Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,4,Mod(51,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.51");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.e (of order \(3\), degree \(2\), 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: | \(10.3253342510\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 51.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.51 |
Dual form | 175.4.e.a.151.1 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | −0.633316 | − | 0.773893i | \(-0.718307\pi\) |
0.986869 | + | 0.161521i | \(0.0516399\pi\) | |||||||
\(3\) | 3.50000 | + | 6.06218i | 0.673575 | + | 1.16667i | 0.976883 | + | 0.213774i | \(0.0685756\pi\) |
−0.303308 | + | 0.952893i | \(0.598091\pi\) | |||||||
\(4\) | 2.00000 | + | 3.46410i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 14.0000 | 0.952579 | ||||||||
\(7\) | −14.0000 | + | 12.1244i | −0.755929 | + | 0.654654i | ||||
\(8\) | 24.0000 | 1.06066 | ||||||||
\(9\) | −11.0000 | + | 19.0526i | −0.407407 | + | 0.705650i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | + | 4.33013i | 0.0685253 | + | 0.118689i | 0.898252 | − | 0.439480i | \(-0.144837\pi\) |
−0.829727 | + | 0.558169i | \(0.811504\pi\) | |||||||
\(12\) | −14.0000 | + | 24.2487i | −0.336788 | + | 0.583333i | ||||
\(13\) | 14.0000 | 0.298685 | 0.149342 | − | 0.988786i | \(-0.452284\pi\) | ||||
0.149342 | + | 0.988786i | \(0.452284\pi\) | |||||||
\(14\) | 7.00000 | + | 36.3731i | 0.133631 | + | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.00000 | − | 13.8564i | 0.125000 | − | 0.216506i | ||||
\(17\) | −10.5000 | − | 18.1865i | −0.149801 | − | 0.259464i | 0.781353 | − | 0.624090i | \(-0.214530\pi\) |
−0.931154 | + | 0.364626i | \(0.881197\pi\) | |||||||
\(18\) | 22.0000 | + | 38.1051i | 0.288081 | + | 0.498970i | ||||
\(19\) | −24.5000 | + | 42.4352i | −0.295826 | + | 0.512385i | −0.975177 | − | 0.221429i | \(-0.928928\pi\) |
0.679351 | + | 0.733813i | \(0.262261\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −122.500 | − | 42.4352i | −1.27294 | − | 0.440959i | ||||
\(22\) | 10.0000 | 0.0969094 | ||||||||
\(23\) | −79.5000 | + | 137.698i | −0.720735 | + | 1.24835i | 0.239971 | + | 0.970780i | \(0.422862\pi\) |
−0.960706 | + | 0.277569i | \(0.910471\pi\) | |||||||
\(24\) | 84.0000 | + | 145.492i | 0.714435 | + | 1.23744i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.0000 | − | 24.2487i | 0.105601 | − | 0.182906i | ||||
\(27\) | 35.0000 | 0.249472 | ||||||||
\(28\) | −70.0000 | − | 24.2487i | −0.472456 | − | 0.163663i | ||||
\(29\) | 58.0000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −73.5000 | − | 127.306i | −0.425838 | − | 0.737574i | 0.570660 | − | 0.821186i | \(-0.306687\pi\) |
−0.996498 | + | 0.0836128i | \(0.973354\pi\) | |||||||
\(32\) | 80.0000 | + | 138.564i | 0.441942 | + | 0.765466i | ||||
\(33\) | −17.5000 | + | 30.3109i | −0.0923139 | + | 0.159892i | ||||
\(34\) | −42.0000 | −0.211851 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −88.0000 | −0.407407 | ||||||||
\(37\) | 109.500 | − | 189.660i | 0.486532 | − | 0.842698i | −0.513348 | − | 0.858181i | \(-0.671595\pi\) |
0.999880 | + | 0.0154821i | \(0.00492832\pi\) | |||||||
\(38\) | 49.0000 | + | 84.8705i | 0.209180 | + | 0.362311i | ||||
\(39\) | 49.0000 | + | 84.8705i | 0.201187 | + | 0.348466i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 350.000 | 1.33319 | 0.666595 | − | 0.745420i | \(-0.267751\pi\) | ||||
0.666595 | + | 0.745420i | \(0.267751\pi\) | |||||||
\(42\) | −196.000 | + | 169.741i | −0.720082 | + | 0.623610i | ||||
\(43\) | 124.000 | 0.439763 | 0.219882 | − | 0.975527i | \(-0.429433\pi\) | ||||
0.219882 | + | 0.975527i | \(0.429433\pi\) | |||||||
\(44\) | −10.0000 | + | 17.3205i | −0.0342627 | + | 0.0593447i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 159.000 | + | 275.396i | 0.509636 | + | 0.882716i | ||||
\(47\) | 262.500 | − | 454.663i | 0.814671 | − | 1.41105i | −0.0948921 | − | 0.995488i | \(-0.530251\pi\) |
0.909564 | − | 0.415565i | \(-0.136416\pi\) | |||||||
\(48\) | 112.000 | 0.336788 | ||||||||
\(49\) | 49.0000 | − | 339.482i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 73.5000 | − | 127.306i | 0.201805 | − | 0.349537i | ||||
\(52\) | 28.0000 | + | 48.4974i | 0.0746712 | + | 0.129334i | ||||
\(53\) | 151.500 | + | 262.406i | 0.392644 | + | 0.680079i | 0.992797 | − | 0.119806i | \(-0.0382272\pi\) |
−0.600153 | + | 0.799885i | \(0.704894\pi\) | |||||||
\(54\) | 35.0000 | − | 60.6218i | 0.0882018 | − | 0.152770i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −336.000 | + | 290.985i | −0.801784 | + | 0.694365i | ||||
\(57\) | −343.000 | −0.797043 | ||||||||
\(58\) | 58.0000 | − | 100.459i | 0.131306 | − | 0.227429i | ||||
\(59\) | 52.5000 | + | 90.9327i | 0.115846 | + | 0.200651i | 0.918118 | − | 0.396308i | \(-0.129709\pi\) |
−0.802272 | + | 0.596959i | \(0.796375\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 206.500 | − | 357.668i | 0.433436 | − | 0.750734i | −0.563730 | − | 0.825959i | \(-0.690634\pi\) |
0.997167 | + | 0.0752252i | \(0.0239676\pi\) | |||||||
\(62\) | −294.000 | −0.602226 | ||||||||
\(63\) | −77.0000 | − | 400.104i | −0.153986 | − | 0.800132i | ||||
\(64\) | 448.000 | 0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 35.0000 | + | 60.6218i | 0.0652758 | + | 0.113061i | ||||
\(67\) | 207.500 | + | 359.401i | 0.378361 | + | 0.655340i | 0.990824 | − | 0.135159i | \(-0.0431546\pi\) |
−0.612463 | + | 0.790499i | \(0.709821\pi\) | |||||||
\(68\) | 42.0000 | − | 72.7461i | 0.0749007 | − | 0.129732i | ||||
\(69\) | −1113.00 | −1.94188 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −432.000 | −0.722098 | −0.361049 | − | 0.932547i | \(-0.617581\pi\) | ||||
−0.361049 | + | 0.932547i | \(0.617581\pi\) | |||||||
\(72\) | −264.000 | + | 457.261i | −0.432121 | + | 0.748455i | ||||
\(73\) | −556.500 | − | 963.886i | −0.892238 | − | 1.54540i | −0.837186 | − | 0.546919i | \(-0.815801\pi\) |
−0.0550526 | − | 0.998483i | \(-0.517533\pi\) | |||||||
\(74\) | −219.000 | − | 379.319i | −0.344030 | − | 0.595878i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −196.000 | −0.295826 | ||||||||
\(77\) | −87.5000 | − | 30.3109i | −0.129501 | − | 0.0448603i | ||||
\(78\) | 196.000 | 0.284521 | ||||||||
\(79\) | 51.5000 | − | 89.2006i | 0.0733443 | − | 0.127036i | −0.827021 | − | 0.562171i | \(-0.809966\pi\) |
0.900365 | + | 0.435135i | \(0.143299\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 419.500 | + | 726.595i | 0.575446 | + | 0.996701i | ||||
\(82\) | 350.000 | − | 606.218i | 0.471354 | − | 0.816409i | ||||
\(83\) | −1092.00 | −1.44413 | −0.722064 | − | 0.691827i | \(-0.756806\pi\) | ||||
−0.722064 | + | 0.691827i | \(0.756806\pi\) | |||||||
\(84\) | −98.0000 | − | 509.223i | −0.127294 | − | 0.661438i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 124.000 | − | 214.774i | 0.155480 | − | 0.269299i | ||||
\(87\) | 203.000 | + | 351.606i | 0.250160 | + | 0.433289i | ||||
\(88\) | 60.0000 | + | 103.923i | 0.0726821 | + | 0.125889i | ||||
\(89\) | 164.500 | − | 284.922i | 0.195921 | − | 0.339345i | −0.751281 | − | 0.659982i | \(-0.770564\pi\) |
0.947202 | + | 0.320637i | \(0.103897\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −196.000 | + | 169.741i | −0.225784 | + | 0.195535i | ||||
\(92\) | −636.000 | −0.720735 | ||||||||
\(93\) | 514.500 | − | 891.140i | 0.573668 | − | 0.993623i | ||||
\(94\) | −525.000 | − | 909.327i | −0.576060 | − | 0.997765i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −560.000 | + | 969.948i | −0.595362 | + | 1.03120i | ||||
\(97\) | 882.000 | 0.923232 | 0.461616 | − | 0.887080i | \(-0.347270\pi\) | ||||
0.461616 | + | 0.887080i | \(0.347270\pi\) | |||||||
\(98\) | −539.000 | − | 424.352i | −0.555584 | − | 0.437409i | ||||
\(99\) | −110.000 | −0.111671 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −689.500 | − | 1194.25i | −0.679285 | − | 1.17656i | −0.975196 | − | 0.221341i | \(-0.928957\pi\) |
0.295911 | − | 0.955215i | \(-0.404377\pi\) | |||||||
\(102\) | −147.000 | − | 254.611i | −0.142698 | − | 0.247160i | ||||
\(103\) | −339.500 | + | 588.031i | −0.324776 | + | 0.562529i | −0.981467 | − | 0.191631i | \(-0.938622\pi\) |
0.656691 | + | 0.754160i | \(0.271956\pi\) | |||||||
\(104\) | 336.000 | 0.316803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 606.000 | 0.555282 | ||||||||
\(107\) | 228.500 | − | 395.774i | 0.206448 | − | 0.357578i | −0.744145 | − | 0.668018i | \(-0.767143\pi\) |
0.950593 | + | 0.310440i | \(0.100476\pi\) | |||||||
\(108\) | 70.0000 | + | 121.244i | 0.0623681 | + | 0.108025i | ||||
\(109\) | 562.500 | + | 974.279i | 0.494291 | + | 0.856137i | 0.999978 | − | 0.00657959i | \(-0.00209436\pi\) |
−0.505687 | + | 0.862717i | \(0.668761\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1533.00 | 1.31086 | ||||||||
\(112\) | 56.0000 | + | 290.985i | 0.0472456 | + | 0.245495i | ||||
\(113\) | 1538.00 | 1.28038 | 0.640190 | − | 0.768217i | \(-0.278856\pi\) | ||||
0.640190 | + | 0.768217i | \(0.278856\pi\) | |||||||
\(114\) | −343.000 | + | 594.093i | −0.281797 | + | 0.488087i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 116.000 | + | 200.918i | 0.0928477 | + | 0.160817i | ||||
\(117\) | −154.000 | + | 266.736i | −0.121686 | + | 0.210767i | ||||
\(118\) | 210.000 | 0.163831 | ||||||||
\(119\) | 367.500 | + | 127.306i | 0.283098 | + | 0.0980680i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 653.000 | − | 1131.03i | 0.490609 | − | 0.849759i | ||||
\(122\) | −413.000 | − | 715.337i | −0.306486 | − | 0.530849i | ||||
\(123\) | 1225.00 | + | 2121.76i | 0.898004 | + | 1.55539i | ||||
\(124\) | 294.000 | − | 509.223i | 0.212919 | − | 0.368787i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −770.000 | − | 266.736i | −0.544421 | − | 0.188593i | ||||
\(127\) | −72.0000 | −0.0503068 | −0.0251534 | − | 0.999684i | \(-0.508007\pi\) | ||||
−0.0251534 | + | 0.999684i | \(0.508007\pi\) | |||||||
\(128\) | −192.000 | + | 332.554i | −0.132583 | + | 0.229640i | ||||
\(129\) | 434.000 | + | 751.710i | 0.296214 | + | 0.513057i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1074.50 | + | 1861.09i | −0.716637 | + | 1.24125i | 0.245687 | + | 0.969349i | \(0.420986\pi\) |
−0.962325 | + | 0.271903i | \(0.912347\pi\) | |||||||
\(132\) | −140.000 | −0.0923139 | ||||||||
\(133\) | −171.500 | − | 891.140i | −0.111812 | − | 0.580990i | ||||
\(134\) | 830.000 | 0.535083 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −252.000 | − | 436.477i | −0.158888 | − | 0.275203i | ||||
\(137\) | −562.500 | − | 974.279i | −0.350786 | − | 0.607578i | 0.635602 | − | 0.772017i | \(-0.280752\pi\) |
−0.986387 | + | 0.164439i | \(0.947419\pi\) | |||||||
\(138\) | −1113.00 | + | 1927.77i | −0.686557 | + | 1.18915i | ||||
\(139\) | 252.000 | 0.153772 | 0.0768862 | − | 0.997040i | \(-0.475502\pi\) | ||||
0.0768862 | + | 0.997040i | \(0.475502\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3675.00 | 2.19497 | ||||||||
\(142\) | −432.000 | + | 748.246i | −0.255300 | + | 0.442193i | ||||
\(143\) | 35.0000 | + | 60.6218i | 0.0204675 | + | 0.0354507i | ||||
\(144\) | 176.000 | + | 304.841i | 0.101852 | + | 0.176413i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2226.00 | −1.26182 | ||||||||
\(147\) | 2229.50 | − | 891.140i | 1.25093 | − | 0.500000i | ||||
\(148\) | 876.000 | 0.486532 | ||||||||
\(149\) | 100.500 | − | 174.071i | 0.0552569 | − | 0.0957078i | −0.837074 | − | 0.547090i | \(-0.815736\pi\) |
0.892331 | + | 0.451382i | \(0.149069\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −809.500 | − | 1402.10i | −0.436266 | − | 0.755635i | 0.561132 | − | 0.827726i | \(-0.310366\pi\) |
−0.997398 | + | 0.0720914i | \(0.977033\pi\) | |||||||
\(152\) | −588.000 | + | 1018.45i | −0.313770 | + | 0.543466i | ||||
\(153\) | 462.000 | 0.244121 | ||||||||
\(154\) | −140.000 | + | 121.244i | −0.0732566 | + | 0.0634421i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −196.000 | + | 339.482i | −0.100593 | + | 0.174233i | ||||
\(157\) | 339.500 | + | 588.031i | 0.172580 | + | 0.298917i | 0.939321 | − | 0.343039i | \(-0.111456\pi\) |
−0.766741 | + | 0.641956i | \(0.778123\pi\) | |||||||
\(158\) | −103.000 | − | 178.401i | −0.0518623 | − | 0.0898281i | ||||
\(159\) | −1060.50 | + | 1836.84i | −0.528950 | + | 0.916169i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −556.500 | − | 2891.66i | −0.272412 | − | 1.41549i | ||||
\(162\) | 1678.00 | 0.813803 | ||||||||
\(163\) | −233.500 | + | 404.434i | −0.112203 | + | 0.194342i | −0.916658 | − | 0.399672i | \(-0.869124\pi\) |
0.804455 | + | 0.594014i | \(0.202457\pi\) | |||||||
\(164\) | 700.000 | + | 1212.44i | 0.333298 | + | 0.577288i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1092.00 | + | 1891.40i | −0.510576 | + | 0.884344i | ||||
\(167\) | −1204.00 | −0.557894 | −0.278947 | − | 0.960306i | \(-0.589985\pi\) | ||||
−0.278947 | + | 0.960306i | \(0.589985\pi\) | |||||||
\(168\) | −2940.00 | − | 1018.45i | −1.35015 | − | 0.467707i | ||||
\(169\) | −2001.00 | −0.910787 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −539.000 | − | 933.575i | −0.241043 | − | 0.417499i | ||||
\(172\) | 248.000 | + | 429.549i | 0.109941 | + | 0.190423i | ||||
\(173\) | −1410.50 | + | 2443.06i | −0.619875 | + | 1.07365i | 0.369633 | + | 0.929178i | \(0.379483\pi\) |
−0.989508 | + | 0.144477i | \(0.953850\pi\) | |||||||
\(174\) | 812.000 | 0.353779 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 80.0000 | 0.0342627 | ||||||||
\(177\) | −367.500 | + | 636.529i | −0.156062 | + | 0.270307i | ||||
\(178\) | −329.000 | − | 569.845i | −0.138537 | − | 0.239953i | ||||
\(179\) | 1626.50 | + | 2817.18i | 0.679164 | + | 1.17635i | 0.975233 | + | 0.221180i | \(0.0709907\pi\) |
−0.296069 | + | 0.955166i | \(0.595676\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1582.00 | 0.649664 | 0.324832 | − | 0.945772i | \(-0.394692\pi\) | ||||
0.324832 | + | 0.945772i | \(0.394692\pi\) | |||||||
\(182\) | 98.0000 | + | 509.223i | 0.0399134 | + | 0.207396i | ||||
\(183\) | 2891.00 | 1.16781 | ||||||||
\(184\) | −1908.00 | + | 3304.75i | −0.764454 | + | 1.32407i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1029.00 | − | 1782.28i | −0.405645 | − | 0.702597i | ||||
\(187\) | 52.5000 | − | 90.9327i | 0.0205304 | − | 0.0355597i | ||||
\(188\) | 2100.00 | 0.814671 | ||||||||
\(189\) | −490.000 | + | 424.352i | −0.188583 | + | 0.163318i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1278.50 | + | 2214.43i | −0.484340 | + | 0.838902i | −0.999838 | − | 0.0179887i | \(-0.994274\pi\) |
0.515498 | + | 0.856891i | \(0.327607\pi\) | |||||||
\(192\) | 1568.00 | + | 2715.86i | 0.589378 | + | 1.02083i | ||||
\(193\) | −198.500 | − | 343.812i | −0.0740329 | − | 0.128229i | 0.826632 | − | 0.562742i | \(-0.190254\pi\) |
−0.900665 | + | 0.434514i | \(0.856920\pi\) | |||||||
\(194\) | 882.000 | − | 1527.67i | 0.326412 | − | 0.565362i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1274.00 | − | 509.223i | 0.464286 | − | 0.185577i | ||||
\(197\) | −2914.00 | −1.05388 | −0.526939 | − | 0.849903i | \(-0.676660\pi\) | ||||
−0.526939 | + | 0.849903i | \(0.676660\pi\) | |||||||
\(198\) | −110.000 | + | 190.526i | −0.0394816 | + | 0.0683842i | ||||
\(199\) | −1669.50 | − | 2891.66i | −0.594712 | − | 1.03007i | −0.993587 | − | 0.113066i | \(-0.963933\pi\) |
0.398875 | − | 0.917005i | \(-0.369401\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1452.50 | + | 2515.80i | −0.509709 | + | 0.882841i | ||||
\(202\) | −2758.00 | −0.960654 | ||||||||
\(203\) | −812.000 | + | 703.213i | −0.280745 | + | 0.243132i | ||||
\(204\) | 588.000 | 0.201805 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 679.000 | + | 1176.06i | 0.229651 | + | 0.397768i | ||||
\(207\) | −1749.00 | − | 3029.36i | −0.587265 | − | 1.01717i | ||||
\(208\) | 112.000 | − | 193.990i | 0.0373356 | − | 0.0646671i | ||||
\(209\) | −245.000 | −0.0810861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1780.00 | 0.580759 | 0.290380 | − | 0.956911i | \(-0.406218\pi\) | ||||
0.290380 | + | 0.956911i | \(0.406218\pi\) | |||||||
\(212\) | −606.000 | + | 1049.62i | −0.196322 | + | 0.340040i | ||||
\(213\) | −1512.00 | − | 2618.86i | −0.486387 | − | 0.842448i | ||||
\(214\) | −457.000 | − | 791.547i | −0.145981 | − | 0.252846i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 840.000 | 0.264605 | ||||||||
\(217\) | 2572.50 | + | 891.140i | 0.804759 | + | 0.278777i | ||||
\(218\) | 2250.00 | 0.699033 | ||||||||
\(219\) | 3895.50 | − | 6747.20i | 1.20198 | − | 2.08189i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −147.000 | − | 254.611i | −0.0447434 | − | 0.0774978i | ||||
\(222\) | 1533.00 | − | 2655.23i | 0.463460 | − | 0.802737i | ||||
\(223\) | 1400.00 | 0.420408 | 0.210204 | − | 0.977658i | \(-0.432587\pi\) | ||||
0.210204 | + | 0.977658i | \(0.432587\pi\) | |||||||
\(224\) | −2800.00 | − | 969.948i | −0.835191 | − | 0.289319i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1538.00 | − | 2663.89i | 0.452682 | − | 0.784069i | ||||
\(227\) | −1102.50 | − | 1909.59i | −0.322359 | − | 0.558342i | 0.658615 | − | 0.752480i | \(-0.271142\pi\) |
−0.980974 | + | 0.194138i | \(0.937809\pi\) | |||||||
\(228\) | −686.000 | − | 1188.19i | −0.199261 | − | 0.345130i | ||||
\(229\) | −143.500 | + | 248.549i | −0.0414094 | + | 0.0717231i | −0.885987 | − | 0.463710i | \(-0.846518\pi\) |
0.844578 | + | 0.535433i | \(0.179851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −122.500 | − | 636.529i | −0.0348914 | − | 0.181301i | ||||
\(232\) | 1392.00 | 0.393919 | ||||||||
\(233\) | 2293.50 | − | 3972.46i | 0.644859 | − | 1.11693i | −0.339475 | − | 0.940615i | \(-0.610249\pi\) |
0.984334 | − | 0.176314i | \(-0.0564173\pi\) | |||||||
\(234\) | 308.000 | + | 533.472i | 0.0860453 | + | 0.149035i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −210.000 | + | 363.731i | −0.0579230 | + | 0.100326i | ||||
\(237\) | 721.000 | 0.197612 | ||||||||
\(238\) | 588.000 | − | 509.223i | 0.160144 | − | 0.138689i | ||||
\(239\) | 1668.00 | 0.451439 | 0.225720 | − | 0.974192i | \(-0.427527\pi\) | ||||
0.225720 | + | 0.974192i | \(0.427527\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1704.50 | + | 2952.28i | 0.455587 | + | 0.789100i | 0.998722 | − | 0.0505456i | \(-0.0160960\pi\) |
−0.543135 | + | 0.839646i | \(0.682763\pi\) | |||||||
\(242\) | −1306.00 | − | 2262.06i | −0.346913 | − | 0.600870i | ||||
\(243\) | −2464.00 | + | 4267.77i | −0.650476 | + | 1.12666i | ||||
\(244\) | 1652.00 | 0.433436 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4900.00 | 1.26997 | ||||||||
\(247\) | −343.000 | + | 594.093i | −0.0883586 | + | 0.153042i | ||||
\(248\) | −1764.00 | − | 3055.34i | −0.451670 | − | 0.782315i | ||||
\(249\) | −3822.00 | − | 6619.90i | −0.972729 | − | 1.68482i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4760.00 | −1.19701 | −0.598503 | − | 0.801121i | \(-0.704238\pi\) | ||||
−0.598503 | + | 0.801121i | \(0.704238\pi\) | |||||||
\(252\) | 1232.00 | − | 1066.94i | 0.307971 | − | 0.266711i | ||||
\(253\) | −795.000 | −0.197554 | ||||||||
\(254\) | −72.0000 | + | 124.708i | −0.0177861 | + | 0.0308065i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2176.00 | + | 3768.94i | 0.531250 | + | 0.920152i | ||||
\(257\) | −402.500 | + | 697.150i | −0.0976936 | + | 0.169210i | −0.910730 | − | 0.413003i | \(-0.864480\pi\) |
0.813036 | + | 0.582213i | \(0.197813\pi\) | |||||||
\(258\) | 1736.00 | 0.418909 | ||||||||
\(259\) | 766.500 | + | 3982.85i | 0.183892 | + | 0.955530i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −638.000 | + | 1105.05i | −0.151307 | + | 0.262072i | ||||
\(262\) | 2149.00 | + | 3722.18i | 0.506739 | + | 0.877698i | ||||
\(263\) | −128.500 | − | 222.569i | −0.0301279 | − | 0.0521831i | 0.850568 | − | 0.525865i | \(-0.176258\pi\) |
−0.880696 | + | 0.473681i | \(0.842925\pi\) | |||||||
\(264\) | −420.000 | + | 727.461i | −0.0979137 | + | 0.169591i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1715.00 | − | 594.093i | −0.395314 | − | 0.136941i | ||||
\(267\) | 2303.00 | 0.527870 | ||||||||
\(268\) | −830.000 | + | 1437.60i | −0.189180 | + | 0.327670i | ||||
\(269\) | −1795.50 | − | 3109.90i | −0.406965 | − | 0.704884i | 0.587583 | − | 0.809164i | \(-0.300080\pi\) |
−0.994548 | + | 0.104280i | \(0.966746\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −696.500 | + | 1206.37i | −0.156123 | + | 0.270413i | −0.933467 | − | 0.358662i | \(-0.883233\pi\) |
0.777344 | + | 0.629075i | \(0.216566\pi\) | |||||||
\(272\) | −336.000 | −0.0749007 | ||||||||
\(273\) | −1715.00 | − | 594.093i | −0.380207 | − | 0.131708i | ||||
\(274\) | −2250.00 | −0.496086 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2226.00 | − | 3855.55i | −0.485469 | − | 0.840857i | ||||
\(277\) | 207.500 | + | 359.401i | 0.0450089 | + | 0.0779577i | 0.887652 | − | 0.460514i | \(-0.152335\pi\) |
−0.842643 | + | 0.538472i | \(0.819002\pi\) | |||||||
\(278\) | 252.000 | − | 436.477i | 0.0543667 | − | 0.0941660i | ||||
\(279\) | 3234.00 | 0.693959 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4954.00 | −1.05171 | −0.525856 | − | 0.850574i | \(-0.676255\pi\) | ||||
−0.525856 | + | 0.850574i | \(0.676255\pi\) | |||||||
\(282\) | 3675.00 | − | 6365.29i | 0.776039 | − | 1.34414i | ||||
\(283\) | −2138.50 | − | 3703.99i | −0.449190 | − | 0.778019i | 0.549144 | − | 0.835728i | \(-0.314954\pi\) |
−0.998333 | + | 0.0577087i | \(0.981621\pi\) | |||||||
\(284\) | −864.000 | − | 1496.49i | −0.180525 | − | 0.312678i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 140.000 | 0.0289454 | ||||||||
\(287\) | −4900.00 | + | 4243.52i | −1.00780 | + | 0.872778i | ||||
\(288\) | −3520.00 | −0.720201 | ||||||||
\(289\) | 2236.00 | − | 3872.87i | 0.455119 | − | 0.788289i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3087.00 | + | 5346.84i | 0.621866 | + | 1.07710i | ||||
\(292\) | 2226.00 | − | 3855.55i | 0.446119 | − | 0.772701i | ||||
\(293\) | −7742.00 | −1.54366 | −0.771830 | − | 0.635829i | \(-0.780658\pi\) | ||||
−0.771830 | + | 0.635829i | \(0.780658\pi\) | |||||||
\(294\) | 686.000 | − | 4752.75i | 0.136083 | − | 0.942809i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2628.00 | − | 4551.83i | 0.516045 | − | 0.893817i | ||||
\(297\) | 87.5000 | + | 151.554i | 0.0170952 | + | 0.0296097i | ||||
\(298\) | −201.000 | − | 348.142i | −0.0390725 | − | 0.0676756i | ||||
\(299\) | −1113.00 | + | 1927.77i | −0.215272 | + | 0.372863i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1736.00 | + | 1503.42i | −0.332430 | + | 0.287893i | ||||
\(302\) | −3238.00 | −0.616973 | ||||||||
\(303\) | 4826.50 | − | 8359.74i | 0.915100 | − | 1.58500i | ||||
\(304\) | 392.000 | + | 678.964i | 0.0739564 | + | 0.128096i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 462.000 | − | 800.207i | 0.0863097 | − | 0.149493i | ||||
\(307\) | 7364.00 | 1.36901 | 0.684504 | − | 0.729009i | \(-0.260019\pi\) | ||||
0.684504 | + | 0.729009i | \(0.260019\pi\) | |||||||
\(308\) | −70.0000 | − | 363.731i | −0.0129501 | − | 0.0672905i | ||||
\(309\) | −4753.00 | −0.875044 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4987.50 | − | 8638.60i | −0.909374 | − | 1.57508i | −0.814936 | − | 0.579550i | \(-0.803228\pi\) |
−0.0944372 | − | 0.995531i | \(-0.530105\pi\) | |||||||
\(312\) | 1176.00 | + | 2036.89i | 0.213391 | + | 0.369603i | ||||
\(313\) | −2376.50 | + | 4116.22i | −0.429162 | + | 0.743330i | −0.996799 | − | 0.0799485i | \(-0.974524\pi\) |
0.567637 | + | 0.823279i | \(0.307858\pi\) | |||||||
\(314\) | 1358.00 | 0.244065 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 412.000 | 0.0733443 | ||||||||
\(317\) | −1738.50 | + | 3011.17i | −0.308025 | + | 0.533515i | −0.977930 | − | 0.208932i | \(-0.933001\pi\) |
0.669905 | + | 0.742447i | \(0.266335\pi\) | |||||||
\(318\) | 2121.00 | + | 3673.68i | 0.374024 | + | 0.647829i | ||||
\(319\) | 145.000 | + | 251.147i | 0.0254497 | + | 0.0440801i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3199.00 | 0.556233 | ||||||||
\(322\) | −5565.00 | − | 1927.77i | −0.963122 | − | 0.333635i | ||||
\(323\) | 1029.00 | 0.177260 | ||||||||
\(324\) | −1678.00 | + | 2906.38i | −0.287723 | + | 0.498351i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 467.000 | + | 808.868i | 0.0793397 | + | 0.137420i | ||||
\(327\) | −3937.50 | + | 6819.95i | −0.665885 | + | 1.15335i | ||||
\(328\) | 8400.00 | 1.41406 | ||||||||
\(329\) | 1837.50 | + | 9547.93i | 0.307917 | + | 1.59998i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1670.50 | + | 2893.39i | −0.277399 | + | 0.480469i | −0.970738 | − | 0.240143i | \(-0.922806\pi\) |
0.693339 | + | 0.720612i | \(0.256139\pi\) | |||||||
\(332\) | −2184.00 | − | 3782.80i | −0.361032 | − | 0.625325i | ||||
\(333\) | 2409.00 | + | 4172.51i | 0.396434 | + | 0.686643i | ||||
\(334\) | −1204.00 | + | 2085.39i | −0.197245 | + | 0.341639i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1568.00 | + | 1357.93i | −0.254588 | + | 0.220479i | ||||
\(337\) | −7366.00 | −1.19066 | −0.595329 | − | 0.803482i | \(-0.702978\pi\) | ||||
−0.595329 | + | 0.803482i | \(0.702978\pi\) | |||||||
\(338\) | −2001.00 | + | 3465.83i | −0.322012 | + | 0.557741i | ||||
\(339\) | 5383.00 | + | 9323.63i | 0.862432 | + | 1.49378i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 367.500 | − | 636.529i | 0.0583614 | − | 0.101085i | ||||
\(342\) | −2156.00 | −0.340886 | ||||||||
\(343\) | 3430.00 | + | 5346.84i | 0.539949 | + | 0.841698i | ||||
\(344\) | 2976.00 | 0.466439 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2821.00 | + | 4886.12i | 0.438318 | + | 0.759188i | ||||
\(347\) | 3707.50 | + | 6421.58i | 0.573571 | + | 0.993454i | 0.996195 | + | 0.0871487i | \(0.0277755\pi\) |
−0.422625 | + | 0.906305i | \(0.638891\pi\) | |||||||
\(348\) | −812.000 | + | 1406.43i | −0.125080 | + | 0.216645i | ||||
\(349\) | −3878.00 | −0.594798 | −0.297399 | − | 0.954753i | \(-0.596119\pi\) | ||||
−0.297399 | + | 0.954753i | \(0.596119\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 490.000 | 0.0745136 | ||||||||
\(352\) | −400.000 | + | 692.820i | −0.0605684 | + | 0.104908i | ||||
\(353\) | 633.500 | + | 1097.25i | 0.0955179 | + | 0.165442i | 0.909825 | − | 0.414993i | \(-0.136216\pi\) |
−0.814307 | + | 0.580435i | \(0.802883\pi\) | |||||||
\(354\) | 735.000 | + | 1273.06i | 0.110353 | + | 0.191136i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1316.00 | 0.195921 | ||||||||
\(357\) | 514.500 | + | 2673.42i | 0.0762751 | + | 0.396337i | ||||
\(358\) | 6506.00 | 0.960483 | ||||||||
\(359\) | −2342.50 | + | 4057.33i | −0.344380 | + | 0.596484i | −0.985241 | − | 0.171173i | \(-0.945244\pi\) |
0.640861 | + | 0.767657i | \(0.278578\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2229.00 | + | 3860.74i | 0.324974 | + | 0.562872i | ||||
\(362\) | 1582.00 | − | 2740.10i | 0.229691 | − | 0.397836i | ||||
\(363\) | 9142.00 | 1.32185 | ||||||||
\(364\) | −980.000 | − | 339.482i | −0.141115 | − | 0.0488838i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2891.00 | − | 5007.36i | 0.412882 | − | 0.715133i | ||||
\(367\) | −2320.50 | − | 4019.22i | −0.330052 | − | 0.571667i | 0.652470 | − | 0.757815i | \(-0.273733\pi\) |
−0.982522 | + | 0.186148i | \(0.940400\pi\) | |||||||
\(368\) | 1272.00 | + | 2203.17i | 0.180184 | + | 0.312087i | ||||
\(369\) | −3850.00 | + | 6668.40i | −0.543152 | + | 0.940766i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5302.50 | − | 1836.84i | −0.742027 | − | 0.257046i | ||||
\(372\) | 4116.00 | 0.573668 | ||||||||
\(373\) | −4398.50 | + | 7618.43i | −0.610578 | + | 1.05755i | 0.380565 | + | 0.924754i | \(0.375730\pi\) |
−0.991143 | + | 0.132798i | \(0.957604\pi\) | |||||||
\(374\) | −105.000 | − | 181.865i | −0.0145172 | − | 0.0251445i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6300.00 | − | 10911.9i | 0.864090 | − | 1.49665i | ||||
\(377\) | 812.000 | 0.110929 | ||||||||
\(378\) | 245.000 | + | 1273.06i | 0.0333371 | + | 0.173225i | ||||
\(379\) | 13680.0 | 1.85407 | 0.927037 | − | 0.374969i | \(-0.122347\pi\) | ||||
0.927037 | + | 0.374969i | \(0.122347\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −252.000 | − | 436.477i | −0.0338854 | − | 0.0586913i | ||||
\(382\) | 2557.00 | + | 4428.85i | 0.342480 | + | 0.593193i | ||||
\(383\) | 4882.50 | − | 8456.74i | 0.651395 | − | 1.12825i | −0.331390 | − | 0.943494i | \(-0.607518\pi\) |
0.982785 | − | 0.184755i | \(-0.0591490\pi\) | |||||||
\(384\) | −2688.00 | −0.357217 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −794.000 | −0.104698 | ||||||||
\(387\) | −1364.00 | + | 2362.52i | −0.179163 | + | 0.310319i | ||||
\(388\) | 1764.00 | + | 3055.34i | 0.230808 | + | 0.399771i | ||||
\(389\) | −865.500 | − | 1499.09i | −0.112809 | − | 0.195390i | 0.804093 | − | 0.594504i | \(-0.202651\pi\) |
−0.916902 | + | 0.399113i | \(0.869318\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3339.00 | 0.431868 | ||||||||
\(392\) | 1176.00 | − | 8147.57i | 0.151523 | − | 1.04978i | ||||
\(393\) | −15043.0 | −1.93084 | ||||||||
\(394\) | −2914.00 | + | 5047.20i | −0.372602 | + | 0.645366i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −220.000 | − | 381.051i | −0.0279177 | − | 0.0483549i | ||||
\(397\) | 5491.50 | − | 9511.56i | 0.694233 | − | 1.20245i | −0.276206 | − | 0.961099i | \(-0.589077\pi\) |
0.970439 | − | 0.241348i | \(-0.0775896\pi\) | |||||||
\(398\) | −6678.00 | −0.841050 | ||||||||
\(399\) | 4802.00 | − | 4158.65i | 0.602508 | − | 0.521787i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3301.50 | + | 5718.37i | −0.411145 | + | 0.712124i | −0.995015 | − | 0.0997232i | \(-0.968204\pi\) |
0.583870 | + | 0.811847i | \(0.301538\pi\) | |||||||
\(402\) | 2905.00 | + | 5031.61i | 0.360418 | + | 0.624263i | ||||
\(403\) | −1029.00 | − | 1782.28i | −0.127191 | − | 0.220302i | ||||
\(404\) | 2758.00 | − | 4777.00i | 0.339643 | − | 0.588278i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 406.000 | + | 2109.64i | 0.0496292 | + | 0.257881i | ||||
\(407\) | 1095.00 | 0.133359 | ||||||||
\(408\) | 1764.00 | − | 3055.34i | 0.214047 | − | 0.370740i | ||||
\(409\) | −5477.50 | − | 9487.31i | −0.662213 | − | 1.14699i | −0.980033 | − | 0.198835i | \(-0.936284\pi\) |
0.317820 | − | 0.948151i | \(-0.397049\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3937.50 | − | 6819.95i | 0.472561 | − | 0.818500i | ||||
\(412\) | −2716.00 | −0.324776 | ||||||||
\(413\) | −1837.50 | − | 636.529i | −0.218928 | − | 0.0758391i | ||||
\(414\) | −6996.00 | −0.830518 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1120.00 | + | 1939.90i | 0.132001 | + | 0.228633i | ||||
\(417\) | 882.000 | + | 1527.67i | 0.103577 | + | 0.179401i | ||||
\(418\) | −245.000 | + | 424.352i | −0.0286683 | + | 0.0496549i | ||||
\(419\) | 6636.00 | 0.773723 | 0.386861 | − | 0.922138i | \(-0.373559\pi\) | ||||
0.386861 | + | 0.922138i | \(0.373559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16630.0 | −1.92517 | −0.962585 | − | 0.270980i | \(-0.912652\pi\) | ||||
−0.962585 | + | 0.270980i | \(0.912652\pi\) | |||||||
\(422\) | 1780.00 | − | 3083.05i | 0.205329 | − | 0.355641i | ||||
\(423\) | 5775.00 | + | 10002.6i | 0.663806 | + | 1.14975i | ||||
\(424\) | 3636.00 | + | 6297.74i | 0.416462 | + | 0.721333i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6048.00 | −0.687856 | ||||||||
\(427\) | 1445.50 | + | 7511.04i | 0.163824 | + | 0.851252i | ||||
\(428\) | 1828.00 | 0.206448 | ||||||||
\(429\) | −245.000 | + | 424.352i | −0.0275728 | + | 0.0477574i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2461.50 | − | 4263.44i | −0.275096 | − | 0.476480i | 0.695064 | − | 0.718948i | \(-0.255376\pi\) |
−0.970159 | + | 0.242468i | \(0.922043\pi\) | |||||||
\(432\) | 280.000 | − | 484.974i | 0.0311840 | − | 0.0540123i | ||||
\(433\) | −8974.00 | −0.995988 | −0.497994 | − | 0.867180i | \(-0.665930\pi\) | ||||
−0.497994 | + | 0.867180i | \(0.665930\pi\) | |||||||
\(434\) | 4116.00 | − | 3564.56i | 0.455240 | − | 0.394250i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2250.00 | + | 3897.11i | −0.247146 | + | 0.428069i | ||||
\(437\) | −3895.50 | − | 6747.20i | −0.426423 | − | 0.738587i | ||||
\(438\) | −7791.00 | − | 13494.4i | −0.849928 | − | 1.47212i | ||||
\(439\) | 2089.50 | − | 3619.12i | 0.227167 | − | 0.393465i | −0.729800 | − | 0.683660i | \(-0.760387\pi\) |
0.956967 | + | 0.290195i | \(0.0937203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5929.00 | + | 4667.88i | 0.640212 | + | 0.504036i | ||||
\(442\) | −588.000 | −0.0632767 | ||||||||
\(443\) | −6463.50 | + | 11195.1i | −0.693206 | + | 1.20067i | 0.277576 | + | 0.960704i | \(0.410469\pi\) |
−0.970782 | + | 0.239964i | \(0.922864\pi\) | |||||||
\(444\) | 3066.00 | + | 5310.47i | 0.327716 | + | 0.567621i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1400.00 | − | 2424.87i | 0.148637 | − | 0.257446i | ||||
\(447\) | 1407.00 | 0.148879 | ||||||||
\(448\) | −6272.00 | + | 5431.71i | −0.661438 | + | 0.572822i | ||||
\(449\) | −2826.00 | −0.297032 | −0.148516 | − | 0.988910i | \(-0.547450\pi\) | ||||
−0.148516 | + | 0.988910i | \(0.547450\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 875.000 | + | 1515.54i | 0.0913573 | + | 0.158235i | ||||
\(452\) | 3076.00 | + | 5327.79i | 0.320095 | + | 0.554421i | ||||
\(453\) | 5666.50 | − | 9814.67i | 0.587716 | − | 1.01795i | ||||
\(454\) | −4410.00 | −0.455884 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8232.00 | −0.845392 | ||||||||
\(457\) | 4239.50 | − | 7343.03i | 0.433951 | − | 0.751625i | −0.563259 | − | 0.826281i | \(-0.690453\pi\) |
0.997209 | + | 0.0746560i | \(0.0237859\pi\) | |||||||
\(458\) | 287.000 | + | 497.099i | 0.0292808 | + | 0.0507159i | ||||
\(459\) | −367.500 | − | 636.529i | −0.0373713 | − | 0.0647290i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9338.00 | 0.943414 | 0.471707 | − | 0.881755i | \(-0.343638\pi\) | ||||
0.471707 | + | 0.881755i | \(0.343638\pi\) | |||||||
\(462\) | −1225.00 | − | 424.352i | −0.123360 | − | 0.0427330i | ||||
\(463\) | 4016.00 | 0.403109 | 0.201554 | − | 0.979477i | \(-0.435401\pi\) | ||||
0.201554 | + | 0.979477i | \(0.435401\pi\) | |||||||
\(464\) | 464.000 | − | 803.672i | 0.0464238 | − | 0.0804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4587.00 | − | 7944.92i | −0.455984 | − | 0.789788i | ||||
\(467\) | −2929.50 | + | 5074.04i | −0.290281 | + | 0.502781i | −0.973876 | − | 0.227080i | \(-0.927082\pi\) |
0.683595 | + | 0.729861i | \(0.260415\pi\) | |||||||
\(468\) | −1232.00 | −0.121686 | ||||||||
\(469\) | −7262.50 | − | 2515.80i | −0.715034 | − | 0.247695i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2376.50 | + | 4116.22i | −0.232491 | + | 0.402687i | ||||
\(472\) | 1260.00 | + | 2182.38i | 0.122873 | + | 0.212823i | ||||
\(473\) | 310.000 | + | 536.936i | 0.0301349 | + | 0.0521952i | ||||
\(474\) | 721.000 | − | 1248.81i | 0.0698663 | − | 0.121012i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 294.000 | + | 1527.67i | 0.0283098 | + | 0.147102i | ||||
\(477\) | −6666.00 | −0.639864 | ||||||||
\(478\) | 1668.00 | − | 2889.06i | 0.159608 | − | 0.276449i | ||||
\(479\) | −3251.50 | − | 5631.76i | −0.310156 | − | 0.537206i | 0.668240 | − | 0.743946i | \(-0.267048\pi\) |
−0.978396 | + | 0.206740i | \(0.933715\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1533.00 | − | 2655.23i | 0.145320 | − | 0.251701i | ||||
\(482\) | 6818.00 | 0.644297 | ||||||||
\(483\) | 15582.0 | − | 13494.4i | 1.46792 | − | 1.27126i | ||||
\(484\) | 5224.00 | 0.490609 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4928.00 | + | 8535.55i | 0.459956 | + | 0.796667i | ||||
\(487\) | −8024.50 | − | 13898.8i | −0.746663 | − | 1.29326i | −0.949414 | − | 0.314028i | \(-0.898322\pi\) |
0.202751 | − | 0.979230i | \(-0.435012\pi\) | |||||||
\(488\) | 4956.00 | − | 8584.04i | 0.459729 | − | 0.796273i | ||||
\(489\) | −3269.00 | −0.302309 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8864.00 | 0.814718 | 0.407359 | − | 0.913268i | \(-0.366450\pi\) | ||||
0.407359 | + | 0.913268i | \(0.366450\pi\) | |||||||
\(492\) | −4900.00 | + | 8487.05i | −0.449002 | + | 0.777695i | ||||
\(493\) | −609.000 | − | 1054.82i | −0.0556348 | − | 0.0963624i | ||||
\(494\) | 686.000 | + | 1188.19i | 0.0624789 | + | 0.108217i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2352.00 | −0.212919 | ||||||||
\(497\) | 6048.00 | − | 5237.72i | 0.545855 | − | 0.472724i | ||||
\(498\) | −15288.0 | −1.37565 | ||||||||
\(499\) | 5105.50 | − | 8842.99i | 0.458023 | − | 0.793319i | −0.540833 | − | 0.841130i | \(-0.681891\pi\) |
0.998856 | + | 0.0478104i | \(0.0152243\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4214.00 | − | 7298.86i | −0.375784 | − | 0.650876i | ||||
\(502\) | −4760.00 | + | 8244.56i | −0.423206 | + | 0.733014i | ||||
\(503\) | 1680.00 | 0.148921 | 0.0744607 | − | 0.997224i | \(-0.476276\pi\) | ||||
0.0744607 | + | 0.997224i | \(0.476276\pi\) | |||||||
\(504\) | −1848.00 | − | 9602.49i | −0.163326 | − | 0.848668i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −795.000 | + | 1376.98i | −0.0698460 | + | 0.120977i | ||||
\(507\) | −7003.50 | − | 12130.4i | −0.613484 | − | 1.06259i | ||||
\(508\) | −144.000 | − | 249.415i | −0.0125767 | − | 0.0217835i | ||||
\(509\) | 4728.50 | − | 8190.00i | 0.411762 | − | 0.713193i | −0.583320 | − | 0.812242i | \(-0.698247\pi\) |
0.995083 | + | 0.0990489i | \(0.0315800\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19477.5 | + | 6747.20i | 1.68617 | + | 0.584107i | ||||
\(512\) | 5632.00 | 0.486136 | ||||||||
\(513\) | −857.500 | + | 1485.23i | −0.0738003 | + | 0.127826i | ||||
\(514\) | 805.000 | + | 1394.30i | 0.0690798 | + | 0.119650i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1736.00 | + | 3006.84i | −0.148107 | + | 0.256529i | ||||
\(517\) | 2625.00 | 0.223302 | ||||||||
\(518\) | 7665.00 | + | 2655.23i | 0.650156 | + | 0.225221i | ||||
\(519\) | −19747.0 | −1.67013 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9040.50 | + | 15658.6i | 0.760214 | + | 1.31673i | 0.942740 | + | 0.333528i | \(0.108239\pi\) |
−0.182526 | + | 0.983201i | \(0.558427\pi\) | |||||||
\(522\) | 1276.00 | + | 2210.10i | 0.106990 | + | 0.185313i | ||||
\(523\) | 10188.5 | − | 17647.0i | 0.851839 | − | 1.47543i | −0.0277071 | − | 0.999616i | \(-0.508821\pi\) |
0.879546 | − | 0.475813i | \(-0.157846\pi\) | |||||||
\(524\) | −8596.00 | −0.716637 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −514.000 | −0.0426073 | ||||||||
\(527\) | −1543.50 | + | 2673.42i | −0.127582 | + | 0.220979i | ||||
\(528\) | 280.000 | + | 484.974i | 0.0230785 | + | 0.0399731i | ||||
\(529\) | −6557.00 | − | 11357.1i | −0.538917 | − | 0.933431i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2310.00 | −0.188786 | ||||||||
\(532\) | 2744.00 | − | 2376.37i | 0.223623 | − | 0.193663i | ||||
\(533\) | 4900.00 | 0.398204 | ||||||||
\(534\) | 2303.00 | − | 3988.91i | 0.186630 | − | 0.323253i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4980.00 | + | 8625.61i | 0.401312 | + | 0.695093i | ||||
\(537\) | −11385.5 | + | 19720.3i | −0.914936 | + | 1.58472i | ||||
\(538\) | −7182.00 | −0.575535 | ||||||||
\(539\) | 1592.50 | − | 636.529i | 0.127261 | − | 0.0508668i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3096.50 | − | 5363.30i | 0.246079 | − | 0.426222i | −0.716355 | − | 0.697736i | \(-0.754191\pi\) |
0.962435 | + | 0.271514i | \(0.0875243\pi\) | |||||||
\(542\) | 1393.00 | + | 2412.75i | 0.110396 | + | 0.191211i | ||||
\(543\) | 5537.00 | + | 9590.37i | 0.437597 | + | 0.757941i | ||||
\(544\) | 1680.00 | − | 2909.85i | 0.132407 | − | 0.229336i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2744.00 | + | 2376.37i | −0.215078 | + | 0.186263i | ||||
\(547\) | 18464.0 | 1.44326 | 0.721630 | − | 0.692279i | \(-0.243393\pi\) | ||||
0.721630 | + | 0.692279i | \(0.243393\pi\) | |||||||
\(548\) | 2250.00 | − | 3897.11i | 0.175393 | − | 0.303789i | ||||
\(549\) | 4543.00 | + | 7868.71i | 0.353170 | + | 0.611709i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1421.00 | + | 2461.24i | −0.109867 | + | 0.190295i | ||||
\(552\) | −26712.0 | −2.05967 | ||||||||
\(553\) | 360.500 | + | 1873.21i | 0.0277216 | + | 0.144045i | ||||
\(554\) | 830.000 | 0.0636522 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 504.000 | + | 872.954i | 0.0384431 | + | 0.0665854i | ||||
\(557\) | −4706.50 | − | 8151.90i | −0.358027 | − | 0.620120i | 0.629604 | − | 0.776916i | \(-0.283217\pi\) |
−0.987631 | + | 0.156796i | \(0.949884\pi\) | |||||||
\(558\) | 3234.00 | − | 5601.45i | 0.245351 | − | 0.424961i | ||||
\(559\) | 1736.00 | 0.131351 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 735.000 | 0.0553150 | ||||||||
\(562\) | −4954.00 | + | 8580.58i | −0.371836 | + | 0.644039i | ||||
\(563\) | 1599.50 | + | 2770.42i | 0.119735 | + | 0.207387i | 0.919663 | − | 0.392709i | \(-0.128462\pi\) |
−0.799928 | + | 0.600097i | \(0.795129\pi\) | |||||||
\(564\) | 7350.00 | + | 12730.6i | 0.548743 | + | 0.950450i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8554.00 | −0.635250 | ||||||||
\(567\) | −14682.5 | − | 5086.17i | −1.08749 | − | 0.376718i | ||||
\(568\) | −10368.0 | −0.765901 | ||||||||
\(569\) | −10791.5 | + | 18691.4i | −0.795085 | + | 1.37713i | 0.127701 | + | 0.991813i | \(0.459240\pi\) |
−0.922785 | + | 0.385314i | \(0.874093\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10133.5 | − | 17551.7i | −0.742686 | − | 1.28637i | −0.951268 | − | 0.308365i | \(-0.900218\pi\) |
0.208582 | − | 0.978005i | \(-0.433115\pi\) | |||||||
\(572\) | −140.000 | + | 242.487i | −0.0102337 | + | 0.0177253i | ||||
\(573\) | −17899.0 | −1.30496 | ||||||||
\(574\) | 2450.00 | + | 12730.6i | 0.178155 | + | 0.925721i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4928.00 | + | 8535.55i | −0.356481 | + | 0.617444i | ||||
\(577\) | 6975.50 | + | 12081.9i | 0.503282 | + | 0.871710i | 0.999993 | + | 0.00379418i | \(0.00120773\pi\) |
−0.496711 | + | 0.867916i | \(0.665459\pi\) | |||||||
\(578\) | −4472.00 | − | 7745.73i | −0.321818 | − | 0.557405i | ||||
\(579\) | 1389.50 | − | 2406.68i | 0.0997334 | − | 0.172743i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15288.0 | − | 13239.8i | 1.09166 | − | 0.945403i | ||||
\(582\) | 12348.0 | 0.879452 | ||||||||
\(583\) | −757.500 | + | 1312.03i | −0.0538121 | + | 0.0932053i | ||||
\(584\) | −13356.0 | − | 23133.3i | −0.946362 | − | 1.63915i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7742.00 | + | 13409.5i | −0.545766 | + | 0.945295i | ||||
\(587\) | 20972.0 | 1.47463 | 0.737314 | − | 0.675550i | \(-0.236094\pi\) | ||||
0.737314 | + | 0.675550i | \(0.236094\pi\) | |||||||
\(588\) | 7546.00 | + | 5940.93i | 0.529238 | + | 0.416667i | ||||
\(589\) | 7203.00 | 0.503895 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10199.0 | − | 17665.2i | −0.709866 | − | 1.22952i | ||||
\(592\) | −1752.00 | − | 3034.55i | −0.121633 | − | 0.210675i | ||||
\(593\) | −94.5000 | + | 163.679i | −0.00654410 | + | 0.0113347i | −0.869279 | − | 0.494322i | \(-0.835416\pi\) |
0.862735 | + | 0.505657i | \(0.168750\pi\) | |||||||
\(594\) | 350.000 | 0.0241762 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 804.000 | 0.0552569 | ||||||||
\(597\) | 11686.5 | − | 20241.6i | 0.801167 | − | 1.38766i | ||||
\(598\) | 2226.00 | + | 3855.55i | 0.152221 | + | 0.263654i | ||||
\(599\) | 5140.50 | + | 8903.61i | 0.350643 | + | 0.607331i | 0.986362 | − | 0.164589i | \(-0.0526297\pi\) |
−0.635719 | + | 0.771920i | \(0.719296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6090.00 | −0.413338 | −0.206669 | − | 0.978411i | \(-0.566262\pi\) | ||||
−0.206669 | + | 0.978411i | \(0.566262\pi\) | |||||||
\(602\) | 868.000 | + | 4510.26i | 0.0587658 | + | 0.305356i | ||||
\(603\) | −9130.00 | −0.616588 | ||||||||
\(604\) | 3238.00 | − | 5608.38i | 0.218133 | − | 0.377817i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9653.00 | − | 16719.5i | −0.647073 | − | 1.12076i | ||||
\(607\) | 2474.50 | − | 4285.96i | 0.165464 | − | 0.286593i | −0.771356 | − | 0.636404i | \(-0.780421\pi\) |
0.936820 | + | 0.349812i | \(0.113754\pi\) | |||||||
\(608\) | −7840.00 | −0.522951 | ||||||||
\(609\) | −7105.00 | − | 2461.24i | −0.472757 | − | 0.163768i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3675.00 | − | 6365.29i | 0.243330 | − | 0.421460i | ||||
\(612\) | 924.000 | + | 1600.41i | 0.0610302 | + | 0.105707i | ||||
\(613\) | −7898.50 | − | 13680.6i | −0.520420 | − | 0.901394i | −0.999718 | − | 0.0237416i | \(-0.992442\pi\) |
0.479298 | − | 0.877652i | \(-0.340891\pi\) | |||||||
\(614\) | 7364.00 | − | 12754.8i | 0.484018 | − | 0.838343i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2100.00 | − | 727.461i | −0.137356 | − | 0.0475816i | ||||
\(617\) | 9378.00 | 0.611903 | 0.305951 | − | 0.952047i | \(-0.401025\pi\) | ||||
0.305951 | + | 0.952047i | \(0.401025\pi\) | |||||||
\(618\) | −4753.00 | + | 8232.44i | −0.309375 | + | 0.535853i | ||||
\(619\) | 12176.5 | + | 21090.3i | 0.790654 | + | 1.36945i | 0.925562 | + | 0.378595i | \(0.123593\pi\) |
−0.134908 | + | 0.990858i | \(0.543074\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2782.50 | + | 4819.43i | −0.179803 | + | 0.311429i | ||||
\(622\) | −19950.0 | −1.28605 | ||||||||
\(623\) | 1151.50 | + | 5983.37i | 0.0740512 | + | 0.384781i | ||||
\(624\) | 1568.00 | 0.100593 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4753.00 | + | 8232.44i | 0.303463 | + | 0.525614i | ||||
\(627\) | −857.500 | − | 1485.23i | −0.0546176 | − | 0.0946005i | ||||
\(628\) | −1358.00 | + | 2352.12i | −0.0862900 | + | 0.149459i | ||||
\(629\) | −4599.00 | −0.291533 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12640.0 | −0.797449 | −0.398725 | − | 0.917071i | \(-0.630547\pi\) | ||||
−0.398725 | + | 0.917071i | \(0.630547\pi\) | |||||||
\(632\) | 1236.00 | − | 2140.81i | 0.0777934 | − | 0.134742i | ||||
\(633\) | 6230.00 | + | 10790.7i | 0.391185 | + | 0.677553i | ||||
\(634\) | 3477.00 | + | 6022.34i | 0.217806 | + | 0.377252i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8484.00 | −0.528950 | ||||||||
\(637\) | 686.000 | − | 4752.75i | 0.0426692 | − | 0.295621i | ||||
\(638\) | 580.000 | 0.0359913 | ||||||||
\(639\) | 4752.00 | − | 8230.71i | 0.294188 | − | 0.509549i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 520.500 | + | 901.532i | 0.0320726 | + | 0.0555513i | 0.881616 | − | 0.471967i | \(-0.156456\pi\) |
−0.849544 | + | 0.527518i | \(0.823123\pi\) | |||||||
\(642\) | 3199.00 | − | 5540.83i | 0.196658 | − | 0.340622i | ||||
\(643\) | −9548.00 | −0.585593 | −0.292797 | − | 0.956175i | \(-0.594586\pi\) | ||||
−0.292797 | + | 0.956175i | \(0.594586\pi\) | |||||||
\(644\) | 8904.00 | − | 7711.09i | 0.544824 | − | 0.471832i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1029.00 | − | 1782.28i | 0.0626710 | − | 0.108549i | ||||
\(647\) | −1620.50 | − | 2806.79i | −0.0984674 | − | 0.170551i | 0.812583 | − | 0.582845i | \(-0.198061\pi\) |
−0.911050 | + | 0.412295i | \(0.864727\pi\) | |||||||
\(648\) | 10068.0 | + | 17438.3i | 0.610352 | + | 1.05716i | ||||
\(649\) | −262.500 | + | 454.663i | −0.0158768 | + | 0.0274994i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3601.50 | + | 18713.9i | 0.216826 | + | 1.12666i | ||||
\(652\) | −1868.00 | −0.112203 | ||||||||
\(653\) | −4426.50 | + | 7666.92i | −0.265272 | + | 0.459464i | −0.967635 | − | 0.252355i | \(-0.918795\pi\) |
0.702363 | + | 0.711819i | \(0.252128\pi\) | |||||||
\(654\) | 7875.00 | + | 13639.9i | 0.470851 | + | 0.815539i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2800.00 | − | 4849.74i | 0.166649 | − | 0.288644i | ||||
\(657\) | 24486.0 | 1.45402 | ||||||||
\(658\) | 18375.0 | + | 6365.29i | 1.08865 | + | 0.377120i | ||||
\(659\) | 7044.00 | 0.416381 | 0.208191 | − | 0.978088i | \(-0.433243\pi\) | ||||
0.208191 | + | 0.978088i | \(0.433243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6044.50 | + | 10469.4i | 0.355679 | + | 0.616054i | 0.987234 | − | 0.159277i | \(-0.0509163\pi\) |
−0.631555 | + | 0.775331i | \(0.717583\pi\) | |||||||
\(662\) | 3341.00 | + | 5786.78i | 0.196151 | + | 0.339743i | ||||
\(663\) | 1029.00 | − | 1782.28i | 0.0602761 | − | 0.104401i | ||||
\(664\) | −26208.0 | −1.53173 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9636.00 | 0.560642 | ||||||||
\(667\) | −4611.00 | + | 7986.49i | −0.267674 | + | 0.463625i | ||||
\(668\) | −2408.00 | − | 4170.78i | −0.139474 | − | 0.241575i | ||||
\(669\) | 4900.00 | + | 8487.05i | 0.283176 | + | 0.490476i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2065.00 | 0.118805 | ||||||||
\(672\) | −3920.00 | − | 20368.9i | −0.225026 | − | 1.16927i | ||||
\(673\) | −982.000 | −0.0562456 | −0.0281228 | − | 0.999604i | \(-0.508953\pi\) | ||||
−0.0281228 | + | 0.999604i | \(0.508953\pi\) | |||||||
\(674\) | −7366.00 | + | 12758.3i | −0.420961 | + | 0.729126i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4002.00 | − | 6931.67i | −0.227697 | − | 0.394383i | ||||
\(677\) | −15256.5 | + | 26425.0i | −0.866108 | + | 1.50014i | −0.000164659 | 1.00000i | \(0.500052\pi\) | |
−0.865943 | + | 0.500143i | \(0.833281\pi\) | |||||||
\(678\) | 21532.0 | 1.21966 | ||||||||
\(679\) | −12348.0 | + | 10693.7i | −0.697898 | + | 0.604397i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7717.50 | − | 13367.1i | 0.434266 | − | 0.752171i | ||||
\(682\) | −735.000 | − | 1273.06i | −0.0412677 | − | 0.0714778i | ||||
\(683\) | 5737.50 | + | 9937.64i | 0.321434 | + | 0.556740i | 0.980784 | − | 0.195096i | \(-0.0625019\pi\) |
−0.659350 | + | 0.751836i | \(0.729169\pi\) | |||||||
\(684\) | 2156.00 | − | 3734.30i | 0.120522 | − | 0.208749i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12691.0 | − | 594.093i | 0.706333 | − | 0.0330650i | ||||
\(687\) | −2009.00 | −0.111569 | ||||||||
\(688\) | 992.000 | − | 1718.19i | 0.0549704 | − | 0.0952116i | ||||
\(689\) | 2121.00 | + | 3673.68i | 0.117277 | + | 0.203129i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14157.5 | − | 24521.5i | 0.779416 | − | 1.34999i | −0.152862 | − | 0.988248i | \(-0.548849\pi\) |
0.932279 | − | 0.361741i | \(-0.117818\pi\) | |||||||
\(692\) | −11284.0 | −0.619875 | ||||||||
\(693\) | 1540.00 | − | 1333.68i | 0.0844152 | − | 0.0731057i | ||||
\(694\) | 14830.0 | 0.811151 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4872.00 | + | 8438.55i | 0.265334 | + | 0.459573i | ||||
\(697\) | −3675.00 | − | 6365.29i | −0.199714 | − | 0.345915i | ||||
\(698\) | −3878.00 | + | 6716.89i | −0.210293 | + | 0.364238i | ||||
\(699\) | 32109.0 | 1.73744 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10614.0 | 0.571876 | 0.285938 | − | 0.958248i | \(-0.407695\pi\) | ||||
0.285938 | + | 0.958248i | \(0.407695\pi\) | |||||||
\(702\) | 490.000 | − | 848.705i | 0.0263445 | − | 0.0456301i | ||||
\(703\) | 5365.50 | + | 9293.32i | 0.287857 | + | 0.498583i | ||||
\(704\) | 1120.00 | + | 1939.90i | 0.0599596 | + | 0.103853i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2534.00 | 0.135083 | ||||||||
\(707\) | 24132.5 | + | 8359.74i | 1.28373 | + | 0.444697i | ||||
\(708\) | −2940.00 | −0.156062 | ||||||||
\(709\) | −5149.50 | + | 8919.20i | −0.272769 | + | 0.472451i | −0.969570 | − | 0.244814i | \(-0.921273\pi\) |
0.696801 | + | 0.717265i | \(0.254606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1133.00 | + | 1962.41i | 0.0597621 | + | 0.103511i | ||||
\(712\) | 3948.00 | − | 6838.14i | 0.207806 | − | 0.359930i | ||||
\(713\) | 23373.0 | 1.22767 | ||||||||
\(714\) | 5145.00 | + | 1782.28i | 0.269673 | + | 0.0934176i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6506.00 | + | 11268.7i | −0.339582 | + | 0.588173i | ||||
\(717\) | 5838.00 | + | 10111.7i | 0.304078 | + | 0.526679i | ||||
\(718\) | 4685.00 | + | 8114.66i | 0.243513 | + | 0.421778i | ||||
\(719\) | −16264.5 | + | 28170.9i | −0.843621 | + | 1.46119i | 0.0431924 | + | 0.999067i | \(0.486247\pi\) |
−0.886813 | + | 0.462128i | \(0.847086\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2376.50 | − | 12348.7i | −0.122754 | − | 0.637847i | ||||
\(722\) | 8916.00 | 0.459583 | ||||||||
\(723\) | −11931.5 | + | 20666.0i | −0.613744 | + | 1.06304i | ||||
\(724\) | 3164.00 | + | 5480.21i | 0.162416 | + | 0.281313i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9142.00 | − | 15834.4i | 0.467344 | − | 0.809463i | ||||
\(727\) | −29456.0 | −1.50270 | −0.751350 | − | 0.659904i | \(-0.770597\pi\) | ||||
−0.751350 | + | 0.659904i | \(0.770597\pi\) | |||||||
\(728\) | −4704.00 | + | 4073.78i | −0.239481 | + | 0.207396i | ||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1302.00 | − | 2255.13i | −0.0658772 | − | 0.114103i | ||||
\(732\) | 5782.00 | + | 10014.7i | 0.291952 | + | 0.505676i | ||||
\(733\) | 13933.5 | − | 24133.5i | 0.702109 | − | 1.21609i | −0.265616 | − | 0.964079i | \(-0.585575\pi\) |
0.967725 | − | 0.252009i | \(-0.0810912\pi\) | |||||||
\(734\) | −9282.00 | −0.466764 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25440.0 | −1.27409 | ||||||||
\(737\) | −1037.50 | + | 1797.00i | −0.0518546 | + | 0.0898147i | ||||
\(738\) | 7700.00 | + | 13336.8i | 0.384066 | + | 0.665222i | ||||
\(739\) | −9769.50 | − | 16921.3i | −0.486302 | − | 0.842299i | 0.513574 | − | 0.858045i | \(-0.328321\pi\) |
−0.999876 | + | 0.0157460i | \(0.994988\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4802.00 | −0.238065 | ||||||||
\(742\) | −8484.00 | + | 7347.36i | −0.419754 | + | 0.363518i | ||||
\(743\) | −1248.00 | −0.0616214 | −0.0308107 | − | 0.999525i | \(-0.509809\pi\) | ||||
−0.0308107 | + | 0.999525i | \(0.509809\pi\) | |||||||
\(744\) | 12348.0 | − | 21387.4i | 0.608467 | − | 1.05390i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8797.00 | + | 15236.9i | 0.431744 | + | 0.747803i | ||||
\(747\) | 12012.0 | − | 20805.4i | 0.588348 | − | 1.01905i | ||||
\(748\) | 420.000 | 0.0205304 | ||||||||
\(749\) | 1599.50 | + | 8311.25i | 0.0780300 | + | 0.405456i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14046.5 | + | 24329.3i | −0.682509 | + | 1.18214i | 0.291704 | + | 0.956509i | \(0.405778\pi\) |
−0.974213 | + | 0.225631i | \(0.927556\pi\) | |||||||
\(752\) | −4200.00 | − | 7274.61i | −0.203668 | − | 0.352763i | ||||
\(753\) | −16660.0 | − | 28856.0i | −0.806274 | − | 1.39651i | ||||
\(754\) | 812.000 | − | 1406.43i | 0.0392192 | − | 0.0679297i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2450.00 | − | 848.705i | −0.117865 | − | 0.0408295i | ||||
\(757\) | −35954.0 | −1.72625 | −0.863124 | − | 0.504991i | \(-0.831496\pi\) | ||||
−0.863124 | + | 0.504991i | \(0.831496\pi\) | |||||||
\(758\) | 13680.0 | − | 23694.5i | 0.655514 | − | 1.13538i | ||||
\(759\) | −2782.50 | − | 4819.43i | −0.133068 | − | 0.230480i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 430.500 | − | 745.648i | 0.0205067 | − | 0.0355187i | −0.855590 | − | 0.517654i | \(-0.826805\pi\) |
0.876097 | + | 0.482136i | \(0.160139\pi\) | |||||||
\(762\) | −1008.00 | −0.0479212 | ||||||||
\(763\) | −19687.5 | − | 6819.95i | −0.934122 | − | 0.323589i | ||||
\(764\) | −10228.0 | −0.484340 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9765.00 | − | 16913.5i | −0.460605 | − | 0.797792i | ||||
\(767\) | 735.000 | + | 1273.06i | 0.0346014 | + | 0.0599315i | ||||
\(768\) | −15232.0 | + | 26382.6i | −0.715674 | + | 1.23958i | ||||
\(769\) | 24710.0 | 1.15873 | 0.579366 | − | 0.815067i | \(-0.303300\pi\) | ||||
0.579366 | + | 0.815067i | \(0.303300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5635.00 | −0.263216 | ||||||||
\(772\) | 794.000 | − | 1375.25i | 0.0370164 | − | 0.0641143i | ||||
\(773\) | 8249.50 | + | 14288.6i | 0.383847 | + | 0.664843i | 0.991609 | − | 0.129277i | \(-0.0412656\pi\) |
−0.607761 | + | 0.794120i | \(0.707932\pi\) | |||||||
\(774\) | 2728.00 | + | 4725.03i | 0.126687 | + | 0.219429i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 21168.0 | 0.979236 | ||||||||
\(777\) | −21462.0 | + | 18586.6i | −0.990920 | + | 0.858162i | ||||
\(778\) | −3462.00 | −0.159536 | ||||||||
\(779\) | −8575.00 | + | 14852.3i | −0.394392 | + | 0.683107i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1080.00 | − | 1870.61i | −0.0494820 | − | 0.0857053i | ||||
\(782\) | 3339.00 | − | 5783.32i | 0.152688 | − | 0.264464i | ||||
\(783\) | 2030.00 | 0.0926517 | ||||||||
\(784\) | −4312.00 | − | 3394.82i | −0.196429 | − | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15043.0 | + | 26055.2i | −0.682654 | + | 1.18239i | ||||
\(787\) | 8235.50 | + | 14264.3i | 0.373016 | + | 0.646083i | 0.990028 | − | 0.140871i | \(-0.0449902\pi\) |
−0.617012 | + | 0.786954i | \(0.711657\pi\) | |||||||
\(788\) | −5828.00 | − | 10094.4i | −0.263469 | − | 0.456342i | ||||
\(789\) | 899.500 | − | 1557.98i | 0.0405869 | − | 0.0702985i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21532.0 | + | 18647.3i | −0.967876 | + | 0.838205i | ||||
\(792\) | −2640.00 | −0.118445 | ||||||||
\(793\) | 2891.00 | − | 5007.36i | 0.129461 | − | 0.224233i | ||||
\(794\) | −10983.0 | − | 19023.1i | −0.490897 | − | 0.850258i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6678.00 | − | 11566.6i | 0.297356 | − | 0.515036i | ||||
\(797\) | 36470.0 | 1.62087 | 0.810435 | − | 0.585828i | \(-0.199231\pi\) | ||||
0.810435 | + | 0.585828i | \(0.199231\pi\) | |||||||
\(798\) | −2401.00 | − | 12476.0i | −0.106509 | − | 0.553439i | ||||
\(799\) | −11025.0 | −0.488156 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3619.00 | + | 6268.29i | 0.159639 | + | 0.276503i | ||||
\(802\) | 6603.00 | + | 11436.7i | 0.290723 | + | 0.503547i | ||||
\(803\) | 2782.50 | − | 4819.43i | 0.122282 | − | 0.211798i | ||||
\(804\) | −11620.0 | −0.509709 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4116.00 | −0.179876 | ||||||||
\(807\) | 12568.5 | − | 21769.3i | 0.548243 | − | 0.949585i | ||||
\(808\) | −16548.0 | − | 28662.0i | −0.720491 | − | 1.24793i | ||||
\(809\) | −17875.5 | − | 30961.3i | −0.776847 | − | 1.34554i | −0.933751 | − | 0.357924i | \(-0.883485\pi\) |
0.156904 | − | 0.987614i | \(-0.449849\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16492.0 | −0.714072 | −0.357036 | − | 0.934091i | \(-0.616213\pi\) | ||||
−0.357036 | + | 0.934091i | \(0.616213\pi\) | |||||||
\(812\) | −4060.00 | − | 1406.43i | −0.175466 | − | 0.0607831i | ||||
\(813\) | −9751.00 | −0.420643 | ||||||||
\(814\) | 1095.00 | − | 1896.60i | 0.0471495 | − | 0.0816654i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1176.00 | − | 2036.89i | −0.0504513 | − | 0.0873842i | ||||
\(817\) | −3038.00 | + | 5261.97i | −0.130093 | + | 0.225328i | ||||
\(818\) | −21910.0 | −0.936510 | ||||||||
\(819\) | −1078.00 | − | 5601.45i | −0.0459931 | − | 0.238987i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20736.5 | − | 35916.7i | 0.881497 | − | 1.52680i | 0.0318198 | − | 0.999494i | \(-0.489870\pi\) |
0.849677 | − | 0.527304i | \(-0.176797\pi\) | |||||||
\(822\) | −7875.00 | − | 13639.9i | −0.334151 | − | 0.578767i | ||||
\(823\) | −12532.5 | − | 21706.9i | −0.530809 | − | 0.919387i | −0.999354 | − | 0.0359479i | \(-0.988555\pi\) |
0.468545 | − | 0.883440i | \(-0.344778\pi\) | |||||||
\(824\) | −8148.00 | + | 14112.7i | −0.344477 | + | 0.596652i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2940.00 | + | 2546.11i | −0.123845 | + | 0.107253i | ||||
\(827\) | −9732.00 | −0.409208 | −0.204604 | − | 0.978845i | \(-0.565591\pi\) | ||||
−0.204604 | + | 0.978845i | \(0.565591\pi\) | |||||||
\(828\) | 6996.00 | − | 12117.4i | 0.293633 | − | 0.508587i | ||||
\(829\) | −13877.5 | − | 24036.5i | −0.581406 | − | 1.00702i | −0.995313 | − | 0.0967055i | \(-0.969170\pi\) |
0.413907 | − | 0.910319i | \(-0.364164\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1452.50 | + | 2515.80i | −0.0606338 | + | 0.105021i | ||||
\(832\) | 6272.00 | 0.261349 | ||||||||
\(833\) | −6688.50 | + | 2673.42i | −0.278203 | + | 0.111199i | ||||
\(834\) | 3528.00 | 0.146480 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −490.000 | − | 848.705i | −0.0202715 | − | 0.0351113i | ||||
\(837\) | −2572.50 | − | 4455.70i | −0.106235 | − | 0.184004i | ||||
\(838\) | 6636.00 | − | 11493.9i | 0.273552 | − | 0.473806i | ||||
\(839\) | 21112.0 | 0.868733 | 0.434367 | − | 0.900736i | \(-0.356972\pi\) | ||||
0.434367 | + | 0.900736i | \(0.356972\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21025.0 | −0.862069 | ||||||||
\(842\) | −16630.0 | + | 28804.0i | −0.680650 | + | 1.17892i | ||||
\(843\) | −17339.0 | − | 30032.0i | −0.708407 | − | 1.22700i | ||||
\(844\) | 3560.00 | + | 6166.10i | 0.145190 | + | 0.251476i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 23100.0 | 0.938764 | ||||||||
\(847\) | 4571.00 | + | 23751.6i | 0.185433 | + | 0.963536i | ||||
\(848\) | 4848.00 | 0.196322 | ||||||||
\(849\) | 14969.5 | − | 25927.9i | 0.605126 | − | 1.04811i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17410.5 | + | 30155.9i | 0.701321 | + | 1.21472i | ||||
\(852\) | 6048.00 | − | 10475.4i | 0.243194 | − | 0.421224i | ||||
\(853\) | 21238.0 | 0.852492 | 0.426246 | − | 0.904607i | \(-0.359836\pi\) | ||||
0.426246 | + | 0.904607i | \(0.359836\pi\) | |||||||
\(854\) | 14455.0 | + | 5007.36i | 0.579204 | + | 0.200642i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5484.00 | − | 9498.57i | 0.218971 | − | 0.379269i | ||||
\(857\) | −17804.5 | − | 30838.3i | −0.709673 | − | 1.22919i | −0.964978 | − | 0.262330i | \(-0.915509\pi\) |
0.255305 | − | 0.966861i | \(-0.417824\pi\) | |||||||
\(858\) | 490.000 | + | 848.705i | 0.0194969 | + | 0.0337696i | ||||
\(859\) | −1088.50 | + | 1885.34i | −0.0432353 | + | 0.0748858i | −0.886833 | − | 0.462090i | \(-0.847100\pi\) |
0.843598 | + | 0.536975i | \(0.180433\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −42875.0 | − | 14852.3i | −1.69707 | − | 0.587882i | ||||
\(862\) | −9846.00 | −0.389044 | ||||||||
\(863\) | −16123.5 | + | 27926.7i | −0.635980 | + | 1.10155i | 0.350327 | + | 0.936627i | \(0.386070\pi\) |
−0.986307 | + | 0.164921i | \(0.947263\pi\) | |||||||
\(864\) | 2800.00 | + | 4849.74i | 0.110252 | + | 0.190962i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8974.00 | + | 15543.4i | −0.352135 | + | 0.609916i | ||||
\(867\) | 31304.0 | 1.22623 | ||||||||
\(868\) | 2058.00 | + | 10693.7i | 0.0804759 | + | 0.418165i | ||||
\(869\) | 515.000 | 0.0201038 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2905.00 | + | 5031.61i | 0.113011 | + | 0.195740i | ||||
\(872\) | 13500.0 | + | 23382.7i | 0.524275 | + | 0.908071i | ||||
\(873\) | −9702.00 | + | 16804.4i | −0.376132 | + | 0.651479i | ||||
\(874\) | −15582.0 | −0.603054 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 31164.0 | 1.20198 | ||||||||
\(877\) | 13815.5 | − | 23929.1i | 0.531946 | − | 0.921357i | −0.467359 | − | 0.884068i | \(-0.654794\pi\) |
0.999305 | − | 0.0372891i | \(-0.0118723\pi\) | |||||||
\(878\) | −4179.00 | − | 7238.24i | −0.160631 | − | 0.278222i | ||||
\(879\) | −27097.0 | − | 46933.4i | −1.03977 | − | 1.80094i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24402.0 | 0.933172 | 0.466586 | − | 0.884476i | \(-0.345484\pi\) | ||||
0.466586 | + | 0.884476i | \(0.345484\pi\) | |||||||
\(882\) | 14014.0 | − | 5601.45i | 0.535007 | − | 0.213844i | ||||
\(883\) | 19612.0 | 0.747448 | 0.373724 | − | 0.927540i | \(-0.378081\pi\) | ||||
0.373724 | + | 0.927540i | \(0.378081\pi\) | |||||||
\(884\) | 588.000 | − | 1018.45i | 0.0223717 | − | 0.0387489i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12927.0 | + | 22390.2i | 0.490170 | + | 0.849000i | ||||
\(887\) | 1130.50 | − | 1958.08i | 0.0427942 | − | 0.0741218i | −0.843835 | − | 0.536603i | \(-0.819707\pi\) |
0.886629 | + | 0.462481i | \(0.153041\pi\) | |||||||
\(888\) | 36792.0 | 1.39038 | ||||||||
\(889\) | 1008.00 | − | 872.954i | 0.0380284 | − | 0.0329335i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2097.50 | + | 3632.98i | −0.0788652 | + | 0.136599i | ||||
\(892\) | 2800.00 | + | 4849.74i | 0.105102 | + | 0.182042i | ||||
\(893\) | 12862.5 | + | 22278.5i | 0.482001 | + | 0.834851i | ||||
\(894\) | 1407.00 | − | 2437.00i | 0.0526366 | − | 0.0911693i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1344.00 | − | 6983.63i | −0.0501115 | − | 0.260387i | ||||
\(897\) | −15582.0 | −0.580009 | ||||||||
\(898\) | −2826.00 | + | 4894.78i | −0.105017 | + | 0.181894i | ||||
\(899\) | −4263.00 | − | 7383.73i | −0.158152 | − | 0.273928i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3181.50 | − | 5510.52i | 0.117637 | − | 0.203754i | ||||
\(902\) | 3500.00 | 0.129199 | ||||||||
\(903\) | −15190.0 | − | 5261.97i | −0.559791 | − | 0.193917i | ||||
\(904\) | 36912.0 | 1.35805 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11333.0 | − | 19629.3i | −0.415578 | − | 0.719802i | ||||
\(907\) | −11916.5 | − | 20640.0i | −0.436252 | − | 0.755611i | 0.561145 | − | 0.827718i | \(-0.310361\pi\) |
−0.997397 | + | 0.0721066i | \(0.977028\pi\) | |||||||
\(908\) | 4410.00 | − | 7638.34i | 0.161180 | − | 0.279171i | ||||
\(909\) | 30338.0 | 1.10698 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31824.0 | 1.15738 | 0.578692 | − | 0.815546i | \(-0.303563\pi\) | ||||
0.578692 | + | 0.815546i | \(0.303563\pi\) | |||||||
\(912\) | −2744.00 | + | 4752.75i | −0.0996304 | + | 0.172565i | ||||
\(913\) | −2730.00 | − | 4728.50i | −0.0989593 | − | 0.171402i | ||||
\(914\) | −8479.00 | − | 14686.1i | −0.306849 | − | 0.531479i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1148.00 | −0.0414094 | ||||||||
\(917\) | −7521.50 | − | 39082.9i | −0.270863 | − | 1.40745i | ||||
\(918\) | −1470.00 | −0.0528510 | ||||||||
\(919\) | 8409.50 | − | 14565.7i | 0.301854 | − | 0.522826i | −0.674702 | − | 0.738090i | \(-0.735728\pi\) |
0.976556 | + | 0.215264i | \(0.0690612\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25774.0 | + | 44641.9i | 0.922130 | + | 1.59718i | ||||
\(922\) | 9338.00 | − | 16173.9i | 0.333547 | − | 0.577721i | ||||
\(923\) | −6048.00 | −0.215680 | ||||||||
\(924\) | 1960.00 | − | 1697.41i | 0.0697828 | − | 0.0604336i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4016.00 | − | 6955.92i | 0.142520 | − | 0.246853i | ||||
\(927\) | −7469.00 | − | 12936.7i | −0.264632 | − | 0.458357i | ||||
\(928\) | 4640.00 | + | 8036.72i | 0.164133 | + | 0.284287i | ||||
\(929\) | −899.500 | + | 1557.98i | −0.0317671 | + | 0.0550222i | −0.881472 | − | 0.472237i | \(-0.843447\pi\) |
0.849705 | + | 0.527259i | \(0.176780\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13205.5 | + | 10396.6i | 0.464869 | + | 0.365989i | ||||
\(932\) | 18348.0 | 0.644859 | ||||||||
\(933\) | 34912.5 | − | 60470.2i | 1.22506 | − | 2.12187i | ||||
\(934\) | 5859.00 | + | 10148.1i | 0.205259 | + | 0.355520i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3696.00 | + | 6401.66i | −0.129068 | + | 0.223552i | ||||
\(937\) | −14154.0 | −0.493480 | −0.246740 | − | 0.969082i | \(-0.579359\pi\) | ||||
−0.246740 | + | 0.969082i | \(0.579359\pi\) | |||||||
\(938\) | −11620.0 | + | 10063.2i | −0.404484 | + | 0.350294i | ||||
\(939\) | −33271.0 | −1.15629 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6023.50 | − | 10433.0i | −0.208672 | − | 0.361431i | 0.742624 | − | 0.669708i | \(-0.233581\pi\) |
−0.951296 | + | 0.308277i | \(0.900247\pi\) | |||||||
\(942\) | 4753.00 | + | 8232.44i | 0.164396 | + | 0.284742i | ||||
\(943\) | −27825.0 | + | 48194.3i | −0.960877 | + | 1.66429i | ||||
\(944\) | 1680.00 | 0.0579230 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1240.00 | 0.0426172 | ||||||||
\(947\) | −12189.5 | + | 21112.8i | −0.418274 | + | 0.724472i | −0.995766 | − | 0.0919245i | \(-0.970698\pi\) |
0.577492 | + | 0.816396i | \(0.304031\pi\) | |||||||
\(948\) | 1442.00 | + | 2497.62i | 0.0494029 | + | 0.0855684i | ||||
\(949\) | −7791.00 | − | 13494.4i | −0.266498 | − | 0.461588i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24339.0 | −0.829912 | ||||||||
\(952\) | 8820.00 | + | 3055.34i | 0.300271 | + | 0.104017i | ||||
\(953\) | 52330.0 | 1.77874 | 0.889368 | − | 0.457192i | \(-0.151145\pi\) | ||||
0.889368 | + | 0.457192i | \(0.151145\pi\) | |||||||
\(954\) | −6666.00 | + | 11545.9i | −0.226226 | + | 0.391835i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3336.00 | + | 5778.12i | 0.112860 | + | 0.195479i | ||||
\(957\) | −1015.00 | + | 1758.03i | −0.0342845 | + | 0.0593825i | ||||
\(958\) | −13006.0 | −0.438627 | ||||||||
\(959\) | 19687.5 | + | 6819.95i | 0.662922 | + | 0.229643i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4091.00 | − | 7085.82i | 0.137323 | − | 0.237851i | ||||
\(962\) | −3066.00 | − | 5310.47i | −0.102757 | − | 0.177980i | ||||
\(963\) | 5027.00 | + | 8707.02i | 0.168217 | + | 0.291360i | ||||
\(964\) | −6818.00 | + | 11809.1i | −0.227794 | + | 0.394550i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7791.00 | − | 40483.2i | −0.259494 | − | 1.34837i | ||||
\(967\) | 12416.0 | 0.412897 | 0.206449 | − | 0.978457i | \(-0.433809\pi\) | ||||
0.206449 | + | 0.978457i | \(0.433809\pi\) | |||||||
\(968\) | 15672.0 | − | 27144.7i | 0.520369 | − | 0.901305i | ||||
\(969\) | 3601.50 | + | 6237.98i | 0.119398 | + | 0.206804i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18406.5 | + | 31881.0i | −0.608334 | + | 1.05367i | 0.383181 | + | 0.923673i | \(0.374829\pi\) |
−0.991515 | + | 0.129993i | \(0.958505\pi\) | |||||||
\(972\) | −19712.0 | −0.650476 | ||||||||
\(973\) | −3528.00 | + | 3055.34i | −0.116241 | + | 0.100668i | ||||
\(974\) | −32098.0 | −1.05594 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3304.00 | − | 5722.70i | −0.108359 | − | 0.187683i | ||||
\(977\) | 17497.5 | + | 30306.6i | 0.572973 | + | 0.992418i | 0.996259 | + | 0.0864221i | \(0.0275434\pi\) |
−0.423286 | + | 0.905996i | \(0.639123\pi\) | |||||||
\(978\) | −3269.00 | + | 5662.07i | −0.106883 | + | 0.185126i | ||||
\(979\) | 1645.00 | 0.0537022 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24750.0 | −0.805511 | ||||||||
\(982\) | 8864.00 | − | 15352.9i | 0.288046 | − | 0.498911i | ||||
\(983\) | −7150.50 | − | 12385.0i | −0.232010 | − | 0.401853i | 0.726390 | − | 0.687283i | \(-0.241197\pi\) |
−0.958399 | + | 0.285430i | \(0.907863\pi\) | |||||||
\(984\) | 29400.0 | + | 50922.3i | 0.952477 | + | 1.64974i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2436.00 | −0.0786796 | ||||||||
\(987\) | −51450.0 | + | 44557.0i | −1.65924 | + | 1.43695i | ||||
\(988\) | −2744.00 | −0.0883586 | ||||||||
\(989\) | −9858.00 | + | 17074.6i | −0.316953 | + | 0.548978i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1332.50 | + | 2307.96i | 0.0427127 | + | 0.0739805i | 0.886591 | − | 0.462553i | \(-0.153067\pi\) |
−0.843879 | + | 0.536534i | \(0.819733\pi\) | |||||||
\(992\) | 11760.0 | − | 20368.9i | 0.376392 | − | 0.651929i | ||||
\(993\) | −23387.0 | −0.747396 | ||||||||
\(994\) | −3024.00 | − | 15713.2i | −0.0964944 | − | 0.501400i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 15288.0 | − | 26479.6i | 0.486364 | − | 0.842408i | ||||
\(997\) | 12435.5 | + | 21538.9i | 0.395021 | + | 0.684197i | 0.993104 | − | 0.117237i | \(-0.0374039\pi\) |
−0.598083 | + | 0.801434i | \(0.704071\pi\) | |||||||
\(998\) | −10211.0 | − | 17686.0i | −0.323871 | − | 0.560962i | ||||
\(999\) | 3832.50 | − | 6638.08i | 0.121376 | − | 0.210230i |
(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 | 175.4.e.a.51.1 | 2 | ||
5.2 | odd | 4 | 175.4.k.a.149.2 | 4 | |||
5.3 | odd | 4 | 175.4.k.a.149.1 | 4 | |||
5.4 | even | 2 | 7.4.c.a.2.1 | ✓ | 2 | ||
7.2 | even | 3 | 1225.4.a.c.1.1 | 1 | |||
7.4 | even | 3 | inner | 175.4.e.a.151.1 | 2 | ||
7.5 | odd | 6 | 1225.4.a.d.1.1 | 1 | |||
15.14 | odd | 2 | 63.4.e.b.37.1 | 2 | |||
20.19 | odd | 2 | 112.4.i.c.65.1 | 2 | |||
35.4 | even | 6 | 7.4.c.a.4.1 | yes | 2 | ||
35.9 | even | 6 | 49.4.a.d.1.1 | 1 | |||
35.18 | odd | 12 | 175.4.k.a.74.2 | 4 | |||
35.19 | odd | 6 | 49.4.a.c.1.1 | 1 | |||
35.24 | odd | 6 | 49.4.c.a.18.1 | 2 | |||
35.32 | odd | 12 | 175.4.k.a.74.1 | 4 | |||
35.34 | odd | 2 | 49.4.c.a.30.1 | 2 | |||
40.19 | odd | 2 | 448.4.i.a.65.1 | 2 | |||
40.29 | even | 2 | 448.4.i.f.65.1 | 2 | |||
105.44 | odd | 6 | 441.4.a.d.1.1 | 1 | |||
105.59 | even | 6 | 441.4.e.k.361.1 | 2 | |||
105.74 | odd | 6 | 63.4.e.b.46.1 | 2 | |||
105.89 | even | 6 | 441.4.a.e.1.1 | 1 | |||
105.104 | even | 2 | 441.4.e.k.226.1 | 2 | |||
140.19 | even | 6 | 784.4.a.r.1.1 | 1 | |||
140.39 | odd | 6 | 112.4.i.c.81.1 | 2 | |||
140.79 | odd | 6 | 784.4.a.b.1.1 | 1 | |||
280.109 | even | 6 | 448.4.i.f.193.1 | 2 | |||
280.179 | odd | 6 | 448.4.i.a.193.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.4.c.a.2.1 | ✓ | 2 | 5.4 | even | 2 | ||
7.4.c.a.4.1 | yes | 2 | 35.4 | even | 6 | ||
49.4.a.c.1.1 | 1 | 35.19 | odd | 6 | |||
49.4.a.d.1.1 | 1 | 35.9 | even | 6 | |||
49.4.c.a.18.1 | 2 | 35.24 | odd | 6 | |||
49.4.c.a.30.1 | 2 | 35.34 | odd | 2 | |||
63.4.e.b.37.1 | 2 | 15.14 | odd | 2 | |||
63.4.e.b.46.1 | 2 | 105.74 | odd | 6 | |||
112.4.i.c.65.1 | 2 | 20.19 | odd | 2 | |||
112.4.i.c.81.1 | 2 | 140.39 | odd | 6 | |||
175.4.e.a.51.1 | 2 | 1.1 | even | 1 | trivial | ||
175.4.e.a.151.1 | 2 | 7.4 | even | 3 | inner | ||
175.4.k.a.74.1 | 4 | 35.32 | odd | 12 | |||
175.4.k.a.74.2 | 4 | 35.18 | odd | 12 | |||
175.4.k.a.149.1 | 4 | 5.3 | odd | 4 | |||
175.4.k.a.149.2 | 4 | 5.2 | odd | 4 | |||
441.4.a.d.1.1 | 1 | 105.44 | odd | 6 | |||
441.4.a.e.1.1 | 1 | 105.89 | even | 6 | |||
441.4.e.k.226.1 | 2 | 105.104 | even | 2 | |||
441.4.e.k.361.1 | 2 | 105.59 | even | 6 | |||
448.4.i.a.65.1 | 2 | 40.19 | odd | 2 | |||
448.4.i.a.193.1 | 2 | 280.179 | odd | 6 | |||
448.4.i.f.65.1 | 2 | 40.29 | even | 2 | |||
448.4.i.f.193.1 | 2 | 280.109 | even | 6 | |||
784.4.a.b.1.1 | 1 | 140.79 | odd | 6 | |||
784.4.a.r.1.1 | 1 | 140.19 | even | 6 | |||
1225.4.a.c.1.1 | 1 | 7.2 | even | 3 | |||
1225.4.a.d.1.1 | 1 | 7.5 | odd | 6 |