Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,4,Mod(74,175)]
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([3, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.74");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.3253342510\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 74.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.74 |
Dual form | 175.4.k.a.149.1 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | + | 1.00000i | −0.612372 | + | 0.353553i | −0.773893 | − | 0.633316i | \(-0.781693\pi\) |
0.161521 | + | 0.986869i | \(0.448360\pi\) | |||||||
\(3\) | −6.06218 | − | 3.50000i | −1.16667 | − | 0.673575i | −0.213774 | − | 0.976883i | \(-0.568576\pi\) |
−0.952893 | + | 0.303308i | \(0.901909\pi\) | |||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 14.0000 | 0.952579 | ||||||||
\(7\) | 12.1244 | − | 14.0000i | 0.654654 | − | 0.755929i | ||||
\(8\) | − | 24.0000i | − | 1.06066i | ||||||
\(9\) | 11.0000 | + | 19.0526i | 0.407407 | + | 0.705650i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | − | 4.33013i | 0.0685253 | − | 0.118689i | −0.829727 | − | 0.558169i | \(-0.811504\pi\) |
0.898252 | + | 0.439480i | \(0.144837\pi\) | |||||||
\(12\) | 24.2487 | − | 14.0000i | 0.583333 | − | 0.336788i | ||||
\(13\) | − | 14.0000i | − | 0.298685i | −0.988786 | − | 0.149342i | \(-0.952284\pi\) | ||
0.988786 | − | 0.149342i | \(-0.0477157\pi\) | |||||||
\(14\) | −7.00000 | + | 36.3731i | −0.133631 | + | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.00000 | + | 13.8564i | 0.125000 | + | 0.216506i | ||||
\(17\) | −18.1865 | − | 10.5000i | −0.259464 | − | 0.149801i | 0.364626 | − | 0.931154i | \(-0.381197\pi\) |
−0.624090 | + | 0.781353i | \(0.714530\pi\) | |||||||
\(18\) | −38.1051 | − | 22.0000i | −0.498970 | − | 0.288081i | ||||
\(19\) | 24.5000 | + | 42.4352i | 0.295826 | + | 0.512385i | 0.975177 | − | 0.221429i | \(-0.0710720\pi\) |
−0.679351 | + | 0.733813i | \(0.737739\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −122.500 | + | 42.4352i | −1.27294 | + | 0.440959i | ||||
\(22\) | 10.0000i | 0.0969094i | ||||||||
\(23\) | −137.698 | + | 79.5000i | −1.24835 | + | 0.720735i | −0.970780 | − | 0.239971i | \(-0.922862\pi\) |
−0.277569 | + | 0.960706i | \(0.589529\pi\) | |||||||
\(24\) | −84.0000 | + | 145.492i | −0.714435 | + | 1.23744i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.0000 | + | 24.2487i | 0.105601 | + | 0.182906i | ||||
\(27\) | 35.0000i | 0.249472i | ||||||||
\(28\) | 24.2487 | + | 70.0000i | 0.163663 | + | 0.472456i | ||||
\(29\) | −58.0000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −73.5000 | + | 127.306i | −0.425838 | + | 0.737574i | −0.996498 | − | 0.0836128i | \(-0.973354\pi\) |
0.570660 | + | 0.821186i | \(0.306687\pi\) | |||||||
\(32\) | 138.564 | + | 80.0000i | 0.765466 | + | 0.441942i | ||||
\(33\) | −30.3109 | + | 17.5000i | −0.159892 | + | 0.0923139i | ||||
\(34\) | 42.0000 | 0.211851 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −88.0000 | −0.407407 | ||||||||
\(37\) | −189.660 | + | 109.500i | −0.842698 | + | 0.486532i | −0.858181 | − | 0.513348i | \(-0.828405\pi\) |
0.0154821 | + | 0.999880i | \(0.495072\pi\) | |||||||
\(38\) | −84.8705 | − | 49.0000i | −0.362311 | − | 0.209180i | ||||
\(39\) | −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 | \(0.267751\pi\) | |||||||
\(42\) | 169.741 | − | 196.000i | 0.623610 | − | 0.720082i | ||||
\(43\) | − | 124.000i | − | 0.439763i | −0.975527 | − | 0.219882i | \(-0.929433\pi\) | ||
0.975527 | − | 0.219882i | \(-0.0705671\pi\) | |||||||
\(44\) | 10.0000 | + | 17.3205i | 0.0342627 | + | 0.0593447i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 159.000 | − | 275.396i | 0.509636 | − | 0.882716i | ||||
\(47\) | −454.663 | + | 262.500i | −1.41105 | + | 0.814671i | −0.995488 | − | 0.0948921i | \(-0.969749\pi\) |
−0.415565 | + | 0.909564i | \(0.636416\pi\) | |||||||
\(48\) | − | 112.000i | − | 0.336788i | ||||||
\(49\) | −49.0000 | − | 339.482i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 73.5000 | + | 127.306i | 0.201805 | + | 0.349537i | ||||
\(52\) | 48.4974 | + | 28.0000i | 0.129334 | + | 0.0746712i | ||||
\(53\) | −262.406 | − | 151.500i | −0.680079 | − | 0.392644i | 0.119806 | − | 0.992797i | \(-0.461773\pi\) |
−0.799885 | + | 0.600153i | \(0.795106\pi\) | |||||||
\(54\) | −35.0000 | − | 60.6218i | −0.0882018 | − | 0.152770i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −336.000 | − | 290.985i | −0.801784 | − | 0.694365i | ||||
\(57\) | − | 343.000i | − | 0.797043i | ||||||
\(58\) | 100.459 | − | 58.0000i | 0.227429 | − | 0.131306i | ||||
\(59\) | −52.5000 | + | 90.9327i | −0.115846 | + | 0.200651i | −0.918118 | − | 0.396308i | \(-0.870291\pi\) |
0.802272 | + | 0.596959i | \(0.203625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 206.500 | + | 357.668i | 0.433436 | + | 0.750734i | 0.997167 | − | 0.0752252i | \(-0.0239676\pi\) |
−0.563730 | + | 0.825959i | \(0.690634\pi\) | |||||||
\(62\) | − | 294.000i | − | 0.602226i | ||||||
\(63\) | 400.104 | + | 77.0000i | 0.800132 | + | 0.153986i | ||||
\(64\) | −448.000 | −0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 35.0000 | − | 60.6218i | 0.0652758 | − | 0.113061i | ||||
\(67\) | 359.401 | + | 207.500i | 0.655340 | + | 0.378361i | 0.790499 | − | 0.612463i | \(-0.209821\pi\) |
−0.135159 | + | 0.990824i | \(0.543155\pi\) | |||||||
\(68\) | 72.7461 | − | 42.0000i | 0.129732 | − | 0.0749007i | ||||
\(69\) | 1113.00 | 1.94188 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −432.000 | −0.722098 | −0.361049 | − | 0.932547i | \(-0.617581\pi\) | ||||
−0.361049 | + | 0.932547i | \(0.617581\pi\) | |||||||
\(72\) | 457.261 | − | 264.000i | 0.748455 | − | 0.432121i | ||||
\(73\) | 963.886 | + | 556.500i | 1.54540 | + | 0.892238i | 0.998483 | + | 0.0550526i | \(0.0175326\pi\) |
0.546919 | + | 0.837186i | \(0.315801\pi\) | |||||||
\(74\) | 219.000 | − | 379.319i | 0.344030 | − | 0.595878i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −196.000 | −0.295826 | ||||||||
\(77\) | −30.3109 | − | 87.5000i | −0.0448603 | − | 0.129501i | ||||
\(78\) | − | 196.000i | − | 0.284521i | ||||||
\(79\) | −51.5000 | − | 89.2006i | −0.0733443 | − | 0.127036i | 0.827021 | − | 0.562171i | \(-0.190034\pi\) |
−0.900365 | + | 0.435135i | \(0.856701\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 419.500 | − | 726.595i | 0.575446 | − | 0.996701i | ||||
\(82\) | −606.218 | + | 350.000i | −0.816409 | + | 0.471354i | ||||
\(83\) | 1092.00i | 1.44413i | 0.691827 | + | 0.722064i | \(0.256806\pi\) | ||||
−0.691827 | + | 0.722064i | \(0.743194\pi\) | |||||||
\(84\) | 98.0000 | − | 509.223i | 0.127294 | − | 0.661438i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 124.000 | + | 214.774i | 0.155480 | + | 0.269299i | ||||
\(87\) | 351.606 | + | 203.000i | 0.433289 | + | 0.250160i | ||||
\(88\) | −103.923 | − | 60.0000i | −0.125889 | − | 0.0726821i | ||||
\(89\) | −164.500 | − | 284.922i | −0.195921 | − | 0.339345i | 0.751281 | − | 0.659982i | \(-0.229436\pi\) |
−0.947202 | + | 0.320637i | \(0.896103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −196.000 | − | 169.741i | −0.225784 | − | 0.195535i | ||||
\(92\) | − | 636.000i | − | 0.720735i | ||||||
\(93\) | 891.140 | − | 514.500i | 0.993623 | − | 0.573668i | ||||
\(94\) | 525.000 | − | 909.327i | 0.576060 | − | 0.997765i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −560.000 | − | 969.948i | −0.595362 | − | 1.03120i | ||||
\(97\) | 882.000i | 0.923232i | 0.887080 | + | 0.461616i | \(0.152730\pi\) | ||||
−0.887080 | + | 0.461616i | \(0.847270\pi\) | |||||||
\(98\) | 424.352 | + | 539.000i | 0.437409 | + | 0.555584i | ||||
\(99\) | 110.000 | 0.111671 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −689.500 | + | 1194.25i | −0.679285 | + | 1.17656i | 0.295911 | + | 0.955215i | \(0.404377\pi\) |
−0.975196 | + | 0.221341i | \(0.928957\pi\) | |||||||
\(102\) | −254.611 | − | 147.000i | −0.247160 | − | 0.142698i | ||||
\(103\) | −588.031 | + | 339.500i | −0.562529 | + | 0.324776i | −0.754160 | − | 0.656691i | \(-0.771956\pi\) |
0.191631 | + | 0.981467i | \(0.438622\pi\) | |||||||
\(104\) | −336.000 | −0.316803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 606.000 | 0.555282 | ||||||||
\(107\) | −395.774 | + | 228.500i | −0.357578 | + | 0.206448i | −0.668018 | − | 0.744145i | \(-0.732857\pi\) |
0.310440 | + | 0.950593i | \(0.399524\pi\) | |||||||
\(108\) | −121.244 | − | 70.0000i | −0.108025 | − | 0.0623681i | ||||
\(109\) | −562.500 | + | 974.279i | −0.494291 | + | 0.856137i | −0.999978 | − | 0.00657959i | \(-0.997906\pi\) |
0.505687 | + | 0.862717i | \(0.331239\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1533.00 | 1.31086 | ||||||||
\(112\) | 290.985 | + | 56.0000i | 0.245495 | + | 0.0472456i | ||||
\(113\) | − | 1538.00i | − | 1.28038i | −0.768217 | − | 0.640190i | \(-0.778856\pi\) | ||
0.768217 | − | 0.640190i | \(-0.221144\pi\) | |||||||
\(114\) | 343.000 | + | 594.093i | 0.281797 | + | 0.488087i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 116.000 | − | 200.918i | 0.0928477 | − | 0.160817i | ||||
\(117\) | 266.736 | − | 154.000i | 0.210767 | − | 0.121686i | ||||
\(118\) | − | 210.000i | − | 0.163831i | ||||||
\(119\) | −367.500 | + | 127.306i | −0.283098 | + | 0.0980680i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 653.000 | + | 1131.03i | 0.490609 | + | 0.849759i | ||||
\(122\) | −715.337 | − | 413.000i | −0.530849 | − | 0.306486i | ||||
\(123\) | −2121.76 | − | 1225.00i | −1.55539 | − | 0.898004i | ||||
\(124\) | −294.000 | − | 509.223i | −0.212919 | − | 0.368787i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −770.000 | + | 266.736i | −0.544421 | + | 0.188593i | ||||
\(127\) | − | 72.0000i | − | 0.0503068i | −0.999684 | − | 0.0251534i | \(-0.991993\pi\) | ||
0.999684 | − | 0.0251534i | \(-0.00800742\pi\) | |||||||
\(128\) | −332.554 | + | 192.000i | −0.229640 | + | 0.132583i | ||||
\(129\) | −434.000 | + | 751.710i | −0.296214 | + | 0.513057i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1074.50 | − | 1861.09i | −0.716637 | − | 1.24125i | −0.962325 | − | 0.271903i | \(-0.912347\pi\) |
0.245687 | − | 0.969349i | \(-0.420986\pi\) | |||||||
\(132\) | − | 140.000i | − | 0.0923139i | ||||||
\(133\) | 891.140 | + | 171.500i | 0.580990 | + | 0.111812i | ||||
\(134\) | −830.000 | −0.535083 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −252.000 | + | 436.477i | −0.158888 | + | 0.275203i | ||||
\(137\) | −974.279 | − | 562.500i | −0.607578 | − | 0.350786i | 0.164439 | − | 0.986387i | \(-0.447419\pi\) |
−0.772017 | + | 0.635602i | \(0.780752\pi\) | |||||||
\(138\) | −1927.77 | + | 1113.00i | −1.18915 | + | 0.686557i | ||||
\(139\) | −252.000 | −0.153772 | −0.0768862 | − | 0.997040i | \(-0.524498\pi\) | ||||
−0.0768862 | + | 0.997040i | \(0.524498\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3675.00 | 2.19497 | ||||||||
\(142\) | 748.246 | − | 432.000i | 0.442193 | − | 0.255300i | ||||
\(143\) | −60.6218 | − | 35.0000i | −0.0354507 | − | 0.0204675i | ||||
\(144\) | −176.000 | + | 304.841i | −0.101852 | + | 0.176413i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2226.00 | −1.26182 | ||||||||
\(147\) | −891.140 | + | 2229.50i | −0.500000 | + | 1.25093i | ||||
\(148\) | − | 876.000i | − | 0.486532i | ||||||
\(149\) | −100.500 | − | 174.071i | −0.0552569 | − | 0.0957078i | 0.837074 | − | 0.547090i | \(-0.184264\pi\) |
−0.892331 | + | 0.451382i | \(0.850931\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −809.500 | + | 1402.10i | −0.436266 | + | 0.755635i | −0.997398 | − | 0.0720914i | \(-0.977033\pi\) |
0.561132 | + | 0.827726i | \(0.310366\pi\) | |||||||
\(152\) | 1018.45 | − | 588.000i | 0.543466 | − | 0.313770i | ||||
\(153\) | − | 462.000i | − | 0.244121i | ||||||
\(154\) | 140.000 | + | 121.244i | 0.0732566 | + | 0.0634421i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −196.000 | − | 339.482i | −0.100593 | − | 0.174233i | ||||
\(157\) | 588.031 | + | 339.500i | 0.298917 | + | 0.172580i | 0.641956 | − | 0.766741i | \(-0.278123\pi\) |
−0.343039 | + | 0.939321i | \(0.611456\pi\) | |||||||
\(158\) | 178.401 | + | 103.000i | 0.0898281 | + | 0.0518623i | ||||
\(159\) | 1060.50 | + | 1836.84i | 0.528950 | + | 0.916169i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −556.500 | + | 2891.66i | −0.272412 | + | 1.41549i | ||||
\(162\) | 1678.00i | 0.813803i | ||||||||
\(163\) | −404.434 | + | 233.500i | −0.194342 | + | 0.112203i | −0.594014 | − | 0.804455i | \(-0.702457\pi\) |
0.399672 | + | 0.916658i | \(0.369124\pi\) | |||||||
\(164\) | −700.000 | + | 1212.44i | −0.333298 | + | 0.577288i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1092.00 | − | 1891.40i | −0.510576 | − | 0.884344i | ||||
\(167\) | − | 1204.00i | − | 0.557894i | −0.960306 | − | 0.278947i | \(-0.910015\pi\) | ||
0.960306 | − | 0.278947i | \(-0.0899854\pi\) | |||||||
\(168\) | 1018.45 | + | 2940.00i | 0.467707 | + | 1.35015i | ||||
\(169\) | 2001.00 | 0.910787 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −539.000 | + | 933.575i | −0.241043 | + | 0.417499i | ||||
\(172\) | 429.549 | + | 248.000i | 0.190423 | + | 0.109941i | ||||
\(173\) | −2443.06 | + | 1410.50i | −1.07365 | + | 0.619875i | −0.929178 | − | 0.369633i | \(-0.879483\pi\) |
−0.144477 | + | 0.989508i | \(0.546150\pi\) | |||||||
\(174\) | −812.000 | −0.353779 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 80.0000 | 0.0342627 | ||||||||
\(177\) | 636.529 | − | 367.500i | 0.270307 | − | 0.156062i | ||||
\(178\) | 569.845 | + | 329.000i | 0.239953 | + | 0.138537i | ||||
\(179\) | −1626.50 | + | 2817.18i | −0.679164 | + | 1.17635i | 0.296069 | + | 0.955166i | \(0.404324\pi\) |
−0.975233 | + | 0.221180i | \(0.929009\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1582.00 | 0.649664 | 0.324832 | − | 0.945772i | \(-0.394692\pi\) | ||||
0.324832 | + | 0.945772i | \(0.394692\pi\) | |||||||
\(182\) | 509.223 | + | 98.0000i | 0.207396 | + | 0.0399134i | ||||
\(183\) | − | 2891.00i | − | 1.16781i | ||||||
\(184\) | 1908.00 | + | 3304.75i | 0.764454 | + | 1.32407i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1029.00 | + | 1782.28i | −0.405645 | + | 0.702597i | ||||
\(187\) | −90.9327 | + | 52.5000i | −0.0355597 | + | 0.0205304i | ||||
\(188\) | − | 2100.00i | − | 0.814671i | ||||||
\(189\) | 490.000 | + | 424.352i | 0.188583 | + | 0.163318i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1278.50 | − | 2214.43i | −0.484340 | − | 0.838902i | 0.515498 | − | 0.856891i | \(-0.327607\pi\) |
−0.999838 | + | 0.0179887i | \(0.994274\pi\) | |||||||
\(192\) | 2715.86 | + | 1568.00i | 1.02083 | + | 0.589378i | ||||
\(193\) | 343.812 | + | 198.500i | 0.128229 | + | 0.0740329i | 0.562742 | − | 0.826632i | \(-0.309746\pi\) |
−0.434514 | + | 0.900665i | \(0.643080\pi\) | |||||||
\(194\) | −882.000 | − | 1527.67i | −0.326412 | − | 0.565362i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1274.00 | + | 509.223i | 0.464286 | + | 0.185577i | ||||
\(197\) | − | 2914.00i | − | 1.05388i | −0.849903 | − | 0.526939i | \(-0.823340\pi\) | ||
0.849903 | − | 0.526939i | \(-0.176660\pi\) | |||||||
\(198\) | −190.526 | + | 110.000i | −0.0683842 | + | 0.0394816i | ||||
\(199\) | 1669.50 | − | 2891.66i | 0.594712 | − | 1.03007i | −0.398875 | − | 0.917005i | \(-0.630599\pi\) |
0.993587 | − | 0.113066i | \(-0.0360673\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1452.50 | − | 2515.80i | −0.509709 | − | 0.882841i | ||||
\(202\) | − | 2758.00i | − | 0.960654i | ||||||
\(203\) | −703.213 | + | 812.000i | −0.243132 | + | 0.280745i | ||||
\(204\) | −588.000 | −0.201805 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 679.000 | − | 1176.06i | 0.229651 | − | 0.397768i | ||||
\(207\) | −3029.36 | − | 1749.00i | −1.01717 | − | 0.587265i | ||||
\(208\) | 193.990 | − | 112.000i | 0.0646671 | − | 0.0373356i | ||||
\(209\) | 245.000 | 0.0810861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1780.00 | 0.580759 | 0.290380 | − | 0.956911i | \(-0.406218\pi\) | ||||
0.290380 | + | 0.956911i | \(0.406218\pi\) | |||||||
\(212\) | 1049.62 | − | 606.000i | 0.340040 | − | 0.196322i | ||||
\(213\) | 2618.86 | + | 1512.00i | 0.842448 | + | 0.486387i | ||||
\(214\) | 457.000 | − | 791.547i | 0.145981 | − | 0.252846i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 840.000 | 0.264605 | ||||||||
\(217\) | 891.140 | + | 2572.50i | 0.278777 | + | 0.804759i | ||||
\(218\) | − | 2250.00i | − | 0.699033i | ||||||
\(219\) | −3895.50 | − | 6747.20i | −1.20198 | − | 2.08189i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −147.000 | + | 254.611i | −0.0447434 | + | 0.0774978i | ||||
\(222\) | −2655.23 | + | 1533.00i | −0.802737 | + | 0.463460i | ||||
\(223\) | − | 1400.00i | − | 0.420408i | −0.977658 | − | 0.210204i | \(-0.932587\pi\) | ||
0.977658 | − | 0.210204i | \(-0.0674128\pi\) | |||||||
\(224\) | 2800.00 | − | 969.948i | 0.835191 | − | 0.289319i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1538.00 | + | 2663.89i | 0.452682 | + | 0.784069i | ||||
\(227\) | −1909.59 | − | 1102.50i | −0.558342 | − | 0.322359i | 0.194138 | − | 0.980974i | \(-0.437809\pi\) |
−0.752480 | + | 0.658615i | \(0.771142\pi\) | |||||||
\(228\) | 1188.19 | + | 686.000i | 0.345130 | + | 0.199261i | ||||
\(229\) | 143.500 | + | 248.549i | 0.0414094 | + | 0.0717231i | 0.885987 | − | 0.463710i | \(-0.153482\pi\) |
−0.844578 | + | 0.535433i | \(0.820149\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −122.500 | + | 636.529i | −0.0348914 | + | 0.181301i | ||||
\(232\) | 1392.00i | 0.393919i | ||||||||
\(233\) | 3972.46 | − | 2293.50i | 1.11693 | − | 0.644859i | 0.176314 | − | 0.984334i | \(-0.443583\pi\) |
0.940615 | + | 0.339475i | \(0.110249\pi\) | |||||||
\(234\) | −308.000 | + | 533.472i | −0.0860453 | + | 0.149035i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −210.000 | − | 363.731i | −0.0579230 | − | 0.100326i | ||||
\(237\) | 721.000i | 0.197612i | ||||||||
\(238\) | 509.223 | − | 588.000i | 0.138689 | − | 0.160144i | ||||
\(239\) | −1668.00 | −0.451439 | −0.225720 | − | 0.974192i | \(-0.572473\pi\) | ||||
−0.225720 | + | 0.974192i | \(0.572473\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1704.50 | − | 2952.28i | 0.455587 | − | 0.789100i | −0.543135 | − | 0.839646i | \(-0.682763\pi\) |
0.998722 | + | 0.0505456i | \(0.0160960\pi\) | |||||||
\(242\) | −2262.06 | − | 1306.00i | −0.600870 | − | 0.346913i | ||||
\(243\) | −4267.77 | + | 2464.00i | −1.12666 | + | 0.650476i | ||||
\(244\) | −1652.00 | −0.433436 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4900.00 | 1.26997 | ||||||||
\(247\) | 594.093 | − | 343.000i | 0.153042 | − | 0.0883586i | ||||
\(248\) | 3055.34 | + | 1764.00i | 0.782315 | + | 0.451670i | ||||
\(249\) | 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 | \(0.704238\pi\) | |||||||
\(252\) | −1066.94 | + | 1232.00i | −0.266711 | + | 0.307971i | ||||
\(253\) | 795.000i | 0.197554i | ||||||||
\(254\) | 72.0000 | + | 124.708i | 0.0177861 | + | 0.0308065i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2176.00 | − | 3768.94i | 0.531250 | − | 0.920152i | ||||
\(257\) | 697.150 | − | 402.500i | 0.169210 | − | 0.0976936i | −0.413003 | − | 0.910730i | \(-0.635520\pi\) |
0.582213 | + | 0.813036i | \(0.302187\pi\) | |||||||
\(258\) | − | 1736.00i | − | 0.418909i | ||||||
\(259\) | −766.500 | + | 3982.85i | −0.183892 | + | 0.955530i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −638.000 | − | 1105.05i | −0.151307 | − | 0.262072i | ||||
\(262\) | 3722.18 | + | 2149.00i | 0.877698 | + | 0.506739i | ||||
\(263\) | 222.569 | + | 128.500i | 0.0521831 | + | 0.0301279i | 0.525865 | − | 0.850568i | \(-0.323742\pi\) |
−0.473681 | + | 0.880696i | \(0.657075\pi\) | |||||||
\(264\) | 420.000 | + | 727.461i | 0.0979137 | + | 0.169591i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1715.00 | + | 594.093i | −0.395314 | + | 0.136941i | ||||
\(267\) | 2303.00i | 0.527870i | ||||||||
\(268\) | −1437.60 | + | 830.000i | −0.327670 | + | 0.189180i | ||||
\(269\) | 1795.50 | − | 3109.90i | 0.406965 | − | 0.704884i | −0.587583 | − | 0.809164i | \(-0.699920\pi\) |
0.994548 | + | 0.104280i | \(0.0332538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −696.500 | − | 1206.37i | −0.156123 | − | 0.270413i | 0.777344 | − | 0.629075i | \(-0.216566\pi\) |
−0.933467 | + | 0.358662i | \(0.883233\pi\) | |||||||
\(272\) | − | 336.000i | − | 0.0749007i | ||||||
\(273\) | 594.093 | + | 1715.00i | 0.131708 | + | 0.380207i | ||||
\(274\) | 2250.00 | 0.496086 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2226.00 | + | 3855.55i | −0.485469 | + | 0.840857i | ||||
\(277\) | 359.401 | + | 207.500i | 0.0779577 | + | 0.0450089i | 0.538472 | − | 0.842643i | \(-0.319002\pi\) |
−0.460514 | + | 0.887652i | \(0.652335\pi\) | |||||||
\(278\) | 436.477 | − | 252.000i | 0.0941660 | − | 0.0543667i | ||||
\(279\) | −3234.00 | −0.693959 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4954.00 | −1.05171 | −0.525856 | − | 0.850574i | \(-0.676255\pi\) | ||||
−0.525856 | + | 0.850574i | \(0.676255\pi\) | |||||||
\(282\) | −6365.29 | + | 3675.00i | −1.34414 | + | 0.776039i | ||||
\(283\) | 3703.99 | + | 2138.50i | 0.778019 | + | 0.449190i | 0.835728 | − | 0.549144i | \(-0.185046\pi\) |
−0.0577087 | + | 0.998333i | \(0.518379\pi\) | |||||||
\(284\) | 864.000 | − | 1496.49i | 0.180525 | − | 0.312678i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 140.000 | 0.0289454 | ||||||||
\(287\) | 4243.52 | − | 4900.00i | 0.872778 | − | 1.00780i | ||||
\(288\) | 3520.00i | 0.720201i | ||||||||
\(289\) | −2236.00 | − | 3872.87i | −0.455119 | − | 0.788289i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3087.00 | − | 5346.84i | 0.621866 | − | 1.07710i | ||||
\(292\) | −3855.55 | + | 2226.00i | −0.772701 | + | 0.446119i | ||||
\(293\) | 7742.00i | 1.54366i | 0.635829 | + | 0.771830i | \(0.280658\pi\) | ||||
−0.635829 | + | 0.771830i | \(0.719342\pi\) | |||||||
\(294\) | −686.000 | − | 4752.75i | −0.136083 | − | 0.942809i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2628.00 | + | 4551.83i | 0.516045 | + | 0.893817i | ||||
\(297\) | 151.554 | + | 87.5000i | 0.0296097 | + | 0.0170952i | ||||
\(298\) | 348.142 | + | 201.000i | 0.0676756 | + | 0.0390725i | ||||
\(299\) | 1113.00 | + | 1927.77i | 0.215272 | + | 0.372863i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1736.00 | − | 1503.42i | −0.332430 | − | 0.287893i | ||||
\(302\) | − | 3238.00i | − | 0.616973i | ||||||
\(303\) | 8359.74 | − | 4826.50i | 1.58500 | − | 0.915100i | ||||
\(304\) | −392.000 | + | 678.964i | −0.0739564 | + | 0.128096i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 462.000 | + | 800.207i | 0.0863097 | + | 0.149493i | ||||
\(307\) | 7364.00i | 1.36901i | 0.729009 | + | 0.684504i | \(0.239981\pi\) | ||||
−0.729009 | + | 0.684504i | \(0.760019\pi\) | |||||||
\(308\) | 363.731 | + | 70.0000i | 0.0672905 | + | 0.0129501i | ||||
\(309\) | 4753.00 | 0.875044 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4987.50 | + | 8638.60i | −0.909374 | + | 1.57508i | −0.0944372 | + | 0.995531i | \(0.530105\pi\) |
−0.814936 | + | 0.579550i | \(0.803228\pi\) | |||||||
\(312\) | 2036.89 | + | 1176.00i | 0.369603 | + | 0.213391i | ||||
\(313\) | −4116.22 | + | 2376.50i | −0.743330 | + | 0.429162i | −0.823279 | − | 0.567637i | \(-0.807858\pi\) |
0.0799485 | + | 0.996799i | \(0.474524\pi\) | |||||||
\(314\) | −1358.00 | −0.244065 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 412.000 | 0.0733443 | ||||||||
\(317\) | 3011.17 | − | 1738.50i | 0.533515 | − | 0.308025i | −0.208932 | − | 0.977930i | \(-0.566999\pi\) |
0.742447 | + | 0.669905i | \(0.233665\pi\) | |||||||
\(318\) | −3673.68 | − | 2121.00i | −0.647829 | − | 0.374024i | ||||
\(319\) | −145.000 | + | 251.147i | −0.0254497 | + | 0.0440801i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3199.00 | 0.556233 | ||||||||
\(322\) | −1927.77 | − | 5565.00i | −0.333635 | − | 0.963122i | ||||
\(323\) | − | 1029.00i | − | 0.177260i | ||||||
\(324\) | 1678.00 | + | 2906.38i | 0.287723 | + | 0.498351i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 467.000 | − | 808.868i | 0.0793397 | − | 0.137420i | ||||
\(327\) | 6819.95 | − | 3937.50i | 1.15335 | − | 0.665885i | ||||
\(328\) | − | 8400.00i | − | 1.41406i | ||||||
\(329\) | −1837.50 | + | 9547.93i | −0.307917 | + | 1.59998i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1670.50 | − | 2893.39i | −0.277399 | − | 0.480469i | 0.693339 | − | 0.720612i | \(-0.256139\pi\) |
−0.970738 | + | 0.240143i | \(0.922806\pi\) | |||||||
\(332\) | −3782.80 | − | 2184.00i | −0.625325 | − | 0.361032i | ||||
\(333\) | −4172.51 | − | 2409.00i | −0.686643 | − | 0.396434i | ||||
\(334\) | 1204.00 | + | 2085.39i | 0.197245 | + | 0.341639i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1568.00 | − | 1357.93i | −0.254588 | − | 0.220479i | ||||
\(337\) | − | 7366.00i | − | 1.19066i | −0.803482 | − | 0.595329i | \(-0.797022\pi\) | ||
0.803482 | − | 0.595329i | \(-0.202978\pi\) | |||||||
\(338\) | −3465.83 | + | 2001.00i | −0.557741 | + | 0.322012i | ||||
\(339\) | −5383.00 | + | 9323.63i | −0.862432 | + | 1.49378i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 367.500 | + | 636.529i | 0.0583614 | + | 0.101085i | ||||
\(342\) | − | 2156.00i | − | 0.340886i | ||||||
\(343\) | −5346.84 | − | 3430.00i | −0.841698 | − | 0.539949i | ||||
\(344\) | −2976.00 | −0.466439 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2821.00 | − | 4886.12i | 0.438318 | − | 0.759188i | ||||
\(347\) | 6421.58 | + | 3707.50i | 0.993454 | + | 0.573571i | 0.906305 | − | 0.422625i | \(-0.138891\pi\) |
0.0871487 | + | 0.996195i | \(0.472224\pi\) | |||||||
\(348\) | −1406.43 | + | 812.000i | −0.216645 | + | 0.125080i | ||||
\(349\) | 3878.00 | 0.594798 | 0.297399 | − | 0.954753i | \(-0.403881\pi\) | ||||
0.297399 | + | 0.954753i | \(0.403881\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 490.000 | 0.0745136 | ||||||||
\(352\) | 692.820 | − | 400.000i | 0.104908 | − | 0.0605684i | ||||
\(353\) | −1097.25 | − | 633.500i | −0.165442 | − | 0.0955179i | 0.414993 | − | 0.909825i | \(-0.363784\pi\) |
−0.580435 | + | 0.814307i | \(0.697117\pi\) | |||||||
\(354\) | −735.000 | + | 1273.06i | −0.110353 | + | 0.191136i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1316.00 | 0.195921 | ||||||||
\(357\) | 2673.42 | + | 514.500i | 0.396337 | + | 0.0762751i | ||||
\(358\) | − | 6506.00i | − | 0.960483i | ||||||
\(359\) | 2342.50 | + | 4057.33i | 0.344380 | + | 0.596484i | 0.985241 | − | 0.171173i | \(-0.0547558\pi\) |
−0.640861 | + | 0.767657i | \(0.721422\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2229.00 | − | 3860.74i | 0.324974 | − | 0.562872i | ||||
\(362\) | −2740.10 | + | 1582.00i | −0.397836 | + | 0.229691i | ||||
\(363\) | − | 9142.00i | − | 1.32185i | ||||||
\(364\) | 980.000 | − | 339.482i | 0.141115 | − | 0.0488838i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2891.00 | + | 5007.36i | 0.412882 | + | 0.715133i | ||||
\(367\) | −4019.22 | − | 2320.50i | −0.571667 | − | 0.330052i | 0.186148 | − | 0.982522i | \(-0.440400\pi\) |
−0.757815 | + | 0.652470i | \(0.773733\pi\) | |||||||
\(368\) | −2203.17 | − | 1272.00i | −0.312087 | − | 0.180184i | ||||
\(369\) | 3850.00 | + | 6668.40i | 0.543152 | + | 0.940766i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5302.50 | + | 1836.84i | −0.742027 | + | 0.257046i | ||||
\(372\) | 4116.00i | 0.573668i | ||||||||
\(373\) | −7618.43 | + | 4398.50i | −1.05755 | + | 0.610578i | −0.924754 | − | 0.380565i | \(-0.875730\pi\) |
−0.132798 | + | 0.991143i | \(0.542396\pi\) | |||||||
\(374\) | 105.000 | − | 181.865i | 0.0145172 | − | 0.0251445i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6300.00 | + | 10911.9i | 0.864090 | + | 1.49665i | ||||
\(377\) | 812.000i | 0.110929i | ||||||||
\(378\) | −1273.06 | − | 245.000i | −0.173225 | − | 0.0333371i | ||||
\(379\) | −13680.0 | −1.85407 | −0.927037 | − | 0.374969i | \(-0.877653\pi\) | ||||
−0.927037 | + | 0.374969i | \(0.877653\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −252.000 | + | 436.477i | −0.0338854 | + | 0.0586913i | ||||
\(382\) | 4428.85 | + | 2557.00i | 0.593193 | + | 0.342480i | ||||
\(383\) | 8456.74 | − | 4882.50i | 1.12825 | − | 0.651395i | 0.184755 | − | 0.982785i | \(-0.440851\pi\) |
0.943494 | + | 0.331390i | \(0.107518\pi\) | |||||||
\(384\) | 2688.00 | 0.357217 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −794.000 | −0.104698 | ||||||||
\(387\) | 2362.52 | − | 1364.00i | 0.310319 | − | 0.179163i | ||||
\(388\) | −3055.34 | − | 1764.00i | −0.399771 | − | 0.230808i | ||||
\(389\) | 865.500 | − | 1499.09i | 0.112809 | − | 0.195390i | −0.804093 | − | 0.594504i | \(-0.797349\pi\) |
0.916902 | + | 0.399113i | \(0.130682\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3339.00 | 0.431868 | ||||||||
\(392\) | −8147.57 | + | 1176.00i | −1.04978 | + | 0.151523i | ||||
\(393\) | 15043.0i | 1.93084i | ||||||||
\(394\) | 2914.00 | + | 5047.20i | 0.372602 | + | 0.645366i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −220.000 | + | 381.051i | −0.0279177 | + | 0.0483549i | ||||
\(397\) | −9511.56 | + | 5491.50i | −1.20245 | + | 0.694233i | −0.961099 | − | 0.276206i | \(-0.910923\pi\) |
−0.241348 | + | 0.970439i | \(0.577590\pi\) | |||||||
\(398\) | 6678.00i | 0.841050i | ||||||||
\(399\) | −4802.00 | − | 4158.65i | −0.602508 | − | 0.521787i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3301.50 | − | 5718.37i | −0.411145 | − | 0.712124i | 0.583870 | − | 0.811847i | \(-0.301538\pi\) |
−0.995015 | + | 0.0997232i | \(0.968204\pi\) | |||||||
\(402\) | 5031.61 | + | 2905.00i | 0.624263 | + | 0.360418i | ||||
\(403\) | 1782.28 | + | 1029.00i | 0.220302 | + | 0.127191i | ||||
\(404\) | −2758.00 | − | 4777.00i | −0.339643 | − | 0.588278i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 406.000 | − | 2109.64i | 0.0496292 | − | 0.257881i | ||||
\(407\) | 1095.00i | 0.133359i | ||||||||
\(408\) | 3055.34 | − | 1764.00i | 0.370740 | − | 0.214047i | ||||
\(409\) | 5477.50 | − | 9487.31i | 0.662213 | − | 1.14699i | −0.317820 | − | 0.948151i | \(-0.602951\pi\) |
0.980033 | − | 0.198835i | \(-0.0637158\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3937.50 | + | 6819.95i | 0.472561 | + | 0.818500i | ||||
\(412\) | − | 2716.00i | − | 0.324776i | ||||||
\(413\) | 636.529 | + | 1837.50i | 0.0758391 | + | 0.218928i | ||||
\(414\) | 6996.00 | 0.830518 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1120.00 | − | 1939.90i | 0.132001 | − | 0.228633i | ||||
\(417\) | 1527.67 | + | 882.000i | 0.179401 | + | 0.103577i | ||||
\(418\) | −424.352 | + | 245.000i | −0.0496549 | + | 0.0286683i | ||||
\(419\) | −6636.00 | −0.773723 | −0.386861 | − | 0.922138i | \(-0.626441\pi\) | ||||
−0.386861 | + | 0.922138i | \(0.626441\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16630.0 | −1.92517 | −0.962585 | − | 0.270980i | \(-0.912652\pi\) | ||||
−0.962585 | + | 0.270980i | \(0.912652\pi\) | |||||||
\(422\) | −3083.05 | + | 1780.00i | −0.355641 | + | 0.205329i | ||||
\(423\) | −10002.6 | − | 5775.00i | −1.14975 | − | 0.663806i | ||||
\(424\) | −3636.00 | + | 6297.74i | −0.416462 | + | 0.721333i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6048.00 | −0.687856 | ||||||||
\(427\) | 7511.04 | + | 1445.50i | 0.851252 | + | 0.163824i | ||||
\(428\) | − | 1828.00i | − | 0.206448i | ||||||
\(429\) | 245.000 | + | 424.352i | 0.0275728 | + | 0.0477574i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2461.50 | + | 4263.44i | −0.275096 | + | 0.476480i | −0.970159 | − | 0.242468i | \(-0.922043\pi\) |
0.695064 | + | 0.718948i | \(0.255376\pi\) | |||||||
\(432\) | −484.974 | + | 280.000i | −0.0540123 | + | 0.0311840i | ||||
\(433\) | 8974.00i | 0.995988i | 0.867180 | + | 0.497994i | \(0.165930\pi\) | ||||
−0.867180 | + | 0.497994i | \(0.834070\pi\) | |||||||
\(434\) | −4116.00 | − | 3564.56i | −0.455240 | − | 0.394250i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2250.00 | − | 3897.11i | −0.247146 | − | 0.428069i | ||||
\(437\) | −6747.20 | − | 3895.50i | −0.738587 | − | 0.426423i | ||||
\(438\) | 13494.4 | + | 7791.00i | 1.47212 | + | 0.849928i | ||||
\(439\) | −2089.50 | − | 3619.12i | −0.227167 | − | 0.393465i | 0.729800 | − | 0.683660i | \(-0.239613\pi\) |
−0.956967 | + | 0.290195i | \(0.906280\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5929.00 | − | 4667.88i | 0.640212 | − | 0.504036i | ||||
\(442\) | − | 588.000i | − | 0.0632767i | ||||||
\(443\) | −11195.1 | + | 6463.50i | −1.20067 | + | 0.693206i | −0.960704 | − | 0.277576i | \(-0.910469\pi\) |
−0.239964 | + | 0.970782i | \(0.577136\pi\) | |||||||
\(444\) | −3066.00 | + | 5310.47i | −0.327716 | + | 0.567621i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1400.00 | + | 2424.87i | 0.148637 | + | 0.257446i | ||||
\(447\) | 1407.00i | 0.148879i | ||||||||
\(448\) | −5431.71 | + | 6272.00i | −0.572822 | + | 0.661438i | ||||
\(449\) | 2826.00 | 0.297032 | 0.148516 | − | 0.988910i | \(-0.452550\pi\) | ||||
0.148516 | + | 0.988910i | \(0.452550\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 875.000 | − | 1515.54i | 0.0913573 | − | 0.158235i | ||||
\(452\) | 5327.79 | + | 3076.00i | 0.554421 | + | 0.320095i | ||||
\(453\) | 9814.67 | − | 5666.50i | 1.01795 | − | 0.587716i | ||||
\(454\) | 4410.00 | 0.455884 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8232.00 | −0.845392 | ||||||||
\(457\) | −7343.03 | + | 4239.50i | −0.751625 | + | 0.433951i | −0.826281 | − | 0.563259i | \(-0.809547\pi\) |
0.0746560 | + | 0.997209i | \(0.476214\pi\) | |||||||
\(458\) | −497.099 | − | 287.000i | −0.0507159 | − | 0.0292808i | ||||
\(459\) | 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 | \(0.343638\pi\) | |||||||
\(462\) | −424.352 | − | 1225.00i | −0.0427330 | − | 0.123360i | ||||
\(463\) | − | 4016.00i | − | 0.403109i | −0.979477 | − | 0.201554i | \(-0.935401\pi\) | ||
0.979477 | − | 0.201554i | \(-0.0645993\pi\) | |||||||
\(464\) | −464.000 | − | 803.672i | −0.0464238 | − | 0.0804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4587.00 | + | 7944.92i | −0.455984 | + | 0.789788i | ||||
\(467\) | 5074.04 | − | 2929.50i | 0.502781 | − | 0.290281i | −0.227080 | − | 0.973876i | \(-0.572918\pi\) |
0.729861 | + | 0.683595i | \(0.239585\pi\) | |||||||
\(468\) | 1232.00i | 0.121686i | ||||||||
\(469\) | 7262.50 | − | 2515.80i | 0.715034 | − | 0.247695i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2376.50 | − | 4116.22i | −0.232491 | − | 0.402687i | ||||
\(472\) | 2182.38 | + | 1260.00i | 0.212823 | + | 0.122873i | ||||
\(473\) | −536.936 | − | 310.000i | −0.0521952 | − | 0.0301349i | ||||
\(474\) | −721.000 | − | 1248.81i | −0.0698663 | − | 0.121012i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 294.000 | − | 1527.67i | 0.0283098 | − | 0.147102i | ||||
\(477\) | − | 6666.00i | − | 0.639864i | ||||||
\(478\) | 2889.06 | − | 1668.00i | 0.276449 | − | 0.159608i | ||||
\(479\) | 3251.50 | − | 5631.76i | 0.310156 | − | 0.537206i | −0.668240 | − | 0.743946i | \(-0.732952\pi\) |
0.978396 | + | 0.206740i | \(0.0662853\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1533.00 | + | 2655.23i | 0.145320 | + | 0.251701i | ||||
\(482\) | 6818.00i | 0.644297i | ||||||||
\(483\) | 13494.4 | − | 15582.0i | 1.27126 | − | 1.46792i | ||||
\(484\) | −5224.00 | −0.490609 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4928.00 | − | 8535.55i | 0.459956 | − | 0.796667i | ||||
\(487\) | −13898.8 | − | 8024.50i | −1.29326 | − | 0.746663i | −0.314028 | − | 0.949414i | \(-0.601678\pi\) |
−0.979230 | + | 0.202751i | \(0.935012\pi\) | |||||||
\(488\) | 8584.04 | − | 4956.00i | 0.796273 | − | 0.459729i | ||||
\(489\) | 3269.00 | 0.302309 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8864.00 | 0.814718 | 0.407359 | − | 0.913268i | \(-0.366450\pi\) | ||||
0.407359 | + | 0.913268i | \(0.366450\pi\) | |||||||
\(492\) | 8487.05 | − | 4900.00i | 0.777695 | − | 0.449002i | ||||
\(493\) | 1054.82 | + | 609.000i | 0.0963624 | + | 0.0556348i | ||||
\(494\) | −686.000 | + | 1188.19i | −0.0624789 | + | 0.108217i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2352.00 | −0.212919 | ||||||||
\(497\) | −5237.72 | + | 6048.00i | −0.472724 | + | 0.545855i | ||||
\(498\) | 15288.0i | 1.37565i | ||||||||
\(499\) | −5105.50 | − | 8842.99i | −0.458023 | − | 0.793319i | 0.540833 | − | 0.841130i | \(-0.318109\pi\) |
−0.998856 | + | 0.0478104i | \(0.984776\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4214.00 | + | 7298.86i | −0.375784 | + | 0.650876i | ||||
\(502\) | 8244.56 | − | 4760.00i | 0.733014 | − | 0.423206i | ||||
\(503\) | − | 1680.00i | − | 0.148921i | −0.997224 | − | 0.0744607i | \(-0.976276\pi\) | ||
0.997224 | − | 0.0744607i | \(-0.0237235\pi\) | |||||||
\(504\) | 1848.00 | − | 9602.49i | 0.163326 | − | 0.848668i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −795.000 | − | 1376.98i | −0.0698460 | − | 0.120977i | ||||
\(507\) | −12130.4 | − | 7003.50i | −1.06259 | − | 0.613484i | ||||
\(508\) | 249.415 | + | 144.000i | 0.0217835 | + | 0.0125767i | ||||
\(509\) | −4728.50 | − | 8190.00i | −0.411762 | − | 0.713193i | 0.583320 | − | 0.812242i | \(-0.301753\pi\) |
−0.995083 | + | 0.0990489i | \(0.968420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19477.5 | − | 6747.20i | 1.68617 | − | 0.584107i | ||||
\(512\) | 5632.00i | 0.486136i | ||||||||
\(513\) | −1485.23 | + | 857.500i | −0.127826 | + | 0.0738003i | ||||
\(514\) | −805.000 | + | 1394.30i | −0.0690798 | + | 0.119650i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1736.00 | − | 3006.84i | −0.148107 | − | 0.256529i | ||||
\(517\) | 2625.00i | 0.223302i | ||||||||
\(518\) | −2655.23 | − | 7665.00i | −0.225221 | − | 0.650156i | ||||
\(519\) | 19747.0 | 1.67013 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9040.50 | − | 15658.6i | 0.760214 | − | 1.31673i | −0.182526 | − | 0.983201i | \(-0.558427\pi\) |
0.942740 | − | 0.333528i | \(-0.108239\pi\) | |||||||
\(522\) | 2210.10 | + | 1276.00i | 0.185313 | + | 0.106990i | ||||
\(523\) | 17647.0 | − | 10188.5i | 1.47543 | − | 0.851839i | 0.475813 | − | 0.879546i | \(-0.342154\pi\) |
0.999616 | + | 0.0277071i | \(0.00882056\pi\) | |||||||
\(524\) | 8596.00 | 0.716637 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −514.000 | −0.0426073 | ||||||||
\(527\) | 2673.42 | − | 1543.50i | 0.220979 | − | 0.127582i | ||||
\(528\) | −484.974 | − | 280.000i | −0.0399731 | − | 0.0230785i | ||||
\(529\) | 6557.00 | − | 11357.1i | 0.538917 | − | 0.933431i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2310.00 | −0.188786 | ||||||||
\(532\) | −2376.37 | + | 2744.00i | −0.193663 | + | 0.223623i | ||||
\(533\) | − | 4900.00i | − | 0.398204i | ||||||
\(534\) | −2303.00 | − | 3988.91i | −0.186630 | − | 0.323253i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4980.00 | − | 8625.61i | 0.401312 | − | 0.695093i | ||||
\(537\) | 19720.3 | − | 11385.5i | 1.58472 | − | 0.914936i | ||||
\(538\) | 7182.00i | 0.575535i | ||||||||
\(539\) | −1592.50 | − | 636.529i | −0.127261 | − | 0.0508668i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3096.50 | + | 5363.30i | 0.246079 | + | 0.426222i | 0.962435 | − | 0.271514i | \(-0.0875243\pi\) |
−0.716355 | + | 0.697736i | \(0.754191\pi\) | |||||||
\(542\) | 2412.75 | + | 1393.00i | 0.191211 | + | 0.110396i | ||||
\(543\) | −9590.37 | − | 5537.00i | −0.757941 | − | 0.437597i | ||||
\(544\) | −1680.00 | − | 2909.85i | −0.132407 | − | 0.229336i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2744.00 | − | 2376.37i | −0.215078 | − | 0.186263i | ||||
\(547\) | 18464.0i | 1.44326i | 0.692279 | + | 0.721630i | \(0.256607\pi\) | ||||
−0.692279 | + | 0.721630i | \(0.743393\pi\) | |||||||
\(548\) | 3897.11 | − | 2250.00i | 0.303789 | − | 0.175393i | ||||
\(549\) | −4543.00 | + | 7868.71i | −0.353170 | + | 0.611709i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1421.00 | − | 2461.24i | −0.109867 | − | 0.190295i | ||||
\(552\) | − | 26712.0i | − | 2.05967i | ||||||
\(553\) | −1873.21 | − | 360.500i | −0.144045 | − | 0.0277216i | ||||
\(554\) | −830.000 | −0.0636522 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 504.000 | − | 872.954i | 0.0384431 | − | 0.0665854i | ||||
\(557\) | −8151.90 | − | 4706.50i | −0.620120 | − | 0.358027i | 0.156796 | − | 0.987631i | \(-0.449884\pi\) |
−0.776916 | + | 0.629604i | \(0.783217\pi\) | |||||||
\(558\) | 5601.45 | − | 3234.00i | 0.424961 | − | 0.245351i | ||||
\(559\) | −1736.00 | −0.131351 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 735.000 | 0.0553150 | ||||||||
\(562\) | 8580.58 | − | 4954.00i | 0.644039 | − | 0.371836i | ||||
\(563\) | −2770.42 | − | 1599.50i | −0.207387 | − | 0.119735i | 0.392709 | − | 0.919663i | \(-0.371538\pi\) |
−0.600097 | + | 0.799928i | \(0.704871\pi\) | |||||||
\(564\) | −7350.00 | + | 12730.6i | −0.548743 | + | 0.950450i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8554.00 | −0.635250 | ||||||||
\(567\) | −5086.17 | − | 14682.5i | −0.376718 | − | 1.08749i | ||||
\(568\) | 10368.0i | 0.765901i | ||||||||
\(569\) | 10791.5 | + | 18691.4i | 0.795085 | + | 1.37713i | 0.922785 | + | 0.385314i | \(0.125907\pi\) |
−0.127701 | + | 0.991813i | \(0.540760\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10133.5 | + | 17551.7i | −0.742686 | + | 1.28637i | 0.208582 | + | 0.978005i | \(0.433115\pi\) |
−0.951268 | + | 0.308365i | \(0.900218\pi\) | |||||||
\(572\) | 242.487 | − | 140.000i | 0.0177253 | − | 0.0102337i | ||||
\(573\) | 17899.0i | 1.30496i | ||||||||
\(574\) | −2450.00 | + | 12730.6i | −0.178155 | + | 0.925721i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4928.00 | − | 8535.55i | −0.356481 | − | 0.617444i | ||||
\(577\) | 12081.9 | + | 6975.50i | 0.871710 | + | 0.503282i | 0.867916 | − | 0.496711i | \(-0.165459\pi\) |
0.00379418 | + | 0.999993i | \(0.498792\pi\) | |||||||
\(578\) | 7745.73 | + | 4472.00i | 0.557405 | + | 0.321818i | ||||
\(579\) | −1389.50 | − | 2406.68i | −0.0997334 | − | 0.172743i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15288.0 | + | 13239.8i | 1.09166 | + | 0.945403i | ||||
\(582\) | 12348.0i | 0.879452i | ||||||||
\(583\) | −1312.03 | + | 757.500i | −0.0932053 | + | 0.0538121i | ||||
\(584\) | 13356.0 | − | 23133.3i | 0.946362 | − | 1.63915i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7742.00 | − | 13409.5i | −0.545766 | − | 0.945295i | ||||
\(587\) | 20972.0i | 1.47463i | 0.675550 | + | 0.737314i | \(0.263906\pi\) | ||||
−0.675550 | + | 0.737314i | \(0.736094\pi\) | |||||||
\(588\) | −5940.93 | − | 7546.00i | −0.416667 | − | 0.529238i | ||||
\(589\) | −7203.00 | −0.503895 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10199.0 | + | 17665.2i | −0.709866 | + | 1.22952i | ||||
\(592\) | −3034.55 | − | 1752.00i | −0.210675 | − | 0.121633i | ||||
\(593\) | −163.679 | + | 94.5000i | −0.0113347 | + | 0.00654410i | −0.505657 | − | 0.862735i | \(-0.668750\pi\) |
0.494322 | + | 0.869279i | \(0.335416\pi\) | |||||||
\(594\) | −350.000 | −0.0241762 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 804.000 | 0.0552569 | ||||||||
\(597\) | −20241.6 | + | 11686.5i | −1.38766 | + | 0.801167i | ||||
\(598\) | −3855.55 | − | 2226.00i | −0.263654 | − | 0.152221i | ||||
\(599\) | −5140.50 | + | 8903.61i | −0.350643 | + | 0.607331i | −0.986362 | − | 0.164589i | \(-0.947370\pi\) |
0.635719 | + | 0.771920i | \(0.280704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6090.00 | −0.413338 | −0.206669 | − | 0.978411i | \(-0.566262\pi\) | ||||
−0.206669 | + | 0.978411i | \(0.566262\pi\) | |||||||
\(602\) | 4510.26 | + | 868.000i | 0.305356 | + | 0.0587658i | ||||
\(603\) | 9130.00i | 0.616588i | ||||||||
\(604\) | −3238.00 | − | 5608.38i | −0.218133 | − | 0.377817i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9653.00 | + | 16719.5i | −0.647073 | + | 1.12076i | ||||
\(607\) | −4285.96 | + | 2474.50i | −0.286593 | + | 0.165464i | −0.636404 | − | 0.771356i | \(-0.719579\pi\) |
0.349812 | + | 0.936820i | \(0.386246\pi\) | |||||||
\(608\) | 7840.00i | 0.522951i | ||||||||
\(609\) | 7105.00 | − | 2461.24i | 0.472757 | − | 0.163768i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3675.00 | + | 6365.29i | 0.243330 | + | 0.421460i | ||||
\(612\) | 1600.41 | + | 924.000i | 0.105707 | + | 0.0610302i | ||||
\(613\) | 13680.6 | + | 7898.50i | 0.901394 | + | 0.520420i | 0.877652 | − | 0.479298i | \(-0.159109\pi\) |
0.0237416 | + | 0.999718i | \(0.492442\pi\) | |||||||
\(614\) | −7364.00 | − | 12754.8i | −0.484018 | − | 0.838343i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2100.00 | + | 727.461i | −0.137356 | + | 0.0475816i | ||||
\(617\) | 9378.00i | 0.611903i | 0.952047 | + | 0.305951i | \(0.0989745\pi\) | ||||
−0.952047 | + | 0.305951i | \(0.901025\pi\) | |||||||
\(618\) | −8232.44 | + | 4753.00i | −0.535853 | + | 0.309375i | ||||
\(619\) | −12176.5 | + | 21090.3i | −0.790654 | + | 1.36945i | 0.134908 | + | 0.990858i | \(0.456926\pi\) |
−0.925562 | + | 0.378595i | \(0.876407\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2782.50 | − | 4819.43i | −0.179803 | − | 0.311429i | ||||
\(622\) | − | 19950.0i | − | 1.28605i | ||||||
\(623\) | −5983.37 | − | 1151.50i | −0.384781 | − | 0.0740512i | ||||
\(624\) | −1568.00 | −0.100593 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4753.00 | − | 8232.44i | 0.303463 | − | 0.525614i | ||||
\(627\) | −1485.23 | − | 857.500i | −0.0946005 | − | 0.0546176i | ||||
\(628\) | −2352.12 | + | 1358.00i | −0.149459 | + | 0.0862900i | ||||
\(629\) | 4599.00 | 0.291533 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12640.0 | −0.797449 | −0.398725 | − | 0.917071i | \(-0.630547\pi\) | ||||
−0.398725 | + | 0.917071i | \(0.630547\pi\) | |||||||
\(632\) | −2140.81 | + | 1236.00i | −0.134742 | + | 0.0777934i | ||||
\(633\) | −10790.7 | − | 6230.00i | −0.677553 | − | 0.391185i | ||||
\(634\) | −3477.00 | + | 6022.34i | −0.217806 | + | 0.377252i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8484.00 | −0.528950 | ||||||||
\(637\) | −4752.75 | + | 686.000i | −0.295621 | + | 0.0426692i | ||||
\(638\) | − | 580.000i | − | 0.0359913i | ||||||
\(639\) | −4752.00 | − | 8230.71i | −0.294188 | − | 0.509549i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 520.500 | − | 901.532i | 0.0320726 | − | 0.0555513i | −0.849544 | − | 0.527518i | \(-0.823123\pi\) |
0.881616 | + | 0.471967i | \(0.156456\pi\) | |||||||
\(642\) | −5540.83 | + | 3199.00i | −0.340622 | + | 0.196658i | ||||
\(643\) | 9548.00i | 0.585593i | 0.956175 | + | 0.292797i | \(0.0945859\pi\) | ||||
−0.956175 | + | 0.292797i | \(0.905414\pi\) | |||||||
\(644\) | −8904.00 | − | 7711.09i | −0.544824 | − | 0.471832i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1029.00 | + | 1782.28i | 0.0626710 | + | 0.108549i | ||||
\(647\) | −2806.79 | − | 1620.50i | −0.170551 | − | 0.0984674i | 0.412295 | − | 0.911050i | \(-0.364727\pi\) |
−0.582845 | + | 0.812583i | \(0.698061\pi\) | |||||||
\(648\) | −17438.3 | − | 10068.0i | −1.05716 | − | 0.610352i | ||||
\(649\) | 262.500 | + | 454.663i | 0.0158768 | + | 0.0274994i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3601.50 | − | 18713.9i | 0.216826 | − | 1.12666i | ||||
\(652\) | − | 1868.00i | − | 0.112203i | ||||||
\(653\) | −7666.92 | + | 4426.50i | −0.459464 | + | 0.265272i | −0.711819 | − | 0.702363i | \(-0.752128\pi\) |
0.252355 | + | 0.967635i | \(0.418795\pi\) | |||||||
\(654\) | −7875.00 | + | 13639.9i | −0.470851 | + | 0.815539i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2800.00 | + | 4849.74i | 0.166649 | + | 0.288644i | ||||
\(657\) | 24486.0i | 1.45402i | ||||||||
\(658\) | −6365.29 | − | 18375.0i | −0.377120 | − | 1.08865i | ||||
\(659\) | −7044.00 | −0.416381 | −0.208191 | − | 0.978088i | \(-0.566757\pi\) | ||||
−0.208191 | + | 0.978088i | \(0.566757\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6044.50 | − | 10469.4i | 0.355679 | − | 0.616054i | −0.631555 | − | 0.775331i | \(-0.717583\pi\) |
0.987234 | + | 0.159277i | \(0.0509163\pi\) | |||||||
\(662\) | 5786.78 | + | 3341.00i | 0.339743 | + | 0.196151i | ||||
\(663\) | 1782.28 | − | 1029.00i | 0.104401 | − | 0.0602761i | ||||
\(664\) | 26208.0 | 1.53173 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9636.00 | 0.560642 | ||||||||
\(667\) | 7986.49 | − | 4611.00i | 0.463625 | − | 0.267674i | ||||
\(668\) | 4170.78 | + | 2408.00i | 0.241575 | + | 0.139474i | ||||
\(669\) | −4900.00 | + | 8487.05i | −0.283176 | + | 0.490476i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2065.00 | 0.118805 | ||||||||
\(672\) | −20368.9 | − | 3920.00i | −1.16927 | − | 0.225026i | ||||
\(673\) | 982.000i | 0.0562456i | 0.999604 | + | 0.0281228i | \(0.00895295\pi\) | ||||
−0.999604 | + | 0.0281228i | \(0.991047\pi\) | |||||||
\(674\) | 7366.00 | + | 12758.3i | 0.420961 | + | 0.729126i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4002.00 | + | 6931.67i | −0.227697 | + | 0.394383i | ||||
\(677\) | 26425.0 | − | 15256.5i | 1.50014 | − | 0.866108i | 0.500143 | − | 0.865943i | \(-0.333281\pi\) |
1.00000 | 0.000164659i | \(-5.24124e-5\pi\) | ||||||||
\(678\) | − | 21532.0i | − | 1.21966i | ||||||
\(679\) | 12348.0 | + | 10693.7i | 0.697898 | + | 0.604397i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7717.50 | + | 13367.1i | 0.434266 | + | 0.752171i | ||||
\(682\) | −1273.06 | − | 735.000i | −0.0714778 | − | 0.0412677i | ||||
\(683\) | −9937.64 | − | 5737.50i | −0.556740 | − | 0.321434i | 0.195096 | − | 0.980784i | \(-0.437498\pi\) |
−0.751836 | + | 0.659350i | \(0.770831\pi\) | |||||||
\(684\) | −2156.00 | − | 3734.30i | −0.120522 | − | 0.208749i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12691.0 | + | 594.093i | 0.706333 | + | 0.0330650i | ||||
\(687\) | − | 2009.00i | − | 0.111569i | ||||||
\(688\) | 1718.19 | − | 992.000i | 0.0952116 | − | 0.0549704i | ||||
\(689\) | −2121.00 | + | 3673.68i | −0.117277 | + | 0.203129i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14157.5 | + | 24521.5i | 0.779416 | + | 1.34999i | 0.932279 | + | 0.361741i | \(0.117818\pi\) |
−0.152862 | + | 0.988248i | \(0.548849\pi\) | |||||||
\(692\) | − | 11284.0i | − | 0.619875i | ||||||
\(693\) | 1333.68 | − | 1540.00i | 0.0731057 | − | 0.0844152i | ||||
\(694\) | −14830.0 | −0.811151 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4872.00 | − | 8438.55i | 0.265334 | − | 0.459573i | ||||
\(697\) | −6365.29 | − | 3675.00i | −0.345915 | − | 0.199714i | ||||
\(698\) | −6716.89 | + | 3878.00i | −0.364238 | + | 0.210293i | ||||
\(699\) | −32109.0 | −1.73744 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10614.0 | 0.571876 | 0.285938 | − | 0.958248i | \(-0.407695\pi\) | ||||
0.285938 | + | 0.958248i | \(0.407695\pi\) | |||||||
\(702\) | −848.705 | + | 490.000i | −0.0456301 | + | 0.0263445i | ||||
\(703\) | −9293.32 | − | 5365.50i | −0.498583 | − | 0.287857i | ||||
\(704\) | −1120.00 | + | 1939.90i | −0.0599596 | + | 0.103853i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2534.00 | 0.135083 | ||||||||
\(707\) | 8359.74 | + | 24132.5i | 0.444697 | + | 1.28373i | ||||
\(708\) | 2940.00i | 0.156062i | ||||||||
\(709\) | 5149.50 | + | 8919.20i | 0.272769 | + | 0.472451i | 0.969570 | − | 0.244814i | \(-0.0787270\pi\) |
−0.696801 | + | 0.717265i | \(0.745394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1133.00 | − | 1962.41i | 0.0597621 | − | 0.103511i | ||||
\(712\) | −6838.14 | + | 3948.00i | −0.359930 | + | 0.207806i | ||||
\(713\) | − | 23373.0i | − | 1.22767i | ||||||
\(714\) | −5145.00 | + | 1782.28i | −0.269673 | + | 0.0934176i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6506.00 | − | 11268.7i | −0.339582 | − | 0.588173i | ||||
\(717\) | 10111.7 | + | 5838.00i | 0.526679 | + | 0.304078i | ||||
\(718\) | −8114.66 | − | 4685.00i | −0.421778 | − | 0.243513i | ||||
\(719\) | 16264.5 | + | 28170.9i | 0.843621 | + | 1.46119i | 0.886813 | + | 0.462128i | \(0.152914\pi\) |
−0.0431924 | + | 0.999067i | \(0.513753\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2376.50 | + | 12348.7i | −0.122754 | + | 0.637847i | ||||
\(722\) | 8916.00i | 0.459583i | ||||||||
\(723\) | −20666.0 | + | 11931.5i | −1.06304 | + | 0.613744i | ||||
\(724\) | −3164.00 | + | 5480.21i | −0.162416 | + | 0.281313i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9142.00 | + | 15834.4i | 0.467344 | + | 0.809463i | ||||
\(727\) | − | 29456.0i | − | 1.50270i | −0.659904 | − | 0.751350i | \(-0.729403\pi\) | ||
0.659904 | − | 0.751350i | \(-0.270597\pi\) | |||||||
\(728\) | −4073.78 | + | 4704.00i | −0.207396 | + | 0.239481i | ||||
\(729\) | 11843.0 | 0.601687 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1302.00 | + | 2255.13i | −0.0658772 | + | 0.114103i | ||||
\(732\) | 10014.7 | + | 5782.00i | 0.505676 | + | 0.291952i | ||||
\(733\) | 24133.5 | − | 13933.5i | 1.21609 | − | 0.702109i | 0.252009 | − | 0.967725i | \(-0.418909\pi\) |
0.964079 | + | 0.265616i | \(0.0855755\pi\) | |||||||
\(734\) | 9282.00 | 0.466764 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25440.0 | −1.27409 | ||||||||
\(737\) | 1797.00 | − | 1037.50i | 0.0898147 | − | 0.0518546i | ||||
\(738\) | −13336.8 | − | 7700.00i | −0.665222 | − | 0.384066i | ||||
\(739\) | 9769.50 | − | 16921.3i | 0.486302 | − | 0.842299i | −0.513574 | − | 0.858045i | \(-0.671679\pi\) |
0.999876 | + | 0.0157460i | \(0.00501231\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4802.00 | −0.238065 | ||||||||
\(742\) | 7347.36 | − | 8484.00i | 0.363518 | − | 0.419754i | ||||
\(743\) | 1248.00i | 0.0616214i | 0.999525 | + | 0.0308107i | \(0.00980890\pi\) | ||||
−0.999525 | + | 0.0308107i | \(0.990191\pi\) | |||||||
\(744\) | −12348.0 | − | 21387.4i | −0.608467 | − | 1.05390i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8797.00 | − | 15236.9i | 0.431744 | − | 0.747803i | ||||
\(747\) | −20805.4 | + | 12012.0i | −1.01905 | + | 0.588348i | ||||
\(748\) | − | 420.000i | − | 0.0205304i | ||||||
\(749\) | −1599.50 | + | 8311.25i | −0.0780300 | + | 0.405456i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14046.5 | − | 24329.3i | −0.682509 | − | 1.18214i | −0.974213 | − | 0.225631i | \(-0.927556\pi\) |
0.291704 | − | 0.956509i | \(-0.405778\pi\) | |||||||
\(752\) | −7274.61 | − | 4200.00i | −0.352763 | − | 0.203668i | ||||
\(753\) | 28856.0 | + | 16660.0i | 1.39651 | + | 0.806274i | ||||
\(754\) | −812.000 | − | 1406.43i | −0.0392192 | − | 0.0679297i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2450.00 | + | 848.705i | −0.117865 | + | 0.0408295i | ||||
\(757\) | − | 35954.0i | − | 1.72625i | −0.504991 | − | 0.863124i | \(-0.668504\pi\) | ||
0.504991 | − | 0.863124i | \(-0.331496\pi\) | |||||||
\(758\) | 23694.5 | − | 13680.0i | 1.13538 | − | 0.655514i | ||||
\(759\) | 2782.50 | − | 4819.43i | 0.133068 | − | 0.230480i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 430.500 | + | 745.648i | 0.0205067 | + | 0.0355187i | 0.876097 | − | 0.482136i | \(-0.160139\pi\) |
−0.855590 | + | 0.517654i | \(0.826805\pi\) | |||||||
\(762\) | − | 1008.00i | − | 0.0479212i | ||||||
\(763\) | 6819.95 | + | 19687.5i | 0.323589 | + | 0.934122i | ||||
\(764\) | 10228.0 | 0.484340 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9765.00 | + | 16913.5i | −0.460605 | + | 0.797792i | ||||
\(767\) | 1273.06 | + | 735.000i | 0.0599315 | + | 0.0346014i | ||||
\(768\) | −26382.6 | + | 15232.0i | −1.23958 | + | 0.715674i | ||||
\(769\) | −24710.0 | −1.15873 | −0.579366 | − | 0.815067i | \(-0.696700\pi\) | ||||
−0.579366 | + | 0.815067i | \(0.696700\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5635.00 | −0.263216 | ||||||||
\(772\) | −1375.25 | + | 794.000i | −0.0641143 | + | 0.0370164i | ||||
\(773\) | −14288.6 | − | 8249.50i | −0.664843 | − | 0.383847i | 0.129277 | − | 0.991609i | \(-0.458734\pi\) |
−0.794120 | + | 0.607761i | \(0.792068\pi\) | |||||||
\(774\) | −2728.00 | + | 4725.03i | −0.126687 | + | 0.219429i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 21168.0 | 0.979236 | ||||||||
\(777\) | 18586.6 | − | 21462.0i | 0.858162 | − | 0.990920i | ||||
\(778\) | 3462.00i | 0.159536i | ||||||||
\(779\) | 8575.00 | + | 14852.3i | 0.394392 | + | 0.683107i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1080.00 | + | 1870.61i | −0.0494820 | + | 0.0857053i | ||||
\(782\) | −5783.32 | + | 3339.00i | −0.264464 | + | 0.152688i | ||||
\(783\) | − | 2030.00i | − | 0.0926517i | ||||||
\(784\) | 4312.00 | − | 3394.82i | 0.196429 | − | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15043.0 | − | 26055.2i | −0.682654 | − | 1.18239i | ||||
\(787\) | 14264.3 | + | 8235.50i | 0.646083 | + | 0.373016i | 0.786954 | − | 0.617012i | \(-0.211657\pi\) |
−0.140871 | + | 0.990028i | \(0.544990\pi\) | |||||||
\(788\) | 10094.4 | + | 5828.00i | 0.456342 | + | 0.263469i | ||||
\(789\) | −899.500 | − | 1557.98i | −0.0405869 | − | 0.0702985i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21532.0 | − | 18647.3i | −0.967876 | − | 0.838205i | ||||
\(792\) | − | 2640.00i | − | 0.118445i | ||||||
\(793\) | 5007.36 | − | 2891.00i | 0.224233 | − | 0.129461i | ||||
\(794\) | 10983.0 | − | 19023.1i | 0.490897 | − | 0.850258i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6678.00 | + | 11566.6i | 0.297356 | + | 0.515036i | ||||
\(797\) | 36470.0i | 1.62087i | 0.585828 | + | 0.810435i | \(0.300769\pi\) | ||||
−0.585828 | + | 0.810435i | \(0.699231\pi\) | |||||||
\(798\) | 12476.0 | + | 2401.00i | 0.553439 | + | 0.106509i | ||||
\(799\) | 11025.0 | 0.488156 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3619.00 | − | 6268.29i | 0.159639 | − | 0.276503i | ||||
\(802\) | 11436.7 | + | 6603.00i | 0.503547 | + | 0.290723i | ||||
\(803\) | 4819.43 | − | 2782.50i | 0.211798 | − | 0.122282i | ||||
\(804\) | 11620.0 | 0.509709 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4116.00 | −0.179876 | ||||||||
\(807\) | −21769.3 | + | 12568.5i | −0.949585 | + | 0.548243i | ||||
\(808\) | 28662.0 | + | 16548.0i | 1.24793 | + | 0.720491i | ||||
\(809\) | 17875.5 | − | 30961.3i | 0.776847 | − | 1.34554i | −0.156904 | − | 0.987614i | \(-0.550151\pi\) |
0.933751 | − | 0.357924i | \(-0.116515\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16492.0 | −0.714072 | −0.357036 | − | 0.934091i | \(-0.616213\pi\) | ||||
−0.357036 | + | 0.934091i | \(0.616213\pi\) | |||||||
\(812\) | −1406.43 | − | 4060.00i | −0.0607831 | − | 0.175466i | ||||
\(813\) | 9751.00i | 0.420643i | ||||||||
\(814\) | −1095.00 | − | 1896.60i | −0.0471495 | − | 0.0816654i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1176.00 | + | 2036.89i | −0.0504513 | + | 0.0873842i | ||||
\(817\) | 5261.97 | − | 3038.00i | 0.225328 | − | 0.130093i | ||||
\(818\) | 21910.0i | 0.936510i | ||||||||
\(819\) | 1078.00 | − | 5601.45i | 0.0459931 | − | 0.238987i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20736.5 | + | 35916.7i | 0.881497 | + | 1.52680i | 0.849677 | + | 0.527304i | \(0.176797\pi\) |
0.0318198 | + | 0.999494i | \(0.489870\pi\) | |||||||
\(822\) | −13639.9 | − | 7875.00i | −0.578767 | − | 0.334151i | ||||
\(823\) | 21706.9 | + | 12532.5i | 0.919387 | + | 0.530809i | 0.883440 | − | 0.468545i | \(-0.155222\pi\) |
0.0359479 | + | 0.999354i | \(0.488555\pi\) | |||||||
\(824\) | 8148.00 | + | 14112.7i | 0.344477 | + | 0.596652i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2940.00 | − | 2546.11i | −0.123845 | − | 0.107253i | ||||
\(827\) | − | 9732.00i | − | 0.409208i | −0.978845 | − | 0.204604i | \(-0.934409\pi\) | ||
0.978845 | − | 0.204604i | \(-0.0655906\pi\) | |||||||
\(828\) | 12117.4 | − | 6996.00i | 0.508587 | − | 0.293633i | ||||
\(829\) | 13877.5 | − | 24036.5i | 0.581406 | − | 1.00702i | −0.413907 | − | 0.910319i | \(-0.635836\pi\) |
0.995313 | − | 0.0967055i | \(-0.0308305\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1452.50 | − | 2515.80i | −0.0606338 | − | 0.105021i | ||||
\(832\) | 6272.00i | 0.261349i | ||||||||
\(833\) | −2673.42 | + | 6688.50i | −0.111199 | + | 0.278203i | ||||
\(834\) | −3528.00 | −0.146480 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −490.000 | + | 848.705i | −0.0202715 | + | 0.0351113i | ||||
\(837\) | −4455.70 | − | 2572.50i | −0.184004 | − | 0.106235i | ||||
\(838\) | 11493.9 | − | 6636.00i | 0.473806 | − | 0.273552i | ||||
\(839\) | −21112.0 | −0.868733 | −0.434367 | − | 0.900736i | \(-0.643028\pi\) | ||||
−0.434367 | + | 0.900736i | \(0.643028\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21025.0 | −0.862069 | ||||||||
\(842\) | 28804.0 | − | 16630.0i | 1.17892 | − | 0.680650i | ||||
\(843\) | 30032.0 | + | 17339.0i | 1.22700 | + | 0.708407i | ||||
\(844\) | −3560.00 | + | 6166.10i | −0.145190 | + | 0.251476i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 23100.0 | 0.938764 | ||||||||
\(847\) | 23751.6 | + | 4571.00i | 0.963536 | + | 0.185433i | ||||
\(848\) | − | 4848.00i | − | 0.196322i | ||||||
\(849\) | −14969.5 | − | 25927.9i | −0.605126 | − | 1.04811i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17410.5 | − | 30155.9i | 0.701321 | − | 1.21472i | ||||
\(852\) | −10475.4 | + | 6048.00i | −0.421224 | + | 0.243194i | ||||
\(853\) | − | 21238.0i | − | 0.852492i | −0.904607 | − | 0.426246i | \(-0.859836\pi\) | ||
0.904607 | − | 0.426246i | \(-0.140164\pi\) | |||||||
\(854\) | −14455.0 | + | 5007.36i | −0.579204 | + | 0.200642i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5484.00 | + | 9498.57i | 0.218971 | + | 0.379269i | ||||
\(857\) | −30838.3 | − | 17804.5i | −1.22919 | − | 0.709673i | −0.262330 | − | 0.964978i | \(-0.584491\pi\) |
−0.966861 | + | 0.255305i | \(0.917824\pi\) | |||||||
\(858\) | −848.705 | − | 490.000i | −0.0337696 | − | 0.0194969i | ||||
\(859\) | 1088.50 | + | 1885.34i | 0.0432353 | + | 0.0748858i | 0.886833 | − | 0.462090i | \(-0.152900\pi\) |
−0.843598 | + | 0.536975i | \(0.819567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −42875.0 | + | 14852.3i | −1.69707 | + | 0.587882i | ||||
\(862\) | − | 9846.00i | − | 0.389044i | ||||||
\(863\) | −27926.7 | + | 16123.5i | −1.10155 | + | 0.635980i | −0.936627 | − | 0.350327i | \(-0.886070\pi\) |
−0.164921 | + | 0.986307i | \(0.552737\pi\) | |||||||
\(864\) | −2800.00 | + | 4849.74i | −0.110252 | + | 0.190962i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8974.00 | − | 15543.4i | −0.352135 | − | 0.609916i | ||||
\(867\) | 31304.0i | 1.22623i | ||||||||
\(868\) | −10693.7 | − | 2058.00i | −0.418165 | − | 0.0804759i | ||||
\(869\) | −515.000 | −0.0201038 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2905.00 | − | 5031.61i | 0.113011 | − | 0.195740i | ||||
\(872\) | 23382.7 | + | 13500.0i | 0.908071 | + | 0.524275i | ||||
\(873\) | −16804.4 | + | 9702.00i | −0.651479 | + | 0.376132i | ||||
\(874\) | 15582.0 | 0.603054 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 31164.0 | 1.20198 | ||||||||
\(877\) | −23929.1 | + | 13815.5i | −0.921357 | + | 0.531946i | −0.884068 | − | 0.467359i | \(-0.845206\pi\) |
−0.0372891 | + | 0.999305i | \(0.511872\pi\) | |||||||
\(878\) | 7238.24 | + | 4179.00i | 0.278222 | + | 0.160631i | ||||
\(879\) | 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 | \(0.345484\pi\) | |||||||
\(882\) | −5601.45 | + | 14014.0i | −0.213844 | + | 0.535007i | ||||
\(883\) | − | 19612.0i | − | 0.747448i | −0.927540 | − | 0.373724i | \(-0.878081\pi\) | ||
0.927540 | − | 0.373724i | \(-0.121919\pi\) | |||||||
\(884\) | −588.000 | − | 1018.45i | −0.0223717 | − | 0.0387489i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12927.0 | − | 22390.2i | 0.490170 | − | 0.849000i | ||||
\(887\) | −1958.08 | + | 1130.50i | −0.0741218 | + | 0.0427942i | −0.536603 | − | 0.843835i | \(-0.680293\pi\) |
0.462481 | + | 0.886629i | \(0.346959\pi\) | |||||||
\(888\) | − | 36792.0i | − | 1.39038i | ||||||
\(889\) | −1008.00 | − | 872.954i | −0.0380284 | − | 0.0329335i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2097.50 | − | 3632.98i | −0.0788652 | − | 0.136599i | ||||
\(892\) | 4849.74 | + | 2800.00i | 0.182042 | + | 0.105102i | ||||
\(893\) | −22278.5 | − | 12862.5i | −0.834851 | − | 0.482001i | ||||
\(894\) | −1407.00 | − | 2437.00i | −0.0526366 | − | 0.0911693i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1344.00 | + | 6983.63i | −0.0501115 | + | 0.260387i | ||||
\(897\) | − | 15582.0i | − | 0.580009i | ||||||
\(898\) | −4894.78 | + | 2826.00i | −0.181894 | + | 0.105017i | ||||
\(899\) | 4263.00 | − | 7383.73i | 0.158152 | − | 0.273928i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3181.50 | + | 5510.52i | 0.117637 | + | 0.203754i | ||||
\(902\) | 3500.00i | 0.129199i | ||||||||
\(903\) | 5261.97 | + | 15190.0i | 0.193917 | + | 0.559791i | ||||
\(904\) | −36912.0 | −1.35805 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11333.0 | + | 19629.3i | −0.415578 | + | 0.719802i | ||||
\(907\) | −20640.0 | − | 11916.5i | −0.755611 | − | 0.436252i | 0.0721066 | − | 0.997397i | \(-0.477028\pi\) |
−0.827718 | + | 0.561145i | \(0.810361\pi\) | |||||||
\(908\) | 7638.34 | − | 4410.00i | 0.279171 | − | 0.161180i | ||||
\(909\) | −30338.0 | −1.10698 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31824.0 | 1.15738 | 0.578692 | − | 0.815546i | \(-0.303563\pi\) | ||||
0.578692 | + | 0.815546i | \(0.303563\pi\) | |||||||
\(912\) | 4752.75 | − | 2744.00i | 0.172565 | − | 0.0996304i | ||||
\(913\) | 4728.50 | + | 2730.00i | 0.171402 | + | 0.0989593i | ||||
\(914\) | 8479.00 | − | 14686.1i | 0.306849 | − | 0.531479i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1148.00 | −0.0414094 | ||||||||
\(917\) | −39082.9 | − | 7521.50i | −1.40745 | − | 0.270863i | ||||
\(918\) | 1470.00i | 0.0528510i | ||||||||
\(919\) | −8409.50 | − | 14565.7i | −0.301854 | − | 0.522826i | 0.674702 | − | 0.738090i | \(-0.264272\pi\) |
−0.976556 | + | 0.215264i | \(0.930939\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25774.0 | − | 44641.9i | 0.922130 | − | 1.59718i | ||||
\(922\) | −16173.9 | + | 9338.00i | −0.577721 | + | 0.333547i | ||||
\(923\) | 6048.00i | 0.215680i | ||||||||
\(924\) | −1960.00 | − | 1697.41i | −0.0697828 | − | 0.0604336i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4016.00 | + | 6955.92i | 0.142520 | + | 0.246853i | ||||
\(927\) | −12936.7 | − | 7469.00i | −0.458357 | − | 0.264632i | ||||
\(928\) | −8036.72 | − | 4640.00i | −0.284287 | − | 0.164133i | ||||
\(929\) | 899.500 | + | 1557.98i | 0.0317671 | + | 0.0550222i | 0.881472 | − | 0.472237i | \(-0.156553\pi\) |
−0.849705 | + | 0.527259i | \(0.823220\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13205.5 | − | 10396.6i | 0.464869 | − | 0.365989i | ||||
\(932\) | 18348.0i | 0.644859i | ||||||||
\(933\) | 60470.2 | − | 34912.5i | 2.12187 | − | 1.22506i | ||||
\(934\) | −5859.00 | + | 10148.1i | −0.205259 | + | 0.355520i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3696.00 | − | 6401.66i | −0.129068 | − | 0.223552i | ||||
\(937\) | − | 14154.0i | − | 0.493480i | −0.969082 | − | 0.246740i | \(-0.920641\pi\) | ||
0.969082 | − | 0.246740i | \(-0.0793594\pi\) | |||||||
\(938\) | −10063.2 | + | 11620.0i | −0.350294 | + | 0.404484i | ||||
\(939\) | 33271.0 | 1.15629 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6023.50 | + | 10433.0i | −0.208672 | + | 0.361431i | −0.951296 | − | 0.308277i | \(-0.900247\pi\) |
0.742624 | + | 0.669708i | \(0.233581\pi\) | |||||||
\(942\) | 8232.44 | + | 4753.00i | 0.284742 | + | 0.164396i | ||||
\(943\) | −48194.3 | + | 27825.0i | −1.66429 | + | 0.960877i | ||||
\(944\) | −1680.00 | −0.0579230 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1240.00 | 0.0426172 | ||||||||
\(947\) | 21112.8 | − | 12189.5i | 0.724472 | − | 0.418274i | −0.0919245 | − | 0.995766i | \(-0.529302\pi\) |
0.816396 | + | 0.577492i | \(0.195969\pi\) | |||||||
\(948\) | −2497.62 | − | 1442.00i | −0.0855684 | − | 0.0494029i | ||||
\(949\) | 7791.00 | − | 13494.4i | 0.266498 | − | 0.461588i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24339.0 | −0.829912 | ||||||||
\(952\) | 3055.34 | + | 8820.00i | 0.104017 | + | 0.300271i | ||||
\(953\) | − | 52330.0i | − | 1.77874i | −0.457192 | − | 0.889368i | \(-0.651145\pi\) | ||
0.457192 | − | 0.889368i | \(-0.348855\pi\) | |||||||
\(954\) | 6666.00 | + | 11545.9i | 0.226226 | + | 0.391835i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3336.00 | − | 5778.12i | 0.112860 | − | 0.195479i | ||||
\(957\) | 1758.03 | − | 1015.00i | 0.0593825 | − | 0.0342845i | ||||
\(958\) | 13006.0i | 0.438627i | ||||||||
\(959\) | −19687.5 | + | 6819.95i | −0.662922 | + | 0.229643i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4091.00 | + | 7085.82i | 0.137323 | + | 0.237851i | ||||
\(962\) | −5310.47 | − | 3066.00i | −0.177980 | − | 0.102757i | ||||
\(963\) | −8707.02 | − | 5027.00i | −0.291360 | − | 0.168217i | ||||
\(964\) | 6818.00 | + | 11809.1i | 0.227794 | + | 0.394550i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7791.00 | + | 40483.2i | −0.259494 | + | 1.34837i | ||||
\(967\) | 12416.0i | 0.412897i | 0.978457 | + | 0.206449i | \(0.0661906\pi\) | ||||
−0.978457 | + | 0.206449i | \(0.933809\pi\) | |||||||
\(968\) | 27144.7 | − | 15672.0i | 0.901305 | − | 0.520369i | ||||
\(969\) | −3601.50 | + | 6237.98i | −0.119398 | + | 0.206804i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18406.5 | − | 31881.0i | −0.608334 | − | 1.05367i | −0.991515 | − | 0.129993i | \(-0.958505\pi\) |
0.383181 | − | 0.923673i | \(-0.374829\pi\) | |||||||
\(972\) | − | 19712.0i | − | 0.650476i | ||||||
\(973\) | −3055.34 | + | 3528.00i | −0.100668 | + | 0.116241i | ||||
\(974\) | 32098.0 | 1.05594 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3304.00 | + | 5722.70i | −0.108359 | + | 0.187683i | ||||
\(977\) | 30306.6 | + | 17497.5i | 0.992418 | + | 0.572973i | 0.905996 | − | 0.423286i | \(-0.139123\pi\) |
0.0864221 | + | 0.996259i | \(0.472457\pi\) | |||||||
\(978\) | −5662.07 | + | 3269.00i | −0.185126 | + | 0.106883i | ||||
\(979\) | −1645.00 | −0.0537022 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24750.0 | −0.805511 | ||||||||
\(982\) | −15352.9 | + | 8864.00i | −0.498911 | + | 0.288046i | ||||
\(983\) | 12385.0 | + | 7150.50i | 0.401853 | + | 0.232010i | 0.687283 | − | 0.726390i | \(-0.258803\pi\) |
−0.285430 | + | 0.958399i | \(0.592137\pi\) | |||||||
\(984\) | −29400.0 | + | 50922.3i | −0.952477 | + | 1.64974i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2436.00 | −0.0786796 | ||||||||
\(987\) | 44557.0 | − | 51450.0i | 1.43695 | − | 1.65924i | ||||
\(988\) | 2744.00i | 0.0883586i | ||||||||
\(989\) | 9858.00 | + | 17074.6i | 0.316953 | + | 0.548978i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1332.50 | − | 2307.96i | 0.0427127 | − | 0.0739805i | −0.843879 | − | 0.536534i | \(-0.819733\pi\) |
0.886591 | + | 0.462553i | \(0.153067\pi\) | |||||||
\(992\) | −20368.9 | + | 11760.0i | −0.651929 | + | 0.376392i | ||||
\(993\) | 23387.0i | 0.747396i | ||||||||
\(994\) | 3024.00 | − | 15713.2i | 0.0964944 | − | 0.501400i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 15288.0 | + | 26479.6i | 0.486364 | + | 0.842408i | ||||
\(997\) | 21538.9 | + | 12435.5i | 0.684197 | + | 0.395021i | 0.801434 | − | 0.598083i | \(-0.204071\pi\) |
−0.117237 | + | 0.993104i | \(0.537404\pi\) | |||||||
\(998\) | 17686.0 | + | 10211.0i | 0.560962 | + | 0.323871i | ||||
\(999\) | −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.k.a.74.1 | 4 | ||
5.2 | odd | 4 | 7.4.c.a.4.1 | yes | 2 | ||
5.3 | odd | 4 | 175.4.e.a.151.1 | 2 | |||
5.4 | even | 2 | inner | 175.4.k.a.74.2 | 4 | ||
7.2 | even | 3 | inner | 175.4.k.a.149.2 | 4 | ||
15.2 | even | 4 | 63.4.e.b.46.1 | 2 | |||
20.7 | even | 4 | 112.4.i.c.81.1 | 2 | |||
35.2 | odd | 12 | 7.4.c.a.2.1 | ✓ | 2 | ||
35.3 | even | 12 | 1225.4.a.d.1.1 | 1 | |||
35.9 | even | 6 | inner | 175.4.k.a.149.1 | 4 | ||
35.12 | even | 12 | 49.4.c.a.30.1 | 2 | |||
35.17 | even | 12 | 49.4.a.c.1.1 | 1 | |||
35.18 | odd | 12 | 1225.4.a.c.1.1 | 1 | |||
35.23 | odd | 12 | 175.4.e.a.51.1 | 2 | |||
35.27 | even | 4 | 49.4.c.a.18.1 | 2 | |||
35.32 | odd | 12 | 49.4.a.d.1.1 | 1 | |||
40.27 | even | 4 | 448.4.i.a.193.1 | 2 | |||
40.37 | odd | 4 | 448.4.i.f.193.1 | 2 | |||
105.2 | even | 12 | 63.4.e.b.37.1 | 2 | |||
105.17 | odd | 12 | 441.4.a.e.1.1 | 1 | |||
105.32 | even | 12 | 441.4.a.d.1.1 | 1 | |||
105.47 | odd | 12 | 441.4.e.k.226.1 | 2 | |||
105.62 | odd | 4 | 441.4.e.k.361.1 | 2 | |||
140.67 | even | 12 | 784.4.a.b.1.1 | 1 | |||
140.87 | odd | 12 | 784.4.a.r.1.1 | 1 | |||
140.107 | even | 12 | 112.4.i.c.65.1 | 2 | |||
280.37 | odd | 12 | 448.4.i.f.65.1 | 2 | |||
280.107 | even | 12 | 448.4.i.a.65.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.4.c.a.2.1 | ✓ | 2 | 35.2 | odd | 12 | ||
7.4.c.a.4.1 | yes | 2 | 5.2 | odd | 4 | ||
49.4.a.c.1.1 | 1 | 35.17 | even | 12 | |||
49.4.a.d.1.1 | 1 | 35.32 | odd | 12 | |||
49.4.c.a.18.1 | 2 | 35.27 | even | 4 | |||
49.4.c.a.30.1 | 2 | 35.12 | even | 12 | |||
63.4.e.b.37.1 | 2 | 105.2 | even | 12 | |||
63.4.e.b.46.1 | 2 | 15.2 | even | 4 | |||
112.4.i.c.65.1 | 2 | 140.107 | even | 12 | |||
112.4.i.c.81.1 | 2 | 20.7 | even | 4 | |||
175.4.e.a.51.1 | 2 | 35.23 | odd | 12 | |||
175.4.e.a.151.1 | 2 | 5.3 | odd | 4 | |||
175.4.k.a.74.1 | 4 | 1.1 | even | 1 | trivial | ||
175.4.k.a.74.2 | 4 | 5.4 | even | 2 | inner | ||
175.4.k.a.149.1 | 4 | 35.9 | even | 6 | inner | ||
175.4.k.a.149.2 | 4 | 7.2 | even | 3 | inner | ||
441.4.a.d.1.1 | 1 | 105.32 | even | 12 | |||
441.4.a.e.1.1 | 1 | 105.17 | odd | 12 | |||
441.4.e.k.226.1 | 2 | 105.47 | odd | 12 | |||
441.4.e.k.361.1 | 2 | 105.62 | odd | 4 | |||
448.4.i.a.65.1 | 2 | 280.107 | even | 12 | |||
448.4.i.a.193.1 | 2 | 40.27 | even | 4 | |||
448.4.i.f.65.1 | 2 | 280.37 | odd | 12 | |||
448.4.i.f.193.1 | 2 | 40.37 | odd | 4 | |||
784.4.a.b.1.1 | 1 | 140.67 | even | 12 | |||
784.4.a.r.1.1 | 1 | 140.87 | odd | 12 | |||
1225.4.a.c.1.1 | 1 | 35.18 | odd | 12 | |||
1225.4.a.d.1.1 | 1 | 35.3 | even | 12 |