Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2520,2,Mod(361,2520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2520.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2520.bi (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.1223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2520.361 |
Dual form | 2520.2.bi.e.1801.1 |
$q$-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 \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(1081\) | \(1261\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | −0.931505 | − | 0.363727i | \(-0.881504\pi\) |
0.780750 | + | 0.624844i | \(0.214837\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | −0.832050 | −0.416025 | − | 0.909353i | \(-0.636577\pi\) | ||||
−0.416025 | + | 0.909353i | \(0.636577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | + | 4.33013i | 0.573539 | + | 0.993399i | 0.996199 | + | 0.0871106i | \(0.0277634\pi\) |
−0.422659 | + | 0.906289i | \(0.638903\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.50000 | + | 6.06218i | 0.729800 | + | 1.26405i | 0.956967 | + | 0.290196i | \(0.0937204\pi\) |
−0.227167 | + | 0.973856i | \(0.572946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.50000 | − | 0.866025i | −0.422577 | − | 0.146385i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50000 | + | 4.33013i | 0.410997 | + | 0.711868i | 0.994999 | − | 0.0998840i | \(-0.0318472\pi\) |
−0.584002 | + | 0.811752i | \(0.698514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00000 | 0.780869 | 0.390434 | − | 0.920631i | \(-0.372325\pi\) | ||||
0.390434 | + | 0.920631i | \(0.372325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | 0.914991 | 0.457496 | − | 0.889212i | \(-0.348747\pi\) | ||||
0.457496 | + | 0.889212i | \(0.348747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.50000 | − | 7.79423i | −0.656392 | − | 1.13691i | −0.981543 | − | 0.191243i | \(-0.938748\pi\) |
0.325150 | − | 0.945662i | \(-0.394585\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.50000 | − | 9.52628i | 0.755483 | − | 1.30854i | −0.189651 | − | 0.981852i | \(-0.560736\pi\) |
0.945134 | − | 0.326683i | \(-0.105931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | − | 6.92820i | 0.520756 | − | 0.901975i | −0.478953 | − | 0.877841i | \(-0.658984\pi\) |
0.999709 | − | 0.0241347i | \(-0.00768307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | + | 10.3923i | 0.768221 | + | 1.33060i | 0.938527 | + | 0.345207i | \(0.112191\pi\) |
−0.170305 | + | 0.985391i | \(0.554475\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.50000 | + | 2.59808i | 0.186052 | + | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | + | 10.3923i | −0.702247 | + | 1.21633i | 0.265429 | + | 0.964130i | \(0.414486\pi\) |
−0.967676 | + | 0.252197i | \(0.918847\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.500000 | + | 2.59808i | 0.0569803 | + | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.00000 | − | 12.1244i | −0.787562 | − | 1.36410i | −0.927457 | − | 0.373930i | \(-0.878010\pi\) |
0.139895 | − | 0.990166i | \(-0.455323\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | + | 5.19615i | −0.628971 | + | 0.544705i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.50000 | − | 4.33013i | 0.256495 | − | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | − | 10.3923i | 0.597022 | − | 1.03407i | −0.396236 | − | 0.918149i | \(-0.629684\pi\) |
0.993258 | − | 0.115924i | \(-0.0369830\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0000 | − | 17.3205i | −0.985329 | − | 1.70664i | −0.640464 | − | 0.767988i | \(-0.721258\pi\) |
−0.344865 | − | 0.938652i | \(-0.612075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | − | 3.46410i | 0.191565 | − | 0.331801i | −0.754204 | − | 0.656640i | \(-0.771977\pi\) |
0.945769 | + | 0.324840i | \(0.105310\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.0000 | −1.88144 | −0.940721 | − | 0.339182i | \(-0.889850\pi\) | ||||
−0.940721 | + | 0.339182i | \(0.889850\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.50000 | − | 6.06218i | 0.326377 | − | 0.565301i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | + | 5.19615i | 0.0916698 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.0000 | 1.50851 | 0.754253 | − | 0.656584i | \(-0.227999\pi\) | ||||
0.754253 | + | 0.656584i | \(0.227999\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.50000 | + | 6.06218i | 0.305796 | + | 0.529655i | 0.977438 | − | 0.211221i | \(-0.0677440\pi\) |
−0.671642 | + | 0.740876i | \(0.734411\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.5000 | + | 4.33013i | 1.08389 | + | 0.375470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.50000 | − | 2.59808i | 0.125436 | − | 0.217262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.00000 | − | 5.19615i | −0.249136 | − | 0.431517i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.00000 | + | 8.66025i | 0.409616 | + | 0.709476i | 0.994847 | − | 0.101391i | \(-0.0323294\pi\) |
−0.585231 | + | 0.810867i | \(0.698996\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | − | 8.66025i | 0.406894 | − | 0.704761i | −0.587646 | − | 0.809118i | \(-0.699945\pi\) |
0.994540 | + | 0.104357i | \(0.0332784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.50000 | + | 4.33013i | −0.199522 | + | 0.345582i | −0.948373 | − | 0.317156i | \(-0.897272\pi\) |
0.748852 | + | 0.662738i | \(0.230606\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.5000 | + | 6.06218i | 1.37919 | + | 0.477767i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | − | 3.46410i | −0.156652 | − | 0.271329i | 0.777007 | − | 0.629492i | \(-0.216737\pi\) |
−0.933659 | + | 0.358162i | \(0.883403\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.00000 | −0.386912 | −0.193456 | − | 0.981109i | \(-0.561970\pi\) | ||||
−0.193456 | + | 0.981109i | \(0.561970\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.50000 | + | 16.4545i | 0.722272 | + | 1.25101i | 0.960087 | + | 0.279701i | \(0.0902353\pi\) |
−0.237816 | + | 0.971310i | \(0.576431\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | + | 2.59808i | 0.0377964 | + | 0.196396i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.50000 | − | 7.79423i | 0.336346 | − | 0.582568i | −0.647397 | − | 0.762153i | \(-0.724142\pi\) |
0.983742 | + | 0.179585i | \(0.0574756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.50000 | − | 4.33013i | 0.183804 | − | 0.318357i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.00000 | − | 1.73205i | −0.0731272 | − | 0.126660i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | + | 10.3923i | 0.434145 | + | 0.751961i | 0.997225 | − | 0.0744412i | \(-0.0237173\pi\) |
−0.563081 | + | 0.826402i | \(0.690384\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0000 | − | 17.3205i | 0.719816 | − | 1.24676i | −0.241257 | − | 0.970461i | \(-0.577560\pi\) |
0.961073 | − | 0.276296i | \(-0.0891071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.0000 | 1.92367 | 0.961835 | − | 0.273629i | \(-0.0882242\pi\) | ||||
0.961835 | + | 0.273629i | \(0.0882242\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | − | 3.46410i | 0.141776 | − | 0.245564i | −0.786389 | − | 0.617731i | \(-0.788052\pi\) |
0.928166 | + | 0.372168i | \(0.121385\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0000 | − | 10.3923i | 0.842235 | − | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.50000 | − | 4.33013i | −0.174608 | − | 0.302429i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.00000 | −0.345857 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0000 | −0.894957 | −0.447478 | − | 0.894295i | \(-0.647678\pi\) | ||||
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.00000 | − | 5.19615i | −0.204598 | − | 0.354375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | + | 10.3923i | 0.135769 | + | 0.705476i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | − | 5.19615i | 0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00000 | + | 6.92820i | −0.265489 | + | 0.459841i | −0.967692 | − | 0.252136i | \(-0.918867\pi\) |
0.702202 | + | 0.711977i | \(0.252200\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | + | 24.2487i | 0.925146 | + | 1.60240i | 0.791326 | + | 0.611394i | \(0.209391\pi\) |
0.133820 | + | 0.991006i | \(0.457276\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.00000 | + | 1.73205i | 0.0655122 | + | 0.113470i | 0.896921 | − | 0.442191i | \(-0.145799\pi\) |
−0.831409 | + | 0.555661i | \(0.812465\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.50000 | + | 7.79423i | −0.293548 | + | 0.508439i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5000 | + | 19.9186i | −0.740780 | + | 1.28307i | 0.211360 | + | 0.977408i | \(0.432211\pi\) |
−0.952141 | + | 0.305661i | \(0.901123\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.50000 | + | 2.59808i | −0.415270 | + | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.50000 | − | 12.9904i | −0.477214 | − | 0.826558i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.0000 | −1.83046 | −0.915232 | − | 0.402928i | \(-0.867993\pi\) | ||||
−0.915232 | + | 0.402928i | \(0.867993\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.00000 | −0.440086 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | + | 10.3923i | 0.374270 | + | 0.648254i | 0.990217 | − | 0.139533i | \(-0.0445601\pi\) |
−0.615948 | + | 0.787787i | \(0.711227\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.5000 | + | 4.33013i | 0.776712 | + | 0.269061i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.00000 | − | 6.92820i | 0.246651 | − | 0.427211i | −0.715944 | − | 0.698158i | \(-0.754003\pi\) |
0.962594 | + | 0.270947i | \(0.0873367\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.0000 | −0.675725 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.00000 | + | 10.3923i | −0.365826 | + | 0.633630i | −0.988908 | − | 0.148527i | \(-0.952547\pi\) |
0.623082 | + | 0.782157i | \(0.285880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.00000 | + | 6.92820i | 0.242983 | + | 0.420858i | 0.961563 | − | 0.274586i | \(-0.0885408\pi\) |
−0.718580 | + | 0.695444i | \(0.755208\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | + | 1.73205i | −0.0600842 | + | 0.104069i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | 0.178965 | 0.0894825 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894825 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0000 | − | 19.0526i | 0.653882 | − | 1.13256i | −0.328291 | − | 0.944577i | \(-0.606473\pi\) |
0.982173 | − | 0.187980i | \(-0.0601941\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.0000 | − | 8.66025i | 0.590281 | − | 0.511199i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.0000 | −1.22683 | −0.613417 | − | 0.789760i | \(-0.710205\pi\) | ||||
−0.613417 | + | 0.789760i | \(0.710205\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.5000 | − | 18.1865i | −0.607231 | − | 1.05175i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | − | 10.3923i | 0.691669 | − | 0.599002i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | − | 10.3923i | 0.343559 | − | 0.595062i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.00000 | −0.342438 | −0.171219 | − | 0.985233i | \(-0.554771\pi\) | ||||
−0.171219 | + | 0.985233i | \(0.554771\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.00000 | + | 3.46410i | −0.113410 | + | 0.196431i | −0.917143 | − | 0.398559i | \(-0.869511\pi\) |
0.803733 | + | 0.594990i | \(0.202844\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.00000 | − | 13.8564i | −0.452187 | − | 0.783210i | 0.546335 | − | 0.837567i | \(-0.316023\pi\) |
−0.998522 | + | 0.0543564i | \(0.982689\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.00000 | + | 1.73205i | 0.0561656 | + | 0.0972817i | 0.892741 | − | 0.450570i | \(-0.148779\pi\) |
−0.836576 | + | 0.547852i | \(0.815446\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | + | 5.19615i | −0.167968 | + | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.0000 | −0.556415 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.50000 | − | 2.59808i | 0.0832050 | − | 0.144115i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.5000 | − | 7.79423i | −1.24047 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5000 | + | 23.3827i | 0.742027 | + | 1.28523i | 0.951571 | + | 0.307429i | \(0.0994688\pi\) |
−0.209544 | + | 0.977799i | \(0.567198\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.0000 | −1.41631 | −0.708155 | − | 0.706057i | \(-0.750472\pi\) | ||||
−0.708155 | + | 0.706057i | \(0.750472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.00000 | − | 3.46410i | −0.108306 | − | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.00000 | − | 6.92820i | 0.214731 | − | 0.371925i | −0.738458 | − | 0.674299i | \(-0.764446\pi\) |
0.953189 | + | 0.302374i | \(0.0977791\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.0000 | − | 17.3205i | 0.532246 | − | 0.921878i | −0.467045 | − | 0.884234i | \(-0.654681\pi\) |
0.999291 | − | 0.0376440i | \(-0.0119853\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.00000 | − | 3.46410i | −0.106149 | − | 0.183855i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0000 | + | 25.9808i | 0.791670 | + | 1.37121i | 0.924932 | + | 0.380131i | \(0.124121\pi\) |
−0.133263 | + | 0.991081i | \(0.542545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | + | 5.19615i | −0.157895 | + | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.0000 | 0.628109 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.50000 | + | 16.4545i | −0.495896 | + | 0.858917i | −0.999989 | − | 0.00473247i | \(-0.998494\pi\) |
0.504093 | + | 0.863649i | \(0.331827\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.50000 | − | 28.5788i | −0.285546 | − | 1.48374i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.00000 | − | 12.1244i | −0.362446 | − | 0.627775i | 0.625917 | − | 0.779890i | \(-0.284725\pi\) |
−0.988363 | + | 0.152115i | \(0.951392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.0000 | −0.927047 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.0000 | −1.07870 | −0.539349 | − | 0.842082i | \(-0.681330\pi\) | ||||
−0.539349 | + | 0.842082i | \(0.681330\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.5000 | − | 18.1865i | −0.536525 | − | 0.929288i | −0.999088 | − | 0.0427020i | \(-0.986403\pi\) |
0.462563 | − | 0.886586i | \(-0.346930\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | − | 1.73205i | 0.101929 | − | 0.0882735i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.00000 | + | 13.8564i | −0.405616 | + | 0.702548i | −0.994393 | − | 0.105748i | \(-0.966276\pi\) |
0.588777 | + | 0.808296i | \(0.299610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.0000 | −0.708010 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.00000 | + | 12.1244i | −0.352208 | + | 0.610043i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.00000 | − | 15.5885i | −0.451697 | − | 0.782362i | 0.546795 | − | 0.837267i | \(-0.315848\pi\) |
−0.998492 | + | 0.0549046i | \(0.982515\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.50000 | + | 11.2583i | 0.324595 | + | 0.562214i | 0.981430 | − | 0.191820i | \(-0.0614388\pi\) |
−0.656836 | + | 0.754034i | \(0.728105\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00000 | − | 10.3923i | 0.298881 | − | 0.517678i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.00000 | −0.247841 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.00000 | − | 5.19615i | 0.148340 | − | 0.256933i | −0.782274 | − | 0.622935i | \(-0.785940\pi\) |
0.930614 | + | 0.366002i | \(0.119274\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.00000 | − | 20.7846i | −0.196827 | − | 1.02274i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.00000 | − | 3.46410i | −0.0981761 | − | 0.170046i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.00000 | 0.244266 | 0.122133 | − | 0.992514i | \(-0.461027\pi\) | ||||
0.122133 | + | 0.992514i | \(0.461027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0000 | 1.46211 | 0.731055 | − | 0.682318i | \(-0.239028\pi\) | ||||
0.731055 | + | 0.682318i | \(0.239028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.00000 | − | 1.73205i | −0.0485071 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 30.0000 | + | 10.3923i | 1.45180 | + | 0.502919i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.00000 | + | 13.8564i | −0.385346 | + | 0.667440i | −0.991817 | − | 0.127666i | \(-0.959251\pi\) |
0.606471 | + | 0.795106i | \(0.292585\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0000 | 1.15337 | 0.576683 | − | 0.816968i | \(-0.304347\pi\) | ||||
0.576683 | + | 0.816968i | \(0.304347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.5000 | + | 30.3109i | −0.837139 | + | 1.44997i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.00000 | + | 8.66025i | 0.238637 | + | 0.413331i | 0.960323 | − | 0.278889i | \(-0.0899661\pi\) |
−0.721686 | + | 0.692220i | \(0.756633\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.0000 | − | 27.7128i | −0.760183 | − | 1.31668i | −0.942756 | − | 0.333483i | \(-0.891776\pi\) |
0.182573 | − | 0.983192i | \(-0.441557\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.00000 | − | 5.19615i | 0.142214 | − | 0.246321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.0000 | −0.613508 | −0.306754 | − | 0.951789i | \(-0.599243\pi\) | ||||
−0.306754 | + | 0.951789i | \(0.599243\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.50000 | + | 4.33013i | −0.117720 | + | 0.203898i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.50000 | + | 2.59808i | 0.351605 | + | 0.121800i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0000 | + | 19.0526i | 0.514558 | + | 0.891241i | 0.999857 | + | 0.0168929i | \(0.00537742\pi\) |
−0.485299 | + | 0.874348i | \(0.661289\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.00000 | 0.418265 | 0.209133 | − | 0.977887i | \(-0.432936\pi\) | ||||
0.209133 | + | 0.977887i | \(0.432936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.00000 | − | 8.66025i | −0.231372 | − | 0.400749i | 0.726840 | − | 0.686807i | \(-0.240988\pi\) |
−0.958212 | + | 0.286058i | \(0.907655\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.00000 | − | 10.3923i | −0.0923514 | − | 0.479872i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.00000 | + | 5.19615i | −0.137940 | + | 0.238919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.00000 | −0.229416 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.00000 | + | 13.8564i | −0.365529 | + | 0.633115i | −0.988861 | − | 0.148842i | \(-0.952445\pi\) |
0.623332 | + | 0.781958i | \(0.285779\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.50000 | − | 12.9904i | −0.341971 | − | 0.592310i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.00000 | − | 5.19615i | −0.136223 | − | 0.235945i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00000 | − | 6.92820i | 0.181257 | − | 0.313947i | −0.761052 | − | 0.648691i | \(-0.775317\pi\) |
0.942309 | + | 0.334744i | \(0.108650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0000 | 0.902587 | 0.451294 | − | 0.892375i | \(-0.350963\pi\) | ||||
0.451294 | + | 0.892375i | \(0.350963\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | + | 10.3923i | −0.270226 | + | 0.468046i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | − | 6.92820i | 0.358849 | − | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0000 | − | 24.2487i | −0.626726 | − | 1.08552i | −0.988204 | − | 0.153141i | \(-0.951061\pi\) |
0.361478 | − | 0.932381i | \(-0.382272\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.00000 | − | 15.5885i | −0.398918 | − | 0.690946i | 0.594675 | − | 0.803966i | \(-0.297281\pi\) |
−0.993593 | + | 0.113020i | \(0.963948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | + | 31.1769i | 0.265424 | + | 1.37919i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.0000 | + | 17.3205i | −0.440653 | + | 0.763233i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.00000 | 0.395820 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.50000 | + | 12.9904i | −0.328581 | + | 0.569119i | −0.982231 | − | 0.187678i | \(-0.939904\pi\) |
0.653650 | + | 0.756797i | \(0.273237\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.0000 | − | 24.2487i | −0.612177 | − | 1.06032i | −0.990873 | − | 0.134801i | \(-0.956961\pi\) |
0.378695 | − | 0.925521i | \(-0.376373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.00000 | − | 6.92820i | −0.174243 | − | 0.301797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | + | 22.5167i | −0.565217 | + | 0.978985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.0000 | −0.649722 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | − | 10.3923i | 0.259403 | − | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.50000 | + | 4.33013i | 0.236902 | + | 0.186512i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0000 | + | 34.6410i | 0.859867 | + | 1.48933i | 0.872055 | + | 0.489408i | \(0.162787\pi\) |
−0.0121878 | + | 0.999926i | \(0.503880\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.00000 | −0.171341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0000 | + | 25.9808i | 0.639021 | + | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.0000 | − | 12.1244i | −1.48835 | − | 0.515580i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.5000 | − | 18.1865i | 0.444899 | − | 0.770588i | −0.553146 | − | 0.833084i | \(-0.686573\pi\) |
0.998045 | + | 0.0624962i | \(0.0199061\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.0000 | −0.761319 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.00000 | − | 5.19615i | 0.126435 | − | 0.218992i | −0.795858 | − | 0.605483i | \(-0.792980\pi\) |
0.922293 | + | 0.386492i | \(0.126313\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | + | 17.3205i | 0.420703 | + | 0.728679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.50000 | − | 9.52628i | −0.230572 | − | 0.399362i | 0.727405 | − | 0.686209i | \(-0.240726\pi\) |
−0.957977 | + | 0.286846i | \(0.907393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0000 | + | 24.2487i | −0.585882 | + | 1.01478i | 0.408883 | + | 0.912587i | \(0.365918\pi\) |
−0.994765 | + | 0.102190i | \(0.967415\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.00000 | −0.291920 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | − | 3.46410i | 0.0832611 | − | 0.144212i | −0.821388 | − | 0.570370i | \(-0.806800\pi\) |
0.904649 | + | 0.426158i | \(0.140133\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00000 | − | 6.92820i | 0.331896 | − | 0.287430i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.50000 | + | 9.52628i | 0.227787 | + | 0.394538i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.0000 | −0.824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00000 | − | 10.3923i | −0.246390 | − | 0.426761i | 0.716131 | − | 0.697966i | \(-0.245911\pi\) |
−0.962522 | + | 0.271205i | \(0.912578\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | − | 3.46410i | 0.163984 | − | 0.142014i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.0000 | − | 29.4449i | 0.694601 | − | 1.20308i | −0.275714 | − | 0.961240i | \(-0.588914\pi\) |
0.970315 | − | 0.241845i | \(-0.0777525\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.00000 | − | 8.66025i | 0.203279 | − | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.5000 | − | 28.5788i | −0.669714 | − | 1.15998i | −0.977984 | − | 0.208680i | \(-0.933083\pi\) |
0.308270 | − | 0.951299i | \(-0.400250\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.5000 | + | 23.3827i | 0.546152 | + | 0.945962i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.5000 | − | 35.5070i | 0.827987 | − | 1.43412i | −0.0716275 | − | 0.997431i | \(-0.522819\pi\) |
0.899615 | − | 0.436684i | \(-0.143847\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.0000 | −1.69086 | −0.845428 | − | 0.534089i | \(-0.820655\pi\) | ||||
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.5000 | + | 30.3109i | −0.703384 | + | 1.21830i | 0.263887 | + | 0.964554i | \(0.414995\pi\) |
−0.967271 | + | 0.253744i | \(0.918338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.0000 | + | 5.19615i | 0.600962 | + | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.0000 | −0.398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.50000 | − | 14.7224i | −0.337312 | − | 0.584242i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00000 | + | 20.7846i | −0.118864 | + | 0.823516i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.5000 | − | 30.3109i | 0.691208 | − | 1.19721i | −0.280234 | − | 0.959932i | \(-0.590412\pi\) |
0.971442 | − | 0.237276i | \(-0.0762547\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.0000 | −1.34083 | −0.670415 | − | 0.741987i | \(-0.733884\pi\) | ||||
−0.670415 | + | 0.741987i | \(0.733884\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.5000 | − | 19.9186i | 0.452112 | − | 0.783080i | −0.546405 | − | 0.837521i | \(-0.684004\pi\) |
0.998517 | + | 0.0544405i | \(0.0173375\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.00000 | + | 6.92820i | 0.157014 | + | 0.271956i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.5000 | + | 38.9711i | 0.880493 | + | 1.52506i | 0.850794 | + | 0.525500i | \(0.176122\pi\) |
0.0296993 | + | 0.999559i | \(0.490545\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.50000 | − | 6.06218i | 0.136756 | − | 0.236869i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.0000 | 0.623272 | 0.311636 | − | 0.950202i | \(-0.399123\pi\) | ||||
0.311636 | + | 0.950202i | \(0.399123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0000 | − | 31.1769i | 0.700119 | − | 1.21264i | −0.268306 | − | 0.963334i | \(-0.586464\pi\) |
0.968424 | − | 0.249308i | \(-0.0802030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.50000 | − | 12.9904i | −0.0969458 | − | 0.503745i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.0000 | + | 36.3731i | 0.813123 | + | 1.40837i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.0000 | −1.61898 | −0.809491 | − | 0.587133i | \(-0.800257\pi\) | ||||
−0.809491 | + | 0.587133i | \(0.800257\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.5000 | + | 18.1865i | 0.403548 | + | 0.698965i | 0.994151 | − | 0.107997i | \(-0.0344436\pi\) |
−0.590603 | + | 0.806962i | \(0.701110\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | − | 10.3923i | 0.460518 | − | 0.398820i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.0000 | + | 31.1769i | −0.688751 | + | 1.19295i | 0.283491 | + | 0.958975i | \(0.408507\pi\) |
−0.972242 | + | 0.233977i | \(0.924826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.5000 | + | 28.5788i | −0.628600 | + | 1.08877i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | − | 6.92820i | −0.152167 | − | 0.263561i | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.00000 | − | 3.46410i | −0.0758643 | − | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.00000 | + | 8.66025i | −0.189389 | + | 0.328031i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.5000 | + | 21.6506i | −0.471446 | + | 0.816569i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.00000 | − | 31.1769i | −0.225653 | − | 1.17253i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.00000 | + | 15.5885i | 0.338002 | + | 0.585437i | 0.984057 | − | 0.177854i | \(-0.0569156\pi\) |
−0.646055 | + | 0.763291i | \(0.723582\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.0000 | −1.04861 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.00000 | −0.112194 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.0000 | − | 31.1769i | −0.671287 | − | 1.16270i | −0.977539 | − | 0.210752i | \(-0.932409\pi\) |
0.306253 | − | 0.951950i | \(-0.400925\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.0000 | − | 17.3205i | −1.86210 | − | 0.645049i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.00000 | + | 5.19615i | −0.111417 | + | 0.192980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.0000 | 1.52061 | 0.760303 | − | 0.649569i | \(-0.225051\pi\) | ||||
0.760303 | + | 0.649569i | \(0.225051\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.00000 | + | 10.3923i | −0.221918 | + | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.5000 | − | 26.8468i | −0.572506 | − | 0.991609i | −0.996308 | − | 0.0858539i | \(-0.972638\pi\) |
0.423802 | − | 0.905755i | \(-0.360695\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.00000 | + | 3.46410i | 0.0736709 | + | 0.127602i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.5000 | − | 35.5070i | 0.754105 | − | 1.30615i | −0.191714 | − | 0.981451i | \(-0.561404\pi\) |
0.945818 | − | 0.324697i | \(-0.105262\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.00000 | 0.110059 | 0.0550297 | − | 0.998485i | \(-0.482475\pi\) | ||||
0.0550297 | + | 0.998485i | \(0.482475\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00000 | − | 8.66025i | 0.183186 | − | 0.317287i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.0000 | + | 10.3923i | 1.09618 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.00000 | − | 15.5885i | −0.328415 | − | 0.568831i | 0.653783 | − | 0.756682i | \(-0.273181\pi\) |
−0.982197 | + | 0.187851i | \(0.939848\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0000 | −0.363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.00000 | −0.218074 | −0.109037 | − | 0.994038i | \(-0.534777\pi\) | ||||
−0.109037 | + | 0.994038i | \(0.534777\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.50000 | − | 2.59808i | −0.0543750 | − | 0.0941802i | 0.837557 | − | 0.546350i | \(-0.183983\pi\) |
−0.891932 | + | 0.452170i | \(0.850650\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | − | 10.3923i | −0.0724049 | − | 0.376227i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | + | 20.7846i | −0.433295 | + | 0.750489i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.0000 | −1.47850 | −0.739249 | − | 0.673432i | \(-0.764819\pi\) | ||||
−0.739249 | + | 0.673432i | \(0.764819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.50000 | − | 12.9904i | 0.269756 | − | 0.467232i | −0.699043 | − | 0.715080i | \(-0.746390\pi\) |
0.968799 | + | 0.247849i | \(0.0797235\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | − | 3.46410i | −0.0718421 | − | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.5000 | + | 21.6506i | 0.447859 | + | 0.775715i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.00000 | + | 3.46410i | −0.0715656 | + | 0.123955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.00000 | 0.178458 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.00000 | − | 15.5885i | 0.320815 | − | 0.555668i | −0.659841 | − | 0.751405i | \(-0.729376\pi\) |
0.980656 | + | 0.195737i | \(0.0627098\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −40.0000 | + | 34.6410i | −1.42224 | + | 1.23169i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.0000 | − | 31.1769i | −0.639199 | − | 1.10712i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.00000 | −0.0708436 | −0.0354218 | − | 0.999372i | \(-0.511277\pi\) | ||||
−0.0354218 | + | 0.999372i | \(0.511277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.00000 | − | 10.3923i | −0.211735 | − | 0.366736i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.50000 | − | 18.1865i | −0.123359 | − | 0.640991i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.5000 | − | 47.6314i | 0.966849 | − | 1.67463i | 0.262284 | − | 0.964991i | \(-0.415524\pi\) |
0.704564 | − | 0.709640i | \(-0.251142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.00000 | −0.175574 | −0.0877869 | − | 0.996139i | \(-0.527979\pi\) | ||||
−0.0877869 | + | 0.996139i | \(0.527979\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | + | 3.46410i | −0.0700569 | + | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.0000 | + | 25.9808i | 0.524784 | + | 0.908952i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.0000 | + | 25.9808i | 0.523504 | + | 0.906735i | 0.999626 | + | 0.0273557i | \(0.00870868\pi\) |
−0.476122 | + | 0.879379i | \(0.657958\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.00000 | + | 3.46410i | −0.0697156 | + | 0.120751i | −0.898776 | − | 0.438408i | \(-0.855543\pi\) |
0.829060 | + | 0.559159i | \(0.188876\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.0000 | 0.486828 | 0.243414 | − | 0.969923i | \(-0.421733\pi\) | ||||
0.243414 | + | 0.969923i | \(0.421733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.0000 | + | 32.9090i | −0.659897 | + | 1.14298i | 0.320745 | + | 0.947166i | \(0.396067\pi\) |
−0.980642 | + | 0.195810i | \(0.937266\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.0000 | + | 8.66025i | 0.381127 | + | 0.300060i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.50000 | + | 4.33013i | 0.0865161 | + | 0.149850i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.0000 | 0.483334 | 0.241667 | − | 0.970359i | \(-0.422306\pi\) | ||||
0.241667 | + | 0.970359i | \(0.422306\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.00000 | + | 3.46410i | 0.0688021 | + | 0.119169i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.0000 | + | 8.66025i | 0.859010 | + | 0.297570i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.5000 | + | 30.3109i | −0.599892 | + | 1.03904i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0000 | 0.787505 | 0.393753 | − | 0.919216i | \(-0.371177\pi\) | ||||
0.393753 | + | 0.919216i | \(0.371177\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0000 | + | 36.3731i | −0.717346 | + | 1.24248i | 0.244701 | + | 0.969599i | \(0.421310\pi\) |
−0.962048 | + | 0.272882i | \(0.912023\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.0000 | − | 34.6410i | −0.682391 | − | 1.18194i | −0.974249 | − | 0.225475i | \(-0.927607\pi\) |
0.291858 | − | 0.956462i | \(-0.405727\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.50000 | − | 11.2583i | −0.221263 | − | 0.383238i | 0.733929 | − | 0.679226i | \(-0.237684\pi\) |
−0.955192 | + | 0.295988i | \(0.904351\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.50000 | − | 16.4545i | 0.323010 | − | 0.559469i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.0000 | 0.474917 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.00000 | + | 10.3923i | −0.203302 | + | 0.352130i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.00000 | − | 1.73205i | 0.0676123 | − | 0.0585540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.50000 | − | 7.79423i | −0.151954 | − | 0.263192i | 0.779992 | − | 0.625790i | \(-0.215223\pi\) |
−0.931946 | + | 0.362598i | \(0.881890\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.00000 | 0.235836 | 0.117918 | − | 0.993023i | \(-0.462378\pi\) | ||||
0.117918 | + | 0.993023i | \(0.462378\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.0000 | − | 29.4449i | 1.14032 | − | 0.987549i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.5000 | − | 38.9711i | 0.752934 | − | 1.30412i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.00000 | −0.300837 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.0000 | + | 20.7846i | −0.400222 | + | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0000 | + | 19.0526i | 0.366463 | + | 0.634733i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.00000 | − | 1.73205i | −0.0332411 | − | 0.0575753i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.0000 | + | 19.0526i | −0.365249 | + | 0.632630i | −0.988816 | − | 0.149140i | \(-0.952349\pi\) |
0.623567 | + | 0.781770i | \(0.285683\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.0000 | −1.39152 | −0.695761 | − | 0.718273i | \(-0.744933\pi\) | ||||
−0.695761 | + | 0.718273i | \(0.744933\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.00000 | + | 3.46410i | −0.0661903 | + | 0.114645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.5000 | + | 6.06218i | 0.577901 | + | 0.200191i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.00000 | + | 15.5885i | 0.296883 | + | 0.514216i | 0.975421 | − | 0.220349i | \(-0.0707197\pi\) |
−0.678538 | + | 0.734565i | \(0.737386\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.0000 | −0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.00000 | −0.164399 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.5000 | − | 26.8468i | −0.508539 | − | 0.880815i | −0.999951 | − | 0.00988764i | \(-0.996853\pi\) |
0.491413 | − | 0.870927i | \(-0.336481\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.5000 | − | 12.9904i | 1.06514 | − | 0.425743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.00000 | + | 1.73205i | −0.0327035 | + | 0.0566441i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.0000 | −1.24141 | −0.620703 | − | 0.784046i | \(-0.713153\pi\) | ||||
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.0000 | − | 20.7846i | 0.391189 | − | 0.677559i | −0.601418 | − | 0.798935i | \(-0.705397\pi\) |
0.992607 | + | 0.121376i | \(0.0387306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.5000 | + | 30.3109i | 0.569878 | + | 0.987058i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.00000 | + | 12.1244i | 0.227469 | + | 0.393989i | 0.957057 | − | 0.289898i | \(-0.0936215\pi\) |
−0.729588 | + | 0.683887i | \(0.760288\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.0000 | − | 31.1769i | 0.584305 | − | 1.01205i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.0000 | 0.647864 | 0.323932 | − | 0.946080i | \(-0.394995\pi\) | ||||
0.323932 | + | 0.946080i | \(0.394995\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.00000 | − | 10.3923i | 0.194155 | − | 0.336287i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.00000 | + | 31.1769i | 0.193750 | + | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.0000 | −0.643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.50000 | + | 6.06218i | 0.112320 | + | 0.194545i | 0.916705 | − | 0.399564i | \(-0.130838\pi\) |
−0.804385 | + | 0.594108i | \(0.797505\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.00000 | − | 6.92820i | 0.256468 | − | 0.222108i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.50000 | + | 2.59808i | −0.0478426 | + | 0.0828658i | −0.888955 | − | 0.457995i | \(-0.848568\pi\) |
0.841112 | + | 0.540860i | \(0.181901\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.5000 | − | 23.3827i | −0.430146 | − | 0.745034i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.0000 | + | 36.3731i | 0.667761 | + | 1.15660i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0000 | + | 38.1051i | −0.698853 | + | 1.21045i | 0.270011 | + | 0.962857i | \(0.412973\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.00000 | −0.126809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.0000 | + | 39.8372i | −0.728417 | + | 1.26166i | 0.229135 | + | 0.973395i | \(0.426410\pi\) |
−0.957552 | + | 0.288261i | \(0.906923\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2520.2.bi.e.361.1 | 2 | ||
3.2 | odd | 2 | 280.2.q.c.81.1 | ✓ | 2 | ||
7.2 | even | 3 | inner | 2520.2.bi.e.1801.1 | 2 | ||
12.11 | even | 2 | 560.2.q.c.81.1 | 2 | |||
15.2 | even | 4 | 1400.2.bh.e.249.1 | 4 | |||
15.8 | even | 4 | 1400.2.bh.e.249.2 | 4 | |||
15.14 | odd | 2 | 1400.2.q.a.1201.1 | 2 | |||
21.2 | odd | 6 | 280.2.q.c.121.1 | yes | 2 | ||
21.5 | even | 6 | 1960.2.q.c.961.1 | 2 | |||
21.11 | odd | 6 | 1960.2.a.a.1.1 | 1 | |||
21.17 | even | 6 | 1960.2.a.m.1.1 | 1 | |||
21.20 | even | 2 | 1960.2.q.c.361.1 | 2 | |||
84.11 | even | 6 | 3920.2.a.bf.1.1 | 1 | |||
84.23 | even | 6 | 560.2.q.c.401.1 | 2 | |||
84.59 | odd | 6 | 3920.2.a.i.1.1 | 1 | |||
105.2 | even | 12 | 1400.2.bh.e.849.2 | 4 | |||
105.23 | even | 12 | 1400.2.bh.e.849.1 | 4 | |||
105.44 | odd | 6 | 1400.2.q.a.401.1 | 2 | |||
105.59 | even | 6 | 9800.2.a.g.1.1 | 1 | |||
105.74 | odd | 6 | 9800.2.a.bi.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.c.81.1 | ✓ | 2 | 3.2 | odd | 2 | ||
280.2.q.c.121.1 | yes | 2 | 21.2 | odd | 6 | ||
560.2.q.c.81.1 | 2 | 12.11 | even | 2 | |||
560.2.q.c.401.1 | 2 | 84.23 | even | 6 | |||
1400.2.q.a.401.1 | 2 | 105.44 | odd | 6 | |||
1400.2.q.a.1201.1 | 2 | 15.14 | odd | 2 | |||
1400.2.bh.e.249.1 | 4 | 15.2 | even | 4 | |||
1400.2.bh.e.249.2 | 4 | 15.8 | even | 4 | |||
1400.2.bh.e.849.1 | 4 | 105.23 | even | 12 | |||
1400.2.bh.e.849.2 | 4 | 105.2 | even | 12 | |||
1960.2.a.a.1.1 | 1 | 21.11 | odd | 6 | |||
1960.2.a.m.1.1 | 1 | 21.17 | even | 6 | |||
1960.2.q.c.361.1 | 2 | 21.20 | even | 2 | |||
1960.2.q.c.961.1 | 2 | 21.5 | even | 6 | |||
2520.2.bi.e.361.1 | 2 | 1.1 | even | 1 | trivial | ||
2520.2.bi.e.1801.1 | 2 | 7.2 | even | 3 | inner | ||
3920.2.a.i.1.1 | 1 | 84.59 | odd | 6 | |||
3920.2.a.bf.1.1 | 1 | 84.11 | even | 6 | |||
9800.2.a.g.1.1 | 1 | 105.59 | even | 6 | |||
9800.2.a.bi.1.1 | 1 | 105.74 | odd | 6 |