Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.a (trivial) |
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: | yes |
Analytic conductor: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −3.30278 | −1.90686 | −0.953429 | − | 0.301617i | \(-0.902474\pi\) | ||||
−0.953429 | + | 0.301617i | \(0.902474\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.302776 | 0.114438 | 0.0572192 | − | 0.998362i | \(-0.481777\pi\) | ||||
0.0572192 | + | 0.998362i | \(0.481777\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.90833 | 2.63611 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.30278 | 1.59885 | 0.799424 | − | 0.600768i | \(-0.205138\pi\) | ||||
0.799424 | + | 0.600768i | \(0.205138\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.302776 | −0.0839749 | −0.0419874 | − | 0.999118i | \(-0.513369\pi\) | ||||
−0.0419874 | + | 0.999118i | \(0.513369\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.30278 | −0.852773 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.90833 | −0.947909 | −0.473954 | − | 0.880549i | \(-0.657174\pi\) | ||||
−0.473954 | + | 0.880549i | \(0.657174\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.90833 | 1.12605 | 0.563024 | − | 0.826441i | \(-0.309638\pi\) | ||||
0.563024 | + | 0.826441i | \(0.309638\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.2111 | −3.11983 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.60555 | 0.855229 | 0.427615 | − | 0.903961i | \(-0.359354\pi\) | ||||
0.427615 | + | 0.903961i | \(0.359354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.90833 | −0.522351 | −0.261175 | − | 0.965291i | \(-0.584110\pi\) | ||||
−0.261175 | + | 0.965291i | \(0.584110\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.5139 | −3.04877 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.302776 | 0.0511784 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.90833 | −1.54742 | −0.773710 | − | 0.633540i | \(-0.781601\pi\) | ||||
−0.773710 | + | 0.633540i | \(0.781601\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.21110 | −0.794686 | −0.397343 | − | 0.917670i | \(-0.630068\pi\) | ||||
−0.397343 | + | 0.917670i | \(0.630068\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.90833 | 1.17890 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.60555 | −0.671789 | −0.335894 | − | 0.941900i | \(-0.609039\pi\) | ||||
−0.335894 | + | 0.941900i | \(0.609039\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.90833 | −0.986904 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.9083 | 1.80753 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.21110 | 0.441079 | 0.220539 | − | 0.975378i | \(-0.429218\pi\) | ||||
0.220539 | + | 0.975378i | \(0.429218\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.30278 | 0.715026 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.2111 | −2.14721 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.6056 | 1.38073 | 0.690363 | − | 0.723464i | \(-0.257451\pi\) | ||||
0.690363 | + | 0.723464i | \(0.257451\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.51388 | −0.834017 | −0.417008 | − | 0.908903i | \(-0.636921\pi\) | ||||
−0.417008 | + | 0.908903i | \(0.636921\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.39445 | 0.301672 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.302776 | −0.0375547 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.30278 | −0.397607 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.6972 | 1.50688 | 0.753442 | − | 0.657515i | \(-0.228392\pi\) | ||||
0.753442 | + | 0.657515i | \(0.228392\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.8167 | 1.85120 | 0.925600 | − | 0.378504i | \(-0.123561\pi\) | ||||
0.925600 | + | 0.378504i | \(0.123561\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.30278 | −0.381372 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.60555 | 0.182970 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.4222 | −1.62262 | −0.811312 | − | 0.584613i | \(-0.801246\pi\) | ||||
−0.811312 | + | 0.584613i | \(0.801246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.8167 | 3.31296 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.21110 | 0.352464 | 0.176232 | − | 0.984349i | \(-0.443609\pi\) | ||||
0.176232 | + | 0.984349i | \(0.443609\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.90833 | −0.423918 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15.2111 | −1.63080 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0916731 | −0.00960995 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.60555 | 0.996049 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.90833 | 0.503584 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.69722 | 0.273862 | 0.136931 | − | 0.990581i | \(-0.456276\pi\) | ||||
0.136931 | + | 0.990581i | \(0.456276\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 41.9361 | 4.21473 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.60555 | −0.458269 | −0.229135 | − | 0.973395i | \(-0.573590\pi\) | ||||
−0.229135 | + | 0.973395i | \(0.573590\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.1194 | 1.68683 | 0.843414 | − | 0.537265i | \(-0.180542\pi\) | ||||
0.843414 | + | 0.537265i | \(0.180542\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.60555 | −0.445235 | −0.222618 | − | 0.974906i | \(-0.571460\pi\) | ||||
−0.222618 | + | 0.974906i | \(0.571460\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.5139 | 1.86909 | 0.934545 | − | 0.355844i | \(-0.115807\pi\) | ||||
0.934545 | + | 0.355844i | \(0.115807\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.4222 | −2.50788 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.4222 | 1.16858 | 0.584291 | − | 0.811544i | \(-0.301373\pi\) | ||||
0.584291 | + | 0.811544i | \(0.301373\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.39445 | −0.221367 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.18335 | −0.108477 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.1194 | 1.55631 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 32.7250 | 2.95071 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8167 | 1.04856 | 0.524279 | − | 0.851546i | \(-0.324335\pi\) | ||||
0.524279 | + | 0.851546i | \(0.324335\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.2111 | 1.51535 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.21110 | −0.280555 | −0.140278 | − | 0.990112i | \(-0.544800\pi\) | ||||
−0.140278 | + | 0.990112i | \(0.544800\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.48612 | 0.128863 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.2111 | −1.39523 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.90833 | −0.590218 | −0.295109 | − | 0.955464i | \(-0.595356\pi\) | ||||
−0.295109 | + | 0.955464i | \(0.595356\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.39445 | 0.457551 | 0.228776 | − | 0.973479i | \(-0.426528\pi\) | ||||
0.228776 | + | 0.973479i | \(0.426528\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.2111 | 1.28101 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.60555 | −0.134263 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.60555 | 0.382470 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 22.8167 | 1.88189 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.69722 | 0.794428 | 0.397214 | − | 0.917726i | \(-0.369977\pi\) | ||||
0.397214 | + | 0.917726i | \(0.369977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.90833 | 0.155297 | 0.0776487 | − | 0.996981i | \(-0.475259\pi\) | ||||
0.0776487 | + | 0.996981i | \(0.475259\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −30.9083 | −2.49879 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.90833 | −0.233602 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3944 | −0.909376 | −0.454688 | − | 0.890651i | \(-0.650249\pi\) | ||||
−0.454688 | + | 0.890651i | \(0.650249\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.6056 | −0.841075 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.302776 | 0.0238621 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.69722 | −0.446241 | −0.223121 | − | 0.974791i | \(-0.571624\pi\) | ||||
−0.223121 | + | 0.974791i | \(0.571624\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −17.5139 | −1.36345 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.2111 | −1.64136 | −0.820682 | − | 0.571385i | \(-0.806406\pi\) | ||||
−0.820682 | + | 0.571385i | \(0.806406\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9083 | −0.992948 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 38.8167 | 2.96838 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.3028 | 1.77168 | 0.885839 | − | 0.463993i | \(-0.153584\pi\) | ||||
0.885839 | + | 0.463993i | \(0.153584\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.302776 | 0.0228877 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −35.0278 | −2.63285 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.6056 | −1.24116 | −0.620579 | − | 0.784144i | \(-0.713102\pi\) | ||||
−0.620579 | + | 0.784144i | \(0.713102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.11943 | −0.603512 | −0.301756 | − | 0.953385i | \(-0.597573\pi\) | ||||
−0.301756 | + | 0.953385i | \(0.597573\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.5139 | 1.59035 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00000 | 0.588172 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.7250 | −1.51556 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.90833 | −0.357028 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.39445 | 0.100899 | 0.0504494 | − | 0.998727i | \(-0.483935\pi\) | ||||
0.0504494 | + | 0.998727i | \(0.483935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.81665 | 0.274729 | 0.137364 | − | 0.990521i | \(-0.456137\pi\) | ||||
0.137364 | + | 0.990521i | \(0.456137\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.697224 | 0.0496752 | 0.0248376 | − | 0.999691i | \(-0.492093\pi\) | ||||
0.0248376 | + | 0.999691i | \(0.492093\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.42221 | −0.597034 | −0.298517 | − | 0.954404i | \(-0.596492\pi\) | ||||
−0.298517 | + | 0.954404i | \(0.596492\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.2111 | −0.931839 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.39445 | 0.0978711 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.90833 | −0.692028 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.90833 | 0.549667 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.0278 | 1.80038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.21110 | 0.496433 | 0.248216 | − | 0.968705i | \(-0.420156\pi\) | ||||
0.248216 | + | 0.968705i | \(0.420156\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −41.9361 | −2.87341 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.21110 | −0.355394 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.880571 | −0.0597770 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −52.2389 | −3.52997 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.18335 | 0.0796005 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000 | 0.267860 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.90833 | 0.527222 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.39445 | 0.490787 | 0.245393 | − | 0.969424i | \(-0.421083\pi\) | ||||
0.245393 | + | 0.969424i | \(0.421083\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.30278 | −0.348897 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.18335 | 0.274060 | 0.137030 | − | 0.990567i | \(-0.456244\pi\) | ||||
0.137030 | + | 0.990567i | \(0.456244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.60555 | −0.300433 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 47.6333 | 3.09412 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.21110 | 0.595817 | 0.297908 | − | 0.954594i | \(-0.403711\pi\) | ||||
0.297908 | + | 0.954594i | \(0.403711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4222 | 0.929016 | 0.464508 | − | 0.885569i | \(-0.346231\pi\) | ||||
0.464508 | + | 0.885569i | \(0.346231\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −49.8444 | −3.19752 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.90833 | −0.441357 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.48612 | −0.0945597 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.6056 | −0.672100 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.51388 | 0.348033 | 0.174016 | − | 0.984743i | \(-0.444325\pi\) | ||||
0.174016 | + | 0.984743i | \(0.444325\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.30278 | 0.333383 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.9083 | 0.808351 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.8167 | 1.23613 | 0.618064 | − | 0.786127i | \(-0.287917\pi\) | ||||
0.618064 | + | 0.786127i | \(0.287917\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.42221 | 0.150509 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 36.4222 | 2.25448 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.5139 | 0.894964 | 0.447482 | − | 0.894293i | \(-0.352321\pi\) | ||||
0.447482 | + | 0.894293i | \(0.352321\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.21110 | 0.197256 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.8167 | 1.57407 | 0.787035 | − | 0.616909i | \(-0.211615\pi\) | ||||
0.787035 | + | 0.616909i | \(0.211615\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.30278 | 0.382866 | 0.191433 | − | 0.981506i | \(-0.438686\pi\) | ||||
0.191433 | + | 0.981506i | \(0.438686\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.302776 | 0.0183248 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.30278 | 0.319769 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.7889 | −0.768410 | −0.384205 | − | 0.923248i | \(-0.625524\pi\) | ||||
−0.384205 | + | 0.923248i | \(0.625524\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.0000 | −1.37697 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.3944 | −1.15698 | −0.578488 | − | 0.815691i | \(-0.696357\pi\) | ||||
−0.578488 | + | 0.815691i | \(0.696357\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | −0.118888 | −0.0594438 | − | 0.998232i | \(-0.518933\pi\) | ||||
−0.0594438 | + | 0.998232i | \(0.518933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.2111 | −0.960263 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.00000 | −0.177084 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.72498 | −0.101469 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.90833 | −0.522215 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.78890 | 0.513453 | 0.256726 | − | 0.966484i | \(-0.417356\pi\) | ||||
0.256726 | + | 0.966484i | \(0.417356\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.6056 | 0.617479 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −85.9638 | −4.98813 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.302776 | −0.0175100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.57779 | −0.0909426 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.2111 | 0.873855 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.51388 | −0.372984 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.3028 | 0.873376 | 0.436688 | − | 0.899613i | \(-0.356151\pi\) | ||||
0.436688 | + | 0.899613i | \(0.356151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −56.5416 | −3.21654 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.42221 | 0.364170 | 0.182085 | − | 0.983283i | \(-0.441715\pi\) | ||||
0.182085 | + | 0.983283i | \(0.441715\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7250 | −0.719258 | −0.359629 | − | 0.933095i | \(-0.617097\pi\) | ||||
−0.359629 | + | 0.933095i | \(0.617097\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.39445 | 0.134912 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.7250 | −0.827037 | −0.413519 | − | 0.910496i | \(-0.635700\pi\) | ||||
−0.413519 | + | 0.910496i | \(0.635700\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.4222 | 1.36738 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.2111 | 0.849001 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.1833 | −1.06739 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.302776 | −0.0167950 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −64.4500 | −3.56409 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.39445 | −0.0768784 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.39445 | −0.516366 | −0.258183 | − | 0.966096i | \(-0.583124\pi\) | ||||
−0.258183 | + | 0.966096i | \(0.583124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 63.2666 | 3.46699 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.48612 | −0.244375 | −0.122187 | − | 0.992507i | \(-0.538991\pi\) | ||||
−0.122187 | + | 0.992507i | \(0.538991\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −41.0278 | −2.22832 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.4222 | −0.835159 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.21110 | −0.227378 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.30278 | −0.177815 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.5416 | 1.37115 | 0.685573 | − | 0.728004i | \(-0.259552\pi\) | ||||
0.685573 | + | 0.728004i | \(0.259552\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7889 | −0.684574 | −0.342287 | − | 0.939595i | \(-0.611202\pi\) | ||||
−0.342287 | + | 0.939595i | \(0.611202\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.90833 | 0.261987 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.4222 | 0.980515 | 0.490258 | − | 0.871578i | \(-0.336903\pi\) | ||||
0.490258 | + | 0.871578i | \(0.336903\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.6972 | 0.673899 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.90833 | 0.206851 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.21110 | 0.169476 | 0.0847378 | − | 0.996403i | \(-0.472995\pi\) | ||||
0.0847378 | + | 0.996403i | \(0.472995\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.09167 | 0.267983 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −56.5416 | −2.96767 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.8167 | 0.827881 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.2111 | −1.52481 | −0.762404 | − | 0.647102i | \(-0.775981\pi\) | ||||
−0.762404 | + | 0.647102i | \(0.775981\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −78.3583 | −4.07917 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.972244 | 0.0504764 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.60555 | −0.134910 | −0.0674552 | − | 0.997722i | \(-0.521488\pi\) | ||||
−0.0674552 | + | 0.997722i | \(0.521488\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.30278 | −0.170555 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.39445 | −0.0718178 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.09167 | −0.210175 | −0.105088 | − | 0.994463i | \(-0.533512\pi\) | ||||
−0.105088 | + | 0.994463i | \(0.533512\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39.0278 | −1.99945 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.60555 | 0.0818265 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −41.2111 | −2.09488 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.9361 | 1.06150 | 0.530751 | − | 0.847528i | \(-0.321910\pi\) | ||||
0.530751 | + | 0.847528i | \(0.321910\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.90833 | −0.197653 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.6056 | 0.534979 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.4222 | −0.725660 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.7250 | −1.09035 | −0.545173 | − | 0.838324i | \(-0.683536\pi\) | ||||
−0.545173 | + | 0.838324i | \(0.683536\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.90833 | −0.245724 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.39445 | −0.0696354 | −0.0348177 | − | 0.999394i | \(-0.511085\pi\) | ||||
−0.0348177 | + | 0.999394i | \(0.511085\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.880571 | 0.0438643 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29.8167 | 1.48160 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 42.4222 | 2.10279 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.0917 | −0.746235 | −0.373118 | − | 0.927784i | \(-0.621711\pi\) | ||||
−0.373118 | + | 0.927784i | \(0.621711\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.8167 | 1.12546 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.21110 | 0.158008 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.21110 | 0.157627 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.8167 | −0.872485 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 39.6333 | 1.93621 | 0.968107 | − | 0.250538i | \(-0.0806073\pi\) | ||||
0.968107 | + | 0.250538i | \(0.0806073\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.3028 | 1.67181 | 0.835907 | − | 0.548870i | \(-0.184942\pi\) | ||||
0.835907 | + | 0.548870i | \(0.184942\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −36.4222 | −1.77091 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.90833 | −0.189582 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.97224 | −0.0954436 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.30278 | 0.256020 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.2389 | −0.974872 | −0.487436 | − | 0.873159i | \(-0.662068\pi\) | ||||
−0.487436 | + | 0.873159i | \(0.662068\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.9083 | −1.67759 | −0.838794 | − | 0.544450i | \(-0.816739\pi\) | ||||
−0.838794 | + | 0.544450i | \(0.816739\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.2111 | −0.729317 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.90833 | 0.234797 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.3028 | 0.873544 | 0.436772 | − | 0.899572i | \(-0.356122\pi\) | ||||
0.436772 | + | 0.899572i | \(0.356122\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −54.6333 | −2.60159 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.5139 | −1.68732 | −0.843658 | − | 0.536882i | \(-0.819602\pi\) | ||||
−0.843658 | + | 0.536882i | \(0.819602\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −32.0278 | −1.51486 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.9083 | −0.609182 | −0.304591 | − | 0.952483i | \(-0.598520\pi\) | ||||
−0.304591 | + | 0.952483i | \(0.598520\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −52.5416 | −2.47409 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.30278 | −0.296130 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0916731 | −0.00429770 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.57779 | −0.167362 | −0.0836811 | − | 0.996493i | \(-0.526668\pi\) | ||||
−0.0836811 | + | 0.996493i | \(0.526668\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 63.3583 | 2.95731 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.8167 | 1.48185 | 0.740925 | − | 0.671588i | \(-0.234388\pi\) | ||||
0.740925 | + | 0.671588i | \(0.234388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.6333 | 1.19128 | 0.595640 | − | 0.803251i | \(-0.296898\pi\) | ||||
0.595640 | + | 0.803251i | \(0.296898\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.60555 | 0.445447 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.8167 | −0.917005 | −0.458503 | − | 0.888693i | \(-0.651614\pi\) | ||||
−0.458503 | + | 0.888693i | \(0.651614\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.21110 | 0.0559235 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 37.6333 | 1.73405 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.6333 | −1.27058 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.90833 | 0.225209 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.3944 | 1.16273 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.0000 | 1.37073 | 0.685367 | − | 0.728197i | \(-0.259642\pi\) | ||||
0.685367 | + | 0.728197i | \(0.259642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.42221 | −0.110443 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.69722 | 0.122475 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.8167 | 0.535464 | 0.267732 | − | 0.963493i | \(-0.413726\pi\) | ||||
0.267732 | + | 0.963493i | \(0.413726\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.8167 | 0.850918 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.8167 | 1.16509 | 0.582545 | − | 0.812799i | \(-0.302057\pi\) | ||||
0.582545 | + | 0.812799i | \(0.302057\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0000 | −0.810679 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 41.9361 | 1.88489 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.84441 | 0.172445 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.6333 | −0.520778 | −0.260389 | − | 0.965504i | \(-0.583851\pi\) | ||||
−0.260389 | + | 0.965504i | \(0.583851\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 70.0555 | 3.12985 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.72498 | 0.121501 | 0.0607504 | − | 0.998153i | \(-0.480651\pi\) | ||||
0.0607504 | + | 0.998153i | \(0.480651\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.60555 | −0.204944 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 42.6333 | 1.89341 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.4500 | 1.30535 | 0.652673 | − | 0.757639i | \(-0.273647\pi\) | ||||
0.652673 | + | 0.757639i | \(0.273647\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.78890 | 0.211848 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −79.5694 | −3.51307 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.1194 | 0.754372 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.4222 | −1.07409 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −76.9638 | −3.37834 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.42221 | −0.368277 | −0.184139 | − | 0.982900i | \(-0.558950\pi\) | ||||
−0.184139 | + | 0.982900i | \(0.558950\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.3667 | 0.495141 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 83.8722 | 3.63974 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.00000 | 0.129944 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.60555 | −0.199115 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 54.8444 | 2.36671 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36.6333 | −1.57791 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.8444 | −1.24012 | −0.620059 | − | 0.784555i | \(-0.712891\pi\) | ||||
−0.620059 | + | 0.784555i | \(0.712891\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 26.8167 | 1.15081 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.5139 | 0.835883 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.51388 | −0.321270 | −0.160635 | − | 0.987014i | \(-0.551354\pi\) | ||||
−0.160635 | + | 0.987014i | \(0.551354\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −51.5139 | −2.19856 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.6056 | 0.963029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.36669 | −0.185691 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26.4222 | −1.12156 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.42221 | −0.272118 | −0.136059 | − | 0.990701i | \(-0.543444\pi\) | ||||
−0.136059 | + | 0.990701i | \(0.543444\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.57779 | 0.0667336 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 68.4500 | 2.88996 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.6333 | −1.67034 | −0.835172 | − | 0.549988i | \(-0.814632\pi\) | ||||
−0.835172 | + | 0.549988i | \(0.814632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.4222 | 0.522606 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.02776 | 0.379130 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.422205 | −0.0176998 | −0.00884988 | − | 0.999961i | \(-0.502817\pi\) | ||||
−0.00884988 | + | 0.999961i | \(0.502817\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.11943 | −0.381636 | −0.190818 | − | 0.981625i | \(-0.561114\pi\) | ||||
−0.190818 | + | 0.981625i | \(0.561114\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.60555 | −0.192400 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.6056 | −0.523869 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.972244 | 0.0403355 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.0278 | 0.705218 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.39445 | −0.0989983 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.5416 | 1.54951 | 0.774755 | − | 0.632262i | \(-0.217873\pi\) | ||||
0.774755 | + | 0.632262i | \(0.217873\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.2750 | −0.588192 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.30278 | −0.0947235 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.8167 | 0.813772 | 0.406886 | − | 0.913479i | \(-0.366615\pi\) | ||||
0.406886 | + | 0.913479i | \(0.366615\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.18335 | −0.0485125 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.8167 | 1.13846 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.33053 | −0.176941 | −0.0884704 | − | 0.996079i | \(-0.528198\pi\) | ||||
−0.0884704 | + | 0.996079i | \(0.528198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.93608 | −0.160556 | −0.0802781 | − | 0.996773i | \(-0.525581\pi\) | ||||
−0.0802781 | + | 0.996773i | \(0.525581\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.6333 | 1.28821 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.1194 | 0.696004 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.0555 | 1.05756 | 0.528780 | − | 0.848759i | \(-0.322650\pi\) | ||||
0.528780 | + | 0.848759i | \(0.322650\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.60555 | −0.186626 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.39445 | 0.0564134 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.4222 | 1.30952 | 0.654760 | − | 0.755837i | \(-0.272770\pi\) | ||||
0.654760 | + | 0.755837i | \(0.272770\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32.7250 | 1.31960 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.09167 | 0.325758 | 0.162879 | − | 0.986646i | \(-0.447922\pi\) | ||||
0.162879 | + | 0.986646i | \(0.447922\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.3305 | −1.09851 | −0.549253 | − | 0.835656i | \(-0.685088\pi\) | ||||
−0.549253 | + | 0.835656i | \(0.685088\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.2111 | −0.650529 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −85.9638 | −3.43307 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.2666 | −1.24668 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.6056 | −1.21839 | −0.609194 | − | 0.793021i | \(-0.708507\pi\) | ||||
−0.609194 | + | 0.793021i | \(0.708507\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.8167 | −0.946627 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.8167 | 0.468930 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.09167 | 0.0828751 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 100.414 | 3.97231 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.0000 | −1.42191 | −0.710957 | − | 0.703235i | \(-0.751738\pi\) | ||||
−0.710957 | + | 0.703235i | \(0.751738\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.2389 | −0.640398 | −0.320199 | − | 0.947350i | \(-0.603750\pi\) | ||||
−0.320199 | + | 0.947350i | \(0.603750\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.2111 | 0.677687 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.8444 | 1.21262 | 0.606309 | − | 0.795229i | \(-0.292649\pi\) | ||||
0.606309 | + | 0.795229i | \(0.292649\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 56.2389 | 2.20757 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.90833 | 0.113986 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.27502 | 0.362960 | 0.181480 | − | 0.983395i | \(-0.441911\pi\) | ||||
0.181480 | + | 0.983395i | \(0.441911\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.21110 | −0.125468 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 125.083 | 4.87996 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.6333 | 1.07644 | 0.538220 | − | 0.842804i | \(-0.319097\pi\) | ||||
0.538220 | + | 0.842804i | \(0.319097\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.0917 | −0.937057 | −0.468529 | − | 0.883448i | \(-0.655216\pi\) | ||||
−0.468529 | + | 0.883448i | \(0.655216\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.90833 | −0.151787 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.48612 | 0.0576293 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.60555 | 0.178328 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.2111 | −0.510771 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.5416 | −1.33347 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.63331 | 0.217148 | 0.108574 | − | 0.994088i | \(-0.465372\pi\) | ||||
0.108574 | + | 0.994088i | \(0.465372\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.2111 | −0.623966 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.4222 | −0.477424 | −0.238712 | − | 0.971090i | \(-0.576725\pi\) | ||||
−0.238712 | + | 0.971090i | \(0.576725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.816654 | 0.0313403 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.4222 | −0.935861 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.7250 | 1.25219 | 0.626093 | − | 0.779748i | \(-0.284653\pi\) | ||||
0.626093 | + | 0.779748i | \(0.284653\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.90833 | −0.263954 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.60555 | −0.252018 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.972244 | −0.0370395 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.1833 | −1.14823 | −0.574114 | − | 0.818775i | \(-0.694653\pi\) | ||||
−0.574114 | + | 0.818775i | \(0.694653\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.6972 | 0.482328 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.39445 | 0.204623 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.7250 | 1.46681 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.8167 | −0.522594 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.9083 | 1.62063 | 0.810313 | − | 0.585998i | \(-0.199297\pi\) | ||||
0.810313 | + | 0.585998i | \(0.199297\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.2666 | 1.48097 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.2111 | 0.572883 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.39445 | −0.0524436 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.1194 | −1.54427 | −0.772136 | − | 0.635457i | \(-0.780812\pi\) | ||||
−0.772136 | + | 0.635457i | \(0.780812\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −114.056 | −4.27742 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.90833 | −0.108918 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.60555 | −0.0600442 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −30.4222 | −1.13614 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.3028 | −0.533404 | −0.266702 | − | 0.963779i | \(-0.585934\pi\) | ||||
−0.266702 | + | 0.963779i | \(0.585934\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.18335 | 0.193038 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −47.6333 | −1.77150 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.60555 | 0.171046 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.90833 | 0.293304 | 0.146652 | − | 0.989188i | \(-0.453150\pi\) | ||||
0.146652 | + | 0.989188i | \(0.453150\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 75.1749 | 2.78426 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.3667 | 0.753289 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.6333 | −0.503558 | −0.251779 | − | 0.967785i | \(-0.581016\pi\) | ||||
−0.251779 | + | 0.967785i | \(0.581016\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.8167 | 0.841605 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.2111 | 0.781321 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.63331 | 0.280796 | 0.140398 | − | 0.990095i | \(-0.455162\pi\) | ||||
0.140398 | + | 0.990095i | \(0.455162\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.90833 | 0.180312 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.33053 | −0.268931 | −0.134466 | − | 0.990918i | \(-0.542932\pi\) | ||||
−0.134466 | + | 0.990918i | \(0.542932\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.69722 | 0.355279 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.3944 | 0.929134 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.39445 | −0.0509520 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.183346 | −0.00669040 | −0.00334520 | − | 0.999994i | \(-0.501065\pi\) | ||||
−0.00334520 | + | 0.999994i | \(0.501065\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.2111 | −0.663649 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.90833 | 0.0694511 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.21110 | −0.0440183 | −0.0220091 | − | 0.999758i | \(-0.507006\pi\) | ||||
−0.0220091 | + | 0.999758i | \(0.507006\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.5139 | −0.635714 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.54163 | 0.164634 | 0.0823171 | − | 0.996606i | \(-0.473768\pi\) | ||||
0.0823171 | + | 0.996606i | \(0.473768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.90833 | 0.213896 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −30.9083 | −1.11749 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.21110 | −0.115946 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.2666 | −1.48811 | −0.744056 | − | 0.668117i | \(-0.767100\pi\) | ||||
−0.744056 | + | 0.668117i | \(0.767100\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −65.4500 | −2.35712 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0000 | 0.431610 | 0.215805 | − | 0.976436i | \(-0.430762\pi\) | ||||
0.215805 | + | 0.976436i | \(0.430762\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.90833 | −0.104470 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.00000 | −0.286998 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −48.6333 | −1.74247 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 67.3305 | 2.40928 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −74.6611 | −2.66817 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.3944 | −0.406685 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.4500 | 0.978485 | 0.489243 | − | 0.872148i | \(-0.337273\pi\) | ||||
0.489243 | + | 0.872148i | \(0.337273\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −47.9361 | −1.70657 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.76114 | 0.133731 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.97224 | 0.0700364 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.6056 | −0.376140 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.8167 | −0.701942 | −0.350971 | − | 0.936386i | \(-0.614148\pi\) | ||||
−0.350971 | + | 0.936386i | \(0.614148\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 83.8722 | 2.95978 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.302776 | 0.0106714 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −85.2666 | −3.00153 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.2750 | 0.642515 | 0.321258 | − | 0.946992i | \(-0.395894\pi\) | ||||
0.321258 | + | 0.946992i | \(0.395894\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.97224 | 0.174599 | 0.0872995 | − | 0.996182i | \(-0.472176\pi\) | ||||
0.0872995 | + | 0.996182i | \(0.472176\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.8167 | −0.730072 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.69722 | −0.199565 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.5778 | −0.894854 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.724981 | −0.0253329 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.0000 | −1.04701 | −0.523504 | − | 0.852023i | \(-0.675375\pi\) | ||||
−0.523504 | + | 0.852023i | \(0.675375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.788897 | 0.0274992 | 0.0137496 | − | 0.999905i | \(-0.495623\pi\) | ||||
0.0137496 | + | 0.999905i | \(0.495623\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.5139 | −0.609755 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.4500 | −1.23272 | −0.616358 | − | 0.787466i | \(-0.711393\pi\) | ||||
−0.616358 | + | 0.787466i | \(0.711393\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.7889 | 0.583103 | 0.291551 | − | 0.956555i | \(-0.405829\pi\) | ||||
0.291551 | + | 0.956555i | \(0.405829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.2389 | 1.46525 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.0000 | 0.935495 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.2111 | −0.734040 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 47.1472 | 1.62965 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.1833 | 0.765854 | 0.382927 | − | 0.923779i | \(-0.374916\pi\) | ||||
0.382927 | + | 0.923779i | \(0.374916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.78890 | −0.268583 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 64.0555 | 2.20619 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.9083 | −0.444060 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.18335 | 0.178102 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.60555 | 0.226702 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00000 | 0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.7250 | 0.367216 | 0.183608 | − | 0.983000i | \(-0.441222\pi\) | ||||
0.183608 | + | 0.983000i | \(0.441222\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 38.8167 | 1.32750 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.6333 | −1.14889 | −0.574446 | − | 0.818543i | \(-0.694782\pi\) | ||||
−0.574446 | + | 0.818543i | \(0.694782\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.1833 | 0.483930 | 0.241965 | − | 0.970285i | \(-0.422208\pi\) | ||||
0.241965 | + | 0.970285i | \(0.422208\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.90833 | 0.337675 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.4500 | −0.798246 | −0.399123 | − | 0.916897i | \(-0.630685\pi\) | ||||
−0.399123 | + | 0.916897i | \(0.630685\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.3028 | 0.792318 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.69722 | 0.193488 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −76.4777 | −2.59433 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.21110 | −0.0410366 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.3305 | 0.721929 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.302776 | 0.0102357 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.1749 | 1.66052 | 0.830260 | − | 0.557376i | \(-0.188192\pi\) | ||||
0.830260 | + | 0.557376i | \(0.188192\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.0278 | −0.979082 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.2666 | −1.05340 | −0.526700 | − | 0.850052i | \(-0.676571\pi\) | ||||
−0.526700 | + | 0.850052i | \(0.676571\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.7250 | −1.37050 | −0.685252 | − | 0.728306i | \(-0.740308\pi\) | ||||
−0.685252 | + | 0.728306i | \(0.740308\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −35.0278 | −1.17745 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.6333 | 0.524915 | 0.262458 | − | 0.964944i | \(-0.415467\pi\) | ||||
0.262458 | + | 0.964944i | \(0.415467\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.57779 | 0.119995 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 158.111 | 5.29692 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.6056 | −0.756466 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.6056 | −0.555062 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.00000 | 0.0333890 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.3944 | −0.446730 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.5500 | −0.418102 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.21110 | 0.173415 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.11943 | −0.269899 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.6611 | 1.01808 | 0.509042 | − | 0.860742i | \(-0.330000\pi\) | ||||
0.509042 | + | 0.860742i | \(0.330000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −36.4222 | −1.20805 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.8167 | 0.855344 | 0.427672 | − | 0.903934i | \(-0.359334\pi\) | ||||
0.427672 | + | 0.903934i | \(0.359334\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.0278 | 0.563536 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.5139 | 0.711227 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.972244 | −0.0321063 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.0000 | −1.45143 | −0.725713 | − | 0.687998i | \(-0.758490\pi\) | ||||
−0.725713 | + | 0.687998i | \(0.758490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −50.5416 | −1.66540 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.84441 | −0.126540 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 135.386 | 4.44666 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −57.6333 | −1.89089 | −0.945444 | − | 0.325785i | \(-0.894371\pi\) | ||||
−0.945444 | + | 0.325785i | \(0.894371\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.9083 | −1.11130 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.2111 | −0.694420 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.7250 | −0.677779 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.9638 | −1.46890 | −0.734452 | − | 0.678660i | \(-0.762561\pi\) | ||||
−0.734452 | + | 0.678660i | \(0.762561\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.0278 | 1.37152 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.9361 | −0.682497 | −0.341248 | − | 0.939973i | \(-0.610850\pi\) | ||||
−0.341248 | + | 0.939973i | \(0.610850\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.90833 | −0.322660 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.90833 | −0.159668 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.9361 | −1.36274 | −0.681370 | − | 0.731939i | \(-0.738615\pi\) | ||||
−0.681370 | + | 0.731939i | \(0.738615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.78890 | −0.155454 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.6333 | 1.57704 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.66947 | −0.0540794 | −0.0270397 | − | 0.999634i | \(-0.508608\pi\) | ||||
−0.0270397 | + | 0.999634i | \(0.508608\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.39445 | 0.0451233 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −80.6611 | −2.60740 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.09167 | −0.0675436 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.5416 | −0.727150 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.4222 | −1.17369 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.81665 | 0.122862 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.39445 | 0.173474 | 0.0867369 | − | 0.996231i | \(-0.472356\pi\) | ||||
0.0867369 | + | 0.996231i | \(0.472356\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 63.3583 | 2.03536 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.9083 | 0.895621 | 0.447810 | − | 0.894129i | \(-0.352204\pi\) | ||||
0.447810 | + | 0.894129i | \(0.352204\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.63331 | 0.0523614 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.00000 | 0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.5139 | −0.368362 | −0.184181 | − | 0.982892i | \(-0.558963\pi\) | ||||
−0.184181 | + | 0.982892i | \(0.558963\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 154.322 | 4.92713 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.5416 | 0.623281 | 0.311641 | − | 0.950200i | \(-0.399121\pi\) | ||||
0.311641 | + | 0.950200i | \(0.399121\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.697224 | 0.0222154 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.60555 | 0.146596 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.21110 | −0.165703 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.3305 | −0.772885 | −0.386442 | − | 0.922314i | \(-0.626296\pi\) | ||||
−0.386442 | + | 0.922314i | \(0.626296\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.0278 | 0.984636 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.42221 | −0.267002 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.2111 | −0.988466 | −0.494233 | − | 0.869330i | \(-0.664551\pi\) | ||||
−0.494233 | + | 0.869330i | \(0.664551\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −129.689 | −4.10317 |
(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 | 1840.2.a.j.1.1 | 2 | ||
4.3 | odd | 2 | 230.2.a.b.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 9200.2.a.ca.1.2 | 2 | |||
8.3 | odd | 2 | 7360.2.a.bc.1.1 | 2 | |||
8.5 | even | 2 | 7360.2.a.bu.1.2 | 2 | |||
12.11 | even | 2 | 2070.2.a.w.1.1 | 2 | |||
20.3 | even | 4 | 1150.2.b.f.599.4 | 4 | |||
20.7 | even | 4 | 1150.2.b.f.599.1 | 4 | |||
20.19 | odd | 2 | 1150.2.a.m.1.1 | 2 | |||
92.91 | even | 2 | 5290.2.a.j.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.a.b.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
1150.2.a.m.1.1 | 2 | 20.19 | odd | 2 | |||
1150.2.b.f.599.1 | 4 | 20.7 | even | 4 | |||
1150.2.b.f.599.4 | 4 | 20.3 | even | 4 | |||
1840.2.a.j.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2070.2.a.w.1.1 | 2 | 12.11 | even | 2 | |||
5290.2.a.j.1.2 | 2 | 92.91 | even | 2 | |||
7360.2.a.bc.1.1 | 2 | 8.3 | odd | 2 | |||
7360.2.a.bu.1.2 | 2 | 8.5 | even | 2 | |||
9200.2.a.ca.1.2 | 2 | 5.4 | even | 2 |