Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,2,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("230.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.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: | \(1.83655924649\) |
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: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 3.30278 | 1.90686 | 0.953429 | − | 0.301617i | \(-0.0975264\pi\) | ||||
0.953429 | + | 0.301617i | \(0.0975264\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −3.30278 | −1.34835 | ||||||||
\(7\) | −0.302776 | −0.114438 | −0.0572192 | − | 0.998362i | \(-0.518223\pi\) | ||||
−0.0572192 | + | 0.998362i | \(0.518223\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.90833 | 2.63611 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −5.30278 | −1.59885 | −0.799424 | − | 0.600768i | \(-0.794862\pi\) | ||||
−0.799424 | + | 0.600768i | \(0.794862\pi\) | |||||||
\(12\) | 3.30278 | 0.953429 | ||||||||
\(13\) | −0.302776 | −0.0839749 | −0.0419874 | − | 0.999118i | \(-0.513369\pi\) | ||||
−0.0419874 | + | 0.999118i | \(0.513369\pi\) | |||||||
\(14\) | 0.302776 | 0.0809202 | ||||||||
\(15\) | 3.30278 | 0.852773 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.90833 | −0.947909 | −0.473954 | − | 0.880549i | \(-0.657174\pi\) | ||||
−0.473954 | + | 0.880549i | \(0.657174\pi\) | |||||||
\(18\) | −7.90833 | −1.86401 | ||||||||
\(19\) | −4.90833 | −1.12605 | −0.563024 | − | 0.826441i | \(-0.690362\pi\) | ||||
−0.563024 | + | 0.826441i | \(0.690362\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 5.30278 | 1.13056 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −3.30278 | −0.674176 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.302776 | 0.0593792 | ||||||||
\(27\) | 16.2111 | 3.11983 | ||||||||
\(28\) | −0.302776 | −0.0572192 | ||||||||
\(29\) | 4.60555 | 0.855229 | 0.427615 | − | 0.903961i | \(-0.359354\pi\) | ||||
0.427615 | + | 0.903961i | \(0.359354\pi\) | |||||||
\(30\) | −3.30278 | −0.603002 | ||||||||
\(31\) | 2.90833 | 0.522351 | 0.261175 | − | 0.965291i | \(-0.415890\pi\) | ||||
0.261175 | + | 0.965291i | \(0.415890\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −17.5139 | −3.04877 | ||||||||
\(34\) | 3.90833 | 0.670273 | ||||||||
\(35\) | −0.302776 | −0.0511784 | ||||||||
\(36\) | 7.90833 | 1.31805 | ||||||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | 4.90833 | 0.796236 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −9.90833 | −1.54742 | −0.773710 | − | 0.633540i | \(-0.781601\pi\) | ||||
−0.773710 | + | 0.633540i | \(0.781601\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | 5.21110 | 0.794686 | 0.397343 | − | 0.917670i | \(-0.369932\pi\) | ||||
0.397343 | + | 0.917670i | \(0.369932\pi\) | |||||||
\(44\) | −5.30278 | −0.799424 | ||||||||
\(45\) | 7.90833 | 1.17890 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 4.60555 | 0.671789 | 0.335894 | − | 0.941900i | \(-0.390961\pi\) | ||||
0.335894 | + | 0.941900i | \(0.390961\pi\) | |||||||
\(48\) | 3.30278 | 0.476715 | ||||||||
\(49\) | −6.90833 | −0.986904 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −12.9083 | −1.80753 | ||||||||
\(52\) | −0.302776 | −0.0419874 | ||||||||
\(53\) | 3.21110 | 0.441079 | 0.220539 | − | 0.975378i | \(-0.429218\pi\) | ||||
0.220539 | + | 0.975378i | \(0.429218\pi\) | |||||||
\(54\) | −16.2111 | −2.20605 | ||||||||
\(55\) | −5.30278 | −0.715026 | ||||||||
\(56\) | 0.302776 | 0.0404601 | ||||||||
\(57\) | −16.2111 | −2.14721 | ||||||||
\(58\) | −4.60555 | −0.604739 | ||||||||
\(59\) | −10.6056 | −1.38073 | −0.690363 | − | 0.723464i | \(-0.742549\pi\) | ||||
−0.690363 | + | 0.723464i | \(0.742549\pi\) | |||||||
\(60\) | 3.30278 | 0.426387 | ||||||||
\(61\) | −6.51388 | −0.834017 | −0.417008 | − | 0.908903i | \(-0.636921\pi\) | ||||
−0.417008 | + | 0.908903i | \(0.636921\pi\) | |||||||
\(62\) | −2.90833 | −0.369358 | ||||||||
\(63\) | −2.39445 | −0.301672 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.302776 | −0.0375547 | ||||||||
\(66\) | 17.5139 | 2.15581 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | −3.90833 | −0.473954 | ||||||||
\(69\) | −3.30278 | −0.397607 | ||||||||
\(70\) | 0.302776 | 0.0361886 | ||||||||
\(71\) | −12.6972 | −1.50688 | −0.753442 | − | 0.657515i | \(-0.771608\pi\) | ||||
−0.753442 | + | 0.657515i | \(0.771608\pi\) | |||||||
\(72\) | −7.90833 | −0.932005 | ||||||||
\(73\) | 15.8167 | 1.85120 | 0.925600 | − | 0.378504i | \(-0.123561\pi\) | ||||
0.925600 | + | 0.378504i | \(0.123561\pi\) | |||||||
\(74\) | −8.00000 | −0.929981 | ||||||||
\(75\) | 3.30278 | 0.381372 | ||||||||
\(76\) | −4.90833 | −0.563024 | ||||||||
\(77\) | 1.60555 | 0.182970 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 14.4222 | 1.62262 | 0.811312 | − | 0.584613i | \(-0.198754\pi\) | ||||
0.811312 | + | 0.584613i | \(0.198754\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 29.8167 | 3.31296 | ||||||||
\(82\) | 9.90833 | 1.09419 | ||||||||
\(83\) | −3.21110 | −0.352464 | −0.176232 | − | 0.984349i | \(-0.556391\pi\) | ||||
−0.176232 | + | 0.984349i | \(0.556391\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −3.90833 | −0.423918 | ||||||||
\(86\) | −5.21110 | −0.561928 | ||||||||
\(87\) | 15.2111 | 1.63080 | ||||||||
\(88\) | 5.30278 | 0.565278 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | −7.90833 | −0.833611 | ||||||||
\(91\) | 0.0916731 | 0.00960995 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 9.60555 | 0.996049 | ||||||||
\(94\) | −4.60555 | −0.475026 | ||||||||
\(95\) | −4.90833 | −0.503584 | ||||||||
\(96\) | −3.30278 | −0.337088 | ||||||||
\(97\) | 2.69722 | 0.273862 | 0.136931 | − | 0.990581i | \(-0.456276\pi\) | ||||
0.136931 | + | 0.990581i | \(0.456276\pi\) | |||||||
\(98\) | 6.90833 | 0.697846 | ||||||||
\(99\) | −41.9361 | −4.21473 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −4.60555 | −0.458269 | −0.229135 | − | 0.973395i | \(-0.573590\pi\) | ||||
−0.229135 | + | 0.973395i | \(0.573590\pi\) | |||||||
\(102\) | 12.9083 | 1.27811 | ||||||||
\(103\) | −17.1194 | −1.68683 | −0.843414 | − | 0.537265i | \(-0.819458\pi\) | ||||
−0.843414 | + | 0.537265i | \(0.819458\pi\) | |||||||
\(104\) | 0.302776 | 0.0296896 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | −3.21110 | −0.311890 | ||||||||
\(107\) | 4.60555 | 0.445235 | 0.222618 | − | 0.974906i | \(-0.428540\pi\) | ||||
0.222618 | + | 0.974906i | \(0.428540\pi\) | |||||||
\(108\) | 16.2111 | 1.55991 | ||||||||
\(109\) | 19.5139 | 1.86909 | 0.934545 | − | 0.355844i | \(-0.115807\pi\) | ||||
0.934545 | + | 0.355844i | \(0.115807\pi\) | |||||||
\(110\) | 5.30278 | 0.505600 | ||||||||
\(111\) | 26.4222 | 2.50788 | ||||||||
\(112\) | −0.302776 | −0.0286096 | ||||||||
\(113\) | 12.4222 | 1.16858 | 0.584291 | − | 0.811544i | \(-0.301373\pi\) | ||||
0.584291 | + | 0.811544i | \(0.301373\pi\) | |||||||
\(114\) | 16.2111 | 1.51831 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 4.60555 | 0.427615 | ||||||||
\(117\) | −2.39445 | −0.221367 | ||||||||
\(118\) | 10.6056 | 0.976320 | ||||||||
\(119\) | 1.18335 | 0.108477 | ||||||||
\(120\) | −3.30278 | −0.301501 | ||||||||
\(121\) | 17.1194 | 1.55631 | ||||||||
\(122\) | 6.51388 | 0.589739 | ||||||||
\(123\) | −32.7250 | −2.95071 | ||||||||
\(124\) | 2.90833 | 0.261175 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.39445 | 0.213314 | ||||||||
\(127\) | −11.8167 | −1.04856 | −0.524279 | − | 0.851546i | \(-0.675665\pi\) | ||||
−0.524279 | + | 0.851546i | \(0.675665\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 17.2111 | 1.51535 | ||||||||
\(130\) | 0.302776 | 0.0265552 | ||||||||
\(131\) | 3.21110 | 0.280555 | 0.140278 | − | 0.990112i | \(-0.455200\pi\) | ||||
0.140278 | + | 0.990112i | \(0.455200\pi\) | |||||||
\(132\) | −17.5139 | −1.52439 | ||||||||
\(133\) | 1.48612 | 0.128863 | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 16.2111 | 1.39523 | ||||||||
\(136\) | 3.90833 | 0.335136 | ||||||||
\(137\) | −6.90833 | −0.590218 | −0.295109 | − | 0.955464i | \(-0.595356\pi\) | ||||
−0.295109 | + | 0.955464i | \(0.595356\pi\) | |||||||
\(138\) | 3.30278 | 0.281151 | ||||||||
\(139\) | −5.39445 | −0.457551 | −0.228776 | − | 0.973479i | \(-0.573472\pi\) | ||||
−0.228776 | + | 0.973479i | \(0.573472\pi\) | |||||||
\(140\) | −0.302776 | −0.0255892 | ||||||||
\(141\) | 15.2111 | 1.28101 | ||||||||
\(142\) | 12.6972 | 1.06553 | ||||||||
\(143\) | 1.60555 | 0.134263 | ||||||||
\(144\) | 7.90833 | 0.659027 | ||||||||
\(145\) | 4.60555 | 0.382470 | ||||||||
\(146\) | −15.8167 | −1.30900 | ||||||||
\(147\) | −22.8167 | −1.88189 | ||||||||
\(148\) | 8.00000 | 0.657596 | ||||||||
\(149\) | 9.69722 | 0.794428 | 0.397214 | − | 0.917726i | \(-0.369977\pi\) | ||||
0.397214 | + | 0.917726i | \(0.369977\pi\) | |||||||
\(150\) | −3.30278 | −0.269671 | ||||||||
\(151\) | −1.90833 | −0.155297 | −0.0776487 | − | 0.996981i | \(-0.524741\pi\) | ||||
−0.0776487 | + | 0.996981i | \(0.524741\pi\) | |||||||
\(152\) | 4.90833 | 0.398118 | ||||||||
\(153\) | −30.9083 | −2.49879 | ||||||||
\(154\) | −1.60555 | −0.129379 | ||||||||
\(155\) | 2.90833 | 0.233602 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −11.3944 | −0.909376 | −0.454688 | − | 0.890651i | \(-0.650249\pi\) | ||||
−0.454688 | + | 0.890651i | \(0.650249\pi\) | |||||||
\(158\) | −14.4222 | −1.14737 | ||||||||
\(159\) | 10.6056 | 0.841075 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0.302776 | 0.0238621 | ||||||||
\(162\) | −29.8167 | −2.34262 | ||||||||
\(163\) | 5.69722 | 0.446241 | 0.223121 | − | 0.974791i | \(-0.428376\pi\) | ||||
0.223121 | + | 0.974791i | \(0.428376\pi\) | |||||||
\(164\) | −9.90833 | −0.773710 | ||||||||
\(165\) | −17.5139 | −1.36345 | ||||||||
\(166\) | 3.21110 | 0.249230 | ||||||||
\(167\) | 21.2111 | 1.64136 | 0.820682 | − | 0.571385i | \(-0.193594\pi\) | ||||
0.820682 | + | 0.571385i | \(0.193594\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | −12.9083 | −0.992948 | ||||||||
\(170\) | 3.90833 | 0.299755 | ||||||||
\(171\) | −38.8167 | −2.96838 | ||||||||
\(172\) | 5.21110 | 0.397343 | ||||||||
\(173\) | 23.3028 | 1.77168 | 0.885839 | − | 0.463993i | \(-0.153584\pi\) | ||||
0.885839 | + | 0.463993i | \(0.153584\pi\) | |||||||
\(174\) | −15.2111 | −1.15315 | ||||||||
\(175\) | −0.302776 | −0.0228877 | ||||||||
\(176\) | −5.30278 | −0.399712 | ||||||||
\(177\) | −35.0278 | −2.63285 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.6056 | 1.24116 | 0.620579 | − | 0.784144i | \(-0.286898\pi\) | ||||
0.620579 | + | 0.784144i | \(0.286898\pi\) | |||||||
\(180\) | 7.90833 | 0.589452 | ||||||||
\(181\) | −8.11943 | −0.603512 | −0.301756 | − | 0.953385i | \(-0.597573\pi\) | ||||
−0.301756 | + | 0.953385i | \(0.597573\pi\) | |||||||
\(182\) | −0.0916731 | −0.00679526 | ||||||||
\(183\) | −21.5139 | −1.59035 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 8.00000 | 0.588172 | ||||||||
\(186\) | −9.60555 | −0.704313 | ||||||||
\(187\) | 20.7250 | 1.51556 | ||||||||
\(188\) | 4.60555 | 0.335894 | ||||||||
\(189\) | −4.90833 | −0.357028 | ||||||||
\(190\) | 4.90833 | 0.356087 | ||||||||
\(191\) | −1.39445 | −0.100899 | −0.0504494 | − | 0.998727i | \(-0.516065\pi\) | ||||
−0.0504494 | + | 0.998727i | \(0.516065\pi\) | |||||||
\(192\) | 3.30278 | 0.238357 | ||||||||
\(193\) | 3.81665 | 0.274729 | 0.137364 | − | 0.990521i | \(-0.456137\pi\) | ||||
0.137364 | + | 0.990521i | \(0.456137\pi\) | |||||||
\(194\) | −2.69722 | −0.193649 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | −6.90833 | −0.493452 | ||||||||
\(197\) | 0.697224 | 0.0496752 | 0.0248376 | − | 0.999691i | \(-0.492093\pi\) | ||||
0.0248376 | + | 0.999691i | \(0.492093\pi\) | |||||||
\(198\) | 41.9361 | 2.98027 | ||||||||
\(199\) | 8.42221 | 0.597034 | 0.298517 | − | 0.954404i | \(-0.403508\pi\) | ||||
0.298517 | + | 0.954404i | \(0.403508\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −13.2111 | −0.931839 | ||||||||
\(202\) | 4.60555 | 0.324045 | ||||||||
\(203\) | −1.39445 | −0.0978711 | ||||||||
\(204\) | −12.9083 | −0.903764 | ||||||||
\(205\) | −9.90833 | −0.692028 | ||||||||
\(206\) | 17.1194 | 1.19277 | ||||||||
\(207\) | −7.90833 | −0.549667 | ||||||||
\(208\) | −0.302776 | −0.0209937 | ||||||||
\(209\) | 26.0278 | 1.80038 | ||||||||
\(210\) | 1.00000 | 0.0690066 | ||||||||
\(211\) | −7.21110 | −0.496433 | −0.248216 | − | 0.968705i | \(-0.579844\pi\) | ||||
−0.248216 | + | 0.968705i | \(0.579844\pi\) | |||||||
\(212\) | 3.21110 | 0.220539 | ||||||||
\(213\) | −41.9361 | −2.87341 | ||||||||
\(214\) | −4.60555 | −0.314829 | ||||||||
\(215\) | 5.21110 | 0.355394 | ||||||||
\(216\) | −16.2111 | −1.10303 | ||||||||
\(217\) | −0.880571 | −0.0597770 | ||||||||
\(218\) | −19.5139 | −1.32165 | ||||||||
\(219\) | 52.2389 | 3.52997 | ||||||||
\(220\) | −5.30278 | −0.357513 | ||||||||
\(221\) | 1.18335 | 0.0796005 | ||||||||
\(222\) | −26.4222 | −1.77334 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 0.302776 | 0.0202300 | ||||||||
\(225\) | 7.90833 | 0.527222 | ||||||||
\(226\) | −12.4222 | −0.826313 | ||||||||
\(227\) | −7.39445 | −0.490787 | −0.245393 | − | 0.969424i | \(-0.578917\pi\) | ||||
−0.245393 | + | 0.969424i | \(0.578917\pi\) | |||||||
\(228\) | −16.2111 | −1.07361 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | 5.30278 | 0.348897 | ||||||||
\(232\) | −4.60555 | −0.302369 | ||||||||
\(233\) | 4.18335 | 0.274060 | 0.137030 | − | 0.990567i | \(-0.456244\pi\) | ||||
0.137030 | + | 0.990567i | \(0.456244\pi\) | |||||||
\(234\) | 2.39445 | 0.156530 | ||||||||
\(235\) | 4.60555 | 0.300433 | ||||||||
\(236\) | −10.6056 | −0.690363 | ||||||||
\(237\) | 47.6333 | 3.09412 | ||||||||
\(238\) | −1.18335 | −0.0767049 | ||||||||
\(239\) | −9.21110 | −0.595817 | −0.297908 | − | 0.954594i | \(-0.596289\pi\) | ||||
−0.297908 | + | 0.954594i | \(0.596289\pi\) | |||||||
\(240\) | 3.30278 | 0.213193 | ||||||||
\(241\) | 14.4222 | 0.929016 | 0.464508 | − | 0.885569i | \(-0.346231\pi\) | ||||
0.464508 | + | 0.885569i | \(0.346231\pi\) | |||||||
\(242\) | −17.1194 | −1.10048 | ||||||||
\(243\) | 49.8444 | 3.19752 | ||||||||
\(244\) | −6.51388 | −0.417008 | ||||||||
\(245\) | −6.90833 | −0.441357 | ||||||||
\(246\) | 32.7250 | 2.08647 | ||||||||
\(247\) | 1.48612 | 0.0945597 | ||||||||
\(248\) | −2.90833 | −0.184679 | ||||||||
\(249\) | −10.6056 | −0.672100 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −5.51388 | −0.348033 | −0.174016 | − | 0.984743i | \(-0.555675\pi\) | ||||
−0.174016 | + | 0.984743i | \(0.555675\pi\) | |||||||
\(252\) | −2.39445 | −0.150836 | ||||||||
\(253\) | 5.30278 | 0.333383 | ||||||||
\(254\) | 11.8167 | 0.741443 | ||||||||
\(255\) | −12.9083 | −0.808351 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.8167 | 1.23613 | 0.618064 | − | 0.786127i | \(-0.287917\pi\) | ||||
0.618064 | + | 0.786127i | \(0.287917\pi\) | |||||||
\(258\) | −17.2111 | −1.07152 | ||||||||
\(259\) | −2.42221 | −0.150509 | ||||||||
\(260\) | −0.302776 | −0.0187773 | ||||||||
\(261\) | 36.4222 | 2.25448 | ||||||||
\(262\) | −3.21110 | −0.198383 | ||||||||
\(263\) | −14.5139 | −0.894964 | −0.447482 | − | 0.894293i | \(-0.647679\pi\) | ||||
−0.447482 | + | 0.894293i | \(0.647679\pi\) | |||||||
\(264\) | 17.5139 | 1.07790 | ||||||||
\(265\) | 3.21110 | 0.197256 | ||||||||
\(266\) | −1.48612 | −0.0911200 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.00000 | −0.244339 | ||||||||
\(269\) | 25.8167 | 1.57407 | 0.787035 | − | 0.616909i | \(-0.211615\pi\) | ||||
0.787035 | + | 0.616909i | \(0.211615\pi\) | |||||||
\(270\) | −16.2111 | −0.986576 | ||||||||
\(271\) | −6.30278 | −0.382866 | −0.191433 | − | 0.981506i | \(-0.561314\pi\) | ||||
−0.191433 | + | 0.981506i | \(0.561314\pi\) | |||||||
\(272\) | −3.90833 | −0.236977 | ||||||||
\(273\) | 0.302776 | 0.0183248 | ||||||||
\(274\) | 6.90833 | 0.417347 | ||||||||
\(275\) | −5.30278 | −0.319769 | ||||||||
\(276\) | −3.30278 | −0.198804 | ||||||||
\(277\) | −12.7889 | −0.768410 | −0.384205 | − | 0.923248i | \(-0.625524\pi\) | ||||
−0.384205 | + | 0.923248i | \(0.625524\pi\) | |||||||
\(278\) | 5.39445 | 0.323538 | ||||||||
\(279\) | 23.0000 | 1.37697 | ||||||||
\(280\) | 0.302776 | 0.0180943 | ||||||||
\(281\) | −19.3944 | −1.15698 | −0.578488 | − | 0.815691i | \(-0.696357\pi\) | ||||
−0.578488 | + | 0.815691i | \(0.696357\pi\) | |||||||
\(282\) | −15.2111 | −0.905808 | ||||||||
\(283\) | 2.00000 | 0.118888 | 0.0594438 | − | 0.998232i | \(-0.481067\pi\) | ||||
0.0594438 | + | 0.998232i | \(0.481067\pi\) | |||||||
\(284\) | −12.6972 | −0.753442 | ||||||||
\(285\) | −16.2111 | −0.960263 | ||||||||
\(286\) | −1.60555 | −0.0949382 | ||||||||
\(287\) | 3.00000 | 0.177084 | ||||||||
\(288\) | −7.90833 | −0.466003 | ||||||||
\(289\) | −1.72498 | −0.101469 | ||||||||
\(290\) | −4.60555 | −0.270447 | ||||||||
\(291\) | 8.90833 | 0.522215 | ||||||||
\(292\) | 15.8167 | 0.925600 | ||||||||
\(293\) | 8.78890 | 0.513453 | 0.256726 | − | 0.966484i | \(-0.417356\pi\) | ||||
0.256726 | + | 0.966484i | \(0.417356\pi\) | |||||||
\(294\) | 22.8167 | 1.33069 | ||||||||
\(295\) | −10.6056 | −0.617479 | ||||||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | −85.9638 | −4.98813 | ||||||||
\(298\) | −9.69722 | −0.561745 | ||||||||
\(299\) | 0.302776 | 0.0175100 | ||||||||
\(300\) | 3.30278 | 0.190686 | ||||||||
\(301\) | −1.57779 | −0.0909426 | ||||||||
\(302\) | 1.90833 | 0.109812 | ||||||||
\(303\) | −15.2111 | −0.873855 | ||||||||
\(304\) | −4.90833 | −0.281512 | ||||||||
\(305\) | −6.51388 | −0.372984 | ||||||||
\(306\) | 30.9083 | 1.76691 | ||||||||
\(307\) | −15.3028 | −0.873376 | −0.436688 | − | 0.899613i | \(-0.643849\pi\) | ||||
−0.436688 | + | 0.899613i | \(0.643849\pi\) | |||||||
\(308\) | 1.60555 | 0.0914848 | ||||||||
\(309\) | −56.5416 | −3.21654 | ||||||||
\(310\) | −2.90833 | −0.165182 | ||||||||
\(311\) | −6.42221 | −0.364170 | −0.182085 | − | 0.983283i | \(-0.558285\pi\) | ||||
−0.182085 | + | 0.983283i | \(0.558285\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −12.7250 | −0.719258 | −0.359629 | − | 0.933095i | \(-0.617097\pi\) | ||||
−0.359629 | + | 0.933095i | \(0.617097\pi\) | |||||||
\(314\) | 11.3944 | 0.643026 | ||||||||
\(315\) | −2.39445 | −0.134912 | ||||||||
\(316\) | 14.4222 | 0.811312 | ||||||||
\(317\) | −14.7250 | −0.827037 | −0.413519 | − | 0.910496i | \(-0.635700\pi\) | ||||
−0.413519 | + | 0.910496i | \(0.635700\pi\) | |||||||
\(318\) | −10.6056 | −0.594730 | ||||||||
\(319\) | −24.4222 | −1.36738 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 15.2111 | 0.849001 | ||||||||
\(322\) | −0.302776 | −0.0168730 | ||||||||
\(323\) | 19.1833 | 1.06739 | ||||||||
\(324\) | 29.8167 | 1.65648 | ||||||||
\(325\) | −0.302776 | −0.0167950 | ||||||||
\(326\) | −5.69722 | −0.315540 | ||||||||
\(327\) | 64.4500 | 3.56409 | ||||||||
\(328\) | 9.90833 | 0.547096 | ||||||||
\(329\) | −1.39445 | −0.0768784 | ||||||||
\(330\) | 17.5139 | 0.964107 | ||||||||
\(331\) | 9.39445 | 0.516366 | 0.258183 | − | 0.966096i | \(-0.416876\pi\) | ||||
0.258183 | + | 0.966096i | \(0.416876\pi\) | |||||||
\(332\) | −3.21110 | −0.176232 | ||||||||
\(333\) | 63.2666 | 3.46699 | ||||||||
\(334\) | −21.2111 | −1.16062 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | −4.48612 | −0.244375 | −0.122187 | − | 0.992507i | \(-0.538991\pi\) | ||||
−0.122187 | + | 0.992507i | \(0.538991\pi\) | |||||||
\(338\) | 12.9083 | 0.702120 | ||||||||
\(339\) | 41.0278 | 2.22832 | ||||||||
\(340\) | −3.90833 | −0.211959 | ||||||||
\(341\) | −15.4222 | −0.835159 | ||||||||
\(342\) | 38.8167 | 2.09896 | ||||||||
\(343\) | 4.21110 | 0.227378 | ||||||||
\(344\) | −5.21110 | −0.280964 | ||||||||
\(345\) | −3.30278 | −0.177815 | ||||||||
\(346\) | −23.3028 | −1.25276 | ||||||||
\(347\) | −25.5416 | −1.37115 | −0.685573 | − | 0.728004i | \(-0.740448\pi\) | ||||
−0.685573 | + | 0.728004i | \(0.740448\pi\) | |||||||
\(348\) | 15.2111 | 0.815401 | ||||||||
\(349\) | −12.7889 | −0.684574 | −0.342287 | − | 0.939595i | \(-0.611202\pi\) | ||||
−0.342287 | + | 0.939595i | \(0.611202\pi\) | |||||||
\(350\) | 0.302776 | 0.0161840 | ||||||||
\(351\) | −4.90833 | −0.261987 | ||||||||
\(352\) | 5.30278 | 0.282639 | ||||||||
\(353\) | 18.4222 | 0.980515 | 0.490258 | − | 0.871578i | \(-0.336903\pi\) | ||||
0.490258 | + | 0.871578i | \(0.336903\pi\) | |||||||
\(354\) | 35.0278 | 1.86170 | ||||||||
\(355\) | −12.6972 | −0.673899 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.90833 | 0.206851 | ||||||||
\(358\) | −16.6056 | −0.877631 | ||||||||
\(359\) | −3.21110 | −0.169476 | −0.0847378 | − | 0.996403i | \(-0.527005\pi\) | ||||
−0.0847378 | + | 0.996403i | \(0.527005\pi\) | |||||||
\(360\) | −7.90833 | −0.416805 | ||||||||
\(361\) | 5.09167 | 0.267983 | ||||||||
\(362\) | 8.11943 | 0.426748 | ||||||||
\(363\) | 56.5416 | 2.96767 | ||||||||
\(364\) | 0.0916731 | 0.00480498 | ||||||||
\(365\) | 15.8167 | 0.827881 | ||||||||
\(366\) | 21.5139 | 1.12455 | ||||||||
\(367\) | 29.2111 | 1.52481 | 0.762404 | − | 0.647102i | \(-0.224019\pi\) | ||||
0.762404 | + | 0.647102i | \(0.224019\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −78.3583 | −4.07917 | ||||||||
\(370\) | −8.00000 | −0.415900 | ||||||||
\(371\) | −0.972244 | −0.0504764 | ||||||||
\(372\) | 9.60555 | 0.498025 | ||||||||
\(373\) | −2.60555 | −0.134910 | −0.0674552 | − | 0.997722i | \(-0.521488\pi\) | ||||
−0.0674552 | + | 0.997722i | \(0.521488\pi\) | |||||||
\(374\) | −20.7250 | −1.07166 | ||||||||
\(375\) | 3.30278 | 0.170555 | ||||||||
\(376\) | −4.60555 | −0.237513 | ||||||||
\(377\) | −1.39445 | −0.0718178 | ||||||||
\(378\) | 4.90833 | 0.252457 | ||||||||
\(379\) | 4.09167 | 0.210175 | 0.105088 | − | 0.994463i | \(-0.466488\pi\) | ||||
0.105088 | + | 0.994463i | \(0.466488\pi\) | |||||||
\(380\) | −4.90833 | −0.251792 | ||||||||
\(381\) | −39.0278 | −1.99945 | ||||||||
\(382\) | 1.39445 | 0.0713462 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | −3.30278 | −0.168544 | ||||||||
\(385\) | 1.60555 | 0.0818265 | ||||||||
\(386\) | −3.81665 | −0.194263 | ||||||||
\(387\) | 41.2111 | 2.09488 | ||||||||
\(388\) | 2.69722 | 0.136931 | ||||||||
\(389\) | 20.9361 | 1.06150 | 0.530751 | − | 0.847528i | \(-0.321910\pi\) | ||||
0.530751 | + | 0.847528i | \(0.321910\pi\) | |||||||
\(390\) | 1.00000 | 0.0506370 | ||||||||
\(391\) | 3.90833 | 0.197653 | ||||||||
\(392\) | 6.90833 | 0.348923 | ||||||||
\(393\) | 10.6056 | 0.534979 | ||||||||
\(394\) | −0.697224 | −0.0351257 | ||||||||
\(395\) | 14.4222 | 0.725660 | ||||||||
\(396\) | −41.9361 | −2.10737 | ||||||||
\(397\) | −21.7250 | −1.09035 | −0.545173 | − | 0.838324i | \(-0.683536\pi\) | ||||
−0.545173 | + | 0.838324i | \(0.683536\pi\) | |||||||
\(398\) | −8.42221 | −0.422167 | ||||||||
\(399\) | 4.90833 | 0.245724 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.39445 | −0.0696354 | −0.0348177 | − | 0.999394i | \(-0.511085\pi\) | ||||
−0.0348177 | + | 0.999394i | \(0.511085\pi\) | |||||||
\(402\) | 13.2111 | 0.658910 | ||||||||
\(403\) | −0.880571 | −0.0438643 | ||||||||
\(404\) | −4.60555 | −0.229135 | ||||||||
\(405\) | 29.8167 | 1.48160 | ||||||||
\(406\) | 1.39445 | 0.0692053 | ||||||||
\(407\) | −42.4222 | −2.10279 | ||||||||
\(408\) | 12.9083 | 0.639057 | ||||||||
\(409\) | −15.0917 | −0.746235 | −0.373118 | − | 0.927784i | \(-0.621711\pi\) | ||||
−0.373118 | + | 0.927784i | \(0.621711\pi\) | |||||||
\(410\) | 9.90833 | 0.489337 | ||||||||
\(411\) | −22.8167 | −1.12546 | ||||||||
\(412\) | −17.1194 | −0.843414 | ||||||||
\(413\) | 3.21110 | 0.158008 | ||||||||
\(414\) | 7.90833 | 0.388673 | ||||||||
\(415\) | −3.21110 | −0.157627 | ||||||||
\(416\) | 0.302776 | 0.0148448 | ||||||||
\(417\) | −17.8167 | −0.872485 | ||||||||
\(418\) | −26.0278 | −1.27306 | ||||||||
\(419\) | −39.6333 | −1.93621 | −0.968107 | − | 0.250538i | \(-0.919393\pi\) | ||||
−0.968107 | + | 0.250538i | \(0.919393\pi\) | |||||||
\(420\) | −1.00000 | −0.0487950 | ||||||||
\(421\) | 34.3028 | 1.67181 | 0.835907 | − | 0.548870i | \(-0.184942\pi\) | ||||
0.835907 | + | 0.548870i | \(0.184942\pi\) | |||||||
\(422\) | 7.21110 | 0.351031 | ||||||||
\(423\) | 36.4222 | 1.77091 | ||||||||
\(424\) | −3.21110 | −0.155945 | ||||||||
\(425\) | −3.90833 | −0.189582 | ||||||||
\(426\) | 41.9361 | 2.03181 | ||||||||
\(427\) | 1.97224 | 0.0954436 | ||||||||
\(428\) | 4.60555 | 0.222618 | ||||||||
\(429\) | 5.30278 | 0.256020 | ||||||||
\(430\) | −5.21110 | −0.251302 | ||||||||
\(431\) | 20.2389 | 0.974872 | 0.487436 | − | 0.873159i | \(-0.337932\pi\) | ||||
0.487436 | + | 0.873159i | \(0.337932\pi\) | |||||||
\(432\) | 16.2111 | 0.779957 | ||||||||
\(433\) | −34.9083 | −1.67759 | −0.838794 | − | 0.544450i | \(-0.816739\pi\) | ||||
−0.838794 | + | 0.544450i | \(0.816739\pi\) | |||||||
\(434\) | 0.880571 | 0.0422687 | ||||||||
\(435\) | 15.2111 | 0.729317 | ||||||||
\(436\) | 19.5139 | 0.934545 | ||||||||
\(437\) | 4.90833 | 0.234797 | ||||||||
\(438\) | −52.2389 | −2.49607 | ||||||||
\(439\) | −18.3028 | −0.873544 | −0.436772 | − | 0.899572i | \(-0.643878\pi\) | ||||
−0.436772 | + | 0.899572i | \(0.643878\pi\) | |||||||
\(440\) | 5.30278 | 0.252800 | ||||||||
\(441\) | −54.6333 | −2.60159 | ||||||||
\(442\) | −1.18335 | −0.0562860 | ||||||||
\(443\) | 35.5139 | 1.68732 | 0.843658 | − | 0.536882i | \(-0.180398\pi\) | ||||
0.843658 | + | 0.536882i | \(0.180398\pi\) | |||||||
\(444\) | 26.4222 | 1.25394 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.00000 | 0.189405 | ||||||||
\(447\) | 32.0278 | 1.51486 | ||||||||
\(448\) | −0.302776 | −0.0143048 | ||||||||
\(449\) | −12.9083 | −0.609182 | −0.304591 | − | 0.952483i | \(-0.598520\pi\) | ||||
−0.304591 | + | 0.952483i | \(0.598520\pi\) | |||||||
\(450\) | −7.90833 | −0.372802 | ||||||||
\(451\) | 52.5416 | 2.47409 | ||||||||
\(452\) | 12.4222 | 0.584291 | ||||||||
\(453\) | −6.30278 | −0.296130 | ||||||||
\(454\) | 7.39445 | 0.347039 | ||||||||
\(455\) | 0.0916731 | 0.00429770 | ||||||||
\(456\) | 16.2111 | 0.759154 | ||||||||
\(457\) | −3.57779 | −0.167362 | −0.0836811 | − | 0.996493i | \(-0.526668\pi\) | ||||
−0.0836811 | + | 0.996493i | \(0.526668\pi\) | |||||||
\(458\) | −2.00000 | −0.0934539 | ||||||||
\(459\) | −63.3583 | −2.95731 | ||||||||
\(460\) | −1.00000 | −0.0466252 | ||||||||
\(461\) | 31.8167 | 1.48185 | 0.740925 | − | 0.671588i | \(-0.234388\pi\) | ||||
0.740925 | + | 0.671588i | \(0.234388\pi\) | |||||||
\(462\) | −5.30278 | −0.246707 | ||||||||
\(463\) | −25.6333 | −1.19128 | −0.595640 | − | 0.803251i | \(-0.703102\pi\) | ||||
−0.595640 | + | 0.803251i | \(0.703102\pi\) | |||||||
\(464\) | 4.60555 | 0.213807 | ||||||||
\(465\) | 9.60555 | 0.445447 | ||||||||
\(466\) | −4.18335 | −0.193790 | ||||||||
\(467\) | 19.8167 | 0.917005 | 0.458503 | − | 0.888693i | \(-0.348386\pi\) | ||||
0.458503 | + | 0.888693i | \(0.348386\pi\) | |||||||
\(468\) | −2.39445 | −0.110683 | ||||||||
\(469\) | 1.21110 | 0.0559235 | ||||||||
\(470\) | −4.60555 | −0.212438 | ||||||||
\(471\) | −37.6333 | −1.73405 | ||||||||
\(472\) | 10.6056 | 0.488160 | ||||||||
\(473\) | −27.6333 | −1.27058 | ||||||||
\(474\) | −47.6333 | −2.18787 | ||||||||
\(475\) | −4.90833 | −0.225209 | ||||||||
\(476\) | 1.18335 | 0.0542386 | ||||||||
\(477\) | 25.3944 | 1.16273 | ||||||||
\(478\) | 9.21110 | 0.421306 | ||||||||
\(479\) | −30.0000 | −1.37073 | −0.685367 | − | 0.728197i | \(-0.740358\pi\) | ||||
−0.685367 | + | 0.728197i | \(0.740358\pi\) | |||||||
\(480\) | −3.30278 | −0.150750 | ||||||||
\(481\) | −2.42221 | −0.110443 | ||||||||
\(482\) | −14.4222 | −0.656913 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 17.1194 | 0.778156 | ||||||||
\(485\) | 2.69722 | 0.122475 | ||||||||
\(486\) | −49.8444 | −2.26099 | ||||||||
\(487\) | −11.8167 | −0.535464 | −0.267732 | − | 0.963493i | \(-0.586274\pi\) | ||||
−0.267732 | + | 0.963493i | \(0.586274\pi\) | |||||||
\(488\) | 6.51388 | 0.294869 | ||||||||
\(489\) | 18.8167 | 0.850918 | ||||||||
\(490\) | 6.90833 | 0.312086 | ||||||||
\(491\) | −25.8167 | −1.16509 | −0.582545 | − | 0.812799i | \(-0.697943\pi\) | ||||
−0.582545 | + | 0.812799i | \(0.697943\pi\) | |||||||
\(492\) | −32.7250 | −1.47536 | ||||||||
\(493\) | −18.0000 | −0.810679 | ||||||||
\(494\) | −1.48612 | −0.0668638 | ||||||||
\(495\) | −41.9361 | −1.88489 | ||||||||
\(496\) | 2.90833 | 0.130588 | ||||||||
\(497\) | 3.84441 | 0.172445 | ||||||||
\(498\) | 10.6056 | 0.475246 | ||||||||
\(499\) | 11.6333 | 0.520778 | 0.260389 | − | 0.965504i | \(-0.416149\pi\) | ||||
0.260389 | + | 0.965504i | \(0.416149\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 70.0555 | 3.12985 | ||||||||
\(502\) | 5.51388 | 0.246096 | ||||||||
\(503\) | −2.72498 | −0.121501 | −0.0607504 | − | 0.998153i | \(-0.519349\pi\) | ||||
−0.0607504 | + | 0.998153i | \(0.519349\pi\) | |||||||
\(504\) | 2.39445 | 0.106657 | ||||||||
\(505\) | −4.60555 | −0.204944 | ||||||||
\(506\) | −5.30278 | −0.235737 | ||||||||
\(507\) | −42.6333 | −1.89341 | ||||||||
\(508\) | −11.8167 | −0.524279 | ||||||||
\(509\) | 29.4500 | 1.30535 | 0.652673 | − | 0.757639i | \(-0.273647\pi\) | ||||
0.652673 | + | 0.757639i | \(0.273647\pi\) | |||||||
\(510\) | 12.9083 | 0.571590 | ||||||||
\(511\) | −4.78890 | −0.211848 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −79.5694 | −3.51307 | ||||||||
\(514\) | −19.8167 | −0.874075 | ||||||||
\(515\) | −17.1194 | −0.754372 | ||||||||
\(516\) | 17.2111 | 0.757677 | ||||||||
\(517\) | −24.4222 | −1.07409 | ||||||||
\(518\) | 2.42221 | 0.106426 | ||||||||
\(519\) | 76.9638 | 3.37834 | ||||||||
\(520\) | 0.302776 | 0.0132776 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | −36.4222 | −1.59416 | ||||||||
\(523\) | 8.42221 | 0.368277 | 0.184139 | − | 0.982900i | \(-0.441050\pi\) | ||||
0.184139 | + | 0.982900i | \(0.441050\pi\) | |||||||
\(524\) | 3.21110 | 0.140278 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 14.5139 | 0.632835 | ||||||||
\(527\) | −11.3667 | −0.495141 | ||||||||
\(528\) | −17.5139 | −0.762194 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −3.21110 | −0.139481 | ||||||||
\(531\) | −83.8722 | −3.63974 | ||||||||
\(532\) | 1.48612 | 0.0644316 | ||||||||
\(533\) | 3.00000 | 0.129944 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.60555 | 0.199115 | ||||||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | 54.8444 | 2.36671 | ||||||||
\(538\) | −25.8167 | −1.11303 | ||||||||
\(539\) | 36.6333 | 1.57791 | ||||||||
\(540\) | 16.2111 | 0.697615 | ||||||||
\(541\) | −28.8444 | −1.24012 | −0.620059 | − | 0.784555i | \(-0.712891\pi\) | ||||
−0.620059 | + | 0.784555i | \(0.712891\pi\) | |||||||
\(542\) | 6.30278 | 0.270727 | ||||||||
\(543\) | −26.8167 | −1.15081 | ||||||||
\(544\) | 3.90833 | 0.167568 | ||||||||
\(545\) | 19.5139 | 0.835883 | ||||||||
\(546\) | −0.302776 | −0.0129576 | ||||||||
\(547\) | 7.51388 | 0.321270 | 0.160635 | − | 0.987014i | \(-0.448646\pi\) | ||||
0.160635 | + | 0.987014i | \(0.448646\pi\) | |||||||
\(548\) | −6.90833 | −0.295109 | ||||||||
\(549\) | −51.5139 | −2.19856 | ||||||||
\(550\) | 5.30278 | 0.226111 | ||||||||
\(551\) | −22.6056 | −0.963029 | ||||||||
\(552\) | 3.30278 | 0.140575 | ||||||||
\(553\) | −4.36669 | −0.185691 | ||||||||
\(554\) | 12.7889 | 0.543348 | ||||||||
\(555\) | 26.4222 | 1.12156 | ||||||||
\(556\) | −5.39445 | −0.228776 | ||||||||
\(557\) | −6.42221 | −0.272118 | −0.136059 | − | 0.990701i | \(-0.543444\pi\) | ||||
−0.136059 | + | 0.990701i | \(0.543444\pi\) | |||||||
\(558\) | −23.0000 | −0.973668 | ||||||||
\(559\) | −1.57779 | −0.0667336 | ||||||||
\(560\) | −0.302776 | −0.0127946 | ||||||||
\(561\) | 68.4500 | 2.88996 | ||||||||
\(562\) | 19.3944 | 0.818105 | ||||||||
\(563\) | 39.6333 | 1.67034 | 0.835172 | − | 0.549988i | \(-0.185368\pi\) | ||||
0.835172 | + | 0.549988i | \(0.185368\pi\) | |||||||
\(564\) | 15.2111 | 0.640503 | ||||||||
\(565\) | 12.4222 | 0.522606 | ||||||||
\(566\) | −2.00000 | −0.0840663 | ||||||||
\(567\) | −9.02776 | −0.379130 | ||||||||
\(568\) | 12.6972 | 0.532764 | ||||||||
\(569\) | −0.422205 | −0.0176998 | −0.00884988 | − | 0.999961i | \(-0.502817\pi\) | ||||
−0.00884988 | + | 0.999961i | \(0.502817\pi\) | |||||||
\(570\) | 16.2111 | 0.679008 | ||||||||
\(571\) | 9.11943 | 0.381636 | 0.190818 | − | 0.981625i | \(-0.438886\pi\) | ||||
0.190818 | + | 0.981625i | \(0.438886\pi\) | |||||||
\(572\) | 1.60555 | 0.0671315 | ||||||||
\(573\) | −4.60555 | −0.192400 | ||||||||
\(574\) | −3.00000 | −0.125218 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 7.90833 | 0.329514 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 1.72498 | 0.0717497 | ||||||||
\(579\) | 12.6056 | 0.523869 | ||||||||
\(580\) | 4.60555 | 0.191235 | ||||||||
\(581\) | 0.972244 | 0.0403355 | ||||||||
\(582\) | −8.90833 | −0.369262 | ||||||||
\(583\) | −17.0278 | −0.705218 | ||||||||
\(584\) | −15.8167 | −0.654498 | ||||||||
\(585\) | −2.39445 | −0.0989983 | ||||||||
\(586\) | −8.78890 | −0.363066 | ||||||||
\(587\) | −37.5416 | −1.54951 | −0.774755 | − | 0.632262i | \(-0.782127\pi\) | ||||
−0.774755 | + | 0.632262i | \(0.782127\pi\) | |||||||
\(588\) | −22.8167 | −0.940943 | ||||||||
\(589\) | −14.2750 | −0.588192 | ||||||||
\(590\) | 10.6056 | 0.436624 | ||||||||
\(591\) | 2.30278 | 0.0947235 | ||||||||
\(592\) | 8.00000 | 0.328798 | ||||||||
\(593\) | 19.8167 | 0.813772 | 0.406886 | − | 0.913479i | \(-0.366615\pi\) | ||||
0.406886 | + | 0.913479i | \(0.366615\pi\) | |||||||
\(594\) | 85.9638 | 3.52714 | ||||||||
\(595\) | 1.18335 | 0.0485125 | ||||||||
\(596\) | 9.69722 | 0.397214 | ||||||||
\(597\) | 27.8167 | 1.13846 | ||||||||
\(598\) | −0.302776 | −0.0123814 | ||||||||
\(599\) | 4.33053 | 0.176941 | 0.0884704 | − | 0.996079i | \(-0.471802\pi\) | ||||
0.0884704 | + | 0.996079i | \(0.471802\pi\) | |||||||
\(600\) | −3.30278 | −0.134835 | ||||||||
\(601\) | −3.93608 | −0.160556 | −0.0802781 | − | 0.996773i | \(-0.525581\pi\) | ||||
−0.0802781 | + | 0.996773i | \(0.525581\pi\) | |||||||
\(602\) | 1.57779 | 0.0643061 | ||||||||
\(603\) | −31.6333 | −1.28821 | ||||||||
\(604\) | −1.90833 | −0.0776487 | ||||||||
\(605\) | 17.1194 | 0.696004 | ||||||||
\(606\) | 15.2111 | 0.617909 | ||||||||
\(607\) | −26.0555 | −1.05756 | −0.528780 | − | 0.848759i | \(-0.677350\pi\) | ||||
−0.528780 | + | 0.848759i | \(0.677350\pi\) | |||||||
\(608\) | 4.90833 | 0.199059 | ||||||||
\(609\) | −4.60555 | −0.186626 | ||||||||
\(610\) | 6.51388 | 0.263739 | ||||||||
\(611\) | −1.39445 | −0.0564134 | ||||||||
\(612\) | −30.9083 | −1.24940 | ||||||||
\(613\) | 32.4222 | 1.30952 | 0.654760 | − | 0.755837i | \(-0.272770\pi\) | ||||
0.654760 | + | 0.755837i | \(0.272770\pi\) | |||||||
\(614\) | 15.3028 | 0.617570 | ||||||||
\(615\) | −32.7250 | −1.31960 | ||||||||
\(616\) | −1.60555 | −0.0646895 | ||||||||
\(617\) | 8.09167 | 0.325758 | 0.162879 | − | 0.986646i | \(-0.447922\pi\) | ||||
0.162879 | + | 0.986646i | \(0.447922\pi\) | |||||||
\(618\) | 56.5416 | 2.27444 | ||||||||
\(619\) | 27.3305 | 1.09851 | 0.549253 | − | 0.835656i | \(-0.314912\pi\) | ||||
0.549253 | + | 0.835656i | \(0.314912\pi\) | |||||||
\(620\) | 2.90833 | 0.116801 | ||||||||
\(621\) | −16.2111 | −0.650529 | ||||||||
\(622\) | 6.42221 | 0.257507 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 12.7250 | 0.508593 | ||||||||
\(627\) | 85.9638 | 3.43307 | ||||||||
\(628\) | −11.3944 | −0.454688 | ||||||||
\(629\) | −31.2666 | −1.24668 | ||||||||
\(630\) | 2.39445 | 0.0953971 | ||||||||
\(631\) | 30.6056 | 1.21839 | 0.609194 | − | 0.793021i | \(-0.291493\pi\) | ||||
0.609194 | + | 0.793021i | \(0.291493\pi\) | |||||||
\(632\) | −14.4222 | −0.573685 | ||||||||
\(633\) | −23.8167 | −0.946627 | ||||||||
\(634\) | 14.7250 | 0.584804 | ||||||||
\(635\) | −11.8167 | −0.468930 | ||||||||
\(636\) | 10.6056 | 0.420537 | ||||||||
\(637\) | 2.09167 | 0.0828751 | ||||||||
\(638\) | 24.4222 | 0.966884 | ||||||||
\(639\) | −100.414 | −3.97231 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −36.0000 | −1.42191 | −0.710957 | − | 0.703235i | \(-0.751738\pi\) | ||||
−0.710957 | + | 0.703235i | \(0.751738\pi\) | |||||||
\(642\) | −15.2111 | −0.600334 | ||||||||
\(643\) | 16.2389 | 0.640398 | 0.320199 | − | 0.947350i | \(-0.396250\pi\) | ||||
0.320199 | + | 0.947350i | \(0.396250\pi\) | |||||||
\(644\) | 0.302776 | 0.0119310 | ||||||||
\(645\) | 17.2111 | 0.677687 | ||||||||
\(646\) | −19.1833 | −0.754759 | ||||||||
\(647\) | −30.8444 | −1.21262 | −0.606309 | − | 0.795229i | \(-0.707351\pi\) | ||||
−0.606309 | + | 0.795229i | \(0.707351\pi\) | |||||||
\(648\) | −29.8167 | −1.17131 | ||||||||
\(649\) | 56.2389 | 2.20757 | ||||||||
\(650\) | 0.302776 | 0.0118758 | ||||||||
\(651\) | −2.90833 | −0.113986 | ||||||||
\(652\) | 5.69722 | 0.223121 | ||||||||
\(653\) | 9.27502 | 0.362960 | 0.181480 | − | 0.983395i | \(-0.441911\pi\) | ||||
0.181480 | + | 0.983395i | \(0.441911\pi\) | |||||||
\(654\) | −64.4500 | −2.52019 | ||||||||
\(655\) | 3.21110 | 0.125468 | ||||||||
\(656\) | −9.90833 | −0.386855 | ||||||||
\(657\) | 125.083 | 4.87996 | ||||||||
\(658\) | 1.39445 | 0.0543613 | ||||||||
\(659\) | −27.6333 | −1.07644 | −0.538220 | − | 0.842804i | \(-0.680903\pi\) | ||||
−0.538220 | + | 0.842804i | \(0.680903\pi\) | |||||||
\(660\) | −17.5139 | −0.681727 | ||||||||
\(661\) | −24.0917 | −0.937057 | −0.468529 | − | 0.883448i | \(-0.655216\pi\) | ||||
−0.468529 | + | 0.883448i | \(0.655216\pi\) | |||||||
\(662\) | −9.39445 | −0.365126 | ||||||||
\(663\) | 3.90833 | 0.151787 | ||||||||
\(664\) | 3.21110 | 0.124615 | ||||||||
\(665\) | 1.48612 | 0.0576293 | ||||||||
\(666\) | −63.2666 | −2.45153 | ||||||||
\(667\) | −4.60555 | −0.178328 | ||||||||
\(668\) | 21.2111 | 0.820682 | ||||||||
\(669\) | −13.2111 | −0.510771 | ||||||||
\(670\) | 4.00000 | 0.154533 | ||||||||
\(671\) | 34.5416 | 1.33347 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 5.63331 | 0.217148 | 0.108574 | − | 0.994088i | \(-0.465372\pi\) | ||||
0.108574 | + | 0.994088i | \(0.465372\pi\) | |||||||
\(674\) | 4.48612 | 0.172799 | ||||||||
\(675\) | 16.2111 | 0.623966 | ||||||||
\(676\) | −12.9083 | −0.496474 | ||||||||
\(677\) | −12.4222 | −0.477424 | −0.238712 | − | 0.971090i | \(-0.576725\pi\) | ||||
−0.238712 | + | 0.971090i | \(0.576725\pi\) | |||||||
\(678\) | −41.0278 | −1.57566 | ||||||||
\(679\) | −0.816654 | −0.0313403 | ||||||||
\(680\) | 3.90833 | 0.149877 | ||||||||
\(681\) | −24.4222 | −0.935861 | ||||||||
\(682\) | 15.4222 | 0.590547 | ||||||||
\(683\) | −32.7250 | −1.25219 | −0.626093 | − | 0.779748i | \(-0.715347\pi\) | ||||
−0.626093 | + | 0.779748i | \(0.715347\pi\) | |||||||
\(684\) | −38.8167 | −1.48419 | ||||||||
\(685\) | −6.90833 | −0.263954 | ||||||||
\(686\) | −4.21110 | −0.160781 | ||||||||
\(687\) | 6.60555 | 0.252018 | ||||||||
\(688\) | 5.21110 | 0.198671 | ||||||||
\(689\) | −0.972244 | −0.0370395 | ||||||||
\(690\) | 3.30278 | 0.125735 | ||||||||
\(691\) | 30.1833 | 1.14823 | 0.574114 | − | 0.818775i | \(-0.305347\pi\) | ||||
0.574114 | + | 0.818775i | \(0.305347\pi\) | |||||||
\(692\) | 23.3028 | 0.885839 | ||||||||
\(693\) | 12.6972 | 0.482328 | ||||||||
\(694\) | 25.5416 | 0.969547 | ||||||||
\(695\) | −5.39445 | −0.204623 | ||||||||
\(696\) | −15.2111 | −0.576575 | ||||||||
\(697\) | 38.7250 | 1.46681 | ||||||||
\(698\) | 12.7889 | 0.484067 | ||||||||
\(699\) | 13.8167 | 0.522594 | ||||||||
\(700\) | −0.302776 | −0.0114438 | ||||||||
\(701\) | 42.9083 | 1.62063 | 0.810313 | − | 0.585998i | \(-0.199297\pi\) | ||||
0.810313 | + | 0.585998i | \(0.199297\pi\) | |||||||
\(702\) | 4.90833 | 0.185253 | ||||||||
\(703\) | −39.2666 | −1.48097 | ||||||||
\(704\) | −5.30278 | −0.199856 | ||||||||
\(705\) | 15.2111 | 0.572883 | ||||||||
\(706\) | −18.4222 | −0.693329 | ||||||||
\(707\) | 1.39445 | 0.0524436 | ||||||||
\(708\) | −35.0278 | −1.31642 | ||||||||
\(709\) | −41.1194 | −1.54427 | −0.772136 | − | 0.635457i | \(-0.780812\pi\) | ||||
−0.772136 | + | 0.635457i | \(0.780812\pi\) | |||||||
\(710\) | 12.6972 | 0.476518 | ||||||||
\(711\) | 114.056 | 4.27742 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.90833 | −0.108918 | ||||||||
\(714\) | −3.90833 | −0.146265 | ||||||||
\(715\) | 1.60555 | 0.0600442 | ||||||||
\(716\) | 16.6056 | 0.620579 | ||||||||
\(717\) | −30.4222 | −1.13614 | ||||||||
\(718\) | 3.21110 | 0.119837 | ||||||||
\(719\) | 14.3028 | 0.533404 | 0.266702 | − | 0.963779i | \(-0.414066\pi\) | ||||
0.266702 | + | 0.963779i | \(0.414066\pi\) | |||||||
\(720\) | 7.90833 | 0.294726 | ||||||||
\(721\) | 5.18335 | 0.193038 | ||||||||
\(722\) | −5.09167 | −0.189492 | ||||||||
\(723\) | 47.6333 | 1.77150 | ||||||||
\(724\) | −8.11943 | −0.301756 | ||||||||
\(725\) | 4.60555 | 0.171046 | ||||||||
\(726\) | −56.5416 | −2.09846 | ||||||||
\(727\) | −7.90833 | −0.293304 | −0.146652 | − | 0.989188i | \(-0.546850\pi\) | ||||
−0.146652 | + | 0.989188i | \(0.546850\pi\) | |||||||
\(728\) | −0.0916731 | −0.00339763 | ||||||||
\(729\) | 75.1749 | 2.78426 | ||||||||
\(730\) | −15.8167 | −0.585401 | ||||||||
\(731\) | −20.3667 | −0.753289 | ||||||||
\(732\) | −21.5139 | −0.795176 | ||||||||
\(733\) | −13.6333 | −0.503558 | −0.251779 | − | 0.967785i | \(-0.581016\pi\) | ||||
−0.251779 | + | 0.967785i | \(0.581016\pi\) | |||||||
\(734\) | −29.2111 | −1.07820 | ||||||||
\(735\) | −22.8167 | −0.841605 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 21.2111 | 0.781321 | ||||||||
\(738\) | 78.3583 | 2.88441 | ||||||||
\(739\) | −7.63331 | −0.280796 | −0.140398 | − | 0.990095i | \(-0.544838\pi\) | ||||
−0.140398 | + | 0.990095i | \(0.544838\pi\) | |||||||
\(740\) | 8.00000 | 0.294086 | ||||||||
\(741\) | 4.90833 | 0.180312 | ||||||||
\(742\) | 0.972244 | 0.0356922 | ||||||||
\(743\) | 7.33053 | 0.268931 | 0.134466 | − | 0.990918i | \(-0.457068\pi\) | ||||
0.134466 | + | 0.990918i | \(0.457068\pi\) | |||||||
\(744\) | −9.60555 | −0.352157 | ||||||||
\(745\) | 9.69722 | 0.355279 | ||||||||
\(746\) | 2.60555 | 0.0953960 | ||||||||
\(747\) | −25.3944 | −0.929134 | ||||||||
\(748\) | 20.7250 | 0.757780 | ||||||||
\(749\) | −1.39445 | −0.0509520 | ||||||||
\(750\) | −3.30278 | −0.120600 | ||||||||
\(751\) | 0.183346 | 0.00669040 | 0.00334520 | − | 0.999994i | \(-0.498935\pi\) | ||||
0.00334520 | + | 0.999994i | \(0.498935\pi\) | |||||||
\(752\) | 4.60555 | 0.167947 | ||||||||
\(753\) | −18.2111 | −0.663649 | ||||||||
\(754\) | 1.39445 | 0.0507828 | ||||||||
\(755\) | −1.90833 | −0.0694511 | ||||||||
\(756\) | −4.90833 | −0.178514 | ||||||||
\(757\) | −1.21110 | −0.0440183 | −0.0220091 | − | 0.999758i | \(-0.507006\pi\) | ||||
−0.0220091 | + | 0.999758i | \(0.507006\pi\) | |||||||
\(758\) | −4.09167 | −0.148616 | ||||||||
\(759\) | 17.5139 | 0.635714 | ||||||||
\(760\) | 4.90833 | 0.178044 | ||||||||
\(761\) | 4.54163 | 0.164634 | 0.0823171 | − | 0.996606i | \(-0.473768\pi\) | ||||
0.0823171 | + | 0.996606i | \(0.473768\pi\) | |||||||
\(762\) | 39.0278 | 1.41383 | ||||||||
\(763\) | −5.90833 | −0.213896 | ||||||||
\(764\) | −1.39445 | −0.0504494 | ||||||||
\(765\) | −30.9083 | −1.11749 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.21110 | 0.115946 | ||||||||
\(768\) | 3.30278 | 0.119179 | ||||||||
\(769\) | −41.2666 | −1.48811 | −0.744056 | − | 0.668117i | \(-0.767100\pi\) | ||||
−0.744056 | + | 0.668117i | \(0.767100\pi\) | |||||||
\(770\) | −1.60555 | −0.0578601 | ||||||||
\(771\) | 65.4500 | 2.35712 | ||||||||
\(772\) | 3.81665 | 0.137364 | ||||||||
\(773\) | 12.0000 | 0.431610 | 0.215805 | − | 0.976436i | \(-0.430762\pi\) | ||||
0.215805 | + | 0.976436i | \(0.430762\pi\) | |||||||
\(774\) | −41.2111 | −1.48130 | ||||||||
\(775\) | 2.90833 | 0.104470 | ||||||||
\(776\) | −2.69722 | −0.0968247 | ||||||||
\(777\) | −8.00000 | −0.286998 | ||||||||
\(778\) | −20.9361 | −0.750595 | ||||||||
\(779\) | 48.6333 | 1.74247 | ||||||||
\(780\) | −1.00000 | −0.0358057 | ||||||||
\(781\) | 67.3305 | 2.40928 | ||||||||
\(782\) | −3.90833 | −0.139761 | ||||||||
\(783\) | 74.6611 | 2.66817 | ||||||||
\(784\) | −6.90833 | −0.246726 | ||||||||
\(785\) | −11.3944 | −0.406685 | ||||||||
\(786\) | −10.6056 | −0.378287 | ||||||||
\(787\) | −27.4500 | −0.978485 | −0.489243 | − | 0.872148i | \(-0.662727\pi\) | ||||
−0.489243 | + | 0.872148i | \(0.662727\pi\) | |||||||
\(788\) | 0.697224 | 0.0248376 | ||||||||
\(789\) | −47.9361 | −1.70657 | ||||||||
\(790\) | −14.4222 | −0.513119 | ||||||||
\(791\) | −3.76114 | −0.133731 | ||||||||
\(792\) | 41.9361 | 1.49013 | ||||||||
\(793\) | 1.97224 | 0.0700364 | ||||||||
\(794\) | 21.7250 | 0.770991 | ||||||||
\(795\) | 10.6056 | 0.376140 | ||||||||
\(796\) | 8.42221 | 0.298517 | ||||||||
\(797\) | −19.8167 | −0.701942 | −0.350971 | − | 0.936386i | \(-0.614148\pi\) | ||||
−0.350971 | + | 0.936386i | \(0.614148\pi\) | |||||||
\(798\) | −4.90833 | −0.173753 | ||||||||
\(799\) | −18.0000 | −0.636794 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.39445 | 0.0492397 | ||||||||
\(803\) | −83.8722 | −2.95978 | ||||||||
\(804\) | −13.2111 | −0.465920 | ||||||||
\(805\) | 0.302776 | 0.0106714 | ||||||||
\(806\) | 0.880571 | 0.0310168 | ||||||||
\(807\) | 85.2666 | 3.00153 | ||||||||
\(808\) | 4.60555 | 0.162023 | ||||||||
\(809\) | 18.2750 | 0.642515 | 0.321258 | − | 0.946992i | \(-0.395894\pi\) | ||||
0.321258 | + | 0.946992i | \(0.395894\pi\) | |||||||
\(810\) | −29.8167 | −1.04765 | ||||||||
\(811\) | −4.97224 | −0.174599 | −0.0872995 | − | 0.996182i | \(-0.527824\pi\) | ||||
−0.0872995 | + | 0.996182i | \(0.527824\pi\) | |||||||
\(812\) | −1.39445 | −0.0489356 | ||||||||
\(813\) | −20.8167 | −0.730072 | ||||||||
\(814\) | 42.4222 | 1.48690 | ||||||||
\(815\) | 5.69722 | 0.199565 | ||||||||
\(816\) | −12.9083 | −0.451882 | ||||||||
\(817\) | −25.5778 | −0.894854 | ||||||||
\(818\) | 15.0917 | 0.527668 | ||||||||
\(819\) | 0.724981 | 0.0253329 | ||||||||
\(820\) | −9.90833 | −0.346014 | ||||||||
\(821\) | −30.0000 | −1.04701 | −0.523504 | − | 0.852023i | \(-0.675375\pi\) | ||||
−0.523504 | + | 0.852023i | \(0.675375\pi\) | |||||||
\(822\) | 22.8167 | 0.795822 | ||||||||
\(823\) | −0.788897 | −0.0274992 | −0.0137496 | − | 0.999905i | \(-0.504377\pi\) | ||||
−0.0137496 | + | 0.999905i | \(0.504377\pi\) | |||||||
\(824\) | 17.1194 | 0.596384 | ||||||||
\(825\) | −17.5139 | −0.609755 | ||||||||
\(826\) | −3.21110 | −0.111729 | ||||||||
\(827\) | 35.4500 | 1.23272 | 0.616358 | − | 0.787466i | \(-0.288607\pi\) | ||||
0.616358 | + | 0.787466i | \(0.288607\pi\) | |||||||
\(828\) | −7.90833 | −0.274833 | ||||||||
\(829\) | 16.7889 | 0.583103 | 0.291551 | − | 0.956555i | \(-0.405829\pi\) | ||||
0.291551 | + | 0.956555i | \(0.405829\pi\) | |||||||
\(830\) | 3.21110 | 0.111459 | ||||||||
\(831\) | −42.2389 | −1.46525 | ||||||||
\(832\) | −0.302776 | −0.0104969 | ||||||||
\(833\) | 27.0000 | 0.935495 | ||||||||
\(834\) | 17.8167 | 0.616940 | ||||||||
\(835\) | 21.2111 | 0.734040 | ||||||||
\(836\) | 26.0278 | 0.900189 | ||||||||
\(837\) | 47.1472 | 1.62965 | ||||||||
\(838\) | 39.6333 | 1.36911 | ||||||||
\(839\) | −22.1833 | −0.765854 | −0.382927 | − | 0.923779i | \(-0.625084\pi\) | ||||
−0.382927 | + | 0.923779i | \(0.625084\pi\) | |||||||
\(840\) | 1.00000 | 0.0345033 | ||||||||
\(841\) | −7.78890 | −0.268583 | ||||||||
\(842\) | −34.3028 | −1.18215 | ||||||||
\(843\) | −64.0555 | −2.20619 | ||||||||
\(844\) | −7.21110 | −0.248216 | ||||||||
\(845\) | −12.9083 | −0.444060 | ||||||||
\(846\) | −36.4222 | −1.25222 | ||||||||
\(847\) | −5.18335 | −0.178102 | ||||||||
\(848\) | 3.21110 | 0.110270 | ||||||||
\(849\) | 6.60555 | 0.226702 | ||||||||
\(850\) | 3.90833 | 0.134055 | ||||||||
\(851\) | −8.00000 | −0.274236 | ||||||||
\(852\) | −41.9361 | −1.43671 | ||||||||
\(853\) | 10.7250 | 0.367216 | 0.183608 | − | 0.983000i | \(-0.441222\pi\) | ||||
0.183608 | + | 0.983000i | \(0.441222\pi\) | |||||||
\(854\) | −1.97224 | −0.0674888 | ||||||||
\(855\) | −38.8167 | −1.32750 | ||||||||
\(856\) | −4.60555 | −0.157415 | ||||||||
\(857\) | −33.6333 | −1.14889 | −0.574446 | − | 0.818543i | \(-0.694782\pi\) | ||||
−0.574446 | + | 0.818543i | \(0.694782\pi\) | |||||||
\(858\) | −5.30278 | −0.181034 | ||||||||
\(859\) | −14.1833 | −0.483930 | −0.241965 | − | 0.970285i | \(-0.577792\pi\) | ||||
−0.241965 | + | 0.970285i | \(0.577792\pi\) | |||||||
\(860\) | 5.21110 | 0.177697 | ||||||||
\(861\) | 9.90833 | 0.337675 | ||||||||
\(862\) | −20.2389 | −0.689338 | ||||||||
\(863\) | 23.4500 | 0.798246 | 0.399123 | − | 0.916897i | \(-0.369315\pi\) | ||||
0.399123 | + | 0.916897i | \(0.369315\pi\) | |||||||
\(864\) | −16.2111 | −0.551513 | ||||||||
\(865\) | 23.3028 | 0.792318 | ||||||||
\(866\) | 34.9083 | 1.18623 | ||||||||
\(867\) | −5.69722 | −0.193488 | ||||||||
\(868\) | −0.880571 | −0.0298885 | ||||||||
\(869\) | −76.4777 | −2.59433 | ||||||||
\(870\) | −15.2111 | −0.515705 | ||||||||
\(871\) | 1.21110 | 0.0410366 | ||||||||
\(872\) | −19.5139 | −0.660823 | ||||||||
\(873\) | 21.3305 | 0.721929 | ||||||||
\(874\) | −4.90833 | −0.166027 | ||||||||
\(875\) | −0.302776 | −0.0102357 | ||||||||
\(876\) | 52.2389 | 1.76499 | ||||||||
\(877\) | 49.1749 | 1.66052 | 0.830260 | − | 0.557376i | \(-0.188192\pi\) | ||||
0.830260 | + | 0.557376i | \(0.188192\pi\) | |||||||
\(878\) | 18.3028 | 0.617689 | ||||||||
\(879\) | 29.0278 | 0.979082 | ||||||||
\(880\) | −5.30278 | −0.178757 | ||||||||
\(881\) | −31.2666 | −1.05340 | −0.526700 | − | 0.850052i | \(-0.676571\pi\) | ||||
−0.526700 | + | 0.850052i | \(0.676571\pi\) | |||||||
\(882\) | 54.6333 | 1.83960 | ||||||||
\(883\) | 40.7250 | 1.37050 | 0.685252 | − | 0.728306i | \(-0.259692\pi\) | ||||
0.685252 | + | 0.728306i | \(0.259692\pi\) | |||||||
\(884\) | 1.18335 | 0.0398002 | ||||||||
\(885\) | −35.0278 | −1.17745 | ||||||||
\(886\) | −35.5139 | −1.19311 | ||||||||
\(887\) | −15.6333 | −0.524915 | −0.262458 | − | 0.964944i | \(-0.584533\pi\) | ||||
−0.262458 | + | 0.964944i | \(0.584533\pi\) | |||||||
\(888\) | −26.4222 | −0.886671 | ||||||||
\(889\) | 3.57779 | 0.119995 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −158.111 | −5.29692 | ||||||||
\(892\) | −4.00000 | −0.133930 | ||||||||
\(893\) | −22.6056 | −0.756466 | ||||||||
\(894\) | −32.0278 | −1.07117 | ||||||||
\(895\) | 16.6056 | 0.555062 | ||||||||
\(896\) | 0.302776 | 0.0101150 | ||||||||
\(897\) | 1.00000 | 0.0333890 | ||||||||
\(898\) | 12.9083 | 0.430756 | ||||||||
\(899\) | 13.3944 | 0.446730 | ||||||||
\(900\) | 7.90833 | 0.263611 | ||||||||
\(901\) | −12.5500 | −0.418102 | ||||||||
\(902\) | −52.5416 | −1.74945 | ||||||||
\(903\) | −5.21110 | −0.173415 | ||||||||
\(904\) | −12.4222 | −0.413156 | ||||||||
\(905\) | −8.11943 | −0.269899 | ||||||||
\(906\) | 6.30278 | 0.209396 | ||||||||
\(907\) | −30.6611 | −1.01808 | −0.509042 | − | 0.860742i | \(-0.670000\pi\) | ||||
−0.509042 | + | 0.860742i | \(0.670000\pi\) | |||||||
\(908\) | −7.39445 | −0.245393 | ||||||||
\(909\) | −36.4222 | −1.20805 | ||||||||
\(910\) | −0.0916731 | −0.00303893 | ||||||||
\(911\) | −25.8167 | −0.855344 | −0.427672 | − | 0.903934i | \(-0.640666\pi\) | ||||
−0.427672 | + | 0.903934i | \(0.640666\pi\) | |||||||
\(912\) | −16.2111 | −0.536803 | ||||||||
\(913\) | 17.0278 | 0.563536 | ||||||||
\(914\) | 3.57779 | 0.118343 | ||||||||
\(915\) | −21.5139 | −0.711227 | ||||||||
\(916\) | 2.00000 | 0.0660819 | ||||||||
\(917\) | −0.972244 | −0.0321063 | ||||||||
\(918\) | 63.3583 | 2.09114 | ||||||||
\(919\) | 44.0000 | 1.45143 | 0.725713 | − | 0.687998i | \(-0.241510\pi\) | ||||
0.725713 | + | 0.687998i | \(0.241510\pi\) | |||||||
\(920\) | 1.00000 | 0.0329690 | ||||||||
\(921\) | −50.5416 | −1.66540 | ||||||||
\(922\) | −31.8167 | −1.04783 | ||||||||
\(923\) | 3.84441 | 0.126540 | ||||||||
\(924\) | 5.30278 | 0.174449 | ||||||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | 25.6333 | 0.842363 | ||||||||
\(927\) | −135.386 | −4.44666 | ||||||||
\(928\) | −4.60555 | −0.151185 | ||||||||
\(929\) | −57.6333 | −1.89089 | −0.945444 | − | 0.325785i | \(-0.894371\pi\) | ||||
−0.945444 | + | 0.325785i | \(0.894371\pi\) | |||||||
\(930\) | −9.60555 | −0.314978 | ||||||||
\(931\) | 33.9083 | 1.11130 | ||||||||
\(932\) | 4.18335 | 0.137030 | ||||||||
\(933\) | −21.2111 | −0.694420 | ||||||||
\(934\) | −19.8167 | −0.648421 | ||||||||
\(935\) | 20.7250 | 0.677779 | ||||||||
\(936\) | 2.39445 | 0.0782650 | ||||||||
\(937\) | −44.9638 | −1.46890 | −0.734452 | − | 0.678660i | \(-0.762561\pi\) | ||||
−0.734452 | + | 0.678660i | \(0.762561\pi\) | |||||||
\(938\) | −1.21110 | −0.0395439 | ||||||||
\(939\) | −42.0278 | −1.37152 | ||||||||
\(940\) | 4.60555 | 0.150217 | ||||||||
\(941\) | −20.9361 | −0.682497 | −0.341248 | − | 0.939973i | \(-0.610850\pi\) | ||||
−0.341248 | + | 0.939973i | \(0.610850\pi\) | |||||||
\(942\) | 37.6333 | 1.22616 | ||||||||
\(943\) | 9.90833 | 0.322660 | ||||||||
\(944\) | −10.6056 | −0.345181 | ||||||||
\(945\) | −4.90833 | −0.159668 | ||||||||
\(946\) | 27.6333 | 0.898436 | ||||||||
\(947\) | 41.9361 | 1.36274 | 0.681370 | − | 0.731939i | \(-0.261385\pi\) | ||||
0.681370 | + | 0.731939i | \(0.261385\pi\) | |||||||
\(948\) | 47.6333 | 1.54706 | ||||||||
\(949\) | −4.78890 | −0.155454 | ||||||||
\(950\) | 4.90833 | 0.159247 | ||||||||
\(951\) | −48.6333 | −1.57704 | ||||||||
\(952\) | −1.18335 | −0.0383525 | ||||||||
\(953\) | −1.66947 | −0.0540794 | −0.0270397 | − | 0.999634i | \(-0.508608\pi\) | ||||
−0.0270397 | + | 0.999634i | \(0.508608\pi\) | |||||||
\(954\) | −25.3944 | −0.822176 | ||||||||
\(955\) | −1.39445 | −0.0451233 | ||||||||
\(956\) | −9.21110 | −0.297908 | ||||||||
\(957\) | −80.6611 | −2.60740 | ||||||||
\(958\) | 30.0000 | 0.969256 | ||||||||
\(959\) | 2.09167 | 0.0675436 | ||||||||
\(960\) | 3.30278 | 0.106597 | ||||||||
\(961\) | −22.5416 | −0.727150 | ||||||||
\(962\) | 2.42221 | 0.0780950 | ||||||||
\(963\) | 36.4222 | 1.17369 | ||||||||
\(964\) | 14.4222 | 0.464508 | ||||||||
\(965\) | 3.81665 | 0.122862 | ||||||||
\(966\) | −1.00000 | −0.0321745 | ||||||||
\(967\) | −5.39445 | −0.173474 | −0.0867369 | − | 0.996231i | \(-0.527644\pi\) | ||||
−0.0867369 | + | 0.996231i | \(0.527644\pi\) | |||||||
\(968\) | −17.1194 | −0.550239 | ||||||||
\(969\) | 63.3583 | 2.03536 | ||||||||
\(970\) | −2.69722 | −0.0866027 | ||||||||
\(971\) | −27.9083 | −0.895621 | −0.447810 | − | 0.894129i | \(-0.647796\pi\) | ||||
−0.447810 | + | 0.894129i | \(0.647796\pi\) | |||||||
\(972\) | 49.8444 | 1.59876 | ||||||||
\(973\) | 1.63331 | 0.0523614 | ||||||||
\(974\) | 11.8167 | 0.378630 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | −6.51388 | −0.208504 | ||||||||
\(977\) | −11.5139 | −0.368362 | −0.184181 | − | 0.982892i | \(-0.558963\pi\) | ||||
−0.184181 | + | 0.982892i | \(0.558963\pi\) | |||||||
\(978\) | −18.8167 | −0.601690 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.90833 | −0.220678 | ||||||||
\(981\) | 154.322 | 4.92713 | ||||||||
\(982\) | 25.8167 | 0.823843 | ||||||||
\(983\) | −19.5416 | −0.623281 | −0.311641 | − | 0.950200i | \(-0.600879\pi\) | ||||
−0.311641 | + | 0.950200i | \(0.600879\pi\) | |||||||
\(984\) | 32.7250 | 1.04323 | ||||||||
\(985\) | 0.697224 | 0.0222154 | ||||||||
\(986\) | 18.0000 | 0.573237 | ||||||||
\(987\) | −4.60555 | −0.146596 | ||||||||
\(988\) | 1.48612 | 0.0472798 | ||||||||
\(989\) | −5.21110 | −0.165703 | ||||||||
\(990\) | 41.9361 | 1.33282 | ||||||||
\(991\) | 24.3305 | 0.772885 | 0.386442 | − | 0.922314i | \(-0.373704\pi\) | ||||
0.386442 | + | 0.922314i | \(0.373704\pi\) | |||||||
\(992\) | −2.90833 | −0.0923395 | ||||||||
\(993\) | 31.0278 | 0.984636 | ||||||||
\(994\) | −3.84441 | −0.121937 | ||||||||
\(995\) | 8.42221 | 0.267002 | ||||||||
\(996\) | −10.6056 | −0.336050 | ||||||||
\(997\) | −31.2111 | −0.988466 | −0.494233 | − | 0.869330i | \(-0.664551\pi\) | ||||
−0.494233 | + | 0.869330i | \(0.664551\pi\) | |||||||
\(998\) | −11.6333 | −0.368246 | ||||||||
\(999\) | 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 | 230.2.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2070.2.a.w.1.1 | 2 | |||
4.3 | odd | 2 | 1840.2.a.j.1.1 | 2 | |||
5.2 | odd | 4 | 1150.2.b.f.599.1 | 4 | |||
5.3 | odd | 4 | 1150.2.b.f.599.4 | 4 | |||
5.4 | even | 2 | 1150.2.a.m.1.1 | 2 | |||
8.3 | odd | 2 | 7360.2.a.bu.1.2 | 2 | |||
8.5 | even | 2 | 7360.2.a.bc.1.1 | 2 | |||
20.19 | odd | 2 | 9200.2.a.ca.1.2 | 2 | |||
23.22 | odd | 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 | 1.1 | even | 1 | trivial | |
1150.2.a.m.1.1 | 2 | 5.4 | even | 2 | |||
1150.2.b.f.599.1 | 4 | 5.2 | odd | 4 | |||
1150.2.b.f.599.4 | 4 | 5.3 | odd | 4 | |||
1840.2.a.j.1.1 | 2 | 4.3 | odd | 2 | |||
2070.2.a.w.1.1 | 2 | 3.2 | odd | 2 | |||
5290.2.a.j.1.2 | 2 | 23.22 | odd | 2 | |||
7360.2.a.bc.1.1 | 2 | 8.5 | even | 2 | |||
7360.2.a.bu.1.2 | 2 | 8.3 | odd | 2 | |||
9200.2.a.ca.1.2 | 2 | 20.19 | odd | 2 |