Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,4,Mod(2,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7.2");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.c (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: | \(0.413013370040\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7.2 |
Dual form | 7.4.c.a.4.1 |
$q$-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 \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 | −0.986869 | − | 0.161521i | \(-0.948360\pi\) |
0.633316 | + | 0.773893i | \(0.281693\pi\) | |||||||
\(3\) | −3.50000 | − | 6.06218i | −0.673575 | − | 1.16667i | −0.976883 | − | 0.213774i | \(-0.931424\pi\) |
0.303308 | − | 0.952893i | \(-0.401909\pi\) | |||||||
\(4\) | 2.00000 | + | 3.46410i | 0.250000 | + | 0.433013i | ||||
\(5\) | −3.50000 | + | 6.06218i | −0.313050 | + | 0.542218i | −0.979021 | − | 0.203760i | \(-0.934684\pi\) |
0.665971 | + | 0.745977i | \(0.268017\pi\) | |||||||
\(6\) | 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 | ||||
\(10\) | −7.00000 | − | 12.1244i | −0.221359 | − | 0.383406i | ||||
\(11\) | 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 | \(-0.547716\pi\) | ||||
−0.149342 | + | 0.988786i | \(0.547716\pi\) | |||||||
\(14\) | 7.00000 | + | 36.3731i | 0.133631 | + | 0.694365i | ||||
\(15\) | 49.0000 | 0.843450 | ||||||||
\(16\) | 8.00000 | − | 13.8564i | 0.125000 | − | 0.216506i | ||||
\(17\) | 10.5000 | + | 18.1865i | 0.149801 | + | 0.259464i | 0.931154 | − | 0.364626i | \(-0.118803\pi\) |
−0.781353 | + | 0.624090i | \(0.785470\pi\) | |||||||
\(18\) | −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 | \(0.262261\pi\) | |||||||
\(20\) | −28.0000 | −0.313050 | ||||||||
\(21\) | −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 | \(-0.577138\pi\) |
0.960706 | − | 0.277569i | \(-0.0895287\pi\) | |||||||
\(24\) | 84.0000 | + | 145.492i | 0.714435 | + | 1.23744i | ||||
\(25\) | 38.0000 | + | 65.8179i | 0.304000 | + | 0.526543i | ||||
\(26\) | 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 | \(0.440546\pi\) | |||||||
\(30\) | −49.0000 | + | 84.8705i | −0.298205 | + | 0.516505i | ||||
\(31\) | −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 | ||||||||
\(35\) | 24.5000 | + | 127.306i | 0.118322 | + | 0.614817i | ||||
\(36\) | −88.0000 | −0.407407 | ||||||||
\(37\) | −109.500 | + | 189.660i | −0.486532 | + | 0.842698i | −0.999880 | − | 0.0154821i | \(-0.995072\pi\) |
0.513348 | + | 0.858181i | \(0.328405\pi\) | |||||||
\(38\) | −49.0000 | − | 84.8705i | −0.209180 | − | 0.362311i | ||||
\(39\) | 49.0000 | + | 84.8705i | 0.201187 | + | 0.348466i | ||||
\(40\) | 84.0000 | − | 145.492i | 0.332039 | − | 0.575109i | ||||
\(41\) | 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 | \(-0.570567\pi\) | ||||
−0.219882 | + | 0.975527i | \(0.570567\pi\) | |||||||
\(44\) | −10.0000 | + | 17.3205i | −0.0342627 | + | 0.0593447i | ||||
\(45\) | −77.0000 | − | 133.368i | −0.255077 | − | 0.441807i | ||||
\(46\) | 159.000 | + | 275.396i | 0.509636 | + | 0.882716i | ||||
\(47\) | −262.500 | + | 454.663i | −0.814671 | + | 1.41105i | 0.0948921 | + | 0.995488i | \(0.469749\pi\) |
−0.909564 | + | 0.415565i | \(0.863584\pi\) | |||||||
\(48\) | −112.000 | −0.336788 | ||||||||
\(49\) | 49.0000 | − | 339.482i | 0.142857 | − | 0.989743i | ||||
\(50\) | −152.000 | −0.429921 | ||||||||
\(51\) | 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 | 0.600153 | − | 0.799885i | \(-0.295106\pi\) |
−0.992797 | + | 0.119806i | \(0.961773\pi\) | |||||||
\(54\) | 35.0000 | − | 60.6218i | 0.0882018 | − | 0.152770i | ||||
\(55\) | −35.0000 | −0.0858073 | ||||||||
\(56\) | −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 | \(0.796375\pi\) | |||||||
\(60\) | 98.0000 | + | 169.741i | 0.210862 | + | 0.365224i | ||||
\(61\) | 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 | ||||||||
\(65\) | 49.0000 | − | 84.8705i | 0.0935031 | − | 0.161952i | ||||
\(66\) | 35.0000 | + | 60.6218i | 0.0652758 | + | 0.113061i | ||||
\(67\) | −207.500 | − | 359.401i | −0.378361 | − | 0.655340i | 0.612463 | − | 0.790499i | \(-0.290179\pi\) |
−0.990824 | + | 0.135159i | \(0.956845\pi\) | |||||||
\(68\) | −42.0000 | + | 72.7461i | −0.0749007 | + | 0.129732i | ||||
\(69\) | −1113.00 | −1.94188 | ||||||||
\(70\) | −245.000 | − | 84.8705i | −0.418330 | − | 0.144914i | ||||
\(71\) | −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 | \(0.184199\pi\) |
0.0550526 | + | 0.998483i | \(0.482467\pi\) | |||||||
\(74\) | −219.000 | − | 379.319i | −0.344030 | − | 0.595878i | ||||
\(75\) | 266.000 | − | 460.726i | 0.409534 | − | 0.709333i | ||||
\(76\) | −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 | \(0.143299\pi\) | |||||||
\(80\) | 56.0000 | + | 96.9948i | 0.0782624 | + | 0.135554i | ||||
\(81\) | 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 | \(-0.243194\pi\) | ||||
0.722064 | + | 0.691827i | \(0.243194\pi\) | |||||||
\(84\) | −98.0000 | − | 509.223i | −0.127294 | − | 0.661438i | ||||
\(85\) | −147.000 | −0.187581 | ||||||||
\(86\) | 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 | \(0.103897\pi\) | |||||||
\(90\) | 308.000 | 0.360734 | ||||||||
\(91\) | −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 | ||||
\(95\) | −171.500 | − | 297.047i | −0.185216 | − | 0.320804i | ||||
\(96\) | −560.000 | + | 969.948i | −0.595362 | + | 1.03120i | ||||
\(97\) | −882.000 | −0.923232 | −0.461616 | − | 0.887080i | \(-0.652730\pi\) | ||||
−0.461616 | + | 0.887080i | \(0.652730\pi\) | |||||||
\(98\) | 539.000 | + | 424.352i | 0.555584 | + | 0.437409i | ||||
\(99\) | −110.000 | −0.111671 | ||||||||
\(100\) | −152.000 | + | 263.272i | −0.152000 | + | 0.263272i | ||||
\(101\) | −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 | −0.656691 | − | 0.754160i | \(-0.728044\pi\) |
0.981467 | + | 0.191631i | \(0.0613777\pi\) | |||||||
\(104\) | 336.000 | 0.316803 | ||||||||
\(105\) | 686.000 | − | 594.093i | 0.637588 | − | 0.552167i | ||||
\(106\) | 606.000 | 0.555282 | ||||||||
\(107\) | −228.500 | + | 395.774i | −0.206448 | + | 0.357578i | −0.950593 | − | 0.310440i | \(-0.899524\pi\) |
0.744145 | + | 0.668018i | \(0.232857\pi\) | |||||||
\(108\) | −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 | \(0.668761\pi\) | |||||||
\(110\) | 35.0000 | − | 60.6218i | 0.0303374 | − | 0.0525460i | ||||
\(111\) | 1533.00 | 1.31086 | ||||||||
\(112\) | −56.0000 | − | 290.985i | −0.0472456 | − | 0.245495i | ||||
\(113\) | −1538.00 | −1.28038 | −0.640190 | − | 0.768217i | \(-0.721144\pi\) | ||||
−0.640190 | + | 0.768217i | \(0.721144\pi\) | |||||||
\(114\) | −343.000 | + | 594.093i | −0.281797 | + | 0.488087i | ||||
\(115\) | 556.500 | + | 963.886i | 0.451251 | + | 0.781590i | ||||
\(116\) | 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 | ||||
\(120\) | −1176.00 | −0.894614 | ||||||||
\(121\) | 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 | ||||
\(125\) | −1407.00 | −1.00677 | ||||||||
\(126\) | −770.000 | − | 266.736i | −0.544421 | − | 0.188593i | ||||
\(127\) | 72.0000 | 0.0503068 | 0.0251534 | − | 0.999684i | \(-0.491993\pi\) | ||||
0.0251534 | + | 0.999684i | \(0.491993\pi\) | |||||||
\(128\) | 192.000 | − | 332.554i | 0.132583 | − | 0.229640i | ||||
\(129\) | 434.000 | + | 751.710i | 0.296214 | + | 0.513057i | ||||
\(130\) | 98.0000 | + | 169.741i | 0.0661167 | + | 0.114517i | ||||
\(131\) | −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 | ||||||||
\(135\) | 122.500 | − | 212.176i | 0.0780972 | − | 0.135268i | ||||
\(136\) | −252.000 | − | 436.477i | −0.158888 | − | 0.275203i | ||||
\(137\) | 562.500 | + | 974.279i | 0.350786 | + | 0.607578i | 0.986387 | − | 0.164439i | \(-0.0525813\pi\) |
−0.635602 | + | 0.772017i | \(0.719248\pi\) | |||||||
\(138\) | 1113.00 | − | 1927.77i | 0.686557 | − | 1.18915i | ||||
\(139\) | 252.000 | 0.153772 | 0.0768862 | − | 0.997040i | \(-0.475502\pi\) | ||||
0.0768862 | + | 0.997040i | \(0.475502\pi\) | |||||||
\(140\) | −392.000 | + | 339.482i | −0.236643 | + | 0.204939i | ||||
\(141\) | 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 | ||||
\(145\) | −203.000 | + | 351.606i | −0.116264 | + | 0.201375i | ||||
\(146\) | −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 | \(0.149069\pi\) | |||||||
\(150\) | 532.000 | + | 921.451i | 0.289584 | + | 0.501574i | ||||
\(151\) | −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 | ||||
\(155\) | 1029.00 | 0.533234 | ||||||||
\(156\) | −196.000 | + | 339.482i | −0.100593 | + | 0.174233i | ||||
\(157\) | −339.500 | − | 588.031i | −0.172580 | − | 0.298917i | 0.766741 | − | 0.641956i | \(-0.221877\pi\) |
−0.939321 | + | 0.343039i | \(0.888544\pi\) | |||||||
\(158\) | 103.000 | + | 178.401i | 0.0518623 | + | 0.0898281i | ||||
\(159\) | −1060.50 | + | 1836.84i | −0.528950 | + | 0.916169i | ||||
\(160\) | 1120.00 | 0.553399 | ||||||||
\(161\) | −556.500 | − | 2891.66i | −0.272412 | − | 1.41549i | ||||
\(162\) | −1678.00 | −0.813803 | ||||||||
\(163\) | 233.500 | − | 404.434i | 0.112203 | − | 0.194342i | −0.804455 | − | 0.594014i | \(-0.797543\pi\) |
0.916658 | + | 0.399672i | \(0.130876\pi\) | |||||||
\(164\) | 700.000 | + | 1212.44i | 0.333298 | + | 0.577288i | ||||
\(165\) | 122.500 | + | 212.176i | 0.0577976 | + | 0.100108i | ||||
\(166\) | −1092.00 | + | 1891.40i | −0.510576 | + | 0.884344i | ||||
\(167\) | 1204.00 | 0.557894 | 0.278947 | − | 0.960306i | \(-0.410015\pi\) | ||||
0.278947 | + | 0.960306i | \(0.410015\pi\) | |||||||
\(168\) | 2940.00 | + | 1018.45i | 1.35015 | + | 0.467707i | ||||
\(169\) | −2001.00 | −0.910787 | ||||||||
\(170\) | 147.000 | − | 254.611i | 0.0663199 | − | 0.114869i | ||||
\(171\) | −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 | \(-0.620517\pi\) |
0.989508 | − | 0.144477i | \(-0.0461499\pi\) | |||||||
\(174\) | 812.000 | 0.353779 | ||||||||
\(175\) | 1330.00 | + | 460.726i | 0.574506 | + | 0.199015i | ||||
\(176\) | 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 | \(0.595676\pi\) | |||||||
\(180\) | 308.000 | − | 533.472i | 0.127539 | − | 0.220903i | ||||
\(181\) | 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 | ||||
\(185\) | −766.500 | − | 1327.62i | −0.304617 | − | 0.527613i | ||||
\(186\) | −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 | ||||
\(190\) | 686.000 | 0.261935 | ||||||||
\(191\) | −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 | 0.900665 | − | 0.434514i | \(-0.143080\pi\) |
−0.826632 | + | 0.562742i | \(0.809746\pi\) | |||||||
\(194\) | 882.000 | − | 1527.67i | 0.326412 | − | 0.565362i | ||||
\(195\) | −686.000 | −0.251926 | ||||||||
\(196\) | 1274.00 | − | 509.223i | 0.464286 | − | 0.185577i | ||||
\(197\) | 2914.00 | 1.05388 | 0.526939 | − | 0.849903i | \(-0.323340\pi\) | ||||
0.526939 | + | 0.849903i | \(0.323340\pi\) | |||||||
\(198\) | 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 | \(-0.369401\pi\) | |||||||
\(200\) | −912.000 | − | 1579.63i | −0.322441 | − | 0.558484i | ||||
\(201\) | −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 | ||||||||
\(205\) | −1225.00 | + | 2121.76i | −0.417355 | + | 0.722880i | ||||
\(206\) | 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 | ||||||||
\(210\) | 343.000 | + | 1782.28i | 0.112711 | + | 0.585662i | ||||
\(211\) | 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 | ||||
\(215\) | 434.000 | − | 751.710i | 0.137668 | − | 0.238447i | ||||
\(216\) | 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 | ||||
\(220\) | −70.0000 | − | 121.244i | −0.0214518 | − | 0.0371556i | ||||
\(221\) | −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 | \(-0.567413\pi\) | ||||
−0.210204 | + | 0.977658i | \(0.567413\pi\) | |||||||
\(224\) | −2800.00 | − | 969.948i | −0.835191 | − | 0.289319i | ||||
\(225\) | −1672.00 | −0.495407 | ||||||||
\(226\) | 1538.00 | − | 2663.89i | 0.452682 | − | 0.784069i | ||||
\(227\) | 1102.50 | + | 1909.59i | 0.322359 | + | 0.558342i | 0.980974 | − | 0.194138i | \(-0.0621908\pi\) |
−0.658615 | + | 0.752480i | \(0.728858\pi\) | |||||||
\(228\) | 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 | \(0.179851\pi\) | |||||||
\(230\) | −2226.00 | −0.638166 | ||||||||
\(231\) | −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 | \(0.389751\pi\) |
−0.984334 | + | 0.176314i | \(0.943583\pi\) | |||||||
\(234\) | 308.000 | + | 533.472i | 0.0860453 | + | 0.149035i | ||||
\(235\) | −1837.50 | − | 3182.64i | −0.510065 | − | 0.883459i | ||||
\(236\) | −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 | \(0.427527\pi\) | |||||||
\(240\) | 392.000 | − | 678.964i | 0.105431 | − | 0.182612i | ||||
\(241\) | 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 | ||||||||
\(245\) | 1886.50 | + | 1485.23i | 0.491935 | + | 0.387298i | ||||
\(246\) | 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 | ||||
\(250\) | 1407.00 | − | 2437.00i | 0.355946 | − | 0.616517i | ||||
\(251\) | −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 | ||||
\(255\) | 514.500 | + | 891.140i | 0.126350 | + | 0.218845i | ||||
\(256\) | 2176.00 | + | 3768.94i | 0.531250 | + | 0.920152i | ||||
\(257\) | 402.500 | − | 697.150i | 0.0976936 | − | 0.169210i | −0.813036 | − | 0.582213i | \(-0.802187\pi\) |
0.910730 | + | 0.413003i | \(0.135520\pi\) | |||||||
\(258\) | −1736.00 | −0.418909 | ||||||||
\(259\) | 766.500 | + | 3982.85i | 0.183892 | + | 0.955530i | ||||
\(260\) | 392.000 | 0.0935031 | ||||||||
\(261\) | −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 | 0.880696 | − | 0.473681i | \(-0.157075\pi\) |
−0.850568 | + | 0.525865i | \(0.823742\pi\) | |||||||
\(264\) | −420.000 | + | 727.461i | −0.0979137 | + | 0.169591i | ||||
\(265\) | 2121.00 | 0.491668 | ||||||||
\(266\) | −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 | \(0.966746\pi\) | |||||||
\(270\) | 245.000 | + | 424.352i | 0.0552231 | + | 0.0956491i | ||||
\(271\) | −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 | ||||||||
\(275\) | −190.000 | + | 329.090i | −0.0416634 | + | 0.0721631i | ||||
\(276\) | −2226.00 | − | 3855.55i | −0.485469 | − | 0.840857i | ||||
\(277\) | −207.500 | − | 359.401i | −0.0450089 | − | 0.0779577i | 0.842643 | − | 0.538472i | \(-0.180998\pi\) |
−0.887652 | + | 0.460514i | \(0.847665\pi\) | |||||||
\(278\) | −252.000 | + | 436.477i | −0.0543667 | + | 0.0941660i | ||||
\(279\) | 3234.00 | 0.693959 | ||||||||
\(280\) | −588.000 | − | 3055.34i | −0.125499 | − | 0.652112i | ||||
\(281\) | −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 | 0.998333 | − | 0.0577087i | \(-0.0183795\pi\) |
−0.549144 | + | 0.835728i | \(0.685046\pi\) | |||||||
\(284\) | −864.000 | − | 1496.49i | −0.180525 | − | 0.312678i | ||||
\(285\) | −1200.50 | + | 2079.33i | −0.249514 | + | 0.432171i | ||||
\(286\) | 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 | ||||
\(290\) | −406.000 | − | 703.213i | −0.0822108 | − | 0.142393i | ||||
\(291\) | 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 | \(-0.219342\pi\) | ||||
0.771830 | + | 0.635829i | \(0.219342\pi\) | |||||||
\(294\) | 686.000 | − | 4752.75i | 0.136083 | − | 0.942809i | ||||
\(295\) | −735.000 | −0.145062 | ||||||||
\(296\) | 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 | ||||
\(300\) | 2128.00 | 0.409534 | ||||||||
\(301\) | −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 | ||||
\(305\) | 1445.50 | + | 2503.68i | 0.271374 | + | 0.470034i | ||||
\(306\) | 462.000 | − | 800.207i | 0.0863097 | − | 0.149493i | ||||
\(307\) | −7364.00 | −1.36901 | −0.684504 | − | 0.729009i | \(-0.739981\pi\) | ||||
−0.684504 | + | 0.729009i | \(0.739981\pi\) | |||||||
\(308\) | 70.0000 | + | 363.731i | 0.0129501 | + | 0.0672905i | ||||
\(309\) | −4753.00 | −0.875044 | ||||||||
\(310\) | −1029.00 | + | 1782.28i | −0.188527 | + | 0.326538i | ||||
\(311\) | −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 | −0.567637 | − | 0.823279i | \(-0.692142\pi\) |
0.996799 | + | 0.0799485i | \(0.0254756\pi\) | |||||||
\(314\) | 1358.00 | 0.244065 | ||||||||
\(315\) | −2695.00 | − | 933.575i | −0.482051 | − | 0.166987i | ||||
\(316\) | 412.000 | 0.0733443 | ||||||||
\(317\) | 1738.50 | − | 3011.17i | 0.308025 | − | 0.533515i | −0.669905 | − | 0.742447i | \(-0.733665\pi\) |
0.977930 | + | 0.208932i | \(0.0669987\pi\) | |||||||
\(318\) | −2121.00 | − | 3673.68i | −0.374024 | − | 0.647829i | ||||
\(319\) | 145.000 | + | 251.147i | 0.0254497 | + | 0.0440801i | ||||
\(320\) | −1568.00 | + | 2715.86i | −0.273918 | + | 0.474440i | ||||
\(321\) | 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 | ||||
\(325\) | −532.000 | − | 921.451i | −0.0908002 | − | 0.157270i | ||||
\(326\) | 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 | ||||
\(330\) | −490.000 | −0.0817382 | ||||||||
\(331\) | −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 | ||||
\(335\) | 2905.00 | 0.473782 | ||||||||
\(336\) | −1568.00 | + | 1357.93i | −0.254588 | + | 0.220479i | ||||
\(337\) | 7366.00 | 1.19066 | 0.595329 | − | 0.803482i | \(-0.297022\pi\) | ||||
0.595329 | + | 0.803482i | \(0.297022\pi\) | |||||||
\(338\) | 2001.00 | − | 3465.83i | 0.322012 | − | 0.557741i | ||||
\(339\) | 5383.00 | + | 9323.63i | 0.862432 | + | 1.49378i | ||||
\(340\) | −294.000 | − | 509.223i | −0.0468953 | − | 0.0812250i | ||||
\(341\) | 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 | ||||||||
\(345\) | 3895.50 | − | 6747.20i | 0.607903 | − | 1.05292i | ||||
\(346\) | 2821.00 | + | 4886.12i | 0.438318 | + | 0.759188i | ||||
\(347\) | −3707.50 | − | 6421.58i | −0.573571 | − | 0.993454i | −0.996195 | − | 0.0871487i | \(-0.972224\pi\) |
0.422625 | − | 0.906305i | \(-0.361109\pi\) | |||||||
\(348\) | 812.000 | − | 1406.43i | 0.125080 | − | 0.216645i | ||||
\(349\) | −3878.00 | −0.594798 | −0.297399 | − | 0.954753i | \(-0.596119\pi\) | ||||
−0.297399 | + | 0.954753i | \(0.596119\pi\) | |||||||
\(350\) | −2128.00 | + | 1842.90i | −0.324990 | + | 0.281449i | ||||
\(351\) | 490.000 | 0.0745136 | ||||||||
\(352\) | 400.000 | − | 692.820i | 0.0605684 | − | 0.104908i | ||||
\(353\) | −633.500 | − | 1097.25i | −0.0955179 | − | 0.165442i | 0.814307 | − | 0.580435i | \(-0.197117\pi\) |
−0.909825 | + | 0.414993i | \(0.863784\pi\) | |||||||
\(354\) | 735.000 | + | 1273.06i | 0.110353 | + | 0.191136i | ||||
\(355\) | 1512.00 | − | 2618.86i | 0.226052 | − | 0.391534i | ||||
\(356\) | 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 | \(0.278578\pi\) | |||||||
\(360\) | 1848.00 | + | 3200.83i | 0.270550 | + | 0.468607i | ||||
\(361\) | 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 | ||||
\(365\) | −7791.00 | −1.11726 | ||||||||
\(366\) | 2891.00 | − | 5007.36i | 0.412882 | − | 0.715133i | ||||
\(367\) | 2320.50 | + | 4019.22i | 0.330052 | + | 0.571667i | 0.982522 | − | 0.186148i | \(-0.0596004\pi\) |
−0.652470 | + | 0.757815i | \(0.726267\pi\) | |||||||
\(368\) | −1272.00 | − | 2203.17i | −0.180184 | − | 0.312087i | ||||
\(369\) | −3850.00 | + | 6668.40i | −0.543152 | + | 0.940766i | ||||
\(370\) | 3066.00 | 0.430794 | ||||||||
\(371\) | −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 | \(-0.624270\pi\) |
0.991143 | − | 0.132798i | \(-0.0423963\pi\) | |||||||
\(374\) | −105.000 | − | 181.865i | −0.0145172 | − | 0.0251445i | ||||
\(375\) | 4924.50 | + | 8529.48i | 0.678134 | + | 1.17456i | ||||
\(376\) | 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 | \(0.122347\pi\) | |||||||
\(380\) | 686.000 | − | 1188.19i | 0.0926080 | − | 0.160402i | ||||
\(381\) | −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 | \(0.392482\pi\) |
−0.982785 | + | 0.184755i | \(0.940851\pi\) | |||||||
\(384\) | −2688.00 | −0.357217 | ||||||||
\(385\) | −490.000 | + | 424.352i | −0.0648642 | + | 0.0561740i | ||||
\(386\) | −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 | \(0.869318\pi\) | |||||||
\(390\) | 686.000 | − | 1188.19i | 0.0890691 | − | 0.154272i | ||||
\(391\) | 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 | ||||
\(395\) | 360.500 | + | 624.404i | 0.0459208 | + | 0.0795372i | ||||
\(396\) | −220.000 | − | 381.051i | −0.0279177 | − | 0.0483549i | ||||
\(397\) | −5491.50 | + | 9511.56i | −0.694233 | + | 1.20245i | 0.276206 | + | 0.961099i | \(0.410923\pi\) |
−0.970439 | + | 0.241348i | \(0.922410\pi\) | |||||||
\(398\) | 6678.00 | 0.841050 | ||||||||
\(399\) | 4802.00 | − | 4158.65i | 0.602508 | − | 0.521787i | ||||
\(400\) | 1216.00 | 0.152000 | ||||||||
\(401\) | −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 | ||||
\(405\) | −5873.00 | −0.720572 | ||||||||
\(406\) | 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 | \(-0.397049\pi\) | |||||||
\(410\) | −2450.00 | − | 4243.52i | −0.295114 | − | 0.511153i | ||||
\(411\) | 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 | ||||||||
\(415\) | −3822.00 | + | 6619.90i | −0.452083 | + | 0.783031i | ||||
\(416\) | 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 | \(0.373559\pi\) | |||||||
\(420\) | 3430.00 | + | 1188.19i | 0.398493 | + | 0.138042i | ||||
\(421\) | −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 | ||||
\(425\) | −798.000 | + | 1382.18i | −0.0910793 | + | 0.157754i | ||||
\(426\) | −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 | ||||
\(430\) | 868.000 | + | 1503.42i | 0.0973458 | + | 0.168608i | ||||
\(431\) | −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 | \(-0.334070\pi\) | ||||
0.497994 | + | 0.867180i | \(0.334070\pi\) | |||||||
\(434\) | 4116.00 | − | 3564.56i | 0.455240 | − | 0.394250i | ||||
\(435\) | 2842.00 | 0.313249 | ||||||||
\(436\) | −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 | \(0.0937203\pi\) | |||||||
\(440\) | 840.000 | 0.0910123 | ||||||||
\(441\) | 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 | \(-0.589531\pi\) |
0.970782 | − | 0.239964i | \(-0.0771356\pi\) | |||||||
\(444\) | 3066.00 | + | 5310.47i | 0.327716 | + | 0.567621i | ||||
\(445\) | 1151.50 | + | 1994.46i | 0.122666 | + | 0.212464i | ||||
\(446\) | 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 | \(0.547450\pi\) | |||||||
\(450\) | 1672.00 | − | 2895.99i | 0.175153 | − | 0.303374i | ||||
\(451\) | 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 | ||||||||
\(455\) | −343.000 | − | 1782.28i | −0.0353409 | − | 0.183636i | ||||
\(456\) | −8232.00 | −0.845392 | ||||||||
\(457\) | −4239.50 | + | 7343.03i | −0.433951 | + | 0.751625i | −0.997209 | − | 0.0746560i | \(-0.976214\pi\) |
0.563259 | + | 0.826281i | \(0.309547\pi\) | |||||||
\(458\) | −287.000 | − | 497.099i | −0.0292808 | − | 0.0507159i | ||||
\(459\) | −367.500 | − | 636.529i | −0.0373713 | − | 0.0647290i | ||||
\(460\) | −2226.00 | + | 3855.55i | −0.225626 | + | 0.390795i | ||||
\(461\) | 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 | \(-0.564599\pi\) | ||||
−0.201554 | + | 0.979477i | \(0.564599\pi\) | |||||||
\(464\) | 464.000 | − | 803.672i | 0.0464238 | − | 0.0804084i | ||||
\(465\) | −3601.50 | − | 6237.98i | −0.359173 | − | 0.622106i | ||||
\(466\) | −4587.00 | − | 7944.92i | −0.455984 | − | 0.789788i | ||||
\(467\) | 2929.50 | − | 5074.04i | 0.290281 | − | 0.502781i | −0.683595 | − | 0.729861i | \(-0.739585\pi\) |
0.973876 | + | 0.227080i | \(0.0729180\pi\) | |||||||
\(468\) | 1232.00 | 0.121686 | ||||||||
\(469\) | −7262.50 | − | 2515.80i | −0.715034 | − | 0.247695i | ||||
\(470\) | 7350.00 | 0.721341 | ||||||||
\(471\) | −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 | ||||
\(475\) | −3724.00 | −0.359724 | ||||||||
\(476\) | 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 | \(0.933715\pi\) | |||||||
\(480\) | −3920.00 | − | 6789.64i | −0.372756 | − | 0.645632i | ||||
\(481\) | 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 | ||||||||
\(485\) | 3087.00 | − | 5346.84i | 0.289017 | − | 0.500593i | ||||
\(486\) | 4928.00 | + | 8535.55i | 0.459956 | + | 0.796667i | ||||
\(487\) | 8024.50 | + | 13898.8i | 0.746663 | + | 1.29326i | 0.949414 | + | 0.314028i | \(0.101678\pi\) |
−0.202751 | + | 0.979230i | \(0.564988\pi\) | |||||||
\(488\) | −4956.00 | + | 8584.04i | −0.459729 | + | 0.796273i | ||||
\(489\) | −3269.00 | −0.302309 | ||||||||
\(490\) | −4459.00 | + | 1782.28i | −0.411096 | + | 0.164317i | ||||
\(491\) | 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 | ||||
\(495\) | 385.000 | − | 666.840i | 0.0349585 | − | 0.0605499i | ||||
\(496\) | −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 | \(0.0152243\pi\) | |||||||
\(500\) | −2814.00 | − | 4873.99i | −0.251692 | − | 0.435943i | ||||
\(501\) | −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 | \(-0.523724\pi\) | ||||
−0.0744607 | + | 0.997224i | \(0.523724\pi\) | |||||||
\(504\) | −1848.00 | − | 9602.49i | −0.163326 | − | 0.848668i | ||||
\(505\) | 9653.00 | 0.850600 | ||||||||
\(506\) | −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 | \(0.0315800\pi\) | |||||||
\(510\) | −2058.00 | −0.178686 | ||||||||
\(511\) | 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 | ||||
\(515\) | 2376.50 | + | 4116.22i | 0.203342 | + | 0.352199i | ||||
\(516\) | −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 | ||||||||
\(520\) | −1176.00 | + | 2036.89i | −0.0991750 | + | 0.171776i | ||||
\(521\) | 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 | \(0.491179\pi\) |
−0.879546 | + | 0.475813i | \(0.842154\pi\) | |||||||
\(524\) | −8596.00 | −0.716637 | ||||||||
\(525\) | −1862.00 | − | 9675.24i | −0.154789 | − | 0.804308i | ||||
\(526\) | −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 | ||||
\(530\) | −2121.00 | + | 3673.68i | −0.173831 | + | 0.301084i | ||||
\(531\) | −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 | ||||
\(535\) | −1599.50 | − | 2770.42i | −0.129257 | − | 0.223879i | ||||
\(536\) | 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 | ||||
\(540\) | 980.000 | 0.0780972 | ||||||||
\(541\) | 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 | ||||
\(545\) | −7875.00 | −0.618950 | ||||||||
\(546\) | −2744.00 | + | 2376.37i | −0.215078 | + | 0.186263i | ||||
\(547\) | −18464.0 | −1.44326 | −0.721630 | − | 0.692279i | \(-0.756607\pi\) | ||||
−0.721630 | + | 0.692279i | \(0.756607\pi\) | |||||||
\(548\) | −2250.00 | + | 3897.11i | −0.175393 | + | 0.303789i | ||||
\(549\) | 4543.00 | + | 7868.71i | 0.353170 | + | 0.611709i | ||||
\(550\) | −380.000 | − | 658.179i | −0.0294605 | − | 0.0510270i | ||||
\(551\) | −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 | ||||||||
\(555\) | −5365.50 | + | 9293.32i | −0.410365 | + | 0.710774i | ||||
\(556\) | 504.000 | + | 872.954i | 0.0384431 | + | 0.0665854i | ||||
\(557\) | 4706.50 | + | 8151.90i | 0.358027 | + | 0.620120i | 0.987631 | − | 0.156796i | \(-0.0501164\pi\) |
−0.629604 | + | 0.776916i | \(0.716783\pi\) | |||||||
\(558\) | −3234.00 | + | 5601.45i | −0.245351 | + | 0.424961i | ||||
\(559\) | 1736.00 | 0.131351 | ||||||||
\(560\) | 1960.00 | + | 678.964i | 0.147902 | + | 0.0512348i | ||||
\(561\) | 735.000 | 0.0553150 | ||||||||
\(562\) | 4954.00 | − | 8580.58i | 0.371836 | − | 0.644039i | ||||
\(563\) | −1599.50 | − | 2770.42i | −0.119735 | − | 0.207387i | 0.799928 | − | 0.600097i | \(-0.204871\pi\) |
−0.919663 | + | 0.392709i | \(0.871538\pi\) | |||||||
\(564\) | 7350.00 | + | 12730.6i | 0.548743 | + | 0.950450i | ||||
\(565\) | 5383.00 | − | 9323.63i | 0.400822 | − | 0.694244i | ||||
\(566\) | −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 | \(0.874093\pi\) | |||||||
\(570\) | −2401.00 | − | 4158.65i | −0.176433 | − | 0.305591i | ||||
\(571\) | −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 | ||||
\(575\) | 12084.0 | 0.876413 | ||||||||
\(576\) | −4928.00 | + | 8535.55i | −0.356481 | + | 0.617444i | ||||
\(577\) | −6975.50 | − | 12081.9i | −0.503282 | − | 0.871710i | −0.999993 | − | 0.00379418i | \(-0.998792\pi\) |
0.496711 | − | 0.867916i | \(-0.334541\pi\) | |||||||
\(578\) | 4472.00 | + | 7745.73i | 0.321818 | + | 0.557405i | ||||
\(579\) | 1389.50 | − | 2406.68i | 0.0997334 | − | 0.172743i | ||||
\(580\) | −1624.00 | −0.116264 | ||||||||
\(581\) | 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 | ||||
\(585\) | 1078.00 | + | 1867.15i | 0.0761877 | + | 0.131961i | ||||
\(586\) | −7742.00 | + | 13409.5i | −0.545766 | + | 0.945295i | ||||
\(587\) | −20972.0 | −1.47463 | −0.737314 | − | 0.675550i | \(-0.763906\pi\) | ||||
−0.737314 | + | 0.675550i | \(0.763906\pi\) | |||||||
\(588\) | −7546.00 | − | 5940.93i | −0.529238 | − | 0.416667i | ||||
\(589\) | 7203.00 | 0.503895 | ||||||||
\(590\) | 735.000 | − | 1273.06i | 0.0512872 | − | 0.0888321i | ||||
\(591\) | −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 | −0.862735 | − | 0.505657i | \(-0.831250\pi\) |
0.869279 | + | 0.494322i | \(0.164584\pi\) | |||||||
\(594\) | 350.000 | 0.0241762 | ||||||||
\(595\) | −2058.00 | + | 1782.28i | −0.141798 | + | 0.122801i | ||||
\(596\) | 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 | \(0.719296\pi\) | |||||||
\(600\) | −6384.00 | + | 11057.4i | −0.434376 | + | 0.752362i | ||||
\(601\) | −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 | ||||
\(605\) | 4571.00 | + | 7917.20i | 0.307170 | + | 0.532033i | ||||
\(606\) | −9653.00 | − | 16719.5i | −0.647073 | − | 1.12076i | ||||
\(607\) | −2474.50 | + | 4285.96i | −0.165464 | + | 0.286593i | −0.936820 | − | 0.349812i | \(-0.886246\pi\) |
0.771356 | + | 0.636404i | \(0.219579\pi\) | |||||||
\(608\) | 7840.00 | 0.522951 | ||||||||
\(609\) | −7105.00 | − | 2461.24i | −0.472757 | − | 0.163768i | ||||
\(610\) | −5782.00 | −0.383781 | ||||||||
\(611\) | 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 | \(0.00755791\pi\) |
−0.479298 | + | 0.877652i | \(0.659109\pi\) | |||||||
\(614\) | 7364.00 | − | 12754.8i | 0.484018 | − | 0.838343i | ||||
\(615\) | 17150.0 | 1.12448 | ||||||||
\(616\) | −2100.00 | − | 727.461i | −0.137356 | − | 0.0475816i | ||||
\(617\) | −9378.00 | −0.611903 | −0.305951 | − | 0.952047i | \(-0.598975\pi\) | ||||
−0.305951 | + | 0.952047i | \(0.598975\pi\) | |||||||
\(618\) | 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 | \(0.543074\pi\) | |||||||
\(620\) | 2058.00 | + | 3564.56i | 0.133308 | + | 0.230897i | ||||
\(621\) | −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 | ||||||||
\(625\) | 174.500 | − | 302.243i | 0.0111680 | − | 0.0193435i | ||||
\(626\) | 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 | ||||||||
\(630\) | 4312.00 | − | 3734.30i | 0.272689 | − | 0.236156i | ||||
\(631\) | −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 | ||||
\(635\) | −252.000 | + | 436.477i | −0.0157485 | + | 0.0272772i | ||||
\(636\) | −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 | ||||
\(640\) | 1344.00 | + | 2327.88i | 0.0830098 | + | 0.143777i | ||||
\(641\) | 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 | \(-0.405414\pi\) | ||||
0.292797 | + | 0.956175i | \(0.405414\pi\) | |||||||
\(644\) | 8904.00 | − | 7711.09i | 0.544824 | − | 0.471832i | ||||
\(645\) | −6076.00 | −0.370918 | ||||||||
\(646\) | 1029.00 | − | 1782.28i | 0.0626710 | − | 0.108549i | ||||
\(647\) | 1620.50 | + | 2806.79i | 0.0984674 | + | 0.170551i | 0.911050 | − | 0.412295i | \(-0.135273\pi\) |
−0.812583 | + | 0.582845i | \(0.801939\pi\) | |||||||
\(648\) | −10068.0 | − | 17438.3i | −0.610352 | − | 1.05716i | ||||
\(649\) | −262.500 | + | 454.663i | −0.0158768 | + | 0.0274994i | ||||
\(650\) | 2128.00 | 0.128411 | ||||||||
\(651\) | 3601.50 | + | 18713.9i | 0.216826 | + | 1.12666i | ||||
\(652\) | 1868.00 | 0.112203 | ||||||||
\(653\) | 4426.50 | − | 7666.92i | 0.265272 | − | 0.459464i | −0.702363 | − | 0.711819i | \(-0.747872\pi\) |
0.967635 | + | 0.252355i | \(0.0812051\pi\) | |||||||
\(654\) | 7875.00 | + | 13639.9i | 0.470851 | + | 0.815539i | ||||
\(655\) | −7521.50 | − | 13027.6i | −0.448686 | − | 0.777147i | ||||
\(656\) | 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 | \(0.433243\pi\) | |||||||
\(660\) | −490.000 | + | 848.705i | −0.0288988 | + | 0.0500542i | ||||
\(661\) | 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 | ||||||||
\(665\) | −6002.50 | − | 2079.33i | −0.350026 | − | 0.121252i | ||||
\(666\) | 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 | ||||
\(670\) | −2905.00 | + | 5031.61i | −0.167507 | + | 0.290131i | ||||
\(671\) | 2065.00 | 0.118805 | ||||||||
\(672\) | 3920.00 | + | 20368.9i | 0.225026 | + | 1.16927i | ||||
\(673\) | 982.000 | 0.0562456 | 0.0281228 | − | 0.999604i | \(-0.491047\pi\) | ||||
0.0281228 | + | 0.999604i | \(0.491047\pi\) | |||||||
\(674\) | −7366.00 | + | 12758.3i | −0.420961 | + | 0.729126i | ||||
\(675\) | −1330.00 | − | 2303.63i | −0.0758396 | − | 0.131358i | ||||
\(676\) | −4002.00 | − | 6931.67i | −0.227697 | − | 0.394383i | ||||
\(677\) | 15256.5 | − | 26425.0i | 0.866108 | − | 1.50014i | 0.000164659 | − | 1.00000i | \(-0.499948\pi\) |
0.865943 | − | 0.500143i | \(-0.166719\pi\) | |||||||
\(678\) | −21532.0 | −1.21966 | ||||||||
\(679\) | −12348.0 | + | 10693.7i | −0.697898 | + | 0.604397i | ||||
\(680\) | 3528.00 | 0.198960 | ||||||||
\(681\) | 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 | 0.659350 | − | 0.751836i | \(-0.270831\pi\) |
−0.980784 | + | 0.195096i | \(0.937498\pi\) | |||||||
\(684\) | 2156.00 | − | 3734.30i | 0.120522 | − | 0.208749i | ||||
\(685\) | −7875.00 | −0.439253 | ||||||||
\(686\) | 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 | ||||
\(690\) | 7791.00 | + | 13494.4i | 0.429853 | + | 0.744527i | ||||
\(691\) | 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 | ||||||||
\(695\) | −882.000 | + | 1527.67i | −0.0481384 | + | 0.0833781i | ||||
\(696\) | 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 | ||||||||
\(700\) | 1064.00 | + | 5528.71i | 0.0574506 | + | 0.298522i | ||||
\(701\) | 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 | ||||
\(705\) | −12862.5 | + | 22278.5i | −0.687134 | + | 1.19015i | ||||
\(706\) | 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 | \(0.254606\pi\) | |||||||
\(710\) | 3024.00 | + | 5237.72i | 0.159843 | + | 0.276857i | ||||
\(711\) | 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 | ||||
\(715\) | 490.000 | 0.0256293 | ||||||||
\(716\) | −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 | \(0.847086\pi\) | |||||||
\(720\) | −2464.00 | −0.127539 | ||||||||
\(721\) | −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 | ||||
\(725\) | 2204.00 | + | 3817.44i | 0.112903 | + | 0.195553i | ||||
\(726\) | 9142.00 | − | 15834.4i | 0.467344 | − | 0.809463i | ||||
\(727\) | 29456.0 | 1.50270 | 0.751350 | − | 0.659904i | \(-0.229403\pi\) | ||||
0.751350 | + | 0.659904i | \(0.229403\pi\) | |||||||
\(728\) | 4704.00 | − | 4073.78i | 0.239481 | − | 0.207396i | ||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | 7791.00 | − | 13494.4i | 0.395011 | − | 0.684179i | ||||
\(731\) | −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 | \(0.414425\pi\) |
−0.967725 | + | 0.252009i | \(0.918909\pi\) | |||||||
\(734\) | −9282.00 | −0.466764 | ||||||||
\(735\) | 2401.00 | − | 16634.6i | 0.120493 | − | 0.834799i | ||||
\(736\) | −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 | \(0.994988\pi\) | |||||||
\(740\) | 3066.00 | − | 5310.47i | 0.152309 | − | 0.263806i | ||||
\(741\) | −4802.00 | −0.238065 | ||||||||
\(742\) | 8484.00 | − | 7347.36i | 0.419754 | − | 0.363518i | ||||
\(743\) | 1248.00 | 0.0616214 | 0.0308107 | − | 0.999525i | \(-0.490191\pi\) | ||||
0.0308107 | + | 0.999525i | \(0.490191\pi\) | |||||||
\(744\) | 12348.0 | − | 21387.4i | 0.608467 | − | 1.05390i | ||||
\(745\) | 703.500 | + | 1218.50i | 0.0345963 | + | 0.0599226i | ||||
\(746\) | 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 | ||||
\(750\) | −19698.0 | −0.959026 | ||||||||
\(751\) | −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 | ||||
\(755\) | 11333.0 | 0.546292 | ||||||||
\(756\) | −2450.00 | − | 848.705i | −0.117865 | − | 0.0408295i | ||||
\(757\) | 35954.0 | 1.72625 | 0.863124 | − | 0.504991i | \(-0.168504\pi\) | ||||
0.863124 | + | 0.504991i | \(0.168504\pi\) | |||||||
\(758\) | −13680.0 | + | 23694.5i | −0.655514 | + | 1.13538i | ||||
\(759\) | −2782.50 | − | 4819.43i | −0.133068 | − | 0.230480i | ||||
\(760\) | 4116.00 | + | 7129.12i | 0.196451 | + | 0.340264i | ||||
\(761\) | 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 | ||||||||
\(765\) | 1617.00 | − | 2800.73i | 0.0764219 | − | 0.132367i | ||||
\(766\) | −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 | \(0.303300\pi\) | |||||||
\(770\) | −245.000 | − | 1273.06i | −0.0114665 | − | 0.0595816i | ||||
\(771\) | −5635.00 | −0.263216 | ||||||||
\(772\) | −794.000 | + | 1375.25i | −0.0370164 | + | 0.0641143i | ||||
\(773\) | −8249.50 | − | 14288.6i | −0.383847 | − | 0.664843i | 0.607761 | − | 0.794120i | \(-0.292068\pi\) |
−0.991609 | + | 0.129277i | \(0.958734\pi\) | |||||||
\(774\) | 2728.00 | + | 4725.03i | 0.126687 | + | 0.219429i | ||||
\(775\) | 5586.00 | − | 9675.24i | 0.258910 | − | 0.448445i | ||||
\(776\) | 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 | ||||
\(780\) | −1372.00 | − | 2376.37i | −0.0629814 | − | 0.109087i | ||||
\(781\) | −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 | ||||
\(785\) | 4753.00 | 0.216104 | ||||||||
\(786\) | −15043.0 | + | 26055.2i | −0.682654 | + | 1.18239i | ||||
\(787\) | −8235.50 | − | 14264.3i | −0.373016 | − | 0.646083i | 0.617012 | − | 0.786954i | \(-0.288343\pi\) |
−0.990028 | + | 0.140871i | \(0.955010\pi\) | |||||||
\(788\) | 5828.00 | + | 10094.4i | 0.263469 | + | 0.456342i | ||||
\(789\) | 899.500 | − | 1557.98i | 0.0405869 | − | 0.0702985i | ||||
\(790\) | −1442.00 | −0.0649418 | ||||||||
\(791\) | −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 | ||||
\(795\) | −7423.50 | − | 12857.9i | −0.331175 | − | 0.573613i | ||||
\(796\) | 6678.00 | − | 11566.6i | 0.297356 | − | 0.515036i | ||||
\(797\) | −36470.0 | −1.62087 | −0.810435 | − | 0.585828i | \(-0.800769\pi\) | ||||
−0.810435 | + | 0.585828i | \(0.800769\pi\) | |||||||
\(798\) | 2401.00 | + | 12476.0i | 0.106509 | + | 0.553439i | ||||
\(799\) | −11025.0 | −0.488156 | ||||||||
\(800\) | 6080.00 | − | 10530.9i | 0.268701 | − | 0.465403i | ||||
\(801\) | 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 | ||||||||
\(805\) | 19477.5 | + | 6747.20i | 0.852785 | + | 0.295413i | ||||
\(806\) | −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 | \(-0.449849\pi\) | |||||||
\(810\) | 5873.00 | − | 10172.3i | 0.254761 | − | 0.441259i | ||||
\(811\) | −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 | ||||
\(815\) | 1634.50 | + | 2831.04i | 0.0702504 | + | 0.121677i | ||||
\(816\) | −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 | ||||
\(820\) | −9800.00 | −0.417355 | ||||||||
\(821\) | 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 | \(0.0114450\pi\) |
−0.468545 | + | 0.883440i | \(0.655222\pi\) | |||||||
\(824\) | −8148.00 | + | 14112.7i | −0.344477 | + | 0.596652i | ||||
\(825\) | 2660.00 | 0.112254 | ||||||||
\(826\) | −2940.00 | + | 2546.11i | −0.123845 | + | 0.107253i | ||||
\(827\) | 9732.00 | 0.409208 | 0.204604 | − | 0.978845i | \(-0.434409\pi\) | ||||
0.204604 | + | 0.978845i | \(0.434409\pi\) | |||||||
\(828\) | −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 | \(-0.364164\pi\) | |||||||
\(830\) | −7644.00 | − | 13239.8i | −0.319671 | − | 0.553687i | ||||
\(831\) | −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 | ||||||||
\(835\) | −4214.00 | + | 7298.86i | −0.174648 | + | 0.302500i | ||||
\(836\) | −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 | \(0.356972\pi\) | |||||||
\(840\) | −16464.0 | + | 14258.2i | −0.676264 | + | 0.585662i | ||||
\(841\) | −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 | ||||
\(845\) | 7003.50 | − | 12130.4i | 0.285122 | − | 0.493845i | ||||
\(846\) | 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 | ||||
\(850\) | −1596.00 | − | 2764.35i | −0.0644028 | − | 0.111549i | ||||
\(851\) | 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 | \(-0.640164\pi\) | ||||
−0.426246 | + | 0.904607i | \(0.640164\pi\) | |||||||
\(854\) | 14455.0 | + | 5007.36i | 0.579204 | + | 0.200642i | ||||
\(855\) | 7546.00 | 0.301834 | ||||||||
\(856\) | 5484.00 | − | 9498.57i | 0.218971 | − | 0.379269i | ||||
\(857\) | 17804.5 | + | 30838.3i | 0.709673 | + | 1.22919i | 0.964978 | + | 0.262330i | \(0.0844908\pi\) |
−0.255305 | + | 0.966861i | \(0.582176\pi\) | |||||||
\(858\) | −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 | \(0.180433\pi\) | |||||||
\(860\) | 3472.00 | 0.137668 | ||||||||
\(861\) | −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 | \(-0.613930\pi\) |
0.986307 | − | 0.164921i | \(-0.0527371\pi\) | |||||||
\(864\) | 2800.00 | + | 4849.74i | 0.110252 | + | 0.190962i | ||||
\(865\) | 9873.50 | + | 17101.4i | 0.388103 | + | 0.672214i | ||||
\(866\) | −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 | ||||||||
\(870\) | −2842.00 | + | 4922.49i | −0.110750 | + | 0.191825i | ||||
\(871\) | 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 | ||||||||
\(875\) | −19698.0 | + | 17059.0i | −0.761045 | + | 0.659084i | ||||
\(876\) | 31164.0 | 1.20198 | ||||||||
\(877\) | −13815.5 | + | 23929.1i | −0.531946 | + | 0.921357i | 0.467359 | + | 0.884068i | \(0.345206\pi\) |
−0.999305 | + | 0.0372891i | \(0.988128\pi\) | |||||||
\(878\) | 4179.00 | + | 7238.24i | 0.160631 | + | 0.278222i | ||||
\(879\) | −27097.0 | − | 46933.4i | −1.03977 | − | 1.80094i | ||||
\(880\) | −280.000 | + | 484.974i | −0.0107259 | + | 0.0185778i | ||||
\(881\) | 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 | \(-0.621919\pi\) | ||||
−0.373724 | + | 0.927540i | \(0.621919\pi\) | |||||||
\(884\) | 588.000 | − | 1018.45i | 0.0223717 | − | 0.0387489i | ||||
\(885\) | 2572.50 | + | 4455.70i | 0.0977103 | + | 0.169239i | ||||
\(886\) | 12927.0 | + | 22390.2i | 0.490170 | + | 0.849000i | ||||
\(887\) | −1130.50 | + | 1958.08i | −0.0427942 | + | 0.0741218i | −0.886629 | − | 0.462481i | \(-0.846959\pi\) |
0.843835 | + | 0.536603i | \(0.180293\pi\) | |||||||
\(888\) | −36792.0 | −1.39038 | ||||||||
\(889\) | 1008.00 | − | 872.954i | 0.0380284 | − | 0.0329335i | ||||
\(890\) | −4606.00 | −0.173476 | ||||||||
\(891\) | −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 | ||||
\(895\) | −22771.0 | −0.850448 | ||||||||
\(896\) | −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 | ||||
\(900\) | −3344.00 | − | 5791.98i | −0.123852 | − | 0.214518i | ||||
\(901\) | 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 | ||||||||
\(905\) | −5537.00 | + | 9590.37i | −0.203377 | + | 0.352259i | ||||
\(906\) | −11333.0 | − | 19629.3i | −0.415578 | − | 0.719802i | ||||
\(907\) | 11916.5 | + | 20640.0i | 0.436252 | + | 0.755611i | 0.997397 | − | 0.0721066i | \(-0.0229722\pi\) |
−0.561145 | + | 0.827718i | \(0.689639\pi\) | |||||||
\(908\) | −4410.00 | + | 7638.34i | −0.161180 | + | 0.279171i | ||||
\(909\) | 30338.0 | 1.10698 | ||||||||
\(910\) | 3430.00 | + | 1188.19i | 0.124949 | + | 0.0432835i | ||||
\(911\) | 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 | ||||
\(915\) | 10118.5 | − | 17525.8i | 0.365582 | − | 0.633206i | ||||
\(916\) | −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 | \(0.0690612\pi\) | |||||||
\(920\) | −13356.0 | − | 23133.3i | −0.478624 | − | 0.829001i | ||||
\(921\) | 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 | ||||
\(925\) | −16644.0 | −0.591623 | ||||||||
\(926\) | 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 | \(0.176780\pi\) | |||||||
\(930\) | 14406.0 | 0.507948 | ||||||||
\(931\) | 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 | ||||
\(935\) | −367.500 | − | 636.529i | −0.0128540 | − | 0.0222639i | ||||
\(936\) | −3696.00 | + | 6401.66i | −0.129068 | + | 0.223552i | ||||
\(937\) | 14154.0 | 0.493480 | 0.246740 | − | 0.969082i | \(-0.420641\pi\) | ||||
0.246740 | + | 0.969082i | \(0.420641\pi\) | |||||||
\(938\) | 11620.0 | − | 10063.2i | 0.404484 | − | 0.350294i | ||||
\(939\) | −33271.0 | −1.15629 | ||||||||
\(940\) | 7350.00 | − | 12730.6i | 0.255033 | − | 0.441729i | ||||
\(941\) | −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 | ||||||||
\(945\) | −857.500 | − | 4455.70i | −0.0295180 | − | 0.153380i | ||||
\(946\) | 1240.00 | 0.0426172 | ||||||||
\(947\) | 12189.5 | − | 21112.8i | 0.418274 | − | 0.724472i | −0.577492 | − | 0.816396i | \(-0.695969\pi\) |
0.995766 | + | 0.0919245i | \(0.0293018\pi\) | |||||||
\(948\) | −1442.00 | − | 2497.62i | −0.0494029 | − | 0.0855684i | ||||
\(949\) | −7791.00 | − | 13494.4i | −0.266498 | − | 0.461588i | ||||
\(950\) | 3724.00 | − | 6450.16i | 0.127182 | − | 0.220285i | ||||
\(951\) | −24339.0 | −0.829912 | ||||||||
\(952\) | −8820.00 | − | 3055.34i | −0.300271 | − | 0.104017i | ||||
\(953\) | −52330.0 | −1.77874 | −0.889368 | − | 0.457192i | \(-0.848855\pi\) | ||||
−0.889368 | + | 0.457192i | \(0.848855\pi\) | |||||||
\(954\) | −6666.00 | + | 11545.9i | −0.226226 | + | 0.391835i | ||||
\(955\) | −8949.50 | − | 15501.0i | −0.303245 | − | 0.525236i | ||||
\(956\) | 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 | ||||
\(960\) | 21952.0 | 0.738018 | ||||||||
\(961\) | 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 | ||||
\(965\) | −2779.00 | −0.0927038 | ||||||||
\(966\) | −7791.00 | − | 40483.2i | −0.259494 | − | 1.34837i | ||||
\(967\) | −12416.0 | −0.412897 | −0.206449 | − | 0.978457i | \(-0.566191\pi\) | ||||
−0.206449 | + | 0.978457i | \(0.566191\pi\) | |||||||
\(968\) | −15672.0 | + | 27144.7i | −0.520369 | + | 0.901305i | ||||
\(969\) | 3601.50 | + | 6237.98i | 0.119398 | + | 0.206804i | ||||
\(970\) | 6174.00 | + | 10693.7i | 0.204366 | + | 0.353973i | ||||
\(971\) | −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 | ||||||||
\(975\) | −3724.00 | + | 6450.16i | −0.122321 | + | 0.211867i | ||||
\(976\) | −3304.00 | − | 5722.70i | −0.108359 | − | 0.187683i | ||||
\(977\) | −17497.5 | − | 30306.6i | −0.572973 | − | 0.992418i | −0.996259 | − | 0.0864221i | \(-0.972457\pi\) |
0.423286 | − | 0.905996i | \(-0.360877\pi\) | |||||||
\(978\) | 3269.00 | − | 5662.07i | 0.106883 | − | 0.185126i | ||||
\(979\) | 1645.00 | 0.0537022 | ||||||||
\(980\) | −1372.00 | + | 9505.49i | −0.0447214 | + | 0.309839i | ||||
\(981\) | −24750.0 | −0.805511 | ||||||||
\(982\) | −8864.00 | + | 15352.9i | −0.288046 | + | 0.498911i | ||||
\(983\) | 7150.50 | + | 12385.0i | 0.232010 | + | 0.401853i | 0.958399 | − | 0.285430i | \(-0.0921366\pi\) |
−0.726390 | + | 0.687283i | \(0.758803\pi\) | |||||||
\(984\) | 29400.0 | + | 50922.3i | 0.952477 | + | 1.64974i | ||||
\(985\) | −10199.0 | + | 17665.2i | −0.329916 | + | 0.571431i | ||||
\(986\) | −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 | ||||
\(990\) | 770.000 | + | 1333.68i | 0.0247194 | + | 0.0428153i | ||||
\(991\) | 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 | ||||
\(995\) | 23373.0 | 0.744697 | ||||||||
\(996\) | 15288.0 | − | 26479.6i | 0.486364 | − | 0.842408i | ||||
\(997\) | −12435.5 | − | 21538.9i | −0.395021 | − | 0.684197i | 0.598083 | − | 0.801434i | \(-0.295929\pi\) |
−0.993104 | + | 0.117237i | \(0.962596\pi\) | |||||||
\(998\) | 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 | 7.4.c.a.2.1 | ✓ | 2 | |
3.2 | odd | 2 | 63.4.e.b.37.1 | 2 | |||
4.3 | odd | 2 | 112.4.i.c.65.1 | 2 | |||
5.2 | odd | 4 | 175.4.k.a.149.1 | 4 | |||
5.3 | odd | 4 | 175.4.k.a.149.2 | 4 | |||
5.4 | even | 2 | 175.4.e.a.51.1 | 2 | |||
7.2 | even | 3 | 49.4.a.d.1.1 | 1 | |||
7.3 | odd | 6 | 49.4.c.a.18.1 | 2 | |||
7.4 | even | 3 | inner | 7.4.c.a.4.1 | yes | 2 | |
7.5 | odd | 6 | 49.4.a.c.1.1 | 1 | |||
7.6 | odd | 2 | 49.4.c.a.30.1 | 2 | |||
8.3 | odd | 2 | 448.4.i.a.65.1 | 2 | |||
8.5 | even | 2 | 448.4.i.f.65.1 | 2 | |||
21.2 | odd | 6 | 441.4.a.d.1.1 | 1 | |||
21.5 | even | 6 | 441.4.a.e.1.1 | 1 | |||
21.11 | odd | 6 | 63.4.e.b.46.1 | 2 | |||
21.17 | even | 6 | 441.4.e.k.361.1 | 2 | |||
21.20 | even | 2 | 441.4.e.k.226.1 | 2 | |||
28.11 | odd | 6 | 112.4.i.c.81.1 | 2 | |||
28.19 | even | 6 | 784.4.a.r.1.1 | 1 | |||
28.23 | odd | 6 | 784.4.a.b.1.1 | 1 | |||
35.4 | even | 6 | 175.4.e.a.151.1 | 2 | |||
35.9 | even | 6 | 1225.4.a.c.1.1 | 1 | |||
35.18 | odd | 12 | 175.4.k.a.74.1 | 4 | |||
35.19 | odd | 6 | 1225.4.a.d.1.1 | 1 | |||
35.32 | odd | 12 | 175.4.k.a.74.2 | 4 | |||
56.11 | odd | 6 | 448.4.i.a.193.1 | 2 | |||
56.53 | even | 6 | 448.4.i.f.193.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.4.c.a.2.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
7.4.c.a.4.1 | yes | 2 | 7.4 | even | 3 | inner | |
49.4.a.c.1.1 | 1 | 7.5 | odd | 6 | |||
49.4.a.d.1.1 | 1 | 7.2 | even | 3 | |||
49.4.c.a.18.1 | 2 | 7.3 | odd | 6 | |||
49.4.c.a.30.1 | 2 | 7.6 | odd | 2 | |||
63.4.e.b.37.1 | 2 | 3.2 | odd | 2 | |||
63.4.e.b.46.1 | 2 | 21.11 | odd | 6 | |||
112.4.i.c.65.1 | 2 | 4.3 | odd | 2 | |||
112.4.i.c.81.1 | 2 | 28.11 | odd | 6 | |||
175.4.e.a.51.1 | 2 | 5.4 | even | 2 | |||
175.4.e.a.151.1 | 2 | 35.4 | even | 6 | |||
175.4.k.a.74.1 | 4 | 35.18 | odd | 12 | |||
175.4.k.a.74.2 | 4 | 35.32 | odd | 12 | |||
175.4.k.a.149.1 | 4 | 5.2 | odd | 4 | |||
175.4.k.a.149.2 | 4 | 5.3 | odd | 4 | |||
441.4.a.d.1.1 | 1 | 21.2 | odd | 6 | |||
441.4.a.e.1.1 | 1 | 21.5 | even | 6 | |||
441.4.e.k.226.1 | 2 | 21.20 | even | 2 | |||
441.4.e.k.361.1 | 2 | 21.17 | even | 6 | |||
448.4.i.a.65.1 | 2 | 8.3 | odd | 2 | |||
448.4.i.a.193.1 | 2 | 56.11 | odd | 6 | |||
448.4.i.f.65.1 | 2 | 8.5 | even | 2 | |||
448.4.i.f.193.1 | 2 | 56.53 | even | 6 | |||
784.4.a.b.1.1 | 1 | 28.23 | odd | 6 | |||
784.4.a.r.1.1 | 1 | 28.19 | even | 6 | |||
1225.4.a.c.1.1 | 1 | 35.9 | even | 6 | |||
1225.4.a.d.1.1 | 1 | 35.19 | odd | 6 |