Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1536,2,Mod(385,1536)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1536, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1536.385");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1536 = 2^{9} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1536.j (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: | \(12.2650217505\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 385.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1536.385 |
Dual form | 1536.2.j.c.1153.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1536\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(517\) | \(1025\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | + | 1.00000i | 0.447214 | + | 0.447214i | 0.894427 | − | 0.447214i | \(-0.147584\pi\) |
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.82843i | − | 1.06904i | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||
0.845154 | − | 0.534522i | \(-0.179509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 3.00000i | −0.832050 | + | 0.832050i | −0.987797 | − | 0.155747i | \(-0.950222\pi\) |
0.155747 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.65685 | − | 5.65685i | 1.29777 | − | 1.29777i | 0.367910 | − | 0.929861i | \(-0.380073\pi\) |
0.929861 | − | 0.367910i | \(-0.119927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | + | 2.00000i | 0.436436 | + | 0.436436i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.65685i | − | 1.17954i | −0.807573 | − | 0.589768i | \(-0.799219\pi\) | ||
0.807573 | − | 0.589768i | \(-0.200781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 3.00000i | − | 0.600000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | − | 1.00000i | 0.185695 | − | 0.185695i | −0.608137 | − | 0.793832i | \(-0.708083\pi\) |
0.793832 | + | 0.608137i | \(0.208083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.82843 | 0.508001 | 0.254000 | − | 0.967204i | \(-0.418254\pi\) | ||||
0.254000 | + | 0.967204i | \(0.418254\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.82843 | − | 2.82843i | 0.478091 | − | 0.478091i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 3.00000i | −0.493197 | − | 0.493197i | 0.416115 | − | 0.909312i | \(-0.363391\pi\) |
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.24264i | − | 0.679366i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000i | 0.624695i | 0.949968 | + | 0.312348i | \(0.101115\pi\) | ||||
−0.949968 | + | 0.312348i | \(0.898885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | − | 1.00000i | 0.149071 | − | 0.149071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3137 | −1.65027 | −0.825137 | − | 0.564933i | \(-0.808902\pi\) | ||||
−0.825137 | + | 0.564933i | \(0.808902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.82843 | − | 2.82843i | 0.396059 | − | 0.396059i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.00000 | − | 5.00000i | −0.686803 | − | 0.686803i | 0.274721 | − | 0.961524i | \(-0.411414\pi\) |
−0.961524 | + | 0.274721i | \(0.911414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.00000i | 1.05963i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.48528 | + | 8.48528i | 1.10469 | + | 1.10469i | 0.993837 | + | 0.110853i | \(0.0353582\pi\) |
0.110853 | + | 0.993837i | \(0.464642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | − | 1.00000i | 0.128037 | − | 0.128037i | −0.640184 | − | 0.768221i | \(-0.721142\pi\) |
0.768221 | + | 0.640184i | \(0.221142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.82843 | −0.356348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.00000 | −0.744208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.82843 | − | 2.82843i | 0.345547 | − | 0.345547i | −0.512901 | − | 0.858448i | \(-0.671429\pi\) |
0.858448 | + | 0.512901i | \(0.171429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | + | 4.00000i | 0.481543 | + | 0.481543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.3137i | − | 1.34269i | −0.741145 | − | 0.671345i | \(-0.765717\pi\) | ||
0.741145 | − | 0.671345i | \(-0.234283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.0000i | − | 1.63858i | −0.573382 | − | 0.819288i | \(-0.694369\pi\) | ||
0.573382 | − | 0.819288i | \(-0.305631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.12132 | + | 2.12132i | 0.244949 | + | 0.244949i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.48528 | −0.954669 | −0.477334 | − | 0.878722i | \(-0.658397\pi\) | ||||
−0.477334 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.3137 | − | 11.3137i | 1.24184 | − | 1.24184i | 0.282604 | − | 0.959237i | \(-0.408802\pi\) |
0.959237 | − | 0.282604i | \(-0.0911983\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | − | 4.00000i | −0.433861 | − | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.41421i | 0.151620i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000i | 0.635999i | 0.948091 | + | 0.317999i | \(0.103011\pi\) | ||||
−0.948091 | + | 0.317999i | \(0.896989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.48528 | + | 8.48528i | 0.889499 | + | 0.889499i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | + | 2.00000i | −0.207390 | + | 0.207390i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.3137 | 1.16076 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0000 | 1.62455 | 0.812277 | − | 0.583272i | \(-0.198228\pi\) | ||||
0.812277 | + | 0.583272i | \(0.198228\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.0000 | + | 11.0000i | 1.09454 | + | 1.09454i | 0.995037 | + | 0.0995037i | \(0.0317255\pi\) |
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 19.7990i | − | 1.95085i | −0.220326 | − | 0.975426i | \(-0.570712\pi\) | ||
0.220326 | − | 0.975426i | \(-0.429288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.00000i | 0.390360i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.48528 | − | 8.48528i | −0.820303 | − | 0.820303i | 0.165848 | − | 0.986151i | \(-0.446964\pi\) |
−0.986151 | + | 0.165848i | \(0.946964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.00000 | − | 3.00000i | 0.287348 | − | 0.287348i | −0.548683 | − | 0.836031i | \(-0.684871\pi\) |
0.836031 | + | 0.548683i | \(0.184871\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.24264 | 0.402694 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.65685 | − | 5.65685i | 0.527504 | − | 0.527504i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.00000 | + | 3.00000i | 0.277350 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.3137i | 1.03713i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 11.0000i | − | 1.00000i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.82843 | − | 2.82843i | −0.255031 | − | 0.255031i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.00000 | − | 8.00000i | 0.715542 | − | 0.715542i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.48528 | −0.752947 | −0.376473 | − | 0.926427i | \(-0.622863\pi\) | ||||
−0.376473 | + | 0.926427i | \(0.622863\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.82843 | + | 2.82843i | −0.247121 | + | 0.247121i | −0.819788 | − | 0.572667i | \(-0.805909\pi\) |
0.572667 | + | 0.819788i | \(0.305909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.0000 | − | 16.0000i | −1.38738 | − | 1.38738i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.41421i | 0.121716i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.0000i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.82843 | − | 2.82843i | −0.239904 | − | 0.239904i | 0.576906 | − | 0.816810i | \(-0.304260\pi\) |
−0.816810 | + | 0.576906i | \(0.804260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | − | 8.00000i | 0.673722 | − | 0.673722i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.707107 | − | 0.707107i | 0.0583212 | − | 0.0583212i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.00000 | + | 9.00000i | 0.737309 | + | 0.737309i | 0.972056 | − | 0.234748i | \(-0.0754264\pi\) |
−0.234748 | + | 0.972056i | \(0.575426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.82843i | − | 0.230174i | −0.993355 | − | 0.115087i | \(-0.963285\pi\) | ||
0.993355 | − | 0.115087i | \(-0.0367147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000i | 0.323381i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.82843 | + | 2.82843i | 0.227185 | + | 0.227185i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.0000 | + | 15.0000i | −1.19713 | + | 1.19713i | −0.222108 | + | 0.975022i | \(0.571294\pi\) |
−0.975022 | + | 0.222108i | \(0.928706\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.07107 | 0.560772 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | −1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3137 | + | 11.3137i | −0.886158 | + | 0.886158i | −0.994152 | − | 0.107994i | \(-0.965557\pi\) |
0.107994 | + | 0.994152i | \(0.465557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 11.3137i | − | 0.875481i | −0.899101 | − | 0.437741i | \(-0.855779\pi\) | ||
0.899101 | − | 0.437741i | \(-0.144221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.65685 | − | 5.65685i | −0.432590 | − | 0.432590i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.00000 | + | 5.00000i | −0.380143 | + | 0.380143i | −0.871154 | − | 0.491011i | \(-0.836628\pi\) |
0.491011 | + | 0.871154i | \(0.336628\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.48528 | −0.641427 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0000 | −0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.82843 | + | 2.82843i | −0.211407 | + | 0.211407i | −0.804865 | − | 0.593458i | \(-0.797762\pi\) |
0.593458 | + | 0.804865i | \(0.297762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.00000 | − | 9.00000i | −0.668965 | − | 0.668965i | 0.288512 | − | 0.957476i | \(-0.406840\pi\) |
−0.957476 | + | 0.288512i | \(0.906840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.41421i | 0.104542i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 6.00000i | − | 0.441129i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.00000 | − | 2.00000i | 0.145479 | − | 0.145479i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.65685 | −0.409316 | −0.204658 | − | 0.978834i | \(-0.565608\pi\) | ||||
−0.204658 | + | 0.978834i | \(0.565608\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.24264 | − | 4.24264i | 0.303822 | − | 0.303822i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00000 | + | 5.00000i | 0.356235 | + | 0.356235i | 0.862423 | − | 0.506188i | \(-0.168946\pi\) |
−0.506188 | + | 0.862423i | \(0.668946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.48528i | 0.601506i | 0.953702 | + | 0.300753i | \(0.0972379\pi\) | ||||
−0.953702 | + | 0.300753i | \(0.902762\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000i | 0.282138i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.82843 | − | 2.82843i | −0.198517 | − | 0.198517i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | + | 4.00000i | −0.279372 | + | 0.279372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.65685 | −0.393179 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.48528 | + | 8.48528i | −0.584151 | + | 0.584151i | −0.936041 | − | 0.351890i | \(-0.885539\pi\) |
0.351890 | + | 0.936041i | \(0.385539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.00000 | + | 8.00000i | 0.548151 | + | 0.548151i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.00000i | − | 0.543075i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.89949 | + | 9.89949i | 0.668946 | + | 0.668946i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | − | 12.0000i | 0.807207 | − | 0.807207i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.4558 | 1.70465 | 0.852325 | − | 0.523013i | \(-0.175192\pi\) | ||||
0.852325 | + | 0.523013i | \(0.175192\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.65685 | + | 5.65685i | −0.375459 | + | 0.375459i | −0.869461 | − | 0.494002i | \(-0.835534\pi\) |
0.494002 | + | 0.869461i | \(0.335534\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.0000 | − | 17.0000i | −1.12339 | − | 1.12339i | −0.991228 | − | 0.132164i | \(-0.957808\pi\) |
−0.132164 | − | 0.991228i | \(-0.542192\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000i | 0.655122i | 0.944830 | + | 0.327561i | \(0.106227\pi\) | ||||
−0.944830 | + | 0.327561i | \(0.893773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.3137 | − | 11.3137i | −0.738025 | − | 0.738025i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.00000 | − | 6.00000i | 0.389742 | − | 0.389742i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.65685 | 0.365911 | 0.182956 | − | 0.983121i | \(-0.441433\pi\) | ||||
0.182956 | + | 0.983121i | \(0.441433\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.00000 | −0.515325 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | − | 1.00000i | −0.0638877 | − | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.9411i | 2.15962i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.0000i | 1.01396i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.65685 | − | 5.65685i | −0.357057 | − | 0.357057i | 0.505670 | − | 0.862727i | \(-0.331245\pi\) |
−0.862727 | + | 0.505670i | \(0.831245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.65685 | 0.354246 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.00000 | 0.124757 | 0.0623783 | − | 0.998053i | \(-0.480131\pi\) | ||||
0.0623783 | + | 0.998053i | \(0.480131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.48528 | + | 8.48528i | −0.527250 | + | 0.527250i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | − | 1.00000i | −0.0618984 | − | 0.0618984i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.2843i | 1.74408i | 0.489432 | + | 0.872041i | \(0.337204\pi\) | ||||
−0.489432 | + | 0.872041i | \(0.662796\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10.0000i | − | 0.614295i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.24264 | − | 4.24264i | −0.259645 | − | 0.259645i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.0000 | + | 15.0000i | −0.914566 | + | 0.914566i | −0.996627 | − | 0.0820612i | \(-0.973850\pi\) |
0.0820612 | + | 0.996627i | \(0.473850\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.48528 | 0.515444 | 0.257722 | − | 0.966219i | \(-0.417028\pi\) | ||||
0.257722 | + | 0.966219i | \(0.417028\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.0000 | −0.726273 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00000 | + | 1.00000i | 0.0600842 | + | 0.0600842i | 0.736510 | − | 0.676426i | \(-0.236472\pi\) |
−0.676426 | + | 0.736510i | \(0.736472\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.82843i | − | 0.169334i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.0000i | − | 1.31241i | −0.754583 | − | 0.656205i | \(-0.772161\pi\) | ||
0.754583 | − | 0.656205i | \(-0.227839\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.82843 | + | 2.82843i | 0.168133 | + | 0.168133i | 0.786158 | − | 0.618026i | \(-0.212067\pi\) |
−0.618026 | + | 0.786158i | \(0.712067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.00000 | + | 8.00000i | −0.473879 | + | 0.473879i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.3137 | 0.667827 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.3137 | + | 11.3137i | −0.663221 | + | 0.663221i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.0000 | + | 13.0000i | 0.759468 | + | 0.759468i | 0.976226 | − | 0.216757i | \(-0.0695481\pi\) |
−0.216757 | + | 0.976226i | \(0.569548\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.9706i | 0.988064i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.9706 | + | 16.9706i | 0.981433 | + | 0.981433i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.5563 | −0.893689 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.82843 | − | 2.82843i | 0.161427 | − | 0.161427i | −0.621772 | − | 0.783199i | \(-0.713587\pi\) |
0.783199 | + | 0.621772i | \(0.213587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.0000 | + | 14.0000i | 0.796432 | + | 0.796432i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.2843i | 1.60385i | 0.597422 | + | 0.801927i | \(0.296192\pi\) | ||||
−0.597422 | + | 0.801927i | \(0.703808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 16.0000i | − | 0.904373i | −0.891923 | − | 0.452187i | \(-0.850644\pi\) | ||
0.891923 | − | 0.452187i | \(-0.149356\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.82843 | − | 2.82843i | −0.159364 | − | 0.159364i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.0000 | + | 15.0000i | −0.842484 | + | 0.842484i | −0.989181 | − | 0.146697i | \(-0.953136\pi\) |
0.146697 | + | 0.989181i | \(0.453136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.6274 | + | 22.6274i | −1.25902 | + | 1.25902i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.00000 | + | 9.00000i | 0.499230 | + | 0.499230i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.24264i | 0.234619i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.0000i | 1.76422i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.82843 | + | 2.82843i | 0.155464 | + | 0.155464i | 0.780553 | − | 0.625089i | \(-0.214937\pi\) |
−0.625089 | + | 0.780553i | \(0.714937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.00000 | + | 3.00000i | −0.164399 | + | 0.164399i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.65685 | 0.309067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.7279 | + | 12.7279i | −0.691286 | + | 0.691286i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.00000i | 0.430706i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.6274 | − | 22.6274i | −1.21470 | − | 1.21470i | −0.969462 | − | 0.245241i | \(-0.921133\pi\) |
−0.245241 | − | 0.969462i | \(-0.578867\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.00000 | + | 9.00000i | −0.481759 | + | 0.481759i | −0.905693 | − | 0.423934i | \(-0.860649\pi\) |
0.423934 | + | 0.905693i | \(0.360649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.24264 | −0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.0000 | −0.958043 | −0.479022 | − | 0.877803i | \(-0.659008\pi\) | ||||
−0.479022 | + | 0.877803i | \(0.659008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.3137 | − | 11.3137i | 0.600469 | − | 0.600469i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.00000 | − | 8.00000i | −0.423405 | − | 0.423405i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.3137i | − | 0.597115i | −0.954392 | − | 0.298557i | \(-0.903495\pi\) | ||
0.954392 | − | 0.298557i | \(-0.0965054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 45.0000i | − | 2.36842i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.77817 | + | 7.77817i | 0.408248 | + | 0.408248i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000 | − | 14.0000i | 0.732793 | − | 0.732793i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.82843 | −0.147643 | −0.0738213 | − | 0.997271i | \(-0.523519\pi\) | ||||
−0.0738213 | + | 0.997271i | \(0.523519\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.00000 | 0.208232 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.1421 | + | 14.1421i | −0.734223 | + | 0.734223i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.00000 | − | 3.00000i | −0.155334 | − | 0.155334i | 0.625161 | − | 0.780496i | \(-0.285033\pi\) |
−0.780496 | + | 0.625161i | \(0.785033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.3137i | 0.584237i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.00000i | 0.309016i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.3137 | − | 11.3137i | −0.581146 | − | 0.581146i | 0.354072 | − | 0.935218i | \(-0.384797\pi\) |
−0.935218 | + | 0.354072i | \(0.884797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.00000 | − | 6.00000i | 0.307389 | − | 0.307389i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.2843 | −1.44526 | −0.722629 | − | 0.691236i | \(-0.757067\pi\) | ||||
−0.722629 | + | 0.691236i | \(0.757067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.00000 | + | 7.00000i | 0.354914 | + | 0.354914i | 0.861934 | − | 0.507020i | \(-0.169253\pi\) |
−0.507020 | + | 0.861934i | \(0.669253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.6274i | 1.14432i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.00000i | − | 0.201773i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.48528 | − | 8.48528i | −0.426941 | − | 0.426941i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.0000 | − | 15.0000i | 0.752828 | − | 0.752828i | −0.222178 | − | 0.975006i | \(-0.571317\pi\) |
0.975006 | + | 0.222178i | \(0.0713165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 22.6274 | 1.13279 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.0000 | 0.998752 | 0.499376 | − | 0.866385i | \(-0.333563\pi\) | ||||
0.499376 | + | 0.866385i | \(0.333563\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.48528 | + | 8.48528i | −0.422682 | + | 0.422682i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | − | 1.00000i | −0.0496904 | − | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.0000i | 1.58230i | 0.611623 | + | 0.791149i | \(0.290517\pi\) | ||||
−0.611623 | + | 0.791149i | \(0.709483\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.48528 | − | 8.48528i | −0.418548 | − | 0.418548i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.0000 | − | 24.0000i | 1.18096 | − | 1.18096i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.6274 | 1.11074 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.00000 | 0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.65685 | + | 5.65685i | −0.276355 | + | 0.276355i | −0.831652 | − | 0.555297i | \(-0.812605\pi\) |
0.555297 | + | 0.831652i | \(0.312605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.00000 | − | 9.00000i | −0.438633 | − | 0.438633i | 0.452919 | − | 0.891552i | \(-0.350383\pi\) |
−0.891552 | + | 0.452919i | \(0.850383\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.3137i | 0.550091i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000i | 0.582086i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.82843 | − | 2.82843i | −0.136877 | − | 0.136877i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3137 | 0.544962 | 0.272481 | − | 0.962161i | \(-0.412156\pi\) | ||||
0.272481 | + | 0.962161i | \(0.412156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.00000 | −0.384455 | −0.192228 | − | 0.981350i | \(-0.561571\pi\) | ||||
−0.192228 | + | 0.981350i | \(0.561571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.41421 | + | 1.41421i | −0.0678064 | + | 0.0678064i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.0000 | − | 32.0000i | −1.53077 | − | 1.53077i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.82843i | 0.134993i | 0.997719 | + | 0.0674967i | \(0.0215012\pi\) | ||||
−0.997719 | + | 0.0674967i | \(0.978499\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000i | 0.0476190i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.9706 | + | 16.9706i | 0.806296 | + | 0.806296i | 0.984071 | − | 0.177775i | \(-0.0568900\pi\) |
−0.177775 | + | 0.984071i | \(0.556890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | + | 6.00000i | −0.284427 | + | 0.284427i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.7279 | −0.602010 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.0000 | −0.566315 | −0.283158 | − | 0.959073i | \(-0.591382\pi\) | ||||
−0.283158 | + | 0.959073i | \(0.591382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.00000 | + | 2.00000i | 0.0939682 | + | 0.0939682i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.9706i | 0.795592i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.82843 | − | 2.82843i | −0.132020 | − | 0.132020i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.0000 | + | 11.0000i | −0.512321 | + | 0.512321i | −0.915237 | − | 0.402916i | \(-0.867997\pi\) |
0.402916 | + | 0.915237i | \(0.367997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.1127 | 1.44593 | 0.722965 | − | 0.690885i | \(-0.242779\pi\) | ||||
0.722965 | + | 0.690885i | \(0.242779\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.00000 | −0.185496 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.65685 | + | 5.65685i | −0.261768 | + | 0.261768i | −0.825772 | − | 0.564004i | \(-0.809260\pi\) |
0.564004 | + | 0.825772i | \(0.309260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | − | 8.00000i | −0.369406 | − | 0.369406i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 21.2132i | − | 0.977453i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.9706 | − | 16.9706i | −0.778663 | − | 0.778663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.00000 | + | 5.00000i | −0.228934 | + | 0.228934i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.2843 | 1.29234 | 0.646171 | − | 0.763193i | \(-0.276369\pi\) | ||||
0.646171 | + | 0.763193i | \(0.276369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.3137 | − | 11.3137i | 0.514792 | − | 0.514792i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.0000 | + | 16.0000i | 0.726523 | + | 0.726523i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.82843i | 0.128168i | 0.997944 | + | 0.0640841i | \(0.0204126\pi\) | ||||
−0.997944 | + | 0.0640841i | \(0.979587\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 16.0000i | − | 0.723545i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.48528 | − | 8.48528i | −0.382935 | − | 0.382935i | 0.489223 | − | 0.872159i | \(-0.337280\pi\) |
−0.872159 | + | 0.489223i | \(0.837280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.00000 | + | 4.00000i | −0.180151 | + | 0.180151i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −32.0000 | −1.43540 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.7990 | + | 19.7990i | −0.886325 | + | 0.886325i | −0.994168 | − | 0.107843i | \(-0.965605\pi\) |
0.107843 | + | 0.994168i | \(0.465605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.00000 | + | 8.00000i | 0.357414 | + | 0.357414i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 11.3137i | − | 0.504453i | −0.967668 | − | 0.252227i | \(-0.918837\pi\) | ||
0.967668 | − | 0.252227i | \(-0.0811629\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.0000i | 0.978987i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.53553 | + | 3.53553i | 0.157019 | + | 0.157019i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.0000 | − | 23.0000i | 1.01946 | − | 1.01946i | 0.0196502 | − | 0.999807i | \(-0.493745\pi\) |
0.999807 | − | 0.0196502i | \(-0.00625524\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.5980 | −1.75171 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.00000 | 0.353209 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.7990 | − | 19.7990i | 0.872448 | − | 0.872448i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 7.07107i | − | 0.310385i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12.0000i | − | 0.525730i | −0.964833 | − | 0.262865i | \(-0.915333\pi\) | ||
0.964833 | − | 0.262865i | \(-0.0846673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.65685 | + | 5.65685i | 0.247357 | + | 0.247357i | 0.819885 | − | 0.572528i | \(-0.194037\pi\) |
−0.572528 | + | 0.819885i | \(0.694037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.00000 | − | 6.00000i | 0.261861 | − | 0.261861i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.3137 | −0.492833 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.00000 | −0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.48528 | − | 8.48528i | 0.368230 | − | 0.368230i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0000 | − | 12.0000i | −0.519778 | − | 0.519778i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 16.9706i | − | 0.733701i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 4.00000i | − | 0.172613i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.00000 | + | 3.00000i | −0.128980 | + | 0.128980i | −0.768650 | − | 0.639670i | \(-0.779071\pi\) |
0.639670 | + | 0.768650i | \(0.279071\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.7279 | 0.546207 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.00000 | 0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.65685 | + | 5.65685i | −0.241870 | + | 0.241870i | −0.817623 | − | 0.575754i | \(-0.804709\pi\) |
0.575754 | + | 0.817623i | \(0.304709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.00000 | − | 1.00000i | −0.0426790 | − | 0.0426790i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11.3137i | − | 0.481980i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.0000i | 1.02058i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.24264 | + | 4.24264i | 0.180090 | + | 0.180090i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.0000 | + | 21.0000i | −0.889799 | + | 0.889799i | −0.994503 | − | 0.104705i | \(-0.966610\pi\) |
0.104705 | + | 0.994503i | \(0.466610\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.65685 | − | 5.65685i | 0.238408 | − | 0.238408i | −0.577783 | − | 0.816191i | \(-0.696082\pi\) |
0.816191 | + | 0.577783i | \(0.196082\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.0000 | + | 18.0000i | 0.757266 | + | 0.757266i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.82843i | 0.118783i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 20.0000i | − | 0.838444i | −0.907884 | − | 0.419222i | \(-0.862303\pi\) | ||
0.907884 | − | 0.419222i | \(-0.137697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.1421 | + | 14.1421i | 0.591830 | + | 0.591830i | 0.938125 | − | 0.346296i | \(-0.112561\pi\) |
−0.346296 | + | 0.938125i | \(0.612561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.00000 | − | 4.00000i | 0.167102 | − | 0.167102i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.9706 | −0.707721 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0000 | 0.915872 | 0.457936 | − | 0.888985i | \(-0.348589\pi\) | ||||
0.457936 | + | 0.888985i | \(0.348589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.0000 | − | 32.0000i | −1.32758 | − | 1.32758i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.00000i | 0.248069i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.82843 | + | 2.82843i | 0.116742 | + | 0.116742i | 0.763064 | − | 0.646323i | \(-0.223694\pi\) |
−0.646323 | + | 0.763064i | \(0.723694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | − | 16.0000i | 0.659269 | − | 0.659269i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.07107 | −0.290865 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.0000 | 1.39621 | 0.698106 | − | 0.715994i | \(-0.254026\pi\) | ||||
0.698106 | + | 0.715994i | \(0.254026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.3137 | + | 11.3137i | −0.463817 | + | 0.463817i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.00000 | − | 6.00000i | −0.245564 | − | 0.245564i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 39.5980i | − | 1.61793i | −0.587857 | − | 0.808965i | \(-0.700028\pi\) | ||
0.587857 | − | 0.808965i | \(-0.299972\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000i | 0.571072i | 0.958368 | + | 0.285536i | \(0.0921716\pi\) | ||||
−0.958368 | + | 0.285536i | \(0.907828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.82843 | − | 2.82843i | −0.115182 | − | 0.115182i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0000 | − | 11.0000i | 0.447214 | − | 0.447214i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.4264 | −1.72203 | −0.861017 | − | 0.508576i | \(-0.830172\pi\) | ||||
−0.861017 | + | 0.508576i | \(0.830172\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00000 | 0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.9411 | − | 33.9411i | 1.37311 | − | 1.37311i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0000 | + | 11.0000i | 0.444286 | + | 0.444286i | 0.893449 | − | 0.449164i | \(-0.148278\pi\) |
−0.449164 | + | 0.893449i | \(0.648278\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 5.65685i | − | 0.228106i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000i | 0.241551i | 0.992680 | + | 0.120775i | \(0.0385381\pi\) | ||||
−0.992680 | + | 0.120775i | \(0.961462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.1127 | + | 31.1127i | 1.25052 | + | 1.25052i | 0.955485 | + | 0.295040i | \(0.0953330\pi\) |
0.295040 | + | 0.955485i | \(0.404667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | − | 4.00000i | 0.160514 | − | 0.160514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.9706 | 0.679911 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0000 | + | 12.0000i | 0.478471 | + | 0.478471i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.48528i | 0.337794i | 0.985634 | + | 0.168897i | \(0.0540205\pi\) | ||||
−0.985634 | + | 0.168897i | \(0.945980\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 12.0000i | − | 0.476957i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.48528 | − | 8.48528i | −0.336728 | − | 0.336728i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | − | 3.00000i | 0.118864 | − | 0.118864i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.3137 | −0.447563 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.0000 | −0.473972 | −0.236986 | − | 0.971513i | \(-0.576159\pi\) | ||||
−0.236986 | + | 0.971513i | \(0.576159\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.3137 | − | 11.3137i | 0.446169 | − | 0.446169i | −0.447910 | − | 0.894079i | \(-0.647831\pi\) |
0.894079 | + | 0.447910i | \(0.147831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.5980i | 1.55676i | 0.627795 | + | 0.778379i | \(0.283958\pi\) | ||||
−0.627795 | + | 0.778379i | \(0.716042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.65685 | + | 5.65685i | 0.221710 | + | 0.221710i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.00000 | + | 3.00000i | −0.117399 | + | 0.117399i | −0.763366 | − | 0.645967i | \(-0.776455\pi\) |
0.645967 | + | 0.763366i | \(0.276455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.65685 | −0.221032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.0000 | −0.546192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.1421 | + | 14.1421i | −0.550899 | + | 0.550899i | −0.926700 | − | 0.375801i | \(-0.877368\pi\) |
0.375801 | + | 0.926700i | \(0.377368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.0000 | + | 19.0000i | 0.739014 | + | 0.739014i | 0.972387 | − | 0.233373i | \(-0.0749763\pi\) |
−0.233373 | + | 0.972387i | \(0.574976\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.9706i | 0.659082i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 32.0000i | − | 1.24091i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.65685 | − | 5.65685i | −0.219034 | − | 0.219034i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.0000 | + | 18.0000i | −0.695920 | + | 0.695920i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.00000 | −0.308377 | −0.154189 | − | 0.988041i | \(-0.549276\pi\) | ||||
−0.154189 | + | 0.988041i | \(0.549276\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.12132 | − | 2.12132i | 0.0816497 | − | 0.0816497i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.0000 | + | 23.0000i | 0.883962 | + | 0.883962i | 0.993935 | − | 0.109973i | \(-0.0350764\pi\) |
−0.109973 | + | 0.993935i | \(0.535076\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 45.2548i | − | 1.73672i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 8.00000i | − | 0.306561i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.6274 | + | 22.6274i | 0.865814 | + | 0.865814i | 0.992006 | − | 0.126192i | \(-0.0402755\pi\) |
−0.126192 | + | 0.992006i | \(0.540275\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | + | 12.0000i | −0.458496 | + | 0.458496i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.0416 | 0.917245 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.0000 | 1.14291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.2843 | − | 28.2843i | 1.07598 | − | 1.07598i | 0.0791192 | − | 0.996865i | \(-0.474789\pi\) |
0.996865 | − | 0.0791192i | \(-0.0252108\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 5.65685i | − | 0.214577i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 16.0000i | − | 0.606043i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.07107 | − | 7.07107i | −0.267452 | − | 0.267452i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.0000 | + | 33.0000i | −1.24639 | + | 1.24639i | −0.289091 | + | 0.957302i | \(0.593353\pi\) |
−0.957302 | + | 0.289091i | \(0.906647\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.9411 | −1.28011 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.0000 | 0.602595 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.1127 | − | 31.1127i | 1.17011 | − | 1.17011i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.0000 | + | 25.0000i | 0.938895 | + | 0.938895i | 0.998238 | − | 0.0593429i | \(-0.0189006\pi\) |
−0.0593429 | + | 0.998238i | \(0.518901\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.48528i | 0.318223i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 16.0000i | − | 0.599205i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.00000 | + | 4.00000i | −0.149383 | + | 0.149383i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.9706 | 0.632895 | 0.316448 | − | 0.948610i | \(-0.397510\pi\) | ||||
0.316448 | + | 0.948610i | \(0.397510\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −56.0000 | −2.08555 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.65685 | − | 5.65685i | 0.210381 | − | 0.210381i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.00000 | − | 3.00000i | −0.111417 | − | 0.111417i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 42.4264i | − | 1.57351i | −0.617266 | − | 0.786754i | \(-0.711760\pi\) | ||
0.617266 | − | 0.786754i | \(-0.288240\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.00000 | − | 3.00000i | 0.110808 | − | 0.110808i | −0.649529 | − | 0.760337i | \(-0.725034\pi\) |
0.760337 | + | 0.649529i | \(0.225034\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.41421 | 0.0521641 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.4558 | − | 25.4558i | 0.936408 | − | 0.936408i | −0.0616872 | − | 0.998096i | \(-0.519648\pi\) |
0.998096 | + | 0.0616872i | \(0.0196481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.0000 | − | 24.0000i | −0.881662 | − | 0.881662i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.3137i | 0.415060i | 0.978229 | + | 0.207530i | \(0.0665424\pi\) | ||||
−0.978229 | + | 0.207530i | \(0.933458\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.0000i | 0.659469i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.3137 | − | 11.3137i | −0.413947 | − | 0.413947i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.0000 | + | 24.0000i | −0.876941 | + | 0.876941i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.48528 | 0.309632 | 0.154816 | − | 0.987943i | \(-0.450521\pi\) | ||||
0.154816 | + | 0.987943i | \(0.450521\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.00000 | 0.291536 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.82843 | − | 2.82843i | 0.102937 | − | 0.102937i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0000 | + | 15.0000i | 0.545184 | + | 0.545184i | 0.925044 | − | 0.379860i | \(-0.124028\pi\) |
−0.379860 | + | 0.925044i | \(0.624028\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.0000i | 1.30500i | 0.757789 | + | 0.652499i | \(0.226280\pi\) | ||||
−0.757789 | + | 0.652499i | \(0.773720\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.48528 | − | 8.48528i | −0.307188 | − | 0.307188i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00000 | + | 4.00000i | −0.144620 | + | 0.144620i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −50.9117 | −1.83831 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.0000 | −1.15395 | −0.576975 | − | 0.816762i | \(-0.695767\pi\) | ||||
−0.576975 | + | 0.816762i | \(0.695767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.41421 | + | 1.41421i | −0.0509317 | + | 0.0509317i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.0000 | − | 13.0000i | −0.467578 | − | 0.467578i | 0.433551 | − | 0.901129i | \(-0.357260\pi\) |
−0.901129 | + | 0.433551i | \(0.857260\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 8.48528i | − | 0.304800i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 12.0000i | − | 0.430498i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.6274 | + | 22.6274i | 0.810711 | + | 0.810711i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.41421 | 0.0505399 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.0000 | −1.07075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.6274 | − | 22.6274i | 0.806580 | − | 0.806580i | −0.177534 | − | 0.984115i | \(-0.556812\pi\) |
0.984115 | + | 0.177534i | \(0.0568121\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.0000 | − | 20.0000i | −0.712019 | − | 0.712019i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 50.9117i | − | 1.81021i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000i | 0.213066i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.07107 | + | 7.07107i | 0.250785 | + | 0.250785i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.0000 | − | 35.0000i | 1.23976 | − | 1.23976i | 0.279666 | − | 0.960097i | \(-0.409776\pi\) |
0.960097 | − | 0.279666i | \(-0.0902238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.2548 | 1.60100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.0000 | − | 16.0000i | −0.563926 | − | 0.563926i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 21.2132i | − | 0.746740i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 4.00000i | − | 0.140633i | −0.997525 | − | 0.0703163i | \(-0.977599\pi\) | ||
0.997525 | − | 0.0703163i | \(-0.0224008\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.2843 | + | 28.2843i | 0.993195 | + | 0.993195i | 0.999977 | − | 0.00678191i | \(-0.00215876\pi\) |
−0.00678191 | + | 0.999977i | \(0.502159\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.00000 | + | 6.00000i | −0.210429 | + | 0.210429i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.6274 | −0.792604 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.48528 | − | 8.48528i | 0.296500 | − | 0.296500i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.00000 | − | 5.00000i | −0.174501 | − | 0.174501i | 0.614453 | − | 0.788954i | \(-0.289377\pi\) |
−0.788954 | + | 0.614453i | \(0.789377\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 25.4558i | − | 0.887335i | −0.896191 | − | 0.443667i | \(-0.853677\pi\) | ||
0.896191 | − | 0.443667i | \(-0.146323\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.1421 | − | 14.1421i | −0.491770 | − | 0.491770i | 0.417093 | − | 0.908864i | \(-0.363049\pi\) |
−0.908864 | + | 0.417093i | \(0.863049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.0000 | − | 37.0000i | 1.28506 | − | 1.28506i | 0.347314 | − | 0.937749i | \(-0.387094\pi\) |
0.937749 | − | 0.347314i | \(-0.112906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.41421 | −0.0490585 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.00000 | 0.138592 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.3137 | − | 11.3137i | 0.391527 | − | 0.391527i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.00000 | + | 2.00000i | 0.0691301 | + | 0.0691301i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 45.2548i | − | 1.56237i | −0.624299 | − | 0.781185i | \(-0.714615\pi\) | ||
0.624299 | − | 0.781185i | \(-0.285385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000i | 0.931034i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.5563 | + | 15.5563i | 0.535789 | + | 0.535789i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.00000 | − | 5.00000i | 0.172005 | − | 0.172005i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.1127 | −1.06904 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.9706 | + | 16.9706i | −0.581743 | + | 0.581743i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.0000 | − | 11.0000i | −0.376633 | − | 0.376633i | 0.493253 | − | 0.869886i | \(-0.335808\pi\) |
−0.869886 | + | 0.493253i | \(0.835808\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 11.3137i | − | 0.386921i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 20.0000i | − | 0.683187i | −0.939848 | − | 0.341593i | \(-0.889033\pi\) | ||
0.939848 | − | 0.341593i | \(-0.110967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.65685 | + | 5.65685i | 0.193009 | + | 0.193009i | 0.796995 | − | 0.603986i | \(-0.206422\pi\) |
−0.603986 | + | 0.796995i | \(0.706422\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | + | 8.00000i | −0.272639 | + | 0.272639i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.65685 | 0.192562 | 0.0962808 | − | 0.995354i | \(-0.469305\pi\) | ||||
0.0962808 | + | 0.995354i | \(0.469305\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0000 | −0.340010 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.707107 | − | 0.707107i | 0.0240146 | − | 0.0240146i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9706i | 0.575026i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 16.0000i | − | 0.541518i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22.6274 | − | 22.6274i | −0.764946 | − | 0.764946i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0000 | − | 23.0000i | 0.776655 | − | 0.776655i | −0.202606 | − | 0.979260i | \(-0.564941\pi\) |
0.979260 | + | 0.202606i | \(0.0649409\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.3848 | −0.620103 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.9706 | + | 16.9706i | −0.571105 | + | 0.571105i | −0.932437 | − | 0.361332i | \(-0.882322\pi\) |
0.361332 | + | 0.932437i | \(0.382322\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.0000 | − | 12.0000i | −0.403376 | − | 0.403376i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 16.9706i | − | 0.569816i | −0.958555 | − | 0.284908i | \(-0.908037\pi\) | ||
0.958555 | − | 0.284908i | \(-0.0919630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.0000i | 0.804934i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −64.0000 | + | 64.0000i | −2.14168 | + | 2.14168i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.65685 | −0.189088 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.0000 | −0.801337 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.82843 | − | 2.82843i | 0.0943333 | − | 0.0943333i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.0000 | + | 20.0000i | 0.666297 | + | 0.666297i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 18.0000i | − | 0.598340i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.6274 | − | 22.6274i | −0.751331 | − | 0.751331i | 0.223397 | − | 0.974728i | \(-0.428286\pi\) |
−0.974728 | + | 0.223397i | \(0.928286\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.0000 | − | 11.0000i | 0.364847 | − | 0.364847i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.65685 | 0.187420 | 0.0937100 | − | 0.995600i | \(-0.470127\pi\) | ||||
0.0937100 | + | 0.995600i | \(0.470127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.41421 | + | 1.41421i | −0.0467525 | + | 0.0467525i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.00000 | + | 8.00000i | 0.264183 | + | 0.264183i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.82843i | − | 0.0933012i | −0.998911 | − | 0.0466506i | \(-0.985145\pi\) | ||
0.998911 | − | 0.0466506i | \(-0.0148547\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.00000i | 0.131804i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33.9411 | + | 33.9411i | 1.11719 | + | 1.11719i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.00000 | + | 9.00000i | −0.295918 | + | 0.295918i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.7990 | −0.650284 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.0000 | −0.656179 | −0.328089 | − | 0.944647i | \(-0.606405\pi\) | ||||
−0.328089 | + | 0.944647i | \(0.606405\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.65685 | + | 5.65685i | −0.185396 | + | 0.185396i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.0000 | − | 20.0000i | −0.654771 | − | 0.654771i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.0000i | 1.37208i | 0.727564 | + | 0.686040i | \(0.240653\pi\) | ||||
−0.727564 | + | 0.686040i | \(0.759347\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.3137 | + | 11.3137i | 0.369209 | + | 0.369209i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.0000 | − | 37.0000i | 1.20617 | − | 1.20617i | 0.233906 | − | 0.972259i | \(-0.424849\pi\) |
0.972259 | − | 0.233906i | \(-0.0751509\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.6274 | 0.736850 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.00000 | 0.130120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.7696 | − | 36.7696i | 1.19485 | − | 1.19485i | 0.219161 | − | 0.975689i | \(-0.429668\pi\) |
0.975689 | − | 0.219161i | \(-0.0703321\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.0000 | + | 42.0000i | 1.36338 | + | 1.36338i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 21.2132i | − | 0.687885i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 36.0000i | − | 1.16615i | −0.812417 | − | 0.583077i | \(-0.801849\pi\) | ||
0.812417 | − | 0.583077i | \(-0.198151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.65685 | − | 5.65685i | −0.183052 | − | 0.183052i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.9411 | 1.09602 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0000 | −0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.48528 | + | 8.48528i | −0.273434 | + | 0.273434i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.4264i | 1.36434i | 0.731193 | + | 0.682171i | \(0.238964\pi\) | ||||
−0.731193 | + | 0.682171i | \(0.761036\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 32.0000i | − | 1.02799i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.9706 | + | 16.9706i | 0.544611 | + | 0.544611i | 0.924877 | − | 0.380266i | \(-0.124168\pi\) |
−0.380266 | + | 0.924877i | \(0.624168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00000 | + | 8.00000i | −0.256468 | + | 0.256468i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.7279 | −0.407620 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.0000 | 1.15174 | 0.575871 | − | 0.817541i | \(-0.304663\pi\) | ||||
0.575871 | + | 0.817541i | \(0.304663\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.00000 | − | 3.00000i | −0.0957826 | − | 0.0957826i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 16.9706i | − | 0.541277i | −0.962681 | − | 0.270638i | \(-0.912765\pi\) | ||
0.962681 | − | 0.270638i | \(-0.0872348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.0000i | 0.318626i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.6274 | − | 22.6274i | −0.720239 | − | 0.720239i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.4558 | 0.808632 | 0.404316 | − | 0.914619i | \(-0.367510\pi\) | ||||
0.404316 | + | 0.914619i | \(0.367510\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.48528 | + | 8.48528i | −0.269002 | + | 0.269002i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.00000 | + | 5.00000i | 0.158352 | + | 0.158352i | 0.781836 | − | 0.623484i | \(-0.214283\pi\) |
−0.623484 | + | 0.781836i | \(0.714283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 4.24264i | − | 0.134231i |
(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 | 1536.2.j.c.385.1 | yes | 4 | |
3.2 | odd | 2 | 4608.2.k.y.3457.1 | 4 | |||
4.3 | odd | 2 | inner | 1536.2.j.c.385.2 | yes | 4 | |
8.3 | odd | 2 | 1536.2.j.b.385.1 | ✓ | 4 | ||
8.5 | even | 2 | 1536.2.j.b.385.2 | yes | 4 | ||
12.11 | even | 2 | 4608.2.k.y.3457.2 | 4 | |||
16.3 | odd | 4 | inner | 1536.2.j.c.1153.2 | yes | 4 | |
16.5 | even | 4 | 1536.2.j.b.1153.2 | yes | 4 | ||
16.11 | odd | 4 | 1536.2.j.b.1153.1 | yes | 4 | ||
16.13 | even | 4 | inner | 1536.2.j.c.1153.1 | yes | 4 | |
24.5 | odd | 2 | 4608.2.k.bb.3457.1 | 4 | |||
24.11 | even | 2 | 4608.2.k.bb.3457.2 | 4 | |||
32.3 | odd | 8 | 3072.2.a.h.1.1 | 2 | |||
32.5 | even | 8 | 3072.2.d.c.1537.2 | 4 | |||
32.11 | odd | 8 | 3072.2.d.c.1537.1 | 4 | |||
32.13 | even | 8 | 3072.2.a.h.1.2 | 2 | |||
32.19 | odd | 8 | 3072.2.a.b.1.2 | 2 | |||
32.21 | even | 8 | 3072.2.d.c.1537.3 | 4 | |||
32.27 | odd | 8 | 3072.2.d.c.1537.4 | 4 | |||
32.29 | even | 8 | 3072.2.a.b.1.1 | 2 | |||
48.5 | odd | 4 | 4608.2.k.bb.1153.2 | 4 | |||
48.11 | even | 4 | 4608.2.k.bb.1153.1 | 4 | |||
48.29 | odd | 4 | 4608.2.k.y.1153.2 | 4 | |||
48.35 | even | 4 | 4608.2.k.y.1153.1 | 4 | |||
96.29 | odd | 8 | 9216.2.a.h.1.2 | 2 | |||
96.35 | even | 8 | 9216.2.a.i.1.2 | 2 | |||
96.77 | odd | 8 | 9216.2.a.i.1.1 | 2 | |||
96.83 | even | 8 | 9216.2.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.j.b.385.1 | ✓ | 4 | 8.3 | odd | 2 | ||
1536.2.j.b.385.2 | yes | 4 | 8.5 | even | 2 | ||
1536.2.j.b.1153.1 | yes | 4 | 16.11 | odd | 4 | ||
1536.2.j.b.1153.2 | yes | 4 | 16.5 | even | 4 | ||
1536.2.j.c.385.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1536.2.j.c.385.2 | yes | 4 | 4.3 | odd | 2 | inner | |
1536.2.j.c.1153.1 | yes | 4 | 16.13 | even | 4 | inner | |
1536.2.j.c.1153.2 | yes | 4 | 16.3 | odd | 4 | inner | |
3072.2.a.b.1.1 | 2 | 32.29 | even | 8 | |||
3072.2.a.b.1.2 | 2 | 32.19 | odd | 8 | |||
3072.2.a.h.1.1 | 2 | 32.3 | odd | 8 | |||
3072.2.a.h.1.2 | 2 | 32.13 | even | 8 | |||
3072.2.d.c.1537.1 | 4 | 32.11 | odd | 8 | |||
3072.2.d.c.1537.2 | 4 | 32.5 | even | 8 | |||
3072.2.d.c.1537.3 | 4 | 32.21 | even | 8 | |||
3072.2.d.c.1537.4 | 4 | 32.27 | odd | 8 | |||
4608.2.k.y.1153.1 | 4 | 48.35 | even | 4 | |||
4608.2.k.y.1153.2 | 4 | 48.29 | odd | 4 | |||
4608.2.k.y.3457.1 | 4 | 3.2 | odd | 2 | |||
4608.2.k.y.3457.2 | 4 | 12.11 | even | 2 | |||
4608.2.k.bb.1153.1 | 4 | 48.11 | even | 4 | |||
4608.2.k.bb.1153.2 | 4 | 48.5 | odd | 4 | |||
4608.2.k.bb.3457.1 | 4 | 24.5 | odd | 2 | |||
4608.2.k.bb.3457.2 | 4 | 24.11 | even | 2 | |||
9216.2.a.h.1.1 | 2 | 96.83 | even | 8 | |||
9216.2.a.h.1.2 | 2 | 96.29 | odd | 8 | |||
9216.2.a.i.1.1 | 2 | 96.77 | odd | 8 | |||
9216.2.a.i.1.2 | 2 | 96.35 | even | 8 |