Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(109,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.l (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 541.7 | ||
Root | \(-1.30887 + 2.01944i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.541 |
Dual form | 2268.2.l.n.109.7 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.30201 | 1.02949 | 0.514746 | − | 0.857343i | \(-0.327886\pi\) | ||||
0.514746 | + | 0.857343i | \(0.327886\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.14324 | − | 1.55130i | −0.810068 | − | 0.586337i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.46291 | −1.34562 | −0.672809 | − | 0.739816i | \(-0.734912\pi\) | ||||
−0.672809 | + | 0.739816i | \(0.734912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.42148 | + | 2.46208i | 0.394248 | + | 0.682858i | 0.993005 | − | 0.118073i | \(-0.0376717\pi\) |
−0.598757 | + | 0.800931i | \(0.704338\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.115312 | + | 0.199726i | 0.0279673 | + | 0.0484408i | 0.879670 | − | 0.475584i | \(-0.157763\pi\) |
−0.851703 | + | 0.524025i | \(0.824430\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.49360 | + | 2.58700i | −0.342656 | + | 0.593498i | −0.984925 | − | 0.172982i | \(-0.944660\pi\) |
0.642269 | + | 0.766479i | \(0.277993\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.800587 | 0.166934 | 0.0834670 | − | 0.996511i | \(-0.473401\pi\) | ||||
0.0834670 | + | 0.996511i | \(0.473401\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.299269 | 0.0598538 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.82751 | + | 6.62944i | −0.710750 | + | 1.23106i | 0.253825 | + | 0.967250i | \(0.418311\pi\) |
−0.964576 | + | 0.263806i | \(0.915022\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.64324 | + | 4.57822i | −0.474739 | + | 0.822273i | −0.999582 | − | 0.0289268i | \(-0.990791\pi\) |
0.524842 | + | 0.851200i | \(0.324124\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.93376 | − | 3.57112i | −0.833958 | − | 0.603629i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.69333 | + | 2.93293i | −0.278382 | + | 0.482171i | −0.970983 | − | 0.239150i | \(-0.923131\pi\) |
0.692601 | + | 0.721321i | \(0.256465\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.899697 | + | 1.55832i | 0.140509 | + | 0.243369i | 0.927688 | − | 0.373355i | \(-0.121793\pi\) |
−0.787179 | + | 0.616724i | \(0.788459\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.85860 | − | 8.41533i | 0.740929 | − | 1.28333i | −0.211144 | − | 0.977455i | \(-0.567719\pi\) |
0.952073 | − | 0.305871i | \(-0.0989478\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.88818 | + | 5.00247i | 0.421284 | + | 0.729686i | 0.996065 | − | 0.0886214i | \(-0.0282461\pi\) |
−0.574781 | + | 0.818307i | \(0.694913\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.18693 | + | 6.64961i | 0.312419 | + | 0.949944i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.31905 | + | 7.48081i | 0.593267 | + | 1.02757i | 0.993789 | + | 0.111281i | \(0.0354954\pi\) |
−0.400522 | + | 0.916287i | \(0.631171\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.2737 | −1.38530 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.17793 | + | 7.23638i | −0.543920 | + | 0.942097i | 0.454754 | + | 0.890617i | \(0.349727\pi\) |
−0.998674 | + | 0.0514798i | \(0.983606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.58675 | + | 11.4086i | 0.843347 | + | 1.46072i | 0.887049 | + | 0.461675i | \(0.152751\pi\) |
−0.0437026 | + | 0.999045i | \(0.513915\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.27227 | + | 5.66774i | 0.405875 | + | 0.702997i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.76545 | − | 6.52195i | 0.460023 | − | 0.796783i | −0.538939 | − | 0.842345i | \(-0.681175\pi\) |
0.998962 | + | 0.0455620i | \(0.0145078\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.59672 | −1.02024 | −0.510122 | − | 0.860102i | \(-0.670400\pi\) | ||||
−0.510122 | + | 0.860102i | \(0.670400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.29287 | − | 3.97137i | −0.268360 | − | 0.464814i | 0.700078 | − | 0.714066i | \(-0.253148\pi\) |
−0.968439 | + | 0.249252i | \(0.919815\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.56507 | + | 6.92331i | 1.09004 | + | 0.788985i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.83657 | − | 8.37718i | −0.544156 | − | 0.942506i | −0.998659 | − | 0.0517612i | \(-0.983517\pi\) |
0.454503 | − | 0.890745i | \(-0.349817\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.46521 | + | 14.6622i | −0.929177 | + | 1.60938i | −0.144476 | + | 0.989508i | \(0.546150\pi\) |
−0.784701 | + | 0.619874i | \(0.787184\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.265450 | + | 0.459773i | 0.0287921 | + | 0.0498694i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.944450 | + | 1.63584i | −0.100111 | + | 0.173398i | −0.911730 | − | 0.410789i | \(-0.865253\pi\) |
0.811619 | + | 0.584187i | \(0.198587\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.772852 | − | 7.48196i | 0.0810169 | − | 0.784323i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.43829 | + | 5.95530i | −0.352762 | + | 0.611001i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.70796 | − | 13.3506i | 0.782624 | − | 1.35555i | −0.147784 | − | 0.989020i | \(-0.547214\pi\) |
0.930408 | − | 0.366525i | \(-0.119453\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.81488 | 0.280091 | 0.140045 | − | 0.990145i | \(-0.455275\pi\) | ||||
0.140045 | + | 0.990145i | \(0.455275\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.11664 | 0.504158 | 0.252079 | − | 0.967707i | \(-0.418886\pi\) | ||||
0.252079 | + | 0.967707i | \(0.418886\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.29487 | − | 2.24278i | 0.125180 | − | 0.216818i | −0.796623 | − | 0.604476i | \(-0.793383\pi\) |
0.921803 | + | 0.387658i | \(0.126716\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.76728 | − | 15.1854i | −0.839753 | − | 1.45450i | −0.890101 | − | 0.455764i | \(-0.849366\pi\) |
0.0503474 | − | 0.998732i | \(-0.483967\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.21711 | + | 14.2325i | 0.773001 | + | 1.33888i | 0.935911 | + | 0.352236i | \(0.114579\pi\) |
−0.162910 | + | 0.986641i | \(0.552088\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.84296 | 0.171857 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0626945 | − | 0.606945i | 0.00574720 | − | 0.0556385i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.91756 | 0.810687 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.8211 | −0.967873 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.13145 | 0.721549 | 0.360775 | − | 0.932653i | \(-0.382512\pi\) | ||||
0.360775 | + | 0.932653i | \(0.382512\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.5118 | 1.09316 | 0.546582 | − | 0.837406i | \(-0.315929\pi\) | ||||
0.546582 | + | 0.837406i | \(0.315929\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.21435 | − | 3.22752i | 0.625564 | − | 0.279861i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.1934 | −1.38349 | −0.691746 | − | 0.722141i | \(-0.743158\pi\) | ||||
−0.691746 | + | 0.722141i | \(0.743158\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.07212 | + | 5.32107i | 0.260574 | + | 0.451327i | 0.966395 | − | 0.257063i | \(-0.0827549\pi\) |
−0.705821 | + | 0.708391i | \(0.749422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.34394 | − | 10.9880i | −0.530507 | − | 0.918866i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.81098 | + | 15.2611i | −0.731712 | + | 1.26736i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.71855 | −0.632328 | −0.316164 | − | 0.948705i | \(-0.602395\pi\) | ||||
−0.316164 | + | 0.948705i | \(0.602395\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.9176 | −1.21397 | −0.606987 | − | 0.794712i | \(-0.707622\pi\) | ||||
−0.606987 | + | 0.794712i | \(0.707622\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.08477 | + | 10.5391i | −0.488740 | + | 0.846523i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.128610 | − | 0.222759i | 0.0102642 | − | 0.0177781i | −0.860848 | − | 0.508863i | \(-0.830066\pi\) |
0.871112 | + | 0.491085i | \(0.163399\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.71585 | − | 1.24195i | −0.135228 | − | 0.0978795i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.28748 | + | 10.8902i | −0.492473 | + | 0.852989i | −0.999962 | − | 0.00866931i | \(-0.997240\pi\) |
0.507489 | + | 0.861658i | \(0.330574\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.8470 | − | 18.7875i | −0.839363 | − | 1.45382i | −0.890428 | − | 0.455123i | \(-0.849595\pi\) |
0.0510657 | − | 0.998695i | \(-0.483738\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.45878 | − | 4.25873i | 0.189137 | − | 0.327595i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.88024 | + | 11.9169i | 0.523095 | + | 0.906026i | 0.999639 | + | 0.0268759i | \(0.00855590\pi\) |
−0.476544 | + | 0.879151i | \(0.658111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.641405 | − | 0.464256i | −0.0484856 | − | 0.0350945i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.448262 | + | 0.776412i | 0.0335046 | + | 0.0580317i | 0.882292 | − | 0.470703i | \(-0.156000\pi\) |
−0.848787 | + | 0.528735i | \(0.822666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.4613 | −1.29788 | −0.648942 | − | 0.760838i | \(-0.724788\pi\) | ||||
−0.648942 | + | 0.760838i | \(0.724788\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.89807 | + | 6.75165i | −0.286592 | + | 0.496391i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.514627 | − | 0.891361i | −0.0376333 | − | 0.0651827i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.734511 | − | 1.27221i | −0.0531474 | − | 0.0920540i | 0.838228 | − | 0.545320i | \(-0.183592\pi\) |
−0.891375 | + | 0.453266i | \(0.850259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.25165 | + | 5.63202i | −0.234059 | + | 0.405402i | −0.958999 | − | 0.283410i | \(-0.908534\pi\) |
0.724940 | + | 0.688812i | \(0.241868\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.9521 | 0.851552 | 0.425776 | − | 0.904828i | \(-0.360001\pi\) | ||||
0.425776 | + | 0.904828i | \(0.360001\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.73886 | + | 16.8682i | 0.690369 | + | 1.19575i | 0.971717 | + | 0.236149i | \(0.0758852\pi\) |
−0.281348 | + | 0.959606i | \(0.590781\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.4875 | − | 8.27084i | 1.29757 | − | 0.580499i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.07112 | + | 3.58728i | 0.144653 | + | 0.250546i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.66581 | − | 11.5455i | 0.461084 | − | 0.798621i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.43611 | + | 11.1477i | 0.443080 | + | 0.767437i | 0.997916 | − | 0.0645225i | \(-0.0205524\pi\) |
−0.554836 | + | 0.831960i | \(0.687219\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.1846 | − | 19.3722i | 0.762780 | − | 1.32117i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.7673 | − | 5.71176i | 0.866700 | − | 0.387739i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.327828 | + | 0.567815i | −0.0220521 | + | 0.0381954i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.92331 | + | 8.52743i | −0.329690 | + | 0.571039i | −0.982450 | − | 0.186525i | \(-0.940277\pi\) |
0.652761 | + | 0.757564i | \(0.273611\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.4507 | −1.62285 | −0.811426 | − | 0.584455i | \(-0.801309\pi\) | ||||
−0.811426 | + | 0.584455i | \(0.801309\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.0037 | −1.45404 | −0.727022 | − | 0.686615i | \(-0.759096\pi\) | ||||
−0.727022 | + | 0.686615i | \(0.759096\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.8179 | + | 18.7372i | −0.708706 | + | 1.22752i | 0.256631 | + | 0.966510i | \(0.417388\pi\) |
−0.965337 | + | 0.261006i | \(0.915946\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.64863 | + | 11.5158i | 0.433709 | + | 0.751206i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.86360 | + | 15.3522i | 0.573338 | + | 0.993051i | 0.996220 | + | 0.0868662i | \(0.0276853\pi\) |
−0.422882 | + | 0.906185i | \(0.638981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.31774 | 0.278130 | 0.139065 | − | 0.990283i | \(-0.455590\pi\) | ||||
0.139065 | + | 0.990283i | \(0.455590\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.03435 | + | 15.3075i | 0.321633 | + | 0.977960i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.49252 | −0.540366 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.2938 | −0.649741 | −0.324870 | − | 0.945759i | \(-0.605321\pi\) | ||||
−0.324870 | + | 0.945759i | \(0.605321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.57295 | −0.224629 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.7914 | −0.735525 | −0.367763 | − | 0.929920i | \(-0.619876\pi\) | ||||
−0.367763 | + | 0.929920i | \(0.619876\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.17907 | − | 3.65911i | 0.508222 | − | 0.227366i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.18719 | −0.319856 | −0.159928 | − | 0.987129i | \(-0.551126\pi\) | ||||
−0.159928 | + | 0.987129i | \(0.551126\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.94251 | + | 17.2209i | 0.610763 | + | 1.05787i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.6103 | + | 25.3058i | 0.890805 | + | 1.54292i | 0.838912 | + | 0.544268i | \(0.183192\pi\) |
0.0518936 | + | 0.998653i | \(0.483474\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2801 | − | 17.8056i | 0.624470 | − | 1.08161i | −0.364173 | − | 0.931331i | \(-0.618648\pi\) |
0.988643 | − | 0.150283i | \(-0.0480184\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.33561 | −0.0805403 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.9567 | −0.718407 | −0.359203 | − | 0.933259i | \(-0.616952\pi\) | ||||
−0.359203 | + | 0.933259i | \(0.616952\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.9166 | − | 25.8363i | 0.889850 | − | 1.54126i | 0.0497975 | − | 0.998759i | \(-0.484142\pi\) |
0.840052 | − | 0.542506i | \(-0.182524\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.78547 | − | 8.28868i | 0.284467 | − | 0.492711i | −0.688013 | − | 0.725698i | \(-0.741517\pi\) |
0.972480 | + | 0.232988i | \(0.0748502\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.489161 | − | 4.73555i | 0.0288742 | − | 0.279531i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.47341 | − | 14.6764i | 0.498436 | − | 0.863316i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.41014 | − | 12.8347i | −0.432905 | − | 0.749813i | 0.564217 | − | 0.825626i | \(-0.309178\pi\) |
−0.997122 | + | 0.0758132i | \(0.975845\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.61765 | + | 16.6583i | −0.559961 | + | 0.969881i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.13802 | + | 1.97111i | 0.0658134 | + | 0.113992i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.4678 | + | 10.4989i | −1.35266 | + | 0.605147i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.1628 | + | 26.2627i | 0.868219 | + | 1.50380i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.88207 | −0.335708 | −0.167854 | − | 0.985812i | \(-0.553684\pi\) | ||||
−0.167854 | + | 0.985812i | \(0.553684\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.11753 | − | 14.0600i | 0.460303 | − | 0.797268i | −0.538673 | − | 0.842515i | \(-0.681074\pi\) |
0.998976 | + | 0.0452468i | \(0.0144074\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.84480 | − | 15.3196i | −0.499937 | − | 0.865917i | 0.500063 | − | 0.865989i | \(-0.333310\pi\) |
−1.00000 | 7.22344e-5i | \(0.999977\pi\) | ||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.64009 | − | 4.57276i | −0.148282 | − | 0.256832i | 0.782311 | − | 0.622889i | \(-0.214041\pi\) |
−0.930593 | + | 0.366057i | \(0.880708\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.0818 | − | 29.5866i | 0.956398 | − | 1.65653i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.688922 | −0.0383326 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.425406 | + | 0.736824i | 0.0235973 | + | 0.0408716i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.57029 | − | 15.2019i | 0.0865727 | − | 0.838109i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.80358 | + | 13.5162i | 0.428923 | + | 0.742917i | 0.996778 | − | 0.0802120i | \(-0.0255597\pi\) |
−0.567855 | + | 0.823129i | \(0.692226\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.66812 | − | 15.0136i | 0.473590 | − | 0.820282i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.77185 | − | 6.53303i | −0.205466 | − | 0.355877i | 0.744815 | − | 0.667271i | \(-0.232538\pi\) |
−0.950281 | + | 0.311394i | \(0.899204\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7965 | − | 20.4322i | 0.638818 | − | 1.10646i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.62843 | − | 17.6443i | 0.303907 | − | 0.952702i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.4502 | + | 23.2963i | −0.722042 | + | 1.25061i | 0.238138 | + | 0.971231i | \(0.423463\pi\) |
−0.960180 | + | 0.279382i | \(0.909870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.00100 | − | 12.1261i | 0.374755 | − | 0.649095i | −0.615535 | − | 0.788109i | \(-0.711060\pi\) |
0.990290 | + | 0.139014i | \(0.0443934\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.3311 | 1.61436 | 0.807180 | − | 0.590306i | \(-0.200993\pi\) | ||||
0.807180 | + | 0.590306i | \(0.200993\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.7898 | −1.05033 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.99876 | + | 12.1222i | −0.369381 | + | 0.639786i | −0.989469 | − | 0.144746i | \(-0.953763\pi\) |
0.620088 | + | 0.784532i | \(0.287097\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.03830 | + | 8.72659i | 0.265174 | + | 0.459294i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.27822 | − | 9.14215i | −0.276275 | − | 0.478522i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.50330 | −0.130671 | −0.0653356 | − | 0.997863i | \(-0.520812\pi\) | ||||
−0.0653356 | + | 0.997863i | \(0.520812\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.34824 | − | 22.7333i | 0.121915 | − | 1.18025i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.6062 | 0.911616 | 0.455808 | − | 0.890078i | \(-0.349350\pi\) | ||||
0.455808 | + | 0.890078i | \(0.349350\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.7629 | −1.12085 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.5474 | 0.541781 | 0.270891 | − | 0.962610i | \(-0.412682\pi\) | ||||
0.270891 | + | 0.962610i | \(0.412682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.6837 | 1.10798 | 0.553992 | − | 0.832522i | \(-0.313104\pi\) | ||||
0.553992 | + | 0.832522i | \(0.313104\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 22.0189 | + | 15.9376i | 1.12219 | + | 0.812254i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.9330 | 0.706434 | 0.353217 | − | 0.935541i | \(-0.385088\pi\) | ||||
0.353217 | + | 0.935541i | \(0.385088\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0923174 | + | 0.159898i | 0.00466869 | + | 0.00808641i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.1338 | − | 19.2844i | −0.560204 | − | 0.970303i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.9542 | − | 24.1694i | 0.700342 | − | 1.21303i | −0.268004 | − | 0.963418i | \(-0.586364\pi\) |
0.968346 | − | 0.249610i | \(-0.0803025\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.9049 | −1.74307 | −0.871534 | − | 0.490335i | \(-0.836874\pi\) | ||||
−0.871534 | + | 0.490335i | \(0.836874\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.0293 | −0.748660 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.55717 | − | 13.0894i | 0.374595 | − | 0.648818i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.3369 | − | 17.9041i | 0.511128 | − | 0.885300i | −0.488789 | − | 0.872402i | \(-0.662561\pi\) |
0.999917 | − | 0.0128979i | \(-0.00410563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.1801 | − | 9.02806i | 0.992998 | − | 0.444242i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.4870 | + | 33.7525i | −0.956581 | + | 1.65685i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.9859 | − | 34.6166i | −0.976376 | − | 1.69113i | −0.675316 | − | 0.737529i | \(-0.735993\pi\) |
−0.301061 | − | 0.953605i | \(-0.597341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.5082 | + | 21.6649i | −0.609614 | + | 1.05588i | 0.381690 | + | 0.924290i | \(0.375342\pi\) |
−0.991304 | + | 0.131592i | \(0.957991\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0345093 | + | 0.0597719i | 0.00167395 | + | 0.00289936i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.58118 | − | 34.6693i | 0.173305 | − | 1.67777i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.05181 | − | 12.2141i | −0.339674 | − | 0.588332i | 0.644698 | − | 0.764438i | \(-0.276983\pi\) |
−0.984371 | + | 0.176106i | \(0.943650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.58941 | 0.0763821 | 0.0381911 | − | 0.999270i | \(-0.487840\pi\) | ||||
0.0381911 | + | 0.999270i | \(0.487840\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.19576 | + | 2.07112i | −0.0572009 | + | 0.0990749i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1884 | + | 21.1109i | 0.581721 | + | 1.00757i | 0.995276 | + | 0.0970905i | \(0.0309536\pi\) |
−0.413555 | + | 0.910479i | \(0.635713\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.28200 | − | 16.0769i | −0.441001 | − | 0.763836i | 0.556763 | − | 0.830671i | \(-0.312043\pi\) |
−0.997764 | + | 0.0668352i | \(0.978710\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.17414 | + | 3.76572i | −0.103064 | + | 0.178512i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.4616 | 1.01284 | 0.506418 | − | 0.862288i | \(-0.330969\pi\) | ||||
0.506418 | + | 0.862288i | \(0.330969\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.01527 | − | 6.95465i | −0.189072 | − | 0.327482i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.77912 | − | 17.2236i | 0.0834062 | − | 0.807454i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.56371 | − | 13.1007i | −0.353816 | − | 0.612827i | 0.633099 | − | 0.774071i | \(-0.281783\pi\) |
−0.986915 | + | 0.161244i | \(0.948449\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.5385 | − | 28.6455i | 0.770273 | − | 1.33415i | −0.167140 | − | 0.985933i | \(-0.553453\pi\) |
0.937413 | − | 0.348219i | \(-0.113213\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.4223 | − | 23.2481i | −0.623788 | − | 1.08043i | −0.988774 | − | 0.149419i | \(-0.952260\pi\) |
0.364986 | − | 0.931013i | \(-0.381074\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.93579 | − | 10.2811i | 0.274675 | − | 0.475752i | −0.695378 | − | 0.718644i | \(-0.744763\pi\) |
0.970053 | + | 0.242893i | \(0.0780963\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.1878 | + | 8.13674i | −0.839833 | + | 0.375720i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.6835 | + | 37.5569i | −0.997007 | + | 1.72687i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.446989 | + | 0.774208i | −0.0205093 | + | 0.0355231i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.4395 | −0.796830 | −0.398415 | − | 0.917205i | \(-0.630440\pi\) | ||||
−0.398415 | + | 0.917205i | \(0.630440\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.62815 | −0.439006 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.7438 | − | 30.7332i | 0.805706 | − | 1.39552i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.3889 | + | 31.8504i | 0.833279 | + | 1.44328i | 0.895424 | + | 0.445214i | \(0.146872\pi\) |
−0.0621458 | + | 0.998067i | \(0.519794\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.54050 | − | 7.86437i | −0.204910 | − | 0.354914i | 0.745194 | − | 0.666847i | \(-0.232357\pi\) |
−0.950104 | + | 0.311933i | \(0.899023\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.76543 | −0.0795110 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.4248 | + | 13.3361i | 0.826466 | + | 0.598206i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.82522 | 0.305539 | 0.152769 | − | 0.988262i | \(-0.451181\pi\) | ||||
0.152769 | + | 0.988262i | \(0.451181\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.09211 | −0.182458 | −0.0912291 | − | 0.995830i | \(-0.529080\pi\) | ||||
−0.0912291 | + | 0.995830i | \(0.529080\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.47989 | 0.288351 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.7982 | 1.27646 | 0.638228 | − | 0.769847i | \(-0.279668\pi\) | ||||
0.638228 | + | 0.769847i | \(0.279668\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.24662 | + | 12.0685i | −0.0551473 | + | 0.533880i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.7786 | 0.519026 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.8897 | − | 22.3256i | −0.566888 | − | 0.981878i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.92170 | + | 10.2567i | 0.259434 | + | 0.449353i | 0.966090 | − | 0.258204i | \(-0.0831306\pi\) |
−0.706656 | + | 0.707557i | \(0.749797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.86664 | − | 11.8934i | 0.300257 | − | 0.520061i | −0.675937 | − | 0.736959i | \(-0.736261\pi\) |
0.976194 | + | 0.216899i | \(0.0695942\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.21919 | −0.0531087 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3591 | −0.972133 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.55781 | + | 4.43025i | −0.110791 | + | 0.191896i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.98081 | − | 5.16291i | 0.128872 | − | 0.223212i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.76008 | − | 29.6766i | −0.420396 | − | 1.27826i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.7425 | − | 37.6592i | 0.934784 | − | 1.61909i | 0.159765 | − | 0.987155i | \(-0.448926\pi\) |
0.775019 | − | 0.631938i | \(-0.217740\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.1824 | − | 34.9570i | −0.864519 | − | 1.49739i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.0307 | + | 19.1058i | −0.471640 | + | 0.816904i | −0.999474 | − | 0.0324437i | \(-0.989671\pi\) |
0.527834 | + | 0.849348i | \(0.323004\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.4336 | − | 19.8035i | −0.487086 | − | 0.843657i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.62961 | + | 25.4573i | −0.111823 | + | 1.08255i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.0925 | + | 27.8730i | 0.681862 | + | 1.18102i | 0.974412 | + | 0.224769i | \(0.0721627\pi\) |
−0.292551 | + | 0.956250i | \(0.594504\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.6256 | 1.16844 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.69369 | − | 2.93355i | 0.0713804 | − | 0.123635i | −0.828126 | − | 0.560542i | \(-0.810593\pi\) |
0.899507 | + | 0.436907i | \(0.143926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.9159 | + | 32.7633i | 0.795798 | + | 1.37836i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.1737 | − | 34.9419i | −0.845726 | − | 1.46484i | −0.884989 | − | 0.465611i | \(-0.845835\pi\) |
0.0392637 | − | 0.999229i | \(-0.487499\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.21928 | − | 9.04006i | 0.218420 | − | 0.378315i | −0.735905 | − | 0.677085i | \(-0.763243\pi\) |
0.954325 | + | 0.298770i | \(0.0965763\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.239591 | 0.00999164 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.55156 | + | 9.61559i | 0.231114 | + | 0.400302i | 0.958136 | − | 0.286312i | \(-0.0924295\pi\) |
−0.727022 | + | 0.686614i | \(0.759096\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.8884 | − | 18.2924i | 1.69634 | − | 0.758898i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.2755 | − | 33.3862i | −0.798310 | − | 1.38271i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.3875 | − | 35.3122i | 0.841482 | − | 1.45749i | −0.0471601 | − | 0.998887i | \(-0.515017\pi\) |
0.888642 | − | 0.458602i | \(-0.151650\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.89589 | − | 13.6761i | −0.325345 | − | 0.563513i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.7930 | + | 25.6221i | −0.607474 | + | 1.05218i | 0.384182 | + | 0.923258i | \(0.374484\pi\) |
−0.991655 | + | 0.128918i | \(0.958850\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.144324 | − | 1.39720i | 0.00591669 | − | 0.0572794i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.17760 | + | 15.8961i | −0.374987 | + | 0.649496i | −0.990325 | − | 0.138767i | \(-0.955686\pi\) |
0.615338 | + | 0.788263i | \(0.289019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.9250 | − | 27.5828i | 0.649593 | − | 1.12513i | −0.333628 | − | 0.942705i | \(-0.608273\pi\) |
0.983220 | − | 0.182423i | \(-0.0583939\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.5283 | 0.834596 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.6903 | 0.961560 | 0.480780 | − | 0.876841i | \(-0.340353\pi\) | ||||
0.480780 | + | 0.876841i | \(0.340353\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.21099 | + | 14.2219i | −0.332181 | + | 0.575354i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.3159 | + | 23.0638i | 0.537824 | + | 0.931539i | 0.999021 | + | 0.0442411i | \(0.0140870\pi\) |
−0.461197 | + | 0.887298i | \(0.652580\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.72483 | − | 8.18364i | −0.190214 | − | 0.329461i | 0.755107 | − | 0.655602i | \(-0.227585\pi\) |
−0.945321 | + | 0.326141i | \(0.894252\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.0947 | −1.45077 | −0.725385 | − | 0.688344i | \(-0.758338\pi\) | ||||
−0.725385 | + | 0.688344i | \(0.758338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.56185 | − | 2.04086i | 0.182767 | − | 0.0817652i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.4068 | −1.05627 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.781045 | −0.0311423 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.0100579 | 0.000400401 | 0.000200200 | − | 1.00000i | \(-0.499936\pi\) | ||||
0.000200200 | 1.00000i | \(0.499936\pi\) | ||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.7187 | 0.742829 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.2632 | + | 14.8367i | −0.525506 | + | 0.587851i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.90453 | 0.193717 | 0.0968587 | − | 0.995298i | \(-0.469121\pi\) | ||||
0.0968587 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0655 | + | 38.2186i | 0.870180 | + | 1.50720i | 0.861810 | + | 0.507231i | \(0.169331\pi\) |
0.00837033 | + | 0.999965i | \(0.497336\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.8813 | + | 43.0957i | 0.978186 | + | 1.69427i | 0.668993 | + | 0.743268i | \(0.266725\pi\) |
0.309192 | + | 0.950999i | \(0.399941\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.6457 | − | 32.2953i | 0.731908 | − | 1.26770i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.9716 | −0.546749 | −0.273375 | − | 0.961908i | \(-0.588140\pi\) | ||||
−0.273375 | + | 0.961908i | \(0.588140\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.8024 | 1.12540 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.9827 | + | 22.4867i | −0.505733 | + | 0.875956i | 0.494245 | + | 0.869323i | \(0.335445\pi\) |
−0.999978 | + | 0.00663317i | \(0.997889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.7681 | + | 22.1150i | −0.496622 | + | 0.860174i | −0.999992 | − | 0.00389626i | \(-0.998760\pi\) |
0.503370 | + | 0.864071i | \(0.332093\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.6075 | − | 7.42979i | 0.644013 | − | 0.288115i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.06425 | + | 5.30744i | −0.118648 | + | 0.205505i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.3961 | − | 50.9155i | −1.13482 | − | 1.96557i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.71472 | − | 4.70203i | 0.104645 | − | 0.181250i | −0.808948 | − | 0.587880i | \(-0.799963\pi\) |
0.913593 | + | 0.406630i | \(0.133296\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.07571 | − | 12.2555i | −0.271942 | − | 0.471017i | 0.697417 | − | 0.716665i | \(-0.254332\pi\) |
−0.969359 | + | 0.245648i | \(0.920999\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.2307 | + | 16.6561i | −1.42878 | + | 0.639202i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.553330 | + | 0.958397i | 0.0211726 | + | 0.0366720i | 0.876418 | − | 0.481552i | \(-0.159927\pi\) |
−0.855245 | + | 0.518224i | \(0.826593\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.2773 | −1.42429 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.2789 | + | 21.2677i | −0.467789 | + | 0.810234i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.4539 | − | 19.8387i | −0.435725 | − | 0.754698i | 0.561629 | − | 0.827389i | \(-0.310175\pi\) |
−0.997355 | + | 0.0726910i | \(0.976841\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.07207 | + | 12.2492i | 0.268259 | + | 0.464638i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.207492 | + | 0.359387i | −0.00785932 | + | 0.0136127i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.4056 | 0.430782 | 0.215391 | − | 0.976528i | \(-0.430897\pi\) | ||||
0.215391 | + | 0.976528i | \(0.430897\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.05832 | − | 8.76127i | −0.190778 | − | 0.330438i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.03295 | − | 4.36672i | −0.226892 | − | 0.164227i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.5336 | + | 32.1011i | 0.696042 | + | 1.20558i | 0.969828 | + | 0.243790i | \(0.0783908\pi\) |
−0.273786 | + | 0.961791i | \(0.588276\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.11614 | + | 3.66527i | −0.0792502 | + | 0.137265i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.6038 | − | 25.2946i | −0.546153 | − | 0.945965i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.459342 | − | 0.795604i | 0.0171306 | − | 0.0296710i | −0.857333 | − | 0.514762i | \(-0.827880\pi\) |
0.874464 | + | 0.485091i | \(0.161214\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.9662 | − | 7.93745i | −0.408402 | − | 0.295606i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.14545 | + | 1.98399i | −0.0425411 | + | 0.0736834i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.34433 | − | 12.7208i | 0.272386 | − | 0.471787i | −0.697086 | − | 0.716987i | \(-0.745521\pi\) |
0.969472 | + | 0.245201i | \(0.0788538\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.24102 | 0.0828871 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.8624 | −0.844441 | −0.422220 | − | 0.906493i | \(-0.638749\pi\) | ||||
−0.422220 | + | 0.906493i | \(0.638749\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.8049 | + | 29.1069i | −0.619015 | + | 1.07217i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.6692 | + | 34.0681i | 0.723544 | + | 1.25321i | 0.959571 | + | 0.281468i | \(0.0908212\pi\) |
−0.236027 | + | 0.971746i | \(0.575845\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.8663 | − | 18.8210i | −0.398647 | − | 0.690477i | 0.594912 | − | 0.803791i | \(-0.297187\pi\) |
−0.993559 | + | 0.113314i | \(0.963853\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.7682 | −0.650977 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.25444 | + | 2.79808i | −0.228532 | + | 0.102240i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.6143 | 0.752225 | 0.376113 | − | 0.926574i | \(-0.377261\pi\) | ||||
0.376113 | + | 0.926574i | \(0.377261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34.3404 | −1.24978 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.8453 | 0.648600 | 0.324300 | − | 0.945954i | \(-0.394871\pi\) | ||||
0.324300 | + | 0.945954i | \(0.394871\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.9427 | 1.23042 | 0.615211 | − | 0.788362i | \(-0.289071\pi\) | ||||
0.615211 | + | 0.788362i | \(0.289071\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.76672 | + | 46.1466i | −0.172567 | + | 1.67062i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.7554 | −0.857757 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.3452 | + | 35.2389i | 0.733665 | + | 1.27075i | 0.955306 | + | 0.295617i | \(0.0955253\pi\) |
−0.221641 | + | 0.975128i | \(0.571141\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.17562 | − | 3.76829i | −0.0782517 | − | 0.135536i | 0.824244 | − | 0.566235i | \(-0.191600\pi\) |
−0.902496 | + | 0.430699i | \(0.858267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.791039 | + | 1.37012i | −0.0284150 | + | 0.0492162i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.37516 | −0.192585 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.3664 | 1.37286 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.296062 | − | 0.512795i | 0.0105669 | − | 0.0183024i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.8110 | + | 32.5816i | −0.670539 | + | 1.16141i | 0.307213 | + | 0.951641i | \(0.400604\pi\) |
−0.977751 | + | 0.209767i | \(0.932730\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.46760 | − | 43.2508i | 0.158850 | − | 1.53782i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.7259 | + | 32.4342i | −0.664976 | + | 1.15177i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.1570 | + | 38.3771i | 0.784842 | + | 1.35939i | 0.929093 | + | 0.369845i | \(0.120589\pi\) |
−0.144251 | + | 0.989541i | \(0.546077\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.666084 | + | 1.15369i | −0.0235644 | + | 0.0408147i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.2329 | + | 17.7239i | 0.361110 | + | 0.625462i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.94991 | − | 2.85899i | −0.139216 | − | 0.100766i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.78609 | + | 16.9500i | 0.344061 | + | 0.595931i | 0.985183 | − | 0.171508i | \(-0.0548641\pi\) |
−0.641122 | + | 0.767439i | \(0.721531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.15430 | −0.145877 | −0.0729386 | − | 0.997336i | \(-0.523238\pi\) | ||||
−0.0729386 | + | 0.997336i | \(0.523238\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.4739 | + | 25.0695i | −0.506997 | + | 0.878145i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.5136 | + | 25.1383i | 0.507767 | + | 0.879479i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.3771 | + | 24.9019i | 0.501764 | + | 0.869081i | 0.999998 | + | 0.00203808i | \(0.000648743\pi\) |
−0.498234 | + | 0.867043i | \(0.666018\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.5441 | − | 18.2628i | 0.367543 | − | 0.636603i | −0.621638 | − | 0.783305i | \(-0.713532\pi\) |
0.989181 | + | 0.146702i | \(0.0468658\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 56.8422 | 1.97660 | 0.988299 | − | 0.152530i | \(-0.0487420\pi\) | ||||
0.988299 | + | 0.152530i | \(0.0487420\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.97588 | − | 15.5467i | −0.311745 | − | 0.539959i | 0.666995 | − | 0.745062i | \(-0.267580\pi\) |
−0.978740 | + | 0.205104i | \(0.934247\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.07592 | + | 1.20357i | −0.0372785 | + | 0.0417012i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.9698 | − | 43.2490i | −0.864117 | − | 1.49669i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.38469 | − | 7.59451i | 0.151376 | − | 0.262192i | −0.780357 | − | 0.625334i | \(-0.784963\pi\) |
0.931734 | + | 0.363142i | \(0.118296\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7996 | − | 25.6337i | −0.510332 | − | 0.883921i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.66014 | − | 9.80366i | 0.194715 | − | 0.337256i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.1124 | − | 13.8338i | −0.656711 | − | 0.475336i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.35566 | + | 2.34807i | −0.0464714 | + | 0.0804908i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0519 | − | 27.8027i | 0.549607 | − | 0.951948i | −0.448694 | − | 0.893686i | \(-0.648111\pi\) |
0.998301 | − | 0.0582625i | \(-0.0185560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.5025 | 0.427078 | 0.213539 | − | 0.976935i | \(-0.431501\pi\) | ||||
0.213539 | + | 0.976935i | \(0.431501\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.56877 | 0.258243 | 0.129121 | − | 0.991629i | \(-0.458784\pi\) | ||||
0.129121 | + | 0.991629i | \(0.458784\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.268987 | + | 0.465899i | −0.00915642 | + | 0.0158594i | −0.870567 | − | 0.492049i | \(-0.836248\pi\) |
0.861411 | + | 0.507909i | \(0.169581\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.8384 | + | 27.4329i | 0.538522 | + | 0.932747i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.5852 | + | 37.3866i | 0.732226 | + | 1.26825i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.4101 | 0.725453 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.1923 | + | 16.7869i | 0.784042 | + | 0.567499i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.7073 | 0.901843 | 0.450921 | − | 0.892564i | \(-0.351096\pi\) | ||||
0.450921 | + | 0.892564i | \(0.351096\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.6239 | −1.13282 | −0.566408 | − | 0.824125i | \(-0.691667\pi\) | ||||
−0.566408 | + | 0.824125i | \(0.691667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.20109 | 0.242336 | 0.121168 | − | 0.992632i | \(-0.461336\pi\) | ||||
0.121168 | + | 0.992632i | \(0.461336\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.78746 | 0.160747 | 0.0803736 | − | 0.996765i | \(-0.474389\pi\) | ||||
0.0803736 | + | 0.996765i | \(0.474389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.4276 | − | 12.6143i | −0.584504 | − | 0.423071i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.2552 | −0.577422 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.03190 | + | 1.78731i | 0.0344928 | + | 0.0597432i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.2340 | − | 35.0464i | −0.674842 | − | 1.16886i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.996076 | + | 1.72525i | −0.0331841 | + | 0.0574766i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.1961 | −1.33616 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.8351 | −1.15668 | −0.578341 | − | 0.815795i | \(-0.696299\pi\) | ||||
−0.578341 | + | 0.815795i | \(0.696299\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.1584 | + | 50.5038i | −0.966060 | + | 1.67326i | −0.259319 | + | 0.965792i | \(0.583498\pi\) |
−0.706740 | + | 0.707473i | \(0.749835\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.7795 | − | 65.4359i | 1.25032 | − | 2.16561i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26.8158 | − | 19.4096i | −0.885536 | − | 0.640962i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.113983 | + | 0.197424i | −0.00375995 | + | 0.00651242i | −0.867899 | − | 0.496740i | \(-0.834530\pi\) |
0.864139 | + | 0.503253i | \(0.167863\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.2201 | − | 21.1658i | −0.402229 | − | 0.696681i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.506761 | + | 0.877736i | −0.0166622 | + | 0.0288598i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.4425 | − | 21.5511i | −0.408226 | − | 0.707069i | 0.586465 | − | 0.809975i | \(-0.300519\pi\) |
−0.994691 | + | 0.102906i | \(0.967186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.4689 | − | 4.27429i | −0.670842 | − | 0.140084i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.18468 | − | 2.05192i | −0.0387432 | − | 0.0671051i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.3194 | −1.44785 | −0.723926 | − | 0.689878i | \(-0.757664\pi\) | ||||
−0.723926 | + | 0.689878i | \(0.757664\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.1410 | − | 52.2057i | 0.982568 | − | 1.70186i | 0.330286 | − | 0.943881i | \(-0.392855\pi\) |
0.652282 | − | 0.757977i | \(-0.273812\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.720286 | + | 1.24757i | 0.0234558 | + | 0.0406266i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.29884 | − | 12.6420i | −0.237180 | − | 0.410808i | 0.722724 | − | 0.691137i | \(-0.242890\pi\) |
−0.959904 | + | 0.280329i | \(0.909557\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.51855 | − | 11.2905i | 0.211601 | − | 0.366504i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.9601 | −0.387427 | −0.193713 | − | 0.981058i | \(-0.562053\pi\) | ||||
−0.193713 | + | 0.981058i | \(0.562053\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.69086 | − | 2.92865i | −0.0547148 | − | 0.0947688i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34.7062 | + | 25.1208i | 1.12072 | + | 0.811192i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.52659 | + | 2.64414i | 0.0492450 | + | 0.0852948i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.48535 | + | 12.9650i | −0.240962 | + | 0.417358i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.8250 | + | 39.5340i | 0.734001 | + | 1.27133i | 0.955160 | + | 0.296090i | \(0.0956828\pi\) |
−0.221159 | + | 0.975238i | \(0.570984\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.25397 | + | 2.17194i | −0.0402418 | + | 0.0697009i | −0.885445 | − | 0.464745i | \(-0.846146\pi\) |
0.845203 | + | 0.534445i | \(0.179479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.67030 | − | 16.1701i | 0.0535472 | − | 0.518390i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.8101 | + | 49.9005i | −0.921715 | + | 1.59646i | −0.124955 | + | 0.992162i | \(0.539879\pi\) |
−0.796760 | + | 0.604296i | \(0.793455\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.21499 | − | 7.30058i | 0.134712 | − | 0.233328i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −59.3736 | −1.89372 | −0.946862 | − | 0.321641i | \(-0.895765\pi\) | ||||
−0.946862 | + | 0.321641i | \(0.895765\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.5139 | 0.876666 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.88973 | − | 6.73721i | 0.123686 | − | 0.214231i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.2341 | − | 35.0465i | −0.642758 | − | 1.11329i | −0.984814 | − | 0.173610i | \(-0.944457\pi\) |
0.342057 | − | 0.939679i | \(-0.388877\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.4190 | + | 38.8308i | 0.710730 | + | 1.23102i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.1422 | −0.447889 | −0.223945 | − | 0.974602i | \(-0.571893\pi\) | ||||
−0.223945 | + | 0.974602i | \(0.571893\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2268.2.l.n.541.7 | 16 | ||
3.2 | odd | 2 | inner | 2268.2.l.n.541.2 | 16 | ||
7.4 | even | 3 | 2268.2.i.n.865.2 | 16 | |||
9.2 | odd | 6 | 2268.2.k.g.1297.7 | yes | 16 | ||
9.4 | even | 3 | 2268.2.i.n.2053.2 | 16 | |||
9.5 | odd | 6 | 2268.2.i.n.2053.7 | 16 | |||
9.7 | even | 3 | 2268.2.k.g.1297.2 | ✓ | 16 | ||
21.11 | odd | 6 | 2268.2.i.n.865.7 | 16 | |||
63.4 | even | 3 | inner | 2268.2.l.n.109.7 | 16 | ||
63.11 | odd | 6 | 2268.2.k.g.1621.7 | yes | 16 | ||
63.25 | even | 3 | 2268.2.k.g.1621.2 | yes | 16 | ||
63.32 | odd | 6 | inner | 2268.2.l.n.109.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2268.2.i.n.865.2 | 16 | 7.4 | even | 3 | |||
2268.2.i.n.865.7 | 16 | 21.11 | odd | 6 | |||
2268.2.i.n.2053.2 | 16 | 9.4 | even | 3 | |||
2268.2.i.n.2053.7 | 16 | 9.5 | odd | 6 | |||
2268.2.k.g.1297.2 | ✓ | 16 | 9.7 | even | 3 | ||
2268.2.k.g.1297.7 | yes | 16 | 9.2 | odd | 6 | ||
2268.2.k.g.1621.2 | yes | 16 | 63.25 | even | 3 | ||
2268.2.k.g.1621.7 | yes | 16 | 63.11 | odd | 6 | ||
2268.2.l.n.109.2 | 16 | 63.32 | odd | 6 | inner | ||
2268.2.l.n.109.7 | 16 | 63.4 | even | 3 | inner | ||
2268.2.l.n.541.2 | 16 | 3.2 | odd | 2 | inner | ||
2268.2.l.n.541.7 | 16 | 1.1 | even | 1 | trivial |