Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [203,3,Mod(115,203)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(203, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("203.115");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 203 = 7 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 203.i (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.53134936651\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Relative dimension: | \(38\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 173.3 | ||
Character | \(\chi\) | \(=\) | 203.173 |
Dual form | 203.3.i.a.115.3 |
$q$-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 \(\left(\mathbb{Z}/203\mathbb{Z}\right)^\times\).
\(n\) | \(59\) | \(176\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.81256 | − | 1.62383i | −1.40628 | − | 0.811917i | −0.411254 | − | 0.911521i | \(-0.634909\pi\) |
−0.995027 | + | 0.0996038i | \(0.968242\pi\) | |||||||
\(3\) | −0.770122 | − | 1.33389i | −0.256707 | − | 0.444630i | 0.708651 | − | 0.705560i | \(-0.249304\pi\) |
−0.965358 | + | 0.260930i | \(0.915971\pi\) | |||||||
\(4\) | 3.27367 | + | 5.67017i | 0.818418 | + | 1.41754i | ||||
\(5\) | 3.06569 | + | 1.76998i | 0.613138 | + | 0.353996i | 0.774193 | − | 0.632950i | \(-0.218156\pi\) |
−0.161054 | + | 0.986946i | \(0.551489\pi\) | |||||||
\(6\) | 5.00220i | 0.833700i | ||||||||
\(7\) | −5.85179 | + | 3.84142i | −0.835970 | + | 0.548775i | ||||
\(8\) | − | 8.27293i | − | 1.03412i | ||||||
\(9\) | 3.31382 | − | 5.73971i | 0.368203 | − | 0.637746i | ||||
\(10\) | −5.74830 | − | 9.95635i | −0.574830 | − | 0.995635i | ||||
\(11\) | 3.51053 | − | 2.02681i | 0.319139 | − | 0.184255i | −0.331870 | − | 0.943325i | \(-0.607679\pi\) |
0.651009 | + | 0.759070i | \(0.274346\pi\) | |||||||
\(12\) | 5.04225 | − | 8.73344i | 0.420188 | − | 0.727787i | ||||
\(13\) | − | 11.5263i | − | 0.886640i | −0.896363 | − | 0.443320i | \(-0.853801\pi\) | ||
0.896363 | − | 0.443320i | \(-0.146199\pi\) | |||||||
\(14\) | 22.6964 | − | 1.30190i | 1.62117 | − | 0.0929930i | ||||
\(15\) | − | 5.45240i | − | 0.363493i | ||||||
\(16\) | −0.339171 | + | 0.587461i | −0.0211982 | + | 0.0367163i | ||||
\(17\) | −5.92333 | − | 10.2595i | −0.348431 | − | 0.603501i | 0.637540 | − | 0.770418i | \(-0.279952\pi\) |
−0.985971 | + | 0.166917i | \(0.946619\pi\) | |||||||
\(18\) | −18.6407 | + | 10.7622i | −1.03559 | + | 0.597900i | ||||
\(19\) | −0.749147 | + | 1.29756i | −0.0394288 | + | 0.0682927i | −0.885066 | − | 0.465465i | \(-0.845887\pi\) |
0.845638 | + | 0.533758i | \(0.179220\pi\) | |||||||
\(20\) | 23.1773i | 1.15887i | ||||||||
\(21\) | 9.63063 | + | 4.84729i | 0.458601 | + | 0.230823i | ||||
\(22\) | −13.1648 | −0.598400 | ||||||||
\(23\) | 0.607982 | − | 1.05306i | 0.0264340 | − | 0.0457850i | −0.852506 | − | 0.522718i | \(-0.824918\pi\) |
0.878940 | + | 0.476933i | \(0.158251\pi\) | |||||||
\(24\) | −11.0352 | + | 6.37116i | −0.459799 | + | 0.265465i | ||||
\(25\) | −6.23435 | − | 10.7982i | −0.249374 | − | 0.431929i | ||||
\(26\) | −18.7168 | + | 32.4185i | −0.719878 | + | 1.24686i | ||||
\(27\) | −24.0704 | −0.891496 | ||||||||
\(28\) | −40.9384 | − | 20.6051i | −1.46208 | − | 0.735896i | ||||
\(29\) | −18.8895 | + | 22.0042i | −0.651363 | + | 0.758766i | ||||
\(30\) | −8.85379 | + | 15.3352i | −0.295126 | + | 0.511174i | ||||
\(31\) | −25.5458 | − | 44.2466i | −0.824057 | − | 1.42731i | −0.902638 | − | 0.430401i | \(-0.858372\pi\) |
0.0785804 | − | 0.996908i | \(-0.474961\pi\) | |||||||
\(32\) | −26.7504 | + | 15.4443i | −0.835950 | + | 0.482636i | ||||
\(33\) | −5.40708 | − | 3.12178i | −0.163851 | − | 0.0945993i | ||||
\(34\) | 38.4740i | 1.13159i | ||||||||
\(35\) | −24.7390 | + | 1.41907i | −0.706829 | + | 0.0405449i | ||||
\(36\) | 43.3935 | 1.20537 | ||||||||
\(37\) | 2.79632 | + | 1.61446i | 0.0755762 | + | 0.0436339i | 0.537312 | − | 0.843384i | \(-0.319440\pi\) |
−0.461736 | + | 0.887018i | \(0.652773\pi\) | |||||||
\(38\) | 4.21405 | − | 2.43298i | 0.110896 | − | 0.0640258i | ||||
\(39\) | −15.3748 | + | 8.87667i | −0.394227 | + | 0.227607i | ||||
\(40\) | 14.6429 | − | 25.3622i | 0.366073 | − | 0.634056i | ||||
\(41\) | 38.6483 | 0.942641 | 0.471321 | − | 0.881962i | \(-0.343777\pi\) | ||||
0.471321 | + | 0.881962i | \(0.343777\pi\) | |||||||
\(42\) | −19.2156 | − | 29.2718i | −0.457513 | − | 0.696949i | ||||
\(43\) | − | 20.2996i | − | 0.472084i | −0.971743 | − | 0.236042i | \(-0.924150\pi\) | ||
0.971743 | − | 0.236042i | \(-0.0758502\pi\) | |||||||
\(44\) | 22.9847 | + | 13.2702i | 0.522379 | + | 0.301596i | ||||
\(45\) | 20.3183 | − | 11.7308i | 0.451518 | − | 0.260684i | ||||
\(46\) | −3.41997 | + | 1.97452i | −0.0743473 | + | 0.0429244i | ||||
\(47\) | −19.3190 | + | 33.4615i | −0.411043 | + | 0.711948i | −0.995004 | − | 0.0998341i | \(-0.968169\pi\) |
0.583961 | + | 0.811782i | \(0.301502\pi\) | |||||||
\(48\) | 1.04481 | 0.0217669 | ||||||||
\(49\) | 19.4870 | − | 44.9584i | 0.397693 | − | 0.917519i | ||||
\(50\) | 40.4942i | 0.809884i | ||||||||
\(51\) | −9.12338 | + | 15.8022i | −0.178890 | + | 0.309846i | ||||
\(52\) | 65.3561 | − | 37.7334i | 1.25685 | − | 0.725642i | ||||
\(53\) | −40.1353 | − | 69.5164i | −0.757271 | − | 1.31163i | −0.944238 | − | 0.329265i | \(-0.893199\pi\) |
0.186967 | − | 0.982366i | \(-0.440134\pi\) | |||||||
\(54\) | 67.6995 | + | 39.0863i | 1.25369 | + | 0.723821i | ||||
\(55\) | 14.3496 | 0.260902 | ||||||||
\(56\) | 31.7798 | + | 48.4115i | 0.567497 | + | 0.864490i | ||||
\(57\) | 2.30774 | 0.0404866 | ||||||||
\(58\) | 88.8592 | − | 31.2148i | 1.53205 | − | 0.538186i | ||||
\(59\) | −9.55587 | + | 5.51709i | −0.161964 | + | 0.0935099i | −0.578791 | − | 0.815476i | \(-0.696475\pi\) |
0.416827 | + | 0.908986i | \(0.363142\pi\) | |||||||
\(60\) | 30.9160 | − | 17.8494i | 0.515267 | − | 0.297489i | ||||
\(61\) | 29.2600 | − | 50.6798i | 0.479672 | − | 0.830817i | −0.520056 | − | 0.854132i | \(-0.674089\pi\) |
0.999728 | + | 0.0233154i | \(0.00742218\pi\) | |||||||
\(62\) | 165.928i | 2.67626i | ||||||||
\(63\) | 2.65685 | + | 46.3174i | 0.0421721 | + | 0.735197i | ||||
\(64\) | 103.030 | 1.60984 | ||||||||
\(65\) | 20.4013 | − | 35.3361i | 0.313867 | − | 0.543633i | ||||
\(66\) | 10.1385 | + | 17.5604i | 0.153614 | + | 0.266067i | ||||
\(67\) | −30.3413 | − | 52.5527i | −0.452856 | − | 0.784369i | 0.545706 | − | 0.837976i | \(-0.316261\pi\) |
−0.998562 | + | 0.0536073i | \(0.982928\pi\) | |||||||
\(68\) | 38.7821 | − | 67.1726i | 0.570325 | − | 0.987832i | ||||
\(69\) | −1.87288 | −0.0271432 | ||||||||
\(70\) | 71.8844 | + | 36.1808i | 1.02692 | + | 0.516869i | ||||
\(71\) | 38.3172 | 0.539679 | 0.269840 | − | 0.962905i | \(-0.413029\pi\) | ||||
0.269840 | + | 0.962905i | \(0.413029\pi\) | |||||||
\(72\) | −47.4842 | − | 27.4150i | −0.659503 | − | 0.380764i | ||||
\(73\) | −50.5622 | − | 87.5763i | −0.692633 | − | 1.19967i | −0.970972 | − | 0.239192i | \(-0.923117\pi\) |
0.278340 | − | 0.960483i | \(-0.410216\pi\) | |||||||
\(74\) | −5.24321 | − | 9.08151i | −0.0708542 | − | 0.122723i | ||||
\(75\) | −9.60243 | + | 16.6319i | −0.128032 | + | 0.221759i | ||||
\(76\) | −9.80985 | −0.129077 | ||||||||
\(77\) | −12.7571 | + | 25.3459i | −0.165676 | + | 0.329168i | ||||
\(78\) | 57.6569 | 0.739192 | ||||||||
\(79\) | 32.2112 | + | 18.5972i | 0.407737 | + | 0.235407i | 0.689817 | − | 0.723984i | \(-0.257691\pi\) |
−0.282080 | + | 0.959391i | \(0.591024\pi\) | |||||||
\(80\) | −2.07959 | + | 1.20065i | −0.0259948 | + | 0.0150081i | ||||
\(81\) | −11.2873 | − | 19.5501i | −0.139349 | − | 0.241360i | ||||
\(82\) | −108.701 | − | 62.7584i | −1.32562 | − | 0.765346i | ||||
\(83\) | 74.9882i | 0.903472i | 0.892152 | + | 0.451736i | \(0.149195\pi\) | ||||
−0.892152 | + | 0.451736i | \(0.850805\pi\) | |||||||
\(84\) | 4.04261 | + | 70.4757i | 0.0481263 | + | 0.838996i | ||||
\(85\) | − | 41.9367i | − | 0.493373i | ||||||
\(86\) | −32.9632 | + | 57.0939i | −0.383293 | + | 0.663882i | ||||
\(87\) | 43.8985 | + | 8.25064i | 0.504580 | + | 0.0948349i | ||||
\(88\) | −16.7676 | − | 29.0424i | −0.190541 | − | 0.330027i | ||||
\(89\) | 20.7592 | − | 35.9559i | 0.233249 | − | 0.403999i | −0.725513 | − | 0.688208i | \(-0.758398\pi\) |
0.958762 | + | 0.284209i | \(0.0917310\pi\) | |||||||
\(90\) | −76.1954 | −0.846616 | ||||||||
\(91\) | 44.2775 | + | 67.4496i | 0.486565 | + | 0.741205i | ||||
\(92\) | 7.96133 | 0.0865362 | ||||||||
\(93\) | −39.3467 | + | 68.1505i | −0.423083 | + | 0.732801i | ||||
\(94\) | 108.672 | − | 62.7418i | 1.15608 | − | 0.667466i | ||||
\(95\) | −4.59331 | + | 2.65195i | −0.0483506 | + | 0.0279152i | ||||
\(96\) | 41.2021 | + | 23.7881i | 0.429189 | + | 0.247792i | ||||
\(97\) | 67.1379 | 0.692144 | 0.346072 | − | 0.938208i | \(-0.387515\pi\) | ||||
0.346072 | + | 0.938208i | \(0.387515\pi\) | |||||||
\(98\) | −127.813 | + | 94.8048i | −1.30422 | + | 0.967396i | ||||
\(99\) | − | 26.8659i | − | 0.271373i | ||||||
\(100\) | 40.8185 | − | 70.6997i | 0.408185 | − | 0.706997i | ||||
\(101\) | 13.4752 | + | 23.3398i | 0.133418 | + | 0.231087i | 0.924992 | − | 0.379987i | \(-0.124071\pi\) |
−0.791574 | + | 0.611073i | \(0.790738\pi\) | |||||||
\(102\) | 51.3202 | − | 29.6297i | 0.503139 | − | 0.290487i | ||||
\(103\) | −98.9946 | − | 57.1546i | −0.961113 | − | 0.554899i | −0.0645976 | − | 0.997911i | \(-0.520576\pi\) |
−0.896515 | + | 0.443013i | \(0.853910\pi\) | |||||||
\(104\) | −95.3564 | −0.916888 | ||||||||
\(105\) | 20.9450 | + | 31.9063i | 0.199476 | + | 0.303869i | ||||
\(106\) | 260.692i | 2.45936i | ||||||||
\(107\) | −57.1020 | + | 98.9035i | −0.533663 | + | 0.924332i | 0.465564 | + | 0.885014i | \(0.345852\pi\) |
−0.999227 | + | 0.0393174i | \(0.987482\pi\) | |||||||
\(108\) | −78.7986 | − | 136.483i | −0.729616 | − | 1.26373i | ||||
\(109\) | 17.8507 | + | 30.9184i | 0.163768 | + | 0.283655i | 0.936217 | − | 0.351422i | \(-0.114302\pi\) |
−0.772449 | + | 0.635077i | \(0.780968\pi\) | |||||||
\(110\) | −40.3592 | − | 23.3014i | −0.366902 | − | 0.211831i | ||||
\(111\) | − | 4.97331i | − | 0.0448046i | ||||||
\(112\) | −0.271929 | − | 4.74060i | −0.00242793 | − | 0.0423268i | ||||
\(113\) | − | 22.8269i | − | 0.202008i | −0.994886 | − | 0.101004i | \(-0.967794\pi\) | ||
0.994886 | − | 0.101004i | \(-0.0322055\pi\) | |||||||
\(114\) | −6.49066 | − | 3.74738i | −0.0569356 | − | 0.0328718i | ||||
\(115\) | 3.72777 | − | 2.15223i | 0.0324154 | − | 0.0187150i | ||||
\(116\) | −186.606 | − | 35.0722i | −1.60867 | − | 0.302347i | ||||
\(117\) | −66.1577 | − | 38.1962i | −0.565451 | − | 0.326463i | ||||
\(118\) | 35.8353 | 0.303689 | ||||||||
\(119\) | 74.0733 | + | 37.2825i | 0.622464 | + | 0.313299i | ||||
\(120\) | −45.1073 | −0.375894 | ||||||||
\(121\) | −52.2841 | + | 90.5587i | −0.432100 | + | 0.748419i | ||||
\(122\) | −164.591 | + | 95.0268i | −1.34911 | + | 0.778908i | ||||
\(123\) | −29.7639 | − | 51.5526i | −0.241983 | − | 0.419127i | ||||
\(124\) | 167.257 | − | 289.698i | 1.34885 | − | 2.33627i | ||||
\(125\) | − | 132.638i | − | 1.06110i | ||||||
\(126\) | 67.7392 | − | 134.585i | 0.537613 | − | 1.06813i | ||||
\(127\) | 132.012i | 1.03947i | 0.854329 | + | 0.519733i | \(0.173969\pi\) | ||||
−0.854329 | + | 0.519733i | \(0.826031\pi\) | |||||||
\(128\) | −182.775 | − | 105.525i | −1.42793 | − | 0.824418i | ||||
\(129\) | −27.0774 | + | 15.6332i | −0.209903 | + | 0.121187i | ||||
\(130\) | −114.760 | + | 66.2567i | −0.882769 | + | 0.509667i | ||||
\(131\) | 56.4098 | − | 97.7047i | 0.430609 | − | 0.745837i | −0.566317 | − | 0.824188i | \(-0.691632\pi\) |
0.996926 | + | 0.0783506i | \(0.0249654\pi\) | |||||||
\(132\) | − | 40.8787i | − | 0.309687i | ||||||
\(133\) | −0.600626 | − | 10.4708i | −0.00451598 | − | 0.0787282i | ||||
\(134\) | 197.077i | 1.47072i | ||||||||
\(135\) | −73.7924 | − | 42.6041i | −0.546610 | − | 0.315586i | ||||
\(136\) | −84.8762 | + | 49.0033i | −0.624090 | + | 0.360319i | ||||
\(137\) | 227.744 | − | 131.488i | 1.66237 | − | 0.959768i | 0.690787 | − | 0.723058i | \(-0.257264\pi\) |
0.971580 | − | 0.236711i | \(-0.0760693\pi\) | |||||||
\(138\) | 5.26759 | + | 3.04125i | 0.0381710 | + | 0.0220380i | ||||
\(139\) | − | 207.520i | − | 1.49295i | −0.665415 | − | 0.746473i | \(-0.731746\pi\) | ||
0.665415 | − | 0.746473i | \(-0.268254\pi\) | |||||||
\(140\) | −89.0338 | − | 135.629i | −0.635956 | − | 0.968777i | ||||
\(141\) | 59.5120 | 0.422071 | ||||||||
\(142\) | −107.770 | − | 62.2208i | −0.758941 | − | 0.438175i | ||||
\(143\) | −23.3616 | − | 40.4635i | −0.163368 | − | 0.282962i | ||||
\(144\) | 2.24790 | + | 3.89348i | 0.0156104 | + | 0.0270381i | ||||
\(145\) | −96.8565 | + | 34.0241i | −0.667976 | + | 0.234649i | ||||
\(146\) | 328.418i | 2.24944i | ||||||||
\(147\) | −74.9769 | + | 8.63000i | −0.510047 | + | 0.0587075i | ||||
\(148\) | 21.1408i | 0.142843i | ||||||||
\(149\) | −59.0283 | + | 102.240i | −0.396163 | + | 0.686175i | −0.993249 | − | 0.116003i | \(-0.962992\pi\) |
0.597086 | + | 0.802177i | \(0.296325\pi\) | |||||||
\(150\) | 54.0149 | − | 31.1855i | 0.360099 | − | 0.207903i | ||||
\(151\) | 131.549 | + | 227.850i | 0.871186 | + | 1.50894i | 0.860771 | + | 0.508992i | \(0.169982\pi\) |
0.0104142 | + | 0.999946i | \(0.496685\pi\) | |||||||
\(152\) | 10.7346 | + | 6.19764i | 0.0706225 | + | 0.0407739i | ||||
\(153\) | −78.5156 | −0.513174 | ||||||||
\(154\) | 77.0376 | − | 50.5715i | 0.500244 | − | 0.328387i | ||||
\(155\) | − | 180.862i | − | 1.16685i | ||||||
\(156\) | −100.664 | − | 58.1186i | −0.645285 | − | 0.372555i | ||||
\(157\) | −25.0478 | − | 43.3841i | −0.159540 | − | 0.276332i | 0.775163 | − | 0.631762i | \(-0.217668\pi\) |
−0.934703 | + | 0.355430i | \(0.884335\pi\) | |||||||
\(158\) | −60.3974 | − | 104.611i | −0.382262 | − | 0.662097i | ||||
\(159\) | −61.8182 | + | 107.072i | −0.388794 | + | 0.673411i | ||||
\(160\) | −109.345 | −0.683404 | ||||||||
\(161\) | 0.487447 | + | 8.49778i | 0.00302762 | + | 0.0527812i | ||||
\(162\) | 73.3147i | 0.452560i | ||||||||
\(163\) | 106.591 | + | 61.5401i | 0.653930 | + | 0.377547i | 0.789960 | − | 0.613158i | \(-0.210101\pi\) |
−0.136030 | + | 0.990705i | \(0.543434\pi\) | |||||||
\(164\) | 126.522 | + | 219.142i | 0.771475 | + | 1.33623i | ||||
\(165\) | −11.0510 | − | 19.1408i | −0.0669755 | − | 0.116005i | ||||
\(166\) | 121.768 | − | 210.909i | 0.733544 | − | 1.27054i | ||||
\(167\) | 209.637i | 1.25531i | 0.778491 | + | 0.627656i | \(0.215985\pi\) | ||||
−0.778491 | + | 0.627656i | \(0.784015\pi\) | |||||||
\(168\) | 40.1012 | − | 79.6735i | 0.238698 | − | 0.474247i | ||||
\(169\) | 36.1440 | 0.213870 | ||||||||
\(170\) | −68.0982 | + | 117.950i | −0.400578 | + | 0.693821i | ||||
\(171\) | 4.96508 | + | 8.59978i | 0.0290356 | + | 0.0502911i | ||||
\(172\) | 115.102 | − | 66.4542i | 0.669198 | − | 0.386362i | ||||
\(173\) | 130.552 | + | 75.3744i | 0.754637 | + | 0.435690i | 0.827367 | − | 0.561662i | \(-0.189838\pi\) |
−0.0727297 | + | 0.997352i | \(0.523171\pi\) | |||||||
\(174\) | −110.069 | − | 94.4892i | −0.632583 | − | 0.543042i | ||||
\(175\) | 77.9627 | + | 39.2401i | 0.445501 | + | 0.224229i | ||||
\(176\) | 2.74973i | 0.0156235i | ||||||||
\(177\) | 14.7184 | + | 8.49766i | 0.0831547 | + | 0.0480094i | ||||
\(178\) | −116.773 | + | 67.4188i | −0.656027 | + | 0.378758i | ||||
\(179\) | 129.981 | + | 225.133i | 0.726149 | + | 1.25773i | 0.958500 | + | 0.285094i | \(0.0920249\pi\) |
−0.232351 | + | 0.972632i | \(0.574642\pi\) | |||||||
\(180\) | 133.031 | + | 76.8055i | 0.739062 | + | 0.426697i | ||||
\(181\) | − | 32.1399i | − | 0.177569i | −0.996051 | − | 0.0887843i | \(-0.971702\pi\) | ||
0.996051 | − | 0.0887843i | \(-0.0282982\pi\) | |||||||
\(182\) | −15.0061 | − | 261.605i | −0.0824513 | − | 1.43739i | ||||
\(183\) | −90.1351 | −0.492542 | ||||||||
\(184\) | −8.71185 | − | 5.02979i | −0.0473470 | − | 0.0273358i | ||||
\(185\) | 5.71510 | + | 9.89884i | 0.0308924 | + | 0.0535073i | ||||
\(186\) | 221.330 | − | 127.785i | 1.18995 | − | 0.687017i | ||||
\(187\) | −41.5881 | − | 24.0109i | −0.222396 | − | 0.128401i | ||||
\(188\) | −252.977 | −1.34562 | ||||||||
\(189\) | 140.855 | − | 92.4645i | 0.745264 | − | 0.489230i | ||||
\(190\) | 17.2253 | 0.0906594 | ||||||||
\(191\) | 233.662 | + | 134.905i | 1.22336 | + | 0.706307i | 0.965633 | − | 0.259911i | \(-0.0836931\pi\) |
0.257727 | + | 0.966218i | \(0.417026\pi\) | |||||||
\(192\) | −79.3453 | − | 137.430i | −0.413257 | − | 0.715782i | ||||
\(193\) | −272.687 | + | 157.436i | −1.41289 | + | 0.815731i | −0.995659 | − | 0.0930711i | \(-0.970332\pi\) |
−0.417228 | + | 0.908802i | \(0.636998\pi\) | |||||||
\(194\) | −188.830 | − | 109.021i | −0.973348 | − | 0.561963i | ||||
\(195\) | −62.8461 | −0.322287 | ||||||||
\(196\) | 318.716 | − | 36.6848i | 1.62610 | − | 0.187168i | ||||
\(197\) | 301.260 | 1.52924 | 0.764618 | − | 0.644483i | \(-0.222927\pi\) | ||||
0.764618 | + | 0.644483i | \(0.222927\pi\) | |||||||
\(198\) | −43.6258 | + | 75.5621i | −0.220332 | + | 0.381627i | ||||
\(199\) | −83.8115 | + | 48.3886i | −0.421163 | + | 0.243159i | −0.695575 | − | 0.718454i | \(-0.744850\pi\) |
0.274412 | + | 0.961612i | \(0.411517\pi\) | |||||||
\(200\) | −89.3329 | + | 51.5764i | −0.446664 | + | 0.257882i | ||||
\(201\) | −46.7331 | + | 80.9440i | −0.232503 | + | 0.402707i | ||||
\(202\) | − | 87.5260i | − | 0.433297i | ||||||
\(203\) | 26.0102 | − | 201.327i | 0.128129 | − | 0.991758i | ||||
\(204\) | −119.468 | −0.585627 | ||||||||
\(205\) | 118.484 | + | 68.4066i | 0.577970 | + | 0.333691i | ||||
\(206\) | 185.619 | + | 321.502i | 0.901064 | + | 1.56069i | ||||
\(207\) | −4.02949 | − | 6.97928i | −0.0194661 | − | 0.0337163i | ||||
\(208\) | 6.77126 | + | 3.90939i | 0.0325541 | + | 0.0187951i | ||||
\(209\) | 6.07351i | 0.0290598i | ||||||||
\(210\) | −7.09849 | − | 123.750i | −0.0338023 | − | 0.589284i | ||||
\(211\) | − | 131.422i | − | 0.622855i | −0.950270 | − | 0.311428i | \(-0.899193\pi\) | ||
0.950270 | − | 0.311428i | \(-0.100807\pi\) | |||||||
\(212\) | 262.780 | − | 455.148i | 1.23953 | − | 2.14692i | ||||
\(213\) | −29.5089 | − | 51.1110i | −0.138540 | − | 0.239958i | ||||
\(214\) | 321.206 | − | 185.448i | 1.50096 | − | 0.866580i | ||||
\(215\) | 35.9298 | − | 62.2323i | 0.167116 | − | 0.289453i | ||||
\(216\) | 199.133i | 0.921910i | ||||||||
\(217\) | 319.458 | + | 160.790i | 1.47216 | + | 0.740966i | ||||
\(218\) | − | 115.947i | − | 0.531865i | ||||||
\(219\) | −77.8781 | + | 134.889i | −0.355608 | + | 0.615931i | ||||
\(220\) | 46.9760 | + | 81.3647i | 0.213527 | + | 0.369840i | ||||
\(221\) | −118.254 | + | 68.2742i | −0.535088 | + | 0.308933i | ||||
\(222\) | −8.07583 | + | 13.9877i | −0.0363776 | + | 0.0630079i | ||||
\(223\) | − | 265.425i | − | 1.19025i | −0.803634 | − | 0.595124i | \(-0.797103\pi\) | ||
0.803634 | − | 0.595124i | \(-0.202897\pi\) | |||||||
\(224\) | 97.2095 | − | 193.137i | 0.433971 | − | 0.862217i | ||||
\(225\) | −82.6382 | −0.367281 | ||||||||
\(226\) | −37.0671 | + | 64.2022i | −0.164014 | + | 0.284080i | ||||
\(227\) | 7.74878 | − | 4.47376i | 0.0341356 | − | 0.0197082i | −0.482835 | − | 0.875711i | \(-0.660393\pi\) |
0.516971 | + | 0.856003i | \(0.327060\pi\) | |||||||
\(228\) | 7.55478 | + | 13.0853i | 0.0331350 | + | 0.0573915i | ||||
\(229\) | −135.411 | + | 234.539i | −0.591316 | + | 1.02419i | 0.402740 | + | 0.915314i | \(0.368058\pi\) |
−0.994056 | + | 0.108874i | \(0.965275\pi\) | |||||||
\(230\) | −13.9794 | −0.0607802 | ||||||||
\(231\) | 43.6332 | − | 2.50287i | 0.188888 | − | 0.0108349i | ||||
\(232\) | 182.039 | + | 156.272i | 0.784652 | + | 0.673585i | ||||
\(233\) | 171.314 | − | 296.724i | 0.735252 | − | 1.27349i | −0.219360 | − | 0.975644i | \(-0.570397\pi\) |
0.954613 | − | 0.297850i | \(-0.0962697\pi\) | |||||||
\(234\) | 124.049 | + | 214.858i | 0.530122 | + | 0.918198i | ||||
\(235\) | −118.452 | + | 68.3885i | −0.504053 | + | 0.291015i | ||||
\(236\) | −62.5656 | − | 36.1223i | −0.265108 | − | 0.153060i | ||||
\(237\) | − | 57.2884i | − | 0.241723i | ||||||
\(238\) | −147.795 | − | 225.142i | −0.620988 | − | 0.945975i | ||||
\(239\) | 51.5305 | 0.215609 | 0.107804 | − | 0.994172i | \(-0.465618\pi\) | ||||
0.107804 | + | 0.994172i | \(0.465618\pi\) | |||||||
\(240\) | 3.20307 | + | 1.84929i | 0.0133461 | + | 0.00770539i | ||||
\(241\) | −42.6231 | + | 24.6085i | −0.176859 | + | 0.102110i | −0.585816 | − | 0.810444i | \(-0.699226\pi\) |
0.408957 | + | 0.912554i | \(0.365893\pi\) | |||||||
\(242\) | 294.105 | − | 169.801i | 1.21531 | − | 0.701659i | ||||
\(243\) | −125.702 | + | 217.722i | −0.517292 | + | 0.895976i | ||||
\(244\) | 383.151 | 1.57029 | ||||||||
\(245\) | 139.316 | − | 103.337i | 0.568638 | − | 0.421784i | ||||
\(246\) | 193.326i | 0.785880i | ||||||||
\(247\) | 14.9561 | + | 8.63491i | 0.0605510 | + | 0.0349591i | ||||
\(248\) | −366.049 | + | 211.338i | −1.47600 | + | 0.852171i | ||||
\(249\) | 100.026 | − | 57.7500i | 0.401711 | − | 0.231928i | ||||
\(250\) | −215.381 | + | 373.052i | −0.861526 | + | 1.49221i | ||||
\(251\) | −385.652 | −1.53646 | −0.768231 | − | 0.640173i | \(-0.778863\pi\) | ||||
−0.768231 | + | 0.640173i | \(0.778863\pi\) | |||||||
\(252\) | −253.930 | + | 166.693i | −1.00766 | + | 0.661479i | ||||
\(253\) | − | 4.92905i | − | 0.0194824i | ||||||
\(254\) | 214.366 | − | 371.293i | 0.843960 | − | 1.46178i | ||||
\(255\) | −55.9390 | + | 32.2964i | −0.219368 | + | 0.126652i | ||||
\(256\) | 136.653 | + | 236.689i | 0.533799 | + | 0.924567i | ||||
\(257\) | −163.195 | − | 94.2205i | −0.634999 | − | 0.366617i | 0.147687 | − | 0.989034i | \(-0.452817\pi\) |
−0.782685 | + | 0.622418i | \(0.786151\pi\) | |||||||
\(258\) | 101.543 | 0.393576 | ||||||||
\(259\) | −22.5653 | + | 1.29438i | −0.0871246 | + | 0.00499762i | ||||
\(260\) | 267.149 | 1.02750 | ||||||||
\(261\) | 63.7013 | + | 181.339i | 0.244066 | + | 0.694784i | ||||
\(262\) | −317.312 | + | 183.200i | −1.21112 | + | 0.699238i | ||||
\(263\) | −232.894 | + | 134.461i | −0.885527 | + | 0.511259i | −0.872477 | − | 0.488656i | \(-0.837487\pi\) |
−0.0130503 | + | 0.999915i | \(0.504154\pi\) | |||||||
\(264\) | −25.8262 | + | 44.7324i | −0.0978267 | + | 0.169441i | ||||
\(265\) | − | 284.155i | − | 1.07228i | ||||||
\(266\) | −15.3136 | + | 30.4252i | −0.0575700 | + | 0.114381i | ||||
\(267\) | −63.9483 | −0.239507 | ||||||||
\(268\) | 198.655 | − | 344.081i | 0.741251 | − | 1.28388i | ||||
\(269\) | −70.8365 | − | 122.692i | −0.263333 | − | 0.456106i | 0.703793 | − | 0.710405i | \(-0.251488\pi\) |
−0.967125 | + | 0.254300i | \(0.918155\pi\) | |||||||
\(270\) | 138.364 | + | 239.653i | 0.512459 | + | 0.887604i | ||||
\(271\) | −44.8903 | + | 77.7523i | −0.165647 | + | 0.286909i | −0.936885 | − | 0.349638i | \(-0.886305\pi\) |
0.771238 | + | 0.636547i | \(0.219638\pi\) | |||||||
\(272\) | 8.03609 | 0.0295444 | ||||||||
\(273\) | 55.8714 | − | 111.006i | 0.204657 | − | 0.406614i | ||||
\(274\) | −854.060 | −3.11701 | ||||||||
\(275\) | −43.7718 | − | 25.2717i | −0.159170 | − | 0.0918970i | ||||
\(276\) | −6.13120 | − | 10.6195i | −0.0222145 | − | 0.0384766i | ||||
\(277\) | 40.3975 | + | 69.9705i | 0.145839 | + | 0.252601i | 0.929686 | − | 0.368354i | \(-0.120078\pi\) |
−0.783846 | + | 0.620955i | \(0.786745\pi\) | |||||||
\(278\) | −336.977 | + | 583.662i | −1.21215 | + | 2.09950i | ||||
\(279\) | −338.617 | −1.21368 | ||||||||
\(280\) | 11.7399 | + | 204.664i | 0.0419282 | + | 0.730944i | ||||
\(281\) | 17.1568 | 0.0610563 | 0.0305281 | − | 0.999534i | \(-0.490281\pi\) | ||||
0.0305281 | + | 0.999534i | \(0.490281\pi\) | |||||||
\(282\) | −167.381 | − | 96.6377i | −0.593551 | − | 0.342687i | ||||
\(283\) | 123.782 | − | 71.4657i | 0.437393 | − | 0.252529i | −0.265098 | − | 0.964221i | \(-0.585404\pi\) |
0.702491 | + | 0.711692i | \(0.252071\pi\) | |||||||
\(284\) | 125.438 | + | 217.265i | 0.441683 | + | 0.765018i | ||||
\(285\) | 7.07481 | + | 4.08465i | 0.0248239 | + | 0.0143321i | ||||
\(286\) | 151.742i | 0.530565i | ||||||||
\(287\) | −226.162 | + | 148.464i | −0.788020 | + | 0.517298i | ||||
\(288\) | 204.719i | 0.710831i | ||||||||
\(289\) | 74.3282 | − | 128.740i | 0.257191 | − | 0.445468i | ||||
\(290\) | 327.664 | + | 61.5839i | 1.12988 | + | 0.212358i | ||||
\(291\) | −51.7044 | − | 89.5546i | −0.177678 | − | 0.307748i | ||||
\(292\) | 331.048 | − | 573.392i | 1.13373 | − | 1.96367i | ||||
\(293\) | −133.067 | −0.454153 | −0.227077 | − | 0.973877i | \(-0.572917\pi\) | ||||
−0.227077 | + | 0.973877i | \(0.572917\pi\) | |||||||
\(294\) | 224.891 | + | 97.4776i | 0.764935 | + | 0.331557i | ||||
\(295\) | −39.0605 | −0.132408 | ||||||||
\(296\) | 13.3563 | − | 23.1337i | 0.0451225 | − | 0.0781545i | ||||
\(297\) | −84.4999 | + | 48.7860i | −0.284511 | + | 0.164263i | ||||
\(298\) | 332.042 | − | 191.704i | 1.11423 | − | 0.643303i | ||||
\(299\) | −12.1378 | − | 7.00779i | −0.0405948 | − | 0.0234374i | ||||
\(300\) | −125.741 | −0.419136 | ||||||||
\(301\) | 77.9793 | + | 118.789i | 0.259067 | + | 0.394648i | ||||
\(302\) | − | 854.455i | − | 2.82932i | ||||||
\(303\) | 20.7551 | − | 35.9489i | 0.0684987 | − | 0.118643i | ||||
\(304\) | −0.508177 | − | 0.880189i | −0.00167164 | − | 0.00289536i | ||||
\(305\) | 179.404 | − | 103.579i | 0.588211 | − | 0.339604i | ||||
\(306\) | 220.830 | + | 127.496i | 0.721666 | + | 0.416654i | ||||
\(307\) | 120.094 | 0.391186 | 0.195593 | − | 0.980685i | \(-0.437337\pi\) | ||||
0.195593 | + | 0.980685i | \(0.437337\pi\) | |||||||
\(308\) | −185.478 | + | 10.6393i | −0.602201 | + | 0.0345433i | ||||
\(309\) | 176.064i | 0.569786i | ||||||||
\(310\) | −293.690 | + | 508.685i | −0.947386 | + | 1.64092i | ||||
\(311\) | −233.800 | − | 404.953i | −0.751768 | − | 1.30210i | −0.946965 | − | 0.321336i | \(-0.895868\pi\) |
0.195197 | − | 0.980764i | \(-0.437465\pi\) | |||||||
\(312\) | 73.4361 | + | 127.195i | 0.235372 | + | 0.407676i | ||||
\(313\) | −278.956 | − | 161.055i | −0.891233 | − | 0.514554i | −0.0168876 | − | 0.999857i | \(-0.505376\pi\) |
−0.874346 | + | 0.485304i | \(0.838709\pi\) | |||||||
\(314\) | 162.694i | 0.518134i | ||||||||
\(315\) | −73.8357 | + | 146.697i | −0.234399 | + | 0.465706i | ||||
\(316\) | 243.524i | 0.770646i | ||||||||
\(317\) | 380.166 | + | 219.489i | 1.19926 | + | 0.692394i | 0.960391 | − | 0.278657i | \(-0.0898893\pi\) |
0.238871 | + | 0.971051i | \(0.423223\pi\) | |||||||
\(318\) | 347.735 | − | 200.765i | 1.09351 | − | 0.631336i | ||||
\(319\) | −21.7140 | + | 115.532i | −0.0680691 | + | 0.362169i | ||||
\(320\) | 315.857 | + | 182.360i | 0.987053 | + | 0.569875i | ||||
\(321\) | 175.902 | 0.547981 | ||||||||
\(322\) | 12.4280 | − | 24.6921i | 0.0385963 | − | 0.0766834i | ||||
\(323\) | 17.7498 | 0.0549529 | ||||||||
\(324\) | 73.9017 | − | 128.002i | 0.228092 | − | 0.395066i | ||||
\(325\) | −124.464 | + | 71.8591i | −0.382965 | + | 0.221105i | ||||
\(326\) | −199.862 | − | 346.171i | −0.613073 | − | 1.06187i | ||||
\(327\) | 27.4945 | − | 47.6219i | 0.0840810 | − | 0.145633i | ||||
\(328\) | − | 319.735i | − | 0.974800i | ||||||
\(329\) | −15.4890 | − | 270.023i | −0.0470789 | − | 0.820737i | ||||
\(330\) | 71.7797i | 0.217514i | ||||||||
\(331\) | 35.1577 | + | 20.2983i | 0.106217 | + | 0.0613242i | 0.552167 | − | 0.833733i | \(-0.313801\pi\) |
−0.445951 | + | 0.895058i | \(0.647134\pi\) | |||||||
\(332\) | −425.195 | + | 245.487i | −1.28071 | + | 0.739418i | ||||
\(333\) | 18.5330 | − | 10.7000i | 0.0556547 | − | 0.0321323i | ||||
\(334\) | 340.416 | − | 589.617i | 1.01921 | − | 1.76532i | ||||
\(335\) | − | 214.814i | − | 0.641236i | ||||||
\(336\) | −6.11402 | + | 4.01356i | −0.0181965 | + | 0.0119451i | ||||
\(337\) | 288.444i | 0.855918i | 0.903798 | + | 0.427959i | \(0.140767\pi\) | ||||
−0.903798 | + | 0.427959i | \(0.859233\pi\) | |||||||
\(338\) | −101.657 | − | 58.6919i | −0.300761 | − | 0.173645i | ||||
\(339\) | −30.4486 | + | 17.5795i | −0.0898190 | + | 0.0518570i | ||||
\(340\) | 237.788 | − | 137.287i | 0.699377 | − | 0.403785i | ||||
\(341\) | −179.359 | − | 103.553i | −0.525978 | − | 0.303674i | ||||
\(342\) | − | 32.2499i | − | 0.0942979i | ||||||
\(343\) | 58.6706 | + | 337.945i | 0.171051 | + | 0.985262i | ||||
\(344\) | −167.937 | −0.488189 | ||||||||
\(345\) | −5.74168 | − | 3.31496i | −0.0166425 | − | 0.00960857i | ||||
\(346\) | −244.791 | − | 423.990i | −0.707488 | − | 1.22541i | ||||
\(347\) | 57.2561 | + | 99.1706i | 0.165003 | + | 0.285794i | 0.936656 | − | 0.350249i | \(-0.113903\pi\) |
−0.771653 | + | 0.636044i | \(0.780570\pi\) | |||||||
\(348\) | 96.9267 | + | 275.921i | 0.278525 | + | 0.792878i | ||||
\(349\) | − | 174.468i | − | 0.499907i | −0.968258 | − | 0.249953i | \(-0.919585\pi\) | ||
0.968258 | − | 0.249953i | \(-0.0804153\pi\) | |||||||
\(350\) | −155.555 | − | 236.964i | −0.444444 | − | 0.677039i | ||||
\(351\) | 277.443i | 0.790436i | ||||||||
\(352\) | −62.6054 | + | 108.436i | −0.177856 | + | 0.308056i | ||||
\(353\) | 534.771 | − | 308.750i | 1.51493 | − | 0.874646i | 0.515084 | − | 0.857140i | \(-0.327761\pi\) |
0.999847 | − | 0.0175060i | \(-0.00557262\pi\) | |||||||
\(354\) | −27.5976 | − | 47.8004i | −0.0779592 | − | 0.135029i | ||||
\(355\) | 117.469 | + | 67.8206i | 0.330898 | + | 0.191044i | ||||
\(356\) | 271.835 | 0.763581 | ||||||||
\(357\) | −7.31463 | − | 127.518i | −0.0204892 | − | 0.357192i | ||||
\(358\) | − | 844.268i | − | 2.35829i | ||||||
\(359\) | −472.963 | − | 273.065i | −1.31745 | − | 0.760628i | −0.334129 | − | 0.942527i | \(-0.608442\pi\) |
−0.983317 | + | 0.181899i | \(0.941776\pi\) | |||||||
\(360\) | −97.0480 | − | 168.092i | −0.269578 | − | 0.466922i | ||||
\(361\) | 179.378 | + | 310.691i | 0.496891 | + | 0.860640i | ||||
\(362\) | −52.1899 | + | 90.3955i | −0.144171 | + | 0.249711i | ||||
\(363\) | 161.061 | 0.443693 | ||||||||
\(364\) | −237.501 | + | 471.868i | −0.652474 | + | 1.29634i | ||||
\(365\) | − | 357.976i | − | 0.980756i | ||||||
\(366\) | 253.511 | + | 146.364i | 0.692652 | + | 0.399903i | ||||
\(367\) | 157.118 | + | 272.136i | 0.428114 | + | 0.741515i | 0.996706 | − | 0.0811050i | \(-0.0258449\pi\) |
−0.568592 | + | 0.822620i | \(0.692512\pi\) | |||||||
\(368\) | 0.412419 | + | 0.714331i | 0.00112070 | + | 0.00194112i | ||||
\(369\) | 128.074 | − | 221.830i | 0.347083 | − | 0.601165i | ||||
\(370\) | − | 37.1215i | − | 0.100328i | ||||||
\(371\) | 501.906 | + | 252.619i | 1.35285 | + | 0.680914i | ||||
\(372\) | −515.233 | −1.38504 | ||||||||
\(373\) | 68.7703 | − | 119.114i | 0.184371 | − | 0.319339i | −0.758994 | − | 0.651098i | \(-0.774309\pi\) |
0.943364 | + | 0.331759i | \(0.107642\pi\) | |||||||
\(374\) | 77.9795 | + | 135.064i | 0.208501 | + | 0.361135i | ||||
\(375\) | −176.924 | + | 102.147i | −0.471797 | + | 0.272392i | ||||
\(376\) | 276.825 | + | 159.825i | 0.736237 | + | 0.425066i | ||||
\(377\) | 253.628 | + | 217.727i | 0.672752 | + | 0.577525i | ||||
\(378\) | −546.310 | + | 31.3373i | −1.44527 | + | 0.0829029i | ||||
\(379\) | − | 683.651i | − | 1.80383i | −0.431915 | − | 0.901914i | \(-0.642162\pi\) | ||
0.431915 | − | 0.901914i | \(-0.357838\pi\) | |||||||
\(380\) | −30.0740 | − | 17.3632i | −0.0791420 | − | 0.0456927i | ||||
\(381\) | 176.090 | − | 101.666i | 0.462178 | − | 0.266839i | ||||
\(382\) | −438.125 | − | 758.856i | −1.14693 | − | 1.98653i | ||||
\(383\) | 101.944 | + | 58.8574i | 0.266172 | + | 0.153675i | 0.627147 | − | 0.778901i | \(-0.284223\pi\) |
−0.360975 | + | 0.932576i | \(0.617556\pi\) | |||||||
\(384\) | 325.070i | 0.846536i | ||||||||
\(385\) | −83.9710 | + | 55.1229i | −0.218106 | + | 0.143176i | ||||
\(386\) | 1022.60 | 2.64922 | ||||||||
\(387\) | −116.514 | − | 67.2693i | −0.301069 | − | 0.173822i | ||||
\(388\) | 219.788 | + | 380.683i | 0.566463 | + | 0.981142i | ||||
\(389\) | −169.492 | + | 97.8564i | −0.435713 | + | 0.251559i | −0.701777 | − | 0.712396i | \(-0.747610\pi\) |
0.266065 | + | 0.963955i | \(0.414277\pi\) | |||||||
\(390\) | 176.758 | + | 102.052i | 0.453227 | + | 0.261671i | ||||
\(391\) | −14.4051 | −0.0368417 | ||||||||
\(392\) | −371.938 | − | 161.214i | −0.948821 | − | 0.411261i | ||||
\(393\) | −173.770 | −0.442162 | ||||||||
\(394\) | −847.312 | − | 489.196i | −2.15054 | − | 1.24161i | ||||
\(395\) | 65.8332 | + | 114.026i | 0.166666 | + | 0.288674i | ||||
\(396\) | 152.334 | − | 87.9503i | 0.384683 | − | 0.222097i | ||||
\(397\) | −5.80765 | − | 3.35305i | −0.0146288 | − | 0.00844596i | 0.492668 | − | 0.870217i | \(-0.336022\pi\) |
−0.507297 | + | 0.861772i | \(0.669355\pi\) | |||||||
\(398\) | 314.300 | 0.789699 | ||||||||
\(399\) | −13.5044 | + | 8.86500i | −0.0338456 | + | 0.0222180i | ||||
\(400\) | 8.45804 | 0.0211451 | ||||||||
\(401\) | −376.011 | + | 651.271i | −0.937684 | + | 1.62412i | −0.167908 | + | 0.985803i | \(0.553701\pi\) |
−0.769776 | + | 0.638314i | \(0.779632\pi\) | |||||||
\(402\) | 262.879 | − | 151.773i | 0.653929 | − | 0.377546i | ||||
\(403\) | −510.000 | + | 294.449i | −1.26551 | + | 0.730642i | ||||
\(404\) | −88.2269 | + | 152.813i | −0.218383 | + | 0.378251i | ||||
\(405\) | − | 79.9130i | − | 0.197316i | ||||||
\(406\) | −400.076 | + | 524.008i | −0.985410 | + | 1.29066i | ||||
\(407\) | 13.0888 | 0.0321591 | ||||||||
\(408\) | 130.730 | + | 75.4771i | 0.320417 | + | 0.184993i | ||||
\(409\) | −263.424 | − | 456.263i | −0.644067 | − | 1.11556i | −0.984516 | − | 0.175294i | \(-0.943912\pi\) |
0.340449 | − | 0.940263i | \(-0.389421\pi\) | |||||||
\(410\) | −222.162 | − | 384.796i | −0.541859 | − | 0.938526i | ||||
\(411\) | −350.782 | − | 202.524i | −0.853484 | − | 0.492759i | ||||
\(412\) | − | 748.421i | − | 1.81656i | ||||||
\(413\) | 34.7255 | − | 68.9930i | 0.0840812 | − | 0.167053i | ||||
\(414\) | 26.1729i | 0.0632195i | ||||||||
\(415\) | −132.727 | + | 229.891i | −0.319825 | + | 0.553953i | ||||
\(416\) | 178.016 | + | 308.333i | 0.427924 | + | 0.741186i | ||||
\(417\) | −276.808 | + | 159.815i | −0.663809 | + | 0.383250i | ||||
\(418\) | 9.86237 | − | 17.0821i | 0.0235942 | − | 0.0408663i | ||||
\(419\) | 632.392i | 1.50929i | 0.656134 | + | 0.754644i | \(0.272191\pi\) | ||||
−0.656134 | + | 0.754644i | \(0.727809\pi\) | |||||||
\(420\) | −112.347 | + | 223.212i | −0.267493 | + | 0.531457i | ||||
\(421\) | 656.784i | 1.56006i | 0.625744 | + | 0.780029i | \(0.284796\pi\) | ||||
−0.625744 | + | 0.780029i | \(0.715204\pi\) | |||||||
\(422\) | −213.408 | + | 369.634i | −0.505707 | + | 0.875910i | ||||
\(423\) | 128.040 | + | 221.771i | 0.302694 | + | 0.524282i | ||||
\(424\) | −575.105 | + | 332.037i | −1.35638 | + | 0.783106i | ||||
\(425\) | −73.8563 | + | 127.923i | −0.173780 | + | 0.300995i | ||||
\(426\) | 191.670i | 0.449930i | ||||||||
\(427\) | 23.4591 | + | 408.968i | 0.0549393 | + | 0.957770i | ||||
\(428\) | −747.733 | −1.74704 | ||||||||
\(429\) | −35.9826 | + | 62.3237i | −0.0838755 | + | 0.145277i | ||||
\(430\) | −202.110 | + | 116.688i | −0.470023 | + | 0.271368i | ||||
\(431\) | −157.219 | − | 272.311i | −0.364776 | − | 0.631811i | 0.623964 | − | 0.781453i | \(-0.285521\pi\) |
−0.988740 | + | 0.149642i | \(0.952188\pi\) | |||||||
\(432\) | 8.16397 | − | 14.1404i | 0.0188981 | − | 0.0327324i | ||||
\(433\) | 766.040 | 1.76915 | 0.884573 | − | 0.466402i | \(-0.154450\pi\) | ||||
0.884573 | + | 0.466402i | \(0.154450\pi\) | |||||||
\(434\) | −637.401 | − | 970.978i | −1.46867 | − | 2.23728i | ||||
\(435\) | 119.976 | + | 102.993i | 0.275806 | + | 0.236766i | ||||
\(436\) | −116.875 | + | 202.433i | −0.268062 | + | 0.464297i | ||||
\(437\) | 0.910935 | + | 1.57779i | 0.00208452 | + | 0.00361050i | ||||
\(438\) | 438.074 | − | 252.922i | 1.00017 | − | 0.577448i | ||||
\(439\) | −622.439 | − | 359.365i | −1.41786 | − | 0.818599i | −0.421745 | − | 0.906714i | \(-0.638582\pi\) |
−0.996110 | + | 0.0881149i | \(0.971916\pi\) | |||||||
\(440\) | − | 118.713i | − | 0.269803i | ||||||
\(441\) | −193.472 | − | 260.834i | −0.438712 | − | 0.591460i | ||||
\(442\) | 443.464 | 1.00331 | ||||||||
\(443\) | 79.4340 | + | 45.8612i | 0.179309 | + | 0.103524i | 0.586968 | − | 0.809610i | \(-0.300321\pi\) |
−0.407659 | + | 0.913134i | \(0.633655\pi\) | |||||||
\(444\) | 28.1995 | − | 16.2810i | 0.0635124 | − | 0.0366689i | ||||
\(445\) | 127.282 | − | 73.4865i | 0.286028 | − | 0.165138i | ||||
\(446\) | −431.007 | + | 746.525i | −0.966383 | + | 1.67382i | ||||
\(447\) | 181.836 | 0.406792 | ||||||||
\(448\) | −602.907 | + | 395.780i | −1.34578 | + | 0.883437i | ||||
\(449\) | − | 244.202i | − | 0.543879i | −0.962314 | − | 0.271940i | \(-0.912335\pi\) | ||
0.962314 | − | 0.271940i | \(-0.0876651\pi\) | |||||||
\(450\) | 232.425 | + | 134.191i | 0.516500 | + | 0.298202i | ||||
\(451\) | 135.676 | − | 78.3326i | 0.300834 | − | 0.173687i | ||||
\(452\) | 129.433 | − | 74.7279i | 0.286355 | − | 0.165327i | ||||
\(453\) | 202.618 | − | 350.944i | 0.447279 | − | 0.774711i | ||||
\(454\) | −29.0586 | −0.0640057 | ||||||||
\(455\) | 16.3567 | + | 285.150i | 0.0359488 | + | 0.626703i | ||||
\(456\) | − | 19.0918i | − | 0.0418679i | ||||||
\(457\) | 131.475 | − | 227.722i | 0.287692 | − | 0.498298i | −0.685566 | − | 0.728010i | \(-0.740445\pi\) |
0.973259 | + | 0.229713i | \(0.0737786\pi\) | |||||||
\(458\) | 761.705 | − | 439.771i | 1.66311 | − | 0.960198i | ||||
\(459\) | 142.577 | + | 246.951i | 0.310625 | + | 0.538019i | ||||
\(460\) | 24.4070 | + | 14.0914i | 0.0530587 | + | 0.0306334i | ||||
\(461\) | 576.134 | 1.24975 | 0.624874 | − | 0.780725i | \(-0.285150\pi\) | ||||
0.624874 | + | 0.780725i | \(0.285150\pi\) | |||||||
\(462\) | −126.785 | − | 63.8135i | −0.274427 | − | 0.138125i | ||||
\(463\) | 333.465 | 0.720227 | 0.360113 | − | 0.932909i | \(-0.382738\pi\) | ||||
0.360113 | + | 0.932909i | \(0.382738\pi\) | |||||||
\(464\) | −6.51984 | − | 18.5600i | −0.0140514 | − | 0.0400001i | ||||
\(465\) | −241.250 | + | 139.286i | −0.518817 | + | 0.299539i | ||||
\(466\) | −963.661 | + | 556.370i | −2.06794 | + | 1.19393i | ||||
\(467\) | 199.814 | − | 346.088i | 0.427867 | − | 0.741088i | −0.568816 | − | 0.822465i | \(-0.692598\pi\) |
0.996683 | + | 0.0813769i | \(0.0259317\pi\) | |||||||
\(468\) | − | 500.167i | − | 1.06873i | ||||||
\(469\) | 379.428 | + | 190.974i | 0.809016 | + | 0.407194i | ||||
\(470\) | 444.206 | 0.945120 | ||||||||
\(471\) | −38.5798 | + | 66.8221i | −0.0819103 | + | 0.141873i | ||||
\(472\) | 45.6425 | + | 79.0550i | 0.0967001 | + | 0.167490i | ||||
\(473\) | −41.1434 | − | 71.2624i | −0.0869839 | − | 0.150660i | ||||
\(474\) | −93.0268 | + | 161.127i | −0.196259 | + | 0.339931i | ||||
\(475\) | 18.6818 | 0.0393301 | ||||||||
\(476\) | 31.0934 | + | 542.059i | 0.0653223 | + | 1.13878i | ||||
\(477\) | −532.006 | −1.11532 | ||||||||
\(478\) | −144.933 | − | 83.6770i | −0.303207 | − | 0.175057i | ||||
\(479\) | −142.075 | − | 246.081i | −0.296608 | − | 0.513740i | 0.678750 | − | 0.734370i | \(-0.262522\pi\) |
−0.975358 | + | 0.220630i | \(0.929189\pi\) | |||||||
\(480\) | 84.2087 | + | 145.854i | 0.175435 | + | 0.303862i | ||||
\(481\) | 18.6087 | − | 32.2313i | 0.0386876 | − | 0.0670088i | ||||
\(482\) | 159.840 | 0.331619 | ||||||||
\(483\) | 10.9597 | − | 7.19453i | 0.0226909 | − | 0.0148955i | ||||
\(484\) | −684.644 | −1.41455 | ||||||||
\(485\) | 205.824 | + | 118.833i | 0.424380 | + | 0.245016i | ||||
\(486\) | 707.089 | − | 408.238i | 1.45492 | − | 0.839996i | ||||
\(487\) | −107.407 | − | 186.035i | −0.220549 | − | 0.382002i | 0.734426 | − | 0.678689i | \(-0.237451\pi\) |
−0.954975 | + | 0.296687i | \(0.904118\pi\) | |||||||
\(488\) | −419.271 | − | 242.066i | −0.859161 | − | 0.496037i | ||||
\(489\) | − | 189.574i | − | 0.387676i | ||||||
\(490\) | −559.638 | + | 64.4156i | −1.14212 | + | 0.131460i | ||||
\(491\) | − | 198.647i | − | 0.404577i | −0.979326 | − | 0.202289i | \(-0.935162\pi\) | ||
0.979326 | − | 0.202289i | \(-0.0648379\pi\) | |||||||
\(492\) | 194.874 | − | 337.533i | 0.396086 | − | 0.686042i | ||||
\(493\) | 337.642 | + | 63.4592i | 0.684871 | + | 0.128720i | ||||
\(494\) | −28.0433 | − | 48.5724i | −0.0567678 | − | 0.0983247i | ||||
\(495\) | 47.5521 | − | 82.3627i | 0.0960649 | − | 0.166389i | ||||
\(496\) | 34.6575 | 0.0698740 | ||||||||
\(497\) | −224.224 | + | 147.193i | −0.451156 | + | 0.296162i | ||||
\(498\) | −375.106 | −0.753225 | ||||||||
\(499\) | 377.735 | − | 654.256i | 0.756984 | − | 1.31113i | −0.187398 | − | 0.982284i | \(-0.560005\pi\) |
0.944382 | − | 0.328850i | \(-0.106661\pi\) | |||||||
\(500\) | 752.077 | − | 434.212i | 1.50415 | − | 0.868424i | ||||
\(501\) | 279.633 | − | 161.446i | 0.558149 | − | 0.322248i | ||||
\(502\) | 1084.67 | + | 626.234i | 2.16070 | + | 1.24748i | ||||
\(503\) | 824.625 | 1.63941 | 0.819706 | − | 0.572784i | \(-0.194137\pi\) | ||||
0.819706 | + | 0.572784i | \(0.194137\pi\) | |||||||
\(504\) | 383.181 | − | 21.9799i | 0.760279 | − | 0.0436109i | ||||
\(505\) | 95.4033i | 0.188917i | ||||||||
\(506\) | −8.00395 | + | 13.8633i | −0.0158181 | + | 0.0273977i | ||||
\(507\) | −27.8353 | − | 48.2122i | −0.0549020 | − | 0.0950930i | ||||
\(508\) | −748.531 | + | 432.165i | −1.47349 | + | 0.850718i | ||||
\(509\) | −322.846 | − | 186.395i | −0.634275 | − | 0.366199i | 0.148131 | − | 0.988968i | \(-0.452674\pi\) |
−0.782406 | + | 0.622769i | \(0.786008\pi\) | |||||||
\(510\) | 209.776 | 0.411325 | ||||||||
\(511\) | 632.297 | + | 318.247i | 1.23737 | + | 0.622793i | ||||
\(512\) | − | 43.4005i | − | 0.0847667i | ||||||
\(513\) | 18.0323 | − | 31.2328i | 0.0351506 | − | 0.0608826i | ||||
\(514\) | 305.997 | + | 530.002i | 0.595325 | + | 1.03113i | ||||
\(515\) | −202.325 | − | 350.437i | −0.392864 | − | 0.680460i | ||||
\(516\) | −177.285 | − | 102.356i | −0.343576 | − | 0.198364i | ||||
\(517\) | 156.624i | 0.302947i | ||||||||
\(518\) | 65.5681 | + | 33.0017i | 0.126579 | + | 0.0637099i | ||||
\(519\) | − | 232.190i | − | 0.447379i | ||||||
\(520\) | −292.333 | − | 168.779i | −0.562179 | − | 0.324574i | ||||
\(521\) | −154.994 | + | 89.4860i | −0.297494 | + | 0.171758i | −0.641316 | − | 0.767276i | \(-0.721611\pi\) |
0.343823 | + | 0.939035i | \(0.388278\pi\) | |||||||
\(522\) | 115.300 | − | 613.466i | 0.220881 | − | 1.17522i | ||||
\(523\) | 720.821 | + | 416.166i | 1.37824 | + | 0.795729i | 0.991948 | − | 0.126646i | \(-0.0404211\pi\) |
0.386296 | + | 0.922375i | \(0.373754\pi\) | |||||||
\(524\) | 738.669 | 1.40967 | ||||||||
\(525\) | −7.69871 | − | 134.213i | −0.0146642 | − | 0.255644i | ||||
\(526\) | 873.371 | 1.66040 | ||||||||
\(527\) | −302.632 | + | 524.175i | −0.574255 | + | 0.994639i | ||||
\(528\) | 3.66784 | − | 2.11763i | 0.00694668 | − | 0.00401066i | ||||
\(529\) | 263.761 | + | 456.847i | 0.498602 | + | 0.863605i | ||||
\(530\) | −461.420 | + | 799.203i | −0.870604 | + | 1.50793i | ||||
\(531\) | 73.1306i | 0.137722i | ||||||||
\(532\) | 57.4052 | − | 37.6838i | 0.107904 | − | 0.0708341i | ||||
\(533\) | − | 445.472i | − | 0.835783i | ||||||
\(534\) | 179.859 | + | 103.841i | 0.336814 | + | 0.194460i | ||||
\(535\) | −350.114 | + | 202.138i | −0.654419 | + | 0.377829i | ||||
\(536\) | −434.765 | + | 251.012i | −0.811129 | + | 0.468305i | ||||
\(537\) | 200.202 | − | 346.760i | 0.372815 | − | 0.645735i | ||||
\(538\) | 460.107i | 0.855217i | ||||||||
\(539\) | −22.7124 | − | 197.324i | −0.0421381 | − | 0.366093i | ||||
\(540\) | − | 557.887i | − | 1.03312i | ||||||
\(541\) | 295.914 | + | 170.846i | 0.546976 | + | 0.315797i | 0.747901 | − | 0.663810i | \(-0.231062\pi\) |
−0.200925 | + | 0.979607i | \(0.564395\pi\) | |||||||
\(542\) | 252.514 | − | 145.789i | 0.465892 | − | 0.268983i | ||||
\(543\) | −42.8711 | + | 24.7516i | −0.0789523 | + | 0.0455831i | ||||
\(544\) | 316.903 | + | 182.964i | 0.582542 | + | 0.336331i | ||||
\(545\) | 126.382i | 0.231893i | ||||||||
\(546\) | −337.396 | + | 221.485i | −0.617942 | + | 0.405650i | ||||
\(547\) | −237.536 | −0.434252 | −0.217126 | − | 0.976144i | \(-0.569668\pi\) | ||||
−0.217126 | + | 0.976144i | \(0.569668\pi\) | |||||||
\(548\) | 1491.12 | + | 860.899i | 2.72102 | + | 1.57098i | ||||
\(549\) | −193.925 | − | 335.888i | −0.353233 | − | 0.611818i | ||||
\(550\) | 82.0740 | + | 142.156i | 0.149225 | + | 0.258466i | ||||
\(551\) | −14.4008 | − | 40.9947i | −0.0261357 | − | 0.0744006i | ||||
\(552\) | 15.4942i | 0.0280692i | ||||||||
\(553\) | −259.933 | + | 14.9102i | −0.470042 | + | 0.0269624i | ||||
\(554\) | − | 262.395i | − | 0.473638i | ||||||
\(555\) | 8.80265 | − | 15.2466i | 0.0158606 | − | 0.0274714i | ||||
\(556\) | 1176.67 | − | 679.351i | 2.11631 | − | 1.22185i | ||||
\(557\) | 42.2915 | + | 73.2511i | 0.0759273 | + | 0.131510i | 0.901489 | − | 0.432802i | \(-0.142475\pi\) |
−0.825562 | + | 0.564312i | \(0.809142\pi\) | |||||||
\(558\) | 952.381 | + | 549.857i | 1.70678 | + | 0.985408i | ||||
\(559\) | −233.980 | −0.418568 | ||||||||
\(560\) | 7.55710 | − | 15.0145i | 0.0134948 | − | 0.0268116i | ||||
\(561\) | 73.9653i | 0.131846i | ||||||||
\(562\) | −48.2546 | − | 27.8598i | −0.0858623 | − | 0.0495726i | ||||
\(563\) | −254.157 | − | 440.213i | −0.451434 | − | 0.781907i | 0.547041 | − | 0.837106i | \(-0.315754\pi\) |
−0.998475 | + | 0.0551989i | \(0.982421\pi\) | |||||||
\(564\) | 194.823 | + | 337.443i | 0.345431 | + | 0.598304i | ||||
\(565\) | 40.4032 | − | 69.9803i | 0.0715100 | − | 0.123859i | ||||
\(566\) | −464.194 | −0.820130 | ||||||||
\(567\) | 141.151 | + | 71.0442i | 0.248944 | + | 0.125298i | ||||
\(568\) | − | 316.996i | − | 0.558091i | ||||||
\(569\) | 148.079 | + | 85.4936i | 0.260245 | + | 0.150252i | 0.624446 | − | 0.781068i | \(-0.285325\pi\) |
−0.364201 | + | 0.931320i | \(0.618658\pi\) | |||||||
\(570\) | −13.2656 | − | 22.9766i | −0.0232729 | − | 0.0403099i | ||||
\(571\) | 76.0554 | + | 131.732i | 0.133197 | + | 0.230704i | 0.924907 | − | 0.380193i | \(-0.124142\pi\) |
−0.791710 | + | 0.610897i | \(0.790809\pi\) | |||||||
\(572\) | 152.957 | − | 264.929i | 0.267407 | − | 0.463162i | ||||
\(573\) | − | 415.572i | − | 0.725257i | ||||||
\(574\) | 877.176 | − | 50.3163i | 1.52818 | − | 0.0876590i | ||||
\(575\) | −15.1615 | −0.0263678 | ||||||||
\(576\) | 341.422 | − | 591.360i | 0.592746 | − | 1.02667i | ||||
\(577\) | −471.575 | − | 816.792i | −0.817287 | − | 1.41558i | −0.907674 | − | 0.419677i | \(-0.862144\pi\) |
0.0903863 | − | 0.995907i | \(-0.471190\pi\) | |||||||
\(578\) | −418.105 | + | 241.393i | −0.723366 | + | 0.417636i | ||||
\(579\) | 420.005 | + | 242.490i | 0.725397 | + | 0.418808i | ||||
\(580\) | −509.999 | − | 437.809i | −0.879308 | − | 0.754843i | ||||
\(581\) | −288.061 | − | 438.815i | −0.495802 | − | 0.755276i | ||||
\(582\) | 335.837i | 0.577040i | ||||||||
\(583\) | −281.793 | − | 162.693i | −0.483350 | − | 0.279062i | ||||
\(584\) | −724.512 | + | 418.297i | −1.24060 | + | 0.716262i | ||||
\(585\) | −135.213 | − | 234.196i | −0.231133 | − | 0.400334i | ||||
\(586\) | 374.259 | + | 216.079i | 0.638667 | + | 0.368735i | ||||
\(587\) | 272.016i | 0.463400i | 0.972787 | + | 0.231700i | \(0.0744288\pi\) | ||||
−0.972787 | + | 0.231700i | \(0.925571\pi\) | |||||||
\(588\) | −294.383 | − | 396.880i | −0.500652 | − | 0.674966i | ||||
\(589\) | 76.5502 | 0.129966 | ||||||||
\(590\) | 109.860 | + | 63.4277i | 0.186203 | + | 0.107505i | ||||
\(591\) | −232.007 | − | 401.847i | −0.392566 | − | 0.679945i | ||||
\(592\) | −1.89686 | + | 1.09515i | −0.00320415 | + | 0.00184992i | ||||
\(593\) | 680.868 | + | 393.099i | 1.14818 | + | 0.662900i | 0.948442 | − | 0.316951i | \(-0.102659\pi\) |
0.199734 | + | 0.979850i | \(0.435992\pi\) | |||||||
\(594\) | 316.882 | 0.533471 | ||||||||
\(595\) | 161.097 | + | 245.405i | 0.270750 | + | 0.412445i | ||||
\(596\) | −772.957 | −1.29691 | ||||||||
\(597\) | 129.090 | + | 74.5303i | 0.216231 | + | 0.124841i | ||||
\(598\) | 22.7590 | + | 39.4197i | 0.0380585 | + | 0.0659192i | ||||
\(599\) | −389.144 | + | 224.673i | −0.649657 | + | 0.375080i | −0.788325 | − | 0.615259i | \(-0.789051\pi\) |
0.138668 | + | 0.990339i | \(0.455718\pi\) | |||||||
\(600\) | 137.594 | + | 79.4402i | 0.229324 | + | 0.132400i | ||||
\(601\) | −1043.45 | −1.73619 | −0.868095 | − | 0.496399i | \(-0.834655\pi\) | ||||
−0.868095 | + | 0.496399i | \(0.834655\pi\) | |||||||
\(602\) | −26.4281 | − | 460.727i | −0.0439005 | − | 0.765327i | ||||
\(603\) | −402.183 | −0.666971 | ||||||||
\(604\) | −861.297 | + | 1491.81i | −1.42599 | + | 2.46988i | ||||
\(605\) | −320.574 | + | 185.083i | −0.529874 | + | 0.305923i | ||||
\(606\) | −116.750 | + | 67.4057i | −0.192657 | + | 0.111231i | ||||
\(607\) | 457.893 | − | 793.093i | 0.754354 | − | 1.30658i | −0.191341 | − | 0.981524i | \(-0.561284\pi\) |
0.945695 | − | 0.325055i | \(-0.105383\pi\) | |||||||
\(608\) | − | 46.2803i | − | 0.0761190i | ||||||
\(609\) | −288.579 | + | 120.351i | −0.473857 | + | 0.197621i | ||||
\(610\) | −672.781 | −1.10292 | ||||||||
\(611\) | 385.688 | + | 222.677i | 0.631241 | + | 0.364447i | ||||
\(612\) | −257.034 | − | 445.196i | −0.419991 | − | 0.727445i | ||||
\(613\) | 161.932 | + | 280.474i | 0.264162 | + | 0.457543i | 0.967344 | − | 0.253468i | \(-0.0815712\pi\) |
−0.703181 | + | 0.711010i | \(0.748238\pi\) | |||||||
\(614\) | −337.773 | − | 195.013i | −0.550118 | − | 0.317611i | ||||
\(615\) | − | 210.726i | − | 0.342644i | ||||||
\(616\) | 209.685 | + | 105.538i | 0.340397 | + | 0.171329i | ||||
\(617\) | − | 111.697i | − | 0.181032i | −0.995895 | − | 0.0905160i | \(-0.971148\pi\) | ||
0.995895 | − | 0.0905160i | \(-0.0288516\pi\) | |||||||
\(618\) | 285.899 | − | 495.191i | 0.462619 | − | 0.801280i | ||||
\(619\) | 375.832 | + | 650.961i | 0.607161 | + | 1.05163i | 0.991706 | + | 0.128527i | \(0.0410249\pi\) |
−0.384545 | + | 0.923106i | \(0.625642\pi\) | |||||||
\(620\) | 1025.52 | − | 592.082i | 1.65406 | − | 0.954972i | ||||
\(621\) | −14.6344 | + | 25.3475i | −0.0235658 | + | 0.0408172i | ||||
\(622\) | 1518.61i | 2.44149i | ||||||||
\(623\) | 16.6436 | + | 290.151i | 0.0267152 | + | 0.465732i | ||||
\(624\) | − | 12.0428i | − | 0.0192994i | ||||||
\(625\) | 78.9068 | − | 136.671i | 0.126251 | − | 0.218673i | ||||
\(626\) | 523.054 | + | 905.956i | 0.835550 | + | 1.44721i | ||||
\(627\) | 8.10139 | − | 4.67734i | 0.0129209 | − | 0.00745987i | ||||
\(628\) | 163.997 | − | 284.051i | 0.261141 | − | 0.452310i | ||||
\(629\) | − | 38.2518i | − | 0.0608137i | ||||||
\(630\) | 445.880 | − | 292.699i | 0.707746 | − | 0.464601i | ||||
\(631\) | −235.755 | −0.373621 | −0.186811 | − | 0.982396i | \(-0.559815\pi\) | ||||
−0.186811 | + | 0.982396i | \(0.559815\pi\) | |||||||
\(632\) | 153.853 | − | 266.481i | 0.243438 | − | 0.421648i | ||||
\(633\) | −175.303 | + | 101.211i | −0.276940 | + | 0.159892i | ||||
\(634\) | −712.827 | − | 1234.65i | −1.12433 | − | 1.94740i | ||||
\(635\) | −233.659 | + | 404.709i | −0.367967 | + | 0.637337i | ||||
\(636\) | −809.490 | −1.27278 | ||||||||
\(637\) | −518.205 | − | 224.613i | −0.813508 | − | 0.352610i | ||||
\(638\) | 248.677 | − | 289.681i | 0.389776 | − | 0.454045i | ||||
\(639\) | 126.977 | − | 219.930i | 0.198711 | − | 0.344178i | ||||
\(640\) | −373.556 | − | 647.017i | −0.583681 | − | 1.01096i | ||||
\(641\) | −248.890 | + | 143.697i | −0.388284 | + | 0.224176i | −0.681416 | − | 0.731896i | \(-0.738636\pi\) |
0.293132 | + | 0.956072i | \(0.405302\pi\) | |||||||
\(642\) | −494.735 | − | 285.635i | −0.770616 | − | 0.444915i | ||||
\(643\) | − | 846.362i | − | 1.31627i | −0.752899 | − | 0.658136i | \(-0.771345\pi\) | ||
0.752899 | − | 0.658136i | \(-0.228655\pi\) | |||||||
\(644\) | −46.5881 | + | 30.5828i | −0.0723417 | + | 0.0474889i | ||||
\(645\) | −110.681 | −0.171599 | ||||||||
\(646\) | −49.9224 | − | 28.8227i | −0.0772793 | − | 0.0446172i | ||||
\(647\) | −770.685 | + | 444.955i | −1.19117 | + | 0.687721i | −0.958571 | − | 0.284853i | \(-0.908055\pi\) |
−0.232596 | + | 0.972574i | \(0.574722\pi\) | |||||||
\(648\) | −161.737 | + | 93.3789i | −0.249594 | + | 0.144103i | ||||
\(649\) | −22.3641 | + | 38.7358i | −0.0344594 | + | 0.0596854i | ||||
\(650\) | 466.749 | 0.718076 | ||||||||
\(651\) | −31.5461 | − | 549.950i | −0.0484579 | − | 0.844777i | ||||
\(652\) | 805.849i | 1.23596i | ||||||||
\(653\) | 48.6873 | + | 28.1096i | 0.0745594 | + | 0.0430469i | 0.536816 | − | 0.843699i | \(-0.319627\pi\) |
−0.462257 | + | 0.886746i | \(0.652960\pi\) | |||||||
\(654\) | −154.660 | + | 89.2930i | −0.236483 | + | 0.136534i | ||||
\(655\) | 345.870 | − | 199.688i | 0.528046 | − | 0.304868i | ||||
\(656\) | −13.1084 | + | 22.7044i | −0.0199823 | + | 0.0346103i | ||||
\(657\) | −670.217 | −1.02012 | ||||||||
\(658\) | −394.908 | + | 784.607i | −0.600164 | + | 1.19241i | ||||
\(659\) | 198.674i | 0.301478i | 0.988574 | + | 0.150739i | \(0.0481653\pi\) | ||||
−0.988574 | + | 0.150739i | \(0.951835\pi\) | |||||||
\(660\) | 72.3544 | − | 125.322i | 0.109628 | − | 0.189881i | ||||
\(661\) | 584.658 | − | 337.552i | 0.884505 | − | 0.510669i | 0.0123638 | − | 0.999924i | \(-0.496064\pi\) |
0.872141 | + | 0.489254i | \(0.162731\pi\) | |||||||
\(662\) | −65.9222 | − | 114.181i | −0.0995803 | − | 0.172478i | ||||
\(663\) | 182.141 | + | 105.159i | 0.274722 | + | 0.158611i | ||||
\(664\) | 620.372 | 0.934295 | ||||||||
\(665\) | 16.6918 | − | 33.1635i | 0.0251005 | − | 0.0498699i | ||||
\(666\) | −69.5003 | −0.104355 | ||||||||
\(667\) | 11.6872 | + | 33.2699i | 0.0175220 | + | 0.0498799i | ||||
\(668\) | −1188.68 | + | 686.283i | −1.77946 | + | 1.02737i | ||||
\(669\) | −354.048 | + | 204.410i | −0.529220 | + | 0.305545i | ||||
\(670\) | −348.822 | + | 604.178i | −0.520630 | + | 0.901758i | ||||
\(671\) | − | 237.218i | − | 0.353529i | ||||||
\(672\) | −332.486 | + | 19.0720i | −0.494771 | + | 0.0283809i | ||||
\(673\) | −1207.98 | −1.79493 | −0.897463 | − | 0.441090i | \(-0.854592\pi\) | ||||
−0.897463 | + | 0.441090i | \(0.854592\pi\) | |||||||
\(674\) | 468.386 | − | 811.268i | 0.694934 | − | 1.20366i | ||||
\(675\) | 150.063 | + | 259.917i | 0.222316 | + | 0.385063i | ||||
\(676\) | 118.324 | + | 204.943i | 0.175035 | + | 0.303169i | ||||
\(677\) | −448.265 | + | 776.418i | −0.662135 | + | 1.14685i | 0.317919 | + | 0.948118i | \(0.397016\pi\) |
−0.980054 | + | 0.198733i | \(0.936317\pi\) | |||||||
\(678\) | 114.185 | 0.168414 | ||||||||
\(679\) | −392.877 | + | 257.905i | −0.578611 | + | 0.379831i | ||||
\(680\) | −346.939 | −0.510205 | ||||||||
\(681\) | −11.9350 | − | 6.89068i | −0.0175257 | − | 0.0101185i | ||||
\(682\) | 336.305 | + | 582.497i | 0.493116 | + | 0.854101i | ||||
\(683\) | −495.667 | − | 858.520i | −0.725720 | − | 1.25698i | −0.958677 | − | 0.284497i | \(-0.908174\pi\) |
0.232957 | − | 0.972487i | \(-0.425160\pi\) | |||||||
\(684\) | −32.5081 | + | 56.3057i | −0.0475265 | + | 0.0823183i | ||||
\(685\) | 930.926 | 1.35902 | ||||||||
\(686\) | 383.751 | − | 1045.76i | 0.559404 | − | 1.52444i | ||||
\(687\) | 417.133 | 0.607180 | ||||||||
\(688\) | 11.9252 | + | 6.88503i | 0.0173332 | + | 0.0100073i | ||||
\(689\) | −801.269 | + | 462.613i | −1.16294 | + | 0.671426i | ||||
\(690\) | 10.7659 | + | 18.6471i | 0.0156027 | + | 0.0270247i | ||||
\(691\) | −635.988 | − | 367.188i | −0.920388 | − | 0.531386i | −0.0366290 | − | 0.999329i | \(-0.511662\pi\) |
−0.883759 | + | 0.467943i | \(0.844995\pi\) | |||||||
\(692\) | 987.004i | 1.42631i | ||||||||
\(693\) | 103.203 | + | 157.214i | 0.148923 | + | 0.226860i | ||||
\(694\) | − | 371.898i | − | 0.535876i | ||||||
\(695\) | 367.305 | − | 636.191i | 0.528497 | − | 0.915383i | ||||
\(696\) | 68.2569 | − | 363.169i | 0.0980703 | − | 0.521794i | ||||
\(697\) | −228.927 | − | 396.513i | −0.328446 | − | 0.568885i | ||||
\(698\) | −283.306 | + | 490.701i | −0.405883 | + | 0.703010i | ||||
\(699\) | −527.730 | −0.754979 | ||||||||
\(700\) | 32.7260 | + | 570.521i | 0.0467515 | + | 0.815030i | ||||
\(701\) | 1039.53 | 1.48292 | 0.741462 | − | 0.670995i | \(-0.234133\pi\) | ||||
0.741462 | + | 0.670995i | \(0.234133\pi\) | |||||||
\(702\) | 450.521 | − | 780.326i | 0.641768 | − | 1.11158i | ||||
\(703\) | −4.18971 | + | 2.41893i | −0.00595975 | + | 0.00344087i | ||||
\(704\) | 361.689 | − | 208.821i | 0.513762 | − | 0.296621i | ||||
\(705\) | 182.446 | + | 105.335i | 0.258788 | + | 0.149411i | ||||
\(706\) | −2005.43 | −2.84056 | ||||||||
\(707\) | −168.512 | − | 84.8154i | −0.238348 | − | 0.119965i | ||||
\(708\) | 111.274i | 0.157167i | ||||||||
\(709\) | 616.675 | − | 1068.11i | 0.869782 | − | 1.50651i | 0.00756252 | − | 0.999971i | \(-0.497593\pi\) |
0.862219 | − | 0.506535i | \(-0.169074\pi\) | |||||||
\(710\) | −220.259 | − | 381.500i | −0.310224 | − | 0.537323i | ||||
\(711\) | 213.485 | − | 123.255i | 0.300260 | − | 0.173355i | ||||
\(712\) | −297.461 | − | 171.739i | −0.417782 | − | 0.241206i | ||||
\(713\) | −62.1255 | −0.0871325 | ||||||||
\(714\) | −186.495 | + | 370.529i | −0.261197 | + | 0.518949i | ||||
\(715\) | − | 165.398i | − | 0.231326i | ||||||
\(716\) | −851.028 | + | 1474.02i | −1.18859 | + | 2.05869i | ||||
\(717\) | −39.6848 | − | 68.7361i | −0.0553484 | − | 0.0958662i | ||||
\(718\) | 886.826 | + | 1536.03i | 1.23513 | + | 2.13931i | ||||
\(719\) | −539.641 | − | 311.562i | −0.750543 | − | 0.433326i | 0.0753469 | − | 0.997157i | \(-0.475994\pi\) |
−0.825890 | + | 0.563831i | \(0.809327\pi\) | |||||||
\(720\) | 15.9150i | 0.0221041i | ||||||||
\(721\) | 798.851 | − | 45.8235i | 1.10798 | − | 0.0635554i | ||||
\(722\) | − | 1165.12i | − | 1.61374i | ||||||
\(723\) | 65.6500 | + | 37.9031i | 0.0908022 | + | 0.0524247i | ||||
\(724\) | 182.239 | − | 105.215i | 0.251711 | − | 0.145325i | ||||
\(725\) | 355.370 | + | 66.7912i | 0.490166 | + | 0.0921259i | ||||
\(726\) | −452.993 | − | 261.536i | −0.623957 | − | 0.360242i | ||||
\(727\) | −15.9778 | −0.0219777 | −0.0109889 | − | 0.999940i | \(-0.503498\pi\) | ||||
−0.0109889 | + | 0.999940i | \(0.503498\pi\) | |||||||
\(728\) | 558.006 | − | 366.304i | 0.766491 | − | 0.503165i | ||||
\(729\) | 184.052 | 0.252472 | ||||||||
\(730\) | −581.293 | + | 1006.83i | −0.796292 | + | 1.37922i | ||||
\(731\) | −208.264 | + | 120.241i | −0.284903 | + | 0.164489i | ||||
\(732\) | −295.073 | − | 511.081i | −0.403105 | − | 0.698198i | ||||
\(733\) | −436.976 | + | 756.865i | −0.596148 | + | 1.03256i | 0.397236 | + | 0.917717i | \(0.369970\pi\) |
−0.993384 | + | 0.114842i | \(0.963364\pi\) | |||||||
\(734\) | − | 1020.53i | − | 1.39037i | ||||||
\(735\) | −245.131 | − | 106.251i | −0.333512 | − | 0.144559i | ||||
\(736\) | 37.5595i | 0.0510319i | ||||||||
\(737\) | −213.029 | − | 122.992i | −0.289048 | − | 0.166882i | ||||
\(738\) | −720.430 | + | 415.941i | −0.976193 | + | 0.563605i | ||||
\(739\) | 940.168 | − | 542.806i | 1.27222 | − | 0.734515i | 0.296812 | − | 0.954936i | \(-0.404077\pi\) |
0.975405 | + | 0.220421i | \(0.0707432\pi\) | |||||||
\(740\) | −37.4187 | + | 64.8111i | −0.0505659 | + | 0.0875826i | ||||
\(741\) | − | 26.5997i | − | 0.0358971i | ||||||
\(742\) | −1001.43 | − | 1525.52i | −1.34964 | − | 2.05595i | ||||
\(743\) | − | 701.352i | − | 0.943946i | −0.881613 | − | 0.471973i | \(-0.843542\pi\) | ||
0.881613 | − | 0.471973i | \(-0.156458\pi\) | |||||||
\(744\) | 563.804 | + | 325.513i | 0.757802 | + | 0.437517i | ||||
\(745\) | −361.925 | + | 208.958i | −0.485806 | + | 0.280480i | ||||
\(746\) | −386.841 | + | 223.343i | −0.518554 | + | 0.299387i | ||||
\(747\) | 430.411 | + | 248.498i | 0.576185 | + | 0.332661i | ||||
\(748\) | − | 314.415i | − | 0.420342i | ||||||
\(749\) | −45.7813 | − | 798.116i | −0.0611232 | − | 1.06557i | ||||
\(750\) | 663.480 | 0.884640 | ||||||||
\(751\) | −1069.02 | − | 617.201i | −1.42347 | − | 0.821839i | −0.426874 | − | 0.904311i | \(-0.640385\pi\) |
−0.996593 | + | 0.0824721i | \(0.973718\pi\) | |||||||
\(752\) | −13.1049 | − | 22.6983i | −0.0174267 | − | 0.0301840i | ||||
\(753\) | 296.999 | + | 514.417i | 0.394421 | + | 0.683157i | ||||
\(754\) | −359.791 | − | 1024.22i | −0.477177 | − | 1.35838i | ||||
\(755\) | 931.356i | 1.23358i | ||||||||
\(756\) | 985.402 | + | 495.972i | 1.30344 | + | 0.656048i | ||||
\(757\) | 1100.36i | 1.45358i | 0.686862 | + | 0.726788i | \(0.258988\pi\) | ||||
−0.686862 | + | 0.726788i | \(0.741012\pi\) | |||||||
\(758\) | −1110.14 | + | 1922.81i | −1.46456 | + | 2.53669i | ||||
\(759\) | −6.57481 | + | 3.79597i | −0.00866246 | + | 0.00500128i | ||||
\(760\) | 21.9394 | + | 38.0001i | 0.0288676 | + | 0.0500001i | ||||
\(761\) | −132.523 | − | 76.5121i | −0.174143 | − | 0.100542i | 0.410395 | − | 0.911908i | \(-0.365391\pi\) |
−0.584538 | + | 0.811366i | \(0.698724\pi\) | |||||||
\(762\) | −660.352 | −0.866603 | ||||||||
\(763\) | −223.229 | − | 112.356i | −0.292568 | − | 0.147255i | ||||
\(764\) | 1766.53i | 2.31222i | ||||||||
\(765\) | −240.705 | − | 138.971i | −0.314646 | − | 0.181661i | ||||
\(766\) | −191.149 | − | 331.080i | −0.249542 | − | 0.432220i | ||||
\(767\) | 63.5917 | + | 110.144i | 0.0829096 | + | 0.143604i | ||||
\(768\) | 210.478 | − | 364.559i | 0.274060 | − | 0.474686i | ||||
\(769\) | 204.903 | 0.266454 | 0.133227 | − | 0.991086i | \(-0.457466\pi\) | ||||
0.133227 | + | 0.991086i | \(0.457466\pi\) | |||||||
\(770\) | 325.684 | − | 18.6818i | 0.422966 | − | 0.0242621i | ||||
\(771\) | 290.245i | 0.376453i | ||||||||
\(772\) | −1785.38 | − | 1030.79i | −2.31266 | − | 1.33522i | ||||
\(773\) | −382.287 | − | 662.140i | −0.494550 | − | 0.856585i | 0.505431 | − | 0.862867i | \(-0.331334\pi\) |
−0.999980 | + | 0.00628211i | \(0.998000\pi\) | |||||||
\(774\) | 218.468 | + | 378.398i | 0.282259 | + | 0.488887i | ||||
\(775\) | −318.523 | + | 551.698i | −0.410997 | + | 0.711868i | ||||
\(776\) | − | 555.427i | − | 0.715757i | ||||||
\(777\) | 19.1046 | + | 29.1028i | 0.0245876 | + | 0.0374553i | ||||
\(778\) | 635.610 | 0.816979 | ||||||||
\(779\) | −28.9532 | + | 50.1485i | −0.0371672 | + | 0.0643755i | ||||
\(780\) | −205.737 | − | 356.348i | −0.263766 | − | 0.456856i | ||||
\(781\) | 134.514 | − | 77.6616i | 0.172233 | − | 0.0994387i | ||||
\(782\) | 40.5153 | + | 23.3915i | 0.0518098 | + | 0.0299124i | ||||
\(783\) | 454.678 | − | 529.650i | 0.580688 | − | 0.676437i | ||||
\(784\) | 19.8019 | + | 26.6964i | 0.0252575 | + | 0.0340515i | ||||
\(785\) | − | 177.336i | − | 0.225906i | ||||||
\(786\) | 488.738 | + | 282.173i | 0.621804 | + | 0.358999i | ||||
\(787\) | 199.251 | − | 115.038i | 0.253178 | − | 0.146172i | −0.368041 | − | 0.929810i | \(-0.619971\pi\) |
0.621218 | + | 0.783637i | \(0.286638\pi\) | |||||||
\(788\) | 986.225 | + | 1708.19i | 1.25156 | + | 2.16776i | ||||
\(789\) | 358.713 | + | 207.103i | 0.454643 | + | 0.262488i | ||||
\(790\) | − | 427.608i | − | 0.541277i | ||||||
\(791\) | 87.6879 | + | 133.578i | 0.110857 | + | 0.168873i | ||||
\(792\) | −222.260 | −0.280631 | ||||||||
\(793\) | −584.152 | − | 337.260i | −0.736635 | − | 0.425297i | ||||
\(794\) | 10.8896 | + | 18.8613i | 0.0137148 | + | 0.0237548i | ||||
\(795\) | −379.031 | + | 218.834i | −0.476769 | + | 0.275263i | ||||
\(796\) | −548.743 | − | 316.817i | −0.689375 | − | 0.398011i | ||||
\(797\) | 1076.68 | 1.35091 | 0.675457 | − | 0.737399i | \(-0.263946\pi\) | ||||
0.675457 | + | 0.737399i | \(0.263946\pi\) | |||||||
\(798\) | 52.3773 | − | 3.00445i | 0.0656357 | − | 0.00376497i | ||||
\(799\) | 457.732 | 0.572882 | ||||||||
\(800\) | 333.543 | + | 192.571i | 0.416928 | + | 0.240714i | ||||
\(801\) | −137.584 | − | 238.303i | −0.171766 | − | 0.297507i | ||||
\(802\) | 2115.11 | − | 1221.16i | 2.63730 | − | 1.52264i | ||||
\(803\) | −355.000 | − | 204.960i | −0.442093 | − | 0.255242i | ||||
\(804\) | −611.955 | −0.761138 | ||||||||
\(805\) | −13.5465 | + | 26.9143i | −0.0168280 | + | 0.0334340i | ||||
\(806\) | 1912.54 | 2.37288 | ||||||||
\(807\) | −109.105 | + | 188.976i | −0.135199 | + | 0.234171i | ||||
\(808\) | 193.088 | − | 111.479i | 0.238970 | − | 0.137970i | ||||
\(809\) | −1152.98 | + | 665.671i | −1.42519 | + | 0.822831i | −0.996736 | − | 0.0807340i | \(-0.974274\pi\) |
−0.428450 | + | 0.903565i | \(0.640940\pi\) | |||||||
\(810\) | −129.765 | + | 224.760i | −0.160204 | + | 0.277482i | ||||
\(811\) | − | 56.1433i | − | 0.0692272i | −0.999401 | − | 0.0346136i | \(-0.988980\pi\) | ||
0.999401 | − | 0.0346136i | \(-0.0110201\pi\) | |||||||
\(812\) | 1226.71 | − | 511.596i | 1.51072 | − | 0.630044i | ||||
\(813\) | 138.284 | 0.170091 | ||||||||
\(814\) | −36.8130 | − | 21.2540i | −0.0452248 | − | 0.0261105i | ||||
\(815\) | 217.849 | + | 377.326i | 0.267300 | + | 0.462977i | ||||
\(816\) | −6.18877 | − | 10.7193i | −0.00758427 | − | 0.0131363i | ||||
\(817\) | 26.3400 | + | 15.2074i | 0.0322398 | + | 0.0186137i | ||||
\(818\) | 1711.02i | 2.09172i | ||||||||
\(819\) | 533.869 | − | 30.6236i | 0.651855 | − | 0.0373915i | ||||
\(820\) | 895.764i | 1.09239i | ||||||||
\(821\) | 707.808 | − | 1225.96i | 0.862129 | − | 1.49325i | −0.00774111 | − | 0.999970i | \(-0.502464\pi\) |
0.869870 | − | 0.493281i | \(-0.164203\pi\) | |||||||
\(822\) | 657.731 | + | 1139.22i | 0.800159 | + | 1.38592i | ||||
\(823\) | 860.951 | − | 497.070i | 1.04611 | − | 0.603973i | 0.124554 | − | 0.992213i | \(-0.460250\pi\) |
0.921559 | + | 0.388239i | \(0.126917\pi\) | |||||||
\(824\) | −472.836 | + | 818.976i | −0.573830 | + | 0.993902i | ||||
\(825\) | 77.8491i | 0.0943625i | ||||||||
\(826\) | −209.701 | + | 137.659i | −0.253875 | + | 0.166657i | ||||
\(827\) | 779.911i | 0.943060i | 0.881850 | + | 0.471530i | \(0.156298\pi\) | ||||
−0.881850 | + | 0.471530i | \(0.843702\pi\) | |||||||
\(828\) | 26.3825 | − | 45.6958i | 0.0318629 | − | 0.0551881i | ||||
\(829\) | 356.152 | + | 616.874i | 0.429617 | + | 0.744118i | 0.996839 | − | 0.0794468i | \(-0.0253154\pi\) |
−0.567222 | + | 0.823565i | \(0.691982\pi\) | |||||||
\(830\) | 746.608 | − | 431.055i | 0.899528 | − | 0.519343i | ||||
\(831\) | 62.2220 | − | 107.772i | 0.0748760 | − | 0.129689i | ||||
\(832\) | − | 1187.55i | − | 1.42735i | ||||||
\(833\) | −576.679 | + | 66.3770i | −0.692292 | + | 0.0796843i | ||||
\(834\) | 1038.05 | 1.24467 | ||||||||
\(835\) | −371.053 | + | 642.683i | −0.444375 | + | 0.769680i | ||||
\(836\) | −34.4378 | + | 19.8827i | −0.0411935 | + | 0.0237831i | ||||
\(837\) | 614.897 | + | 1065.03i | 0.734644 | + | 1.27244i | ||||
\(838\) | 1026.90 | − | 1778.64i | 1.22542 | − | 2.12248i | ||||
\(839\) | 1424.96 | 1.69841 | 0.849204 | − | 0.528065i | \(-0.177082\pi\) | ||||
0.849204 | + | 0.528065i | \(0.177082\pi\) | |||||||
\(840\) | 263.958 | − | 173.276i | 0.314236 | − | 0.206281i | ||||
\(841\) | −127.371 | − | 831.299i | −0.151452 | − | 0.988465i | ||||
\(842\) | 1066.51 | − | 1847.25i | 1.26664 | − | 2.19388i | ||||
\(843\) | −13.2128 | − | 22.8853i | −0.0156736 | − | 0.0271475i | ||||
\(844\) | 745.187 | − | 430.234i | 0.882923 | − | 0.509756i | ||||
\(845\) | 110.806 | + | 63.9741i | 0.131132 | + | 0.0757090i | ||||
\(846\) | − | 831.661i | − | 0.983051i | ||||||
\(847\) | −41.9186 | − | 730.776i | −0.0494906 | − | 0.862782i | ||||
\(848\) | 54.4509 | 0.0642110 | ||||||||
\(849\) | −190.655 | − | 110.075i | −0.224564 | − | 0.129652i | ||||
\(850\) | 415.451 | − | 239.861i | 0.488766 | − | 0.282189i | ||||
\(851\) | 3.40022 | − | 1.96312i | 0.00399556 | − | 0.00230684i | ||||
\(852\) | 193.205 | − | 334.641i | 0.226767 | − | 0.392771i | ||||
\(853\) | 109.195 | 0.128013 | 0.0640067 | − | 0.997949i | \(-0.479612\pi\) | ||||
0.0640067 | + | 0.997949i | \(0.479612\pi\) | |||||||
\(854\) | 598.116 | − | 1188.34i | 0.700370 | − | 1.39150i | ||||
\(855\) | 35.1524i | 0.0411139i | ||||||||
\(856\) | 818.222 | + | 472.400i | 0.955866 | + | 0.551870i | ||||
\(857\) | −1292.86 | + | 746.431i | −1.50858 | + | 0.870981i | −0.508634 | + | 0.860983i | \(0.669849\pi\) |
−0.999950 | + | 0.00999828i | \(0.996817\pi\) | |||||||
\(858\) | 202.407 | − | 116.860i | 0.235905 | − | 0.136200i | ||||
\(859\) | 742.885 | − | 1286.72i | 0.864826 | − | 1.49792i | −0.00239449 | − | 0.999997i | \(-0.500762\pi\) |
0.867220 | − | 0.497925i | \(-0.165904\pi\) | |||||||
\(860\) | 470.490 | 0.547081 | ||||||||
\(861\) | 372.207 | + | 187.339i | 0.432297 | + | 0.217583i | ||||
\(862\) | 1021.19i | 1.18467i | ||||||||
\(863\) | 139.103 | − | 240.933i | 0.161185 | − | 0.279180i | −0.774109 | − | 0.633052i | \(-0.781802\pi\) |
0.935294 | + | 0.353872i | \(0.115135\pi\) | |||||||
\(864\) | 643.892 | − | 371.751i | 0.745246 | − | 0.430268i | ||||
\(865\) | 266.822 | + | 462.149i | 0.308465 | + | 0.534277i | ||||
\(866\) | −2154.54 | − | 1243.92i | −2.48792 | − | 1.43640i | ||||
\(867\) | −228.967 | −0.264091 | ||||||||
\(868\) | 134.098 | + | 2337.75i | 0.154490 | + | 2.69327i | ||||
\(869\) | 150.772 | 0.173500 | ||||||||
\(870\) | −170.195 | − | 484.496i | −0.195627 | − | 0.556891i | ||||
\(871\) | −605.739 | + | 349.724i | −0.695453 | + | 0.401520i | ||||
\(872\) | 255.786 | − | 147.678i | 0.293332 | − | 0.169355i | ||||
\(873\) | 222.483 | − | 385.352i | 0.254849 | − | 0.441412i | ||||
\(874\) | − | 5.91683i | − | 0.00676983i | ||||||
\(875\) | 509.517 | + | 776.168i | 0.582305 | + | 0.887049i | ||||
\(876\) | −1019.79 | −1.16414 | ||||||||
\(877\) | 476.282 | − | 824.945i | 0.543081 | − | 0.940644i | −0.455644 | − | 0.890162i | \(-0.650591\pi\) |
0.998725 | − | 0.0504820i | \(-0.0160757\pi\) | |||||||
\(878\) | 1167.10 | + | 2021.47i | 1.32927 | + | 2.30236i | ||||
\(879\) | 102.478 | + | 177.497i | 0.116585 | + | 0.201930i | ||||
\(880\) | −4.86697 | + | 8.42984i | −0.00553065 | + | 0.00957936i | ||||
\(881\) | −1529.47 | −1.73606 | −0.868030 | − | 0.496512i | \(-0.834614\pi\) | ||||
−0.868030 | + | 0.496512i | \(0.834614\pi\) | |||||||
\(882\) | 120.601 | + | 1047.78i | 0.136736 | + | 1.18796i | ||||
\(883\) | −437.558 | −0.495536 | −0.247768 | − | 0.968819i | \(-0.579697\pi\) | ||||
−0.247768 | + | 0.968819i | \(0.579697\pi\) | |||||||
\(884\) | −774.253 | − | 447.015i | −0.875851 | − | 0.505673i | ||||
\(885\) | 30.0813 | + | 52.1024i | 0.0339902 | + | 0.0588728i | ||||
\(886\) | −148.942 | − | 257.975i | −0.168106 | − | 0.291168i | ||||
\(887\) | 418.020 | − | 724.032i | 0.471274 | − | 0.816271i | −0.528186 | − | 0.849129i | \(-0.677128\pi\) |
0.999460 | + | 0.0328578i | \(0.0104608\pi\) | |||||||
\(888\) | −41.1438 | −0.0463331 | ||||||||
\(889\) | −507.115 | − | 772.508i | −0.570433 | − | 0.868963i | ||||
\(890\) | −477.320 | −0.536314 | ||||||||
\(891\) | −79.2487 | − | 45.7543i | −0.0889436 | − | 0.0513516i | ||||
\(892\) | 1505.01 | − | 868.916i | 1.68723 | − | 0.974121i | ||||
\(893\) | −28.9456 | − | 50.1352i | −0.0324139 | − | 0.0561425i | ||||
\(894\) | −511.425 | − | 295.271i | −0.572064 | − | 0.330281i | ||||
\(895\) | 920.251i | 1.02821i | ||||||||
\(896\) | 1474.93 | − | 84.6046i | 1.64613 | − | 0.0944248i | ||||
\(897\) | 21.5874i | 0.0240662i | ||||||||
\(898\) | −396.543 | + | 686.833i | −0.441585 | + | 0.764848i | ||||
\(899\) | 1456.16 | + | 273.683i | 1.61975 | + | 0.304430i | ||||
\(900\) | −270.530 | − | 468.572i | −0.300589 | − | 0.520636i | ||||
\(901\) | −475.470 | + | 823.538i | −0.527714 | + | 0.914027i | ||||
\(902\) | −508.797 | −0.564076 | ||||||||
\(903\) | 98.3979 | − | 195.498i | 0.108968 | − | 0.216498i | ||||
\(904\) | −188.846 | −0.208900 | ||||||||
\(905\) | 56.8869 | − | 98.5310i | 0.0628585 | − | 0.108874i | ||||
\(906\) | −1139.75 | + | 658.035i | −1.25800 | + | 0.726307i | ||||
\(907\) | 182.405 | − | 105.312i | 0.201108 | − | 0.116110i | −0.396064 | − | 0.918223i | \(-0.629624\pi\) |
0.597172 | + | 0.802113i | \(0.296291\pi\) | |||||||
\(908\) | 50.7339 | + | 29.2912i | 0.0558744 | + | 0.0322591i | ||||
\(909\) | 178.618 | 0.196499 | ||||||||
\(910\) | 417.032 | − | 828.562i | 0.458277 | − | 0.910508i | ||||
\(911\) | 1074.63i | 1.17962i | 0.807544 | + | 0.589808i | \(0.200796\pi\) | ||||
−0.807544 | + | 0.589808i | \(0.799204\pi\) | |||||||
\(912\) | −0.782717 | + | 1.35571i | −0.000858242 | + | 0.00148652i | ||||
\(913\) | 151.987 | + | 263.248i | 0.166469 | + | 0.288334i | ||||
\(914\) | −739.565 | + | 426.988i | −0.809153 | + | 0.467164i | ||||
\(915\) | −276.327 | − | 159.537i | −0.301996 | − | 0.174358i | ||||
\(916\) | −1773.17 | −1.93577 | ||||||||
\(917\) | 45.2263 | + | 788.441i | 0.0493199 | + | 0.859805i | ||||
\(918\) | − | 926.085i | − | 1.00881i | ||||||
\(919\) | −150.978 | + | 261.502i | −0.164285 | + | 0.284550i | −0.936401 | − | 0.350931i | \(-0.885865\pi\) |
0.772116 | + | 0.635482i | \(0.219198\pi\) | |||||||
\(920\) | −17.8052 | − | 30.8396i | −0.0193535 | − | 0.0335213i | ||||
\(921\) | −92.4872 | − | 160.193i | −0.100420 | − | 0.173933i | ||||
\(922\) | −1620.41 | − | 935.546i | −1.75750 | − | 1.01469i | ||||
\(923\) | − | 441.656i | − | 0.478501i | ||||||
\(924\) | 157.032 | + | 239.214i | 0.169948 | + | 0.258889i | ||||
\(925\) | − | 40.2603i | − | 0.0435247i | ||||||
\(926\) | −937.891 | − | 541.492i | −1.01284 | − | 0.584764i | ||||
\(927\) | −656.102 | + | 378.800i | −0.707769 | + | 0.408631i | ||||
\(928\) | 165.462 | − | 880.358i | 0.178299 | − | 0.948661i | ||||
\(929\) | 1296.33 | + | 748.439i | 1.39541 | + | 0.805639i | 0.993907 | − | 0.110220i | \(-0.0351555\pi\) |
0.401500 | + | 0.915859i | \(0.368489\pi\) | |||||||
\(930\) | 904.707 | 0.972803 | ||||||||
\(931\) | 43.7377 | + | 58.9660i | 0.0469792 | + | 0.0633362i | ||||
\(932\) | 2243.30 | 2.40698 | ||||||||
\(933\) | −360.109 | + | 623.727i | −0.385969 | + | 0.668517i | ||||
\(934\) | −1123.98 | + | 648.929i | −1.20340 | + | 0.694785i | ||||
\(935\) | −84.9976 | − | 147.220i | −0.0909065 | − | 0.157455i | ||||
\(936\) | −315.994 | + | 547.318i | −0.337601 | + | 0.584742i | ||||
\(937\) | − | 59.0010i | − | 0.0629680i | −0.999504 | − | 0.0314840i | \(-0.989977\pi\) | ||
0.999504 | − | 0.0314840i | \(-0.0100233\pi\) | |||||||
\(938\) | −757.056 | − | 1153.25i | −0.807096 | − | 1.22948i | ||||
\(939\) | 496.129i | 0.528359i | ||||||||
\(940\) | −775.549 | − | 447.763i | −0.825052 | − | 0.476344i | ||||
\(941\) | −102.176 | + | 58.9914i | −0.108583 | + | 0.0626901i | −0.553308 | − | 0.832977i | \(-0.686635\pi\) |
0.444725 | + | 0.895667i | \(0.353301\pi\) | |||||||
\(942\) | 217.016 | − | 125.294i | 0.230378 | − | 0.133009i | ||||
\(943\) | 23.4975 | − | 40.6988i | 0.0249178 | − | 0.0431588i | ||||
\(944\) | − | 7.48493i | − | 0.00792896i | ||||||
\(945\) | 595.478 | − | 34.1576i | 0.630136 | − | 0.0361456i | ||||
\(946\) | 267.240i | 0.282495i | ||||||||
\(947\) | −1298.76 | − | 749.838i | −1.37144 | − | 0.791804i | −0.380335 | − | 0.924849i | \(-0.624191\pi\) |
−0.991110 | + | 0.133045i | \(0.957525\pi\) | |||||||
\(948\) | 324.835 | − | 187.543i | 0.342652 | − | 0.197830i | ||||
\(949\) | −1009.43 | + | 582.796i | −1.06368 | + | 0.614116i | ||||
\(950\) | −52.5437 | − | 30.3361i | −0.0553092 | − | 0.0319328i | ||||
\(951\) | − | 676.133i | − | 0.710971i | ||||||
\(952\) | 308.436 | − | 612.803i | 0.323987 | − | 0.643700i | ||||
\(953\) | −1015.35 | −1.06543 | −0.532715 | − | 0.846295i | \(-0.678828\pi\) | ||||
−0.532715 | + | 0.846295i | \(0.678828\pi\) | |||||||
\(954\) | 1496.30 | + | 863.889i | 1.56845 | + | 0.905544i | ||||
\(955\) | 477.557 | + | 827.152i | 0.500059 | + | 0.866128i | ||||
\(956\) | 168.694 | + | 292.187i | 0.176458 | + | 0.305635i | ||||
\(957\) | 170.829 | − | 60.0096i | 0.178505 | − | 0.0627059i | ||||
\(958\) | 922.825i | 0.963283i | ||||||||
\(959\) | −827.611 | + | 1644.30i | −0.862994 | + | 1.71460i | ||||
\(960\) | − | 561.758i | − | 0.585164i | ||||||
\(961\) | −824.673 | + | 1428.38i | −0.858141 | + | 1.48634i | ||||
\(962\) | −104.676 | + | 60.4349i | −0.108811 | + | 0.0628222i | ||||
\(963\) | 378.452 | + | 655.498i | 0.392992 | + | 0.680683i | ||||
\(964\) | −279.068 | − | 161.120i | −0.289490 | − | 0.167137i | ||||
\(965\) | −1114.63 | −1.15506 | ||||||||
\(966\) | −42.5076 | + | 2.43831i | −0.0440037 | + | 0.00252413i | ||||
\(967\) | 872.337i | 0.902106i | 0.892497 | + | 0.451053i | \(0.148952\pi\) | ||||
−0.892497 | + | 0.451053i | \(0.851048\pi\) | |||||||
\(968\) | 749.186 | + | 432.543i | 0.773952 | + | 0.446842i | ||||
\(969\) | −13.6695 | − | 23.6763i | −0.0141068 | − | 0.0244337i | ||||
\(970\) | −385.929 | − | 668.449i | −0.397865 | − | 0.689122i | ||||
\(971\) | 685.157 | − | 1186.73i | 0.705620 | − | 1.22217i | −0.260847 | − | 0.965380i | \(-0.584002\pi\) |
0.966467 | − | 0.256790i | \(-0.0826650\pi\) | |||||||
\(972\) | −1646.03 | −1.69344 | ||||||||
\(973\) | 797.170 | + | 1214.36i | 0.819291 | + | 1.24806i | ||||
\(974\) | 697.646i | 0.716269i | ||||||||
\(975\) | 191.704 | + | 110.681i | 0.196620 | + | 0.113519i | ||||
\(976\) | 19.8483 | + | 34.3782i | 0.0203364 | + | 0.0352236i | ||||
\(977\) | −219.578 | − | 380.320i | −0.224747 | − | 0.389273i | 0.731496 | − | 0.681845i | \(-0.238822\pi\) |
−0.956244 | + | 0.292572i | \(0.905489\pi\) | |||||||
\(978\) | −307.836 | + | 533.188i | −0.314761 | + | 0.545182i | ||||
\(979\) | − | 168.299i | − | 0.171909i | ||||||
\(980\) | 1042.02 | + | 451.655i | 1.06328 | + | 0.460873i | ||||
\(981\) | 236.617 | 0.241200 | ||||||||
\(982\) | −322.570 | + | 558.708i | −0.328483 | + | 0.568949i | ||||
\(983\) | −253.547 | − | 439.156i | −0.257932 | − | 0.446751i | 0.707756 | − | 0.706457i | \(-0.249708\pi\) |
−0.965688 | + | 0.259706i | \(0.916374\pi\) | |||||||
\(984\) | −426.491 | + | 246.235i | −0.433426 | + | 0.250238i | ||||
\(985\) | 923.569 | + | 533.223i | 0.937634 | + | 0.541343i | ||||
\(986\) | −846.591 | − | 726.757i | −0.858612 | − | 0.737076i | ||||
\(987\) | −348.252 | + | 228.611i | −0.352839 | + | 0.231622i | ||||
\(988\) | 113.071i | 0.114445i | ||||||||
\(989\) | −21.3766 | − | 12.3418i | −0.0216144 | − | 0.0124791i | ||||
\(990\) | −267.487 | + | 154.433i | −0.270188 | + | 0.155993i | ||||
\(991\) | 171.380 | + | 296.839i | 0.172937 | + | 0.299535i | 0.939445 | − | 0.342699i | \(-0.111341\pi\) |
−0.766509 | + | 0.642234i | \(0.778008\pi\) | |||||||
\(992\) | 1366.72 | + | 789.075i | 1.37774 | + | 0.795439i | ||||
\(993\) | − | 62.5287i | − | 0.0629695i | ||||||
\(994\) | 869.661 | − | 49.8853i | 0.874911 | − | 0.0501864i | ||||
\(995\) | −342.587 | −0.344309 | ||||||||
\(996\) | 654.905 | + | 378.109i | 0.657535 | + | 0.379628i | ||||
\(997\) | 882.925 | + | 1529.27i | 0.885582 | + | 1.53387i | 0.845046 | + | 0.534694i | \(0.179573\pi\) |
0.0405359 | + | 0.999178i | \(0.487093\pi\) | |||||||
\(998\) | −2124.81 | + | 1226.76i | −2.12906 | + | 1.22922i | ||||
\(999\) | −67.3085 | − | 38.8606i | −0.0673758 | − | 0.0388995i |
(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 | 203.3.i.a.173.3 | yes | 76 | |
7.3 | odd | 6 | inner | 203.3.i.a.115.36 | yes | 76 | |
29.28 | even | 2 | inner | 203.3.i.a.173.36 | yes | 76 | |
203.115 | odd | 6 | inner | 203.3.i.a.115.3 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
203.3.i.a.115.3 | ✓ | 76 | 203.115 | odd | 6 | inner | |
203.3.i.a.115.36 | yes | 76 | 7.3 | odd | 6 | inner | |
203.3.i.a.173.3 | yes | 76 | 1.1 | even | 1 | trivial | |
203.3.i.a.173.36 | yes | 76 | 29.28 | even | 2 | inner |