Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(449,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.c (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.29 | ||
Character | \(\chi\) | \(=\) | 1050.449 |
Dual form | 1050.3.c.c.449.30 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 2.88800 | − | 0.812085i | 0.962665 | − | 0.270695i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.08424 | − | 1.14846i | 0.680707 | − | 0.191410i | ||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 7.68104 | − | 4.69059i | 0.853449 | − | 0.521177i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.7741i | 1.79765i | 0.438309 | + | 0.898824i | \(0.355577\pi\) | ||||
−0.438309 | + | 0.898824i | \(0.644423\pi\) | |||||||
\(12\) | 5.77599 | − | 1.62417i | 0.481333 | − | 0.135347i | ||||
\(13\) | 18.5947i | 1.43036i | 0.698940 | + | 0.715181i | \(0.253656\pi\) | ||||
−0.698940 | + | 0.715181i | \(0.746344\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 13.2896 | 0.781743 | 0.390872 | − | 0.920445i | \(-0.372174\pi\) | ||||
0.390872 | + | 0.920445i | \(0.372174\pi\) | |||||||
\(18\) | 10.8626 | − | 6.63350i | 0.603479 | − | 0.368528i | ||||
\(19\) | 5.47422 | 0.288117 | 0.144058 | − | 0.989569i | \(-0.453985\pi\) | ||||
0.144058 | + | 0.989569i | \(0.453985\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.14857 | + | 7.64092i | 0.102313 | + | 0.363853i | ||||
\(22\) | 27.9648i | 1.27113i | ||||||||
\(23\) | −34.8062 | −1.51331 | −0.756656 | − | 0.653814i | \(-0.773168\pi\) | ||||
−0.756656 | + | 0.653814i | \(0.773168\pi\) | |||||||
\(24\) | 8.16849 | − | 2.29692i | 0.340354 | − | 0.0957051i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 26.2969i | 1.01142i | ||||||||
\(27\) | 18.3736 | − | 19.7841i | 0.680505 | − | 0.732743i | ||||
\(28\) | 5.29150i | 0.188982i | ||||||||
\(29\) | 6.83287i | 0.235616i | 0.993036 | + | 0.117808i | \(0.0375867\pi\) | ||||
−0.993036 | + | 0.117808i | \(0.962413\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −31.4842 | −1.01562 | −0.507810 | − | 0.861469i | \(-0.669545\pi\) | ||||
−0.507810 | + | 0.861469i | \(0.669545\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 16.0583 | + | 57.1076i | 0.486614 | + | 1.73053i | ||||
\(34\) | 18.7944 | 0.552776 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 15.3621 | − | 9.38119i | 0.426724 | − | 0.260589i | ||||
\(37\) | 10.1809i | 0.275159i | 0.990491 | + | 0.137580i | \(0.0439323\pi\) | ||||
−0.990491 | + | 0.137580i | \(0.956068\pi\) | |||||||
\(38\) | 7.74172 | 0.203729 | ||||||||
\(39\) | 15.1005 | + | 53.7014i | 0.387191 | + | 1.37696i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 28.9124i | − | 0.705180i | −0.935778 | − | 0.352590i | \(-0.885301\pi\) | ||
0.935778 | − | 0.352590i | \(-0.114699\pi\) | |||||||
\(42\) | 3.03854 | + | 10.8059i | 0.0723462 | + | 0.257283i | ||||
\(43\) | − | 19.1117i | − | 0.444458i | −0.974995 | − | 0.222229i | \(-0.928667\pi\) | ||
0.974995 | − | 0.222229i | \(-0.0713332\pi\) | |||||||
\(44\) | 39.5483i | 0.898824i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −49.2233 | −1.07007 | ||||||||
\(47\) | 45.1245 | 0.960096 | 0.480048 | − | 0.877242i | \(-0.340619\pi\) | ||||
0.480048 | + | 0.877242i | \(0.340619\pi\) | |||||||
\(48\) | 11.5520 | − | 3.24834i | 0.240666 | − | 0.0676737i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 38.3804 | − | 10.7923i | 0.752557 | − | 0.211614i | ||||
\(52\) | 37.1894i | 0.715181i | ||||||||
\(53\) | 74.1324 | 1.39872 | 0.699362 | − | 0.714767i | \(-0.253467\pi\) | ||||
0.699362 | + | 0.714767i | \(0.253467\pi\) | |||||||
\(54\) | 25.9843 | − | 27.9789i | 0.481190 | − | 0.518128i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.48331i | 0.133631i | ||||||||
\(57\) | 15.8095 | − | 4.44553i | 0.277360 | − | 0.0779918i | ||||
\(58\) | 9.66313i | 0.166606i | ||||||||
\(59\) | − | 32.5630i | − | 0.551916i | −0.961170 | − | 0.275958i | \(-0.911005\pi\) | ||
0.961170 | − | 0.275958i | \(-0.0889950\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 71.7631 | 1.17644 | 0.588222 | − | 0.808700i | \(-0.299828\pi\) | ||||
0.588222 | + | 0.808700i | \(0.299828\pi\) | |||||||
\(62\) | −44.5254 | −0.718152 | ||||||||
\(63\) | 12.4101 | + | 20.3221i | 0.196986 | + | 0.322573i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 22.7098 | + | 80.7624i | 0.344088 | + | 1.22367i | ||||
\(67\) | − | 66.6261i | − | 0.994419i | −0.867631 | − | 0.497210i | \(-0.834358\pi\) | ||
0.867631 | − | 0.497210i | \(-0.165642\pi\) | |||||||
\(68\) | 26.5793 | 0.390872 | ||||||||
\(69\) | −100.520 | + | 28.2655i | −1.45681 | + | 0.409646i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 101.245i | − | 1.42599i | −0.701170 | − | 0.712994i | \(-0.747339\pi\) | ||
0.701170 | − | 0.712994i | \(-0.252661\pi\) | |||||||
\(72\) | 21.7253 | − | 13.2670i | 0.301740 | − | 0.184264i | ||||
\(73\) | 45.9939i | 0.630053i | 0.949083 | + | 0.315026i | \(0.102013\pi\) | ||||
−0.949083 | + | 0.315026i | \(0.897987\pi\) | |||||||
\(74\) | 14.3979i | 0.194567i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.9484 | 0.144058 | ||||||||
\(77\) | −52.3174 | −0.679447 | ||||||||
\(78\) | 21.3553 | + | 75.9452i | 0.273786 | + | 0.973657i | ||||
\(79\) | 140.809 | 1.78239 | 0.891195 | − | 0.453620i | \(-0.149868\pi\) | ||||
0.891195 | + | 0.453620i | \(0.149868\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 36.9967 | − | 72.0572i | 0.456749 | − | 0.889596i | ||||
\(82\) | − | 40.8883i | − | 0.498637i | ||||||
\(83\) | −100.622 | −1.21231 | −0.606154 | − | 0.795347i | \(-0.707288\pi\) | ||||
−0.606154 | + | 0.795347i | \(0.707288\pi\) | |||||||
\(84\) | 4.29715 | + | 15.2818i | 0.0511565 | + | 0.181927i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 27.0280i | − | 0.314279i | ||||||
\(87\) | 5.54887 | + | 19.7333i | 0.0637801 | + | 0.226819i | ||||
\(88\) | 55.9297i | 0.635565i | ||||||||
\(89\) | − | 11.2035i | − | 0.125882i | −0.998017 | − | 0.0629410i | \(-0.979952\pi\) | ||
0.998017 | − | 0.0629410i | \(-0.0200480\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −49.1969 | −0.540626 | ||||||||
\(92\) | −69.6123 | −0.756656 | ||||||||
\(93\) | −90.9263 | + | 25.5678i | −0.977702 | + | 0.274923i | ||||
\(94\) | 63.8157 | 0.678890 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 16.3370 | − | 4.59384i | 0.170177 | − | 0.0478525i | ||||
\(97\) | − | 102.496i | − | 1.05666i | −0.849038 | − | 0.528332i | \(-0.822818\pi\) | ||
0.849038 | − | 0.528332i | \(-0.177182\pi\) | |||||||
\(98\) | −9.89949 | −0.101015 | ||||||||
\(99\) | 92.7524 | + | 151.886i | 0.936893 | + | 1.53420i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 141.006i | 1.39610i | 0.716050 | + | 0.698049i | \(0.245948\pi\) | ||||
−0.716050 | + | 0.698049i | \(0.754052\pi\) | |||||||
\(102\) | 54.2781 | − | 15.2626i | 0.532138 | − | 0.149634i | ||||
\(103\) | 59.0361i | 0.573166i | 0.958055 | + | 0.286583i | \(0.0925194\pi\) | ||||
−0.958055 | + | 0.286583i | \(0.907481\pi\) | |||||||
\(104\) | 52.5937i | 0.505709i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 104.839 | 0.989048 | ||||||||
\(107\) | −90.2764 | −0.843705 | −0.421852 | − | 0.906664i | \(-0.638620\pi\) | ||||
−0.421852 | + | 0.906664i | \(0.638620\pi\) | |||||||
\(108\) | 36.7473 | − | 39.5681i | 0.340253 | − | 0.366372i | ||||
\(109\) | 92.1672 | 0.845570 | 0.422785 | − | 0.906230i | \(-0.361052\pi\) | ||||
0.422785 | + | 0.906230i | \(0.361052\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.26774 | + | 29.4024i | 0.0744842 | + | 0.264886i | ||||
\(112\) | 10.5830i | 0.0944911i | ||||||||
\(113\) | −148.929 | −1.31795 | −0.658977 | − | 0.752163i | \(-0.729011\pi\) | ||||
−0.658977 | + | 0.752163i | \(0.729011\pi\) | |||||||
\(114\) | 22.3580 | − | 6.28693i | 0.196123 | − | 0.0551485i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 13.6657i | 0.117808i | ||||||||
\(117\) | 87.2202 | + | 142.827i | 0.745471 | + | 1.22074i | ||||
\(118\) | − | 46.0511i | − | 0.390263i | ||||||
\(119\) | 35.1611i | 0.295471i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −270.016 | −2.23154 | ||||||||
\(122\) | 101.488 | 0.831871 | ||||||||
\(123\) | −23.4793 | − | 83.4988i | −0.190889 | − | 0.678852i | ||||
\(124\) | −62.9684 | −0.507810 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 17.5506 | + | 28.7398i | 0.139290 | + | 0.228094i | ||||
\(127\) | − | 77.7817i | − | 0.612455i | −0.951958 | − | 0.306227i | \(-0.900933\pi\) | ||
0.951958 | − | 0.306227i | \(-0.0990668\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | −15.5203 | − | 55.1944i | −0.120312 | − | 0.427864i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 229.780i | − | 1.75405i | −0.480447 | − | 0.877024i | \(-0.659526\pi\) | ||
0.480447 | − | 0.877024i | \(-0.340474\pi\) | |||||||
\(132\) | 32.1165 | + | 114.215i | 0.243307 | + | 0.865267i | ||||
\(133\) | 14.4834i | 0.108898i | ||||||||
\(134\) | − | 94.2235i | − | 0.703160i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 37.5888 | 0.276388 | ||||||||
\(137\) | −143.560 | −1.04788 | −0.523941 | − | 0.851754i | \(-0.675539\pi\) | ||||
−0.523941 | + | 0.851754i | \(0.675539\pi\) | |||||||
\(138\) | −142.157 | + | 39.9735i | −1.03012 | + | 0.289663i | ||||
\(139\) | 257.958 | 1.85581 | 0.927906 | − | 0.372815i | \(-0.121607\pi\) | ||||
0.927906 | + | 0.372815i | \(0.121607\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 130.319 | − | 36.6449i | 0.924251 | − | 0.259893i | ||||
\(142\) | − | 143.182i | − | 1.00833i | ||||||
\(143\) | −367.694 | −2.57129 | ||||||||
\(144\) | 30.7241 | − | 18.7624i | 0.213362 | − | 0.130294i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 65.0451i | 0.445515i | ||||||||
\(147\) | −20.2160 | + | 5.68459i | −0.137524 | + | 0.0386707i | ||||
\(148\) | 20.3618i | 0.137580i | ||||||||
\(149\) | − | 117.530i | − | 0.788791i | −0.918941 | − | 0.394396i | \(-0.870954\pi\) | ||
0.918941 | − | 0.394396i | \(-0.129046\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 251.056 | 1.66262 | 0.831311 | − | 0.555808i | \(-0.187591\pi\) | ||||
0.831311 | + | 0.555808i | \(0.187591\pi\) | |||||||
\(152\) | 15.4834 | 0.101865 | ||||||||
\(153\) | 102.078 | − | 62.3363i | 0.667178 | − | 0.407427i | ||||
\(154\) | −73.9880 | −0.480442 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 30.2009 | + | 107.403i | 0.193596 | + | 0.688479i | ||||
\(157\) | − | 18.6419i | − | 0.118738i | −0.998236 | − | 0.0593690i | \(-0.981091\pi\) | ||
0.998236 | − | 0.0593690i | \(-0.0189089\pi\) | |||||||
\(158\) | 199.134 | 1.26034 | ||||||||
\(159\) | 214.094 | − | 60.2018i | 1.34650 | − | 0.378628i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 92.0884i | − | 0.571978i | ||||||
\(162\) | 52.3212 | − | 101.904i | 0.322970 | − | 0.629039i | ||||
\(163\) | − | 14.1896i | − | 0.0870529i | −0.999052 | − | 0.0435265i | \(-0.986141\pi\) | ||
0.999052 | − | 0.0435265i | \(-0.0138593\pi\) | |||||||
\(164\) | − | 57.8247i | − | 0.352590i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −142.300 | −0.857231 | ||||||||
\(167\) | −173.839 | −1.04095 | −0.520476 | − | 0.853877i | \(-0.674245\pi\) | ||||
−0.520476 | + | 0.853877i | \(0.674245\pi\) | |||||||
\(168\) | 6.07708 | + | 21.6118i | 0.0361731 | + | 0.128642i | ||||
\(169\) | −176.763 | −1.04593 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 42.0477 | − | 25.6773i | 0.245893 | − | 0.150160i | ||||
\(172\) | − | 38.2233i | − | 0.222229i | ||||||
\(173\) | −164.076 | −0.948415 | −0.474207 | − | 0.880413i | \(-0.657265\pi\) | ||||
−0.474207 | + | 0.880413i | \(0.657265\pi\) | |||||||
\(174\) | 7.84728 | + | 27.9071i | 0.0450993 | + | 0.160386i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 79.0965i | 0.449412i | ||||||||
\(177\) | −26.4439 | − | 94.0419i | −0.149401 | − | 0.531310i | ||||
\(178\) | − | 15.8441i | − | 0.0890120i | ||||||
\(179\) | − | 267.494i | − | 1.49438i | −0.664611 | − | 0.747189i | \(-0.731403\pi\) | ||
0.664611 | − | 0.747189i | \(-0.268597\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 188.355 | 1.04063 | 0.520317 | − | 0.853973i | \(-0.325814\pi\) | ||||
0.520317 | + | 0.853973i | \(0.325814\pi\) | |||||||
\(182\) | −69.5750 | −0.382280 | ||||||||
\(183\) | 207.251 | − | 58.2777i | 1.13252 | − | 0.318457i | ||||
\(184\) | −98.4467 | −0.535036 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −128.589 | + | 36.1584i | −0.691340 | + | 0.194400i | ||||
\(187\) | 262.791i | 1.40530i | ||||||||
\(188\) | 90.2490 | 0.480048 | ||||||||
\(189\) | 52.3437 | + | 48.6121i | 0.276951 | + | 0.257207i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 300.383i | 1.57268i | 0.617791 | + | 0.786342i | \(0.288028\pi\) | ||||
−0.617791 | + | 0.786342i | \(0.711972\pi\) | |||||||
\(192\) | 23.1040 | − | 6.49668i | 0.120333 | − | 0.0338369i | ||||
\(193\) | 209.232i | 1.08410i | 0.840345 | + | 0.542051i | \(0.182352\pi\) | ||||
−0.840345 | + | 0.542051i | \(0.817648\pi\) | |||||||
\(194\) | − | 144.952i | − | 0.747175i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 97.0683 | 0.492733 | 0.246366 | − | 0.969177i | \(-0.420763\pi\) | ||||
0.246366 | + | 0.969177i | \(0.420763\pi\) | |||||||
\(198\) | 131.172 | + | 214.799i | 0.662483 | + | 1.08484i | ||||
\(199\) | −292.070 | −1.46769 | −0.733845 | − | 0.679317i | \(-0.762276\pi\) | ||||
−0.733845 | + | 0.679317i | \(0.762276\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −54.1060 | − | 192.416i | −0.269184 | − | 0.957293i | ||||
\(202\) | 199.413i | 0.987191i | ||||||||
\(203\) | −18.0781 | −0.0890545 | ||||||||
\(204\) | 76.7608 | − | 21.5846i | 0.376279 | − | 0.105807i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 83.4897i | 0.405290i | ||||||||
\(207\) | −267.347 | + | 163.262i | −1.29153 | + | 0.788703i | ||||
\(208\) | 74.3788i | 0.357590i | ||||||||
\(209\) | 108.248i | 0.517933i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −88.4332 | −0.419115 | −0.209557 | − | 0.977796i | \(-0.567202\pi\) | ||||
−0.209557 | + | 0.977796i | \(0.567202\pi\) | |||||||
\(212\) | 148.265 | 0.699362 | ||||||||
\(213\) | −82.2196 | − | 292.396i | −0.386008 | − | 1.37275i | ||||
\(214\) | −127.670 | −0.596590 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 51.9685 | − | 55.9578i | 0.240595 | − | 0.259064i | ||||
\(217\) | − | 83.2994i | − | 0.383868i | ||||||
\(218\) | 130.344 | 0.597909 | ||||||||
\(219\) | 37.3509 | + | 132.830i | 0.170552 | + | 0.606530i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 247.117i | 1.11818i | ||||||||
\(222\) | 11.6924 | + | 41.5812i | 0.0526683 | + | 0.187303i | ||||
\(223\) | 330.233i | 1.48087i | 0.672130 | + | 0.740433i | \(0.265380\pi\) | ||||
−0.672130 | + | 0.740433i | \(0.734620\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −210.617 | −0.931935 | ||||||||
\(227\) | −283.024 | −1.24680 | −0.623402 | − | 0.781902i | \(-0.714250\pi\) | ||||
−0.623402 | + | 0.781902i | \(0.714250\pi\) | |||||||
\(228\) | 31.6191 | − | 8.89106i | 0.138680 | − | 0.0389959i | ||||
\(229\) | 17.0978 | 0.0746629 | 0.0373314 | − | 0.999303i | \(-0.488114\pi\) | ||||
0.0373314 | + | 0.999303i | \(0.488114\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −151.093 | + | 42.4862i | −0.654080 | + | 0.183923i | ||||
\(232\) | 19.3263i | 0.0833029i | ||||||||
\(233\) | 223.943 | 0.961129 | 0.480564 | − | 0.876960i | \(-0.340432\pi\) | ||||
0.480564 | + | 0.876960i | \(0.340432\pi\) | |||||||
\(234\) | 123.348 | + | 201.987i | 0.527128 | + | 0.863193i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 65.1261i | − | 0.275958i | ||||||
\(237\) | 406.655 | − | 114.349i | 1.71584 | − | 0.482484i | ||||
\(238\) | 49.7253i | 0.208930i | ||||||||
\(239\) | 10.9304i | 0.0457340i | 0.999739 | + | 0.0228670i | \(0.00727942\pi\) | ||||
−0.999739 | + | 0.0228670i | \(0.992721\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 177.306 | 0.735710 | 0.367855 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367855 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(242\) | −381.861 | −1.57794 | ||||||||
\(243\) | 48.3296 | − | 238.145i | 0.198887 | − | 0.980022i | ||||
\(244\) | 143.526 | 0.588222 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −33.2047 | − | 118.085i | −0.134979 | − | 0.480021i | ||||
\(247\) | 101.791i | 0.412111i | ||||||||
\(248\) | −89.0508 | −0.359076 | ||||||||
\(249\) | −290.595 | + | 81.7132i | −1.16705 | + | 0.328166i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 182.001i | − | 0.725103i | −0.931964 | − | 0.362551i | \(-0.881906\pi\) | ||
0.931964 | − | 0.362551i | \(-0.118094\pi\) | |||||||
\(252\) | 24.8203 | + | 40.6442i | 0.0984932 | + | 0.161287i | ||||
\(253\) | − | 688.262i | − | 2.72040i | ||||||
\(254\) | − | 110.000i | − | 0.433071i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −155.204 | −0.603906 | −0.301953 | − | 0.953323i | \(-0.597639\pi\) | ||||
−0.301953 | + | 0.953323i | \(0.597639\pi\) | |||||||
\(258\) | −21.9490 | − | 78.0567i | −0.0850737 | − | 0.302545i | ||||
\(259\) | −26.9361 | −0.104000 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 32.0502 | + | 52.4835i | 0.122798 | + | 0.201086i | ||||
\(262\) | − | 324.958i | − | 1.24030i | ||||||
\(263\) | 159.605 | 0.606861 | 0.303431 | − | 0.952854i | \(-0.401868\pi\) | ||||
0.303431 | + | 0.952854i | \(0.401868\pi\) | |||||||
\(264\) | 45.4196 | + | 161.525i | 0.172044 | + | 0.611836i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 20.4827i | 0.0770025i | ||||||||
\(267\) | −9.09818 | − | 32.3556i | −0.0340756 | − | 0.121182i | ||||
\(268\) | − | 133.252i | − | 0.497210i | ||||||
\(269\) | 198.340i | 0.737323i | 0.929564 | + | 0.368661i | \(0.120184\pi\) | ||||
−0.929564 | + | 0.368661i | \(0.879816\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 46.2341 | 0.170606 | 0.0853028 | − | 0.996355i | \(-0.472814\pi\) | ||||
0.0853028 | + | 0.996355i | \(0.472814\pi\) | |||||||
\(272\) | 53.1586 | 0.195436 | ||||||||
\(273\) | −142.081 | + | 39.9521i | −0.520442 | + | 0.146345i | ||||
\(274\) | −203.024 | −0.740965 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −201.040 | + | 56.5311i | −0.728406 | + | 0.204823i | ||||
\(277\) | − | 387.786i | − | 1.39995i | −0.714168 | − | 0.699974i | \(-0.753195\pi\) | ||
0.714168 | − | 0.699974i | \(-0.246805\pi\) | |||||||
\(278\) | 364.807 | 1.31226 | ||||||||
\(279\) | −241.831 | + | 147.680i | −0.866779 | + | 0.529318i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 46.9368i | − | 0.167035i | −0.996506 | − | 0.0835174i | \(-0.973385\pi\) | ||
0.996506 | − | 0.0835174i | \(-0.0266154\pi\) | |||||||
\(282\) | 184.299 | − | 51.8237i | 0.653544 | − | 0.183772i | ||||
\(283\) | − | 32.3428i | − | 0.114286i | −0.998366 | − | 0.0571428i | \(-0.981801\pi\) | ||
0.998366 | − | 0.0571428i | \(-0.0181990\pi\) | |||||||
\(284\) | − | 202.490i | − | 0.712994i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −519.998 | −1.81817 | ||||||||
\(287\) | 76.4949 | 0.266533 | ||||||||
\(288\) | 43.4505 | − | 26.5340i | 0.150870 | − | 0.0921320i | ||||
\(289\) | −112.386 | −0.388877 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −83.2358 | − | 296.009i | −0.286034 | − | 1.01721i | ||||
\(292\) | 91.9877i | 0.315026i | ||||||||
\(293\) | 36.5402 | 0.124711 | 0.0623553 | − | 0.998054i | \(-0.480139\pi\) | ||||
0.0623553 | + | 0.998054i | \(0.480139\pi\) | |||||||
\(294\) | −28.5897 | + | 8.03923i | −0.0972439 | + | 0.0273443i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 28.7959i | 0.0972834i | ||||||||
\(297\) | 391.213 | + | 363.323i | 1.31721 | + | 1.22331i | ||||
\(298\) | − | 166.212i | − | 0.557760i | ||||||
\(299\) | − | 647.210i | − | 2.16458i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 50.5647 | 0.167989 | ||||||||
\(302\) | 355.047 | 1.17565 | ||||||||
\(303\) | 114.509 | + | 407.225i | 0.377917 | + | 1.34398i | ||||
\(304\) | 21.8969 | 0.0720292 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 144.360 | − | 88.1568i | 0.471766 | − | 0.288094i | ||||
\(307\) | 57.4988i | 0.187292i | 0.995606 | + | 0.0936462i | \(0.0298523\pi\) | ||||
−0.995606 | + | 0.0936462i | \(0.970148\pi\) | |||||||
\(308\) | −104.635 | −0.339724 | ||||||||
\(309\) | 47.9423 | + | 170.496i | 0.155153 | + | 0.551767i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 230.523i | 0.741231i | 0.928786 | + | 0.370615i | \(0.120853\pi\) | ||||
−0.928786 | + | 0.370615i | \(0.879147\pi\) | |||||||
\(312\) | 42.7106 | + | 151.890i | 0.136893 | + | 0.486828i | ||||
\(313\) | 449.686i | 1.43670i | 0.695684 | + | 0.718348i | \(0.255101\pi\) | ||||
−0.695684 | + | 0.718348i | \(0.744899\pi\) | |||||||
\(314\) | − | 26.3636i | − | 0.0839605i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 281.618 | 0.891195 | ||||||||
\(317\) | −370.113 | −1.16755 | −0.583775 | − | 0.811916i | \(-0.698425\pi\) | ||||
−0.583775 | + | 0.811916i | \(0.698425\pi\) | |||||||
\(318\) | 302.775 | − | 85.1382i | 0.952122 | − | 0.267730i | ||||
\(319\) | −135.114 | −0.423555 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −260.718 | + | 73.3121i | −0.812205 | + | 0.228387i | ||||
\(322\) | − | 130.233i | − | 0.404449i | ||||||
\(323\) | 72.7504 | 0.225233 | ||||||||
\(324\) | 73.9933 | − | 144.114i | 0.228374 | − | 0.444798i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 20.0672i | − | 0.0615557i | ||||||
\(327\) | 266.178 | − | 74.8475i | 0.814001 | − | 0.228892i | ||||
\(328\) | − | 81.7765i | − | 0.249319i | ||||||
\(329\) | 119.388i | 0.362882i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −125.253 | −0.378409 | −0.189204 | − | 0.981938i | \(-0.560591\pi\) | ||||
−0.189204 | + | 0.981938i | \(0.560591\pi\) | |||||||
\(332\) | −201.243 | −0.606154 | ||||||||
\(333\) | 47.7544 | + | 78.1998i | 0.143407 | + | 0.234834i | ||||
\(334\) | −245.845 | −0.736064 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.59430 | + | 30.5637i | 0.0255783 | + | 0.0909633i | ||||
\(337\) | − | 5.34562i | − | 0.0158624i | −0.999969 | − | 0.00793119i | \(-0.997475\pi\) | ||
0.999969 | − | 0.00793119i | \(-0.00252460\pi\) | |||||||
\(338\) | −249.980 | −0.739586 | ||||||||
\(339\) | −430.106 | + | 120.943i | −1.26875 | + | 0.356764i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 622.573i | − | 1.82573i | ||||||
\(342\) | 59.4644 | − | 36.3133i | 0.173873 | − | 0.106179i | ||||
\(343\) | − | 18.5203i | − | 0.0539949i | ||||||
\(344\) | − | 54.0560i | − | 0.157139i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −232.038 | −0.670630 | ||||||||
\(347\) | 277.074 | 0.798485 | 0.399242 | − | 0.916845i | \(-0.369273\pi\) | ||||
0.399242 | + | 0.916845i | \(0.369273\pi\) | |||||||
\(348\) | 11.0977 | + | 39.4666i | 0.0318900 | + | 0.113410i | ||||
\(349\) | −371.020 | −1.06309 | −0.531547 | − | 0.847029i | \(-0.678389\pi\) | ||||
−0.531547 | + | 0.847029i | \(0.678389\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 367.879 | + | 341.652i | 1.04809 | + | 0.973368i | ||||
\(352\) | 111.859i | 0.317782i | ||||||||
\(353\) | 200.070 | 0.566770 | 0.283385 | − | 0.959006i | \(-0.408543\pi\) | ||||
0.283385 | + | 0.959006i | \(0.408543\pi\) | |||||||
\(354\) | −37.3974 | − | 132.995i | −0.105642 | − | 0.375693i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 22.4070i | − | 0.0629410i | ||||||
\(357\) | 28.5538 | + | 101.545i | 0.0799825 | + | 0.284440i | ||||
\(358\) | − | 378.293i | − | 1.05669i | ||||||
\(359\) | − | 13.1711i | − | 0.0366884i | −0.999832 | − | 0.0183442i | \(-0.994161\pi\) | ||
0.999832 | − | 0.0183442i | \(-0.00583947\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −331.033 | −0.916989 | ||||||||
\(362\) | 266.374 | 0.735839 | ||||||||
\(363\) | −779.806 | + | 219.276i | −2.14823 | + | 0.604066i | ||||
\(364\) | −98.3939 | −0.270313 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 293.098 | − | 82.4171i | 0.800814 | − | 0.225183i | ||||
\(367\) | − | 347.808i | − | 0.947706i | −0.880604 | − | 0.473853i | \(-0.842863\pi\) | ||
0.880604 | − | 0.473853i | \(-0.157137\pi\) | |||||||
\(368\) | −139.225 | −0.378328 | ||||||||
\(369\) | −135.616 | − | 222.077i | −0.367523 | − | 0.601835i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 196.136i | 0.528668i | ||||||||
\(372\) | −181.853 | + | 51.1357i | −0.488851 | + | 0.137462i | ||||
\(373\) | − | 558.926i | − | 1.49846i | −0.662310 | − | 0.749230i | \(-0.730424\pi\) | ||
0.662310 | − | 0.749230i | \(-0.269576\pi\) | |||||||
\(374\) | 371.643i | 0.993697i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 127.631 | 0.339445 | ||||||||
\(377\) | −127.055 | −0.337016 | ||||||||
\(378\) | 74.0252 | + | 68.7479i | 0.195834 | + | 0.181873i | ||||
\(379\) | 585.239 | 1.54417 | 0.772083 | − | 0.635522i | \(-0.219215\pi\) | ||||
0.772083 | + | 0.635522i | \(0.219215\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −63.1654 | − | 224.633i | −0.165788 | − | 0.589589i | ||||
\(382\) | 424.805i | 1.11206i | ||||||||
\(383\) | −391.278 | −1.02161 | −0.510807 | − | 0.859696i | \(-0.670653\pi\) | ||||
−0.510807 | + | 0.859696i | \(0.670653\pi\) | |||||||
\(384\) | 32.6739 | − | 9.18769i | 0.0850884 | − | 0.0239263i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 295.899i | 0.766577i | ||||||||
\(387\) | −89.6451 | − | 146.797i | −0.231641 | − | 0.379322i | ||||
\(388\) | − | 204.993i | − | 0.528332i | ||||||
\(389\) | − | 412.091i | − | 1.05936i | −0.848197 | − | 0.529680i | \(-0.822312\pi\) | ||
0.848197 | − | 0.529680i | \(-0.177688\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −462.561 | −1.18302 | ||||||||
\(392\) | −19.7990 | −0.0505076 | ||||||||
\(393\) | −186.601 | − | 663.604i | −0.474812 | − | 1.68856i | ||||
\(394\) | 137.275 | 0.348415 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 185.505 | + | 303.772i | 0.468447 | + | 0.767100i | ||||
\(397\) | 620.931i | 1.56406i | 0.623243 | + | 0.782028i | \(0.285815\pi\) | ||||
−0.623243 | + | 0.782028i | \(0.714185\pi\) | |||||||
\(398\) | −413.050 | −1.03781 | ||||||||
\(399\) | 11.7618 | + | 41.8281i | 0.0294781 | + | 0.104832i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 517.392i | − | 1.29025i | −0.764075 | − | 0.645127i | \(-0.776804\pi\) | ||
0.764075 | − | 0.645127i | \(-0.223196\pi\) | |||||||
\(402\) | −76.5175 | − | 272.117i | −0.190342 | − | 0.676908i | ||||
\(403\) | − | 585.439i | − | 1.45270i | ||||||
\(404\) | 282.012i | 0.698049i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.5662 | −0.0629710 | ||||||||
\(407\) | −201.318 | −0.494639 | ||||||||
\(408\) | 108.556 | − | 30.5253i | 0.266069 | − | 0.0748168i | ||||
\(409\) | 46.7243 | 0.114240 | 0.0571202 | − | 0.998367i | \(-0.481808\pi\) | ||||
0.0571202 | + | 0.998367i | \(0.481808\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −414.600 | + | 116.583i | −1.00876 | + | 0.283656i | ||||
\(412\) | 118.072i | 0.286583i | ||||||||
\(413\) | 86.1537 | 0.208605 | ||||||||
\(414\) | −378.086 | + | 230.887i | −0.913252 | + | 0.557697i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 105.187i | 0.252855i | ||||||||
\(417\) | 744.981 | − | 209.484i | 1.78652 | − | 0.502359i | ||||
\(418\) | 153.086i | 0.366234i | ||||||||
\(419\) | 165.753i | 0.395591i | 0.980243 | + | 0.197796i | \(0.0633783\pi\) | ||||
−0.980243 | + | 0.197796i | \(0.936622\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 660.766 | 1.56952 | 0.784758 | − | 0.619802i | \(-0.212787\pi\) | ||||
0.784758 | + | 0.619802i | \(0.212787\pi\) | |||||||
\(422\) | −125.063 | −0.296359 | ||||||||
\(423\) | 346.603 | − | 211.661i | 0.819392 | − | 0.500380i | ||||
\(424\) | 209.678 | 0.494524 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −116.276 | − | 413.510i | −0.272949 | − | 0.970680i | ||||
\(427\) | 189.867i | 0.444654i | ||||||||
\(428\) | −180.553 | −0.421852 | ||||||||
\(429\) | −1061.90 | + | 298.599i | −2.47529 | + | 0.696034i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 182.301i | − | 0.422972i | −0.977381 | − | 0.211486i | \(-0.932170\pi\) | ||
0.977381 | − | 0.211486i | \(-0.0678303\pi\) | |||||||
\(432\) | 73.4946 | − | 79.1363i | 0.170126 | − | 0.183186i | ||||
\(433\) | 116.523i | 0.269106i | 0.990906 | + | 0.134553i | \(0.0429598\pi\) | ||||
−0.990906 | + | 0.134553i | \(0.957040\pi\) | |||||||
\(434\) | − | 117.803i | − | 0.271436i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 184.334 | 0.422785 | ||||||||
\(437\) | −190.537 | −0.436010 | ||||||||
\(438\) | 52.8222 | + | 187.850i | 0.120599 | + | 0.428881i | ||||
\(439\) | −377.751 | −0.860481 | −0.430240 | − | 0.902714i | \(-0.641571\pi\) | ||||
−0.430240 | + | 0.902714i | \(0.641571\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −53.7673 | + | 32.8342i | −0.121921 | + | 0.0744539i | ||||
\(442\) | 349.476i | 0.790669i | ||||||||
\(443\) | −152.788 | −0.344893 | −0.172447 | − | 0.985019i | \(-0.555167\pi\) | ||||
−0.172447 | + | 0.985019i | \(0.555167\pi\) | |||||||
\(444\) | 16.5355 | + | 58.8047i | 0.0372421 | + | 0.132443i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 467.020i | 1.04713i | ||||||||
\(447\) | −95.4442 | − | 339.426i | −0.213522 | − | 0.759342i | ||||
\(448\) | 21.1660i | 0.0472456i | ||||||||
\(449\) | − | 201.173i | − | 0.448047i | −0.974584 | − | 0.224023i | \(-0.928081\pi\) | ||
0.974584 | − | 0.224023i | \(-0.0719192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 571.717 | 1.26767 | ||||||||
\(452\) | −297.858 | −0.658977 | ||||||||
\(453\) | 725.048 | − | 203.879i | 1.60055 | − | 0.450063i | ||||
\(454\) | −400.257 | −0.881623 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 44.7161 | − | 12.5739i | 0.0980616 | − | 0.0275743i | ||||
\(457\) | 718.056i | 1.57124i | 0.618710 | + | 0.785620i | \(0.287656\pi\) | ||||
−0.618710 | + | 0.785620i | \(0.712344\pi\) | |||||||
\(458\) | 24.1799 | 0.0527946 | ||||||||
\(459\) | 244.179 | − | 262.923i | 0.531981 | − | 0.572817i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 344.884i | 0.748121i | 0.927404 | + | 0.374061i | \(0.122035\pi\) | ||||
−0.927404 | + | 0.374061i | \(0.877965\pi\) | |||||||
\(462\) | −213.677 | + | 60.0845i | −0.462505 | + | 0.130053i | ||||
\(463\) | − | 561.331i | − | 1.21238i | −0.795321 | − | 0.606189i | \(-0.792697\pi\) | ||
0.795321 | − | 0.606189i | \(-0.207303\pi\) | |||||||
\(464\) | 27.3315i | 0.0589040i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 316.703 | 0.679621 | ||||||||
\(467\) | −146.016 | −0.312668 | −0.156334 | − | 0.987704i | \(-0.549968\pi\) | ||||
−0.156334 | + | 0.987704i | \(0.549968\pi\) | |||||||
\(468\) | 174.440 | + | 285.653i | 0.372736 | + | 0.610370i | ||||
\(469\) | 176.276 | 0.375855 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.1388 | − | 53.8377i | −0.0321418 | − | 0.114305i | ||||
\(472\) | − | 92.1022i | − | 0.195132i | ||||||
\(473\) | 377.917 | 0.798978 | ||||||||
\(474\) | 575.097 | − | 161.713i | 1.21329 | − | 0.341168i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 70.3222i | 0.147736i | ||||||||
\(477\) | 569.414 | − | 347.725i | 1.19374 | − | 0.728983i | ||||
\(478\) | 15.4579i | 0.0323388i | ||||||||
\(479\) | − | 48.7573i | − | 0.101790i | −0.998704 | − | 0.0508949i | \(-0.983793\pi\) | ||
0.998704 | − | 0.0508949i | \(-0.0162074\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −189.310 | −0.393577 | ||||||||
\(482\) | 250.749 | 0.520226 | ||||||||
\(483\) | −74.7836 | − | 265.951i | −0.154831 | − | 0.550623i | ||||
\(484\) | −540.033 | −1.11577 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 68.3484 | − | 336.788i | 0.140635 | − | 0.692980i | ||||
\(487\) | − | 562.319i | − | 1.15466i | −0.816511 | − | 0.577329i | \(-0.804095\pi\) | ||
0.816511 | − | 0.577329i | \(-0.195905\pi\) | |||||||
\(488\) | 202.977 | 0.415936 | ||||||||
\(489\) | −11.5232 | − | 40.9796i | −0.0235648 | − | 0.0838028i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 124.234i | 0.253022i | 0.991965 | + | 0.126511i | \(0.0403778\pi\) | ||||
−0.991965 | + | 0.126511i | \(0.959622\pi\) | |||||||
\(492\) | −46.9586 | − | 166.998i | −0.0954443 | − | 0.339426i | ||||
\(493\) | 90.8063i | 0.184191i | ||||||||
\(494\) | 143.955i | 0.291407i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −125.937 | −0.253905 | ||||||||
\(497\) | 267.870 | 0.538973 | ||||||||
\(498\) | −410.963 | + | 115.560i | −0.825227 | + | 0.232048i | ||||
\(499\) | 751.671 | 1.50635 | 0.753177 | − | 0.657817i | \(-0.228520\pi\) | ||||
0.753177 | + | 0.657817i | \(0.228520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −502.046 | + | 141.172i | −1.00209 | + | 0.281780i | ||||
\(502\) | − | 257.388i | − | 0.512725i | ||||||
\(503\) | −725.516 | −1.44238 | −0.721189 | − | 0.692739i | \(-0.756404\pi\) | ||||
−0.721189 | + | 0.692739i | \(0.756404\pi\) | |||||||
\(504\) | 35.1012 | + | 57.4796i | 0.0696452 | + | 0.114047i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 973.349i | − | 1.92361i | ||||||
\(507\) | −510.490 | + | 143.546i | −1.00688 | + | 0.283129i | ||||
\(508\) | − | 155.563i | − | 0.306227i | ||||||
\(509\) | 495.288i | 0.973062i | 0.873663 | + | 0.486531i | \(0.161738\pi\) | ||||
−0.873663 | + | 0.486531i | \(0.838262\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −121.688 | −0.238138 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 100.581 | − | 108.302i | 0.196065 | − | 0.211116i | ||||
\(514\) | −219.492 | −0.427026 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −31.0406 | − | 110.389i | −0.0601562 | − | 0.213932i | ||||
\(517\) | 892.298i | 1.72591i | ||||||||
\(518\) | −38.0934 | −0.0735394 | ||||||||
\(519\) | −473.850 | + | 133.243i | −0.913006 | + | 0.256731i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 496.127i | − | 0.952260i | −0.879375 | − | 0.476130i | \(-0.842039\pi\) | ||
0.879375 | − | 0.476130i | \(-0.157961\pi\) | |||||||
\(522\) | 45.3258 | + | 74.2229i | 0.0868311 | + | 0.142189i | ||||
\(523\) | 863.914i | 1.65184i | 0.563785 | + | 0.825922i | \(0.309345\pi\) | ||||
−0.563785 | + | 0.825922i | \(0.690655\pi\) | |||||||
\(524\) | − | 459.560i | − | 0.877024i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 225.715 | 0.429116 | ||||||||
\(527\) | −418.414 | −0.793954 | ||||||||
\(528\) | 64.2331 | + | 228.430i | 0.121654 | + | 0.432633i | ||||
\(529\) | 682.468 | 1.29011 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −152.740 | − | 250.118i | −0.287646 | − | 0.471032i | ||||
\(532\) | 28.9669i | 0.0544490i | ||||||||
\(533\) | 537.617 | 1.00866 | ||||||||
\(534\) | −12.8668 | − | 45.7578i | −0.0240951 | − | 0.0856887i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 188.447i | − | 0.351580i | ||||||
\(537\) | −217.228 | − | 772.521i | −0.404521 | − | 1.43859i | ||||
\(538\) | 280.495i | 0.521366i | ||||||||
\(539\) | − | 138.419i | − | 0.256807i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −606.291 | −1.12069 | −0.560343 | − | 0.828261i | \(-0.689331\pi\) | ||||
−0.560343 | + | 0.828261i | \(0.689331\pi\) | |||||||
\(542\) | 65.3849 | 0.120636 | ||||||||
\(543\) | 543.968 | − | 152.960i | 1.00178 | − | 0.281694i | ||||
\(544\) | 75.1775 | 0.138194 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −200.932 | + | 56.5008i | −0.368008 | + | 0.103481i | ||||
\(547\) | − | 940.119i | − | 1.71868i | −0.511404 | − | 0.859341i | \(-0.670874\pi\) | ||
0.511404 | − | 0.859341i | \(-0.329126\pi\) | |||||||
\(548\) | −287.120 | −0.523941 | ||||||||
\(549\) | 551.215 | − | 336.611i | 1.00403 | − | 0.613135i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.4046i | 0.0678850i | ||||||||
\(552\) | −284.314 | + | 79.9470i | −0.515061 | + | 0.144832i | ||||
\(553\) | 372.545i | 0.673680i | ||||||||
\(554\) | − | 548.412i | − | 0.989913i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 515.916 | 0.927906 | ||||||||
\(557\) | 302.696 | 0.543439 | 0.271720 | − | 0.962376i | \(-0.412408\pi\) | ||||
0.271720 | + | 0.962376i | \(0.412408\pi\) | |||||||
\(558\) | −342.001 | + | 208.851i | −0.612905 | + | 0.374284i | ||||
\(559\) | 355.376 | 0.635735 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 213.409 | + | 758.939i | 0.380407 | + | 1.35283i | ||||
\(562\) | − | 66.3786i | − | 0.118111i | ||||||
\(563\) | 705.188 | 1.25255 | 0.626277 | − | 0.779601i | \(-0.284578\pi\) | ||||
0.626277 | + | 0.779601i | \(0.284578\pi\) | |||||||
\(564\) | 260.639 | − | 73.2898i | 0.462125 | − | 0.129946i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 45.7396i | − | 0.0808121i | ||||||
\(567\) | 190.646 | + | 97.8840i | 0.336236 | + | 0.172635i | ||||
\(568\) | − | 286.365i | − | 0.504163i | ||||||
\(569\) | 428.736i | 0.753491i | 0.926317 | + | 0.376746i | \(0.122957\pi\) | ||||
−0.926317 | + | 0.376746i | \(0.877043\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 222.414 | 0.389517 | 0.194758 | − | 0.980851i | \(-0.437608\pi\) | ||||
0.194758 | + | 0.980851i | \(0.437608\pi\) | |||||||
\(572\) | −735.388 | −1.28564 | ||||||||
\(573\) | 243.936 | + | 867.504i | 0.425718 | + | 1.51397i | ||||
\(574\) | 108.180 | 0.188467 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 61.4483 | − | 37.5247i | 0.106681 | − | 0.0651471i | ||||
\(577\) | 677.458i | 1.17410i | 0.809549 | + | 0.587052i | \(0.199712\pi\) | ||||
−0.809549 | + | 0.587052i | \(0.800288\pi\) | |||||||
\(578\) | −158.937 | −0.274978 | ||||||||
\(579\) | 169.914 | + | 604.261i | 0.293461 | + | 1.04363i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 266.220i | − | 0.458209i | ||||||
\(582\) | −117.713 | − | 418.620i | −0.202256 | − | 0.719279i | ||||
\(583\) | 1465.90i | 2.51441i | ||||||||
\(584\) | 130.090i | 0.222757i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 51.6757 | 0.0881837 | ||||||||
\(587\) | −681.642 | −1.16123 | −0.580615 | − | 0.814178i | \(-0.697188\pi\) | ||||
−0.580615 | + | 0.814178i | \(0.697188\pi\) | |||||||
\(588\) | −40.4319 | + | 11.3692i | −0.0687618 | + | 0.0193353i | ||||
\(589\) | −172.352 | −0.292617 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 280.333 | − | 78.8277i | 0.474337 | − | 0.133380i | ||||
\(592\) | 40.7235i | 0.0687898i | ||||||||
\(593\) | −39.3230 | −0.0663120 | −0.0331560 | − | 0.999450i | \(-0.510556\pi\) | ||||
−0.0331560 | + | 0.999450i | \(0.510556\pi\) | |||||||
\(594\) | 553.258 | + | 513.816i | 0.931411 | + | 0.865010i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 235.060i | − | 0.394396i | ||||||
\(597\) | −843.498 | + | 237.186i | −1.41289 | + | 0.397296i | ||||
\(598\) | − | 915.293i | − | 1.53059i | ||||||
\(599\) | − | 564.730i | − | 0.942788i | −0.881923 | − | 0.471394i | \(-0.843751\pi\) | ||
0.881923 | − | 0.471394i | \(-0.156249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −223.287 | −0.371527 | −0.185763 | − | 0.982595i | \(-0.559476\pi\) | ||||
−0.185763 | + | 0.982595i | \(0.559476\pi\) | |||||||
\(602\) | 71.5093 | 0.118786 | ||||||||
\(603\) | −312.516 | − | 511.757i | −0.518268 | − | 0.848686i | ||||
\(604\) | 502.112 | 0.831311 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 161.940 | + | 575.903i | 0.267228 | + | 0.950334i | ||||
\(607\) | − | 343.966i | − | 0.566665i | −0.959022 | − | 0.283332i | \(-0.908560\pi\) | ||
0.959022 | − | 0.283332i | \(-0.0914400\pi\) | |||||||
\(608\) | 30.9669 | 0.0509324 | ||||||||
\(609\) | −52.2094 | + | 14.6809i | −0.0857297 | + | 0.0241066i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 839.076i | 1.37328i | ||||||||
\(612\) | 204.156 | − | 124.673i | 0.333589 | − | 0.203713i | ||||
\(613\) | 532.494i | 0.868668i | 0.900752 | + | 0.434334i | \(0.143016\pi\) | ||||
−0.900752 | + | 0.434334i | \(0.856984\pi\) | |||||||
\(614\) | 81.3156i | 0.132436i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −147.976 | −0.240221 | ||||||||
\(617\) | 553.837 | 0.897630 | 0.448815 | − | 0.893625i | \(-0.351846\pi\) | ||||
0.448815 | + | 0.893625i | \(0.351846\pi\) | |||||||
\(618\) | 67.8007 | + | 241.118i | 0.109710 | + | 0.390158i | ||||
\(619\) | −467.768 | −0.755684 | −0.377842 | − | 0.925870i | \(-0.623334\pi\) | ||||
−0.377842 | + | 0.925870i | \(0.623334\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −639.516 | + | 688.607i | −1.02982 | + | 1.10887i | ||||
\(622\) | 326.008i | 0.524129i | ||||||||
\(623\) | 29.6416 | 0.0475789 | ||||||||
\(624\) | 60.4019 | + | 214.806i | 0.0967979 | + | 0.344240i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 635.952i | 1.01590i | ||||||||
\(627\) | 87.9065 | + | 312.620i | 0.140202 | + | 0.498596i | ||||
\(628\) | − | 37.2838i | − | 0.0593690i | ||||||
\(629\) | 135.300i | 0.215104i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 822.827 | 1.30400 | 0.652002 | − | 0.758217i | \(-0.273929\pi\) | ||||
0.652002 | + | 0.758217i | \(0.273929\pi\) | |||||||
\(632\) | 398.267 | 0.630170 | ||||||||
\(633\) | −255.395 | + | 71.8152i | −0.403467 | + | 0.113452i | ||||
\(634\) | −523.419 | −0.825582 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 428.188 | − | 120.404i | 0.673252 | − | 0.189314i | ||||
\(637\) | − | 130.163i | − | 0.204337i | ||||||
\(638\) | −191.080 | −0.299499 | ||||||||
\(639\) | −474.900 | − | 777.668i | −0.743192 | − | 1.21701i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 64.4367i | 0.100525i | 0.998736 | + | 0.0502626i | \(0.0160058\pi\) | ||||
−0.998736 | + | 0.0502626i | \(0.983994\pi\) | |||||||
\(642\) | −368.711 | + | 103.679i | −0.574316 | + | 0.161494i | ||||
\(643\) | − | 367.448i | − | 0.571458i | −0.958310 | − | 0.285729i | \(-0.907764\pi\) | ||
0.958310 | − | 0.285729i | \(-0.0922357\pi\) | |||||||
\(644\) | − | 184.177i | − | 0.285989i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 102.885 | 0.159264 | ||||||||
\(647\) | 335.963 | 0.519262 | 0.259631 | − | 0.965708i | \(-0.416399\pi\) | ||||
0.259631 | + | 0.965708i | \(0.416399\pi\) | |||||||
\(648\) | 104.642 | − | 203.809i | 0.161485 | − | 0.314520i | ||||
\(649\) | 643.906 | 0.992151 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −67.6462 | − | 240.568i | −0.103911 | − | 0.369537i | ||||
\(652\) | − | 28.3793i | − | 0.0435265i | ||||||
\(653\) | −365.159 | −0.559202 | −0.279601 | − | 0.960116i | \(-0.590202\pi\) | ||||
−0.279601 | + | 0.960116i | \(0.590202\pi\) | |||||||
\(654\) | 376.433 | − | 105.850i | 0.575586 | − | 0.161851i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 115.649i | − | 0.176295i | ||||||
\(657\) | 215.739 | + | 353.281i | 0.328369 | + | 0.537718i | ||||
\(658\) | 168.840i | 0.256596i | ||||||||
\(659\) | − | 895.096i | − | 1.35826i | −0.734016 | − | 0.679132i | \(-0.762357\pi\) | ||
0.734016 | − | 0.679132i | \(-0.237643\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 511.388 | 0.773658 | 0.386829 | − | 0.922151i | \(-0.373570\pi\) | ||||
0.386829 | + | 0.922151i | \(0.373570\pi\) | |||||||
\(662\) | −177.135 | −0.267575 | ||||||||
\(663\) | 200.680 | + | 713.672i | 0.302684 | + | 1.07643i | ||||
\(664\) | −284.601 | −0.428616 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 67.5349 | + | 110.591i | 0.101404 | + | 0.166053i | ||||
\(667\) | − | 237.826i | − | 0.356560i | ||||||
\(668\) | −347.678 | −0.520476 | ||||||||
\(669\) | 268.177 | + | 953.712i | 0.400863 | + | 1.42558i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1419.05i | 2.11483i | ||||||||
\(672\) | 12.1542 | + | 43.2236i | 0.0180866 | + | 0.0643208i | ||||
\(673\) | 265.771i | 0.394904i | 0.980313 | + | 0.197452i | \(0.0632667\pi\) | ||||
−0.980313 | + | 0.197452i | \(0.936733\pi\) | |||||||
\(674\) | − | 7.55985i | − | 0.0112164i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −353.525 | −0.522967 | ||||||||
\(677\) | 788.674 | 1.16495 | 0.582477 | − | 0.812847i | \(-0.302083\pi\) | ||||
0.582477 | + | 0.812847i | \(0.302083\pi\) | |||||||
\(678\) | −608.262 | + | 171.039i | −0.897141 | + | 0.252270i | ||||
\(679\) | 271.180 | 0.399382 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −817.373 | + | 229.840i | −1.20025 | + | 0.337503i | ||||
\(682\) | − | 880.451i | − | 1.29098i | ||||||
\(683\) | −644.795 | −0.944062 | −0.472031 | − | 0.881582i | \(-0.656479\pi\) | ||||
−0.472031 | + | 0.881582i | \(0.656479\pi\) | |||||||
\(684\) | 84.0954 | − | 51.3547i | 0.122946 | − | 0.0750800i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 26.1916i | − | 0.0381802i | ||||||
\(687\) | 49.3784 | − | 13.8849i | 0.0718753 | − | 0.0202109i | ||||
\(688\) | − | 76.4467i | − | 0.111114i | ||||||
\(689\) | 1378.47i | 2.00068i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −758.839 | −1.09818 | −0.549088 | − | 0.835765i | \(-0.685025\pi\) | ||||
−0.549088 | + | 0.835765i | \(0.685025\pi\) | |||||||
\(692\) | −328.151 | −0.474207 | ||||||||
\(693\) | −401.852 | + | 245.400i | −0.579873 | + | 0.354112i | ||||
\(694\) | 391.842 | 0.564614 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 15.6946 | + | 55.8142i | 0.0225497 | + | 0.0801928i | ||||
\(697\) | − | 384.235i | − | 0.551270i | ||||||
\(698\) | −524.701 | −0.751721 | ||||||||
\(699\) | 646.746 | − | 181.861i | 0.925245 | − | 0.260173i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 633.097i | 0.903134i | 0.892237 | + | 0.451567i | \(0.149135\pi\) | ||||
−0.892237 | + | 0.451567i | \(0.850865\pi\) | |||||||
\(702\) | 520.259 | + | 483.169i | 0.741110 | + | 0.688275i | ||||
\(703\) | 55.7324i | 0.0792780i | ||||||||
\(704\) | 158.193i | 0.224706i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 282.942 | 0.400767 | ||||||||
\(707\) | −373.067 | −0.527676 | ||||||||
\(708\) | −52.8879 | − | 188.084i | −0.0747004 | − | 0.265655i | ||||
\(709\) | 906.040 | 1.27791 | 0.638956 | − | 0.769243i | \(-0.279366\pi\) | ||||
0.638956 | + | 0.769243i | \(0.279366\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1081.56 | − | 660.477i | 1.52118 | − | 0.928941i | ||||
\(712\) | − | 31.6883i | − | 0.0445060i | ||||||
\(713\) | 1095.84 | 1.53695 | ||||||||
\(714\) | 40.3811 | + | 143.606i | 0.0565562 | + | 0.201129i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 534.988i | − | 0.747189i | ||||||
\(717\) | 8.87642 | + | 31.5670i | 0.0123799 | + | 0.0440265i | ||||
\(718\) | − | 18.6268i | − | 0.0259426i | ||||||
\(719\) | − | 144.683i | − | 0.201228i | −0.994926 | − | 0.100614i | \(-0.967919\pi\) | ||
0.994926 | − | 0.100614i | \(-0.0320806\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −156.195 | −0.216636 | ||||||||
\(722\) | −468.151 | −0.648409 | ||||||||
\(723\) | 512.059 | − | 143.988i | 0.708243 | − | 0.199153i | ||||
\(724\) | 376.709 | 0.520317 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1102.81 | + | 310.103i | −1.51902 | + | 0.427139i | ||||
\(727\) | 194.850i | 0.268019i | 0.990980 | + | 0.134009i | \(0.0427853\pi\) | ||||
−0.990980 | + | 0.134009i | \(0.957215\pi\) | |||||||
\(728\) | −139.150 | −0.191140 | ||||||||
\(729\) | −53.8185 | − | 727.011i | −0.0738251 | − | 0.997271i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 253.987i | − | 0.347452i | ||||||
\(732\) | 414.503 | − | 116.555i | 0.566261 | − | 0.159229i | ||||
\(733\) | 883.063i | 1.20472i | 0.798223 | + | 0.602362i | \(0.205774\pi\) | ||||
−0.798223 | + | 0.602362i | \(0.794226\pi\) | |||||||
\(734\) | − | 491.875i | − | 0.670129i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −196.893 | −0.267518 | ||||||||
\(737\) | 1317.47 | 1.78762 | ||||||||
\(738\) | −191.790 | − | 314.064i | −0.259878 | − | 0.425561i | ||||
\(739\) | 679.219 | 0.919106 | 0.459553 | − | 0.888150i | \(-0.348010\pi\) | ||||
0.459553 | + | 0.888150i | \(0.348010\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 82.6633 | + | 293.973i | 0.111556 | + | 0.396725i | ||||
\(742\) | 277.378i | 0.373825i | ||||||||
\(743\) | 1349.22 | 1.81591 | 0.907953 | − | 0.419073i | \(-0.137645\pi\) | ||||
0.907953 | + | 0.419073i | \(0.137645\pi\) | |||||||
\(744\) | −257.178 | + | 72.3168i | −0.345670 | + | 0.0972000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 790.440i | − | 1.05957i | ||||||
\(747\) | −772.878 | + | 471.975i | −1.03464 | + | 0.631827i | ||||
\(748\) | 525.582i | 0.702650i | ||||||||
\(749\) | − | 238.849i | − | 0.318891i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 171.226 | 0.227997 | 0.113998 | − | 0.993481i | \(-0.463634\pi\) | ||||
0.113998 | + | 0.993481i | \(0.463634\pi\) | |||||||
\(752\) | 180.498 | 0.240024 | ||||||||
\(753\) | −147.800 | − | 525.618i | −0.196282 | − | 0.698031i | ||||
\(754\) | −179.683 | −0.238306 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 104.687 | + | 97.2242i | 0.138475 | + | 0.128603i | ||||
\(757\) | 317.899i | 0.419946i | 0.977707 | + | 0.209973i | \(0.0673376\pi\) | ||||
−0.977707 | + | 0.209973i | \(0.932662\pi\) | |||||||
\(758\) | 827.653 | 1.09189 | ||||||||
\(759\) | −558.927 | − | 1987.70i | −0.736399 | − | 2.61884i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 423.830i | 0.556938i | 0.960445 | + | 0.278469i | \(0.0898269\pi\) | ||||
−0.960445 | + | 0.278469i | \(0.910173\pi\) | |||||||
\(762\) | −89.3293 | − | 317.680i | −0.117230 | − | 0.416902i | ||||
\(763\) | 243.851i | 0.319596i | ||||||||
\(764\) | 600.766i | 0.786342i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −553.351 | −0.722390 | ||||||||
\(767\) | 605.500 | 0.789439 | ||||||||
\(768\) | 46.2079 | − | 12.9934i | 0.0601666 | − | 0.0169184i | ||||
\(769\) | −169.095 | −0.219889 | −0.109945 | − | 0.993938i | \(-0.535067\pi\) | ||||
−0.109945 | + | 0.993938i | \(0.535067\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −448.228 | + | 126.039i | −0.581360 | + | 0.163474i | ||||
\(772\) | 418.464i | 0.542051i | ||||||||
\(773\) | −603.486 | −0.780706 | −0.390353 | − | 0.920665i | \(-0.627647\pi\) | ||||
−0.390353 | + | 0.920665i | \(0.627647\pi\) | |||||||
\(774\) | −126.777 | − | 207.603i | −0.163795 | − | 0.268221i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 289.904i | − | 0.373587i | ||||||
\(777\) | −77.7913 | + | 21.8744i | −0.100118 | + | 0.0281524i | ||||
\(778\) | − | 582.785i | − | 0.749081i | ||||||
\(779\) | − | 158.273i | − | 0.203174i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2002.04 | 2.56343 | ||||||||
\(782\) | −654.160 | −0.836522 | ||||||||
\(783\) | 135.182 | + | 125.545i | 0.172646 | + | 0.160338i | ||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −263.894 | − | 938.478i | −0.335743 | − | 1.19399i | ||||
\(787\) | − | 1458.37i | − | 1.85307i | −0.376205 | − | 0.926536i | \(-0.622771\pi\) | ||
0.376205 | − | 0.926536i | \(-0.377229\pi\) | |||||||
\(788\) | 194.137 | 0.246366 | ||||||||
\(789\) | 460.937 | − | 129.612i | 0.584204 | − | 0.164274i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 394.029i | − | 0.498140i | ||||||
\(792\) | 262.343 | + | 429.598i | 0.331242 | + | 0.542422i | ||||
\(793\) | 1334.41i | 1.68274i | ||||||||
\(794\) | 878.128i | 1.10596i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −584.141 | −0.733845 | ||||||||
\(797\) | 47.8528 | 0.0600412 | 0.0300206 | − | 0.999549i | \(-0.490443\pi\) | ||||
0.0300206 | + | 0.999549i | \(0.490443\pi\) | |||||||
\(798\) | 16.6337 | + | 59.1538i | 0.0208442 | + | 0.0741276i | ||||
\(799\) | 599.688 | 0.750548 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −52.5510 | − | 86.0544i | −0.0656068 | − | 0.107434i | ||||
\(802\) | − | 731.703i | − | 0.912347i | ||||||
\(803\) | −909.489 | −1.13261 | ||||||||
\(804\) | −108.212 | − | 384.832i | −0.134592 | − | 0.478646i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 827.936i | − | 1.02722i | ||||||
\(807\) | 161.069 | + | 572.804i | 0.199589 | + | 0.709795i | ||||
\(808\) | 398.825i | 0.493595i | ||||||||
\(809\) | − | 267.783i | − | 0.331005i | −0.986209 | − | 0.165503i | \(-0.947075\pi\) | ||
0.986209 | − | 0.165503i | \(-0.0529247\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −658.395 | −0.811831 | −0.405915 | − | 0.913911i | \(-0.633047\pi\) | ||||
−0.405915 | + | 0.913911i | \(0.633047\pi\) | |||||||
\(812\) | −36.1561 | −0.0445273 | ||||||||
\(813\) | 133.524 | − | 37.5460i | 0.164236 | − | 0.0461820i | ||||
\(814\) | −284.707 | −0.349763 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 153.522 | − | 43.1692i | 0.188139 | − | 0.0529035i | ||||
\(817\) | − | 104.622i | − | 0.128056i | ||||||
\(818\) | 66.0782 | 0.0807802 | ||||||||
\(819\) | −377.884 | + | 230.763i | −0.461396 | + | 0.281762i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1104.72i | 1.34558i | 0.739833 | + | 0.672791i | \(0.234905\pi\) | ||||
−0.739833 | + | 0.672791i | \(0.765095\pi\) | |||||||
\(822\) | −586.333 | + | 164.873i | −0.713301 | + | 0.200575i | ||||
\(823\) | − | 1044.86i | − | 1.26957i | −0.772688 | − | 0.634787i | \(-0.781088\pi\) | ||
0.772688 | − | 0.634787i | \(-0.218912\pi\) | |||||||
\(824\) | 166.979i | 0.202645i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 121.840 | 0.147506 | ||||||||
\(827\) | −1417.09 | −1.71354 | −0.856768 | − | 0.515702i | \(-0.827531\pi\) | ||||
−0.856768 | + | 0.515702i | \(0.827531\pi\) | |||||||
\(828\) | −534.695 | + | 326.523i | −0.645767 | + | 0.394352i | ||||
\(829\) | 1178.56 | 1.42166 | 0.710832 | − | 0.703362i | \(-0.248319\pi\) | ||||
0.710832 | + | 0.703362i | \(0.248319\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −314.915 | − | 1119.92i | −0.378959 | − | 1.34768i | ||||
\(832\) | 148.758i | 0.178795i | ||||||||
\(833\) | −93.0275 | −0.111678 | ||||||||
\(834\) | 1053.56 | − | 296.254i | 1.26326 | − | 0.355221i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 216.496i | 0.258966i | ||||||||
\(837\) | −578.480 | + | 622.886i | −0.691135 | + | 0.744188i | ||||
\(838\) | 234.410i | 0.279725i | ||||||||
\(839\) | 631.629i | 0.752836i | 0.926450 | + | 0.376418i | \(0.122844\pi\) | ||||
−0.926450 | + | 0.376418i | \(0.877156\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 794.312 | 0.944485 | ||||||||
\(842\) | 934.465 | 1.10982 | ||||||||
\(843\) | −38.1166 | − | 135.553i | −0.0452155 | − | 0.160799i | ||||
\(844\) | −176.866 | −0.209557 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 490.171 | − | 299.333i | 0.579398 | − | 0.353822i | ||||
\(847\) | − | 714.396i | − | 0.843443i | ||||||
\(848\) | 296.530 | 0.349681 | ||||||||
\(849\) | −26.2651 | − | 93.4059i | −0.0309365 | − | 0.110019i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 354.358i | − | 0.416401i | ||||||
\(852\) | −164.439 | − | 584.791i | −0.193004 | − | 0.686375i | ||||
\(853\) | 274.418i | 0.321710i | 0.986978 | + | 0.160855i | \(0.0514251\pi\) | ||||
−0.986978 | + | 0.160855i | \(0.948575\pi\) | |||||||
\(854\) | 268.513i | 0.314418i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −255.340 | −0.298295 | ||||||||
\(857\) | 1272.83 | 1.48521 | 0.742606 | − | 0.669729i | \(-0.233590\pi\) | ||||
0.742606 | + | 0.669729i | \(0.233590\pi\) | |||||||
\(858\) | −1501.75 | + | 422.282i | −1.75029 | + | 0.492170i | ||||
\(859\) | −1092.97 | −1.27237 | −0.636185 | − | 0.771537i | \(-0.719488\pi\) | ||||
−0.636185 | + | 0.771537i | \(0.719488\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 220.917 | − | 62.1204i | 0.256582 | − | 0.0721491i | ||||
\(862\) | − | 257.813i | − | 0.299086i | ||||||
\(863\) | −782.875 | −0.907155 | −0.453577 | − | 0.891217i | \(-0.649852\pi\) | ||||
−0.453577 | + | 0.891217i | \(0.649852\pi\) | |||||||
\(864\) | 103.937 | − | 111.916i | 0.120297 | − | 0.129532i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 164.788i | 0.190286i | ||||||||
\(867\) | −324.569 | + | 91.2665i | −0.374359 | + | 0.105267i | ||||
\(868\) | − | 166.599i | − | 0.191934i | ||||||
\(869\) | 2784.37i | 3.20411i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1238.89 | 1.42238 | ||||||||
\(872\) | 260.688 | 0.298954 | ||||||||
\(873\) | −480.769 | − | 787.279i | −0.550709 | − | 0.901809i | ||||
\(874\) | −269.459 | −0.308306 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 74.7018 | + | 265.660i | 0.0852760 | + | 0.303265i | ||||
\(877\) | − | 240.309i | − | 0.274012i | −0.990570 | − | 0.137006i | \(-0.956252\pi\) | ||
0.990570 | − | 0.137006i | \(-0.0437480\pi\) | |||||||
\(878\) | −534.221 | −0.608452 | ||||||||
\(879\) | 105.528 | − | 29.6737i | 0.120055 | − | 0.0337585i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 402.445i | − | 0.456805i | −0.973567 | − | 0.228403i | \(-0.926650\pi\) | ||
0.973567 | − | 0.228403i | \(-0.0733502\pi\) | |||||||
\(882\) | −76.0384 | + | 46.4345i | −0.0862113 | + | 0.0526468i | ||||
\(883\) | 99.2223i | 0.112370i | 0.998420 | + | 0.0561848i | \(0.0178936\pi\) | ||||
−0.998420 | + | 0.0561848i | \(0.982106\pi\) | |||||||
\(884\) | 494.234i | 0.559088i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −216.074 | −0.243876 | ||||||||
\(887\) | −197.974 | −0.223195 | −0.111597 | − | 0.993754i | \(-0.535597\pi\) | ||||
−0.111597 | + | 0.993754i | \(0.535597\pi\) | |||||||
\(888\) | 23.3847 | + | 83.1624i | 0.0263341 | + | 0.0936514i | ||||
\(889\) | 205.791 | 0.231486 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1424.87 | + | 731.577i | 1.59918 | + | 0.821074i | ||||
\(892\) | 660.466i | 0.740433i | ||||||||
\(893\) | 247.021 | 0.276620 | ||||||||
\(894\) | −134.979 | − | 480.021i | −0.150983 | − | 0.536936i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.9333i | 0.0334077i | ||||||||
\(897\) | −525.589 | − | 1869.14i | −0.585941 | − | 2.08377i | ||||
\(898\) | − | 284.501i | − | 0.316817i | ||||||
\(899\) | − | 215.127i | − | 0.239296i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 985.193 | 1.09344 | ||||||||
\(902\) | 808.530 | 0.896375 | ||||||||
\(903\) | 146.031 | − | 41.0628i | 0.161717 | − | 0.0454738i | ||||
\(904\) | −421.234 | −0.465967 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1025.37 | − | 288.328i | 1.13176 | − | 0.318243i | ||||
\(907\) | 1429.61i | 1.57620i | 0.615550 | + | 0.788098i | \(0.288934\pi\) | ||||
−0.615550 | + | 0.788098i | \(0.711066\pi\) | |||||||
\(908\) | −566.049 | −0.623402 | ||||||||
\(909\) | 661.402 | + | 1083.07i | 0.727615 | + | 1.19150i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 291.143i | 0.319587i | 0.987150 | + | 0.159793i | \(0.0510828\pi\) | ||||
−0.987150 | + | 0.159793i | \(0.948917\pi\) | |||||||
\(912\) | 63.2381 | − | 17.7821i | 0.0693400 | − | 0.0194979i | ||||
\(913\) | − | 1989.70i | − | 2.17930i | ||||||
\(914\) | 1015.49i | 1.11103i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 34.1956 | 0.0373314 | ||||||||
\(917\) | 607.941 | 0.662968 | ||||||||
\(918\) | 345.321 | − | 371.829i | 0.376167 | − | 0.405043i | ||||
\(919\) | −1118.26 | −1.21682 | −0.608412 | − | 0.793621i | \(-0.708193\pi\) | ||||
−0.608412 | + | 0.793621i | \(0.708193\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46.6939 | + | 166.056i | 0.0506991 | + | 0.180300i | ||||
\(922\) | 487.740i | 0.529002i | ||||||||
\(923\) | 1882.62 | 2.03968 | ||||||||
\(924\) | −302.185 | + | 84.9724i | −0.327040 | + | 0.0919614i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 793.842i | − | 0.857281i | ||||||
\(927\) | 276.914 | + | 453.459i | 0.298721 | + | 0.489168i | ||||
\(928\) | 38.6525i | 0.0416514i | ||||||||
\(929\) | 1182.23i | 1.27258i | 0.771449 | + | 0.636292i | \(0.219532\pi\) | ||||
−0.771449 | + | 0.636292i | \(0.780468\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.3195 | −0.0411596 | ||||||||
\(932\) | 447.886 | 0.480564 | ||||||||
\(933\) | 187.204 | + | 665.749i | 0.200647 | + | 0.713557i | ||||
\(934\) | −206.498 | −0.221089 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 246.696 | + | 403.974i | 0.263564 | + | 0.431597i | ||||
\(937\) | − | 1442.28i | − | 1.53925i | −0.638494 | − | 0.769627i | \(-0.720442\pi\) | ||
0.638494 | − | 0.769627i | \(-0.279558\pi\) | |||||||
\(938\) | 249.292 | 0.265770 | ||||||||
\(939\) | 365.183 | + | 1298.69i | 0.388906 | + | 1.38306i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 617.890i | − | 0.656631i | −0.944568 | − | 0.328315i | \(-0.893519\pi\) | ||
0.944568 | − | 0.328315i | \(-0.106481\pi\) | |||||||
\(942\) | −21.4095 | − | 76.1380i | −0.0227277 | − | 0.0808259i | ||||
\(943\) | 1006.33i | 1.06716i | ||||||||
\(944\) | − | 130.252i | − | 0.137979i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 534.455 | 0.564963 | ||||||||
\(947\) | −850.033 | −0.897606 | −0.448803 | − | 0.893631i | \(-0.648149\pi\) | ||||
−0.448803 | + | 0.893631i | \(0.648149\pi\) | |||||||
\(948\) | 813.311 | − | 228.697i | 0.857922 | − | 0.241242i | ||||
\(949\) | −855.242 | −0.901203 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1068.88 | + | 300.563i | −1.12396 | + | 0.316050i | ||||
\(952\) | 99.4505i | 0.104465i | ||||||||
\(953\) | 774.098 | 0.812275 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(954\) | 805.273 | − | 491.757i | 0.844101 | − | 0.515469i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 21.8608i | 0.0228670i | ||||||||
\(957\) | −390.209 | + | 109.724i | −0.407742 | + | 0.114654i | ||||
\(958\) | − | 68.9533i | − | 0.0719763i | ||||||
\(959\) | − | 379.824i | − | 0.396062i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.2557 | 0.0314835 | ||||||||
\(962\) | −267.725 | −0.278301 | ||||||||
\(963\) | −693.417 | + | 423.450i | −0.720059 | + | 0.439720i | ||||
\(964\) | 354.612 | 0.367855 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −105.760 | − | 376.111i | −0.109482 | − | 0.389349i | ||||
\(967\) | 1167.79i | 1.20764i | 0.797122 | + | 0.603819i | \(0.206355\pi\) | ||||
−0.797122 | + | 0.603819i | \(0.793645\pi\) | |||||||
\(968\) | −763.721 | −0.788968 | ||||||||
\(969\) | 210.103 | − | 59.0795i | 0.216824 | − | 0.0609695i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 624.999i | 0.643665i | 0.946797 | + | 0.321833i | \(0.104299\pi\) | ||||
−0.946797 | + | 0.321833i | \(0.895701\pi\) | |||||||
\(972\) | 96.6593 | − | 476.291i | 0.0994437 | − | 0.490011i | ||||
\(973\) | 682.492i | 0.701431i | ||||||||
\(974\) | − | 795.239i | − | 0.816467i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 287.052 | 0.294111 | ||||||||
\(977\) | 258.970 | 0.265066 | 0.132533 | − | 0.991179i | \(-0.457689\pi\) | ||||
0.132533 | + | 0.991179i | \(0.457689\pi\) | |||||||
\(978\) | −16.2962 | − | 57.9539i | −0.0166628 | − | 0.0592575i | ||||
\(979\) | 221.539 | 0.226291 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 707.939 | − | 432.319i | 0.721651 | − | 0.440692i | ||||
\(982\) | 175.693i | 0.178913i | ||||||||
\(983\) | −1153.22 | −1.17316 | −0.586582 | − | 0.809890i | \(-0.699527\pi\) | ||||
−0.586582 | + | 0.809890i | \(0.699527\pi\) | |||||||
\(984\) | −66.4095 | − | 236.170i | −0.0674893 | − | 0.240010i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 128.420i | 0.130243i | ||||||||
\(987\) | 96.9533 | + | 344.793i | 0.0982303 | + | 0.349334i | ||||
\(988\) | 203.583i | 0.206056i | ||||||||
\(989\) | 665.204i | 0.672603i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −977.180 | −0.986054 | −0.493027 | − | 0.870014i | \(-0.664110\pi\) | ||||
−0.493027 | + | 0.870014i | \(0.664110\pi\) | |||||||
\(992\) | −178.102 | −0.179538 | ||||||||
\(993\) | −361.731 | + | 101.716i | −0.364281 | + | 0.102433i | ||||
\(994\) | 378.825 | 0.381111 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −581.189 | + | 163.426i | −0.583523 | + | 0.164083i | ||||
\(997\) | 1274.45i | 1.27829i | 0.769087 | + | 0.639144i | \(0.220711\pi\) | ||||
−0.769087 | + | 0.639144i | \(0.779289\pi\) | |||||||
\(998\) | 1063.02 | 1.06515 | ||||||||
\(999\) | 201.419 | + | 187.060i | 0.201621 | + | 0.187247i |
(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 | 1050.3.c.c.449.29 | 32 | ||
3.2 | odd | 2 | inner | 1050.3.c.c.449.3 | 32 | ||
5.2 | odd | 4 | 210.3.e.a.71.13 | yes | 16 | ||
5.3 | odd | 4 | 1050.3.e.d.701.4 | 16 | |||
5.4 | even | 2 | inner | 1050.3.c.c.449.4 | 32 | ||
15.2 | even | 4 | 210.3.e.a.71.5 | ✓ | 16 | ||
15.8 | even | 4 | 1050.3.e.d.701.12 | 16 | |||
15.14 | odd | 2 | inner | 1050.3.c.c.449.30 | 32 | ||
20.7 | even | 4 | 1680.3.l.c.1121.8 | 16 | |||
60.47 | odd | 4 | 1680.3.l.c.1121.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.e.a.71.5 | ✓ | 16 | 15.2 | even | 4 | ||
210.3.e.a.71.13 | yes | 16 | 5.2 | odd | 4 | ||
1050.3.c.c.449.3 | 32 | 3.2 | odd | 2 | inner | ||
1050.3.c.c.449.4 | 32 | 5.4 | even | 2 | inner | ||
1050.3.c.c.449.29 | 32 | 1.1 | even | 1 | trivial | ||
1050.3.c.c.449.30 | 32 | 15.14 | odd | 2 | inner | ||
1050.3.e.d.701.4 | 16 | 5.3 | odd | 4 | |||
1050.3.e.d.701.12 | 16 | 15.8 | even | 4 | |||
1680.3.l.c.1121.7 | 16 | 60.47 | odd | 4 | |||
1680.3.l.c.1121.8 | 16 | 20.7 | even | 4 |