Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,3,Mod(3,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.3");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.d (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: | \(0.381472370104\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 5.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 14.5 |
Dual form | 14.3.d.a.3.2 |
$q$-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 \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 1.22474i | 0.353553 | − | 0.612372i | ||||
\(3\) | −3.62132 | + | 2.09077i | −1.20711 | + | 0.696923i | −0.962126 | − | 0.272605i | \(-0.912115\pi\) |
−0.244981 | + | 0.969528i | \(0.578782\pi\) | |||||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.74264 | + | 1.58346i | 0.548528 | + | 0.316693i | 0.748528 | − | 0.663103i | \(-0.230761\pi\) |
−0.200000 | + | 0.979796i | \(0.564094\pi\) | |||||||
\(6\) | 5.91359i | 0.985599i | ||||||||
\(7\) | −2.24264 | − | 6.63103i | −0.320377 | − | 0.947290i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 4.24264 | − | 7.34847i | 0.471405 | − | 0.816497i | ||||
\(10\) | 3.87868 | − | 2.23936i | 0.387868 | − | 0.223936i | ||||
\(11\) | 6.62132 | + | 11.4685i | 0.601938 | + | 1.04259i | 0.992527 | + | 0.122022i | \(0.0389380\pi\) |
−0.390589 | + | 0.920565i | \(0.627729\pi\) | |||||||
\(12\) | 7.24264 | + | 4.18154i | 0.603553 | + | 0.348462i | ||||
\(13\) | − | 5.49333i | − | 0.422563i | −0.977425 | − | 0.211282i | \(-0.932236\pi\) | ||
0.977425 | − | 0.211282i | \(-0.0677638\pi\) | |||||||
\(14\) | −9.70711 | − | 1.94218i | −0.693365 | − | 0.138727i | ||||
\(15\) | −13.2426 | −0.882843 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | −11.7426 | + | 6.77962i | −0.690744 | + | 0.398801i | −0.803891 | − | 0.594777i | \(-0.797240\pi\) |
0.113147 | + | 0.993578i | \(0.463907\pi\) | |||||||
\(18\) | −6.00000 | − | 10.3923i | −0.333333 | − | 0.577350i | ||||
\(19\) | −0.621320 | − | 0.358719i | −0.0327011 | − | 0.0188800i | 0.483560 | − | 0.875311i | \(-0.339343\pi\) |
−0.516261 | + | 0.856431i | \(0.672677\pi\) | |||||||
\(20\) | − | 6.33386i | − | 0.316693i | ||||||
\(21\) | 21.9853 | + | 19.3242i | 1.04692 | + | 0.920202i | ||||
\(22\) | 18.7279 | 0.851269 | ||||||||
\(23\) | 1.13604 | − | 1.96768i | 0.0493930 | − | 0.0855512i | −0.840272 | − | 0.542165i | \(-0.817605\pi\) |
0.889665 | + | 0.456614i | \(0.150938\pi\) | |||||||
\(24\) | 10.2426 | − | 5.91359i | 0.426777 | − | 0.246400i | ||||
\(25\) | −7.48528 | − | 12.9649i | −0.299411 | − | 0.518596i | ||||
\(26\) | −6.72792 | − | 3.88437i | −0.258766 | − | 0.149399i | ||||
\(27\) | − | 2.15232i | − | 0.0797154i | ||||||
\(28\) | −9.24264 | + | 10.5154i | −0.330094 | + | 0.375550i | ||||
\(29\) | 20.4853 | 0.706389 | 0.353195 | − | 0.935550i | \(-0.385095\pi\) | ||||
0.353195 | + | 0.935550i | \(0.385095\pi\) | |||||||
\(30\) | −9.36396 | + | 16.2189i | −0.312132 | + | 0.540629i | ||||
\(31\) | 21.3198 | − | 12.3090i | 0.687736 | − | 0.397064i | −0.115028 | − | 0.993362i | \(-0.536696\pi\) |
0.802763 | + | 0.596298i | \(0.203362\pi\) | |||||||
\(32\) | 2.82843 | + | 4.89898i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −47.9558 | − | 27.6873i | −1.45321 | − | 0.839010i | ||||
\(34\) | 19.1757i | 0.563990i | ||||||||
\(35\) | 4.34924 | − | 21.7377i | 0.124264 | − | 0.621076i | ||||
\(36\) | −16.9706 | −0.471405 | ||||||||
\(37\) | −32.4706 | + | 56.2407i | −0.877583 | + | 1.52002i | −0.0235970 | + | 0.999722i | \(0.507512\pi\) |
−0.853986 | + | 0.520296i | \(0.825821\pi\) | |||||||
\(38\) | −0.878680 | + | 0.507306i | −0.0231231 | + | 0.0133502i | ||||
\(39\) | 11.4853 | + | 19.8931i | 0.294494 | + | 0.510079i | ||||
\(40\) | −7.75736 | − | 4.47871i | −0.193934 | − | 0.111968i | ||||
\(41\) | − | 21.0308i | − | 0.512946i | −0.966551 | − | 0.256473i | \(-0.917439\pi\) | ||
0.966551 | − | 0.256473i | \(-0.0825605\pi\) | |||||||
\(42\) | 39.2132 | − | 13.2621i | 0.933648 | − | 0.315763i | ||||
\(43\) | 6.48528 | 0.150820 | 0.0754102 | − | 0.997153i | \(-0.475973\pi\) | ||||
0.0754102 | + | 0.997153i | \(0.475973\pi\) | |||||||
\(44\) | 13.2426 | − | 22.9369i | 0.300969 | − | 0.521294i | ||||
\(45\) | 23.2721 | − | 13.4361i | 0.517157 | − | 0.298581i | ||||
\(46\) | −1.60660 | − | 2.78272i | −0.0349261 | − | 0.0604938i | ||||
\(47\) | 41.3787 | + | 23.8900i | 0.880397 | + | 0.508298i | 0.870789 | − | 0.491656i | \(-0.163608\pi\) |
0.00960801 | + | 0.999954i | \(0.496942\pi\) | |||||||
\(48\) | − | 16.7262i | − | 0.348462i | ||||||
\(49\) | −38.9411 | + | 29.7420i | −0.794717 | + | 0.606980i | ||||
\(50\) | −21.1716 | −0.423431 | ||||||||
\(51\) | 28.3492 | − | 49.1023i | 0.555867 | − | 0.962791i | ||||
\(52\) | −9.51472 | + | 5.49333i | −0.182975 | + | 0.105641i | ||||
\(53\) | −11.0147 | − | 19.0781i | −0.207825 | − | 0.359963i | 0.743204 | − | 0.669065i | \(-0.233305\pi\) |
−0.951029 | + | 0.309101i | \(0.899972\pi\) | |||||||
\(54\) | −2.63604 | − | 1.52192i | −0.0488155 | − | 0.0281837i | ||||
\(55\) | 41.9385i | 0.762518i | ||||||||
\(56\) | 6.34315 | + | 18.7554i | 0.113270 | + | 0.334918i | ||||
\(57\) | 3.00000 | 0.0526316 | ||||||||
\(58\) | 14.4853 | − | 25.0892i | 0.249746 | − | 0.432573i | ||||
\(59\) | −72.5330 | + | 41.8770i | −1.22937 | + | 0.709779i | −0.966899 | − | 0.255160i | \(-0.917872\pi\) |
−0.262474 | + | 0.964939i | \(0.584538\pi\) | |||||||
\(60\) | 13.2426 | + | 22.9369i | 0.220711 | + | 0.382282i | ||||
\(61\) | 57.3823 | + | 33.1297i | 0.940693 | + | 0.543109i | 0.890177 | − | 0.455614i | \(-0.150580\pi\) |
0.0505153 | + | 0.998723i | \(0.483914\pi\) | |||||||
\(62\) | − | 34.8151i | − | 0.561534i | ||||||
\(63\) | −58.2426 | − | 11.6531i | −0.924486 | − | 0.184970i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 8.69848 | − | 15.0662i | 0.133823 | − | 0.231788i | ||||
\(66\) | −67.8198 | + | 39.1558i | −1.02757 | + | 0.593269i | ||||
\(67\) | −46.3198 | − | 80.2283i | −0.691340 | − | 1.19744i | −0.971399 | − | 0.237454i | \(-0.923687\pi\) |
0.280058 | − | 0.959983i | \(-0.409646\pi\) | |||||||
\(68\) | 23.4853 | + | 13.5592i | 0.345372 | + | 0.199400i | ||||
\(69\) | 9.50079i | 0.137693i | ||||||||
\(70\) | −23.5477 | − | 20.6976i | −0.336396 | − | 0.295680i | ||||
\(71\) | −48.4264 | −0.682062 | −0.341031 | − | 0.940052i | \(-0.610776\pi\) | ||||
−0.341031 | + | 0.940052i | \(0.610776\pi\) | |||||||
\(72\) | −12.0000 | + | 20.7846i | −0.166667 | + | 0.288675i | ||||
\(73\) | 113.441 | − | 65.4953i | 1.55399 | − | 0.897195i | 0.556177 | − | 0.831064i | \(-0.312268\pi\) |
0.997811 | − | 0.0661316i | \(-0.0210657\pi\) | |||||||
\(74\) | 45.9203 | + | 79.5363i | 0.620545 | + | 1.07482i | ||||
\(75\) | 54.2132 | + | 31.3000i | 0.722843 | + | 0.417333i | ||||
\(76\) | 1.43488i | 0.0188800i | ||||||||
\(77\) | 61.1985 | − | 69.6258i | 0.794786 | − | 0.904231i | ||||
\(78\) | 32.4853 | 0.416478 | ||||||||
\(79\) | 38.1066 | − | 66.0026i | 0.482362 | − | 0.835476i | −0.517433 | − | 0.855724i | \(-0.673112\pi\) |
0.999795 | + | 0.0202482i | \(0.00644564\pi\) | |||||||
\(80\) | −10.9706 | + | 6.33386i | −0.137132 | + | 0.0791732i | ||||
\(81\) | 42.6838 | + | 73.9305i | 0.526960 | + | 0.912722i | ||||
\(82\) | −25.7574 | − | 14.8710i | −0.314114 | − | 0.181354i | ||||
\(83\) | 107.981i | 1.30098i | 0.759514 | + | 0.650491i | \(0.225437\pi\) | ||||
−0.759514 | + | 0.650491i | \(0.774563\pi\) | |||||||
\(84\) | 11.4853 | − | 57.4039i | 0.136730 | − | 0.683379i | ||||
\(85\) | −42.9411 | −0.505190 | ||||||||
\(86\) | 4.58579 | − | 7.94282i | 0.0533231 | − | 0.0923583i | ||||
\(87\) | −74.1838 | + | 42.8300i | −0.852687 | + | 0.492299i | ||||
\(88\) | −18.7279 | − | 32.4377i | −0.212817 | − | 0.368610i | ||||
\(89\) | −145.412 | − | 83.9535i | −1.63384 | − | 0.943297i | −0.982894 | − | 0.184173i | \(-0.941039\pi\) |
−0.650945 | − | 0.759125i | \(-0.725627\pi\) | |||||||
\(90\) | − | 38.0031i | − | 0.422257i | ||||||
\(91\) | −36.4264 | + | 12.3196i | −0.400290 | + | 0.135380i | ||||
\(92\) | −4.54416 | −0.0493930 | ||||||||
\(93\) | −51.4706 | + | 89.1496i | −0.553447 | + | 0.958598i | ||||
\(94\) | 58.5183 | − | 33.7856i | 0.622535 | − | 0.359421i | ||||
\(95\) | −1.13604 | − | 1.96768i | −0.0119583 | − | 0.0207124i | ||||
\(96\) | −20.4853 | − | 11.8272i | −0.213388 | − | 0.123200i | ||||
\(97\) | 25.5816i | 0.263728i | 0.991268 | + | 0.131864i | \(0.0420962\pi\) | ||||
−0.991268 | + | 0.131864i | \(0.957904\pi\) | |||||||
\(98\) | 8.89087 | + | 68.7237i | 0.0907232 | + | 0.701263i | ||||
\(99\) | 112.368 | 1.13503 | ||||||||
\(100\) | −14.9706 | + | 25.9298i | −0.149706 | + | 0.259298i | ||||
\(101\) | 24.6838 | − | 14.2512i | 0.244394 | − | 0.141101i | −0.372801 | − | 0.927911i | \(-0.621603\pi\) |
0.617194 | + | 0.786811i | \(0.288269\pi\) | |||||||
\(102\) | −40.0919 | − | 69.4412i | −0.393058 | − | 0.680796i | ||||
\(103\) | 48.9228 | + | 28.2456i | 0.474979 | + | 0.274229i | 0.718322 | − | 0.695711i | \(-0.244911\pi\) |
−0.243343 | + | 0.969940i | \(0.578244\pi\) | |||||||
\(104\) | 15.5375i | 0.149399i | ||||||||
\(105\) | 29.6985 | + | 87.8124i | 0.282843 | + | 0.836308i | ||||
\(106\) | −31.1543 | −0.293909 | ||||||||
\(107\) | −23.8051 | + | 41.2316i | −0.222477 | + | 0.385342i | −0.955560 | − | 0.294798i | \(-0.904748\pi\) |
0.733082 | + | 0.680140i | \(0.238081\pi\) | |||||||
\(108\) | −3.72792 | + | 2.15232i | −0.0345178 | + | 0.0199289i | ||||
\(109\) | −37.6543 | − | 65.2192i | −0.345453 | − | 0.598341i | 0.639983 | − | 0.768389i | \(-0.278941\pi\) |
−0.985436 | + | 0.170047i | \(0.945608\pi\) | |||||||
\(110\) | 51.3640 | + | 29.6550i | 0.466945 | + | 0.269591i | ||||
\(111\) | − | 271.554i | − | 2.44643i | ||||||
\(112\) | 27.4558 | + | 5.49333i | 0.245141 | + | 0.0490475i | ||||
\(113\) | 85.4558 | 0.756246 | 0.378123 | − | 0.925755i | \(-0.376570\pi\) | ||||
0.378123 | + | 0.925755i | \(0.376570\pi\) | |||||||
\(114\) | 2.12132 | − | 3.67423i | 0.0186081 | − | 0.0322301i | ||||
\(115\) | 6.23149 | − | 3.59775i | 0.0541869 | − | 0.0312848i | ||||
\(116\) | −20.4853 | − | 35.4815i | −0.176597 | − | 0.305875i | ||||
\(117\) | −40.3675 | − | 23.3062i | −0.345022 | − | 0.199198i | ||||
\(118\) | 118.446i | 1.00378i | ||||||||
\(119\) | 71.2904 | + | 62.6616i | 0.599079 | + | 0.526568i | ||||
\(120\) | 37.4558 | 0.312132 | ||||||||
\(121\) | −27.1838 | + | 47.0837i | −0.224659 | + | 0.389121i | ||||
\(122\) | 81.1508 | − | 46.8524i | 0.665170 | − | 0.384036i | ||||
\(123\) | 43.9706 | + | 76.1592i | 0.357484 | + | 0.619181i | ||||
\(124\) | −42.6396 | − | 24.6180i | −0.343868 | − | 0.198532i | ||||
\(125\) | − | 126.584i | − | 1.01267i | ||||||
\(126\) | −55.4558 | + | 63.0924i | −0.440126 | + | 0.500733i | ||||
\(127\) | −60.6619 | −0.477653 | −0.238826 | − | 0.971062i | \(-0.576763\pi\) | ||||
−0.238826 | + | 0.971062i | \(0.576763\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −23.4853 | + | 13.5592i | −0.182056 | + | 0.105110i | ||||
\(130\) | −12.3015 | − | 21.3068i | −0.0946270 | − | 0.163899i | ||||
\(131\) | −115.136 | − | 66.4738i | −0.878901 | − | 0.507434i | −0.00860515 | − | 0.999963i | \(-0.502739\pi\) |
−0.870296 | + | 0.492529i | \(0.836072\pi\) | |||||||
\(132\) | 110.749i | 0.839010i | ||||||||
\(133\) | −0.985281 | + | 4.92447i | −0.00740813 | + | 0.0370261i | ||||
\(134\) | −131.012 | −0.977703 | ||||||||
\(135\) | 3.40812 | − | 5.90303i | 0.0252453 | − | 0.0437262i | ||||
\(136\) | 33.2132 | − | 19.1757i | 0.244215 | − | 0.140997i | ||||
\(137\) | 58.7132 | + | 101.694i | 0.428564 | + | 0.742294i | 0.996746 | − | 0.0806089i | \(-0.0256865\pi\) |
−0.568182 | + | 0.822903i | \(0.692353\pi\) | |||||||
\(138\) | 11.6360 | + | 6.71807i | 0.0843191 | + | 0.0486817i | ||||
\(139\) | 68.5857i | 0.493422i | 0.969089 | + | 0.246711i | \(0.0793499\pi\) | ||||
−0.969089 | + | 0.246711i | \(0.920650\pi\) | |||||||
\(140\) | −42.0000 | + | 14.2046i | −0.300000 | + | 0.101461i | ||||
\(141\) | −199.794 | −1.41698 | ||||||||
\(142\) | −34.2426 | + | 59.3100i | −0.241145 | + | 0.417676i | ||||
\(143\) | 63.0000 | − | 36.3731i | 0.440559 | − | 0.254357i | ||||
\(144\) | 16.9706 | + | 29.3939i | 0.117851 | + | 0.204124i | ||||
\(145\) | 56.1838 | + | 32.4377i | 0.387474 | + | 0.223708i | ||||
\(146\) | − | 185.249i | − | 1.26883i | ||||||
\(147\) | 78.8345 | − | 189.122i | 0.536289 | − | 1.28655i | ||||
\(148\) | 129.882 | 0.877583 | ||||||||
\(149\) | 13.1985 | − | 22.8604i | 0.0885804 | − | 0.153426i | −0.818331 | − | 0.574747i | \(-0.805100\pi\) |
0.906911 | + | 0.421322i | \(0.138434\pi\) | |||||||
\(150\) | 76.6690 | − | 44.2649i | 0.511127 | − | 0.295099i | ||||
\(151\) | 67.1066 | + | 116.232i | 0.444415 | + | 0.769749i | 0.998011 | − | 0.0630363i | \(-0.0200784\pi\) |
−0.553597 | + | 0.832785i | \(0.686745\pi\) | |||||||
\(152\) | 1.75736 | + | 1.01461i | 0.0115616 | + | 0.00667508i | ||||
\(153\) | 115.054i | 0.751986i | ||||||||
\(154\) | −42.0000 | − | 124.185i | −0.272727 | − | 0.806399i | ||||
\(155\) | 77.9634 | 0.502990 | ||||||||
\(156\) | 22.9706 | − | 39.7862i | 0.147247 | − | 0.255040i | ||||
\(157\) | −196.323 | + | 113.347i | −1.25047 | + | 0.721958i | −0.971202 | − | 0.238256i | \(-0.923424\pi\) |
−0.279265 | + | 0.960214i | \(0.590091\pi\) | |||||||
\(158\) | −53.8909 | − | 93.3417i | −0.341081 | − | 0.590770i | ||||
\(159\) | 79.7756 | + | 46.0585i | 0.501734 | + | 0.289676i | ||||
\(160\) | 17.9149i | 0.111968i | ||||||||
\(161\) | −15.5955 | − | 3.12032i | −0.0968662 | − | 0.0193808i | ||||
\(162\) | 120.728 | 0.745234 | ||||||||
\(163\) | 45.9889 | − | 79.6550i | 0.282140 | − | 0.488681i | −0.689771 | − | 0.724027i | \(-0.742289\pi\) |
0.971912 | + | 0.235346i | \(0.0756223\pi\) | |||||||
\(164\) | −36.4264 | + | 21.0308i | −0.222112 | + | 0.128237i | ||||
\(165\) | −87.6838 | − | 151.873i | −0.531417 | − | 0.920441i | ||||
\(166\) | 132.250 | + | 76.3544i | 0.796685 | + | 0.459967i | ||||
\(167\) | 203.482i | 1.21845i | 0.792996 | + | 0.609227i | \(0.208520\pi\) | ||||
−0.792996 | + | 0.609227i | \(0.791480\pi\) | |||||||
\(168\) | −62.1838 | − | 54.6572i | −0.370141 | − | 0.325340i | ||||
\(169\) | 138.823 | 0.821440 | ||||||||
\(170\) | −30.3640 | + | 52.5919i | −0.178612 | + | 0.309364i | ||||
\(171\) | −5.27208 | + | 3.04384i | −0.0308309 | + | 0.0178002i | ||||
\(172\) | −6.48528 | − | 11.2328i | −0.0377051 | − | 0.0653072i | ||||
\(173\) | 61.3234 | + | 35.4051i | 0.354470 | + | 0.204654i | 0.666652 | − | 0.745369i | \(-0.267727\pi\) |
−0.312182 | + | 0.950022i | \(0.601060\pi\) | |||||||
\(174\) | 121.142i | 0.696216i | ||||||||
\(175\) | −69.1838 | + | 78.7107i | −0.395336 | + | 0.449775i | ||||
\(176\) | −52.9706 | −0.300969 | ||||||||
\(177\) | 175.110 | − | 303.300i | 0.989323 | − | 1.71356i | ||||
\(178\) | −205.643 | + | 118.728i | −1.15530 | + | 0.667012i | ||||
\(179\) | −54.4081 | − | 94.2376i | −0.303956 | − | 0.526467i | 0.673072 | − | 0.739577i | \(-0.264974\pi\) |
−0.977028 | + | 0.213109i | \(0.931641\pi\) | |||||||
\(180\) | −46.5442 | − | 26.8723i | −0.258579 | − | 0.149290i | ||||
\(181\) | − | 99.6607i | − | 0.550611i | −0.961357 | − | 0.275306i | \(-0.911221\pi\) | ||
0.961357 | − | 0.275306i | \(-0.0887791\pi\) | |||||||
\(182\) | −10.6690 | + | 53.3243i | −0.0586211 | + | 0.292991i | ||||
\(183\) | −277.066 | −1.51402 | ||||||||
\(184\) | −3.21320 | + | 5.56543i | −0.0174631 | + | 0.0302469i | ||||
\(185\) | −178.110 | + | 102.832i | −0.962758 | + | 0.555848i | ||||
\(186\) | 72.7904 | + | 126.077i | 0.391346 | + | 0.677831i | ||||
\(187\) | −155.504 | − | 89.7800i | −0.831570 | − | 0.480107i | ||||
\(188\) | − | 95.5600i | − | 0.508298i | ||||||
\(189\) | −14.2721 | + | 4.82687i | −0.0755136 | + | 0.0255390i | ||||
\(190\) | −3.21320 | −0.0169116 | ||||||||
\(191\) | −34.9523 | + | 60.5391i | −0.182996 | + | 0.316959i | −0.942899 | − | 0.333077i | \(-0.891913\pi\) |
0.759903 | + | 0.650036i | \(0.225246\pi\) | |||||||
\(192\) | −28.9706 | + | 16.7262i | −0.150888 | + | 0.0871154i | ||||
\(193\) | 16.1690 | + | 28.0056i | 0.0837774 | + | 0.145107i | 0.904870 | − | 0.425689i | \(-0.139968\pi\) |
−0.821092 | + | 0.570796i | \(0.806635\pi\) | |||||||
\(194\) | 31.3310 | + | 18.0889i | 0.161500 | + | 0.0932419i | ||||
\(195\) | 72.7461i | 0.373057i | ||||||||
\(196\) | 90.4558 | + | 37.7060i | 0.461509 | + | 0.192377i | ||||
\(197\) | 277.103 | 1.40661 | 0.703306 | − | 0.710887i | \(-0.251706\pi\) | ||||
0.703306 | + | 0.710887i | \(0.251706\pi\) | |||||||
\(198\) | 79.4558 | − | 137.622i | 0.401292 | − | 0.695058i | ||||
\(199\) | 145.011 | − | 83.7222i | 0.728699 | − | 0.420715i | −0.0892469 | − | 0.996010i | \(-0.528446\pi\) |
0.817946 | + | 0.575295i | \(0.195113\pi\) | |||||||
\(200\) | 21.1716 | + | 36.6702i | 0.105858 | + | 0.183351i | ||||
\(201\) | 335.478 | + | 193.688i | 1.66904 | + | 0.963623i | ||||
\(202\) | − | 40.3084i | − | 0.199547i | ||||||
\(203\) | −45.9411 | − | 135.839i | −0.226311 | − | 0.669155i | ||||
\(204\) | −113.397 | −0.555867 | ||||||||
\(205\) | 33.3015 | − | 57.6799i | 0.162446 | − | 0.281365i | ||||
\(206\) | 69.1873 | − | 39.9453i | 0.335861 | − | 0.193909i | ||||
\(207\) | −9.63961 | − | 16.6963i | −0.0465682 | − | 0.0806584i | ||||
\(208\) | 19.0294 | + | 10.9867i | 0.0914877 | + | 0.0528204i | ||||
\(209\) | − | 9.50079i | − | 0.0454583i | ||||||
\(210\) | 128.548 | + | 25.7196i | 0.612132 | + | 0.122474i | ||||
\(211\) | −128.073 | −0.606982 | −0.303491 | − | 0.952834i | \(-0.598152\pi\) | ||||
−0.303491 | + | 0.952834i | \(0.598152\pi\) | |||||||
\(212\) | −22.0294 | + | 38.1561i | −0.103912 | + | 0.179982i | ||||
\(213\) | 175.368 | − | 101.248i | 0.823322 | − | 0.475345i | ||||
\(214\) | 33.6655 | + | 58.3103i | 0.157315 | + | 0.272478i | ||||
\(215\) | 17.7868 | + | 10.2692i | 0.0827293 | + | 0.0477638i | ||||
\(216\) | 6.08767i | 0.0281837i | ||||||||
\(217\) | −129.434 | − | 113.768i | −0.596470 | − | 0.524275i | ||||
\(218\) | −106.503 | −0.488544 | ||||||||
\(219\) | −273.871 | + | 474.359i | −1.25055 | + | 2.16602i | ||||
\(220\) | 72.6396 | − | 41.9385i | 0.330180 | − | 0.190630i | ||||
\(221\) | 37.2426 | + | 64.5061i | 0.168519 | + | 0.291883i | ||||
\(222\) | −332.584 | − | 192.018i | −1.49813 | − | 0.864944i | ||||
\(223\) | − | 417.169i | − | 1.87071i | −0.353705 | − | 0.935357i | \(-0.615078\pi\) | ||
0.353705 | − | 0.935357i | \(-0.384922\pi\) | |||||||
\(224\) | 26.1421 | − | 29.7420i | 0.116706 | − | 0.132777i | ||||
\(225\) | −127.029 | −0.564575 | ||||||||
\(226\) | 60.4264 | − | 104.662i | 0.267373 | − | 0.463104i | ||||
\(227\) | 201.143 | − | 116.130i | 0.886093 | − | 0.511586i | 0.0134307 | − | 0.999910i | \(-0.495725\pi\) |
0.872663 | + | 0.488324i | \(0.162391\pi\) | |||||||
\(228\) | −3.00000 | − | 5.19615i | −0.0131579 | − | 0.0227901i | ||||
\(229\) | −72.4188 | − | 41.8110i | −0.316239 | − | 0.182581i | 0.333476 | − | 0.942759i | \(-0.391778\pi\) |
−0.649715 | + | 0.760178i | \(0.725112\pi\) | |||||||
\(230\) | − | 10.1760i | − | 0.0442434i | ||||||
\(231\) | −76.0477 | + | 380.089i | −0.329211 | + | 1.64541i | ||||
\(232\) | −57.9411 | −0.249746 | ||||||||
\(233\) | −109.537 | + | 189.723i | −0.470114 | + | 0.814261i | −0.999416 | − | 0.0341721i | \(-0.989121\pi\) |
0.529302 | + | 0.848434i | \(0.322454\pi\) | |||||||
\(234\) | −57.0883 | + | 32.9600i | −0.243967 | + | 0.140854i | ||||
\(235\) | 75.6579 | + | 131.043i | 0.321949 | + | 0.557631i | ||||
\(236\) | 145.066 | + | 83.7539i | 0.614687 | + | 0.354889i | ||||
\(237\) | 318.689i | 1.34468i | ||||||||
\(238\) | 127.154 | − | 43.0041i | 0.534262 | − | 0.180689i | ||||
\(239\) | 193.103 | 0.807961 | 0.403980 | − | 0.914768i | \(-0.367626\pi\) | ||||
0.403980 | + | 0.914768i | \(0.367626\pi\) | |||||||
\(240\) | 26.4853 | − | 45.8739i | 0.110355 | − | 0.191141i | ||||
\(241\) | 42.8970 | − | 24.7666i | 0.177996 | − | 0.102766i | −0.408355 | − | 0.912823i | \(-0.633897\pi\) |
0.586351 | + | 0.810057i | \(0.300564\pi\) | |||||||
\(242\) | 38.4437 | + | 66.5864i | 0.158858 | + | 0.275150i | ||||
\(243\) | −292.368 | − | 168.798i | −1.20316 | − | 0.694644i | ||||
\(244\) | − | 132.519i | − | 0.543109i | ||||||
\(245\) | −153.897 | + | 19.9098i | −0.628151 | + | 0.0812646i | ||||
\(246\) | 124.368 | 0.505559 | ||||||||
\(247\) | −1.97056 | + | 3.41311i | −0.00797799 | + | 0.0138183i | ||||
\(248\) | −60.3015 | + | 34.8151i | −0.243151 | + | 0.140383i | ||||
\(249\) | −225.765 | − | 391.036i | −0.906685 | − | 1.57042i | ||||
\(250\) | −155.033 | − | 89.5083i | −0.620132 | − | 0.358033i | ||||
\(251\) | 162.524i | 0.647507i | 0.946141 | + | 0.323754i | \(0.104945\pi\) | ||||
−0.946141 | + | 0.323754i | \(0.895055\pi\) | |||||||
\(252\) | 38.0589 | + | 112.532i | 0.151027 | + | 0.446557i | ||||
\(253\) | 30.0883 | 0.118926 | ||||||||
\(254\) | −42.8944 | + | 74.2954i | −0.168876 | + | 0.292501i | ||||
\(255\) | 155.504 | − | 89.7800i | 0.609818 | − | 0.352079i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −85.8747 | − | 49.5798i | −0.334143 | − | 0.192917i | 0.323536 | − | 0.946216i | \(-0.395128\pi\) |
−0.657679 | + | 0.753298i | \(0.728462\pi\) | |||||||
\(258\) | 38.3513i | 0.148648i | ||||||||
\(259\) | 445.753 | + | 89.1857i | 1.72106 | + | 0.344346i | ||||
\(260\) | −34.7939 | −0.133823 | ||||||||
\(261\) | 86.9117 | − | 150.535i | 0.332995 | − | 0.576764i | ||||
\(262\) | −162.827 | + | 94.0082i | −0.621477 | + | 0.358810i | ||||
\(263\) | −217.173 | − | 376.154i | −0.825751 | − | 1.43024i | −0.901344 | − | 0.433105i | \(-0.857418\pi\) |
0.0755923 | − | 0.997139i | \(-0.475915\pi\) | |||||||
\(264\) | 135.640 | + | 78.3116i | 0.513786 | + | 0.296635i | ||||
\(265\) | − | 69.7657i | − | 0.263267i | ||||||
\(266\) | 5.33452 | + | 4.68885i | 0.0200546 | + | 0.0176272i | ||||
\(267\) | 702.110 | 2.62962 | ||||||||
\(268\) | −92.6396 | + | 160.457i | −0.345670 | + | 0.598718i | ||||
\(269\) | −79.1619 | + | 45.7041i | −0.294282 | + | 0.169904i | −0.639871 | − | 0.768482i | \(-0.721012\pi\) |
0.345589 | + | 0.938386i | \(0.387679\pi\) | |||||||
\(270\) | −4.81981 | − | 8.34815i | −0.0178511 | − | 0.0309191i | ||||
\(271\) | 14.8051 | + | 8.54772i | 0.0546313 | + | 0.0315414i | 0.527067 | − | 0.849824i | \(-0.323292\pi\) |
−0.472436 | + | 0.881365i | \(0.656625\pi\) | |||||||
\(272\) | − | 54.2369i | − | 0.199400i | ||||||
\(273\) | 106.154 | − | 120.772i | 0.388844 | − | 0.442389i | ||||
\(274\) | 166.066 | 0.606080 | ||||||||
\(275\) | 99.1249 | − | 171.689i | 0.360454 | − | 0.624325i | ||||
\(276\) | 16.4558 | − | 9.50079i | 0.0596226 | − | 0.0344231i | ||||
\(277\) | 200.206 | + | 346.766i | 0.722764 | + | 1.25186i | 0.959888 | + | 0.280385i | \(0.0904620\pi\) |
−0.237124 | + | 0.971479i | \(0.576205\pi\) | |||||||
\(278\) | 84.0000 | + | 48.4974i | 0.302158 | + | 0.174451i | ||||
\(279\) | − | 208.891i | − | 0.748712i | ||||||
\(280\) | −12.3015 | + | 61.4834i | −0.0439340 | + | 0.219584i | ||||
\(281\) | −538.690 | −1.91705 | −0.958524 | − | 0.285012i | \(-0.908002\pi\) | ||||
−0.958524 | + | 0.285012i | \(0.908002\pi\) | |||||||
\(282\) | −141.276 | + | 244.697i | −0.500977 | + | 0.867718i | ||||
\(283\) | −267.783 | + | 154.604i | −0.946229 | + | 0.546306i | −0.891907 | − | 0.452218i | \(-0.850633\pi\) |
−0.0543215 | + | 0.998523i | \(0.517300\pi\) | |||||||
\(284\) | 48.4264 | + | 83.8770i | 0.170516 | + | 0.295342i | ||||
\(285\) | 8.22792 | + | 4.75039i | 0.0288699 | + | 0.0166680i | ||||
\(286\) | − | 102.879i | − | 0.359715i | ||||||
\(287\) | −139.456 | + | 47.1645i | −0.485909 | + | 0.164336i | ||||
\(288\) | 48.0000 | 0.166667 | ||||||||
\(289\) | −52.5736 | + | 91.0601i | −0.181916 | + | 0.315087i | ||||
\(290\) | 79.4558 | − | 45.8739i | 0.273986 | − | 0.158186i | ||||
\(291\) | −53.4853 | − | 92.6392i | −0.183798 | − | 0.318348i | ||||
\(292\) | −226.882 | − | 130.991i | −0.776994 | − | 0.448598i | ||||
\(293\) | 327.391i | 1.11738i | 0.829378 | + | 0.558688i | \(0.188695\pi\) | ||||
−0.829378 | + | 0.558688i | \(0.811305\pi\) | |||||||
\(294\) | −175.882 | − | 230.282i | −0.598239 | − | 0.783272i | ||||
\(295\) | −265.243 | −0.899128 | ||||||||
\(296\) | 91.8406 | − | 159.073i | 0.310272 | − | 0.537408i | ||||
\(297\) | 24.6838 | − | 14.2512i | 0.0831103 | − | 0.0479838i | ||||
\(298\) | −18.6655 | − | 32.3296i | −0.0626358 | − | 0.108488i | ||||
\(299\) | −10.8091 | − | 6.24063i | −0.0361508 | − | 0.0208717i | ||||
\(300\) | − | 125.200i | − | 0.417333i | ||||||
\(301\) | −14.5442 | − | 43.0041i | −0.0483195 | − | 0.142871i | ||||
\(302\) | 189.806 | 0.628497 | ||||||||
\(303\) | −59.5919 | + | 103.216i | −0.196673 | + | 0.340647i | ||||
\(304\) | 2.48528 | − | 1.43488i | 0.00817527 | − | 0.00471999i | ||||
\(305\) | 104.919 | + | 181.725i | 0.343998 | + | 0.595821i | ||||
\(306\) | 140.912 | + | 81.3554i | 0.460496 | + | 0.265867i | ||||
\(307\) | 256.140i | 0.834331i | 0.908831 | + | 0.417165i | \(0.136976\pi\) | ||||
−0.908831 | + | 0.417165i | \(0.863024\pi\) | |||||||
\(308\) | −181.794 | − | 36.3731i | −0.590240 | − | 0.118094i | ||||
\(309\) | −236.220 | −0.764467 | ||||||||
\(310\) | 55.1285 | − | 95.4853i | 0.177834 | − | 0.308017i | ||||
\(311\) | 187.349 | − | 108.166i | 0.602409 | − | 0.347801i | −0.167580 | − | 0.985859i | \(-0.553595\pi\) |
0.769989 | + | 0.638057i | \(0.220262\pi\) | |||||||
\(312\) | −32.4853 | − | 56.2662i | −0.104119 | − | 0.180340i | ||||
\(313\) | 135.809 | + | 78.4092i | 0.433893 | + | 0.250509i | 0.701004 | − | 0.713157i | \(-0.252736\pi\) |
−0.267110 | + | 0.963666i | \(0.586069\pi\) | |||||||
\(314\) | 320.595i | 1.02100i | ||||||||
\(315\) | −141.286 | − | 124.185i | −0.448528 | − | 0.394239i | ||||
\(316\) | −152.426 | −0.482362 | ||||||||
\(317\) | 224.015 | − | 388.005i | 0.706671 | − | 1.22399i | −0.259414 | − | 0.965766i | \(-0.583529\pi\) |
0.966085 | − | 0.258224i | \(-0.0831372\pi\) | |||||||
\(318\) | 112.820 | − | 65.1365i | 0.354779 | − | 0.204832i | ||||
\(319\) | 135.640 | + | 234.935i | 0.425203 | + | 0.736472i | ||||
\(320\) | 21.9411 | + | 12.6677i | 0.0685660 | + | 0.0395866i | ||||
\(321\) | − | 199.084i | − | 0.620199i | ||||||
\(322\) | −14.8492 | + | 16.8941i | −0.0461157 | + | 0.0524660i | ||||
\(323\) | 9.72792 | 0.0301174 | ||||||||
\(324\) | 85.3675 | − | 147.861i | 0.263480 | − | 0.456361i | ||||
\(325\) | −71.2203 | + | 41.1191i | −0.219140 | + | 0.126520i | ||||
\(326\) | −65.0381 | − | 112.649i | −0.199503 | − | 0.345550i | ||||
\(327\) | 272.717 | + | 157.453i | 0.833996 | + | 0.481508i | ||||
\(328\) | 59.4841i | 0.181354i | ||||||||
\(329\) | 65.6177 | − | 327.960i | 0.199446 | − | 0.996839i | ||||
\(330\) | −248.007 | −0.751537 | ||||||||
\(331\) | 27.5036 | − | 47.6376i | 0.0830924 | − | 0.143920i | −0.821484 | − | 0.570231i | \(-0.806854\pi\) |
0.904577 | + | 0.426311i | \(0.140187\pi\) | |||||||
\(332\) | 187.029 | − | 107.981i | 0.563342 | − | 0.325245i | ||||
\(333\) | 275.522 | + | 477.218i | 0.827393 | + | 1.43309i | ||||
\(334\) | 249.213 | + | 143.883i | 0.746147 | + | 0.430788i | ||||
\(335\) | − | 293.383i | − | 0.875770i | ||||||
\(336\) | −110.912 | + | 37.5108i | −0.330094 | + | 0.111639i | ||||
\(337\) | −111.632 | −0.331254 | −0.165627 | − | 0.986189i | \(-0.552965\pi\) | ||||
−0.165627 | + | 0.986189i | \(0.552965\pi\) | |||||||
\(338\) | 98.1630 | − | 170.023i | 0.290423 | − | 0.503027i | ||||
\(339\) | −309.463 | + | 178.669i | −0.912870 | + | 0.527046i | ||||
\(340\) | 42.9411 | + | 74.3762i | 0.126297 | + | 0.218754i | ||||
\(341\) | 282.331 | + | 163.004i | 0.827949 | + | 0.478016i | ||||
\(342\) | 8.60927i | 0.0251733i | ||||||||
\(343\) | 284.551 | + | 191.519i | 0.829596 | + | 0.558365i | ||||
\(344\) | −18.3431 | −0.0533231 | ||||||||
\(345\) | −15.0442 | + | 26.0572i | −0.0436062 | + | 0.0755282i | ||||
\(346\) | 86.7244 | − | 50.0703i | 0.250648 | − | 0.144712i | ||||
\(347\) | −188.628 | − | 326.714i | −0.543598 | − | 0.941539i | −0.998694 | − | 0.0510967i | \(-0.983728\pi\) |
0.455096 | − | 0.890442i | \(-0.349605\pi\) | |||||||
\(348\) | 148.368 | + | 85.6600i | 0.426343 | + | 0.246150i | ||||
\(349\) | − | 204.034i | − | 0.584624i | −0.956323 | − | 0.292312i | \(-0.905575\pi\) | ||
0.956323 | − | 0.292312i | \(-0.0944246\pi\) | |||||||
\(350\) | 47.4802 | + | 140.389i | 0.135658 | + | 0.401112i | ||||
\(351\) | −11.8234 | −0.0336848 | ||||||||
\(352\) | −37.4558 | + | 64.8754i | −0.106409 | + | 0.184305i | ||||
\(353\) | −361.198 | + | 208.538i | −1.02323 | + | 0.590759i | −0.915036 | − | 0.403371i | \(-0.867838\pi\) |
−0.108189 | + | 0.994130i | \(0.534505\pi\) | |||||||
\(354\) | −247.643 | − | 428.931i | −0.699557 | − | 1.21167i | ||||
\(355\) | −132.816 | − | 76.6815i | −0.374130 | − | 0.216004i | ||||
\(356\) | 335.814i | 0.943297i | ||||||||
\(357\) | −389.176 | − | 77.8658i | −1.09013 | − | 0.218112i | ||||
\(358\) | −153.889 | −0.429859 | ||||||||
\(359\) | 89.4153 | − | 154.872i | 0.249068 | − | 0.431398i | −0.714200 | − | 0.699942i | \(-0.753209\pi\) |
0.963267 | + | 0.268544i | \(0.0865425\pi\) | |||||||
\(360\) | −65.8234 | + | 38.0031i | −0.182843 | + | 0.105564i | ||||
\(361\) | −180.243 | − | 312.189i | −0.499287 | − | 0.864791i | ||||
\(362\) | −122.059 | − | 70.4707i | −0.337179 | − | 0.194671i | ||||
\(363\) | − | 227.340i | − | 0.626281i | ||||||
\(364\) | 57.7645 | + | 50.7728i | 0.158694 | + | 0.139486i | ||||
\(365\) | 414.838 | 1.13654 | ||||||||
\(366\) | −195.915 | + | 339.335i | −0.535288 | + | 0.927145i | ||||
\(367\) | −544.724 | + | 314.497i | −1.48426 | + | 0.856939i | −0.999840 | − | 0.0178960i | \(-0.994303\pi\) |
−0.484422 | + | 0.874835i | \(0.660970\pi\) | |||||||
\(368\) | 4.54416 | + | 7.87071i | 0.0123482 | + | 0.0213878i | ||||
\(369\) | −154.544 | − | 89.2261i | −0.418819 | − | 0.241805i | ||||
\(370\) | 290.853i | 0.786088i | ||||||||
\(371\) | −101.805 | + | 115.824i | −0.274407 | + | 0.312194i | ||||
\(372\) | 205.882 | 0.553447 | ||||||||
\(373\) | 127.779 | − | 221.320i | 0.342572 | − | 0.593351i | −0.642338 | − | 0.766422i | \(-0.722035\pi\) |
0.984910 | + | 0.173070i | \(0.0553687\pi\) | |||||||
\(374\) | −219.915 | + | 126.968i | −0.588009 | + | 0.339487i | ||||
\(375\) | 264.658 | + | 458.401i | 0.705754 | + | 1.22240i | ||||
\(376\) | −117.037 | − | 67.5711i | −0.311267 | − | 0.179710i | ||||
\(377\) | − | 112.532i | − | 0.298494i | ||||||
\(378\) | −4.18019 | + | 20.8928i | −0.0110587 | + | 0.0552719i | ||||
\(379\) | 219.750 | 0.579816 | 0.289908 | − | 0.957055i | \(-0.406375\pi\) | ||||
0.289908 | + | 0.957055i | \(0.406375\pi\) | |||||||
\(380\) | −2.27208 | + | 3.93535i | −0.00597915 | + | 0.0103562i | ||||
\(381\) | 219.676 | − | 126.830i | 0.576578 | − | 0.332887i | ||||
\(382\) | 49.4300 | + | 85.6152i | 0.129398 | + | 0.224124i | ||||
\(383\) | −14.7534 | − | 8.51785i | −0.0385205 | − | 0.0222398i | 0.480616 | − | 0.876931i | \(-0.340413\pi\) |
−0.519137 | + | 0.854691i | \(0.673746\pi\) | |||||||
\(384\) | 47.3087i | 0.123200i | ||||||||
\(385\) | 278.095 | − | 94.0530i | 0.722326 | − | 0.244293i | ||||
\(386\) | 45.7330 | 0.118479 | ||||||||
\(387\) | 27.5147 | − | 47.6569i | 0.0710975 | − | 0.123144i | ||||
\(388\) | 44.3087 | − | 25.5816i | 0.114198 | − | 0.0659320i | ||||
\(389\) | 76.1102 | + | 131.827i | 0.195656 | + | 0.338886i | 0.947115 | − | 0.320893i | \(-0.103983\pi\) |
−0.751459 | + | 0.659779i | \(0.770650\pi\) | |||||||
\(390\) | 89.0955 | + | 51.4393i | 0.228450 | + | 0.131896i | ||||
\(391\) | 30.8076i | 0.0787919i | ||||||||
\(392\) | 110.142 | − | 84.1232i | 0.280975 | − | 0.214600i | ||||
\(393\) | 555.926 | 1.41457 | ||||||||
\(394\) | 195.941 | − | 339.380i | 0.497313 | − | 0.861371i | ||||
\(395\) | 209.025 | − | 120.681i | 0.529178 | − | 0.305521i | ||||
\(396\) | −112.368 | − | 194.626i | −0.283756 | − | 0.491480i | ||||
\(397\) | −322.786 | − | 186.361i | −0.813064 | − | 0.469423i | 0.0349549 | − | 0.999389i | \(-0.488871\pi\) |
−0.848019 | + | 0.529966i | \(0.822205\pi\) | |||||||
\(398\) | − | 236.802i | − | 0.594980i | ||||||
\(399\) | −6.72792 | − | 19.8931i | −0.0168620 | − | 0.0498574i | ||||
\(400\) | 59.8823 | 0.149706 | ||||||||
\(401\) | −325.786 | + | 564.279i | −0.812435 | + | 1.40718i | 0.0987205 | + | 0.995115i | \(0.468525\pi\) |
−0.911155 | + | 0.412063i | \(0.864808\pi\) | |||||||
\(402\) | 474.437 | − | 273.916i | 1.18019 | − | 0.681384i | ||||
\(403\) | −67.6173 | − | 117.117i | −0.167785 | − | 0.290612i | ||||
\(404\) | −49.3675 | − | 28.5024i | −0.122197 | − | 0.0705504i | ||||
\(405\) | 270.353i | 0.667538i | ||||||||
\(406\) | −198.853 | − | 39.7862i | −0.489785 | − | 0.0979955i | ||||
\(407\) | −859.992 | −2.11300 | ||||||||
\(408\) | −80.1838 | + | 138.882i | −0.196529 | + | 0.340398i | ||||
\(409\) | 462.081 | − | 266.782i | 1.12978 | − | 0.652280i | 0.185902 | − | 0.982568i | \(-0.440479\pi\) |
0.943880 | + | 0.330289i | \(0.107146\pi\) | |||||||
\(410\) | −47.0955 | − | 81.5717i | −0.114867 | − | 0.198955i | ||||
\(411\) | −425.239 | − | 245.512i | −1.03464 | − | 0.597352i | ||||
\(412\) | − | 112.982i | − | 0.274229i | ||||||
\(413\) | 440.353 | + | 387.054i | 1.06623 | + | 0.937176i | ||||
\(414\) | −27.2649 | −0.0658573 | ||||||||
\(415\) | −170.985 | + | 296.154i | −0.412012 | + | 0.713625i | ||||
\(416\) | 26.9117 | − | 15.5375i | 0.0646916 | − | 0.0373497i | ||||
\(417\) | −143.397 | − | 248.371i | −0.343878 | − | 0.595614i | ||||
\(418\) | −11.6360 | − | 6.71807i | −0.0278374 | − | 0.0160719i | ||||
\(419\) | 534.252i | 1.27507i | 0.770423 | + | 0.637533i | \(0.220045\pi\) | ||||
−0.770423 | + | 0.637533i | \(0.779955\pi\) | |||||||
\(420\) | 122.397 | − | 139.252i | 0.291421 | − | 0.331552i | ||||
\(421\) | 157.220 | 0.373445 | 0.186723 | − | 0.982413i | \(-0.440213\pi\) | ||||
0.186723 | + | 0.982413i | \(0.440213\pi\) | |||||||
\(422\) | −90.5614 | + | 156.857i | −0.214600 | + | 0.371699i | ||||
\(423\) | 351.110 | − | 202.713i | 0.830047 | − | 0.479228i | ||||
\(424\) | 31.1543 | + | 53.9609i | 0.0734772 | + | 0.127266i | ||||
\(425\) | 175.794 | + | 101.495i | 0.413633 | + | 0.238811i | ||||
\(426\) | − | 286.374i | − | 0.672239i | ||||||
\(427\) | 90.9960 | − | 454.801i | 0.213105 | − | 1.06511i | ||||
\(428\) | 95.2203 | 0.222477 | ||||||||
\(429\) | −152.095 | + | 263.437i | −0.354535 | + | 0.614072i | ||||
\(430\) | 25.1543 | − | 14.5229i | 0.0584984 | − | 0.0337741i | ||||
\(431\) | 114.268 | + | 197.918i | 0.265123 | + | 0.459207i | 0.967596 | − | 0.252504i | \(-0.0812541\pi\) |
−0.702473 | + | 0.711711i | \(0.747921\pi\) | |||||||
\(432\) | 7.45584 | + | 4.30463i | 0.0172589 | + | 0.00996443i | ||||
\(433\) | − | 47.5549i | − | 0.109827i | −0.998491 | − | 0.0549133i | \(-0.982512\pi\) | ||
0.998491 | − | 0.0549133i | \(-0.0174882\pi\) | |||||||
\(434\) | −230.860 | + | 78.0778i | −0.531935 | + | 0.179903i | ||||
\(435\) | −271.279 | −0.623630 | ||||||||
\(436\) | −75.3087 | + | 130.438i | −0.172726 | + | 0.299171i | ||||
\(437\) | −1.41169 | + | 0.815039i | −0.00323041 | + | 0.00186508i | ||||
\(438\) | 387.312 | + | 670.844i | 0.884274 | + | 1.53161i | ||||
\(439\) | −63.9594 | − | 36.9270i | −0.145693 | − | 0.0841161i | 0.425381 | − | 0.905014i | \(-0.360140\pi\) |
−0.571075 | + | 0.820898i | \(0.693473\pi\) | |||||||
\(440\) | − | 118.620i | − | 0.269591i | ||||||
\(441\) | 53.3452 | + | 412.342i | 0.120964 | + | 0.935017i | ||||
\(442\) | 105.338 | 0.238321 | ||||||||
\(443\) | −117.320 | + | 203.204i | −0.264830 | + | 0.458699i | −0.967519 | − | 0.252798i | \(-0.918649\pi\) |
0.702689 | + | 0.711497i | \(0.251983\pi\) | |||||||
\(444\) | −470.345 | + | 271.554i | −1.05934 | + | 0.611608i | ||||
\(445\) | −265.875 | − | 460.508i | −0.597471 | − | 1.03485i | ||||
\(446\) | −510.926 | − | 294.983i | −1.14557 | − | 0.661397i | ||||
\(447\) | 110.380i | 0.246935i | ||||||||
\(448\) | −17.9411 | − | 53.0482i | −0.0400472 | − | 0.118411i | ||||
\(449\) | −255.161 | −0.568288 | −0.284144 | − | 0.958782i | \(-0.591709\pi\) | ||||
−0.284144 | + | 0.958782i | \(0.591709\pi\) | |||||||
\(450\) | −89.8234 | + | 155.579i | −0.199608 | + | 0.345730i | ||||
\(451\) | 241.191 | − | 139.252i | 0.534791 | − | 0.308762i | ||||
\(452\) | −85.4558 | − | 148.014i | −0.189062 | − | 0.327464i | ||||
\(453\) | −486.029 | − | 280.609i | −1.07291 | − | 0.619446i | ||||
\(454\) | − | 328.465i | − | 0.723492i | ||||||
\(455\) | −119.412 | − | 23.8918i | −0.262444 | − | 0.0525095i | ||||
\(456\) | −8.48528 | −0.0186081 | ||||||||
\(457\) | 72.8675 | − | 126.210i | 0.159448 | − | 0.276171i | −0.775222 | − | 0.631689i | \(-0.782362\pi\) |
0.934670 | + | 0.355518i | \(0.115695\pi\) | |||||||
\(458\) | −102.416 | + | 59.1297i | −0.223615 | + | 0.129104i | ||||
\(459\) | 14.5919 | + | 25.2739i | 0.0317906 | + | 0.0550629i | ||||
\(460\) | −12.4630 | − | 7.19551i | −0.0270934 | − | 0.0156424i | ||||
\(461\) | − | 888.329i | − | 1.92696i | −0.267777 | − | 0.963481i | \(-0.586289\pi\) | ||
0.267777 | − | 0.963481i | \(-0.413711\pi\) | |||||||
\(462\) | 411.739 | + | 361.903i | 0.891209 | + | 0.783339i | ||||
\(463\) | 234.014 | 0.505430 | 0.252715 | − | 0.967541i | \(-0.418676\pi\) | ||||
0.252715 | + | 0.967541i | \(0.418676\pi\) | |||||||
\(464\) | −40.9706 | + | 70.9631i | −0.0882986 | + | 0.152938i | ||||
\(465\) | −282.331 | + | 163.004i | −0.607162 | + | 0.350545i | ||||
\(466\) | 154.908 | + | 268.309i | 0.332421 | + | 0.575770i | ||||
\(467\) | 681.231 | + | 393.309i | 1.45874 | + | 0.842204i | 0.998950 | − | 0.0458237i | \(-0.0145912\pi\) |
0.459790 | + | 0.888028i | \(0.347925\pi\) | |||||||
\(468\) | 93.2248i | 0.199198i | ||||||||
\(469\) | −428.117 | + | 487.071i | −0.912830 | + | 1.03853i | ||||
\(470\) | 213.993 | 0.455304 | ||||||||
\(471\) | 473.967 | − | 820.934i | 1.00630 | − | 1.74296i | ||||
\(472\) | 205.154 | − | 118.446i | 0.434649 | − | 0.250945i | ||||
\(473\) | 42.9411 | + | 74.3762i | 0.0907846 | + | 0.157244i | ||||
\(474\) | 390.312 | + | 225.347i | 0.823444 | + | 0.475415i | ||||
\(475\) | 10.7405i | 0.0226115i | ||||||||
\(476\) | 37.2426 | − | 186.140i | 0.0782408 | − | 0.391051i | ||||
\(477\) | −186.926 | −0.391878 | ||||||||
\(478\) | 136.544 | − | 236.501i | 0.285657 | − | 0.494773i | ||||
\(479\) | 638.202 | − | 368.466i | 1.33236 | − | 0.769240i | 0.346702 | − | 0.937975i | \(-0.387302\pi\) |
0.985661 | + | 0.168735i | \(0.0539682\pi\) | |||||||
\(480\) | −37.4558 | − | 64.8754i | −0.0780330 | − | 0.135157i | ||||
\(481\) | 308.948 | + | 178.371i | 0.642304 | + | 0.370834i | ||||
\(482\) | − | 70.0505i | − | 0.145333i | ||||||
\(483\) | 63.0000 | − | 21.3068i | 0.130435 | − | 0.0441136i | ||||
\(484\) | 108.735 | 0.224659 | ||||||||
\(485\) | −40.5076 | + | 70.1612i | −0.0835208 | + | 0.144662i | ||||
\(486\) | −413.470 | + | 238.717i | −0.850762 | + | 0.491187i | ||||
\(487\) | −135.349 | − | 234.432i | −0.277925 | − | 0.481379i | 0.692944 | − | 0.720991i | \(-0.256313\pi\) |
−0.970869 | + | 0.239612i | \(0.922980\pi\) | |||||||
\(488\) | −162.302 | − | 93.7048i | −0.332585 | − | 0.192018i | ||||
\(489\) | 384.609i | 0.786520i | ||||||||
\(490\) | −84.4371 | + | 202.563i | −0.172321 | + | 0.413394i | ||||
\(491\) | 760.161 | 1.54819 | 0.774094 | − | 0.633070i | \(-0.218206\pi\) | ||||
0.774094 | + | 0.633070i | \(0.218206\pi\) | |||||||
\(492\) | 87.9411 | − | 152.318i | 0.178742 | − | 0.309590i | ||||
\(493\) | −240.551 | + | 138.882i | −0.487934 | + | 0.281709i | ||||
\(494\) | 2.78680 | + | 4.82687i | 0.00564129 | + | 0.00977100i | ||||
\(495\) | 308.184 | + | 177.930i | 0.622593 | + | 0.359455i | ||||
\(496\) | 98.4720i | 0.198532i | ||||||||
\(497\) | 108.603 | + | 321.117i | 0.218517 | + | 0.646111i | ||||
\(498\) | −638.558 | −1.28225 | ||||||||
\(499\) | −62.7462 | + | 108.680i | −0.125744 | + | 0.217795i | −0.922023 | − | 0.387134i | \(-0.873465\pi\) |
0.796280 | + | 0.604929i | \(0.206798\pi\) | |||||||
\(500\) | −219.250 | + | 126.584i | −0.438500 | + | 0.253168i | ||||
\(501\) | −425.434 | − | 736.873i | −0.849169 | − | 1.47080i | ||||
\(502\) | 199.051 | + | 114.922i | 0.396516 | + | 0.228928i | ||||
\(503\) | − | 117.083i | − | 0.232770i | −0.993204 | − | 0.116385i | \(-0.962869\pi\) | ||
0.993204 | − | 0.116385i | \(-0.0371306\pi\) | |||||||
\(504\) | 164.735 | + | 32.9600i | 0.326855 | + | 0.0653967i | ||||
\(505\) | 90.2649 | 0.178742 | ||||||||
\(506\) | 21.2756 | − | 36.8505i | 0.0420467 | − | 0.0728271i | ||||
\(507\) | −502.724 | + | 290.248i | −0.991566 | + | 0.572481i | ||||
\(508\) | 60.6619 | + | 105.070i | 0.119413 | + | 0.206830i | ||||
\(509\) | −574.110 | − | 331.463i | −1.12792 | − | 0.651204i | −0.184507 | − | 0.982831i | \(-0.559069\pi\) |
−0.943410 | + | 0.331627i | \(0.892402\pi\) | |||||||
\(510\) | − | 253.936i | − | 0.497914i | ||||||
\(511\) | −688.709 | − | 605.349i | −1.34777 | − | 1.18464i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −0.772078 | + | 1.33728i | −0.00150503 | + | 0.00260678i | ||||
\(514\) | −121.445 | + | 70.1164i | −0.236275 | + | 0.136413i | ||||
\(515\) | 89.4518 | + | 154.935i | 0.173693 | + | 0.300845i | ||||
\(516\) | 46.9706 | + | 27.1185i | 0.0910282 | + | 0.0525552i | ||||
\(517\) | 632.733i | 1.22386i | ||||||||
\(518\) | 424.425 | − | 482.870i | 0.819353 | − | 0.932182i | ||||
\(519\) | −296.095 | −0.570511 | ||||||||
\(520\) | −24.6030 | + | 42.6137i | −0.0473135 | + | 0.0819494i | ||||
\(521\) | −40.8229 | + | 23.5691i | −0.0783550 | + | 0.0452383i | −0.538666 | − | 0.842520i | \(-0.681071\pi\) |
0.460311 | + | 0.887758i | \(0.347738\pi\) | |||||||
\(522\) | −122.912 | − | 212.889i | −0.235463 | − | 0.407834i | ||||
\(523\) | 432.554 | + | 249.735i | 0.827064 | + | 0.477506i | 0.852846 | − | 0.522162i | \(-0.174874\pi\) |
−0.0257824 | + | 0.999668i | \(0.508208\pi\) | |||||||
\(524\) | 265.895i | 0.507434i | ||||||||
\(525\) | 85.9706 | − | 429.684i | 0.163753 | − | 0.818446i | ||||
\(526\) | −614.257 | −1.16779 | ||||||||
\(527\) | −166.901 | + | 289.080i | −0.316699 | + | 0.548539i | ||||
\(528\) | 191.823 | − | 110.749i | 0.363302 | − | 0.209752i | ||||
\(529\) | 261.919 | + | 453.657i | 0.495121 | + | 0.857574i | ||||
\(530\) | −85.4451 | − | 49.3318i | −0.161217 | − | 0.0930788i | ||||
\(531\) | 710.675i | 1.33837i | ||||||||
\(532\) | 9.51472 | − | 3.21792i | 0.0178848 | − | 0.00604871i | ||||
\(533\) | −115.529 | −0.216752 | ||||||||
\(534\) | 496.467 | − | 859.905i | 0.929713 | − | 1.61031i | ||||
\(535\) | −130.578 | + | 75.3890i | −0.244070 | + | 0.140914i | ||||
\(536\) | 131.012 | + | 226.920i | 0.244426 | + | 0.423358i | ||||
\(537\) | 394.058 | + | 227.510i | 0.733815 | + | 0.423668i | ||||
\(538\) | 129.271i | 0.240280i | ||||||||
\(539\) | −598.937 | − | 249.663i | −1.11120 | − | 0.463197i | ||||
\(540\) | −13.6325 | −0.0252453 | ||||||||
\(541\) | −249.405 | + | 431.981i | −0.461007 | + | 0.798487i | −0.999011 | − | 0.0444550i | \(-0.985845\pi\) |
0.538005 | + | 0.842942i | \(0.319178\pi\) | |||||||
\(542\) | 20.9376 | − | 12.0883i | 0.0386302 | − | 0.0223031i | ||||
\(543\) | 208.368 | + | 360.903i | 0.383734 | + | 0.664647i | ||||
\(544\) | −66.4264 | − | 38.3513i | −0.122107 | − | 0.0704987i | ||||
\(545\) | − | 238.497i | − | 0.437609i | ||||||
\(546\) | −72.8528 | − | 215.411i | −0.133430 | − | 0.394525i | ||||
\(547\) | −279.897 | −0.511694 | −0.255847 | − | 0.966717i | \(-0.582354\pi\) | ||||
−0.255847 | + | 0.966717i | \(0.582354\pi\) | |||||||
\(548\) | 117.426 | − | 203.389i | 0.214282 | − | 0.371147i | ||||
\(549\) | 486.905 | − | 281.114i | 0.886894 | − | 0.512048i | ||||
\(550\) | −140.184 | − | 242.805i | −0.254880 | − | 0.441464i | ||||
\(551\) | −12.7279 | − | 7.34847i | −0.0230997 | − | 0.0133366i | ||||
\(552\) | − | 26.8723i | − | 0.0486817i | ||||||
\(553\) | −523.124 | − | 104.666i | −0.945976 | − | 0.189269i | ||||
\(554\) | 566.267 | 1.02214 | ||||||||
\(555\) | 429.996 | − | 744.775i | 0.774768 | − | 1.34194i | ||||
\(556\) | 118.794 | − | 68.5857i | 0.213658 | − | 0.123356i | ||||
\(557\) | 130.890 | + | 226.708i | 0.234991 | + | 0.407016i | 0.959270 | − | 0.282491i | \(-0.0911607\pi\) |
−0.724279 | + | 0.689507i | \(0.757827\pi\) | |||||||
\(558\) | −255.838 | − | 147.708i | −0.458490 | − | 0.264710i | ||||
\(559\) | − | 35.6258i | − | 0.0637312i | ||||||
\(560\) | 66.6030 | + | 58.5416i | 0.118934 | + | 0.104539i | ||||
\(561\) | 750.838 | 1.33839 | ||||||||
\(562\) | −380.912 | + | 659.758i | −0.677779 | + | 1.17395i | ||||
\(563\) | −420.076 | + | 242.531i | −0.746139 | + | 0.430784i | −0.824297 | − | 0.566157i | \(-0.808429\pi\) |
0.0781581 | + | 0.996941i | \(0.475096\pi\) | |||||||
\(564\) | 199.794 | + | 346.053i | 0.354245 | + | 0.613570i | ||||
\(565\) | 234.375 | + | 135.316i | 0.414822 | + | 0.239498i | ||||
\(566\) | 437.287i | 0.772593i | ||||||||
\(567\) | 394.511 | − | 448.837i | 0.695786 | − | 0.791599i | ||||
\(568\) | 136.971 | 0.241145 | ||||||||
\(569\) | 227.000 | − | 393.175i | 0.398945 | − | 0.690993i | −0.594651 | − | 0.803984i | \(-0.702710\pi\) |
0.993596 | + | 0.112991i | \(0.0360432\pi\) | |||||||
\(570\) | 11.6360 | − | 6.71807i | 0.0204141 | − | 0.0117861i | ||||
\(571\) | 115.769 | + | 200.517i | 0.202747 | + | 0.351168i | 0.949413 | − | 0.314032i | \(-0.101680\pi\) |
−0.746666 | + | 0.665200i | \(0.768346\pi\) | |||||||
\(572\) | −126.000 | − | 72.7461i | −0.220280 | − | 0.127179i | ||||
\(573\) | − | 292.309i | − | 0.510137i | ||||||
\(574\) | −40.8457 | + | 204.148i | −0.0711597 | + | 0.355659i | ||||
\(575\) | −34.0143 | −0.0591553 | ||||||||
\(576\) | 33.9411 | − | 58.7878i | 0.0589256 | − | 0.102062i | ||||
\(577\) | 564.014 | − | 325.634i | 0.977494 | − | 0.564356i | 0.0759812 | − | 0.997109i | \(-0.475791\pi\) |
0.901513 | + | 0.432753i | \(0.142458\pi\) | |||||||
\(578\) | 74.3503 | + | 128.778i | 0.128634 | + | 0.222800i | ||||
\(579\) | −117.107 | − | 67.6115i | −0.202257 | − | 0.116773i | ||||
\(580\) | − | 129.751i | − | 0.223708i | ||||||
\(581\) | 716.029 | − | 242.164i | 1.23241 | − | 0.416805i | ||||
\(582\) | −151.279 | −0.259930 | ||||||||
\(583\) | 145.864 | − | 252.644i | 0.250195 | − | 0.433351i | ||||
\(584\) | −320.860 | + | 185.249i | −0.549418 | + | 0.317206i | ||||
\(585\) | −73.8091 | − | 127.841i | −0.126169 | − | 0.218532i | ||||
\(586\) | 400.971 | + | 231.500i | 0.684250 | + | 0.395052i | ||||
\(587\) | − | 823.029i | − | 1.40209i | −0.713116 | − | 0.701046i | \(-0.752717\pi\) | ||
0.713116 | − | 0.701046i | \(-0.247283\pi\) | |||||||
\(588\) | −406.404 | + | 52.5770i | −0.691163 | + | 0.0894166i | ||||
\(589\) | −17.6619 | −0.0299863 | ||||||||
\(590\) | −187.555 | + | 324.855i | −0.317890 | + | 0.550601i | ||||
\(591\) | −1003.48 | + | 579.358i | −1.69793 | + | 0.980301i | ||||
\(592\) | −129.882 | − | 224.963i | −0.219396 | − | 0.380004i | ||||
\(593\) | −700.110 | − | 404.209i | −1.18062 | − | 0.681634i | −0.224465 | − | 0.974482i | \(-0.572064\pi\) |
−0.956159 | + | 0.292848i | \(0.905397\pi\) | |||||||
\(594\) | − | 40.3084i | − | 0.0678593i | ||||||
\(595\) | 96.3015 | + | 284.744i | 0.161851 | + | 0.478561i | ||||
\(596\) | −52.7939 | −0.0885804 | ||||||||
\(597\) | −350.088 | + | 606.370i | −0.586412 | + | 1.01570i | ||||
\(598\) | −15.2864 | + | 8.82559i | −0.0255625 | + | 0.0147585i | ||||
\(599\) | −265.422 | − | 459.725i | −0.443109 | − | 0.767488i | 0.554809 | − | 0.831978i | \(-0.312791\pi\) |
−0.997918 | + | 0.0644900i | \(0.979458\pi\) | |||||||
\(600\) | −153.338 | − | 88.5298i | −0.255563 | − | 0.147550i | ||||
\(601\) | 936.503i | 1.55824i | 0.626874 | + | 0.779121i | \(0.284334\pi\) | ||||
−0.626874 | + | 0.779121i | \(0.715666\pi\) | |||||||
\(602\) | −62.9533 | − | 12.5956i | −0.104574 | − | 0.0209229i | ||||
\(603\) | −786.073 | −1.30360 | ||||||||
\(604\) | 134.213 | − | 232.464i | 0.222207 | − | 0.384874i | ||||
\(605\) | −149.111 | + | 86.0890i | −0.246464 | + | 0.142296i | ||||
\(606\) | 84.2756 | + | 145.970i | 0.139069 | + | 0.240874i | ||||
\(607\) | 521.452 | + | 301.060i | 0.859064 | + | 0.495981i | 0.863699 | − | 0.504008i | \(-0.168142\pi\) |
−0.00463474 | + | 0.999989i | \(0.501475\pi\) | |||||||
\(608\) | − | 4.05845i | − | 0.00667508i | ||||||
\(609\) | 450.375 | + | 395.862i | 0.739531 | + | 0.650020i | ||||
\(610\) | 296.756 | 0.486486 | ||||||||
\(611\) | 131.235 | − | 227.307i | 0.214788 | − | 0.372024i | ||||
\(612\) | 199.279 | − | 115.054i | 0.325620 | − | 0.187997i | ||||
\(613\) | −548.448 | − | 949.940i | −0.894695 | − | 1.54966i | −0.834181 | − | 0.551491i | \(-0.814059\pi\) |
−0.0605142 | − | 0.998167i | \(-0.519274\pi\) | |||||||
\(614\) | 313.706 | + | 181.118i | 0.510921 | + | 0.294981i | ||||
\(615\) | 278.503i | 0.452851i | ||||||||
\(616\) | −173.095 | + | 196.932i | −0.280999 | + | 0.319694i | ||||
\(617\) | −432.956 | −0.701712 | −0.350856 | − | 0.936429i | \(-0.614109\pi\) | ||||
−0.350856 | + | 0.936429i | \(0.614109\pi\) | |||||||
\(618\) | −167.033 | + | 289.310i | −0.270280 | + | 0.468139i | ||||
\(619\) | 194.951 | − | 112.555i | 0.314946 | − | 0.181834i | −0.334192 | − | 0.942505i | \(-0.608463\pi\) |
0.649137 | + | 0.760671i | \(0.275130\pi\) | |||||||
\(620\) | −77.9634 | − | 135.037i | −0.125747 | − | 0.217801i | ||||
\(621\) | −4.23506 | − | 2.44512i | −0.00681975 | − | 0.00393738i | ||||
\(622\) | − | 305.940i | − | 0.491865i | ||||||
\(623\) | −230.592 | + | 1152.51i | −0.370131 | + | 1.84993i | ||||
\(624\) | −91.8823 | −0.147247 | ||||||||
\(625\) | 13.3091 | − | 23.0520i | 0.0212945 | − | 0.0368832i | ||||
\(626\) | 192.062 | − | 110.887i | 0.306809 | − | 0.177136i | ||||
\(627\) | 19.8640 | + | 34.4054i | 0.0316810 | + | 0.0548730i | ||||
\(628\) | 392.647 | + | 226.695i | 0.625234 | + | 0.360979i | ||||
\(629\) | − | 880.552i | − | 1.39992i | ||||||
\(630\) | −252.000 | + | 85.2274i | −0.400000 | + | 0.135282i | ||||
\(631\) | 750.514 | 1.18940 | 0.594702 | − | 0.803946i | \(-0.297270\pi\) | ||||
0.594702 | + | 0.803946i | \(0.297270\pi\) | |||||||
\(632\) | −107.782 | + | 186.683i | −0.170541 | + | 0.295385i | ||||
\(633\) | 463.794 | − | 267.772i | 0.732692 | − | 0.423020i | ||||
\(634\) | −316.805 | − | 548.722i | −0.499692 | − | 0.865492i | ||||
\(635\) | −166.374 | − | 96.0560i | −0.262006 | − | 0.151269i | ||||
\(636\) | − | 184.234i | − | 0.289676i | ||||||
\(637\) | 163.383 | + | 213.916i | 0.256488 | + | 0.335818i | ||||
\(638\) | 383.647 | 0.601327 | ||||||||
\(639\) | −205.456 | + | 355.860i | −0.321527 | + | 0.556901i | ||||
\(640\) | 31.0294 | − | 17.9149i | 0.0484835 | − | 0.0279920i | ||||
\(641\) | 580.926 | + | 1006.19i | 0.906281 | + | 1.56973i | 0.819188 | + | 0.573525i | \(0.194425\pi\) |
0.0870937 | + | 0.996200i | \(0.472242\pi\) | |||||||
\(642\) | −243.827 | − | 140.774i | −0.379793 | − | 0.219273i | ||||
\(643\) | − | 121.957i | − | 0.189669i | −0.995493 | − | 0.0948347i | \(-0.969768\pi\) | ||
0.995493 | − | 0.0948347i | \(-0.0302322\pi\) | |||||||
\(644\) | 10.1909 | + | 30.1324i | 0.0158244 | + | 0.0467895i | ||||
\(645\) | −85.8823 | −0.133151 | ||||||||
\(646\) | 6.87868 | − | 11.9142i | 0.0106481 | − | 0.0184431i | ||||
\(647\) | −137.504 | + | 79.3877i | −0.212525 | + | 0.122701i | −0.602484 | − | 0.798131i | \(-0.705822\pi\) |
0.389959 | + | 0.920832i | \(0.372489\pi\) | |||||||
\(648\) | −120.728 | − | 209.107i | −0.186309 | − | 0.322696i | ||||
\(649\) | −960.529 | − | 554.561i | −1.48001 | − | 0.854486i | ||||
\(650\) | 116.302i | 0.178927i | ||||||||
\(651\) | 706.584 | + | 141.372i | 1.08538 | + | 0.217162i | ||||
\(652\) | −183.955 | −0.282140 | ||||||||
\(653\) | 195.471 | − | 338.565i | 0.299342 | − | 0.518476i | −0.676643 | − | 0.736311i | \(-0.736566\pi\) |
0.975986 | + | 0.217835i | \(0.0698994\pi\) | |||||||
\(654\) | 385.680 | − | 222.672i | 0.589724 | − | 0.340478i | ||||
\(655\) | −210.518 | − | 364.628i | −0.321401 | − | 0.556683i | ||||
\(656\) | 72.8528 | + | 42.0616i | 0.111056 | + | 0.0641183i | ||||
\(657\) | − | 1111.49i | − | 1.69177i | ||||||
\(658\) | −355.269 | − | 312.268i | −0.539922 | − | 0.474571i | ||||
\(659\) | −331.955 | −0.503726 | −0.251863 | − | 0.967763i | \(-0.581043\pi\) | ||||
−0.251863 | + | 0.967763i | \(0.581043\pi\) | |||||||
\(660\) | −175.368 | + | 303.745i | −0.265708 | + | 0.460220i | ||||
\(661\) | 561.029 | − | 323.910i | 0.848758 | − | 0.490031i | −0.0114736 | − | 0.999934i | \(-0.503652\pi\) |
0.860232 | + | 0.509904i | \(0.170319\pi\) | |||||||
\(662\) | −38.8959 | − | 67.3697i | −0.0587552 | − | 0.101767i | ||||
\(663\) | −269.735 | − | 155.732i | −0.406840 | − | 0.234889i | ||||
\(664\) | − | 305.418i | − | 0.459967i | ||||||
\(665\) | −10.5000 | + | 11.9459i | −0.0157895 | + | 0.0179638i | ||||
\(666\) | 779.294 | 1.17011 | ||||||||
\(667\) | 23.2721 | − | 40.3084i | 0.0348907 | − | 0.0604324i | ||||
\(668\) | 352.441 | − | 203.482i | 0.527606 | − | 0.304613i | ||||
\(669\) | 872.205 | + | 1510.70i | 1.30374 | + | 2.25815i | ||||
\(670\) | −359.319 | − | 207.453i | −0.536298 | − | 0.309632i | ||||
\(671\) | 877.448i | 1.30767i | ||||||||
\(672\) | −32.4853 | + | 162.363i | −0.0483412 | + | 0.241611i | ||||
\(673\) | 100.956 | 0.150009 | 0.0750047 | − | 0.997183i | \(-0.476103\pi\) | ||||
0.0750047 | + | 0.997183i | \(0.476103\pi\) | |||||||
\(674\) | −78.9361 | + | 136.721i | −0.117116 | + | 0.202851i | ||||
\(675\) | −27.9045 | + | 16.1107i | −0.0413401 | + | 0.0238677i | ||||
\(676\) | −138.823 | − | 240.449i | −0.205360 | − | 0.355694i | ||||
\(677\) | 643.610 | + | 371.588i | 0.950679 | + | 0.548875i | 0.893292 | − | 0.449477i | \(-0.148390\pi\) |
0.0573873 | + | 0.998352i | \(0.481723\pi\) | |||||||
\(678\) | 505.351i | 0.745355i | ||||||||
\(679\) | 169.632 | − | 57.3704i | 0.249827 | − | 0.0844924i | ||||
\(680\) | 121.456 | 0.178612 | ||||||||
\(681\) | −485.603 | + | 841.088i | −0.713073 | + | 1.23508i | ||||
\(682\) | 399.276 | − | 230.522i | 0.585448 | − | 0.338009i | ||||
\(683\) | −2.21721 | − | 3.84032i | −0.00324628 | − | 0.00562272i | 0.864398 | − | 0.502809i | \(-0.167700\pi\) |
−0.867644 | + | 0.497186i | \(0.834367\pi\) | |||||||
\(684\) | 10.5442 | + | 6.08767i | 0.0154154 | + | 0.00890010i | ||||
\(685\) | 371.881i | 0.542892i | ||||||||
\(686\) | 435.770 | − | 213.078i | 0.635233 | − | 0.310610i | ||||
\(687\) | 349.669 | 0.508980 | ||||||||
\(688\) | −12.9706 | + | 22.4657i | −0.0188526 | + | 0.0326536i | ||||
\(689\) | −104.802 | + | 60.5074i | −0.152107 | + | 0.0878192i | ||||
\(690\) | 21.2756 | + | 36.8505i | 0.0308343 | + | 0.0534065i | ||||
\(691\) | −846.253 | − | 488.584i | −1.22468 | − | 0.707069i | −0.258767 | − | 0.965940i | \(-0.583316\pi\) |
−0.965912 | + | 0.258871i | \(0.916649\pi\) | |||||||
\(692\) | − | 141.620i | − | 0.204654i | ||||||
\(693\) | −252.000 | − | 745.113i | −0.363636 | − | 1.07520i | ||||
\(694\) | −533.522 | −0.768763 | ||||||||
\(695\) | −108.603 | + | 188.106i | −0.156263 | + | 0.270656i | ||||
\(696\) | 209.823 | − | 121.142i | 0.301470 | − | 0.174054i | ||||
\(697\) | 142.581 | + | 246.957i | 0.204563 | + | 0.354314i | ||||
\(698\) | −249.889 | − | 144.274i | −0.358008 | − | 0.206696i | ||||
\(699\) | − | 916.063i | − | 1.31053i | ||||||
\(700\) | 205.515 | + | 41.1191i | 0.293592 | + | 0.0587416i | ||||
\(701\) | −840.177 | −1.19854 | −0.599270 | − | 0.800547i | \(-0.704542\pi\) | ||||
−0.599270 | + | 0.800547i | \(0.704542\pi\) | |||||||
\(702\) | −8.36039 | + | 14.4806i | −0.0119094 | + | 0.0206277i | ||||
\(703\) | 40.3492 | − | 23.2956i | 0.0573958 | − | 0.0331375i | ||||
\(704\) | 52.9706 | + | 91.7477i | 0.0752423 | + | 0.130323i | ||||
\(705\) | −547.963 | − | 316.367i | −0.777252 | − | 0.448747i | ||||
\(706\) | 589.835i | 0.835460i | ||||||||
\(707\) | −149.857 | − | 131.719i | −0.211962 | − | 0.186306i | ||||
\(708\) | −700.441 | −0.989323 | ||||||||
\(709\) | −341.279 | + | 591.112i | −0.481352 | + | 0.833727i | −0.999771 | − | 0.0214003i | \(-0.993188\pi\) |
0.518419 | + | 0.855127i | \(0.326521\pi\) | |||||||
\(710\) | −187.831 | + | 108.444i | −0.264550 | + | 0.152738i | ||||
\(711\) | −323.345 | − | 560.050i | −0.454775 | − | 0.787694i | ||||
\(712\) | 411.286 | + | 237.456i | 0.577649 | + | 0.333506i | ||||
\(713\) | − | 55.9340i | − | 0.0784488i | ||||||
\(714\) | −370.555 | + | 421.582i | −0.518984 | + | 0.590451i | ||||
\(715\) | 230.382 | 0.322212 | ||||||||
\(716\) | −108.816 | + | 188.475i | −0.151978 | + | 0.263234i | ||||
\(717\) | −699.286 | + | 403.733i | −0.975295 | + | 0.563087i | ||||
\(718\) | −126.452 | − | 219.022i | −0.176117 | − | 0.305044i | ||||
\(719\) | 119.187 | + | 68.8126i | 0.165768 | + | 0.0957060i | 0.580589 | − | 0.814197i | \(-0.302822\pi\) |
−0.414821 | + | 0.909903i | \(0.636156\pi\) | |||||||
\(720\) | 107.489i | 0.149290i | ||||||||
\(721\) | 77.5812 | − | 387.754i | 0.107602 | − | 0.537800i | ||||
\(722\) | −509.803 | −0.706099 | ||||||||
\(723\) | −103.562 | + | 179.375i | −0.143240 | + | 0.248099i | ||||
\(724\) | −172.617 | + | 99.6607i | −0.238422 | + | 0.137653i | ||||
\(725\) | −153.338 | − | 265.589i | −0.211501 | − | 0.366330i | ||||
\(726\) | −278.434 | − | 160.754i | −0.383517 | − | 0.221424i | ||||
\(727\) | − | 264.137i | − | 0.363325i | −0.983361 | − | 0.181662i | \(-0.941852\pi\) | ||
0.983361 | − | 0.181662i | \(-0.0581478\pi\) | |||||||
\(728\) | 103.029 | − | 34.8450i | 0.141524 | − | 0.0478640i | ||||
\(729\) | 643.368 | 0.882534 | ||||||||
\(730\) | 293.335 | − | 508.070i | 0.401828 | − | 0.695987i | ||||
\(731\) | −76.1543 | + | 43.9677i | −0.104178 | + | 0.0601474i | ||||
\(732\) | 277.066 | + | 479.892i | 0.378505 | + | 0.655591i | ||||
\(733\) | 501.705 | + | 289.660i | 0.684455 | + | 0.395170i | 0.801531 | − | 0.597953i | \(-0.204019\pi\) |
−0.117077 | + | 0.993123i | \(0.537352\pi\) | |||||||
\(734\) | 889.530i | 1.21189i | ||||||||
\(735\) | 515.683 | − | 393.863i | 0.701610 | − | 0.535868i | ||||
\(736\) | 12.8528 | 0.0174631 | ||||||||
\(737\) | 613.397 | − | 1062.43i | 0.832288 | − | 1.44157i | ||||
\(738\) | −218.558 | + | 126.185i | −0.296150 | + | 0.170982i | ||||
\(739\) | 99.0477 | + | 171.556i | 0.134029 | + | 0.232146i | 0.925226 | − | 0.379416i | \(-0.123875\pi\) |
−0.791197 | + | 0.611562i | \(0.790542\pi\) | |||||||
\(740\) | 356.220 | + | 205.664i | 0.481379 | + | 0.277924i | ||||
\(741\) | − | 16.4800i | − | 0.0222402i | ||||||
\(742\) | 69.8680 | + | 206.585i | 0.0941617 | + | 0.278417i | ||||
\(743\) | 976.690 | 1.31452 | 0.657261 | − | 0.753663i | \(-0.271715\pi\) | ||||
0.657261 | + | 0.753663i | \(0.271715\pi\) | |||||||
\(744\) | 145.581 | − | 252.153i | 0.195673 | − | 0.338916i | ||||
\(745\) | 72.3974 | − | 41.7987i | 0.0971777 | − | 0.0561056i | ||||
\(746\) | −180.707 | − | 312.994i | −0.242235 | − | 0.419563i | ||||
\(747\) | 793.499 | + | 458.127i | 1.06225 | + | 0.613289i | ||||
\(748\) | 359.120i | 0.480107i | ||||||||
\(749\) | 326.794 | + | 65.3845i | 0.436308 | + | 0.0872958i | ||||
\(750\) | 748.566 | 0.998087 | ||||||||
\(751\) | 417.665 | − | 723.417i | 0.556145 | − | 0.963272i | −0.441668 | − | 0.897178i | \(-0.645613\pi\) |
0.997813 | − | 0.0660933i | \(-0.0210535\pi\) | |||||||
\(752\) | −165.515 | + | 95.5600i | −0.220099 | + | 0.127074i | ||||
\(753\) | −339.801 | − | 588.553i | −0.451263 | − | 0.781611i | ||||
\(754\) | −137.823 | − | 79.5724i | −0.182790 | − | 0.105534i | ||||
\(755\) | 425.044i | 0.562972i | ||||||||
\(756\) | 22.6325 | + | 19.8931i | 0.0299371 | + | 0.0263136i | ||||
\(757\) | 104.221 | 0.137677 | 0.0688383 | − | 0.997628i | \(-0.478071\pi\) | ||||
0.0688383 | + | 0.997628i | \(0.478071\pi\) | |||||||
\(758\) | 155.387 | − | 269.138i | 0.204996 | − | 0.355063i | ||||
\(759\) | −108.959 | + | 62.9077i | −0.143557 | + | 0.0828824i | ||||
\(760\) | 3.21320 | + | 5.56543i | 0.00422790 | + | 0.00732294i | ||||
\(761\) | −473.785 | − | 273.540i | −0.622583 | − | 0.359448i | 0.155291 | − | 0.987869i | \(-0.450368\pi\) |
−0.777874 | + | 0.628420i | \(0.783702\pi\) | |||||||
\(762\) | − | 358.730i | − | 0.470774i | ||||||
\(763\) | −348.025 | + | 395.950i | −0.456128 | + | 0.518939i | ||||
\(764\) | 139.809 | 0.182996 | ||||||||
\(765\) | −182.184 | + | 315.552i | −0.238149 | + | 0.412486i | ||||
\(766\) | −20.8644 | + | 12.0461i | −0.0272381 | + | 0.0157259i | ||||
\(767\) | 230.044 | + | 398.447i | 0.299927 | + | 0.519488i | ||||
\(768\) | 57.9411 | + | 33.4523i | 0.0754442 | + | 0.0435577i | ||||
\(769\) | 341.205i | 0.443700i | 0.975081 | + | 0.221850i | \(0.0712095\pi\) | ||||
−0.975081 | + | 0.221850i | \(0.928790\pi\) | |||||||
\(770\) | 81.4523 | − | 407.101i | 0.105782 | − | 0.528703i | ||||
\(771\) | 414.640 | 0.537795 | ||||||||
\(772\) | 32.3381 | − | 56.0112i | 0.0418887 | − | 0.0725534i | ||||
\(773\) | −425.213 | + | 245.497i | −0.550081 | + | 0.317590i | −0.749155 | − | 0.662395i | \(-0.769540\pi\) |
0.199074 | + | 0.979985i | \(0.436207\pi\) | |||||||
\(774\) | −38.9117 | − | 67.3970i | −0.0502735 | − | 0.0870763i | ||||
\(775\) | −319.169 | − | 184.273i | −0.411832 | − | 0.237771i | ||||
\(776\) | − | 72.3557i | − | 0.0932419i | ||||||
\(777\) | −1800.68 | + | 608.998i | −2.31748 | + | 0.783781i | ||||
\(778\) | 215.272 | 0.276699 | ||||||||
\(779\) | −7.54416 | + | 13.0669i | −0.00968441 | + | 0.0167739i | ||||
\(780\) | 126.000 | − | 72.7461i | 0.161538 | − | 0.0932643i | ||||
\(781\) | −320.647 | − | 555.376i | −0.410559 | − | 0.711109i | ||||
\(782\) | 37.7315 | + | 21.7843i | 0.0482500 | + | 0.0278571i | ||||
\(783\) | − | 44.0908i | − | 0.0563101i | ||||||
\(784\) | −25.1472 | − | 194.380i | −0.0320755 | − | 0.247934i | ||||
\(785\) | −717.926 | −0.914555 | ||||||||
\(786\) | 393.099 | − | 680.867i | 0.500126 | − | 0.866244i | ||||
\(787\) | 260.202 | − | 150.228i | 0.330625 | − | 0.190887i | −0.325493 | − | 0.945544i | \(-0.605530\pi\) |
0.656119 | + | 0.754658i | \(0.272197\pi\) | |||||||
\(788\) | −277.103 | − | 479.956i | −0.351653 | − | 0.609081i | ||||
\(789\) | 1572.90 | + | 908.116i | 1.99354 | + | 1.15097i | ||||
\(790\) | − | 341.337i | − | 0.432072i | ||||||
\(791\) | −191.647 | − | 566.660i | −0.242284 | − | 0.716385i | ||||
\(792\) | −317.823 | −0.401292 | ||||||||
\(793\) | 181.992 | − | 315.219i | 0.229498 | − | 0.397502i | ||||
\(794\) | −456.489 | + | 263.554i | −0.574923 | + | 0.331932i | ||||
\(795\) | 145.864 | + | 252.644i | 0.183477 | + | 0.317791i | ||||
\(796\) | −290.022 | − | 167.444i | −0.364350 | − | 0.210357i | ||||
\(797\) | 370.072i | 0.464331i | 0.972676 | + | 0.232165i | \(0.0745811\pi\) | ||||
−0.972676 | + | 0.232165i | \(0.925419\pi\) | |||||||
\(798\) | −29.1213 | − | 5.82655i | −0.0364929 | − | 0.00730144i | ||||
\(799\) | −647.860 | −0.810838 | ||||||||
\(800\) | 42.3431 | − | 73.3405i | 0.0529289 | − | 0.0916756i | ||||
\(801\) | −1233.86 | + | 712.369i | −1.54040 | + | 0.889349i | ||||
\(802\) | 460.731 | + | 798.010i | 0.574478 | + | 0.995025i | ||||
\(803\) | 1502.26 | + | 867.330i | 1.87081 | + | 1.08011i | ||||
\(804\) | − | 774.753i | − | 0.963623i | ||||||
\(805\) | −37.8318 | − | 33.2528i | −0.0469960 | − | 0.0413078i | ||||
\(806\) | −191.251 | −0.237284 | ||||||||
\(807\) | 191.114 | − | 331.019i | 0.236820 | − | 0.410184i | ||||
\(808\) | −69.8162 | + | 40.3084i | −0.0864062 | + | 0.0498867i | ||||
\(809\) | −245.618 | − | 425.422i | −0.303607 | − | 0.525862i | 0.673344 | − | 0.739330i | \(-0.264858\pi\) |
−0.976950 | + | 0.213468i | \(0.931524\pi\) | |||||||
\(810\) | 331.113 | + | 191.168i | 0.408782 | + | 0.236010i | ||||
\(811\) | − | 156.802i | − | 0.193344i | −0.995316 | − | 0.0966722i | \(-0.969180\pi\) | ||
0.995316 | − | 0.0966722i | \(-0.0308199\pi\) | |||||||
\(812\) | −189.338 | + | 215.411i | −0.233175 | + | 0.265284i | ||||
\(813\) | −71.4853 | −0.0879278 | ||||||||
\(814\) | −608.106 | + | 1053.27i | −0.747059 | + | 1.29394i | ||||
\(815\) | 252.262 | − | 145.643i | 0.309524 | − | 0.178704i | ||||
\(816\) | 113.397 | + | 196.409i | 0.138967 | + | 0.240698i | ||||
\(817\) | −4.02944 | − | 2.32640i | −0.00493199 | − | 0.00284749i | ||||
\(818\) | − | 754.575i | − | 0.922463i | ||||||
\(819\) | −64.0143 | + | 319.946i | −0.0781615 | + | 0.390654i | ||||
\(820\) | −133.206 | −0.162446 | ||||||||
\(821\) | 215.316 | − | 372.939i | 0.262261 | − | 0.454249i | −0.704581 | − | 0.709623i | \(-0.748865\pi\) |
0.966842 | + | 0.255374i | \(0.0821986\pi\) | |||||||
\(822\) | −601.378 | + | 347.206i | −0.731604 | + | 0.422392i | ||||
\(823\) | 354.371 | + | 613.788i | 0.430584 | + | 0.745793i | 0.996924 | − | 0.0783785i | \(-0.0249743\pi\) |
−0.566340 | + | 0.824172i | \(0.691641\pi\) | |||||||
\(824\) | −138.375 | − | 79.8907i | −0.167930 | − | 0.0969547i | ||||
\(825\) | 828.990i | 1.00484i | ||||||||
\(826\) | 785.418 | − | 265.632i | 0.950870 | − | 0.321588i | ||||
\(827\) | −1460.10 | −1.76554 | −0.882770 | − | 0.469805i | \(-0.844324\pi\) | ||||
−0.882770 | + | 0.469805i | \(0.844324\pi\) | |||||||
\(828\) | −19.2792 | + | 33.3926i | −0.0232841 | + | 0.0403292i | ||||
\(829\) | −223.095 | + | 128.804i | −0.269113 | + | 0.155373i | −0.628485 | − | 0.777822i | \(-0.716325\pi\) |
0.359371 | + | 0.933195i | \(0.382991\pi\) | |||||||
\(830\) | 241.809 | + | 418.826i | 0.291336 | + | 0.504609i | ||||
\(831\) | −1450.02 | − | 837.168i | −1.74491 | − | 1.00742i | ||||
\(832\) | − | 43.9466i | − | 0.0528204i | ||||||
\(833\) | 255.632 | − | 613.256i | 0.306881 | − | 0.736202i | ||||
\(834\) | −405.588 | −0.486316 | ||||||||
\(835\) | −322.206 | + | 558.077i | −0.385876 | + | 0.668356i | ||||
\(836\) | −16.4558 | + | 9.50079i | −0.0196840 | + | 0.0113646i | ||||
\(837\) | −26.4929 | − | 45.8870i | −0.0316522 | − | 0.0548231i | ||||
\(838\) | 654.323 | + | 377.774i | 0.780815 | + | 0.450804i | ||||
\(839\) | 213.621i | 0.254613i | 0.991863 | + | 0.127307i | \(0.0406332\pi\) | ||||
−0.991863 | + | 0.127307i | \(0.959367\pi\) | |||||||
\(840\) | −84.0000 | − | 248.371i | −0.100000 | − | 0.295680i | ||||
\(841\) | −421.353 | −0.501015 | ||||||||
\(842\) | 111.172 | − | 192.555i | 0.132033 | − | 0.228687i | ||||
\(843\) | 1950.77 | − | 1126.28i | 2.31408 | − | 1.33604i | ||||
\(844\) | 128.073 | + | 221.829i | 0.151745 | + | 0.262831i | ||||
\(845\) | 380.743 | + | 219.822i | 0.450583 | + | 0.260144i | ||||
\(846\) | − | 573.360i | − | 0.677730i | ||||||
\(847\) | 373.177 | + | 74.6646i | 0.440586 | + | 0.0881519i | ||||
\(848\) | 88.1177 | 0.103912 | ||||||||
\(849\) | 646.485 | − | 1119.74i | 0.761466 | − | 1.31890i | ||||
\(850\) | 248.610 | − | 143.535i | 0.292483 | − | 0.168865i | ||||
\(851\) | 73.7756 | + | 127.783i | 0.0866929 | + | 0.150156i | ||||
\(852\) | −350.735 | − | 202.497i | −0.411661 | − | 0.237673i | ||||
\(853\) | 1127.37i | 1.32165i | 0.750539 | + | 0.660826i | \(0.229794\pi\) | ||||
−0.750539 | + | 0.660826i | \(0.770206\pi\) | |||||||
\(854\) | −492.672 | − | 433.040i | −0.576899 | − | 0.507073i | ||||
\(855\) | −19.2792 | −0.0225488 | ||||||||
\(856\) | 67.3310 | − | 116.621i | 0.0786577 | − | 0.136239i | ||||
\(857\) | 1100.22 | − | 635.212i | 1.28380 | − | 0.741204i | 0.306261 | − | 0.951947i | \(-0.400922\pi\) |
0.977541 | + | 0.210744i | \(0.0675885\pi\) | |||||||
\(858\) | 215.095 | + | 372.556i | 0.250694 | + | 0.434215i | ||||
\(859\) | −221.488 | − | 127.876i | −0.257844 | − | 0.148867i | 0.365506 | − | 0.930809i | \(-0.380896\pi\) |
−0.623351 | + | 0.781942i | \(0.714229\pi\) | |||||||
\(860\) | − | 41.0768i | − | 0.0477638i | ||||||
\(861\) | 406.404 | − | 462.368i | 0.472014 | − | 0.537013i | ||||
\(862\) | 323.199 | 0.374941 | ||||||||
\(863\) | −557.364 | + | 965.382i | −0.645844 | + | 1.11863i | 0.338262 | + | 0.941052i | \(0.390161\pi\) |
−0.984106 | + | 0.177583i | \(0.943172\pi\) | |||||||
\(864\) | 10.5442 | − | 6.08767i | 0.0122039 | − | 0.00704592i | ||||
\(865\) | 112.125 | + | 194.207i | 0.129625 | + | 0.224516i | ||||
\(866\) | −58.2426 | − | 33.6264i | −0.0672548 | − | 0.0388296i | ||||
\(867\) | − | 439.677i | − | 0.507125i | ||||||
\(868\) | −67.6173 | + | 337.954i | −0.0779001 | + | 0.389348i | ||||
\(869\) | 1009.26 | 1.16141 | ||||||||
\(870\) | −191.823 | + | 332.248i | −0.220487 | + | 0.381894i | ||||
\(871\) | −440.720 | + | 254.450i | −0.505993 | + | 0.292135i | ||||
\(872\) | 106.503 | + | 184.468i | 0.122136 | + | 0.211546i | ||||
\(873\) | 187.986 | + | 108.534i | 0.215333 | + | 0.124323i | ||||
\(874\) | 2.30528i | 0.00263762i | ||||||||
\(875\) | −839.382 | + | 283.882i | −0.959294 | + | 0.324437i | ||||
\(876\) | 1095.48 | 1.25055 | ||||||||
\(877\) | 550.904 | − | 954.194i | 0.628169 | − | 1.08802i | −0.359750 | − | 0.933049i | \(-0.617138\pi\) |
0.987919 | − | 0.154972i | \(-0.0495286\pi\) | |||||||
\(878\) | −90.4523 | + | 52.2226i | −0.103021 | + | 0.0594791i | ||||
\(879\) | −684.500 | − | 1185.59i | −0.778725 | − | 1.34879i | ||||
\(880\) | −145.279 | − | 83.8770i | −0.165090 | − | 0.0953148i | ||||
\(881\) | − | 217.067i | − | 0.246387i | −0.992383 | − | 0.123194i | \(-0.960686\pi\) | ||
0.992383 | − | 0.123194i | \(-0.0393136\pi\) | |||||||
\(882\) | 542.735 | + | 226.236i | 0.615346 | + | 0.256503i | ||||
\(883\) | −516.544 | −0.584988 | −0.292494 | − | 0.956267i | \(-0.594485\pi\) | ||||
−0.292494 | + | 0.956267i | \(0.594485\pi\) | |||||||
\(884\) | 74.4853 | − | 129.012i | 0.0842594 | − | 0.145942i | ||||
\(885\) | 960.529 | − | 554.561i | 1.08534 | − | 0.626623i | ||||
\(886\) | 165.915 | + | 287.374i | 0.187263 | + | 0.324350i | ||||
\(887\) | −978.445 | − | 564.905i | −1.10309 | − | 0.636872i | −0.166062 | − | 0.986115i | \(-0.553105\pi\) |
−0.937032 | + | 0.349243i | \(0.886439\pi\) | |||||||
\(888\) | 768.071i | 0.864944i | ||||||||
\(889\) | 136.043 | + | 402.251i | 0.153029 | + | 0.452476i | ||||
\(890\) | −752.007 | −0.844952 | ||||||||
\(891\) | −565.246 | + | 979.034i | −0.634395 | + | 1.09880i | ||||
\(892\) | −722.558 | + | 417.169i | −0.810043 | + | 0.467679i | ||||
\(893\) | −17.1396 | − | 29.6867i | −0.0191933 | − | 0.0332438i | ||||
\(894\) | 135.187 | + | 78.0504i | 0.151216 | + | 0.0873047i | ||||
\(895\) | − | 344.613i | − | 0.385043i | ||||||
\(896\) | −77.6569 | − | 15.5375i | −0.0866706 | − | 0.0173409i | ||||
\(897\) | 52.1909 | 0.0581838 | ||||||||
\(898\) | −180.426 | + | 312.508i | −0.200920 | + | 0.348004i | ||||
\(899\) | 436.742 | − | 252.153i | 0.485809 | − | 0.280482i | ||||
\(900\) | 127.029 | + | 220.021i | 0.141144 | + | 0.244468i | ||||
\(901\) | 258.684 | + | 149.351i | 0.287107 | + | 0.165762i | ||||
\(902\) | − | 393.863i | − | 0.436655i | ||||||
\(903\) | 142.581 | + | 125.323i | 0.157897 | + | 0.138785i | ||||
\(904\) | −241.706 | −0.267373 | ||||||||
\(905\) | 157.809 | − | 273.333i | 0.174375 | − | 0.302026i | ||||
\(906\) | −687.349 | + | 396.841i | −0.758663 | + | 0.438014i | ||||
\(907\) | −30.0111 | − | 51.9808i | −0.0330884 | − | 0.0573107i | 0.849007 | − | 0.528382i | \(-0.177201\pi\) |
−0.882095 | + | 0.471071i | \(0.843868\pi\) | |||||||
\(908\) | −402.286 | − | 232.260i | −0.443047 | − | 0.255793i | ||||
\(909\) | − | 241.851i | − | 0.266062i | ||||||
\(910\) | −113.698 | + | 129.355i | −0.124943 | + | 0.142149i | ||||
\(911\) | 1422.25 | 1.56120 | 0.780598 | − | 0.625033i | \(-0.214915\pi\) | ||||
0.780598 | + | 0.625033i | \(0.214915\pi\) | |||||||
\(912\) | −6.00000 | + | 10.3923i | −0.00657895 | + | 0.0113951i | ||||
\(913\) | −1238.38 | + | 714.980i | −1.35639 | + | 0.783111i | ||||
\(914\) | −103.050 | − | 178.488i | −0.112746 | − | 0.195283i | ||||
\(915\) | −759.893 | − | 438.724i | −0.830484 | − | 0.479480i | ||||
\(916\) | 167.244i | 0.182581i | ||||||||
\(917\) | −182.581 | + | 912.547i | −0.199107 | + | 0.995144i | ||||
\(918\) | 41.2721 | 0.0449587 | ||||||||
\(919\) | −834.849 | + | 1446.00i | −0.908432 | + | 1.57345i | −0.0921886 | + | 0.995742i | \(0.529386\pi\) |
−0.816243 | + | 0.577708i | \(0.803947\pi\) | |||||||
\(920\) | −17.6253 | + | 10.1760i | −0.0191580 | + | 0.0110609i | ||||
\(921\) | −535.529 | − | 927.563i | −0.581465 | − | 1.00713i | ||||
\(922\) | −1087.98 | − | 628.144i | −1.18002 | − | 0.681284i | ||||
\(923\) | 266.022i | 0.288215i | ||||||||
\(924\) | 734.382 | − | 248.371i | 0.794786 | − | 0.268800i | ||||
\(925\) | 972.205 | 1.05103 | ||||||||
\(926\) | 165.473 | − | 286.608i | 0.178697 | − | 0.309512i | ||||
\(927\) | 415.124 | − | 239.672i | 0.447814 | − | 0.258546i | ||||
\(928\) | 57.9411 | + | 100.357i | 0.0624366 | + | 0.108143i | ||||
\(929\) | 839.058 | + | 484.430i | 0.903184 | + | 0.521453i | 0.878232 | − | 0.478235i | \(-0.158723\pi\) |
0.0249519 | + | 0.999689i | \(0.492057\pi\) | |||||||
\(930\) | 461.044i | 0.495746i | ||||||||
\(931\) | 34.8640 | − | 4.51039i | 0.0374479 | − | 0.00484468i | ||||
\(932\) | 438.146 | 0.470114 | ||||||||
\(933\) | −452.301 | + | 783.408i | −0.484781 | + | 0.839666i | ||||
\(934\) | 963.407 | − | 556.223i | 1.03148 | − | 0.595528i | ||||
\(935\) | −284.327 | − | 492.469i | −0.304093 | − | 0.526705i | ||||
\(936\) | 114.177 | + | 65.9199i | 0.121984 | + | 0.0704272i | ||||
\(937\) | − | 1212.57i | − | 1.29410i | −0.762449 | − | 0.647049i | \(-0.776003\pi\) | ||
0.762449 | − | 0.647049i | \(-0.223997\pi\) | |||||||
\(938\) | 293.813 | + | 868.746i | 0.313234 | + | 0.926168i | ||||
\(939\) | −655.742 | −0.698341 | ||||||||
\(940\) | 151.316 | − | 262.087i | 0.160974 | − | 0.278816i | ||||
\(941\) | −1293.90 | + | 747.032i | −1.37502 | + | 0.793870i | −0.991555 | − | 0.129684i | \(-0.958604\pi\) |
−0.383468 | + | 0.923554i | \(0.625270\pi\) | |||||||
\(942\) | −670.290 | − | 1160.98i | −0.711560 | − | 1.23246i | ||||
\(943\) | −41.3818 | − | 23.8918i | −0.0438832 | − | 0.0253360i | ||||
\(944\) | − | 335.016i | − | 0.354889i | ||||||
\(945\) | −46.7864 | − | 9.36095i | −0.0495094 | − | 0.00990576i | ||||
\(946\) | 121.456 | 0.128389 | ||||||||
\(947\) | −387.731 | + | 671.570i | −0.409431 | + | 0.709155i | −0.994826 | − | 0.101593i | \(-0.967606\pi\) |
0.585395 | + | 0.810748i | \(0.300939\pi\) | |||||||
\(948\) | 551.985 | − | 318.689i | 0.582262 | − | 0.336169i | ||||
\(949\) | −359.787 | − | 623.169i | −0.379122 | − | 0.656659i | ||||
\(950\) | 13.1543 | + | 7.59466i | 0.0138467 | + | 0.00799437i | ||||
\(951\) | 1873.45i | 1.96998i | ||||||||
\(952\) | −201.640 | − | 177.234i | −0.211806 | − | 0.186170i | ||||
\(953\) | 1055.40 | 1.10745 | 0.553723 | − | 0.832701i | \(-0.313206\pi\) | ||||
0.553723 | + | 0.832701i | \(0.313206\pi\) | |||||||
\(954\) | −132.177 | + | 228.937i | −0.138550 | + | 0.239976i | ||||
\(955\) | −191.723 | + | 110.691i | −0.200757 | + | 0.115907i | ||||
\(956\) | −193.103 | − | 334.464i | −0.201990 | − | 0.349857i | ||||
\(957\) | −982.389 | − | 567.183i | −1.02653 | − | 0.592667i | ||||
\(958\) | − | 1042.18i | − | 1.08787i | ||||||
\(959\) | 542.665 | − | 617.393i | 0.565866 | − | 0.643788i | ||||
\(960\) | −105.941 | −0.110355 | ||||||||
\(961\) | −177.477 | + | 307.400i | −0.184680 | + | 0.319875i | ||||
\(962\) | 436.919 | − | 252.255i | 0.454178 | − | 0.262220i | ||||
\(963\) | 201.993 | + | 349.862i | 0.209754 | + | 0.363304i | ||||
\(964\) | −85.7939 | − | 49.5332i | −0.0889979 | − | 0.0513829i | ||||
\(965\) | 102.412i | 0.106127i | ||||||||
\(966\) | 18.4523 | − | 92.2251i | 0.0191017 | − | 0.0954712i | ||||
\(967\) | 1221.63 | 1.26332 | 0.631661 | − | 0.775245i | \(-0.282373\pi\) | ||||
0.631661 | + | 0.775245i | \(0.282373\pi\) | |||||||
\(968\) | 76.8873 | − | 133.173i | 0.0794290 | − | 0.137575i | ||||
\(969\) | −35.2279 | + | 20.3389i | −0.0363549 | + | 0.0209895i | ||||
\(970\) | 57.2864 | + | 99.2229i | 0.0590581 | + | 0.102292i | ||||
\(971\) | −455.753 | − | 263.129i | −0.469365 | − | 0.270988i | 0.246609 | − | 0.969115i | \(-0.420684\pi\) |
−0.715974 | + | 0.698127i | \(0.754017\pi\) | |||||||
\(972\) | 675.194i | 0.694644i | ||||||||
\(973\) | 454.794 | − | 153.813i | 0.467414 | − | 0.158081i | ||||
\(974\) | −382.825 | −0.393045 | ||||||||
\(975\) | 171.941 | − | 297.811i | 0.176350 | − | 0.305447i | ||||
\(976\) | −229.529 | + | 132.519i | −0.235173 | + | 0.135777i | ||||
\(977\) | 500.051 | + | 866.114i | 0.511823 | + | 0.886504i | 0.999906 | + | 0.0137065i | \(0.00436306\pi\) |
−0.488083 | + | 0.872797i | \(0.662304\pi\) | |||||||
\(978\) | 471.047 | + | 271.959i | 0.481643 | + | 0.278077i | ||||
\(979\) | − | 2223.53i | − | 2.27123i | ||||||
\(980\) | 188.382 | + | 246.648i | 0.192226 | + | 0.251681i | ||||
\(981\) | −639.015 | −0.651392 | ||||||||
\(982\) | 537.515 | − | 931.003i | 0.547367 | − | 0.948068i | ||||
\(983\) | 931.584 | − | 537.850i | 0.947695 | − | 0.547152i | 0.0553306 | − | 0.998468i | \(-0.482379\pi\) |
0.892364 | + | 0.451316i | \(0.149045\pi\) | |||||||
\(984\) | −124.368 | − | 215.411i | −0.126390 | − | 0.218914i | ||||
\(985\) | 759.993 | + | 438.782i | 0.771566 | + | 0.445464i | ||||
\(986\) | 392.819i | 0.398396i | ||||||||
\(987\) | 448.066 | + | 1324.84i | 0.453968 | + | 1.34229i | ||||
\(988\) | 7.88225 | 0.00797799 | ||||||||
\(989\) | 7.36753 | − | 12.7609i | 0.00744948 | − | 0.0129029i | ||||
\(990\) | 435.838 | − | 251.631i | 0.440240 | − | 0.254173i | ||||
\(991\) | 938.017 | + | 1624.69i | 0.946536 | + | 1.63945i | 0.752646 | + | 0.658426i | \(0.228777\pi\) |
0.193891 | + | 0.981023i | \(0.437889\pi\) | |||||||
\(992\) | 120.603 | + | 69.6302i | 0.121576 | + | 0.0701917i | ||||
\(993\) | 230.015i | 0.231636i | ||||||||
\(994\) | 470.080 | + | 94.0530i | 0.472918 | + | 0.0946207i | ||||
\(995\) | 530.285 | 0.532949 | ||||||||
\(996\) | −451.529 | + | 782.071i | −0.453342 | + | 0.785212i | ||||
\(997\) | 504.221 | − | 291.112i | 0.505738 | − | 0.291988i | −0.225342 | − | 0.974280i | \(-0.572350\pi\) |
0.731080 | + | 0.682292i | \(0.239017\pi\) | |||||||
\(998\) | 88.7365 | + | 153.696i | 0.0889144 | + | 0.154004i | ||||
\(999\) | 121.048 | + | 69.8869i | 0.121169 | + | 0.0699569i |
(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 | 14.3.d.a.5.2 | yes | 4 | |
3.2 | odd | 2 | 126.3.n.c.19.1 | 4 | |||
4.3 | odd | 2 | 112.3.s.b.33.2 | 4 | |||
5.2 | odd | 4 | 350.3.i.a.299.4 | 8 | |||
5.3 | odd | 4 | 350.3.i.a.299.1 | 8 | |||
5.4 | even | 2 | 350.3.k.a.201.1 | 4 | |||
7.2 | even | 3 | 98.3.b.b.97.1 | 4 | |||
7.3 | odd | 6 | inner | 14.3.d.a.3.2 | ✓ | 4 | |
7.4 | even | 3 | 98.3.d.a.31.2 | 4 | |||
7.5 | odd | 6 | 98.3.b.b.97.2 | 4 | |||
7.6 | odd | 2 | 98.3.d.a.19.2 | 4 | |||
8.3 | odd | 2 | 448.3.s.c.257.1 | 4 | |||
8.5 | even | 2 | 448.3.s.d.257.2 | 4 | |||
12.11 | even | 2 | 1008.3.cg.l.145.1 | 4 | |||
21.2 | odd | 6 | 882.3.c.f.685.4 | 4 | |||
21.5 | even | 6 | 882.3.c.f.685.3 | 4 | |||
21.11 | odd | 6 | 882.3.n.b.325.1 | 4 | |||
21.17 | even | 6 | 126.3.n.c.73.1 | 4 | |||
21.20 | even | 2 | 882.3.n.b.19.1 | 4 | |||
28.3 | even | 6 | 112.3.s.b.17.2 | 4 | |||
28.11 | odd | 6 | 784.3.s.c.129.1 | 4 | |||
28.19 | even | 6 | 784.3.c.e.97.1 | 4 | |||
28.23 | odd | 6 | 784.3.c.e.97.4 | 4 | |||
28.27 | even | 2 | 784.3.s.c.705.1 | 4 | |||
35.3 | even | 12 | 350.3.i.a.199.4 | 8 | |||
35.17 | even | 12 | 350.3.i.a.199.1 | 8 | |||
35.24 | odd | 6 | 350.3.k.a.101.1 | 4 | |||
56.3 | even | 6 | 448.3.s.c.129.1 | 4 | |||
56.45 | odd | 6 | 448.3.s.d.129.2 | 4 | |||
84.59 | odd | 6 | 1008.3.cg.l.577.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.3.d.a.3.2 | ✓ | 4 | 7.3 | odd | 6 | inner | |
14.3.d.a.5.2 | yes | 4 | 1.1 | even | 1 | trivial | |
98.3.b.b.97.1 | 4 | 7.2 | even | 3 | |||
98.3.b.b.97.2 | 4 | 7.5 | odd | 6 | |||
98.3.d.a.19.2 | 4 | 7.6 | odd | 2 | |||
98.3.d.a.31.2 | 4 | 7.4 | even | 3 | |||
112.3.s.b.17.2 | 4 | 28.3 | even | 6 | |||
112.3.s.b.33.2 | 4 | 4.3 | odd | 2 | |||
126.3.n.c.19.1 | 4 | 3.2 | odd | 2 | |||
126.3.n.c.73.1 | 4 | 21.17 | even | 6 | |||
350.3.i.a.199.1 | 8 | 35.17 | even | 12 | |||
350.3.i.a.199.4 | 8 | 35.3 | even | 12 | |||
350.3.i.a.299.1 | 8 | 5.3 | odd | 4 | |||
350.3.i.a.299.4 | 8 | 5.2 | odd | 4 | |||
350.3.k.a.101.1 | 4 | 35.24 | odd | 6 | |||
350.3.k.a.201.1 | 4 | 5.4 | even | 2 | |||
448.3.s.c.129.1 | 4 | 56.3 | even | 6 | |||
448.3.s.c.257.1 | 4 | 8.3 | odd | 2 | |||
448.3.s.d.129.2 | 4 | 56.45 | odd | 6 | |||
448.3.s.d.257.2 | 4 | 8.5 | even | 2 | |||
784.3.c.e.97.1 | 4 | 28.19 | even | 6 | |||
784.3.c.e.97.4 | 4 | 28.23 | odd | 6 | |||
784.3.s.c.129.1 | 4 | 28.11 | odd | 6 | |||
784.3.s.c.705.1 | 4 | 28.27 | even | 2 | |||
882.3.c.f.685.3 | 4 | 21.5 | even | 6 | |||
882.3.c.f.685.4 | 4 | 21.2 | odd | 6 | |||
882.3.n.b.19.1 | 4 | 21.20 | even | 2 | |||
882.3.n.b.325.1 | 4 | 21.11 | odd | 6 | |||
1008.3.cg.l.145.1 | 4 | 12.11 | even | 2 | |||
1008.3.cg.l.577.1 | 4 | 84.59 | odd | 6 |