Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(107,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.f (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: | \(10.7798042729\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.2 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.593 |
Dual form | 1350.2.f.a.107.2 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.366025 | − | 0.366025i | 0.138345 | − | 0.138345i | −0.634543 | − | 0.772888i | \(-0.718812\pi\) |
0.772888 | + | 0.634543i | \(0.218812\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.76028i | 1.43528i | 0.696415 | + | 0.717639i | \(0.254777\pi\) | ||||
−0.696415 | + | 0.717639i | \(0.745223\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.46410 | − | 3.46410i | −0.960769 | − | 0.960769i | 0.0384901 | − | 0.999259i | \(-0.487745\pi\) |
−0.999259 | + | 0.0384901i | \(0.987745\pi\) | |||||||
\(14\) | −0.517638 | −0.138345 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.03528 | + | 1.03528i | 0.251091 | + | 0.251091i | 0.821418 | − | 0.570327i | \(-0.193183\pi\) |
−0.570327 | + | 0.821418i | \(0.693183\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.46410i | − | 1.71238i | −0.516659 | − | 0.856191i | \(-0.672825\pi\) | ||
0.516659 | − | 0.856191i | \(-0.327175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.36603 | − | 3.36603i | 0.717639 | − | 0.717639i | ||||
\(23\) | 1.41421 | − | 1.41421i | 0.294884 | − | 0.294884i | −0.544122 | − | 0.839006i | \(-0.683137\pi\) |
0.839006 | + | 0.544122i | \(0.183137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.89898i | 0.960769i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.366025 | + | 0.366025i | 0.0691723 | + | 0.0691723i | ||||
\(29\) | 6.31319 | 1.17233 | 0.586165 | − | 0.810192i | \(-0.300637\pi\) | ||||
0.586165 | + | 0.810192i | \(0.300637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.66025 | 1.19622 | 0.598108 | − | 0.801415i | \(-0.295919\pi\) | ||||
0.598108 | + | 0.801415i | \(0.295919\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.46410i | − | 0.251091i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.19615 | − | 2.19615i | 0.361045 | − | 0.361045i | −0.503152 | − | 0.864198i | \(-0.667827\pi\) |
0.864198 | + | 0.503152i | \(0.167827\pi\) | |||||||
\(38\) | −5.27792 | + | 5.27792i | −0.856191 | + | 0.856191i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.62158i | − | 0.721769i | −0.932610 | − | 0.360885i | \(-0.882475\pi\) | ||
0.932610 | − | 0.360885i | \(-0.117525\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.26795 | + | 1.26795i | 0.193360 | + | 0.193360i | 0.797146 | − | 0.603786i | \(-0.206342\pi\) |
−0.603786 | + | 0.797146i | \(0.706342\pi\) | |||||||
\(44\) | −4.76028 | −0.717639 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | 4.24264 | + | 4.24264i | 0.618853 | + | 0.618853i | 0.945237 | − | 0.326384i | \(-0.105830\pi\) |
−0.326384 | + | 0.945237i | \(0.605830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.73205i | 0.961722i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.46410 | − | 3.46410i | 0.480384 | − | 0.480384i | ||||
\(53\) | −5.08845 | + | 5.08845i | −0.698952 | + | 0.698952i | −0.964185 | − | 0.265232i | \(-0.914551\pi\) |
0.265232 | + | 0.964185i | \(0.414551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 0.517638i | − | 0.0691723i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.46410 | − | 4.46410i | −0.586165 | − | 0.586165i | ||||
\(59\) | 4.52004 | 0.588459 | 0.294230 | − | 0.955735i | \(-0.404937\pi\) | ||||
0.294230 | + | 0.955735i | \(0.404937\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.46410 | 1.21175 | 0.605877 | − | 0.795558i | \(-0.292822\pi\) | ||||
0.605877 | + | 0.795558i | \(0.292822\pi\) | |||||||
\(62\) | −4.70951 | − | 4.70951i | −0.598108 | − | 0.598108i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.19615 | − | 6.19615i | 0.756980 | − | 0.756980i | −0.218791 | − | 0.975772i | \(-0.570211\pi\) |
0.975772 | + | 0.218791i | \(0.0702114\pi\) | |||||||
\(68\) | −1.03528 | + | 1.03528i | −0.125546 | + | 0.125546i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 15.4548i | − | 1.83415i | −0.398716 | − | 0.917074i | \(-0.630544\pi\) | ||
0.398716 | − | 0.917074i | \(-0.369456\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.36603 | − | 9.36603i | −1.09621 | − | 1.09621i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
−0.101361 | − | 0.994850i | \(-0.532320\pi\) | |||||||
\(74\) | −3.10583 | −0.361045 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.46410 | 0.856191 | ||||||||
\(77\) | 1.74238 | + | 1.74238i | 0.198563 | + | 0.198563i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.46410i | − | 0.389742i | −0.980829 | − | 0.194871i | \(-0.937571\pi\) | ||
0.980829 | − | 0.194871i | \(-0.0624288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.26795 | + | 3.26795i | −0.360885 | + | 0.360885i | ||||
\(83\) | −1.46498 | + | 1.46498i | −0.160803 | + | 0.160803i | −0.782922 | − | 0.622120i | \(-0.786272\pi\) |
0.622120 | + | 0.782922i | \(0.286272\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1.79315i | − | 0.193360i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.36603 | + | 3.36603i | 0.358820 | + | 0.358820i | ||||
\(89\) | 5.93426 | 0.629030 | 0.314515 | − | 0.949253i | \(-0.398158\pi\) | ||||
0.314515 | + | 0.949253i | \(0.398158\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.53590 | −0.265834 | ||||||||
\(92\) | 1.41421 | + | 1.41421i | 0.147442 | + | 0.147442i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 6.00000i | − | 0.618853i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.5622 | − | 13.5622i | 1.37703 | − | 1.37703i | 0.527435 | − | 0.849595i | \(-0.323154\pi\) |
0.849595 | − | 0.527435i | \(-0.176846\pi\) | |||||||
\(98\) | 4.76028 | − | 4.76028i | 0.480861 | − | 0.480861i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.6598i | 1.45870i | 0.684140 | + | 0.729351i | \(0.260178\pi\) | ||||
−0.684140 | + | 0.729351i | \(0.739822\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.73205 | + | 9.73205i | 0.958927 | + | 0.958927i | 0.999189 | − | 0.0402617i | \(-0.0128192\pi\) |
−0.0402617 | + | 0.999189i | \(0.512819\pi\) | |||||||
\(104\) | −4.89898 | −0.480384 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.19615 | 0.698952 | ||||||||
\(107\) | 1.36345 | + | 1.36345i | 0.131809 | + | 0.131809i | 0.769933 | − | 0.638124i | \(-0.220289\pi\) |
−0.638124 | + | 0.769933i | \(0.720289\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.00000i | − | 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.366025 | + | 0.366025i | −0.0345861 | + | 0.0345861i | ||||
\(113\) | 11.9700 | − | 11.9700i | 1.12605 | − | 1.12605i | 0.135234 | − | 0.990814i | \(-0.456822\pi\) |
0.990814 | − | 0.135234i | \(-0.0431785\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.31319i | 0.586165i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.19615 | − | 3.19615i | −0.294230 | − | 0.294230i | ||||
\(119\) | 0.757875 | 0.0694743 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.6603 | −1.06002 | ||||||||
\(122\) | −6.69213 | − | 6.69213i | −0.605877 | − | 0.605877i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.66025i | 0.598108i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.16987 | − | 1.16987i | 0.103809 | − | 0.103809i | −0.653294 | − | 0.757104i | \(-0.726614\pi\) |
0.757104 | + | 0.653294i | \(0.226614\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 14.1793i | − | 1.23885i | −0.785055 | − | 0.619426i | \(-0.787366\pi\) | ||
0.785055 | − | 0.619426i | \(-0.212634\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.73205 | − | 2.73205i | −0.236899 | − | 0.236899i | ||||
\(134\) | −8.76268 | −0.756980 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.46410 | 0.125546 | ||||||||
\(137\) | 2.44949 | + | 2.44949i | 0.209274 | + | 0.209274i | 0.803959 | − | 0.594685i | \(-0.202723\pi\) |
−0.594685 | + | 0.803959i | \(0.702723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.85641i | − | 0.836009i | −0.908445 | − | 0.418005i | \(-0.862730\pi\) | ||
0.908445 | − | 0.418005i | \(-0.137270\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.9282 | + | 10.9282i | −0.917074 | + | 0.917074i | ||||
\(143\) | 16.4901 | − | 16.4901i | 1.37897 | − | 1.37897i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.2456i | 1.09621i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.19615 | + | 2.19615i | 0.180523 | + | 0.180523i | ||||
\(149\) | −12.4877 | −1.02303 | −0.511516 | − | 0.859274i | \(-0.670916\pi\) | ||||
−0.511516 | + | 0.859274i | \(0.670916\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.46410 | −0.688799 | −0.344399 | − | 0.938823i | \(-0.611917\pi\) | ||||
−0.344399 | + | 0.938823i | \(0.611917\pi\) | |||||||
\(152\) | −5.27792 | − | 5.27792i | −0.428096 | − | 0.428096i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 2.46410i | − | 0.198563i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0000 | + | 12.0000i | −0.957704 | + | 0.957704i | −0.999141 | − | 0.0414369i | \(-0.986806\pi\) |
0.0414369 | + | 0.999141i | \(0.486806\pi\) | |||||||
\(158\) | −2.44949 | + | 2.44949i | −0.194871 | + | 0.194871i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.03528i | − | 0.0815912i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.46410 | − | 5.46410i | −0.427981 | − | 0.427981i | 0.459959 | − | 0.887940i | \(-0.347864\pi\) |
−0.887940 | + | 0.459959i | \(0.847864\pi\) | |||||||
\(164\) | 4.62158 | 0.360885 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.07180 | 0.160803 | ||||||||
\(167\) | −11.9700 | − | 11.9700i | −0.926270 | − | 0.926270i | 0.0711925 | − | 0.997463i | \(-0.477320\pi\) |
−0.997463 | + | 0.0711925i | \(0.977320\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000i | 0.846154i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.26795 | + | 1.26795i | −0.0966802 | + | 0.0966802i | ||||
\(173\) | −7.39924 | + | 7.39924i | −0.562554 | + | 0.562554i | −0.930032 | − | 0.367478i | \(-0.880221\pi\) |
0.367478 | + | 0.930032i | \(0.380221\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.76028i | − | 0.358820i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.19615 | − | 4.19615i | −0.314515 | − | 0.314515i | ||||
\(179\) | −5.41662 | −0.404857 | −0.202429 | − | 0.979297i | \(-0.564883\pi\) | ||||
−0.202429 | + | 0.979297i | \(0.564883\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9282 | 1.10960 | 0.554802 | − | 0.831982i | \(-0.312794\pi\) | ||||
0.554802 | + | 0.831982i | \(0.312794\pi\) | |||||||
\(182\) | 1.79315 | + | 1.79315i | 0.132917 | + | 0.132917i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 2.00000i | − | 0.147442i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.92820 | + | 4.92820i | −0.360386 | + | 0.360386i | ||||
\(188\) | −4.24264 | + | 4.24264i | −0.309426 | + | 0.309426i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.38323i | − | 0.244802i | −0.992481 | − | 0.122401i | \(-0.960941\pi\) | ||
0.992481 | − | 0.122401i | \(-0.0390594\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.02628 | + | 8.02628i | 0.577744 | + | 0.577744i | 0.934281 | − | 0.356537i | \(-0.116043\pi\) |
−0.356537 | + | 0.934281i | \(0.616043\pi\) | |||||||
\(194\) | −19.1798 | −1.37703 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.73205 | −0.480861 | ||||||||
\(197\) | 3.01790 | + | 3.01790i | 0.215016 | + | 0.215016i | 0.806394 | − | 0.591378i | \(-0.201416\pi\) |
−0.591378 | + | 0.806394i | \(0.701416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3205i | 1.01515i | 0.861606 | + | 0.507577i | \(0.169459\pi\) | ||||
−0.861606 | + | 0.507577i | \(0.830541\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.3660 | − | 10.3660i | 0.729351 | − | 0.729351i | ||||
\(203\) | 2.31079 | − | 2.31079i | 0.162186 | − | 0.162186i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 13.7632i | − | 0.958927i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.46410 | + | 3.46410i | 0.240192 | + | 0.240192i | ||||
\(209\) | 35.5312 | 2.45774 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.3205 | −1.46776 | −0.733882 | − | 0.679277i | \(-0.762294\pi\) | ||||
−0.733882 | + | 0.679277i | \(0.762294\pi\) | |||||||
\(212\) | −5.08845 | − | 5.08845i | −0.349476 | − | 0.349476i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 1.92820i | − | 0.131809i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.43782 | − | 2.43782i | 0.165490 | − | 0.165490i | ||||
\(218\) | −1.41421 | + | 1.41421i | −0.0957826 | + | 0.0957826i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 7.17260i | − | 0.482482i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.26795 | − | 4.26795i | −0.285803 | − | 0.285803i | 0.549615 | − | 0.835418i | \(-0.314774\pi\) |
−0.835418 | + | 0.549615i | \(0.814774\pi\) | |||||||
\(224\) | 0.517638 | 0.0345861 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.9282 | −1.12605 | ||||||||
\(227\) | 3.20736 | + | 3.20736i | 0.212880 | + | 0.212880i | 0.805490 | − | 0.592610i | \(-0.201902\pi\) |
−0.592610 | + | 0.805490i | \(0.701902\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.60770i | − | 0.106239i | −0.998588 | − | 0.0531197i | \(-0.983083\pi\) | ||
0.998588 | − | 0.0531197i | \(-0.0169165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.46410 | − | 4.46410i | 0.293083 | − | 0.293083i | ||||
\(233\) | −5.55532 | + | 5.55532i | −0.363941 | + | 0.363941i | −0.865262 | − | 0.501321i | \(-0.832848\pi\) |
0.501321 | + | 0.865262i | \(0.332848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.52004i | 0.294230i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.535898 | − | 0.535898i | −0.0347371 | − | 0.0347371i | ||||
\(239\) | −5.37945 | −0.347968 | −0.173984 | − | 0.984748i | \(-0.555664\pi\) | ||||
−0.173984 | + | 0.984748i | \(0.555664\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(242\) | 8.24504 | + | 8.24504i | 0.530012 | + | 0.530012i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.46410i | 0.605877i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.8564 | + | 25.8564i | −1.64520 | + | 1.64520i | ||||
\(248\) | 4.70951 | − | 4.70951i | 0.299054 | − | 0.299054i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 14.5211i | − | 0.916562i | −0.888807 | − | 0.458281i | \(-0.848465\pi\) | ||
0.888807 | − | 0.458281i | \(-0.151535\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.73205 | + | 6.73205i | 0.423240 | + | 0.423240i | ||||
\(254\) | −1.65445 | −0.103809 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.3538 | + | 20.3538i | 1.26963 | + | 1.26963i | 0.946277 | + | 0.323358i | \(0.104812\pi\) |
0.323358 | + | 0.946277i | \(0.395188\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.60770i | − | 0.0998973i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.0263 | + | 10.0263i | −0.619426 | + | 0.619426i | ||||
\(263\) | −9.89949 | + | 9.89949i | −0.610429 | + | 0.610429i | −0.943058 | − | 0.332629i | \(-0.892064\pi\) |
0.332629 | + | 0.943058i | \(0.392064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.86370i | 0.236899i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.19615 | + | 6.19615i | 0.378490 | + | 0.378490i | ||||
\(269\) | 7.62587 | 0.464958 | 0.232479 | − | 0.972601i | \(-0.425316\pi\) | ||||
0.232479 | + | 0.972601i | \(0.425316\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.60770 | 0.279898 | 0.139949 | − | 0.990159i | \(-0.455306\pi\) | ||||
0.139949 | + | 0.990159i | \(0.455306\pi\) | |||||||
\(272\) | −1.03528 | − | 1.03528i | −0.0627728 | − | 0.0627728i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 3.46410i | − | 0.209274i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.8564 | + | 19.8564i | −1.19306 | + | 1.19306i | −0.216851 | + | 0.976205i | \(0.569579\pi\) |
−0.976205 | + | 0.216851i | \(0.930421\pi\) | |||||||
\(278\) | −6.96953 | + | 6.96953i | −0.418005 | + | 0.418005i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.3843i | 0.798438i | 0.916856 | + | 0.399219i | \(0.130719\pi\) | ||||
−0.916856 | + | 0.399219i | \(0.869281\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.73205 | + | 8.73205i | 0.519067 | + | 0.519067i | 0.917289 | − | 0.398222i | \(-0.130373\pi\) |
−0.398222 | + | 0.917289i | \(0.630373\pi\) | |||||||
\(284\) | 15.4548 | 0.917074 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.3205 | −1.37897 | ||||||||
\(287\) | −1.69161 | − | 1.69161i | −0.0998529 | − | 0.0998529i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 14.8564i | − | 0.873906i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.36603 | − | 9.36603i | 0.548105 | − | 0.548105i | ||||
\(293\) | −8.48528 | + | 8.48528i | −0.495715 | + | 0.495715i | −0.910101 | − | 0.414386i | \(-0.863996\pi\) |
0.414386 | + | 0.910101i | \(0.363996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 3.10583i | − | 0.180523i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.83013 | + | 8.83013i | 0.511516 | + | 0.511516i | ||||
\(299\) | −9.79796 | −0.566631 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.928203 | 0.0535007 | ||||||||
\(302\) | 5.98502 | + | 5.98502i | 0.344399 | + | 0.344399i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.46410i | 0.428096i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | −1.74238 | + | 1.74238i | −0.0992815 | + | 0.0992815i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3.86370i | − | 0.219091i | −0.993982 | − | 0.109545i | \(-0.965061\pi\) | ||
0.993982 | − | 0.109545i | \(-0.0349395\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0263 | + | 20.0263i | 1.13195 | + | 1.13195i | 0.989852 | + | 0.142100i | \(0.0453854\pi\) |
0.142100 | + | 0.989852i | \(0.454615\pi\) | |||||||
\(314\) | 16.9706 | 0.957704 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.46410 | 0.194871 | ||||||||
\(317\) | 8.81345 | + | 8.81345i | 0.495013 | + | 0.495013i | 0.909881 | − | 0.414869i | \(-0.136172\pi\) |
−0.414869 | + | 0.909881i | \(0.636172\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.0526i | 1.68262i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.732051 | + | 0.732051i | −0.0407956 | + | 0.0407956i | ||||
\(323\) | 7.72741 | − | 7.72741i | 0.429964 | − | 0.429964i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.72741i | 0.427981i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.26795 | − | 3.26795i | −0.180442 | − | 0.180442i | ||||
\(329\) | 3.10583 | 0.171230 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.46410 | 0.410264 | 0.205132 | − | 0.978734i | \(-0.434238\pi\) | ||||
0.205132 | + | 0.978734i | \(0.434238\pi\) | |||||||
\(332\) | −1.46498 | − | 1.46498i | −0.0804013 | − | 0.0804013i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.9282i | 0.926270i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.464102 | + | 0.464102i | −0.0252812 | + | 0.0252812i | −0.719634 | − | 0.694353i | \(-0.755691\pi\) |
0.694353 | + | 0.719634i | \(0.255691\pi\) | |||||||
\(338\) | 7.77817 | − | 7.77817i | 0.423077 | − | 0.423077i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.7047i | 1.71690i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.02628 | + | 5.02628i | 0.271394 | + | 0.271394i | ||||
\(344\) | 1.79315 | 0.0966802 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.4641 | 0.562554 | ||||||||
\(347\) | −20.2659 | − | 20.2659i | −1.08793 | − | 1.08793i | −0.995742 | − | 0.0921866i | \(-0.970614\pi\) |
−0.0921866 | − | 0.995742i | \(-0.529386\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.60770i | − | 0.300173i | −0.988673 | − | 0.150087i | \(-0.952045\pi\) | ||
0.988673 | − | 0.150087i | \(-0.0479552\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.36603 | + | 3.36603i | −0.179410 | + | 0.179410i | ||||
\(353\) | −14.0406 | + | 14.0406i | −0.747306 | + | 0.747306i | −0.973972 | − | 0.226667i | \(-0.927217\pi\) |
0.226667 | + | 0.973972i | \(0.427217\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.93426i | 0.314515i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.83013 | + | 3.83013i | 0.202429 | + | 0.202429i | ||||
\(359\) | −23.4596 | −1.23815 | −0.619076 | − | 0.785331i | \(-0.712493\pi\) | ||||
−0.619076 | + | 0.785331i | \(0.712493\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −36.7128 | −1.93225 | ||||||||
\(362\) | −10.5558 | − | 10.5558i | −0.554802 | − | 0.554802i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 2.53590i | − | 0.132917i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.02628 | − | 3.02628i | 0.157971 | − | 0.157971i | −0.623696 | − | 0.781667i | \(-0.714370\pi\) |
0.781667 | + | 0.623696i | \(0.214370\pi\) | |||||||
\(368\) | −1.41421 | + | 1.41421i | −0.0737210 | + | 0.0737210i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.72500i | 0.193392i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.39230 | − | 8.39230i | −0.434537 | − | 0.434537i | 0.455631 | − | 0.890169i | \(-0.349414\pi\) |
−0.890169 | + | 0.455631i | \(0.849414\pi\) | |||||||
\(374\) | 6.96953 | 0.360386 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | −21.8695 | − | 21.8695i | −1.12634 | − | 1.12634i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000i | 0.410932i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.39230 | + | 2.39230i | −0.122401 | + | 0.122401i | ||||
\(383\) | 0.480473 | − | 0.480473i | 0.0245510 | − | 0.0245510i | −0.694725 | − | 0.719276i | \(-0.744474\pi\) |
0.719276 | + | 0.694725i | \(0.244474\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 11.3509i | − | 0.577744i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.5622 | + | 13.5622i | 0.688515 | + | 0.688515i | ||||
\(389\) | −13.1440 | −0.666428 | −0.333214 | − | 0.942851i | \(-0.608133\pi\) | ||||
−0.333214 | + | 0.942851i | \(0.608133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.92820 | 0.148086 | ||||||||
\(392\) | 4.76028 | + | 4.76028i | 0.240430 | + | 0.240430i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 4.26795i | − | 0.215016i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.92820 | + | 4.92820i | −0.247339 | + | 0.247339i | −0.819878 | − | 0.572538i | \(-0.805959\pi\) |
0.572538 | + | 0.819878i | \(0.305959\pi\) | |||||||
\(398\) | 10.1261 | − | 10.1261i | 0.507577 | − | 0.507577i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.2832i | 0.913021i | 0.889718 | + | 0.456511i | \(0.150901\pi\) | ||||
−0.889718 | + | 0.456511i | \(0.849099\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.0718 | − | 23.0718i | −1.14929 | − | 1.14929i | ||||
\(404\) | −14.6598 | −0.729351 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.26795 | −0.162186 | ||||||||
\(407\) | 10.4543 | + | 10.4543i | 0.518200 | + | 0.518200i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.33975i | 0.165140i | 0.996585 | + | 0.0825699i | \(0.0263128\pi\) | ||||
−0.996585 | + | 0.0825699i | \(0.973687\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.73205 | + | 9.73205i | −0.479464 | + | 0.479464i | ||||
\(413\) | 1.65445 | − | 1.65445i | 0.0814102 | − | 0.0814102i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 4.89898i | − | 0.240192i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −25.1244 | − | 25.1244i | −1.22887 | − | 1.22887i | ||||
\(419\) | 13.2084 | 0.645272 | 0.322636 | − | 0.946523i | \(-0.395431\pi\) | ||||
0.322636 | + | 0.946523i | \(0.395431\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.8564 | −0.870268 | −0.435134 | − | 0.900366i | \(-0.643299\pi\) | ||||
−0.435134 | + | 0.900366i | \(0.643299\pi\) | |||||||
\(422\) | 15.0759 | + | 15.0759i | 0.733882 | + | 0.733882i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.19615i | 0.349476i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.46410 | − | 3.46410i | 0.167640 | − | 0.167640i | ||||
\(428\) | −1.36345 | + | 1.36345i | −0.0659046 | + | 0.0659046i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.7332i | 1.23953i | 0.784789 | + | 0.619763i | \(0.212771\pi\) | ||||
−0.784789 | + | 0.619763i | \(0.787229\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.83013 | + | 9.83013i | 0.472406 | + | 0.472406i | 0.902692 | − | 0.430287i | \(-0.141587\pi\) |
−0.430287 | + | 0.902692i | \(0.641587\pi\) | |||||||
\(434\) | −3.44760 | −0.165490 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | −10.5558 | − | 10.5558i | −0.504954 | − | 0.504954i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 29.2487i | − | 1.39596i | −0.716115 | − | 0.697982i | \(-0.754081\pi\) | ||
0.716115 | − | 0.697982i | \(-0.245919\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.07180 | + | 5.07180i | −0.241241 | + | 0.241241i | ||||
\(443\) | 25.6317 | − | 25.6317i | 1.21780 | − | 1.21780i | 0.249398 | − | 0.968401i | \(-0.419767\pi\) |
0.968401 | − | 0.249398i | \(-0.0802328\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.03579i | 0.285803i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.366025 | − | 0.366025i | −0.0172931 | − | 0.0172931i | ||||
\(449\) | 14.9743 | 0.706683 | 0.353341 | − | 0.935494i | \(-0.385045\pi\) | ||||
0.353341 | + | 0.935494i | \(0.385045\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.0000 | 1.03594 | ||||||||
\(452\) | 11.9700 | + | 11.9700i | 0.563024 | + | 0.563024i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 4.53590i | − | 0.212880i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.70577 | − | 8.70577i | 0.407239 | − | 0.407239i | −0.473536 | − | 0.880775i | \(-0.657023\pi\) |
0.880775 | + | 0.473536i | \(0.157023\pi\) | |||||||
\(458\) | −1.13681 | + | 1.13681i | −0.0531197 | + | 0.0531197i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.7699i | 0.967350i | 0.875248 | + | 0.483675i | \(0.160698\pi\) | ||||
−0.875248 | + | 0.483675i | \(0.839302\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.29423 | − | 8.29423i | −0.385465 | − | 0.385465i | 0.487601 | − | 0.873067i | \(-0.337872\pi\) |
−0.873067 | + | 0.487601i | \(0.837872\pi\) | |||||||
\(464\) | −6.31319 | −0.293083 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.85641 | 0.363941 | ||||||||
\(467\) | 9.19239 | + | 9.19239i | 0.425373 | + | 0.425373i | 0.887049 | − | 0.461676i | \(-0.152752\pi\) |
−0.461676 | + | 0.887049i | \(0.652752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.53590i | − | 0.209448i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.19615 | − | 3.19615i | 0.147115 | − | 0.147115i | ||||
\(473\) | −6.03579 | + | 6.03579i | −0.277526 | + | 0.277526i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.757875i | 0.0347371i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.80385 | + | 3.80385i | 0.173984 | + | 0.173984i | ||||
\(479\) | 11.0363 | 0.504262 | 0.252131 | − | 0.967693i | \(-0.418869\pi\) | ||||
0.252131 | + | 0.967693i | \(0.418869\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.2154 | −0.693762 | ||||||||
\(482\) | −2.82843 | − | 2.82843i | −0.128831 | − | 0.128831i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 11.6603i | − | 0.530012i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.1962 | − | 23.1962i | 1.05112 | − | 1.05112i | 0.0524969 | − | 0.998621i | \(-0.483282\pi\) |
0.998621 | − | 0.0524969i | \(-0.0167180\pi\) | |||||||
\(488\) | 6.69213 | − | 6.69213i | 0.302939 | − | 0.302939i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.5630i | − | 1.01826i | −0.860691 | − | 0.509128i | \(-0.829968\pi\) | ||
0.860691 | − | 0.509128i | \(-0.170032\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.53590 | + | 6.53590i | 0.294362 | + | 0.294362i | ||||
\(494\) | 36.5665 | 1.64520 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.66025 | −0.299054 | ||||||||
\(497\) | −5.65685 | − | 5.65685i | −0.253745 | − | 0.253745i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.8564i | 1.60515i | 0.596549 | + | 0.802577i | \(0.296538\pi\) | ||||
−0.596549 | + | 0.802577i | \(0.703462\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.2679 | + | 10.2679i | −0.458281 | + | 0.458281i | ||||
\(503\) | −1.13681 | + | 1.13681i | −0.0506879 | + | 0.0506879i | −0.731996 | − | 0.681308i | \(-0.761411\pi\) |
0.681308 | + | 0.731996i | \(0.261411\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 9.52056i | − | 0.423240i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.16987 | + | 1.16987i | 0.0519047 | + | 0.0519047i | ||||
\(509\) | −30.6694 | −1.35940 | −0.679698 | − | 0.733492i | \(-0.737889\pi\) | ||||
−0.679698 | + | 0.733492i | \(0.737889\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.85641 | −0.303310 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 28.7846i | − | 1.26963i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.1962 | + | 20.1962i | −0.888226 | + | 0.888226i | ||||
\(518\) | −1.13681 | + | 1.13681i | −0.0499487 | + | 0.0499487i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.58630i | − | 0.157119i | −0.996909 | − | 0.0785594i | \(-0.974968\pi\) | ||
0.996909 | − | 0.0785594i | \(-0.0250320\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.4641 | + | 21.4641i | 0.938560 | + | 0.938560i | 0.998219 | − | 0.0596592i | \(-0.0190014\pi\) |
−0.0596592 | + | 0.998219i | \(0.519001\pi\) | |||||||
\(524\) | 14.1793 | 0.619426 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.0000 | 0.610429 | ||||||||
\(527\) | 6.89520 | + | 6.89520i | 0.300360 | + | 0.300360i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0000i | 0.826087i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.73205 | − | 2.73205i | 0.118449 | − | 0.118449i | ||||
\(533\) | −16.0096 | + | 16.0096i | −0.693453 | + | 0.693453i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 8.76268i | − | 0.378490i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.39230 | − | 5.39230i | −0.232479 | − | 0.232479i | ||||
\(539\) | −32.0464 | −1.38034 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.3205 | 1.17460 | 0.587300 | − | 0.809369i | \(-0.300191\pi\) | ||||
0.587300 | + | 0.809369i | \(0.300191\pi\) | |||||||
\(542\) | −3.25813 | − | 3.25813i | −0.139949 | − | 0.139949i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.46410i | 0.0627728i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.928203 | − | 0.928203i | 0.0396871 | − | 0.0396871i | −0.686985 | − | 0.726672i | \(-0.741066\pi\) |
0.726672 | + | 0.686985i | \(0.241066\pi\) | |||||||
\(548\) | −2.44949 | + | 2.44949i | −0.104637 | + | 0.104637i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 47.1223i | − | 2.00748i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.26795 | − | 1.26795i | −0.0539187 | − | 0.0539187i | ||||
\(554\) | 28.0812 | 1.19306 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.85641 | 0.418005 | ||||||||
\(557\) | −1.88108 | − | 1.88108i | −0.0797041 | − | 0.0797041i | 0.666131 | − | 0.745835i | \(-0.267949\pi\) |
−0.745835 | + | 0.666131i | \(0.767949\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.78461i | − | 0.371549i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.46410 | − | 9.46410i | 0.399219 | − | 0.399219i | ||||
\(563\) | −4.81105 | + | 4.81105i | −0.202761 | + | 0.202761i | −0.801182 | − | 0.598421i | \(-0.795795\pi\) |
0.598421 | + | 0.801182i | \(0.295795\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 12.3490i | − | 0.519067i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.9282 | − | 10.9282i | −0.458537 | − | 0.458537i | ||||
\(569\) | −26.2137 | −1.09894 | −0.549468 | − | 0.835515i | \(-0.685170\pi\) | ||||
−0.549468 | + | 0.835515i | \(0.685170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.46410 | −0.0612707 | −0.0306354 | − | 0.999531i | \(-0.509753\pi\) | ||||
−0.0306354 | + | 0.999531i | \(0.509753\pi\) | |||||||
\(572\) | 16.4901 | + | 16.4901i | 0.689485 | + | 0.689485i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.39230i | 0.0998529i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.3923 | − | 15.3923i | 0.640790 | − | 0.640790i | −0.309960 | − | 0.950750i | \(-0.600316\pi\) |
0.950750 | + | 0.309960i | \(0.100316\pi\) | |||||||
\(578\) | −10.5051 | + | 10.5051i | −0.436953 | + | 0.436953i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.07244i | 0.0444923i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.2224 | − | 24.2224i | −1.00319 | − | 1.00319i | ||||
\(584\) | −13.2456 | −0.548105 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | −31.5152 | − | 31.5152i | −1.30077 | − | 1.30077i | −0.927872 | − | 0.372900i | \(-0.878364\pi\) |
−0.372900 | − | 0.927872i | \(-0.621636\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 49.7128i | − | 2.04838i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.19615 | + | 2.19615i | −0.0902613 | + | 0.0902613i | ||||
\(593\) | −8.86422 | + | 8.86422i | −0.364010 | + | 0.364010i | −0.865287 | − | 0.501277i | \(-0.832864\pi\) |
0.501277 | + | 0.865287i | \(0.332864\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 12.4877i | − | 0.511516i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.92820 | + | 6.92820i | 0.283315 | + | 0.283315i | ||||
\(599\) | 7.45001 | 0.304399 | 0.152199 | − | 0.988350i | \(-0.451364\pi\) | ||||
0.152199 | + | 0.988350i | \(0.451364\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0000 | −0.530281 | −0.265141 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265141 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(602\) | −0.656339 | − | 0.656339i | −0.0267504 | − | 0.0267504i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 8.46410i | − | 0.344399i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5885 | − | 21.5885i | 0.876248 | − | 0.876248i | −0.116896 | − | 0.993144i | \(-0.537294\pi\) |
0.993144 | + | 0.116896i | \(0.0372943\pi\) | |||||||
\(608\) | 5.27792 | − | 5.27792i | 0.214048 | − | 0.214048i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 29.3939i | − | 1.18915i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.6603 | − | 17.6603i | −0.713291 | − | 0.713291i | 0.253931 | − | 0.967222i | \(-0.418276\pi\) |
−0.967222 | + | 0.253931i | \(0.918276\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.46410 | 0.0992815 | ||||||||
\(617\) | 29.2180 | + | 29.2180i | 1.17627 | + | 1.17627i | 0.980686 | + | 0.195586i | \(0.0626610\pi\) |
0.195586 | + | 0.980686i | \(0.437339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.60770i | − | 0.305779i | −0.988243 | − | 0.152890i | \(-0.951142\pi\) | ||
0.988243 | − | 0.152890i | \(-0.0488579\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.73205 | + | 2.73205i | −0.109545 | + | 0.109545i | ||||
\(623\) | 2.17209 | − | 2.17209i | 0.0870229 | − | 0.0870229i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 28.3214i | − | 1.13195i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.0000 | − | 12.0000i | −0.478852 | − | 0.478852i | ||||
\(629\) | 4.54725 | 0.181311 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.9090 | 1.23047 | 0.615233 | − | 0.788345i | \(-0.289062\pi\) | ||||
0.615233 | + | 0.788345i | \(0.289062\pi\) | |||||||
\(632\) | −2.44949 | − | 2.44949i | −0.0974355 | − | 0.0974355i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 12.4641i | − | 0.495013i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.3205 | − | 23.3205i | 0.923992 | − | 0.923992i | ||||
\(638\) | 21.2504 | − | 21.2504i | 0.841310 | − | 0.841310i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 25.7332i | − | 1.01640i | −0.861238 | − | 0.508201i | \(-0.830311\pi\) | ||
0.861238 | − | 0.508201i | \(-0.169689\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.46410 | − | 3.46410i | −0.136611 | − | 0.136611i | 0.635495 | − | 0.772105i | \(-0.280796\pi\) |
−0.772105 | + | 0.635495i | \(0.780796\pi\) | |||||||
\(644\) | 1.03528 | 0.0407956 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.9282 | −0.429964 | ||||||||
\(647\) | −15.7322 | − | 15.7322i | −0.618497 | − | 0.618497i | 0.326649 | − | 0.945146i | \(-0.394081\pi\) |
−0.945146 | + | 0.326649i | \(0.894081\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.5167i | 0.844603i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.46410 | − | 5.46410i | 0.213991 | − | 0.213991i | ||||
\(653\) | −10.1261 | + | 10.1261i | −0.396266 | + | 0.396266i | −0.876914 | − | 0.480648i | \(-0.840402\pi\) |
0.480648 | + | 0.876914i | \(0.340402\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.62158i | 0.180442i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.19615 | − | 2.19615i | −0.0856149 | − | 0.0856149i | ||||
\(659\) | −48.4994 | −1.88927 | −0.944633 | − | 0.328127i | \(-0.893582\pi\) | ||||
−0.944633 | + | 0.328127i | \(0.893582\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.39230 | −0.0930499 | −0.0465249 | − | 0.998917i | \(-0.514815\pi\) | ||||
−0.0465249 | + | 0.998917i | \(0.514815\pi\) | |||||||
\(662\) | −5.27792 | − | 5.27792i | −0.205132 | − | 0.205132i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.07180i | 0.0804013i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.92820 | − | 8.92820i | 0.345701 | − | 0.345701i | ||||
\(668\) | 11.9700 | − | 11.9700i | 0.463135 | − | 0.463135i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 45.0518i | 1.73920i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.02628 | − | 3.02628i | −0.116654 | − | 0.116654i | 0.646370 | − | 0.763024i | \(-0.276286\pi\) |
−0.763024 | + | 0.646370i | \(0.776286\pi\) | |||||||
\(674\) | 0.656339 | 0.0252812 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | −0.423077 | ||||||||
\(677\) | −29.4954 | − | 29.4954i | −1.13360 | − | 1.13360i | −0.989574 | − | 0.144027i | \(-0.953995\pi\) |
−0.144027 | − | 0.989574i | \(-0.546005\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 9.92820i | − | 0.381009i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 22.4186 | − | 22.4186i | 0.858452 | − | 0.858452i | ||||
\(683\) | −21.8695 | + | 21.8695i | −0.836815 | + | 0.836815i | −0.988438 | − | 0.151624i | \(-0.951550\pi\) |
0.151624 | + | 0.988438i | \(0.451550\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 7.10823i | − | 0.271394i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.26795 | − | 1.26795i | −0.0483401 | − | 0.0483401i | ||||
\(689\) | 35.2538 | 1.34306 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.6410 | 1.31781 | 0.658903 | − | 0.752228i | \(-0.271021\pi\) | ||||
0.658903 | + | 0.752228i | \(0.271021\pi\) | |||||||
\(692\) | −7.39924 | − | 7.39924i | −0.281277 | − | 0.281277i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.6603i | 1.08793i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.78461 | − | 4.78461i | 0.181230 | − | 0.181230i | ||||
\(698\) | −3.96524 | + | 3.96524i | −0.150087 | + | 0.150087i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.8677i | 0.863699i | 0.901946 | + | 0.431850i | \(0.142139\pi\) | ||||
−0.901946 | + | 0.431850i | \(0.857861\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.3923 | − | 16.3923i | −0.618247 | − | 0.618247i | ||||
\(704\) | 4.76028 | 0.179410 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.8564 | 0.747306 | ||||||||
\(707\) | 5.36585 | + | 5.36585i | 0.201804 | + | 0.201804i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 12.7846i | − | 0.480136i | −0.970756 | − | 0.240068i | \(-0.922830\pi\) | ||
0.970756 | − | 0.240068i | \(-0.0771698\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.19615 | − | 4.19615i | 0.157257 | − | 0.157257i | ||||
\(713\) | 9.41902 | − | 9.41902i | 0.352745 | − | 0.352745i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 5.41662i | − | 0.202429i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.5885 | + | 16.5885i | 0.619076 | + | 0.619076i | ||||
\(719\) | −9.04008 | −0.337138 | −0.168569 | − | 0.985690i | \(-0.553915\pi\) | ||||
−0.168569 | + | 0.985690i | \(0.553915\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.12436 | 0.265325 | ||||||||
\(722\) | 25.9599 | + | 25.9599i | 0.966127 | + | 0.966127i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.9282i | 0.554802i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.973721 | + | 0.973721i | −0.0361133 | + | 0.0361133i | −0.724933 | − | 0.688820i | \(-0.758129\pi\) |
0.688820 | + | 0.724933i | \(0.258129\pi\) | |||||||
\(728\) | −1.79315 | + | 1.79315i | −0.0664586 | + | 0.0664586i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.62536i | 0.0971023i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.1244 | + | 11.1244i | 0.410887 | + | 0.410887i | 0.882048 | − | 0.471160i | \(-0.156165\pi\) |
−0.471160 | + | 0.882048i | \(0.656165\pi\) | |||||||
\(734\) | −4.27981 | −0.157971 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | 29.4954 | + | 29.4954i | 1.08648 | + | 1.08648i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.07180i | 0.333711i | 0.985981 | + | 0.166856i | \(0.0533614\pi\) | ||||
−0.985981 | + | 0.166856i | \(0.946639\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.63397 | − | 2.63397i | 0.0966962 | − | 0.0966962i | ||||
\(743\) | 30.4292 | − | 30.4292i | 1.11634 | − | 1.11634i | 0.124063 | − | 0.992274i | \(-0.460408\pi\) |
0.992274 | − | 0.124063i | \(-0.0395925\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.8685i | 0.434537i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.92820 | − | 4.92820i | −0.180193 | − | 0.180193i | ||||
\(749\) | 0.998111 | 0.0364702 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.41154 | 0.0879984 | 0.0439992 | − | 0.999032i | \(-0.485990\pi\) | ||||
0.0439992 | + | 0.999032i | \(0.485990\pi\) | |||||||
\(752\) | −4.24264 | − | 4.24264i | −0.154713 | − | 0.154713i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 30.9282i | 1.12634i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.19615 | − | 2.19615i | 0.0798205 | − | 0.0798205i | −0.666069 | − | 0.745890i | \(-0.732025\pi\) |
0.745890 | + | 0.666069i | \(0.232025\pi\) | |||||||
\(758\) | 5.65685 | − | 5.65685i | 0.205466 | − | 0.205466i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.4970i | 1.61301i | 0.591225 | + | 0.806507i | \(0.298645\pi\) | ||||
−0.591225 | + | 0.806507i | \(0.701355\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.732051 | − | 0.732051i | −0.0265020 | − | 0.0265020i | ||||
\(764\) | 3.38323 | 0.122401 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.679492 | −0.0245510 | ||||||||
\(767\) | −15.6579 | − | 15.6579i | −0.565373 | − | 0.565373i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.7846i | − | 1.14618i | −0.819492 | − | 0.573091i | \(-0.805744\pi\) | ||
0.819492 | − | 0.573091i | \(-0.194256\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.02628 | + | 8.02628i | −0.288872 | + | 0.288872i | ||||
\(773\) | 11.4152 | − | 11.4152i | 0.410578 | − | 0.410578i | −0.471362 | − | 0.881940i | \(-0.656237\pi\) |
0.881940 | + | 0.471362i | \(0.156237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 19.1798i | − | 0.688515i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.29423 | + | 9.29423i | 0.333214 | + | 0.333214i | ||||
\(779\) | −34.4959 | −1.23594 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 73.5692 | 2.63251 | ||||||||
\(782\) | −2.07055 | − | 2.07055i | −0.0740428 | − | 0.0740428i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 6.73205i | − | 0.240430i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.07180 | + | 3.07180i | −0.109498 | + | 0.109498i | −0.759733 | − | 0.650235i | \(-0.774670\pi\) |
0.650235 | + | 0.759733i | \(0.274670\pi\) | |||||||
\(788\) | −3.01790 | + | 3.01790i | −0.107508 | + | 0.107508i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8.76268i | − | 0.311565i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.7846 | − | 32.7846i | −1.16422 | − | 1.16422i | ||||
\(794\) | 6.96953 | 0.247339 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.3205 | −0.507577 | ||||||||
\(797\) | −23.5104 | − | 23.5104i | −0.832781 | − | 0.832781i | 0.155116 | − | 0.987896i | \(-0.450425\pi\) |
−0.987896 | + | 0.155116i | \(0.950425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.78461i | 0.310777i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.9282 | − | 12.9282i | 0.456511 | − | 0.456511i | ||||
\(803\) | 44.5849 | − | 44.5849i | 1.57337 | − | 1.57337i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.6284i | 1.14929i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.3660 | + | 10.3660i | 0.364676 | + | 0.364676i | ||||
\(809\) | 19.3185 | 0.679203 | 0.339601 | − | 0.940569i | \(-0.389708\pi\) | ||||
0.339601 | + | 0.940569i | \(0.389708\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.9282 | −1.01581 | −0.507903 | − | 0.861414i | \(-0.669579\pi\) | ||||
−0.507903 | + | 0.861414i | \(0.669579\pi\) | |||||||
\(812\) | 2.31079 | + | 2.31079i | 0.0810928 | + | 0.0810928i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 14.7846i | − | 0.518200i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.46410 | − | 9.46410i | 0.331107 | − | 0.331107i | ||||
\(818\) | 2.36156 | − | 2.36156i | 0.0825699 | − | 0.0825699i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.93855i | 0.311957i | 0.987760 | + | 0.155979i | \(0.0498531\pi\) | ||||
−0.987760 | + | 0.155979i | \(0.950147\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.2942 | + | 31.2942i | 1.09085 | + | 1.09085i | 0.995438 | + | 0.0954102i | \(0.0304163\pi\) |
0.0954102 | + | 0.995438i | \(0.469584\pi\) | |||||||
\(824\) | 13.7632 | 0.479464 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.33975 | −0.0814102 | ||||||||
\(827\) | −4.72311 | − | 4.72311i | −0.164239 | − | 0.164239i | 0.620203 | − | 0.784442i | \(-0.287050\pi\) |
−0.784442 | + | 0.620203i | \(0.787050\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.67949i | − | 0.0930626i | −0.998917 | − | 0.0465313i | \(-0.985183\pi\) | ||
0.998917 | − | 0.0465313i | \(-0.0148167\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.46410 | + | 3.46410i | −0.120096 | + | 0.120096i | ||||
\(833\) | −6.96953 | + | 6.96953i | −0.241480 | + | 0.241480i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 35.5312i | 1.22887i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.33975 | − | 9.33975i | −0.322636 | − | 0.322636i | ||||
\(839\) | −28.8391 | −0.995635 | −0.497818 | − | 0.867282i | \(-0.665865\pi\) | ||||
−0.497818 | + | 0.867282i | \(0.665865\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8564 | 0.374359 | ||||||||
\(842\) | 12.6264 | + | 12.6264i | 0.435134 | + | 0.435134i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 21.3205i | − | 0.733882i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.26795 | + | 4.26795i | −0.146648 | + | 0.146648i | ||||
\(848\) | 5.08845 | − | 5.08845i | 0.174738 | − | 0.174738i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 6.21166i | − | 0.212933i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.8756 | + | 10.8756i | 0.372375 | + | 0.372375i | 0.868342 | − | 0.495967i | \(-0.165186\pi\) |
−0.495967 | + | 0.868342i | \(0.665186\pi\) | |||||||
\(854\) | −4.89898 | −0.167640 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.92820 | 0.0659046 | ||||||||
\(857\) | 32.9802 | + | 32.9802i | 1.12658 | + | 1.12658i | 0.990729 | + | 0.135852i | \(0.0433773\pi\) |
0.135852 | + | 0.990729i | \(0.456623\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 31.3205i | − | 1.06864i | −0.845282 | − | 0.534321i | \(-0.820567\pi\) | ||
0.845282 | − | 0.534321i | \(-0.179433\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.1962 | − | 18.1962i | 0.619763 | − | 0.619763i | ||||
\(863\) | −19.3185 | + | 19.3185i | −0.657610 | + | 0.657610i | −0.954814 | − | 0.297204i | \(-0.903946\pi\) |
0.297204 | + | 0.954814i | \(0.403946\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 13.9019i | − | 0.472406i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.43782 | + | 2.43782i | 0.0827451 | + | 0.0827451i | ||||
\(869\) | 16.4901 | 0.559388 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42.9282 | −1.45457 | ||||||||
\(872\) | −1.41421 | − | 1.41421i | −0.0478913 | − | 0.0478913i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.9282i | 0.504954i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.26795 | − | 1.26795i | 0.0428156 | − | 0.0428156i | −0.685375 | − | 0.728190i | \(-0.740362\pi\) |
0.728190 | + | 0.685375i | \(0.240362\pi\) | |||||||
\(878\) | −20.6820 | + | 20.6820i | −0.697982 | + | 0.697982i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6.41473i | − | 0.216118i | −0.994144 | − | 0.108059i | \(-0.965537\pi\) | ||
0.994144 | − | 0.108059i | \(-0.0344635\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.1244 | − | 19.1244i | −0.643586 | − | 0.643586i | 0.307849 | − | 0.951435i | \(-0.400391\pi\) |
−0.951435 | + | 0.307849i | \(0.900391\pi\) | |||||||
\(884\) | 7.17260 | 0.241241 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.2487 | −1.21780 | ||||||||
\(887\) | −29.8744 | − | 29.8744i | −1.00308 | − | 1.00308i | −0.999995 | − | 0.00308728i | \(-0.999017\pi\) |
−0.00308728 | − | 0.999995i | \(-0.500983\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 0.856406i | − | 0.0287230i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.26795 | − | 4.26795i | 0.142902 | − | 0.142902i | ||||
\(893\) | 31.6675 | − | 31.6675i | 1.05971 | − | 1.05971i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.517638i | 0.0172931i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.5885 | − | 10.5885i | −0.353341 | − | 0.353341i | ||||
\(899\) | 42.0475 | 1.40236 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.5359 | −0.351002 | ||||||||
\(902\) | −15.5563 | − | 15.5563i | −0.517970 | − | 0.517970i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 16.9282i | − | 0.563024i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.9808 | + | 26.9808i | −0.895882 | + | 0.895882i | −0.995069 | − | 0.0991873i | \(-0.968376\pi\) |
0.0991873 | + | 0.995069i | \(0.468376\pi\) | |||||||
\(908\) | −3.20736 | + | 3.20736i | −0.106440 | + | 0.106440i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 51.1891i | − | 1.69597i | −0.530020 | − | 0.847985i | \(-0.677816\pi\) | ||
0.530020 | − | 0.847985i | \(-0.322184\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.97372 | − | 6.97372i | −0.230796 | − | 0.230796i | ||||
\(914\) | −12.3118 | −0.407239 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.60770 | 0.0531197 | ||||||||
\(917\) | −5.18998 | − | 5.18998i | −0.171388 | − | 0.171388i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 41.5885i | − | 1.37188i | −0.727660 | − | 0.685938i | \(-0.759392\pi\) | ||
0.727660 | − | 0.685938i | \(-0.240608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.6865 | − | 14.6865i | 0.483675 | − | 0.483675i | ||||
\(923\) | −53.5370 | + | 53.5370i | −1.76219 | + | 1.76219i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.7298i | 0.385465i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.46410 | + | 4.46410i | 0.146541 | + | 0.146541i | ||||
\(929\) | −17.1736 | −0.563449 | −0.281724 | − | 0.959495i | \(-0.590906\pi\) | ||||
−0.281724 | + | 0.959495i | \(0.590906\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.2487 | 1.64683 | ||||||||
\(932\) | −5.55532 | − | 5.55532i | −0.181971 | − | 0.181971i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 13.0000i | − | 0.425373i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.8301 | + | 18.8301i | −0.615153 | + | 0.615153i | −0.944284 | − | 0.329131i | \(-0.893244\pi\) |
0.329131 | + | 0.944284i | \(0.393244\pi\) | |||||||
\(938\) | −3.20736 | + | 3.20736i | −0.104724 | + | 0.104724i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.4988i | 1.41802i | 0.705197 | + | 0.709011i | \(0.250858\pi\) | ||||
−0.705197 | + | 0.709011i | \(0.749142\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.53590 | − | 6.53590i | −0.212838 | − | 0.212838i | ||||
\(944\) | −4.52004 | −0.147115 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.53590 | 0.277526 | ||||||||
\(947\) | −11.5775 | − | 11.5775i | −0.376218 | − | 0.376218i | 0.493517 | − | 0.869736i | \(-0.335711\pi\) |
−0.869736 | + | 0.493517i | \(0.835711\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 64.8897i | 2.10641i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.535898 | − | 0.535898i | 0.0173686 | − | 0.0173686i | ||||
\(953\) | −10.2784 | + | 10.2784i | −0.332951 | + | 0.332951i | −0.853706 | − | 0.520755i | \(-0.825650\pi\) |
0.520755 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 5.37945i | − | 0.173984i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.80385 | − | 7.80385i | −0.252131 | − | 0.252131i | ||||
\(959\) | 1.79315 | 0.0579039 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.3590 | 0.430935 | ||||||||
\(962\) | 10.7589 | + | 10.7589i | 0.346881 | + | 0.346881i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.00000i | 0.128831i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.50962 | − | 2.50962i | 0.0807039 | − | 0.0807039i | −0.665603 | − | 0.746306i | \(-0.731825\pi\) |
0.746306 | + | 0.665603i | \(0.231825\pi\) | |||||||
\(968\) | −8.24504 | + | 8.24504i | −0.265006 | + | 0.265006i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.6303i | 1.01507i | 0.861632 | + | 0.507533i | \(0.169442\pi\) | ||||
−0.861632 | + | 0.507533i | \(0.830558\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.60770 | − | 3.60770i | −0.115657 | − | 0.115657i | ||||
\(974\) | −32.8043 | −1.05112 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.46410 | −0.302939 | ||||||||
\(977\) | 2.92996 | + | 2.92996i | 0.0937378 | + | 0.0937378i | 0.752421 | − | 0.658683i | \(-0.228886\pi\) |
−0.658683 | + | 0.752421i | \(0.728886\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.2487i | 0.902833i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.9545 | + | 15.9545i | −0.509128 | + | 0.509128i | ||||
\(983\) | −31.2886 | + | 31.2886i | −0.997950 | + | 0.997950i | −0.999998 | − | 0.00204770i | \(-0.999348\pi\) |
0.00204770 | + | 0.999998i | \(0.499348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 9.24316i | − | 0.294362i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25.8564 | − | 25.8564i | −0.822602 | − | 0.822602i | ||||
\(989\) | 3.58630 | 0.114038 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.60770 | 0.0828362 | 0.0414181 | − | 0.999142i | \(-0.486812\pi\) | ||||
0.0414181 | + | 0.999142i | \(0.486812\pi\) | |||||||
\(992\) | 4.70951 | + | 4.70951i | 0.149527 | + | 0.149527i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.00000i | 0.253745i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.8564 | − | 33.8564i | 1.07224 | − | 1.07224i | 0.0750645 | − | 0.997179i | \(-0.476084\pi\) |
0.997179 | − | 0.0750645i | \(-0.0239163\pi\) | |||||||
\(998\) | 25.3543 | − | 25.3543i | 0.802577 | − | 0.802577i | ||||
\(999\) | 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 | 1350.2.f.a.593.2 | 8 | ||
3.2 | odd | 2 | inner | 1350.2.f.a.593.4 | 8 | ||
5.2 | odd | 4 | inner | 1350.2.f.a.107.4 | 8 | ||
5.3 | odd | 4 | 270.2.f.b.107.2 | yes | 8 | ||
5.4 | even | 2 | 270.2.f.b.53.3 | yes | 8 | ||
15.2 | even | 4 | inner | 1350.2.f.a.107.2 | 8 | ||
15.8 | even | 4 | 270.2.f.b.107.3 | yes | 8 | ||
15.14 | odd | 2 | 270.2.f.b.53.2 | ✓ | 8 | ||
20.3 | even | 4 | 2160.2.w.b.1457.3 | 8 | |||
20.19 | odd | 2 | 2160.2.w.b.593.2 | 8 | |||
45.4 | even | 6 | 810.2.m.d.593.1 | 8 | |||
45.13 | odd | 12 | 810.2.m.e.107.1 | 8 | |||
45.14 | odd | 6 | 810.2.m.d.593.2 | 8 | |||
45.23 | even | 12 | 810.2.m.e.107.2 | 8 | |||
45.29 | odd | 6 | 810.2.m.e.53.1 | 8 | |||
45.34 | even | 6 | 810.2.m.e.53.2 | 8 | |||
45.38 | even | 12 | 810.2.m.d.377.1 | 8 | |||
45.43 | odd | 12 | 810.2.m.d.377.2 | 8 | |||
60.23 | odd | 4 | 2160.2.w.b.1457.2 | 8 | |||
60.59 | even | 2 | 2160.2.w.b.593.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.2.f.b.53.2 | ✓ | 8 | 15.14 | odd | 2 | ||
270.2.f.b.53.3 | yes | 8 | 5.4 | even | 2 | ||
270.2.f.b.107.2 | yes | 8 | 5.3 | odd | 4 | ||
270.2.f.b.107.3 | yes | 8 | 15.8 | even | 4 | ||
810.2.m.d.377.1 | 8 | 45.38 | even | 12 | |||
810.2.m.d.377.2 | 8 | 45.43 | odd | 12 | |||
810.2.m.d.593.1 | 8 | 45.4 | even | 6 | |||
810.2.m.d.593.2 | 8 | 45.14 | odd | 6 | |||
810.2.m.e.53.1 | 8 | 45.29 | odd | 6 | |||
810.2.m.e.53.2 | 8 | 45.34 | even | 6 | |||
810.2.m.e.107.1 | 8 | 45.13 | odd | 12 | |||
810.2.m.e.107.2 | 8 | 45.23 | even | 12 | |||
1350.2.f.a.107.2 | 8 | 15.2 | even | 4 | inner | ||
1350.2.f.a.107.4 | 8 | 5.2 | odd | 4 | inner | ||
1350.2.f.a.593.2 | 8 | 1.1 | even | 1 | trivial | ||
1350.2.f.a.593.4 | 8 | 3.2 | odd | 2 | inner | ||
2160.2.w.b.593.2 | 8 | 20.19 | odd | 2 | |||
2160.2.w.b.593.3 | 8 | 60.59 | even | 2 | |||
2160.2.w.b.1457.2 | 8 | 60.23 | odd | 4 | |||
2160.2.w.b.1457.3 | 8 | 20.3 | even | 4 |