Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,3,Mod(133,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.133");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.b (of order \(2\), degree \(1\), 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: | \(5.47685331364\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 133.10 | ||
Character | \(\chi\) | \(=\) | 201.133 |
Dual form | 201.3.b.a.133.13 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.858352i | − | 0.429176i | −0.976705 | − | 0.214588i | \(-0.931159\pi\) | ||
0.976705 | − | 0.214588i | \(-0.0688409\pi\) | |||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 3.26323 | 0.815808 | ||||||||
\(5\) | − | 8.02842i | − | 1.60568i | −0.596191 | − | 0.802842i | \(-0.703320\pi\) | ||
0.596191 | − | 0.802842i | \(-0.296680\pi\) | |||||||
\(6\) | −1.48671 | −0.247785 | ||||||||
\(7\) | 1.82241i | 0.260344i | 0.991491 | + | 0.130172i | \(0.0415529\pi\) | ||||
−0.991491 | + | 0.130172i | \(0.958447\pi\) | |||||||
\(8\) | − | 6.23441i | − | 0.779301i | ||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | −6.89121 | −0.689121 | ||||||||
\(11\) | − | 0.484291i | − | 0.0440265i | −0.999758 | − | 0.0220132i | \(-0.992992\pi\) | ||
0.999758 | − | 0.0220132i | \(-0.00700760\pi\) | |||||||
\(12\) | − | 5.65208i | − | 0.471007i | ||||||
\(13\) | 10.0249i | 0.771143i | 0.922678 | + | 0.385571i | \(0.125996\pi\) | ||||
−0.922678 | + | 0.385571i | \(0.874004\pi\) | |||||||
\(14\) | 1.56427 | 0.111733 | ||||||||
\(15\) | −13.9056 | −0.927042 | ||||||||
\(16\) | 7.70161 | 0.481350 | ||||||||
\(17\) | −2.19758 | −0.129269 | −0.0646347 | − | 0.997909i | \(-0.520588\pi\) | ||||
−0.0646347 | + | 0.997909i | \(0.520588\pi\) | |||||||
\(18\) | 2.57506i | 0.143059i | ||||||||
\(19\) | −6.71186 | −0.353256 | −0.176628 | − | 0.984278i | \(-0.556519\pi\) | ||||
−0.176628 | + | 0.984278i | \(0.556519\pi\) | |||||||
\(20\) | − | 26.1986i | − | 1.30993i | ||||||
\(21\) | 3.15650 | 0.150309 | ||||||||
\(22\) | −0.415692 | −0.0188951 | ||||||||
\(23\) | 11.9565 | 0.519848 | 0.259924 | − | 0.965629i | \(-0.416303\pi\) | ||||
0.259924 | + | 0.965629i | \(0.416303\pi\) | |||||||
\(24\) | −10.7983 | −0.449930 | ||||||||
\(25\) | −39.4556 | −1.57822 | ||||||||
\(26\) | 8.60486 | 0.330956 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 5.94693i | 0.212390i | ||||||||
\(29\) | 1.08392 | 0.0373767 | 0.0186883 | − | 0.999825i | \(-0.494051\pi\) | ||||
0.0186883 | + | 0.999825i | \(0.494051\pi\) | |||||||
\(30\) | 11.9359i | 0.397864i | ||||||||
\(31\) | − | 42.5045i | − | 1.37111i | −0.728020 | − | 0.685556i | \(-0.759559\pi\) | ||
0.728020 | − | 0.685556i | \(-0.240441\pi\) | |||||||
\(32\) | − | 31.5483i | − | 0.985885i | ||||||
\(33\) | −0.838817 | −0.0254187 | ||||||||
\(34\) | 1.88630i | 0.0554794i | ||||||||
\(35\) | 14.6310 | 0.418030 | ||||||||
\(36\) | −9.78969 | −0.271936 | ||||||||
\(37\) | 21.6619 | 0.585457 | 0.292728 | − | 0.956196i | \(-0.405437\pi\) | ||||
0.292728 | + | 0.956196i | \(0.405437\pi\) | |||||||
\(38\) | 5.76114i | 0.151609i | ||||||||
\(39\) | 17.3636 | 0.445220 | ||||||||
\(40\) | −50.0525 | −1.25131 | ||||||||
\(41\) | 40.8070i | 0.995292i | 0.867380 | + | 0.497646i | \(0.165802\pi\) | ||||
−0.867380 | + | 0.497646i | \(0.834198\pi\) | |||||||
\(42\) | − | 2.70939i | − | 0.0645092i | ||||||
\(43\) | 15.1894i | 0.353243i | 0.984279 | + | 0.176621i | \(0.0565168\pi\) | ||||
−0.984279 | + | 0.176621i | \(0.943483\pi\) | |||||||
\(44\) | − | 1.58035i | − | 0.0359171i | ||||||
\(45\) | 24.0853i | 0.535228i | ||||||||
\(46\) | − | 10.2629i | − | 0.223106i | ||||||
\(47\) | −19.5302 | −0.415535 | −0.207768 | − | 0.978178i | \(-0.566620\pi\) | ||||
−0.207768 | + | 0.978178i | \(0.566620\pi\) | |||||||
\(48\) | − | 13.3396i | − | 0.277908i | ||||||
\(49\) | 45.6788 | 0.932221 | ||||||||
\(50\) | 33.8668i | 0.677336i | ||||||||
\(51\) | 3.80632i | 0.0746337i | ||||||||
\(52\) | 32.7134i | 0.629104i | ||||||||
\(53\) | − | 29.3759i | − | 0.554263i | −0.960832 | − | 0.277132i | \(-0.910616\pi\) | ||
0.960832 | − | 0.277132i | \(-0.0893838\pi\) | |||||||
\(54\) | 4.46013 | 0.0825950 | ||||||||
\(55\) | −3.88810 | −0.0706926 | ||||||||
\(56\) | 11.3616 | 0.202886 | ||||||||
\(57\) | 11.6253i | 0.203952i | ||||||||
\(58\) | − | 0.930388i | − | 0.0160412i | ||||||
\(59\) | 104.153 | 1.76530 | 0.882652 | − | 0.470027i | \(-0.155756\pi\) | ||||
0.882652 | + | 0.470027i | \(0.155756\pi\) | |||||||
\(60\) | −45.3773 | −0.756289 | ||||||||
\(61\) | 109.511i | 1.79526i | 0.440754 | + | 0.897628i | \(0.354711\pi\) | ||||
−0.440754 | + | 0.897628i | \(0.645289\pi\) | |||||||
\(62\) | −36.4838 | −0.588449 | ||||||||
\(63\) | − | 5.46722i | − | 0.0867812i | ||||||
\(64\) | 3.72684 | 0.0582319 | ||||||||
\(65\) | 80.4838 | 1.23821 | ||||||||
\(66\) | 0.720000i | 0.0109091i | ||||||||
\(67\) | 55.3048 | + | 37.8203i | 0.825445 | + | 0.564482i | ||||
\(68\) | −7.17121 | −0.105459 | ||||||||
\(69\) | − | 20.7093i | − | 0.300134i | ||||||
\(70\) | − | 12.5586i | − | 0.179408i | ||||||
\(71\) | 110.740 | 1.55972 | 0.779858 | − | 0.625956i | \(-0.215291\pi\) | ||||
0.779858 | + | 0.625956i | \(0.215291\pi\) | |||||||
\(72\) | 18.7032i | 0.259767i | ||||||||
\(73\) | −7.70418 | −0.105537 | −0.0527683 | − | 0.998607i | \(-0.516804\pi\) | ||||
−0.0527683 | + | 0.998607i | \(0.516804\pi\) | |||||||
\(74\) | − | 18.5935i | − | 0.251264i | ||||||
\(75\) | 68.3391i | 0.911188i | ||||||||
\(76\) | −21.9024 | −0.288189 | ||||||||
\(77\) | 0.882575 | 0.0114620 | ||||||||
\(78\) | − | 14.9041i | − | 0.191078i | ||||||
\(79\) | − | 42.4445i | − | 0.537273i | −0.963242 | − | 0.268636i | \(-0.913427\pi\) | ||
0.963242 | − | 0.268636i | \(-0.0865730\pi\) | |||||||
\(80\) | − | 61.8318i | − | 0.772897i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 35.0268 | 0.427156 | ||||||||
\(83\) | −78.6551 | −0.947651 | −0.473826 | − | 0.880619i | \(-0.657127\pi\) | ||||
−0.473826 | + | 0.880619i | \(0.657127\pi\) | |||||||
\(84\) | 10.3004 | 0.122624 | ||||||||
\(85\) | 17.6431i | 0.207566i | ||||||||
\(86\) | 13.0379 | 0.151603 | ||||||||
\(87\) | − | 1.87741i | − | 0.0215794i | ||||||
\(88\) | −3.01927 | −0.0343099 | ||||||||
\(89\) | −59.7970 | −0.671876 | −0.335938 | − | 0.941884i | \(-0.609053\pi\) | ||||
−0.335938 | + | 0.941884i | \(0.609053\pi\) | |||||||
\(90\) | 20.6736 | 0.229707 | ||||||||
\(91\) | −18.2694 | −0.200762 | ||||||||
\(92\) | 39.0168 | 0.424096 | ||||||||
\(93\) | −73.6199 | −0.791612 | ||||||||
\(94\) | 16.7638i | 0.178338i | ||||||||
\(95\) | 53.8857i | 0.567218i | ||||||||
\(96\) | −54.6433 | −0.569201 | ||||||||
\(97\) | − | 9.72666i | − | 0.100275i | −0.998742 | − | 0.0501374i | \(-0.984034\pi\) | ||
0.998742 | − | 0.0501374i | \(-0.0159659\pi\) | |||||||
\(98\) | − | 39.2085i | − | 0.400087i | ||||||
\(99\) | 1.45287i | 0.0146755i | ||||||||
\(100\) | −128.753 | −1.28753 | ||||||||
\(101\) | − | 81.6063i | − | 0.807983i | −0.914763 | − | 0.403991i | \(-0.867623\pi\) | ||
0.914763 | − | 0.403991i | \(-0.132377\pi\) | |||||||
\(102\) | 3.26716 | 0.0320310 | ||||||||
\(103\) | −40.2157 | −0.390444 | −0.195222 | − | 0.980759i | \(-0.562543\pi\) | ||||
−0.195222 | + | 0.980759i | \(0.562543\pi\) | |||||||
\(104\) | 62.4991 | 0.600953 | ||||||||
\(105\) | − | 25.3417i | − | 0.241350i | ||||||
\(106\) | −25.2149 | −0.237876 | ||||||||
\(107\) | −81.3778 | −0.760541 | −0.380270 | − | 0.924875i | \(-0.624169\pi\) | ||||
−0.380270 | + | 0.924875i | \(0.624169\pi\) | |||||||
\(108\) | 16.9562i | 0.157002i | ||||||||
\(109\) | 153.719i | 1.41027i | 0.709073 | + | 0.705135i | \(0.249114\pi\) | ||||
−0.709073 | + | 0.705135i | \(0.750886\pi\) | |||||||
\(110\) | 3.33736i | 0.0303396i | ||||||||
\(111\) | − | 37.5195i | − | 0.338014i | ||||||
\(112\) | 14.0355i | 0.125317i | ||||||||
\(113\) | 166.349i | 1.47212i | 0.676917 | + | 0.736059i | \(0.263316\pi\) | ||||
−0.676917 | + | 0.736059i | \(0.736684\pi\) | |||||||
\(114\) | 9.97859 | 0.0875315 | ||||||||
\(115\) | − | 95.9918i | − | 0.834711i | ||||||
\(116\) | 3.53709 | 0.0304922 | ||||||||
\(117\) | − | 30.0746i | − | 0.257048i | ||||||
\(118\) | − | 89.3999i | − | 0.757626i | ||||||
\(119\) | − | 4.00488i | − | 0.0336545i | ||||||
\(120\) | 86.6935i | 0.722445i | ||||||||
\(121\) | 120.765 | 0.998062 | ||||||||
\(122\) | 93.9987 | 0.770481 | ||||||||
\(123\) | 70.6798 | 0.574632 | ||||||||
\(124\) | − | 138.702i | − | 1.11856i | ||||||
\(125\) | 116.055i | 0.928444i | ||||||||
\(126\) | −4.69280 | −0.0372444 | ||||||||
\(127\) | −157.450 | −1.23977 | −0.619883 | − | 0.784694i | \(-0.712820\pi\) | ||||
−0.619883 | + | 0.784694i | \(0.712820\pi\) | |||||||
\(128\) | − | 129.392i | − | 1.01088i | ||||||
\(129\) | 26.3089 | 0.203945 | ||||||||
\(130\) | − | 69.0834i | − | 0.531411i | ||||||
\(131\) | −161.155 | −1.23019 | −0.615095 | − | 0.788453i | \(-0.710882\pi\) | ||||
−0.615095 | + | 0.788453i | \(0.710882\pi\) | |||||||
\(132\) | −2.73725 | −0.0207368 | ||||||||
\(133\) | − | 12.2317i | − | 0.0919680i | ||||||
\(134\) | 32.4632 | − | 47.4710i | 0.242262 | − | 0.354261i | ||||
\(135\) | 41.7169 | 0.309014 | ||||||||
\(136\) | 13.7006i | 0.100740i | ||||||||
\(137\) | − | 164.030i | − | 1.19730i | −0.801012 | − | 0.598648i | \(-0.795705\pi\) | ||
0.801012 | − | 0.598648i | \(-0.204295\pi\) | |||||||
\(138\) | −17.7758 | −0.128810 | ||||||||
\(139\) | − | 152.105i | − | 1.09428i | −0.837041 | − | 0.547140i | \(-0.815717\pi\) | ||
0.837041 | − | 0.547140i | \(-0.184283\pi\) | |||||||
\(140\) | 47.7445 | 0.341032 | ||||||||
\(141\) | 33.8272i | 0.239909i | ||||||||
\(142\) | − | 95.0538i | − | 0.669393i | ||||||
\(143\) | 4.85495 | 0.0339507 | ||||||||
\(144\) | −23.1048 | −0.160450 | ||||||||
\(145\) | − | 8.70219i | − | 0.0600151i | ||||||
\(146\) | 6.61290i | 0.0452938i | ||||||||
\(147\) | − | 79.1181i | − | 0.538218i | ||||||
\(148\) | 70.6878 | 0.477620 | ||||||||
\(149\) | 126.451 | 0.848663 | 0.424332 | − | 0.905507i | \(-0.360509\pi\) | ||||
0.424332 | + | 0.905507i | \(0.360509\pi\) | |||||||
\(150\) | 58.6590 | 0.391060 | ||||||||
\(151\) | 145.917 | 0.966339 | 0.483169 | − | 0.875527i | \(-0.339486\pi\) | ||||
0.483169 | + | 0.875527i | \(0.339486\pi\) | |||||||
\(152\) | 41.8445i | 0.275293i | ||||||||
\(153\) | 6.59274 | 0.0430898 | ||||||||
\(154\) | − | 0.757560i | − | 0.00491922i | ||||||
\(155\) | −341.244 | −2.20157 | ||||||||
\(156\) | 56.6613 | 0.363214 | ||||||||
\(157\) | 135.904 | 0.865631 | 0.432815 | − | 0.901483i | \(-0.357520\pi\) | ||||
0.432815 | + | 0.901483i | \(0.357520\pi\) | |||||||
\(158\) | −36.4324 | −0.230585 | ||||||||
\(159\) | −50.8806 | −0.320004 | ||||||||
\(160\) | −253.283 | −1.58302 | ||||||||
\(161\) | 21.7896i | 0.135339i | ||||||||
\(162\) | − | 7.72517i | − | 0.0476862i | ||||||
\(163\) | −227.905 | −1.39819 | −0.699095 | − | 0.715029i | \(-0.746413\pi\) | ||||
−0.699095 | + | 0.715029i | \(0.746413\pi\) | |||||||
\(164\) | 133.163i | 0.811967i | ||||||||
\(165\) | 6.73438i | 0.0408144i | ||||||||
\(166\) | 67.5137i | 0.406709i | ||||||||
\(167\) | −318.507 | −1.90723 | −0.953613 | − | 0.301036i | \(-0.902668\pi\) | ||||
−0.953613 | + | 0.301036i | \(0.902668\pi\) | |||||||
\(168\) | − | 19.6789i | − | 0.117136i | ||||||
\(169\) | 68.5023 | 0.405339 | ||||||||
\(170\) | 15.1440 | 0.0890823 | ||||||||
\(171\) | 20.1356 | 0.117752 | ||||||||
\(172\) | 49.5666i | 0.288178i | ||||||||
\(173\) | −186.601 | −1.07862 | −0.539310 | − | 0.842107i | \(-0.681315\pi\) | ||||
−0.539310 | + | 0.842107i | \(0.681315\pi\) | |||||||
\(174\) | −1.61148 | −0.00926137 | ||||||||
\(175\) | − | 71.9041i | − | 0.410880i | ||||||
\(176\) | − | 3.72982i | − | 0.0211922i | ||||||
\(177\) | − | 180.398i | − | 1.01920i | ||||||
\(178\) | 51.3269i | 0.288353i | ||||||||
\(179\) | 162.498i | 0.907808i | 0.891051 | + | 0.453904i | \(0.149969\pi\) | ||||
−0.891051 | + | 0.453904i | \(0.850031\pi\) | |||||||
\(180\) | 78.5958i | 0.436643i | ||||||||
\(181\) | −28.2924 | −0.156311 | −0.0781557 | − | 0.996941i | \(-0.524903\pi\) | ||||
−0.0781557 | + | 0.996941i | \(0.524903\pi\) | |||||||
\(182\) | 15.6815i | 0.0861623i | ||||||||
\(183\) | 189.678 | 1.03649 | ||||||||
\(184\) | − | 74.5417i | − | 0.405118i | ||||||
\(185\) | − | 173.911i | − | 0.940059i | ||||||
\(186\) | 63.1918i | 0.339741i | ||||||||
\(187\) | 1.06427i | 0.00569128i | ||||||||
\(188\) | −63.7314 | −0.338997 | ||||||||
\(189\) | −9.46950 | −0.0501032 | ||||||||
\(190\) | 46.2529 | 0.243436 | ||||||||
\(191\) | − | 9.47516i | − | 0.0496082i | −0.999692 | − | 0.0248041i | \(-0.992104\pi\) | ||
0.999692 | − | 0.0248041i | \(-0.00789619\pi\) | |||||||
\(192\) | − | 6.45508i | − | 0.0336202i | ||||||
\(193\) | 254.816 | 1.32029 | 0.660146 | − | 0.751137i | \(-0.270494\pi\) | ||||
0.660146 | + | 0.751137i | \(0.270494\pi\) | |||||||
\(194\) | −8.34890 | −0.0430356 | ||||||||
\(195\) | − | 139.402i | − | 0.714882i | ||||||
\(196\) | 149.061 | 0.760513 | ||||||||
\(197\) | 225.629i | 1.14533i | 0.819791 | + | 0.572663i | \(0.194090\pi\) | ||||
−0.819791 | + | 0.572663i | \(0.805910\pi\) | |||||||
\(198\) | 1.24708 | 0.00629837 | ||||||||
\(199\) | 170.579 | 0.857180 | 0.428590 | − | 0.903499i | \(-0.359010\pi\) | ||||
0.428590 | + | 0.903499i | \(0.359010\pi\) | |||||||
\(200\) | 245.982i | 1.22991i | ||||||||
\(201\) | 65.5067 | − | 95.7908i | 0.325904 | − | 0.476571i | ||||
\(202\) | −70.0469 | −0.346767 | ||||||||
\(203\) | 1.97535i | 0.00973078i | ||||||||
\(204\) | 12.4209i | 0.0608868i | ||||||||
\(205\) | 327.616 | 1.59813 | ||||||||
\(206\) | 34.5192i | 0.167569i | ||||||||
\(207\) | −35.8695 | −0.173283 | ||||||||
\(208\) | 77.2075i | 0.371190i | ||||||||
\(209\) | 3.25050i | 0.0155526i | ||||||||
\(210\) | −21.7521 | −0.103581 | ||||||||
\(211\) | −216.886 | −1.02789 | −0.513947 | − | 0.857822i | \(-0.671817\pi\) | ||||
−0.513947 | + | 0.857822i | \(0.671817\pi\) | |||||||
\(212\) | − | 95.8605i | − | 0.452172i | ||||||
\(213\) | − | 191.807i | − | 0.900503i | ||||||
\(214\) | 69.8508i | 0.326406i | ||||||||
\(215\) | 121.947 | 0.567196 | ||||||||
\(216\) | 32.3949 | 0.149977 | ||||||||
\(217\) | 77.4604 | 0.356961 | ||||||||
\(218\) | 131.945 | 0.605254 | ||||||||
\(219\) | 13.3440i | 0.0609316i | ||||||||
\(220\) | −12.6878 | −0.0576716 | ||||||||
\(221\) | − | 22.0304i | − | 0.0996852i | ||||||
\(222\) | −32.2050 | −0.145067 | ||||||||
\(223\) | 274.408 | 1.23053 | 0.615264 | − | 0.788321i | \(-0.289049\pi\) | ||||
0.615264 | + | 0.788321i | \(0.289049\pi\) | |||||||
\(224\) | 57.4939 | 0.256669 | ||||||||
\(225\) | 118.367 | 0.526074 | ||||||||
\(226\) | 142.786 | 0.631798 | ||||||||
\(227\) | −199.016 | −0.876723 | −0.438361 | − | 0.898799i | \(-0.644441\pi\) | ||||
−0.438361 | + | 0.898799i | \(0.644441\pi\) | |||||||
\(228\) | 37.9360i | 0.166386i | ||||||||
\(229\) | 336.853i | 1.47098i | 0.677538 | + | 0.735488i | \(0.263047\pi\) | ||||
−0.677538 | + | 0.735488i | \(0.736953\pi\) | |||||||
\(230\) | −82.3948 | −0.358238 | ||||||||
\(231\) | − | 1.52867i | − | 0.00661760i | ||||||
\(232\) | − | 6.75762i | − | 0.0291277i | ||||||
\(233\) | 325.037i | 1.39501i | 0.716581 | + | 0.697504i | \(0.245706\pi\) | ||||
−0.716581 | + | 0.697504i | \(0.754294\pi\) | |||||||
\(234\) | −25.8146 | −0.110319 | ||||||||
\(235\) | 156.796i | 0.667218i | ||||||||
\(236\) | 339.875 | 1.44015 | ||||||||
\(237\) | −73.5161 | −0.310195 | ||||||||
\(238\) | −3.43760 | −0.0144437 | ||||||||
\(239\) | − | 14.6583i | − | 0.0613316i | −0.999530 | − | 0.0306658i | \(-0.990237\pi\) | ||
0.999530 | − | 0.0306658i | \(-0.00976276\pi\) | |||||||
\(240\) | −107.096 | −0.446232 | ||||||||
\(241\) | 87.0662 | 0.361271 | 0.180635 | − | 0.983550i | \(-0.442185\pi\) | ||||
0.180635 | + | 0.983550i | \(0.442185\pi\) | |||||||
\(242\) | − | 103.659i | − | 0.428344i | ||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 357.358i | 1.46458i | ||||||||
\(245\) | − | 366.729i | − | 1.49685i | ||||||
\(246\) | − | 60.6681i | − | 0.246618i | ||||||
\(247\) | − | 67.2855i | − | 0.272411i | ||||||
\(248\) | −264.990 | −1.06851 | ||||||||
\(249\) | 136.235i | 0.547127i | ||||||||
\(250\) | 99.6165 | 0.398466 | ||||||||
\(251\) | 91.9893i | 0.366491i | 0.983067 | + | 0.183246i | \(0.0586603\pi\) | ||||
−0.983067 | + | 0.183246i | \(0.941340\pi\) | |||||||
\(252\) | − | 17.8408i | − | 0.0707968i | ||||||
\(253\) | − | 5.79043i | − | 0.0228871i | ||||||
\(254\) | 135.148i | 0.532078i | ||||||||
\(255\) | 30.5588 | 0.119838 | ||||||||
\(256\) | −96.1568 | −0.375612 | ||||||||
\(257\) | −219.195 | −0.852898 | −0.426449 | − | 0.904512i | \(-0.640236\pi\) | ||||
−0.426449 | + | 0.904512i | \(0.640236\pi\) | |||||||
\(258\) | − | 22.5823i | − | 0.0875282i | ||||||
\(259\) | 39.4768i | 0.152420i | ||||||||
\(260\) | 262.637 | 1.01014 | ||||||||
\(261\) | −3.25177 | −0.0124589 | ||||||||
\(262\) | 138.328i | 0.527968i | ||||||||
\(263\) | −7.87641 | −0.0299483 | −0.0149742 | − | 0.999888i | \(-0.504767\pi\) | ||||
−0.0149742 | + | 0.999888i | \(0.504767\pi\) | |||||||
\(264\) | 5.22953i | 0.0198088i | ||||||||
\(265\) | −235.843 | −0.889972 | ||||||||
\(266\) | −10.4991 | −0.0394705 | ||||||||
\(267\) | 103.571i | 0.387908i | ||||||||
\(268\) | 180.472 | + | 123.416i | 0.673405 | + | 0.460509i | ||||
\(269\) | −311.628 | −1.15847 | −0.579235 | − | 0.815161i | \(-0.696648\pi\) | ||||
−0.579235 | + | 0.815161i | \(0.696648\pi\) | |||||||
\(270\) | − | 35.8078i | − | 0.132621i | ||||||
\(271\) | − | 159.485i | − | 0.588505i | −0.955728 | − | 0.294252i | \(-0.904929\pi\) | ||
0.955728 | − | 0.294252i | \(-0.0950706\pi\) | |||||||
\(272\) | −16.9249 | −0.0622239 | ||||||||
\(273\) | 31.6435i | 0.115910i | ||||||||
\(274\) | −140.795 | −0.513851 | ||||||||
\(275\) | 19.1080i | 0.0694836i | ||||||||
\(276\) | − | 67.5791i | − | 0.244852i | ||||||
\(277\) | −126.187 | −0.455548 | −0.227774 | − | 0.973714i | \(-0.573145\pi\) | ||||
−0.227774 | + | 0.973714i | \(0.573145\pi\) | |||||||
\(278\) | −130.560 | −0.469639 | ||||||||
\(279\) | 127.513i | 0.457038i | ||||||||
\(280\) | − | 91.2159i | − | 0.325771i | ||||||
\(281\) | 239.093i | 0.850863i | 0.904991 | + | 0.425432i | \(0.139878\pi\) | ||||
−0.904991 | + | 0.425432i | \(0.860122\pi\) | |||||||
\(282\) | 29.0357 | 0.102963 | ||||||||
\(283\) | −201.395 | −0.711644 | −0.355822 | − | 0.934554i | \(-0.615799\pi\) | ||||
−0.355822 | + | 0.934554i | \(0.615799\pi\) | |||||||
\(284\) | 361.370 | 1.27243 | ||||||||
\(285\) | 93.3327 | 0.327483 | ||||||||
\(286\) | − | 4.16726i | − | 0.0145708i | ||||||
\(287\) | −74.3669 | −0.259118 | ||||||||
\(288\) | 94.6450i | 0.328628i | ||||||||
\(289\) | −284.171 | −0.983289 | ||||||||
\(290\) | −7.46955 | −0.0257571 | ||||||||
\(291\) | −16.8471 | −0.0578937 | ||||||||
\(292\) | −25.1405 | −0.0860977 | ||||||||
\(293\) | 16.4586 | 0.0561727 | 0.0280863 | − | 0.999606i | \(-0.491059\pi\) | ||||
0.0280863 | + | 0.999606i | \(0.491059\pi\) | |||||||
\(294\) | −67.9112 | −0.230990 | ||||||||
\(295\) | − | 836.184i | − | 2.83452i | ||||||
\(296\) | − | 135.049i | − | 0.456247i | ||||||
\(297\) | 2.51645 | 0.00847290 | ||||||||
\(298\) | − | 108.539i | − | 0.364226i | ||||||
\(299\) | 119.862i | 0.400877i | ||||||||
\(300\) | 223.006i | 0.743354i | ||||||||
\(301\) | −27.6813 | −0.0919645 | ||||||||
\(302\) | − | 125.248i | − | 0.414729i | ||||||
\(303\) | −141.346 | −0.466489 | ||||||||
\(304\) | −51.6921 | −0.170040 | ||||||||
\(305\) | 879.197 | 2.88261 | ||||||||
\(306\) | − | 5.65889i | − | 0.0184931i | ||||||
\(307\) | −393.009 | −1.28016 | −0.640080 | − | 0.768308i | \(-0.721099\pi\) | ||||
−0.640080 | + | 0.768308i | \(0.721099\pi\) | |||||||
\(308\) | 2.88005 | 0.00935080 | ||||||||
\(309\) | 69.6556i | 0.225423i | ||||||||
\(310\) | 292.908i | 0.944863i | ||||||||
\(311\) | 52.7513i | 0.169618i | 0.996397 | + | 0.0848092i | \(0.0270281\pi\) | ||||
−0.996397 | + | 0.0848092i | \(0.972972\pi\) | |||||||
\(312\) | − | 108.252i | − | 0.346960i | ||||||
\(313\) | 238.740i | 0.762747i | 0.924421 | + | 0.381373i | \(0.124549\pi\) | ||||
−0.924421 | + | 0.381373i | \(0.875451\pi\) | |||||||
\(314\) | − | 116.654i | − | 0.371508i | ||||||
\(315\) | −43.8931 | −0.139343 | ||||||||
\(316\) | − | 138.506i | − | 0.438311i | ||||||
\(317\) | −99.9853 | −0.315411 | −0.157706 | − | 0.987486i | \(-0.550410\pi\) | ||||
−0.157706 | + | 0.987486i | \(0.550410\pi\) | |||||||
\(318\) | 43.6735i | 0.137338i | ||||||||
\(319\) | − | 0.524935i | − | 0.00164556i | ||||||
\(320\) | − | 29.9207i | − | 0.0935021i | ||||||
\(321\) | 140.951i | 0.439098i | ||||||||
\(322\) | 18.7031 | 0.0580843 | ||||||||
\(323\) | 14.7499 | 0.0456652 | ||||||||
\(324\) | 29.3691 | 0.0906453 | ||||||||
\(325\) | − | 395.536i | − | 1.21704i | ||||||
\(326\) | 195.623i | 0.600070i | ||||||||
\(327\) | 266.250 | 0.814220 | ||||||||
\(328\) | 254.407 | 0.775633 | ||||||||
\(329\) | − | 35.5919i | − | 0.108182i | ||||||
\(330\) | 5.78047 | 0.0175166 | ||||||||
\(331\) | − | 491.470i | − | 1.48480i | −0.669955 | − | 0.742402i | \(-0.733686\pi\) | ||
0.669955 | − | 0.742402i | \(-0.266314\pi\) | |||||||
\(332\) | −256.670 | −0.773101 | ||||||||
\(333\) | −64.9857 | −0.195152 | ||||||||
\(334\) | 273.391i | 0.818536i | ||||||||
\(335\) | 303.638 | − | 444.010i | 0.906381 | − | 1.32540i | ||||
\(336\) | 24.3101 | 0.0723515 | ||||||||
\(337\) | − | 385.089i | − | 1.14270i | −0.820707 | − | 0.571349i | \(-0.806420\pi\) | ||
0.820707 | − | 0.571349i | \(-0.193580\pi\) | |||||||
\(338\) | − | 58.7991i | − | 0.173962i | ||||||
\(339\) | 288.126 | 0.849928 | ||||||||
\(340\) | 57.5735i | 0.169334i | ||||||||
\(341\) | −20.5846 | −0.0603653 | ||||||||
\(342\) | − | 17.2834i | − | 0.0505363i | ||||||
\(343\) | 172.543i | 0.503042i | ||||||||
\(344\) | 94.6972 | 0.275283 | ||||||||
\(345\) | −166.263 | −0.481921 | ||||||||
\(346\) | 160.170i | 0.462918i | ||||||||
\(347\) | − | 422.486i | − | 1.21754i | −0.793347 | − | 0.608770i | \(-0.791663\pi\) | ||
0.793347 | − | 0.608770i | \(-0.208337\pi\) | |||||||
\(348\) | − | 6.12642i | − | 0.0176047i | ||||||
\(349\) | 159.657 | 0.457469 | 0.228734 | − | 0.973489i | \(-0.426541\pi\) | ||||
0.228734 | + | 0.973489i | \(0.426541\pi\) | |||||||
\(350\) | −61.7190 | −0.176340 | ||||||||
\(351\) | −52.0907 | −0.148407 | ||||||||
\(352\) | −15.2786 | −0.0434051 | ||||||||
\(353\) | 406.964i | 1.15287i | 0.817142 | + | 0.576437i | \(0.195557\pi\) | ||||
−0.817142 | + | 0.576437i | \(0.804443\pi\) | |||||||
\(354\) | −154.845 | −0.437416 | ||||||||
\(355\) | − | 889.067i | − | 2.50441i | ||||||
\(356\) | −195.131 | −0.548122 | ||||||||
\(357\) | −6.93666 | −0.0194304 | ||||||||
\(358\) | 139.480 | 0.389609 | ||||||||
\(359\) | −252.187 | −0.702470 | −0.351235 | − | 0.936287i | \(-0.614238\pi\) | ||||
−0.351235 | + | 0.936287i | \(0.614238\pi\) | |||||||
\(360\) | 150.157 | 0.417104 | ||||||||
\(361\) | −315.951 | −0.875210 | ||||||||
\(362\) | 24.2848i | 0.0670851i | ||||||||
\(363\) | − | 209.172i | − | 0.576231i | ||||||
\(364\) | −59.6171 | −0.163783 | ||||||||
\(365\) | 61.8524i | 0.169459i | ||||||||
\(366\) | − | 162.810i | − | 0.444837i | ||||||
\(367\) | − | 330.938i | − | 0.901738i | −0.892590 | − | 0.450869i | \(-0.851114\pi\) | ||
0.892590 | − | 0.450869i | \(-0.148886\pi\) | |||||||
\(368\) | 92.0842 | 0.250229 | ||||||||
\(369\) | − | 122.421i | − | 0.331764i | ||||||
\(370\) | −149.277 | −0.403451 | ||||||||
\(371\) | 53.5349 | 0.144299 | ||||||||
\(372\) | −240.239 | −0.645803 | ||||||||
\(373\) | 661.975i | 1.77473i | 0.461066 | + | 0.887366i | \(0.347467\pi\) | ||||
−0.461066 | + | 0.887366i | \(0.652533\pi\) | |||||||
\(374\) | 0.913518 | 0.00244256 | ||||||||
\(375\) | 201.014 | 0.536037 | ||||||||
\(376\) | 121.759i | 0.323827i | ||||||||
\(377\) | 10.8662i | 0.0288227i | ||||||||
\(378\) | 8.12816i | 0.0215031i | ||||||||
\(379\) | 435.877i | 1.15007i | 0.818128 | + | 0.575036i | \(0.195012\pi\) | ||||
−0.818128 | + | 0.575036i | \(0.804988\pi\) | |||||||
\(380\) | 175.841i | 0.462741i | ||||||||
\(381\) | 272.712i | 0.715779i | ||||||||
\(382\) | −8.13302 | −0.0212906 | ||||||||
\(383\) | − | 205.665i | − | 0.536984i | −0.963282 | − | 0.268492i | \(-0.913475\pi\) | ||
0.963282 | − | 0.268492i | \(-0.0865253\pi\) | |||||||
\(384\) | −224.114 | −0.583630 | ||||||||
\(385\) | − | 7.08569i | − | 0.0184044i | ||||||
\(386\) | − | 218.722i | − | 0.566638i | ||||||
\(387\) | − | 45.5683i | − | 0.117748i | ||||||
\(388\) | − | 31.7403i | − | 0.0818050i | ||||||
\(389\) | 539.491 | 1.38687 | 0.693433 | − | 0.720521i | \(-0.256097\pi\) | ||||
0.693433 | + | 0.720521i | \(0.256097\pi\) | |||||||
\(390\) | −119.656 | −0.306810 | ||||||||
\(391\) | −26.2754 | −0.0672004 | ||||||||
\(392\) | − | 284.781i | − | 0.726481i | ||||||
\(393\) | 279.129i | 0.710251i | ||||||||
\(394\) | 193.669 | 0.491546 | ||||||||
\(395\) | −340.763 | −0.862690 | ||||||||
\(396\) | 4.74106i | 0.0119724i | ||||||||
\(397\) | −360.077 | −0.906995 | −0.453498 | − | 0.891257i | \(-0.649824\pi\) | ||||
−0.453498 | + | 0.891257i | \(0.649824\pi\) | |||||||
\(398\) | − | 146.417i | − | 0.367881i | ||||||
\(399\) | −21.1860 | −0.0530977 | ||||||||
\(400\) | −303.871 | −0.759678 | ||||||||
\(401\) | − | 612.829i | − | 1.52825i | −0.645068 | − | 0.764126i | \(-0.723171\pi\) | ||
0.645068 | − | 0.764126i | \(-0.276829\pi\) | |||||||
\(402\) | −82.2222 | − | 56.2278i | −0.204533 | − | 0.139870i | ||||
\(403\) | 426.101 | 1.05732 | ||||||||
\(404\) | − | 266.300i | − | 0.659159i | ||||||
\(405\) | − | 72.2558i | − | 0.178409i | ||||||
\(406\) | 1.69554 | 0.00417622 | ||||||||
\(407\) | − | 10.4907i | − | 0.0257756i | ||||||
\(408\) | 23.7302 | 0.0581622 | ||||||||
\(409\) | − | 346.344i | − | 0.846806i | −0.905941 | − | 0.423403i | \(-0.860835\pi\) | ||
0.905941 | − | 0.423403i | \(-0.139165\pi\) | |||||||
\(410\) | − | 281.210i | − | 0.685877i | ||||||
\(411\) | −284.108 | −0.691259 | ||||||||
\(412\) | −131.233 | −0.318527 | ||||||||
\(413\) | 189.809i | 0.459586i | ||||||||
\(414\) | 30.7886i | 0.0743687i | ||||||||
\(415\) | 631.476i | 1.52163i | ||||||||
\(416\) | 316.268 | 0.760258 | ||||||||
\(417\) | −263.453 | −0.631782 | ||||||||
\(418\) | 2.79007 | 0.00667481 | ||||||||
\(419\) | −409.264 | −0.976764 | −0.488382 | − | 0.872630i | \(-0.662413\pi\) | ||||
−0.488382 | + | 0.872630i | \(0.662413\pi\) | |||||||
\(420\) | − | 82.6959i | − | 0.196895i | ||||||
\(421\) | −392.331 | −0.931903 | −0.465952 | − | 0.884810i | \(-0.654288\pi\) | ||||
−0.465952 | + | 0.884810i | \(0.654288\pi\) | |||||||
\(422\) | 186.164i | 0.441147i | ||||||||
\(423\) | 58.5905 | 0.138512 | ||||||||
\(424\) | −183.142 | −0.431938 | ||||||||
\(425\) | 86.7068 | 0.204016 | ||||||||
\(426\) | −164.638 | −0.386474 | ||||||||
\(427\) | −199.573 | −0.467383 | ||||||||
\(428\) | −265.555 | −0.620455 | ||||||||
\(429\) | − | 8.40902i | − | 0.0196014i | ||||||
\(430\) | − | 104.674i | − | 0.243427i | ||||||
\(431\) | 86.3386 | 0.200322 | 0.100161 | − | 0.994971i | \(-0.468064\pi\) | ||||
0.100161 | + | 0.994971i | \(0.468064\pi\) | |||||||
\(432\) | 40.0187i | 0.0926359i | ||||||||
\(433\) | 228.984i | 0.528831i | 0.964409 | + | 0.264415i | \(0.0851790\pi\) | ||||
−0.964409 | + | 0.264415i | \(0.914821\pi\) | |||||||
\(434\) | − | 66.4883i | − | 0.153199i | ||||||
\(435\) | −15.0726 | −0.0346498 | ||||||||
\(436\) | 501.622i | 1.15051i | ||||||||
\(437\) | −80.2504 | −0.183639 | ||||||||
\(438\) | 11.4539 | 0.0261504 | ||||||||
\(439\) | 639.389 | 1.45647 | 0.728233 | − | 0.685329i | \(-0.240342\pi\) | ||||
0.728233 | + | 0.685329i | \(0.240342\pi\) | |||||||
\(440\) | 24.2400i | 0.0550909i | ||||||||
\(441\) | −137.037 | −0.310740 | ||||||||
\(442\) | −18.9099 | −0.0427825 | ||||||||
\(443\) | − | 2.41341i | − | 0.00544787i | −0.999996 | − | 0.00272394i | \(-0.999133\pi\) | ||
0.999996 | − | 0.00272394i | \(-0.000867057\pi\) | |||||||
\(444\) | − | 122.435i | − | 0.275754i | ||||||
\(445\) | 480.075i | 1.07882i | ||||||||
\(446\) | − | 235.539i | − | 0.528113i | ||||||
\(447\) | − | 219.019i | − | 0.489976i | ||||||
\(448\) | 6.79182i | 0.0151603i | ||||||||
\(449\) | 887.102 | 1.97573 | 0.987864 | − | 0.155320i | \(-0.0496408\pi\) | ||||
0.987864 | + | 0.155320i | \(0.0496408\pi\) | |||||||
\(450\) | − | 101.600i | − | 0.225779i | ||||||
\(451\) | 19.7625 | 0.0438192 | ||||||||
\(452\) | 542.837i | 1.20097i | ||||||||
\(453\) | − | 252.736i | − | 0.557916i | ||||||
\(454\) | 170.826i | 0.376268i | ||||||||
\(455\) | 146.674i | 0.322361i | ||||||||
\(456\) | 72.4768 | 0.158940 | ||||||||
\(457\) | 203.749 | 0.445841 | 0.222921 | − | 0.974837i | \(-0.428441\pi\) | ||||
0.222921 | + | 0.974837i | \(0.428441\pi\) | |||||||
\(458\) | 289.139 | 0.631307 | ||||||||
\(459\) | − | 11.4190i | − | 0.0248779i | ||||||
\(460\) | − | 313.243i | − | 0.680964i | ||||||
\(461\) | −503.081 | −1.09128 | −0.545641 | − | 0.838019i | \(-0.683714\pi\) | ||||
−0.545641 | + | 0.838019i | \(0.683714\pi\) | |||||||
\(462\) | −1.31213 | −0.00284011 | ||||||||
\(463\) | 585.201i | 1.26393i | 0.774996 | + | 0.631966i | \(0.217752\pi\) | ||||
−0.774996 | + | 0.631966i | \(0.782248\pi\) | |||||||
\(464\) | 8.34795 | 0.0179913 | ||||||||
\(465\) | 591.052i | 1.27108i | ||||||||
\(466\) | 278.996 | 0.598704 | ||||||||
\(467\) | 83.3835 | 0.178551 | 0.0892757 | − | 0.996007i | \(-0.471545\pi\) | ||||
0.0892757 | + | 0.996007i | \(0.471545\pi\) | |||||||
\(468\) | − | 98.1403i | − | 0.209701i | ||||||
\(469\) | −68.9240 | + | 100.788i | −0.146959 | + | 0.214899i | ||||
\(470\) | 134.586 | 0.286354 | ||||||||
\(471\) | − | 235.393i | − | 0.499772i | ||||||
\(472\) | − | 649.332i | − | 1.37570i | ||||||
\(473\) | 7.35611 | 0.0155520 | ||||||||
\(474\) | 63.1027i | 0.133128i | ||||||||
\(475\) | 264.820 | 0.557517 | ||||||||
\(476\) | − | 13.0689i | − | 0.0274556i | ||||||
\(477\) | 88.1278i | 0.184754i | ||||||||
\(478\) | −12.5820 | −0.0263221 | ||||||||
\(479\) | 292.164 | 0.609947 | 0.304973 | − | 0.952361i | \(-0.401352\pi\) | ||||
0.304973 | + | 0.952361i | \(0.401352\pi\) | |||||||
\(480\) | 438.700i | 0.913958i | ||||||||
\(481\) | 217.157i | 0.451471i | ||||||||
\(482\) | − | 74.7335i | − | 0.155049i | ||||||
\(483\) | 37.7407 | 0.0781380 | ||||||||
\(484\) | 394.086 | 0.814227 | ||||||||
\(485\) | −78.0897 | −0.161010 | ||||||||
\(486\) | −13.3804 | −0.0275317 | ||||||||
\(487\) | − | 125.844i | − | 0.258407i | −0.991618 | − | 0.129203i | \(-0.958758\pi\) | ||
0.991618 | − | 0.129203i | \(-0.0412420\pi\) | |||||||
\(488\) | 682.734 | 1.39905 | ||||||||
\(489\) | 394.743i | 0.807245i | ||||||||
\(490\) | −314.783 | −0.642414 | ||||||||
\(491\) | 558.781 | 1.13805 | 0.569023 | − | 0.822322i | \(-0.307322\pi\) | ||||
0.569023 | + | 0.822322i | \(0.307322\pi\) | |||||||
\(492\) | 230.644 | 0.468790 | ||||||||
\(493\) | −2.38201 | −0.00483166 | ||||||||
\(494\) | −57.7546 | −0.116912 | ||||||||
\(495\) | 11.6643 | 0.0235642 | ||||||||
\(496\) | − | 327.353i | − | 0.659986i | ||||||
\(497\) | 201.813i | 0.406062i | ||||||||
\(498\) | 116.937 | 0.234814 | ||||||||
\(499\) | 362.983i | 0.727421i | 0.931512 | + | 0.363710i | \(0.118490\pi\) | ||||
−0.931512 | + | 0.363710i | \(0.881510\pi\) | |||||||
\(500\) | 378.716i | 0.757432i | ||||||||
\(501\) | 551.670i | 1.10114i | ||||||||
\(502\) | 78.9592 | 0.157289 | ||||||||
\(503\) | 480.564i | 0.955396i | 0.878524 | + | 0.477698i | \(0.158529\pi\) | ||||
−0.878524 | + | 0.477698i | \(0.841471\pi\) | |||||||
\(504\) | −34.0849 | −0.0676287 | ||||||||
\(505\) | −655.170 | −1.29737 | ||||||||
\(506\) | −4.97022 | −0.00982258 | ||||||||
\(507\) | − | 118.649i | − | 0.234022i | ||||||
\(508\) | −513.797 | −1.01141 | ||||||||
\(509\) | −140.767 | −0.276556 | −0.138278 | − | 0.990393i | \(-0.544157\pi\) | ||||
−0.138278 | + | 0.990393i | \(0.544157\pi\) | |||||||
\(510\) | − | 26.2302i | − | 0.0514317i | ||||||
\(511\) | − | 14.0401i | − | 0.0274758i | ||||||
\(512\) | − | 435.033i | − | 0.849673i | ||||||
\(513\) | − | 34.8759i | − | 0.0679841i | ||||||
\(514\) | 188.146i | 0.366043i | ||||||||
\(515\) | 322.869i | 0.626929i | ||||||||
\(516\) | 85.8520 | 0.166380 | ||||||||
\(517\) | 9.45828i | 0.0182946i | ||||||||
\(518\) | 33.8850 | 0.0654150 | ||||||||
\(519\) | 323.203i | 0.622742i | ||||||||
\(520\) | − | 501.769i | − | 0.964940i | ||||||
\(521\) | − | 54.1161i | − | 0.103870i | −0.998650 | − | 0.0519349i | \(-0.983461\pi\) | ||
0.998650 | − | 0.0519349i | \(-0.0165388\pi\) | |||||||
\(522\) | 2.79116i | 0.00534706i | ||||||||
\(523\) | 146.612 | 0.280330 | 0.140165 | − | 0.990128i | \(-0.455237\pi\) | ||||
0.140165 | + | 0.990128i | \(0.455237\pi\) | |||||||
\(524\) | −525.886 | −1.00360 | ||||||||
\(525\) | −124.542 | −0.237222 | ||||||||
\(526\) | 6.76073i | 0.0128531i | ||||||||
\(527\) | 93.4070i | 0.177243i | ||||||||
\(528\) | −6.46024 | −0.0122353 | ||||||||
\(529\) | −386.042 | −0.729759 | ||||||||
\(530\) | 202.436i | 0.381955i | ||||||||
\(531\) | −312.459 | −0.588435 | ||||||||
\(532\) | − | 39.9150i | − | 0.0750282i | ||||||
\(533\) | −409.084 | −0.767512 | ||||||||
\(534\) | 88.9008 | 0.166481 | ||||||||
\(535\) | 653.336i | 1.22119i | ||||||||
\(536\) | 235.787 | − | 344.793i | 0.439902 | − | 0.643270i | ||||
\(537\) | 281.454 | 0.524123 | ||||||||
\(538\) | 267.487i | 0.497187i | ||||||||
\(539\) | − | 22.1219i | − | 0.0410424i | ||||||
\(540\) | 136.132 | 0.252096 | ||||||||
\(541\) | 953.817i | 1.76306i | 0.472125 | + | 0.881531i | \(0.343487\pi\) | ||||
−0.472125 | + | 0.881531i | \(0.656513\pi\) | |||||||
\(542\) | −136.894 | −0.252572 | ||||||||
\(543\) | 49.0038i | 0.0902464i | ||||||||
\(544\) | 69.3300i | 0.127445i | ||||||||
\(545\) | 1234.12 | 2.26445 | ||||||||
\(546\) | 27.1612 | 0.0497458 | ||||||||
\(547\) | − | 880.448i | − | 1.60960i | −0.593549 | − | 0.804798i | \(-0.702274\pi\) | ||
0.593549 | − | 0.804798i | \(-0.297726\pi\) | |||||||
\(548\) | − | 535.266i | − | 0.976764i | ||||||
\(549\) | − | 328.532i | − | 0.598419i | ||||||
\(550\) | 16.4014 | 0.0298207 | ||||||||
\(551\) | −7.27515 | −0.0132035 | ||||||||
\(552\) | −129.110 | −0.233895 | ||||||||
\(553\) | 77.3512 | 0.139876 | ||||||||
\(554\) | 108.313i | 0.195510i | ||||||||
\(555\) | −301.223 | −0.542743 | ||||||||
\(556\) | − | 496.353i | − | 0.892722i | ||||||
\(557\) | 243.499 | 0.437162 | 0.218581 | − | 0.975819i | \(-0.429857\pi\) | ||||
0.218581 | + | 0.975819i | \(0.429857\pi\) | |||||||
\(558\) | 109.451 | 0.196150 | ||||||||
\(559\) | −152.272 | −0.272401 | ||||||||
\(560\) | 112.683 | 0.201219 | ||||||||
\(561\) | 1.84337 | 0.00328586 | ||||||||
\(562\) | 205.226 | 0.365170 | ||||||||
\(563\) | 241.358i | 0.428700i | 0.976757 | + | 0.214350i | \(0.0687633\pi\) | ||||
−0.976757 | + | 0.214350i | \(0.931237\pi\) | |||||||
\(564\) | 110.386i | 0.195720i | ||||||||
\(565\) | 1335.52 | 2.36376 | ||||||||
\(566\) | 172.868i | 0.305421i | ||||||||
\(567\) | 16.4017i | 0.0289271i | ||||||||
\(568\) | − | 690.398i | − | 1.21549i | ||||||
\(569\) | 556.193 | 0.977492 | 0.488746 | − | 0.872426i | \(-0.337454\pi\) | ||||
0.488746 | + | 0.872426i | \(0.337454\pi\) | |||||||
\(570\) | − | 80.1124i | − | 0.140548i | ||||||
\(571\) | −385.003 | −0.674262 | −0.337131 | − | 0.941458i | \(-0.609456\pi\) | ||||
−0.337131 | + | 0.941458i | \(0.609456\pi\) | |||||||
\(572\) | 15.8428 | 0.0276973 | ||||||||
\(573\) | −16.4115 | −0.0286413 | ||||||||
\(574\) | 63.8330i | 0.111207i | ||||||||
\(575\) | −471.750 | −0.820435 | ||||||||
\(576\) | −11.1805 | −0.0194106 | ||||||||
\(577\) | − | 282.772i | − | 0.490072i | −0.969514 | − | 0.245036i | \(-0.921200\pi\) | ||
0.969514 | − | 0.245036i | \(-0.0787999\pi\) | |||||||
\(578\) | 243.918i | 0.422004i | ||||||||
\(579\) | − | 441.355i | − | 0.762271i | ||||||
\(580\) | − | 28.3973i | − | 0.0489608i | ||||||
\(581\) | − | 143.341i | − | 0.246715i | ||||||
\(582\) | 14.4607i | 0.0248466i | ||||||||
\(583\) | −14.2265 | −0.0244023 | ||||||||
\(584\) | 48.0310i | 0.0822449i | ||||||||
\(585\) | −241.451 | −0.412737 | ||||||||
\(586\) | − | 14.1273i | − | 0.0241080i | ||||||
\(587\) | − | 1042.24i | − | 1.77554i | −0.460290 | − | 0.887769i | \(-0.652255\pi\) | ||
0.460290 | − | 0.887769i | \(-0.347745\pi\) | |||||||
\(588\) | − | 258.181i | − | 0.439083i | ||||||
\(589\) | 285.284i | 0.484354i | ||||||||
\(590\) | −717.740 | −1.21651 | ||||||||
\(591\) | 390.801 | 0.661254 | ||||||||
\(592\) | 166.831 | 0.281810 | ||||||||
\(593\) | − | 185.863i | − | 0.313429i | −0.987644 | − | 0.156714i | \(-0.949910\pi\) | ||
0.987644 | − | 0.156714i | \(-0.0500902\pi\) | |||||||
\(594\) | − | 2.16000i | − | 0.00363637i | ||||||
\(595\) | −32.1529 | −0.0540385 | ||||||||
\(596\) | 412.638 | 0.692346 | ||||||||
\(597\) | − | 295.451i | − | 0.494893i | ||||||
\(598\) | 102.884 | 0.172047 | ||||||||
\(599\) | 921.879i | 1.53903i | 0.638629 | + | 0.769515i | \(0.279502\pi\) | ||||
−0.638629 | + | 0.769515i | \(0.720498\pi\) | |||||||
\(600\) | 426.054 | 0.710090 | ||||||||
\(601\) | −657.867 | −1.09462 | −0.547310 | − | 0.836930i | \(-0.684348\pi\) | ||||
−0.547310 | + | 0.836930i | \(0.684348\pi\) | |||||||
\(602\) | 23.7603i | 0.0394690i | ||||||||
\(603\) | −165.914 | − | 113.461i | −0.275148 | − | 0.188161i | ||||
\(604\) | 476.161 | 0.788347 | ||||||||
\(605\) | − | 969.556i | − | 1.60257i | ||||||
\(606\) | 121.325i | 0.200206i | ||||||||
\(607\) | 591.641 | 0.974697 | 0.487348 | − | 0.873208i | \(-0.337964\pi\) | ||||
0.487348 | + | 0.873208i | \(0.337964\pi\) | |||||||
\(608\) | 211.748i | 0.348270i | ||||||||
\(609\) | 3.42140 | 0.00561807 | ||||||||
\(610\) | − | 754.661i | − | 1.23715i | ||||||
\(611\) | − | 195.787i | − | 0.320437i | ||||||
\(612\) | 21.5136 | 0.0351530 | ||||||||
\(613\) | 654.685 | 1.06800 | 0.534000 | − | 0.845484i | \(-0.320688\pi\) | ||||
0.534000 | + | 0.845484i | \(0.320688\pi\) | |||||||
\(614\) | 337.340i | 0.549414i | ||||||||
\(615\) | − | 567.447i | − | 0.922678i | ||||||
\(616\) | − | 5.50234i | − | 0.00893236i | ||||||
\(617\) | −885.383 | −1.43498 | −0.717490 | − | 0.696569i | \(-0.754709\pi\) | ||||
−0.717490 | + | 0.696569i | \(0.754709\pi\) | |||||||
\(618\) | 59.7891 | 0.0967461 | ||||||||
\(619\) | −214.765 | −0.346954 | −0.173477 | − | 0.984838i | \(-0.555500\pi\) | ||||
−0.173477 | + | 0.984838i | \(0.555500\pi\) | |||||||
\(620\) | −1113.56 | −1.79606 | ||||||||
\(621\) | 62.1278i | 0.100045i | ||||||||
\(622\) | 45.2792 | 0.0727962 | ||||||||
\(623\) | − | 108.974i | − | 0.174919i | ||||||
\(624\) | 133.727 | 0.214307 | ||||||||
\(625\) | −54.6468 | −0.0874350 | ||||||||
\(626\) | 204.923 | 0.327353 | ||||||||
\(627\) | 5.63003 | 0.00897931 | ||||||||
\(628\) | 443.486 | 0.706188 | ||||||||
\(629\) | −47.6038 | −0.0756817 | ||||||||
\(630\) | 37.6758i | 0.0598028i | ||||||||
\(631\) | 985.057i | 1.56110i | 0.625091 | + | 0.780552i | \(0.285062\pi\) | ||||
−0.625091 | + | 0.780552i | \(0.714938\pi\) | |||||||
\(632\) | −264.617 | −0.418697 | ||||||||
\(633\) | 375.657i | 0.593455i | ||||||||
\(634\) | 85.8226i | 0.135367i | ||||||||
\(635\) | 1264.08i | 1.99067i | ||||||||
\(636\) | −166.035 | −0.261062 | ||||||||
\(637\) | 457.924i | 0.718876i | ||||||||
\(638\) | −0.450579 | −0.000706236 | ||||||||
\(639\) | −332.220 | −0.519906 | ||||||||
\(640\) | −1038.82 | −1.62315 | ||||||||
\(641\) | − | 360.413i | − | 0.562267i | −0.959669 | − | 0.281134i | \(-0.909290\pi\) | ||
0.959669 | − | 0.281134i | \(-0.0907104\pi\) | |||||||
\(642\) | 120.985 | 0.188450 | ||||||||
\(643\) | 1081.75 | 1.68234 | 0.841172 | − | 0.540768i | \(-0.181866\pi\) | ||||
0.841172 | + | 0.540768i | \(0.181866\pi\) | |||||||
\(644\) | 71.1044i | 0.110411i | ||||||||
\(645\) | − | 211.219i | − | 0.327471i | ||||||
\(646\) | − | 12.6606i | − | 0.0195984i | ||||||
\(647\) | 72.9948i | 0.112820i | 0.998408 | + | 0.0564102i | \(0.0179655\pi\) | ||||
−0.998408 | + | 0.0564102i | \(0.982035\pi\) | |||||||
\(648\) | − | 56.1097i | − | 0.0865890i | ||||||
\(649\) | − | 50.4404i | − | 0.0777201i | ||||||
\(650\) | −339.510 | −0.522322 | ||||||||
\(651\) | − | 134.165i | − | 0.206091i | ||||||
\(652\) | −743.707 | −1.14065 | ||||||||
\(653\) | 391.601i | 0.599695i | 0.953987 | + | 0.299848i | \(0.0969359\pi\) | ||||
−0.953987 | + | 0.299848i | \(0.903064\pi\) | |||||||
\(654\) | − | 228.536i | − | 0.349444i | ||||||
\(655\) | 1293.82i | 1.97530i | ||||||||
\(656\) | 314.279i | 0.479084i | ||||||||
\(657\) | 23.1125 | 0.0351789 | ||||||||
\(658\) | −30.5504 | −0.0464291 | ||||||||
\(659\) | −1137.91 | −1.72673 | −0.863363 | − | 0.504583i | \(-0.831646\pi\) | ||||
−0.863363 | + | 0.504583i | \(0.831646\pi\) | |||||||
\(660\) | 21.9758i | 0.0332967i | ||||||||
\(661\) | − | 1133.56i | − | 1.71492i | −0.514553 | − | 0.857459i | \(-0.672042\pi\) | ||
0.514553 | − | 0.857459i | \(-0.327958\pi\) | |||||||
\(662\) | −421.854 | −0.637242 | ||||||||
\(663\) | −38.1578 | −0.0575533 | ||||||||
\(664\) | 490.368i | 0.738506i | ||||||||
\(665\) | −98.2016 | −0.147672 | ||||||||
\(666\) | 55.7806i | 0.0837547i | ||||||||
\(667\) | 12.9599 | 0.0194302 | ||||||||
\(668\) | −1039.36 | −1.55593 | ||||||||
\(669\) | − | 475.288i | − | 0.710446i | ||||||
\(670\) | −381.117 | − | 260.628i | −0.568832 | − | 0.388997i | ||||
\(671\) | 53.0350 | 0.0790388 | ||||||||
\(672\) | − | 99.5823i | − | 0.148188i | ||||||
\(673\) | − | 1145.47i | − | 1.70203i | −0.525141 | − | 0.851015i | \(-0.675987\pi\) | ||
0.525141 | − | 0.851015i | \(-0.324013\pi\) | |||||||
\(674\) | −330.542 | −0.490418 | ||||||||
\(675\) | − | 205.017i | − | 0.303729i | ||||||
\(676\) | 223.539 | 0.330679 | ||||||||
\(677\) | 662.472i | 0.978541i | 0.872132 | + | 0.489270i | \(0.162737\pi\) | ||||
−0.872132 | + | 0.489270i | \(0.837263\pi\) | |||||||
\(678\) | − | 247.313i | − | 0.364769i | ||||||
\(679\) | 17.7259 | 0.0261059 | ||||||||
\(680\) | 109.994 | 0.161756 | ||||||||
\(681\) | 344.706i | 0.506176i | ||||||||
\(682\) | 17.6688i | 0.0259073i | ||||||||
\(683\) | − | 1073.18i | − | 1.57127i | −0.618691 | − | 0.785634i | \(-0.712337\pi\) | ||
0.618691 | − | 0.785634i | \(-0.287663\pi\) | |||||||
\(684\) | 65.7071 | 0.0960630 | ||||||||
\(685\) | −1316.90 | −1.92248 | ||||||||
\(686\) | 148.103 | 0.215893 | ||||||||
\(687\) | 583.447 | 0.849268 | ||||||||
\(688\) | 116.983i | 0.170034i | ||||||||
\(689\) | 294.490 | 0.427416 | ||||||||
\(690\) | 142.712i | 0.206829i | ||||||||
\(691\) | 996.055 | 1.44147 | 0.720734 | − | 0.693211i | \(-0.243805\pi\) | ||||
0.720734 | + | 0.693211i | \(0.243805\pi\) | |||||||
\(692\) | −608.923 | −0.879947 | ||||||||
\(693\) | −2.64773 | −0.00382067 | ||||||||
\(694\) | −362.642 | −0.522539 | ||||||||
\(695\) | −1221.16 | −1.75707 | ||||||||
\(696\) | −11.7045 | −0.0168169 | ||||||||
\(697\) | − | 89.6766i | − | 0.128661i | ||||||
\(698\) | − | 137.042i | − | 0.196335i | ||||||
\(699\) | 562.980 | 0.805408 | ||||||||
\(700\) | − | 234.640i | − | 0.335199i | ||||||
\(701\) | 149.187i | 0.212820i | 0.994322 | + | 0.106410i | \(0.0339356\pi\) | ||||
−0.994322 | + | 0.106410i | \(0.966064\pi\) | |||||||
\(702\) | 44.7122i | 0.0636925i | ||||||||
\(703\) | −145.392 | −0.206816 | ||||||||
\(704\) | − | 1.80488i | − | 0.00256375i | ||||||
\(705\) | 271.579 | 0.385219 | ||||||||
\(706\) | 349.319 | 0.494786 | ||||||||
\(707\) | 148.720 | 0.210353 | ||||||||
\(708\) | − | 588.681i | − | 0.831470i | ||||||
\(709\) | 1282.28 | 1.80858 | 0.904290 | − | 0.426918i | \(-0.140401\pi\) | ||||
0.904290 | + | 0.426918i | \(0.140401\pi\) | |||||||
\(710\) | −763.132 | −1.07483 | ||||||||
\(711\) | 127.334i | 0.179091i | ||||||||
\(712\) | 372.799i | 0.523594i | ||||||||
\(713\) | − | 508.205i | − | 0.712769i | ||||||
\(714\) | 5.95410i | 0.00833907i | ||||||||
\(715\) | − | 38.9776i | − | 0.0545141i | ||||||
\(716\) | 530.267i | 0.740597i | ||||||||
\(717\) | −25.3889 | −0.0354098 | ||||||||
\(718\) | 216.465i | 0.301483i | ||||||||
\(719\) | −203.704 | −0.283315 | −0.141658 | − | 0.989916i | \(-0.545243\pi\) | ||||
−0.141658 | + | 0.989916i | \(0.545243\pi\) | |||||||
\(720\) | 185.495i | 0.257632i | ||||||||
\(721\) | − | 73.2893i | − | 0.101650i | ||||||
\(722\) | 271.197i | 0.375619i | ||||||||
\(723\) | − | 150.803i | − | 0.208580i | ||||||
\(724\) | −92.3245 | −0.127520 | ||||||||
\(725\) | −42.7668 | −0.0589887 | ||||||||
\(726\) | −179.543 | −0.247305 | ||||||||
\(727\) | − | 1288.60i | − | 1.77249i | −0.463213 | − | 0.886247i | \(-0.653304\pi\) | ||
0.463213 | − | 0.886247i | \(-0.346696\pi\) | |||||||
\(728\) | 113.899i | 0.156454i | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 53.0911 | 0.0727276 | ||||||||
\(731\) | − | 33.3800i | − | 0.0456635i | ||||||
\(732\) | 618.963 | 0.845578 | ||||||||
\(733\) | 234.758i | 0.320271i | 0.987095 | + | 0.160135i | \(0.0511931\pi\) | ||||
−0.987095 | + | 0.160135i | \(0.948807\pi\) | |||||||
\(734\) | −284.061 | −0.387004 | ||||||||
\(735\) | −635.193 | −0.864209 | ||||||||
\(736\) | − | 377.207i | − | 0.512510i | ||||||
\(737\) | 18.3161 | − | 26.7836i | 0.0248522 | − | 0.0363414i | ||||
\(738\) | −105.080 | −0.142385 | ||||||||
\(739\) | − | 314.604i | − | 0.425716i | −0.977083 | − | 0.212858i | \(-0.931723\pi\) | ||
0.977083 | − | 0.212858i | \(-0.0682772\pi\) | |||||||
\(740\) | − | 567.512i | − | 0.766908i | ||||||
\(741\) | −116.542 | −0.157276 | ||||||||
\(742\) | − | 45.9518i | − | 0.0619296i | ||||||
\(743\) | 1151.64 | 1.54998 | 0.774992 | − | 0.631970i | \(-0.217754\pi\) | ||||
0.774992 | + | 0.631970i | \(0.217754\pi\) | |||||||
\(744\) | 458.977i | 0.616904i | ||||||||
\(745\) | − | 1015.20i | − | 1.36269i | ||||||
\(746\) | 568.208 | 0.761672 | ||||||||
\(747\) | 235.965 | 0.315884 | ||||||||
\(748\) | 3.47296i | 0.00464299i | ||||||||
\(749\) | − | 148.303i | − | 0.198002i | ||||||
\(750\) | − | 172.541i | − | 0.230054i | ||||||
\(751\) | −1418.44 | −1.88873 | −0.944367 | − | 0.328892i | \(-0.893325\pi\) | ||||
−0.944367 | + | 0.328892i | \(0.893325\pi\) | |||||||
\(752\) | −150.414 | −0.200018 | ||||||||
\(753\) | 159.330 | 0.211594 | ||||||||
\(754\) | 9.32701 | 0.0123700 | ||||||||
\(755\) | − | 1171.48i | − | 1.55164i | ||||||
\(756\) | −30.9012 | −0.0408746 | ||||||||
\(757\) | − | 933.164i | − | 1.23271i | −0.787467 | − | 0.616357i | \(-0.788608\pi\) | ||
0.787467 | − | 0.616357i | \(-0.211392\pi\) | |||||||
\(758\) | 374.136 | 0.493583 | ||||||||
\(759\) | −10.0293 | −0.0132138 | ||||||||
\(760\) | 335.945 | 0.442034 | ||||||||
\(761\) | 547.932 | 0.720016 | 0.360008 | − | 0.932949i | \(-0.382774\pi\) | ||||
0.360008 | + | 0.932949i | \(0.382774\pi\) | |||||||
\(762\) | 234.083 | 0.307195 | ||||||||
\(763\) | −280.139 | −0.367155 | ||||||||
\(764\) | − | 30.9196i | − | 0.0404707i | ||||||
\(765\) | − | 52.9293i | − | 0.0691887i | ||||||
\(766\) | −176.533 | −0.230461 | ||||||||
\(767\) | 1044.12i | 1.36130i | ||||||||
\(768\) | 166.548i | 0.216860i | ||||||||
\(769\) | − | 1154.35i | − | 1.50111i | −0.660807 | − | 0.750556i | \(-0.729786\pi\) | ||
0.660807 | − | 0.750556i | \(-0.270214\pi\) | |||||||
\(770\) | −6.08202 | −0.00789872 | ||||||||
\(771\) | 379.656i | 0.492421i | ||||||||
\(772\) | 831.525 | 1.07710 | ||||||||
\(773\) | 1283.57 | 1.66050 | 0.830252 | − | 0.557389i | \(-0.188197\pi\) | ||||
0.830252 | + | 0.557389i | \(0.188197\pi\) | |||||||
\(774\) | −39.1137 | −0.0505344 | ||||||||
\(775\) | 1677.04i | 2.16392i | ||||||||
\(776\) | −60.6400 | −0.0781443 | ||||||||
\(777\) | 68.3758 | 0.0879997 | ||||||||
\(778\) | − | 463.073i | − | 0.595210i | ||||||
\(779\) | − | 273.891i | − | 0.351593i | ||||||
\(780\) | − | 454.901i | − | 0.583206i | ||||||
\(781\) | − | 53.6304i | − | 0.0686688i | ||||||
\(782\) | 22.5535i | 0.0288408i | ||||||||
\(783\) | 5.63223i | 0.00719314i | ||||||||
\(784\) | 351.800 | 0.448725 | ||||||||
\(785\) | − | 1091.09i | − | 1.38993i | ||||||
\(786\) | 239.591 | 0.304823 | ||||||||
\(787\) | − | 765.804i | − | 0.973068i | −0.873662 | − | 0.486534i | \(-0.838261\pi\) | ||
0.873662 | − | 0.486534i | \(-0.161739\pi\) | |||||||
\(788\) | 736.280i | 0.934366i | ||||||||
\(789\) | 13.6423i | 0.0172907i | ||||||||
\(790\) | 292.494i | 0.370246i | ||||||||
\(791\) | −303.156 | −0.383257 | ||||||||
\(792\) | 9.05781 | 0.0114366 | ||||||||
\(793\) | −1097.83 | −1.38440 | ||||||||
\(794\) | 309.073i | 0.389261i | ||||||||
\(795\) | 408.491i | 0.513825i | ||||||||
\(796\) | 556.638 | 0.699295 | ||||||||
\(797\) | 1056.70 | 1.32584 | 0.662922 | − | 0.748688i | \(-0.269316\pi\) | ||||
0.662922 | + | 0.748688i | \(0.269316\pi\) | |||||||
\(798\) | 18.1850i | 0.0227883i | ||||||||
\(799\) | 42.9191 | 0.0537160 | ||||||||
\(800\) | 1244.76i | 1.55595i | ||||||||
\(801\) | 179.391 | 0.223959 | ||||||||
\(802\) | −526.023 | −0.655889 | ||||||||
\(803\) | 3.73107i | 0.00464641i | ||||||||
\(804\) | 213.764 | − | 312.587i | 0.265875 | − | 0.388790i | ||||
\(805\) | 174.936 | 0.217312 | ||||||||
\(806\) | − | 365.745i | − | 0.453778i | ||||||
\(807\) | 539.756i | 0.668842i | ||||||||
\(808\) | −508.767 | −0.629662 | ||||||||
\(809\) | 1507.68i | 1.86363i | 0.362935 | + | 0.931814i | \(0.381775\pi\) | ||||
−0.362935 | + | 0.931814i | \(0.618225\pi\) | |||||||
\(810\) | −62.0209 | −0.0765691 | ||||||||
\(811\) | − | 1241.66i | − | 1.53102i | −0.643425 | − | 0.765509i | \(-0.722487\pi\) | ||
0.643425 | − | 0.765509i | \(-0.277513\pi\) | |||||||
\(812\) | 6.44602i | 0.00793845i | ||||||||
\(813\) | −276.236 | −0.339773 | ||||||||
\(814\) | −9.00469 | −0.0110623 | ||||||||
\(815\) | 1829.72i | 2.24505i | ||||||||
\(816\) | 29.3148i | 0.0359250i | ||||||||
\(817\) | − | 101.949i | − | 0.124785i | ||||||
\(818\) | −297.285 | −0.363429 | ||||||||
\(819\) | 54.8081 | 0.0669207 | ||||||||
\(820\) | 1069.09 | 1.30376 | ||||||||
\(821\) | 244.688 | 0.298037 | 0.149018 | − | 0.988834i | \(-0.452389\pi\) | ||||
0.149018 | + | 0.988834i | \(0.452389\pi\) | |||||||
\(822\) | 243.864i | 0.296672i | ||||||||
\(823\) | 616.466 | 0.749048 | 0.374524 | − | 0.927217i | \(-0.377806\pi\) | ||||
0.374524 | + | 0.927217i | \(0.377806\pi\) | |||||||
\(824\) | 250.721i | 0.304273i | ||||||||
\(825\) | 33.0960 | 0.0401164 | ||||||||
\(826\) | 162.923 | 0.197243 | ||||||||
\(827\) | −962.213 | −1.16350 | −0.581749 | − | 0.813368i | \(-0.697631\pi\) | ||||
−0.581749 | + | 0.813368i | \(0.697631\pi\) | |||||||
\(828\) | −117.050 | −0.141365 | ||||||||
\(829\) | −133.378 | −0.160890 | −0.0804450 | − | 0.996759i | \(-0.525634\pi\) | ||||
−0.0804450 | + | 0.996759i | \(0.525634\pi\) | |||||||
\(830\) | 542.029 | 0.653047 | ||||||||
\(831\) | 218.562i | 0.263011i | ||||||||
\(832\) | 37.3611i | 0.0449051i | ||||||||
\(833\) | −100.383 | −0.120508 | ||||||||
\(834\) | 226.136i | 0.271146i | ||||||||
\(835\) | 2557.11i | 3.06240i | ||||||||
\(836\) | 10.6071i | 0.0126879i | ||||||||
\(837\) | 220.860 | 0.263871 | ||||||||
\(838\) | 351.293i | 0.419204i | ||||||||
\(839\) | −575.860 | −0.686365 | −0.343183 | − | 0.939269i | \(-0.611505\pi\) | ||||
−0.343183 | + | 0.939269i | \(0.611505\pi\) | |||||||
\(840\) | −157.991 | −0.188084 | ||||||||
\(841\) | −839.825 | −0.998603 | ||||||||
\(842\) | 336.758i | 0.399951i | ||||||||
\(843\) | 414.120 | 0.491246 | ||||||||
\(844\) | −707.748 | −0.838564 | ||||||||
\(845\) | − | 549.965i | − | 0.650846i | ||||||
\(846\) | − | 50.2913i | − | 0.0594459i | ||||||
\(847\) | 220.084i | 0.259839i | ||||||||
\(848\) | − | 226.242i | − | 0.266795i | ||||||
\(849\) | 348.827i | 0.410868i | ||||||||
\(850\) | − | 74.4250i | − | 0.0875588i | ||||||
\(851\) | 259.000 | 0.304348 | ||||||||
\(852\) | − | 625.911i | − | 0.734637i | ||||||
\(853\) | −178.625 | −0.209408 | −0.104704 | − | 0.994503i | \(-0.533389\pi\) | ||||
−0.104704 | + | 0.994503i | \(0.533389\pi\) | |||||||
\(854\) | 171.304i | 0.200590i | ||||||||
\(855\) | − | 161.657i | − | 0.189073i | ||||||
\(856\) | 507.343i | 0.592690i | ||||||||
\(857\) | − | 1266.31i | − | 1.47761i | −0.673918 | − | 0.738806i | \(-0.735390\pi\) | ||
0.673918 | − | 0.738806i | \(-0.264610\pi\) | |||||||
\(858\) | −7.21790 | −0.00841247 | ||||||||
\(859\) | −116.665 | −0.135815 | −0.0679076 | − | 0.997692i | \(-0.521632\pi\) | ||||
−0.0679076 | + | 0.997692i | \(0.521632\pi\) | |||||||
\(860\) | 397.942 | 0.462723 | ||||||||
\(861\) | 128.807i | 0.149602i | ||||||||
\(862\) | − | 74.1089i | − | 0.0859733i | ||||||
\(863\) | −820.416 | −0.950656 | −0.475328 | − | 0.879809i | \(-0.657671\pi\) | ||||
−0.475328 | + | 0.879809i | \(0.657671\pi\) | |||||||
\(864\) | 163.930 | 0.189734 | ||||||||
\(865\) | 1498.11i | 1.73192i | ||||||||
\(866\) | 196.549 | 0.226962 | ||||||||
\(867\) | 492.198i | 0.567702i | ||||||||
\(868\) | 252.771 | 0.291211 | ||||||||
\(869\) | −20.5555 | −0.0236542 | ||||||||
\(870\) | 12.9376i | 0.0148708i | ||||||||
\(871\) | −379.143 | + | 554.423i | −0.435297 | + | 0.636536i | ||||
\(872\) | 958.350 | 1.09903 | ||||||||
\(873\) | 29.1800i | 0.0334249i | ||||||||
\(874\) | 68.8831i | 0.0788136i | ||||||||
\(875\) | −211.500 | −0.241715 | ||||||||
\(876\) | 43.5446i | 0.0497085i | ||||||||
\(877\) | −157.796 | −0.179927 | −0.0899637 | − | 0.995945i | \(-0.528675\pi\) | ||||
−0.0899637 | + | 0.995945i | \(0.528675\pi\) | |||||||
\(878\) | − | 548.821i | − | 0.625081i | ||||||
\(879\) | − | 28.5071i | − | 0.0324313i | ||||||
\(880\) | −29.9446 | −0.0340279 | ||||||||
\(881\) | 1255.19 | 1.42474 | 0.712368 | − | 0.701807i | \(-0.247623\pi\) | ||||
0.712368 | + | 0.701807i | \(0.247623\pi\) | |||||||
\(882\) | 117.626i | 0.133362i | ||||||||
\(883\) | 91.7520i | 0.103909i | 0.998649 | + | 0.0519547i | \(0.0165451\pi\) | ||||
−0.998649 | + | 0.0519547i | \(0.983455\pi\) | |||||||
\(884\) | − | 71.8904i | − | 0.0813240i | ||||||
\(885\) | −1448.31 | −1.63651 | ||||||||
\(886\) | −2.07155 | −0.00233810 | ||||||||
\(887\) | −953.087 | −1.07451 | −0.537253 | − | 0.843421i | \(-0.680538\pi\) | ||||
−0.537253 | + | 0.843421i | \(0.680538\pi\) | |||||||
\(888\) | −233.912 | −0.263415 | ||||||||
\(889\) | − | 286.938i | − | 0.322765i | ||||||
\(890\) | 412.074 | 0.463004 | ||||||||
\(891\) | − | 4.35862i | − | 0.00489183i | ||||||
\(892\) | 895.456 | 1.00387 | ||||||||
\(893\) | 131.084 | 0.146790 | ||||||||
\(894\) | −187.996 | −0.210286 | ||||||||
\(895\) | 1304.60 | 1.45765 | ||||||||
\(896\) | 235.805 | 0.263175 | ||||||||
\(897\) | 207.607 | 0.231446 | ||||||||
\(898\) | − | 761.446i | − | 0.847935i | ||||||
\(899\) | − | 46.0716i | − | 0.0512476i | ||||||
\(900\) | 386.258 | 0.429176 | ||||||||
\(901\) | 64.5560i | 0.0716493i | ||||||||
\(902\) | − | 16.9632i | − | 0.0188062i | ||||||
\(903\) | 47.9454i | 0.0530957i | ||||||||
\(904\) | 1037.09 | 1.14722 | ||||||||
\(905\) | 227.143i | 0.250987i | ||||||||
\(906\) | −216.936 | −0.239444 | ||||||||
\(907\) | −161.062 | −0.177577 | −0.0887885 | − | 0.996051i | \(-0.528300\pi\) | ||||
−0.0887885 | + | 0.996051i | \(0.528300\pi\) | |||||||
\(908\) | −649.436 | −0.715237 | ||||||||
\(909\) | 244.819i | 0.269328i | ||||||||
\(910\) | 125.898 | 0.138350 | ||||||||
\(911\) | 345.660 | 0.379429 | 0.189715 | − | 0.981839i | \(-0.439244\pi\) | ||||
0.189715 | + | 0.981839i | \(0.439244\pi\) | |||||||
\(912\) | 89.5334i | 0.0981726i | ||||||||
\(913\) | 38.0920i | 0.0417217i | ||||||||
\(914\) | − | 174.889i | − | 0.191344i | ||||||
\(915\) | − | 1522.81i | − | 1.66428i | ||||||
\(916\) | 1099.23i | 1.20003i | ||||||||
\(917\) | − | 293.690i | − | 0.320272i | ||||||
\(918\) | −9.80149 | −0.0106770 | ||||||||
\(919\) | − | 1647.79i | − | 1.79302i | −0.443020 | − | 0.896512i | \(-0.646093\pi\) | ||
0.443020 | − | 0.896512i | \(-0.353907\pi\) | |||||||
\(920\) | −598.452 | −0.650492 | ||||||||
\(921\) | 680.712i | 0.739101i | ||||||||
\(922\) | 431.821i | 0.468353i | ||||||||
\(923\) | 1110.15i | 1.20276i | ||||||||
\(924\) | − | 4.98839i | − | 0.00539869i | ||||||
\(925\) | −854.683 | −0.923982 | ||||||||
\(926\) | 502.308 | 0.542449 | ||||||||
\(927\) | 120.647 | 0.130148 | ||||||||
\(928\) | − | 34.1960i | − | 0.0368491i | ||||||
\(929\) | 850.797i | 0.915821i | 0.888998 | + | 0.457910i | \(0.151402\pi\) | ||||
−0.888998 | + | 0.457910i | \(0.848598\pi\) | |||||||
\(930\) | 507.331 | 0.545517 | ||||||||
\(931\) | −306.590 | −0.329313 | ||||||||
\(932\) | 1060.67i | 1.13806i | ||||||||
\(933\) | 91.3680 | 0.0979293 | ||||||||
\(934\) | − | 71.5724i | − | 0.0766300i | ||||||
\(935\) | 8.54440 | 0.00913840 | ||||||||
\(936\) | −187.497 | −0.200318 | ||||||||
\(937\) | 627.669i | 0.669871i | 0.942241 | + | 0.334935i | \(0.108715\pi\) | ||||
−0.942241 | + | 0.334935i | \(0.891285\pi\) | |||||||
\(938\) | 86.5114 | + | 59.1610i | 0.0922297 | + | 0.0630715i | ||||
\(939\) | 413.509 | 0.440372 | ||||||||
\(940\) | 511.663i | 0.544322i | ||||||||
\(941\) | − | 248.878i | − | 0.264482i | −0.991218 | − | 0.132241i | \(-0.957783\pi\) | ||
0.991218 | − | 0.132241i | \(-0.0422173\pi\) | |||||||
\(942\) | −202.050 | −0.214490 | ||||||||
\(943\) | 487.908i | 0.517400i | ||||||||
\(944\) | 802.145 | 0.849730 | ||||||||
\(945\) | 76.0251i | 0.0804499i | ||||||||
\(946\) | − | 6.31413i | − | 0.00667456i | ||||||
\(947\) | 247.947 | 0.261824 | 0.130912 | − | 0.991394i | \(-0.458210\pi\) | ||||
0.130912 | + | 0.991394i | \(0.458210\pi\) | |||||||
\(948\) | −239.900 | −0.253059 | ||||||||
\(949\) | − | 77.2333i | − | 0.0813838i | ||||||
\(950\) | − | 227.309i | − | 0.239273i | ||||||
\(951\) | 173.180i | 0.182103i | ||||||||
\(952\) | −24.9681 | −0.0262270 | ||||||||
\(953\) | −721.778 | −0.757375 | −0.378687 | − | 0.925525i | \(-0.623624\pi\) | ||||
−0.378687 | + | 0.925525i | \(0.623624\pi\) | |||||||
\(954\) | 75.6447 | 0.0792922 | ||||||||
\(955\) | −76.0706 | −0.0796551 | ||||||||
\(956\) | − | 47.8333i | − | 0.0500348i | ||||||
\(957\) | −0.909213 | −0.000950066 | ||||||||
\(958\) | − | 250.780i | − | 0.261775i | ||||||
\(959\) | 298.928 | 0.311708 | ||||||||
\(960\) | −51.8241 | −0.0539835 | ||||||||
\(961\) | −845.632 | −0.879950 | ||||||||
\(962\) | 186.398 | 0.193760 | ||||||||
\(963\) | 244.134 | 0.253514 | ||||||||
\(964\) | 284.117 | 0.294727 | ||||||||
\(965\) | − | 2045.77i | − | 2.11997i | ||||||
\(966\) | − | 32.3948i | − | 0.0335350i | ||||||
\(967\) | 528.165 | 0.546190 | 0.273095 | − | 0.961987i | \(-0.411953\pi\) | ||||
0.273095 | + | 0.961987i | \(0.411953\pi\) | |||||||
\(968\) | − | 752.901i | − | 0.777791i | ||||||
\(969\) | − | 25.5475i | − | 0.0263648i | ||||||
\(970\) | 67.0285i | 0.0691015i | ||||||||
\(971\) | −167.452 | −0.172454 | −0.0862268 | − | 0.996276i | \(-0.527481\pi\) | ||||
−0.0862268 | + | 0.996276i | \(0.527481\pi\) | |||||||
\(972\) | − | 50.8687i | − | 0.0523341i | ||||||
\(973\) | 277.197 | 0.284889 | ||||||||
\(974\) | −108.019 | −0.110902 | ||||||||
\(975\) | −685.089 | −0.702656 | ||||||||
\(976\) | 843.407i | 0.864147i | ||||||||
\(977\) | −1.54853 | −0.00158499 | −0.000792493 | − | 1.00000i | \(-0.500252\pi\) | ||||
−0.000792493 | 1.00000i | \(0.500252\pi\) | ||||||||
\(978\) | 338.828 | 0.346450 | ||||||||
\(979\) | 28.9592i | 0.0295803i | ||||||||
\(980\) | − | 1196.72i | − | 1.22114i | ||||||
\(981\) | − | 461.158i | − | 0.470090i | ||||||
\(982\) | − | 479.631i | − | 0.488422i | ||||||
\(983\) | 257.390i | 0.261842i | 0.991393 | + | 0.130921i | \(0.0417934\pi\) | ||||
−0.991393 | + | 0.130921i | \(0.958207\pi\) | |||||||
\(984\) | − | 440.647i | − | 0.447812i | ||||||
\(985\) | 1811.45 | 1.83903 | ||||||||
\(986\) | 2.04460i | 0.00207363i | ||||||||
\(987\) | −61.6469 | −0.0624589 | ||||||||
\(988\) | − | 219.568i | − | 0.222235i | ||||||
\(989\) | 181.612i | 0.183632i | ||||||||
\(990\) | − | 10.0121i | − | 0.0101132i | ||||||
\(991\) | − | 192.643i | − | 0.194392i | −0.995265 | − | 0.0971961i | \(-0.969013\pi\) | ||
0.995265 | − | 0.0971961i | \(-0.0309874\pi\) | |||||||
\(992\) | −1340.95 | −1.35176 | ||||||||
\(993\) | −851.251 | −0.857252 | ||||||||
\(994\) | 173.227 | 0.174272 | ||||||||
\(995\) | − | 1369.48i | − | 1.37636i | ||||||
\(996\) | 444.565i | 0.446350i | ||||||||
\(997\) | −1386.10 | −1.39027 | −0.695133 | − | 0.718881i | \(-0.744655\pi\) | ||||
−0.695133 | + | 0.718881i | \(0.744655\pi\) | |||||||
\(998\) | 311.567 | 0.312192 | ||||||||
\(999\) | 112.559i | 0.112671i |
(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 | 201.3.b.a.133.10 | ✓ | 22 | |
3.2 | odd | 2 | 603.3.b.e.334.13 | 22 | |||
67.66 | odd | 2 | inner | 201.3.b.a.133.13 | yes | 22 | |
201.200 | even | 2 | 603.3.b.e.334.10 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.3.b.a.133.10 | ✓ | 22 | 1.1 | even | 1 | trivial | |
201.3.b.a.133.13 | yes | 22 | 67.66 | odd | 2 | inner | |
603.3.b.e.334.10 | 22 | 201.200 | even | 2 | |||
603.3.b.e.334.13 | 22 | 3.2 | odd | 2 |