Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(37,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.v (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Character | \(\chi\) | \(=\) | 210.67 |
Dual form | 210.3.v.b.163.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | + | 1.36603i | −0.183013 | + | 0.683013i | ||||
\(3\) | −0.448288 | − | 1.67303i | −0.149429 | − | 0.557678i | ||||
\(4\) | −1.73205 | − | 1.00000i | −0.433013 | − | 0.250000i | ||||
\(5\) | −3.76724 | + | 3.28753i | −0.753449 | + | 0.657507i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | 5.65016 | − | 4.13228i | 0.807166 | − | 0.590325i | ||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | −2.59808 | + | 1.50000i | −0.288675 | + | 0.166667i | ||||
\(10\) | −3.11195 | − | 6.34947i | −0.311195 | − | 0.634947i | ||||
\(11\) | 2.47138 | − | 4.28056i | 0.224671 | − | 0.389141i | −0.731550 | − | 0.681788i | \(-0.761203\pi\) |
0.956221 | + | 0.292647i | \(0.0945360\pi\) | |||||||
\(12\) | −0.896575 | + | 3.34607i | −0.0747146 | + | 0.278839i | ||||
\(13\) | 7.82868 | − | 7.82868i | 0.602206 | − | 0.602206i | −0.338692 | − | 0.940897i | \(-0.609984\pi\) |
0.940897 | + | 0.338692i | \(0.109984\pi\) | |||||||
\(14\) | 3.57669 | + | 9.23078i | 0.255478 | + | 0.659341i | ||||
\(15\) | 7.18896 | + | 4.82896i | 0.479264 | + | 0.321931i | ||||
\(16\) | 2.00000 | + | 3.46410i | 0.125000 | + | 0.216506i | ||||
\(17\) | 3.41115 | − | 0.914015i | 0.200656 | − | 0.0537656i | −0.157091 | − | 0.987584i | \(-0.550212\pi\) |
0.357747 | + | 0.933819i | \(0.383545\pi\) | |||||||
\(18\) | −1.09808 | − | 4.09808i | −0.0610042 | − | 0.227671i | ||||
\(19\) | 26.8487 | − | 15.5011i | 1.41309 | − | 0.815848i | 0.417412 | − | 0.908718i | \(-0.362937\pi\) |
0.995678 | + | 0.0928696i | \(0.0296040\pi\) | |||||||
\(20\) | 9.81259 | − | 1.92693i | 0.490630 | − | 0.0963467i | ||||
\(21\) | −9.44633 | − | 7.60045i | −0.449825 | − | 0.361926i | ||||
\(22\) | 4.94276 | + | 4.94276i | 0.224671 | + | 0.224671i | ||||
\(23\) | 17.2084 | + | 4.61097i | 0.748191 | + | 0.200477i | 0.612715 | − | 0.790304i | \(-0.290077\pi\) |
0.135475 | + | 0.990781i | \(0.456744\pi\) | |||||||
\(24\) | −4.24264 | − | 2.44949i | −0.176777 | − | 0.102062i | ||||
\(25\) | 3.38424 | − | 24.7699i | 0.135369 | − | 0.990795i | ||||
\(26\) | 7.82868 | + | 13.5597i | 0.301103 | + | 0.521526i | ||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | −13.9186 | + | 1.50715i | −0.497094 | + | 0.0538269i | ||||
\(29\) | − | 24.0299i | − | 0.828619i | −0.910136 | − | 0.414309i | \(-0.864023\pi\) | ||
0.910136 | − | 0.414309i | \(-0.135977\pi\) | |||||||
\(30\) | −9.22782 | + | 8.05278i | −0.307594 | + | 0.268426i | ||||
\(31\) | 7.79698 | − | 13.5048i | 0.251515 | − | 0.435638i | −0.712428 | − | 0.701745i | \(-0.752404\pi\) |
0.963943 | + | 0.266108i | \(0.0857377\pi\) | |||||||
\(32\) | −5.46410 | + | 1.46410i | −0.170753 | + | 0.0457532i | ||||
\(33\) | −8.26940 | − | 2.21578i | −0.250588 | − | 0.0671448i | ||||
\(34\) | 4.99427i | 0.146890i | ||||||||
\(35\) | −7.70052 | + | 34.1424i | −0.220015 | + | 0.975496i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −8.92003 | + | 33.2900i | −0.241082 | + | 0.899730i | 0.734231 | + | 0.678900i | \(0.237543\pi\) |
−0.975312 | + | 0.220830i | \(0.929124\pi\) | |||||||
\(38\) | 11.3476 | + | 42.3498i | 0.298621 | + | 1.11447i | ||||
\(39\) | −16.6071 | − | 9.58813i | −0.425824 | − | 0.245850i | ||||
\(40\) | −0.959417 | + | 14.1096i | −0.0239854 | + | 0.352739i | ||||
\(41\) | −19.3822 | −0.472736 | −0.236368 | − | 0.971664i | \(-0.575957\pi\) | ||||
−0.236368 | + | 0.971664i | \(0.575957\pi\) | |||||||
\(42\) | 13.8400 | − | 10.1220i | 0.329524 | − | 0.240999i | ||||
\(43\) | −11.5955 | + | 11.5955i | −0.269662 | + | 0.269662i | −0.828964 | − | 0.559302i | \(-0.811069\pi\) |
0.559302 | + | 0.828964i | \(0.311069\pi\) | |||||||
\(44\) | −8.56111 | + | 4.94276i | −0.194571 | + | 0.112335i | ||||
\(45\) | 4.85628 | − | 14.1921i | 0.107917 | − | 0.315381i | ||||
\(46\) | −12.5974 | + | 21.8194i | −0.273857 | + | 0.474334i | ||||
\(47\) | 8.13382 | − | 30.3558i | 0.173060 | − | 0.645869i | −0.823814 | − | 0.566860i | \(-0.808158\pi\) |
0.996874 | − | 0.0790084i | \(-0.0251754\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | 14.8486 | − | 46.6960i | 0.303033 | − | 0.952980i | ||||
\(50\) | 32.5976 | + | 13.6894i | 0.651951 | + | 0.273787i | ||||
\(51\) | −3.05835 | − | 5.29722i | −0.0599677 | − | 0.103867i | ||||
\(52\) | −21.3883 | + | 5.73099i | −0.411314 | + | 0.110211i | ||||
\(53\) | 26.9228 | + | 100.477i | 0.507977 | + | 1.89580i | 0.439735 | + | 0.898128i | \(0.355072\pi\) |
0.0682425 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(54\) | −6.36396 | + | 3.67423i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 4.76218 | + | 24.2506i | 0.0865852 | + | 0.440921i | ||||
\(56\) | 3.03577 | − | 19.5649i | 0.0542101 | − | 0.349373i | ||||
\(57\) | −37.9698 | − | 37.9698i | −0.666137 | − | 0.666137i | ||||
\(58\) | 32.8255 | + | 8.79557i | 0.565957 | + | 0.151648i | ||||
\(59\) | 13.5357 | + | 7.81482i | 0.229418 | + | 0.132455i | 0.610304 | − | 0.792168i | \(-0.291047\pi\) |
−0.380885 | + | 0.924622i | \(0.624381\pi\) | |||||||
\(60\) | −7.62269 | − | 15.5530i | −0.127045 | − | 0.259216i | ||||
\(61\) | −44.1937 | − | 76.5457i | −0.724486 | − | 1.25485i | −0.959185 | − | 0.282779i | \(-0.908744\pi\) |
0.234699 | − | 0.972068i | \(-0.424590\pi\) | |||||||
\(62\) | 15.5940 | + | 15.5940i | 0.251515 | + | 0.251515i | ||||
\(63\) | −8.48113 | + | 19.2112i | −0.134621 | + | 0.304940i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −3.75548 | + | 55.2296i | −0.0577767 | + | 0.849686i | ||||
\(66\) | 6.05362 | − | 10.4852i | 0.0917215 | − | 0.158866i | ||||
\(67\) | −75.6604 | + | 20.2731i | −1.12926 | + | 0.302584i | −0.774625 | − | 0.632421i | \(-0.782061\pi\) |
−0.354634 | + | 0.935005i | \(0.615395\pi\) | |||||||
\(68\) | −6.82230 | − | 1.82803i | −0.100328 | − | 0.0268828i | ||||
\(69\) | − | 30.8572i | − | 0.447206i | ||||||
\(70\) | −43.8208 | − | 23.0161i | −0.626011 | − | 0.328801i | ||||
\(71\) | −59.7196 | −0.841121 | −0.420560 | − | 0.907265i | \(-0.638167\pi\) | ||||
−0.420560 | + | 0.907265i | \(0.638167\pi\) | |||||||
\(72\) | −2.19615 | + | 8.19615i | −0.0305021 | + | 0.113835i | ||||
\(73\) | −27.5699 | − | 102.892i | −0.377670 | − | 1.40948i | −0.849404 | − | 0.527743i | \(-0.823038\pi\) |
0.471734 | − | 0.881741i | \(-0.343628\pi\) | |||||||
\(74\) | −42.2100 | − | 24.3700i | −0.570406 | − | 0.329324i | ||||
\(75\) | −42.9579 | + | 5.44209i | −0.572772 | + | 0.0725613i | ||||
\(76\) | −62.0044 | −0.815848 | ||||||||
\(77\) | −3.72475 | − | 34.3982i | −0.0483733 | − | 0.446730i | ||||
\(78\) | 19.1763 | − | 19.1763i | 0.245850 | − | 0.245850i | ||||
\(79\) | −23.6823 | + | 13.6730i | −0.299776 | + | 0.173076i | −0.642342 | − | 0.766418i | \(-0.722037\pi\) |
0.342566 | + | 0.939494i | \(0.388704\pi\) | |||||||
\(80\) | −18.9228 | − | 6.47504i | −0.236535 | − | 0.0809380i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 7.09436 | − | 26.4765i | 0.0865166 | − | 0.322884i | ||||
\(83\) | −48.9951 | + | 48.9951i | −0.590302 | + | 0.590302i | −0.937713 | − | 0.347411i | \(-0.887061\pi\) |
0.347411 | + | 0.937713i | \(0.387061\pi\) | |||||||
\(84\) | 8.76107 | + | 22.6107i | 0.104298 | + | 0.269175i | ||||
\(85\) | −9.84577 | + | 14.6576i | −0.115833 | + | 0.172442i | ||||
\(86\) | −11.5955 | − | 20.0839i | −0.134831 | − | 0.233534i | ||||
\(87\) | −40.2029 | + | 10.7723i | −0.462102 | + | 0.123820i | ||||
\(88\) | −3.61835 | − | 13.5039i | −0.0411176 | − | 0.153453i | ||||
\(89\) | 98.6980 | − | 56.9833i | 1.10897 | − | 0.640262i | 0.170405 | − | 0.985374i | \(-0.445492\pi\) |
0.938561 | + | 0.345112i | \(0.112159\pi\) | |||||||
\(90\) | 17.6093 | + | 11.8285i | 0.195659 | + | 0.131428i | ||||
\(91\) | 11.8830 | − | 76.5835i | 0.130583 | − | 0.841577i | ||||
\(92\) | −25.1948 | − | 25.1948i | −0.273857 | − | 0.273857i | ||||
\(93\) | −26.0892 | − | 6.99058i | −0.280529 | − | 0.0751675i | ||||
\(94\) | 38.4896 | + | 22.2220i | 0.409464 | + | 0.236404i | ||||
\(95\) | −50.1852 | + | 146.662i | −0.528265 | + | 1.54382i | ||||
\(96\) | 4.89898 | + | 8.48528i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 99.3285 | + | 99.3285i | 1.02400 | + | 1.02400i | 0.999705 | + | 0.0243000i | \(0.00773568\pi\) |
0.0243000 | + | 0.999705i | \(0.492264\pi\) | |||||||
\(98\) | 58.3530 | + | 37.3755i | 0.595439 | + | 0.381383i | ||||
\(99\) | 14.8283i | 0.149781i | ||||||||
\(100\) | −30.6316 | + | 39.5185i | −0.306316 | + | 0.395185i | ||||
\(101\) | 39.4954 | − | 68.4080i | 0.391043 | − | 0.677307i | −0.601544 | − | 0.798839i | \(-0.705448\pi\) |
0.992587 | + | 0.121533i | \(0.0387810\pi\) | |||||||
\(102\) | 8.35558 | − | 2.23887i | 0.0819174 | − | 0.0219497i | ||||
\(103\) | 87.6811 | + | 23.4941i | 0.851272 | + | 0.228098i | 0.657972 | − | 0.753042i | \(-0.271414\pi\) |
0.193300 | + | 0.981140i | \(0.438081\pi\) | |||||||
\(104\) | − | 31.3147i | − | 0.301103i | ||||||
\(105\) | 60.5734 | − | 2.42238i | 0.576889 | − | 0.0230703i | ||||
\(106\) | −147.109 | −1.38782 | ||||||||
\(107\) | −20.5193 | + | 76.5792i | −0.191770 | + | 0.715694i | 0.801310 | + | 0.598250i | \(0.204137\pi\) |
−0.993079 | + | 0.117444i | \(0.962530\pi\) | |||||||
\(108\) | −2.68973 | − | 10.0382i | −0.0249049 | − | 0.0929463i | ||||
\(109\) | 37.6062 | + | 21.7120i | 0.345011 | + | 0.199192i | 0.662486 | − | 0.749074i | \(-0.269501\pi\) |
−0.317475 | + | 0.948267i | \(0.602835\pi\) | |||||||
\(110\) | −34.8701 | − | 2.37108i | −0.317001 | − | 0.0215553i | ||||
\(111\) | 59.6940 | 0.537784 | ||||||||
\(112\) | 25.6149 | + | 11.3082i | 0.228705 | + | 0.100966i | ||||
\(113\) | 129.101 | − | 129.101i | 1.14249 | − | 1.14249i | 0.154493 | − | 0.987994i | \(-0.450625\pi\) |
0.987994 | − | 0.154493i | \(-0.0493745\pi\) | |||||||
\(114\) | 65.7656 | − | 37.9698i | 0.576892 | − | 0.333068i | ||||
\(115\) | −79.9869 | + | 39.2025i | −0.695538 | + | 0.340891i | ||||
\(116\) | −24.0299 | + | 41.6211i | −0.207155 | + | 0.358802i | ||||
\(117\) | −8.59648 | + | 32.0825i | −0.0734742 | + | 0.274209i | ||||
\(118\) | −15.6296 | + | 15.6296i | −0.132455 | + | 0.132455i | ||||
\(119\) | 15.4966 | − | 19.2601i | 0.130223 | − | 0.161850i | ||||
\(120\) | 24.0358 | − | 4.72000i | 0.200299 | − | 0.0393334i | ||||
\(121\) | 48.2846 | + | 83.6313i | 0.399046 | + | 0.691168i | ||||
\(122\) | 120.739 | − | 32.3520i | 0.989666 | − | 0.265180i | ||||
\(123\) | 8.68879 | + | 32.4270i | 0.0706405 | + | 0.263634i | ||||
\(124\) | −27.0095 | + | 15.5940i | −0.217819 | + | 0.125758i | ||||
\(125\) | 68.6826 | + | 104.440i | 0.549461 | + | 0.835520i | ||||
\(126\) | −23.1387 | − | 18.6172i | −0.183640 | − | 0.147756i | ||||
\(127\) | 152.616 | + | 152.616i | 1.20170 | + | 1.20170i | 0.973648 | + | 0.228056i | \(0.0732370\pi\) |
0.228056 | + | 0.973648i | \(0.426763\pi\) | |||||||
\(128\) | 10.9282 | + | 2.92820i | 0.0853766 | + | 0.0228766i | ||||
\(129\) | 24.5977 | + | 14.2015i | 0.190680 | + | 0.110089i | ||||
\(130\) | −74.0704 | − | 25.3455i | −0.569772 | − | 0.194965i | ||||
\(131\) | −97.2153 | − | 168.382i | −0.742102 | − | 1.28536i | −0.951537 | − | 0.307535i | \(-0.900496\pi\) |
0.209435 | − | 0.977823i | \(-0.432838\pi\) | |||||||
\(132\) | 12.1072 | + | 12.1072i | 0.0917215 | + | 0.0917215i | ||||
\(133\) | 87.6446 | − | 198.530i | 0.658982 | − | 1.49271i | ||||
\(134\) | − | 110.774i | − | 0.826675i | ||||||
\(135\) | −25.9209 | − | 1.76256i | −0.192007 | − | 0.0130560i | ||||
\(136\) | 4.99427 | − | 8.65033i | 0.0367226 | − | 0.0636054i | ||||
\(137\) | −179.801 | + | 48.1776i | −1.31242 | + | 0.351661i | −0.846132 | − | 0.532973i | \(-0.821075\pi\) |
−0.466285 | + | 0.884634i | \(0.654408\pi\) | |||||||
\(138\) | 42.1518 | + | 11.2945i | 0.305448 | + | 0.0818445i | ||||
\(139\) | 202.296i | 1.45537i | 0.685913 | + | 0.727683i | \(0.259403\pi\) | ||||
−0.685913 | + | 0.727683i | \(0.740597\pi\) | |||||||
\(140\) | 47.4801 | − | 51.4358i | 0.339143 | − | 0.367399i | ||||
\(141\) | −54.4326 | −0.386047 | ||||||||
\(142\) | 21.8589 | − | 81.5785i | 0.153936 | − | 0.574496i | ||||
\(143\) | −14.1634 | − | 52.8587i | −0.0990451 | − | 0.369641i | ||||
\(144\) | −10.3923 | − | 6.00000i | −0.0721688 | − | 0.0416667i | ||||
\(145\) | 78.9993 | + | 90.5266i | 0.544822 | + | 0.624322i | ||||
\(146\) | 150.645 | 1.03181 | ||||||||
\(147\) | −84.7804 | − | 3.90893i | −0.576738 | − | 0.0265913i | ||||
\(148\) | 48.7399 | − | 48.7399i | 0.329324 | − | 0.329324i | ||||
\(149\) | −89.3747 | + | 51.6005i | −0.599830 | + | 0.346312i | −0.768975 | − | 0.639279i | \(-0.779233\pi\) |
0.169144 | + | 0.985591i | \(0.445900\pi\) | |||||||
\(150\) | 8.28965 | − | 60.6736i | 0.0552644 | − | 0.404490i | ||||
\(151\) | 37.3443 | − | 64.6822i | 0.247313 | − | 0.428359i | −0.715466 | − | 0.698647i | \(-0.753786\pi\) |
0.962779 | + | 0.270288i | \(0.0871190\pi\) | |||||||
\(152\) | 22.6952 | − | 84.6996i | 0.149311 | − | 0.557234i | ||||
\(153\) | −7.49140 | + | 7.49140i | −0.0489634 | + | 0.0489634i | ||||
\(154\) | 48.3522 | + | 7.50253i | 0.313975 | + | 0.0487177i | ||||
\(155\) | 15.0243 | + | 76.5086i | 0.0969307 | + | 0.493604i | ||||
\(156\) | 19.1763 | + | 33.2143i | 0.122925 | + | 0.212912i | ||||
\(157\) | −195.069 | + | 52.2685i | −1.24248 | + | 0.332920i | −0.819425 | − | 0.573186i | \(-0.805707\pi\) |
−0.423050 | + | 0.906106i | \(0.639041\pi\) | |||||||
\(158\) | −10.0093 | − | 37.3553i | −0.0633502 | − | 0.236426i | ||||
\(159\) | 156.033 | − | 90.0854i | 0.981336 | − | 0.566575i | ||||
\(160\) | 15.7713 | − | 23.4790i | 0.0985707 | − | 0.146744i | ||||
\(161\) | 116.284 | − | 45.0571i | 0.722261 | − | 0.279858i | ||||
\(162\) | 9.00000 | + | 9.00000i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | 159.904 | + | 42.8461i | 0.981004 | + | 0.262859i | 0.713467 | − | 0.700688i | \(-0.247124\pi\) |
0.267537 | + | 0.963548i | \(0.413790\pi\) | |||||||
\(164\) | 33.5709 | + | 19.3822i | 0.204701 | + | 0.118184i | ||||
\(165\) | 38.4373 | − | 18.8386i | 0.232953 | − | 0.114173i | ||||
\(166\) | −48.9951 | − | 84.8619i | −0.295151 | − | 0.511216i | ||||
\(167\) | 129.993 | + | 129.993i | 0.778403 | + | 0.778403i | 0.979559 | − | 0.201156i | \(-0.0644698\pi\) |
−0.201156 | + | 0.979559i | \(0.564470\pi\) | |||||||
\(168\) | −34.0936 | + | 3.69175i | −0.202938 | + | 0.0219747i | ||||
\(169\) | 46.4237i | 0.274696i | ||||||||
\(170\) | −16.4188 | − | 18.8146i | −0.0965814 | − | 0.110674i | ||||
\(171\) | −46.5033 | + | 80.5461i | −0.271949 | + | 0.471030i | ||||
\(172\) | 31.6794 | − | 8.48846i | 0.184182 | − | 0.0493515i | ||||
\(173\) | −28.5654 | − | 7.65408i | −0.165118 | − | 0.0442432i | 0.175313 | − | 0.984513i | \(-0.443906\pi\) |
−0.340431 | + | 0.940270i | \(0.610573\pi\) | |||||||
\(174\) | − | 58.8611i | − | 0.338282i | ||||||
\(175\) | −83.2345 | − | 153.938i | −0.475626 | − | 0.879648i | ||||
\(176\) | 19.7710 | 0.112335 | ||||||||
\(177\) | 7.00658 | − | 26.1489i | 0.0395852 | − | 0.147734i | ||||
\(178\) | 41.7147 | + | 155.681i | 0.234352 | + | 0.874614i | ||||
\(179\) | −187.148 | − | 108.050i | −1.04552 | − | 0.603629i | −0.124126 | − | 0.992266i | \(-0.539613\pi\) |
−0.921391 | + | 0.388637i | \(0.872946\pi\) | |||||||
\(180\) | −22.6035 | + | 19.7252i | −0.125575 | + | 0.109584i | ||||
\(181\) | 138.273 | 0.763937 | 0.381968 | − | 0.924175i | \(-0.375246\pi\) | ||||
0.381968 | + | 0.924175i | \(0.375246\pi\) | |||||||
\(182\) | 100.266 | + | 44.2640i | 0.550910 | + | 0.243209i | ||||
\(183\) | −108.252 | + | 108.252i | −0.591540 | + | 0.591540i | ||||
\(184\) | 43.6387 | − | 25.1948i | 0.237167 | − | 0.136928i | ||||
\(185\) | −75.8381 | − | 154.736i | −0.409936 | − | 0.836413i | ||||
\(186\) | 19.0986 | − | 33.0798i | 0.102681 | − | 0.177848i | ||||
\(187\) | 4.51775 | − | 16.8605i | 0.0241591 | − | 0.0901631i | ||||
\(188\) | −44.4440 | + | 44.4440i | −0.236404 | + | 0.236404i | ||||
\(189\) | 35.9430 | + | 5.57706i | 0.190174 | + | 0.0295083i | ||||
\(190\) | −181.976 | − | 122.236i | −0.957767 | − | 0.643350i | ||||
\(191\) | −76.7883 | − | 133.001i | −0.402033 | − | 0.696342i | 0.591938 | − | 0.805983i | \(-0.298363\pi\) |
−0.993971 | + | 0.109642i | \(0.965030\pi\) | |||||||
\(192\) | −13.3843 | + | 3.58630i | −0.0697097 | + | 0.0186787i | ||||
\(193\) | −80.5552 | − | 300.636i | −0.417385 | − | 1.55770i | −0.780011 | − | 0.625766i | \(-0.784787\pi\) |
0.362627 | − | 0.931935i | \(-0.381880\pi\) | |||||||
\(194\) | −172.042 | + | 99.3285i | −0.886814 | + | 0.512002i | ||||
\(195\) | 94.0844 | − | 18.4757i | 0.482484 | − | 0.0947471i | ||||
\(196\) | −72.4146 | + | 66.0313i | −0.369462 | + | 0.336894i | ||||
\(197\) | 67.5608 | + | 67.5608i | 0.342948 | + | 0.342948i | 0.857475 | − | 0.514526i | \(-0.172032\pi\) |
−0.514526 | + | 0.857475i | \(0.672032\pi\) | |||||||
\(198\) | −20.2558 | − | 5.42753i | −0.102302 | − | 0.0274118i | ||||
\(199\) | 279.894 | + | 161.597i | 1.40650 | + | 0.812044i | 0.995049 | − | 0.0993866i | \(-0.0316880\pi\) |
0.411453 | + | 0.911431i | \(0.365021\pi\) | |||||||
\(200\) | −42.7713 | − | 56.3082i | −0.213856 | − | 0.281541i | ||||
\(201\) | 67.8352 | + | 117.494i | 0.337489 | + | 0.584548i | ||||
\(202\) | 78.9907 | + | 78.9907i | 0.391043 | + | 0.391043i | ||||
\(203\) | −99.2983 | − | 135.773i | −0.489154 | − | 0.668833i | ||||
\(204\) | 12.2334i | 0.0599677i | ||||||||
\(205\) | 73.0173 | − | 63.7195i | 0.356182 | − | 0.310827i | ||||
\(206\) | −64.1870 | + | 111.175i | −0.311587 | + | 0.539685i | ||||
\(207\) | −51.6252 | + | 13.8329i | −0.249397 | + | 0.0668257i | ||||
\(208\) | 42.7767 | + | 11.4620i | 0.205657 | + | 0.0551057i | ||||
\(209\) | − | 153.237i | − | 0.733189i | ||||||
\(210\) | −18.8624 | + | 83.6314i | −0.0898207 | + | 0.398245i | ||||
\(211\) | −327.292 | −1.55115 | −0.775575 | − | 0.631256i | \(-0.782540\pi\) | ||||
−0.775575 | + | 0.631256i | \(0.782540\pi\) | |||||||
\(212\) | 53.8456 | − | 200.954i | 0.253989 | − | 0.947898i | ||||
\(213\) | 26.7716 | + | 99.9128i | 0.125688 | + | 0.469074i | ||||
\(214\) | −97.0986 | − | 56.0599i | −0.453732 | − | 0.261962i | ||||
\(215\) | 5.56244 | − | 81.8033i | 0.0258718 | − | 0.380481i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −11.7512 | − | 108.523i | −0.0541532 | − | 0.500108i | ||||
\(218\) | −43.4239 | + | 43.4239i | −0.199192 | + | 0.199192i | ||||
\(219\) | −159.783 | + | 92.2507i | −0.729603 | + | 0.421236i | ||||
\(220\) | 16.0023 | − | 46.7655i | 0.0727377 | − | 0.212571i | ||||
\(221\) | 19.5493 | − | 33.8603i | 0.0884582 | − | 0.153214i | ||||
\(222\) | −21.8495 | + | 81.5435i | −0.0984213 | + | 0.367313i | ||||
\(223\) | 87.5407 | − | 87.5407i | 0.392559 | − | 0.392559i | −0.483040 | − | 0.875599i | \(-0.660467\pi\) |
0.875599 | + | 0.483040i | \(0.160467\pi\) | |||||||
\(224\) | −24.8230 | + | 30.8516i | −0.110817 | + | 0.137730i | ||||
\(225\) | 28.3623 | + | 69.4304i | 0.126055 | + | 0.308580i | ||||
\(226\) | 129.101 | + | 223.610i | 0.571244 | + | 0.989423i | ||||
\(227\) | −281.372 | + | 75.3933i | −1.23952 | + | 0.332129i | −0.818280 | − | 0.574819i | \(-0.805072\pi\) |
−0.421242 | + | 0.906948i | \(0.638406\pi\) | |||||||
\(228\) | 27.7958 | + | 103.735i | 0.121912 | + | 0.454980i | ||||
\(229\) | 56.5510 | − | 32.6497i | 0.246948 | − | 0.142575i | −0.371418 | − | 0.928466i | \(-0.621128\pi\) |
0.618366 | + | 0.785890i | \(0.287795\pi\) | |||||||
\(230\) | −24.2744 | − | 123.613i | −0.105541 | − | 0.537449i | ||||
\(231\) | −55.8796 | + | 21.6519i | −0.241903 | + | 0.0937313i | ||||
\(232\) | −48.0599 | − | 48.0599i | −0.207155 | − | 0.207155i | ||||
\(233\) | −159.294 | − | 42.6828i | −0.683667 | − | 0.183188i | −0.0997635 | − | 0.995011i | \(-0.531809\pi\) |
−0.583903 | + | 0.811823i | \(0.698475\pi\) | |||||||
\(234\) | −40.6790 | − | 23.4860i | −0.173842 | − | 0.100368i | ||||
\(235\) | 69.1537 | + | 141.098i | 0.294271 | + | 0.600417i | ||||
\(236\) | −15.6296 | − | 27.0713i | −0.0662273 | − | 0.114709i | ||||
\(237\) | 33.4919 | + | 33.4919i | 0.141316 | + | 0.141316i | ||||
\(238\) | 20.6377 | + | 28.2184i | 0.0867130 | + | 0.118565i | ||||
\(239\) | 84.6324i | 0.354110i | 0.984201 | + | 0.177055i | \(0.0566571\pi\) | ||||
−0.984201 | + | 0.177055i | \(0.943343\pi\) | |||||||
\(240\) | −2.35008 | + | 34.5612i | −0.00979201 | + | 0.144005i | ||||
\(241\) | −220.268 | + | 381.516i | −0.913976 | + | 1.58305i | −0.105583 | + | 0.994410i | \(0.533671\pi\) |
−0.808393 | + | 0.588643i | \(0.799662\pi\) | |||||||
\(242\) | −131.916 | + | 35.3468i | −0.545107 | + | 0.146061i | ||||
\(243\) | −15.0573 | − | 4.03459i | −0.0619642 | − | 0.0166032i | ||||
\(244\) | 176.775i | 0.724486i | ||||||||
\(245\) | 97.5765 | + | 224.731i | 0.398272 | + | 0.917268i | ||||
\(246\) | −47.4764 | −0.192994 | ||||||||
\(247\) | 88.8367 | − | 331.543i | 0.359663 | − | 1.34228i | ||||
\(248\) | −11.4156 | − | 42.6035i | −0.0460305 | − | 0.171788i | ||||
\(249\) | 103.934 | + | 60.0064i | 0.417406 | + | 0.240990i | ||||
\(250\) | −167.807 | + | 55.5945i | −0.671229 | + | 0.222378i | ||||
\(251\) | −78.4347 | −0.312489 | −0.156244 | − | 0.987718i | \(-0.549939\pi\) | ||||
−0.156244 | + | 0.987718i | \(0.549939\pi\) | |||||||
\(252\) | 33.9010 | − | 24.7937i | 0.134528 | − | 0.0983875i | ||||
\(253\) | 62.2660 | − | 62.2660i | 0.246111 | − | 0.246111i | ||||
\(254\) | −264.339 | + | 152.616i | −1.04071 | + | 0.600852i | ||||
\(255\) | 28.9364 | + | 9.90148i | 0.113476 | + | 0.0388293i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 103.036 | − | 384.537i | 0.400920 | − | 1.49625i | −0.410540 | − | 0.911843i | \(-0.634660\pi\) |
0.811459 | − | 0.584409i | \(-0.198674\pi\) | |||||||
\(258\) | −28.4029 | + | 28.4029i | −0.110089 | + | 0.110089i | ||||
\(259\) | 87.1639 | + | 224.954i | 0.336540 | + | 0.868548i | ||||
\(260\) | 61.7343 | − | 91.9049i | 0.237439 | − | 0.353480i | ||||
\(261\) | 36.0449 | + | 62.4316i | 0.138103 | + | 0.239202i | ||||
\(262\) | 265.597 | − | 71.1666i | 1.01373 | − | 0.271628i | ||||
\(263\) | 104.904 | + | 391.508i | 0.398876 | + | 1.48862i | 0.815077 | + | 0.579352i | \(0.196694\pi\) |
−0.416201 | + | 0.909272i | \(0.636639\pi\) | |||||||
\(264\) | −20.9704 | + | 12.1072i | −0.0794332 | + | 0.0458608i | ||||
\(265\) | −431.747 | − | 290.012i | −1.62923 | − | 1.09439i | ||||
\(266\) | 239.117 | + | 192.392i | 0.898936 | + | 0.723277i | ||||
\(267\) | −139.580 | − | 139.580i | −0.522772 | − | 0.522772i | ||||
\(268\) | 151.321 | + | 40.5463i | 0.564630 | + | 0.151292i | ||||
\(269\) | −113.642 | − | 65.6115i | −0.422463 | − | 0.243909i | 0.273668 | − | 0.961824i | \(-0.411763\pi\) |
−0.696130 | + | 0.717915i | \(0.745096\pi\) | |||||||
\(270\) | 11.8954 | − | 34.7635i | 0.0440571 | − | 0.128754i | ||||
\(271\) | 31.0750 | + | 53.8235i | 0.114668 | + | 0.198611i | 0.917647 | − | 0.397397i | \(-0.130086\pi\) |
−0.802979 | + | 0.596007i | \(0.796753\pi\) | |||||||
\(272\) | 9.98854 | + | 9.98854i | 0.0367226 | + | 0.0367226i | ||||
\(273\) | −133.454 | + | 14.4508i | −0.488841 | + | 0.0529332i | ||||
\(274\) | − | 263.247i | − | 0.960756i | ||||||
\(275\) | −97.6651 | − | 75.7022i | −0.355146 | − | 0.275281i | ||||
\(276\) | −30.8572 | + | 53.4463i | −0.111802 | + | 0.193646i | ||||
\(277\) | 86.7411 | − | 23.2422i | 0.313145 | − | 0.0839068i | −0.0988239 | − | 0.995105i | \(-0.531508\pi\) |
0.411968 | + | 0.911198i | \(0.364841\pi\) | |||||||
\(278\) | −276.341 | − | 74.0454i | −0.994034 | − | 0.266351i | ||||
\(279\) | 46.7819i | 0.167677i | ||||||||
\(280\) | 52.8837 | + | 83.6858i | 0.188870 | + | 0.298878i | ||||
\(281\) | −3.27031 | −0.0116381 | −0.00581906 | − | 0.999983i | \(-0.501852\pi\) | ||||
−0.00581906 | + | 0.999983i | \(0.501852\pi\) | |||||||
\(282\) | 19.9237 | − | 74.3563i | 0.0706514 | − | 0.263675i | ||||
\(283\) | 52.8584 | + | 197.270i | 0.186779 | + | 0.697068i | 0.994243 | + | 0.107151i | \(0.0341729\pi\) |
−0.807464 | + | 0.589917i | \(0.799160\pi\) | |||||||
\(284\) | 103.437 | + | 59.7196i | 0.364216 | + | 0.210280i | ||||
\(285\) | 267.869 | + | 18.2144i | 0.939890 | + | 0.0639103i | ||||
\(286\) | 77.3905 | 0.270596 | ||||||||
\(287\) | −109.512 | + | 80.0924i | −0.381576 | + | 0.279068i | ||||
\(288\) | 12.0000 | − | 12.0000i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | −239.481 | + | 138.264i | −0.828653 | + | 0.478423i | ||||
\(290\) | −152.577 | + | 74.7799i | −0.526129 | + | 0.257862i | ||||
\(291\) | 121.652 | − | 210.707i | 0.418048 | − | 0.724081i | ||||
\(292\) | −55.1398 | + | 205.785i | −0.188835 | + | 0.704742i | ||||
\(293\) | −269.541 | + | 269.541i | −0.919935 | + | 0.919935i | −0.997024 | − | 0.0770891i | \(-0.975437\pi\) |
0.0770891 | + | 0.997024i | \(0.475437\pi\) | |||||||
\(294\) | 36.3715 | − | 114.381i | 0.123713 | − | 0.389053i | ||||
\(295\) | −76.6837 | + | 15.0586i | −0.259945 | + | 0.0510463i | ||||
\(296\) | 48.7399 | + | 84.4201i | 0.164662 | + | 0.285203i | ||||
\(297\) | 24.8082 | − | 6.64734i | 0.0835293 | − | 0.0223816i | ||||
\(298\) | −37.7742 | − | 140.975i | −0.126759 | − | 0.473071i | ||||
\(299\) | 170.817 | − | 98.6211i | 0.571293 | − | 0.329836i | ||||
\(300\) | 79.8474 | + | 33.5319i | 0.266158 | + | 0.111773i | ||||
\(301\) | −17.6005 | + | 113.432i | −0.0584736 | + | 0.376850i | ||||
\(302\) | 74.6886 | + | 74.6886i | 0.247313 | + | 0.247313i | ||||
\(303\) | −132.154 | − | 35.4106i | −0.436152 | − | 0.116867i | ||||
\(304\) | 107.395 | + | 62.0044i | 0.353272 | + | 0.203962i | ||||
\(305\) | 418.135 | + | 143.078i | 1.37093 | + | 0.469108i | ||||
\(306\) | −7.49140 | − | 12.9755i | −0.0244817 | − | 0.0424036i | ||||
\(307\) | 167.472 | + | 167.472i | 0.545511 | + | 0.545511i | 0.925139 | − | 0.379628i | \(-0.123948\pi\) |
−0.379628 | + | 0.925139i | \(0.623948\pi\) | |||||||
\(308\) | −27.9468 | + | 63.3042i | −0.0907363 | + | 0.205533i | ||||
\(309\) | − | 157.225i | − | 0.508820i | ||||||
\(310\) | −110.012 | − | 7.48056i | −0.354877 | − | 0.0241308i | ||||
\(311\) | 275.366 | − | 476.948i | 0.885422 | − | 1.53360i | 0.0401933 | − | 0.999192i | \(-0.487203\pi\) |
0.845229 | − | 0.534404i | \(-0.179464\pi\) | |||||||
\(312\) | −52.3905 | + | 14.0380i | −0.167918 | + | 0.0449936i | ||||
\(313\) | −274.100 | − | 73.4448i | −0.875718 | − | 0.234648i | −0.207159 | − | 0.978307i | \(-0.566422\pi\) |
−0.668559 | + | 0.743659i | \(0.733088\pi\) | |||||||
\(314\) | − | 285.600i | − | 0.909555i | ||||||
\(315\) | −31.2070 | − | 100.255i | −0.0990699 | − | 0.318271i | ||||
\(316\) | 54.6920 | 0.173076 | ||||||||
\(317\) | 97.6208 | − | 364.326i | 0.307952 | − | 1.14929i | −0.622422 | − | 0.782682i | \(-0.713851\pi\) |
0.930374 | − | 0.366611i | \(-0.119482\pi\) | |||||||
\(318\) | 65.9471 | + | 246.118i | 0.207381 | + | 0.773956i | ||||
\(319\) | −102.861 | − | 59.3871i | −0.322450 | − | 0.186167i | ||||
\(320\) | 26.3003 | + | 30.1379i | 0.0821884 | + | 0.0941811i | ||||
\(321\) | 137.318 | 0.427782 | ||||||||
\(322\) | 18.9862 | + | 175.339i | 0.0589634 | + | 0.544531i | ||||
\(323\) | 77.4167 | − | 77.4167i | 0.239680 | − | 0.239680i | ||||
\(324\) | −15.5885 | + | 9.00000i | −0.0481125 | + | 0.0277778i | ||||
\(325\) | −167.421 | − | 220.409i | −0.515142 | − | 0.678183i | ||||
\(326\) | −117.058 | + | 202.750i | −0.359072 | + | 0.621932i | ||||
\(327\) | 19.4664 | − | 72.6497i | 0.0595303 | − | 0.222170i | ||||
\(328\) | −38.7643 | + | 38.7643i | −0.118184 | + | 0.118184i | ||||
\(329\) | −79.4813 | − | 205.126i | −0.241584 | − | 0.623485i | ||||
\(330\) | 11.6649 | + | 59.4017i | 0.0353482 | + | 0.180005i | ||||
\(331\) | 203.687 | + | 352.797i | 0.615369 | + | 1.06585i | 0.990320 | + | 0.138806i | \(0.0443264\pi\) |
−0.374950 | + | 0.927045i | \(0.622340\pi\) | |||||||
\(332\) | 133.857 | − | 35.8669i | 0.403184 | − | 0.108033i | ||||
\(333\) | −26.7601 | − | 99.8700i | −0.0803606 | − | 0.299910i | ||||
\(334\) | −225.155 | + | 129.993i | −0.674117 | + | 0.389202i | ||||
\(335\) | 218.382 | − | 325.110i | 0.651888 | − | 0.970477i | ||||
\(336\) | 7.43608 | − | 47.9239i | 0.0221312 | − | 0.142631i | ||||
\(337\) | −51.7090 | − | 51.7090i | −0.153439 | − | 0.153439i | 0.626213 | − | 0.779652i | \(-0.284604\pi\) |
−0.779652 | + | 0.626213i | \(0.784604\pi\) | |||||||
\(338\) | −63.4159 | − | 16.9922i | −0.187621 | − | 0.0502729i | ||||
\(339\) | −273.865 | − | 158.116i | −0.807860 | − | 0.466418i | ||||
\(340\) | 31.7110 | − | 15.5419i | 0.0932675 | − | 0.0457115i | ||||
\(341\) | −38.5386 | − | 66.7508i | −0.113016 | − | 0.195750i | ||||
\(342\) | −93.0067 | − | 93.0067i | −0.271949 | − | 0.271949i | ||||
\(343\) | −109.064 | − | 325.198i | −0.317971 | − | 0.948101i | ||||
\(344\) | 46.3818i | 0.134831i | ||||||||
\(345\) | 101.444 | + | 116.247i | 0.294041 | + | 0.336947i | ||||
\(346\) | 20.9113 | − | 36.2195i | 0.0604374 | − | 0.104681i | ||||
\(347\) | −465.261 | + | 124.666i | −1.34081 | + | 0.359269i | −0.856734 | − | 0.515758i | \(-0.827510\pi\) |
−0.484075 | + | 0.875027i | \(0.660844\pi\) | |||||||
\(348\) | 80.4058 | + | 21.5447i | 0.231051 | + | 0.0619099i | ||||
\(349\) | − | 165.950i | − | 0.475501i | −0.971326 | − | 0.237750i | \(-0.923590\pi\) | ||
0.971326 | − | 0.237750i | \(-0.0764100\pi\) | |||||||
\(350\) | 240.750 | − | 57.3551i | 0.687856 | − | 0.163872i | ||||
\(351\) | 57.5288 | 0.163900 | ||||||||
\(352\) | −7.23670 | + | 27.0077i | −0.0205588 | + | 0.0767265i | ||||
\(353\) | 16.3422 | + | 60.9899i | 0.0462951 | + | 0.172776i | 0.985203 | − | 0.171394i | \(-0.0548271\pi\) |
−0.938907 | + | 0.344170i | \(0.888160\pi\) | |||||||
\(354\) | 33.1555 | + | 19.1423i | 0.0936596 | + | 0.0540744i | ||||
\(355\) | 224.978 | − | 196.330i | 0.633741 | − | 0.553043i | ||||
\(356\) | −227.933 | −0.640262 | ||||||||
\(357\) | −39.1698 | − | 17.2922i | −0.109719 | − | 0.0484375i | ||||
\(358\) | 216.099 | − | 216.099i | 0.603629 | − | 0.603629i | ||||
\(359\) | −140.408 | + | 81.0646i | −0.391109 | + | 0.225807i | −0.682640 | − | 0.730754i | \(-0.739168\pi\) |
0.291532 | + | 0.956561i | \(0.405835\pi\) | |||||||
\(360\) | −18.6717 | − | 38.0968i | −0.0518658 | − | 0.105825i | ||||
\(361\) | 300.069 | − | 519.734i | 0.831215 | − | 1.43971i | ||||
\(362\) | −50.6113 | + | 188.884i | −0.139810 | + | 0.521778i | ||||
\(363\) | 118.273 | − | 118.273i | 0.325820 | − | 0.325820i | ||||
\(364\) | −97.1655 | + | 120.764i | −0.266938 | + | 0.331768i | ||||
\(365\) | 442.125 | + | 296.983i | 1.21130 | + | 0.813653i | ||||
\(366\) | −108.252 | − | 187.498i | −0.295770 | − | 0.512289i | ||||
\(367\) | 18.5994 | − | 4.98370i | 0.0506796 | − | 0.0135796i | −0.233390 | − | 0.972383i | \(-0.574982\pi\) |
0.284070 | + | 0.958804i | \(0.408315\pi\) | |||||||
\(368\) | 18.4439 | + | 68.8336i | 0.0501193 | + | 0.187048i | ||||
\(369\) | 50.3563 | − | 29.0732i | 0.136467 | − | 0.0787893i | ||||
\(370\) | 239.133 | − | 46.9593i | 0.646304 | − | 0.126917i | ||||
\(371\) | 567.318 | + | 456.460i | 1.52916 | + | 1.23035i | ||||
\(372\) | 38.1972 | + | 38.1972i | 0.102681 | + | 0.102681i | ||||
\(373\) | −326.843 | − | 87.5772i | −0.876253 | − | 0.234791i | −0.207463 | − | 0.978243i | \(-0.566521\pi\) |
−0.668790 | + | 0.743451i | \(0.733187\pi\) | |||||||
\(374\) | 21.3782 | + | 12.3427i | 0.0571611 | + | 0.0330020i | ||||
\(375\) | 143.942 | − | 161.727i | 0.383845 | − | 0.431273i | ||||
\(376\) | −44.4440 | − | 76.9793i | −0.118202 | − | 0.204732i | ||||
\(377\) | −188.123 | − | 188.123i | −0.498999 | − | 0.498999i | ||||
\(378\) | −20.7744 | + | 47.0577i | −0.0549588 | + | 0.124491i | ||||
\(379\) | 531.207i | 1.40160i | 0.713357 | + | 0.700801i | \(0.247174\pi\) | ||||
−0.713357 | + | 0.700801i | \(0.752826\pi\) | |||||||
\(380\) | 233.586 | − | 203.842i | 0.614699 | − | 0.536426i | ||||
\(381\) | 186.916 | − | 323.748i | 0.490594 | − | 0.849733i | ||||
\(382\) | 209.790 | − | 56.2129i | 0.549187 | − | 0.147154i | ||||
\(383\) | −96.4442 | − | 25.8421i | −0.251813 | − | 0.0674730i | 0.130705 | − | 0.991421i | \(-0.458276\pi\) |
−0.382517 | + | 0.923948i | \(0.624943\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 127.117 | + | 117.341i | 0.330175 | + | 0.304783i | ||||
\(386\) | 440.162 | 1.14032 | ||||||||
\(387\) | 12.7327 | − | 47.5191i | 0.0329010 | − | 0.122788i | ||||
\(388\) | −72.7135 | − | 271.370i | −0.187406 | − | 0.699408i | ||||
\(389\) | 528.011 | + | 304.848i | 1.35736 | + | 0.783670i | 0.989267 | − | 0.146121i | \(-0.0466788\pi\) |
0.368089 | + | 0.929791i | \(0.380012\pi\) | |||||||
\(390\) | −9.19902 | + | 135.284i | −0.0235872 | + | 0.346883i | ||||
\(391\) | 62.9149 | 0.160908 | ||||||||
\(392\) | −63.6949 | − | 123.089i | −0.162487 | − | 0.314003i | ||||
\(393\) | −238.128 | + | 238.128i | −0.605924 | + | 0.605924i | ||||
\(394\) | −117.019 | + | 67.5608i | −0.297002 | + | 0.171474i | ||||
\(395\) | 44.2666 | − | 129.366i | 0.112067 | − | 0.327509i | ||||
\(396\) | 14.8283 | − | 25.6833i | 0.0374451 | − | 0.0648569i | ||||
\(397\) | −173.904 | + | 649.017i | −0.438044 | + | 1.63480i | 0.295631 | + | 0.955302i | \(0.404470\pi\) |
−0.733675 | + | 0.679501i | \(0.762196\pi\) | |||||||
\(398\) | −323.194 | + | 323.194i | −0.812044 | + | 0.812044i | ||||
\(399\) | −371.437 | − | 57.6337i | −0.930920 | − | 0.144445i | ||||
\(400\) | 92.5739 | − | 37.8164i | 0.231435 | − | 0.0945410i | ||||
\(401\) | 304.095 | + | 526.709i | 0.758343 | + | 1.31349i | 0.943695 | + | 0.330816i | \(0.107324\pi\) |
−0.185353 | + | 0.982672i | \(0.559343\pi\) | |||||||
\(402\) | −185.329 | + | 49.6588i | −0.461018 | + | 0.123529i | ||||
\(403\) | −44.6844 | − | 166.764i | −0.110879 | − | 0.413808i | ||||
\(404\) | −136.816 | + | 78.9907i | −0.338653 | + | 0.195522i | ||||
\(405\) | 8.67120 | + | 44.1567i | 0.0214104 | + | 0.109029i | ||||
\(406\) | 221.815 | − | 85.9477i | 0.546343 | − | 0.211694i | ||||
\(407\) | 120.455 | + | 120.455i | 0.295958 | + | 0.295958i | ||||
\(408\) | −16.7112 | − | 4.47774i | −0.0409587 | − | 0.0109749i | ||||
\(409\) | −322.212 | − | 186.029i | −0.787804 | − | 0.454839i | 0.0513849 | − | 0.998679i | \(-0.483636\pi\) |
−0.839189 | + | 0.543840i | \(0.816970\pi\) | |||||||
\(410\) | 60.3163 | + | 123.066i | 0.147113 | + | 0.300162i | ||||
\(411\) | 161.205 | + | 279.216i | 0.392227 | + | 0.679357i | ||||
\(412\) | −128.374 | − | 128.374i | −0.311587 | − | 0.311587i | ||||
\(413\) | 108.772 | − | 11.7781i | 0.263370 | − | 0.0285185i | ||||
\(414\) | − | 75.5845i | − | 0.182571i | ||||||
\(415\) | 23.5033 | − | 345.649i | 0.0566346 | − | 0.832890i | ||||
\(416\) | −31.3147 | + | 54.2387i | −0.0752757 | + | 0.130381i | ||||
\(417\) | 338.448 | − | 90.6868i | 0.811625 | − | 0.217474i | ||||
\(418\) | 209.325 | + | 56.0885i | 0.500777 | + | 0.134183i | ||||
\(419\) | − | 338.166i | − | 0.807079i | −0.914962 | − | 0.403540i | \(-0.867780\pi\) | ||
0.914962 | − | 0.403540i | \(-0.132220\pi\) | |||||||
\(420\) | −107.339 | − | 56.3777i | −0.255568 | − | 0.134233i | ||||
\(421\) | 13.7324 | 0.0326186 | 0.0163093 | − | 0.999867i | \(-0.494808\pi\) | ||||
0.0163093 | + | 0.999867i | \(0.494808\pi\) | |||||||
\(422\) | 119.797 | − | 447.090i | 0.283880 | − | 1.05945i | ||||
\(423\) | 24.4015 | + | 91.0675i | 0.0576867 | + | 0.215290i | ||||
\(424\) | 254.800 | + | 147.109i | 0.600943 | + | 0.346955i | ||||
\(425\) | −11.0959 | − | 87.5870i | −0.0261080 | − | 0.206087i | ||||
\(426\) | −146.282 | −0.343386 | ||||||||
\(427\) | −566.009 | − | 249.875i | −1.32555 | − | 0.585187i | ||||
\(428\) | 112.120 | − | 112.120i | 0.261962 | − | 0.261962i | ||||
\(429\) | −82.0851 | + | 47.3918i | −0.191340 | + | 0.110470i | ||||
\(430\) | 109.709 | + | 37.5405i | 0.255138 | + | 0.0873036i | ||||
\(431\) | −54.4290 | + | 94.2738i | −0.126285 | + | 0.218733i | −0.922235 | − | 0.386631i | \(-0.873639\pi\) |
0.795949 | + | 0.605363i | \(0.206972\pi\) | |||||||
\(432\) | −5.37945 | + | 20.0764i | −0.0124524 | + | 0.0464731i | ||||
\(433\) | −449.174 | + | 449.174i | −1.03735 | + | 1.03735i | −0.0380787 | + | 0.999275i | \(0.512124\pi\) |
−0.999275 | + | 0.0380787i | \(0.987876\pi\) | |||||||
\(434\) | 152.547 | + | 23.6698i | 0.351491 | + | 0.0545387i | ||||
\(435\) | 116.040 | − | 172.750i | 0.266758 | − | 0.397127i | ||||
\(436\) | −43.4239 | − | 75.2125i | −0.0995962 | − | 0.172506i | ||||
\(437\) | 533.498 | − | 142.950i | 1.22082 | − | 0.327118i | ||||
\(438\) | −67.5322 | − | 252.034i | −0.154183 | − | 0.575419i | ||||
\(439\) | 97.0976 | − | 56.0593i | 0.221179 | − | 0.127698i | −0.385317 | − | 0.922784i | \(-0.625908\pi\) |
0.606496 | + | 0.795086i | \(0.292575\pi\) | |||||||
\(440\) | 58.0256 | + | 38.9769i | 0.131876 | + | 0.0885839i | ||||
\(441\) | 31.4663 | + | 143.593i | 0.0713521 | + | 0.325607i | ||||
\(442\) | 39.0985 | + | 39.0985i | 0.0884582 | + | 0.0884582i | ||||
\(443\) | 614.169 | + | 164.566i | 1.38639 | + | 0.371481i | 0.873437 | − | 0.486938i | \(-0.161886\pi\) |
0.512950 | + | 0.858419i | \(0.328553\pi\) | |||||||
\(444\) | −103.393 | − | 59.6940i | −0.232867 | − | 0.134446i | ||||
\(445\) | −184.485 | + | 539.143i | −0.414572 | + | 1.21156i | ||||
\(446\) | 87.5407 | + | 151.625i | 0.196279 | + | 0.339966i | ||||
\(447\) | 126.395 | + | 126.395i | 0.282763 | + | 0.282763i | ||||
\(448\) | −33.0582 | − | 45.2013i | −0.0737906 | − | 0.100896i | ||||
\(449\) | 199.822i | 0.445038i | 0.974928 | + | 0.222519i | \(0.0714279\pi\) | ||||
−0.974928 | + | 0.222519i | \(0.928572\pi\) | |||||||
\(450\) | −105.225 | + | 13.3304i | −0.233833 | + | 0.0296230i | ||||
\(451\) | −47.9007 | + | 82.9664i | −0.106210 | + | 0.183961i | ||||
\(452\) | −352.711 | + | 94.5085i | −0.780333 | + | 0.209090i | ||||
\(453\) | −124.956 | − | 33.4820i | −0.275842 | − | 0.0739116i | ||||
\(454\) | − | 411.957i | − | 0.907393i | ||||||
\(455\) | 207.005 | + | 327.575i | 0.454955 | + | 0.719944i | ||||
\(456\) | −151.879 | −0.333068 | ||||||||
\(457\) | 109.714 | − | 409.459i | 0.240075 | − | 0.895971i | −0.735720 | − | 0.677285i | \(-0.763156\pi\) |
0.975795 | − | 0.218686i | \(-0.0701771\pi\) | |||||||
\(458\) | 23.9013 | + | 89.2008i | 0.0521862 | + | 0.194761i | ||||
\(459\) | 15.8917 | + | 9.17506i | 0.0346224 | + | 0.0199892i | ||||
\(460\) | 177.744 | + | 12.0862i | 0.386400 | + | 0.0262743i | ||||
\(461\) | −768.361 | −1.66673 | −0.833364 | − | 0.552725i | \(-0.813588\pi\) | ||||
−0.833364 | + | 0.552725i | \(0.813588\pi\) | |||||||
\(462\) | −9.12373 | − | 84.2581i | −0.0197483 | − | 0.182377i | ||||
\(463\) | −2.18079 | + | 2.18079i | −0.00471013 | + | 0.00471013i | −0.709458 | − | 0.704748i | \(-0.751060\pi\) |
0.704748 | + | 0.709458i | \(0.251060\pi\) | |||||||
\(464\) | 83.2422 | − | 48.0599i | 0.179401 | − | 0.103577i | ||||
\(465\) | 121.266 | − | 59.4339i | 0.260787 | − | 0.127815i | ||||
\(466\) | 116.612 | − | 201.977i | 0.250239 | − | 0.433427i | ||||
\(467\) | −222.687 | + | 831.079i | −0.476846 | + | 1.77961i | 0.137419 | + | 0.990513i | \(0.456119\pi\) |
−0.614265 | + | 0.789100i | \(0.710547\pi\) | |||||||
\(468\) | 46.9721 | − | 46.9721i | 0.100368 | − | 0.100368i | ||||
\(469\) | −343.719 | + | 427.196i | −0.732876 | + | 0.910866i | ||||
\(470\) | −218.055 | + | 42.8203i | −0.463948 | + | 0.0911071i | ||||
\(471\) | 174.894 | + | 302.925i | 0.371324 | + | 0.643153i | ||||
\(472\) | 42.7010 | − | 11.4417i | 0.0904682 | − | 0.0242409i | ||||
\(473\) | 20.9782 | + | 78.2918i | 0.0443514 | + | 0.165522i | ||||
\(474\) | −58.0096 | + | 33.4919i | −0.122383 | + | 0.0706579i | ||||
\(475\) | −293.098 | − | 717.499i | −0.617049 | − | 1.51052i | ||||
\(476\) | −46.1010 | + | 17.8630i | −0.0968508 | + | 0.0375272i | ||||
\(477\) | −220.663 | − | 220.663i | −0.462606 | − | 0.462606i | ||||
\(478\) | −115.610 | − | 30.9776i | −0.241862 | − | 0.0648067i | ||||
\(479\) | 440.106 | + | 254.095i | 0.918801 | + | 0.530470i | 0.883252 | − | 0.468898i | \(-0.155349\pi\) |
0.0355485 | + | 0.999368i | \(0.488682\pi\) | |||||||
\(480\) | −46.3513 | − | 15.8606i | −0.0965652 | − | 0.0330428i | ||||
\(481\) | 190.785 | + | 330.449i | 0.396642 | + | 0.687003i | ||||
\(482\) | −440.537 | − | 440.537i | −0.913976 | − | 0.913976i | ||||
\(483\) | −127.511 | − | 174.348i | −0.263997 | − | 0.360970i | ||||
\(484\) | − | 193.138i | − | 0.399046i | ||||||
\(485\) | −700.740 | − | 47.6487i | −1.44482 | − | 0.0982448i | ||||
\(486\) | 11.0227 | − | 19.0919i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 733.901 | − | 196.648i | 1.50698 | − | 0.403795i | 0.591551 | − | 0.806268i | \(-0.298516\pi\) |
0.915432 | + | 0.402473i | \(0.131849\pi\) | |||||||
\(488\) | −241.479 | − | 64.7040i | −0.494833 | − | 0.132590i | ||||
\(489\) | − | 286.731i | − | 0.586363i | ||||||
\(490\) | −342.703 | + | 51.0349i | −0.699394 | + | 0.104153i | ||||
\(491\) | −160.570 | −0.327027 | −0.163514 | − | 0.986541i | \(-0.552283\pi\) | ||||
−0.163514 | + | 0.986541i | \(0.552283\pi\) | |||||||
\(492\) | 17.3776 | − | 64.8540i | 0.0353203 | − | 0.131817i | ||||
\(493\) | −21.9637 | − | 81.9697i | −0.0445512 | − | 0.166267i | ||||
\(494\) | 420.380 | + | 242.706i | 0.850971 | + | 0.491308i | ||||
\(495\) | −48.7485 | − | 55.8617i | −0.0984818 | − | 0.112852i | ||||
\(496\) | 62.3758 | 0.125758 | ||||||||
\(497\) | −337.425 | + | 246.778i | −0.678924 | + | 0.496535i | ||||
\(498\) | −120.013 | + | 120.013i | −0.240990 | + | 0.240990i | ||||
\(499\) | −53.3534 | + | 30.8036i | −0.106921 | + | 0.0617307i | −0.552507 | − | 0.833508i | \(-0.686329\pi\) |
0.445586 | + | 0.895239i | \(0.352995\pi\) | |||||||
\(500\) | −14.5218 | − | 249.578i | −0.0290436 | − | 0.499156i | ||||
\(501\) | 159.209 | − | 275.758i | 0.317782 | − | 0.550414i | ||||
\(502\) | 28.7091 | − | 107.144i | 0.0571894 | − | 0.213434i | ||||
\(503\) | 10.2453 | − | 10.2453i | 0.0203684 | − | 0.0203684i | −0.696849 | − | 0.717218i | \(-0.745415\pi\) |
0.717218 | + | 0.696849i | \(0.245415\pi\) | |||||||
\(504\) | 21.4602 | + | 55.3847i | 0.0425797 | + | 0.109890i | ||||
\(505\) | 76.1049 | + | 387.552i | 0.150703 | + | 0.767429i | ||||
\(506\) | 62.2660 | + | 107.848i | 0.123055 | + | 0.213138i | ||||
\(507\) | 77.6683 | − | 20.8112i | 0.153192 | − | 0.0410476i | ||||
\(508\) | −111.723 | − | 416.956i | −0.219927 | − | 0.820779i | ||||
\(509\) | 447.613 | − | 258.430i | 0.879398 | − | 0.507720i | 0.00893787 | − | 0.999960i | \(-0.497155\pi\) |
0.870460 | + | 0.492240i | \(0.163822\pi\) | |||||||
\(510\) | −24.1171 | + | 35.9036i | −0.0472885 | + | 0.0703992i | ||||
\(511\) | −580.954 | − | 467.432i | −1.13690 | − | 0.914739i | ||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 155.603 | + | 41.6937i | 0.303320 | + | 0.0812744i | ||||
\(514\) | 487.573 | + | 281.500i | 0.948586 | + | 0.547666i | ||||
\(515\) | −407.553 | + | 199.747i | −0.791366 | + | 0.387858i | ||||
\(516\) | −28.4029 | − | 49.1953i | −0.0550445 | − | 0.0953398i | ||||
\(517\) | −109.838 | − | 109.838i | −0.212453 | − | 0.212453i | ||||
\(518\) | −339.197 | + | 36.7293i | −0.654820 | + | 0.0709059i | ||||
\(519\) | 51.2221i | 0.0986938i | ||||||||
\(520\) | 102.948 | + | 117.970i | 0.197977 | + | 0.226866i | ||||
\(521\) | −319.243 | + | 552.945i | −0.612751 | + | 1.06132i | 0.378024 | + | 0.925796i | \(0.376604\pi\) |
−0.990775 | + | 0.135520i | \(0.956730\pi\) | |||||||
\(522\) | −98.4765 | + | 26.3867i | −0.188652 | + | 0.0505492i | ||||
\(523\) | 664.497 | + | 178.051i | 1.27055 | + | 0.340442i | 0.830241 | − | 0.557405i | \(-0.188203\pi\) |
0.440307 | + | 0.897847i | \(0.354870\pi\) | |||||||
\(524\) | 388.861i | 0.742102i | ||||||||
\(525\) | −220.231 | + | 208.263i | −0.419487 | + | 0.396691i | ||||
\(526\) | −573.208 | −1.08975 | ||||||||
\(527\) | 14.2531 | − | 53.1933i | 0.0270457 | − | 0.100936i | ||||
\(528\) | −8.86311 | − | 33.0776i | −0.0167862 | − | 0.0626470i | ||||
\(529\) | −183.260 | − | 105.805i | −0.346427 | − | 0.200010i | ||||
\(530\) | 554.195 | − | 483.625i | 1.04565 | − | 0.912501i | ||||
\(531\) | −46.8889 | −0.0883031 | ||||||||
\(532\) | −350.335 | + | 256.219i | −0.658524 | + | 0.481615i | ||||
\(533\) | −151.737 | + | 151.737i | −0.284684 | + | 0.284684i | ||||
\(534\) | 241.760 | − | 139.580i | 0.452734 | − | 0.261386i | ||||
\(535\) | −174.456 | − | 355.951i | −0.326085 | − | 0.665328i | ||||
\(536\) | −110.774 | + | 191.867i | −0.206669 | + | 0.357961i | ||||
\(537\) | −96.8747 | + | 361.541i | −0.180400 | + | 0.673261i | ||||
\(538\) | 131.223 | − | 131.223i | 0.243909 | − | 0.243909i | ||||
\(539\) | −163.188 | − | 178.964i | −0.302761 | − | 0.332029i | ||||
\(540\) | 43.1338 | + | 28.9738i | 0.0798773 | + | 0.0536551i | ||||
\(541\) | 63.2590 | + | 109.568i | 0.116930 | + | 0.202528i | 0.918550 | − | 0.395306i | \(-0.129361\pi\) |
−0.801620 | + | 0.597834i | \(0.796028\pi\) | |||||||
\(542\) | −84.8985 | + | 22.7485i | −0.156639 | + | 0.0419714i | ||||
\(543\) | −61.9859 | − | 231.334i | −0.114154 | − | 0.426030i | ||||
\(544\) | −17.3007 | + | 9.98854i | −0.0318027 | + | 0.0183613i | ||||
\(545\) | −213.051 | + | 41.8375i | −0.390919 | + | 0.0767661i | ||||
\(546\) | 29.1073 | − | 187.591i | 0.0533101 | − | 0.343572i | ||||
\(547\) | 425.173 | + | 425.173i | 0.777281 | + | 0.777281i | 0.979368 | − | 0.202087i | \(-0.0647723\pi\) |
−0.202087 | + | 0.979368i | \(0.564772\pi\) | |||||||
\(548\) | 359.602 | + | 96.3552i | 0.656209 | + | 0.175831i | ||||
\(549\) | 229.637 | + | 132.581i | 0.418282 | + | 0.241495i | ||||
\(550\) | 139.159 | − | 105.704i | 0.253016 | − | 0.192189i | ||||
\(551\) | −372.491 | − | 645.173i | −0.676027 | − | 1.17091i | ||||
\(552\) | −61.7145 | − | 61.7145i | −0.111802 | − | 0.111802i | ||||
\(553\) | −77.3083 | + | 175.116i | −0.139798 | + | 0.316666i | ||||
\(554\) | 126.998i | 0.229238i | ||||||||
\(555\) | −224.882 | + | 196.246i | −0.405192 | + | 0.353596i | ||||
\(556\) | 202.296 | − | 350.387i | 0.363842 | − | 0.630192i | ||||
\(557\) | −14.7556 | + | 3.95376i | −0.0264912 | + | 0.00709831i | −0.272040 | − | 0.962286i | \(-0.587698\pi\) |
0.245549 | + | 0.969384i | \(0.421032\pi\) | |||||||
\(558\) | −63.9052 | − | 17.1234i | −0.114526 | − | 0.0306870i | ||||
\(559\) | 181.554i | 0.324784i | ||||||||
\(560\) | −133.674 | + | 41.6094i | −0.238703 | + | 0.0743024i | ||||
\(561\) | −30.2334 | −0.0538920 | ||||||||
\(562\) | 1.19702 | − | 4.46733i | 0.00212992 | − | 0.00794899i | ||||
\(563\) | −61.5366 | − | 229.658i | −0.109301 | − | 0.407918i | 0.889496 | − | 0.456942i | \(-0.151055\pi\) |
−0.998798 | + | 0.0490246i | \(0.984389\pi\) | |||||||
\(564\) | 94.2800 | + | 54.4326i | 0.167163 | + | 0.0965117i | ||||
\(565\) | −61.9309 | + | 910.779i | −0.109612 | + | 1.61200i | ||||
\(566\) | −288.824 | −0.510290 | ||||||||
\(567\) | −6.78219 | − | 62.6339i | −0.0119615 | − | 0.110465i | ||||
\(568\) | −119.439 | + | 119.439i | −0.210280 | + | 0.210280i | ||||
\(569\) | 179.993 | − | 103.919i | 0.316331 | − | 0.182634i | −0.333425 | − | 0.942777i | \(-0.608204\pi\) |
0.649756 | + | 0.760143i | \(0.274871\pi\) | |||||||
\(570\) | −122.928 | + | 359.248i | −0.215663 | + | 0.630260i | ||||
\(571\) | −214.885 | + | 372.192i | −0.376331 | + | 0.651824i | −0.990525 | − | 0.137331i | \(-0.956148\pi\) |
0.614194 | + | 0.789155i | \(0.289481\pi\) | |||||||
\(572\) | −28.3269 | + | 105.717i | −0.0495226 | + | 0.184821i | ||||
\(573\) | −188.092 | + | 188.092i | −0.328259 | + | 0.328259i | ||||
\(574\) | −69.3240 | − | 178.912i | −0.120774 | − | 0.311694i | ||||
\(575\) | 172.451 | − | 410.645i | 0.299914 | − | 0.714165i | ||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 357.130 | − | 95.6927i | 0.618943 | − | 0.165845i | 0.0642958 | − | 0.997931i | \(-0.479520\pi\) |
0.554647 | + | 0.832086i | \(0.312853\pi\) | |||||||
\(578\) | −101.217 | − | 377.745i | −0.175115 | − | 0.653538i | ||||
\(579\) | −466.862 | + | 269.543i | −0.806325 | + | 0.465532i | ||||
\(580\) | −46.3041 | − | 235.796i | −0.0798347 | − | 0.406545i | ||||
\(581\) | −74.3688 | + | 479.291i | −0.128001 | + | 0.824941i | ||||
\(582\) | 243.304 | + | 243.304i | 0.418048 | + | 0.418048i | ||||
\(583\) | 496.635 | + | 133.073i | 0.851861 | + | 0.228255i | ||||
\(584\) | −260.924 | − | 150.645i | −0.446788 | − | 0.257953i | ||||
\(585\) | −73.0873 | − | 149.124i | −0.124936 | − | 0.254913i | ||||
\(586\) | −269.541 | − | 466.859i | −0.459968 | − | 0.796687i | ||||
\(587\) | 425.963 | + | 425.963i | 0.725661 | + | 0.725661i | 0.969752 | − | 0.244091i | \(-0.0784897\pi\) |
−0.244091 | + | 0.969752i | \(0.578490\pi\) | |||||||
\(588\) | 142.935 | + | 91.5509i | 0.243087 | + | 0.155699i | ||||
\(589\) | − | 483.447i | − | 0.820794i | ||||||
\(590\) | 7.49768 | − | 110.264i | 0.0127079 | − | 0.186888i | ||||
\(591\) | 82.7447 | − | 143.318i | 0.140008 | − | 0.242501i | ||||
\(592\) | −133.160 | + | 35.6801i | −0.224932 | + | 0.0602705i | ||||
\(593\) | −183.152 | − | 49.0753i | −0.308856 | − | 0.0827577i | 0.101062 | − | 0.994880i | \(-0.467776\pi\) |
−0.409918 | + | 0.912122i | \(0.634443\pi\) | |||||||
\(594\) | 36.3217i | 0.0611477i | ||||||||
\(595\) | 4.93900 | + | 123.503i | 0.00830084 | + | 0.207568i | ||||
\(596\) | 206.402 | 0.346312 | ||||||||
\(597\) | 144.884 | − | 540.714i | 0.242686 | − | 0.905718i | ||||
\(598\) | 72.1956 | + | 269.438i | 0.120729 | + | 0.450565i | ||||
\(599\) | −238.166 | − | 137.505i | −0.397605 | − | 0.229557i | 0.287845 | − | 0.957677i | \(-0.407061\pi\) |
−0.685450 | + | 0.728120i | \(0.740395\pi\) | |||||||
\(600\) | −75.0317 | + | 96.8000i | −0.125053 | + | 0.161333i | ||||
\(601\) | −1029.92 | −1.71368 | −0.856842 | − | 0.515580i | \(-0.827577\pi\) | ||||
−0.856842 | + | 0.515580i | \(0.827577\pi\) | |||||||
\(602\) | −148.508 | − | 65.5617i | −0.246692 | − | 0.108906i | ||||
\(603\) | 166.162 | − | 166.162i | 0.275558 | − | 0.275558i | ||||
\(604\) | −129.364 | + | 74.6886i | −0.214179 | + | 0.123657i | ||||
\(605\) | −456.840 | − | 156.322i | −0.755108 | − | 0.258384i | ||||
\(606\) | 96.7435 | − | 167.565i | 0.159643 | − | 0.276509i | ||||
\(607\) | 6.83168 | − | 25.4962i | 0.0112548 | − | 0.0420036i | −0.960070 | − | 0.279760i | \(-0.909745\pi\) |
0.971325 | + | 0.237756i | \(0.0764119\pi\) | |||||||
\(608\) | −124.009 | + | 124.009i | −0.203962 | + | 0.203962i | ||||
\(609\) | −182.638 | + | 226.995i | −0.299899 | + | 0.372734i | ||||
\(610\) | −348.496 | + | 518.812i | −0.571305 | + | 0.850512i | ||||
\(611\) | −173.969 | − | 301.323i | −0.284728 | − | 0.493164i | ||||
\(612\) | 20.4669 | − | 5.48409i | 0.0334426 | − | 0.00896093i | ||||
\(613\) | −8.97661 | − | 33.5012i | −0.0146437 | − | 0.0546511i | 0.958217 | − | 0.286041i | \(-0.0923394\pi\) |
−0.972861 | + | 0.231390i | \(0.925673\pi\) | |||||||
\(614\) | −290.070 | + | 167.472i | −0.472427 | + | 0.272756i | ||||
\(615\) | −139.338 | − | 93.5957i | −0.226565 | − | 0.152188i | ||||
\(616\) | −76.2460 | − | 61.3470i | −0.123776 | − | 0.0995893i | ||||
\(617\) | 349.027 | + | 349.027i | 0.565684 | + | 0.565684i | 0.930916 | − | 0.365232i | \(-0.119011\pi\) |
−0.365232 | + | 0.930916i | \(0.619011\pi\) | |||||||
\(618\) | 214.774 | + | 57.5485i | 0.347530 | + | 0.0931205i | ||||
\(619\) | −942.217 | − | 543.989i | −1.52216 | − | 0.878820i | −0.999657 | − | 0.0261820i | \(-0.991665\pi\) |
−0.522503 | − | 0.852638i | \(-0.675002\pi\) | |||||||
\(620\) | 50.4858 | − | 147.541i | 0.0814287 | − | 0.237969i | ||||
\(621\) | 46.2859 | + | 80.1695i | 0.0745344 | + | 0.129097i | ||||
\(622\) | 550.733 | + | 550.733i | 0.885422 | + | 0.885422i | ||||
\(623\) | 322.189 | − | 729.812i | 0.517157 | − | 1.17145i | ||||
\(624\) | − | 76.7050i | − | 0.122925i | ||||||
\(625\) | −602.094 | − | 167.654i | −0.963350 | − | 0.268247i | ||||
\(626\) | 200.655 | − | 347.544i | 0.320535 | − | 0.555183i | ||||
\(627\) | −256.370 | + | 68.6940i | −0.408883 | + | 0.109560i | ||||
\(628\) | 390.137 | + | 104.537i | 0.621238 | + | 0.166460i | ||||
\(629\) | 121.710i | 0.193498i | ||||||||
\(630\) | 148.374 | − | 5.93360i | 0.235514 | − | 0.00941841i | ||||
\(631\) | 573.080 | 0.908209 | 0.454104 | − | 0.890949i | \(-0.349959\pi\) | ||||
0.454104 | + | 0.890949i | \(0.349959\pi\) | |||||||
\(632\) | −20.0187 | + | 74.7106i | −0.0316751 | + | 0.118213i | ||||
\(633\) | 146.721 | + | 547.571i | 0.231787 | + | 0.865041i | ||||
\(634\) | 461.947 | + | 266.705i | 0.728623 | + | 0.420671i | ||||
\(635\) | −1076.67 | − | 73.2114i | −1.69555 | − | 0.115294i | ||||
\(636\) | −360.342 | −0.566575 | ||||||||
\(637\) | −249.323 | − | 481.813i | −0.391402 | − | 0.756378i | ||||
\(638\) | 118.774 | − | 118.774i | 0.186167 | − | 0.186167i | ||||
\(639\) | 155.156 | − | 89.5794i | 0.242811 | − | 0.140187i | ||||
\(640\) | −50.7958 | + | 24.8956i | −0.0793684 | + | 0.0388994i | ||||
\(641\) | 515.594 | − | 893.035i | 0.804359 | − | 1.39319i | −0.112364 | − | 0.993667i | \(-0.535842\pi\) |
0.916723 | − | 0.399523i | \(-0.130824\pi\) | |||||||
\(642\) | −50.2619 | + | 187.580i | −0.0782896 | + | 0.292181i | ||||
\(643\) | 413.439 | − | 413.439i | 0.642985 | − | 0.642985i | −0.308303 | − | 0.951288i | \(-0.599761\pi\) |
0.951288 | + | 0.308303i | \(0.0997612\pi\) | |||||||
\(644\) | −246.467 | − | 38.2428i | −0.382712 | − | 0.0593833i | ||||
\(645\) | −139.353 | + | 27.3653i | −0.216052 | + | 0.0424268i | ||||
\(646\) | 77.4167 | + | 134.090i | 0.119840 | + | 0.207569i | ||||
\(647\) | 732.536 | − | 196.283i | 1.13220 | − | 0.303373i | 0.356392 | − | 0.934337i | \(-0.384007\pi\) |
0.775813 | + | 0.630963i | \(0.217340\pi\) | |||||||
\(648\) | −6.58846 | − | 24.5885i | −0.0101674 | − | 0.0379452i | ||||
\(649\) | 66.9036 | − | 38.6268i | 0.103087 | − | 0.0595174i | ||||
\(650\) | 362.365 | − | 148.026i | 0.557485 | − | 0.227733i | ||||
\(651\) | −176.295 | + | 68.3099i | −0.270807 | + | 0.104931i | ||||
\(652\) | −234.115 | − | 234.115i | −0.359072 | − | 0.359072i | ||||
\(653\) | 710.307 | + | 190.326i | 1.08776 | + | 0.291464i | 0.757771 | − | 0.652521i | \(-0.226288\pi\) |
0.329988 | + | 0.943985i | \(0.392955\pi\) | |||||||
\(654\) | 92.1161 | + | 53.1832i | 0.140850 | + | 0.0813199i | ||||
\(655\) | 919.795 | + | 314.737i | 1.40427 | + | 0.480514i | ||||
\(656\) | −38.7643 | − | 67.1418i | −0.0590920 | − | 0.102350i | ||||
\(657\) | 225.967 | + | 225.967i | 0.343938 | + | 0.343938i | ||||
\(658\) | 309.300 | − | 33.4919i | 0.470061 | − | 0.0508996i | ||||
\(659\) | − | 913.700i | − | 1.38650i | −0.720700 | − | 0.693248i | \(-0.756179\pi\) | ||
0.720700 | − | 0.693248i | \(-0.243821\pi\) | |||||||
\(660\) | −85.4139 | − | 5.80795i | −0.129415 | − | 0.00879992i | ||||
\(661\) | −27.1929 | + | 47.0994i | −0.0411390 | + | 0.0712548i | −0.885862 | − | 0.463949i | \(-0.846432\pi\) |
0.844723 | + | 0.535204i | \(0.179765\pi\) | |||||||
\(662\) | −556.484 | + | 149.109i | −0.840610 | + | 0.225241i | ||||
\(663\) | −65.4131 | − | 17.5274i | −0.0986623 | − | 0.0264365i | ||||
\(664\) | 195.980i | 0.295151i | ||||||||
\(665\) | 322.496 | + | 1036.05i | 0.484956 | + | 1.55796i | ||||
\(666\) | 146.220 | 0.219549 | ||||||||
\(667\) | 110.801 | − | 413.517i | 0.166119 | − | 0.619965i | ||||
\(668\) | −95.1617 | − | 355.148i | −0.142458 | − | 0.531659i | ||||
\(669\) | −185.702 | − | 107.215i | −0.277581 | − | 0.160262i | ||||
\(670\) | 364.175 | + | 417.314i | 0.543545 | + | 0.622857i | ||||
\(671\) | −436.877 | −0.651084 | ||||||||
\(672\) | 62.7435 | + | 27.6993i | 0.0933684 | + | 0.0412191i | ||||
\(673\) | −93.9180 | + | 93.9180i | −0.139551 | + | 0.139551i | −0.773431 | − | 0.633880i | \(-0.781461\pi\) |
0.633880 | + | 0.773431i | \(0.281461\pi\) | |||||||
\(674\) | 89.5626 | − | 51.7090i | 0.132882 | − | 0.0767196i | ||||
\(675\) | 103.445 | − | 78.5759i | 0.153252 | − | 0.116409i | ||||
\(676\) | 46.4237 | − | 80.4081i | 0.0686741 | − | 0.118947i | ||||
\(677\) | 60.8859 | − | 227.229i | 0.0899349 | − | 0.335642i | −0.906268 | − | 0.422704i | \(-0.861081\pi\) |
0.996203 | + | 0.0870620i | \(0.0277478\pi\) | |||||||
\(678\) | 316.232 | − | 316.232i | 0.466418 | − | 0.466418i | ||||
\(679\) | 971.674 | + | 150.769i | 1.43104 | + | 0.222046i | ||||
\(680\) | 9.62362 | + | 49.0067i | 0.0141524 | + | 0.0720687i | ||||
\(681\) | 252.271 | + | 436.946i | 0.370442 | + | 0.641624i | ||||
\(682\) | 105.289 | − | 28.2122i | 0.154383 | − | 0.0413669i | ||||
\(683\) | 140.148 | + | 523.038i | 0.205194 | + | 0.765795i | 0.989390 | + | 0.145282i | \(0.0464089\pi\) |
−0.784196 | + | 0.620513i | \(0.786924\pi\) | |||||||
\(684\) | 161.092 | − | 93.0067i | 0.235515 | − | 0.135975i | ||||
\(685\) | 518.969 | − | 772.599i | 0.757619 | − | 1.12788i | ||||
\(686\) | 484.150 | − | 29.9532i | 0.705757 | − | 0.0436636i | ||||
\(687\) | −79.9752 | − | 79.9752i | −0.116412 | − | 0.116412i | ||||
\(688\) | −63.3587 | − | 16.9769i | −0.0920912 | − | 0.0246758i | ||||
\(689\) | 997.373 | + | 575.834i | 1.44757 | + | 0.835753i | ||||
\(690\) | −195.927 | + | 96.0262i | −0.283952 | + | 0.139168i | ||||
\(691\) | −245.831 | − | 425.792i | −0.355761 | − | 0.616196i | 0.631487 | − | 0.775387i | \(-0.282445\pi\) |
−0.987248 | + | 0.159190i | \(0.949112\pi\) | |||||||
\(692\) | 41.8227 | + | 41.8227i | 0.0604374 | + | 0.0604374i | ||||
\(693\) | 61.2745 | + | 83.7821i | 0.0884192 | + | 0.120898i | ||||
\(694\) | − | 681.189i | − | 0.981540i | ||||||
\(695\) | −665.055 | − | 762.098i | −0.956913 | − | 1.09654i | ||||
\(696\) | −58.8611 | + | 101.950i | −0.0845705 | + | 0.146480i | ||||
\(697\) | −66.1155 | + | 17.7156i | −0.0948572 | + | 0.0254169i | ||||
\(698\) | 226.692 | + | 60.7418i | 0.324773 | + | 0.0870226i | ||||
\(699\) | 285.639i | 0.408639i | ||||||||
\(700\) | −9.77199 | + | 349.864i | −0.0139600 | + | 0.499805i | ||||
\(701\) | −372.833 | −0.531858 | −0.265929 | − | 0.963993i | \(-0.585679\pi\) | ||||
−0.265929 | + | 0.963993i | \(0.585679\pi\) | |||||||
\(702\) | −21.0570 | + | 78.5858i | −0.0299957 | + | 0.111946i | ||||
\(703\) | 276.541 | + | 1032.06i | 0.393372 | + | 1.46809i | ||||
\(704\) | −34.2444 | − | 19.7710i | −0.0486427 | − | 0.0280839i | ||||
\(705\) | 205.061 | − | 178.949i | 0.290866 | − | 0.253828i | ||||
\(706\) | −89.2954 | −0.126481 | ||||||||
\(707\) | −59.5255 | − | 549.722i | −0.0841945 | − | 0.777541i | ||||
\(708\) | −38.2847 | + | 38.2847i | −0.0540744 | + | 0.0540744i | ||||
\(709\) | 471.040 | − | 271.955i | 0.664372 | − | 0.383575i | −0.129569 | − | 0.991570i | \(-0.541359\pi\) |
0.793941 | + | 0.607995i | \(0.208026\pi\) | |||||||
\(710\) | 185.844 | + | 379.188i | 0.261752 | + | 0.534067i | ||||
\(711\) | 41.0190 | − | 71.0470i | 0.0576920 | − | 0.0999254i | ||||
\(712\) | 83.4294 | − | 311.363i | 0.117176 | − | 0.437307i | ||||
\(713\) | 196.444 | − | 196.444i | 0.275517 | − | 0.275517i | ||||
\(714\) | 37.9587 | − | 47.1775i | 0.0531634 | − | 0.0660749i | ||||
\(715\) | 227.132 | + | 152.569i | 0.317667 | + | 0.213383i | ||||
\(716\) | 216.099 | + | 374.295i | 0.301815 | + | 0.522758i | ||||
\(717\) | 141.593 | − | 37.9396i | 0.197479 | − | 0.0529144i | ||||
\(718\) | −59.3434 | − | 221.473i | −0.0826510 | − | 0.308458i | ||||
\(719\) | −479.506 | + | 276.843i | −0.666906 | + | 0.385039i | −0.794903 | − | 0.606736i | \(-0.792479\pi\) |
0.127997 | + | 0.991775i | \(0.459145\pi\) | |||||||
\(720\) | 58.8755 | − | 11.5616i | 0.0817716 | − | 0.0160578i | ||||
\(721\) | 592.496 | − | 229.577i | 0.821770 | − | 0.318415i | ||||
\(722\) | 600.138 | + | 600.138i | 0.831215 | + | 0.831215i | ||||
\(723\) | 737.032 | + | 197.487i | 1.01941 | + | 0.273150i | ||||
\(724\) | −239.495 | − | 138.273i | −0.330794 | − | 0.190984i | ||||
\(725\) | −595.219 | − | 81.3230i | −0.820991 | − | 0.112170i | ||||
\(726\) | 118.273 | + | 204.854i | 0.162910 | + | 0.282168i | ||||
\(727\) | 544.208 | + | 544.208i | 0.748566 | + | 0.748566i | 0.974210 | − | 0.225644i | \(-0.0724485\pi\) |
−0.225644 | + | 0.974210i | \(0.572449\pi\) | |||||||
\(728\) | −129.401 | − | 176.933i | −0.177749 | − | 0.243040i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −567.516 | + | 495.250i | −0.777419 | + | 0.678425i | ||||
\(731\) | −28.9554 | + | 50.1522i | −0.0396107 | + | 0.0686077i | ||||
\(732\) | 295.750 | − | 79.2459i | 0.404030 | − | 0.108259i | ||||
\(733\) | −29.6500 | − | 7.94468i | −0.0404501 | − | 0.0108386i | 0.238537 | − | 0.971133i | \(-0.423332\pi\) |
−0.278987 | + | 0.960295i | \(0.589999\pi\) | |||||||
\(734\) | 27.2314i | 0.0371001i | ||||||||
\(735\) | 332.239 | − | 263.993i | 0.452026 | − | 0.359174i | ||||
\(736\) | −100.779 | −0.136928 | ||||||||
\(737\) | −100.205 | + | 373.971i | −0.135964 | + | 0.507423i | ||||
\(738\) | 21.2831 | + | 79.4296i | 0.0288389 | + | 0.107628i | ||||
\(739\) | 70.2506 | + | 40.5592i | 0.0950616 | + | 0.0548839i | 0.546777 | − | 0.837278i | \(-0.315854\pi\) |
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(740\) | −23.3810 | + | 343.849i | −0.0315959 | + | 0.464661i | ||||
\(741\) | −594.507 | −0.802303 | ||||||||
\(742\) | −831.188 | + | 607.894i | −1.12020 | + | 0.819265i | ||||
\(743\) | 824.672 | − | 824.672i | 1.10992 | − | 1.10992i | 0.116761 | − | 0.993160i | \(-0.462749\pi\) |
0.993160 | − | 0.116761i | \(-0.0372513\pi\) | |||||||
\(744\) | −66.1596 | + | 38.1972i | −0.0889242 | + | 0.0513404i | ||||
\(745\) | 167.058 | − | 488.214i | 0.224239 | − | 0.655321i | ||||
\(746\) | 239.265 | − | 414.420i | 0.320731 | − | 0.555522i | ||||
\(747\) | 53.8003 | − | 200.785i | 0.0720218 | − | 0.268789i | ||||
\(748\) | −24.6855 | + | 24.6855i | −0.0330020 | + | 0.0330020i | ||||
\(749\) | 200.509 | + | 517.477i | 0.267702 | + | 0.690890i | ||||
\(750\) | 168.237 | + | 255.825i | 0.224316 | + | 0.341099i | ||||
\(751\) | 91.6006 | + | 158.657i | 0.121972 | + | 0.211261i | 0.920545 | − | 0.390636i | \(-0.127745\pi\) |
−0.798574 | + | 0.601897i | \(0.794412\pi\) | |||||||
\(752\) | 121.423 | − | 32.5353i | 0.161467 | − | 0.0432650i | ||||
\(753\) | 35.1613 | + | 131.224i | 0.0466950 | + | 0.174268i | ||||
\(754\) | 325.838 | − | 188.123i | 0.432146 | − | 0.249500i | ||||
\(755\) | 71.9600 | + | 366.444i | 0.0953112 | + | 0.485357i | ||||
\(756\) | −56.6780 | − | 45.6027i | −0.0749709 | − | 0.0603210i | ||||
\(757\) | 298.331 | + | 298.331i | 0.394096 | + | 0.394096i | 0.876145 | − | 0.482048i | \(-0.160107\pi\) |
−0.482048 | + | 0.876145i | \(0.660107\pi\) | |||||||
\(758\) | −725.642 | − | 194.435i | −0.957312 | − | 0.256511i | ||||
\(759\) | −132.086 | − | 76.2600i | −0.174027 | − | 0.100474i | ||||
\(760\) | 192.955 | + | 393.695i | 0.253888 | + | 0.518020i | ||||
\(761\) | 16.0986 | + | 27.8836i | 0.0211546 | + | 0.0366408i | 0.876409 | − | 0.481568i | \(-0.159932\pi\) |
−0.855254 | + | 0.518208i | \(0.826599\pi\) | |||||||
\(762\) | 373.832 | + | 373.832i | 0.490594 | + | 0.490594i | ||||
\(763\) | 302.201 | − | 32.7232i | 0.396069 | − | 0.0428876i | ||||
\(764\) | 307.153i | 0.402033i | ||||||||
\(765\) | 3.59369 | − | 52.8502i | 0.00469763 | − | 0.0690852i | ||||
\(766\) | 70.6020 | − | 122.286i | 0.0921698 | − | 0.159643i | ||||
\(767\) | 167.146 | − | 44.7867i | 0.217922 | − | 0.0583920i | ||||
\(768\) | 26.7685 | + | 7.17260i | 0.0348548 | + | 0.00933933i | ||||
\(769\) | − | 210.008i | − | 0.273092i | −0.990634 | − | 0.136546i | \(-0.956400\pi\) | ||
0.990634 | − | 0.136546i | \(-0.0436002\pi\) | |||||||
\(770\) | −206.819 | + | 130.696i | −0.268597 | + | 0.169735i | ||||
\(771\) | −689.532 | −0.894335 | ||||||||
\(772\) | −161.110 | + | 601.272i | −0.208692 | + | 0.778850i | ||||
\(773\) | −90.9196 | − | 339.317i | −0.117619 | − | 0.438961i | 0.881850 | − | 0.471529i | \(-0.156298\pi\) |
−0.999470 | + | 0.0325686i | \(0.989631\pi\) | |||||||
\(774\) | 60.2518 | + | 34.7864i | 0.0778446 | + | 0.0449436i | ||||
\(775\) | −308.125 | − | 238.834i | −0.397580 | − | 0.308172i | ||||
\(776\) | 397.314 | 0.512002 | ||||||||
\(777\) | 337.281 | − | 246.672i | 0.434081 | − | 0.317467i | ||||
\(778\) | −609.695 | + | 609.695i | −0.783670 | + | 0.783670i | ||||
\(779\) | −520.386 | + | 300.445i | −0.668018 | + | 0.385680i | ||||
\(780\) | −181.435 | − | 62.0836i | −0.232609 | − | 0.0795943i | ||||
\(781\) | −147.590 | + | 255.633i | −0.188975 | + | 0.327315i | ||||
\(782\) | −23.0284 | + | 85.9433i | −0.0294481 | + | 0.109902i | ||||
\(783\) | 88.2916 | − | 88.2916i | 0.112761 | − | 0.112761i | ||||
\(784\) | 191.457 | − | 41.9550i | 0.244205 | − | 0.0535140i | ||||
\(785\) | 563.037 | − | 838.203i | 0.717244 | − | 1.06777i | ||||
\(786\) | −238.128 | − | 412.450i | −0.302962 | − | 0.524745i | ||||
\(787\) | −712.746 | + | 190.980i | −0.905649 | + | 0.242668i | −0.681441 | − | 0.731873i | \(-0.738646\pi\) |
−0.224209 | + | 0.974541i | \(0.571980\pi\) | |||||||
\(788\) | −49.4579 | − | 184.579i | −0.0627639 | − | 0.234238i | ||||
\(789\) | 607.979 | − | 351.017i | 0.770569 | − | 0.444888i | ||||
\(790\) | 160.514 | + | 107.821i | 0.203183 | + | 0.136482i | ||||
\(791\) | 195.960 | − | 1262.92i | 0.247737 | − | 1.59662i | ||||
\(792\) | 29.6566 | + | 29.6566i | 0.0374451 | + | 0.0374451i | ||||
\(793\) | −945.229 | − | 253.273i | −1.19197 | − | 0.319386i | ||||
\(794\) | −822.920 | − | 475.113i | −1.03642 | − | 0.598379i | ||||
\(795\) | −291.653 | + | 852.336i | −0.366860 | + | 1.07212i | ||||
\(796\) | −323.194 | − | 559.788i | −0.406022 | − | 0.703251i | ||||
\(797\) | −34.9409 | − | 34.9409i | −0.0438406 | − | 0.0438406i | 0.684847 | − | 0.728687i | \(-0.259869\pi\) |
−0.728687 | + | 0.684847i | \(0.759869\pi\) | |||||||
\(798\) | 214.685 | − | 486.297i | 0.269028 | − | 0.609395i | ||||
\(799\) | − | 110.983i | − | 0.138902i | ||||||
\(800\) | 17.7738 | + | 140.300i | 0.0222173 | + | 0.175375i | ||||
\(801\) | −170.950 | + | 296.094i | −0.213421 | + | 0.369655i | ||||
\(802\) | −830.804 | + | 222.613i | −1.03592 | + | 0.277573i | ||||
\(803\) | −508.572 | − | 136.271i | −0.633340 | − | 0.169703i | ||||
\(804\) | − | 271.341i | − | 0.337489i | ||||||
\(805\) | −289.943 | + | 552.028i | −0.360178 | + | 0.685750i | ||||
\(806\) | 244.160 | 0.302928 | ||||||||
\(807\) | −58.8257 | + | 219.540i | −0.0728943 | + | 0.272045i | ||||
\(808\) | −57.8252 | − | 215.807i | −0.0715659 | − | 0.267087i | ||||
\(809\) | −226.253 | − | 130.627i | −0.279670 | − | 0.161468i | 0.353604 | − | 0.935395i | \(-0.384956\pi\) |
−0.633274 | + | 0.773928i | \(0.718289\pi\) | |||||||
\(810\) | −63.4930 | − | 4.31738i | −0.0783864 | − | 0.00533010i | ||||
\(811\) | 1476.16 | 1.82018 | 0.910089 | − | 0.414413i | \(-0.136013\pi\) | ||||
0.910089 | + | 0.414413i | \(0.136013\pi\) | |||||||
\(812\) | 36.2168 | + | 334.464i | 0.0446019 | + | 0.411902i | ||||
\(813\) | 76.1179 | − | 76.1179i | 0.0936260 | − | 0.0936260i | ||||
\(814\) | −208.634 | + | 120.455i | −0.256307 | + | 0.147979i | ||||
\(815\) | −743.254 | + | 364.277i | −0.911968 | + | 0.446966i | ||||
\(816\) | 12.2334 | − | 21.1889i | 0.0149919 | − | 0.0259668i | ||||
\(817\) | −131.581 | + | 491.065i | −0.161053 | + | 0.601059i | ||||
\(818\) | 372.058 | − | 372.058i | 0.454839 | − | 0.454839i | ||||
\(819\) | 84.0023 | + | 216.794i | 0.102567 | + | 0.264706i | ||||
\(820\) | −190.189 | + | 37.3481i | −0.231938 | + | 0.0455465i | ||||
\(821\) | −644.418 | − | 1116.16i | −0.784918 | − | 1.35952i | −0.929048 | − | 0.369959i | \(-0.879372\pi\) |
0.144130 | − | 0.989559i | \(-0.453962\pi\) | |||||||
\(822\) | −440.421 | + | 118.011i | −0.535792 | + | 0.143565i | ||||
\(823\) | 33.4443 | + | 124.816i | 0.0406371 | + | 0.151660i | 0.983263 | − | 0.182190i | \(-0.0583187\pi\) |
−0.942626 | + | 0.333850i | \(0.891652\pi\) | |||||||
\(824\) | 222.350 | − | 128.374i | 0.269843 | − | 0.155794i | ||||
\(825\) | −82.8702 | + | 197.333i | −0.100449 | + | 0.239192i | ||||
\(826\) | −23.7240 | + | 152.896i | −0.0287215 | + | 0.185104i | ||||
\(827\) | −830.887 | − | 830.887i | −1.00470 | − | 1.00470i | −0.999989 | − | 0.00471131i | \(-0.998500\pi\) |
−0.00471131 | − | 0.999989i | \(-0.501500\pi\) | |||||||
\(828\) | 103.250 | + | 27.6658i | 0.124698 | + | 0.0334129i | ||||
\(829\) | −371.475 | − | 214.471i | −0.448100 | − | 0.258711i | 0.258928 | − | 0.965897i | \(-0.416631\pi\) |
−0.707027 | + | 0.707186i | \(0.749964\pi\) | |||||||
\(830\) | 463.563 | + | 158.623i | 0.558509 | + | 0.191111i | ||||
\(831\) | −77.7699 | − | 134.701i | −0.0935859 | − | 0.162096i | ||||
\(832\) | −62.6294 | − | 62.6294i | −0.0752757 | − | 0.0752757i | ||||
\(833\) | 7.96992 | − | 172.859i | 0.00956773 | − | 0.207514i | ||||
\(834\) | 495.522i | 0.594151i | ||||||||
\(835\) | −917.074 | − | 62.3589i | −1.09829 | − | 0.0746814i | ||||
\(836\) | −153.237 | + | 265.413i | −0.183297 | + | 0.317480i | ||||
\(837\) | 78.2676 | − | 20.9717i | 0.0935097 | − | 0.0250558i | ||||
\(838\) | 461.944 | + | 123.777i | 0.551245 | + | 0.147706i | ||||
\(839\) | − | 1335.08i | − | 1.59127i | −0.605775 | − | 0.795636i | \(-0.707137\pi\) | ||
0.605775 | − | 0.795636i | \(-0.292863\pi\) | |||||||
\(840\) | 116.302 | − | 125.991i | 0.138455 | − | 0.149990i | ||||
\(841\) | 263.562 | 0.313391 | ||||||||
\(842\) | −5.02642 | + | 18.7588i | −0.00596962 | + | 0.0222789i | ||||
\(843\) | 1.46604 | + | 5.47134i | 0.00173908 | + | 0.00649032i | ||||
\(844\) | 566.887 | + | 327.292i | 0.671667 | + | 0.387787i | ||||
\(845\) | −152.619 | − | 174.889i | −0.180615 | − | 0.206969i | ||||
\(846\) | −133.332 | −0.157603 | ||||||||
\(847\) | 618.403 | + | 273.005i | 0.730110 | + | 0.322320i | ||||
\(848\) | −294.218 | + | 294.218i | −0.346955 | + | 0.346955i | ||||
\(849\) | 306.344 | − | 176.868i | 0.360829 | − | 0.208325i | ||||
\(850\) | 123.707 | + | 16.9018i | 0.145538 | + | 0.0198845i | ||||
\(851\) | −306.999 | + | 531.737i | −0.360750 | + | 0.624838i | ||||
\(852\) | 53.5431 | − | 199.826i | 0.0628440 | − | 0.234537i | ||||
\(853\) | −650.928 | + | 650.928i | −0.763104 | + | 0.763104i | −0.976882 | − | 0.213778i | \(-0.931423\pi\) |
0.213778 | + | 0.976882i | \(0.431423\pi\) | |||||||
\(854\) | 548.509 | − | 681.722i | 0.642282 | − | 0.798269i | ||||
\(855\) | −89.6088 | − | 456.318i | −0.104806 | − | 0.533705i | ||||
\(856\) | 112.120 | + | 194.197i | 0.130981 | + | 0.226866i | ||||
\(857\) | 677.342 | − | 181.493i | 0.790364 | − | 0.211777i | 0.159015 | − | 0.987276i | \(-0.449168\pi\) |
0.631349 | + | 0.775499i | \(0.282501\pi\) | |||||||
\(858\) | −34.6932 | − | 129.477i | −0.0404350 | − | 0.150905i | ||||
\(859\) | −267.011 | + | 154.159i | −0.310839 | + | 0.179463i | −0.647302 | − | 0.762234i | \(-0.724103\pi\) |
0.336463 | + | 0.941697i | \(0.390769\pi\) | |||||||
\(860\) | −91.4378 | + | 136.125i | −0.106323 | + | 0.158285i | ||||
\(861\) | 183.090 | + | 147.313i | 0.212648 | + | 0.171095i | ||||
\(862\) | −108.858 | − | 108.858i | −0.126285 | − | 0.126285i | ||||
\(863\) | 1213.32 | + | 325.107i | 1.40593 | + | 0.376717i | 0.880470 | − | 0.474102i | \(-0.157227\pi\) |
0.525458 | + | 0.850819i | \(0.323894\pi\) | |||||||
\(864\) | −25.4558 | − | 14.6969i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 132.776 | − | 65.0750i | 0.153498 | − | 0.0752312i | ||||
\(866\) | −449.174 | − | 777.992i | −0.518677 | − | 0.898374i | ||||
\(867\) | 338.677 | + | 338.677i | 0.390631 | + | 0.390631i | ||||
\(868\) | −88.1696 | + | 199.719i | −0.101578 | + | 0.230091i | ||||
\(869\) | 135.165i | 0.155540i | ||||||||
\(870\) | 193.508 | + | 221.744i | 0.222423 | + | 0.254878i | ||||
\(871\) | −433.609 | + | 751.032i | −0.497829 | + | 0.862265i | ||||
\(872\) | 118.636 | − | 31.7885i | 0.136051 | − | 0.0364547i | ||||
\(873\) | −407.056 | − | 109.070i | −0.466272 | − | 0.124937i | ||||
\(874\) | 781.096i | 0.893702i | ||||||||
\(875\) | 819.642 | + | 306.287i | 0.936734 | + | 0.350042i | ||||
\(876\) | 369.003 | 0.421236 | ||||||||
\(877\) | 352.556 | − | 1315.76i | 0.402002 | − | 1.50029i | −0.407516 | − | 0.913198i | \(-0.633605\pi\) |
0.809518 | − | 0.587094i | \(-0.199728\pi\) | |||||||
\(878\) | 41.0383 | + | 153.157i | 0.0467406 | + | 0.174438i | ||||
\(879\) | 571.783 | + | 330.119i | 0.650492 | + | 0.375562i | ||||
\(880\) | −74.4823 | + | 64.9980i | −0.0846390 | + | 0.0738613i | ||||
\(881\) | −717.855 | −0.814818 | −0.407409 | − | 0.913246i | \(-0.633568\pi\) | ||||
−0.407409 | + | 0.913246i | \(0.633568\pi\) | |||||||
\(882\) | −207.669 | − | 9.57488i | −0.235452 | − | 0.0108559i | ||||
\(883\) | −385.364 | + | 385.364i | −0.436426 | + | 0.436426i | −0.890807 | − | 0.454381i | \(-0.849860\pi\) |
0.454381 | + | 0.890807i | \(0.349860\pi\) | |||||||
\(884\) | −67.7206 | + | 39.0985i | −0.0766070 | + | 0.0442291i | ||||
\(885\) | 59.5700 | + | 121.544i | 0.0673107 | + | 0.137337i | ||||
\(886\) | −449.603 | + | 778.735i | −0.507453 | + | 0.878934i | ||||
\(887\) | 42.9913 | − | 160.446i | 0.0484682 | − | 0.180886i | −0.937448 | − | 0.348125i | \(-0.886819\pi\) |
0.985916 | + | 0.167239i | \(0.0534852\pi\) | |||||||
\(888\) | 119.388 | − | 119.388i | 0.134446 | − | 0.134446i | ||||
\(889\) | 1492.96 | + | 231.654i | 1.67937 | + | 0.260578i | ||||
\(890\) | −668.957 | − | 449.351i | −0.751637 | − | 0.504889i | ||||
\(891\) | −22.2424 | − | 38.5250i | −0.0249634 | − | 0.0432379i | ||||
\(892\) | −239.166 | + | 64.0842i | −0.268123 | + | 0.0718433i | ||||
\(893\) | −252.166 | − | 941.098i | −0.282381 | − | 1.05386i | ||||
\(894\) | −218.922 | + | 126.395i | −0.244880 | + | 0.141381i | ||||
\(895\) | 1060.25 | − | 208.205i | 1.18463 | − | 0.232631i | ||||
\(896\) | 73.8462 | − | 28.6135i | 0.0824177 | − | 0.0319347i | ||||
\(897\) | −241.571 | − | 241.571i | −0.269310 | − | 0.269310i | ||||
\(898\) | −272.962 | − | 73.1399i | −0.303966 | − | 0.0814476i | ||||
\(899\) | −324.519 | − | 187.361i | −0.360977 | − | 0.208410i | ||||
\(900\) | 20.3054 | − | 148.619i | 0.0225616 | − | 0.165133i | ||||
\(901\) | 183.675 | + | 318.135i | 0.203857 | + | 0.353091i | ||||
\(902\) | −95.8014 | − | 95.8014i | −0.106210 | − | 0.106210i | ||||
\(903\) | 197.665 | − | 21.4038i | 0.218898 | − | 0.0237030i | ||||
\(904\) | − | 516.404i | − | 0.571244i | ||||||
\(905\) | −520.906 | + | 454.576i | −0.575587 | + | 0.502293i | ||||
\(906\) | 91.4745 | − | 158.438i | 0.100965 | − | 0.174877i | ||||
\(907\) | −1406.38 | + | 376.838i | −1.55058 | + | 0.415478i | −0.929668 | − | 0.368400i | \(-0.879906\pi\) |
−0.620916 | + | 0.783877i | \(0.713239\pi\) | |||||||
\(908\) | 562.743 | + | 150.787i | 0.619761 | + | 0.166064i | ||||
\(909\) | 236.972i | 0.260695i | ||||||||
\(910\) | −523.244 | + | 162.873i | −0.574994 | + | 0.178981i | ||||
\(911\) | −1585.71 | −1.74062 | −0.870311 | − | 0.492502i | \(-0.836082\pi\) | ||||
−0.870311 | + | 0.492502i | \(0.836082\pi\) | |||||||
\(912\) | 55.5917 | − | 207.471i | 0.0609558 | − | 0.227490i | ||||
\(913\) | 88.6406 | + | 330.811i | 0.0970872 | + | 0.362335i | ||||
\(914\) | 519.173 | + | 299.745i | 0.568023 | + | 0.327948i | ||||
\(915\) | 51.9294 | − | 763.693i | 0.0567534 | − | 0.834637i | ||||
\(916\) | −130.599 | −0.142575 | ||||||||
\(917\) | −1245.08 | − | 549.664i | −1.35778 | − | 0.599415i | ||||
\(918\) | −18.3501 | + | 18.3501i | −0.0199892 | + | 0.0199892i | ||||
\(919\) | −255.071 | + | 147.266i | −0.277553 | + | 0.160245i | −0.632315 | − | 0.774711i | \(-0.717895\pi\) |
0.354762 | + | 0.934957i | \(0.384562\pi\) | |||||||
\(920\) | −81.5688 | + | 238.379i | −0.0886618 | + | 0.259107i | ||||
\(921\) | 205.110 | − | 355.262i | 0.222704 | − | 0.385735i | ||||
\(922\) | 281.240 | − | 1049.60i | 0.305032 | − | 1.13840i | ||||
\(923\) | −467.525 | + | 467.525i | −0.506528 | + | 0.506528i | ||||
\(924\) | 118.438 | + | 18.3774i | 0.128180 | + | 0.0198889i | ||||
\(925\) | 794.402 | + | 333.609i | 0.858813 | + | 0.360659i | ||||
\(926\) | −2.18079 | − | 3.77724i | −0.00235507 | − | 0.00407909i | ||||
\(927\) | −263.043 | + | 70.4822i | −0.283757 | + | 0.0760326i | ||||
\(928\) | 35.1823 | + | 131.302i | 0.0379119 | + | 0.141489i | ||||
\(929\) | 910.483 | − | 525.668i | 0.980068 | − | 0.565842i | 0.0777771 | − | 0.996971i | \(-0.475218\pi\) |
0.902291 | + | 0.431128i | \(0.141884\pi\) | |||||||
\(930\) | 36.8018 | + | 187.407i | 0.0395718 | + | 0.201513i | ||||
\(931\) | −325.175 | − | 1483.90i | −0.349275 | − | 1.59388i | ||||
\(932\) | 233.223 | + | 233.223i | 0.250239 | + | 0.250239i | ||||
\(933\) | −921.394 | − | 246.887i | −0.987560 | − | 0.264616i | ||||
\(934\) | −1053.77 | − | 608.392i | −1.12823 | − | 0.651383i | ||||
\(935\) | 38.4100 | + | 78.3698i | 0.0410802 | + | 0.0838180i | ||||
\(936\) | 46.9721 | + | 81.3580i | 0.0501838 | + | 0.0869209i | ||||
\(937\) | −839.139 | − | 839.139i | −0.895559 | − | 0.895559i | 0.0994803 | − | 0.995040i | \(-0.468282\pi\) |
−0.995040 | + | 0.0994803i | \(0.968282\pi\) | |||||||
\(938\) | −457.751 | − | 625.893i | −0.488007 | − | 0.667264i | ||||
\(939\) | 491.502i | 0.523431i | ||||||||
\(940\) | 21.3202 | − | 313.543i | 0.0226810 | − | 0.333556i | ||||
\(941\) | −244.702 | + | 423.836i | −0.260045 | + | 0.450411i | −0.966254 | − | 0.257593i | \(-0.917071\pi\) |
0.706209 | + | 0.708004i | \(0.250404\pi\) | |||||||
\(942\) | −477.819 | + | 128.031i | −0.507239 | + | 0.135914i | ||||
\(943\) | −333.536 | − | 89.3707i | −0.353697 | − | 0.0947727i | ||||
\(944\) | 62.5186i | 0.0662273i | ||||||||
\(945\) | −153.741 | + | 97.1536i | −0.162689 | + | 0.102808i | ||||
\(946\) | −114.627 | −0.121170 | ||||||||
\(947\) | −239.947 | + | 895.495i | −0.253376 | + | 0.945612i | 0.715611 | + | 0.698499i | \(0.246148\pi\) |
−0.968987 | + | 0.247113i | \(0.920518\pi\) | |||||||
\(948\) | −24.5177 | − | 91.5015i | −0.0258626 | − | 0.0965205i | ||||
\(949\) | −1021.35 | − | 589.675i | −1.07623 | − | 0.621364i | ||||
\(950\) | 1087.40 | − | 137.757i | 1.14463 | − | 0.145007i | ||||
\(951\) | −653.291 | −0.686952 | ||||||||
\(952\) | −7.52712 | − | 69.5134i | −0.00790664 | − | 0.0730183i | ||||
\(953\) | −1057.61 | + | 1057.61i | −1.10977 | + | 1.10977i | −0.116587 | + | 0.993181i | \(0.537195\pi\) |
−0.993181 | + | 0.116587i | \(0.962805\pi\) | |||||||
\(954\) | 382.200 | − | 220.663i | 0.400629 | − | 0.231303i | ||||
\(955\) | 726.526 | + | 248.604i | 0.760761 | + | 0.260318i | ||||
\(956\) | 84.6324 | − | 146.588i | 0.0885276 | − | 0.153334i | ||||
\(957\) | −53.2450 | + | 198.713i | −0.0556374 | + | 0.207642i | ||||
\(958\) | −508.190 | + | 508.190i | −0.530470 | + | 0.530470i | ||||
\(959\) | −816.822 | + | 1015.20i | −0.851744 | + | 1.05860i | ||||
\(960\) | 38.6317 | − | 57.5117i | 0.0402413 | − | 0.0599080i | ||||
\(961\) | 358.914 | + | 621.658i | 0.373480 | + | 0.646886i | ||||
\(962\) | −521.233 | + | 139.664i | −0.541822 | + | 0.145181i | ||||
\(963\) | −61.5580 | − | 229.738i | −0.0639232 | − | 0.238565i | ||||
\(964\) | 763.032 | − | 440.537i | 0.791527 | − | 0.456988i | ||||
\(965\) | 1291.82 | + | 867.741i | 1.33868 | + | 0.899214i | ||||
\(966\) | 284.836 | − | 110.367i | 0.294862 | − | 0.114251i | ||||
\(967\) | −607.869 | − | 607.869i | −0.628613 | − | 0.628613i | 0.319106 | − | 0.947719i | \(-0.396617\pi\) |
−0.947719 | + | 0.319106i | \(0.896617\pi\) | |||||||
\(968\) | 263.832 | + | 70.6935i | 0.272553 | + | 0.0730305i | ||||
\(969\) | −164.226 | − | 94.8157i | −0.169480 | − | 0.0978490i | ||||
\(970\) | 321.578 | − | 939.788i | 0.331524 | − | 0.968854i | ||||
\(971\) | 328.192 | + | 568.446i | 0.337994 | + | 0.585423i | 0.984055 | − | 0.177863i | \(-0.0569183\pi\) |
−0.646061 | + | 0.763286i | \(0.723585\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 835.943 | + | 1143.00i | 0.859139 | + | 1.17472i | ||||
\(974\) | 1074.51i | 1.10319i | ||||||||
\(975\) | −293.699 | + | 378.908i | −0.301230 | + | 0.388624i | ||||
\(976\) | 176.775 | − | 306.183i | 0.181122 | − | 0.313712i | ||||
\(977\) | −764.332 | + | 204.802i | −0.782326 | + | 0.209624i | −0.627810 | − | 0.778367i | \(-0.716048\pi\) |
−0.154516 | + | 0.987990i | \(0.549382\pi\) | |||||||
\(978\) | 391.682 | + | 104.951i | 0.400493 | + | 0.107312i | ||||
\(979\) | − | 563.310i | − | 0.575393i | ||||||
\(980\) | 55.7230 | − | 486.821i | 0.0568602 | − | 0.496756i | ||||
\(981\) | −130.272 | −0.132795 | ||||||||
\(982\) | 58.7728 | − | 219.343i | 0.0598501 | − | 0.223364i | ||||
\(983\) | 159.927 | + | 596.854i | 0.162692 | + | 0.607176i | 0.998323 | + | 0.0578848i | \(0.0184356\pi\) |
−0.835631 | + | 0.549291i | \(0.814898\pi\) | |||||||
\(984\) | 82.2316 | + | 47.4764i | 0.0835687 | + | 0.0482484i | ||||
\(985\) | −476.626 | − | 32.4095i | −0.483884 | − | 0.0329030i | ||||
\(986\) | 120.012 | 0.121716 | ||||||||
\(987\) | −307.553 | + | 224.930i | −0.311604 | + | 0.227893i | ||||
\(988\) | −485.413 | + | 485.413i | −0.491308 | + | 0.491308i | ||||
\(989\) | −253.005 | + | 146.073i | −0.255819 | + | 0.147697i | ||||
\(990\) | 94.1517 | − | 46.1448i | 0.0951027 | − | 0.0466110i | ||||
\(991\) | −241.741 | + | 418.708i | −0.243937 | + | 0.422511i | −0.961832 | − | 0.273640i | \(-0.911772\pi\) |
0.717895 | + | 0.696151i | \(0.245106\pi\) | |||||||
\(992\) | −22.8311 | + | 85.2070i | −0.0230153 | + | 0.0858941i | ||||
\(993\) | 498.930 | − | 498.930i | 0.502447 | − | 0.502447i | ||||
\(994\) | −213.599 | − | 551.258i | −0.214888 | − | 0.554586i | ||||
\(995\) | −1585.68 | + | 311.386i | −1.59365 | + | 0.312951i | ||||
\(996\) | −120.013 | − | 207.868i | −0.120495 | − | 0.208703i | ||||
\(997\) | −157.380 | + | 42.1697i | −0.157853 | + | 0.0422966i | −0.336880 | − | 0.941548i | \(-0.609372\pi\) |
0.179027 | + | 0.983844i | \(0.442705\pi\) | |||||||
\(998\) | −22.5498 | − | 84.1570i | −0.0225950 | − | 0.0843257i | ||||
\(999\) | −155.090 | + | 89.5410i | −0.155245 | + | 0.0896306i |
(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 | 210.3.v.b.67.1 | yes | 32 | |
5.3 | odd | 4 | inner | 210.3.v.b.193.8 | yes | 32 | |
7.2 | even | 3 | inner | 210.3.v.b.37.8 | ✓ | 32 | |
35.23 | odd | 12 | inner | 210.3.v.b.163.1 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.v.b.37.8 | ✓ | 32 | 7.2 | even | 3 | inner | |
210.3.v.b.67.1 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.v.b.163.1 | yes | 32 | 35.23 | odd | 12 | inner | |
210.3.v.b.193.8 | yes | 32 | 5.3 | odd | 4 | inner |