Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1457,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.m (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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2843.4 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.2843 |
Dual form | 3150.2.m.k.1457.4 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.41421i | − | 1.02942i | −0.857363 | − | 0.514712i | \(-0.827899\pi\) | ||
0.857363 | − | 0.514712i | \(-0.172101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.02494 | + | 2.02494i | 0.561618 | + | 0.561618i | 0.929767 | − | 0.368149i | \(-0.120008\pi\) |
−0.368149 | + | 0.929767i | \(0.620008\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.37101 | − | 4.37101i | −1.06013 | − | 1.06013i | −0.998073 | − | 0.0620526i | \(-0.980235\pi\) |
−0.0620526 | − | 0.998073i | \(-0.519765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.87832i | 1.11916i | 0.828776 | + | 0.559581i | \(0.189038\pi\) | ||||
−0.828776 | + | 0.559581i | \(0.810962\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.41421 | − | 2.41421i | 0.514712 | − | 0.514712i | ||||
\(23\) | −3.74238 | + | 3.74238i | −0.780341 | + | 0.780341i | −0.979888 | − | 0.199547i | \(-0.936053\pi\) |
0.199547 | + | 0.979888i | \(0.436053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.86370i | 0.561618i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.707107 | − | 0.707107i | −0.133631 | − | 0.133631i | ||||
\(29\) | 5.21682 | 0.968739 | 0.484369 | − | 0.874864i | \(-0.339049\pi\) | ||||
0.484369 | + | 0.874864i | \(0.339049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.93942 | −0.887145 | −0.443573 | − | 0.896238i | \(-0.646289\pi\) | ||||
−0.443573 | + | 0.896238i | \(0.646289\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.18154i | − | 1.06013i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.87832 | + | 6.87832i | −1.13079 | + | 1.13079i | −0.140742 | + | 0.990046i | \(0.544949\pi\) |
−0.990046 | + | 0.140742i | \(0.955051\pi\) | |||||||
\(38\) | −3.44949 | + | 3.44949i | −0.559581 | + | 0.559581i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.77729i | 1.37078i | 0.728175 | + | 0.685392i | \(0.240369\pi\) | ||||
−0.728175 | + | 0.685392i | \(0.759631\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.174857 | − | 0.174857i | −0.0266654 | − | 0.0266654i | 0.693648 | − | 0.720314i | \(-0.256002\pi\) |
−0.720314 | + | 0.693648i | \(0.756002\pi\) | |||||||
\(44\) | 3.41421 | 0.514712 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.29253 | −0.780341 | ||||||||
\(47\) | 3.42883 | + | 3.42883i | 0.500146 | + | 0.500146i | 0.911483 | − | 0.411338i | \(-0.134938\pi\) |
−0.411338 | + | 0.911483i | \(0.634938\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.02494 | + | 2.02494i | −0.280809 | + | 0.280809i | ||||
\(53\) | −6.43916 | + | 6.43916i | −0.884486 | + | 0.884486i | −0.993987 | − | 0.109500i | \(-0.965075\pi\) |
0.109500 | + | 0.993987i | \(0.465075\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.68885 | + | 3.68885i | 0.484369 | + | 0.484369i | ||||
\(59\) | 2.22803 | 0.290065 | 0.145032 | − | 0.989427i | \(-0.453671\pi\) | ||||
0.145032 | + | 0.989427i | \(0.453671\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.2526 | −1.95290 | −0.976448 | − | 0.215752i | \(-0.930780\pi\) | ||||
−0.976448 | + | 0.215752i | \(0.930780\pi\) | |||||||
\(62\) | −3.49269 | − | 3.49269i | −0.443573 | − | 0.443573i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.81382 | − | 3.81382i | 0.465932 | − | 0.465932i | −0.434662 | − | 0.900594i | \(-0.643132\pi\) |
0.900594 | + | 0.434662i | \(0.143132\pi\) | |||||||
\(68\) | 4.37101 | − | 4.37101i | 0.530063 | − | 0.530063i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.9282i | − | 1.29694i | −0.761241 | − | 0.648470i | \(-0.775409\pi\) | ||
0.761241 | − | 0.648470i | \(-0.224591\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.51059 | − | 2.51059i | −0.293842 | − | 0.293842i | 0.544754 | − | 0.838596i | \(-0.316623\pi\) |
−0.838596 | + | 0.544754i | \(0.816623\pi\) | |||||||
\(74\) | −9.72741 | −1.13079 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.87832 | −0.559581 | ||||||||
\(77\) | 2.41421 | + | 2.41421i | 0.275125 | + | 0.275125i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.98414i | 1.12330i | 0.827374 | + | 0.561652i | \(0.189834\pi\) | ||||
−0.827374 | + | 0.561652i | \(0.810166\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.20648 | + | 6.20648i | −0.685392 | + | 0.685392i | ||||
\(83\) | −2.35640 | + | 2.35640i | −0.258648 | + | 0.258648i | −0.824504 | − | 0.565856i | \(-0.808546\pi\) |
0.565856 | + | 0.824504i | \(0.308546\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 0.247285i | − | 0.0266654i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.41421 | + | 2.41421i | 0.257356 | + | 0.257356i | ||||
\(89\) | 4.07055 | 0.431478 | 0.215739 | − | 0.976451i | \(-0.430784\pi\) | ||||
0.215739 | + | 0.976451i | \(0.430784\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.86370 | −0.300198 | ||||||||
\(92\) | −3.74238 | − | 3.74238i | −0.390170 | − | 0.390170i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.84909i | 0.500146i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.64564 | + | 5.64564i | −0.573228 | + | 0.573228i | −0.933029 | − | 0.359801i | \(-0.882845\pi\) |
0.359801 | + | 0.933029i | \(0.382845\pi\) | |||||||
\(98\) | 0.707107 | − | 0.707107i | 0.0714286 | − | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 4.91484i | − | 0.489044i | −0.969644 | − | 0.244522i | \(-0.921369\pi\) | ||
0.969644 | − | 0.244522i | \(-0.0786311\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.07019 | + | 8.07019i | 0.795179 | + | 0.795179i | 0.982331 | − | 0.187152i | \(-0.0599256\pi\) |
−0.187152 | + | 0.982331i | \(0.559926\pi\) | |||||||
\(104\) | −2.86370 | −0.280809 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.10634 | −0.884486 | ||||||||
\(107\) | −5.77729 | − | 5.77729i | −0.558512 | − | 0.558512i | 0.370372 | − | 0.928884i | \(-0.379230\pi\) |
−0.928884 | + | 0.370372i | \(0.879230\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.07712i | − | 0.582083i | −0.956710 | − | 0.291041i | \(-0.905998\pi\) | ||
0.956710 | − | 0.291041i | \(-0.0940017\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | −6.76733 | + | 6.76733i | −0.636617 | + | 0.636617i | −0.949719 | − | 0.313103i | \(-0.898632\pi\) |
0.313103 | + | 0.949719i | \(0.398632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.21682i | 0.484369i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.57545 | + | 1.57545i | 0.145032 | + | 0.145032i | ||||
\(119\) | 6.18154 | 0.566661 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.656854 | −0.0597140 | ||||||||
\(122\) | −10.7852 | − | 10.7852i | −0.976448 | − | 0.976448i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 4.93942i | − | 0.443573i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0345 | + | 11.0345i | −0.979158 | + | 0.979158i | −0.999787 | − | 0.0206295i | \(-0.993433\pi\) |
0.0206295 | + | 0.999787i | \(0.493433\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.41370i | − | 0.210886i | −0.994425 | − | 0.105443i | \(-0.966374\pi\) | ||
0.994425 | − | 0.105443i | \(-0.0336260\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.44949 | − | 3.44949i | −0.299109 | − | 0.299109i | ||||
\(134\) | 5.39355 | 0.465932 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.18154 | 0.530063 | ||||||||
\(137\) | −9.39836 | − | 9.39836i | −0.802956 | − | 0.802956i | 0.180601 | − | 0.983557i | \(-0.442196\pi\) |
−0.983557 | + | 0.180601i | \(0.942196\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.2621i | − | 0.955236i | −0.878568 | − | 0.477618i | \(-0.841500\pi\) | ||
0.878568 | − | 0.477618i | \(-0.158500\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.72741 | − | 7.72741i | 0.648470 | − | 0.648470i | ||||
\(143\) | 6.91359 | − | 6.91359i | 0.578144 | − | 0.578144i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 3.55051i | − | 0.293842i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.87832 | − | 6.87832i | −0.565394 | − | 0.565394i | ||||
\(149\) | 3.18759 | 0.261138 | 0.130569 | − | 0.991439i | \(-0.458320\pi\) | ||||
0.130569 | + | 0.991439i | \(0.458320\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.80725 | 0.147072 | 0.0735359 | − | 0.997293i | \(-0.476572\pi\) | ||||
0.0735359 | + | 0.997293i | \(0.476572\pi\) | |||||||
\(152\) | −3.44949 | − | 3.44949i | −0.279791 | − | 0.279791i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.41421i | 0.275125i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.8577 | + | 12.8577i | −1.02615 | + | 1.02615i | −0.0265035 | + | 0.999649i | \(0.508437\pi\) |
−0.999649 | + | 0.0265035i | \(0.991563\pi\) | |||||||
\(158\) | −7.05986 | + | 7.05986i | −0.561652 | + | 0.561652i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 5.29253i | − | 0.417110i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0884 | − | 10.0884i | −0.790188 | − | 0.790188i | 0.191336 | − | 0.981525i | \(-0.438718\pi\) |
−0.981525 | + | 0.191336i | \(0.938718\pi\) | |||||||
\(164\) | −8.77729 | −0.685392 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.33245 | −0.258648 | ||||||||
\(167\) | −3.31319 | − | 3.31319i | −0.256383 | − | 0.256383i | 0.567199 | − | 0.823581i | \(-0.308027\pi\) |
−0.823581 | + | 0.567199i | \(0.808027\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 4.79920i | − | 0.369169i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.174857 | − | 0.174857i | 0.0133327 | − | 0.0133327i | ||||
\(173\) | −8.88437 | + | 8.88437i | −0.675466 | + | 0.675466i | −0.958971 | − | 0.283505i | \(-0.908503\pi\) |
0.283505 | + | 0.958971i | \(0.408503\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.41421i | 0.257356i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.87832 | + | 2.87832i | 0.215739 | + | 0.215739i | ||||
\(179\) | 24.6556 | 1.84285 | 0.921423 | − | 0.388560i | \(-0.127027\pi\) | ||||
0.921423 | + | 0.388560i | \(0.127027\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.2432 | −0.984356 | −0.492178 | − | 0.870495i | \(-0.663799\pi\) | ||||
−0.492178 | + | 0.870495i | \(0.663799\pi\) | |||||||
\(182\) | −2.02494 | − | 2.02494i | −0.150099 | − | 0.150099i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 5.29253i | − | 0.390170i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.9236 | + | 14.9236i | −1.09132 | + | 1.09132i | ||||
\(188\) | −3.42883 | + | 3.42883i | −0.250073 | + | 0.250073i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 19.7228i | − | 1.42709i | −0.700610 | − | 0.713545i | \(-0.747089\pi\) | ||
0.700610 | − | 0.713545i | \(-0.252911\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.01461 | + | 7.01461i | 0.504923 | + | 0.504923i | 0.912964 | − | 0.408041i | \(-0.133788\pi\) |
−0.408041 | + | 0.912964i | \(0.633788\pi\) | |||||||
\(194\) | −7.98414 | −0.573228 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 17.5394 | + | 17.5394i | 1.24963 | + | 1.24963i | 0.955882 | + | 0.293752i | \(0.0949041\pi\) |
0.293752 | + | 0.955882i | \(0.405096\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.9683i | 1.13196i | 0.824418 | + | 0.565981i | \(0.191502\pi\) | ||||
−0.824418 | + | 0.565981i | \(0.808498\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.47531 | − | 3.47531i | 0.244522 | − | 0.244522i | ||||
\(203\) | −3.68885 | + | 3.68885i | −0.258906 | + | 0.258906i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.4130i | 0.795179i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.02494 | − | 2.02494i | −0.140405 | − | 0.140405i | ||||
\(209\) | 16.6556 | 1.15209 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.2686 | −1.80841 | −0.904203 | − | 0.427102i | \(-0.859535\pi\) | ||||
−0.904203 | + | 0.427102i | \(0.859535\pi\) | |||||||
\(212\) | −6.43916 | − | 6.43916i | −0.442243 | − | 0.442243i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 8.17033i | − | 0.558512i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.49269 | − | 3.49269i | 0.237100 | − | 0.237100i | ||||
\(218\) | 4.29717 | − | 4.29717i | 0.291041 | − | 0.291041i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 17.7021i | − | 1.19077i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.6061 | + | 12.6061i | 0.844166 | + | 0.844166i | 0.989398 | − | 0.145232i | \(-0.0463928\pi\) |
−0.145232 | + | 0.989398i | \(0.546393\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.57045 | −0.636617 | ||||||||
\(227\) | −3.02786 | − | 3.02786i | −0.200966 | − | 0.200966i | 0.599448 | − | 0.800414i | \(-0.295387\pi\) |
−0.800414 | + | 0.599448i | \(0.795387\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.50543i | 0.231645i | 0.993270 | + | 0.115823i | \(0.0369504\pi\) | ||||
−0.993270 | + | 0.115823i | \(0.963050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.68885 | + | 3.68885i | −0.242185 | + | 0.242185i | ||||
\(233\) | 8.98074 | − | 8.98074i | 0.588348 | − | 0.588348i | −0.348836 | − | 0.937184i | \(-0.613423\pi\) |
0.937184 | + | 0.348836i | \(0.113423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.22803i | 0.145032i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.37101 | + | 4.37101i | 0.283330 | + | 0.283330i | ||||
\(239\) | −16.4853 | −1.06634 | −0.533172 | − | 0.846007i | \(-0.679000\pi\) | ||||
−0.533172 | + | 0.846007i | \(0.679000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.8179 | 1.79191 | 0.895954 | − | 0.444147i | \(-0.146493\pi\) | ||||
0.895954 | + | 0.444147i | \(0.146493\pi\) | |||||||
\(242\) | −0.464466 | − | 0.464466i | −0.0298570 | − | 0.0298570i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 15.2526i | − | 0.976448i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.87832 | + | 9.87832i | −0.628542 | + | 0.628542i | ||||
\(248\) | 3.49269 | − | 3.49269i | 0.221786 | − | 0.221786i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 8.43969i | − | 0.532708i | −0.963875 | − | 0.266354i | \(-0.914181\pi\) | ||
0.963875 | − | 0.266354i | \(-0.0858191\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.7773 | + | 12.7773i | 0.803302 | + | 0.803302i | ||||
\(254\) | −15.6052 | −0.979158 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.7275 | + | 14.7275i | 0.918678 | + | 0.918678i | 0.996933 | − | 0.0782557i | \(-0.0249351\pi\) |
−0.0782557 | + | 0.996933i | \(0.524935\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 9.72741i | − | 0.604432i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.70674 | − | 1.70674i | 0.105443 | − | 0.105443i | ||||
\(263\) | 3.42919 | − | 3.42919i | 0.211453 | − | 0.211453i | −0.593432 | − | 0.804884i | \(-0.702227\pi\) |
0.804884 | + | 0.593432i | \(0.202227\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 4.87832i | − | 0.299109i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.81382 | + | 3.81382i | 0.232966 | + | 0.232966i | ||||
\(269\) | 5.33510 | 0.325287 | 0.162643 | − | 0.986685i | \(-0.447998\pi\) | ||||
0.162643 | + | 0.986685i | \(0.447998\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.0479 | 1.03559 | 0.517794 | − | 0.855506i | \(-0.326754\pi\) | ||||
0.517794 | + | 0.855506i | \(0.326754\pi\) | |||||||
\(272\) | 4.37101 | + | 4.37101i | 0.265031 | + | 0.265031i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 13.2913i | − | 0.802956i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.36360 | + | 6.36360i | −0.382351 | + | 0.382351i | −0.871949 | − | 0.489597i | \(-0.837144\pi\) |
0.489597 | + | 0.871949i | \(0.337144\pi\) | |||||||
\(278\) | 7.96348 | − | 7.96348i | 0.477618 | − | 0.477618i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.14214i | 0.366409i | 0.983075 | + | 0.183205i | \(0.0586471\pi\) | ||||
−0.983075 | + | 0.183205i | \(0.941353\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.4600 | + | 14.4600i | 0.859556 | + | 0.859556i | 0.991286 | − | 0.131730i | \(-0.0420530\pi\) |
−0.131730 | + | 0.991286i | \(0.542053\pi\) | |||||||
\(284\) | 10.9282 | 0.648470 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.77729 | 0.578144 | ||||||||
\(287\) | −6.20648 | − | 6.20648i | −0.366357 | − | 0.366357i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.2114i | 1.24773i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.51059 | − | 2.51059i | 0.146921 | − | 0.146921i | ||||
\(293\) | −3.55708 | + | 3.55708i | −0.207807 | + | 0.207807i | −0.803335 | − | 0.595528i | \(-0.796943\pi\) |
0.595528 | + | 0.803335i | \(0.296943\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 9.72741i | − | 0.565394i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.25397 | + | 2.25397i | 0.130569 | + | 0.130569i | ||||
\(299\) | −15.1562 | −0.876508 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.247285 | 0.0142533 | ||||||||
\(302\) | 1.27792 | + | 1.27792i | 0.0735359 | + | 0.0735359i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 4.87832i | − | 0.279791i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.32729 | − | 4.32729i | 0.246971 | − | 0.246971i | −0.572755 | − | 0.819727i | \(-0.694125\pi\) |
0.819727 | + | 0.572755i | \(0.194125\pi\) | |||||||
\(308\) | −2.41421 | + | 2.41421i | −0.137563 | + | 0.137563i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.69537i | 0.209545i | 0.994496 | + | 0.104773i | \(0.0334114\pi\) | ||||
−0.994496 | + | 0.104773i | \(0.966589\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.3390 | − | 13.3390i | −0.753966 | − | 0.753966i | 0.221251 | − | 0.975217i | \(-0.428986\pi\) |
−0.975217 | + | 0.221251i | \(0.928986\pi\) | |||||||
\(314\) | −18.1835 | −1.02615 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.98414 | −0.561652 | ||||||||
\(317\) | −13.5601 | − | 13.5601i | −0.761612 | − | 0.761612i | 0.215002 | − | 0.976614i | \(-0.431024\pi\) |
−0.976614 | + | 0.215002i | \(0.931024\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 17.8113i | − | 0.997243i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.74238 | − | 3.74238i | 0.208555 | − | 0.208555i | ||||
\(323\) | 21.3232 | − | 21.3232i | 1.18645 | − | 1.18645i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 14.2672i | − | 0.790188i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.20648 | − | 6.20648i | −0.342696 | − | 0.342696i | ||||
\(329\) | −4.84909 | −0.267339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.1849 | 0.669745 | 0.334872 | − | 0.942263i | \(-0.391307\pi\) | ||||
0.334872 | + | 0.942263i | \(0.391307\pi\) | |||||||
\(332\) | −2.35640 | − | 2.35640i | −0.129324 | − | 0.129324i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 4.68556i | − | 0.256383i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8403 | − | 14.8403i | 0.808401 | − | 0.808401i | −0.175991 | − | 0.984392i | \(-0.556313\pi\) |
0.984392 | + | 0.175991i | \(0.0563129\pi\) | |||||||
\(338\) | 3.39355 | − | 3.39355i | 0.184585 | − | 0.184585i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.8642i | 0.913249i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 0.247285 | 0.0133327 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.5644 | −0.675466 | ||||||||
\(347\) | 13.5731 | + | 13.5731i | 0.728642 | + | 0.728642i | 0.970349 | − | 0.241707i | \(-0.0777073\pi\) |
−0.241707 | + | 0.970349i | \(0.577707\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.9467i | 1.28184i | 0.767608 | + | 0.640920i | \(0.221447\pi\) | ||||
−0.767608 | + | 0.640920i | \(0.778553\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.41421 | + | 2.41421i | −0.128678 | + | 0.128678i | ||||
\(353\) | −17.0693 | + | 17.0693i | −0.908508 | + | 0.908508i | −0.996152 | − | 0.0876442i | \(-0.972066\pi\) |
0.0876442 | + | 0.996152i | \(0.472066\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.07055i | 0.215739i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.4341 | + | 17.4341i | 0.921423 | + | 0.921423i | ||||
\(359\) | −11.9223 | −0.629236 | −0.314618 | − | 0.949218i | \(-0.601876\pi\) | ||||
−0.314618 | + | 0.949218i | \(0.601876\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.79796 | −0.252524 | ||||||||
\(362\) | −9.36433 | − | 9.36433i | −0.492178 | − | 0.492178i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 2.86370i | − | 0.150099i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.6572 | + | 17.6572i | −0.921699 | + | 0.921699i | −0.997150 | − | 0.0754503i | \(-0.975961\pi\) |
0.0754503 | + | 0.997150i | \(0.475961\pi\) | |||||||
\(368\) | 3.74238 | − | 3.74238i | 0.195085 | − | 0.195085i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 9.10634i | − | 0.472778i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.7980 | − | 16.7980i | −0.869765 | − | 0.869765i | 0.122681 | − | 0.992446i | \(-0.460851\pi\) |
−0.992446 | + | 0.122681i | \(0.960851\pi\) | |||||||
\(374\) | −21.1051 | −1.09132 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.84909 | −0.250073 | ||||||||
\(377\) | 10.5638 | + | 10.5638i | 0.544061 | + | 0.544061i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 14.7821i | − | 0.759306i | −0.925129 | − | 0.379653i | \(-0.876043\pi\) | ||
0.925129 | − | 0.379653i | \(-0.123957\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.9461 | − | 13.9461i | 0.713545 | − | 0.713545i | ||||
\(383\) | 19.2573 | − | 19.2573i | 0.984000 | − | 0.984000i | −0.0158744 | − | 0.999874i | \(-0.505053\pi\) |
0.999874 | + | 0.0158744i | \(0.00505318\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.92016i | 0.504923i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.64564 | − | 5.64564i | −0.286614 | − | 0.286614i | ||||
\(389\) | 7.50397 | 0.380466 | 0.190233 | − | 0.981739i | \(-0.439076\pi\) | ||||
0.190233 | + | 0.981739i | \(0.439076\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.7160 | 1.65452 | ||||||||
\(392\) | 0.707107 | + | 0.707107i | 0.0357143 | + | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.8045i | 1.24963i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.67324 | + | 7.67324i | −0.385109 | + | 0.385109i | −0.872939 | − | 0.487830i | \(-0.837789\pi\) |
0.487830 | + | 0.872939i | \(0.337789\pi\) | |||||||
\(398\) | −11.2913 | + | 11.2913i | −0.565981 | + | 0.565981i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.80828i | − | 0.0903011i | −0.998980 | − | 0.0451506i | \(-0.985623\pi\) | ||
0.998980 | − | 0.0451506i | \(-0.0143768\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0020 | − | 10.0020i | −0.498237 | − | 0.498237i | ||||
\(404\) | 4.91484 | 0.244522 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.21682 | −0.258906 | ||||||||
\(407\) | 23.4840 | + | 23.4840i | 1.16406 | + | 1.16406i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.3440i | 1.74765i | 0.486243 | + | 0.873824i | \(0.338367\pi\) | ||||
−0.486243 | + | 0.873824i | \(0.661633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.07019 | + | 8.07019i | −0.397590 | + | 0.397590i | ||||
\(413\) | −1.57545 | + | 1.57545i | −0.0775230 | + | 0.0775230i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 2.86370i | − | 0.140405i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11.7773 | + | 11.7773i | 0.576046 | + | 0.576046i | ||||
\(419\) | 27.4979 | 1.34336 | 0.671681 | − | 0.740841i | \(-0.265573\pi\) | ||||
0.671681 | + | 0.740841i | \(0.265573\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.86194 | −0.285694 | −0.142847 | − | 0.989745i | \(-0.545626\pi\) | ||||
−0.142847 | + | 0.989745i | \(0.545626\pi\) | |||||||
\(422\) | −18.5747 | − | 18.5747i | −0.904203 | − | 0.904203i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 9.10634i | − | 0.442243i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.7852 | − | 10.7852i | 0.521934 | − | 0.521934i | ||||
\(428\) | 5.77729 | − | 5.77729i | 0.279256 | − | 0.279256i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 21.4794i | − | 1.03463i | −0.855796 | − | 0.517313i | \(-0.826932\pi\) | ||
0.855796 | − | 0.517313i | \(-0.173068\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.0406 | + | 16.0406i | 0.770862 | + | 0.770862i | 0.978257 | − | 0.207395i | \(-0.0664986\pi\) |
−0.207395 | + | 0.978257i | \(0.566499\pi\) | |||||||
\(434\) | 4.93942 | 0.237100 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.07712 | 0.291041 | ||||||||
\(437\) | −18.2565 | − | 18.2565i | −0.873328 | − | 0.873328i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.8583i | 0.565967i | 0.959125 | + | 0.282984i | \(0.0913242\pi\) | ||||
−0.959125 | + | 0.282984i | \(0.908676\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.5173 | − | 12.5173i | 0.595386 | − | 0.595386i | ||||
\(443\) | −19.9223 | + | 19.9223i | −0.946538 | + | 0.946538i | −0.998642 | − | 0.0521039i | \(-0.983407\pi\) |
0.0521039 | + | 0.998642i | \(0.483407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 17.8277i | 0.844166i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.707107 | + | 0.707107i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | 23.6138 | 1.11440 | 0.557201 | − | 0.830377i | \(-0.311875\pi\) | ||||
0.557201 | + | 0.830377i | \(0.311875\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.9676 | 1.41112 | ||||||||
\(452\) | −6.76733 | − | 6.76733i | −0.318308 | − | 0.318308i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 4.28205i | − | 0.200966i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.4150 | − | 19.4150i | 0.908196 | − | 0.908196i | −0.0879308 | − | 0.996127i | \(-0.528025\pi\) |
0.996127 | + | 0.0879308i | \(0.0280254\pi\) | |||||||
\(458\) | −2.47871 | + | 2.47871i | −0.115823 | + | 0.115823i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 29.8406i | − | 1.38981i | −0.719100 | − | 0.694906i | \(-0.755446\pi\) | ||
0.719100 | − | 0.694906i | \(-0.244554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.13505 | − | 9.13505i | −0.424542 | − | 0.424542i | 0.462222 | − | 0.886764i | \(-0.347052\pi\) |
−0.886764 | + | 0.462222i | \(0.847052\pi\) | |||||||
\(464\) | −5.21682 | −0.242185 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.7007 | 0.588348 | ||||||||
\(467\) | 2.03591 | + | 2.03591i | 0.0942106 | + | 0.0942106i | 0.752641 | − | 0.658431i | \(-0.228779\pi\) |
−0.658431 | + | 0.752641i | \(0.728779\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.39355i | 0.249051i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.57545 | + | 1.57545i | −0.0725162 | + | 0.0725162i | ||||
\(473\) | −0.596999 | + | 0.596999i | −0.0274500 | + | 0.0274500i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.18154i | 0.283330i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.6569 | − | 11.6569i | −0.533172 | − | 0.533172i | ||||
\(479\) | −38.9202 | −1.77831 | −0.889154 | − | 0.457608i | \(-0.848706\pi\) | ||||
−0.889154 | + | 0.457608i | \(0.848706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.8564 | −1.27014 | ||||||||
\(482\) | 19.6702 | + | 19.6702i | 0.895954 | + | 0.895954i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 0.656854i | − | 0.0298570i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.6040 | − | 23.6040i | 1.06960 | − | 1.06960i | 0.0722080 | − | 0.997390i | \(-0.476995\pi\) |
0.997390 | − | 0.0722080i | \(-0.0230045\pi\) | |||||||
\(488\) | 10.7852 | − | 10.7852i | 0.488224 | − | 0.488224i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.4735i | − | 1.19473i | −0.801969 | − | 0.597366i | \(-0.796214\pi\) | ||
0.801969 | − | 0.597366i | \(-0.203786\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.8028 | − | 22.8028i | −1.02698 | − | 1.02698i | ||||
\(494\) | −13.9700 | −0.628542 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.93942 | 0.221786 | ||||||||
\(497\) | 7.72741 | + | 7.72741i | 0.346622 | + | 0.346622i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 40.3855i | − | 1.80790i | −0.427634 | − | 0.903952i | \(-0.640653\pi\) | ||
0.427634 | − | 0.903952i | \(-0.359347\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.96776 | − | 5.96776i | 0.266354 | − | 0.266354i | ||||
\(503\) | 18.8113 | − | 18.8113i | 0.838756 | − | 0.838756i | −0.149940 | − | 0.988695i | \(-0.547908\pi\) |
0.988695 | + | 0.149940i | \(0.0479079\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 18.0698i | 0.803302i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.0345 | − | 11.0345i | −0.489579 | − | 0.489579i | ||||
\(509\) | −28.6793 | −1.27119 | −0.635594 | − | 0.772024i | \(-0.719245\pi\) | ||||
−0.635594 | + | 0.772024i | \(0.719245\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.55051 | 0.157065 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.8279i | 0.918678i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.7067 | − | 11.7067i | 0.514862 | − | 0.514862i | ||||
\(518\) | 6.87832 | − | 6.87832i | 0.302216 | − | 0.302216i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.4916i | 0.722509i | 0.932467 | + | 0.361254i | \(0.117651\pi\) | ||||
−0.932467 | + | 0.361254i | \(0.882349\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.8596 | + | 22.8596i | 0.999579 | + | 0.999579i | 1.00000 | 0.000420508i | \(-0.000133852\pi\) | |
−0.000420508 | 1.00000i | \(0.500134\pi\) | ||||||||
\(524\) | 2.41370 | 0.105443 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.84961 | 0.211453 | ||||||||
\(527\) | 21.5902 | + | 21.5902i | 0.940485 | + | 0.940485i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 5.01086i | − | 0.217863i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.44949 | − | 3.44949i | 0.149554 | − | 0.149554i | ||||
\(533\) | −17.7735 | + | 17.7735i | −0.769857 | + | 0.769857i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.39355i | 0.232966i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.77249 | + | 3.77249i | 0.162643 | + | 0.162643i | ||||
\(539\) | −3.41421 | −0.147061 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.4412 | 1.30877 | 0.654385 | − | 0.756161i | \(-0.272927\pi\) | ||||
0.654385 | + | 0.756161i | \(0.272927\pi\) | |||||||
\(542\) | 12.0547 | + | 12.0547i | 0.517794 | + | 0.517794i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.18154i | 0.265031i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.9103 | − | 22.9103i | 0.979574 | − | 0.979574i | −0.0202215 | − | 0.999796i | \(-0.506437\pi\) |
0.999796 | + | 0.0202215i | \(0.00643715\pi\) | |||||||
\(548\) | 9.39836 | − | 9.39836i | 0.401478 | − | 0.401478i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.4493i | 1.08418i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.05986 | − | 7.05986i | −0.300216 | − | 0.300216i | ||||
\(554\) | −8.99948 | −0.382351 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.2621 | 0.477618 | ||||||||
\(557\) | 4.43612 | + | 4.43612i | 0.187965 | + | 0.187965i | 0.794816 | − | 0.606851i | \(-0.207568\pi\) |
−0.606851 | + | 0.794816i | \(0.707568\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.708151i | − | 0.0299516i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.34315 | + | 4.34315i | −0.183205 | + | 0.183205i | ||||
\(563\) | 8.80589 | − | 8.80589i | 0.371124 | − | 0.371124i | −0.496763 | − | 0.867886i | \(-0.665478\pi\) |
0.867886 | + | 0.496763i | \(0.165478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 20.4495i | 0.859556i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.72741 | + | 7.72741i | 0.324235 | + | 0.324235i | ||||
\(569\) | −17.6654 | −0.740573 | −0.370286 | − | 0.928918i | \(-0.620740\pi\) | ||||
−0.370286 | + | 0.928918i | \(0.620740\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.9852 | 1.29669 | 0.648345 | − | 0.761347i | \(-0.275462\pi\) | ||||
0.648345 | + | 0.761347i | \(0.275462\pi\) | |||||||
\(572\) | 6.91359 | + | 6.91359i | 0.289072 | + | 0.289072i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 8.77729i | − | 0.366357i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.4860 | + | 16.4860i | −0.686322 | + | 0.686322i | −0.961417 | − | 0.275095i | \(-0.911291\pi\) |
0.275095 | + | 0.961417i | \(0.411291\pi\) | |||||||
\(578\) | −14.9988 | + | 14.9988i | −0.623866 | + | 0.623866i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 3.33245i | − | 0.138253i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.9847 | + | 21.9847i | 0.910512 | + | 0.910512i | ||||
\(584\) | 3.55051 | 0.146921 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.03047 | −0.207807 | ||||||||
\(587\) | 29.4681 | + | 29.4681i | 1.21628 | + | 1.21628i | 0.968926 | + | 0.247351i | \(0.0795602\pi\) |
0.247351 | + | 0.968926i | \(0.420440\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 24.0960i | − | 0.992859i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.87832 | − | 6.87832i | 0.282697 | − | 0.282697i | ||||
\(593\) | 22.7874 | − | 22.7874i | 0.935767 | − | 0.935767i | −0.0622906 | − | 0.998058i | \(-0.519841\pi\) |
0.998058 | + | 0.0622906i | \(0.0198406\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.18759i | 0.130569i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.7171 | − | 10.7171i | −0.438254 | − | 0.438254i | ||||
\(599\) | 34.9314 | 1.42726 | 0.713629 | − | 0.700524i | \(-0.247050\pi\) | ||||
0.713629 | + | 0.700524i | \(0.247050\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.8254 | −1.62451 | −0.812256 | − | 0.583301i | \(-0.801761\pi\) | ||||
−0.812256 | + | 0.583301i | \(0.801761\pi\) | |||||||
\(602\) | 0.174857 | + | 0.174857i | 0.00712663 | + | 0.00712663i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.80725i | 0.0735359i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.7675 | + | 22.7675i | −0.924104 | + | 0.924104i | −0.997316 | − | 0.0732124i | \(-0.976675\pi\) |
0.0732124 | + | 0.997316i | \(0.476675\pi\) | |||||||
\(608\) | 3.44949 | − | 3.44949i | 0.139895 | − | 0.139895i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.8864i | 0.561782i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.99446 | − | 3.99446i | −0.161335 | − | 0.161335i | 0.621823 | − | 0.783158i | \(-0.286392\pi\) |
−0.783158 | + | 0.621823i | \(0.786392\pi\) | |||||||
\(614\) | 6.11971 | 0.246971 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.41421 | −0.137563 | ||||||||
\(617\) | −1.46002 | − | 1.46002i | −0.0587783 | − | 0.0587783i | 0.677107 | − | 0.735885i | \(-0.263234\pi\) |
−0.735885 | + | 0.677107i | \(0.763234\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.4138i | 1.90572i | 0.303407 | + | 0.952861i | \(0.401876\pi\) | ||||
−0.303407 | + | 0.952861i | \(0.598124\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.61302 | + | 2.61302i | −0.104773 | + | 0.104773i | ||||
\(623\) | −2.87832 | + | 2.87832i | −0.115317 | + | 0.115317i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 18.8642i | − | 0.753966i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.8577 | − | 12.8577i | −0.513076 | − | 0.513076i | ||||
\(629\) | 60.1304 | 2.39755 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.98665 | 0.198515 | 0.0992577 | − | 0.995062i | \(-0.468353\pi\) | ||||
0.0992577 | + | 0.995062i | \(0.468353\pi\) | |||||||
\(632\) | −7.05986 | − | 7.05986i | −0.280826 | − | 0.280826i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 19.1769i | − | 0.761612i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.02494 | − | 2.02494i | 0.0802312 | − | 0.0802312i | ||||
\(638\) | 12.5945 | − | 12.5945i | 0.498621 | − | 0.498621i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.4961i | 1.48101i | 0.672052 | + | 0.740504i | \(0.265413\pi\) | ||||
−0.672052 | + | 0.740504i | \(0.734587\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.58970 | − | 4.58970i | −0.181000 | − | 0.181000i | 0.610791 | − | 0.791792i | \(-0.290851\pi\) |
−0.791792 | + | 0.610791i | \(0.790851\pi\) | |||||||
\(644\) | 5.29253 | 0.208555 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 30.1555 | 1.18645 | ||||||||
\(647\) | −27.4412 | − | 27.4412i | −1.07883 | − | 1.07883i | −0.996615 | − | 0.0822112i | \(-0.973802\pi\) |
−0.0822112 | − | 0.996615i | \(-0.526198\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7.60697i | − | 0.298600i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0884 | − | 10.0884i | 0.395094 | − | 0.395094i | ||||
\(653\) | −13.3212 | + | 13.3212i | −0.521300 | + | 0.521300i | −0.917964 | − | 0.396664i | \(-0.870168\pi\) |
0.396664 | + | 0.917964i | \(0.370168\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 8.77729i | − | 0.342696i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.42883 | − | 3.42883i | −0.133670 | − | 0.133670i | ||||
\(659\) | 13.9355 | 0.542851 | 0.271425 | − | 0.962459i | \(-0.412505\pi\) | ||||
0.271425 | + | 0.962459i | \(0.412505\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.5879 | 1.50089 | 0.750447 | − | 0.660930i | \(-0.229838\pi\) | ||||
0.750447 | + | 0.660930i | \(0.229838\pi\) | |||||||
\(662\) | 8.61605 | + | 8.61605i | 0.334872 | + | 0.334872i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 3.33245i | − | 0.129324i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.5233 | + | 19.5233i | −0.755946 | + | 0.755946i | ||||
\(668\) | 3.31319 | − | 3.31319i | 0.128191 | − | 0.128191i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 52.0757i | 2.01036i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.1223 | − | 28.1223i | −1.08403 | − | 1.08403i | −0.996129 | − | 0.0879048i | \(-0.971983\pi\) |
−0.0879048 | − | 0.996129i | \(-0.528017\pi\) | |||||||
\(674\) | 20.9873 | 0.808401 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.79920 | 0.184585 | ||||||||
\(677\) | 22.7408 | + | 22.7408i | 0.873999 | + | 0.873999i | 0.992905 | − | 0.118907i | \(-0.0379389\pi\) |
−0.118907 | + | 0.992905i | \(0.537939\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 7.98414i | − | 0.306403i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.9248 | + | 11.9248i | −0.456624 | + | 0.456624i | ||||
\(683\) | 11.9549 | − | 11.9549i | 0.457442 | − | 0.457442i | −0.440373 | − | 0.897815i | \(-0.645154\pi\) |
0.897815 | + | 0.440373i | \(0.145154\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.174857 | + | 0.174857i | 0.00666635 | + | 0.00666635i | ||||
\(689\) | −26.0779 | −0.993488 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.79167 | 0.258367 | 0.129184 | − | 0.991621i | \(-0.458764\pi\) | ||||
0.129184 | + | 0.991621i | \(0.458764\pi\) | |||||||
\(692\) | −8.88437 | − | 8.88437i | −0.337733 | − | 0.337733i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.1953i | 0.728642i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.3656 | − | 38.3656i | 1.45320 | − | 1.45320i | ||||
\(698\) | −16.9329 | + | 16.9329i | −0.640920 | + | 0.640920i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.7354i | 1.53855i | 0.638915 | + | 0.769277i | \(0.279383\pi\) | ||||
−0.638915 | + | 0.769277i | \(0.720617\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.5546 | − | 33.5546i | −1.26554 | − | 1.26554i | ||||
\(704\) | −3.41421 | −0.128678 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.1396 | −0.908508 | ||||||||
\(707\) | 3.47531 | + | 3.47531i | 0.130703 | + | 0.130703i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.8035i | 1.15685i | 0.815735 | + | 0.578425i | \(0.196333\pi\) | ||||
−0.815735 | + | 0.578425i | \(0.803667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.87832 | + | 2.87832i | −0.107869 | + | 0.107869i | ||||
\(713\) | 18.4852 | − | 18.4852i | 0.692276 | − | 0.692276i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.6556i | 0.921423i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.43035 | − | 8.43035i | −0.314618 | − | 0.314618i | ||||
\(719\) | 13.0945 | 0.488341 | 0.244170 | − | 0.969732i | \(-0.421484\pi\) | ||||
0.244170 | + | 0.969732i | \(0.421484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.4130 | −0.425041 | ||||||||
\(722\) | −3.39267 | − | 3.39267i | −0.126262 | − | 0.126262i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 13.2432i | − | 0.492178i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.4418 | − | 34.4418i | 1.27738 | − | 1.27738i | 0.335246 | − | 0.942131i | \(-0.391181\pi\) |
0.942131 | − | 0.335246i | \(-0.108819\pi\) | |||||||
\(728\) | 2.02494 | − | 2.02494i | 0.0750494 | − | 0.0750494i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.52860i | 0.0565374i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.9524 | − | 20.9524i | −0.773895 | − | 0.773895i | 0.204890 | − | 0.978785i | \(-0.434316\pi\) |
−0.978785 | + | 0.204890i | \(0.934316\pi\) | |||||||
\(734\) | −24.9711 | −0.921699 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.29253 | 0.195085 | ||||||||
\(737\) | −13.0212 | − | 13.0212i | −0.479641 | − | 0.479641i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.0850i | 1.87919i | 0.342288 | + | 0.939595i | \(0.388798\pi\) | ||||
−0.342288 | + | 0.939595i | \(0.611202\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.43916 | − | 6.43916i | 0.236389 | − | 0.236389i | ||||
\(743\) | −23.2763 | + | 23.2763i | −0.853925 | + | 0.853925i | −0.990614 | − | 0.136689i | \(-0.956354\pi\) |
0.136689 | + | 0.990614i | \(0.456354\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 23.7559i | − | 0.869765i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.9236 | − | 14.9236i | −0.545659 | − | 0.545659i | ||||
\(749\) | 8.17033 | 0.298537 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.7035 | 0.609520 | 0.304760 | − | 0.952429i | \(-0.401424\pi\) | ||||
0.304760 | + | 0.952429i | \(0.401424\pi\) | |||||||
\(752\) | −3.42883 | − | 3.42883i | −0.125036 | − | 0.125036i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.9394i | 0.544061i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.56461 | − | 6.56461i | 0.238595 | − | 0.238595i | −0.577673 | − | 0.816268i | \(-0.696039\pi\) |
0.816268 | + | 0.577673i | \(0.196039\pi\) | |||||||
\(758\) | 10.4525 | − | 10.4525i | 0.379653 | − | 0.379653i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.4642i | 1.68433i | 0.539223 | + | 0.842163i | \(0.318718\pi\) | ||||
−0.539223 | + | 0.842163i | \(0.681282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.29717 | + | 4.29717i | 0.155568 | + | 0.155568i | ||||
\(764\) | 19.7228 | 0.713545 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.2339 | 0.984000 | ||||||||
\(767\) | 4.51163 | + | 4.51163i | 0.162906 | + | 0.162906i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 39.1177i | − | 1.41062i | −0.708898 | − | 0.705311i | \(-0.750807\pi\) | ||
0.708898 | − | 0.705311i | \(-0.249193\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.01461 | + | 7.01461i | −0.252461 | + | 0.252461i | ||||
\(773\) | 4.88918 | − | 4.88918i | 0.175851 | − | 0.175851i | −0.613693 | − | 0.789545i | \(-0.710317\pi\) |
0.789545 | + | 0.613693i | \(0.210317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 7.98414i | − | 0.286614i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.30611 | + | 5.30611i | 0.190233 | + | 0.190233i | ||||
\(779\) | −42.8184 | −1.53413 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.3112 | −1.33510 | ||||||||
\(782\) | 23.1337 | + | 23.1337i | 0.827259 | + | 0.827259i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.6549 | − | 10.6549i | 0.379805 | − | 0.379805i | −0.491226 | − | 0.871032i | \(-0.663451\pi\) |
0.871032 | + | 0.491226i | \(0.163451\pi\) | |||||||
\(788\) | −17.5394 | + | 17.5394i | −0.624817 | + | 0.624817i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 9.57045i | − | 0.340286i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.8857 | − | 30.8857i | −1.09678 | − | 1.09678i | ||||
\(794\) | −10.8516 | −0.385109 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.9683 | −0.565981 | ||||||||
\(797\) | −8.27135 | − | 8.27135i | −0.292986 | − | 0.292986i | 0.545273 | − | 0.838259i | \(-0.316426\pi\) |
−0.838259 | + | 0.545273i | \(0.816426\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 29.9749i | − | 1.06043i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.27865 | − | 1.27865i | 0.0451506 | − | 0.0451506i | ||||
\(803\) | −8.57169 | + | 8.57169i | −0.302488 | + | 0.302488i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 14.1450i | − | 0.498237i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.47531 | + | 3.47531i | 0.122261 | + | 0.122261i | ||||
\(809\) | 28.7785 | 1.01180 | 0.505900 | − | 0.862592i | \(-0.331161\pi\) | ||||
0.505900 | + | 0.862592i | \(0.331161\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.8874 | 0.698341 | 0.349170 | − | 0.937059i | \(-0.386463\pi\) | ||||
0.349170 | + | 0.937059i | \(0.386463\pi\) | |||||||
\(812\) | −3.68885 | − | 3.68885i | −0.129453 | − | 0.129453i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 33.2114i | 1.16406i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.853007 | − | 0.853007i | 0.0298429 | − | 0.0298429i | ||||
\(818\) | −24.9920 | + | 24.9920i | −0.873824 | + | 0.873824i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.3394i | 0.884352i | 0.896928 | + | 0.442176i | \(0.145793\pi\) | ||||
−0.896928 | + | 0.442176i | \(0.854207\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.0270 | + | 22.0270i | 0.767814 | + | 0.767814i | 0.977721 | − | 0.209908i | \(-0.0673163\pi\) |
−0.209908 | + | 0.977721i | \(0.567316\pi\) | |||||||
\(824\) | −11.4130 | −0.397590 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.22803 | −0.0775230 | ||||||||
\(827\) | −3.83272 | − | 3.83272i | −0.133277 | − | 0.133277i | 0.637321 | − | 0.770598i | \(-0.280042\pi\) |
−0.770598 | + | 0.637321i | \(0.780042\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.3021i | 1.36502i | 0.730877 | + | 0.682509i | \(0.239111\pi\) | ||||
−0.730877 | + | 0.682509i | \(0.760889\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.02494 | − | 2.02494i | 0.0702023 | − | 0.0702023i | ||||
\(833\) | −4.37101 | + | 4.37101i | −0.151446 | + | 0.151446i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.6556i | 0.576046i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.4440 | + | 19.4440i | 0.671681 | + | 0.671681i | ||||
\(839\) | −47.1174 | −1.62667 | −0.813337 | − | 0.581792i | \(-0.802352\pi\) | ||||
−0.813337 | + | 0.581792i | \(0.802352\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.78482 | −0.0615456 | ||||||||
\(842\) | −4.14502 | − | 4.14502i | −0.142847 | − | 0.142847i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 26.2686i | − | 0.904203i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.464466 | − | 0.464466i | 0.0159592 | − | 0.0159592i | ||||
\(848\) | 6.43916 | − | 6.43916i | 0.221122 | − | 0.221122i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 51.4826i | − | 1.76480i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.5412 | − | 10.5412i | −0.360924 | − | 0.360924i | 0.503229 | − | 0.864153i | \(-0.332145\pi\) |
−0.864153 | + | 0.503229i | \(0.832145\pi\) | |||||||
\(854\) | 15.2526 | 0.521934 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.17033 | 0.279256 | ||||||||
\(857\) | −30.2006 | − | 30.2006i | −1.03163 | − | 1.03163i | −0.999483 | − | 0.0321492i | \(-0.989765\pi\) |
−0.0321492 | − | 0.999483i | \(-0.510235\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 16.5437i | − | 0.564465i | −0.959346 | − | 0.282232i | \(-0.908925\pi\) | ||
0.959346 | − | 0.282232i | \(-0.0910749\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.1882 | − | 15.1882i | 0.517313 | − | 0.517313i | ||||
\(863\) | 8.61783 | − | 8.61783i | 0.293354 | − | 0.293354i | −0.545050 | − | 0.838404i | \(-0.683489\pi\) |
0.838404 | + | 0.545050i | \(0.183489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22.6848i | 0.770862i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.49269 | + | 3.49269i | 0.118550 | + | 0.118550i | ||||
\(869\) | 34.0880 | 1.15636 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.4455 | 0.523352 | ||||||||
\(872\) | 4.29717 | + | 4.29717i | 0.145521 | + | 0.145521i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 25.8186i | − | 0.873328i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.75539 | − | 4.75539i | 0.160578 | − | 0.160578i | −0.622245 | − | 0.782823i | \(-0.713779\pi\) |
0.782823 | + | 0.622245i | \(0.213779\pi\) | |||||||
\(878\) | −8.38511 | + | 8.38511i | −0.282984 | + | 0.282984i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.5569i | 0.658888i | 0.944175 | + | 0.329444i | \(0.106861\pi\) | ||||
−0.944175 | + | 0.329444i | \(0.893139\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.46863 | + | 1.46863i | 0.0494233 | + | 0.0494233i | 0.731387 | − | 0.681963i | \(-0.238874\pi\) |
−0.681963 | + | 0.731387i | \(0.738874\pi\) | |||||||
\(884\) | 17.7021 | 0.595386 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.1744 | −0.946538 | ||||||||
\(887\) | 20.5833 | + | 20.5833i | 0.691119 | + | 0.691119i | 0.962478 | − | 0.271359i | \(-0.0874730\pi\) |
−0.271359 | + | 0.962478i | \(0.587473\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 15.6052i | − | 0.523382i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.6061 | + | 12.6061i | −0.422083 | + | 0.422083i | ||||
\(893\) | −16.7269 | + | 16.7269i | −0.559744 | + | 0.559744i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.6975 | + | 16.6975i | 0.557201 | + | 0.557201i | ||||
\(899\) | −25.7680 | −0.859412 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.2912 | 1.87533 | ||||||||
\(902\) | 21.1903 | + | 21.1903i | 0.705559 | + | 0.705559i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 9.57045i | − | 0.318308i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5032 | − | 18.5032i | 0.614388 | − | 0.614388i | −0.329698 | − | 0.944086i | \(-0.606947\pi\) |
0.944086 | + | 0.329698i | \(0.106947\pi\) | |||||||
\(908\) | 3.02786 | − | 3.02786i | 0.100483 | − | 0.100483i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 7.35968i | − | 0.243837i | −0.992540 | − | 0.121919i | \(-0.961095\pi\) | ||
0.992540 | − | 0.121919i | \(-0.0389047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.04524 | + | 8.04524i | 0.266259 | + | 0.266259i | ||||
\(914\) | 27.4570 | 0.908196 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.50543 | −0.115823 | ||||||||
\(917\) | 1.70674 | + | 1.70674i | 0.0563616 | + | 0.0563616i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.7527i | 0.618593i | 0.950966 | + | 0.309297i | \(0.100094\pi\) | ||||
−0.950966 | + | 0.309297i | \(0.899906\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 21.1005 | − | 21.1005i | 0.694906 | − | 0.694906i | ||||
\(923\) | 22.1290 | − | 22.1290i | 0.728385 | − | 0.728385i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 12.9189i | − | 0.424542i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.68885 | − | 3.68885i | −0.121092 | − | 0.121092i | ||||
\(929\) | −25.9196 | −0.850396 | −0.425198 | − | 0.905100i | \(-0.639796\pi\) | ||||
−0.425198 | + | 0.905100i | \(0.639796\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.87832 | 0.159880 | ||||||||
\(932\) | 8.98074 | + | 8.98074i | 0.294174 | + | 0.294174i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.87921i | 0.0942106i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.24994 | − | 6.24994i | 0.204177 | − | 0.204177i | −0.597610 | − | 0.801787i | \(-0.703883\pi\) |
0.801787 | + | 0.597610i | \(0.203883\pi\) | |||||||
\(938\) | −3.81382 | + | 3.81382i | −0.124525 | + | 0.124525i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.7955i | 1.55809i | 0.626969 | + | 0.779044i | \(0.284295\pi\) | ||||
−0.626969 | + | 0.779044i | \(0.715705\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.8480 | − | 32.8480i | −1.06968 | − | 1.06968i | ||||
\(944\) | −2.22803 | −0.0725162 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.844283 | −0.0274500 | ||||||||
\(947\) | −7.01173 | − | 7.01173i | −0.227851 | − | 0.227851i | 0.583944 | − | 0.811794i | \(-0.301509\pi\) |
−0.811794 | + | 0.583944i | \(0.801509\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 10.1676i | − | 0.330055i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.37101 | + | 4.37101i | −0.141665 | + | 0.141665i | ||||
\(953\) | 4.50419 | − | 4.50419i | 0.145905 | − | 0.145905i | −0.630381 | − | 0.776286i | \(-0.717101\pi\) |
0.776286 | + | 0.630381i | \(0.217101\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 16.4853i | − | 0.533172i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −27.5207 | − | 27.5207i | −0.889154 | − | 0.889154i | ||||
\(959\) | 13.2913 | 0.429198 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.60218 | −0.212973 | ||||||||
\(962\) | −19.6975 | − | 19.6975i | −0.635071 | − | 0.635071i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 27.8179i | 0.895954i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.4951 | − | 10.4951i | 0.337499 | − | 0.337499i | −0.517926 | − | 0.855425i | \(-0.673296\pi\) |
0.855425 | + | 0.517926i | \(0.173296\pi\) | |||||||
\(968\) | 0.464466 | − | 0.464466i | 0.0149285 | − | 0.0149285i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 6.79671i | − | 0.218117i | −0.994035 | − | 0.109058i | \(-0.965216\pi\) | ||
0.994035 | − | 0.109058i | \(-0.0347836\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.96348 | + | 7.96348i | 0.255297 | + | 0.255297i | ||||
\(974\) | 33.3810 | 1.06960 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.2526 | 0.488224 | ||||||||
\(977\) | −12.0348 | − | 12.0348i | −0.385026 | − | 0.385026i | 0.487883 | − | 0.872909i | \(-0.337769\pi\) |
−0.872909 | + | 0.487883i | \(0.837769\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 13.8977i | − | 0.444174i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.7196 | − | 18.7196i | 0.597366 | − | 0.597366i | ||||
\(983\) | 39.3016 | − | 39.3016i | 1.25353 | − | 1.25353i | 0.299398 | − | 0.954128i | \(-0.403214\pi\) |
0.954128 | − | 0.299398i | \(-0.0967859\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 32.2480i | − | 1.02698i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.87832 | − | 9.87832i | −0.314271 | − | 0.314271i | ||||
\(989\) | 1.30876 | 0.0416162 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.6002 | −0.908516 | −0.454258 | − | 0.890870i | \(-0.650096\pi\) | ||||
−0.454258 | + | 0.890870i | \(0.650096\pi\) | |||||||
\(992\) | 3.49269 | + | 3.49269i | 0.110893 | + | 0.110893i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.9282i | 0.346622i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.3736 | + | 13.3736i | −0.423547 | + | 0.423547i | −0.886423 | − | 0.462876i | \(-0.846817\pi\) |
0.462876 | + | 0.886423i | \(0.346817\pi\) | |||||||
\(998\) | 28.5569 | − | 28.5569i | 0.903952 | − | 0.903952i | ||||
\(999\) | 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 | 3150.2.m.k.2843.4 | yes | 8 | |
3.2 | odd | 2 | 3150.2.m.l.2843.2 | yes | 8 | ||
5.2 | odd | 4 | 3150.2.m.l.1457.2 | yes | 8 | ||
5.3 | odd | 4 | 3150.2.m.h.1457.3 | yes | 8 | ||
5.4 | even | 2 | 3150.2.m.g.2843.1 | yes | 8 | ||
15.2 | even | 4 | inner | 3150.2.m.k.1457.4 | yes | 8 | |
15.8 | even | 4 | 3150.2.m.g.1457.1 | ✓ | 8 | ||
15.14 | odd | 2 | 3150.2.m.h.2843.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.m.g.1457.1 | ✓ | 8 | 15.8 | even | 4 | ||
3150.2.m.g.2843.1 | yes | 8 | 5.4 | even | 2 | ||
3150.2.m.h.1457.3 | yes | 8 | 5.3 | odd | 4 | ||
3150.2.m.h.2843.3 | yes | 8 | 15.14 | odd | 2 | ||
3150.2.m.k.1457.4 | yes | 8 | 15.2 | even | 4 | inner | |
3150.2.m.k.2843.4 | yes | 8 | 1.1 | even | 1 | trivial | |
3150.2.m.l.1457.2 | yes | 8 | 5.2 | odd | 4 | ||
3150.2.m.l.2843.2 | yes | 8 | 3.2 | odd | 2 |