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.a.239.2 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 1.41421 | + | 1.00000i | 0.816497 | + | 0.577350i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.414214 | + | 0.414214i | −0.185242 | + | 0.185242i | −0.793635 | − | 0.608394i | \(-0.791814\pi\) |
0.608394 | + | 0.793635i | \(0.291814\pi\) | |||||||
\(6\) | 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 | \(-0.946064\pi\) |
−0.168636 | − | 0.985678i | \(-0.553936\pi\) | |||||||
\(12\) | 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 | \(0.0453771\pi\) | ||||
−0.989856 | + | 0.142074i | \(0.954623\pi\) | |||||||
\(18\) | 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 | ||||||||
\(21\) | 1.41421 | + | 1.00000i | 0.308607 | + | 0.218218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.65685i | 1.59656i | 0.602284 | + | 0.798282i | \(0.294258\pi\) | ||||
−0.602284 | + | 0.798282i | \(0.705742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.65685i | 0.931371i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.41421 | + | 5.00000i | −0.272166 | + | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | + | 3.00000i | 0.557086 | + | 0.557086i | 0.928477 | − | 0.371391i | \(-0.121119\pi\) |
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 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 | \(-0.491470\pi\) | ||||
0.0267952 | + | 0.999641i | \(0.491470\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | −1.58579 | − | 0.757359i | −0.236395 | − | 0.112900i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.65685 | −0.825137 | −0.412568 | − | 0.910927i | \(-0.635368\pi\) | ||||
−0.412568 | + | 0.910927i | \(0.635368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.17157 | + | 1.65685i | −0.164053 | + | 0.232006i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.82843 | − | 5.82843i | 0.800596 | − | 0.800596i | −0.182593 | − | 0.983189i | \(-0.558449\pi\) |
0.983189 | + | 0.182593i | \(0.0584489\pi\) | |||||||
\(54\) | 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 | \(-0.872279\pi\) |
−0.390567 | − | 0.920575i | \(-0.627721\pi\) | |||||||
\(60\) | 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 | ||||||||
\(69\) | −7.65685 | + | 10.8284i | −0.921777 | + | 1.30359i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000i | 0.712069i | 0.934473 | + | 0.356034i | \(0.115871\pi\) | ||||
−0.934473 | + | 0.356034i | \(0.884129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.17157i | − | 0.605287i | −0.953104 | − | 0.302643i | \(-0.902131\pi\) | ||
0.953104 | − | 0.302643i | \(-0.0978691\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.65685 | + | 6.58579i | −0.537727 | + | 0.760461i | ||||
\(76\) | 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 | −0.0228915 | − | 0.999738i | \(-0.507287\pi\) |
0.999738 | + | 0.0228915i | \(0.00728722\pi\) | |||||||
\(84\) | 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 | \(-0.188448\pi\) | ||||
0.829812 | + | 0.558044i | \(0.188448\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.41421 | + | 4.41421i | −0.462735 | + | 0.462735i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.48528 | + | 9.17157i | −0.672492 | + | 0.951048i | ||||
\(94\) | 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 | ||||||||
\(99\) | 7.00000 | − | 14.6569i | 0.703526 | − | 1.47307i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0711 | + | 10.0711i | −1.00211 | + | 1.00211i | −0.00211093 | + | 0.999998i | \(0.500672\pi\) |
−0.999998 | + | 0.00211093i | \(0.999328\pi\) | |||||||
\(102\) | 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 | 0.422837 | − | 0.906206i | \(-0.361034\pi\) |
−0.906206 | + | 0.422837i | \(0.861034\pi\) | |||||||
\(108\) | 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 | \(0.0248317\pi\) | ||||
−0.996959 | + | 0.0779319i | \(0.975168\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.17157 | − | 3.17157i | −0.295751 | − | 0.295751i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.8995 | − | 8.07107i | −1.56236 | − | 0.746170i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.17157i | 0.107398i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3137i | 1.66488i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.485281 | + | 0.343146i | 0.0437563 | + | 0.0309404i | ||||
\(124\) | 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 | −0.862222 | − | 0.506531i | \(-0.830928\pi\) |
0.506531 | + | 0.862222i | \(0.330928\pi\) | |||||||
\(132\) | 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 | \(-0.393934\pi\) | ||||
0.327085 | + | 0.944995i | \(0.393934\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | −8.00000 | − | 5.65685i | −0.673722 | − | 0.476393i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 33.7990 | 2.82641 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.48528 | −0.206391 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.41421 | + | 1.00000i | 0.116642 | + | 0.0824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.48528 | + | 9.48528i | −0.777065 | + | 0.777065i | −0.979331 | − | 0.202266i | \(-0.935169\pi\) |
0.202266 | + | 0.979331i | \(0.435169\pi\) | |||||||
\(150\) | 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 | ||||||||
\(165\) | 4.48528 | + | 3.17157i | 0.349179 | + | 0.246907i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 7.17157i | − | 0.554953i | −0.960732 | − | 0.277476i | \(-0.910502\pi\) | ||
0.960732 | − | 0.277476i | \(-0.0894981\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 25.9706i | − | 1.99774i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.757359 | − | 1.58579i | 0.0579167 | − | 0.121268i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.89949 | − | 4.89949i | −0.372502 | − | 0.372502i | 0.495886 | − | 0.868388i | \(-0.334843\pi\) |
−0.868388 | + | 0.495886i | \(0.834843\pi\) | |||||||
\(174\) | 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 | \(0.541364\pi\) |
−0.991568 | + | 0.129584i | \(0.958636\pi\) | |||||||
\(180\) | 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 | ||||||||
\(189\) | −1.41421 | + | 5.00000i | −0.102869 | + | 0.363696i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.34315 | −0.458974 | −0.229487 | − | 0.973312i | \(-0.573705\pi\) | ||||
−0.229487 | + | 0.973312i | \(0.573705\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6569 | 1.12701 | 0.563503 | − | 0.826114i | \(-0.309454\pi\) | ||||
0.563503 | + | 0.826114i | \(0.309454\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.65685 | − | 5.17157i | 0.261873 | − | 0.370344i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.82843 | − | 5.82843i | 0.415258 | − | 0.415258i | −0.468307 | − | 0.883566i | \(-0.655136\pi\) |
0.883566 | + | 0.468307i | \(0.155136\pi\) | |||||||
\(198\) | 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 | ||||||||
\(213\) | −6.00000 | + | 8.48528i | −0.411113 | + | 0.581402i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.17157i | 0.216299i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.48528i | 0.440250i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.17157 | − | 7.31371i | 0.349463 | − | 0.494215i | ||||
\(220\) | 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 | −0.922262 | − | 0.386566i | \(-0.873661\pi\) |
0.386566 | + | 0.922262i | \(0.373661\pi\) | |||||||
\(228\) | 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 | \(-0.486298\pi\) | ||||
0.0430320 | + | 0.999074i | \(0.486298\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.34315 | − | 2.34315i | 0.152850 | − | 0.152850i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.00000 | + | 2.82843i | −0.129914 | + | 0.183726i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3137 | 0.731823 | 0.365911 | − | 0.930650i | \(-0.380757\pi\) | ||||
0.365911 | + | 0.930650i | \(0.380757\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.343146 | 0.0221040 | 0.0110520 | − | 0.999939i | \(-0.496482\pi\) | ||||
0.0110520 | + | 0.999939i | \(0.496482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5563 | + | 1.00000i | −0.997940 | + | 0.0641500i | ||||
\(244\) | 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 | 0.779182 | − | 0.626798i | \(-0.215635\pi\) |
−0.626798 | + | 0.779182i | \(0.715635\pi\) | |||||||
\(252\) | 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 | \(0.315551\pi\) | ||||
−0.547576 | + | 0.836756i | \(0.684449\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.82843 | + | 1.82843i | 0.113613 | + | 0.113613i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.48528 | + | 11.4853i | −0.339530 | + | 0.710921i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.6569i | 0.718792i | 0.933185 | + | 0.359396i | \(0.117017\pi\) | ||||
−0.933185 | + | 0.359396i | \(0.882983\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.82843i | 0.296608i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.1421 | + | 15.6569i | 1.35508 | + | 0.958184i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.58579 | − | 5.58579i | −0.340571 | − | 0.340571i | 0.516011 | − | 0.856582i | \(-0.327416\pi\) |
−0.856582 | + | 0.516011i | \(0.827416\pi\) | |||||||
\(270\) | 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 | \(-0.563911\pi\) | ||||
−0.199435 | + | 0.979911i | \(0.563911\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | 0.485281 | + | 0.343146i | 0.0287456 | + | 0.0203262i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.343146 | 0.0202553 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.6274 | 0.919260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.82843 | − | 2.00000i | −0.165805 | − | 0.117242i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.24264 | − | 9.24264i | 0.539961 | − | 0.539961i | −0.383557 | − | 0.923517i | \(-0.625301\pi\) |
0.923517 | + | 0.383557i | \(0.125301\pi\) | |||||||
\(294\) | 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 | ||||||||
\(309\) | −16.0000 | − | 11.3137i | −0.910208 | − | 0.643614i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.51472i | − | 0.0858918i | −0.999077 | − | 0.0429459i | \(-0.986326\pi\) | ||
0.999077 | − | 0.0429459i | \(-0.0136743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 20.4853i | − | 1.15790i | −0.815364 | − | 0.578948i | \(-0.803463\pi\) | ||
0.815364 | − | 0.578948i | \(-0.196537\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.58579 | − | 0.757359i | −0.0893489 | − | 0.0426724i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.1421 | + | 13.1421i | 0.738136 | + | 0.738136i | 0.972217 | − | 0.234081i | \(-0.0752082\pi\) |
−0.234081 | + | 0.972217i | \(0.575208\pi\) | |||||||
\(318\) | 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 | ||||||||
\(333\) | −3.34315 | + | 7.00000i | −0.183203 | + | 0.383598i | ||||
\(334\) | 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 | ||||||||
\(339\) | −1.65685 | + | 2.34315i | −0.0899880 | + | 0.127262i | ||||
\(340\) | 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 | 0.965587 | − | 0.260080i | \(-0.0837490\pi\) |
−0.260080 | + | 0.965587i | \(0.583749\pi\) | |||||||
\(348\) | 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 | \(-0.927496\pi\) | ||
0.974171 | − | 0.225813i | \(-0.0725038\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.48528 | − | 2.48528i | −0.131905 | − | 0.131905i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.17157 | + | 1.65685i | −0.0620062 | + | 0.0876900i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.3431i | 1.07367i | 0.843687 | + | 0.536835i | \(0.180380\pi\) | ||||
−0.843687 | + | 0.536835i | \(0.819620\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.6569i | − | 0.981940i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.3137 | + | 25.8995i | −0.961220 | + | 1.35937i | ||||
\(364\) | 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 | ||||||||
\(381\) | 15.6569 | − | 22.1421i | 0.802125 | − | 1.13438i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.3137 | 0.986884 | 0.493442 | − | 0.869779i | \(-0.335738\pi\) | ||||
0.493442 | + | 0.869779i | \(0.335738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.17157 | 0.161638 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.6569 | + | 7.00000i | 0.745050 | + | 0.355830i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.9706 | − | 19.9706i | 1.01255 | − | 1.01255i | 0.0126275 | − | 0.999920i | \(-0.495980\pi\) |
0.999920 | − | 0.0126275i | \(-0.00401955\pi\) | |||||||
\(390\) | 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 | \(-0.839823\pi\) | ||
0.876039 | − | 0.482240i | \(-0.160177\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.6274 | − | 28.6274i | −1.42603 | − | 1.42603i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.556349 | − | 5.24264i | 0.0276452 | − | 0.260509i | ||||
\(406\) | 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 | ||||||||
\(411\) | 10.8284 | + | 7.65685i | 0.534127 | + | 0.377685i | ||||
\(412\) | 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 | −0.952254 | − | 0.305308i | \(-0.901241\pi\) |
0.305308 | + | 0.952254i | \(0.401241\pi\) | |||||||
\(420\) | 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 | ||||||||
\(429\) | 47.7990 | + | 33.7990i | 2.30776 | + | 1.63183i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.31371 | −0.159616 | −0.0798079 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798079 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.6863 | −0.705778 | −0.352889 | − | 0.935665i | \(-0.614801\pi\) | ||||
−0.352889 | + | 0.935665i | \(0.614801\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.51472 | − | 2.48528i | −0.168518 | − | 0.119160i | ||||
\(436\) | 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 | 0.981720 | − | 0.190329i | \(-0.0609556\pi\) |
−0.190329 | + | 0.981720i | \(0.560956\pi\) | |||||||
\(444\) | 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 | \(0.0990106\pi\) | ||||
−0.952012 | + | 0.306059i | \(0.900989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.31371 | − | 1.31371i | −0.0618601 | − | 0.0618601i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.9706 | + | 17.6569i | 1.17322 | + | 0.829591i | ||||
\(454\) | 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 | ||||||||
\(459\) | −5.85786 | − | 1.65685i | −0.273422 | − | 0.0773353i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.4142 | + | 22.4142i | 1.04393 | + | 1.04393i | 0.998989 | + | 0.0449445i | \(0.0143111\pi\) |
0.0449445 | + | 0.998989i | \(0.485689\pi\) | |||||||
\(462\) | 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 | −0.957023 | − | 0.290013i | \(-0.906341\pi\) |
0.290013 | + | 0.957023i | \(0.406341\pi\) | |||||||
\(468\) | 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 | ||||||||
\(477\) | 22.3137 | + | 10.6569i | 1.02167 | + | 0.487944i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.3137 | 1.24800 | 0.623998 | − | 0.781426i | \(-0.285507\pi\) | ||||
0.623998 | + | 0.781426i | \(0.285507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.1421 | −0.736018 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.65685 | + | 10.8284i | −0.348399 | + | 0.492710i | ||||
\(484\) | 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 | 0.900437 | − | 0.434986i | \(-0.143247\pi\) |
−0.434986 | + | 0.900437i | \(0.643247\pi\) | |||||||
\(492\) | 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 | ||||||||
\(501\) | 7.17157 | − | 10.1421i | 0.320402 | − | 0.453117i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.8284i | 0.750342i | 0.926956 | + | 0.375171i | \(0.122416\pi\) | ||||
−0.926956 | + | 0.375171i | \(0.877584\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 8.34315i | − | 0.371265i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.9706 | − | 36.7279i | 1.15339 | − | 1.63114i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.24264 | − | 7.24264i | −0.321024 | − | 0.321024i | 0.528136 | − | 0.849160i | \(-0.322891\pi\) |
−0.849160 | + | 0.528136i | \(0.822891\pi\) | |||||||
\(510\) | 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 | \(-0.594202\pi\) | ||||
−0.291642 | + | 0.956528i | \(0.594202\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | −4.65685 | + | 6.58579i | −0.203242 | + | 0.287427i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.59798 | −0.330973 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −35.6274 | −1.54902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.4142 | − | 38.5563i | 0.799109 | − | 1.67320i | ||||
\(532\) | 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 | ||||||||
\(549\) | 9.24264 | + | 4.41421i | 0.394466 | + | 0.188394i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.48528i | − | 0.105877i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.00000i | 0.0850487i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.14214 | − | 1.51472i | −0.0909286 | − | 0.0642962i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.1421 | − | 15.1421i | −0.641593 | − | 0.641593i | 0.309354 | − | 0.950947i | \(-0.399887\pi\) |
−0.950947 | + | 0.309354i | \(0.899887\pi\) | |||||||
\(558\) | 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 | −0.986883 | − | 0.161440i | \(-0.948386\pi\) |
0.161440 | + | 0.986883i | \(0.448386\pi\) | |||||||
\(564\) | 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 | \(-0.739720\pi\) | ||||
−0.683906 | + | 0.729570i | \(0.739720\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | −8.97056 | − | 6.34315i | −0.374751 | − | 0.264989i | ||||
\(574\) | 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 | ||||||||
\(579\) | 22.1421 | + | 15.6569i | 0.920196 | + | 0.650677i | ||||
\(580\) | 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 | 0.956162 | − | 0.292838i | \(-0.0945997\pi\) |
−0.292838 | + | 0.956162i | \(0.594600\pi\) | |||||||
\(588\) | 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 | \(0.0121454\pi\) | ||||
−0.999272 | + | 0.0381467i | \(0.987855\pi\) | |||||||
\(594\) | 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 | \(-0.658967\pi\) | ||
0.478909 | − | 0.877865i | \(-0.341033\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.4853i | 0.672449i | 0.941782 | + | 0.336224i | \(0.109150\pi\) | ||||
−0.941782 | + | 0.336224i | \(0.890850\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.7990 | + | 26.7990i | −0.521215 | + | 1.09134i | ||||
\(604\) | 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 | \(-0.324678\pi\) | ||||
0.523360 | + | 0.852111i | \(0.324678\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | −38.2843 | − | 10.8284i | −1.53629 | − | 0.434530i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.6569 | 0.627279 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.9706 | −0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.17157 | + | 4.48528i | −0.126660 | + | 0.179125i | ||||
\(628\) | 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 | \(0.351920\pi\) | ||||
−0.448607 | + | 0.893729i | \(0.648080\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | −3.17157 | + | 4.48528i | −0.124881 | + | 0.176608i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 16.1421i | − | 0.634613i | −0.948323 | − | 0.317306i | \(-0.897222\pi\) | ||
0.948323 | − | 0.317306i | \(-0.102778\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 77.1127i | 3.02694i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.48528 | + | 9.17157i | −0.254178 | + | 0.359462i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.3431 | − | 11.3431i | −0.443892 | − | 0.443892i | 0.449426 | − | 0.893318i | \(-0.351629\pi\) |
−0.893318 | + | 0.449426i | \(0.851629\pi\) | |||||||
\(654\) | 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 | −0.00720841 | − | 0.999974i | \(-0.502295\pi\) |
0.999974 | + | 0.00720841i | \(0.00229453\pi\) | |||||||
\(660\) | 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 | ||||||||
\(669\) | 7.17157 | − | 10.1421i | 0.277269 | − | 0.392118i | ||||
\(670\) | 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 | ||||||||
\(675\) | −23.2843 | − | 6.58579i | −0.896212 | − | 0.253487i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.8995 | + | 20.8995i | −0.803233 | + | 0.803233i | −0.983599 | − | 0.180367i | \(-0.942272\pi\) |
0.180367 | + | 0.983599i | \(0.442272\pi\) | |||||||
\(678\) | 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 | 0.701079 | − | 0.713083i | \(-0.252702\pi\) |
−0.713083 | + | 0.701079i | \(0.752702\pi\) | |||||||
\(684\) | 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 | ||||||||
\(693\) | 7.00000 | − | 14.6569i | 0.265908 | − | 0.556768i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.65685i | 0.138712i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.402020i | 0.0152276i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.85786 | + | 1.31371i | 0.0702709 | + | 0.0496890i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.656854 | + | 0.656854i | 0.0248090 | + | 0.0248090i | 0.719402 | − | 0.694593i | \(-0.244416\pi\) |
−0.694593 | + | 0.719402i | \(0.744416\pi\) | |||||||
\(702\) | 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 | ||||||||
\(717\) | 16.0000 | + | 11.3137i | 0.597531 | + | 0.422518i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0000 | −0.596699 | −0.298350 | − | 0.954457i | \(-0.596436\pi\) | ||||
−0.298350 | + | 0.954457i | \(0.596436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.3137 | −0.421345 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.485281 | + | 0.343146i | 0.0180478 | + | 0.0127617i | ||||
\(724\) | 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 | ||||||||
\(741\) | 5.17157 | + | 3.65685i | 0.189982 | + | 0.134338i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.34315i | 0.159335i | 0.996822 | + | 0.0796673i | \(0.0253858\pi\) | ||||
−0.996822 | + | 0.0796673i | \(0.974614\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 7.85786i | − | 0.287890i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.0711 | + | 16.2721i | 1.24660 | + | 0.595364i | ||||
\(748\) | 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 | \(-0.268912\pi\) | ||||
0.663871 | + | 0.747847i | \(0.268912\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.82843 | − | 5.82843i | 0.211003 | − | 0.211003i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.887302 | − | 1.85786i | 0.0320805 | − | 0.0671712i | ||||
\(766\) | 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 | ||||||||
\(771\) | −26.8284 | + | 37.9411i | −0.966202 | + | 1.36642i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.5563 | − | 36.5563i | 1.31484 | − | 1.31484i | 0.397039 | − | 0.917802i | \(-0.370038\pi\) |
0.917802 | − | 0.397039i | \(-0.129962\pi\) | |||||||
\(774\) | 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 | ||||||||
\(789\) | −11.6569 | + | 16.4853i | −0.414995 | + | 0.586892i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.65685i | 0.0589110i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.3137i | 0.756872i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.82843 | + | 6.82843i | −0.171247 | + | 0.242179i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.4142 | + | 34.4142i | 1.21901 | + | 1.21901i | 0.967978 | + | 0.251036i | \(0.0807714\pi\) |
0.251036 | + | 0.967978i | \(0.419229\pi\) | |||||||
\(798\) | 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 | \(-0.630575\pi\) | ||||
−0.398804 | + | 0.917036i | \(0.630575\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | −16.8284 | + | 23.7990i | −0.590199 | + | 0.834667i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.51472 | −0.0530583 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.17157 | −0.110959 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.8995 | − | 8.07107i | −0.590516 | − | 0.282026i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.4853 | − | 15.4853i | 0.540440 | − | 0.540440i | −0.383218 | − | 0.923658i | \(-0.625184\pi\) |
0.923658 | + | 0.383218i | \(0.125184\pi\) | |||||||
\(822\) | 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 | 0.533095 | − | 0.846055i | \(-0.321029\pi\) |
−0.846055 | + | 0.533095i | \(0.821029\pi\) | |||||||
\(828\) | 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 | ||||||||
\(837\) | −32.4264 | − | 9.17157i | −1.12082 | − | 0.317016i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 51.4558i | − | 1.77645i | −0.459406 | − | 0.888227i | \(-0.651938\pi\) | ||
0.459406 | − | 0.888227i | \(-0.348062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 11.0000i | − | 0.379310i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.45584 | − | 6.68629i | −0.325677 | − | 0.230288i | ||||
\(844\) | 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 | \(-0.316323\pi\) | ||||
0.545544 | + | 0.838082i | \(0.316323\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | 0.485281 | + | 0.343146i | 0.0165383 | + | 0.0116944i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.3137 | −1.33825 | −0.669127 | − | 0.743148i | \(-0.733332\pi\) | ||||
−0.669127 | + | 0.743148i | \(0.733332\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.05887 | 0.138006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.1005 | + | 15.6274i | 0.750573 | + | 0.530735i | ||||
\(868\) | 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 | \(-0.695771\pi\) | ||
0.576984 | − | 0.816755i | \(-0.304229\pi\) | |||||||
\(882\) | 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 | ||||||||
\(885\) | 11.7990 | + | 8.34315i | 0.396619 | + | 0.280452i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 39.1716i | − | 1.31525i | −0.753344 | − | 0.657626i | \(-0.771561\pi\) | ||
0.753344 | − | 0.657626i | \(-0.228439\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 15.6569i | − | 0.525114i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 48.4558 | + | 5.14214i | 1.62333 | + | 0.172268i | ||||
\(892\) | 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 | ||||||||
\(909\) | −38.5563 | − | 18.4142i | −1.27883 | − | 0.610761i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.2843 | −1.46720 | −0.733602 | − | 0.679580i | \(-0.762162\pi\) | ||||
−0.733602 | + | 0.679580i | \(0.762162\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −68.1421 | −2.25518 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.00000 | + | 2.82843i | −0.0661180 | + | 0.0935049i | ||||
\(916\) | 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 | \(0.101513\pi\) | ||||
−0.949577 | + | 0.313534i | \(0.898487\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.414214 | − | 0.414214i | −0.0135753 | − | 0.0135753i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.51472 | − | 2.14214i | 0.0495897 | − | 0.0701304i | ||||
\(934\) | 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 | ||||||||
\(939\) | 20.4853 | − | 28.9706i | 0.668512 | − | 0.945419i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.3553 | − | 42.3553i | −1.38074 | − | 1.38074i | −0.843297 | − | 0.537447i | \(-0.819389\pi\) |
−0.537447 | − | 0.843297i | \(-0.680611\pi\) | |||||||
\(942\) | 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 | −0.324016 | − | 0.946052i | \(-0.605033\pi\) |
0.946052 | + | 0.324016i | \(0.105033\pi\) | |||||||
\(948\) | 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 | \(-0.393123\pi\) | ||||
0.329490 | + | 0.944159i | \(0.393123\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.62742 | − | 2.62742i | 0.0850212 | − | 0.0850212i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.9706 | − | 32.4853i | 0.742533 | − | 1.05010i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.65685 | 0.247253 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0589 | −0.356738 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.14214 | − | 19.1421i | 0.294601 | − | 0.616847i | ||||
\(964\) | 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 | 0.752099 | − | 0.659050i | \(-0.229041\pi\) |
−0.659050 | + | 0.752099i | \(0.729041\pi\) | |||||||
\(972\) | 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 | \(0.0443726\pi\) | ||||
−0.990299 | + | 0.138950i | \(0.955627\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −59.9411 | − | 59.9411i | −1.91573 | − | 1.91573i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.3137 | + | 10.6569i | 0.712422 | + | 0.340247i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.5147i | 1.19653i | 0.801297 | + | 0.598267i | \(0.204144\pi\) | ||||
−0.801297 | + | 0.598267i | \(0.795856\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.82843i | 0.153846i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.00000 | − | 5.65685i | −0.254643 | − | 0.180060i | ||||
\(988\) | 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.a.911.2 | 4 | ||
3.2 | odd | 2 | 1344.2.s.b.911.2 | 4 | |||
4.3 | odd | 2 | 336.2.s.b.155.1 | yes | 4 | ||
12.11 | even | 2 | 336.2.s.a.155.1 | ✓ | 4 | ||
16.3 | odd | 4 | 1344.2.s.b.239.1 | 4 | |||
16.13 | even | 4 | 336.2.s.a.323.2 | yes | 4 | ||
48.29 | odd | 4 | 336.2.s.b.323.1 | yes | 4 | ||
48.35 | even | 4 | inner | 1344.2.s.a.239.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.s.a.155.1 | ✓ | 4 | 12.11 | even | 2 | ||
336.2.s.a.323.2 | yes | 4 | 16.13 | even | 4 | ||
336.2.s.b.155.1 | yes | 4 | 4.3 | odd | 2 | ||
336.2.s.b.323.1 | yes | 4 | 48.29 | odd | 4 | ||
1344.2.s.a.239.2 | 4 | 48.35 | even | 4 | inner | ||
1344.2.s.a.911.2 | 4 | 1.1 | even | 1 | trivial | ||
1344.2.s.b.239.1 | 4 | 16.3 | odd | 4 | |||
1344.2.s.b.911.2 | 4 | 3.2 | odd | 2 |