24.2487i | −0.456630 | − | 0.790906i | ||||
\(941\) | 12.0000 | + | 20.7846i | 0.391189 | + | 0.677559i | 0.992607 | − | 0.121376i | \(-0.0387306\pi\) |
−0.601418 | + | 0.798935i | \(0.705397\pi\) | |||||||
\(942\) | 48.4974i | 1.58013i | ||||||||
\(943\) | −1.00000 | + | 1.73205i | −0.0325645 | + | 0.0564033i | ||||
\(944\) | −44.0000 | −1.43208 | ||||||||
\(945\) | − | 41.5692i | − | 1.35225i | ||||||
\(946\) | −24.0000 | −0.780307 | ||||||||
\(947\) | −6.00000 | + | 10.3923i | −0.194974 | + | 0.337705i | −0.946892 | − | 0.321552i | \(-0.895796\pi\) |
0.751918 | + | 0.659256i | \(0.229129\pi\) | |||||||
\(948\) | 34.6410i | 1.12509i | ||||||||
\(949\) | 16.0000 | + | 27.7128i | 0.519382 | + | 0.899596i | ||||
\(950\) | 6.00000 | + | 10.3923i | 0.194666 | + | 0.337171i | ||||
\(951\) | 19.5000 | + | 11.2583i | 0.632331 | + | 0.365076i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.0000 | −0.647864 | −0.323932 | − | 0.946080i | \(-0.605005\pi\) | ||||
−0.323932 | + | 0.946080i | \(0.605005\pi\) | |||||||
\(954\) | −9.00000 | + | 15.5885i | −0.291386 | + | 0.504695i | ||||
\(955\) | −40.0000 | −1.29437 | ||||||||
\(956\) | 24.0000 | − | 41.5692i | 0.776215 | − | 1.34444i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.0000 | − | 58.8897i | −1.09849 | − | 1.90264i | ||||
\(959\) | 14.0000 | + | 24.2487i | 0.452084 | + | 0.783032i | ||||
\(960\) | −24.0000 | + | 13.8564i | −0.774597 | + | 0.447214i | ||||
\(961\) | 15.0000 | − | 25.9808i | 0.483871 | − | 0.838089i | ||||
\(962\) | −24.0000 | −0.773791 | ||||||||
\(963\) | 18.0000 | 0.580042 | ||||||||
\(964\) | 20.0000 | 0.644157 | ||||||||
\(965\) | −14.0000 | + | 24.2487i | −0.450676 | + | 0.780594i | ||||
\(966\) | 12.0000 | + | 6.92820i | 0.386094 | + | 0.222911i | ||||
\(967\) | −29.0000 | − | 50.2295i | −0.932577 | − | 1.61527i | −0.778898 | − | 0.627150i | \(-0.784221\pi\) |
−0.153679 | − | 0.988121i | \(-0.549112\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 41.5692i | 1.33540i | ||||||||
\(970\) | −34.0000 | + | 58.8897i | −1.09167 | + | 1.89084i | ||||
\(971\) | 35.0000 | 1.12320 | 0.561602 | − | 0.827408i | \(-0.310185\pi\) | ||||
0.561602 | + | 0.827408i | \(0.310185\pi\) | |||||||
\(972\) | −27.0000 | + | 15.5885i | −0.866025 | + | 0.500000i | ||||
\(973\) | 64.0000 | 2.05175 | ||||||||
\(974\) | −19.0000 | + | 32.9090i | −0.608799 | + | 1.05447i | ||||
\(975\) | 6.92820i | 0.221880i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.5000 | + | 23.3827i | 0.431903 | + | 0.748078i | 0.997037 | − | 0.0769208i | \(-0.0245089\pi\) |
−0.565134 | + | 0.824999i | \(0.691176\pi\) | |||||||
\(978\) | −39.0000 | − | 22.5167i | −1.24708 | − | 0.720003i | ||||
\(979\) | −1.50000 | + | 2.59808i | −0.0479402 | + | 0.0830349i | ||||
\(980\) | −36.0000 | −1.14998 | ||||||||
\(981\) | −30.0000 | −0.957826 | ||||||||
\(982\) | −20.0000 | −0.638226 | ||||||||
\(983\) | −16.5000 | + | 28.5788i | −0.526268 | + | 0.911523i | 0.473263 | + | 0.880921i | \(0.343076\pi\) |
−0.999532 | + | 0.0306024i | \(0.990257\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00000 | − | 3.46410i | −0.0637253 | − | 0.110375i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42.0000 | − | 24.2487i | 1.33687 | − | 0.771845i | ||||
\(988\) | 24.0000 | − | 41.5692i | 0.763542 | − | 1.32249i | ||||
\(989\) | −12.0000 | −0.381578 | ||||||||
\(990\) | 6.00000 | − | 10.3923i | 0.190693 | − | 0.330289i | ||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | −4.00000 | + | 6.92820i | −0.127000 | + | 0.219971i | ||||
\(993\) | 6.00000 | + | 3.46410i | 0.190404 | + | 0.109930i | ||||
\(994\) | 60.0000 | + | 103.923i | 1.90308 | + | 3.29624i | ||||
\(995\) | −15.0000 | − | 25.9808i | −0.475532 | − | 0.823646i | ||||
\(996\) | − | 41.5692i | − | 1.31717i | ||||||
\(997\) | 26.0000 | − | 45.0333i | 0.823428 | − | 1.42622i | −0.0796863 | − | 0.996820i | \(-0.525392\pi\) |
0.903115 | − | 0.429400i | \(-0.141275\pi\) | |||||||
\(998\) | 50.0000 | 1.58272 | ||||||||
\(999\) | 15.5885i | 0.493197i |
(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 | 99.2.e.c.34.1 | ✓ | 2 | |
3.2 | odd | 2 | 297.2.e.a.100.1 | 2 | |||
9.2 | odd | 6 | 891.2.a.h.1.1 | 1 | |||
9.4 | even | 3 | inner | 99.2.e.c.67.1 | yes | 2 | |
9.5 | odd | 6 | 297.2.e.a.199.1 | 2 | |||
9.7 | even | 3 | 891.2.a.a.1.1 | 1 | |||
11.10 | odd | 2 | 1089.2.e.a.727.1 | 2 | |||
99.43 | odd | 6 | 9801.2.a.l.1.1 | 1 | |||
99.65 | even | 6 | 9801.2.a.a.1.1 | 1 | |||
99.76 | odd | 6 | 1089.2.e.a.364.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.e.c.34.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
99.2.e.c.67.1 | yes | 2 | 9.4 | even | 3 | inner | |
297.2.e.a.100.1 | 2 | 3.2 | odd | 2 | |||
297.2.e.a.199.1 | 2 | 9.5 | odd | 6 | |||
891.2.a.a.1.1 | 1 | 9.7 | even | 3 | |||
891.2.a.h.1.1 | 1 | 9.2 | odd | 6 | |||
1089.2.e.a.364.1 | 2 | 99.76 | odd | 6 | |||
1089.2.e.a.727.1 | 2 | 11.10 | odd | 2 | |||
9801.2.a.a.1.1 | 1 | 99.65 | even | 6 | |||
9801.2.a.l.1.1 | 1 | 99.43 | odd | 6 |