Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(64,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.d (of order \(2\), degree \(1\), 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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.1 | ||
Root | \(-0.854638 + 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.64 |
Dual form | 315.2.d.e.64.6 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.70928i | − | 1.91575i | −0.287190 | − | 0.957873i | \(-0.592721\pi\) | ||
0.287190 | − | 0.957873i | \(-0.407279\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.34017 | −2.67009 | ||||||||
\(5\) | −2.17009 | − | 0.539189i | −0.970492 | − | 0.241133i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 9.04945i | 3.19946i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.46081 | + | 5.87936i | −0.461949 | + | 1.85922i | ||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.921622i | 0.255612i | 0.991799 | + | 0.127806i | \(0.0407935\pi\) | ||||
−0.991799 | + | 0.127806i | \(0.959207\pi\) | |||||||
\(14\) | −2.70928 | −0.724084 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.8371 | 3.45928 | ||||||||
\(17\) | 1.07838i | 0.261545i | 0.991412 | + | 0.130773i | \(0.0417457\pi\) | ||||
−0.991412 | + | 0.130773i | \(0.958254\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.07838 | −0.706228 | −0.353114 | − | 0.935580i | \(-0.614877\pi\) | ||||
−0.353114 | + | 0.935580i | \(0.614877\pi\) | |||||||
\(20\) | 11.5886 | + | 2.87936i | 2.59130 | + | 0.643845i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.41855i | 1.15524i | ||||||||
\(23\) | − | 2.34017i | − | 0.487960i | −0.969780 | − | 0.243980i | \(-0.921547\pi\) | ||
0.969780 | − | 0.243980i | \(-0.0784531\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.41855 | + | 2.34017i | 0.883710 | + | 0.468035i | ||||
\(26\) | 2.49693 | 0.489688 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.34017i | 1.00920i | ||||||||
\(29\) | −6.68035 | −1.24051 | −0.620255 | − | 0.784401i | \(-0.712971\pi\) | ||||
−0.620255 | + | 0.784401i | \(0.712971\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.75872 | −1.39351 | −0.696754 | − | 0.717310i | \(-0.745373\pi\) | ||||
−0.696754 | + | 0.717310i | \(0.745373\pi\) | |||||||
\(32\) | − | 19.3896i | − | 3.42763i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.92162 | 0.501054 | ||||||||
\(35\) | −0.539189 | + | 2.17009i | −0.0911396 | + | 0.366812i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.8371i | − | 1.78161i | −0.454387 | − | 0.890804i | \(-0.650142\pi\) | ||
0.454387 | − | 0.890804i | \(-0.349858\pi\) | |||||||
\(38\) | 8.34017i | 1.35295i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.87936 | − | 19.6381i | 0.771495 | − | 3.10505i | ||||
\(41\) | −6.49693 | −1.01465 | −0.507325 | − | 0.861755i | \(-0.669366\pi\) | ||||
−0.507325 | + | 0.861755i | \(0.669366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.52359i | − | 0.994838i | −0.867510 | − | 0.497419i | \(-0.834281\pi\) | ||
0.867510 | − | 0.497419i | \(-0.165719\pi\) | |||||||
\(44\) | 10.6803 | 1.61012 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.34017 | −0.934808 | ||||||||
\(47\) | 4.68035i | 0.682699i | 0.939937 | + | 0.341349i | \(0.110884\pi\) | ||||
−0.939937 | + | 0.341349i | \(0.889116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 6.34017 | − | 11.9711i | 0.896636 | − | 1.69297i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.92162i | − | 0.682506i | ||||||
\(53\) | − | 3.75872i | − | 0.516300i | −0.966105 | − | 0.258150i | \(-0.916887\pi\) | ||
0.966105 | − | 0.258150i | \(-0.0831129\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.34017 | + | 1.07838i | 0.585229 | + | 0.145408i | ||||
\(56\) | 9.04945 | 1.20928 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 18.0989i | 2.37650i | ||||||||
\(59\) | 10.5236 | 1.37005 | 0.685027 | − | 0.728517i | \(-0.259790\pi\) | ||||
0.685027 | + | 0.728517i | \(0.259790\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.15676 | −0.532218 | −0.266109 | − | 0.963943i | \(-0.585738\pi\) | ||||
−0.266109 | + | 0.963943i | \(0.585738\pi\) | |||||||
\(62\) | 21.0205i | 2.66961i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −24.8576 | −3.10720 | ||||||||
\(65\) | 0.496928 | − | 2.00000i | 0.0616364 | − | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.68035i | − | 0.571795i | −0.958260 | − | 0.285898i | \(-0.907708\pi\) | ||
0.958260 | − | 0.285898i | \(-0.0922917\pi\) | |||||||
\(68\) | − | 5.75872i | − | 0.698348i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.87936 | + | 1.46081i | 0.702718 | + | 0.174600i | ||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.07838i | 0.828461i | 0.910172 | + | 0.414231i | \(0.135949\pi\) | ||||
−0.910172 | + | 0.414231i | \(0.864051\pi\) | |||||||
\(74\) | −29.3607 | −3.41311 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16.4391 | 1.88569 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.15676 | −0.692689 | −0.346345 | − | 0.938107i | \(-0.612577\pi\) | ||||
−0.346345 | + | 0.938107i | \(0.612577\pi\) | |||||||
\(80\) | −30.0277 | − | 7.46081i | −3.35720 | − | 0.834144i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 17.6020i | 1.94381i | ||||||||
\(83\) | − | 6.83710i | − | 0.750469i | −0.926930 | − | 0.375235i | \(-0.877562\pi\) | ||
0.926930 | − | 0.375235i | \(-0.122438\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.581449 | − | 2.34017i | 0.0630670 | − | 0.253827i | ||||
\(86\) | −17.6742 | −1.90586 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 18.0989i | − | 1.92935i | ||||||
\(89\) | 8.34017 | 0.884057 | 0.442028 | − | 0.897001i | \(-0.354259\pi\) | ||||
0.442028 | + | 0.897001i | \(0.354259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.921622 | 0.0966123 | ||||||||
\(92\) | 12.4969i | 1.30289i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.6803 | 1.30788 | ||||||||
\(95\) | 6.68035 | + | 1.65983i | 0.685389 | + | 0.170295i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.43907i | 0.856858i | 0.903576 | + | 0.428429i | \(0.140933\pi\) | ||||
−0.903576 | + | 0.428429i | \(0.859067\pi\) | |||||||
\(98\) | 2.70928i | 0.273678i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −23.5958 | − | 12.4969i | −2.35958 | − | 1.24969i | ||||
\(101\) | 5.81658 | 0.578772 | 0.289386 | − | 0.957213i | \(-0.406549\pi\) | ||||
0.289386 | + | 0.957213i | \(0.406549\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.15676i | − | 0.212511i | −0.994339 | − | 0.106256i | \(-0.966114\pi\) | ||
0.994339 | − | 0.106256i | \(-0.0338862\pi\) | |||||||
\(104\) | −8.34017 | −0.817821 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.1834 | −0.989101 | ||||||||
\(107\) | − | 16.4969i | − | 1.59482i | −0.603439 | − | 0.797409i | \(-0.706203\pi\) | ||
0.603439 | − | 0.797409i | \(-0.293797\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8371 | 1.22957 | 0.614786 | − | 0.788694i | \(-0.289243\pi\) | ||||
0.614786 | + | 0.788694i | \(0.289243\pi\) | |||||||
\(110\) | 2.92162 | − | 11.7587i | 0.278566 | − | 1.12115i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 13.8371i | − | 1.30748i | ||||||
\(113\) | 5.23513i | 0.492480i | 0.969209 | + | 0.246240i | \(0.0791951\pi\) | ||||
−0.969209 | + | 0.246240i | \(0.920805\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.26180 | + | 5.07838i | −0.117663 | + | 0.473561i | ||||
\(116\) | 35.6742 | 3.31227 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 28.5113i | − | 2.62468i | ||||||
\(119\) | 1.07838 | 0.0988547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 11.2618i | 1.01960i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 41.4329 | 3.72079 | ||||||||
\(125\) | −8.32684 | − | 7.46081i | −0.744775 | − | 0.667315i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.84324i | − | 0.163562i | −0.996650 | − | 0.0817808i | \(-0.973939\pi\) | ||
0.996650 | − | 0.0817808i | \(-0.0260607\pi\) | |||||||
\(128\) | 28.5669i | 2.52498i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.41855 | − | 1.34632i | −0.475238 | − | 0.118080i | ||||
\(131\) | −1.47641 | −0.128995 | −0.0644973 | − | 0.997918i | \(-0.520544\pi\) | ||||
−0.0644973 | + | 0.997918i | \(0.520544\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.07838i | 0.266929i | ||||||||
\(134\) | −12.6803 | −1.09542 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.75872 | −0.836804 | ||||||||
\(137\) | 4.43907i | 0.379255i | 0.981856 | + | 0.189628i | \(0.0607281\pi\) | ||||
−0.981856 | + | 0.189628i | \(0.939272\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.6020 | −1.15370 | −0.576852 | − | 0.816849i | \(-0.695719\pi\) | ||||
−0.576852 | + | 0.816849i | \(0.695719\pi\) | |||||||
\(140\) | 2.87936 | − | 11.5886i | 0.243350 | − | 0.979419i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.41855i | 0.454715i | ||||||||
\(143\) | − | 1.84324i | − | 0.154140i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.4969 | + | 3.60197i | 1.20390 | + | 0.299127i | ||||
\(146\) | 19.1773 | 1.58712 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 57.8720i | 4.75705i | ||||||||
\(149\) | 15.6742 | 1.28408 | 0.642040 | − | 0.766671i | \(-0.278088\pi\) | ||||
0.642040 | + | 0.766671i | \(0.278088\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.84324 | 0.475516 | 0.237758 | − | 0.971324i | \(-0.423587\pi\) | ||||
0.237758 | + | 0.971324i | \(0.423587\pi\) | |||||||
\(152\) | − | 27.8576i | − | 2.25955i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.41855 | 0.436639 | ||||||||
\(155\) | 16.8371 | + | 4.18342i | 1.35239 | + | 0.336020i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.92162i | − | 0.392788i | −0.980525 | − | 0.196394i | \(-0.937077\pi\) | ||
0.980525 | − | 0.196394i | \(-0.0629232\pi\) | |||||||
\(158\) | 16.6803i | 1.32702i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.4547 | + | 42.0772i | −0.826514 | + | 3.32649i | ||||
\(161\) | −2.34017 | −0.184431 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 9.84324i | − | 0.770982i | −0.922712 | − | 0.385491i | \(-0.874032\pi\) | ||
0.922712 | − | 0.385491i | \(-0.125968\pi\) | |||||||
\(164\) | 34.6947 | 2.70920 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.5236 | −1.43771 | ||||||||
\(167\) | − | 19.2039i | − | 1.48605i | −0.669266 | − | 0.743023i | \(-0.733391\pi\) | ||
0.669266 | − | 0.743023i | \(-0.266609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1506 | 0.934662 | ||||||||
\(170\) | −6.34017 | − | 1.57531i | −0.486269 | − | 0.120820i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 34.8371i | 2.65630i | ||||||||
\(173\) | 22.4391i | 1.70601i | 0.521902 | + | 0.853005i | \(0.325223\pi\) | ||||
−0.521902 | + | 0.853005i | \(0.674777\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.34017 | − | 4.41855i | 0.176900 | − | 0.334011i | ||||
\(176\) | −27.6742 | −2.08602 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 22.5958i | − | 1.69363i | ||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.52359 | −0.633553 | −0.316777 | − | 0.948500i | \(-0.602601\pi\) | ||||
−0.316777 | + | 0.948500i | \(0.602601\pi\) | |||||||
\(182\) | − | 2.49693i | − | 0.185085i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 21.1773 | 1.56121 | ||||||||
\(185\) | −5.84324 | + | 23.5174i | −0.429604 | + | 1.72904i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.15676i | − | 0.157718i | ||||||
\(188\) | − | 24.9939i | − | 1.82286i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.49693 | − | 18.0989i | 0.326241 | − | 1.31303i | ||||
\(191\) | −15.3607 | −1.11146 | −0.555730 | − | 0.831363i | \(-0.687561\pi\) | ||||
−0.555730 | + | 0.831363i | \(0.687561\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.36683i | 0.602258i | 0.953583 | + | 0.301129i | \(0.0973635\pi\) | ||||
−0.953583 | + | 0.301129i | \(0.902637\pi\) | |||||||
\(194\) | 22.8638 | 1.64152 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.34017 | 0.381441 | ||||||||
\(197\) | − | 11.7587i | − | 0.837774i | −0.908038 | − | 0.418887i | \(-0.862420\pi\) | ||
0.908038 | − | 0.418887i | \(-0.137580\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.5958 | 1.60178 | 0.800888 | − | 0.598814i | \(-0.204361\pi\) | ||||
0.800888 | + | 0.598814i | \(0.204361\pi\) | |||||||
\(200\) | −21.1773 | + | 39.9854i | −1.49746 | + | 2.82740i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 15.7587i | − | 1.10878i | ||||||
\(203\) | 6.68035i | 0.468868i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.0989 | + | 3.50307i | 0.984710 | + | 0.244665i | ||||
\(206\) | −5.84324 | −0.407118 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.7526i | 0.884232i | ||||||||
\(209\) | 6.15676 | 0.425872 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.6742 | −0.941371 | −0.470685 | − | 0.882301i | \(-0.655993\pi\) | ||||
−0.470685 | + | 0.882301i | \(0.655993\pi\) | |||||||
\(212\) | 20.0722i | 1.37857i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −44.6947 | −3.05527 | ||||||||
\(215\) | −3.51745 | + | 14.1568i | −0.239888 | + | 0.965483i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.75872i | 0.526696i | ||||||||
\(218\) | − | 34.7792i | − | 2.35555i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −23.1773 | − | 5.75872i | −1.56261 | − | 0.388253i | ||||
\(221\) | −0.993857 | −0.0668541 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 21.6742i | − | 1.45141i | −0.688005 | − | 0.725706i | \(-0.741513\pi\) | ||
0.688005 | − | 0.725706i | \(-0.258487\pi\) | |||||||
\(224\) | −19.3896 | −1.29552 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.1834 | 0.943467 | ||||||||
\(227\) | − | 11.5174i | − | 0.764440i | −0.924071 | − | 0.382220i | \(-0.875160\pi\) | ||
0.924071 | − | 0.382220i | \(-0.124840\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.8371 | −0.848300 | −0.424150 | − | 0.905592i | \(-0.639427\pi\) | ||||
−0.424150 | + | 0.905592i | \(0.639427\pi\) | |||||||
\(230\) | 13.7587 | + | 3.41855i | 0.907223 | + | 0.225413i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 60.4534i | − | 3.96896i | ||||||
\(233\) | 6.76487i | 0.443181i | 0.975140 | + | 0.221591i | \(0.0711248\pi\) | ||||
−0.975140 | + | 0.221591i | \(0.928875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.52359 | − | 10.1568i | 0.164621 | − | 0.662554i | ||||
\(236\) | −56.1978 | −3.65816 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 2.92162i | − | 0.189381i | ||||||
\(239\) | −23.3607 | −1.51108 | −0.755539 | − | 0.655104i | \(-0.772625\pi\) | ||||
−0.755539 | + | 0.655104i | \(0.772625\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.6803 | −0.945644 | −0.472822 | − | 0.881158i | \(-0.656765\pi\) | ||||
−0.472822 | + | 0.881158i | \(0.656765\pi\) | |||||||
\(242\) | 18.9649i | 1.21911i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 22.1978 | 1.42107 | ||||||||
\(245\) | 2.17009 | + | 0.539189i | 0.138642 | + | 0.0344475i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.83710i | − | 0.180520i | ||||||
\(248\) | − | 70.2122i | − | 4.45848i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −20.2134 | + | 22.5597i | −1.27841 | + | 1.42680i | ||||
\(251\) | −9.16290 | −0.578357 | −0.289179 | − | 0.957275i | \(-0.593382\pi\) | ||||
−0.289179 | + | 0.957275i | \(0.593382\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.68035i | 0.294251i | ||||||||
\(254\) | −4.99386 | −0.313342 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 27.6803 | 1.73002 | ||||||||
\(257\) | − | 5.07838i | − | 0.316781i | −0.987377 | − | 0.158390i | \(-0.949370\pi\) | ||
0.987377 | − | 0.158390i | \(-0.0506304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.8371 | −0.673385 | ||||||||
\(260\) | −2.65368 | + | 10.6803i | −0.164574 | + | 0.662367i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.00000i | 0.247121i | ||||||||
\(263\) | − | 5.65983i | − | 0.349000i | −0.984657 | − | 0.174500i | \(-0.944169\pi\) | ||
0.984657 | − | 0.174500i | \(-0.0558309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.02666 | + | 8.15676i | −0.124497 | + | 0.501066i | ||||
\(266\) | 8.34017 | 0.511369 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 24.9939i | 1.52674i | ||||||||
\(269\) | −27.8576 | −1.69851 | −0.849255 | − | 0.527984i | \(-0.822948\pi\) | ||||
−0.849255 | + | 0.527984i | \(0.822948\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.1194 | 1.52590 | 0.762948 | − | 0.646460i | \(-0.223751\pi\) | ||||
0.762948 | + | 0.646460i | \(0.223751\pi\) | |||||||
\(272\) | 14.9216i | 0.904756i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0267 | 0.726557 | ||||||||
\(275\) | −8.83710 | − | 4.68035i | −0.532897 | − | 0.282235i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.1978i | 1.69424i | 0.531401 | + | 0.847121i | \(0.321666\pi\) | ||||
−0.531401 | + | 0.847121i | \(0.678334\pi\) | |||||||
\(278\) | 36.8515i | 2.21020i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19.6381 | − | 4.87936i | −1.17360 | − | 0.291598i | ||||
\(281\) | 20.3545 | 1.21425 | 0.607125 | − | 0.794606i | \(-0.292323\pi\) | ||||
0.607125 | + | 0.794606i | \(0.292323\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.5174i | 1.39797i | 0.715138 | + | 0.698984i | \(0.246364\pi\) | ||||
−0.715138 | + | 0.698984i | \(0.753636\pi\) | |||||||
\(284\) | 10.6803 | 0.633762 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.99386 | −0.295293 | ||||||||
\(287\) | 6.49693i | 0.383502i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8371 | 0.931594 | ||||||||
\(290\) | 9.75872 | − | 39.2762i | 0.573052 | − | 2.30638i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 37.7998i | − | 2.21206i | ||||||
\(293\) | 2.92162i | 0.170683i | 0.996352 | + | 0.0853415i | \(0.0271981\pi\) | ||||
−0.996352 | + | 0.0853415i | \(0.972802\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.8371 | − | 5.67420i | −1.32963 | − | 0.330365i | ||||
\(296\) | 98.0698 | 5.70019 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 42.4657i | − | 2.45997i | ||||||
\(299\) | 2.15676 | 0.124728 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.52359 | −0.376014 | ||||||||
\(302\) | − | 15.8310i | − | 0.910969i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −42.5958 | −2.44304 | ||||||||
\(305\) | 9.02052 | + | 2.24128i | 0.516513 | + | 0.128335i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.4703i | 0.597570i | 0.954321 | + | 0.298785i | \(0.0965813\pi\) | ||||
−0.954321 | + | 0.298785i | \(0.903419\pi\) | |||||||
\(308\) | − | 10.6803i | − | 0.608569i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11.3340 | − | 45.6163i | 0.643730 | − | 2.59083i | ||||
\(311\) | −23.8310 | −1.35133 | −0.675665 | − | 0.737209i | \(-0.736143\pi\) | ||||
−0.675665 | + | 0.737209i | \(0.736143\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.7526i | 1.85129i | 0.378399 | + | 0.925643i | \(0.376475\pi\) | ||||
−0.378399 | + | 0.925643i | \(0.623525\pi\) | |||||||
\(314\) | −13.3340 | −0.752483 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.8781 | 1.84954 | ||||||||
\(317\) | − | 17.9155i | − | 1.00623i | −0.864218 | − | 0.503117i | \(-0.832187\pi\) | ||
0.864218 | − | 0.503117i | \(-0.167813\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.3607 | 0.748055 | ||||||||
\(320\) | 53.9432 | + | 13.4030i | 3.01552 | + | 0.749248i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.34017i | 0.353324i | ||||||||
\(323\) | − | 3.31965i | − | 0.184710i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.15676 | + | 4.07223i | −0.119635 | + | 0.225887i | ||||
\(326\) | −26.6681 | −1.47701 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 58.7936i | − | 3.24633i | ||||||
\(329\) | 4.68035 | 0.258036 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.36069 | −0.0747904 | −0.0373952 | − | 0.999301i | \(-0.511906\pi\) | ||||
−0.0373952 | + | 0.999301i | \(0.511906\pi\) | |||||||
\(332\) | 36.5113i | 2.00382i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −52.0288 | −2.84689 | ||||||||
\(335\) | −2.52359 | + | 10.1568i | −0.137878 | + | 0.554923i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.3607i | 1.38148i | 0.723101 | + | 0.690742i | \(0.242716\pi\) | ||||
−0.723101 | + | 0.690742i | \(0.757284\pi\) | |||||||
\(338\) | − | 32.9194i | − | 1.79058i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.10504 | + | 12.4969i | −0.168394 | + | 0.677741i | ||||
\(341\) | 15.5174 | 0.840317 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 59.0349 | 3.18295 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 60.7936 | 3.26829 | ||||||||
\(347\) | 16.8638i | 0.905294i | 0.891690 | + | 0.452647i | \(0.149520\pi\) | ||||
−0.891690 | + | 0.452647i | \(0.850480\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.51745 | −0.509457 | −0.254729 | − | 0.967013i | \(-0.581986\pi\) | ||||
−0.254729 | + | 0.967013i | \(0.581986\pi\) | |||||||
\(350\) | −11.9711 | − | 6.34017i | −0.639881 | − | 0.338897i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 38.7792i | 2.06694i | ||||||||
\(353\) | 35.7998i | 1.90543i | 0.303867 | + | 0.952715i | \(0.401722\pi\) | ||||
−0.303867 | + | 0.952715i | \(0.598278\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.34017 | + | 1.07838i | 0.230352 | + | 0.0572343i | ||||
\(356\) | −44.5380 | −2.36051 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 27.0928i | − | 1.43190i | ||||||
\(359\) | −22.3135 | −1.17766 | −0.588831 | − | 0.808256i | \(-0.700412\pi\) | ||||
−0.588831 | + | 0.808256i | \(0.700412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.52359 | −0.501242 | ||||||||
\(362\) | 23.0928i | 1.21373i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.92162 | −0.257963 | ||||||||
\(365\) | 3.81658 | − | 15.3607i | 0.199769 | − | 0.804015i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 20.3135i | − | 1.06036i | −0.847886 | − | 0.530178i | \(-0.822125\pi\) | ||
0.847886 | − | 0.530178i | \(-0.177875\pi\) | |||||||
\(368\) | − | 32.3812i | − | 1.68799i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 63.7152 | + | 15.8310i | 3.31240 | + | 0.823012i | ||||
\(371\) | −3.75872 | −0.195143 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16.0000i | − | 0.828449i | −0.910175 | − | 0.414224i | \(-0.864053\pi\) | ||
0.910175 | − | 0.414224i | \(-0.135947\pi\) | |||||||
\(374\) | −5.84324 | −0.302147 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −42.3545 | −2.18427 | ||||||||
\(377\) | − | 6.15676i | − | 0.317089i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.15676 | −0.316251 | −0.158126 | − | 0.987419i | \(-0.550545\pi\) | ||||
−0.158126 | + | 0.987419i | \(0.550545\pi\) | |||||||
\(380\) | −35.6742 | − | 8.86376i | −1.83005 | − | 0.454701i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 41.6163i | 2.12928i | ||||||||
\(383\) | − | 26.8371i | − | 1.37131i | −0.727926 | − | 0.685656i | \(-0.759515\pi\) | ||
0.727926 | − | 0.685656i | \(-0.240485\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.07838 | − | 4.34017i | 0.0549592 | − | 0.221196i | ||||
\(386\) | 22.6681 | 1.15377 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 45.0661i | − | 2.28788i | ||||||
\(389\) | −5.63317 | −0.285613 | −0.142806 | − | 0.989751i | \(-0.545613\pi\) | ||||
−0.142806 | + | 0.989751i | \(0.545613\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.52359 | 0.127623 | ||||||||
\(392\) | − | 9.04945i | − | 0.457066i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −31.8576 | −1.60496 | ||||||||
\(395\) | 13.3607 | + | 3.31965i | 0.672249 | + | 0.167030i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 37.7998i | − | 1.89712i | −0.316604 | − | 0.948558i | \(-0.602543\pi\) | ||
0.316604 | − | 0.948558i | \(-0.397457\pi\) | |||||||
\(398\) | − | 61.2183i | − | 3.06860i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 61.1399 | + | 32.3812i | 3.05700 | + | 1.61906i | ||||
\(401\) | 13.6332 | 0.680808 | 0.340404 | − | 0.940279i | \(-0.389436\pi\) | ||||
0.340404 | + | 0.940279i | \(0.389436\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.15061i | − | 0.356197i | ||||||
\(404\) | −31.0616 | −1.54537 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.0989 | 0.898233 | ||||||||
\(407\) | 21.6742i | 1.07435i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.3545 | −0.610893 | −0.305447 | − | 0.952209i | \(-0.598806\pi\) | ||||
−0.305447 | + | 0.952209i | \(0.598806\pi\) | |||||||
\(410\) | 9.49079 | − | 38.1978i | 0.468716 | − | 1.88645i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.5174i | 0.567424i | ||||||||
\(413\) | − | 10.5236i | − | 0.517832i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.68649 | + | 14.8371i | −0.180963 | + | 0.728325i | ||||
\(416\) | 17.8699 | 0.876144 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 16.6803i | − | 0.815862i | ||||||
\(419\) | 28.9939 | 1.41644 | 0.708221 | − | 0.705991i | \(-0.249498\pi\) | ||||
0.708221 | + | 0.705991i | \(0.249498\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1629 | −0.738994 | −0.369497 | − | 0.929232i | \(-0.620470\pi\) | ||||
−0.369497 | + | 0.929232i | \(0.620470\pi\) | |||||||
\(422\) | 37.0472i | 1.80343i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 34.0144 | 1.65188 | ||||||||
\(425\) | −2.52359 | + | 4.76487i | −0.122412 | + | 0.231130i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.15676i | 0.201159i | ||||||||
\(428\) | 88.0965i | 4.25830i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 38.3545 | + | 9.52973i | 1.84962 | + | 0.459565i | ||||
\(431\) | 10.3135 | 0.496784 | 0.248392 | − | 0.968660i | \(-0.420098\pi\) | ||||
0.248392 | + | 0.968660i | \(0.420098\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.4391i | 0.982239i | 0.871092 | + | 0.491120i | \(0.163412\pi\) | ||||
−0.871092 | + | 0.491120i | \(0.836588\pi\) | |||||||
\(434\) | 21.0205 | 1.00902 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −68.5523 | −3.28306 | ||||||||
\(437\) | 7.20394i | 0.344611i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.9216 | 0.807625 | 0.403812 | − | 0.914842i | \(-0.367685\pi\) | ||||
0.403812 | + | 0.914842i | \(0.367685\pi\) | |||||||
\(440\) | −9.75872 | + | 39.2762i | −0.465229 | + | 1.87242i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.69263i | 0.128075i | ||||||||
\(443\) | 12.8104i | 0.608642i | 0.952569 | + | 0.304321i | \(0.0984296\pi\) | ||||
−0.952569 | + | 0.304321i | \(0.901570\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.0989 | − | 4.49693i | −0.857970 | − | 0.213175i | ||||
\(446\) | −58.7214 | −2.78054 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 24.8576i | 1.17441i | ||||||||
\(449\) | −14.6270 | −0.690292 | −0.345146 | − | 0.938549i | \(-0.612171\pi\) | ||||
−0.345146 | + | 0.938549i | \(0.612171\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.9939 | 0.611857 | ||||||||
\(452\) | − | 27.9565i | − | 1.31496i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −31.2039 | −1.46447 | ||||||||
\(455\) | −2.00000 | − | 0.496928i | −0.0937614 | − | 0.0232964i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 14.1568i | − | 0.662225i | −0.943591 | − | 0.331113i | \(-0.892576\pi\) | ||
0.943591 | − | 0.331113i | \(-0.107424\pi\) | |||||||
\(458\) | 34.7792i | 1.62513i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.73820 | − | 27.1194i | 0.314170 | − | 1.26445i | ||||
\(461\) | −0.340173 | −0.0158434 | −0.00792172 | − | 0.999969i | \(-0.502522\pi\) | ||||
−0.00792172 | + | 0.999969i | \(0.502522\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 9.84324i | − | 0.457454i | −0.973491 | − | 0.228727i | \(-0.926544\pi\) | ||
0.973491 | − | 0.228727i | \(-0.0734564\pi\) | |||||||
\(464\) | −92.4366 | −4.29126 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.3279 | 0.849023 | ||||||||
\(467\) | − | 11.5174i | − | 0.532964i | −0.963840 | − | 0.266482i | \(-0.914139\pi\) | ||
0.963840 | − | 0.266482i | \(-0.0858613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.68035 | −0.216118 | ||||||||
\(470\) | −27.5174 | − | 6.83710i | −1.26929 | − | 0.315372i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 95.2327i | 4.38344i | ||||||||
\(473\) | 13.0472i | 0.599910i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.6020 | − | 7.20394i | −0.624101 | − | 0.330539i | ||||
\(476\) | −5.75872 | −0.263951 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 63.2905i | 2.89484i | ||||||||
\(479\) | −19.5174 | −0.891775 | −0.445887 | − | 0.895089i | \(-0.647112\pi\) | ||||
−0.445887 | + | 0.895089i | \(0.647112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.98771 | 0.455401 | ||||||||
\(482\) | 39.7731i | 1.81162i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 37.3812 | 1.69915 | ||||||||
\(485\) | 4.55025 | − | 18.3135i | 0.206616 | − | 0.831574i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 23.1506i | − | 1.04905i | −0.851394 | − | 0.524527i | \(-0.824242\pi\) | ||
0.851394 | − | 0.524527i | \(-0.175758\pi\) | |||||||
\(488\) | − | 37.6163i | − | 1.70281i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.46081 | − | 5.87936i | 0.0659927 | − | 0.265602i | ||||
\(491\) | −2.00000 | −0.0902587 | −0.0451294 | − | 0.998981i | \(-0.514370\pi\) | ||||
−0.0451294 | + | 0.998981i | \(0.514370\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.20394i | − | 0.324449i | ||||||
\(494\) | −7.68649 | −0.345831 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −107.358 | −4.82053 | ||||||||
\(497\) | 2.00000i | 0.0897123i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.2039 | −1.21782 | −0.608908 | − | 0.793241i | \(-0.708392\pi\) | ||||
−0.608908 | + | 0.793241i | \(0.708392\pi\) | |||||||
\(500\) | 44.4668 | + | 39.8420i | 1.98861 | + | 1.78179i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.8248i | 1.10799i | ||||||||
\(503\) | 18.8371i | 0.839905i | 0.907546 | + | 0.419952i | \(0.137953\pi\) | ||||
−0.907546 | + | 0.419952i | \(0.862047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.6225 | − | 3.13624i | −0.561693 | − | 0.139561i | ||||
\(506\) | 12.6803 | 0.563710 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.84324i | 0.436723i | ||||||||
\(509\) | 6.81044 | 0.301867 | 0.150934 | − | 0.988544i | \(-0.451772\pi\) | ||||
0.150934 | + | 0.988544i | \(0.451772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.07838 | 0.313129 | ||||||||
\(512\) | − | 17.8599i | − | 0.789303i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.7587 | −0.606871 | ||||||||
\(515\) | −1.16290 | + | 4.68035i | −0.0512434 | + | 0.206241i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.36069i | − | 0.411683i | ||||||
\(518\) | 29.3607i | 1.29003i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 18.0989 | + | 4.49693i | 0.793689 | + | 0.197203i | ||||
\(521\) | 25.8166 | 1.13105 | 0.565523 | − | 0.824733i | \(-0.308675\pi\) | ||||
0.565523 | + | 0.824733i | \(0.308675\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000i | 0.174908i | 0.996169 | + | 0.0874539i | \(0.0278730\pi\) | ||||
−0.996169 | + | 0.0874539i | \(0.972127\pi\) | |||||||
\(524\) | 7.88428 | 0.344426 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.3340 | −0.668595 | ||||||||
\(527\) | − | 8.36683i | − | 0.364465i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.5236 | 0.761895 | ||||||||
\(530\) | 22.0989 | + | 5.49079i | 0.959915 | + | 0.238504i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 16.4391i | − | 0.712724i | ||||||
\(533\) | − | 5.98771i | − | 0.259357i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.89496 | + | 35.7998i | −0.384563 | + | 1.54776i | ||||
\(536\) | 42.3545 | 1.82944 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 75.4740i | 3.25391i | ||||||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.8843 | 1.11285 | 0.556426 | − | 0.830897i | \(-0.312172\pi\) | ||||
0.556426 | + | 0.830897i | \(0.312172\pi\) | |||||||
\(542\) | − | 68.0554i | − | 2.92323i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20.9093 | 0.896480 | ||||||||
\(545\) | −27.8576 | − | 6.92162i | −1.19329 | − | 0.296490i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 11.3197i | − | 0.483993i | −0.970277 | − | 0.241997i | \(-0.922198\pi\) | ||
0.970277 | − | 0.241997i | \(-0.0778023\pi\) | |||||||
\(548\) | − | 23.7054i | − | 1.01264i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.6803 | + | 23.9421i | −0.540692 | + | 1.02090i | ||||
\(551\) | 20.5646 | 0.876083 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.15676i | 0.261812i | ||||||||
\(554\) | 76.3956 | 3.24574 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 72.6369 | 3.08049 | ||||||||
\(557\) | − | 26.6491i | − | 1.12916i | −0.825378 | − | 0.564580i | \(-0.809038\pi\) | ||
0.825378 | − | 0.564580i | \(-0.190962\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.01229 | 0.254293 | ||||||||
\(560\) | −7.46081 | + | 30.0277i | −0.315277 | + | 1.26890i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 55.1461i | − | 2.32620i | ||||||
\(563\) | − | 46.3545i | − | 1.95361i | −0.214128 | − | 0.976806i | \(-0.568691\pi\) | ||
0.214128 | − | 0.976806i | \(-0.431309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.82273 | − | 11.3607i | 0.118753 | − | 0.477948i | ||||
\(566\) | 63.7152 | 2.67815 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 18.0989i | − | 0.759413i | ||||||
\(569\) | −14.3668 | −0.602289 | −0.301145 | − | 0.953579i | \(-0.597369\pi\) | ||||
−0.301145 | + | 0.953579i | \(0.597369\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.7214 | 1.62044 | 0.810220 | − | 0.586126i | \(-0.199348\pi\) | ||||
0.810220 | + | 0.586126i | \(0.199348\pi\) | |||||||
\(572\) | 9.84324i | 0.411567i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.6020 | 0.734692 | ||||||||
\(575\) | 5.47641 | − | 10.3402i | 0.228382 | − | 0.431215i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 43.4740i | − | 1.80984i | −0.425577 | − | 0.904922i | \(-0.639929\pi\) | ||
0.425577 | − | 0.904922i | \(-0.360071\pi\) | |||||||
\(578\) | − | 42.9071i | − | 1.78470i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −77.4161 | − | 19.2351i | −3.21453 | − | 0.798695i | ||||
\(581\) | −6.83710 | −0.283651 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.51745i | 0.311341i | ||||||||
\(584\) | −64.0554 | −2.65063 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.91548 | 0.326985 | ||||||||
\(587\) | 36.0288i | 1.48707i | 0.668699 | + | 0.743533i | \(0.266851\pi\) | ||||
−0.668699 | + | 0.743533i | \(0.733149\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.8843 | 0.984135 | ||||||||
\(590\) | −15.3730 | + | 61.8720i | −0.632895 | + | 2.54723i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 149.954i | − | 6.16307i | ||||||
\(593\) | − | 31.4863i | − | 1.29299i | −0.762920 | − | 0.646493i | \(-0.776235\pi\) | ||
0.762920 | − | 0.646493i | \(-0.223765\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.34017 | − | 0.581449i | −0.0959377 | − | 0.0238371i | ||||
\(596\) | −83.7030 | −3.42861 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 5.84324i | − | 0.238948i | ||||||
\(599\) | 29.0349 | 1.18633 | 0.593167 | − | 0.805080i | \(-0.297877\pi\) | ||||
0.593167 | + | 0.805080i | \(0.297877\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.3607 | 0.626576 | 0.313288 | − | 0.949658i | \(-0.398570\pi\) | ||||
0.313288 | + | 0.949658i | \(0.398570\pi\) | |||||||
\(602\) | 17.6742i | 0.720347i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −31.2039 | −1.26967 | ||||||||
\(605\) | 15.1906 | + | 3.77432i | 0.617586 | + | 0.153448i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.0472i | 0.529569i | 0.964308 | + | 0.264784i | \(0.0853008\pi\) | ||||
−0.964308 | + | 0.264784i | \(0.914699\pi\) | |||||||
\(608\) | 59.6886i | 2.42069i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.07223 | − | 24.4391i | 0.245858 | − | 0.989509i | ||||
\(611\) | −4.31351 | −0.174506 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 15.5174i | − | 0.626744i | −0.949630 | − | 0.313372i | \(-0.898541\pi\) | ||
0.949630 | − | 0.313372i | \(-0.101459\pi\) | |||||||
\(614\) | 28.3668 | 1.14479 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.0989 | −0.729225 | ||||||||
\(617\) | − | 22.7649i | − | 0.916479i | −0.888829 | − | 0.458240i | \(-0.848480\pi\) | ||
0.888829 | − | 0.458240i | \(-0.151520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.92777 | −0.318644 | −0.159322 | − | 0.987227i | \(-0.550931\pi\) | ||||
−0.159322 | + | 0.987227i | \(0.550931\pi\) | |||||||
\(620\) | −89.9130 | − | 22.3402i | −3.61099 | − | 0.897203i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 64.5646i | 2.58881i | ||||||||
\(623\) | − | 8.34017i | − | 0.334142i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0472 | + | 20.6803i | 0.561887 | + | 0.827214i | ||||
\(626\) | 88.7358 | 3.54659 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 26.2823i | 1.04878i | ||||||||
\(629\) | 11.6865 | 0.465971 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.2039 | 0.764497 | 0.382248 | − | 0.924060i | \(-0.375150\pi\) | ||||
0.382248 | + | 0.924060i | \(0.375150\pi\) | |||||||
\(632\) | − | 55.7152i | − | 2.21623i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −48.5380 | −1.92769 | ||||||||
\(635\) | −0.993857 | + | 4.00000i | −0.0394400 | + | 0.158735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.921622i | − | 0.0365160i | ||||||
\(638\) | − | 36.1978i | − | 1.43308i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15.4030 | − | 61.9926i | 0.608855 | − | 2.45047i | ||||
\(641\) | 5.94668 | 0.234880 | 0.117440 | − | 0.993080i | \(-0.462531\pi\) | ||||
0.117440 | + | 0.993080i | \(0.462531\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 30.8904i | − | 1.21820i | −0.793094 | − | 0.609100i | \(-0.791531\pi\) | ||
0.793094 | − | 0.609100i | \(-0.208469\pi\) | |||||||
\(644\) | 12.4969 | 0.492448 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.99386 | −0.353859 | ||||||||
\(647\) | − | 19.2039i | − | 0.754985i | −0.926013 | − | 0.377492i | \(-0.876786\pi\) | ||
0.926013 | − | 0.377492i | \(-0.123214\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.0472 | −0.826174 | ||||||||
\(650\) | 11.0328 | + | 5.84324i | 0.432742 | + | 0.229191i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 52.5646i | 2.05859i | ||||||||
\(653\) | 28.5548i | 1.11744i | 0.829358 | + | 0.558718i | \(0.188706\pi\) | ||||
−0.829358 | + | 0.558718i | \(0.811294\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.20394 | + | 0.796064i | 0.125188 | + | 0.0311048i | ||||
\(656\) | −89.8987 | −3.50995 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 12.6803i | − | 0.494331i | ||||||
\(659\) | −27.9877 | −1.09025 | −0.545123 | − | 0.838356i | \(-0.683517\pi\) | ||||
−0.545123 | + | 0.838356i | \(0.683517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.1445 | −0.861320 | −0.430660 | − | 0.902514i | \(-0.641719\pi\) | ||||
−0.430660 | + | 0.902514i | \(0.641719\pi\) | |||||||
\(662\) | 3.68649i | 0.143279i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 61.8720 | 2.40110 | ||||||||
\(665\) | 1.65983 | − | 6.68035i | 0.0643653 | − | 0.259053i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.6332i | 0.605319i | ||||||||
\(668\) | 102.552i | 3.96787i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 27.5174 | + | 6.83710i | 1.06309 | + | 0.264140i | ||||
\(671\) | 8.31351 | 0.320940 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.21008i | 0.0851923i | 0.999092 | + | 0.0425962i | \(0.0135629\pi\) | ||||
−0.999092 | + | 0.0425962i | \(0.986437\pi\) | |||||||
\(674\) | 68.7091 | 2.64658 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −64.8864 | −2.49563 | ||||||||
\(677\) | 19.5486i | 0.751315i | 0.926758 | + | 0.375658i | \(0.122583\pi\) | ||||
−0.926758 | + | 0.375658i | \(0.877417\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.43907 | 0.323862 | ||||||||
\(680\) | 21.1773 | + | 5.26180i | 0.812111 | + | 0.201781i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 42.0410i | − | 1.60983i | ||||||
\(683\) | − | 11.8166i | − | 0.452149i | −0.974110 | − | 0.226074i | \(-0.927411\pi\) | ||
0.974110 | − | 0.226074i | \(-0.0725893\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.39350 | − | 9.63317i | 0.0914508 | − | 0.368064i | ||||
\(686\) | 2.70928 | 0.103441 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 90.2676i | − | 3.44142i | ||||||
\(689\) | 3.46412 | 0.131973 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.7587 | 0.447323 | 0.223661 | − | 0.974667i | \(-0.428199\pi\) | ||||
0.223661 | + | 0.974667i | \(0.428199\pi\) | |||||||
\(692\) | − | 119.829i | − | 4.55520i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 45.6886 | 1.73431 | ||||||||
\(695\) | 29.5174 | + | 7.33403i | 1.11966 | + | 0.278196i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 7.00614i | − | 0.265377i | ||||||
\(698\) | 25.7854i | 0.975991i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.4969 | + | 23.5958i | −0.472339 | + | 0.891838i | ||||
\(701\) | −9.94668 | −0.375681 | −0.187840 | − | 0.982200i | \(-0.560149\pi\) | ||||
−0.187840 | + | 0.982200i | \(0.560149\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.3607i | 1.25822i | ||||||||
\(704\) | 49.7152 | 1.87371 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 96.9914 | 3.65032 | ||||||||
\(707\) | − | 5.81658i | − | 0.218755i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.0472 | 0.414886 | 0.207443 | − | 0.978247i | \(-0.433486\pi\) | ||||
0.207443 | + | 0.978247i | \(0.433486\pi\) | |||||||
\(710\) | 2.92162 | − | 11.7587i | 0.109647 | − | 0.441297i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 75.4740i | 2.82851i | ||||||||
\(713\) | 18.1568i | 0.679976i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.993857 | + | 4.00000i | −0.0371681 | + | 0.149592i | ||||
\(716\) | −53.4017 | −1.99572 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 60.4534i | 2.25610i | ||||||||
\(719\) | −6.15676 | −0.229608 | −0.114804 | − | 0.993388i | \(-0.536624\pi\) | ||||
−0.114804 | + | 0.993388i | \(0.536624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.15676 | −0.0803218 | ||||||||
\(722\) | 25.8020i | 0.960252i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 45.5174 | 1.69164 | ||||||||
\(725\) | −29.5174 | − | 15.6332i | −1.09625 | − | 0.580601i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.89043i | − | 0.107200i | −0.998562 | − | 0.0536000i | \(-0.982930\pi\) | ||
0.998562 | − | 0.0536000i | \(-0.0170696\pi\) | |||||||
\(728\) | 8.34017i | 0.309107i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −41.6163 | − | 10.3402i | −1.54029 | − | 0.382707i | ||||
\(731\) | 7.03489 | 0.260195 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 25.7998i | − | 0.952936i | −0.879192 | − | 0.476468i | \(-0.841917\pi\) | ||
0.879192 | − | 0.476468i | \(-0.158083\pi\) | |||||||
\(734\) | −55.0349 | −2.03138 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −45.3751 | −1.67255 | ||||||||
\(737\) | 9.36069i | 0.344806i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.04718 | 0.0385212 | 0.0192606 | − | 0.999814i | \(-0.493869\pi\) | ||||
0.0192606 | + | 0.999814i | \(0.493869\pi\) | |||||||
\(740\) | 31.2039 | − | 125.587i | 1.14708 | − | 4.61668i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.1834i | 0.373845i | ||||||||
\(743\) | 9.97334i | 0.365886i | 0.983123 | + | 0.182943i | \(0.0585624\pi\) | ||||
−0.983123 | + | 0.182943i | \(0.941438\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.0144 | − | 8.45136i | −1.24619 | − | 0.309634i | ||||
\(746\) | −43.3484 | −1.58710 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.5174i | 0.421120i | ||||||||
\(749\) | −16.4969 | −0.602785 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.26633 | 0.119190 | 0.0595950 | − | 0.998223i | \(-0.481019\pi\) | ||||
0.0595950 | + | 0.998223i | \(0.481019\pi\) | |||||||
\(752\) | 64.7624i | 2.36164i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.6803 | −0.607462 | ||||||||
\(755\) | −12.6803 | − | 3.15061i | −0.461485 | − | 0.114663i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.9877i | 1.81683i | 0.418065 | + | 0.908417i | \(0.362708\pi\) | ||||
−0.418065 | + | 0.908417i | \(0.637292\pi\) | |||||||
\(758\) | 16.6803i | 0.605857i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15.0205 | + | 60.4534i | −0.544851 | + | 2.19288i | ||||
\(761\) | −2.61265 | −0.0947083 | −0.0473542 | − | 0.998878i | \(-0.515079\pi\) | ||||
−0.0473542 | + | 0.998878i | \(0.515079\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 12.8371i | − | 0.464734i | ||||||
\(764\) | 82.0288 | 2.96770 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −72.7091 | −2.62709 | ||||||||
\(767\) | 9.69878i | 0.350202i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.6742 | 0.565226 | 0.282613 | − | 0.959234i | \(-0.408799\pi\) | ||||
0.282613 | + | 0.959234i | \(0.408799\pi\) | |||||||
\(770\) | −11.7587 | − | 2.92162i | −0.423755 | − | 0.105288i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 44.6803i | − | 1.60808i | ||||||
\(773\) | − | 5.81205i | − | 0.209045i | −0.994523 | − | 0.104522i | \(-0.966669\pi\) | ||
0.994523 | − | 0.104522i | \(-0.0333314\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.2823 | − | 18.1568i | −1.23146 | − | 0.652210i | ||||
\(776\) | −76.3689 | −2.74148 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.2618i | 0.547162i | ||||||||
\(779\) | 20.0000 | 0.716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | − | 6.83710i | − | 0.244494i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13.8371 | −0.494182 | ||||||||
\(785\) | −2.65368 | + | 10.6803i | −0.0947140 | + | 0.381198i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 39.3484i | − | 1.40262i | −0.712857 | − | 0.701310i | \(-0.752599\pi\) | ||
0.712857 | − | 0.701310i | \(-0.247401\pi\) | |||||||
\(788\) | 62.7936i | 2.23693i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.99386 | − | 36.1978i | 0.319987 | − | 1.28786i | ||||
\(791\) | 5.23513 | 0.186140 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.83096i | − | 0.136041i | ||||||
\(794\) | −102.410 | −3.63439 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −120.666 | −4.27688 | ||||||||
\(797\) | 28.2823i | 1.00181i | 0.865502 | + | 0.500905i | \(0.167000\pi\) | ||||
−0.865502 | + | 0.500905i | \(0.833000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.04718 | −0.178556 | ||||||||
\(800\) | 45.3751 | − | 85.6740i | 1.60425 | − | 3.02903i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 36.9360i | − | 1.30426i | ||||||
\(803\) | − | 14.1568i | − | 0.499581i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.07838 | + | 1.26180i | 0.178989 | + | 0.0444724i | ||||
\(806\) | −19.3730 | −0.682384 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 52.6369i | 1.85176i | ||||||||
\(809\) | −15.6742 | −0.551076 | −0.275538 | − | 0.961290i | \(-0.588856\pi\) | ||||
−0.275538 | + | 0.961290i | \(0.588856\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.1666 | −1.48067 | −0.740335 | − | 0.672238i | \(-0.765333\pi\) | ||||
−0.740335 | + | 0.672238i | \(0.765333\pi\) | |||||||
\(812\) | − | 35.6742i | − | 1.25192i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 58.7214 | 2.05818 | ||||||||
\(815\) | −5.30737 | + | 21.3607i | −0.185909 | + | 0.748232i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.0821i | 0.702583i | ||||||||
\(818\) | 33.4719i | 1.17032i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −75.2905 | − | 18.7070i | −2.62926 | − | 0.653277i | ||||
\(821\) | 39.0472 | 1.36276 | 0.681378 | − | 0.731932i | \(-0.261381\pi\) | ||||
0.681378 | + | 0.731932i | \(0.261381\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 36.5646i | − | 1.27456i | −0.770631 | − | 0.637281i | \(-0.780059\pi\) | ||
0.770631 | − | 0.637281i | \(-0.219941\pi\) | |||||||
\(824\) | 19.5174 | 0.679922 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.5113 | −0.992035 | ||||||||
\(827\) | 50.2245i | 1.74648i | 0.487294 | + | 0.873238i | \(0.337984\pi\) | ||||
−0.487294 | + | 0.873238i | \(0.662016\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.8371 | −1.14048 | −0.570240 | − | 0.821478i | \(-0.693150\pi\) | ||||
−0.570240 | + | 0.821478i | \(0.693150\pi\) | |||||||
\(830\) | 40.1978 | + | 9.98771i | 1.39529 | + | 0.346679i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 22.9093i | − | 0.794238i | ||||||
\(833\) | − | 1.07838i | − | 0.0373636i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.3545 | + | 41.6742i | −0.358334 | + | 1.44220i | ||||
\(836\) | −32.8781 | −1.13711 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 78.5523i | − | 2.71355i | ||||||
\(839\) | −13.3607 | −0.461262 | −0.230631 | − | 0.973041i | \(-0.574079\pi\) | ||||
−0.230631 | + | 0.973041i | \(0.574079\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6270 | 0.538863 | ||||||||
\(842\) | 41.0805i | 1.41573i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 73.0226 | 2.51354 | ||||||||
\(845\) | −26.3679 | − | 6.55148i | −0.907083 | − | 0.225378i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000i | 0.240523i | ||||||||
\(848\) | − | 52.0098i | − | 1.78603i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.9093 | + | 6.83710i | 0.442787 | + | 0.234511i | ||||
\(851\) | −25.3607 | −0.869353 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 39.6430i | − | 1.35735i | −0.734438 | − | 0.678675i | \(-0.762554\pi\) | ||
0.734438 | − | 0.678675i | \(-0.237446\pi\) | |||||||
\(854\) | 11.2618 | 0.385371 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 149.288 | 5.10256 | ||||||||
\(857\) | − | 29.7054i | − | 1.01472i | −0.861735 | − | 0.507359i | \(-0.830622\pi\) | ||
0.861735 | − | 0.507359i | \(-0.169378\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.07838 | 0.105033 | 0.0525164 | − | 0.998620i | \(-0.483276\pi\) | ||||
0.0525164 | + | 0.998620i | \(0.483276\pi\) | |||||||
\(860\) | 18.7838 | − | 75.5995i | 0.640521 | − | 2.57792i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 27.9421i | − | 0.951713i | ||||||
\(863\) | 6.39350i | 0.217637i | 0.994062 | + | 0.108819i | \(0.0347068\pi\) | ||||
−0.994062 | + | 0.108819i | \(0.965293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0989 | − | 48.6947i | 0.411375 | − | 1.65567i | ||||
\(866\) | 55.3751 | 1.88172 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 41.4329i | − | 1.40633i | ||||||
\(869\) | 12.3135 | 0.417707 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.31351 | 0.146158 | ||||||||
\(872\) | 116.169i | 3.93397i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.5174 | 0.660188 | ||||||||
\(875\) | −7.46081 | + | 8.32684i | −0.252221 | + | 0.281499i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.21622i | 0.0410689i | 0.999789 | + | 0.0205345i | \(0.00653678\pi\) | ||||
−0.999789 | + | 0.0205345i | \(0.993463\pi\) | |||||||
\(878\) | − | 45.8453i | − | 1.54721i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 60.0554 | + | 14.9216i | 2.02447 | + | 0.503008i | ||||
\(881\) | −15.9733 | −0.538155 | −0.269078 | − | 0.963118i | \(-0.586719\pi\) | ||||
−0.269078 | + | 0.963118i | \(0.586719\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.6865i | 0.393282i | 0.980476 | + | 0.196641i | \(0.0630033\pi\) | ||||
−0.980476 | + | 0.196641i | \(0.936997\pi\) | |||||||
\(884\) | 5.30737 | 0.178506 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34.7070 | 1.16600 | ||||||||
\(887\) | − | 25.6209i | − | 0.860265i | −0.902766 | − | 0.430132i | \(-0.858467\pi\) | ||
0.902766 | − | 0.430132i | \(-0.141533\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.84324 | −0.0618204 | ||||||||
\(890\) | −12.1834 | + | 49.0349i | −0.408389 | + | 1.64365i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 115.744i | 3.87540i | ||||||||
\(893\) | − | 14.4079i | − | 0.482141i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.7009 | − | 5.39189i | −0.725380 | − | 0.180231i | ||||
\(896\) | 28.5669 | 0.954353 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39.6286i | 1.32242i | ||||||||
\(899\) | 51.8310 | 1.72866 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.05332 | 0.135036 | ||||||||
\(902\) | − | 35.2039i | − | 1.17216i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −47.3751 | −1.57567 | ||||||||
\(905\) | 18.4969 | + | 4.59583i | 0.614859 | + | 0.152770i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 57.7563i | 1.91777i | 0.283802 | + | 0.958883i | \(0.408404\pi\) | ||||
−0.283802 | + | 0.958883i | \(0.591596\pi\) | |||||||
\(908\) | 61.5052i | 2.04112i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.34632 | + | 5.41855i | −0.0446299 | + | 0.179623i | ||||
\(911\) | 35.9877 | 1.19233 | 0.596163 | − | 0.802863i | \(-0.296691\pi\) | ||||
0.596163 | + | 0.802863i | \(0.296691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.6742i | 0.452550i | ||||||||
\(914\) | −38.3545 | −1.26866 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 68.5523 | 2.26503 | ||||||||
\(917\) | 1.47641i | 0.0487553i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.7214 | −1.54120 | −0.770598 | − | 0.637321i | \(-0.780042\pi\) | ||||
−0.770598 | + | 0.637321i | \(0.780042\pi\) | |||||||
\(920\) | −45.9565 | − | 11.4186i | −1.51514 | − | 0.376458i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.921622i | 0.0303520i | ||||||||
\(923\) | − | 1.84324i | − | 0.0606711i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.3607 | − | 47.8843i | 0.833854 | − | 1.57443i | ||||
\(926\) | −26.6681 | −0.876367 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 129.529i | 4.25201i | ||||||||
\(929\) | −53.0493 | −1.74049 | −0.870245 | − | 0.492619i | \(-0.836040\pi\) | ||||
−0.870245 | + | 0.492619i | \(0.836040\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.07838 | 0.100890 | ||||||||
\(932\) | − | 36.1256i | − | 1.18333i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −31.2039 | −1.02102 | ||||||||
\(935\) | −1.16290 | + | 4.68035i | −0.0380308 | + | 0.153064i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.1256i | 0.526799i | 0.964687 | + | 0.263400i | \(0.0848437\pi\) | ||||
−0.964687 | + | 0.263400i | \(0.915156\pi\) | |||||||
\(938\) | 12.6803i | 0.414028i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.4764 | + | 54.2388i | −0.439552 | + | 1.76908i | ||||
\(941\) | −24.7070 | −0.805425 | −0.402713 | − | 0.915326i | \(-0.631933\pi\) | ||||
−0.402713 | + | 0.915326i | \(0.631933\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.2039i | 0.495108i | ||||||||
\(944\) | 145.616 | 4.73940 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.3484 | 1.14928 | ||||||||
\(947\) | − | 6.53797i | − | 0.212455i | −0.994342 | − | 0.106228i | \(-0.966123\pi\) | ||
0.994342 | − | 0.106228i | \(-0.0338772\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.52359 | −0.211765 | ||||||||
\(950\) | −19.5174 | + | 36.8515i | −0.633230 | + | 1.19562i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.75872i | 0.316282i | ||||||||
\(953\) | − | 6.11327i | − | 0.198028i | −0.995086 | − | 0.0990142i | \(-0.968431\pi\) | ||
0.995086 | − | 0.0990142i | \(-0.0315689\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33.3340 | + | 8.28231i | 1.07866 | + | 0.268009i | ||||
\(956\) | 124.750 | 4.03471 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 52.8781i | 1.70842i | ||||||||
\(959\) | 4.43907 | 0.143345 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.1978 | 0.941864 | ||||||||
\(962\) | − | 27.0595i | − | 0.872432i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 78.3956 | 2.52495 | ||||||||
\(965\) | 4.51130 | − | 18.1568i | 0.145224 | − | 0.584487i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.6209i | 0.823912i | 0.911204 | + | 0.411956i | \(0.135154\pi\) | ||||
−0.911204 | + | 0.411956i | \(0.864846\pi\) | |||||||
\(968\) | − | 63.3461i | − | 2.03602i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −49.6163 | − | 12.3279i | −1.59308 | − | 0.395825i | ||||
\(971\) | −4.05332 | −0.130077 | −0.0650387 | − | 0.997883i | \(-0.520717\pi\) | ||||
−0.0650387 | + | 0.997883i | \(0.520717\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.6020i | 0.436059i | ||||||||
\(974\) | −62.7214 | −2.00972 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −57.5174 | −1.84109 | ||||||||
\(977\) | − | 3.81205i | − | 0.121958i | −0.998139 | − | 0.0609791i | \(-0.980578\pi\) | ||
0.998139 | − | 0.0609791i | \(-0.0194223\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.6803 | −0.533106 | ||||||||
\(980\) | −11.5886 | − | 2.87936i | −0.370185 | − | 0.0919778i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.41855i | 0.172913i | ||||||||
\(983\) | − | 24.0000i | − | 0.765481i | −0.923856 | − | 0.382741i | \(-0.874980\pi\) | ||
0.923856 | − | 0.382741i | \(-0.125020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.34017 | + | 25.5174i | −0.202015 | + | 0.813053i | ||||
\(986\) | −19.5174 | −0.621562 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.1506i | 0.482005i | ||||||||
\(989\) | −15.2663 | −0.485441 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.4079 | −1.34713 | −0.673565 | − | 0.739128i | \(-0.735238\pi\) | ||||
−0.673565 | + | 0.739128i | \(0.735238\pi\) | |||||||
\(992\) | 150.439i | 4.77643i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.41855 | 0.171866 | ||||||||
\(995\) | −49.0349 | − | 12.1834i | −1.55451 | − | 0.386240i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 43.4740i | − | 1.37683i | −0.725315 | − | 0.688417i | \(-0.758306\pi\) | ||
0.725315 | − | 0.688417i | \(-0.241694\pi\) | |||||||
\(998\) | 73.7030i | 2.33303i | ||||||||
\(999\) | 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 | 315.2.d.e.64.1 | 6 | ||
3.2 | odd | 2 | 105.2.d.b.64.6 | yes | 6 | ||
4.3 | odd | 2 | 5040.2.t.v.1009.1 | 6 | |||
5.2 | odd | 4 | 1575.2.a.x.1.3 | 3 | |||
5.3 | odd | 4 | 1575.2.a.w.1.1 | 3 | |||
5.4 | even | 2 | inner | 315.2.d.e.64.6 | 6 | ||
7.6 | odd | 2 | 2205.2.d.l.1324.1 | 6 | |||
12.11 | even | 2 | 1680.2.t.k.1009.3 | 6 | |||
15.2 | even | 4 | 525.2.a.j.1.1 | 3 | |||
15.8 | even | 4 | 525.2.a.k.1.3 | 3 | |||
15.14 | odd | 2 | 105.2.d.b.64.1 | ✓ | 6 | ||
20.19 | odd | 2 | 5040.2.t.v.1009.2 | 6 | |||
21.2 | odd | 6 | 735.2.q.e.214.6 | 12 | |||
21.5 | even | 6 | 735.2.q.f.214.6 | 12 | |||
21.11 | odd | 6 | 735.2.q.e.79.1 | 12 | |||
21.17 | even | 6 | 735.2.q.f.79.1 | 12 | |||
21.20 | even | 2 | 735.2.d.b.589.6 | 6 | |||
35.34 | odd | 2 | 2205.2.d.l.1324.6 | 6 | |||
60.23 | odd | 4 | 8400.2.a.dj.1.2 | 3 | |||
60.47 | odd | 4 | 8400.2.a.dg.1.2 | 3 | |||
60.59 | even | 2 | 1680.2.t.k.1009.6 | 6 | |||
105.44 | odd | 6 | 735.2.q.e.214.1 | 12 | |||
105.59 | even | 6 | 735.2.q.f.79.6 | 12 | |||
105.62 | odd | 4 | 3675.2.a.bi.1.1 | 3 | |||
105.74 | odd | 6 | 735.2.q.e.79.6 | 12 | |||
105.83 | odd | 4 | 3675.2.a.bj.1.3 | 3 | |||
105.89 | even | 6 | 735.2.q.f.214.1 | 12 | |||
105.104 | even | 2 | 735.2.d.b.589.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.b.64.1 | ✓ | 6 | 15.14 | odd | 2 | ||
105.2.d.b.64.6 | yes | 6 | 3.2 | odd | 2 | ||
315.2.d.e.64.1 | 6 | 1.1 | even | 1 | trivial | ||
315.2.d.e.64.6 | 6 | 5.4 | even | 2 | inner | ||
525.2.a.j.1.1 | 3 | 15.2 | even | 4 | |||
525.2.a.k.1.3 | 3 | 15.8 | even | 4 | |||
735.2.d.b.589.1 | 6 | 105.104 | even | 2 | |||
735.2.d.b.589.6 | 6 | 21.20 | even | 2 | |||
735.2.q.e.79.1 | 12 | 21.11 | odd | 6 | |||
735.2.q.e.79.6 | 12 | 105.74 | odd | 6 | |||
735.2.q.e.214.1 | 12 | 105.44 | odd | 6 | |||
735.2.q.e.214.6 | 12 | 21.2 | odd | 6 | |||
735.2.q.f.79.1 | 12 | 21.17 | even | 6 | |||
735.2.q.f.79.6 | 12 | 105.59 | even | 6 | |||
735.2.q.f.214.1 | 12 | 105.89 | even | 6 | |||
735.2.q.f.214.6 | 12 | 21.5 | even | 6 | |||
1575.2.a.w.1.1 | 3 | 5.3 | odd | 4 | |||
1575.2.a.x.1.3 | 3 | 5.2 | odd | 4 | |||
1680.2.t.k.1009.3 | 6 | 12.11 | even | 2 | |||
1680.2.t.k.1009.6 | 6 | 60.59 | even | 2 | |||
2205.2.d.l.1324.1 | 6 | 7.6 | odd | 2 | |||
2205.2.d.l.1324.6 | 6 | 35.34 | odd | 2 | |||
3675.2.a.bi.1.1 | 3 | 105.62 | odd | 4 | |||
3675.2.a.bj.1.3 | 3 | 105.83 | odd | 4 | |||
5040.2.t.v.1009.1 | 6 | 4.3 | odd | 2 | |||
5040.2.t.v.1009.2 | 6 | 20.19 | odd | 2 | |||
8400.2.a.dg.1.2 | 3 | 60.47 | odd | 4 | |||
8400.2.a.dj.1.2 | 3 | 60.23 | odd | 4 |