Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(8,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.n (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.8 |
Dual form | 273.2.n.a.239.1 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(3\) | −1.70711 | − | 0.292893i | −0.985599 | − | 0.169102i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.70711 | + | 2.70711i | −1.21065 | + | 1.21065i | −0.239843 | + | 0.970812i | \(0.577096\pi\) |
−0.970812 | + | 0.239843i | \(0.922904\pi\) | |||||||
\(6\) | 2.00000 | − | 1.41421i | 0.816497 | − | 0.577350i | ||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | 2.82843 | + | 1.00000i | 0.942809 | + | 0.333333i | ||||
\(10\) | − | 5.41421i | − | 1.71212i | ||||||
\(11\) | 1.41421 | + | 1.41421i | 0.426401 | + | 0.426401i | 0.887401 | − | 0.460999i | \(-0.152509\pi\) |
−0.460999 | + | 0.887401i | \(0.652509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.707107 | − | 3.53553i | 0.196116 | − | 0.980581i | ||||
\(14\) | − | 1.41421i | − | 0.377964i | ||||||
\(15\) | 5.41421 | − | 3.82843i | 1.39794 | − | 0.988496i | ||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | −3.82843 | + | 1.82843i | −0.902369 | + | 0.430964i | ||||
\(19\) | −1.87868 | − | 1.87868i | −0.430999 | − | 0.430999i | 0.457969 | − | 0.888968i | \(-0.348577\pi\) |
−0.888968 | + | 0.457969i | \(0.848577\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.41421 | − | 1.00000i | 0.308607 | − | 0.218218i | ||||
\(22\) | −2.82843 | −0.603023 | ||||||||
\(23\) | 1.82843 | 0.381253 | 0.190627 | − | 0.981663i | \(-0.438948\pi\) | ||||
0.190627 | + | 0.981663i | \(0.438948\pi\) | |||||||
\(24\) | 2.82843 | + | 4.00000i | 0.577350 | + | 0.816497i | ||||
\(25\) | − | 9.65685i | − | 1.93137i | ||||||
\(26\) | 2.82843 | + | 4.24264i | 0.554700 | + | 0.832050i | ||||
\(27\) | −4.53553 | − | 2.53553i | −0.872864 | − | 0.487964i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.65685i | − | 1.23615i | −0.786120 | − | 0.618073i | \(-0.787913\pi\) | ||
0.786120 | − | 0.618073i | \(-0.212087\pi\) | |||||||
\(30\) | −1.58579 | + | 9.24264i | −0.289524 | + | 1.68747i | ||||
\(31\) | 2.94975 | + | 2.94975i | 0.529790 | + | 0.529790i | 0.920510 | − | 0.390720i | \(-0.127774\pi\) |
−0.390720 | + | 0.920510i | \(0.627774\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | − | 2.82843i | −0.348155 | − | 0.492366i | ||||
\(34\) | 4.00000 | − | 4.00000i | 0.685994 | − | 0.685994i | ||||
\(35\) | − | 3.82843i | − | 0.647122i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.41421 | + | 6.41421i | −1.05449 | + | 1.05449i | −0.0560630 | + | 0.998427i | \(0.517855\pi\) |
−0.998427 | + | 0.0560630i | \(0.982145\pi\) | |||||||
\(38\) | 3.75736 | 0.609524 | ||||||||
\(39\) | −2.24264 | + | 5.82843i | −0.359110 | + | 0.933295i | ||||
\(40\) | 10.8284 | 1.71212 | ||||||||
\(41\) | −0.242641 | + | 0.242641i | −0.0378941 | + | 0.0378941i | −0.725800 | − | 0.687906i | \(-0.758530\pi\) |
0.687906 | + | 0.725800i | \(0.258530\pi\) | |||||||
\(42\) | −0.414214 | + | 2.41421i | −0.0639145 | + | 0.372521i | ||||
\(43\) | 6.65685i | 1.01516i | 0.861604 | + | 0.507580i | \(0.169460\pi\) | ||||
−0.861604 | + | 0.507580i | \(0.830540\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.3640 | + | 4.94975i | −1.54497 | + | 0.737865i | ||||
\(46\) | −1.82843 | + | 1.82843i | −0.269587 | + | 0.269587i | ||||
\(47\) | 1.87868 | + | 1.87868i | 0.274034 | + | 0.274034i | 0.830722 | − | 0.556688i | \(-0.187928\pi\) |
−0.556688 | + | 0.830722i | \(0.687928\pi\) | |||||||
\(48\) | −6.82843 | − | 1.17157i | −0.985599 | − | 0.169102i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 9.65685 | + | 9.65685i | 1.36569 | + | 1.36569i | ||||
\(51\) | 6.82843 | + | 1.17157i | 0.956171 | + | 0.164053i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 12.3137i | − | 1.69142i | −0.533644 | − | 0.845709i | \(-0.679178\pi\) | ||
0.533644 | − | 0.845709i | \(-0.320822\pi\) | |||||||
\(54\) | 7.07107 | − | 2.00000i | 0.962250 | − | 0.272166i | ||||
\(55\) | −7.65685 | −1.03245 | ||||||||
\(56\) | 2.82843 | 0.377964 | ||||||||
\(57\) | 2.65685 | + | 3.75736i | 0.351909 | + | 0.497674i | ||||
\(58\) | 6.65685 | + | 6.65685i | 0.874088 | + | 0.874088i | ||||
\(59\) | −1.41421 | − | 1.41421i | −0.184115 | − | 0.184115i | 0.609031 | − | 0.793146i | \(-0.291558\pi\) |
−0.793146 | + | 0.609031i | \(0.791558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.8995 | −1.77965 | −0.889824 | − | 0.456304i | \(-0.849173\pi\) | ||||
−0.889824 | + | 0.456304i | \(0.849173\pi\) | |||||||
\(62\) | −5.89949 | −0.749237 | ||||||||
\(63\) | −2.70711 | + | 1.29289i | −0.341063 | + | 0.162889i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 7.65685 | + | 11.4853i | 0.949716 | + | 1.42457i | ||||
\(66\) | 4.82843 | + | 0.828427i | 0.594338 | + | 0.101972i | ||||
\(67\) | −9.07107 | − | 9.07107i | −1.10821 | − | 1.10821i | −0.993386 | − | 0.114821i | \(-0.963371\pi\) |
−0.114821 | − | 0.993386i | \(-0.536629\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.12132 | − | 0.535534i | −0.375763 | − | 0.0644707i | ||||
\(70\) | 3.82843 | + | 3.82843i | 0.457585 | + | 0.457585i | ||||
\(71\) | −11.2426 | + | 11.2426i | −1.33426 | + | 1.33426i | −0.432735 | + | 0.901521i | \(0.642451\pi\) |
−0.901521 | + | 0.432735i | \(0.857549\pi\) | |||||||
\(72\) | −3.65685 | − | 7.65685i | −0.430964 | − | 0.902369i | ||||
\(73\) | 0.121320 | − | 0.121320i | 0.0141995 | − | 0.0141995i | −0.699971 | − | 0.714171i | \(-0.746804\pi\) |
0.714171 | + | 0.699971i | \(0.246804\pi\) | |||||||
\(74\) | − | 12.8284i | − | 1.49127i | ||||||
\(75\) | −2.82843 | + | 16.4853i | −0.326599 | + | 1.90356i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | −0.227921 | ||||||||
\(78\) | −3.58579 | − | 8.07107i | −0.406010 | − | 0.913868i | ||||
\(79\) | 5.82843 | 0.655749 | 0.327875 | − | 0.944721i | \(-0.393668\pi\) | ||||
0.327875 | + | 0.944721i | \(0.393668\pi\) | |||||||
\(80\) | −10.8284 | + | 10.8284i | −1.21065 | + | 1.21065i | ||||
\(81\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(82\) | − | 0.485281i | − | 0.0535904i | ||||||
\(83\) | −0.707107 | + | 0.707107i | −0.0776151 | + | 0.0776151i | −0.744849 | − | 0.667234i | \(-0.767478\pi\) |
0.667234 | + | 0.744849i | \(0.267478\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.8284 | − | 10.8284i | 1.17451 | − | 1.17451i | ||||
\(86\) | −6.65685 | − | 6.65685i | −0.717827 | − | 0.717827i | ||||
\(87\) | −1.94975 | + | 11.3640i | −0.209035 | + | 1.21834i | ||||
\(88\) | − | 5.65685i | − | 0.603023i | ||||||
\(89\) | −5.87868 | − | 5.87868i | −0.623139 | − | 0.623139i | 0.323194 | − | 0.946333i | \(-0.395243\pi\) |
−0.946333 | + | 0.323194i | \(0.895243\pi\) | |||||||
\(90\) | 5.41421 | − | 15.3137i | 0.570708 | − | 1.61421i | ||||
\(91\) | 2.00000 | + | 3.00000i | 0.209657 | + | 0.314485i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.17157 | − | 5.89949i | −0.432572 | − | 0.611749i | ||||
\(94\) | −3.75736 | −0.387542 | ||||||||
\(95\) | 10.1716 | 1.04358 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.29289 | − | 7.29289i | −0.740481 | − | 0.740481i | 0.232189 | − | 0.972671i | \(-0.425411\pi\) |
−0.972671 | + | 0.232189i | \(0.925411\pi\) | |||||||
\(98\) | 1.00000 | + | 1.00000i | 0.101015 | + | 0.101015i | ||||
\(99\) | 2.58579 | + | 5.41421i | 0.259881 | + | 0.544149i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.65685 | 0.761885 | 0.380943 | − | 0.924599i | \(-0.375599\pi\) | ||||
0.380943 | + | 0.924599i | \(0.375599\pi\) | |||||||
\(102\) | −8.00000 | + | 5.65685i | −0.792118 | + | 0.560112i | ||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | −8.48528 | + | 5.65685i | −0.832050 | + | 0.554700i | ||||
\(105\) | −1.12132 | + | 6.53553i | −0.109430 | + | 0.637803i | ||||
\(106\) | 12.3137 | + | 12.3137i | 1.19601 | + | 1.19601i | ||||
\(107\) | 0.828427i | 0.0800871i | 0.999198 | + | 0.0400435i | \(0.0127497\pi\) | ||||
−0.999198 | + | 0.0400435i | \(0.987250\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.17157 | + | 4.17157i | 0.399564 | + | 0.399564i | 0.878079 | − | 0.478515i | \(-0.158825\pi\) |
−0.478515 | + | 0.878079i | \(0.658825\pi\) | |||||||
\(110\) | 7.65685 | − | 7.65685i | 0.730052 | − | 0.730052i | ||||
\(111\) | 12.8284 | − | 9.07107i | 1.21762 | − | 0.860988i | ||||
\(112\) | −2.82843 | + | 2.82843i | −0.267261 | + | 0.267261i | ||||
\(113\) | − | 9.82843i | − | 0.924581i | −0.886729 | − | 0.462290i | \(-0.847028\pi\) | ||
0.886729 | − | 0.462290i | \(-0.152972\pi\) | |||||||
\(114\) | −6.41421 | − | 1.10051i | −0.600746 | − | 0.103072i | ||||
\(115\) | −4.94975 | + | 4.94975i | −0.461566 | + | 0.461566i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.53553 | − | 9.29289i | 0.511760 | − | 0.859128i | ||||
\(118\) | 2.82843 | 0.260378 | ||||||||
\(119\) | 2.82843 | − | 2.82843i | 0.259281 | − | 0.259281i | ||||
\(120\) | −18.4853 | − | 3.17157i | −1.68747 | − | 0.289524i | ||||
\(121\) | − | 7.00000i | − | 0.636364i | ||||||
\(122\) | 13.8995 | − | 13.8995i | 1.25840 | − | 1.25840i | ||||
\(123\) | 0.485281 | − | 0.343146i | 0.0437563 | − | 0.0309404i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.6066 | + | 12.6066i | 1.12757 | + | 1.12757i | ||||
\(126\) | 1.41421 | − | 4.00000i | 0.125988 | − | 0.356348i | ||||
\(127\) | − | 2.00000i | − | 0.177471i | −0.996055 | − | 0.0887357i | \(-0.971717\pi\) | ||
0.996055 | − | 0.0887357i | \(-0.0282826\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.707107 | − | 0.707107i | ||||
\(129\) | 1.94975 | − | 11.3640i | 0.171666 | − | 1.00054i | ||||
\(130\) | −19.1421 | − | 3.82843i | −1.67888 | − | 0.335775i | ||||
\(131\) | − | 9.07107i | − | 0.792543i | −0.918133 | − | 0.396271i | \(-0.870304\pi\) | ||
0.918133 | − | 0.396271i | \(-0.129696\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.65685 | 0.230378 | ||||||||
\(134\) | 18.1421 | 1.56724 | ||||||||
\(135\) | 19.1421 | − | 5.41421i | 1.64749 | − | 0.465981i | ||||
\(136\) | 8.00000 | + | 8.00000i | 0.685994 | + | 0.685994i | ||||
\(137\) | 6.41421 | + | 6.41421i | 0.548003 | + | 0.548003i | 0.925863 | − | 0.377860i | \(-0.123340\pi\) |
−0.377860 | + | 0.925863i | \(0.623340\pi\) | |||||||
\(138\) | 3.65685 | − | 2.58579i | 0.311292 | − | 0.220117i | ||||
\(139\) | −8.82843 | −0.748817 | −0.374409 | − | 0.927264i | \(-0.622154\pi\) | ||||
−0.374409 | + | 0.927264i | \(0.622154\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.65685 | − | 3.75736i | −0.223747 | − | 0.316427i | ||||
\(142\) | − | 22.4853i | − | 1.88692i | ||||||
\(143\) | 6.00000 | − | 4.00000i | 0.501745 | − | 0.334497i | ||||
\(144\) | 11.3137 | + | 4.00000i | 0.942809 | + | 0.333333i | ||||
\(145\) | 18.0208 | + | 18.0208i | 1.49655 | + | 1.49655i | ||||
\(146\) | 0.242641i | 0.0200811i | ||||||||
\(147\) | −0.292893 | + | 1.70711i | −0.0241574 | + | 0.140800i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.24264 | + | 4.24264i | −0.347571 | + | 0.347571i | −0.859204 | − | 0.511633i | \(-0.829041\pi\) |
0.511633 | + | 0.859204i | \(0.329041\pi\) | |||||||
\(150\) | −13.6569 | − | 19.3137i | −1.11508 | − | 1.57696i | ||||
\(151\) | 10.8995 | − | 10.8995i | 0.886988 | − | 0.886988i | −0.107244 | − | 0.994233i | \(-0.534203\pi\) |
0.994233 | + | 0.107244i | \(0.0342027\pi\) | |||||||
\(152\) | 7.51472i | 0.609524i | ||||||||
\(153\) | −11.3137 | − | 4.00000i | −0.914659 | − | 0.323381i | ||||
\(154\) | 2.00000 | − | 2.00000i | 0.161165 | − | 0.161165i | ||||
\(155\) | −15.9706 | −1.28279 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.48528 | −0.677199 | −0.338600 | − | 0.940931i | \(-0.609953\pi\) | ||||
−0.338600 | + | 0.940931i | \(0.609953\pi\) | |||||||
\(158\) | −5.82843 | + | 5.82843i | −0.463685 | + | 0.463685i | ||||
\(159\) | −3.60660 | + | 21.0208i | −0.286022 | + | 1.66706i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.29289 | + | 1.29289i | −0.101894 | + | 0.101894i | ||||
\(162\) | −12.6569 | + | 1.34315i | −0.994416 | + | 0.105527i | ||||
\(163\) | −15.2426 | + | 15.2426i | −1.19390 | + | 1.19390i | −0.217932 | + | 0.975964i | \(0.569931\pi\) |
−0.975964 | + | 0.217932i | \(0.930069\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.0711 | + | 2.24264i | 1.01758 | + | 0.174589i | ||||
\(166\) | − | 1.41421i | − | 0.109764i | ||||||
\(167\) | 2.94975 | + | 2.94975i | 0.228258 | + | 0.228258i | 0.811965 | − | 0.583706i | \(-0.198398\pi\) |
−0.583706 | + | 0.811965i | \(0.698398\pi\) | |||||||
\(168\) | −4.82843 | − | 0.828427i | −0.372521 | − | 0.0639145i | ||||
\(169\) | −12.0000 | − | 5.00000i | −0.923077 | − | 0.384615i | ||||
\(170\) | 21.6569i | 1.66100i | ||||||||
\(171\) | −3.43503 | − | 7.19239i | −0.262683 | − | 0.550016i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.75736 | −0.741838 | −0.370919 | − | 0.928665i | \(-0.620957\pi\) | ||||
−0.370919 | + | 0.928665i | \(0.620957\pi\) | |||||||
\(174\) | −9.41421 | − | 13.3137i | −0.713690 | − | 1.00931i | ||||
\(175\) | 6.82843 | + | 6.82843i | 0.516181 | + | 0.516181i | ||||
\(176\) | 5.65685 | + | 5.65685i | 0.426401 | + | 0.426401i | ||||
\(177\) | 2.00000 | + | 2.82843i | 0.150329 | + | 0.212598i | ||||
\(178\) | 11.7574 | 0.881251 | ||||||||
\(179\) | −23.8284 | −1.78102 | −0.890510 | − | 0.454963i | \(-0.849652\pi\) | ||||
−0.890510 | + | 0.454963i | \(0.849652\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.00000i | − | 0.148659i | −0.997234 | − | 0.0743294i | \(-0.976318\pi\) | ||
0.997234 | − | 0.0743294i | \(-0.0236816\pi\) | |||||||
\(182\) | −5.00000 | − | 1.00000i | −0.370625 | − | 0.0741249i | ||||
\(183\) | 23.7279 | + | 4.07107i | 1.75402 | + | 0.300942i | ||||
\(184\) | −3.65685 | − | 3.65685i | −0.269587 | − | 0.269587i | ||||
\(185\) | − | 34.7279i | − | 2.55325i | ||||||
\(186\) | 10.0711 | + | 1.72792i | 0.738447 | + | 0.126697i | ||||
\(187\) | −5.65685 | − | 5.65685i | −0.413670 | − | 0.413670i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.00000 | − | 1.41421i | 0.363696 | − | 0.102869i | ||||
\(190\) | −10.1716 | + | 10.1716i | −0.737923 | + | 0.737923i | ||||
\(191\) | 9.31371i | 0.673916i | 0.941520 | + | 0.336958i | \(0.109398\pi\) | ||||
−0.941520 | + | 0.336958i | \(0.890602\pi\) | |||||||
\(192\) | 2.34315 | − | 13.6569i | 0.169102 | − | 0.985599i | ||||
\(193\) | −3.75736 | + | 3.75736i | −0.270461 | + | 0.270461i | −0.829286 | − | 0.558825i | \(-0.811252\pi\) |
0.558825 | + | 0.829286i | \(0.311252\pi\) | |||||||
\(194\) | 14.5858 | 1.04720 | ||||||||
\(195\) | −9.70711 | − | 21.8492i | −0.695140 | − | 1.56466i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.65685 | − | 8.65685i | 0.616775 | − | 0.616775i | −0.327928 | − | 0.944703i | \(-0.606350\pi\) |
0.944703 | + | 0.327928i | \(0.106350\pi\) | |||||||
\(198\) | −8.00000 | − | 2.82843i | −0.568535 | − | 0.201008i | ||||
\(199\) | 17.6569i | 1.25166i | 0.779959 | + | 0.625831i | \(0.215240\pi\) | ||||
−0.779959 | + | 0.625831i | \(0.784760\pi\) | |||||||
\(200\) | −19.3137 | + | 19.3137i | −1.36569 | + | 1.36569i | ||||
\(201\) | 12.8284 | + | 18.1421i | 0.904847 | + | 1.27965i | ||||
\(202\) | −7.65685 | + | 7.65685i | −0.538734 | + | 0.538734i | ||||
\(203\) | 4.70711 | + | 4.70711i | 0.330374 | + | 0.330374i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.31371i | − | 0.0917534i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.17157 | + | 1.82843i | 0.359449 | + | 0.127084i | ||||
\(208\) | 2.82843 | − | 14.1421i | 0.196116 | − | 0.980581i | ||||
\(209\) | − | 5.31371i | − | 0.367557i | ||||||
\(210\) | −5.41421 | − | 7.65685i | −0.373616 | − | 0.528373i | ||||
\(211\) | 17.4853 | 1.20374 | 0.601868 | − | 0.798595i | \(-0.294423\pi\) | ||||
0.601868 | + | 0.798595i | \(0.294423\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.4853 | − | 15.8995i | 1.54067 | − | 1.08942i | ||||
\(214\) | −0.828427 | − | 0.828427i | −0.0566301 | − | 0.0566301i | ||||
\(215\) | −18.0208 | − | 18.0208i | −1.22901 | − | 1.22901i | ||||
\(216\) | 4.00000 | + | 14.1421i | 0.272166 | + | 0.962250i | ||||
\(217\) | −4.17157 | −0.283185 | ||||||||
\(218\) | −8.34315 | −0.565069 | ||||||||
\(219\) | −0.242641 | + | 0.171573i | −0.0163961 | + | 0.0115938i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.82843 | + | 14.1421i | −0.190261 | + | 0.951303i | ||||
\(222\) | −3.75736 | + | 21.8995i | −0.252177 | + | 1.46980i | ||||
\(223\) | 11.7782 | + | 11.7782i | 0.788725 | + | 0.788725i | 0.981285 | − | 0.192560i | \(-0.0616791\pi\) |
−0.192560 | + | 0.981285i | \(0.561679\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.65685 | − | 27.3137i | 0.643790 | − | 1.82091i | ||||
\(226\) | 9.82843 | + | 9.82843i | 0.653777 | + | 0.653777i | ||||
\(227\) | −0.928932 | + | 0.928932i | −0.0616554 | + | 0.0616554i | −0.737262 | − | 0.675607i | \(-0.763882\pi\) |
0.675607 | + | 0.737262i | \(0.263882\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.48528 | − | 6.48528i | 0.428559 | − | 0.428559i | −0.459578 | − | 0.888137i | \(-0.651999\pi\) |
0.888137 | + | 0.459578i | \(0.151999\pi\) | |||||||
\(230\) | − | 9.89949i | − | 0.652753i | ||||||
\(231\) | 3.41421 | + | 0.585786i | 0.224639 | + | 0.0385419i | ||||
\(232\) | −13.3137 | + | 13.3137i | −0.874088 | + | 0.874088i | ||||
\(233\) | −16.3137 | −1.06875 | −0.534373 | − | 0.845249i | \(-0.679452\pi\) | ||||
−0.534373 | + | 0.845249i | \(0.679452\pi\) | |||||||
\(234\) | 3.75736 | + | 14.8284i | 0.245626 | + | 0.969365i | ||||
\(235\) | −10.1716 | −0.663520 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.94975 | − | 1.70711i | −0.646306 | − | 0.110889i | ||||
\(238\) | 5.65685i | 0.366679i | ||||||||
\(239\) | −10.0711 | + | 10.0711i | −0.651443 | + | 0.651443i | −0.953340 | − | 0.301897i | \(-0.902380\pi\) |
0.301897 | + | 0.953340i | \(0.402380\pi\) | |||||||
\(240\) | 21.6569 | − | 15.3137i | 1.39794 | − | 0.988496i | ||||
\(241\) | 6.70711 | − | 6.70711i | 0.432043 | − | 0.432043i | −0.457280 | − | 0.889323i | \(-0.651176\pi\) |
0.889323 | + | 0.457280i | \(0.151176\pi\) | |||||||
\(242\) | 7.00000 | + | 7.00000i | 0.449977 | + | 0.449977i | ||||
\(243\) | −10.2929 | − | 11.7071i | −0.660289 | − | 0.751011i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.70711 | + | 2.70711i | 0.172951 | + | 0.172951i | ||||
\(246\) | −0.142136 | + | 0.828427i | −0.00906224 | + | 0.0528186i | ||||
\(247\) | −7.97056 | + | 5.31371i | −0.507155 | + | 0.338103i | ||||
\(248\) | − | 11.7990i | − | 0.749237i | ||||||
\(249\) | 1.41421 | − | 1.00000i | 0.0896221 | − | 0.0633724i | ||||
\(250\) | −25.2132 | −1.59462 | ||||||||
\(251\) | −18.9706 | −1.19741 | −0.598706 | − | 0.800969i | \(-0.704318\pi\) | ||||
−0.598706 | + | 0.800969i | \(0.704318\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.58579 | + | 2.58579i | 0.162567 | + | 0.162567i | ||||
\(254\) | 2.00000 | + | 2.00000i | 0.125491 | + | 0.125491i | ||||
\(255\) | −21.6569 | + | 15.3137i | −1.35620 | + | 0.958982i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.1421 | 1.75546 | 0.877729 | − | 0.479157i | \(-0.159058\pi\) | ||||
0.877729 | + | 0.479157i | \(0.159058\pi\) | |||||||
\(258\) | 9.41421 | + | 13.3137i | 0.586103 | + | 0.828875i | ||||
\(259\) | − | 9.07107i | − | 0.563649i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.65685 | − | 18.8284i | 0.412049 | − | 1.16545i | ||||
\(262\) | 9.07107 | + | 9.07107i | 0.560412 | + | 0.560412i | ||||
\(263\) | 27.4853i | 1.69482i | 0.530943 | + | 0.847408i | \(0.321838\pi\) | ||||
−0.530943 | + | 0.847408i | \(0.678162\pi\) | |||||||
\(264\) | −1.65685 | + | 9.65685i | −0.101972 | + | 0.594338i | ||||
\(265\) | 33.3345 | + | 33.3345i | 2.04772 | + | 2.04772i | ||||
\(266\) | −2.65685 | + | 2.65685i | −0.162902 | + | 0.162902i | ||||
\(267\) | 8.31371 | + | 11.7574i | 0.508791 | + | 0.719539i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.6985i | 1.93269i | 0.257248 | + | 0.966345i | \(0.417184\pi\) | ||||
−0.257248 | + | 0.966345i | \(0.582816\pi\) | |||||||
\(270\) | −13.7279 | + | 24.5563i | −0.835455 | + | 1.49445i | ||||
\(271\) | −11.8995 | + | 11.8995i | −0.722843 | + | 0.722843i | −0.969183 | − | 0.246341i | \(-0.920772\pi\) |
0.246341 | + | 0.969183i | \(0.420772\pi\) | |||||||
\(272\) | −16.0000 | −0.970143 | ||||||||
\(273\) | −2.53553 | − | 5.70711i | −0.153457 | − | 0.345410i | ||||
\(274\) | −12.8284 | −0.774994 | ||||||||
\(275\) | 13.6569 | − | 13.6569i | 0.823539 | − | 0.823539i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.51472i | − | 0.151095i | −0.997142 | − | 0.0755474i | \(-0.975930\pi\) | ||
0.997142 | − | 0.0755474i | \(-0.0240704\pi\) | |||||||
\(278\) | 8.82843 | − | 8.82843i | 0.529494 | − | 0.529494i | ||||
\(279\) | 5.39340 | + | 11.2929i | 0.322894 | + | 0.676088i | ||||
\(280\) | −7.65685 | + | 7.65685i | −0.457585 | + | 0.457585i | ||||
\(281\) | −11.1421 | − | 11.1421i | −0.664684 | − | 0.664684i | 0.291796 | − | 0.956480i | \(-0.405747\pi\) |
−0.956480 | + | 0.291796i | \(0.905747\pi\) | |||||||
\(282\) | 6.41421 | + | 1.10051i | 0.381961 | + | 0.0655341i | ||||
\(283\) | 6.82843i | 0.405908i | 0.979188 | + | 0.202954i | \(0.0650542\pi\) | ||||
−0.979188 | + | 0.202954i | \(0.934946\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.3640 | − | 2.97918i | −1.02855 | − | 0.176472i | ||||
\(286\) | −2.00000 | + | 10.0000i | −0.118262 | + | 0.591312i | ||||
\(287\) | − | 0.343146i | − | 0.0202553i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −36.0416 | −2.11644 | ||||||||
\(291\) | 10.3137 | + | 14.5858i | 0.604600 | + | 0.855034i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.9497 | + | 12.9497i | 0.756532 | + | 0.756532i | 0.975690 | − | 0.219157i | \(-0.0703308\pi\) |
−0.219157 | + | 0.975690i | \(0.570331\pi\) | |||||||
\(294\) | −1.41421 | − | 2.00000i | −0.0824786 | − | 0.116642i | ||||
\(295\) | 7.65685 | 0.445799 | ||||||||
\(296\) | 25.6569 | 1.49127 | ||||||||
\(297\) | −2.82843 | − | 10.0000i | −0.164122 | − | 0.580259i | ||||
\(298\) | − | 8.48528i | − | 0.491539i | ||||||
\(299\) | 1.29289 | − | 6.46447i | 0.0747699 | − | 0.373850i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.70711 | − | 4.70711i | −0.271313 | − | 0.271313i | ||||
\(302\) | 21.7990i | 1.25439i | ||||||||
\(303\) | −13.0711 | − | 2.24264i | −0.750913 | − | 0.128836i | ||||
\(304\) | −7.51472 | − | 7.51472i | −0.430999 | − | 0.430999i | ||||
\(305\) | 37.6274 | − | 37.6274i | 2.15454 | − | 2.15454i | ||||
\(306\) | 15.3137 | − | 7.31371i | 0.875426 | − | 0.418097i | ||||
\(307\) | 4.36396 | − | 4.36396i | 0.249064 | − | 0.249064i | −0.571522 | − | 0.820587i | \(-0.693647\pi\) |
0.820587 | + | 0.571522i | \(0.193647\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.9706 | − | 15.9706i | 0.907067 | − | 0.907067i | ||||
\(311\) | 31.5563 | 1.78940 | 0.894698 | − | 0.446671i | \(-0.147391\pi\) | ||||
0.894698 | + | 0.446671i | \(0.147391\pi\) | |||||||
\(312\) | 16.1421 | − | 7.17157i | 0.913868 | − | 0.406010i | ||||
\(313\) | −12.1421 | −0.686314 | −0.343157 | − | 0.939278i | \(-0.611496\pi\) | ||||
−0.343157 | + | 0.939278i | \(0.611496\pi\) | |||||||
\(314\) | 8.48528 | − | 8.48528i | 0.478852 | − | 0.478852i | ||||
\(315\) | 3.82843 | − | 10.8284i | 0.215707 | − | 0.610113i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.2426 | + | 11.2426i | −0.631450 | + | 0.631450i | −0.948432 | − | 0.316982i | \(-0.897331\pi\) |
0.316982 | + | 0.948432i | \(0.397331\pi\) | |||||||
\(318\) | −17.4142 | − | 24.6274i | −0.976541 | − | 1.38104i | ||||
\(319\) | 9.41421 | − | 9.41421i | 0.527095 | − | 0.527095i | ||||
\(320\) | −21.6569 | − | 21.6569i | −1.21065 | − | 1.21065i | ||||
\(321\) | 0.242641 | − | 1.41421i | 0.0135429 | − | 0.0789337i | ||||
\(322\) | − | 2.58579i | − | 0.144100i | ||||||
\(323\) | 7.51472 | + | 7.51472i | 0.418130 | + | 0.418130i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −34.1421 | − | 6.82843i | −1.89386 | − | 0.378773i | ||||
\(326\) | − | 30.4853i | − | 1.68842i | ||||||
\(327\) | −5.89949 | − | 8.34315i | −0.326243 | − | 0.461377i | ||||
\(328\) | 0.970563 | 0.0535904 | ||||||||
\(329\) | −2.65685 | −0.146477 | ||||||||
\(330\) | −15.3137 | + | 10.8284i | −0.842992 | + | 0.596085i | ||||
\(331\) | −8.65685 | − | 8.65685i | −0.475824 | − | 0.475824i | 0.427969 | − | 0.903793i | \(-0.359229\pi\) |
−0.903793 | + | 0.427969i | \(0.859229\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.5563 | + | 11.7279i | −1.34568 | + | 0.642686i | ||||
\(334\) | −5.89949 | −0.322806 | ||||||||
\(335\) | 49.1127 | 2.68331 | ||||||||
\(336\) | 5.65685 | − | 4.00000i | 0.308607 | − | 0.218218i | ||||
\(337\) | 21.1421i | 1.15169i | 0.817560 | + | 0.575843i | \(0.195326\pi\) | ||||
−0.817560 | + | 0.575843i | \(0.804674\pi\) | |||||||
\(338\) | 17.0000 | − | 7.00000i | 0.924678 | − | 0.380750i | ||||
\(339\) | −2.87868 | + | 16.7782i | −0.156348 | + | 0.911265i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.34315i | 0.451807i | ||||||||
\(342\) | 10.6274 | + | 3.75736i | 0.574665 | + | 0.203175i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 13.3137 | − | 13.3137i | 0.717827 | − | 0.717827i | ||||
\(345\) | 9.89949 | − | 7.00000i | 0.532971 | − | 0.376867i | ||||
\(346\) | 9.75736 | − | 9.75736i | 0.524559 | − | 0.524559i | ||||
\(347\) | 6.00000i | 0.322097i | 0.986947 | + | 0.161048i | \(0.0514875\pi\) | ||||
−0.986947 | + | 0.161048i | \(0.948512\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0503 | − | 13.0503i | 0.698564 | − | 0.698564i | −0.265537 | − | 0.964101i | \(-0.585549\pi\) |
0.964101 | + | 0.265537i | \(0.0855492\pi\) | |||||||
\(350\) | −13.6569 | −0.729990 | ||||||||
\(351\) | −12.1716 | + | 14.2426i | −0.649670 | + | 0.760216i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.3137 | + | 17.3137i | −0.921516 | + | 0.921516i | −0.997137 | − | 0.0756209i | \(-0.975906\pi\) |
0.0756209 | + | 0.997137i | \(0.475906\pi\) | |||||||
\(354\) | −4.82843 | − | 0.828427i | −0.256628 | − | 0.0440304i | ||||
\(355\) | − | 60.8701i | − | 3.23065i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.65685 | + | 4.00000i | −0.299392 | + | 0.211702i | ||||
\(358\) | 23.8284 | − | 23.8284i | 1.25937 | − | 1.25937i | ||||
\(359\) | −16.8284 | − | 16.8284i | −0.888170 | − | 0.888170i | 0.106177 | − | 0.994347i | \(-0.466139\pi\) |
−0.994347 | + | 0.106177i | \(0.966139\pi\) | |||||||
\(360\) | 30.6274 | + | 10.8284i | 1.61421 | + | 0.570708i | ||||
\(361\) | − | 11.9411i | − | 0.628480i | ||||||
\(362\) | 2.00000 | + | 2.00000i | 0.105118 | + | 0.105118i | ||||
\(363\) | −2.05025 | + | 11.9497i | −0.107610 | + | 0.627199i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.656854i | 0.0343813i | ||||||||
\(366\) | −27.7990 | + | 19.6569i | −1.45308 | + | 1.02748i | ||||
\(367\) | 25.6985 | 1.34145 | 0.670725 | − | 0.741706i | \(-0.265983\pi\) | ||||
0.670725 | + | 0.741706i | \(0.265983\pi\) | |||||||
\(368\) | 7.31371 | 0.381253 | ||||||||
\(369\) | −0.928932 | + | 0.443651i | −0.0483583 | + | 0.0230955i | ||||
\(370\) | 34.7279 | + | 34.7279i | 1.80542 | + | 1.80542i | ||||
\(371\) | 8.70711 | + | 8.70711i | 0.452050 | + | 0.452050i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.6274 | −1.17160 | −0.585802 | − | 0.810454i | \(-0.699220\pi\) | ||||
−0.585802 | + | 0.810454i | \(0.699220\pi\) | |||||||
\(374\) | 11.3137 | 0.585018 | ||||||||
\(375\) | −17.8284 | − | 25.2132i | −0.920656 | − | 1.30200i | ||||
\(376\) | − | 7.51472i | − | 0.387542i | ||||||
\(377\) | −23.5355 | − | 4.70711i | −1.21214 | − | 0.242428i | ||||
\(378\) | −3.58579 | + | 6.41421i | −0.184433 | + | 0.329912i | ||||
\(379\) | −4.58579 | − | 4.58579i | −0.235556 | − | 0.235556i | 0.579451 | − | 0.815007i | \(-0.303267\pi\) |
−0.815007 | + | 0.579451i | \(0.803267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.585786 | + | 3.41421i | −0.0300107 | + | 0.174915i | ||||
\(382\) | −9.31371 | − | 9.31371i | −0.476531 | − | 0.476531i | ||||
\(383\) | 6.10051 | − | 6.10051i | 0.311721 | − | 0.311721i | −0.533855 | − | 0.845576i | \(-0.679257\pi\) |
0.845576 | + | 0.533855i | \(0.179257\pi\) | |||||||
\(384\) | 11.3137 | + | 16.0000i | 0.577350 | + | 0.816497i | ||||
\(385\) | 5.41421 | − | 5.41421i | 0.275934 | − | 0.275934i | ||||
\(386\) | − | 7.51472i | − | 0.382489i | ||||||
\(387\) | −6.65685 | + | 18.8284i | −0.338387 | + | 0.957103i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.82843 | −0.346215 | −0.173107 | − | 0.984903i | \(-0.555381\pi\) | ||||
−0.173107 | + | 0.984903i | \(0.555381\pi\) | |||||||
\(390\) | 31.5563 | + | 12.1421i | 1.59792 | + | 0.614841i | ||||
\(391\) | −7.31371 | −0.369870 | ||||||||
\(392\) | −2.00000 | + | 2.00000i | −0.101015 | + | 0.101015i | ||||
\(393\) | −2.65685 | + | 15.4853i | −0.134021 | + | 0.781129i | ||||
\(394\) | 17.3137i | 0.872252i | ||||||||
\(395\) | −15.7782 | + | 15.7782i | −0.793886 | + | 0.793886i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.39340 | + | 3.39340i | −0.170310 | + | 0.170310i | −0.787115 | − | 0.616806i | \(-0.788426\pi\) |
0.616806 | + | 0.787115i | \(0.288426\pi\) | |||||||
\(398\) | −17.6569 | − | 17.6569i | −0.885058 | − | 0.885058i | ||||
\(399\) | −4.53553 | − | 0.778175i | −0.227061 | − | 0.0389575i | ||||
\(400\) | − | 38.6274i | − | 1.93137i | ||||||
\(401\) | −3.92893 | − | 3.92893i | −0.196202 | − | 0.196202i | 0.602168 | − | 0.798369i | \(-0.294304\pi\) |
−0.798369 | + | 0.602168i | \(0.794304\pi\) | |||||||
\(402\) | −30.9706 | − | 5.31371i | −1.54467 | − | 0.265024i | ||||
\(403\) | 12.5147 | − | 8.34315i | 0.623403 | − | 0.415602i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −34.2635 | + | 3.63604i | −1.70256 | + | 0.180676i | ||||
\(406\) | −9.41421 | −0.467220 | ||||||||
\(407\) | −18.1421 | −0.899272 | ||||||||
\(408\) | −11.3137 | − | 16.0000i | −0.560112 | − | 0.792118i | ||||
\(409\) | −2.36396 | − | 2.36396i | −0.116890 | − | 0.116890i | 0.646242 | − | 0.763132i | \(-0.276340\pi\) |
−0.763132 | + | 0.646242i | \(0.776340\pi\) | |||||||
\(410\) | 1.31371 | + | 1.31371i | 0.0648794 | + | 0.0648794i | ||||
\(411\) | −9.07107 | − | 12.8284i | −0.447443 | − | 0.632780i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.00000 | 0.0984136 | ||||||||
\(414\) | −7.00000 | + | 3.34315i | −0.344031 | + | 0.164307i | ||||
\(415\) | − | 3.82843i | − | 0.187930i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.0711 | + | 2.58579i | 0.738033 | + | 0.126627i | ||||
\(418\) | 5.31371 | + | 5.31371i | 0.259902 | + | 0.259902i | ||||
\(419\) | − | 16.6274i | − | 0.812302i | −0.913806 | − | 0.406151i | \(-0.866871\pi\) | ||
0.913806 | − | 0.406151i | \(-0.133129\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(422\) | −17.4853 | + | 17.4853i | −0.851170 | + | 0.851170i | ||||
\(423\) | 3.43503 | + | 7.19239i | 0.167017 | + | 0.349706i | ||||
\(424\) | −24.6274 | + | 24.6274i | −1.19601 | + | 1.19601i | ||||
\(425\) | 38.6274i | 1.87370i | ||||||||
\(426\) | −6.58579 | + | 38.3848i | −0.319082 | + | 1.85975i | ||||
\(427\) | 9.82843 | − | 9.82843i | 0.475631 | − | 0.475631i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.4142 | + | 5.07107i | −0.551083 | + | 0.244833i | ||||
\(430\) | 36.0416 | 1.73808 | ||||||||
\(431\) | 15.4853 | − | 15.4853i | 0.745900 | − | 0.745900i | −0.227807 | − | 0.973706i | \(-0.573155\pi\) |
0.973706 | + | 0.227807i | \(0.0731554\pi\) | |||||||
\(432\) | −18.1421 | − | 10.1421i | −0.872864 | − | 0.487964i | ||||
\(433\) | 11.4142i | 0.548532i | 0.961654 | + | 0.274266i | \(0.0884349\pi\) | ||||
−0.961654 | + | 0.274266i | \(0.911565\pi\) | |||||||
\(434\) | 4.17157 | − | 4.17157i | 0.200242 | − | 0.200242i | ||||
\(435\) | −25.4853 | − | 36.0416i | −1.22193 | − | 1.72806i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.43503 | − | 3.43503i | −0.164320 | − | 0.164320i | ||||
\(438\) | 0.0710678 | − | 0.414214i | 0.00339575 | − | 0.0197919i | ||||
\(439\) | − | 21.2132i | − | 1.01245i | −0.862401 | − | 0.506225i | \(-0.831040\pi\) | ||
0.862401 | − | 0.506225i | \(-0.168960\pi\) | |||||||
\(440\) | 15.3137 | + | 15.3137i | 0.730052 | + | 0.730052i | ||||
\(441\) | 1.00000 | − | 2.82843i | 0.0476190 | − | 0.134687i | ||||
\(442\) | −11.3137 | − | 16.9706i | −0.538138 | − | 0.807207i | ||||
\(443\) | 7.34315i | 0.348883i | 0.984668 | + | 0.174442i | \(0.0558121\pi\) | ||||
−0.984668 | + | 0.174442i | \(0.944188\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.8284 | 1.50881 | ||||||||
\(446\) | −23.5563 | −1.11543 | ||||||||
\(447\) | 8.48528 | − | 6.00000i | 0.401340 | − | 0.283790i | ||||
\(448\) | −5.65685 | − | 5.65685i | −0.267261 | − | 0.267261i | ||||
\(449\) | −18.4142 | − | 18.4142i | −0.869020 | − | 0.869020i | 0.123344 | − | 0.992364i | \(-0.460638\pi\) |
−0.992364 | + | 0.123344i | \(0.960638\pi\) | |||||||
\(450\) | 17.6569 | + | 36.9706i | 0.832352 | + | 1.74281i | ||||
\(451\) | −0.686292 | −0.0323162 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.7990 | + | 15.4142i | −1.02421 | + | 0.724223i | ||||
\(454\) | − | 1.85786i | − | 0.0871939i | ||||||
\(455\) | −13.5355 | − | 2.70711i | −0.634556 | − | 0.126911i | ||||
\(456\) | 2.20101 | − | 12.8284i | 0.103072 | − | 0.600746i | ||||
\(457\) | −5.17157 | − | 5.17157i | −0.241916 | − | 0.241916i | 0.575726 | − | 0.817642i | \(-0.304719\pi\) |
−0.817642 | + | 0.575726i | \(0.804719\pi\) | |||||||
\(458\) | 12.9706i | 0.606075i | ||||||||
\(459\) | 18.1421 | + | 10.1421i | 0.846802 | + | 0.473394i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.51472 | + | 1.51472i | −0.0705475 | + | 0.0705475i | −0.741500 | − | 0.670953i | \(-0.765885\pi\) |
0.670953 | + | 0.741500i | \(0.265885\pi\) | |||||||
\(462\) | −4.00000 | + | 2.82843i | −0.186097 | + | 0.131590i | ||||
\(463\) | 3.34315 | − | 3.34315i | 0.155369 | − | 0.155369i | −0.625142 | − | 0.780511i | \(-0.714959\pi\) |
0.780511 | + | 0.625142i | \(0.214959\pi\) | |||||||
\(464\) | − | 26.6274i | − | 1.23615i | ||||||
\(465\) | 27.2635 | + | 4.67767i | 1.26431 | + | 0.216922i | ||||
\(466\) | 16.3137 | − | 16.3137i | 0.755718 | − | 0.755718i | ||||
\(467\) | 33.2132 | 1.53692 | 0.768462 | − | 0.639896i | \(-0.221022\pi\) | ||||
0.768462 | + | 0.639896i | \(0.221022\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.8284 | 0.592362 | ||||||||
\(470\) | 10.1716 | − | 10.1716i | 0.469180 | − | 0.469180i | ||||
\(471\) | 14.4853 | + | 2.48528i | 0.667447 | + | 0.114516i | ||||
\(472\) | 5.65685i | 0.260378i | ||||||||
\(473\) | −9.41421 | + | 9.41421i | −0.432866 | + | 0.432866i | ||||
\(474\) | 11.6569 | − | 8.24264i | 0.535417 | − | 0.378597i | ||||
\(475\) | −18.1421 | + | 18.1421i | −0.832418 | + | 0.832418i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.3137 | − | 34.8284i | 0.563806 | − | 1.59468i | ||||
\(478\) | − | 20.1421i | − | 0.921280i | ||||||
\(479\) | 8.02082 | + | 8.02082i | 0.366480 | + | 0.366480i | 0.866192 | − | 0.499712i | \(-0.166561\pi\) |
−0.499712 | + | 0.866192i | \(0.666561\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.1421 | + | 27.2132i | 0.827210 | + | 1.24082i | ||||
\(482\) | 13.4142i | 0.611001i | ||||||||
\(483\) | 2.58579 | − | 1.82843i | 0.117657 | − | 0.0831963i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 39.4853 | 1.79293 | ||||||||
\(486\) | 22.0000 | + | 1.41421i | 0.997940 | + | 0.0641500i | ||||
\(487\) | −20.1716 | − | 20.1716i | −0.914061 | − | 0.914061i | 0.0825276 | − | 0.996589i | \(-0.473701\pi\) |
−0.996589 | + | 0.0825276i | \(0.973701\pi\) | |||||||
\(488\) | 27.7990 | + | 27.7990i | 1.25840 | + | 1.25840i | ||||
\(489\) | 30.4853 | − | 21.5563i | 1.37859 | − | 0.974812i | ||||
\(490\) | −5.41421 | −0.244589 | ||||||||
\(491\) | 28.9706 | 1.30742 | 0.653712 | − | 0.756744i | \(-0.273211\pi\) | ||||
0.653712 | + | 0.756744i | \(0.273211\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.6274i | 1.19924i | ||||||||
\(494\) | 2.65685 | − | 13.2843i | 0.119538 | − | 0.597688i | ||||
\(495\) | −21.6569 | − | 7.65685i | −0.973403 | − | 0.344150i | ||||
\(496\) | 11.7990 | + | 11.7990i | 0.529790 | + | 0.529790i | ||||
\(497\) | − | 15.8995i | − | 0.713190i | ||||||
\(498\) | −0.414214 | + | 2.41421i | −0.0185614 | + | 0.108183i | ||||
\(499\) | −14.0000 | − | 14.0000i | −0.626726 | − | 0.626726i | 0.320517 | − | 0.947243i | \(-0.396143\pi\) |
−0.947243 | + | 0.320517i | \(0.896143\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.17157 | − | 5.89949i | −0.186372 | − | 0.263570i | ||||
\(502\) | 18.9706 | − | 18.9706i | 0.846698 | − | 0.846698i | ||||
\(503\) | − | 3.07107i | − | 0.136932i | −0.997653 | − | 0.0684661i | \(-0.978190\pi\) | ||
0.997653 | − | 0.0684661i | \(-0.0218105\pi\) | |||||||
\(504\) | 8.00000 | + | 2.82843i | 0.356348 | + | 0.125988i | ||||
\(505\) | −20.7279 | + | 20.7279i | −0.922380 | + | 0.922380i | ||||
\(506\) | −5.17157 | −0.229904 | ||||||||
\(507\) | 19.0208 | + | 12.0503i | 0.844744 | + | 0.535171i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.1213 | + | 26.1213i | −1.15781 | + | 1.15781i | −0.172861 | + | 0.984946i | \(0.555301\pi\) |
−0.984946 | + | 0.172861i | \(0.944699\pi\) | |||||||
\(510\) | 6.34315 | − | 36.9706i | 0.280879 | − | 1.63708i | ||||
\(511\) | 0.171573i | 0.00758994i | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | 3.75736 | + | 13.2843i | 0.165891 | + | 0.586515i | ||||
\(514\) | −28.1421 | + | 28.1421i | −1.24130 | + | 1.24130i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.31371i | 0.233697i | ||||||||
\(518\) | 9.07107 | + | 9.07107i | 0.398560 | + | 0.398560i | ||||
\(519\) | 16.6569 | + | 2.85786i | 0.731155 | + | 0.125446i | ||||
\(520\) | 7.65685 | − | 38.2843i | 0.335775 | − | 1.67888i | ||||
\(521\) | 16.2843i | 0.713427i | 0.934214 | + | 0.356713i | \(0.116103\pi\) | ||||
−0.934214 | + | 0.356713i | \(0.883897\pi\) | |||||||
\(522\) | 12.1716 | + | 25.4853i | 0.532735 | + | 1.11546i | ||||
\(523\) | −4.72792 | −0.206738 | −0.103369 | − | 0.994643i | \(-0.532962\pi\) | ||||
−0.103369 | + | 0.994643i | \(0.532962\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.65685 | − | 13.6569i | −0.421460 | − | 0.596034i | ||||
\(526\) | −27.4853 | − | 27.4853i | −1.19842 | − | 1.19842i | ||||
\(527\) | −11.7990 | − | 11.7990i | −0.513972 | − | 0.513972i | ||||
\(528\) | −8.00000 | − | 11.3137i | −0.348155 | − | 0.492366i | ||||
\(529\) | −19.6569 | −0.854646 | ||||||||
\(530\) | −66.6690 | −2.89592 | ||||||||
\(531\) | −2.58579 | − | 5.41421i | −0.112214 | − | 0.234957i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.686292 | + | 1.02944i | 0.0297266 | + | 0.0445899i | ||||
\(534\) | −20.0711 | − | 3.44365i | −0.868560 | − | 0.149021i | ||||
\(535\) | −2.24264 | − | 2.24264i | −0.0969578 | − | 0.0969578i | ||||
\(536\) | 36.2843i | 1.56724i | ||||||||
\(537\) | 40.6777 | + | 6.97918i | 1.75537 | + | 0.301174i | ||||
\(538\) | −31.6985 | − | 31.6985i | −1.36662 | − | 1.36662i | ||||
\(539\) | 1.41421 | − | 1.41421i | 0.0609145 | − | 0.0609145i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0711 | − | 14.0711i | 0.604962 | − | 0.604962i | −0.336663 | − | 0.941625i | \(-0.609298\pi\) |
0.941625 | + | 0.336663i | \(0.109298\pi\) | |||||||
\(542\) | − | 23.7990i | − | 1.02225i | ||||||
\(543\) | −0.585786 | + | 3.41421i | −0.0251385 | + | 0.146518i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22.5858 | −0.967469 | ||||||||
\(546\) | 8.24264 | + | 3.17157i | 0.352752 | + | 0.135731i | ||||
\(547\) | −14.6569 | −0.626682 | −0.313341 | − | 0.949641i | \(-0.601448\pi\) | ||||
−0.313341 | + | 0.949641i | \(0.601448\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −39.3137 | − | 13.8995i | −1.67787 | − | 0.593216i | ||||
\(550\) | 27.3137i | 1.16466i | ||||||||
\(551\) | −12.5061 | + | 12.5061i | −0.532778 | + | 0.532778i | ||||
\(552\) | 5.17157 | + | 7.31371i | 0.220117 | + | 0.311292i | ||||
\(553\) | −4.12132 | + | 4.12132i | −0.175256 | + | 0.175256i | ||||
\(554\) | 2.51472 | + | 2.51472i | 0.106840 | + | 0.106840i | ||||
\(555\) | −10.1716 | + | 59.2843i | −0.431759 | + | 2.51648i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.7990 | − | 27.7990i | −1.17788 | − | 1.17788i | −0.980283 | − | 0.197598i | \(-0.936686\pi\) |
−0.197598 | − | 0.980283i | \(-0.563314\pi\) | |||||||
\(558\) | −16.6863 | − | 5.89949i | −0.706387 | − | 0.249746i | ||||
\(559\) | 23.5355 | + | 4.70711i | 0.995447 | + | 0.199089i | ||||
\(560\) | − | 15.3137i | − | 0.647122i | ||||||
\(561\) | 8.00000 | + | 11.3137i | 0.337760 | + | 0.477665i | ||||
\(562\) | 22.2843 | 0.940005 | ||||||||
\(563\) | 1.07107 | 0.0451401 | 0.0225701 | − | 0.999745i | \(-0.492815\pi\) | ||||
0.0225701 | + | 0.999745i | \(0.492815\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.6066 | + | 26.6066i | 1.11935 | + | 1.11935i | ||||
\(566\) | −6.82843 | − | 6.82843i | −0.287020 | − | 0.287020i | ||||
\(567\) | −8.94975 | + | 0.949747i | −0.375854 | + | 0.0398856i | ||||
\(568\) | 44.9706 | 1.88692 | ||||||||
\(569\) | −7.48528 | −0.313799 | −0.156900 | − | 0.987615i | \(-0.550150\pi\) | ||||
−0.156900 | + | 0.987615i | \(0.550150\pi\) | |||||||
\(570\) | 20.3431 | − | 14.3848i | 0.852081 | − | 0.602512i | ||||
\(571\) | 36.4558i | 1.52563i | 0.646617 | + | 0.762815i | \(0.276183\pi\) | ||||
−0.646617 | + | 0.762815i | \(0.723817\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.72792 | − | 15.8995i | 0.113961 | − | 0.664211i | ||||
\(574\) | 0.343146 | + | 0.343146i | 0.0143226 | + | 0.0143226i | ||||
\(575\) | − | 17.6569i | − | 0.736342i | ||||||
\(576\) | −8.00000 | + | 22.6274i | −0.333333 | + | 0.942809i | ||||
\(577\) | −14.8284 | − | 14.8284i | −0.617315 | − | 0.617315i | 0.327526 | − | 0.944842i | \(-0.393785\pi\) |
−0.944842 | + | 0.327526i | \(0.893785\pi\) | |||||||
\(578\) | 1.00000 | − | 1.00000i | 0.0415945 | − | 0.0415945i | ||||
\(579\) | 7.51472 | − | 5.31371i | 0.312301 | − | 0.220830i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.00000i | − | 0.0414870i | ||||||
\(582\) | −24.8995 | − | 4.27208i | −1.03212 | − | 0.177083i | ||||
\(583\) | 17.4142 | − | 17.4142i | 0.721223 | − | 0.721223i | ||||
\(584\) | −0.485281 | −0.0200811 | ||||||||
\(585\) | 10.1716 | + | 40.1421i | 0.420543 | + | 1.65967i | ||||
\(586\) | −25.8995 | −1.06990 | ||||||||
\(587\) | 11.1924 | − | 11.1924i | 0.461959 | − | 0.461959i | −0.437338 | − | 0.899297i | \(-0.644079\pi\) |
0.899297 | + | 0.437338i | \(0.144079\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 11.0833i | − | 0.456678i | ||||||
\(590\) | −7.65685 | + | 7.65685i | −0.315228 | + | 0.315228i | ||||
\(591\) | −17.3137 | + | 12.2426i | −0.712191 | + | 0.503595i | ||||
\(592\) | −25.6569 | + | 25.6569i | −1.05449 | + | 1.05449i | ||||
\(593\) | 21.0919 | + | 21.0919i | 0.866140 | + | 0.866140i | 0.992043 | − | 0.125903i | \(-0.0401827\pi\) |
−0.125903 | + | 0.992043i | \(0.540183\pi\) | |||||||
\(594\) | 12.8284 | + | 7.17157i | 0.526357 | + | 0.294253i | ||||
\(595\) | 15.3137i | 0.627801i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.17157 | − | 30.1421i | 0.211658 | − | 1.23364i | ||||
\(598\) | 5.17157 | + | 7.75736i | 0.211481 | + | 0.317222i | ||||
\(599\) | 16.4558i | 0.672368i | 0.941796 | + | 0.336184i | \(0.109136\pi\) | ||||
−0.941796 | + | 0.336184i | \(0.890864\pi\) | |||||||
\(600\) | 38.6274 | − | 27.3137i | 1.57696 | − | 1.11508i | ||||
\(601\) | 2.48528 | 0.101377 | 0.0506884 | − | 0.998715i | \(-0.483858\pi\) | ||||
0.0506884 | + | 0.998715i | \(0.483858\pi\) | |||||||
\(602\) | 9.41421 | 0.383695 | ||||||||
\(603\) | −16.5858 | − | 34.7279i | −0.675425 | − | 1.41423i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.9497 | + | 18.9497i | 0.770417 | + | 0.770417i | ||||
\(606\) | 15.3137 | − | 10.8284i | 0.622077 | − | 0.439875i | ||||
\(607\) | 8.82843 | 0.358335 | 0.179167 | − | 0.983819i | \(-0.442660\pi\) | ||||
0.179167 | + | 0.983819i | \(0.442660\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.65685 | − | 9.41421i | −0.269749 | − | 0.381483i | ||||
\(610\) | 75.2548i | 3.04698i | ||||||||
\(611\) | 7.97056 | − | 5.31371i | 0.322454 | − | 0.214970i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.7574 | + | 10.7574i | 0.434486 | + | 0.434486i | 0.890151 | − | 0.455665i | \(-0.150599\pi\) |
−0.455665 | + | 0.890151i | \(0.650599\pi\) | |||||||
\(614\) | 8.72792i | 0.352230i | ||||||||
\(615\) | −0.384776 | + | 2.24264i | −0.0155157 | + | 0.0904320i | ||||
\(616\) | 4.00000 | + | 4.00000i | 0.161165 | + | 0.161165i | ||||
\(617\) | −9.68629 | + | 9.68629i | −0.389955 | + | 0.389955i | −0.874672 | − | 0.484716i | \(-0.838923\pi\) |
0.484716 | + | 0.874672i | \(0.338923\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.8995 | + | 15.8995i | −0.639055 | + | 0.639055i | −0.950322 | − | 0.311268i | \(-0.899246\pi\) |
0.311268 | + | 0.950322i | \(0.399246\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.29289 | − | 4.63604i | −0.332782 | − | 0.186038i | ||||
\(622\) | −31.5563 | + | 31.5563i | −1.26529 | + | 1.26529i | ||||
\(623\) | 8.31371 | 0.333082 | ||||||||
\(624\) | −8.97056 | + | 23.3137i | −0.359110 | + | 0.933295i | ||||
\(625\) | −19.9706 | −0.798823 | ||||||||
\(626\) | 12.1421 | − | 12.1421i | 0.485297 | − | 0.485297i | ||||
\(627\) | −1.55635 | + | 9.07107i | −0.0621546 | + | 0.362264i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.6569 | − | 25.6569i | 1.02301 | − | 1.02301i | ||||
\(630\) | 7.00000 | + | 14.6569i | 0.278887 | + | 0.583943i | ||||
\(631\) | 20.6569 | − | 20.6569i | 0.822336 | − | 0.822336i | −0.164106 | − | 0.986443i | \(-0.552474\pi\) |
0.986443 | + | 0.164106i | \(0.0524740\pi\) | |||||||
\(632\) | −11.6569 | − | 11.6569i | −0.463685 | − | 0.463685i | ||||
\(633\) | −29.8492 | − | 5.12132i | −1.18640 | − | 0.203554i | ||||
\(634\) | − | 22.4853i | − | 0.893005i | ||||||
\(635\) | 5.41421 | + | 5.41421i | 0.214857 | + | 0.214857i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.53553 | − | 0.707107i | −0.140083 | − | 0.0280166i | ||||
\(638\) | 18.8284i | 0.745425i | ||||||||
\(639\) | −43.0416 | + | 20.5563i | −1.70270 | + | 0.813197i | ||||
\(640\) | 43.3137 | 1.71212 | ||||||||
\(641\) | 31.0000 | 1.22443 | 0.612213 | − | 0.790693i | \(-0.290279\pi\) | ||||
0.612213 | + | 0.790693i | \(0.290279\pi\) | |||||||
\(642\) | 1.17157 | + | 1.65685i | 0.0462383 | + | 0.0653908i | ||||
\(643\) | 4.92893 | + | 4.92893i | 0.194378 | + | 0.194378i | 0.797585 | − | 0.603207i | \(-0.206111\pi\) |
−0.603207 | + | 0.797585i | \(0.706111\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.4853 | + | 36.0416i | 1.00348 | + | 1.41914i | ||||
\(646\) | −15.0294 | −0.591325 | ||||||||
\(647\) | −33.8995 | −1.33273 | −0.666363 | − | 0.745627i | \(-0.732150\pi\) | ||||
−0.666363 | + | 0.745627i | \(0.732150\pi\) | |||||||
\(648\) | −2.68629 | − | 25.3137i | −0.105527 | − | 0.994416i | ||||
\(649\) | − | 4.00000i | − | 0.157014i | ||||||
\(650\) | 40.9706 | − | 27.3137i | 1.60700 | − | 1.07133i | ||||
\(651\) | 7.12132 | + | 1.22183i | 0.279107 | + | 0.0478871i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.5147i | 0.450606i | 0.974289 | + | 0.225303i | \(0.0723372\pi\) | ||||
−0.974289 | + | 0.225303i | \(0.927663\pi\) | |||||||
\(654\) | 14.2426 | + | 2.44365i | 0.556931 | + | 0.0955543i | ||||
\(655\) | 24.5563 | + | 24.5563i | 0.959496 | + | 0.959496i | ||||
\(656\) | −0.970563 | + | 0.970563i | −0.0378941 | + | 0.0378941i | ||||
\(657\) | 0.464466 | − | 0.221825i | 0.0181205 | − | 0.00865423i | ||||
\(658\) | 2.65685 | − | 2.65685i | 0.103575 | − | 0.103575i | ||||
\(659\) | 27.9706i | 1.08958i | 0.838573 | + | 0.544789i | \(0.183390\pi\) | ||||
−0.838573 | + | 0.544789i | \(0.816610\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.849242 | − | 0.849242i | 0.0330317 | − | 0.0330317i | −0.690398 | − | 0.723430i | \(-0.742565\pi\) |
0.723430 | + | 0.690398i | \(0.242565\pi\) | |||||||
\(662\) | 17.3137 | 0.672916 | ||||||||
\(663\) | 8.97056 | − | 23.3137i | 0.348388 | − | 0.905429i | ||||
\(664\) | 2.82843 | 0.109764 | ||||||||
\(665\) | −7.19239 | + | 7.19239i | −0.278909 | + | 0.278909i | ||||
\(666\) | 12.8284 | − | 36.2843i | 0.497091 | − | 1.40599i | ||||
\(667\) | − | 12.1716i | − | 0.471285i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.6569 | − | 23.5563i | −0.643991 | − | 0.910741i | ||||
\(670\) | −49.1127 | + | 49.1127i | −1.89739 | + | 1.89739i | ||||
\(671\) | −19.6569 | − | 19.6569i | −0.758844 | − | 0.758844i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 27.0000i | − | 1.04077i | −0.853931 | − | 0.520387i | \(-0.825788\pi\) | ||
0.853931 | − | 0.520387i | \(-0.174212\pi\) | |||||||
\(674\) | −21.1421 | − | 21.1421i | −0.814365 | − | 0.814365i | ||||
\(675\) | −24.4853 | + | 43.7990i | −0.942439 | + | 1.68582i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.41421i | − | 0.208085i | −0.994573 | − | 0.104043i | \(-0.966822\pi\) | ||
0.994573 | − | 0.104043i | \(-0.0331778\pi\) | |||||||
\(678\) | −13.8995 | − | 19.6569i | −0.533807 | − | 0.754917i | ||||
\(679\) | 10.3137 | 0.395804 | ||||||||
\(680\) | −43.3137 | −1.66100 | ||||||||
\(681\) | 1.85786 | − | 1.31371i | 0.0711935 | − | 0.0503414i | ||||
\(682\) | −8.34315 | − | 8.34315i | −0.319476 | − | 0.319476i | ||||
\(683\) | −11.7990 | − | 11.7990i | −0.451476 | − | 0.451476i | 0.444368 | − | 0.895844i | \(-0.353428\pi\) |
−0.895844 | + | 0.444368i | \(0.853428\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34.7279 | −1.32689 | ||||||||
\(686\) | −1.41421 | −0.0539949 | ||||||||
\(687\) | −12.9706 | + | 9.17157i | −0.494858 | + | 0.349917i | ||||
\(688\) | 26.6274i | 1.01516i | ||||||||
\(689\) | −43.5355 | − | 8.70711i | −1.65857 | − | 0.331714i | ||||
\(690\) | −2.89949 | + | 16.8995i | −0.110382 | + | 0.643353i | ||||
\(691\) | −26.6066 | − | 26.6066i | −1.01216 | − | 1.01216i | −0.999925 | − | 0.0122377i | \(-0.996105\pi\) |
−0.0122377 | − | 0.999925i | \(-0.503895\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.65685 | − | 2.00000i | −0.214886 | − | 0.0759737i | ||||
\(694\) | −6.00000 | − | 6.00000i | −0.227757 | − | 0.227757i | ||||
\(695\) | 23.8995 | − | 23.8995i | 0.906560 | − | 0.906560i | ||||
\(696\) | 26.6274 | − | 18.8284i | 1.00931 | − | 0.713690i | ||||
\(697\) | 0.970563 | − | 0.970563i | 0.0367627 | − | 0.0367627i | ||||
\(698\) | 26.1005i | 0.987919i | ||||||||
\(699\) | 27.8492 | + | 4.77817i | 1.05336 | + | 0.180727i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.48528 | −0.282715 | −0.141358 | − | 0.989959i | \(-0.545147\pi\) | ||||
−0.141358 | + | 0.989959i | \(0.545147\pi\) | |||||||
\(702\) | −2.07107 | − | 26.4142i | −0.0781674 | − | 0.996940i | ||||
\(703\) | 24.1005 | 0.908968 | ||||||||
\(704\) | −11.3137 | + | 11.3137i | −0.426401 | + | 0.426401i | ||||
\(705\) | 17.3640 | + | 2.97918i | 0.653965 | + | 0.112203i | ||||
\(706\) | − | 34.6274i | − | 1.30322i | ||||||
\(707\) | −5.41421 | + | 5.41421i | −0.203622 | + | 0.203622i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.6985 | + | 31.6985i | −1.19046 | + | 1.19046i | −0.213524 | + | 0.976938i | \(0.568494\pi\) |
−0.976938 | + | 0.213524i | \(0.931506\pi\) | |||||||
\(710\) | 60.8701 | + | 60.8701i | 2.28441 | + | 2.28441i | ||||
\(711\) | 16.4853 | + | 5.82843i | 0.618246 | + | 0.218583i | ||||
\(712\) | 23.5147i | 0.881251i | ||||||||
\(713\) | 5.39340 | + | 5.39340i | 0.201984 | + | 0.201984i | ||||
\(714\) | 1.65685 | − | 9.65685i | 0.0620062 | − | 0.361399i | ||||
\(715\) | −5.41421 | + | 27.0711i | −0.202480 | + | 1.01240i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.1421 | − | 14.2426i | 0.752222 | − | 0.531901i | ||||
\(718\) | 33.6569 | 1.25606 | ||||||||
\(719\) | 6.38478 | 0.238112 | 0.119056 | − | 0.992888i | \(-0.462013\pi\) | ||||
0.119056 | + | 0.992888i | \(0.462013\pi\) | |||||||
\(720\) | −41.4558 | + | 19.7990i | −1.54497 | + | 0.737865i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 11.9411 | + | 11.9411i | 0.444403 | + | 0.444403i | ||||
\(723\) | −13.4142 | + | 9.48528i | −0.498880 | + | 0.352761i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −64.2843 | −2.38746 | ||||||||
\(726\) | −9.89949 | − | 14.0000i | −0.367405 | − | 0.519589i | ||||
\(727\) | − | 7.45584i | − | 0.276522i | −0.990396 | − | 0.138261i | \(-0.955849\pi\) | ||
0.990396 | − | 0.138261i | \(-0.0441513\pi\) | |||||||
\(728\) | 2.00000 | − | 10.0000i | 0.0741249 | − | 0.370625i | ||||
\(729\) | 14.1421 | + | 23.0000i | 0.523783 | + | 0.851852i | ||||
\(730\) | −0.656854 | − | 0.656854i | −0.0243113 | − | 0.0243113i | ||||
\(731\) | − | 26.6274i | − | 0.984851i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.8787 | + | 19.8787i | 0.734236 | + | 0.734236i | 0.971456 | − | 0.237220i | \(-0.0762363\pi\) |
−0.237220 | + | 0.971456i | \(0.576236\pi\) | |||||||
\(734\) | −25.6985 | + | 25.6985i | −0.948548 | + | 0.948548i | ||||
\(735\) | −3.82843 | − | 5.41421i | −0.141214 | − | 0.199706i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 25.6569i | − | 0.945082i | ||||||
\(738\) | 0.485281 | − | 1.37258i | 0.0178635 | − | 0.0505255i | ||||
\(739\) | 16.0416 | − | 16.0416i | 0.590101 | − | 0.590101i | −0.347558 | − | 0.937659i | \(-0.612989\pi\) |
0.937659 | + | 0.347558i | \(0.112989\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.1630 | − | 6.73654i | 0.557025 | − | 0.247473i | ||||
\(742\) | −17.4142 | −0.639296 | ||||||||
\(743\) | −12.2132 | + | 12.2132i | −0.448059 | + | 0.448059i | −0.894709 | − | 0.446650i | \(-0.852617\pi\) |
0.446650 | + | 0.894709i | \(0.352617\pi\) | |||||||
\(744\) | −3.45584 | + | 20.1421i | −0.126697 | + | 0.738447i | ||||
\(745\) | − | 22.9706i | − | 0.841576i | ||||||
\(746\) | 22.6274 | − | 22.6274i | 0.828449 | − | 0.828449i | ||||
\(747\) | −2.70711 | + | 1.29289i | −0.0990479 | + | 0.0473045i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.585786 | − | 0.585786i | −0.0214042 | − | 0.0214042i | ||||
\(750\) | 43.0416 | + | 7.38478i | 1.57166 | + | 0.269654i | ||||
\(751\) | 49.6274i | 1.81093i | 0.424421 | + | 0.905465i | \(0.360478\pi\) | ||||
−0.424421 | + | 0.905465i | \(0.639522\pi\) | |||||||
\(752\) | 7.51472 | + | 7.51472i | 0.274034 | + | 0.274034i | ||||
\(753\) | 32.3848 | + | 5.55635i | 1.18017 | + | 0.202485i | ||||
\(754\) | 28.2426 | − | 18.8284i | 1.02854 | − | 0.685691i | ||||
\(755\) | 59.0122i | 2.14767i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.68629 | −0.279363 | −0.139682 | − | 0.990196i | \(-0.544608\pi\) | ||||
−0.139682 | + | 0.990196i | \(0.544608\pi\) | |||||||
\(758\) | 9.17157 | 0.333127 | ||||||||
\(759\) | −3.65685 | − | 5.17157i | −0.132735 | − | 0.187716i | ||||
\(760\) | −20.3431 | − | 20.3431i | −0.737923 | − | 0.737923i | ||||
\(761\) | −36.8492 | − | 36.8492i | −1.33578 | − | 1.33578i | −0.900099 | − | 0.435685i | \(-0.856506\pi\) |
−0.435685 | − | 0.900099i | \(-0.643494\pi\) | |||||||
\(762\) | −2.82843 | − | 4.00000i | −0.102463 | − | 0.144905i | ||||
\(763\) | −5.89949 | −0.213576 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 41.4558 | − | 19.7990i | 1.49884 | − | 0.715834i | ||||
\(766\) | 12.2010i | 0.440840i | ||||||||
\(767\) | −6.00000 | + | 4.00000i | −0.216647 | + | 0.144432i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.36396 | − | 6.36396i | −0.229490 | − | 0.229490i | 0.582989 | − | 0.812480i | \(-0.301883\pi\) |
−0.812480 | + | 0.582989i | \(0.801883\pi\) | |||||||
\(770\) | 10.8284i | 0.390229i | ||||||||
\(771\) | −48.0416 | − | 8.24264i | −1.73018 | − | 0.296851i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.1421 | + | 22.1421i | −0.796397 | + | 0.796397i | −0.982525 | − | 0.186128i | \(-0.940406\pi\) |
0.186128 | + | 0.982525i | \(0.440406\pi\) | |||||||
\(774\) | −12.1716 | − | 25.4853i | −0.437498 | − | 0.916050i | ||||
\(775\) | 28.4853 | − | 28.4853i | 1.02322 | − | 1.02322i | ||||
\(776\) | 29.1716i | 1.04720i | ||||||||
\(777\) | −2.65685 | + | 15.4853i | −0.0953141 | + | 0.555531i | ||||
\(778\) | 6.82843 | − | 6.82843i | 0.244811 | − | 0.244811i | ||||
\(779\) | 0.911688 | 0.0326646 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.7990 | −1.13786 | ||||||||
\(782\) | 7.31371 | − | 7.31371i | 0.261538 | − | 0.261538i | ||||
\(783\) | −16.8787 | + | 30.1924i | −0.603195 | + | 1.07899i | ||||
\(784\) | − | 4.00000i | − | 0.142857i | ||||||
\(785\) | 22.9706 | − | 22.9706i | 0.819855 | − | 0.819855i | ||||
\(786\) | −12.8284 | − | 18.1421i | −0.457575 | − | 0.647109i | ||||
\(787\) | 33.5355 | − | 33.5355i | 1.19541 | − | 1.19541i | 0.219887 | − | 0.975525i | \(-0.429431\pi\) |
0.975525 | − | 0.219887i | \(-0.0705690\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.05025 | − | 46.9203i | 0.286597 | − | 1.67041i | ||||
\(790\) | − | 31.5563i | − | 1.12272i | ||||||
\(791\) | 6.94975 | + | 6.94975i | 0.247105 | + | 0.247105i | ||||
\(792\) | 5.65685 | − | 16.0000i | 0.201008 | − | 0.568535i | ||||
\(793\) | −9.82843 | + | 49.1421i | −0.349018 | + | 1.74509i | ||||
\(794\) | − | 6.78680i | − | 0.240854i | ||||||
\(795\) | −47.1421 | − | 66.6690i | −1.67196 | − | 2.36451i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.7990 | 0.630473 | 0.315236 | − | 0.949013i | \(-0.397916\pi\) | ||||
0.315236 | + | 0.949013i | \(0.397916\pi\) | |||||||
\(798\) | 5.31371 | − | 3.75736i | 0.188103 | − | 0.133009i | ||||
\(799\) | −7.51472 | − | 7.51472i | −0.265852 | − | 0.265852i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.7487 | − | 22.5061i | −0.379788 | − | 0.795214i | ||||
\(802\) | 7.85786 | 0.277471 | ||||||||
\(803\) | 0.343146 | 0.0121094 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 7.00000i | − | 0.246718i | ||||||
\(806\) | −4.17157 | + | 20.8579i | −0.146937 | + | 0.734687i | ||||
\(807\) | 9.28427 | − | 54.1127i | 0.326822 | − | 1.90486i | ||||
\(808\) | −15.3137 | − | 15.3137i | −0.538734 | − | 0.538734i | ||||
\(809\) | − | 3.97056i | − | 0.139598i | −0.997561 | − | 0.0697988i | \(-0.977764\pi\) | ||
0.997561 | − | 0.0697988i | \(-0.0222357\pi\) | |||||||
\(810\) | 30.6274 | − | 37.8995i | 1.07614 | − | 1.33165i | ||||
\(811\) | −11.7574 | − | 11.7574i | −0.412857 | − | 0.412857i | 0.469876 | − | 0.882733i | \(-0.344299\pi\) |
−0.882733 | + | 0.469876i | \(0.844299\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.7990 | − | 16.8284i | 0.834667 | − | 0.590199i | ||||
\(814\) | 18.1421 | − | 18.1421i | 0.635882 | − | 0.635882i | ||||
\(815\) | − | 82.5269i | − | 2.89079i | ||||||
\(816\) | 27.3137 | + | 4.68629i | 0.956171 | + | 0.164053i | ||||
\(817\) | 12.5061 | − | 12.5061i | 0.437533 | − | 0.437533i | ||||
\(818\) | 4.72792 | 0.165308 | ||||||||
\(819\) | 2.65685 | + | 10.4853i | 0.0928380 | + | 0.366385i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.2426 | − | 30.2426i | 1.05548 | − | 1.05548i | 0.0571074 | − | 0.998368i | \(-0.481812\pi\) |
0.998368 | − | 0.0571074i | \(-0.0181877\pi\) | |||||||
\(822\) | 21.8995 | + | 3.75736i | 0.763833 | + | 0.131053i | ||||
\(823\) | 11.3137i | 0.394371i | 0.980366 | + | 0.197186i | \(0.0631801\pi\) | ||||
−0.980366 | + | 0.197186i | \(0.936820\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.3137 | + | 19.3137i | −0.950941 | + | 0.672417i | ||||
\(826\) | −2.00000 | + | 2.00000i | −0.0695889 | + | 0.0695889i | ||||
\(827\) | 27.8701 | + | 27.8701i | 0.969137 | + | 0.969137i | 0.999538 | − | 0.0304009i | \(-0.00967841\pi\) |
−0.0304009 | + | 0.999538i | \(0.509678\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.89949i | − | 0.204898i | −0.994738 | − | 0.102449i | \(-0.967332\pi\) | ||
0.994738 | − | 0.102449i | \(-0.0326678\pi\) | |||||||
\(830\) | 3.82843 | + | 3.82843i | 0.132887 | + | 0.132887i | ||||
\(831\) | −0.736544 | + | 4.29289i | −0.0255504 | + | 0.148919i | ||||
\(832\) | 28.2843 | + | 5.65685i | 0.980581 | + | 0.196116i | ||||
\(833\) | 4.00000i | 0.138592i | ||||||||
\(834\) | −17.6569 | + | 12.4853i | −0.611407 | + | 0.432330i | ||||
\(835\) | −15.9706 | −0.552684 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.89949 | − | 20.8579i | −0.203916 | − | 0.720953i | ||||
\(838\) | 16.6274 | + | 16.6274i | 0.574385 | + | 0.574385i | ||||
\(839\) | −37.2132 | − | 37.2132i | −1.28474 | − | 1.28474i | −0.937937 | − | 0.346805i | \(-0.887266\pi\) |
−0.346805 | − | 0.937937i | \(-0.612734\pi\) | |||||||
\(840\) | 15.3137 | − | 10.8284i | 0.528373 | − | 0.373616i | ||||
\(841\) | −15.3137 | −0.528059 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.7574 | + | 22.2843i | 0.542712 | + | 0.767511i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 46.0208 | − | 18.9497i | 1.58316 | − | 0.651891i | ||||
\(846\) | −10.6274 | − | 3.75736i | −0.365378 | − | 0.129181i | ||||
\(847\) | 4.94975 | + | 4.94975i | 0.170075 | + | 0.170075i | ||||
\(848\) | − | 49.2548i | − | 1.69142i | ||||||
\(849\) | 2.00000 | − | 11.6569i | 0.0686398 | − | 0.400062i | ||||
\(850\) | −38.6274 | − | 38.6274i | −1.32491 | − | 1.32491i | ||||
\(851\) | −11.7279 | + | 11.7279i | −0.402028 | + | 0.402028i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.02082 | − | 6.02082i | 0.206149 | − | 0.206149i | −0.596480 | − | 0.802628i | \(-0.703434\pi\) |
0.802628 | + | 0.596480i | \(0.203434\pi\) | |||||||
\(854\) | 19.6569i | 0.672644i | ||||||||
\(855\) | 28.7696 | + | 10.1716i | 0.983898 | + | 0.347860i | ||||
\(856\) | 1.65685 | − | 1.65685i | 0.0566301 | − | 0.0566301i | ||||
\(857\) | −1.21320 | −0.0414422 | −0.0207211 | − | 0.999785i | \(-0.506596\pi\) | ||||
−0.0207211 | + | 0.999785i | \(0.506596\pi\) | |||||||
\(858\) | 6.34315 | − | 16.4853i | 0.216551 | − | 0.562798i | ||||
\(859\) | −23.6569 | −0.807161 | −0.403581 | − | 0.914944i | \(-0.632235\pi\) | ||||
−0.403581 | + | 0.914944i | \(0.632235\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.100505 | + | 0.585786i | −0.00342520 | + | 0.0199635i | ||||
\(862\) | 30.9706i | 1.05486i | ||||||||
\(863\) | 13.7990 | − | 13.7990i | 0.469723 | − | 0.469723i | −0.432102 | − | 0.901825i | \(-0.642228\pi\) |
0.901825 | + | 0.432102i | \(0.142228\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.4142 | − | 26.4142i | 0.898110 | − | 0.898110i | ||||
\(866\) | −11.4142 | − | 11.4142i | −0.387871 | − | 0.387871i | ||||
\(867\) | 1.70711 | + | 0.292893i | 0.0579764 | + | 0.00994718i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.24264 | + | 8.24264i | 0.279612 | + | 0.279612i | ||||
\(870\) | 61.5269 | + | 10.5563i | 2.08596 | + | 0.357894i | ||||
\(871\) | −38.4853 | + | 25.6569i | −1.30402 | + | 0.869349i | ||||
\(872\) | − | 16.6863i | − | 0.565069i | ||||||
\(873\) | −13.3345 | − | 27.9203i | −0.451305 | − | 0.944959i | ||||
\(874\) | 6.87006 | 0.232383 | ||||||||
\(875\) | −17.8284 | −0.602711 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.4853 | + | 26.4853i | 0.894344 | + | 0.894344i | 0.994929 | − | 0.100584i | \(-0.0320712\pi\) |
−0.100584 | + | 0.994929i | \(0.532071\pi\) | |||||||
\(878\) | 21.2132 | + | 21.2132i | 0.715911 | + | 0.715911i | ||||
\(879\) | −18.3137 | − | 25.8995i | −0.617706 | − | 0.873568i | ||||
\(880\) | −30.6274 | −1.03245 | ||||||||
\(881\) | −10.2843 | −0.346486 | −0.173243 | − | 0.984879i | \(-0.555425\pi\) | ||||
−0.173243 | + | 0.984879i | \(0.555425\pi\) | |||||||
\(882\) | 1.82843 | + | 3.82843i | 0.0615663 | + | 0.128910i | ||||
\(883\) | 8.68629i | 0.292317i | 0.989261 | + | 0.146158i | \(0.0466909\pi\) | ||||
−0.989261 | + | 0.146158i | \(0.953309\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.0711 | − | 2.24264i | −0.439379 | − | 0.0753855i | ||||
\(886\) | −7.34315 | − | 7.34315i | −0.246698 | − | 0.246698i | ||||
\(887\) | 24.8701i | 0.835055i | 0.908664 | + | 0.417527i | \(0.137103\pi\) | ||||
−0.908664 | + | 0.417527i | \(0.862897\pi\) | |||||||
\(888\) | −43.7990 | − | 7.51472i | −1.46980 | − | 0.252177i | ||||
\(889\) | 1.41421 | + | 1.41421i | 0.0474312 | + | 0.0474312i | ||||
\(890\) | −31.8284 | + | 31.8284i | −1.06689 | + | 1.06689i | ||||
\(891\) | 1.89949 | + | 17.8995i | 0.0636355 | + | 0.599656i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 7.05887i | − | 0.236216i | ||||||
\(894\) | −2.48528 | + | 14.4853i | −0.0831202 | + | 0.484460i | ||||
\(895\) | 64.5061 | − | 64.5061i | 2.15620 | − | 2.15620i | ||||
\(896\) | 11.3137 | 0.377964 | ||||||||
\(897\) | −4.10051 | + | 10.6569i | −0.136912 | + | 0.355822i | ||||
\(898\) | 36.8284 | 1.22898 | ||||||||
\(899\) | 19.6360 | − | 19.6360i | 0.654899 | − | 0.654899i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.2548i | 1.64092i | ||||||||
\(902\) | 0.686292 | − | 0.686292i | 0.0228510 | − | 0.0228510i | ||||
\(903\) | 6.65685 | + | 9.41421i | 0.221526 | + | 0.313285i | ||||
\(904\) | −19.6569 | + | 19.6569i | −0.653777 | + | 0.653777i | ||||
\(905\) | 5.41421 | + | 5.41421i | 0.179975 | + | 0.179975i | ||||
\(906\) | 6.38478 | − | 37.2132i | 0.212120 | − | 1.23633i | ||||
\(907\) | − | 0.372583i | − | 0.0123714i | −0.999981 | − | 0.00618571i | \(-0.998031\pi\) | ||
0.999981 | − | 0.00618571i | \(-0.00196898\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.6569 | + | 7.65685i | 0.718313 | + | 0.253962i | ||||
\(910\) | 16.2426 | − | 10.8284i | 0.538438 | − | 0.358959i | ||||
\(911\) | − | 18.1716i | − | 0.602051i | −0.953616 | − | 0.301026i | \(-0.902671\pi\) | ||
0.953616 | − | 0.301026i | \(-0.0973289\pi\) | |||||||
\(912\) | 10.6274 | + | 15.0294i | 0.351909 | + | 0.497674i | ||||
\(913\) | −2.00000 | −0.0661903 | ||||||||
\(914\) | 10.3431 | 0.342121 | ||||||||
\(915\) | −75.2548 | + | 53.2132i | −2.48785 | + | 1.75917i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.41421 | + | 6.41421i | 0.211816 | + | 0.211816i | ||||
\(918\) | −28.2843 | + | 8.00000i | −0.933520 | + | 0.264039i | ||||
\(919\) | 47.1716 | 1.55605 | 0.778023 | − | 0.628235i | \(-0.216223\pi\) | ||||
0.778023 | + | 0.628235i | \(0.216223\pi\) | |||||||
\(920\) | 19.7990 | 0.652753 | ||||||||
\(921\) | −8.72792 | + | 6.17157i | −0.287595 | + | 0.203360i | ||||
\(922\) | − | 3.02944i | − | 0.0997692i | ||||||
\(923\) | 31.7990 | + | 47.6985i | 1.04668 | + | 1.57001i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 61.9411 | + | 61.9411i | 2.03661 | + | 2.03661i | ||||
\(926\) | 6.68629i | 0.219725i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.9203 | − | 35.9203i | 1.17851 | − | 1.17851i | 0.198382 | − | 0.980125i | \(-0.436431\pi\) |
0.980125 | − | 0.198382i | \(-0.0635688\pi\) | |||||||
\(930\) | −31.9411 | + | 22.5858i | −1.04739 | + | 0.740617i | ||||
\(931\) | −1.87868 | + | 1.87868i | −0.0615712 | + | 0.0615712i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −53.8701 | − | 9.24264i | −1.76363 | − | 0.302590i | ||||
\(934\) | −33.2132 | + | 33.2132i | −1.08677 | + | 1.08677i | ||||
\(935\) | 30.6274 | 1.00162 | ||||||||
\(936\) | −29.6569 | + | 7.51472i | −0.969365 | + | 0.245626i | ||||
\(937\) | −32.8701 | −1.07382 | −0.536909 | − | 0.843640i | \(-0.680408\pi\) | ||||
−0.536909 | + | 0.843640i | \(0.680408\pi\) | |||||||
\(938\) | −12.8284 | + | 12.8284i | −0.418863 | + | 0.418863i | ||||
\(939\) | 20.7279 | + | 3.55635i | 0.676430 | + | 0.116057i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.6066 | + | 26.6066i | −0.867350 | + | 0.867350i | −0.992178 | − | 0.124828i | \(-0.960162\pi\) |
0.124828 | + | 0.992178i | \(0.460162\pi\) | |||||||
\(942\) | −16.9706 | + | 12.0000i | −0.552931 | + | 0.390981i | ||||
\(943\) | −0.443651 | + | 0.443651i | −0.0144473 | + | 0.0144473i | ||||
\(944\) | −5.65685 | − | 5.65685i | −0.184115 | − | 0.184115i | ||||
\(945\) | −9.70711 | + | 17.3640i | −0.315772 | + | 0.564850i | ||||
\(946\) | − | 18.8284i | − | 0.612165i | ||||||
\(947\) | 16.5858 | + | 16.5858i | 0.538966 | + | 0.538966i | 0.923225 | − | 0.384259i | \(-0.125543\pi\) |
−0.384259 | + | 0.923225i | \(0.625543\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.343146 | − | 0.514719i | −0.0111390 | − | 0.0167085i | ||||
\(950\) | − | 36.2843i | − | 1.17722i | ||||||
\(951\) | 22.4853 | − | 15.8995i | 0.729135 | − | 0.515576i | ||||
\(952\) | −11.3137 | −0.366679 | ||||||||
\(953\) | −3.97056 | −0.128619 | −0.0643096 | − | 0.997930i | \(-0.520485\pi\) | ||||
−0.0643096 | + | 0.997930i | \(0.520485\pi\) | |||||||
\(954\) | 22.5147 | + | 47.1421i | 0.728941 | + | 1.52628i | ||||
\(955\) | −25.2132 | − | 25.2132i | −0.815880 | − | 0.815880i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18.8284 | + | 13.3137i | −0.608637 | + | 0.430371i | ||||
\(958\) | −16.0416 | −0.518282 | ||||||||
\(959\) | −9.07107 | −0.292920 | ||||||||
\(960\) | 30.6274 | + | 43.3137i | 0.988496 | + | 1.39794i | ||||
\(961\) | − | 13.5980i | − | 0.438645i | ||||||
\(962\) | −45.3553 | − | 9.07107i | −1.46231 | − | 0.292463i | ||||
\(963\) | −0.828427 | + | 2.34315i | −0.0266957 | + | 0.0755068i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 20.3431i | − | 0.654869i | ||||||
\(966\) | −0.757359 | + | 4.41421i | −0.0243676 | + | 0.142025i | ||||
\(967\) | −16.3848 | − | 16.3848i | −0.526899 | − | 0.526899i | 0.392747 | − | 0.919646i | \(-0.371525\pi\) |
−0.919646 | + | 0.392747i | \(0.871525\pi\) | |||||||
\(968\) | −14.0000 | + | 14.0000i | −0.449977 | + | 0.449977i | ||||
\(969\) | −10.6274 | − | 15.0294i | −0.341402 | − | 0.482815i | ||||
\(970\) | −39.4853 | + | 39.4853i | −1.26780 | + | 1.26780i | ||||
\(971\) | − | 8.52691i | − | 0.273642i | −0.990596 | − | 0.136821i | \(-0.956312\pi\) | ||
0.990596 | − | 0.136821i | \(-0.0436885\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.24264 | − | 6.24264i | 0.200130 | − | 0.200130i | ||||
\(974\) | 40.3431 | 1.29268 | ||||||||
\(975\) | 56.2843 | + | 21.6569i | 1.80254 | + | 0.693574i | ||||
\(976\) | −55.5980 | −1.77965 | ||||||||
\(977\) | −23.5563 | + | 23.5563i | −0.753634 | + | 0.753634i | −0.975156 | − | 0.221521i | \(-0.928898\pi\) |
0.221521 | + | 0.975156i | \(0.428898\pi\) | |||||||
\(978\) | −8.92893 | + | 52.0416i | −0.285516 | + | 1.66411i | ||||
\(979\) | − | 16.6274i | − | 0.531415i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.62742 | + | 15.9706i | 0.243525 | + | 0.509901i | ||||
\(982\) | −28.9706 | + | 28.9706i | −0.924488 | + | 0.924488i | ||||
\(983\) | −11.1924 | − | 11.1924i | −0.356982 | − | 0.356982i | 0.505717 | − | 0.862699i | \(-0.331228\pi\) |
−0.862699 | + | 0.505717i | \(0.831228\pi\) | |||||||
\(984\) | −1.65685 | − | 0.284271i | −0.0528186 | − | 0.00906224i | ||||
\(985\) | 46.8701i | 1.49340i | ||||||||
\(986\) | −26.6274 | − | 26.6274i | −0.847990 | − | 0.847990i | ||||
\(987\) | 4.53553 | + | 0.778175i | 0.144368 | + | 0.0247696i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.1716i | 0.387034i | ||||||||
\(990\) | 29.3137 | − | 14.0000i | 0.931651 | − | 0.444949i | ||||
\(991\) | −42.9706 | −1.36500 | −0.682502 | − | 0.730883i | \(-0.739108\pi\) | ||||
−0.682502 | + | 0.730883i | \(0.739108\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.2426 | + | 17.3137i | 0.388508 | + | 0.549434i | ||||
\(994\) | 15.8995 | + | 15.8995i | 0.504301 | + | 0.504301i | ||||
\(995\) | −47.7990 | − | 47.7990i | −1.51533 | − | 1.51533i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.3137 | 1.62512 | 0.812561 | − | 0.582877i | \(-0.198073\pi\) | ||||
0.812561 | + | 0.582877i | \(0.198073\pi\) | |||||||
\(998\) | 28.0000 | 0.886325 | ||||||||
\(999\) | 45.3553 | − | 12.8284i | 1.43498 | − | 0.405873i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 273.2.n.a.8.1 | ✓ | 4 | |
3.2 | odd | 2 | 273.2.n.b.8.1 | yes | 4 | ||
13.5 | odd | 4 | 273.2.n.b.239.1 | yes | 4 | ||
39.5 | even | 4 | inner | 273.2.n.a.239.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.n.a.8.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
273.2.n.a.239.1 | yes | 4 | 39.5 | even | 4 | inner | |
273.2.n.b.8.1 | yes | 4 | 3.2 | odd | 2 | ||
273.2.n.b.239.1 | yes | 4 | 13.5 | odd | 4 |