Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(51,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.51");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.bb (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.855355656503296000000000000.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 12x^{14} + 95x^{12} + 552x^{10} + 1969x^{8} + 27048x^{6} + 228095x^{4} + 1411788x^{2} + 5764801 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 259.3 | ||
Root | \(2.47822 - 0.926503i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 572.259 |
Dual form | 572.2.bb.a.519.3 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{9}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34500 | − | 0.437016i | 0.951057 | − | 0.309017i | ||||
\(3\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(4\) | 1.61803 | − | 1.17557i | 0.809017 | − | 0.587785i | ||||
\(5\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.10731 | − | 4.27685i | −1.17445 | − | 1.61650i | −0.622496 | − | 0.782623i | \(-0.713881\pi\) |
−0.551957 | − | 0.833873i | \(-0.686119\pi\) | |||||||
\(8\) | 1.66251 | − | 2.28825i | 0.587785 | − | 0.809017i | ||||
\(9\) | 0.927051 | + | 2.85317i | 0.309017 | + | 0.951057i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.30948 | + | 0.217620i | 0.997845 | + | 0.0656149i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.42908 | − | 1.11418i | 0.951057 | − | 0.309017i | ||||
\(14\) | −6.04837 | − | 4.39440i | −1.61650 | − | 1.17445i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.23607 | − | 3.80423i | 0.309017 | − | 0.951057i | ||||
\(17\) | −5.73732 | − | 1.86417i | −1.39151 | − | 0.452128i | −0.485071 | − | 0.874475i | \(-0.661206\pi\) |
−0.906434 | + | 0.422347i | \(0.861206\pi\) | |||||||
\(18\) | 2.49376 | + | 3.43237i | 0.587785 | + | 0.809017i | ||||
\(19\) | 1.60082 | − | 2.20335i | 0.367254 | − | 0.505482i | −0.584898 | − | 0.811107i | \(-0.698865\pi\) |
0.952152 | + | 0.305625i | \(0.0988653\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.54634 | − | 1.15360i | 0.969283 | − | 0.245948i | ||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04508 | − | 2.93893i | −0.809017 | − | 0.587785i | ||||
\(26\) | 4.12519 | − | 2.99713i | 0.809017 | − | 0.587785i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.0555 | − | 3.26722i | −1.90030 | − | 0.617446i | ||||
\(29\) | 6.19302 | + | 8.52395i | 1.15001 | + | 1.58286i | 0.742781 | + | 0.669534i | \(0.233506\pi\) |
0.407233 | + | 0.913324i | \(0.366494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.523346 | − | 1.61069i | −0.0939957 | − | 0.289289i | 0.892995 | − | 0.450067i | \(-0.148600\pi\) |
−0.986991 | + | 0.160778i | \(0.948600\pi\) | |||||||
\(32\) | − | 5.65685i | − | 1.00000i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.53136 | −1.46312 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.85410 | + | 3.52671i | 0.809017 | + | 0.587785i | ||||
\(37\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(38\) | 1.19021 | − | 3.66308i | 0.193077 | − | 0.594230i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 5.61067 | − | 3.53841i | 0.845841 | − | 0.533435i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.51837 | + | 6.18896i | 1.24253 | + | 0.902753i | 0.997764 | − | 0.0668289i | \(-0.0212882\pi\) |
0.244768 | + | 0.969582i | \(0.421288\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.47291 | + | 19.9216i | −0.924702 | + | 2.84594i | ||||
\(50\) | −6.72499 | − | 2.18508i | −0.951057 | − | 0.309017i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.23858 | − | 5.83390i | 0.587785 | − | 0.809017i | ||||
\(53\) | 3.11959 | + | 9.60110i | 0.428508 | + | 1.31881i | 0.899595 | + | 0.436726i | \(0.143862\pi\) |
−0.471087 | + | 0.882087i | \(0.656138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −14.9524 | −1.99810 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.0547 | + | 8.75825i | 1.58286 | + | 1.15001i | ||||
\(59\) | −10.6846 | + | 7.76278i | −1.39101 | + | 1.01063i | −0.395257 | + | 0.918571i | \(0.629344\pi\) |
−0.995754 | + | 0.0920575i | \(0.970656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.74264 | + | 2.51574i | 0.991344 | + | 0.322107i | 0.759401 | − | 0.650622i | \(-0.225492\pi\) |
0.231942 | + | 0.972730i | \(0.425492\pi\) | |||||||
\(62\) | −1.40780 | − | 1.93767i | −0.178791 | − | 0.246084i | ||||
\(63\) | 9.32193 | − | 12.8305i | 1.17445 | − | 1.61650i | ||||
\(64\) | −2.47214 | − | 7.60845i | −0.309017 | − | 0.951057i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.09902 | 0.622944 | 0.311472 | − | 0.950255i | \(-0.399178\pi\) | ||||
0.311472 | + | 0.950255i | \(0.399178\pi\) | |||||||
\(68\) | −11.4746 | + | 3.72834i | −1.39151 | + | 0.452128i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.617396 | + | 1.90015i | −0.0732714 | + | 0.225506i | −0.980985 | − | 0.194085i | \(-0.937826\pi\) |
0.907713 | + | 0.419591i | \(0.137826\pi\) | |||||||
\(72\) | 8.06998 | + | 2.62210i | 0.951057 | + | 0.309017i | ||||
\(73\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 5.44697i | − | 0.624810i | ||||||
\(77\) | −9.35285 | − | 14.8303i | −1.06586 | − | 1.69007i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.28115 | + | 5.29007i | −0.809017 | + | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.1682 | − | 5.25336i | −1.77469 | − | 0.576632i | −0.776145 | − | 0.630555i | \(-0.782827\pi\) |
−0.998545 | + | 0.0539231i | \(0.982827\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.00000 | − | 7.21110i | 0.639602 | − | 0.768706i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.4204 | − | 11.2036i | −1.61650 | − | 1.17445i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.1619 | + | 4.60147i | 1.46068 | + | 0.474605i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(98\) | 29.6232i | 2.99240i | ||||||||
\(99\) | 2.44715 | + | 9.64425i | 0.245948 | + | 0.969283i | ||||
\(100\) | −10.0000 | −1.00000 | ||||||||
\(101\) | 8.42454 | − | 2.73730i | 0.838273 | − | 0.272371i | 0.141747 | − | 0.989903i | \(-0.454728\pi\) |
0.696526 | + | 0.717532i | \(0.254728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(104\) | 3.15137 | − | 9.69891i | 0.309017 | − | 0.951057i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.39167 | + | 11.5501i | 0.815071 | + | 1.12185i | ||||
\(107\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −20.1109 | + | 6.53444i | −1.90030 | + | 0.617446i | ||||
\(113\) | −0.548373 | − | 0.398416i | −0.0515866 | − | 0.0374798i | 0.561693 | − | 0.827346i | \(-0.310150\pi\) |
−0.613280 | + | 0.789866i | \(0.710150\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 20.0410 | + | 6.51172i | 1.86076 | + | 0.604598i | ||||
\(117\) | 6.35787 | + | 8.75086i | 0.587785 | + | 0.809017i | ||||
\(118\) | −10.9782 | + | 15.1102i | −1.01063 | + | 1.39101i | ||||
\(119\) | 9.85488 | + | 30.3302i | 0.903395 | + | 2.78036i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9053 | + | 1.44042i | 0.991389 | + | 0.130947i | ||||
\(122\) | 11.5133 | 1.04236 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.74028 | − | 1.99093i | −0.246084 | − | 0.178791i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.93082 | − | 21.3309i | 0.617446 | − | 1.90030i | ||||
\(127\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(128\) | −6.65003 | − | 9.15298i | −0.587785 | − | 0.809017i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.3976 | −1.24843 | ||||||||
\(134\) | 6.85817 | − | 2.22835i | 0.592455 | − | 0.192500i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.8040 | + | 10.0292i | −1.18369 | + | 0.859998i | ||||
\(137\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.82551i | 0.237111i | ||||||||
\(143\) | 11.5909 | − | 2.94111i | 0.969283 | − | 0.245948i | ||||
\(144\) | 12.0000 | 1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.1941 | + | 18.1602i | −1.07372 | + | 1.47785i | −0.207476 | + | 0.978240i | \(0.566525\pi\) |
−0.866248 | + | 0.499614i | \(0.833475\pi\) | |||||||
\(152\) | −2.38041 | − | 7.32616i | −0.193077 | − | 0.594230i | ||||
\(153\) | − | 18.0977i | − | 1.46312i | ||||||
\(154\) | −19.0606 | − | 15.8594i | −1.53595 | − | 1.27799i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5484 | − | 8.39038i | −0.921660 | − | 0.669626i | 0.0222763 | − | 0.999752i | \(-0.492909\pi\) |
−0.943937 | + | 0.330126i | \(0.892909\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.48128 | + | 10.2971i | −0.587785 | + | 0.809017i | ||||
\(163\) | 2.01894 | + | 6.21365i | 0.158135 | + | 0.486691i | 0.998465 | − | 0.0553849i | \(-0.0176386\pi\) |
−0.840330 | + | 0.542076i | \(0.817639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −24.0420 | −1.86602 | ||||||||
\(167\) | 10.9878 | − | 3.57016i | 0.850263 | − | 0.276267i | 0.148707 | − | 0.988881i | \(-0.452489\pi\) |
0.701556 | + | 0.712614i | \(0.252489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5172 | − | 7.64121i | 0.809017 | − | 0.587785i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.77057 | + | 2.52481i | 0.594230 | + | 0.193077i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.47716 | − | 11.6678i | 0.644506 | − | 0.887087i | −0.354339 | − | 0.935117i | \(-0.615294\pi\) |
0.998846 | + | 0.0480298i | \(0.0152942\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 26.4324i | 1.99810i | ||||||||
\(176\) | 4.91861 | − | 12.3210i | 0.370755 | − | 0.928731i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.83001 | − | 14.8652i | 0.359011 | − | 1.10492i | −0.594635 | − | 0.803996i | \(-0.702704\pi\) |
0.953647 | − | 0.300928i | \(-0.0972964\pi\) | |||||||
\(182\) | −25.6365 | − | 8.32981i | −1.90030 | − | 0.617446i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.5819 | − | 7.41798i | −1.35884 | − | 0.542457i | ||||
\(188\) | 21.0586 | 1.53585 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.9458 | + | 39.8432i | 0.924702 | + | 2.84594i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 7.50610 | + | 11.9020i | 0.533435 | + | 0.845841i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | −13.4500 | + | 4.37016i | −0.951057 | + | 0.309017i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.1347 | − | 7.36332i | 0.713078 | − | 0.518081i | ||||
\(203\) | 17.2120 | − | 52.9731i | 1.20805 | − | 3.71799i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 14.4222i | − | 1.00000i | ||||||
\(209\) | 5.77739 | − | 6.94355i | 0.399630 | − | 0.480296i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(212\) | 16.3344 | + | 11.8676i | 1.12185 | + | 0.815071i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.26249 | + | 7.24320i | −0.357241 | + | 0.491700i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.7508 | −1.46312 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.6260 | − | 14.9856i | −1.38122 | − | 1.00351i | −0.996765 | − | 0.0803677i | \(-0.974391\pi\) |
−0.384452 | − | 0.923145i | \(-0.625609\pi\) | |||||||
\(224\) | −24.1935 | + | 17.5776i | −1.61650 | + | 1.17445i | ||||
\(225\) | 4.63525 | − | 14.2658i | 0.309017 | − | 0.951057i | ||||
\(226\) | −0.911674 | − | 0.296221i | −0.0606437 | − | 0.0197043i | ||||
\(227\) | 2.54386 | + | 3.50133i | 0.168842 | + | 0.232391i | 0.885050 | − | 0.465495i | \(-0.154124\pi\) |
−0.716208 | + | 0.697887i | \(0.754124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 29.8008 | 1.95652 | ||||||||
\(233\) | 27.7837 | − | 9.02746i | 1.82017 | − | 0.591408i | 0.820360 | − | 0.571848i | \(-0.193773\pi\) |
0.999809 | − | 0.0195604i | \(-0.00622666\pi\) | |||||||
\(234\) | 12.3756 | + | 8.99139i | 0.809017 | + | 0.587785i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.16227 | + | 25.1209i | −0.531319 | + | 1.63523i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 26.5096 | + | 36.4873i | 1.71836 | + | 2.36512i | ||||
\(239\) | 3.67076 | − | 5.05236i | 0.237441 | − | 0.326810i | −0.673622 | − | 0.739076i | \(-0.735262\pi\) |
0.911064 | + | 0.412266i | \(0.135262\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 15.2971 | − | 2.82843i | 0.983332 | − | 0.181818i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.4853 | − | 5.03147i | 0.991344 | − | 0.322107i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.03444 | − | 9.33906i | 0.193077 | − | 0.594230i | ||||
\(248\) | −4.55573 | − | 1.48025i | −0.289289 | − | 0.0939957i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(252\) | − | 31.7188i | − | 1.99810i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | − | 9.40456i | −0.809017 | − | 0.587785i | ||||
\(257\) | −18.6935 | + | 13.5816i | −1.16607 | + | 0.847198i | −0.990533 | − | 0.137275i | \(-0.956166\pi\) |
−0.175535 | + | 0.984473i | \(0.556166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.5790 | + | 25.5719i | −1.15001 | + | 1.58286i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −19.3648 | + | 6.29199i | −1.18733 | + | 0.385787i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.25039 | − | 5.99426i | 0.503973 | − | 0.366158i | ||||
\(269\) | 6.69021 | − | 20.5903i | 0.407909 | − | 1.25542i | −0.510532 | − | 0.859858i | \(-0.670552\pi\) |
0.918442 | − | 0.395557i | \(-0.129448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.75848 | − | 12.0550i | −0.532040 | − | 0.732290i | 0.455400 | − | 0.890287i | \(-0.349496\pi\) |
−0.987440 | + | 0.157997i | \(0.949496\pi\) | |||||||
\(272\) | −14.1834 | + | 19.5218i | −0.859998 | + | 1.18369i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.7475 | − | 10.6066i | −0.768706 | − | 0.639602i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.3738 | + | 10.1940i | −1.88507 | + | 0.612497i | −0.901263 | + | 0.433273i | \(0.857359\pi\) |
−0.983808 | + | 0.179224i | \(0.942641\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.11041 | − | 2.98639i | 0.246084 | − | 0.178791i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(284\) | 1.23479 | + | 3.80030i | 0.0732714 | + | 0.225506i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.3045 | − | 9.02120i | 0.845841 | − | 0.533435i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 16.1400 | − | 5.24419i | 0.951057 | − | 0.309017i | ||||
\(289\) | 15.6885 | + | 11.3983i | 0.922851 | + | 0.670491i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.80979 | + | 30.1914i | −0.564490 | + | 1.73732i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.40330 | − | 8.81338i | −0.367254 | − | 0.505482i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.90900 | − | 24.3414i | −0.452128 | − | 1.39151i | ||||
\(307\) | 16.8180i | 0.959854i | 0.877308 | + | 0.479927i | \(0.159337\pi\) | ||||
−0.877308 | + | 0.479927i | \(0.840663\pi\) | |||||||
\(308\) | −32.5673 | − | 13.0011i | −1.85570 | − | 0.740804i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.03163 | − | 27.7965i | 0.510498 | − | 1.57115i | −0.280829 | − | 0.959758i | \(-0.590609\pi\) |
0.791327 | − | 0.611393i | \(-0.209391\pi\) | |||||||
\(314\) | −19.1993 | − | 6.23822i | −1.08348 | − | 0.352043i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.6407 | + | 29.5576i | 1.04368 | + | 1.65491i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.2919 | + | 9.65710i | −0.739579 | + | 0.537336i | ||||
\(324\) | −5.56231 | + | 17.1190i | −0.309017 | + | 0.951057i | ||||
\(325\) | −17.1454 | − | 5.57088i | −0.951057 | − | 0.309017i | ||||
\(326\) | 5.43093 | + | 7.47504i | 0.300791 | + | 0.414004i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 55.6628i | − | 3.06879i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.7201 | −1.35874 | −0.679369 | − | 0.733796i | \(-0.737747\pi\) | ||||
−0.679369 | + | 0.733796i | \(0.737747\pi\) | |||||||
\(332\) | −32.3364 | + | 10.5067i | −1.77469 | + | 0.576632i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.2184 | − | 9.60370i | 0.723277 | − | 0.525491i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.00861 | − | 12.3993i | −0.490730 | − | 0.675432i | 0.489792 | − | 0.871839i | \(-0.337073\pi\) |
−0.980522 | + | 0.196407i | \(0.937073\pi\) | |||||||
\(338\) | 10.8063 | − | 14.8736i | 0.587785 | − | 0.809017i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.38148 | − | 5.44445i | −0.0748115 | − | 0.294833i | ||||
\(342\) | 11.5548 | 0.624810 | ||||||||
\(343\) | 70.1207 | − | 22.7836i | 3.78616 | − | 1.23020i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.30273 | − | 19.3978i | 0.338837 | − | 1.04283i | ||||
\(347\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(350\) | 11.5514 | + | 35.5514i | 0.617446 | + | 1.90030i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.23104 | − | 18.7212i | 0.0656149 | − | 0.997845i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.3842 | − | 25.3036i | −0.970279 | − | 1.33547i | −0.941906 | − | 0.335877i | \(-0.890967\pi\) |
−0.0283731 | − | 0.999597i | \(-0.509033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.57923 | + | 11.0157i | 0.188380 | + | 0.579775i | ||||
\(362\) | − | 22.1045i | − | 1.16179i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −38.1213 | −1.99810 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 31.3689 | − | 43.1756i | 1.62859 | − | 2.24156i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.7487i | 1.22966i | 0.788658 | + | 0.614832i | \(0.210776\pi\) | ||||
−0.788658 | + | 0.614832i | \(0.789224\pi\) | |||||||
\(374\) | −28.2343 | − | 1.85659i | −1.45996 | − | 0.0960022i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 28.3237 | − | 9.20294i | 1.46068 | − | 0.474605i | ||||
\(377\) | 30.7336 | + | 22.3292i | 1.58286 | + | 1.15001i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.0298 | + | 33.9462i | −0.566562 | + | 1.74370i | 0.0967022 | + | 0.995313i | \(0.469171\pi\) |
−0.663264 | + | 0.748385i | \(0.730829\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.1627 | + | 34.3554i | 0.570389 | + | 1.75548i | 0.651369 | + | 0.758761i | \(0.274195\pi\) |
−0.0809804 | + | 0.996716i | \(0.525805\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.6176 | − | 20.0653i | 1.40027 | − | 1.01735i | 0.405616 | − | 0.914044i | \(-0.367057\pi\) |
0.994649 | − | 0.103309i | \(-0.0329430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 34.8242 | + | 47.9314i | 1.75889 | + | 2.42090i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 15.2971 | + | 12.7279i | 0.768706 | + | 0.639602i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.1803 | + | 11.7557i | −0.809017 | + | 0.587785i | ||||
\(401\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.58919 | − | 4.94010i | −0.178791 | − | 0.246084i | ||||
\(404\) | 10.4133 | − | 14.3327i | 0.518081 | − | 0.713078i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 78.7706i | − | 3.90932i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 66.4004 | + | 21.5748i | 3.26735 | + | 1.06163i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.30273 | − | 19.3978i | −0.309017 | − | 0.951057i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.73612 | − | 11.8639i | 0.231651 | − | 0.580281i | ||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.76119 | + | 30.0418i | −0.474605 | + | 1.46068i | ||||
\(424\) | 27.1560 | + | 8.82352i | 1.31881 | + | 0.428508i | ||||
\(425\) | 17.7293 | + | 24.4023i | 0.859998 | + | 1.18369i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.2994 | − | 40.9313i | −0.643602 | − | 1.98080i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.0503 | − | 8.46427i | 1.25480 | − | 0.407709i | 0.395162 | − | 0.918612i | \(-0.370689\pi\) |
0.859639 | + | 0.510902i | \(0.170689\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.6935 | + | 21.5736i | −1.42698 | + | 1.03676i | −0.436409 | + | 0.899749i | \(0.643750\pi\) |
−0.990569 | + | 0.137012i | \(0.956250\pi\) | |||||||
\(434\) | −3.91264 | + | 12.0419i | −0.187813 | + | 0.578028i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −62.8404 | −2.99240 | ||||||||
\(442\) | −29.2547 | + | 9.50544i | −1.39151 | + | 0.452128i | ||||
\(443\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −34.2908 | − | 11.1418i | −1.62372 | − | 0.527578i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −24.8585 | + | 34.2148i | −1.17445 | + | 1.61650i | ||||
\(449\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(450\) | − | 21.2132i | − | 1.00000i | ||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.35565 | −0.0637645 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.95163 | + | 3.59757i | 0.232391 | + | 0.168842i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −43.0077 | −1.99874 | −0.999368 | − | 0.0355482i | \(-0.988682\pi\) | ||||
−0.999368 | + | 0.0355482i | \(0.988682\pi\) | |||||||
\(464\) | 40.0820 | − | 13.0234i | 1.86076 | − | 0.604598i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 33.4238 | − | 24.2838i | 1.54833 | − | 1.12493i | ||||
\(467\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(468\) | 20.5745 | + | 6.68506i | 0.951057 | + | 0.309017i | ||||
\(469\) | −15.8442 | − | 21.8077i | −0.731619 | − | 1.00699i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 37.3546i | 1.71938i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.9509 | + | 4.20802i | −0.594230 | + | 0.193077i | ||||
\(476\) | 51.6008 | + | 37.4902i | 2.36512 | + | 1.71836i | ||||
\(477\) | −24.5015 | + | 17.8014i | −1.12185 | + | 0.815071i | ||||
\(478\) | 2.72919 | − | 8.39959i | 0.124830 | − | 0.384188i | ||||
\(479\) | −40.1070 | − | 13.0315i | −1.83253 | − | 0.595426i | −0.999082 | − | 0.0428332i | \(-0.986362\pi\) |
−0.833451 | − | 0.552593i | \(-0.813638\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.3384 | − | 10.4893i | 0.879020 | − | 0.476786i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.4571 | + | 23.5815i | 1.47077 | + | 1.06858i | 0.980389 | + | 0.197073i | \(0.0631436\pi\) |
0.490384 | + | 0.871506i | \(0.336856\pi\) | |||||||
\(488\) | 18.6288 | − | 13.5346i | 0.843288 | − | 0.612684i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.6412 | − | 60.4495i | −0.884597 | − | 2.72251i | ||||
\(494\) | − | 13.8871i | − | 0.624810i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.77433 | −0.304177 | ||||||||
\(497\) | 10.0451 | − | 3.26384i | 0.450583 | − | 0.146403i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.7511 | + | 8.53767i | −0.526051 | + | 0.382199i | −0.818879 | − | 0.573967i | \(-0.805404\pi\) |
0.292827 | + | 0.956165i | \(0.405404\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(504\) | −13.8616 | − | 42.6617i | −0.617446 | − | 1.90030i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −21.5200 | − | 6.99226i | −0.951057 | − | 0.309017i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.2073 | + | 26.4366i | −0.847198 | + | 1.16607i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.8445 | + | 22.3360i | 1.18062 | + | 0.982336i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.18082 | + | 0.857918i | −0.0517328 | + | 0.0375861i | −0.613351 | − | 0.789810i | \(-0.710179\pi\) |
0.561618 | + | 0.827396i | \(0.310179\pi\) | |||||||
\(522\) | −13.8134 | + | 42.5134i | −0.604598 | + | 1.86076i | ||||
\(523\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.2167i | 0.445045i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −32.0537 | − | 23.2883i | −1.39101 | − | 1.01063i | ||||
\(532\) | −23.2959 | + | 16.9254i | −1.01000 | + | 0.733810i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.47716 | − | 11.6678i | 0.366158 | − | 0.503973i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 30.6177i | − | 1.32002i | ||||||
\(539\) | −25.7573 | + | 64.5214i | −1.10945 | + | 2.77913i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(542\) | −17.0484 | − | 12.3864i | −0.732290 | − | 0.532040i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.5453 | + | 32.4552i | −0.452128 | + | 1.39151i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 24.4233i | 1.04236i | ||||||||
\(550\) | −21.7807 | − | 8.69496i | −0.928731 | − | 0.370755i | ||||
\(551\) | 28.6952 | 1.22245 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −37.7428 | + | 27.4217i | −1.60354 | + | 1.16504i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(558\) | 4.22339 | − | 5.81300i | 0.178791 | − | 0.246084i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 45.2496 | + | 14.7025i | 1.90030 | + | 0.617446i | ||||
\(568\) | 3.32158 | + | 4.57176i | 0.139370 | + | 0.191827i | ||||
\(569\) | −26.4818 | + | 36.4491i | −1.11018 | + | 1.52803i | −0.289018 | + | 0.957324i | \(0.593329\pi\) |
−0.821157 | + | 0.570702i | \(0.806671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 15.2971 | − | 18.3848i | 0.639602 | − | 0.768706i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 19.4164 | − | 14.1068i | 0.809017 | − | 0.587785i | ||||
\(577\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(578\) | 26.0822 | + | 8.47462i | 1.08488 | + | 0.352498i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.7718 | + | 85.4727i | 1.15217 | + | 3.54601i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.23481 | + | 32.4535i | 0.341051 | + | 1.34409i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.1267 | + | 26.9742i | −1.53238 | + | 1.11334i | −0.577490 | + | 0.816398i | \(0.695968\pi\) |
−0.954895 | + | 0.296945i | \(0.904032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.38670 | − | 1.42533i | −0.180751 | − | 0.0587295i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.7157 | + | 17.5017i | 0.518686 | + | 0.713910i | 0.985354 | − | 0.170523i | \(-0.0545457\pi\) |
−0.466668 | + | 0.884433i | \(0.654546\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.72705 | + | 14.5484i | 0.192500 | + | 0.592455i | ||||
\(604\) | 44.8944i | 1.82673i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(608\) | −12.4640 | − | 9.05563i | −0.505482 | − | 0.367254i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.1058 | + | 11.7315i | 1.46068 | + | 0.474605i | ||||
\(612\) | −21.2752 | − | 29.2828i | −0.859998 | − | 1.18369i | ||||
\(613\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(614\) | 7.34974 | + | 22.6202i | 0.296611 | + | 0.912876i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −49.4846 | − | 3.25394i | −1.99379 | − | 0.131105i | ||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.3591 | − | 28.5961i | −1.58198 | − | 1.14937i | −0.914384 | − | 0.404848i | \(-0.867324\pi\) |
−0.667594 | − | 0.744526i | \(-0.732676\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.72542 | + | 23.7764i | 0.309017 | + | 0.951057i | ||||
\(626\) | − | 41.3332i | − | 1.65201i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.5491 | −1.13924 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.1264 | − | 26.2474i | 1.43817 | − | 1.04489i | 0.449749 | − | 0.893155i | \(-0.351513\pi\) |
0.988421 | − | 0.151737i | \(-0.0484866\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 75.5247i | 2.99240i | ||||||||
\(638\) | 37.9888 | + | 31.6086i | 1.50399 | + | 1.25139i | ||||
\(639\) | −5.99380 | −0.237111 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.3855 | − | 15.5375i | −0.844678 | − | 0.613695i | 0.0789953 | − | 0.996875i | \(-0.474829\pi\) |
−0.923674 | + | 0.383180i | \(0.874829\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.3368 | − | 44.1241i | 0.565388 | − | 1.74009i | −0.101408 | − | 0.994845i | \(-0.532335\pi\) |
0.666796 | − | 0.745240i | \(-0.267665\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.6572 | + | 18.7975i | −0.537336 | + | 0.739579i | ||||
\(647\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(648\) | 25.4558i | 1.00000i | ||||||||
\(649\) | −37.0496 | + | 23.3656i | −1.45433 | + | 0.917179i | ||||
\(650\) | −25.4951 | −1.00000 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.5713 | + | 7.68050i | 0.414004 | + | 0.300791i | ||||
\(653\) | 36.8386 | − | 26.7648i | 1.44161 | − | 1.04739i | 0.453902 | − | 0.891051i | \(-0.350031\pi\) |
0.987704 | − | 0.156337i | \(-0.0499685\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.3255 | − | 74.8663i | −0.948308 | − | 2.91859i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | −33.2484 | + | 10.8031i | −1.29224 | + | 0.419873i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −38.9007 | + | 28.2630i | −1.50964 | + | 1.09682i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 13.5817 | − | 18.6936i | 0.525491 | − | 0.723277i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.0766 | + | 10.0107i | 0.968073 | + | 0.386460i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.5468 | + | 14.7991i | −1.75570 | + | 0.570462i | −0.996740 | − | 0.0806753i | \(-0.974292\pi\) |
−0.758960 | + | 0.651137i | \(0.774292\pi\) | |||||||
\(674\) | −17.5352 | − | 12.7401i | −0.675432 | − | 0.490730i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.03444 | − | 24.7275i | 0.309017 | − | 0.951057i | ||||
\(677\) | −16.8541 | − | 5.47623i | −0.647756 | − | 0.210469i | −0.0333315 | − | 0.999444i | \(-0.510612\pi\) |
−0.614424 | + | 0.788976i | \(0.710612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.23740 | − | 6.71903i | −0.162258 | − | 0.257285i | ||||
\(683\) | −6.43250 | −0.246133 | −0.123066 | − | 0.992398i | \(-0.539273\pi\) | ||||
−0.123066 | + | 0.992398i | \(0.539273\pi\) | |||||||
\(684\) | 15.5411 | − | 5.04962i | 0.594230 | − | 0.193077i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 84.3553 | − | 61.2877i | 3.22070 | − | 2.33998i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.3946 | + | 29.4472i | 0.815071 | + | 1.12185i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.7790 | + | 33.1744i | 0.410053 | + | 1.26201i | 0.916602 | + | 0.399801i | \(0.130921\pi\) |
−0.506549 | + | 0.862211i | \(0.669079\pi\) | |||||||
\(692\) | − | 28.8444i | − | 1.09650i | ||||||
\(693\) | 33.6429 | − | 40.4337i | 1.27799 | − | 1.53595i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 31.0731 | + | 42.7685i | 1.17445 | + | 1.61650i | ||||
\(701\) | 0.224280 | − | 0.308695i | 0.00847095 | − | 0.0116593i | −0.804761 | − | 0.593600i | \(-0.797706\pi\) |
0.813231 | + | 0.581940i | \(0.197706\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −6.52573 | − | 25.7180i | −0.245948 | − | 0.969283i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −37.8847 | − | 27.5248i | −1.42480 | − | 1.03518i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −35.7847 | − | 25.9991i | −1.33547 | − | 0.970279i | ||||
\(719\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.62810 | + | 13.2519i | 0.358321 | + | 0.493186i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.66001 | − | 29.7305i | −0.359011 | − | 1.10492i | ||||
\(725\) | − | 52.6809i | − | 1.95652i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | −51.2730 | + | 16.6596i | −1.90030 | + | 0.617446i | ||||
\(729\) | −21.8435 | − | 15.8702i | −0.809017 | − | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.8751 | + | 1.10965i | 0.621602 | + | 0.0408744i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.3379 | − | 14.4063i | 1.63100 | − | 0.529943i | 0.656497 | − | 0.754329i | \(-0.272038\pi\) |
0.974500 | + | 0.224386i | \(0.0720376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 23.3227 | − | 71.7797i | 0.856201 | − | 2.63512i | ||||
\(743\) | 31.7093 | + | 10.3030i | 1.16330 | + | 0.377980i | 0.826139 | − | 0.563466i | \(-0.190533\pi\) |
0.337163 | + | 0.941446i | \(0.390533\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.3786 | + | 31.9420i | 0.379987 | + | 1.16948i | ||||
\(747\) | − | 51.0007i | − | 1.86602i | ||||||
\(748\) | −38.7864 | + | 9.84174i | −1.41817 | + | 0.359850i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(752\) | 34.0735 | − | 24.7558i | 1.24253 | − | 0.902753i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 51.0948 | + | 16.6017i | 1.86076 | + | 0.604598i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.9625 | − | 49.1274i | −0.580165 | − | 1.78556i | −0.617876 | − | 0.786276i | \(-0.712006\pi\) |
0.0377104 | − | 0.999289i | \(-0.487994\pi\) | |||||||
\(758\) | 50.4777i | 1.83343i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.0277 | + | 41.3296i | 1.08494 | + | 1.49330i | ||||
\(767\) | −27.9891 | + | 38.5237i | −1.01063 | + | 1.39101i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.61673 | + | 8.05347i | −0.0939957 | + | 0.289289i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.3767 | − | 39.0571i | 1.01735 | − | 1.40027i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.45677 | + | 6.15414i | −0.0879100 | + | 0.220212i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 67.7852 | + | 49.2488i | 2.42090 | + | 1.75889i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.34500 | + | 0.437016i | 0.0479440 | + | 0.0155779i | 0.332891 | − | 0.942965i | \(-0.391976\pi\) |
−0.284947 | + | 0.958543i | \(0.591976\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.58331i | 0.127408i | ||||||||
\(792\) | 26.1368 | + | 10.4340i | 0.928731 | + | 0.370755i | ||||
\(793\) | 29.3531 | 1.04236 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.3098 | + | 47.1187i | −0.542301 | + | 1.66903i | 0.185022 | + | 0.982734i | \(0.440764\pi\) |
−0.727323 | + | 0.686296i | \(0.759236\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.3354 | − | 51.3878i | −1.32083 | − | 1.81797i | ||||
\(800\) | −16.6251 | + | 22.8825i | −0.587785 | + | 0.809017i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.98636 | − | 5.07589i | −0.246084 | − | 0.178791i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.74225 | − | 23.8282i | 0.272371 | − | 0.838273i | ||||
\(809\) | −34.2908 | − | 11.1418i | −1.20560 | − | 0.391724i | −0.363783 | − | 0.931484i | \(-0.618515\pi\) |
−0.841819 | + | 0.539760i | \(0.818515\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.81878 | + | 8.00886i | −0.204325 | + | 0.281229i | −0.898866 | − | 0.438224i | \(-0.855608\pi\) |
0.694541 | + | 0.719453i | \(0.255608\pi\) | |||||||
\(812\) | −34.4240 | − | 105.946i | −1.20805 | − | 3.71799i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.6702 | − | 54.3833i | 0.617446 | − | 1.90030i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 98.7369 | 3.43550 | ||||||||
\(827\) | −12.1050 | + | 3.93314i | −0.420931 | + | 0.136769i | −0.511821 | − | 0.859092i | \(-0.671029\pi\) |
0.0908898 | + | 0.995861i | \(0.471029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.29682 | − | 3.12183i | 0.149235 | − | 0.108425i | −0.510662 | − | 0.859781i | \(-0.670600\pi\) |
0.659897 | + | 0.751356i | \(0.270600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16.9543 | − | 23.3356i | −0.587785 | − | 0.809017i | ||||
\(833\) | 74.2744 | − | 102.230i | 2.57345 | − | 3.54206i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.18537 | − | 18.0266i | 0.0409969 | − | 0.623464i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.8486 | − | 34.0375i | −1.61739 | − | 1.17511i | −0.825225 | − | 0.564805i | \(-0.808951\pi\) |
−0.792170 | − | 0.610301i | \(-0.791049\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.3429 | + | 77.9973i | −0.873892 | + | 2.68956i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 44.6720i | 1.53585i | ||||||||
\(847\) | −27.7257 | − | 51.1160i | −0.952665 | − | 1.75637i | ||||
\(848\) | 40.3808 | 1.38668 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 34.5101 | + | 25.0730i | 1.18369 | + | 0.859998i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(854\) | −35.7752 | − | 49.2404i | −1.22420 | − | 1.68497i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.3374i | 0.933827i | 0.884303 | + | 0.466914i | \(0.154634\pi\) | ||||
−0.884303 | + | 0.466914i | \(0.845366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31.3386 | − | 22.7688i | 1.06740 | − | 0.775510i | ||||
\(863\) | −11.0298 | + | 33.9462i | −0.375458 | + | 1.15554i | 0.567711 | + | 0.823228i | \(0.307829\pi\) |
−0.943169 | + | 0.332314i | \(0.892171\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30.5097 | + | 41.9929i | −1.03676 | + | 1.42698i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 17.9062i | 0.607775i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.4850 | − | 5.68121i | 0.592455 | − | 0.192500i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.5824 | 0.760820 | 0.380410 | − | 0.924818i | \(-0.375783\pi\) | ||||
0.380410 | + | 0.924818i | \(0.375783\pi\) | |||||||
\(882\) | −84.5201 | + | 27.4622i | −2.84594 | + | 0.924702i | ||||
\(883\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(884\) | −35.1935 | + | 25.5696i | −1.18369 | + | 0.859998i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.2480 | + | 15.9228i | −0.845841 | + | 0.533435i | ||||
\(892\) | −50.9902 | −1.70728 | ||||||||
\(893\) | 27.2728 | − | 8.86149i | 0.912651 | − | 0.296538i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18.4822 | + | 56.8823i | −0.617446 | + | 1.90030i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.4884 | − | 14.4360i | 0.349807 | − | 0.481469i | ||||
\(900\) | −9.27051 | − | 28.5317i | −0.309017 | − | 0.951057i | ||||
\(901\) | − | 60.9001i | − | 2.02887i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.82335 | + | 0.592442i | −0.0606437 | + | 0.0197043i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(908\) | 8.23212 | + | 2.67478i | 0.273192 | + | 0.0887656i | ||||
\(909\) | 15.6200 | + | 21.4990i | 0.518081 | + | 0.713078i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.3650 | − | 20.9044i | −1.73303 | − | 0.691835i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.20365i | 0.237111i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −57.8452 | + | 18.7950i | −1.90091 | + | 0.617643i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 48.2188 | − | 35.0330i | 1.58286 | − | 1.15001i | ||||
\(929\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.5321 | + | 46.1530i | 1.09897 | + | 1.51260i | ||||
\(932\) | 34.3425 | − | 47.2684i | 1.12493 | − | 1.54833i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 30.5941 | 1.00000 | ||||||||
\(937\) | 52.3804 | − | 17.0194i | 1.71119 | − | 0.556000i | 0.720662 | − | 0.693287i | \(-0.243838\pi\) |
0.990531 | + | 0.137286i | \(0.0438380\pi\) | |||||||
\(938\) | −30.8408 | − | 22.4071i | −1.00699 | − | 0.731619i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 16.3245 | + | 50.2418i | 0.531319 | + | 1.63523i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 53.1861 | 1.72831 | 0.864157 | − | 0.503221i | \(-0.167852\pi\) | ||||
0.864157 | + | 0.503221i | \(0.167852\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −15.5800 | + | 11.3195i | −0.505482 | + | 0.367254i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 85.7868 | + | 27.8738i | 2.78036 | + | 0.903395i | ||||
\(953\) | −33.9086 | − | 46.6712i | −1.09841 | − | 1.51183i | −0.837477 | − | 0.546472i | \(-0.815970\pi\) |
−0.260931 | − | 0.965357i | \(-0.584030\pi\) | |||||||
\(954\) | −25.1750 | + | 34.6504i | −0.815071 | + | 1.12185i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 12.4901i | − | 0.403960i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −59.6387 | −1.92684 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.7591 | − | 16.5354i | 0.734164 | − | 0.533401i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 26.8701i | − | 0.864083i | −0.901854 | − | 0.432041i | \(-0.857793\pi\) | ||
0.901854 | − | 0.432041i | \(-0.142207\pi\) | |||||||
\(968\) | 21.4261 | − | 22.5593i | 0.688662 | − | 0.725082i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 53.9602 | + | 17.5327i | 1.72900 | + | 0.561785i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.1409 | − | 26.3451i | 0.612684 | − | 0.843288i | ||||
\(977\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.9054 | − | 13.7356i | 0.602988 | − | 0.438096i | −0.243950 | − | 0.969788i | \(-0.578443\pi\) |
0.846938 | + | 0.531691i | \(0.178443\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −52.8348 | − | 72.7209i | −1.68260 | − | 2.31590i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.06889 | − | 18.6781i | −0.193077 | − | 0.594230i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | −9.11146 | + | 2.96049i | −0.289289 | + | 0.0939957i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.0843 | − | 8.77972i | 0.383289 | − | 0.278476i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.5735 | − | 46.2100i | −1.06328 | − | 1.46349i | −0.876694 | − | 0.481048i | \(-0.840256\pi\) |
−0.186590 | − | 0.982438i | \(-0.559744\pi\) | |||||||
\(998\) | −12.0741 | + | 16.6186i | −0.382199 | + | 0.526051i | ||||
\(999\) | 0 | 0 |
(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 | 572.2.bb.a.259.3 | yes | 16 | |
4.3 | odd | 2 | inner | 572.2.bb.a.259.2 | ✓ | 16 | |
11.2 | odd | 10 | inner | 572.2.bb.a.519.3 | yes | 16 | |
13.12 | even | 2 | inner | 572.2.bb.a.259.2 | ✓ | 16 | |
44.35 | even | 10 | inner | 572.2.bb.a.519.2 | yes | 16 | |
52.51 | odd | 2 | CM | 572.2.bb.a.259.3 | yes | 16 | |
143.90 | odd | 10 | inner | 572.2.bb.a.519.2 | yes | 16 | |
572.519 | even | 10 | inner | 572.2.bb.a.519.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.bb.a.259.2 | ✓ | 16 | 4.3 | odd | 2 | inner | |
572.2.bb.a.259.2 | ✓ | 16 | 13.12 | even | 2 | inner | |
572.2.bb.a.259.3 | yes | 16 | 1.1 | even | 1 | trivial | |
572.2.bb.a.259.3 | yes | 16 | 52.51 | odd | 2 | CM | |
572.2.bb.a.519.2 | yes | 16 | 44.35 | even | 10 | inner | |
572.2.bb.a.519.2 | yes | 16 | 143.90 | odd | 10 | inner | |
572.2.bb.a.519.3 | yes | 16 | 11.2 | odd | 10 | inner | |
572.2.bb.a.519.3 | yes | 16 | 572.519 | even | 10 | inner |