Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(239,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.s (of order \(4\), degree \(2\), not 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: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 911.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.911 |
Dual form | 1344.2.s.b.239.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | 0 | ||||||||
\(3\) | 1.00000 | + | 1.41421i | 0.577350 | + | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.414214 | − | 0.414214i | 0.185242 | − | 0.185242i | −0.608394 | − | 0.793635i | \(-0.708186\pi\) |
0.793635 | + | 0.608394i | \(0.208186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.82843 | + | 3.82843i | 1.15431 | + | 1.15431i | 0.985678 | + | 0.168636i | \(0.0539362\pi\) |
0.168636 | + | 0.985678i | \(0.446064\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.41421 | + | 4.41421i | −1.22428 | + | 1.22428i | −0.258188 | + | 0.966095i | \(0.583125\pi\) |
−0.966095 | + | 0.258188i | \(0.916875\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | + | 0.171573i | 0.258199 | + | 0.0442999i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.17157i | − | 0.284148i | −0.989856 | − | 0.142074i | \(-0.954623\pi\) | ||
0.989856 | − | 0.142074i | \(-0.0453771\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.414214 | − | 0.414214i | −0.0950271 | − | 0.0950271i | 0.657995 | − | 0.753022i | \(-0.271405\pi\) |
−0.753022 | + | 0.657995i | \(0.771405\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | + | 1.41421i | 0.218218 | + | 0.308607i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.65685i | − | 1.59656i | −0.602284 | − | 0.798282i | \(-0.705742\pi\) | ||
0.602284 | − | 0.798282i | \(-0.294258\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.65685i | 0.931371i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | + | 1.41421i | −0.962250 | + | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | − | 3.00000i | −0.557086 | − | 0.557086i | 0.371391 | − | 0.928477i | \(-0.378881\pi\) |
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.48528i | 1.16479i | 0.812906 | + | 0.582395i | \(0.197884\pi\) | ||||
−0.812906 | + | 0.582395i | \(0.802116\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.58579 | + | 9.24264i | −0.276050 | + | 1.60894i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.414214 | − | 0.414214i | 0.0700149 | − | 0.0700149i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.82843 | + | 1.82843i | 0.300592 | + | 0.300592i | 0.841245 | − | 0.540654i | \(-0.181823\pi\) |
−0.540654 | + | 0.841245i | \(0.681823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.6569 | − | 1.82843i | −1.70646 | − | 0.292783i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.343146 | −0.0535904 | −0.0267952 | − | 0.999641i | \(-0.508530\pi\) | ||||
−0.0267952 | + | 0.999641i | \(0.508530\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.82843 | − | 3.82843i | 0.583830 | − | 0.583830i | −0.352124 | − | 0.935953i | \(-0.614540\pi\) |
0.935953 | + | 0.352124i | \(0.114540\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.757359 | + | 1.58579i | 0.112900 | + | 0.236395i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.65685 | 0.825137 | 0.412568 | − | 0.910927i | \(-0.364632\pi\) | ||||
0.412568 | + | 0.910927i | \(0.364632\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.65685 | − | 1.17157i | 0.232006 | − | 0.164053i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.82843 | + | 5.82843i | −0.800596 | + | 0.800596i | −0.983189 | − | 0.182593i | \(-0.941551\pi\) |
0.182593 | + | 0.983189i | \(0.441551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.17157 | 0.427655 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.171573 | − | 1.00000i | 0.0227254 | − | 0.132453i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.0711 | + | 10.0711i | 1.31114 | + | 1.31114i | 0.920575 | + | 0.390567i | \(0.127721\pi\) |
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.41421 | − | 2.41421i | 0.309108 | − | 0.309108i | −0.535455 | − | 0.844564i | \(-0.679860\pi\) |
0.844564 | + | 0.535455i | \(0.179860\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | + | 2.82843i | −0.125988 | + | 0.356348i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.65685i | 0.453577i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.00000 | + | 7.00000i | 0.855186 | + | 0.855186i | 0.990766 | − | 0.135580i | \(-0.0432899\pi\) |
−0.135580 | + | 0.990766i | \(0.543290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.8284 | − | 7.65685i | 1.30359 | − | 0.921777i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.00000i | − | 0.712069i | −0.934473 | − | 0.356034i | \(-0.884129\pi\) | ||
0.934473 | − | 0.356034i | \(-0.115871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.17157i | − | 0.605287i | −0.953104 | − | 0.302643i | \(-0.902131\pi\) | ||
0.953104 | − | 0.302643i | \(-0.0978691\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.58579 | + | 4.65685i | −0.760461 | + | 0.537727i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.82843 | + | 3.82843i | 0.436290 | + | 0.436290i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000i | 0.225018i | 0.993651 | + | 0.112509i | \(0.0358886\pi\) | ||||
−0.993651 | + | 0.112509i | \(0.964111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.89949 | + | 8.89949i | −0.976846 | + | 0.976846i | −0.999738 | − | 0.0228915i | \(-0.992713\pi\) |
0.0228915 | + | 0.999738i | \(0.492713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.485281 | − | 0.485281i | −0.0526362 | − | 0.0526362i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.24264 | − | 7.24264i | 0.133225 | − | 0.776493i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.6569 | −1.65962 | −0.829812 | − | 0.558044i | \(-0.811552\pi\) | ||||
−0.829812 | + | 0.558044i | \(0.811552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.41421 | + | 4.41421i | −0.462735 | + | 0.462735i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.17157 | + | 6.48528i | −0.951048 | + | 0.672492i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.343146 | −0.0352060 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.6569 | + | 7.00000i | −1.47307 | + | 0.703526i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0711 | − | 10.0711i | 1.00211 | − | 1.00211i | 0.00211093 | − | 0.999998i | \(-0.499328\pi\) |
0.999998 | − | 0.00211093i | \(-0.000671930\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.3137 | −1.11477 | −0.557386 | − | 0.830253i | \(-0.688196\pi\) | ||||
−0.557386 | + | 0.830253i | \(0.688196\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | + | 0.171573i | 0.0975900 | + | 0.0167438i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.00000 | + | 5.00000i | 0.483368 | + | 0.483368i | 0.906206 | − | 0.422837i | \(-0.138966\pi\) |
−0.422837 | + | 0.906206i | \(0.638966\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.82843 | − | 5.82843i | 0.558262 | − | 0.558262i | −0.370550 | − | 0.928812i | \(-0.620831\pi\) |
0.928812 | + | 0.370550i | \(0.120831\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.757359 | + | 4.41421i | −0.0718854 | + | 0.418979i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.65685i | − | 0.155864i | −0.996959 | − | 0.0779319i | \(-0.975168\pi\) | ||
0.996959 | − | 0.0779319i | \(-0.0248317\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.17157 | − | 3.17157i | −0.295751 | − | 0.295751i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.07107 | − | 16.8995i | −0.746170 | − | 1.56236i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.17157i | − | 0.107398i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3137i | 1.66488i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.343146 | − | 0.485281i | −0.0309404 | − | 0.0437563i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.00000 | + | 4.00000i | 0.357771 | + | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.6569i | − | 1.38932i | −0.719338 | − | 0.694661i | \(-0.755555\pi\) | ||
0.719338 | − | 0.694661i | \(-0.244445\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.24264 | + | 1.58579i | 0.813769 | + | 0.139621i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.07107 | − | 4.07107i | 0.355691 | − | 0.355691i | −0.506531 | − | 0.862222i | \(-0.669072\pi\) |
0.862222 | + | 0.506531i | \(0.169072\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.414214 | − | 0.414214i | −0.0359169 | − | 0.0359169i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.48528 | + | 2.65685i | −0.127833 | + | 0.228666i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.65685 | −0.654169 | −0.327085 | − | 0.944995i | \(-0.606066\pi\) | ||||
−0.327085 | + | 0.944995i | \(0.606066\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.41421 | − | 4.41421i | 0.374409 | − | 0.374409i | −0.494671 | − | 0.869080i | \(-0.664712\pi\) |
0.869080 | + | 0.494671i | \(0.164712\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.65685 | + | 8.00000i | 0.476393 | + | 0.673722i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −33.7990 | −2.82641 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.48528 | −0.206391 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | + | 1.41421i | 0.0824786 | + | 0.116642i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.48528 | − | 9.48528i | 0.777065 | − | 0.777065i | −0.202266 | − | 0.979331i | \(-0.564831\pi\) |
0.979331 | + | 0.202266i | \(0.0648306\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.6569 | 1.43689 | 0.718447 | − | 0.695581i | \(-0.244853\pi\) | ||||
0.718447 | + | 0.695581i | \(0.244853\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.31371 | + | 1.17157i | 0.267897 | + | 0.0947161i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.68629 | + | 2.68629i | 0.215768 | + | 0.215768i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.89949 | − | 2.89949i | 0.231405 | − | 0.231405i | −0.581874 | − | 0.813279i | \(-0.697680\pi\) |
0.813279 | + | 0.581874i | \(0.197680\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.0711 | − | 2.41421i | −1.11591 | − | 0.191460i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.65685i | − | 0.603445i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.82843 | + | 1.82843i | 0.143213 | + | 0.143213i | 0.775078 | − | 0.631865i | \(-0.217710\pi\) |
−0.631865 | + | 0.775078i | \(0.717710\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.17157 | + | 4.48528i | 0.246907 | + | 0.349179i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.17157i | 0.554953i | 0.960732 | + | 0.277476i | \(0.0894981\pi\) | ||||
−0.960732 | + | 0.277476i | \(0.910502\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 25.9706i | − | 1.99774i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.58579 | − | 0.757359i | 0.121268 | − | 0.0579167i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.89949 | + | 4.89949i | 0.372502 | + | 0.372502i | 0.868388 | − | 0.495886i | \(-0.165157\pi\) |
−0.495886 | + | 0.868388i | \(0.665157\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.65685i | 0.352025i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.17157 | + | 24.3137i | −0.313555 | + | 1.82753i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.0000 | − | 15.0000i | 1.12115 | − | 1.12115i | 0.129584 | − | 0.991568i | \(-0.458636\pi\) |
0.991568 | − | 0.129584i | \(-0.0413643\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.07107 | − | 2.07107i | −0.153941 | − | 0.153941i | 0.625934 | − | 0.779876i | \(-0.284718\pi\) |
−0.779876 | + | 0.625934i | \(0.784718\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.82843 | + | 1.00000i | 0.430850 | + | 0.0739221i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.51472 | 0.111364 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.48528 | − | 4.48528i | 0.327996 | − | 0.327996i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.00000 | + | 1.41421i | −0.363696 | + | 0.102869i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.34315 | 0.458974 | 0.229487 | − | 0.973312i | \(-0.426295\pi\) | ||||
0.229487 | + | 0.973312i | \(0.426295\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6569 | 1.12701 | 0.563503 | − | 0.826114i | \(-0.309454\pi\) | ||||
0.563503 | + | 0.826114i | \(0.309454\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.17157 | + | 3.65685i | −0.370344 | + | 0.261873i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.82843 | + | 5.82843i | −0.415258 | + | 0.415258i | −0.883566 | − | 0.468307i | \(-0.844864\pi\) |
0.468307 | + | 0.883566i | \(0.344864\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.89949 | + | 16.8995i | −0.204515 | + | 1.19200i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.00000 | − | 3.00000i | −0.210559 | − | 0.210559i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.142136 | + | 0.142136i | −0.00992718 | + | 0.00992718i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.6569 | + | 7.65685i | 1.50526 | + | 0.532188i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.17157i | − | 0.219382i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.00000 | − | 5.00000i | −0.344214 | − | 0.344214i | 0.513735 | − | 0.857949i | \(-0.328262\pi\) |
−0.857949 | + | 0.513735i | \(0.828262\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.48528 | − | 6.00000i | 0.581402 | − | 0.411113i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3.17157i | − | 0.216299i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.48528i | 0.440250i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.31371 | − | 5.17157i | 0.494215 | − | 0.349463i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.17157 | + | 5.17157i | 0.347878 | + | 0.347878i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 7.17157i | − | 0.480244i | −0.970743 | − | 0.240122i | \(-0.922813\pi\) | ||
0.970743 | − | 0.240122i | \(-0.0771875\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.1716 | − | 4.65685i | −0.878105 | − | 0.310457i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.07107 | − | 8.07107i | 0.535696 | − | 0.535696i | −0.386566 | − | 0.922262i | \(-0.626339\pi\) |
0.922262 | + | 0.386566i | \(0.126339\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.8995 | + | 10.8995i | 0.720259 | + | 0.720259i | 0.968658 | − | 0.248399i | \(-0.0799044\pi\) |
−0.248399 | + | 0.968658i | \(0.579904\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.58579 | + | 9.24264i | −0.104337 | + | 0.608121i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.31371 | −0.0860639 | −0.0430320 | − | 0.999074i | \(-0.513702\pi\) | ||||
−0.0430320 | + | 0.999074i | \(0.513702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.34315 | − | 2.34315i | 0.152850 | − | 0.152850i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.82843 | + | 2.00000i | −0.183726 | + | 0.129914i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3137 | −0.731823 | −0.365911 | − | 0.930650i | \(-0.619243\pi\) | ||||
−0.365911 | + | 0.930650i | \(0.619243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.343146 | 0.0221040 | 0.0110520 | − | 0.999939i | \(-0.496482\pi\) | ||||
0.0110520 | + | 0.999939i | \(0.496482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | − | 15.5563i | 0.0641500 | − | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.414214 | − | 0.414214i | 0.0264631 | − | 0.0264631i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.65685 | 0.232680 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.4853 | − | 3.68629i | −1.36157 | − | 0.233609i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.41421 | − | 2.41421i | −0.152384 | − | 0.152384i | 0.626798 | − | 0.779182i | \(-0.284365\pi\) |
−0.779182 | + | 0.626798i | \(0.784365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.3137 | − | 29.3137i | 1.84294 | − | 1.84294i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.201010 | − | 1.17157i | 0.0125877 | − | 0.0733667i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 26.8284i | − | 1.67351i | −0.547576 | − | 0.836756i | \(-0.684449\pi\) | ||
0.547576 | − | 0.836756i | \(-0.315551\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.82843 | + | 1.82843i | 0.113613 | + | 0.113613i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.4853 | − | 5.48528i | 0.710921 | − | 0.339530i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 11.6569i | − | 0.718792i | −0.933185 | − | 0.359396i | \(-0.882983\pi\) | ||
0.933185 | − | 0.359396i | \(-0.117017\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.82843i | 0.296608i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.6569 | − | 22.1421i | −0.958184 | − | 1.35508i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.58579 | + | 5.58579i | 0.340571 | + | 0.340571i | 0.856582 | − | 0.516011i | \(-0.172584\pi\) |
−0.516011 | + | 0.856582i | \(0.672584\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.8284i | 1.02225i | 0.859505 | + | 0.511127i | \(0.170772\pi\) | ||||
−0.859505 | + | 0.511127i | \(0.829228\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.6569 | − | 1.82843i | −0.644982 | − | 0.110661i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.8284 | + | 17.8284i | −1.07509 | + | 1.07509i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.31371 | + | 6.31371i | 0.379354 | + | 0.379354i | 0.870869 | − | 0.491515i | \(-0.163557\pi\) |
−0.491515 | + | 0.870869i | \(0.663557\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.3431 | − | 6.48528i | −1.09818 | − | 0.388264i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.68629 | 0.398871 | 0.199435 | − | 0.979911i | \(-0.436089\pi\) | ||||
0.199435 | + | 0.979911i | \(0.436089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.8995 | − | 12.8995i | 0.766795 | − | 0.766795i | −0.210746 | − | 0.977541i | \(-0.567589\pi\) |
0.977541 | + | 0.210746i | \(0.0675892\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.343146 | − | 0.485281i | −0.0203262 | − | 0.0287456i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.343146 | −0.0202553 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.6274 | 0.919260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.00000 | − | 2.82843i | −0.117242 | − | 0.165805i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.24264 | + | 9.24264i | −0.539961 | + | 0.539961i | −0.923517 | − | 0.383557i | \(-0.874699\pi\) |
0.383557 | + | 0.923517i | \(0.374699\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.34315 | 0.485757 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.5563 | − | 13.7279i | −1.42490 | − | 0.796575i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 33.7990 | + | 33.7990i | 1.95465 | + | 1.95465i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.82843 | − | 3.82843i | 0.220667 | − | 0.220667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.3137 | + | 4.17157i | 1.39679 | + | 0.239651i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.00000i | − | 0.114520i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.8995 | + | 14.8995i | 0.850359 | + | 0.850359i | 0.990177 | − | 0.139818i | \(-0.0446518\pi\) |
−0.139818 | + | 0.990177i | \(0.544652\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.3137 | − | 16.0000i | −0.643614 | − | 0.910208i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.51472i | 0.0858918i | 0.999077 | + | 0.0429459i | \(0.0136743\pi\) | ||||
−0.999077 | + | 0.0429459i | \(0.986326\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 20.4853i | − | 1.15790i | −0.815364 | − | 0.578948i | \(-0.803463\pi\) | ||
0.815364 | − | 0.578948i | \(-0.196537\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.757359 | + | 1.58579i | 0.0426724 | + | 0.0893489i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.1421 | − | 13.1421i | −0.738136 | − | 0.738136i | 0.234081 | − | 0.972217i | \(-0.424792\pi\) |
−0.972217 | + | 0.234081i | \(0.924792\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 22.9706i | − | 1.28610i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.07107 | + | 12.0711i | −0.115596 | + | 0.673741i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.485281 | + | 0.485281i | −0.0270018 | + | 0.0270018i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.5563 | − | 20.5563i | −1.14026 | − | 1.14026i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.0711 | + | 2.41421i | 0.778132 | + | 0.133506i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.65685 | 0.311872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.1421 | + | 17.1421i | −0.942217 | + | 0.942217i | −0.998419 | − | 0.0562024i | \(-0.982101\pi\) |
0.0562024 | + | 0.998419i | \(0.482101\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.00000 | + | 3.34315i | −0.383598 | + | 0.183203i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.79899 | 0.316833 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.3137 | 1.37893 | 0.689463 | − | 0.724321i | \(-0.257847\pi\) | ||||
0.689463 | + | 0.724321i | \(0.257847\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.34315 | − | 1.65685i | 0.127262 | − | 0.0899880i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.8284 | + | 24.8284i | −1.34453 | + | 1.34453i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.31371 | − | 7.65685i | 0.0707277 | − | 0.412231i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.1421 | − | 13.1421i | −0.705507 | − | 0.705507i | 0.260080 | − | 0.965587i | \(-0.416251\pi\) |
−0.965587 | + | 0.260080i | \(0.916251\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.07107 | + | 2.07107i | −0.110862 | + | 0.110862i | −0.760362 | − | 0.649500i | \(-0.774978\pi\) |
0.649500 | + | 0.760362i | \(0.274978\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.8284 | − | 28.3137i | 0.844859 | − | 1.51127i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.48528i | 0.451626i | 0.974171 | + | 0.225813i | \(0.0725038\pi\) | ||||
−0.974171 | + | 0.225813i | \(0.927496\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.48528 | − | 2.48528i | −0.131905 | − | 0.131905i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.65685 | − | 1.17157i | 0.0876900 | − | 0.0620062i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 20.3431i | − | 1.07367i | −0.843687 | − | 0.536835i | \(-0.819620\pi\) | ||
0.843687 | − | 0.536835i | \(-0.180380\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.6569i | − | 0.981940i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.8995 | + | 18.3137i | −1.35937 | + | 0.961220i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.14214 | − | 2.14214i | −0.112125 | − | 0.112125i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 16.1421i | − | 0.842613i | −0.906918 | − | 0.421306i | \(-0.861572\pi\) | ||
0.906918 | − | 0.421306i | \(-0.138428\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.343146 | − | 0.970563i | 0.0178635 | − | 0.0505255i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.82843 | + | 5.82843i | −0.302597 | + | 0.302597i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.31371 | − | 8.31371i | −0.430468 | − | 0.430468i | 0.458320 | − | 0.888787i | \(-0.348451\pi\) |
−0.888787 | + | 0.458320i | \(0.848451\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.65685 | + | 9.65685i | −0.0855596 | + | 0.498678i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.4853 | 1.36406 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.1421 | − | 27.1421i | 1.39420 | − | 1.39420i | 0.578553 | − | 0.815645i | \(-0.303618\pi\) |
0.815645 | − | 0.578553i | \(-0.196382\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.1421 | − | 15.6569i | 1.13438 | − | 0.802125i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.3137 | −0.986884 | −0.493442 | − | 0.869779i | \(-0.664262\pi\) | ||||
−0.493442 | + | 0.869779i | \(0.664262\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.17157 | 0.161638 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.00000 | + | 14.6569i | 0.355830 | + | 0.745050i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.9706 | + | 19.9706i | −1.01255 | + | 1.01255i | −0.0126275 | + | 0.999920i | \(0.504020\pi\) |
−0.999920 | + | 0.0126275i | \(0.995980\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.97056 | −0.453661 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.82843 | + | 1.68629i | 0.495779 | + | 0.0850622i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.828427 | + | 0.828427i | 0.0416827 | + | 0.0416827i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.7279 | + | 23.7279i | −1.19087 | + | 1.19087i | −0.214047 | + | 0.976823i | \(0.568665\pi\) |
−0.976823 | + | 0.214047i | \(0.931335\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.171573 | − | 1.00000i | 0.00858939 | − | 0.0500626i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.3137i | 0.964481i | 0.876039 | + | 0.482240i | \(0.160177\pi\) | ||||
−0.876039 | + | 0.482240i | \(0.839823\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.6274 | − | 28.6274i | −1.42603 | − | 1.42603i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.24264 | + | 0.556349i | −0.260509 | + | 0.0276452i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.0000i | 0.693954i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.1716i | 1.24465i | 0.782757 | + | 0.622327i | \(0.213813\pi\) | ||||
−0.782757 | + | 0.622327i | \(0.786187\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.65685 | − | 10.8284i | −0.377685 | − | 0.534127i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.0711 | + | 10.0711i | 0.495565 | + | 0.495565i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.37258i | 0.361906i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.6569 | + | 1.82843i | 0.521868 | + | 0.0895385i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.2426 | − | 13.2426i | 0.646945 | − | 0.646945i | −0.305308 | − | 0.952254i | \(-0.598759\pi\) |
0.952254 | + | 0.305308i | \(0.0987595\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.68629 | − | 1.68629i | −0.0821848 | − | 0.0821848i | 0.664819 | − | 0.747004i | \(-0.268509\pi\) |
−0.747004 | + | 0.664819i | \(0.768509\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.65685 | + | 16.0000i | −0.275046 | + | 0.777947i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.45584 | 0.264647 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.41421 | − | 2.41421i | 0.116832 | − | 0.116832i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −33.7990 | − | 47.7990i | −1.63183 | − | 2.30776i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.31371 | 0.159616 | 0.0798079 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798079 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.6863 | −0.705778 | −0.352889 | − | 0.935665i | \(-0.614801\pi\) | ||||
−0.352889 | + | 0.935665i | \(0.614801\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.48528 | − | 3.51472i | −0.119160 | − | 0.168518i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.17157 | + | 3.17157i | −0.151717 | + | 0.151717i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.970563 | 0.0463224 | 0.0231612 | − | 0.999732i | \(-0.492627\pi\) | ||||
0.0231612 | + | 0.999732i | \(0.492627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | + | 2.82843i | −0.0476190 | + | 0.134687i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.6569 | − | 16.6569i | −0.791391 | − | 0.791391i | 0.190329 | − | 0.981720i | \(-0.439044\pi\) |
−0.981720 | + | 0.190329i | \(0.939044\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.48528 | + | 6.48528i | −0.307432 | + | 0.307432i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.8995 | + | 3.92893i | 1.08311 | + | 0.185832i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 12.9706i | − | 0.612119i | −0.952012 | − | 0.306059i | \(-0.900989\pi\) | ||
0.952012 | − | 0.306059i | \(-0.0990106\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.31371 | − | 1.31371i | −0.0618601 | − | 0.0618601i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.6569 | + | 24.9706i | 0.829591 | + | 1.17322i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.65685i | 0.171436i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 29.9411i | − | 1.40059i | −0.713855 | − | 0.700293i | \(-0.753053\pi\) | ||
0.713855 | − | 0.700293i | \(-0.246947\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.65685 | + | 5.85786i | 0.0773353 | + | 0.273422i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.4142 | − | 22.4142i | −1.04393 | − | 1.04393i | −0.998989 | − | 0.0449445i | \(-0.985689\pi\) |
−0.0449445 | − | 0.998989i | \(-0.514311\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11.6569i | − | 0.541740i | −0.962616 | − | 0.270870i | \(-0.912689\pi\) | ||
0.962616 | − | 0.270870i | \(-0.0873113\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.11270 | + | 6.48528i | −0.0516002 | + | 0.300748i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.4142 | − | 14.4142i | 0.667010 | − | 0.667010i | −0.290013 | − | 0.957023i | \(-0.593659\pi\) |
0.957023 | + | 0.290013i | \(0.0936595\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.00000 | + | 7.00000i | 0.323230 | + | 0.323230i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.00000 | + | 1.20101i | 0.322543 | + | 0.0553396i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29.3137 | 1.34785 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.92893 | − | 1.92893i | 0.0885055 | − | 0.0885055i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.6569 | − | 22.3137i | −0.487944 | − | 1.02167i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.3137 | −1.24800 | −0.623998 | − | 0.781426i | \(-0.714493\pi\) | ||||
−0.623998 | + | 0.781426i | \(0.714493\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.1421 | −0.736018 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.8284 | − | 7.65685i | 0.492710 | − | 0.348399i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.828427 | + | 0.828427i | −0.0376169 | + | 0.0376169i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.2843 | 0.737911 | 0.368955 | − | 0.929447i | \(-0.379716\pi\) | ||||
0.368955 | + | 0.929447i | \(0.379716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.757359 | + | 4.41421i | −0.0342490 | + | 0.199618i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.3137 | − | 10.3137i | −0.465451 | − | 0.465451i | 0.434986 | − | 0.900437i | \(-0.356753\pi\) |
−0.900437 | + | 0.434986i | \(0.856753\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.51472 | + | 3.51472i | −0.158295 | + | 0.158295i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.17157 | + | 8.97056i | −0.142552 | + | 0.403197i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6.00000i | − | 0.269137i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.68629 | − | 5.68629i | −0.254553 | − | 0.254553i | 0.568281 | − | 0.822834i | \(-0.307609\pi\) |
−0.822834 | + | 0.568281i | \(0.807609\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.1421 | + | 7.17157i | −0.453117 | + | 0.320402i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 16.8284i | − | 0.750342i | −0.926956 | − | 0.375171i | \(-0.877584\pi\) | ||
0.926956 | − | 0.375171i | \(-0.122416\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 8.34315i | − | 0.371265i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 36.7279 | − | 25.9706i | 1.63114 | − | 1.15339i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.24264 | + | 7.24264i | 0.321024 | + | 0.321024i | 0.849160 | − | 0.528136i | \(-0.177109\pi\) |
−0.528136 | + | 0.849160i | \(0.677109\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5.17157i | − | 0.228777i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.65685 | + | 1.48528i | 0.117303 | + | 0.0655768i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.68629 | + | 4.68629i | −0.206503 | + | 0.206503i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.6569 | + | 21.6569i | 0.952467 | + | 0.952467i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.02944 | + | 11.8284i | −0.0890824 | + | 0.519210i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.3137 | 0.583284 | 0.291642 | − | 0.956528i | \(-0.405798\pi\) | ||||
0.291642 | + | 0.956528i | \(0.405798\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.0416 | + | 21.0416i | −0.920086 | + | 0.920086i | −0.997035 | − | 0.0769488i | \(-0.975482\pi\) |
0.0769488 | + | 0.997035i | \(0.475482\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.58579 | + | 4.65685i | −0.287427 | + | 0.203242i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.59798 | 0.330973 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −35.6274 | −1.54902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −38.5563 | + | 18.4142i | −1.67320 | + | 0.799109i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.51472 | − | 1.51472i | 0.0656097 | − | 0.0656097i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.14214 | 0.179080 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 36.2132 | + | 6.21320i | 1.56272 | + | 0.268120i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.82843 | + | 3.82843i | 0.164902 | + | 0.164902i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0000 | + | 21.0000i | −0.902861 | + | 0.902861i | −0.995683 | − | 0.0928222i | \(-0.970411\pi\) |
0.0928222 | + | 0.995683i | \(0.470411\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.857864 | − | 5.00000i | 0.0368145 | − | 0.214571i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4.82843i | − | 0.206827i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.1421 | + | 17.1421i | 0.732945 | + | 0.732945i | 0.971202 | − | 0.238257i | \(-0.0765761\pi\) |
−0.238257 | + | 0.971202i | \(0.576576\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.41421 | + | 9.24264i | 0.188394 | + | 0.394466i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.48528i | 0.105877i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.00000i | 0.0850487i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.51472 | + | 2.14214i | 0.0642962 | + | 0.0909286i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.1421 | + | 15.1421i | 0.641593 | + | 0.641593i | 0.950947 | − | 0.309354i | \(-0.100113\pi\) |
−0.309354 | + | 0.950947i | \(0.600113\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.7990i | 1.42954i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.8284 | + | 1.85786i | 0.457177 | + | 0.0784391i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.5858 | − | 19.5858i | 0.825442 | − | 0.825442i | −0.161440 | − | 0.986883i | \(-0.551614\pi\) |
0.986883 | + | 0.161440i | \(0.0516138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.686292 | − | 0.686292i | −0.0288725 | − | 0.0288725i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.00000 | − | 5.65685i | −0.293972 | − | 0.237566i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.6274 | 1.36781 | 0.683906 | − | 0.729570i | \(-0.260280\pi\) | ||||
0.683906 | + | 0.729570i | \(0.260280\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.17157 | − | 6.17157i | 0.258272 | − | 0.258272i | −0.566079 | − | 0.824351i | \(-0.691540\pi\) |
0.824351 | + | 0.566079i | \(0.191540\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.34315 | + | 8.97056i | 0.264989 | + | 0.374751i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 35.6569 | 1.48699 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.343146 | −0.0142853 | −0.00714267 | − | 0.999974i | \(-0.502274\pi\) | ||||
−0.00714267 | + | 0.999974i | \(0.502274\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.6569 | + | 22.1421i | 0.650677 | + | 0.920196i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.89949 | + | 8.89949i | −0.369213 | + | 0.369213i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −44.6274 | −1.84828 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.3431 | − | 3.65685i | −0.427636 | − | 0.151192i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.0711 | − | 16.0711i | −0.663324 | − | 0.663324i | 0.292838 | − | 0.956162i | \(-0.405400\pi\) |
−0.956162 | + | 0.292838i | \(0.905400\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.68629 | − | 2.68629i | 0.110687 | − | 0.110687i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.0711 | − | 2.41421i | −0.578806 | − | 0.0993075i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.85786i | − | 0.0762933i | −0.999272 | − | 0.0381467i | \(-0.987855\pi\) | ||
0.999272 | − | 0.0381467i | \(-0.0121454\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.485281 | − | 0.485281i | −0.0198946 | − | 0.0198946i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.9706i | 1.75573i | 0.478909 | + | 0.877865i | \(0.341033\pi\) | ||||
−0.478909 | + | 0.877865i | \(0.658967\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.4853i | 0.672449i | 0.941782 | + | 0.336224i | \(0.109150\pi\) | ||||
−0.941782 | + | 0.336224i | \(0.890850\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.7990 | + | 12.7990i | −1.09134 | + | 0.521215i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.58579 | + | 7.58579i | 0.308406 | + | 0.308406i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.1127i | 0.856938i | 0.903556 | + | 0.428469i | \(0.140947\pi\) | ||||
−0.903556 | + | 0.428469i | \(0.859053\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.24264 | − | 7.24264i | 0.0503543 | − | 0.293487i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.9706 | + | 24.9706i | −1.01020 | + | 1.01020i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.1716 | − | 14.1716i | −0.572384 | − | 0.572384i | 0.360410 | − | 0.932794i | \(-0.382637\pi\) |
−0.932794 | + | 0.360410i | \(0.882637\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.343146 | − | 0.0588745i | −0.0138370 | − | 0.00237405i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.0000 | −1.04672 | −0.523360 | − | 0.852111i | \(-0.675322\pi\) | ||||
−0.523360 | + | 0.852111i | \(0.675322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.4142 | + | 26.4142i | −1.06168 | + | 1.06168i | −0.0637083 | + | 0.997969i | \(0.520293\pi\) |
−0.997969 | + | 0.0637083i | \(0.979707\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.8284 | + | 38.2843i | 0.434530 | + | 1.53629i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.6569 | −0.627279 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.9706 | −0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.48528 | − | 3.17157i | 0.179125 | − | 0.126660i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.14214 | − | 2.14214i | 0.0854125 | − | 0.0854125i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.6569 | 0.543671 | 0.271835 | − | 0.962344i | \(-0.412369\pi\) | ||||
0.271835 | + | 0.962344i | \(0.412369\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.07107 | − | 12.0711i | 0.0823176 | − | 0.479782i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.48528 | − | 6.48528i | −0.257361 | − | 0.257361i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.41421 | + | 4.41421i | −0.174898 | + | 0.174898i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.9706 | + | 6.00000i | 0.671345 | + | 0.237356i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 45.2548i | − | 1.78746i | −0.448607 | − | 0.893729i | \(-0.648080\pi\) | ||
0.448607 | − | 0.893729i | \(-0.351920\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.0416 | + | 21.0416i | 0.829801 | + | 0.829801i | 0.987489 | − | 0.157688i | \(-0.0504040\pi\) |
−0.157688 | + | 0.987489i | \(0.550404\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.48528 | − | 3.17157i | 0.176608 | − | 0.124881i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.1421i | 0.634613i | 0.948323 | + | 0.317306i | \(0.102778\pi\) | ||||
−0.948323 | + | 0.317306i | \(0.897222\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 77.1127i | 3.02694i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.17157 | + | 6.48528i | −0.359462 | + | 0.254178i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.3431 | + | 11.3431i | 0.443892 | + | 0.443892i | 0.893318 | − | 0.449426i | \(-0.148371\pi\) |
−0.449426 | + | 0.893318i | \(0.648371\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3.37258i | − | 0.131778i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6274 | + | 5.17157i | 0.570670 | + | 0.201762i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.4853 | + | 25.4853i | −0.992766 | + | 0.992766i | −0.999974 | − | 0.00720841i | \(-0.997705\pi\) |
0.00720841 | + | 0.999974i | \(0.497705\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.3848 | + | 11.3848i | 0.442816 | + | 0.442816i | 0.892957 | − | 0.450141i | \(-0.148626\pi\) |
−0.450141 | + | 0.892957i | \(0.648626\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.14214 | + | 12.4853i | −0.0831937 | + | 0.484888i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.343146 | −0.0133066 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.9706 | + | 22.9706i | −0.889424 | + | 0.889424i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.1421 | − | 7.17157i | 0.392118 | − | 0.277269i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.4853 | 0.713616 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.00000 | −0.0770943 | −0.0385472 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385472 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.58579 | − | 23.2843i | −0.253487 | − | 0.896212i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.8995 | − | 20.8995i | 0.803233 | − | 0.803233i | −0.180367 | − | 0.983599i | \(-0.557728\pi\) |
0.983599 | + | 0.180367i | \(0.0577284\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.00000 | −0.0767530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.4853 | + | 3.34315i | 0.746678 | + | 0.128110i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.313708 | + | 0.313708i | 0.0120037 | + | 0.0120037i | 0.713083 | − | 0.701079i | \(-0.247298\pi\) |
−0.701079 | + | 0.713083i | \(0.747298\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.17157 | + | 3.17157i | −0.121180 | + | 0.121180i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.51472 | + | 26.3137i | −0.172247 | + | 1.00393i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 51.4558i | − | 1.96031i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.8995 | + | 14.8995i | 0.566803 | + | 0.566803i | 0.931232 | − | 0.364428i | \(-0.118735\pi\) |
−0.364428 | + | 0.931232i | \(0.618735\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.6569 | + | 7.00000i | −0.556768 | + | 0.265908i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.65685i | − | 0.138712i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.402020i | 0.0152276i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.31371 | − | 1.85786i | −0.0496890 | − | 0.0702709i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.656854 | − | 0.656854i | −0.0248090 | − | 0.0248090i | 0.694593 | − | 0.719402i | \(-0.255584\pi\) |
−0.719402 | + | 0.694593i | \(0.755584\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.51472i | − | 0.0571287i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.65685 | + | 0.970563i | 0.213049 | + | 0.0365535i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0711 | − | 10.0711i | 0.378761 | − | 0.378761i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.17157 | − | 2.17157i | −0.0815551 | − | 0.0815551i | 0.665152 | − | 0.746708i | \(-0.268367\pi\) |
−0.746708 | + | 0.665152i | \(0.768367\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.65685 | − | 2.00000i | −0.212149 | − | 0.0750059i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 49.6569 | 1.85966 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.0000 | + | 14.0000i | −0.523570 | + | 0.523570i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.3137 | − | 16.0000i | −0.422518 | − | 0.597531i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.0000 | 0.596699 | 0.298350 | − | 0.954457i | \(-0.403564\pi\) | ||||
0.298350 | + | 0.954457i | \(0.403564\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.3137 | −0.421345 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.343146 | + | 0.485281i | 0.0127617 | + | 0.0180478i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.9706 | − | 13.9706i | 0.518854 | − | 0.518854i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.3137 | 1.30971 | 0.654856 | − | 0.755753i | \(-0.272729\pi\) | ||||
0.654856 | + | 0.755753i | \(0.272729\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.48528 | − | 4.48528i | −0.165894 | − | 0.165894i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.27208 | + | 2.27208i | −0.0839211 | + | 0.0839211i | −0.747821 | − | 0.663900i | \(-0.768900\pi\) |
0.663900 | + | 0.747821i | \(0.268900\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.00000 | + | 0.171573i | 0.0368856 | + | 0.00632856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 53.5980i | 1.97431i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.8284 | + | 21.8284i | 0.802972 | + | 0.802972i | 0.983559 | − | 0.180587i | \(-0.0577998\pi\) |
−0.180587 | + | 0.983559i | \(0.557800\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.65685 | + | 5.17157i | 0.134338 | + | 0.189982i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4.34315i | − | 0.159335i | −0.996822 | − | 0.0796673i | \(-0.974614\pi\) | ||
0.996822 | − | 0.0796673i | \(-0.0253858\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 7.85786i | − | 0.287890i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.2721 | − | 34.0711i | −0.595364 | − | 1.24660i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.00000 | + | 5.00000i | 0.182696 | + | 0.182696i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.6863i | 0.681872i | 0.940086 | + | 0.340936i | \(0.110744\pi\) | ||||
−0.940086 | + | 0.340936i | \(0.889256\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.00000 | − | 5.82843i | 0.0364420 | − | 0.212400i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.31371 | − | 7.31371i | 0.266173 | − | 0.266173i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.5147 | + | 14.5147i | 0.527546 | + | 0.527546i | 0.919840 | − | 0.392294i | \(-0.128318\pi\) |
−0.392294 | + | 0.919840i | \(0.628318\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 70.7696 | + | 12.1421i | 2.56877 | + | 0.440732i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.6274 | −1.32774 | −0.663871 | − | 0.747847i | \(-0.731088\pi\) | ||||
−0.663871 | + | 0.747847i | \(0.731088\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.82843 | − | 5.82843i | 0.211003 | − | 0.211003i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.85786 | − | 0.887302i | 0.0671712 | − | 0.0320805i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −88.9117 | −3.21041 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.3431 | 0.877836 | 0.438918 | − | 0.898527i | \(-0.355362\pi\) | ||||
0.438918 | + | 0.898527i | \(0.355362\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.9411 | − | 26.8284i | 1.36642 | − | 0.966202i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.5563 | + | 36.5563i | −1.31484 | + | 1.31484i | −0.397039 | + | 0.917802i | \(0.629962\pi\) |
−0.917802 | + | 0.397039i | \(0.870038\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30.2010 | −1.08485 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.757359 | + | 4.41421i | −0.0271701 | + | 0.158359i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.142136 | + | 0.142136i | 0.00509254 | + | 0.00509254i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.9706 | − | 22.9706i | 0.821951 | − | 0.821951i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.2426 | + | 10.7574i | 0.687676 | + | 0.384437i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.40202i | − | 0.0857318i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.0416 | − | 23.0416i | −0.821345 | − | 0.821345i | 0.164956 | − | 0.986301i | \(-0.447252\pi\) |
−0.986301 | + | 0.164956i | \(0.947252\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.4853 | − | 11.6569i | 0.586892 | − | 0.414995i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.65685i | − | 0.0589110i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.3137i | 0.756872i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.82843 | + | 4.82843i | −0.242179 | + | 0.171247i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.4142 | − | 34.4142i | −1.21901 | − | 1.21901i | −0.967978 | − | 0.251036i | \(-0.919229\pi\) |
−0.251036 | − | 0.967978i | \(-0.580771\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.62742i | − | 0.234461i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.6569 | − | 44.2843i | 0.553208 | − | 1.56471i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.7990 | − | 19.7990i | 0.698691 | − | 0.698691i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.17157 | − | 3.17157i | −0.111783 | − | 0.111783i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.31371 | + | 13.4853i | −0.0814464 | + | 0.474704i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.6863 | 0.797608 | 0.398804 | − | 0.917036i | \(-0.369425\pi\) | ||||
0.398804 | + | 0.917036i | \(0.369425\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0711 | + | 16.0711i | −0.564332 | + | 0.564332i | −0.930535 | − | 0.366203i | \(-0.880657\pi\) |
0.366203 | + | 0.930535i | \(0.380657\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.7990 | + | 16.8284i | −0.834667 | + | 0.590199i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.51472 | 0.0530583 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.17157 | −0.110959 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.07107 | − | 16.8995i | −0.282026 | − | 0.590516i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.4853 | + | 15.4853i | −0.540440 | + | 0.540440i | −0.923658 | − | 0.383218i | \(-0.874816\pi\) |
0.383218 | + | 0.923658i | \(0.374816\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.9706 | −0.870419 | −0.435210 | − | 0.900329i | \(-0.643326\pi\) | ||||
−0.435210 | + | 0.900329i | \(0.643326\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −43.0416 | − | 7.38478i | −1.49852 | − | 0.257105i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.00000 | + | 9.00000i | 0.312961 | + | 0.312961i | 0.846055 | − | 0.533095i | \(-0.178971\pi\) |
−0.533095 | + | 0.846055i | \(0.678971\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.8995 | + | 24.8995i | −0.864795 | + | 0.864795i | −0.991891 | − | 0.127095i | \(-0.959435\pi\) |
0.127095 | + | 0.991891i | \(0.459435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.61522 | + | 15.2426i | −0.0907211 | + | 0.528761i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.17157i | − | 0.0405926i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.97056 | + | 2.97056i | 0.102801 | + | 0.102801i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.17157 | − | 32.4264i | −0.317016 | − | 1.12082i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.4558i | 1.77645i | 0.459406 | + | 0.888227i | \(0.348062\pi\) | ||||
−0.459406 | + | 0.888227i | \(0.651938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 11.0000i | − | 0.379310i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.68629 | + | 9.45584i | 0.230288 | + | 0.325677i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.7574 | − | 10.7574i | −0.370064 | − | 0.370064i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.3137i | 0.629266i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.1421 | + | 5.34315i | 1.06880 | + | 0.183376i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.0000 | − | 14.0000i | 0.479914 | − | 0.479914i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.4142 | − | 28.4142i | −0.972884 | − | 0.972884i | 0.0267578 | − | 0.999642i | \(-0.491482\pi\) |
−0.999642 | + | 0.0267578i | \(0.991482\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.343146 | − | 0.970563i | 0.0117353 | − | 0.0331925i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.9411 | −1.09109 | −0.545544 | − | 0.838082i | \(-0.683677\pi\) | ||||
−0.545544 | + | 0.838082i | \(0.683677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.8995 | + | 22.8995i | −0.781321 | + | 0.781321i | −0.980054 | − | 0.198733i | \(-0.936317\pi\) |
0.198733 | + | 0.980054i | \(0.436317\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.343146 | − | 0.485281i | −0.0116944 | − | 0.0165383i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.3137 | 1.33825 | 0.669127 | − | 0.743148i | \(-0.266668\pi\) | ||||
0.669127 | + | 0.743148i | \(0.266668\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.05887 | 0.138006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.6274 | + | 22.1005i | 0.530735 | + | 0.750573i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.65685 | + | 7.65685i | −0.259741 | + | 0.259741i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −61.7990 | −2.09398 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.00000 | − | 5.65685i | 0.0676897 | − | 0.191456i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.00000 | + | 4.00000i | 0.135225 | + | 0.135225i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.51472 | − | 6.51472i | 0.219986 | − | 0.219986i | −0.588506 | − | 0.808493i | \(-0.700284\pi\) |
0.808493 | + | 0.588506i | \(0.200284\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.3137 | − | 3.82843i | −0.752623 | − | 0.129130i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.4853i | 1.63351i | 0.576984 | + | 0.816755i | \(0.304229\pi\) | ||||
−0.576984 | + | 0.816755i | \(0.695771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.9411 | − | 38.9411i | −1.31047 | − | 1.31047i | −0.921065 | − | 0.389408i | \(-0.872680\pi\) |
−0.389408 | − | 0.921065i | \(-0.627320\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.34315 | + | 11.7990i | 0.280452 | + | 0.396619i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.1716i | 1.31525i | 0.753344 | + | 0.657626i | \(0.228439\pi\) | ||||
−0.753344 | + | 0.657626i | \(0.771561\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 15.6569i | − | 0.525114i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.14214 | − | 48.4558i | −0.172268 | − | 1.62333i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.34315 | − | 2.34315i | −0.0784104 | − | 0.0784104i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 12.4264i | − | 0.415369i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.0000 | + | 81.5980i | −0.467446 | + | 2.72448i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.4558 | − | 19.4558i | 0.648889 | − | 0.648889i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.82843 | + | 6.82843i | 0.227488 | + | 0.227488i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.24264 | + | 1.58579i | 0.307576 | + | 0.0527717i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.71573 | −0.0570328 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.3137 | − | 20.3137i | 0.674506 | − | 0.674506i | −0.284246 | − | 0.958751i | \(-0.591743\pi\) |
0.958751 | + | 0.284246i | \(0.0917432\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.4142 | + | 38.5563i | 0.610761 | + | 1.27883i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.2843 | 1.46720 | 0.733602 | − | 0.679580i | \(-0.237838\pi\) | ||||
0.733602 | + | 0.679580i | \(0.237838\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −68.1421 | −2.25518 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.82843 | − | 2.00000i | 0.0935049 | − | 0.0661180i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.07107 | − | 4.07107i | 0.134439 | − | 0.134439i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.34315 | 0.0772932 | 0.0386466 | − | 0.999253i | \(-0.487695\pi\) | ||||
0.0386466 | + | 0.999253i | \(0.487695\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.17157 | + | 35.9706i | −0.203360 | + | 1.18527i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26.4853 | + | 26.4853i | 0.871774 | + | 0.871774i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.51472 | + | 8.51472i | −0.279962 | + | 0.279962i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.3137 | − | 32.0000i | 0.371591 | − | 1.05102i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 19.1127i | − | 0.627067i | −0.949577 | − | 0.313534i | \(-0.898487\pi\) | ||
0.949577 | − | 0.313534i | \(-0.101513\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.414214 | − | 0.414214i | −0.0135753 | − | 0.0135753i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.14214 | + | 1.51472i | −0.0701304 | + | 0.0495897i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 3.71573i | − | 0.121517i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.85786i | − | 0.0606938i | −0.999539 | − | 0.0303469i | \(-0.990339\pi\) | ||
0.999539 | − | 0.0303469i | \(-0.00966120\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.9706 | − | 20.4853i | 0.945419 | − | 0.668512i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.3553 | + | 42.3553i | 1.38074 | + | 1.38074i | 0.843297 | + | 0.537447i | \(0.180611\pi\) |
0.537447 | + | 0.843297i | \(0.319389\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.62742i | 0.0855605i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.48528 | + | 2.65685i | −0.0483162 | + | 0.0864275i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.1421 | + | 19.1421i | −0.622036 | + | 0.622036i | −0.946052 | − | 0.324016i | \(-0.894967\pi\) |
0.324016 | + | 0.946052i | \(0.394967\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.8284 | + | 22.8284i | 0.741042 | + | 0.741042i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.44365 | − | 31.7279i | 0.176522 | − | 1.02885i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.3431 | −0.658979 | −0.329490 | − | 0.944159i | \(-0.606877\pi\) | ||||
−0.329490 | + | 0.944159i | \(0.606877\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.62742 | − | 2.62742i | 0.0850212 | − | 0.0850212i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32.4853 | − | 22.9706i | 1.05010 | − | 0.742533i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.65685 | −0.247253 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0589 | −0.356738 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.1421 | + | 9.14214i | −0.616847 | + | 0.294601i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.48528 | − | 6.48528i | 0.208769 | − | 0.208769i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3137 | 0.749718 | 0.374859 | − | 0.927082i | \(-0.377691\pi\) | ||||
0.374859 | + | 0.927082i | \(0.377691\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.17157 | − | 0.201010i | −0.0376363 | − | 0.00645738i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.89949 | − | 2.89949i | −0.0930492 | − | 0.0930492i | 0.659050 | − | 0.752099i | \(-0.270959\pi\) |
−0.752099 | + | 0.659050i | \(0.770959\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.41421 | − | 4.41421i | 0.141513 | − | 0.141513i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.51472 | − | 49.6274i | 0.272689 | − | 1.58935i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 8.68629i | − | 0.277899i | −0.990299 | − | 0.138950i | \(-0.955627\pi\) | ||
0.990299 | − | 0.138950i | \(-0.0443726\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −59.9411 | − | 59.9411i | −1.91573 | − | 1.91573i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.6569 | + | 22.3137i | 0.340247 | + | 0.712422i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 37.5147i | − | 1.19653i | −0.801297 | − | 0.598267i | \(-0.795856\pi\) | ||
0.801297 | − | 0.598267i | \(-0.204144\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.82843i | 0.153846i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.65685 | + | 8.00000i | 0.180060 | + | 0.254643i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29.3137 | − | 29.3137i | −0.932122 | − | 0.932122i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.6863i | 0.720654i | 0.932826 | + | 0.360327i | \(0.117335\pi\) | ||||
−0.932826 | + | 0.360327i | \(0.882665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −41.3848 | − | 7.10051i | −1.31331 | − | 0.225328i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.9289 | − | 19.9289i | −0.631156 | − | 0.631156i | 0.317202 | − | 0.948358i | \(-0.397257\pi\) |
−0.948358 | + | 0.317202i | \(0.897257\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.7279 | − | 6.55635i | −0.371055 | − | 0.207434i |
(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 | 1344.2.s.b.911.2 | 4 | ||
3.2 | odd | 2 | 1344.2.s.a.911.2 | 4 | |||
4.3 | odd | 2 | 336.2.s.a.155.1 | ✓ | 4 | ||
12.11 | even | 2 | 336.2.s.b.155.1 | yes | 4 | ||
16.3 | odd | 4 | 1344.2.s.a.239.2 | 4 | |||
16.13 | even | 4 | 336.2.s.b.323.1 | yes | 4 | ||
48.29 | odd | 4 | 336.2.s.a.323.2 | yes | 4 | ||
48.35 | even | 4 | inner | 1344.2.s.b.239.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.s.a.155.1 | ✓ | 4 | 4.3 | odd | 2 | ||
336.2.s.a.323.2 | yes | 4 | 48.29 | odd | 4 | ||
336.2.s.b.155.1 | yes | 4 | 12.11 | even | 2 | ||
336.2.s.b.323.1 | yes | 4 | 16.13 | even | 4 | ||
1344.2.s.a.239.2 | 4 | 16.3 | odd | 4 | |||
1344.2.s.a.911.2 | 4 | 3.2 | odd | 2 | |||
1344.2.s.b.239.1 | 4 | 48.35 | even | 4 | inner | ||
1344.2.s.b.911.2 | 4 | 1.1 | even | 1 | trivial |