Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [880,2,Mod(81,880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(880, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("880.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 880 = 2^{4} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 880.bo (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.02683537787\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 401.1 | ||
Root | \(-0.386111 - 0.280526i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 880.401 |
Dual form | 880.2.bo.h.801.1 |
$q$-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 \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(321\) | \(661\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.261370 | + | 0.189896i | 0.150902 | + | 0.109637i | 0.660674 | − | 0.750673i | \(-0.270270\pi\) |
−0.509772 | + | 0.860309i | \(0.670270\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.309017 | + | 0.951057i | −0.138197 | + | 0.425325i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.17239 | − | 1.57833i | 0.821086 | − | 0.596554i | −0.0959376 | − | 0.995387i | \(-0.530585\pi\) |
0.917023 | + | 0.398834i | \(0.130585\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.894797 | − | 2.75390i | −0.298266 | − | 0.917968i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.79042 | − | 1.79264i | 0.841344 | − | 0.540500i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.44244 | − | 4.43939i | −0.400062 | − | 1.23126i | −0.924949 | − | 0.380092i | \(-0.875892\pi\) |
0.524886 | − | 0.851172i | \(-0.324108\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.261370 | + | 0.189896i | −0.0674854 | + | 0.0490310i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.42961 | + | 4.39990i | −0.346732 | + | 1.06713i | 0.613918 | + | 0.789370i | \(0.289593\pi\) |
−0.960650 | + | 0.277762i | \(0.910407\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.51149 | − | 2.55125i | −0.805592 | − | 0.585297i | 0.106958 | − | 0.994264i | \(-0.465889\pi\) |
−0.912549 | + | 0.408967i | \(0.865889\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.867517 | 0.189308 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.77222 | −0.578048 | −0.289024 | − | 0.957322i | \(-0.593331\pi\) | ||||
−0.289024 | + | 0.957322i | \(0.593331\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.588587 | − | 1.81148i | 0.113274 | − | 0.348620i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.43790 | − | 1.77124i | 0.452707 | − | 0.328911i | −0.337956 | − | 0.941162i | \(-0.609736\pi\) |
0.790664 | + | 0.612251i | \(0.209736\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.737407 | − | 2.26951i | −0.132442 | − | 0.407615i | 0.862741 | − | 0.505646i | \(-0.168746\pi\) |
−0.995183 | + | 0.0980305i | \(0.968746\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.06975 | + | 0.0613500i | 0.186219 | + | 0.0106797i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.829779 | + | 2.55380i | 0.140258 | + | 0.431670i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.61029 | − | 6.25574i | 1.41552 | − | 1.02844i | 0.423033 | − | 0.906114i | \(-0.360965\pi\) |
0.992490 | − | 0.122324i | \(-0.0390346\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.466012 | − | 1.43424i | 0.0746217 | − | 0.229662i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.78826 | + | 1.29924i | 0.279279 | + | 0.202908i | 0.718603 | − | 0.695421i | \(-0.244782\pi\) |
−0.439324 | + | 0.898329i | \(0.644782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.06719 | 1.07774 | 0.538868 | − | 0.842390i | \(-0.318852\pi\) | ||||
0.538868 | + | 0.842390i | \(0.318852\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.89563 | 0.431654 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.52905 | + | 2.56401i | 0.514765 | + | 0.373999i | 0.814628 | − | 0.579983i | \(-0.196941\pi\) |
−0.299863 | + | 0.953982i | \(0.596941\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0650188 | − | 0.200107i | 0.00928840 | − | 0.0285868i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.20918 | + | 0.878523i | −0.169319 | + | 0.123018i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.95733 | − | 6.02403i | −0.268859 | − | 0.827464i | −0.990779 | − | 0.135487i | \(-0.956740\pi\) |
0.721920 | − | 0.691977i | \(-0.243260\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.842610 | + | 3.20780i | 0.113617 | + | 0.432540i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.433326 | − | 1.33364i | −0.0573954 | − | 0.176645i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.50375 | − | 6.90488i | 1.23728 | − | 0.898939i | 0.239869 | − | 0.970805i | \(-0.422896\pi\) |
0.997414 | + | 0.0718667i | \(0.0228956\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.23070 | + | 3.78770i | −0.157575 | + | 0.484966i | −0.998413 | − | 0.0563214i | \(-0.982063\pi\) |
0.840838 | + | 0.541287i | \(0.182063\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.29042 | − | 4.57026i | −0.792519 | − | 0.575799i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.66785 | 0.578975 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.31984 | −0.894260 | −0.447130 | − | 0.894469i | \(-0.647554\pi\) | ||||
−0.447130 | + | 0.894469i | \(0.647554\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.724576 | − | 0.526435i | −0.0872287 | − | 0.0633754i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.369495 | + | 1.13719i | −0.0438510 | + | 0.134960i | −0.970585 | − | 0.240758i | \(-0.922604\pi\) |
0.926734 | + | 0.375718i | \(0.122604\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.826577 | + | 0.600544i | −0.0967436 | + | 0.0702883i | −0.635105 | − | 0.772425i | \(-0.719043\pi\) |
0.538362 | + | 0.842714i | \(0.319043\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0998345 | − | 0.307259i | −0.0115279 | − | 0.0354792i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.23251 | − | 8.29852i | 0.368378 | − | 0.945704i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.08222 | − | 3.33073i | −0.121759 | − | 0.374736i | 0.871538 | − | 0.490329i | \(-0.163123\pi\) |
−0.993297 | + | 0.115593i | \(0.963123\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.53000 | + | 4.74432i | −0.725555 | + | 0.527147i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.43498 | + | 10.5718i | −0.377038 | + | 1.16040i | 0.565055 | + | 0.825053i | \(0.308855\pi\) |
−0.942093 | + | 0.335351i | \(0.891145\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.74278 | − | 2.71929i | −0.405961 | − | 0.294948i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.973547 | 0.104375 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.76978 | 0.293596 | 0.146798 | − | 0.989167i | \(-0.453103\pi\) | ||||
0.146798 | + | 0.989167i | \(0.453103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.1404 | − | 7.36742i | −1.06300 | − | 0.772315i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.238235 | − | 0.733212i | 0.0247038 | − | 0.0760305i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.51149 | − | 2.55125i | 0.360271 | − | 0.261753i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.72738 | + | 17.6271i | 0.581528 | + | 1.78976i | 0.612789 | + | 0.790247i | \(0.290048\pi\) |
−0.0312615 | + | 0.999511i | \(0.509952\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.43361 | − | 6.08051i | −0.747106 | − | 0.611114i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.19852 | − | 6.76634i | −0.218761 | − | 0.673276i | −0.998865 | − | 0.0476270i | \(-0.984834\pi\) |
0.780104 | − | 0.625649i | \(-0.215166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.09056 | − | 4.42505i | 0.600121 | − | 0.436014i | −0.245801 | − | 0.969320i | \(-0.579051\pi\) |
0.845922 | + | 0.533307i | \(0.179051\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.268077 | + | 0.825058i | −0.0261617 | + | 0.0805174i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.5859 | + | 10.5973i | 1.41008 | + | 1.02448i | 0.993312 | + | 0.115465i | \(0.0368358\pi\) |
0.416764 | + | 0.909015i | \(0.363164\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.3653 | −1.56751 | −0.783756 | − | 0.621068i | \(-0.786699\pi\) | ||||
−0.783756 | + | 0.621068i | \(0.786699\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.43842 | 0.326360 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.66154 | + | 1.20718i | 0.156304 | + | 0.113562i | 0.663188 | − | 0.748453i | \(-0.269203\pi\) |
−0.506884 | + | 0.862014i | \(0.669203\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.856664 | − | 2.63654i | 0.0798843 | − | 0.245859i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.9349 | + | 7.94470i | −1.01094 | + | 0.734488i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.83883 | + | 11.8147i | 0.351905 | + | 1.08305i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.57291 | − | 10.0044i | 0.415720 | − | 0.909493i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.220675 | + | 0.679167i | 0.0198976 | + | 0.0612384i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.809017 | − | 0.587785i | 0.0723607 | − | 0.0525731i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0235677 | − | 0.0725340i | 0.00209130 | − | 0.00643635i | −0.950005 | − | 0.312233i | \(-0.898923\pi\) |
0.952097 | + | 0.305797i | \(0.0989229\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.84715 | + | 1.34203i | 0.162633 | + | 0.118159i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4831 | 1.00328 | 0.501642 | − | 0.865075i | \(-0.332730\pi\) | ||||
0.501642 | + | 0.865075i | \(0.332730\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.6550 | −1.01062 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.54094 | + | 1.11956i | 0.132623 | + | 0.0963562i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.66406 | + | 17.4322i | −0.483914 | + | 1.48933i | 0.349635 | + | 0.936886i | \(0.386306\pi\) |
−0.833548 | + | 0.552447i | \(0.813694\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.7590 | + | 13.6292i | −1.59111 | + | 1.15601i | −0.688785 | + | 0.724966i | \(0.741855\pi\) |
−0.902330 | + | 0.431046i | \(0.858145\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.435493 | + | 1.34031i | 0.0366751 | + | 0.112874i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.9832 | − | 9.80199i | −1.00209 | − | 0.819683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.931196 | + | 2.86593i | 0.0773317 | + | 0.238002i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.0549936 | − | 0.0399552i | 0.00453580 | − | 0.00329545i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.53161 | − | 13.9469i | 0.371244 | − | 1.14257i | −0.574733 | − | 0.818341i | \(-0.694894\pi\) |
0.945978 | − | 0.324232i | \(-0.105106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.08301 | − | 4.41957i | −0.495028 | − | 0.359659i | 0.312086 | − | 0.950054i | \(-0.398972\pi\) |
−0.807115 | + | 0.590394i | \(0.798972\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.3961 | 1.08301 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.38630 | 0.191672 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.8262 | + | 7.86568i | 0.864023 | + | 0.627750i | 0.928977 | − | 0.370139i | \(-0.120690\pi\) |
−0.0649531 | + | 0.997888i | \(0.520690\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.632355 | − | 1.94619i | 0.0501491 | − | 0.154343i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.02234 | + | 4.37549i | −0.474627 | + | 0.344837i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.238558 | + | 0.734206i | 0.0186853 | + | 0.0575075i | 0.959964 | − | 0.280122i | \(-0.0903749\pi\) |
−0.941279 | + | 0.337629i | \(0.890375\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.388918 | + | 0.998432i | −0.0302772 | + | 0.0777279i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.62118 | + | 8.06716i | 0.202833 | + | 0.624256i | 0.999795 | + | 0.0202268i | \(0.00643884\pi\) |
−0.796962 | + | 0.604029i | \(0.793561\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.11029 | + | 5.16593i | −0.546946 | + | 0.397379i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.88382 | + | 11.9532i | −0.297003 | + | 0.914081i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.10876 | − | 2.98519i | −0.312384 | − | 0.226960i | 0.420535 | − | 0.907276i | \(-0.361842\pi\) |
−0.732919 | + | 0.680316i | \(0.761842\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.68522 | −0.202984 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.79521 | 0.285265 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.15568 | − | 6.65199i | −0.684328 | − | 0.497193i | 0.190463 | − | 0.981694i | \(-0.439001\pi\) |
−0.874791 | + | 0.484501i | \(0.839001\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.28674 | − | 7.03787i | 0.169972 | − | 0.523121i | −0.829396 | − | 0.558661i | \(-0.811315\pi\) |
0.999368 | + | 0.0355402i | \(0.0113152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.04094 | + | 0.756287i | −0.0769485 | + | 0.0559063i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.28884 | + | 10.1220i | 0.241800 | + | 0.744185i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.89819 | + | 14.8403i | 0.285064 | + | 1.08523i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.58048 | − | 4.86423i | −0.114963 | − | 0.353821i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.17135 | + | 3.03067i | −0.301829 | + | 0.219291i | −0.728382 | − | 0.685171i | \(-0.759728\pi\) |
0.426554 | + | 0.904462i | \(0.359728\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.24605 | + | 3.83494i | −0.0896925 | + | 0.276045i | −0.985834 | − | 0.167723i | \(-0.946359\pi\) |
0.896142 | + | 0.443768i | \(0.146359\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.22004 | + | 0.886408i | 0.0873686 | + | 0.0634770i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.4176 | 0.813469 | 0.406734 | − | 0.913547i | \(-0.366667\pi\) | ||||
0.406734 | + | 0.913547i | \(0.366667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.16644 | 0.508015 | 0.254008 | − | 0.967202i | \(-0.418251\pi\) | ||||
0.254008 | + | 0.967202i | \(0.418251\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.91319 | − | 1.39001i | −0.134946 | − | 0.0980438i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.50047 | − | 7.69565i | 0.175498 | − | 0.540128i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.78826 | + | 1.29924i | −0.124897 | + | 0.0907431i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.48058 | + | 7.63443i | 0.172412 | + | 0.530630i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.3720 | − | 0.824235i | −0.994132 | − | 0.0570135i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.07649 | − | 3.31309i | −0.0741086 | − | 0.228083i | 0.907140 | − | 0.420829i | \(-0.138261\pi\) |
−0.981249 | + | 0.192746i | \(0.938261\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.312523 | + | 0.227061i | −0.0214137 | + | 0.0155580i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.18388 | + | 6.72129i | −0.148939 | + | 0.458388i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.18397 | − | 3.76638i | −0.351911 | − | 0.255678i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.330084 | −0.0223050 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.5950 | 1.45264 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.53103 | + | 6.19816i | 0.571280 | + | 0.415059i | 0.835570 | − | 0.549384i | \(-0.185138\pi\) |
−0.264290 | + | 0.964443i | \(0.585138\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.894797 | + | 2.75390i | −0.0596532 | + | 0.183594i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.174762 | − | 0.126972i | 0.0115994 | − | 0.00842743i | −0.581970 | − | 0.813210i | \(-0.697718\pi\) |
0.593570 | + | 0.804782i | \(0.297718\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.0233956 | − | 0.0720042i | −0.00154602 | − | 0.00475817i | 0.950281 | − | 0.311395i | \(-0.100796\pi\) |
−0.951827 | + | 0.306637i | \(0.900796\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.42074 | − | 1.55514i | 0.159273 | − | 0.102321i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.67235 | + | 14.3800i | 0.306096 | + | 0.942067i | 0.979266 | + | 0.202579i | \(0.0649323\pi\) |
−0.673170 | + | 0.739488i | \(0.735068\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.52905 | + | 2.56401i | −0.230210 | + | 0.167257i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.349634 | − | 1.07606i | 0.0227111 | − | 0.0698977i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.7406 | − | 13.6158i | −1.21223 | − | 0.880734i | −0.216796 | − | 0.976217i | \(-0.569561\pi\) |
−0.995431 | + | 0.0954825i | \(0.969561\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.3349 | −1.37430 | −0.687151 | − | 0.726515i | \(-0.741139\pi\) | ||||
−0.687151 | + | 0.726515i | \(0.741139\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.32179 | −0.533843 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.170221 | + | 0.123673i | 0.0108750 | + | 0.00790119i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.26085 | + | 19.2689i | −0.398368 | + | 1.22605i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.90535 | + | 2.11086i | −0.184119 | + | 0.133770i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.92266 | + | 5.91734i | 0.121357 | + | 0.373499i | 0.993220 | − | 0.116251i | \(-0.0370878\pi\) |
−0.871863 | + | 0.489751i | \(0.837088\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.73567 | + | 4.96959i | −0.486338 | + | 0.312435i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.461867 | − | 1.42148i | −0.0289232 | − | 0.0890165i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.5611 | − | 8.39964i | 0.721163 | − | 0.523955i | −0.165593 | − | 0.986194i | \(-0.552954\pi\) |
0.886755 | + | 0.462239i | \(0.152954\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.83126 | − | 27.1798i | 0.548748 | − | 1.68887i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.05926 | − | 5.12885i | −0.436957 | − | 0.317468i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.13132 | −0.254748 | −0.127374 | − | 0.991855i | \(-0.540655\pi\) | ||||
−0.127374 | + | 0.991855i | \(0.540655\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.33404 | 0.389097 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.723937 | + | 0.525971i | 0.0443042 | + | 0.0321889i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.520367 | + | 1.60152i | −0.0317273 | + | 0.0976466i | −0.965666 | − | 0.259786i | \(-0.916348\pi\) |
0.933939 | + | 0.357433i | \(0.116348\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.9110 | + | 10.8335i | −0.905778 | + | 0.658086i | −0.939943 | − | 0.341330i | \(-0.889123\pi\) |
0.0341657 | + | 0.999416i | \(0.489123\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.25134 | − | 3.85124i | −0.0757348 | − | 0.233088i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.31118 | − | 0.189896i | −0.199672 | − | 0.0114512i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.05914 | − | 3.25969i | −0.0636375 | − | 0.195856i | 0.914183 | − | 0.405303i | \(-0.132834\pi\) |
−0.977820 | + | 0.209446i | \(0.932834\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.59017 | + | 4.06150i | −0.334675 | + | 0.243155i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.05230 | + | 21.7048i | −0.420705 | + | 1.29480i | 0.486342 | + | 0.873769i | \(0.338331\pi\) |
−0.907047 | + | 0.421029i | \(0.861669\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.5416 | − | 17.1040i | −1.39941 | − | 1.01673i | −0.994758 | − | 0.102255i | \(-0.967394\pi\) |
−0.404647 | − | 0.914473i | \(-0.632606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.40227 | 0.0830634 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.93542 | 0.350357 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.56201 | − | 2.58795i | −0.209530 | − | 0.152232i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.85035 | + | 5.69480i | −0.108470 | + | 0.333835i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.1621 | + | 12.4690i | −1.00262 | + | 0.728448i | −0.962649 | − | 0.270753i | \(-0.912727\pi\) |
−0.0399740 | + | 0.999201i | \(0.512727\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.63011 | + | 11.1723i | 0.211353 | + | 0.650478i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.60492 | − | 6.10992i | −0.0931271 | − | 0.354534i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.99878 | + | 12.3070i | 0.231255 | + | 0.711731i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.3527 | − | 11.1544i | 0.884913 | − | 0.642927i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.710278 | − | 2.18601i | 0.0408044 | − | 0.125583i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.22201 | − | 2.34093i | −0.184492 | − | 0.134041i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.87520 | 0.392388 | 0.196194 | − | 0.980565i | \(-0.437142\pi\) | ||||
0.196194 | + | 0.980565i | \(0.437142\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.43219 | 0.138363 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.3530 | + | 14.7873i | 1.15411 | + | 0.838511i | 0.989022 | − | 0.147768i | \(-0.0472087\pi\) |
0.165089 | + | 0.986279i | \(0.447209\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.57821 | + | 11.0126i | −0.202252 | + | 0.622469i | 0.797563 | + | 0.603236i | \(0.206122\pi\) |
−0.999815 | + | 0.0192328i | \(0.993878\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.29042 | − | 4.57026i | 0.354425 | − | 0.257505i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.40940 | + | 19.7261i | 0.359988 | + | 1.10793i | 0.953061 | + | 0.302780i | \(0.0979146\pi\) |
−0.593073 | + | 0.805149i | \(0.702085\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.62759 | − | 9.31278i | 0.203106 | − | 0.521416i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.79994 | + | 5.53963i | 0.100463 | + | 0.309192i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.2453 | − | 11.8029i | 0.903913 | − | 0.656731i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.44244 | + | 4.43939i | −0.0800124 | + | 0.246253i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.27740 | − | 3.10771i | −0.236541 | − | 0.171857i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.7133 | 0.645777 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.1415 | 1.76665 | 0.883327 | − | 0.468757i | \(-0.155298\pi\) | ||||
0.883327 | + | 0.468757i | \(0.155298\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.9322 | − | 18.1143i | −1.36627 | − | 0.992657i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.26195 | − | 6.96158i | 0.123584 | − | 0.380352i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5594 | − | 10.5780i | 0.793100 | − | 0.576221i | −0.115782 | − | 0.993275i | \(-0.536937\pi\) |
0.908882 | + | 0.417054i | \(0.136937\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.205037 | + | 0.631039i | 0.0111361 | + | 0.0342734i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.12608 | − | 5.01098i | −0.331746 | − | 0.271360i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.63386 | + | 17.3392i | 0.304200 | + | 0.936231i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.724576 | − | 0.526435i | 0.0390099 | − | 0.0283423i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.48753 | − | 7.65583i | 0.133538 | − | 0.410986i | −0.861822 | − | 0.507211i | \(-0.830677\pi\) |
0.995360 | + | 0.0962243i | \(0.0306766\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.5569 | − | 11.3027i | −0.832741 | − | 0.605022i | 0.0875926 | − | 0.996156i | \(-0.472083\pi\) |
−0.920333 | + | 0.391135i | \(0.872083\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.89088 | −0.474560 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.8497 | 0.790371 | 0.395186 | − | 0.918601i | \(-0.370680\pi\) | ||||
0.395186 | + | 0.918601i | \(0.370680\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.967351 | − | 0.702822i | −0.0513417 | − | 0.0373019i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.24021 | + | 3.81698i | −0.0656391 | + | 0.202016i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.27079 | − | 6.00908i | 0.436516 | − | 0.317147i | −0.347733 | − | 0.937594i | \(-0.613048\pi\) |
0.784249 | + | 0.620446i | \(0.213048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.0496143 | − | 0.152697i | −0.00261128 | − | 0.00803670i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.09503 | − | 1.74648i | 0.162447 | − | 0.0916662i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.315724 | − | 0.971700i | −0.0165258 | − | 0.0508611i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.4422 | − | 8.31327i | 0.597280 | − | 0.433949i | −0.247632 | − | 0.968854i | \(-0.579653\pi\) |
0.844912 | + | 0.534905i | \(0.179653\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.97786 | − | 6.08724i | 0.102964 | − | 0.316889i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.7600 | − | 9.99722i | −0.714383 | − | 0.519030i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.4600 | 0.645154 | 0.322577 | − | 0.946543i | \(-0.395451\pi\) | ||||
0.322577 | + | 0.946543i | \(0.395451\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.323071 | 0.0166833 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.3798 | − | 8.26788i | −0.586088 | − | 0.425818i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.04840 | + | 15.5374i | −0.259319 | + | 0.798102i | 0.733629 | + | 0.679550i | \(0.237825\pi\) |
−0.992948 | + | 0.118552i | \(0.962175\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0199338 | − | 0.0144828i | 0.00102124 | − | 0.000741975i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.251122 | + | 0.772874i | 0.0128317 | + | 0.0394920i | 0.957267 | − | 0.289204i | \(-0.0933907\pi\) |
−0.944436 | + | 0.328696i | \(0.893391\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.89346 | + | 5.63868i | 0.351323 | + | 0.287374i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.32370 | − | 19.4623i | −0.321452 | − | 0.989327i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.5894 | − | 17.8652i | 1.24673 | − | 0.905802i | 0.248702 | − | 0.968580i | \(-0.419996\pi\) |
0.998028 | + | 0.0627780i | \(0.0199960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.96321 | − | 12.1975i | 0.200428 | − | 0.616854i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.00134 | + | 2.18060i | 0.151398 | + | 0.109997i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.50213 | 0.176211 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.8996 | −0.747789 | −0.373894 | − | 0.927471i | \(-0.621978\pi\) | ||||
−0.373894 | + | 0.927471i | \(0.621978\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.04628 | − | 2.21325i | −0.152505 | − | 0.110801i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.76049 | − | 11.5736i | 0.187790 | − | 0.577957i | −0.812196 | − | 0.583385i | \(-0.801728\pi\) |
0.999985 | + | 0.00542792i | \(0.00172777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.01155 | + | 6.54727i | −0.448897 | + | 0.326143i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.49424 | − | 7.67647i | −0.123940 | − | 0.381447i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.8121 | − | 32.8913i | 0.635071 | − | 1.63036i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.0809957 | − | 0.249279i | −0.00400498 | − | 0.0123261i | 0.949034 | − | 0.315174i | \(-0.102063\pi\) |
−0.953039 | + | 0.302847i | \(0.902063\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.79073 | + | 3.48067i | −0.236309 | + | 0.171689i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.74764 | − | 30.0002i | 0.479650 | − | 1.47621i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.99290 | − | 6.53372i | −0.441444 | − | 0.320728i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.49116 | −0.366844 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.26916 | 0.0620023 | 0.0310012 | − | 0.999519i | \(-0.490130\pi\) | ||||
0.0310012 | + | 0.999519i | \(0.490130\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.9999 | + | 17.4369i | 1.16968 | + | 0.849824i | 0.990971 | − | 0.134078i | \(-0.0428071\pi\) |
0.178712 | + | 0.983902i | \(0.442807\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.90324 | − | 12.0129i | 0.189782 | − | 0.584089i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.74278 | − | 2.71929i | 0.181551 | − | 0.131905i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.30470 | + | 10.1708i | 0.159926 | + | 0.492200i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.27070 | − | 4.83752i | −0.0613497 | − | 0.233558i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.68919 | − | 29.8203i | −0.466712 | − | 1.43639i | −0.856817 | − | 0.515621i | \(-0.827561\pi\) |
0.390105 | − | 0.920771i | \(-0.372439\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.0607 | − | 15.3015i | 1.01212 | − | 0.735345i | 0.0474634 | − | 0.998873i | \(-0.484886\pi\) |
0.964652 | + | 0.263528i | \(0.0848863\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.300843 | + | 0.925898i | −0.0144243 | + | 0.0443934i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.73464 | + | 7.07263i | 0.465671 | + | 0.338330i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.4191 | −0.688185 | −0.344093 | − | 0.938936i | \(-0.611813\pi\) | ||||
−0.344093 | + | 0.938936i | \(0.611813\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.609255 | −0.0290121 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.267467 | − | 0.194326i | −0.0127078 | − | 0.00923273i | 0.581413 | − | 0.813608i | \(-0.302500\pi\) |
−0.594121 | + | 0.804376i | \(0.702500\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.855908 | + | 2.63421i | −0.0405739 | + | 0.124874i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.83289 | − | 2.78476i | 0.181289 | − | 0.131715i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.62920 | + | 8.09185i | 0.124080 | + | 0.381878i | 0.993732 | − | 0.111786i | \(-0.0356571\pi\) |
−0.869653 | + | 0.493664i | \(0.835657\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.31906 | + | 0.419748i | 0.344641 | + | 0.0197652i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.750657 | − | 2.31028i | −0.0352689 | − | 0.108547i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.1404 | − | 7.36742i | 0.475388 | − | 0.345390i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.351807 | − | 1.08275i | 0.0164569 | − | 0.0506490i | −0.942491 | − | 0.334232i | \(-0.891523\pi\) |
0.958948 | + | 0.283583i | \(0.0915231\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.12889 | + | 5.17944i | 0.332748 | + | 0.241756i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.5073 | 0.675670 | 0.337835 | − | 0.941205i | \(-0.390305\pi\) | ||||
0.337835 | + | 0.941205i | \(0.390305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.89739 | 0.227601 | 0.113801 | − | 0.993504i | \(-0.463698\pi\) | ||||
0.113801 | + | 0.993504i | \(0.463698\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.623707 | + | 0.453150i | 0.0289237 | + | 0.0210143i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.0193 | + | 30.8361i | −0.463637 | + | 1.42693i | 0.397053 | + | 0.917796i | \(0.370033\pi\) |
−0.860689 | + | 0.509131i | \(0.829967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.9015 | + | 11.5531i | −0.734264 | + | 0.533474i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.33597 | + | 4.11171i | 0.0615585 | + | 0.189457i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.7204 | − | 12.6689i | 0.906747 | − | 0.582516i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.34127 | + | 4.12801i | 0.0615417 | + | 0.189406i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.8382 | + | 10.7806i | −0.679394 | + | 0.493609i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.48054 | + | 16.8674i | −0.250412 | + | 0.770690i | 0.744287 | + | 0.667860i | \(0.232790\pi\) |
−0.994699 | + | 0.102830i | \(0.967210\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.1915 | − | 29.2009i | −1.83258 | − | 1.33144i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.40495 | −0.109429 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.5342 | −0.841595 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.9347 | − | 10.8507i | −0.676754 | − | 0.491691i | 0.195525 | − | 0.980699i | \(-0.437359\pi\) |
−0.872279 | + | 0.489008i | \(0.837359\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0770712 | + | 0.237201i | −0.00348528 | + | 0.0107266i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.25018 | + | 6.72065i | −0.417455 | + | 0.303299i | −0.776613 | − | 0.629978i | \(-0.783064\pi\) |
0.359158 | + | 0.933277i | \(0.383064\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.30802 | + | 13.2587i | 0.194023 | + | 0.597142i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.08002 | − | 5.19080i | 0.363170 | − | 0.233309i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.992176 | + | 3.05360i | 0.0445052 | + | 0.136973i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.80335 | − | 6.39601i | 0.394092 | − | 0.286325i | −0.373038 | − | 0.927816i | \(-0.621684\pi\) |
0.767130 | + | 0.641491i | \(0.221684\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.846827 | + | 2.60627i | −0.0378335 | + | 0.116439i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.1830 | + | 26.2885i | 1.61332 | + | 1.17215i | 0.851490 | + | 0.524371i | \(0.175699\pi\) |
0.761831 | + | 0.647776i | \(0.224301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.11455 | 0.316594 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.83941 | −0.126103 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.1720 | + | 8.11693i | 0.495190 | + | 0.359777i | 0.807177 | − | 0.590310i | \(-0.200994\pi\) |
−0.311987 | + | 0.950086i | \(0.600994\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.847790 | + | 2.60923i | −0.0375040 | + | 0.115425i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.68836 | + | 4.85938i | −0.295298 | + | 0.214547i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.32639 | + | 7.15989i | 0.102513 | + | 0.315502i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.4439 | + | 0.828356i | 0.635241 | + | 0.0364311i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.507030 | − | 1.56048i | −0.0222562 | − | 0.0684974i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.95269 | − | 2.14525i | 0.129360 | − | 0.0939852i | −0.521224 | − | 0.853420i | \(-0.674524\pi\) |
0.650584 | + | 0.759435i | \(0.274524\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.54109 | − | 4.74299i | 0.0673872 | − | 0.207396i | −0.911693 | − | 0.410873i | \(-0.865224\pi\) |
0.979080 | + | 0.203476i | \(0.0652240\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.701836 | − | 0.509914i | −0.0306306 | − | 0.0222545i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.0398 | 0.480901 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3148 | −0.665860 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.5193 | − | 19.9939i | −1.19424 | − | 0.867663i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.18839 | − | 9.81284i | 0.138104 | − | 0.425041i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.5859 | + | 10.5973i | −0.630605 | + | 0.458161i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.12983 | − | 3.47726i | −0.0487558 | − | 0.150055i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.177290 | − | 0.674939i | −0.00763640 | − | 0.0290717i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.0765109 | + | 0.235476i | 0.00328946 | + | 0.0101239i | 0.952688 | − | 0.303951i | \(-0.0983058\pi\) |
−0.949398 | + | 0.314075i | \(0.898306\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.93415 | − | 1.40524i | 0.0830025 | − | 0.0603048i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.05716 | − | 15.5643i | 0.216625 | − | 0.666703i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.4779 | − | 14.8780i | −0.875570 | − | 0.636139i | 0.0565056 | − | 0.998402i | \(-0.482004\pi\) |
−0.932076 | + | 0.362263i | \(0.882004\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.5322 | 0.492182 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.0796 | −0.557208 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.60799 | − | 5.52753i | −0.323525 | − | 0.235054i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.06253 | + | 3.27013i | −0.0451018 | + | 0.138809i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.2824 | − | 22.7280i | 1.32548 | − | 0.963015i | 0.325630 | − | 0.945497i | \(-0.394424\pi\) |
0.999847 | − | 0.0175177i | \(-0.00557635\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.1940 | − | 31.3740i | −0.431161 | − | 1.32698i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.79926 | + | 4.61907i | −0.0759648 | + | 0.195017i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.30653 | − | 13.2541i | −0.181498 | − | 0.558595i | 0.818372 | − | 0.574689i | \(-0.194877\pi\) |
−0.999870 | + | 0.0160940i | \(0.994877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.66154 | + | 1.20718i | −0.0699013 | + | 0.0507863i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.69757 | + | 20.6130i | −0.281272 | + | 0.865665i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.5817 | − | 16.4065i | −0.946672 | − | 0.687798i | 0.00334520 | − | 0.999994i | \(-0.498935\pi\) |
−0.950017 | + | 0.312197i | \(0.898935\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.4113 | 1.31452 | 0.657261 | − | 0.753663i | \(-0.271715\pi\) | ||||
0.657261 | + | 0.753663i | \(0.271715\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.66578 | −0.0695889 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.24278 | + | 1.62947i | 0.0935302 | + | 0.0679537i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.40744 | − | 19.7201i | 0.266745 | − | 0.820958i | −0.724541 | − | 0.689232i | \(-0.757948\pi\) |
0.991286 | − | 0.131726i | \(-0.0420519\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.05392 | + | 0.765719i | −0.0437995 | + | 0.0318222i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.22368 | + | 28.3876i | 0.382663 | + | 1.17771i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.2607 | − | 13.3008i | −0.673448 | − | 0.550864i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.17678 | − | 12.8548i | −0.172689 | − | 0.531481i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.3267 | − | 8.95591i | 0.508779 | − | 0.369650i | −0.303581 | − | 0.952806i | \(-0.598182\pi\) |
0.812360 | + | 0.583156i | \(0.198182\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.20067 | + | 9.85066i | −0.131881 | + | 0.405889i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.98421 | + | 2.16816i | 0.122754 | + | 0.0891860i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.5413 | 1.13098 | 0.565492 | − | 0.824754i | \(-0.308686\pi\) | ||||
0.565492 | + | 0.824754i | \(0.308686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.4227 | −0.509281 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.87309 | + | 1.36088i | 0.0766605 | + | 0.0556971i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.26097 | − | 25.4247i | 0.337534 | − | 1.03882i | −0.627926 | − | 0.778273i | \(-0.716096\pi\) |
0.965460 | − | 0.260551i | \(-0.0839041\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.94714 | + | 1.41468i | −0.0794255 | + | 0.0577060i | −0.626789 | − | 0.779189i | \(-0.715631\pi\) |
0.547364 | + | 0.836895i | \(0.315631\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.54977 | + | 20.1581i | 0.266727 | + | 0.820902i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.10166 | + | 7.44064i | 0.329379 | + | 0.302505i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.18067 | − | 9.78909i | −0.129099 | − | 0.397327i | 0.865526 | − | 0.500864i | \(-0.166984\pi\) |
−0.994626 | + | 0.103536i | \(0.966984\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.11492 | − | 1.53658i | 0.0857010 | − | 0.0622654i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.29216 | − | 19.3653i | 0.254553 | − | 0.783435i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.5519 | − | 16.3849i | −0.910861 | − | 0.661779i | 0.0303715 | − | 0.999539i | \(-0.490331\pi\) |
−0.941232 | + | 0.337759i | \(0.890331\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.714118 | −0.0287960 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.7216 | −1.15629 | −0.578143 | − | 0.815935i | \(-0.696222\pi\) | ||||
−0.578143 | + | 0.815935i | \(0.696222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.3621 | + | 13.3408i | 0.738035 | + | 0.536214i | 0.892095 | − | 0.451848i | \(-0.149235\pi\) |
−0.154060 | + | 0.988061i | \(0.549235\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.63169 | + | 5.02183i | −0.0654776 | + | 0.201519i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.01703 | − | 4.37163i | 0.241067 | − | 0.175146i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.59989 | − | 2.94462i | −0.143766 | − | 0.117597i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.2152 | + | 46.8277i | 0.606671 | + | 1.86714i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.0864 | − | 16.7733i | 0.919056 | − | 0.667733i | −0.0242327 | − | 0.999706i | \(-0.507714\pi\) |
0.943289 | + | 0.331973i | \(0.107714\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.347783 | − | 1.07037i | 0.0138231 | − | 0.0425432i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.0617011 | + | 0.0448285i | 0.00244853 | + | 0.00177896i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.982140 | −0.0389138 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.46233 | 0.136968 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.92040 | − | 1.39526i | −0.0758514 | − | 0.0551093i | 0.549213 | − | 0.835682i | \(-0.314927\pi\) |
−0.625065 | + | 0.780573i | \(0.714927\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.51053 | + | 10.8043i | −0.138442 | + | 0.426080i | −0.996109 | − | 0.0881244i | \(-0.971913\pi\) |
0.857668 | + | 0.514204i | \(0.171913\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.84715 | + | 1.34203i | −0.0727315 | + | 0.0528425i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.9632 | + | 46.0520i | 0.588264 | + | 1.81049i | 0.585746 | + | 0.810495i | \(0.300802\pi\) |
0.00251822 | + | 0.999997i | \(0.499198\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.1415 | − | 36.3043i | 0.555104 | − | 1.42507i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.639713 | − | 1.96883i | −0.0250723 | − | 0.0771647i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.0722 | + | 17.4894i | −0.942016 | + | 0.684415i | −0.948905 | − | 0.315562i | \(-0.897807\pi\) |
0.00688905 | + | 0.999976i | \(0.497807\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.54847 | + | 10.9211i | −0.138650 | + | 0.426722i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.39346 | + | 1.73895i | 0.0933777 | + | 0.0678429i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.4931 | 1.10993 | 0.554966 | − | 0.831873i | \(-0.312731\pi\) | ||||
0.554966 | + | 0.831873i | \(0.312731\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.02875 | −0.0400139 | −0.0200070 | − | 0.999800i | \(-0.506369\pi\) | ||||
−0.0200070 | + | 0.999800i | \(0.506369\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.64428 | + | 4.10081i | 0.219206 | + | 0.159262i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.60161 | − | 11.0846i | 0.139664 | − | 0.429843i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.75841 | + | 4.91027i | −0.261687 | + | 0.190127i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.05275 | + | 3.24002i | 0.0407016 | + | 0.125267i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.35580 | + | 12.7755i | 0.129549 | + | 0.493192i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.02863 | + | 12.3988i | 0.155292 | + | 0.477940i | 0.998190 | − | 0.0601327i | \(-0.0191524\pi\) |
−0.842898 | + | 0.538073i | \(0.819152\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.54094 | + | 1.11956i | −0.0593108 | + | 0.0430918i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.4665 | + | 35.2903i | −0.440694 | + | 1.35632i | 0.446444 | + | 0.894812i | \(0.352690\pi\) |
−0.887138 | + | 0.461505i | \(0.847310\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.2635 | + | 29.2531i | 1.54517 | + | 1.12263i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0697890 | 0.00267432 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.8992 | 1.25885 | 0.629426 | − | 0.777061i | \(-0.283290\pi\) | ||||
0.629426 | + | 0.777061i | \(0.283290\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.8287 | − | 10.7737i | −0.566576 | − | 0.411641i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.00755844 | − | 0.0232625i | 0.000288372 | − | 0.000887519i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.9197 | + | 17.3787i | −0.911267 | + | 0.662074i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.3409 | − | 34.9036i | −0.431427 | − | 1.32780i | −0.896704 | − | 0.442631i | \(-0.854045\pi\) |
0.465277 | − | 0.885165i | \(-0.345955\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −25.7457 | − | 1.47652i | −0.978000 | − | 0.0560883i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.16529 | − | 22.0525i | −0.271795 | − | 0.836498i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.27305 | + | 6.01072i | −0.313364 | + | 0.227672i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.50950 | + | 4.64577i | −0.0570946 | + | 0.175719i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.3266 | + | 21.3070i | 1.10765 | + | 0.804755i | 0.982292 | − | 0.187356i | \(-0.0599919\pi\) |
0.125359 | + | 0.992111i | \(0.459992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −46.1949 | −1.74227 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.40928 | −0.0530767 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.4556 | − | 11.2291i | −0.581267 | − | 0.422315i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.74811 | + | 17.6909i | −0.215875 | + | 0.664394i | 0.783216 | + | 0.621750i | \(0.213578\pi\) |
−0.999090 | + | 0.0426440i | \(0.986422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.20413 | + | 5.96065i | −0.307679 | + | 0.223542i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.04426 | + | 6.29158i | 0.0765580 | + | 0.235621i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.0253 | − | 8.36775i | 0.487117 | − | 0.312936i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.31263 | − | 7.11754i | −0.0863667 | − | 0.265809i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.2799 | + | 21.9996i | −1.12925 | + | 0.820447i | −0.985585 | − | 0.169179i | \(-0.945888\pi\) |
−0.143664 | + | 0.989627i | \(0.545888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.24687 | − | 19.2259i | 0.232645 | − | 0.716009i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.57630 | − | 4.05142i | −0.207385 | − | 0.150674i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.01341 | −0.111915 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.6011 | −0.541526 | −0.270763 | − | 0.962646i | \(-0.587276\pi\) | ||||
−0.270763 | + | 0.962646i | \(0.587276\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.4149 | + | 12.6527i | 0.644997 | + | 0.468618i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.1033 | + | 31.0949i | −0.373686 | + | 1.15009i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.8468 | + | 24.5911i | −1.25016 | + | 0.908293i | −0.998231 | − | 0.0594528i | \(-0.981064\pi\) |
−0.251927 | + | 0.967746i | \(0.581064\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0210057 | + | 0.0646489i | 0.000774807 | + | 0.00238461i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.4254 | + | 13.1218i | −0.752381 | + | 0.483348i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.68654 | + | 11.3460i | 0.135612 | + | 0.417370i | 0.995685 | − | 0.0928012i | \(-0.0295821\pi\) |
−0.860073 | + | 0.510171i | \(0.829582\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.29549 | + | 3.84740i | −0.194535 | + | 0.141338i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.4250 | + | 44.3956i | −0.529202 | + | 1.62872i | 0.226652 | + | 0.973976i | \(0.427222\pi\) |
−0.755854 | + | 0.654740i | \(0.772778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.8639 | + | 8.61964i | 0.434660 | + | 0.315799i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 32.1873 | 1.17767 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.4124 | 1.76895 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.6530 | + | 8.46642i | 0.425225 | + | 0.308944i | 0.779737 | − | 0.626108i | \(-0.215353\pi\) |
−0.354512 | + | 0.935052i | \(0.615353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.621156 | + | 1.91172i | −0.0226362 | + | 0.0696670i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.08301 | − | 4.41957i | 0.221383 | − | 0.160845i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.96330 | − | 15.2755i | −0.180394 | − | 0.555196i | 0.819444 | − | 0.573159i | \(-0.194282\pi\) |
−0.999839 | + | 0.0179624i | \(0.994282\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.96558 | − | 0.170076i | −0.107644 | − | 0.00617337i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.0158 | − | 36.9809i | −0.435573 | − | 1.34056i | −0.892498 | − | 0.451051i | \(-0.851049\pi\) |
0.456925 | − | 0.889505i | \(-0.348951\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.5518 | + | 25.8299i | −1.28706 | + | 0.935106i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.13962 | + | 12.7405i | −0.149668 | + | 0.460632i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −44.3621 | − | 32.2309i | −1.60182 | − | 1.16379i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.0017 | 1.55068 | 0.775341 | − | 0.631543i | \(-0.217578\pi\) | ||||
0.775341 | + | 0.631543i | \(0.217578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.61679 | 0.166270 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.35452 | + | 4.61683i | 0.228556 | + | 0.166056i | 0.696170 | − | 0.717877i | \(-0.254886\pi\) |
−0.467613 | + | 0.883933i | \(0.654886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.737407 | + | 2.26951i | −0.0264885 | + | 0.0815231i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.46957 | − | 5.42696i | 0.267969 | − | 0.194691i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.96475 | − | 9.12457i | −0.106223 | − | 0.326922i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.00752 | + | 3.83561i | 0.0360519 | + | 0.137249i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.77366 | − | 5.45875i | −0.0633853 | − | 0.195080i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.8262 | + | 7.86568i | −0.386403 | + | 0.280738i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.53048 | − | 10.8657i | 0.125848 | − | 0.387321i | −0.868206 | − | 0.496203i | \(-0.834727\pi\) |
0.994055 | + | 0.108882i | \(0.0347271\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.07980 | − | 0.784522i | −0.0384420 | − | 0.0279297i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.51483 | 0.196085 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.5903 | 0.660161 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.65553 | + | 1.20281i | 0.0587155 | + | 0.0426593i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.32414 | + | 4.07529i | −0.0469035 | + | 0.144354i | −0.971766 | − | 0.235949i | \(-0.924180\pi\) |
0.924862 | + | 0.380303i | \(0.124180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.3265 | + | 11.8619i | −0.577592 | + | 0.419645i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.47839 | − | 7.62770i | −0.0875696 | − | 0.269511i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.22994 | + | 3.15752i | −0.0434038 | + | 0.111427i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.30033 | − | 7.07969i | −0.0810760 | − | 0.249526i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.440132 | + | 0.319774i | −0.0154934 | + | 0.0112566i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.13350 | + | 18.8770i | −0.215642 | + | 0.663679i | 0.783465 | + | 0.621436i | \(0.213450\pi\) |
−0.999107 | + | 0.0422430i | \(0.986550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.53899 | − | 1.84468i | −0.0891559 | − | 0.0647756i | 0.542314 | − | 0.840176i | \(-0.317548\pi\) |
−0.631470 | + | 0.775400i | \(0.717548\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.95452 | −0.208834 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.771990 | −0.0270416 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.8164 | − | 18.0301i | −0.868215 | − | 0.630795i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.2156 | + | 34.5180i | −0.391904 | + | 1.20616i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.0118 | + | 13.8129i | −0.663516 | + | 0.482073i | −0.867849 | − | 0.496829i | \(-0.834498\pi\) |
0.204332 | + | 0.978902i | \(0.434498\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.91103 | + | 12.0369i | 0.136330 | + | 0.419580i | 0.995795 | − | 0.0916150i | \(-0.0292029\pi\) |
−0.859465 | + | 0.511195i | \(0.829203\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.829384 | − | 0.678415i | −0.0288754 | − | 0.0236194i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.33959 | − | 28.7443i | −0.324770 | − | 0.999538i | −0.971545 | − | 0.236857i | \(-0.923883\pi\) |
0.646775 | − | 0.762681i | \(-0.276117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.61937 | + | 1.17654i | −0.0562432 | + | 0.0408630i | −0.615552 | − | 0.788097i | \(-0.711067\pi\) |
0.559308 | + | 0.828960i | \(0.311067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.342177 | − | 1.05311i | 0.0118700 | − | 0.0365321i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.787500 | + | 0.572152i | 0.0272852 | + | 0.0198239i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.48232 | −0.293543 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.54520 | −0.157105 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.6185 | + | 20.7925i | 0.988019 | + | 0.717838i | 0.959486 | − | 0.281755i | \(-0.0909166\pi\) |
0.0285326 | + | 0.999593i | \(0.490917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.15541 | + | 18.9444i | −0.212256 | + | 0.653255i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.96492 | + | 4.33377i | −0.205443 | + | 0.149263i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.71589 | − | 8.35865i | −0.0934295 | − | 0.287546i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.85616 | − | 28.9511i | −0.201220 | − | 0.994771i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.90509 | − | 8.94095i | −0.0997024 | − | 0.306853i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.8696 | + | 17.3423i | −0.818241 | + | 0.594487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.62515 | + | 17.3124i | −0.192602 | + | 0.592767i | 0.807395 | + | 0.590012i | \(0.200877\pi\) |
−0.999996 | + | 0.00275489i | \(0.999123\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.1680 | − | 7.38746i | −0.347737 | − | 0.252646i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.2837 | −1.00031 | −0.500156 | − | 0.865935i | \(-0.666724\pi\) | ||||
−0.500156 | + | 0.865935i | \(0.666724\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.44030 | −0.287979 | −0.143990 | − | 0.989579i | \(-0.545993\pi\) | ||||
−0.143990 | + | 0.989579i | \(0.545993\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.55134 | + | 1.12712i | 0.0528696 | + | 0.0384120i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.97907 | − | 18.4017i | 0.203530 | − | 0.626400i | −0.796241 | − | 0.604980i | \(-0.793181\pi\) |
0.999771 | − | 0.0214204i | \(-0.00681885\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.10876 | − | 2.98519i | 0.139702 | − | 0.101500i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.439559 | − | 1.35282i | −0.0149282 | − | 0.0459443i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.99063 | − | 7.35411i | −0.304986 | − | 0.249471i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5585 | + | 32.4956i | 0.357760 | + | 1.10107i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 43.4184 | − | 31.5453i | 1.46949 | − | 1.06765i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.829779 | − | 2.55380i | 0.0280516 | − | 0.0863341i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.1691 | − | 10.2945i | −0.478456 | − | 0.347619i | 0.322271 | − | 0.946647i | \(-0.395554\pi\) |
−0.800728 | + | 0.599028i | \(0.795554\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.85349 | −0.231163 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.0575 | −0.675754 | −0.337877 | − | 0.941190i | \(-0.609709\pi\) | ||||
−0.337877 | + | 0.941190i | \(0.609709\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.7609 | + | 15.8102i | 0.732313 | + | 0.532057i | 0.890294 | − | 0.455386i | \(-0.150499\pi\) |
−0.157981 | + | 0.987442i | \(0.550499\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.17278 | + | 3.60946i | −0.0394227 | + | 0.121331i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.50591 | − | 4.00028i | 0.184870 | − | 0.134316i | −0.491501 | − | 0.870877i | \(-0.663552\pi\) |
0.676371 | + | 0.736561i | \(0.263552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0632845 | − | 0.194770i | −0.00212249 | − | 0.00653237i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.71661 | + | 24.9446i | −0.325519 | + | 0.835674i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.85082 | − | 18.0070i | −0.195790 | − | 0.602581i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.15568 | − | 6.65199i | 0.306041 | − | 0.222352i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.29189 | + | 3.97603i | −0.0431349 | + | 0.132756i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.81757 | − | 4.22671i | −0.194027 | − | 0.140969i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.3033 | 0.976235 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.13090 | 0.204024 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.98677 | + | 4.34965i | 0.199007 | + | 0.144587i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.59174 | − | 20.2873i | 0.218875 | − | 0.673629i | −0.779981 | − | 0.625804i | \(-0.784771\pi\) |
0.998856 | − | 0.0478248i | \(-0.0152289\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.6666 | + | 12.1090i | −0.552797 | + | 0.401631i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.52542 | + | 26.2385i | 0.282460 | + | 0.869322i | 0.987149 | + | 0.159805i | \(0.0510866\pi\) |
−0.704689 | + | 0.709516i | \(0.748913\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.36631 | + | 35.6574i | 0.309980 | + | 1.18009i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.397604 | − | 1.22370i | −0.0131444 | − | 0.0404542i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.9458 | − | 18.1242i | 0.823782 | − | 0.598512i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.85685 | − | 5.71479i | 0.0612518 | − | 0.188514i | −0.915748 | − | 0.401752i | \(-0.868401\pi\) |
0.977000 | + | 0.213239i | \(0.0684012\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.79697 | + | 1.30558i | 0.0592122 | + | 0.0430202i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.58140 | 0.183714 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.6429 | −0.349937 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.6360 | − | 12.8133i | −0.579242 | − | 0.420844i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.96576 | − | 9.12766i | 0.0973034 | − | 0.299469i | −0.890544 | − | 0.454898i | \(-0.849676\pi\) |
0.987847 | + | 0.155429i | \(0.0496759\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.738836 | + | 0.536796i | −0.0242144 | + | 0.0175928i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.51160 | + | 7.72992i | 0.0822261 | + | 0.253066i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.3186 | − | 0.878523i | −0.500972 | − | 0.0287308i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.9255 | − | 36.7029i | −0.389589 | − | 1.19903i | −0.933096 | − | 0.359628i | \(-0.882904\pi\) |
0.543507 | − | 0.839405i | \(-0.317096\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.02649 | + | 2.19887i | −0.0987658 | + | 0.0717575i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.01854 | + | 27.7562i | −0.293996 | + | 0.904826i | 0.689561 | + | 0.724228i | \(0.257804\pi\) |
−0.983557 | + | 0.180599i | \(0.942196\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.95744 | − | 3.60179i | −0.161437 | − | 0.117291i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.11455 | 0.166376 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.7623 | −1.51957 | −0.759785 | − | 0.650174i | \(-0.774696\pi\) | ||||
−0.759785 | + | 0.650174i | \(0.774696\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.85834 | + | 2.80325i | 0.125247 | + | 0.0909972i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.07069 | + | 6.37293i | −0.0671468 | + | 0.206657i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.97738 | − | 3.61628i | 0.161233 | − | 0.117143i | −0.504243 | − | 0.863562i | \(-0.668228\pi\) |
0.665476 | + | 0.746419i | \(0.268228\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.59332 | − | 4.90372i | −0.0515585 | − | 0.158681i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.71661 | − | 1.74522i | 0.0878155 | − | 0.0564148i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.2093 | + | 46.8093i | 0.491132 | + | 1.51155i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.4726 | − | 14.8742i | 0.660408 | − | 0.479814i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.1325 | − | 49.6507i | 0.519862 | − | 1.59997i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.26220 | − | 2.37013i | −0.105014 | − | 0.0762970i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.39625 | −0.109216 | −0.0546080 | − | 0.998508i | \(-0.517391\pi\) | ||||
−0.0546080 | + | 0.998508i | \(0.517391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.48736 | 0.208404 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.60072 | − | 5.52224i | −0.243919 | − | 0.177217i | 0.459109 | − | 0.888380i | \(-0.348169\pi\) |
−0.703027 | + | 0.711163i | \(0.748169\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.2404 | + | 59.2158i | −0.616818 | + | 1.89837i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.22004 | + | 0.886408i | −0.0390724 | + | 0.0283878i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.11585 | − | 15.7450i | −0.163671 | − | 0.503726i | 0.835265 | − | 0.549847i | \(-0.185314\pi\) |
−0.998936 | + | 0.0461210i | \(0.985314\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.72885 | − | 4.96520i | 0.247015 | − | 0.158689i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.6436 | + | 45.0685i | 0.467535 | + | 1.43893i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.1126 | − | 29.8701i | 1.31129 | − | 0.952707i | 0.311291 | − | 0.950315i | \(-0.399238\pi\) |
0.999997 | − | 0.00239240i | \(-0.000761525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.52822 | + | 10.8588i | −0.112419 | + | 0.345989i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.06151 | + | 2.22432i | 0.0974490 | + | 0.0708009i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.5918 | −0.622983 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.3642 | −0.360996 | −0.180498 | − | 0.983575i | \(-0.557771\pi\) | ||||
−0.180498 | + | 0.983575i | \(0.557771\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.40081 | + | 6.10355i | 0.266592 | + | 0.193690i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.21455 | + | 6.81569i | −0.0702060 | + | 0.216072i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.5945 | − | 17.1424i | 0.747246 | − | 0.542906i | −0.147726 | − | 0.989028i | \(-0.547195\pi\) |
0.894972 | + | 0.446122i | \(0.147195\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.26427 | − | 19.2794i | −0.198193 | − | 0.609975i |
(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 | 880.2.bo.h.401.1 | 8 | ||
4.3 | odd | 2 | 55.2.g.b.16.2 | ✓ | 8 | ||
11.3 | even | 5 | 9680.2.a.cn.1.3 | 4 | |||
11.8 | odd | 10 | 9680.2.a.cm.1.3 | 4 | |||
11.9 | even | 5 | inner | 880.2.bo.h.801.1 | 8 | ||
12.11 | even | 2 | 495.2.n.e.181.1 | 8 | |||
20.3 | even | 4 | 275.2.z.a.49.3 | 16 | |||
20.7 | even | 4 | 275.2.z.a.49.2 | 16 | |||
20.19 | odd | 2 | 275.2.h.a.126.1 | 8 | |||
44.3 | odd | 10 | 605.2.a.j.1.3 | 4 | |||
44.7 | even | 10 | 605.2.g.e.366.2 | 8 | |||
44.15 | odd | 10 | 605.2.g.m.366.1 | 8 | |||
44.19 | even | 10 | 605.2.a.k.1.2 | 4 | |||
44.27 | odd | 10 | 605.2.g.m.81.1 | 8 | |||
44.31 | odd | 10 | 55.2.g.b.31.2 | yes | 8 | ||
44.35 | even | 10 | 605.2.g.k.251.1 | 8 | |||
44.39 | even | 10 | 605.2.g.e.81.2 | 8 | |||
44.43 | even | 2 | 605.2.g.k.511.1 | 8 | |||
132.47 | even | 10 | 5445.2.a.bp.1.2 | 4 | |||
132.107 | odd | 10 | 5445.2.a.bi.1.3 | 4 | |||
132.119 | even | 10 | 495.2.n.e.361.1 | 8 | |||
220.19 | even | 10 | 3025.2.a.w.1.3 | 4 | |||
220.119 | odd | 10 | 275.2.h.a.251.1 | 8 | |||
220.163 | even | 20 | 275.2.z.a.174.2 | 16 | |||
220.179 | odd | 10 | 3025.2.a.bd.1.2 | 4 | |||
220.207 | even | 20 | 275.2.z.a.174.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.b.16.2 | ✓ | 8 | 4.3 | odd | 2 | ||
55.2.g.b.31.2 | yes | 8 | 44.31 | odd | 10 | ||
275.2.h.a.126.1 | 8 | 20.19 | odd | 2 | |||
275.2.h.a.251.1 | 8 | 220.119 | odd | 10 | |||
275.2.z.a.49.2 | 16 | 20.7 | even | 4 | |||
275.2.z.a.49.3 | 16 | 20.3 | even | 4 | |||
275.2.z.a.174.2 | 16 | 220.163 | even | 20 | |||
275.2.z.a.174.3 | 16 | 220.207 | even | 20 | |||
495.2.n.e.181.1 | 8 | 12.11 | even | 2 | |||
495.2.n.e.361.1 | 8 | 132.119 | even | 10 | |||
605.2.a.j.1.3 | 4 | 44.3 | odd | 10 | |||
605.2.a.k.1.2 | 4 | 44.19 | even | 10 | |||
605.2.g.e.81.2 | 8 | 44.39 | even | 10 | |||
605.2.g.e.366.2 | 8 | 44.7 | even | 10 | |||
605.2.g.k.251.1 | 8 | 44.35 | even | 10 | |||
605.2.g.k.511.1 | 8 | 44.43 | even | 2 | |||
605.2.g.m.81.1 | 8 | 44.27 | odd | 10 | |||
605.2.g.m.366.1 | 8 | 44.15 | odd | 10 | |||
880.2.bo.h.401.1 | 8 | 1.1 | even | 1 | trivial | ||
880.2.bo.h.801.1 | 8 | 11.9 | even | 5 | inner | ||
3025.2.a.w.1.3 | 4 | 220.19 | even | 10 | |||
3025.2.a.bd.1.2 | 4 | 220.179 | odd | 10 | |||
5445.2.a.bi.1.3 | 4 | 132.107 | odd | 10 | |||
5445.2.a.bp.1.2 | 4 | 132.47 | even | 10 | |||
9680.2.a.cm.1.3 | 4 | 11.8 | odd | 10 | |||
9680.2.a.cn.1.3 | 4 | 11.3 | even | 5 |