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 | 64.6 | ||
Root | \(-0.854638 - 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.64 |
Dual form | 315.2.d.e.64.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | \(0.407279\pi\) | ||||
−0.287190 | + | 0.957873i | \(0.592721\pi\) | |||||||
\(3\) | 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 | \(-0.959207\pi\) | ||
0.991799 | − | 0.127806i | \(-0.0407935\pi\) | |||||||
\(14\) | −2.70928 | −0.724084 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.8371 | 3.45928 | ||||||||
\(17\) | − | 1.07838i | − | 0.261545i | −0.991412 | − | 0.130773i | \(-0.958254\pi\) | ||
0.991412 | − | 0.130773i | \(-0.0417457\pi\) | |||||||
\(18\) | 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 | \(0.0784531\pi\) | ||||
−0.969780 | + | 0.243980i | \(0.921547\pi\) | |||||||
\(24\) | 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 | \(0.349858\pi\) | ||||
−0.454387 | + | 0.890804i | \(0.650142\pi\) | |||||||
\(38\) | − | 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 | \(0.165719\pi\) | ||||
−0.867510 | + | 0.497419i | \(0.834281\pi\) | |||||||
\(44\) | 10.6803 | 1.61012 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.34017 | −0.934808 | ||||||||
\(47\) | − | 4.68035i | − | 0.682699i | −0.939937 | − | 0.341349i | \(-0.889116\pi\) | ||
0.939937 | − | 0.341349i | \(-0.110884\pi\) | |||||||
\(48\) | 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 | \(0.0831129\pi\) | ||||
−0.966105 | + | 0.258150i | \(0.916887\pi\) | |||||||
\(54\) | 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 | \(0.0922917\pi\) | ||||
−0.958260 | + | 0.285898i | \(0.907708\pi\) | |||||||
\(68\) | 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 | \(-0.864051\pi\) | ||
0.910172 | − | 0.414231i | \(-0.135949\pi\) | |||||||
\(74\) | −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 | \(0.122438\pi\) | ||||
−0.926930 | + | 0.375235i | \(0.877562\pi\) | |||||||
\(84\) | 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 | \(-0.859067\pi\) | ||
0.903576 | − | 0.428429i | \(-0.140933\pi\) | |||||||
\(98\) | − | 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 | \(0.0338862\pi\) | ||||
−0.994339 | + | 0.106256i | \(0.966114\pi\) | |||||||
\(104\) | −8.34017 | −0.817821 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.1834 | −0.989101 | ||||||||
\(107\) | 16.4969i | 1.59482i | 0.603439 | + | 0.797409i | \(0.293797\pi\) | ||||
−0.603439 | + | 0.797409i | \(0.706203\pi\) | |||||||
\(108\) | 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 | \(-0.920805\pi\) | ||
0.969209 | − | 0.246240i | \(-0.0791951\pi\) | |||||||
\(114\) | 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 | \(0.0260607\pi\) | ||||
−0.996650 | + | 0.0817808i | \(0.973939\pi\) | |||||||
\(128\) | − | 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 | \(-0.939272\pi\) | ||
0.981856 | − | 0.189628i | \(-0.0607281\pi\) | |||||||
\(138\) | 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 | \(0.0629232\pi\) | ||||
−0.980525 | + | 0.196394i | \(0.937077\pi\) | |||||||
\(158\) | − | 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 | \(0.125968\pi\) | ||||
−0.922712 | + | 0.385491i | \(0.874032\pi\) | |||||||
\(164\) | 34.6947 | 2.70920 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.5236 | −1.43771 | ||||||||
\(167\) | 19.2039i | 1.48605i | 0.669266 | + | 0.743023i | \(0.266609\pi\) | ||||
−0.669266 | + | 0.743023i | \(0.733391\pi\) | |||||||
\(168\) | 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 | \(-0.674777\pi\) | ||
0.521902 | − | 0.853005i | \(-0.325223\pi\) | |||||||
\(174\) | 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 | \(-0.902637\pi\) | ||
0.953583 | − | 0.301129i | \(-0.0973635\pi\) | |||||||
\(194\) | 22.8638 | 1.64152 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.34017 | 0.381441 | ||||||||
\(197\) | 11.7587i | 0.837774i | 0.908038 | + | 0.418887i | \(0.137580\pi\) | ||||
−0.908038 | + | 0.418887i | \(0.862420\pi\) | |||||||
\(198\) | 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 | \(0.258487\pi\) | ||||
−0.688005 | + | 0.725706i | \(0.741513\pi\) | |||||||
\(224\) | −19.3896 | −1.29552 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.1834 | 0.943467 | ||||||||
\(227\) | 11.5174i | 0.764440i | 0.924071 | + | 0.382220i | \(0.124840\pi\) | ||||
−0.924071 | + | 0.382220i | \(0.875160\pi\) | |||||||
\(228\) | 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 | \(-0.928875\pi\) | ||
0.975140 | − | 0.221591i | \(-0.0711248\pi\) | |||||||
\(234\) | 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 | \(0.0506304\pi\) | ||||
−0.987377 | + | 0.158390i | \(0.949370\pi\) | |||||||
\(258\) | 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 | \(0.0558309\pi\) | ||||
−0.984657 | + | 0.174500i | \(0.944169\pi\) | |||||||
\(264\) | 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 | \(-0.678334\pi\) | ||
0.531401 | − | 0.847121i | \(-0.321666\pi\) | |||||||
\(278\) | − | 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 | \(-0.753636\pi\) | ||
0.715138 | − | 0.698984i | \(-0.246364\pi\) | |||||||
\(284\) | 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 | \(-0.972802\pi\) | ||
0.996352 | − | 0.0853415i | \(-0.0271981\pi\) | |||||||
\(294\) | 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 | \(-0.903419\pi\) | ||
0.954321 | − | 0.298785i | \(-0.0965813\pi\) | |||||||
\(308\) | 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 | \(-0.623525\pi\) | ||
0.378399 | − | 0.925643i | \(-0.376475\pi\) | |||||||
\(314\) | −13.3340 | −0.752483 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.8781 | 1.84954 | ||||||||
\(317\) | 17.9155i | 1.00623i | 0.864218 | + | 0.503117i | \(0.167813\pi\) | ||||
−0.864218 | + | 0.503117i | \(0.832187\pi\) | |||||||
\(318\) | 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 | \(-0.757284\pi\) | ||
0.723101 | − | 0.690742i | \(-0.242716\pi\) | |||||||
\(338\) | 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 | \(-0.850480\pi\) | ||
0.891690 | − | 0.452647i | \(-0.149520\pi\) | |||||||
\(348\) | 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 | \(-0.598278\pi\) | ||
0.303867 | − | 0.952715i | \(-0.401722\pi\) | |||||||
\(354\) | 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 | \(0.177875\pi\) | ||||
−0.847886 | + | 0.530178i | \(0.822125\pi\) | |||||||
\(368\) | 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 | \(0.135947\pi\) | ||||
−0.910175 | + | 0.414224i | \(0.864053\pi\) | |||||||
\(374\) | −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 | \(0.240485\pi\) | ||||
−0.727926 | + | 0.685656i | \(0.759515\pi\) | |||||||
\(384\) | 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 | \(0.397457\pi\) | ||||
−0.316604 | + | 0.948558i | \(0.602543\pi\) | |||||||
\(398\) | 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 | \(-0.836588\pi\) | ||
0.871092 | − | 0.491120i | \(-0.163412\pi\) | |||||||
\(434\) | 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 | \(-0.901570\pi\) | ||
0.952569 | − | 0.304321i | \(-0.0984296\pi\) | |||||||
\(444\) | 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 | \(0.107424\pi\) | ||||
−0.943591 | + | 0.331113i | \(0.892576\pi\) | |||||||
\(458\) | − | 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 | \(0.0734564\pi\) | ||||
−0.973491 | + | 0.228727i | \(0.926544\pi\) | |||||||
\(464\) | −92.4366 | −4.29126 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.3279 | 0.849023 | ||||||||
\(467\) | 11.5174i | 0.532964i | 0.963840 | + | 0.266482i | \(0.0858613\pi\) | ||||
−0.963840 | + | 0.266482i | \(0.914139\pi\) | |||||||
\(468\) | 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 | \(0.175758\pi\) | ||||
−0.851394 | + | 0.524527i | \(0.824242\pi\) | |||||||
\(488\) | 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 | \(-0.862047\pi\) | ||
0.907546 | − | 0.419952i | \(-0.137953\pi\) | |||||||
\(504\) | 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 | \(-0.972127\pi\) | ||
0.996169 | − | 0.0874539i | \(-0.0278730\pi\) | |||||||
\(524\) | 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 | \(0.0778023\pi\) | ||||
−0.970277 | + | 0.241997i | \(0.922198\pi\) | |||||||
\(548\) | 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 | \(0.190962\pi\) | ||||
−0.825378 | + | 0.564580i | \(0.809038\pi\) | |||||||
\(558\) | 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 | \(0.431309\pi\) | ||||
−0.214128 | + | 0.976806i | \(0.568691\pi\) | |||||||
\(564\) | 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 | \(0.360071\pi\) | ||||
−0.425577 | + | 0.904922i | \(0.639929\pi\) | |||||||
\(578\) | 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 | \(-0.733149\pi\) | ||
0.668699 | − | 0.743533i | \(-0.266851\pi\) | |||||||
\(588\) | 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 | \(0.223765\pi\) | ||||
−0.762920 | + | 0.646493i | \(0.776235\pi\) | |||||||
\(594\) | 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 | \(-0.914699\pi\) | ||
0.964308 | − | 0.264784i | \(-0.0853008\pi\) | |||||||
\(608\) | − | 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 | \(0.101459\pi\) | ||||
−0.949630 | + | 0.313372i | \(0.898541\pi\) | |||||||
\(614\) | 28.3668 | 1.14479 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.0989 | −0.729225 | ||||||||
\(617\) | 22.7649i | 0.916479i | 0.888829 | + | 0.458240i | \(0.151520\pi\) | ||||
−0.888829 | + | 0.458240i | \(0.848480\pi\) | |||||||
\(618\) | 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 | \(0.208469\pi\) | ||||
−0.793094 | + | 0.609100i | \(0.791531\pi\) | |||||||
\(644\) | 12.4969 | 0.492448 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.99386 | −0.353859 | ||||||||
\(647\) | 19.2039i | 0.754985i | 0.926013 | + | 0.377492i | \(0.123214\pi\) | ||||
−0.926013 | + | 0.377492i | \(0.876786\pi\) | |||||||
\(648\) | 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 | \(-0.811294\pi\) | ||
0.829358 | − | 0.558718i | \(-0.188706\pi\) | |||||||
\(654\) | 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 | \(-0.986437\pi\) | ||
0.999092 | − | 0.0425962i | \(-0.0135629\pi\) | |||||||
\(674\) | 68.7091 | 2.64658 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −64.8864 | −2.49563 | ||||||||
\(677\) | − | 19.5486i | − | 0.751315i | −0.926758 | − | 0.375658i | \(-0.877417\pi\) | ||
0.926758 | − | 0.375658i | \(-0.122583\pi\) | |||||||
\(678\) | 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 | \(0.0725893\pi\) | ||||
−0.974110 | + | 0.226074i | \(0.927411\pi\) | |||||||
\(684\) | 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 | \(0.0170696\pi\) | ||||
−0.998562 | + | 0.0536000i | \(0.982930\pi\) | |||||||
\(728\) | − | 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 | \(0.158083\pi\) | ||||
−0.879192 | + | 0.476468i | \(0.841917\pi\) | |||||||
\(734\) | −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 | \(-0.941438\pi\) | ||
0.983123 | − | 0.182943i | \(-0.0585624\pi\) | |||||||
\(744\) | 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 | \(-0.637292\pi\) | ||
0.418065 | − | 0.908417i | \(-0.362708\pi\) | |||||||
\(758\) | − | 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 | \(0.0333314\pi\) | ||||
−0.994523 | + | 0.104522i | \(0.966669\pi\) | |||||||
\(774\) | 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 | \(0.247401\pi\) | ||||
−0.712857 | + | 0.701310i | \(0.752599\pi\) | |||||||
\(788\) | − | 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 | \(-0.833000\pi\) | ||
0.865502 | − | 0.500905i | \(-0.167000\pi\) | |||||||
\(798\) | 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 | \(0.219941\pi\) | ||||
−0.770631 | + | 0.637281i | \(0.780059\pi\) | |||||||
\(824\) | 19.5174 | 0.679922 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.5113 | −0.992035 | ||||||||
\(827\) | − | 50.2245i | − | 1.74648i | −0.487294 | − | 0.873238i | \(-0.662016\pi\) | ||
0.487294 | − | 0.873238i | \(-0.337984\pi\) | |||||||
\(828\) | 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 | \(0.237446\pi\) | ||||
−0.734438 | + | 0.678675i | \(0.762554\pi\) | |||||||
\(854\) | 11.2618 | 0.385371 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 149.288 | 5.10256 | ||||||||
\(857\) | 29.7054i | 1.01472i | 0.861735 | + | 0.507359i | \(0.169378\pi\) | ||||
−0.861735 | + | 0.507359i | \(0.830622\pi\) | |||||||
\(858\) | 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 | \(-0.965293\pi\) | ||
0.994062 | − | 0.108819i | \(-0.0347068\pi\) | |||||||
\(864\) | 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 | \(-0.993463\pi\) | ||
0.999789 | − | 0.0205345i | \(-0.00653678\pi\) | |||||||
\(878\) | 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 | \(-0.936997\pi\) | ||
0.980476 | − | 0.196641i | \(-0.0630033\pi\) | |||||||
\(884\) | 5.30737 | 0.178506 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34.7070 | 1.16600 | ||||||||
\(887\) | 25.6209i | 0.860265i | 0.902766 | + | 0.430132i | \(0.141533\pi\) | ||||
−0.902766 | + | 0.430132i | \(0.858467\pi\) | |||||||
\(888\) | 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 | \(-0.591596\pi\) | ||
0.283802 | − | 0.958883i | \(-0.408404\pi\) | |||||||
\(908\) | − | 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 | \(-0.915156\pi\) | ||
0.964687 | − | 0.263400i | \(-0.0848437\pi\) | |||||||
\(938\) | − | 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 | \(0.0338772\pi\) | ||||
−0.994342 | + | 0.106228i | \(0.966123\pi\) | |||||||
\(948\) | 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 | \(0.0315689\pi\) | ||||
−0.995086 | + | 0.0990142i | \(0.968431\pi\) | |||||||
\(954\) | 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 | \(-0.864846\pi\) | ||
0.911204 | − | 0.411956i | \(-0.135154\pi\) | |||||||
\(968\) | 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 | \(0.0194223\pi\) | ||||
−0.998139 | + | 0.0609791i | \(0.980578\pi\) | |||||||
\(978\) | 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 | \(0.125020\pi\) | ||||
−0.923856 | + | 0.382741i | \(0.874980\pi\) | |||||||
\(984\) | 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 | \(0.241694\pi\) | ||||
−0.725315 | + | 0.688417i | \(0.758306\pi\) | |||||||
\(998\) | − | 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.64.6 | 6 | ||
3.2 | odd | 2 | 105.2.d.b.64.1 | ✓ | 6 | ||
4.3 | odd | 2 | 5040.2.t.v.1009.2 | 6 | |||
5.2 | odd | 4 | 1575.2.a.w.1.1 | 3 | |||
5.3 | odd | 4 | 1575.2.a.x.1.3 | 3 | |||
5.4 | even | 2 | inner | 315.2.d.e.64.1 | 6 | ||
7.6 | odd | 2 | 2205.2.d.l.1324.6 | 6 | |||
12.11 | even | 2 | 1680.2.t.k.1009.6 | 6 | |||
15.2 | even | 4 | 525.2.a.k.1.3 | 3 | |||
15.8 | even | 4 | 525.2.a.j.1.1 | 3 | |||
15.14 | odd | 2 | 105.2.d.b.64.6 | yes | 6 | ||
20.19 | odd | 2 | 5040.2.t.v.1009.1 | 6 | |||
21.2 | odd | 6 | 735.2.q.e.214.1 | 12 | |||
21.5 | even | 6 | 735.2.q.f.214.1 | 12 | |||
21.11 | odd | 6 | 735.2.q.e.79.6 | 12 | |||
21.17 | even | 6 | 735.2.q.f.79.6 | 12 | |||
21.20 | even | 2 | 735.2.d.b.589.1 | 6 | |||
35.34 | odd | 2 | 2205.2.d.l.1324.1 | 6 | |||
60.23 | odd | 4 | 8400.2.a.dg.1.2 | 3 | |||
60.47 | odd | 4 | 8400.2.a.dj.1.2 | 3 | |||
60.59 | even | 2 | 1680.2.t.k.1009.3 | 6 | |||
105.44 | odd | 6 | 735.2.q.e.214.6 | 12 | |||
105.59 | even | 6 | 735.2.q.f.79.1 | 12 | |||
105.62 | odd | 4 | 3675.2.a.bj.1.3 | 3 | |||
105.74 | odd | 6 | 735.2.q.e.79.1 | 12 | |||
105.83 | odd | 4 | 3675.2.a.bi.1.1 | 3 | |||
105.89 | even | 6 | 735.2.q.f.214.6 | 12 | |||
105.104 | even | 2 | 735.2.d.b.589.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.b.64.1 | ✓ | 6 | 3.2 | odd | 2 | ||
105.2.d.b.64.6 | yes | 6 | 15.14 | odd | 2 | ||
315.2.d.e.64.1 | 6 | 5.4 | even | 2 | inner | ||
315.2.d.e.64.6 | 6 | 1.1 | even | 1 | trivial | ||
525.2.a.j.1.1 | 3 | 15.8 | even | 4 | |||
525.2.a.k.1.3 | 3 | 15.2 | even | 4 | |||
735.2.d.b.589.1 | 6 | 21.20 | even | 2 | |||
735.2.d.b.589.6 | 6 | 105.104 | even | 2 | |||
735.2.q.e.79.1 | 12 | 105.74 | odd | 6 | |||
735.2.q.e.79.6 | 12 | 21.11 | odd | 6 | |||
735.2.q.e.214.1 | 12 | 21.2 | odd | 6 | |||
735.2.q.e.214.6 | 12 | 105.44 | odd | 6 | |||
735.2.q.f.79.1 | 12 | 105.59 | even | 6 | |||
735.2.q.f.79.6 | 12 | 21.17 | even | 6 | |||
735.2.q.f.214.1 | 12 | 21.5 | even | 6 | |||
735.2.q.f.214.6 | 12 | 105.89 | even | 6 | |||
1575.2.a.w.1.1 | 3 | 5.2 | odd | 4 | |||
1575.2.a.x.1.3 | 3 | 5.3 | odd | 4 | |||
1680.2.t.k.1009.3 | 6 | 60.59 | even | 2 | |||
1680.2.t.k.1009.6 | 6 | 12.11 | even | 2 | |||
2205.2.d.l.1324.1 | 6 | 35.34 | odd | 2 | |||
2205.2.d.l.1324.6 | 6 | 7.6 | odd | 2 | |||
3675.2.a.bi.1.1 | 3 | 105.83 | odd | 4 | |||
3675.2.a.bj.1.3 | 3 | 105.62 | odd | 4 | |||
5040.2.t.v.1009.1 | 6 | 20.19 | odd | 2 | |||
5040.2.t.v.1009.2 | 6 | 4.3 | odd | 2 | |||
8400.2.a.dg.1.2 | 3 | 60.23 | odd | 4 | |||
8400.2.a.dj.1.2 | 3 | 60.47 | odd | 4 |