Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.5 | ||
Root | \(1.80194i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.s.1351.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | − 1.00000i | − 0.408248i | ||||||||
\(7\) | 1.35690i | 0.512858i | 0.966563 | + | 0.256429i | \(0.0825461\pi\) | ||||
−0.966563 | + | 0.256429i | \(0.917454\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 3.19806i | 0.964252i | 0.876102 | + | 0.482126i | \(0.160135\pi\) | ||||
−0.876102 | + | 0.482126i | \(0.839865\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.35690 | −0.362646 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.04892 | 0.496935 | 0.248468 | − | 0.968640i | \(-0.420073\pi\) | ||||
0.248468 | + | 0.968640i | \(0.420073\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 5.34481i | 1.22618i | 0.790011 | + | 0.613092i | \(0.210075\pi\) | ||||
−0.790011 | + | 0.613092i | \(0.789925\pi\) | |||||||
\(20\) | − 1.00000i | − 0.223607i | ||||||||
\(21\) | − 1.35690i | − 0.296099i | ||||||||
\(22\) | −3.19806 | −0.681829 | ||||||||
\(23\) | 8.32304 | 1.73547 | 0.867737 | − | 0.497023i | \(-0.165574\pi\) | ||||
0.867737 | + | 0.497023i | \(0.165574\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | − 1.35690i | − 0.256429i | ||||||||
\(29\) | 8.07069 | 1.49869 | 0.749345 | − | 0.662180i | \(-0.230369\pi\) | ||||
0.749345 | + | 0.662180i | \(0.230369\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 0.185981i | 0.0334031i | 0.999861 | + | 0.0167016i | \(0.00531652\pi\) | ||||
−0.999861 | + | 0.0167016i | \(0.994683\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 3.19806i | − 0.556711i | ||||||||
\(34\) | 2.04892i | 0.351386i | ||||||||
\(35\) | −1.35690 | −0.229357 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 2.46681i | − 0.405541i | −0.979226 | − | 0.202771i | \(-0.935005\pi\) | ||||
0.979226 | − | 0.202771i | \(-0.0649946\pi\) | |||||||
\(38\) | −5.34481 | −0.867043 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | − 12.2349i | − 1.91077i | −0.295363 | − | 0.955385i | \(-0.595441\pi\) | ||||
0.295363 | − | 0.955385i | \(-0.404559\pi\) | |||||||
\(42\) | 1.35690 | 0.209374 | ||||||||
\(43\) | 2.91185 | 0.444054 | 0.222027 | − | 0.975041i | \(-0.428733\pi\) | ||||
0.222027 | + | 0.975041i | \(0.428733\pi\) | |||||||
\(44\) | − 3.19806i | − 0.482126i | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 8.32304i | 1.22717i | ||||||||
\(47\) | 13.0978i | 1.91052i | 0.295775 | + | 0.955258i | \(0.404422\pi\) | ||||
−0.295775 | + | 0.955258i | \(0.595578\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 5.15883 | 0.736976 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | −2.04892 | −0.286906 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.74094 | 0.788579 | 0.394289 | − | 0.918986i | \(-0.370991\pi\) | ||||
0.394289 | + | 0.918986i | \(0.370991\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | −3.19806 | −0.431227 | ||||||||
\(56\) | 1.35690 | 0.181323 | ||||||||
\(57\) | − 5.34481i | − 0.707938i | ||||||||
\(58\) | 8.07069i | 1.05973i | ||||||||
\(59\) | − 1.62565i | − 0.211641i | −0.994385 | − | 0.105821i | \(-0.966253\pi\) | ||||
0.994385 | − | 0.105821i | \(-0.0337469\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | 5.28382 | 0.676523 | 0.338262 | − | 0.941052i | \(-0.390161\pi\) | ||||
0.338262 | + | 0.941052i | \(0.390161\pi\) | |||||||
\(62\) | −0.185981 | −0.0236196 | ||||||||
\(63\) | 1.35690i | 0.170953i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.19806 | 0.393654 | ||||||||
\(67\) | − 1.55496i | − 0.189968i | −0.995479 | − | 0.0949842i | \(-0.969720\pi\) | ||||
0.995479 | − | 0.0949842i | \(-0.0302801\pi\) | |||||||
\(68\) | −2.04892 | −0.248468 | ||||||||
\(69\) | −8.32304 | −1.00198 | ||||||||
\(70\) | − 1.35690i | − 0.162180i | ||||||||
\(71\) | 2.32304i | 0.275695i | 0.990453 | + | 0.137847i | \(0.0440183\pi\) | ||||
−0.990453 | + | 0.137847i | \(0.955982\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | − 5.11529i | − 0.598700i | −0.954143 | − | 0.299350i | \(-0.903230\pi\) | ||||
0.954143 | − | 0.299350i | \(-0.0967698\pi\) | |||||||
\(74\) | 2.46681 | 0.286761 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | − 5.34481i | − 0.613092i | ||||||||
\(77\) | −4.33944 | −0.494525 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.42327 | −0.160131 | −0.0800653 | − | 0.996790i | \(-0.525513\pi\) | ||||
−0.0800653 | + | 0.996790i | \(0.525513\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.2349 | 1.35112 | ||||||||
\(83\) | − 11.1196i | − 1.22054i | −0.792195 | − | 0.610268i | \(-0.791062\pi\) | ||||
0.792195 | − | 0.610268i | \(-0.208938\pi\) | |||||||
\(84\) | 1.35690i | 0.148049i | ||||||||
\(85\) | 2.04892i | 0.222236i | ||||||||
\(86\) | 2.91185i | 0.313993i | ||||||||
\(87\) | −8.07069 | −0.865269 | ||||||||
\(88\) | 3.19806 | 0.340915 | ||||||||
\(89\) | 3.37867i | 0.358138i | 0.983837 | + | 0.179069i | \(0.0573085\pi\) | ||||
−0.983837 | + | 0.179069i | \(0.942691\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.32304 | −0.867737 | ||||||||
\(93\) | − 0.185981i | − 0.0192853i | ||||||||
\(94\) | −13.0978 | −1.35094 | ||||||||
\(95\) | −5.34481 | −0.548366 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | 4.74094i | 0.481369i | 0.970603 | + | 0.240685i | \(0.0773720\pi\) | ||||
−0.970603 | + | 0.240685i | \(0.922628\pi\) | |||||||
\(98\) | 5.15883i | 0.521121i | ||||||||
\(99\) | 3.19806i | 0.321417i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 12.5918 | 1.25293 | 0.626465 | − | 0.779449i | \(-0.284501\pi\) | ||||
0.626465 | + | 0.779449i | \(0.284501\pi\) | |||||||
\(102\) | − 2.04892i | − 0.202873i | ||||||||
\(103\) | 9.00000 | 0.886796 | 0.443398 | − | 0.896325i | \(-0.353773\pi\) | ||||
0.443398 | + | 0.896325i | \(0.353773\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.35690 | 0.132419 | ||||||||
\(106\) | 5.74094i | 0.557609i | ||||||||
\(107\) | −5.08815 | −0.491890 | −0.245945 | − | 0.969284i | \(-0.579098\pi\) | ||||
−0.245945 | + | 0.969284i | \(0.579098\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | − 6.43296i | − 0.616166i | −0.951360 | − | 0.308083i | \(-0.900313\pi\) | ||||
0.951360 | − | 0.308083i | \(-0.0996874\pi\) | |||||||
\(110\) | − 3.19806i | − 0.304923i | ||||||||
\(111\) | 2.46681i | 0.234139i | ||||||||
\(112\) | 1.35690i | 0.128215i | ||||||||
\(113\) | −18.6571 | −1.75511 | −0.877556 | − | 0.479473i | \(-0.840828\pi\) | ||||
−0.877556 | + | 0.479473i | \(0.840828\pi\) | |||||||
\(114\) | 5.34481 | 0.500588 | ||||||||
\(115\) | 8.32304i | 0.776128i | ||||||||
\(116\) | −8.07069 | −0.749345 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.62565 | 0.149653 | ||||||||
\(119\) | 2.78017i | 0.254858i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 0.772398 | 0.0702180 | ||||||||
\(122\) | 5.28382i | 0.478374i | ||||||||
\(123\) | 12.2349i | 1.10318i | ||||||||
\(124\) | − 0.185981i | − 0.0167016i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | −1.35690 | −0.120882 | ||||||||
\(127\) | 16.3763 | 1.45316 | 0.726580 | − | 0.687082i | \(-0.241109\pi\) | ||||
0.726580 | + | 0.687082i | \(0.241109\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −2.91185 | −0.256374 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00969 | 0.262958 | 0.131479 | − | 0.991319i | \(-0.458027\pi\) | ||||
0.131479 | + | 0.991319i | \(0.458027\pi\) | |||||||
\(132\) | 3.19806i | 0.278356i | ||||||||
\(133\) | −7.25236 | −0.628859 | ||||||||
\(134\) | 1.55496 | 0.134328 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | − 2.04892i | − 0.175693i | ||||||||
\(137\) | 20.2892i | 1.73342i | 0.498810 | + | 0.866711i | \(0.333771\pi\) | ||||
−0.498810 | + | 0.866711i | \(0.666229\pi\) | |||||||
\(138\) | − 8.32304i | − 0.708505i | ||||||||
\(139\) | −0.153457 | −0.0130160 | −0.00650802 | − | 0.999979i | \(-0.502072\pi\) | ||||
−0.00650802 | + | 0.999979i | \(0.502072\pi\) | |||||||
\(140\) | 1.35690 | 0.114679 | ||||||||
\(141\) | − 13.0978i | − 1.10304i | ||||||||
\(142\) | −2.32304 | −0.194946 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.07069i | 0.670234i | ||||||||
\(146\) | 5.11529 | 0.423345 | ||||||||
\(147\) | −5.15883 | −0.425493 | ||||||||
\(148\) | 2.46681i | 0.202771i | ||||||||
\(149\) | 10.7724i | 0.882509i | 0.897382 | + | 0.441255i | \(0.145466\pi\) | ||||
−0.897382 | + | 0.441255i | \(0.854534\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | 17.3817i | 1.41450i | 0.706964 | + | 0.707249i | \(0.250064\pi\) | ||||
−0.706964 | + | 0.707249i | \(0.749936\pi\) | |||||||
\(152\) | 5.34481 | 0.433522 | ||||||||
\(153\) | 2.04892 | 0.165645 | ||||||||
\(154\) | − 4.33944i | − 0.349682i | ||||||||
\(155\) | −0.185981 | −0.0149383 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5429 | 1.24046 | 0.620228 | − | 0.784421i | \(-0.287040\pi\) | ||||
0.620228 | + | 0.784421i | \(0.287040\pi\) | |||||||
\(158\) | − 1.42327i | − 0.113229i | ||||||||
\(159\) | −5.74094 | −0.455286 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 11.2935i | 0.890053i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − 2.00239i | − 0.156840i | −0.996920 | − | 0.0784198i | \(-0.975013\pi\) | ||||
0.996920 | − | 0.0784198i | \(-0.0249874\pi\) | |||||||
\(164\) | 12.2349i | 0.955385i | ||||||||
\(165\) | 3.19806 | 0.248969 | ||||||||
\(166\) | 11.1196 | 0.863049 | ||||||||
\(167\) | − 8.24027i | − 0.637652i | −0.947813 | − | 0.318826i | \(-0.896712\pi\) | ||||
0.947813 | − | 0.318826i | \(-0.103288\pi\) | |||||||
\(168\) | −1.35690 | −0.104687 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.04892 | −0.157145 | ||||||||
\(171\) | 5.34481i | 0.408728i | ||||||||
\(172\) | −2.91185 | −0.222027 | ||||||||
\(173\) | −12.7463 | −0.969084 | −0.484542 | − | 0.874768i | \(-0.661014\pi\) | ||||
−0.484542 | + | 0.874768i | \(0.661014\pi\) | |||||||
\(174\) | − 8.07069i | − 0.611837i | ||||||||
\(175\) | − 1.35690i | − 0.102572i | ||||||||
\(176\) | 3.19806i | 0.241063i | ||||||||
\(177\) | 1.62565i | 0.122191i | ||||||||
\(178\) | −3.37867 | −0.253242 | ||||||||
\(179\) | −16.0422 | −1.19905 | −0.599526 | − | 0.800356i | \(-0.704644\pi\) | ||||
−0.599526 | + | 0.800356i | \(0.704644\pi\) | |||||||
\(180\) | − 1.00000i | − 0.0745356i | ||||||||
\(181\) | −3.85086 | −0.286232 | −0.143116 | − | 0.989706i | \(-0.545712\pi\) | ||||
−0.143116 | + | 0.989706i | \(0.545712\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.28382 | −0.390591 | ||||||||
\(184\) | − 8.32304i | − 0.613583i | ||||||||
\(185\) | 2.46681 | 0.181364 | ||||||||
\(186\) | 0.185981 | 0.0136368 | ||||||||
\(187\) | 6.55257i | 0.479171i | ||||||||
\(188\) | − 13.0978i | − 0.955258i | ||||||||
\(189\) | − 1.35690i | − 0.0986997i | ||||||||
\(190\) | − 5.34481i | − 0.387754i | ||||||||
\(191\) | 11.8280 | 0.855845 | 0.427923 | − | 0.903815i | \(-0.359246\pi\) | ||||
0.427923 | + | 0.903815i | \(0.359246\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 0.872625i | 0.0628129i | 0.999507 | + | 0.0314065i | \(0.00999864\pi\) | ||||
−0.999507 | + | 0.0314065i | \(0.990001\pi\) | |||||||
\(194\) | −4.74094 | −0.340380 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.15883 | −0.368488 | ||||||||
\(197\) | − 10.6213i | − 0.756739i | −0.925655 | − | 0.378369i | \(-0.876485\pi\) | ||||
0.925655 | − | 0.378369i | \(-0.123515\pi\) | |||||||
\(198\) | −3.19806 | −0.227276 | ||||||||
\(199\) | −12.3424 | −0.874931 | −0.437466 | − | 0.899235i | \(-0.644124\pi\) | ||||
−0.437466 | + | 0.899235i | \(0.644124\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 1.55496i | 0.109678i | ||||||||
\(202\) | 12.5918i | 0.885956i | ||||||||
\(203\) | 10.9511i | 0.768615i | ||||||||
\(204\) | 2.04892 | 0.143453 | ||||||||
\(205\) | 12.2349 | 0.854522 | ||||||||
\(206\) | 9.00000i | 0.627060i | ||||||||
\(207\) | 8.32304 | 0.578492 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.0930 | −1.18235 | ||||||||
\(210\) | 1.35690i | 0.0936347i | ||||||||
\(211\) | 6.75733 | 0.465194 | 0.232597 | − | 0.972573i | \(-0.425278\pi\) | ||||
0.232597 | + | 0.972573i | \(0.425278\pi\) | |||||||
\(212\) | −5.74094 | −0.394289 | ||||||||
\(213\) | − 2.32304i | − 0.159172i | ||||||||
\(214\) | − 5.08815i | − 0.347819i | ||||||||
\(215\) | 2.91185i | 0.198587i | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −0.252356 | −0.0171311 | ||||||||
\(218\) | 6.43296 | 0.435695 | ||||||||
\(219\) | 5.11529i | 0.345659i | ||||||||
\(220\) | 3.19806 | 0.215613 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.46681 | −0.165562 | ||||||||
\(223\) | − 21.5972i | − 1.44625i | −0.690715 | − | 0.723127i | \(-0.742704\pi\) | ||||
0.690715 | − | 0.723127i | \(-0.257296\pi\) | |||||||
\(224\) | −1.35690 | −0.0906614 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | − 18.6571i | − 1.24105i | ||||||||
\(227\) | − 10.2862i | − 0.682720i | −0.939933 | − | 0.341360i | \(-0.889113\pi\) | ||||
0.939933 | − | 0.341360i | \(-0.110887\pi\) | |||||||
\(228\) | 5.34481i | 0.353969i | ||||||||
\(229\) | 4.25906i | 0.281447i | 0.990049 | + | 0.140723i | \(0.0449428\pi\) | ||||
−0.990049 | + | 0.140723i | \(0.955057\pi\) | |||||||
\(230\) | −8.32304 | −0.548805 | ||||||||
\(231\) | 4.33944 | 0.285514 | ||||||||
\(232\) | − 8.07069i | − 0.529867i | ||||||||
\(233\) | −19.5133 | −1.27836 | −0.639181 | − | 0.769057i | \(-0.720726\pi\) | ||||
−0.639181 | + | 0.769057i | \(0.720726\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.0978 | −0.854409 | ||||||||
\(236\) | 1.62565i | 0.105821i | ||||||||
\(237\) | 1.42327 | 0.0924514 | ||||||||
\(238\) | −2.78017 | −0.180211 | ||||||||
\(239\) | 7.16315i | 0.463345i | 0.972794 | + | 0.231673i | \(0.0744198\pi\) | ||||
−0.972794 | + | 0.231673i | \(0.925580\pi\) | |||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | 17.9584i | 1.15680i | 0.815753 | + | 0.578400i | \(0.196323\pi\) | ||||
−0.815753 | + | 0.578400i | \(0.803677\pi\) | |||||||
\(242\) | 0.772398i | 0.0496516i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.28382 | −0.338262 | ||||||||
\(245\) | 5.15883i | 0.329586i | ||||||||
\(246\) | −12.2349 | −0.780069 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.185981 | 0.0118098 | ||||||||
\(249\) | 11.1196i | 0.704676i | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 6.68425 | 0.421906 | 0.210953 | − | 0.977496i | \(-0.432343\pi\) | ||||
0.210953 | + | 0.977496i | \(0.432343\pi\) | |||||||
\(252\) | − 1.35690i | − 0.0854764i | ||||||||
\(253\) | 26.6176i | 1.67343i | ||||||||
\(254\) | 16.3763i | 1.02754i | ||||||||
\(255\) | − 2.04892i | − 0.128308i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.91484 | −0.618471 | −0.309235 | − | 0.950986i | \(-0.600073\pi\) | ||||
−0.309235 | + | 0.950986i | \(0.600073\pi\) | |||||||
\(258\) | − 2.91185i | − 0.181284i | ||||||||
\(259\) | 3.34721 | 0.207985 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.07069 | 0.499563 | ||||||||
\(262\) | 3.00969i | 0.185939i | ||||||||
\(263\) | 13.8509 | 0.854080 | 0.427040 | − | 0.904233i | \(-0.359556\pi\) | ||||
0.427040 | + | 0.904233i | \(0.359556\pi\) | |||||||
\(264\) | −3.19806 | −0.196827 | ||||||||
\(265\) | 5.74094i | 0.352663i | ||||||||
\(266\) | − 7.25236i | − 0.444671i | ||||||||
\(267\) | − 3.37867i | − 0.206771i | ||||||||
\(268\) | 1.55496i | 0.0949842i | ||||||||
\(269\) | −17.8756 | −1.08990 | −0.544948 | − | 0.838470i | \(-0.683450\pi\) | ||||
−0.544948 | + | 0.838470i | \(0.683450\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 31.2083i | 1.89577i | 0.318610 | + | 0.947886i | \(0.396784\pi\) | ||||
−0.318610 | + | 0.947886i | \(0.603216\pi\) | |||||||
\(272\) | 2.04892 | 0.124234 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.2892 | −1.22571 | ||||||||
\(275\) | − 3.19806i | − 0.192850i | ||||||||
\(276\) | 8.32304 | 0.500988 | ||||||||
\(277\) | −22.9245 | −1.37740 | −0.688701 | − | 0.725046i | \(-0.741819\pi\) | ||||
−0.688701 | + | 0.725046i | \(0.741819\pi\) | |||||||
\(278\) | − 0.153457i | − 0.00920373i | ||||||||
\(279\) | 0.185981i | 0.0111344i | ||||||||
\(280\) | 1.35690i | 0.0810900i | ||||||||
\(281\) | 28.0683i | 1.67441i | 0.546886 | + | 0.837207i | \(0.315813\pi\) | ||||
−0.546886 | + | 0.837207i | \(0.684187\pi\) | |||||||
\(282\) | 13.0978 | 0.779965 | ||||||||
\(283\) | 24.8364 | 1.47637 | 0.738185 | − | 0.674599i | \(-0.235683\pi\) | ||||
0.738185 | + | 0.674599i | \(0.235683\pi\) | |||||||
\(284\) | − 2.32304i | − 0.137847i | ||||||||
\(285\) | 5.34481 | 0.316599 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.6015 | 0.979955 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −12.8019 | −0.753055 | ||||||||
\(290\) | −8.07069 | −0.473927 | ||||||||
\(291\) | − 4.74094i | − 0.277919i | ||||||||
\(292\) | 5.11529i | 0.299350i | ||||||||
\(293\) | − 28.4349i | − 1.66118i | −0.556882 | − | 0.830592i | \(-0.688002\pi\) | ||||
0.556882 | − | 0.830592i | \(-0.311998\pi\) | |||||||
\(294\) | − 5.15883i | − 0.300869i | ||||||||
\(295\) | 1.62565 | 0.0946488 | ||||||||
\(296\) | −2.46681 | −0.143381 | ||||||||
\(297\) | − 3.19806i | − 0.185570i | ||||||||
\(298\) | −10.7724 | −0.624028 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 3.95108i | 0.227737i | ||||||||
\(302\) | −17.3817 | −1.00020 | ||||||||
\(303\) | −12.5918 | −0.723380 | ||||||||
\(304\) | 5.34481i | 0.306546i | ||||||||
\(305\) | 5.28382i | 0.302550i | ||||||||
\(306\) | 2.04892i | 0.117129i | ||||||||
\(307\) | − 10.1347i | − 0.578416i | −0.957266 | − | 0.289208i | \(-0.906608\pi\) | ||||
0.957266 | − | 0.289208i | \(-0.0933920\pi\) | |||||||
\(308\) | 4.33944 | 0.247262 | ||||||||
\(309\) | −9.00000 | −0.511992 | ||||||||
\(310\) | − 0.185981i | − 0.0105630i | ||||||||
\(311\) | −20.0218 | −1.13533 | −0.567665 | − | 0.823259i | \(-0.692153\pi\) | ||||
−0.567665 | + | 0.823259i | \(0.692153\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.63640 | 0.488158 | 0.244079 | − | 0.969755i | \(-0.421514\pi\) | ||||
0.244079 | + | 0.969755i | \(0.421514\pi\) | |||||||
\(314\) | 15.5429i | 0.877135i | ||||||||
\(315\) | −1.35690 | −0.0764524 | ||||||||
\(316\) | 1.42327 | 0.0800653 | ||||||||
\(317\) | − 17.6256i | − 0.989955i | −0.868906 | − | 0.494977i | \(-0.835176\pi\) | ||||
0.868906 | − | 0.494977i | \(-0.164824\pi\) | |||||||
\(318\) | − 5.74094i | − 0.321936i | ||||||||
\(319\) | 25.8106i | 1.44511i | ||||||||
\(320\) | − 1.00000i | − 0.0559017i | ||||||||
\(321\) | 5.08815 | 0.283993 | ||||||||
\(322\) | −11.2935 | −0.629362 | ||||||||
\(323\) | 10.9511i | 0.609335i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00239 | 0.110902 | ||||||||
\(327\) | 6.43296i | 0.355744i | ||||||||
\(328\) | −12.2349 | −0.675559 | ||||||||
\(329\) | −17.7724 | −0.979824 | ||||||||
\(330\) | 3.19806i | 0.176048i | ||||||||
\(331\) | 31.5163i | 1.73229i | 0.499790 | + | 0.866147i | \(0.333411\pi\) | ||||
−0.499790 | + | 0.866147i | \(0.666589\pi\) | |||||||
\(332\) | 11.1196i | 0.610268i | ||||||||
\(333\) | − 2.46681i | − 0.135180i | ||||||||
\(334\) | 8.24027 | 0.450888 | ||||||||
\(335\) | 1.55496 | 0.0849564 | ||||||||
\(336\) | − 1.35690i | − 0.0740247i | ||||||||
\(337\) | 11.8116 | 0.643420 | 0.321710 | − | 0.946838i | \(-0.395742\pi\) | ||||
0.321710 | + | 0.946838i | \(0.395742\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.6571 | 1.01331 | ||||||||
\(340\) | − 2.04892i | − 0.111118i | ||||||||
\(341\) | −0.594778 | −0.0322090 | ||||||||
\(342\) | −5.34481 | −0.289014 | ||||||||
\(343\) | 16.4983i | 0.890823i | ||||||||
\(344\) | − 2.91185i | − 0.156997i | ||||||||
\(345\) | − 8.32304i | − 0.448098i | ||||||||
\(346\) | − 12.7463i | − 0.685246i | ||||||||
\(347\) | −17.4101 | −0.934624 | −0.467312 | − | 0.884092i | \(-0.654778\pi\) | ||||
−0.467312 | + | 0.884092i | \(0.654778\pi\) | |||||||
\(348\) | 8.07069 | 0.432634 | ||||||||
\(349\) | 18.6799i | 0.999914i | 0.866050 | + | 0.499957i | \(0.166651\pi\) | ||||
−0.866050 | + | 0.499957i | \(0.833349\pi\) | |||||||
\(350\) | 1.35690 | 0.0725291 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.19806 | −0.170457 | ||||||||
\(353\) | − 25.3991i | − 1.35186i | −0.736967 | − | 0.675929i | \(-0.763743\pi\) | ||||
0.736967 | − | 0.675929i | \(-0.236257\pi\) | |||||||
\(354\) | −1.62565 | −0.0864021 | ||||||||
\(355\) | −2.32304 | −0.123294 | ||||||||
\(356\) | − 3.37867i | − 0.179069i | ||||||||
\(357\) | − 2.78017i | − 0.147142i | ||||||||
\(358\) | − 16.0422i | − 0.847857i | ||||||||
\(359\) | 34.0103i | 1.79499i | 0.441021 | + | 0.897497i | \(0.354617\pi\) | ||||
−0.441021 | + | 0.897497i | \(0.645383\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −9.56704 | −0.503528 | ||||||||
\(362\) | − 3.85086i | − 0.202396i | ||||||||
\(363\) | −0.772398 | −0.0405404 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.11529 | 0.267747 | ||||||||
\(366\) | − 5.28382i | − 0.276189i | ||||||||
\(367\) | −25.6437 | −1.33859 | −0.669295 | − | 0.742997i | \(-0.733404\pi\) | ||||
−0.669295 | + | 0.742997i | \(0.733404\pi\) | |||||||
\(368\) | 8.32304 | 0.433869 | ||||||||
\(369\) | − 12.2349i | − 0.636923i | ||||||||
\(370\) | 2.46681i | 0.128243i | ||||||||
\(371\) | 7.78986i | 0.404429i | ||||||||
\(372\) | 0.185981i | 0.00964265i | ||||||||
\(373\) | −16.3612 | −0.847151 | −0.423576 | − | 0.905861i | \(-0.639225\pi\) | ||||
−0.423576 | + | 0.905861i | \(0.639225\pi\) | |||||||
\(374\) | −6.55257 | −0.338825 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 13.0978 | 0.675469 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.35690 | 0.0697912 | ||||||||
\(379\) | − 22.8823i | − 1.17539i | −0.809084 | − | 0.587693i | \(-0.800036\pi\) | ||||
0.809084 | − | 0.587693i | \(-0.199964\pi\) | |||||||
\(380\) | 5.34481 | 0.274183 | ||||||||
\(381\) | −16.3763 | −0.838982 | ||||||||
\(382\) | 11.8280i | 0.605174i | ||||||||
\(383\) | − 11.9191i | − 0.609040i | −0.952506 | − | 0.304520i | \(-0.901504\pi\) | ||||
0.952506 | − | 0.304520i | \(-0.0984961\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | − 4.33944i | − 0.221158i | ||||||||
\(386\) | −0.872625 | −0.0444155 | ||||||||
\(387\) | 2.91185 | 0.148018 | ||||||||
\(388\) | − 4.74094i | − 0.240685i | ||||||||
\(389\) | −8.07606 | −0.409473 | −0.204736 | − | 0.978817i | \(-0.565634\pi\) | ||||
−0.204736 | + | 0.978817i | \(0.565634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.0532 | 0.862419 | ||||||||
\(392\) | − 5.15883i | − 0.260560i | ||||||||
\(393\) | −3.00969 | −0.151819 | ||||||||
\(394\) | 10.6213 | 0.535095 | ||||||||
\(395\) | − 1.42327i | − 0.0716126i | ||||||||
\(396\) | − 3.19806i | − 0.160709i | ||||||||
\(397\) | − 20.5230i | − 1.03002i | −0.857184 | − | 0.515011i | \(-0.827788\pi\) | ||||
0.857184 | − | 0.515011i | \(-0.172212\pi\) | |||||||
\(398\) | − 12.3424i | − 0.618670i | ||||||||
\(399\) | 7.25236 | 0.363072 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − 18.3274i | − 0.915224i | −0.889152 | − | 0.457612i | \(-0.848705\pi\) | ||||
0.889152 | − | 0.457612i | \(-0.151295\pi\) | |||||||
\(402\) | −1.55496 | −0.0775543 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12.5918 | −0.626465 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −10.9511 | −0.543493 | ||||||||
\(407\) | 7.88902 | 0.391044 | ||||||||
\(408\) | 2.04892i | 0.101437i | ||||||||
\(409\) | − 9.00000i | − 0.445021i | −0.974930 | − | 0.222511i | \(-0.928575\pi\) | ||||
0.974930 | − | 0.222511i | \(-0.0714252\pi\) | |||||||
\(410\) | 12.2349i | 0.604239i | ||||||||
\(411\) | − 20.2892i | − 1.00079i | ||||||||
\(412\) | −9.00000 | −0.443398 | ||||||||
\(413\) | 2.20583 | 0.108542 | ||||||||
\(414\) | 8.32304i | 0.409055i | ||||||||
\(415\) | 11.1196 | 0.545840 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.153457 | 0.00751481 | ||||||||
\(418\) | − 17.0930i | − 0.836048i | ||||||||
\(419\) | −14.4185 | −0.704389 | −0.352195 | − | 0.935927i | \(-0.614564\pi\) | ||||
−0.352195 | + | 0.935927i | \(0.614564\pi\) | |||||||
\(420\) | −1.35690 | −0.0662097 | ||||||||
\(421\) | 19.9801i | 0.973773i | 0.873465 | + | 0.486886i | \(0.161867\pi\) | ||||
−0.873465 | + | 0.486886i | \(0.838133\pi\) | |||||||
\(422\) | 6.75733i | 0.328942i | ||||||||
\(423\) | 13.0978i | 0.636839i | ||||||||
\(424\) | − 5.74094i | − 0.278805i | ||||||||
\(425\) | −2.04892 | −0.0993871 | ||||||||
\(426\) | 2.32304 | 0.112552 | ||||||||
\(427\) | 7.16959i | 0.346961i | ||||||||
\(428\) | 5.08815 | 0.245945 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.91185 | −0.140422 | ||||||||
\(431\) | 21.1812i | 1.02026i | 0.860097 | + | 0.510131i | \(0.170403\pi\) | ||||
−0.860097 | + | 0.510131i | \(0.829597\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −31.0291 | −1.49116 | −0.745581 | − | 0.666415i | \(-0.767828\pi\) | ||||
−0.745581 | + | 0.666415i | \(0.767828\pi\) | |||||||
\(434\) | − 0.252356i | − 0.0121135i | ||||||||
\(435\) | − 8.07069i | − 0.386960i | ||||||||
\(436\) | 6.43296i | 0.308083i | ||||||||
\(437\) | 44.4851i | 2.12801i | ||||||||
\(438\) | −5.11529 | −0.244418 | ||||||||
\(439\) | −7.33406 | −0.350036 | −0.175018 | − | 0.984565i | \(-0.555998\pi\) | ||||
−0.175018 | + | 0.984565i | \(0.555998\pi\) | |||||||
\(440\) | 3.19806i | 0.152462i | ||||||||
\(441\) | 5.15883 | 0.245659 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.1360 | −0.861667 | −0.430834 | − | 0.902431i | \(-0.641780\pi\) | ||||
−0.430834 | + | 0.902431i | \(0.641780\pi\) | |||||||
\(444\) | − 2.46681i | − 0.117070i | ||||||||
\(445\) | −3.37867 | −0.160164 | ||||||||
\(446\) | 21.5972 | 1.02266 | ||||||||
\(447\) | − 10.7724i | − 0.509517i | ||||||||
\(448\) | − 1.35690i | − 0.0641073i | ||||||||
\(449\) | 4.55496i | 0.214962i | 0.994207 | + | 0.107481i | \(0.0342784\pi\) | ||||
−0.994207 | + | 0.107481i | \(0.965722\pi\) | |||||||
\(450\) | − 1.00000i | − 0.0471405i | ||||||||
\(451\) | 39.1280 | 1.84246 | ||||||||
\(452\) | 18.6571 | 0.877556 | ||||||||
\(453\) | − 17.3817i | − 0.816661i | ||||||||
\(454\) | 10.2862 | 0.482756 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.34481 | −0.250294 | ||||||||
\(457\) | 9.98121i | 0.466901i | 0.972369 | + | 0.233451i | \(0.0750018\pi\) | ||||
−0.972369 | + | 0.233451i | \(0.924998\pi\) | |||||||
\(458\) | −4.25906 | −0.199013 | ||||||||
\(459\) | −2.04892 | −0.0956353 | ||||||||
\(460\) | − 8.32304i | − 0.388064i | ||||||||
\(461\) | − 16.1672i | − 0.752981i | −0.926420 | − | 0.376491i | \(-0.877131\pi\) | ||||
0.926420 | − | 0.376491i | \(-0.122869\pi\) | |||||||
\(462\) | 4.33944i | 0.201889i | ||||||||
\(463\) | − 3.88902i | − 0.180738i | −0.995908 | − | 0.0903690i | \(-0.971195\pi\) | ||||
0.995908 | − | 0.0903690i | \(-0.0288046\pi\) | |||||||
\(464\) | 8.07069 | 0.374672 | ||||||||
\(465\) | 0.185981 | 0.00862465 | ||||||||
\(466\) | − 19.5133i | − 0.903938i | ||||||||
\(467\) | 0.872625 | 0.0403803 | 0.0201901 | − | 0.999796i | \(-0.493573\pi\) | ||||
0.0201901 | + | 0.999796i | \(0.493573\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.10992 | 0.0974269 | ||||||||
\(470\) | − 13.0978i | − 0.604158i | ||||||||
\(471\) | −15.5429 | −0.716178 | ||||||||
\(472\) | −1.62565 | −0.0748264 | ||||||||
\(473\) | 9.31229i | 0.428180i | ||||||||
\(474\) | 1.42327i | 0.0653730i | ||||||||
\(475\) | − 5.34481i | − 0.245237i | ||||||||
\(476\) | − 2.78017i | − 0.127429i | ||||||||
\(477\) | 5.74094 | 0.262860 | ||||||||
\(478\) | −7.16315 | −0.327635 | ||||||||
\(479\) | 31.6305i | 1.44524i | 0.691247 | + | 0.722618i | \(0.257062\pi\) | ||||
−0.691247 | + | 0.722618i | \(0.742938\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −17.9584 | −0.817982 | ||||||||
\(483\) | − 11.2935i | − 0.513872i | ||||||||
\(484\) | −0.772398 | −0.0351090 | ||||||||
\(485\) | −4.74094 | −0.215275 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | 21.7748i | 0.986710i | 0.869828 | + | 0.493355i | \(0.164230\pi\) | ||||
−0.869828 | + | 0.493355i | \(0.835770\pi\) | |||||||
\(488\) | − 5.28382i | − 0.239187i | ||||||||
\(489\) | 2.00239i | 0.0905513i | ||||||||
\(490\) | −5.15883 | −0.233052 | ||||||||
\(491\) | −42.9590 | −1.93871 | −0.969356 | − | 0.245662i | \(-0.920995\pi\) | ||||
−0.969356 | + | 0.245662i | \(0.920995\pi\) | |||||||
\(492\) | − 12.2349i | − 0.551592i | ||||||||
\(493\) | 16.5362 | 0.744752 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.19806 | −0.143742 | ||||||||
\(496\) | 0.185981i | 0.00835078i | ||||||||
\(497\) | −3.15213 | −0.141392 | ||||||||
\(498\) | −11.1196 | −0.498281 | ||||||||
\(499\) | − 36.0978i | − 1.61596i | −0.589209 | − | 0.807981i | \(-0.700561\pi\) | ||||
0.589209 | − | 0.807981i | \(-0.299439\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 8.24027i | 0.368148i | ||||||||
\(502\) | 6.68425i | 0.298333i | ||||||||
\(503\) | −21.4534 | −0.956560 | −0.478280 | − | 0.878207i | \(-0.658740\pi\) | ||||
−0.478280 | + | 0.878207i | \(0.658740\pi\) | |||||||
\(504\) | 1.35690 | 0.0604409 | ||||||||
\(505\) | 12.5918i | 0.560327i | ||||||||
\(506\) | −26.6176 | −1.18330 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.3763 | −0.726580 | ||||||||
\(509\) | 0.545860i | 0.0241948i | 0.999927 | + | 0.0120974i | \(0.00385082\pi\) | ||||
−0.999927 | + | 0.0120974i | \(0.996149\pi\) | |||||||
\(510\) | 2.04892 | 0.0907276 | ||||||||
\(511\) | 6.94092 | 0.307048 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 5.34481i | − 0.235979i | ||||||||
\(514\) | − 9.91484i | − 0.437325i | ||||||||
\(515\) | 9.00000i | 0.396587i | ||||||||
\(516\) | 2.91185 | 0.128187 | ||||||||
\(517\) | −41.8877 | −1.84222 | ||||||||
\(518\) | 3.34721i | 0.147068i | ||||||||
\(519\) | 12.7463 | 0.559501 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.6136 | 1.29739 | 0.648697 | − | 0.761047i | \(-0.275314\pi\) | ||||
0.648697 | + | 0.761047i | \(0.275314\pi\) | |||||||
\(522\) | 8.07069i | 0.353244i | ||||||||
\(523\) | 44.4543 | 1.94385 | 0.971924 | − | 0.235293i | \(-0.0756050\pi\) | ||||
0.971924 | + | 0.235293i | \(0.0756050\pi\) | |||||||
\(524\) | −3.00969 | −0.131479 | ||||||||
\(525\) | 1.35690i | 0.0592198i | ||||||||
\(526\) | 13.8509i | 0.603926i | ||||||||
\(527\) | 0.381059i | 0.0165992i | ||||||||
\(528\) | − 3.19806i | − 0.139178i | ||||||||
\(529\) | 46.2731 | 2.01187 | ||||||||
\(530\) | −5.74094 | −0.249370 | ||||||||
\(531\) | − 1.62565i | − 0.0705470i | ||||||||
\(532\) | 7.25236 | 0.314430 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.37867 | 0.146209 | ||||||||
\(535\) | − 5.08815i | − 0.219980i | ||||||||
\(536\) | −1.55496 | −0.0671640 | ||||||||
\(537\) | 16.0422 | 0.692273 | ||||||||
\(538\) | − 17.8756i | − 0.770672i | ||||||||
\(539\) | 16.4983i | 0.710631i | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | − 18.7651i | − 0.806775i | −0.915029 | − | 0.403387i | \(-0.867833\pi\) | ||||
0.915029 | − | 0.403387i | \(-0.132167\pi\) | |||||||
\(542\) | −31.2083 | −1.34051 | ||||||||
\(543\) | 3.85086 | 0.165256 | ||||||||
\(544\) | 2.04892i | 0.0878466i | ||||||||
\(545\) | 6.43296 | 0.275558 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0116 | 1.36872 | 0.684359 | − | 0.729145i | \(-0.260082\pi\) | ||||
0.684359 | + | 0.729145i | \(0.260082\pi\) | |||||||
\(548\) | − 20.2892i | − 0.866711i | ||||||||
\(549\) | 5.28382 | 0.225508 | ||||||||
\(550\) | 3.19806 | 0.136366 | ||||||||
\(551\) | 43.1363i | 1.83767i | ||||||||
\(552\) | 8.32304i | 0.354252i | ||||||||
\(553\) | − 1.93123i | − 0.0821243i | ||||||||
\(554\) | − 22.9245i | − 0.973970i | ||||||||
\(555\) | −2.46681 | −0.104710 | ||||||||
\(556\) | 0.153457 | 0.00650802 | ||||||||
\(557\) | 8.23490i | 0.348924i | 0.984664 | + | 0.174462i | \(0.0558186\pi\) | ||||
−0.984664 | + | 0.174462i | \(0.944181\pi\) | |||||||
\(558\) | −0.185981 | −0.00787319 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.35690 | −0.0573393 | ||||||||
\(561\) | − 6.55257i | − 0.276650i | ||||||||
\(562\) | −28.0683 | −1.18399 | ||||||||
\(563\) | 30.2295 | 1.27402 | 0.637011 | − | 0.770855i | \(-0.280170\pi\) | ||||
0.637011 | + | 0.770855i | \(0.280170\pi\) | |||||||
\(564\) | 13.0978i | 0.551518i | ||||||||
\(565\) | − 18.6571i | − 0.784910i | ||||||||
\(566\) | 24.8364i | 1.04395i | ||||||||
\(567\) | 1.35690i | 0.0569843i | ||||||||
\(568\) | 2.32304 | 0.0974728 | ||||||||
\(569\) | −44.3110 | −1.85761 | −0.928806 | − | 0.370566i | \(-0.879164\pi\) | ||||
−0.928806 | + | 0.370566i | \(0.879164\pi\) | |||||||
\(570\) | 5.34481i | 0.223870i | ||||||||
\(571\) | −34.4873 | −1.44325 | −0.721623 | − | 0.692286i | \(-0.756604\pi\) | ||||
−0.721623 | + | 0.692286i | \(0.756604\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.8280 | −0.494123 | ||||||||
\(574\) | 16.6015i | 0.692932i | ||||||||
\(575\) | −8.32304 | −0.347095 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 14.1715i | − 0.589968i | −0.955502 | − | 0.294984i | \(-0.904686\pi\) | ||||
0.955502 | − | 0.294984i | \(-0.0953142\pi\) | |||||||
\(578\) | − 12.8019i | − 0.532490i | ||||||||
\(579\) | − 0.872625i | − 0.0362651i | ||||||||
\(580\) | − 8.07069i | − 0.335117i | ||||||||
\(581\) | 15.0881 | 0.625962 | ||||||||
\(582\) | 4.74094 | 0.196518 | ||||||||
\(583\) | 18.3599i | 0.760389i | ||||||||
\(584\) | −5.11529 | −0.211672 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.4349 | 1.17463 | ||||||||
\(587\) | − 1.12737i | − 0.0465317i | −0.999729 | − | 0.0232659i | \(-0.992594\pi\) | ||||
0.999729 | − | 0.0232659i | \(-0.00740642\pi\) | |||||||
\(588\) | 5.15883 | 0.212747 | ||||||||
\(589\) | −0.994032 | −0.0409584 | ||||||||
\(590\) | 1.62565i | 0.0669268i | ||||||||
\(591\) | 10.6213i | 0.436903i | ||||||||
\(592\) | − 2.46681i | − 0.101385i | ||||||||
\(593\) | − 18.3913i | − 0.755242i | −0.925960 | − | 0.377621i | \(-0.876742\pi\) | ||||
0.925960 | − | 0.377621i | \(-0.123258\pi\) | |||||||
\(594\) | 3.19806 | 0.131218 | ||||||||
\(595\) | −2.78017 | −0.113976 | ||||||||
\(596\) | − 10.7724i | − 0.441255i | ||||||||
\(597\) | 12.3424 | 0.505142 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.1226 | 0.536174 | 0.268087 | − | 0.963395i | \(-0.413608\pi\) | ||||
0.268087 | + | 0.963395i | \(0.413608\pi\) | |||||||
\(600\) | − 1.00000i | − 0.0408248i | ||||||||
\(601\) | 25.5754 | 1.04324 | 0.521621 | − | 0.853177i | \(-0.325327\pi\) | ||||
0.521621 | + | 0.853177i | \(0.325327\pi\) | |||||||
\(602\) | −3.95108 | −0.161034 | ||||||||
\(603\) | − 1.55496i | − 0.0633228i | ||||||||
\(604\) | − 17.3817i | − 0.707249i | ||||||||
\(605\) | 0.772398i | 0.0314024i | ||||||||
\(606\) | − 12.5918i | − 0.511507i | ||||||||
\(607\) | 44.4782 | 1.80531 | 0.902656 | − | 0.430362i | \(-0.141614\pi\) | ||||
0.902656 | + | 0.430362i | \(0.141614\pi\) | |||||||
\(608\) | −5.34481 | −0.216761 | ||||||||
\(609\) | − 10.9511i | − 0.443760i | ||||||||
\(610\) | −5.28382 | −0.213935 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.04892 | −0.0828226 | ||||||||
\(613\) | − 21.7657i | − 0.879108i | −0.898216 | − | 0.439554i | \(-0.855137\pi\) | ||||
0.898216 | − | 0.439554i | \(-0.144863\pi\) | |||||||
\(614\) | 10.1347 | 0.409002 | ||||||||
\(615\) | −12.2349 | −0.493359 | ||||||||
\(616\) | 4.33944i | 0.174841i | ||||||||
\(617\) | − 17.3569i | − 0.698762i | −0.936981 | − | 0.349381i | \(-0.886392\pi\) | ||||
0.936981 | − | 0.349381i | \(-0.113608\pi\) | |||||||
\(618\) | − 9.00000i | − 0.362033i | ||||||||
\(619\) | − 36.8049i | − 1.47931i | −0.672984 | − | 0.739657i | \(-0.734988\pi\) | ||||
0.672984 | − | 0.739657i | \(-0.265012\pi\) | |||||||
\(620\) | 0.185981 | 0.00746916 | ||||||||
\(621\) | −8.32304 | −0.333992 | ||||||||
\(622\) | − 20.0218i | − 0.802800i | ||||||||
\(623\) | −4.58450 | −0.183674 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 8.63640i | 0.345180i | ||||||||
\(627\) | 17.0930 | 0.682631 | ||||||||
\(628\) | −15.5429 | −0.620228 | ||||||||
\(629\) | − 5.05429i | − 0.201528i | ||||||||
\(630\) | − 1.35690i | − 0.0540600i | ||||||||
\(631\) | − 11.7554i | − 0.467976i | −0.972240 | − | 0.233988i | \(-0.924822\pi\) | ||||
0.972240 | − | 0.233988i | \(-0.0751776\pi\) | |||||||
\(632\) | 1.42327i | 0.0566147i | ||||||||
\(633\) | −6.75733 | −0.268580 | ||||||||
\(634\) | 17.6256 | 0.700004 | ||||||||
\(635\) | 16.3763i | 0.649873i | ||||||||
\(636\) | 5.74094 | 0.227643 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25.8106 | −1.02185 | ||||||||
\(639\) | 2.32304i | 0.0918982i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −33.0858 | −1.30681 | −0.653404 | − | 0.757009i | \(-0.726660\pi\) | ||||
−0.653404 | + | 0.757009i | \(0.726660\pi\) | |||||||
\(642\) | 5.08815i | 0.200813i | ||||||||
\(643\) | − 10.3461i | − 0.408012i | −0.978970 | − | 0.204006i | \(-0.934604\pi\) | ||||
0.978970 | − | 0.204006i | \(-0.0653962\pi\) | |||||||
\(644\) | − 11.2935i | − 0.445026i | ||||||||
\(645\) | − 2.91185i | − 0.114654i | ||||||||
\(646\) | −10.9511 | −0.430865 | ||||||||
\(647\) | 11.0030 | 0.432572 | 0.216286 | − | 0.976330i | \(-0.430606\pi\) | ||||
0.216286 | + | 0.976330i | \(0.430606\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 5.19892 | 0.204075 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.252356 | 0.00989063 | ||||||||
\(652\) | 2.00239i | 0.0784198i | ||||||||
\(653\) | −30.8224 | −1.20617 | −0.603086 | − | 0.797676i | \(-0.706063\pi\) | ||||
−0.603086 | + | 0.797676i | \(0.706063\pi\) | |||||||
\(654\) | −6.43296 | −0.251549 | ||||||||
\(655\) | 3.00969i | 0.117598i | ||||||||
\(656\) | − 12.2349i | − 0.477693i | ||||||||
\(657\) | − 5.11529i | − 0.199567i | ||||||||
\(658\) | − 17.7724i | − 0.692840i | ||||||||
\(659\) | −33.2010 | −1.29333 | −0.646665 | − | 0.762774i | \(-0.723837\pi\) | ||||
−0.646665 | + | 0.762774i | \(0.723837\pi\) | |||||||
\(660\) | −3.19806 | −0.124484 | ||||||||
\(661\) | − 37.4252i | − 1.45567i | −0.685752 | − | 0.727836i | \(-0.740526\pi\) | ||||
0.685752 | − | 0.727836i | \(-0.259474\pi\) | |||||||
\(662\) | −31.5163 | −1.22492 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.1196 | −0.431524 | ||||||||
\(665\) | − 7.25236i | − 0.281234i | ||||||||
\(666\) | 2.46681 | 0.0955870 | ||||||||
\(667\) | 67.1727 | 2.60094 | ||||||||
\(668\) | 8.24027i | 0.318826i | ||||||||
\(669\) | 21.5972i | 0.834995i | ||||||||
\(670\) | 1.55496i | 0.0600733i | ||||||||
\(671\) | 16.8980i | 0.652339i | ||||||||
\(672\) | 1.35690 | 0.0523434 | ||||||||
\(673\) | 34.9409 | 1.34687 | 0.673437 | − | 0.739245i | \(-0.264817\pi\) | ||||
0.673437 | + | 0.739245i | \(0.264817\pi\) | |||||||
\(674\) | 11.8116i | 0.454967i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.3913 | 1.12960 | 0.564800 | − | 0.825228i | \(-0.308953\pi\) | ||||
0.564800 | + | 0.825228i | \(0.308953\pi\) | |||||||
\(678\) | 18.6571i | 0.716522i | ||||||||
\(679\) | −6.43296 | −0.246874 | ||||||||
\(680\) | 2.04892 | 0.0785724 | ||||||||
\(681\) | 10.2862i | 0.394168i | ||||||||
\(682\) | − 0.594778i | − 0.0227752i | ||||||||
\(683\) | − 28.9855i | − 1.10910i | −0.832150 | − | 0.554550i | \(-0.812890\pi\) | ||||
0.832150 | − | 0.554550i | \(-0.187110\pi\) | |||||||
\(684\) | − 5.34481i | − 0.204364i | ||||||||
\(685\) | −20.2892 | −0.775210 | ||||||||
\(686\) | −16.4983 | −0.629907 | ||||||||
\(687\) | − 4.25906i | − 0.162493i | ||||||||
\(688\) | 2.91185 | 0.111013 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 8.32304 | 0.316853 | ||||||||
\(691\) | − 1.37627i | − 0.0523559i | −0.999657 | − | 0.0261780i | \(-0.991666\pi\) | ||||
0.999657 | − | 0.0261780i | \(-0.00833365\pi\) | |||||||
\(692\) | 12.7463 | 0.484542 | ||||||||
\(693\) | −4.33944 | −0.164842 | ||||||||
\(694\) | − 17.4101i | − 0.660879i | ||||||||
\(695\) | − 0.153457i | − 0.00582095i | ||||||||
\(696\) | 8.07069i | 0.305919i | ||||||||
\(697\) | − 25.0683i | − 0.949529i | ||||||||
\(698\) | −18.6799 | −0.707046 | ||||||||
\(699\) | 19.5133 | 0.738062 | ||||||||
\(700\) | 1.35690i | 0.0512858i | ||||||||
\(701\) | −9.21014 | −0.347862 | −0.173931 | − | 0.984758i | \(-0.555647\pi\) | ||||
−0.173931 | + | 0.984758i | \(0.555647\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.1847 | 0.497269 | ||||||||
\(704\) | − 3.19806i | − 0.120532i | ||||||||
\(705\) | 13.0978 | 0.493293 | ||||||||
\(706\) | 25.3991 | 0.955908 | ||||||||
\(707\) | 17.0858i | 0.642576i | ||||||||
\(708\) | − 1.62565i | − 0.0610955i | ||||||||
\(709\) | 46.1613i | 1.73363i | 0.498634 | + | 0.866813i | \(0.333835\pi\) | ||||
−0.498634 | + | 0.866813i | \(0.666165\pi\) | |||||||
\(710\) | − 2.32304i | − 0.0871823i | ||||||||
\(711\) | −1.42327 | −0.0533769 | ||||||||
\(712\) | 3.37867 | 0.126621 | ||||||||
\(713\) | 1.54793i | 0.0579703i | ||||||||
\(714\) | 2.78017 | 0.104045 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.0422 | 0.599526 | ||||||||
\(717\) | − 7.16315i | − 0.267513i | ||||||||
\(718\) | −34.0103 | −1.26925 | ||||||||
\(719\) | 46.3588 | 1.72889 | 0.864446 | − | 0.502726i | \(-0.167669\pi\) | ||||
0.864446 | + | 0.502726i | \(0.167669\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | 12.2121i | 0.454801i | ||||||||
\(722\) | − 9.56704i | − 0.356048i | ||||||||
\(723\) | − 17.9584i | − 0.667879i | ||||||||
\(724\) | 3.85086 | 0.143116 | ||||||||
\(725\) | −8.07069 | −0.299738 | ||||||||
\(726\) | − 0.772398i | − 0.0286664i | ||||||||
\(727\) | 1.67217 | 0.0620174 | 0.0310087 | − | 0.999519i | \(-0.490128\pi\) | ||||
0.0310087 | + | 0.999519i | \(0.490128\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.11529i | 0.189325i | ||||||||
\(731\) | 5.96615 | 0.220666 | ||||||||
\(732\) | 5.28382 | 0.195295 | ||||||||
\(733\) | 33.6189i | 1.24174i | 0.783912 | + | 0.620872i | \(0.213221\pi\) | ||||
−0.783912 | + | 0.620872i | \(0.786779\pi\) | |||||||
\(734\) | − 25.6437i | − 0.946526i | ||||||||
\(735\) | − 5.15883i | − 0.190286i | ||||||||
\(736\) | 8.32304i | 0.306791i | ||||||||
\(737\) | 4.97285 | 0.183177 | ||||||||
\(738\) | 12.2349 | 0.450373 | ||||||||
\(739\) | − 31.8437i | − 1.17139i | −0.810532 | − | 0.585694i | \(-0.800822\pi\) | ||||
0.810532 | − | 0.585694i | \(-0.199178\pi\) | |||||||
\(740\) | −2.46681 | −0.0906818 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.78986 | −0.285975 | ||||||||
\(743\) | − 23.4010i | − 0.858500i | −0.903186 | − | 0.429250i | \(-0.858778\pi\) | ||||
0.903186 | − | 0.429250i | \(-0.141222\pi\) | |||||||
\(744\) | −0.185981 | −0.00681838 | ||||||||
\(745\) | −10.7724 | −0.394670 | ||||||||
\(746\) | − 16.3612i | − 0.599026i | ||||||||
\(747\) | − 11.1196i | − 0.406845i | ||||||||
\(748\) | − 6.55257i | − 0.239586i | ||||||||
\(749\) | − 6.90408i | − 0.252270i | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 39.0146 | 1.42366 | 0.711831 | − | 0.702350i | \(-0.247866\pi\) | ||||
0.711831 | + | 0.702350i | \(0.247866\pi\) | |||||||
\(752\) | 13.0978i | 0.477629i | ||||||||
\(753\) | −6.68425 | −0.243588 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.3817 | −0.632583 | ||||||||
\(756\) | 1.35690i | 0.0493498i | ||||||||
\(757\) | 43.0224 | 1.56367 | 0.781837 | − | 0.623483i | \(-0.214283\pi\) | ||||
0.781837 | + | 0.623483i | \(0.214283\pi\) | |||||||
\(758\) | 22.8823 | 0.831123 | ||||||||
\(759\) | − 26.6176i | − 0.966158i | ||||||||
\(760\) | 5.34481i | 0.193877i | ||||||||
\(761\) | 14.9903i | 0.543398i | 0.962382 | + | 0.271699i | \(0.0875856\pi\) | ||||
−0.962382 | + | 0.271699i | \(0.912414\pi\) | |||||||
\(762\) | − 16.3763i | − 0.593250i | ||||||||
\(763\) | 8.72886 | 0.316006 | ||||||||
\(764\) | −11.8280 | −0.427923 | ||||||||
\(765\) | 2.04892i | 0.0740788i | ||||||||
\(766\) | 11.9191 | 0.430656 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 19.9138i | 0.718109i | 0.933317 | + | 0.359055i | \(0.116901\pi\) | ||||
−0.933317 | + | 0.359055i | \(0.883099\pi\) | |||||||
\(770\) | 4.33944 | 0.156382 | ||||||||
\(771\) | 9.91484 | 0.357074 | ||||||||
\(772\) | − 0.872625i | − 0.0314065i | ||||||||
\(773\) | − 25.5566i | − 0.919208i | −0.888124 | − | 0.459604i | \(-0.847991\pi\) | ||||
0.888124 | − | 0.459604i | \(-0.152009\pi\) | |||||||
\(774\) | 2.91185i | 0.104664i | ||||||||
\(775\) | − 0.185981i | − 0.00668062i | ||||||||
\(776\) | 4.74094 | 0.170190 | ||||||||
\(777\) | −3.34721 | −0.120080 | ||||||||
\(778\) | − 8.07606i | − 0.289541i | ||||||||
\(779\) | 65.3933 | 2.34296 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.42924 | −0.265839 | ||||||||
\(782\) | 17.0532i | 0.609822i | ||||||||
\(783\) | −8.07069 | −0.288423 | ||||||||
\(784\) | 5.15883 | 0.184244 | ||||||||
\(785\) | 15.5429i | 0.554749i | ||||||||
\(786\) | − 3.00969i | − 0.107352i | ||||||||
\(787\) | 28.6297i | 1.02054i | 0.860015 | + | 0.510269i | \(0.170454\pi\) | ||||
−0.860015 | + | 0.510269i | \(0.829546\pi\) | |||||||
\(788\) | 10.6213i | 0.378369i | ||||||||
\(789\) | −13.8509 | −0.493103 | ||||||||
\(790\) | 1.42327 | 0.0506377 | ||||||||
\(791\) | − 25.3157i | − 0.900124i | ||||||||
\(792\) | 3.19806 | 0.113638 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 20.5230 | 0.728335 | ||||||||
\(795\) | − 5.74094i | − 0.203610i | ||||||||
\(796\) | 12.3424 | 0.437466 | ||||||||
\(797\) | −1.00431 | −0.0355746 | −0.0177873 | − | 0.999842i | \(-0.505662\pi\) | ||||
−0.0177873 | + | 0.999842i | \(0.505662\pi\) | |||||||
\(798\) | 7.25236i | 0.256731i | ||||||||
\(799\) | 26.8364i | 0.949403i | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | 3.37867i | 0.119379i | ||||||||
\(802\) | 18.3274 | 0.647161 | ||||||||
\(803\) | 16.3590 | 0.577297 | ||||||||
\(804\) | − 1.55496i | − 0.0548391i | ||||||||
\(805\) | −11.2935 | −0.398044 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.8756 | 0.629251 | ||||||||
\(808\) | − 12.5918i | − 0.442978i | ||||||||
\(809\) | 49.8743 | 1.75349 | 0.876743 | − | 0.480959i | \(-0.159711\pi\) | ||||
0.876743 | + | 0.480959i | \(0.159711\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 7.95646i | 0.279389i | 0.990195 | + | 0.139695i | \(0.0446121\pi\) | ||||
−0.990195 | + | 0.139695i | \(0.955388\pi\) | |||||||
\(812\) | − 10.9511i | − 0.384308i | ||||||||
\(813\) | − 31.2083i | − 1.09452i | ||||||||
\(814\) | 7.88902i | 0.276510i | ||||||||
\(815\) | 2.00239 | 0.0701408 | ||||||||
\(816\) | −2.04892 | −0.0717265 | ||||||||
\(817\) | 15.5633i | 0.544492i | ||||||||
\(818\) | 9.00000 | 0.314678 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.2349 | −0.427261 | ||||||||
\(821\) | 52.9071i | 1.84647i | 0.384236 | + | 0.923235i | \(0.374465\pi\) | ||||
−0.384236 | + | 0.923235i | \(0.625535\pi\) | |||||||
\(822\) | 20.2892 | 0.707667 | ||||||||
\(823\) | −21.8006 | −0.759921 | −0.379961 | − | 0.925003i | \(-0.624063\pi\) | ||||
−0.379961 | + | 0.925003i | \(0.624063\pi\) | |||||||
\(824\) | − 9.00000i | − 0.313530i | ||||||||
\(825\) | 3.19806i | 0.111342i | ||||||||
\(826\) | 2.20583i | 0.0767507i | ||||||||
\(827\) | 27.3139i | 0.949799i | 0.880040 | + | 0.474899i | \(0.157516\pi\) | ||||
−0.880040 | + | 0.474899i | \(0.842484\pi\) | |||||||
\(828\) | −8.32304 | −0.289246 | ||||||||
\(829\) | −40.8471 | −1.41868 | −0.709340 | − | 0.704867i | \(-0.751007\pi\) | ||||
−0.709340 | + | 0.704867i | \(0.751007\pi\) | |||||||
\(830\) | 11.1196i | 0.385967i | ||||||||
\(831\) | 22.9245 | 0.795243 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5700 | 0.366230 | ||||||||
\(834\) | 0.153457i | 0.00531377i | ||||||||
\(835\) | 8.24027 | 0.285166 | ||||||||
\(836\) | 17.0930 | 0.591175 | ||||||||
\(837\) | − 0.185981i | − 0.00642843i | ||||||||
\(838\) | − 14.4185i | − 0.498078i | ||||||||
\(839\) | − 43.0823i | − 1.48737i | −0.668532 | − | 0.743683i | \(-0.733077\pi\) | ||||
0.668532 | − | 0.743683i | \(-0.266923\pi\) | |||||||
\(840\) | − 1.35690i | − 0.0468174i | ||||||||
\(841\) | 36.1360 | 1.24607 | ||||||||
\(842\) | −19.9801 | −0.688561 | ||||||||
\(843\) | − 28.0683i | − 0.966723i | ||||||||
\(844\) | −6.75733 | −0.232597 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13.0978 | −0.450313 | ||||||||
\(847\) | 1.04806i | 0.0360119i | ||||||||
\(848\) | 5.74094 | 0.197145 | ||||||||
\(849\) | −24.8364 | −0.852382 | ||||||||
\(850\) | − 2.04892i | − 0.0702773i | ||||||||
\(851\) | − 20.5314i | − 0.703807i | ||||||||
\(852\) | 2.32304i | 0.0795862i | ||||||||
\(853\) | 24.6813i | 0.845071i | 0.906346 | + | 0.422535i | \(0.138860\pi\) | ||||
−0.906346 | + | 0.422535i | \(0.861140\pi\) | |||||||
\(854\) | −7.16959 | −0.245338 | ||||||||
\(855\) | −5.34481 | −0.182789 | ||||||||
\(856\) | 5.08815i | 0.173909i | ||||||||
\(857\) | −43.1075 | −1.47252 | −0.736262 | − | 0.676696i | \(-0.763411\pi\) | ||||
−0.736262 | + | 0.676696i | \(0.763411\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.1323 | −1.43753 | −0.718767 | − | 0.695251i | \(-0.755293\pi\) | ||||
−0.718767 | + | 0.695251i | \(0.755293\pi\) | |||||||
\(860\) | − 2.91185i | − 0.0992934i | ||||||||
\(861\) | −16.6015 | −0.565777 | ||||||||
\(862\) | −21.1812 | −0.721434 | ||||||||
\(863\) | 47.9342i | 1.63170i | 0.578264 | + | 0.815850i | \(0.303730\pi\) | ||||
−0.578264 | + | 0.815850i | \(0.696270\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | − 12.7463i | − 0.433388i | ||||||||
\(866\) | − 31.0291i | − 1.05441i | ||||||||
\(867\) | 12.8019 | 0.434777 | ||||||||
\(868\) | 0.252356 | 0.00856553 | ||||||||
\(869\) | − 4.55171i | − 0.154406i | ||||||||
\(870\) | 8.07069 | 0.273622 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.43296 | −0.217848 | ||||||||
\(873\) | 4.74094i | 0.160456i | ||||||||
\(874\) | −44.4851 | −1.50473 | ||||||||
\(875\) | 1.35690 | 0.0458715 | ||||||||
\(876\) | − 5.11529i | − 0.172830i | ||||||||
\(877\) | − 38.6674i | − 1.30570i | −0.757485 | − | 0.652852i | \(-0.773572\pi\) | ||||
0.757485 | − | 0.652852i | \(-0.226428\pi\) | |||||||
\(878\) | − 7.33406i | − 0.247513i | ||||||||
\(879\) | 28.4349i | 0.959085i | ||||||||
\(880\) | −3.19806 | −0.107807 | ||||||||
\(881\) | −25.4980 | −0.859050 | −0.429525 | − | 0.903055i | \(-0.641319\pi\) | ||||
−0.429525 | + | 0.903055i | \(0.641319\pi\) | |||||||
\(882\) | 5.15883i | 0.173707i | ||||||||
\(883\) | 31.8377 | 1.07142 | 0.535712 | − | 0.844401i | \(-0.320043\pi\) | ||||
0.535712 | + | 0.844401i | \(0.320043\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.62565 | −0.0546455 | ||||||||
\(886\) | − 18.1360i | − 0.609291i | ||||||||
\(887\) | −7.83446 | −0.263055 | −0.131528 | − | 0.991312i | \(-0.541988\pi\) | ||||
−0.131528 | + | 0.991312i | \(0.541988\pi\) | |||||||
\(888\) | 2.46681 | 0.0827808 | ||||||||
\(889\) | 22.2209i | 0.745265i | ||||||||
\(890\) | − 3.37867i | − 0.113253i | ||||||||
\(891\) | 3.19806i | 0.107139i | ||||||||
\(892\) | 21.5972i | 0.723127i | ||||||||
\(893\) | −70.0055 | −2.34264 | ||||||||
\(894\) | 10.7724 | 0.360283 | ||||||||
\(895\) | − 16.0422i | − 0.536232i | ||||||||
\(896\) | 1.35690 | 0.0453307 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.55496 | −0.152001 | ||||||||
\(899\) | 1.50099i | 0.0500609i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 11.7627 | 0.391873 | ||||||||
\(902\) | 39.1280i | 1.30282i | ||||||||
\(903\) | − 3.95108i | − 0.131484i | ||||||||
\(904\) | 18.6571i | 0.620526i | ||||||||
\(905\) | − 3.85086i | − 0.128007i | ||||||||
\(906\) | 17.3817 | 0.577467 | ||||||||
\(907\) | −33.1089 | −1.09936 | −0.549681 | − | 0.835375i | \(-0.685251\pi\) | ||||
−0.549681 | + | 0.835375i | \(0.685251\pi\) | |||||||
\(908\) | 10.2862i | 0.341360i | ||||||||
\(909\) | 12.5918 | 0.417643 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.0556 | −0.465684 | −0.232842 | − | 0.972515i | \(-0.574802\pi\) | ||||
−0.232842 | + | 0.972515i | \(0.574802\pi\) | |||||||
\(912\) | − 5.34481i | − 0.176984i | ||||||||
\(913\) | 35.5612 | 1.17690 | ||||||||
\(914\) | −9.98121 | −0.330149 | ||||||||
\(915\) | − 5.28382i | − 0.174678i | ||||||||
\(916\) | − 4.25906i | − 0.140723i | ||||||||
\(917\) | 4.08383i | 0.134860i | ||||||||
\(918\) | − 2.04892i | − 0.0676243i | ||||||||
\(919\) | −27.1830 | −0.896684 | −0.448342 | − | 0.893862i | \(-0.647985\pi\) | ||||
−0.448342 | + | 0.893862i | \(0.647985\pi\) | |||||||
\(920\) | 8.32304 | 0.274403 | ||||||||
\(921\) | 10.1347i | 0.333949i | ||||||||
\(922\) | 16.1672 | 0.532438 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −4.33944 | −0.142757 | ||||||||
\(925\) | 2.46681i | 0.0811083i | ||||||||
\(926\) | 3.88902 | 0.127801 | ||||||||
\(927\) | 9.00000 | 0.295599 | ||||||||
\(928\) | 8.07069i | 0.264933i | ||||||||
\(929\) | − 50.3521i | − 1.65200i | −0.563671 | − | 0.826000i | \(-0.690611\pi\) | ||||
0.563671 | − | 0.826000i | \(-0.309389\pi\) | |||||||
\(930\) | 0.185981i | 0.00609855i | ||||||||
\(931\) | 27.5730i | 0.903669i | ||||||||
\(932\) | 19.5133 | 0.639181 | ||||||||
\(933\) | 20.0218 | 0.655483 | ||||||||
\(934\) | 0.872625i | 0.0285532i | ||||||||
\(935\) | −6.55257 | −0.214292 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.6394 | 0.870271 | 0.435135 | − | 0.900365i | \(-0.356701\pi\) | ||||
0.435135 | + | 0.900365i | \(0.356701\pi\) | |||||||
\(938\) | 2.10992i | 0.0688912i | ||||||||
\(939\) | −8.63640 | −0.281838 | ||||||||
\(940\) | 13.0978 | 0.427204 | ||||||||
\(941\) | − 25.7198i | − 0.838440i | −0.907885 | − | 0.419220i | \(-0.862304\pi\) | ||||
0.907885 | − | 0.419220i | \(-0.137696\pi\) | |||||||
\(942\) | − 15.5429i | − 0.506414i | ||||||||
\(943\) | − 101.832i | − 3.31609i | ||||||||
\(944\) | − 1.62565i | − 0.0529103i | ||||||||
\(945\) | 1.35690 | 0.0441398 | ||||||||
\(946\) | −9.31229 | −0.302769 | ||||||||
\(947\) | − 14.4862i | − 0.470738i | −0.971906 | − | 0.235369i | \(-0.924370\pi\) | ||||
0.971906 | − | 0.235369i | \(-0.0756298\pi\) | |||||||
\(948\) | −1.42327 | −0.0462257 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 5.34481 | 0.173409 | ||||||||
\(951\) | 17.6256i | 0.571551i | ||||||||
\(952\) | 2.78017 | 0.0901057 | ||||||||
\(953\) | 29.3690 | 0.951354 | 0.475677 | − | 0.879620i | \(-0.342203\pi\) | ||||
0.475677 | + | 0.879620i | \(0.342203\pi\) | |||||||
\(954\) | 5.74094i | 0.185870i | ||||||||
\(955\) | 11.8280i | 0.382746i | ||||||||
\(956\) | − 7.16315i | − 0.231673i | ||||||||
\(957\) | − 25.8106i | − 0.834337i | ||||||||
\(958\) | −31.6305 | −1.02194 | ||||||||
\(959\) | −27.5303 | −0.889000 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | 30.9654 | 0.998884 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.08815 | −0.163963 | ||||||||
\(964\) | − 17.9584i | − 0.578400i | ||||||||
\(965\) | −0.872625 | −0.0280908 | ||||||||
\(966\) | 11.2935 | 0.363363 | ||||||||
\(967\) | − 21.9360i | − 0.705415i | −0.935734 | − | 0.352707i | \(-0.885261\pi\) | ||||
0.935734 | − | 0.352707i | \(-0.114739\pi\) | |||||||
\(968\) | − 0.772398i | − 0.0248258i | ||||||||
\(969\) | − 10.9511i | − 0.351799i | ||||||||
\(970\) | − 4.74094i | − 0.152222i | ||||||||
\(971\) | 34.9754 | 1.12241 | 0.561206 | − | 0.827676i | \(-0.310337\pi\) | ||||
0.561206 | + | 0.827676i | \(0.310337\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | − 0.208225i | − 0.00667538i | ||||||||
\(974\) | −21.7748 | −0.697709 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.28382 | 0.169131 | ||||||||
\(977\) | − 7.72289i | − 0.247077i | −0.992340 | − | 0.123539i | \(-0.960576\pi\) | ||||
0.992340 | − | 0.123539i | \(-0.0394243\pi\) | |||||||
\(978\) | −2.00239 | −0.0640295 | ||||||||
\(979\) | −10.8052 | −0.345335 | ||||||||
\(980\) | − 5.15883i | − 0.164793i | ||||||||
\(981\) | − 6.43296i | − 0.205389i | ||||||||
\(982\) | − 42.9590i | − 1.37088i | ||||||||
\(983\) | − 29.0489i | − 0.926517i | −0.886223 | − | 0.463258i | \(-0.846680\pi\) | ||||
0.886223 | − | 0.463258i | \(-0.153320\pi\) | |||||||
\(984\) | 12.2349 | 0.390034 | ||||||||
\(985\) | 10.6213 | 0.338424 | ||||||||
\(986\) | 16.5362i | 0.526619i | ||||||||
\(987\) | 17.7724 | 0.565702 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.2355 | 0.770644 | ||||||||
\(990\) | − 3.19806i | − 0.101641i | ||||||||
\(991\) | 37.7192 | 1.19819 | 0.599094 | − | 0.800678i | \(-0.295527\pi\) | ||||
0.599094 | + | 0.800678i | \(0.295527\pi\) | |||||||
\(992\) | −0.185981 | −0.00590489 | ||||||||
\(993\) | − 31.5163i | − 1.00014i | ||||||||
\(994\) | − 3.15213i | − 0.0999795i | ||||||||
\(995\) | − 12.3424i | − 0.391281i | ||||||||
\(996\) | − 11.1196i | − 0.352338i | ||||||||
\(997\) | −7.18060 | −0.227412 | −0.113706 | − | 0.993514i | \(-0.536272\pi\) | ||||
−0.113706 | + | 0.993514i | \(0.536272\pi\) | |||||||
\(998\) | 36.0978 | 1.14266 | ||||||||
\(999\) | 2.46681i | 0.0780465i |
(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 | 5070.2.b.s.1351.5 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bt.1.2 | yes | 3 | ||
13.8 | odd | 4 | 5070.2.a.bk.1.2 | ✓ | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.s.1351.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bk.1.2 | ✓ | 3 | 13.8 | odd | 4 | ||
5070.2.a.bt.1.2 | yes | 3 | 13.5 | odd | 4 | ||
5070.2.b.s.1351.2 | 6 | 13.12 | even | 2 | inner | ||
5070.2.b.s.1351.5 | 6 | 1.1 | even | 1 | trivial |