Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(353,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.353");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.bi (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.66563859404\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 353.3 | ||
Root | \(-1.14412 + 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.353 |
Dual form | 960.2.bi.f.737.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.70711 | − | 0.292893i | 0.985599 | − | 0.169102i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.58114 | − | 1.58114i | −0.707107 | − | 0.707107i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.23607 | + | 2.23607i | −0.845154 | + | 0.845154i | −0.989524 | − | 0.144370i | \(-0.953885\pi\) |
0.144370 | + | 0.989524i | \(0.453885\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | − | 1.00000i | 0.942809 | − | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.24264 | −1.27920 | −0.639602 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639602 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47214 | + | 4.47214i | −1.24035 | + | 1.24035i | −0.280491 | + | 0.959857i | \(0.590497\pi\) |
−0.959857 | + | 0.280491i | \(0.909503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.16228 | − | 2.23607i | −0.816497 | − | 0.577350i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.82843 | − | 2.82843i | −0.685994 | − | 0.685994i | 0.275350 | − | 0.961344i | \(-0.411206\pi\) |
−0.961344 | + | 0.275350i | \(0.911206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.16228 | + | 4.47214i | −0.690066 | + | 0.975900i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.16228 | + | 3.16228i | −0.659380 | + | 0.659380i | −0.955233 | − | 0.295853i | \(-0.904396\pi\) |
0.295853 | + | 0.955233i | \(0.404396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000i | 1.00000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.53553 | − | 2.53553i | 0.872864 | − | 0.487964i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.48683i | − | 1.76166i | −0.473432 | − | 0.880830i | \(-0.656985\pi\) | ||
0.473432 | − | 0.880830i | \(-0.343015\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.47214 | 0.803219 | 0.401610 | − | 0.915811i | \(-0.368451\pi\) | ||||
0.401610 | + | 0.915811i | \(0.368451\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.24264 | + | 1.24264i | −1.26078 | + | 0.216316i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.07107 | 1.19523 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.32456 | + | 8.94427i | −1.01274 | + | 1.43223i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.82843i | 0.441726i | 0.975305 | + | 0.220863i | \(0.0708874\pi\) | ||||
−0.975305 | + | 0.220863i | \(0.929113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | + | 4.00000i | −0.609994 | + | 0.609994i | −0.942944 | − | 0.332950i | \(-0.891956\pi\) |
0.332950 | + | 0.942944i | \(0.391956\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.05327 | − | 2.89100i | −0.902369 | − | 0.430964i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.16228 | + | 3.16228i | 0.461266 | + | 0.461266i | 0.899070 | − | 0.437805i | \(-0.144244\pi\) |
−0.437805 | + | 0.899070i | \(0.644244\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.00000i | − | 0.428571i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.65685 | − | 4.00000i | −0.792118 | − | 0.560112i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.32456 | − | 6.32456i | −0.868744 | − | 0.868744i | 0.123589 | − | 0.992333i | \(-0.460560\pi\) |
−0.992333 | + | 0.123589i | \(0.960560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.70820 | + | 6.70820i | 0.904534 | + | 0.904534i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.41421 | + | 0.585786i | −0.452224 | + | 0.0775893i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.07107i | 0.920575i | 0.887770 | + | 0.460287i | \(0.152254\pi\) | ||||
−0.887770 | + | 0.460287i | \(0.847746\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.94427i | − | 1.14520i | −0.819836 | − | 0.572598i | \(-0.805935\pi\) | ||
0.819836 | − | 0.572598i | \(-0.194065\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.08849 | + | 8.56062i | −0.515101 | + | 1.07854i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.1421 | 1.75412 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | + | 6.00000i | 0.733017 | + | 0.733017i | 0.971216 | − | 0.238200i | \(-0.0765572\pi\) |
−0.238200 | + | 0.971216i | \(0.576557\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.47214 | + | 6.32456i | −0.538382 | + | 0.761387i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.32456i | 0.750587i | 0.926906 | + | 0.375293i | \(0.122458\pi\) | ||||
−0.926906 | + | 0.375293i | \(0.877542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00000 | − | 3.00000i | −0.351123 | − | 0.351123i | 0.509404 | − | 0.860527i | \(-0.329866\pi\) |
−0.860527 | + | 0.509404i | \(0.829866\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.46447 | + | 8.53553i | 0.169102 | + | 0.985599i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.48683 | − | 9.48683i | 1.08112 | − | 1.08112i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.47214i | − | 0.503155i | −0.967837 | − | 0.251577i | \(-0.919051\pi\) | ||
0.967837 | − | 0.251577i | \(-0.0809493\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.65685 | − | 5.65685i | −0.620920 | − | 0.620920i | 0.324846 | − | 0.945767i | \(-0.394687\pi\) |
−0.945767 | + | 0.324846i | \(0.894687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.94427i | 0.970143i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.77863 | − | 16.1950i | −0.297900 | − | 1.73629i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.48528 | −0.899438 | −0.449719 | − | 0.893170i | \(-0.648476\pi\) | ||||
−0.449719 | + | 0.893170i | \(0.648476\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 20.0000i | − | 2.09657i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.63441 | − | 1.30986i | 0.791652 | − | 0.135826i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.16228 | + | 3.16228i | 0.324443 | + | 0.324443i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | − | 3.00000i | 0.304604 | − | 0.304604i | −0.538208 | − | 0.842812i | \(-0.680899\pi\) |
0.842812 | + | 0.538208i | \(0.180899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.0000 | + | 4.24264i | −1.20605 | + | 0.426401i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.16228 | −0.314658 | −0.157329 | − | 0.987546i | \(-0.550288\pi\) | ||||
−0.157329 | + | 0.987546i | \(0.550288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.23607 | + | 2.23607i | 0.220326 | + | 0.220326i | 0.808636 | − | 0.588310i | \(-0.200206\pi\) |
−0.588310 | + | 0.808636i | \(0.700206\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.0711 | − | 2.07107i | 1.17802 | − | 0.202116i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3137 | − | 11.3137i | 1.09374 | − | 1.09374i | 0.0986115 | − | 0.995126i | \(-0.468560\pi\) |
0.995126 | − | 0.0986115i | \(-0.0314401\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.48528 | + | 8.48528i | −0.798228 | + | 0.798228i | −0.982816 | − | 0.184588i | \(-0.940905\pi\) |
0.184588 | + | 0.982816i | \(0.440905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.0000 | 0.932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.17697 | + | 17.1212i | −0.755962 | + | 1.58286i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.6491 | 1.15954 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.828427 | + | 4.82843i | 0.0746968 | + | 0.435365i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.90569 | − | 7.90569i | 0.707107 | − | 0.707107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.23607 | + | 2.23607i | −0.198419 | + | 0.198419i | −0.799322 | − | 0.600903i | \(-0.794808\pi\) |
0.600903 | + | 0.799322i | \(0.294808\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.65685 | + | 8.00000i | −0.498058 | + | 0.704361i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.07107 | −0.617802 | −0.308901 | − | 0.951094i | \(-0.599961\pi\) | ||||
−0.308901 | + | 0.951094i | \(0.599961\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.47214 | − | 4.47214i | 0.387783 | − | 0.387783i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.1803 | − | 3.16228i | −0.962250 | − | 0.272166i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.82843 | + | 2.82843i | 0.241649 | + | 0.241649i | 0.817532 | − | 0.575883i | \(-0.195342\pi\) |
−0.575883 | + | 0.817532i | \(0.695342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.32456 | + | 4.47214i | 0.532624 | + | 0.376622i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.9737 | − | 18.9737i | 1.58666 | − | 1.58666i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.0000 | + | 15.0000i | −1.24568 | + | 1.24568i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.878680 | − | 5.12132i | −0.0724723 | − | 0.422399i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.16228i | 0.259064i | 0.991575 | + | 0.129532i | \(0.0413475\pi\) | ||||
−0.991575 | + | 0.129532i | \(0.958653\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.8885 | −1.45575 | −0.727875 | − | 0.685710i | \(-0.759492\pi\) | ||||
−0.727875 | + | 0.685710i | \(0.759492\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.8284 | − | 5.17157i | −0.875426 | − | 0.418097i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.07107 | − | 7.07107i | −0.567962 | − | 0.567962i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.94427 | − | 8.94427i | −0.713831 | − | 0.713831i | 0.253504 | − | 0.967334i | \(-0.418417\pi\) |
−0.967334 | + | 0.253504i | \(0.918417\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.6491 | − | 8.94427i | −1.00314 | − | 0.709327i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 14.1421i | − | 1.11456i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | + | 12.0000i | −0.939913 | + | 0.939913i | −0.998294 | − | 0.0583818i | \(-0.981406\pi\) |
0.0583818 | + | 0.998294i | \(0.481406\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.4164 | + | 9.48683i | 1.04447 | + | 0.738549i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.48683 | + | 9.48683i | 0.734113 | + | 0.734113i | 0.971432 | − | 0.237319i | \(-0.0762686\pi\) |
−0.237319 | + | 0.971432i | \(0.576269\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 27.0000i | − | 2.07692i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.65685 | + | 2.00000i | −0.432590 | + | 0.152944i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.16228 | + | 3.16228i | 0.240424 | + | 0.240424i | 0.817025 | − | 0.576602i | \(-0.195622\pi\) |
−0.576602 | + | 0.817025i | \(0.695622\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.1803 | − | 11.1803i | −0.845154 | − | 0.845154i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.07107 | + | 12.0711i | 0.155671 | + | 0.907317i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.5563i | 1.16274i | 0.813641 | + | 0.581368i | \(0.197482\pi\) | ||||
−0.813641 | + | 0.581368i | \(0.802518\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.8885i | 1.32964i | 0.747001 | + | 0.664822i | \(0.231493\pi\) | ||||
−0.747001 | + | 0.664822i | \(0.768507\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.61972 | − | 15.2688i | −0.193655 | − | 1.12870i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0000 | + | 12.0000i | 0.877527 | + | 0.877527i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.47214 | + | 15.8114i | −0.325300 | + | 1.15011i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 12.6491i | − | 0.915258i | −0.889143 | − | 0.457629i | \(-0.848699\pi\) | ||
0.889143 | − | 0.457629i | \(-0.151301\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.00000 | − | 3.00000i | −0.215945 | − | 0.215945i | 0.590842 | − | 0.806787i | \(-0.298796\pi\) |
−0.806787 | + | 0.590842i | \(0.798796\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 24.1421 | − | 4.14214i | 1.72885 | − | 0.296624i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.32456 | + | 6.32456i | −0.450606 | + | 0.450606i | −0.895556 | − | 0.444950i | \(-0.853222\pi\) |
0.444950 | + | 0.895556i | \(0.353222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 17.8885i | − | 1.26809i | −0.773298 | − | 0.634043i | \(-0.781394\pi\) | ||
0.773298 | − | 0.634043i | \(-0.218606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0000 | + | 8.48528i | 0.846415 | + | 0.598506i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.2132 | + | 21.2132i | 1.48888 | + | 1.48888i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.47214 | − | 4.47214i | 0.312348 | − | 0.312348i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.78199 | + | 12.1065i | −0.401876 | + | 0.841463i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.48528 | 0.586939 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.0000i | − | 0.963800i | −0.876226 | − | 0.481900i | \(-0.839947\pi\) | ||
0.876226 | − | 0.481900i | \(-0.160053\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.85242 | + | 10.7967i | 0.126926 | + | 0.739777i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.6491 | 0.862662 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.0000 | + | 10.0000i | −0.678844 | + | 0.678844i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.00000 | − | 4.24264i | −0.405442 | − | 0.286691i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.2982 | 1.70174 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.23607 | + | 2.23607i | 0.149738 | + | 0.149738i | 0.778001 | − | 0.628263i | \(-0.216234\pi\) |
−0.628263 | + | 0.778001i | \(0.716234\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | + | 14.1421i | 0.333333 | + | 0.942809i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.07107 | + | 7.07107i | −0.469323 | + | 0.469323i | −0.901695 | − | 0.432372i | \(-0.857677\pi\) |
0.432372 | + | 0.901695i | \(0.357677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.8328 | 1.77316 | 0.886581 | − | 0.462573i | \(-0.153074\pi\) | ||||
0.886581 | + | 0.462573i | \(0.153074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.4164 | − | 18.9737i | 0.882735 | − | 1.24838i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 10.0000i | − | 0.652328i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.30986 | − | 7.63441i | −0.0850844 | − | 0.495908i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.9737 | 1.22730 | 0.613652 | − | 0.789576i | \(-0.289700\pi\) | ||||
0.613652 | + | 0.789576i | \(0.289700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.0000 | 1.54598 | 0.772988 | − | 0.634421i | \(-0.218761\pi\) | ||||
0.772988 | + | 0.634421i | \(0.218761\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.2929 | − | 11.7071i | 0.660289 | − | 0.751011i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.74342 | + | 4.74342i | −0.303046 | + | 0.303046i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.94427 | − | 8.94427i | 0.569110 | − | 0.569110i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.3137 | − | 8.00000i | −0.716977 | − | 0.506979i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0416 | −1.51749 | −0.758747 | − | 0.651385i | \(-0.774188\pi\) | ||||
−0.758747 | + | 0.651385i | \(0.774188\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.4164 | − | 13.4164i | 0.843482 | − | 0.843482i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.61972 | + | 15.2688i | 0.164053 | + | 0.956171i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.48683 | − | 26.8328i | −0.587220 | − | 1.66091i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.16228 | + | 3.16228i | −0.194994 | + | 0.194994i | −0.797850 | − | 0.602856i | \(-0.794029\pi\) |
0.602856 | + | 0.797850i | \(0.294029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.0000i | 1.22859i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.4853 | + | 2.48528i | −0.886485 | + | 0.152097i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.16228i | − | 0.192807i | −0.995342 | − | 0.0964037i | \(-0.969266\pi\) | ||
0.995342 | − | 0.0964037i | \(-0.0307340\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.85786 | − | 34.1421i | −0.354534 | − | 2.06638i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 21.2132i | − | 1.27920i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.94427 | + | 8.94427i | 0.537409 | + | 0.537409i | 0.922767 | − | 0.385358i | \(-0.125922\pi\) |
−0.385358 | + | 0.922767i | \(0.625922\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.6491 | − | 4.47214i | 0.757282 | − | 0.267740i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 28.2843i | − | 1.68730i | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||
0.536895 | − | 0.843649i | \(-0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.0000 | + | 22.0000i | −1.30776 | + | 1.30776i | −0.384739 | + | 0.923026i | \(0.625708\pi\) |
−0.923026 | + | 0.384739i | \(0.874292\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.32456 | + | 4.47214i | 0.374634 | + | 0.264906i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.32456 | − | 6.32456i | −0.373327 | − | 0.373327i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.24264 | − | 6.00000i | 0.248708 | − | 0.351726i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.6491 | + | 12.6491i | 0.738969 | + | 0.738969i | 0.972379 | − | 0.233410i | \(-0.0749883\pi\) |
−0.233410 | + | 0.972379i | \(0.574988\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.1803 | − | 11.1803i | 0.650945 | − | 0.650945i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.2426 | + | 10.7574i | −1.11657 | + | 0.624205i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 28.2843i | − | 1.63572i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 17.8885i | − | 1.03108i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.39835 | + | 0.926210i | −0.310127 | + | 0.0532094i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.1421 | + | 14.1421i | −0.809776 | + | 0.809776i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.00000 | − | 4.00000i | −0.228292 | − | 0.228292i | 0.583687 | − | 0.811979i | \(-0.301610\pi\) |
−0.811979 | + | 0.583687i | \(0.801610\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.47214 | + | 3.16228i | 0.254411 | + | 0.179896i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.9737i | 1.07590i | 0.842977 | + | 0.537949i | \(0.180801\pi\) | ||||
−0.842977 | + | 0.537949i | \(0.819199\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.0000 | + | 19.0000i | 1.07394 | + | 1.07394i | 0.997038 | + | 0.0769051i | \(0.0245038\pi\) |
0.0769051 | + | 0.997038i | \(0.475496\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 20.0000 | − | 7.07107i | 1.12687 | − | 0.398410i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.16228 | − | 3.16228i | 0.177611 | − | 0.177611i | −0.612702 | − | 0.790314i | \(-0.709918\pi\) |
0.790314 | + | 0.612702i | \(0.209918\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 40.2492i | 2.25352i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.0000 | − | 22.6274i | 0.893033 | − | 1.26294i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.65685 | + | 5.65685i | 0.314756 | + | 0.314756i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.3607 | − | 22.3607i | −1.24035 | − | 1.24035i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.1421 | −0.779681 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 6.00000i | − | 0.329790i | −0.986311 | − | 0.164895i | \(-0.947272\pi\) | ||
0.986311 | − | 0.164895i | \(-0.0527285\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 18.9737i | − | 1.03664i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | − | 11.0000i | 0.599208 | − | 0.599208i | −0.340894 | − | 0.940102i | \(-0.610730\pi\) |
0.940102 | + | 0.340894i | \(0.110730\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.0000 | + | 16.9706i | −0.651751 | + | 0.921714i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.9737 | −1.02748 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.94427 | − | 8.94427i | −0.482945 | − | 0.482945i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.0711 | − | 2.92893i | 0.919075 | − | 0.157688i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.24264 | + | 4.24264i | −0.227757 | + | 0.227757i | −0.811755 | − | 0.583998i | \(-0.801488\pi\) |
0.583998 | + | 0.811755i | \(0.301488\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.8328 | −1.43633 | −0.718164 | − | 0.695874i | \(-0.755017\pi\) | ||||
−0.718164 | + | 0.695874i | \(0.755017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.94427 | + | 31.6228i | −0.477410 | + | 1.68790i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.1421 | + | 14.1421i | −0.752710 | + | 0.752710i | −0.974984 | − | 0.222274i | \(-0.928652\pi\) |
0.222274 | + | 0.974984i | \(0.428652\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.0000 | − | 10.0000i | 0.530745 | − | 0.530745i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.5934 | − | 3.70484i | 1.14284 | − | 0.196081i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.9737 | −1.00139 | −0.500696 | − | 0.865623i | \(-0.666923\pi\) | ||||
−0.500696 | + | 0.865623i | \(0.666923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.9497 | − | 2.05025i | 0.627199 | − | 0.107610i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.48683i | 0.496564i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.70820 | − | 6.70820i | 0.350165 | − | 0.350165i | −0.510006 | − | 0.860171i | \(-0.670357\pi\) |
0.860171 | + | 0.510006i | \(0.170357\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.82843 | + | 8.00000i | 0.147242 | + | 0.416463i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.2843 | 1.46845 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.94427 | + | 8.94427i | −0.463117 | + | 0.463117i | −0.899676 | − | 0.436559i | \(-0.856197\pi\) |
0.436559 | + | 0.899676i | \(0.356197\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.1803 | − | 15.8114i | 0.577350 | − | 0.816497i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 42.4264 | + | 42.4264i | 2.18507 | + | 2.18507i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.16228 | + | 4.47214i | −0.162008 | + | 0.229114i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.1359 | + | 22.1359i | −1.13109 | + | 1.13109i | −0.141098 | + | 0.989996i | \(0.545063\pi\) |
−0.989996 | + | 0.141098i | \(0.954937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −30.0000 | −1.52894 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.31371 | + | 15.3137i | −0.371777 | + | 0.778440i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.16228i | − | 0.160334i | −0.996781 | − | 0.0801669i | \(-0.974455\pi\) | ||
0.996781 | − | 0.0801669i | \(-0.0255453\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.8885 | 0.904663 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0711 | + | 2.07107i | −0.608905 | + | 0.104472i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.07107 | + | 7.07107i | −0.355784 | + | 0.355784i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.4164 | + | 13.4164i | 0.673350 | + | 0.673350i | 0.958487 | − | 0.285137i | \(-0.0920390\pi\) |
−0.285137 | + | 0.958487i | \(0.592039\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.32456 | − | 8.94427i | 0.316624 | − | 0.447774i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.82843i | − | 0.141245i | −0.997503 | − | 0.0706225i | \(-0.977501\pi\) | ||
0.997503 | − | 0.0706225i | \(-0.0224986\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.0000 | + | 20.0000i | −0.996271 | + | 0.996271i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.0122 | − | 2.12370i | −0.994416 | − | 0.105527i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 28.0000i | − | 1.38451i | −0.721653 | − | 0.692255i | \(-0.756617\pi\) | ||
0.721653 | − | 0.692255i | \(-0.243383\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.65685 | + | 4.00000i | 0.279032 | + | 0.197305i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.8114 | − | 15.8114i | −0.778028 | − | 0.778028i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.8885i | 0.878114i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.41421 | + | 0.585786i | −0.167195 | + | 0.0286861i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.41421i | − | 0.0690889i | −0.999403 | − | 0.0345444i | \(-0.989002\pi\) | ||
0.999403 | − | 0.0345444i | \(-0.0109980\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.8885i | 0.871834i | 0.899987 | + | 0.435917i | \(0.143576\pi\) | ||||
−0.899987 | + | 0.435917i | \(0.856424\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.1065 | + | 5.78199i | 0.588641 | + | 0.281130i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.1421 | − | 14.1421i | 0.685994 | − | 0.685994i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0000 | + | 20.0000i | 0.967868 | + | 0.967868i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.8328 | − | 37.9473i | 1.29550 | − | 1.83211i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 31.6228i | − | 1.52322i | −0.648038 | − | 0.761608i | \(-0.724410\pi\) | ||
0.648038 | − | 0.761608i | \(-0.275590\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.00000 | + | 3.00000i | 0.144171 | + | 0.144171i | 0.775508 | − | 0.631337i | \(-0.217494\pi\) |
−0.631337 | + | 0.775508i | \(0.717494\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.2132 | + | 30.0000i | −1.01710 | + | 1.43839i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.32456 | − | 6.32456i | 0.302545 | − | 0.302545i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.8885i | 0.853774i | 0.904305 | + | 0.426887i | \(0.140390\pi\) | ||||
−0.904305 | + | 0.426887i | \(0.859610\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | − | 8.48528i | −0.142857 | − | 0.404061i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.7279 | + | 12.7279i | 0.604722 | + | 0.604722i | 0.941562 | − | 0.336840i | \(-0.109358\pi\) |
−0.336840 | + | 0.941562i | \(0.609358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.4164 | + | 13.4164i | 0.635999 | + | 0.635999i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.926210 | + | 5.39835i | 0.0438082 | + | 0.255333i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.65685 | −0.266963 | −0.133482 | − | 0.991051i | \(-0.542616\pi\) | ||||
−0.133482 | + | 0.991051i | \(0.542616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 12.0000i | − | 0.565058i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −30.5377 | + | 5.23943i | −1.43478 | + | 0.246170i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −31.6228 | + | 31.6228i | −1.48250 | + | 1.48250i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | + | 1.00000i | −0.0467780 | + | 0.0467780i | −0.730109 | − | 0.683331i | \(-0.760531\pi\) |
0.683331 | + | 0.730109i | \(0.260531\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20.0000 | − | 5.65685i | −0.933520 | − | 0.264039i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.4605 | −1.32554 | −0.662769 | − | 0.748824i | \(-0.730619\pi\) | ||||
−0.662769 | + | 0.748824i | \(0.730619\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.1803 | − | 11.1803i | −0.519594 | − | 0.519594i | 0.397854 | − | 0.917449i | \(-0.369755\pi\) |
−0.917449 | + | 0.397854i | \(0.869755\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.1421 | − | 10.0000i | −0.655826 | − | 0.463739i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.8328 | −1.23902 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.8885 | − | 12.6491i | −0.824261 | − | 0.582840i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.9706 | − | 16.9706i | 0.780307 | − | 0.780307i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 10.0000i | − | 0.458831i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.2131 | − | 11.5640i | −1.10864 | − | 0.529479i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.6228 | −1.44488 | −0.722441 | − | 0.691433i | \(-0.756980\pi\) | ||||
−0.722441 | + | 0.691433i | \(0.756980\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.14214 | − | 24.1421i | −0.188474 | − | 1.09851i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.48683 | −0.430775 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.5967 | + | 24.5967i | −1.11459 | + | 1.11459i | −0.122063 | + | 0.992522i | \(0.538951\pi\) |
−0.992522 | + | 0.122063i | \(0.961049\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.9706 | + | 24.0000i | −0.767435 | + | 1.08532i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.07107 | 0.319113 | 0.159556 | − | 0.987189i | \(-0.448994\pi\) | ||||
0.159556 | + | 0.987189i | \(0.448994\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.8328 | + | 26.8328i | −1.20849 | + | 1.20849i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 25.6819 | + | 12.2655i | 1.15431 | + | 0.551292i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.1421 | − | 14.1421i | −0.634361 | − | 0.634361i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.0000 | 1.16392 | 0.581960 | − | 0.813217i | \(-0.302286\pi\) | ||||
0.581960 | + | 0.813217i | \(0.302286\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.9737 | + | 13.4164i | 0.847681 | + | 0.599401i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.48683 | + | 9.48683i | −0.422997 | + | 0.422997i | −0.886234 | − | 0.463237i | \(-0.846688\pi\) |
0.463237 | + | 0.886234i | \(0.346688\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.00000 | + | 5.00000i | 0.222497 | + | 0.222497i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.90812 | − | 46.0919i | −0.351212 | − | 2.04701i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.8114i | 0.700827i | 0.936595 | + | 0.350414i | \(0.113959\pi\) | ||||
−0.936595 | + | 0.350414i | \(0.886041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.4164 | 0.593507 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.07107 | + | 5.07107i | −0.400497 | + | 0.223893i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 7.07107i | − | 0.311588i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.4164 | − | 13.4164i | −0.590053 | − | 0.590053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.32456 | + | 4.47214i | 0.277617 | + | 0.196305i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.3137i | 0.495663i | 0.968803 | + | 0.247831i | \(0.0797179\pi\) | ||||
−0.968803 | + | 0.247831i | \(0.920282\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.00000 | − | 2.00000i | 0.0874539 | − | 0.0874539i | −0.662027 | − | 0.749480i | \(-0.730303\pi\) |
0.749480 | + | 0.662027i | \(0.230303\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.3607 | − | 15.8114i | −0.975900 | − | 0.690066i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.6491 | − | 12.6491i | −0.551004 | − | 0.551004i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.00000i | 0.130435i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.07107 | + | 20.0000i | 0.306858 | + | 0.867926i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.6491 | − | 12.6491i | −0.547894 | − | 0.547894i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.7771 | −1.54678 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.55635 | + | 26.5563i | 0.196621 | + | 1.14599i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.7279i | 0.548230i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.8328i | 1.15363i | 0.816874 | + | 0.576816i | \(0.195705\pi\) | ||||
−0.816874 | + | 0.576816i | \(0.804295\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.23943 | + | 30.5377i | 0.224846 | + | 1.31050i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0000 | − | 16.0000i | −0.684111 | − | 0.684111i | 0.276813 | − | 0.960924i | \(-0.410722\pi\) |
−0.960924 | + | 0.276813i | \(0.910722\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.94427 | − | 25.2982i | −0.381732 | − | 1.07970i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.9737i | 0.808305i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0000 | + | 10.0000i | 0.425243 | + | 0.425243i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.2982 | + | 25.2982i | −1.07192 | + | 1.07192i | −0.0747151 | + | 0.997205i | \(0.523805\pi\) |
−0.997205 | + | 0.0747151i | \(0.976195\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 35.7771i | − | 1.51321i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | + | 16.9706i | 1.01328 | + | 0.716498i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.2132 | − | 21.2132i | −0.894030 | − | 0.894030i | 0.100870 | − | 0.994900i | \(-0.467837\pi\) |
−0.994900 | + | 0.100870i | \(0.967837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.8328 | 1.12887 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.00337 | + | 28.3016i | −0.126129 | + | 1.18855i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.7696 | −1.54146 | −0.770730 | − | 0.637162i | \(-0.780108\pi\) | ||||
−0.770730 | + | 0.637162i | \(0.780108\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 18.0000i | − | 0.753277i | −0.926360 | − | 0.376638i | \(-0.877080\pi\) | ||
0.926360 | − | 0.376638i | \(-0.122920\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.70484 | − | 21.5934i | −0.154772 | − | 0.902076i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.8114 | − | 15.8114i | −0.659380 | − | 0.659380i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.0000 | − | 21.0000i | 0.874241 | − | 0.874241i | −0.118690 | − | 0.992931i | \(-0.537869\pi\) |
0.992931 | + | 0.118690i | \(0.0378694\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.00000 | − | 4.24264i | −0.249351 | − | 0.176318i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.2982 | 1.04955 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.8328 | + | 26.8328i | 1.11130 | + | 1.11130i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 40.0000 | − | 14.1421i | 1.65380 | − | 0.584705i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.3137 | + | 11.3137i | −0.466967 | + | 0.466967i | −0.900930 | − | 0.433964i | \(-0.857115\pi\) |
0.433964 | + | 0.900930i | \(0.357115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.94427 | −0.368542 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.94427 | + | 12.6491i | −0.367918 | + | 0.520315i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.6274 | − | 22.6274i | 0.929197 | − | 0.929197i | −0.0684574 | − | 0.997654i | \(-0.521808\pi\) |
0.997654 | + | 0.0684574i | \(0.0218077\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.0000 | − | 20.0000i | −0.819920 | − | 0.819920i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.23943 | − | 30.5377i | −0.214436 | − | 1.24982i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.2719 | −1.80890 | −0.904450 | − | 0.426579i | \(-0.859718\pi\) | ||||
−0.904450 | + | 0.426579i | \(0.859718\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.9706 | + | 10.9706i | 0.935434 | + | 0.446756i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.0680 | − | 11.0680i | −0.449977 | − | 0.449977i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.1246 | − | 20.1246i | 0.816833 | − | 0.816833i | −0.168815 | − | 0.985648i | \(-0.553994\pi\) |
0.985648 | + | 0.168815i | \(0.0539940\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 42.4264 | + | 30.0000i | 1.71920 | + | 1.21566i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.2843 | −1.14426 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.3607 | − | 22.3607i | 0.903139 | − | 0.903139i | −0.0925671 | − | 0.995706i | \(-0.529507\pi\) |
0.995706 | + | 0.0925671i | \(0.0295073\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.32456 | − | 8.94427i | 0.255031 | − | 0.360668i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.2843 | − | 28.2843i | −1.13868 | − | 1.13868i | −0.988687 | − | 0.149995i | \(-0.952074\pi\) |
−0.149995 | − | 0.988687i | \(-0.547926\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.0000 | 1.36658 | 0.683288 | − | 0.730149i | \(-0.260549\pi\) | ||||
0.683288 | + | 0.730149i | \(0.260549\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.32456 | + | 22.3607i | −0.253796 | + | 0.897303i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.9737 | − | 18.9737i | 0.760164 | − | 0.760164i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.4853 | − | 2.48528i | 0.578486 | − | 0.0992526i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.2492 | 1.60230 | 0.801148 | − | 0.598466i | \(-0.204223\pi\) | ||||
0.801148 | + | 0.598466i | \(0.204223\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.10051 | − | 23.8995i | −0.162980 | − | 0.949920i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.07107 | 0.280607 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.4164 | + | 13.4164i | 0.531577 | + | 0.531577i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.32456 | + | 17.8885i | 0.250196 | + | 0.707660i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.2843i | 1.11716i | 0.829450 | + | 0.558581i | \(0.188654\pi\) | ||||
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.00000 | − | 4.00000i | 0.157745 | − | 0.157745i | −0.623822 | − | 0.781567i | \(-0.714421\pi\) |
0.781567 | + | 0.623822i | \(0.214421\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.5934 | − | 3.70484i | 0.850239 | − | 0.145878i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.8114 | − | 15.8114i | −0.621610 | − | 0.621610i | 0.324333 | − | 0.945943i | \(-0.394860\pi\) |
−0.945943 | + | 0.324333i | \(0.894860\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 30.0000i | − | 1.17760i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.1421 | + | 20.0000i | −0.554274 | + | 0.783862i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.4605 | + | 28.4605i | 1.11375 | + | 1.11375i | 0.992640 | + | 0.121106i | \(0.0386440\pi\) |
0.121106 | + | 0.992640i | \(0.461356\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.1803 | + | 11.1803i | 0.436852 | + | 0.436852i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.4853 | − | 5.48528i | −0.448084 | − | 0.214001i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.8701i | 1.04671i | 0.852115 | + | 0.523354i | \(0.175320\pi\) | ||||
−0.852115 | + | 0.523354i | \(0.824680\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 44.7214i | − | 1.73946i | −0.493528 | − | 0.869730i | \(-0.664293\pi\) | ||
0.493528 | − | 0.869730i | \(-0.335707\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 43.1868 | − | 7.40968i | 1.67723 | − | 0.287768i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.1421 | −0.548408 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.0000 | + | 30.0000i | 1.16160 | + | 1.16160i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.47214 | + | 3.16228i | 0.172903 | + | 0.122261i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.9473i | 1.46494i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.00000 | + | 9.00000i | 0.346925 | + | 0.346925i | 0.858963 | − | 0.512038i | \(-0.171109\pi\) |
−0.512038 | + | 0.858963i | \(0.671109\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.6777 | + | 22.6777i | 0.487964 | + | 0.872864i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.8114 | + | 15.8114i | −0.607681 | + | 0.607681i | −0.942339 | − | 0.334658i | \(-0.891379\pi\) |
0.334658 | + | 0.942339i | \(0.391379\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.4164i | 0.514874i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.0000 | + | 14.1421i | −0.383201 | + | 0.541928i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.9411 | − | 33.9411i | −1.29872 | − | 1.29872i | −0.929237 | − | 0.369484i | \(-0.879534\pi\) |
−0.369484 | − | 0.929237i | \(-0.620466\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 8.94427i | − | 0.341743i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 45.8065 | − | 7.85915i | 1.74763 | − | 0.299845i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 56.5685 | 2.15509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.0000i | 1.29342i | 0.762736 | + | 0.646710i | \(0.223856\pi\) | ||||
−0.762736 | + | 0.646710i | \(0.776144\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.3460 | − | 36.3196i | 0.658919 | − | 1.37967i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.16228 | + | 3.16228i | 0.119952 | + | 0.119952i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.00000 | − | 8.00000i | 0.303022 | − | 0.303022i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.4605 | −1.07494 | −0.537469 | − | 0.843283i | \(-0.680620\pi\) | ||||
−0.537469 | + | 0.843283i | \(0.680620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.92893 | − | 17.0711i | −0.110310 | − | 0.642934i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.07107 | − | 7.07107i | 0.265935 | − | 0.265935i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.8885 | −0.671818 | −0.335909 | − | 0.941894i | \(-0.609044\pi\) | ||||
−0.335909 | + | 0.941894i | \(0.609044\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.47214 | − | 12.6491i | −0.167718 | − | 0.474379i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.1421 | + | 14.1421i | −0.529627 | + | 0.529627i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −60.0000 | −2.24387 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.3901 | − | 5.55726i | 1.20963 | − | 0.207540i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.2982 | 0.943464 | 0.471732 | − | 0.881742i | \(-0.343629\pi\) | ||||
0.471732 | + | 0.881742i | \(0.343629\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | −0.372419 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 40.9706 | − | 7.02944i | 1.52371 | − | 0.261428i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 47.4342 | 1.76166 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.1803 | − | 11.1803i | 0.414656 | − | 0.414656i | −0.468701 | − | 0.883357i | \(-0.655278\pi\) |
0.883357 | + | 0.468701i | \(0.155278\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.1421 | − | 23.0000i | 0.523783 | − | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.6274 | 0.836905 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.70820 | + | 9.48683i | −0.247436 | + | 0.349927i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.4558 | − | 25.4558i | −0.937678 | − | 0.937678i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.00000 | 0.220714 | 0.110357 | − | 0.993892i | \(-0.464801\pi\) | ||||
0.110357 | + | 0.993892i | \(0.464801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.6491 | − | 17.8885i | 0.464677 | − | 0.657152i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.4605 | + | 28.4605i | −1.04411 | + | 1.04411i | −0.0451335 | + | 0.998981i | \(0.514371\pi\) |
−0.998981 | + | 0.0451335i | \(0.985629\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00000 | − | 5.00000i | 0.183186 | − | 0.183186i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21.6569 | − | 10.3431i | −0.792383 | − | 0.378436i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 50.5964i | 1.84875i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.2492 | −1.46872 | −0.734358 | − | 0.678763i | \(-0.762516\pi\) | ||||
−0.734358 | + | 0.678763i | \(0.762516\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −41.0416 | + | 7.04163i | −1.49564 | + | 0.256611i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.2843 | + | 28.2843i | 1.02937 | + | 1.02937i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.8885 | − | 17.8885i | −0.650170 | − | 0.650170i | 0.302864 | − | 0.953034i | \(-0.402057\pi\) |
−0.953034 | + | 0.302864i | \(0.902057\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.9737 | − | 26.8328i | 0.688700 | − | 0.973970i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.5980i | 1.43543i | 0.696339 | + | 0.717713i | \(0.254811\pi\) | ||||
−0.696339 | + | 0.717713i | \(0.745189\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.94427 | + | 25.2982i | 0.323381 | + | 0.914659i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31.6228 | − | 31.6228i | −1.14183 | − | 1.14183i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.0000i | 1.51456i | 0.653091 | + | 0.757279i | \(0.273472\pi\) | ||||
−0.653091 | + | 0.757279i | \(0.726528\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.48683 | + | 9.48683i | 0.341218 | + | 0.341218i | 0.856825 | − | 0.515607i | \(-0.172434\pi\) |
−0.515607 | + | 0.856825i | \(0.672434\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.3607i | 0.803219i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 5.65685i | − | 0.202678i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 26.8328i | − | 0.960154i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.0542 | − | 43.0279i | −0.859627 | − | 1.53769i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.2843i | 1.00951i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.00000 | + | 2.00000i | 0.0712923 | + | 0.0712923i | 0.741854 | − | 0.670562i | \(-0.233947\pi\) |
−0.670562 | + | 0.741854i | \(0.733947\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.47214 | + | 6.32456i | −0.159212 | + | 0.225160i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 37.9473i | − | 1.34925i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.0000 | + | 40.0000i | 1.42044 | + | 1.42044i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.85786 | + | 34.1421i | 0.207757 | + | 1.21090i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.16228 | + | 3.16228i | −0.112014 | + | 0.112014i | −0.760892 | − | 0.648878i | \(-0.775238\pi\) |
0.648878 | + | 0.760892i | \(0.275238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 17.8885i | − | 0.632851i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.0000 | + | 8.48528i | −0.847998 | + | 0.299813i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.7279 | + | 12.7279i | 0.449159 | + | 0.449159i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.3607 | + | 22.3607i | −0.788110 | + | 0.788110i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.926210 | − | 5.39835i | −0.0326041 | − | 0.190031i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.2843 | 0.994422 | 0.497211 | − | 0.867630i | \(-0.334357\pi\) | ||||
0.497211 | + | 0.867630i | \(0.334357\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.0000i | 0.632065i | 0.948748 | + | 0.316033i | \(0.102351\pi\) | ||||
−0.948748 | + | 0.316033i | \(0.897649\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37.9473 | 1.32924 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | − | 8.00000i | 0.279885 | − | 0.279885i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20.0000 | − | 56.5685i | −0.698857 | − | 1.97666i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.4605 | 0.993278 | 0.496639 | − | 0.867957i | \(-0.334567\pi\) | ||||
0.496639 | + | 0.867957i | \(0.334567\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.1246 | − | 20.1246i | −0.701500 | − | 0.701500i | 0.263233 | − | 0.964732i | \(-0.415211\pi\) |
−0.964732 | + | 0.263233i | \(0.915211\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.21320 | − | 36.2132i | −0.216316 | − | 1.26078i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.0416 | − | 24.0416i | 0.836009 | − | 0.836009i | −0.152322 | − | 0.988331i | \(-0.548675\pi\) |
0.988331 | + | 0.152322i | \(0.0486749\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.6656 | 1.86388 | 0.931942 | − | 0.362607i | \(-0.118113\pi\) | ||||
0.931942 | + | 0.362607i | \(0.118113\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.8885 | + | 12.6491i | 0.620547 | + | 0.438793i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.48528 | + | 8.48528i | −0.293998 | + | 0.293998i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 30.0000i | − | 1.03819i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.2835 | − | 11.3393i | 0.701101 | − | 0.391942i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.9737 | 0.655044 | 0.327522 | − | 0.944844i | \(-0.393786\pi\) | ||||
0.327522 | + | 0.944844i | \(0.393786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −61.0000 | −2.10345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.28427 | − | 48.2843i | −0.285325 | − | 1.66300i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −42.6907 | + | 42.6907i | −1.46861 | + | 1.46861i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.6525 | + | 15.6525i | −0.537825 | + | 0.537825i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.1127 | + | 44.0000i | −1.06779 | + | 1.51008i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.4164 | − | 13.4164i | 0.459369 | − | 0.459369i | −0.439079 | − | 0.898448i | \(-0.644695\pi\) |
0.898448 | + | 0.439079i | \(0.144695\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.1065 | + | 5.78199i | 0.414035 | + | 0.197740i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.9706 | − | 16.9706i | −0.579703 | − | 0.579703i | 0.355118 | − | 0.934821i | \(-0.384441\pi\) |
−0.934821 | + | 0.355118i | \(0.884441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.0000 | −0.614152 | −0.307076 | − | 0.951685i | \(-0.599351\pi\) | ||||
−0.307076 | + | 0.951685i | \(0.599351\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.6491 | − | 8.94427i | −0.431081 | − | 0.304820i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.8114 | − | 15.8114i | 0.538226 | − | 0.538226i | −0.384782 | − | 0.923008i | \(-0.625723\pi\) |
0.923008 | + | 0.384782i | \(0.125723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 10.0000i | − | 0.340010i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.292893 | − | 1.70711i | −0.00994718 | − | 0.0579764i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.9737i | 0.643638i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.6656 | −1.81839 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.48528 | − | 11.4853i | 0.185649 | − | 0.388718i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 35.3553i | 1.19523i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.8885 | + | 17.8885i | 0.604053 | + | 0.604053i | 0.941386 | − | 0.337332i | \(-0.109525\pi\) |
−0.337332 | + | 0.941386i | \(0.609525\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.2982 | + | 17.8885i | 0.853288 | + | 0.603366i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 42.4264i | − | 1.42938i | −0.699440 | − | 0.714691i | \(-0.746567\pi\) | ||
0.699440 | − | 0.714691i | \(-0.253433\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.0000 | + | 12.0000i | −0.403832 | + | 0.403832i | −0.879581 | − | 0.475749i | \(-0.842177\pi\) |
0.475749 | + | 0.879581i | \(0.342177\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.8114 | − | 22.3607i | 0.531494 | − | 0.751646i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.7851 | + | 34.7851i | 1.16797 | + | 1.16797i | 0.982685 | + | 0.185283i | \(0.0593200\pi\) |
0.185283 | + | 0.982685i | \(0.440680\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 10.0000i | − | 0.335389i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.6985 | + | 24.0000i | −0.994937 | + | 0.804030i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.32456 | − | 6.32456i | −0.211643 | − | 0.211643i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.5967 | − | 24.5967i | 0.822179 | − | 0.822179i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.28427 | − | 48.2843i | −0.276604 | − | 1.61216i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 42.4264i | − | 1.41500i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.7771i | 1.19191i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.23943 | − | 30.5377i | −0.174357 | − | 1.01623i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.2843 | − | 28.2843i | 0.940201 | − | 0.940201i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0000 | − | 22.0000i | −0.730498 | − | 0.730498i | 0.240220 | − | 0.970718i | \(-0.422780\pi\) |
−0.970718 | + | 0.240220i | \(0.922780\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.94427 | + | 3.16228i | −0.296663 | + | 0.104886i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 56.9210i | − | 1.88588i | −0.332967 | − | 0.942938i | \(-0.608050\pi\) | ||
0.332967 | − | 0.942938i | \(-0.391950\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0000 | + | 24.0000i | 0.794284 | + | 0.794284i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.0000 | + | 28.2843i | −0.661180 | + | 0.935049i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.8114 | − | 15.8114i | 0.522138 | − | 0.522138i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 13.4164i | − | 0.442566i | −0.975210 | − | 0.221283i | \(-0.928975\pi\) | ||
0.975210 | − | 0.221283i | \(-0.0710245\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.00000 | − | 5.65685i | −0.263609 | − | 0.186400i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.2843 | − | 28.2843i | −0.930988 | − | 0.930988i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.56062 | + | 4.08849i | 0.281168 | + | 0.134284i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.2843 | 0.927977 | 0.463988 | − | 0.885841i | \(-0.346418\pi\) | ||||
0.463988 | + | 0.885841i | \(0.346418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000i | 0.196642i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.55726 | + | 32.3901i | 0.181936 | + | 1.06040i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 37.9473i | − | 1.24101i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.0000 | − | 21.0000i | 0.686040 | − | 0.686040i | −0.275314 | − | 0.961354i | \(-0.588782\pi\) |
0.961354 | + | 0.275314i | \(0.0887819\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.0000 | + | 26.8701i | 1.24008 | + | 0.876871i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.4605 | 0.927786 | 0.463893 | − | 0.885891i | \(-0.346452\pi\) | ||||
0.463893 | + | 0.885891i | \(0.346452\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.94427 | − | 8.94427i | −0.291266 | − | 0.291266i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 32.0711 | − | 17.9289i | 1.04327 | − | 0.583228i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.07107 | + | 7.07107i | −0.229779 | + | 0.229779i | −0.812600 | − | 0.582821i | \(-0.801949\pi\) |
0.582821 | + | 0.812600i | \(0.301949\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.8328 | 0.871030 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.47214 | − | 6.32456i | 0.145019 | − | 0.205088i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.65685 | − | 5.65685i | 0.183243 | − | 0.183243i | −0.609524 | − | 0.792768i | \(-0.708639\pi\) |
0.792768 | + | 0.609524i | \(0.208639\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.0000 | + | 20.0000i | −0.647185 | + | 0.647185i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.7887 | + | 68.7097i | 0.381075 | + | 2.22107i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.6491 | −0.408461 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0000 | −0.354839 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.6863 | − | 43.3137i | 0.666606 | − | 1.39576i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.48683i | 0.305392i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.70820 | − | 6.70820i | 0.215721 | − | 0.215721i | −0.590971 | − | 0.806693i | \(-0.701255\pi\) |
0.806693 | + | 0.590971i | \(0.201255\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.3137 | + | 8.00000i | 0.363449 | + | 0.256997i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.3259 | 1.67922 | 0.839609 | − | 0.543191i | \(-0.182784\pi\) | ||||
0.839609 | + | 0.543191i | \(0.182784\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.47214 | − | 4.47214i | 0.143370 | − | 0.143370i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −44.7214 | − | 31.6228i | −1.43223 | − | 1.01274i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.9706 | + | 16.9706i | 0.542936 | + | 0.542936i | 0.924389 | − | 0.381452i | \(-0.124576\pi\) |
−0.381452 | + | 0.924389i | \(0.624576\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.0000 | 1.15056 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.1359 | − | 22.1359i | 0.706027 | − | 0.706027i | −0.259670 | − | 0.965697i | \(-0.583614\pi\) |
0.965697 | + | 0.259670i | \(0.0836139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.0000 | 0.637253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.1421 | + | 4.14214i | −0.768453 | + | 0.131846i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 25.2982i | − | 0.804437i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.75736 | − | 10.2426i | −0.0557681 | − | 0.325040i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.2843 | + | 28.2843i | −0.896672 | + | 0.896672i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.47214 | − | 4.47214i | −0.141634 | − | 0.141634i | 0.632735 | − | 0.774369i | \(-0.281932\pi\) |
−0.774369 | + | 0.632735i | \(0.781932\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 960.2.bi.f.353.3 | yes | 8 | |
3.2 | odd | 2 | inner | 960.2.bi.f.353.2 | yes | 8 | |
4.3 | odd | 2 | 960.2.bi.e.353.1 | ✓ | 8 | ||
5.2 | odd | 4 | 960.2.bi.e.737.3 | yes | 8 | ||
8.3 | odd | 2 | inner | 960.2.bi.f.353.4 | yes | 8 | |
8.5 | even | 2 | 960.2.bi.e.353.2 | yes | 8 | ||
12.11 | even | 2 | 960.2.bi.e.353.4 | yes | 8 | ||
15.2 | even | 4 | 960.2.bi.e.737.2 | yes | 8 | ||
20.7 | even | 4 | inner | 960.2.bi.f.737.1 | yes | 8 | |
24.5 | odd | 2 | 960.2.bi.e.353.3 | yes | 8 | ||
24.11 | even | 2 | inner | 960.2.bi.f.353.1 | yes | 8 | |
40.27 | even | 4 | 960.2.bi.e.737.4 | yes | 8 | ||
40.37 | odd | 4 | inner | 960.2.bi.f.737.2 | yes | 8 | |
60.47 | odd | 4 | inner | 960.2.bi.f.737.4 | yes | 8 | |
120.77 | even | 4 | inner | 960.2.bi.f.737.3 | yes | 8 | |
120.107 | odd | 4 | 960.2.bi.e.737.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
960.2.bi.e.353.1 | ✓ | 8 | 4.3 | odd | 2 | ||
960.2.bi.e.353.2 | yes | 8 | 8.5 | even | 2 | ||
960.2.bi.e.353.3 | yes | 8 | 24.5 | odd | 2 | ||
960.2.bi.e.353.4 | yes | 8 | 12.11 | even | 2 | ||
960.2.bi.e.737.1 | yes | 8 | 120.107 | odd | 4 | ||
960.2.bi.e.737.2 | yes | 8 | 15.2 | even | 4 | ||
960.2.bi.e.737.3 | yes | 8 | 5.2 | odd | 4 | ||
960.2.bi.e.737.4 | yes | 8 | 40.27 | even | 4 | ||
960.2.bi.f.353.1 | yes | 8 | 24.11 | even | 2 | inner | |
960.2.bi.f.353.2 | yes | 8 | 3.2 | odd | 2 | inner | |
960.2.bi.f.353.3 | yes | 8 | 1.1 | even | 1 | trivial | |
960.2.bi.f.353.4 | yes | 8 | 8.3 | odd | 2 | inner | |
960.2.bi.f.737.1 | yes | 8 | 20.7 | even | 4 | inner | |
960.2.bi.f.737.2 | yes | 8 | 40.37 | odd | 4 | inner | |
960.2.bi.f.737.3 | yes | 8 | 120.77 | even | 4 | inner | |
960.2.bi.f.737.4 | yes | 8 | 60.47 | odd | 4 | inner |