Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(49,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bx (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 499.1 | ||
Root | \(0.280526 - 0.386111i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.499 |
Dual form | 825.2.bx.h.124.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.62947 | + | 2.24278i | −1.15221 | + | 1.58588i | −0.415627 | + | 0.909535i | \(0.636438\pi\) |
−0.736584 | + | 0.676347i | \(0.763562\pi\) | |||||||
\(3\) | 0.951057 | + | 0.309017i | 0.549093 | + | 0.178411i | ||||
\(4\) | −1.75683 | − | 5.40697i | −0.878415 | − | 2.70348i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.24278 | + | 1.62947i | −0.915609 | + | 0.665229i | ||||
\(7\) | −2.16612 | + | 0.703814i | −0.818716 | + | 0.266017i | −0.688285 | − | 0.725441i | \(-0.741636\pi\) |
−0.130431 | + | 0.991457i | \(0.541636\pi\) | |||||||
\(8\) | 9.71623 | + | 3.15700i | 3.43521 | + | 1.11617i | ||||
\(9\) | 0.809017 | + | 0.587785i | 0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.105203 | − | 3.31496i | −0.0317198 | − | 0.999497i | ||||
\(12\) | − | 5.68522i | − | 1.64118i | ||||||
\(13\) | −0.256120 | + | 0.352519i | −0.0710348 | + | 0.0977711i | −0.843056 | − | 0.537826i | \(-0.819246\pi\) |
0.772021 | + | 0.635597i | \(0.219246\pi\) | |||||||
\(14\) | 1.95113 | − | 6.00496i | 0.521461 | − | 1.60489i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −13.7139 | + | 9.96371i | −3.42847 | + | 2.49093i | ||||
\(17\) | 2.93893 | + | 4.04508i | 0.712794 | + | 0.981077i | 0.999733 | + | 0.0231281i | \(0.00736256\pi\) |
−0.286938 | + | 0.957949i | \(0.592637\pi\) | |||||||
\(18\) | −2.63654 | + | 0.856664i | −0.621439 | + | 0.201918i | ||||
\(19\) | −1.45113 | + | 4.46612i | −0.332912 | + | 1.02460i | 0.634829 | + | 0.772652i | \(0.281070\pi\) |
−0.967741 | + | 0.251946i | \(0.918930\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.27759 | −0.497011 | ||||||||
\(22\) | 7.60613 | + | 5.16568i | 1.62163 | + | 1.10133i | ||||
\(23\) | − | 0.845811i | − | 0.176364i | −0.996104 | − | 0.0881819i | \(-0.971894\pi\) | ||
0.996104 | − | 0.0881819i | \(-0.0281057\pi\) | |||||||
\(24\) | 8.26512 | + | 6.00496i | 1.68711 | + | 1.22576i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.373280 | − | 1.14884i | −0.0732063 | − | 0.225306i | ||||
\(27\) | 0.587785 | + | 0.809017i | 0.113119 | + | 0.155695i | ||||
\(28\) | 7.61100 | + | 10.4756i | 1.43834 | + | 1.97971i | ||||
\(29\) | 0.821093 | + | 2.52706i | 0.152473 | + | 0.469264i | 0.997896 | − | 0.0648334i | \(-0.0206516\pi\) |
−0.845423 | + | 0.534097i | \(0.820652\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.77637 | + | 2.74369i | 0.678256 | + | 0.492782i | 0.872779 | − | 0.488116i | \(-0.162316\pi\) |
−0.194523 | + | 0.980898i | \(0.562316\pi\) | |||||||
\(32\) | − | 26.5602i | − | 4.69523i | ||||||
\(33\) | 0.924324 | − | 3.18522i | 0.160904 | − | 0.554476i | ||||
\(34\) | −13.8611 | −2.37716 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.75683 | − | 5.40697i | 0.292805 | − | 0.901161i | ||||
\(37\) | −8.42864 | + | 2.73863i | −1.38566 | + | 0.450228i | −0.904526 | − | 0.426419i | \(-0.859775\pi\) |
−0.481134 | + | 0.876647i | \(0.659775\pi\) | |||||||
\(38\) | −7.65193 | − | 10.5320i | −1.24131 | − | 1.70851i | ||||
\(39\) | −0.352519 | + | 0.256120i | −0.0564481 | + | 0.0410120i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.32697 | + | 4.08400i | −0.207238 | + | 0.637814i | 0.792376 | + | 0.610033i | \(0.208844\pi\) |
−0.999614 | + | 0.0277805i | \(0.991156\pi\) | |||||||
\(42\) | 3.71127 | − | 5.10813i | 0.572661 | − | 0.788201i | ||||
\(43\) | 7.00317i | 1.06797i | 0.845493 | + | 0.533986i | \(0.179307\pi\) | ||||
−0.845493 | + | 0.533986i | \(0.820693\pi\) | |||||||
\(44\) | −17.7390 | + | 6.39264i | −2.67426 | + | 0.963727i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.89696 | + | 1.37823i | 0.279692 | + | 0.203208i | ||||
\(47\) | −0.445265 | − | 0.144675i | −0.0649485 | − | 0.0211031i | 0.276363 | − | 0.961053i | \(-0.410871\pi\) |
−0.341311 | + | 0.939950i | \(0.610871\pi\) | |||||||
\(48\) | −16.1216 | + | 5.23823i | −2.32696 | + | 0.756074i | ||||
\(49\) | −1.46641 | + | 1.06541i | −0.209487 | + | 0.152201i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.54508 | + | 4.75528i | 0.216355 | + | 0.665873i | ||||
\(52\) | 2.35601 | + | 0.765515i | 0.326720 | + | 0.106158i | ||||
\(53\) | −6.37078 | + | 8.76863i | −0.875094 | + | 1.20446i | 0.102662 | + | 0.994716i | \(0.467264\pi\) |
−0.977756 | + | 0.209747i | \(0.932736\pi\) | |||||||
\(54\) | −2.77222 | −0.377252 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −23.2684 | −3.10938 | ||||||||
\(57\) | −2.76021 | + | 3.79911i | −0.365599 | + | 0.503204i | ||||
\(58\) | −7.00558 | − | 2.27625i | −0.919878 | − | 0.298887i | ||||
\(59\) | −1.21629 | − | 3.74334i | −0.158347 | − | 0.487341i | 0.840138 | − | 0.542373i | \(-0.182474\pi\) |
−0.998485 | + | 0.0550316i | \(0.982474\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.39913 | + | 1.74307i | −0.307177 | + | 0.223177i | −0.730684 | − | 0.682715i | \(-0.760799\pi\) |
0.423507 | + | 0.905893i | \(0.360799\pi\) | |||||||
\(62\) | −12.3070 | + | 3.99878i | −1.56299 | + | 0.507845i | ||||
\(63\) | −2.16612 | − | 0.703814i | −0.272905 | − | 0.0886723i | ||||
\(64\) | 32.1409 | + | 23.3517i | 4.01761 | + | 2.91897i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.63757 | + | 7.26328i | 0.693937 | + | 0.894048i | ||||
\(67\) | 2.47048i | 0.301817i | 0.988548 | + | 0.150909i | \(0.0482199\pi\) | ||||
−0.988548 | + | 0.150909i | \(0.951780\pi\) | |||||||
\(68\) | 16.7084 | − | 22.9972i | 2.02620 | − | 2.78882i | ||||
\(69\) | 0.261370 | − | 0.804414i | 0.0314653 | − | 0.0968401i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.15321 | − | 6.65020i | 1.08629 | − | 0.789233i | 0.107518 | − | 0.994203i | \(-0.465710\pi\) |
0.978768 | + | 0.204970i | \(0.0657097\pi\) | |||||||
\(72\) | 6.00496 | + | 8.26512i | 0.707691 | + | 0.974054i | ||||
\(73\) | −8.01655 | + | 2.60474i | −0.938266 | + | 0.304861i | −0.737939 | − | 0.674868i | \(-0.764201\pi\) |
−0.200328 | + | 0.979729i | \(0.564201\pi\) | |||||||
\(74\) | 7.59209 | − | 23.3661i | 0.882563 | − | 2.71625i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 26.6975 | 3.06242 | ||||||||
\(77\) | 2.56099 | + | 7.10654i | 0.291852 | + | 0.809866i | ||||
\(78\) | − | 1.20796i | − | 0.136775i | ||||||
\(79\) | −8.79457 | − | 6.38963i | −0.989466 | − | 0.718889i | −0.0296621 | − | 0.999560i | \(-0.509443\pi\) |
−0.959804 | + | 0.280671i | \(0.909443\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −6.99723 | − | 9.63087i | −0.772715 | − | 1.06355i | ||||
\(83\) | 3.47998 | + | 4.78978i | 0.381978 | + | 0.525747i | 0.956107 | − | 0.293017i | \(-0.0946594\pi\) |
−0.574130 | + | 0.818764i | \(0.694659\pi\) | |||||||
\(84\) | 4.00134 | + | 12.3149i | 0.436582 | + | 1.34366i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −15.7065 | − | 11.4115i | −1.69368 | − | 1.23053i | ||||
\(87\) | 2.65711i | 0.284872i | ||||||||
\(88\) | 9.44313 | − | 32.5410i | 1.00664 | − | 3.46888i | ||||
\(89\) | −5.89958 | −0.625354 | −0.312677 | − | 0.949859i | \(-0.601226\pi\) | ||||
−0.312677 | + | 0.949859i | \(0.601226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.306678 | − | 0.943857i | 0.0321486 | − | 0.0989431i | ||||
\(92\) | −4.57327 | + | 1.48595i | −0.476796 | + | 0.154921i | ||||
\(93\) | 2.74369 | + | 3.77637i | 0.284508 | + | 0.391591i | ||||
\(94\) | 1.05002 | − | 0.762885i | 0.108301 | − | 0.0786855i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.20756 | − | 25.2603i | 0.837681 | − | 2.57812i | ||||
\(97\) | 5.08318 | − | 6.99640i | 0.516119 | − | 0.710377i | −0.468817 | − | 0.883295i | \(-0.655320\pi\) |
0.984936 | + | 0.172918i | \(0.0553196\pi\) | |||||||
\(98\) | − | 5.02487i | − | 0.507589i | ||||||
\(99\) | 1.86337 | − | 2.74369i | 0.187276 | − | 0.275751i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.59624 | + | 3.33936i | 0.457343 | + | 0.332279i | 0.792488 | − | 0.609887i | \(-0.208785\pi\) |
−0.335145 | + | 0.942166i | \(0.608785\pi\) | |||||||
\(102\) | −13.1827 | − | 4.28332i | −1.30528 | − | 0.424112i | ||||
\(103\) | 1.23269 | − | 0.400526i | 0.121461 | − | 0.0394650i | −0.247656 | − | 0.968848i | \(-0.579660\pi\) |
0.369117 | + | 0.929383i | \(0.379660\pi\) | |||||||
\(104\) | −3.60142 | + | 2.61658i | −0.353148 | + | 0.256577i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.28505 | − | 28.5765i | −0.901844 | − | 2.77559i | ||||
\(107\) | 11.6036 | + | 3.77024i | 1.12176 | + | 0.364483i | 0.810441 | − | 0.585821i | \(-0.199228\pi\) |
0.311324 | + | 0.950304i | \(0.399228\pi\) | |||||||
\(108\) | 3.34169 | − | 4.59944i | 0.321554 | − | 0.442581i | ||||
\(109\) | 12.1644 | 1.16514 | 0.582568 | − | 0.812782i | \(-0.302048\pi\) | ||||
0.582568 | + | 0.812782i | \(0.302048\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.86239 | −0.841181 | ||||||||
\(112\) | 22.6933 | − | 31.2346i | 2.14431 | − | 2.95139i | ||||
\(113\) | 0.135100 | + | 0.0438966i | 0.0127091 | + | 0.00412944i | 0.315365 | − | 0.948971i | \(-0.397873\pi\) |
−0.302656 | + | 0.953100i | \(0.597873\pi\) | |||||||
\(114\) | −4.02286 | − | 12.3811i | −0.376775 | − | 1.15959i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.2212 | − | 8.87924i | 1.13471 | − | 0.824417i | ||||
\(117\) | −0.414410 | + | 0.134650i | −0.0383123 | + | 0.0124484i | ||||
\(118\) | 10.3774 | + | 3.37181i | 0.955315 | + | 0.310401i | ||||
\(119\) | −9.21305 | − | 6.69367i | −0.844559 | − | 0.613608i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9779 | + | 0.697484i | −0.997988 | + | 0.0634077i | ||||
\(122\) | − | 8.22100i | − | 0.744294i | ||||||
\(123\) | −2.52405 | + | 3.47406i | −0.227586 | + | 0.313245i | ||||
\(124\) | 8.20061 | − | 25.2389i | 0.736437 | − | 2.26652i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.10813 | − | 3.71127i | 0.455068 | − | 0.330626i | ||||
\(127\) | −0.296075 | − | 0.407512i | −0.0262724 | − | 0.0361609i | 0.795679 | − | 0.605719i | \(-0.207114\pi\) |
−0.821951 | + | 0.569558i | \(0.807114\pi\) | |||||||
\(128\) | −54.2248 | + | 17.6187i | −4.79284 | + | 1.55729i | ||||
\(129\) | −2.16410 | + | 6.66041i | −0.190538 | + | 0.586416i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.1098 | 1.66963 | 0.834816 | − | 0.550529i | \(-0.185574\pi\) | ||||
0.834816 | + | 0.550529i | \(0.185574\pi\) | |||||||
\(132\) | −18.8463 | + | 0.598100i | −1.64036 | + | 0.0520579i | ||||
\(133\) | − | 10.6955i | − | 0.927415i | ||||||
\(134\) | −5.54073 | − | 4.02558i | −0.478646 | − | 0.347757i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.7850 | + | 48.5812i | 1.35355 | + | 4.16580i | ||||
\(137\) | 7.25608 | + | 9.98713i | 0.619929 | + | 0.853258i | 0.997348 | − | 0.0727841i | \(-0.0231884\pi\) |
−0.377419 | + | 0.926043i | \(0.623188\pi\) | |||||||
\(138\) | 1.37823 | + | 1.89696i | 0.117322 | + | 0.161480i | ||||
\(139\) | 2.38943 | + | 7.35391i | 0.202669 | + | 0.623750i | 0.999801 | + | 0.0199456i | \(0.00634930\pi\) |
−0.797132 | + | 0.603805i | \(0.793651\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.378765 | − | 0.275189i | −0.0318978 | − | 0.0231751i | ||||
\(142\) | 31.3649i | 2.63208i | ||||||||
\(143\) | 1.19553 | + | 0.811940i | 0.0999751 | + | 0.0678978i | ||||
\(144\) | −16.9513 | −1.41261 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.22091 | − | 22.2237i | 0.597607 | − | 1.83924i | ||||
\(147\) | −1.72386 | + | 0.560118i | −0.142182 | + | 0.0461977i | ||||
\(148\) | 29.6154 | + | 40.7620i | 2.43437 | + | 3.35062i | ||||
\(149\) | 6.15577 | − | 4.47243i | 0.504301 | − | 0.366396i | −0.306357 | − | 0.951917i | \(-0.599110\pi\) |
0.810657 | + | 0.585521i | \(0.199110\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.826389 | + | 2.54336i | −0.0672506 | + | 0.206976i | −0.979035 | − | 0.203694i | \(-0.934705\pi\) |
0.911784 | + | 0.410670i | \(0.134705\pi\) | |||||||
\(152\) | −28.1990 | + | 38.8126i | −2.28724 | + | 3.14812i | ||||
\(153\) | 5.00000i | 0.404226i | ||||||||
\(154\) | −20.1114 | − | 5.83617i | −1.62063 | − | 0.470292i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00415 | + | 1.45610i | 0.160460 | + | 0.116581i | ||||
\(157\) | −19.2113 | − | 6.24214i | −1.53323 | − | 0.498177i | −0.583731 | − | 0.811947i | \(-0.698408\pi\) |
−0.949499 | + | 0.313770i | \(0.898408\pi\) | |||||||
\(158\) | 28.6610 | − | 9.31252i | 2.28015 | − | 0.740865i | ||||
\(159\) | −8.76863 | + | 6.37078i | −0.695397 | + | 0.505236i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.595294 | + | 1.83213i | 0.0469157 | + | 0.144392i | ||||
\(162\) | −2.63654 | − | 0.856664i | −0.207146 | − | 0.0673059i | ||||
\(163\) | −5.75784 | + | 7.92498i | −0.450989 | + | 0.620733i | −0.972610 | − | 0.232445i | \(-0.925328\pi\) |
0.521621 | + | 0.853177i | \(0.325328\pi\) | |||||||
\(164\) | 24.4133 | 1.90636 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.4129 | −1.27389 | ||||||||
\(167\) | −15.0341 | + | 20.6927i | −1.16338 | + | 1.60125i | −0.465467 | + | 0.885065i | \(0.654114\pi\) |
−0.697910 | + | 0.716185i | \(0.745886\pi\) | |||||||
\(168\) | −22.1296 | − | 7.19034i | −1.70734 | − | 0.554747i | ||||
\(169\) | 3.95855 | + | 12.1832i | 0.304504 | + | 0.937166i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.79911 | + | 2.76021i | −0.290525 | + | 0.211079i | ||||
\(172\) | 37.8659 | − | 12.3034i | 2.88725 | − | 0.938123i | ||||
\(173\) | −6.42349 | − | 2.08712i | −0.488369 | − | 0.158681i | 0.0544734 | − | 0.998515i | \(-0.482652\pi\) |
−0.542843 | + | 0.839834i | \(0.682652\pi\) | |||||||
\(174\) | −5.95930 | − | 4.32969i | −0.451774 | − | 0.328233i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 34.4720 | + | 44.4127i | 2.59843 | + | 3.34773i | ||||
\(177\) | − | 3.93598i | − | 0.295846i | ||||||
\(178\) | 9.61320 | − | 13.2314i | 0.720540 | − | 0.991738i | ||||
\(179\) | −2.01539 | + | 6.20274i | −0.150638 | + | 0.463615i | −0.997693 | − | 0.0678901i | \(-0.978373\pi\) |
0.847055 | + | 0.531505i | \(0.178373\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1257 | + | 8.08332i | −0.826970 | + | 0.600829i | −0.918700 | − | 0.394955i | \(-0.870760\pi\) |
0.0917306 | + | 0.995784i | \(0.470760\pi\) | |||||||
\(182\) | 1.61714 | + | 2.22580i | 0.119870 | + | 0.164987i | ||||
\(183\) | −2.82035 | + | 0.916387i | −0.208486 | + | 0.0677412i | ||||
\(184\) | 2.67022 | − | 8.21810i | 0.196851 | − | 0.605846i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −12.9403 | −0.948830 | ||||||||
\(187\) | 13.1001 | − | 10.1680i | 0.957974 | − | 0.743555i | ||||
\(188\) | 2.66170i | 0.194124i | ||||||||
\(189\) | −1.84261 | − | 1.33873i | −0.134030 | − | 0.0973786i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00607 | − | 18.4848i | −0.434584 | − | 1.33751i | −0.893512 | − | 0.449038i | \(-0.851767\pi\) |
0.458929 | − | 0.888473i | \(-0.348233\pi\) | |||||||
\(192\) | 23.3517 | + | 32.1409i | 1.68527 | + | 2.31957i | ||||
\(193\) | −13.2912 | − | 18.2938i | −0.956722 | − | 1.31681i | −0.948476 | − | 0.316849i | \(-0.897375\pi\) |
−0.00824604 | − | 0.999966i | \(-0.502625\pi\) | |||||||
\(194\) | 7.40846 | + | 22.8009i | 0.531896 | + | 1.63701i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.33685 | + | 6.05707i | 0.595489 | + | 0.432648i | ||||
\(197\) | − | 23.0300i | − | 1.64082i | −0.571776 | − | 0.820410i | \(-0.693745\pi\) | ||
0.571776 | − | 0.820410i | \(-0.306255\pi\) | |||||||
\(198\) | 3.11717 | + | 8.64989i | 0.221528 | + | 0.614721i | ||||
\(199\) | 19.6216 | 1.39094 | 0.695468 | − | 0.718557i | \(-0.255197\pi\) | ||||
0.695468 | + | 0.718557i | \(0.255197\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.763420 | + | 2.34957i | −0.0538475 | + | 0.165726i | ||||
\(202\) | −14.9789 | + | 4.86693i | −1.05391 | + | 0.342436i | ||||
\(203\) | −3.55717 | − | 4.89602i | −0.249664 | − | 0.343633i | ||||
\(204\) | 22.9972 | − | 16.7084i | 1.61013 | − | 1.16982i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.11035 | + | 3.41730i | −0.0773616 | + | 0.238095i | ||||
\(207\) | 0.497155 | − | 0.684276i | 0.0345547 | − | 0.0475604i | ||||
\(208\) | − | 7.38630i | − | 0.512148i | ||||||
\(209\) | 14.9577 | + | 4.34059i | 1.03464 | + | 0.300245i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0403903 | − | 0.0293453i | −0.00278059 | − | 0.00202021i | 0.586394 | − | 0.810026i | \(-0.300547\pi\) |
−0.589175 | + | 0.808006i | \(0.700547\pi\) | |||||||
\(212\) | 58.6040 | + | 19.0416i | 4.02494 | + | 1.30778i | ||||
\(213\) | 10.7602 | − | 3.49622i | 0.737280 | − | 0.239557i | ||||
\(214\) | −27.3636 | + | 19.8808i | −1.87054 | + | 1.35902i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.15700 | + | 9.71623i | 0.214806 | + | 0.661106i | ||||
\(217\) | −10.1111 | − | 3.28530i | −0.686387 | − | 0.223021i | ||||
\(218\) | −19.8215 | + | 27.2819i | −1.34248 | + | 1.84777i | ||||
\(219\) | −8.42910 | −0.569586 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.17868 | −0.146554 | ||||||||
\(222\) | 14.4410 | − | 19.8764i | 0.969218 | − | 1.33401i | ||||
\(223\) | 0.718012 | + | 0.233296i | 0.0480816 | + | 0.0156227i | 0.332959 | − | 0.942941i | \(-0.391953\pi\) |
−0.284877 | + | 0.958564i | \(0.591953\pi\) | |||||||
\(224\) | 18.6935 | + | 57.5326i | 1.24901 | + | 3.84406i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.318592 | + | 0.231470i | −0.0211924 | + | 0.0153972i | ||||
\(227\) | 7.87855 | − | 2.55989i | 0.522917 | − | 0.169906i | −0.0356515 | − | 0.999364i | \(-0.511351\pi\) |
0.558569 | + | 0.829458i | \(0.311351\pi\) | |||||||
\(228\) | 25.3909 | + | 8.24999i | 1.68155 | + | 0.546369i | ||||
\(229\) | −2.32691 | − | 1.69060i | −0.153767 | − | 0.111718i | 0.508242 | − | 0.861214i | \(-0.330296\pi\) |
−0.662008 | + | 0.749496i | \(0.730296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.239609 | + | 7.55011i | 0.0157651 | + | 0.496761i | ||||
\(232\) | 27.1457i | 1.78220i | ||||||||
\(233\) | −3.04395 | + | 4.18964i | −0.199416 | + | 0.274473i | −0.897000 | − | 0.442030i | \(-0.854258\pi\) |
0.697584 | + | 0.716503i | \(0.254258\pi\) | |||||||
\(234\) | 0.373280 | − | 1.14884i | 0.0244021 | − | 0.0751019i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −18.1033 | + | 13.1528i | −1.17842 | + | 0.856176i | ||||
\(237\) | −6.38963 | − | 8.79457i | −0.415051 | − | 0.571269i | ||||
\(238\) | 30.0248 | − | 9.75565i | 1.94622 | − | 0.632365i | ||||
\(239\) | −3.34751 | + | 10.3026i | −0.216532 | + | 0.666418i | 0.782509 | + | 0.622640i | \(0.213940\pi\) |
−0.999041 | + | 0.0437789i | \(0.986060\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.96526 | −0.191009 | −0.0955045 | − | 0.995429i | \(-0.530446\pi\) | ||||
−0.0955045 | + | 0.995429i | \(0.530446\pi\) | |||||||
\(242\) | 16.3238 | − | 25.7574i | 1.04933 | − | 1.65575i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 13.6396 | + | 9.90974i | 0.873185 | + | 0.634406i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.67866 | − | 11.3218i | −0.234543 | − | 0.721849i | ||||
\(247\) | −1.20273 | − | 1.65541i | −0.0765277 | − | 0.105331i | ||||
\(248\) | 28.0302 | + | 38.5803i | 1.77992 | + | 2.44985i | ||||
\(249\) | 1.82953 | + | 5.63073i | 0.115942 | + | 0.356833i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.2504 | + | 10.3535i | 0.899475 | + | 0.653507i | 0.938331 | − | 0.345738i | \(-0.112371\pi\) |
−0.0388560 | + | 0.999245i | \(0.512371\pi\) | |||||||
\(252\) | 12.9486i | 0.815685i | ||||||||
\(253\) | −2.80383 | + | 0.0889816i | −0.176275 | + | 0.00559422i | ||||
\(254\) | 1.39640 | 0.0876182 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 24.2895 | − | 74.7554i | 1.51809 | − | 4.67221i | ||||
\(257\) | 19.9386 | − | 6.47845i | 1.24374 | − | 0.404115i | 0.388064 | − | 0.921632i | \(-0.373144\pi\) |
0.855672 | + | 0.517518i | \(0.173144\pi\) | |||||||
\(258\) | −11.4115 | − | 15.7065i | −0.710447 | − | 0.977846i | ||||
\(259\) | 16.3299 | − | 11.8644i | 1.01469 | − | 0.737217i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.821093 | + | 2.52706i | −0.0508244 | + | 0.156421i | ||||
\(262\) | −31.1389 | + | 42.8590i | −1.92377 | + | 2.64784i | ||||
\(263\) | 8.43471i | 0.520107i | 0.965594 | + | 0.260053i | \(0.0837402\pi\) | ||||
−0.965594 | + | 0.260053i | \(0.916260\pi\) | |||||||
\(264\) | 19.0367 | − | 28.0302i | 1.17163 | − | 1.72514i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 23.9875 | + | 17.4280i | 1.47077 | + | 1.06858i | ||||
\(267\) | −5.61084 | − | 1.82307i | −0.343378 | − | 0.111570i | ||||
\(268\) | 13.3578 | − | 4.34021i | 0.815958 | − | 0.265121i | ||||
\(269\) | 7.80173 | − | 5.66829i | 0.475680 | − | 0.345601i | −0.323971 | − | 0.946067i | \(-0.605018\pi\) |
0.799651 | + | 0.600466i | \(0.205018\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.16056 | + | 9.72719i | 0.191990 | + | 0.590885i | 0.999999 | + | 0.00171395i | \(0.000545568\pi\) |
−0.808008 | + | 0.589171i | \(0.799454\pi\) | |||||||
\(272\) | −80.6081 | − | 26.1912i | −4.88759 | − | 1.58807i | ||||
\(273\) | 0.583336 | − | 0.802893i | 0.0353051 | − | 0.0485933i | ||||
\(274\) | −34.2225 | −2.06746 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.80862 | −0.289445 | ||||||||
\(277\) | 3.43210 | − | 4.72388i | 0.206215 | − | 0.283830i | −0.693365 | − | 0.720586i | \(-0.743873\pi\) |
0.899580 | + | 0.436756i | \(0.143873\pi\) | |||||||
\(278\) | −20.3867 | − | 6.62403i | −1.22271 | − | 0.397283i | ||||
\(279\) | 1.44244 | + | 4.43939i | 0.0863569 | + | 0.265779i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.6611 | + | 8.47225i | −0.695640 | + | 0.505412i | −0.878509 | − | 0.477725i | \(-0.841461\pi\) |
0.182869 | + | 0.983137i | \(0.441461\pi\) | |||||||
\(282\) | 1.23437 | − | 0.401072i | 0.0735058 | − | 0.0238835i | ||||
\(283\) | −10.1130 | − | 3.28592i | −0.601156 | − | 0.195327i | −0.00740011 | − | 0.999973i | \(-0.502356\pi\) |
−0.593756 | + | 0.804645i | \(0.702356\pi\) | |||||||
\(284\) | −52.0380 | − | 37.8078i | −3.08789 | − | 2.24348i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.76908 | + | 1.35827i | −0.222870 | + | 0.0803161i | ||||
\(287\) | − | 9.78037i | − | 0.577317i | ||||||
\(288\) | 15.6117 | − | 21.4877i | 0.919929 | − | 1.26617i | ||||
\(289\) | −2.47214 | + | 7.60845i | −0.145420 | + | 0.447556i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.99640 | − | 5.08318i | 0.410136 | − | 0.297982i | ||||
\(292\) | 28.1674 | + | 38.7691i | 1.64837 | + | 2.26879i | ||||
\(293\) | 7.98484 | − | 2.59443i | 0.466479 | − | 0.151568i | −0.0663405 | − | 0.997797i | \(-0.521132\pi\) |
0.532820 | + | 0.846229i | \(0.321132\pi\) | |||||||
\(294\) | 1.55277 | − | 4.77894i | 0.0905594 | − | 0.278713i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −90.5404 | −5.26256 | ||||||||
\(297\) | 2.62002 | − | 2.03359i | 0.152029 | − | 0.118001i | ||||
\(298\) | 21.0937i | 1.22193i | ||||||||
\(299\) | 0.298164 | + | 0.216629i | 0.0172433 | + | 0.0125280i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.92893 | − | 15.1697i | −0.284099 | − | 0.874366i | ||||
\(302\) | −4.35762 | − | 5.99774i | −0.250753 | − | 0.345131i | ||||
\(303\) | 3.33936 | + | 4.59624i | 0.191841 | + | 0.264047i | ||||
\(304\) | −24.5985 | − | 75.7065i | −1.41082 | − | 4.34206i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −11.2139 | − | 8.14736i | −0.641055 | − | 0.465753i | ||||
\(307\) | − | 4.51902i | − | 0.257914i | −0.991650 | − | 0.128957i | \(-0.958837\pi\) | ||
0.991650 | − | 0.128957i | \(-0.0411629\pi\) | |||||||
\(308\) | 33.9256 | − | 26.3322i | 1.93309 | − | 1.50042i | ||||
\(309\) | 1.29613 | 0.0737343 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.41548 | − | 22.8225i | 0.420493 | − | 1.29415i | −0.486751 | − | 0.873541i | \(-0.661818\pi\) |
0.907244 | − | 0.420604i | \(-0.138182\pi\) | |||||||
\(312\) | −4.23372 | + | 1.37562i | −0.239687 | + | 0.0778791i | ||||
\(313\) | 15.2052 | + | 20.9281i | 0.859448 | + | 1.18293i | 0.981701 | + | 0.190430i | \(0.0609882\pi\) |
−0.122253 | + | 0.992499i | \(0.539012\pi\) | |||||||
\(314\) | 45.3040 | − | 32.9153i | 2.55665 | − | 1.85752i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.0979 | + | 58.7774i | −1.07434 | + | 3.30649i | ||||
\(317\) | −1.70645 | + | 2.34873i | −0.0958441 | + | 0.131918i | −0.854246 | − | 0.519869i | \(-0.825981\pi\) |
0.758402 | + | 0.651787i | \(0.225981\pi\) | |||||||
\(318\) | − | 30.0471i | − | 1.68496i | ||||||
\(319\) | 8.29072 | − | 2.98774i | 0.464191 | − | 0.167281i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.87063 | + | 7.17143i | 0.550925 | + | 0.400270i | ||||
\(322\) | −5.07906 | − | 1.65029i | −0.283045 | − | 0.0919669i | ||||
\(323\) | −22.3306 | + | 7.25565i | −1.24251 | + | 0.403715i | ||||
\(324\) | 4.59944 | − | 3.34169i | 0.255524 | − | 0.185649i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.39172 | − | 25.8271i | −0.464775 | − | 1.43043i | ||||
\(327\) | 11.5690 | + | 3.75900i | 0.639767 | + | 0.207873i | ||||
\(328\) | −25.7863 | + | 35.4919i | −1.42381 | + | 1.95971i | ||||
\(329\) | 1.06632 | 0.0587881 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9837 | 0.603720 | 0.301860 | − | 0.953352i | \(-0.402392\pi\) | ||||
0.301860 | + | 0.953352i | \(0.402392\pi\) | |||||||
\(332\) | 19.7845 | − | 27.2310i | 1.08581 | − | 1.49449i | ||||
\(333\) | −8.42864 | − | 2.73863i | −0.461886 | − | 0.150076i | ||||
\(334\) | −21.9114 | − | 67.4364i | −1.19894 | − | 3.68996i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 31.2346 | − | 22.6933i | 1.70399 | − | 1.23802i | ||||
\(337\) | 12.2174 | − | 3.96968i | 0.665525 | − | 0.216242i | 0.0432780 | − | 0.999063i | \(-0.486220\pi\) |
0.622247 | + | 0.782821i | \(0.286220\pi\) | |||||||
\(338\) | −33.7744 | − | 10.9740i | −1.83709 | − | 0.596906i | ||||
\(339\) | 0.114923 | + | 0.0834963i | 0.00624175 | + | 0.00453490i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.69793 | − | 12.8071i | 0.471020 | − | 0.693545i | ||||
\(342\) | − | 13.0182i | − | 0.703946i | ||||||
\(343\) | 11.7977 | − | 16.2381i | 0.637016 | − | 0.876777i | ||||
\(344\) | −22.1090 | + | 68.0444i | −1.19204 | + | 3.66871i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.1478 | − | 11.0056i | 0.814353 | − | 0.591662i | ||||
\(347\) | −1.11074 | − | 1.52881i | −0.0596279 | − | 0.0820707i | 0.778162 | − | 0.628064i | \(-0.216152\pi\) |
−0.837790 | + | 0.545993i | \(0.816152\pi\) | |||||||
\(348\) | 14.3669 | − | 4.66809i | 0.770147 | − | 0.250236i | ||||
\(349\) | −7.34802 | + | 22.6149i | −0.393330 | + | 1.21055i | 0.536924 | + | 0.843631i | \(0.319586\pi\) |
−0.930254 | + | 0.366915i | \(0.880414\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.435737 | −0.0232579 | ||||||||
\(352\) | −88.0460 | + | 2.79421i | −4.69287 | + | 0.148932i | ||||
\(353\) | − | 20.2294i | − | 1.07670i | −0.842720 | − | 0.538352i | \(-0.819047\pi\) | ||
0.842720 | − | 0.538352i | \(-0.180953\pi\) | |||||||
\(354\) | 8.82752 | + | 6.41357i | 0.469177 | + | 0.340877i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.3646 | + | 31.8988i | 0.549321 | + | 1.69063i | ||||
\(357\) | −6.69367 | − | 9.21305i | −0.354267 | − | 0.487606i | ||||
\(358\) | −10.6273 | − | 14.6273i | −0.561672 | − | 0.773075i | ||||
\(359\) | 5.74455 | + | 17.6799i | 0.303186 | + | 0.933109i | 0.980348 | + | 0.197276i | \(0.0632094\pi\) |
−0.677162 | + | 0.735834i | \(0.736791\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.46912 | − | 1.79392i | −0.129954 | − | 0.0944170i | ||||
\(362\) | − | 38.1241i | − | 2.00376i | ||||||
\(363\) | −10.6561 | − | 2.72900i | −0.559300 | − | 0.143235i | ||||
\(364\) | −5.64219 | −0.295731 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.54043 | − | 7.81863i | 0.132790 | − | 0.408687i | ||||
\(367\) | 5.61894 | − | 1.82571i | 0.293306 | − | 0.0953010i | −0.158668 | − | 0.987332i | \(-0.550720\pi\) |
0.451974 | + | 0.892031i | \(0.350720\pi\) | |||||||
\(368\) | 8.42742 | + | 11.5993i | 0.439310 | + | 0.604658i | ||||
\(369\) | −3.47406 | + | 2.52405i | −0.180852 | + | 0.131397i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.62838 | − | 23.4777i | 0.396046 | − | 1.21890i | ||||
\(372\) | 15.5985 | − | 21.4695i | 0.808744 | − | 1.11314i | ||||
\(373\) | − | 1.66992i | − | 0.0864650i | −0.999065 | − | 0.0432325i | \(-0.986234\pi\) | ||
0.999065 | − | 0.0432325i | \(-0.0137656\pi\) | |||||||
\(374\) | 1.45823 | + | 45.9490i | 0.0754031 | + | 2.37597i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.86956 | − | 2.81140i | −0.199557 | − | 0.144987i | ||||
\(377\) | −1.10113 | − | 0.357780i | −0.0567113 | − | 0.0184266i | ||||
\(378\) | 6.00496 | − | 1.95113i | 0.308862 | − | 0.100355i | ||||
\(379\) | 6.82420 | − | 4.95807i | 0.350536 | − | 0.254679i | −0.398558 | − | 0.917143i | \(-0.630489\pi\) |
0.749094 | + | 0.662464i | \(0.230489\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.155656 | − | 0.479059i | −0.00797449 | − | 0.0245430i | ||||
\(382\) | 51.2439 | + | 16.6502i | 2.62187 | + | 0.851896i | ||||
\(383\) | 12.8616 | − | 17.7025i | 0.657199 | − | 0.904558i | −0.342185 | − | 0.939633i | \(-0.611167\pi\) |
0.999385 | + | 0.0350750i | \(0.0111670\pi\) | |||||||
\(384\) | −57.0153 | −2.90955 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 62.6865 | 3.19066 | ||||||||
\(387\) | −4.11636 | + | 5.66568i | −0.209246 | + | 0.288003i | ||||
\(388\) | −46.7596 | − | 15.1931i | −2.37386 | − | 0.771314i | ||||
\(389\) | 0.121163 | + | 0.372902i | 0.00614322 | + | 0.0189069i | 0.954081 | − | 0.299548i | \(-0.0968360\pi\) |
−0.947938 | + | 0.318455i | \(0.896836\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.42138 | − | 2.48578i | 0.173027 | − | 0.125711i | ||||
\(392\) | −17.6114 | + | 5.72230i | −0.889512 | + | 0.289020i | ||||
\(393\) | 18.1745 | + | 5.90526i | 0.916783 | + | 0.297881i | ||||
\(394\) | 51.6511 | + | 37.5267i | 2.60215 | + | 1.89057i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −18.1087 | − | 5.25499i | −0.909995 | − | 0.264073i | ||||
\(397\) | − | 35.7823i | − | 1.79586i | −0.440134 | − | 0.897932i | \(-0.645069\pi\) | ||
0.440134 | − | 0.897932i | \(-0.354931\pi\) | |||||||
\(398\) | −31.9728 | + | 44.0068i | −1.60265 | + | 2.20586i | ||||
\(399\) | 3.30508 | − | 10.1720i | 0.165461 | − | 0.509237i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.6074 | + | 17.8783i | −1.22884 | + | 0.892802i | −0.996802 | − | 0.0799056i | \(-0.974538\pi\) |
−0.232034 | + | 0.972708i | \(0.574538\pi\) | |||||||
\(402\) | −4.02558 | − | 5.54073i | −0.200778 | − | 0.276347i | ||||
\(403\) | −1.93440 | + | 0.628526i | −0.0963596 | + | 0.0313091i | ||||
\(404\) | 9.98101 | − | 30.7184i | 0.496574 | − | 1.52830i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.7770 | 0.832627 | ||||||||
\(407\) | 9.96515 | + | 27.6524i | 0.493954 | + | 1.37068i | ||||
\(408\) | 51.0813i | 2.52890i | ||||||||
\(409\) | −13.1625 | − | 9.56310i | −0.650843 | − | 0.472865i | 0.212715 | − | 0.977114i | \(-0.431769\pi\) |
−0.863558 | + | 0.504249i | \(0.831769\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.81475 | + | 11.7406i | 0.188168 | + | 0.579120i | ||||
\(412\) | −4.33126 | − | 5.96147i | −0.213386 | − | 0.293701i | ||||
\(413\) | 5.26923 | + | 7.25248i | 0.259282 | + | 0.356871i | ||||
\(414\) | 0.724576 | + | 2.23002i | 0.0356110 | + | 0.109599i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.36298 | + | 6.80260i | 0.459058 | + | 0.333525i | ||||
\(417\) | 7.73236i | 0.378655i | ||||||||
\(418\) | −34.1080 | + | 26.4738i | −1.66828 | + | 1.29488i | ||||
\(419\) | 40.0703 | 1.95756 | 0.978781 | − | 0.204910i | \(-0.0656903\pi\) | ||||
0.978781 | + | 0.204910i | \(0.0656903\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.99316 | + | 18.4450i | −0.292089 | + | 0.898956i | 0.692095 | + | 0.721806i | \(0.256688\pi\) |
−0.984184 | + | 0.177150i | \(0.943312\pi\) | |||||||
\(422\) | 0.131630 | − | 0.0427691i | 0.00640764 | − | 0.00208197i | ||||
\(423\) | −0.275189 | − | 0.378765i | −0.0133801 | − | 0.0184162i | ||||
\(424\) | −89.5825 | + | 65.0855i | −4.35051 | + | 3.16083i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.69229 | + | 29.8298i | −0.469593 | + | 1.44526i | ||||
\(427\) | 3.97000 | − | 5.46424i | 0.192122 | − | 0.264433i | ||||
\(428\) | − | 69.3640i | − | 3.35284i | ||||||
\(429\) | 0.886111 | + | 1.14164i | 0.0427819 | + | 0.0551188i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.4616 | − | 19.9520i | −1.32278 | − | 0.961056i | −0.999893 | − | 0.0146183i | \(-0.995347\pi\) |
−0.322887 | − | 0.946438i | \(-0.604653\pi\) | |||||||
\(432\) | −16.1216 | − | 5.23823i | −0.775652 | − | 0.252025i | ||||
\(433\) | 12.4736 | − | 4.05291i | 0.599442 | − | 0.194770i | 0.00645020 | − | 0.999979i | \(-0.497947\pi\) |
0.592991 | + | 0.805209i | \(0.297947\pi\) | |||||||
\(434\) | 23.8440 | − | 17.3236i | 1.14455 | − | 0.831562i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.3707 | − | 65.7723i | −1.02347 | − | 3.14992i | ||||
\(437\) | 3.77749 | + | 1.22738i | 0.180702 | + | 0.0587136i | ||||
\(438\) | 13.7350 | − | 18.9046i | 0.656283 | − | 0.903296i | ||||
\(439\) | 9.64731 | 0.460441 | 0.230220 | − | 0.973138i | \(-0.426055\pi\) | ||||
0.230220 | + | 0.973138i | \(0.426055\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.81258 | −0.0863133 | ||||||||
\(442\) | 3.55010 | − | 4.88630i | 0.168861 | − | 0.232418i | ||||
\(443\) | −8.47781 | − | 2.75461i | −0.402793 | − | 0.130875i | 0.100613 | − | 0.994926i | \(-0.467920\pi\) |
−0.503405 | + | 0.864050i | \(0.667920\pi\) | |||||||
\(444\) | 15.5697 | + | 47.9187i | 0.738906 | + | 2.27412i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.69321 | + | 1.23019i | −0.0801759 | + | 0.0582512i | ||||
\(447\) | 7.23654 | − | 2.35130i | 0.342277 | − | 0.111212i | ||||
\(448\) | −86.0562 | − | 27.9614i | −4.06578 | − | 1.32105i | ||||
\(449\) | −10.0616 | − | 7.31019i | −0.474837 | − | 0.344989i | 0.324487 | − | 0.945890i | \(-0.394809\pi\) |
−0.799323 | + | 0.600901i | \(0.794809\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.6779 | + | 3.96921i | 0.644066 | + | 0.186903i | ||||
\(452\) | − | 0.807599i | − | 0.0379863i | ||||||
\(453\) | −1.57188 | + | 2.16351i | −0.0738536 | + | 0.101651i | ||||
\(454\) | −7.09660 | + | 21.8411i | −0.333060 | + | 1.02505i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −38.8126 | + | 28.1990i | −1.81757 | + | 1.32054i | ||||
\(457\) | −22.4289 | − | 30.8707i | −1.04918 | − | 1.44407i | −0.889519 | − | 0.456898i | \(-0.848960\pi\) |
−0.159659 | − | 0.987172i | \(-0.551040\pi\) | |||||||
\(458\) | 7.58327 | − | 2.46395i | 0.354343 | − | 0.115133i | ||||
\(459\) | −1.54508 | + | 4.75528i | −0.0721184 | + | 0.221958i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.3847 | 1.60145 | 0.800726 | − | 0.599030i | \(-0.204447\pi\) | ||||
0.800726 | + | 0.599030i | \(0.204447\pi\) | |||||||
\(462\) | −17.3236 | − | 11.7653i | −0.805969 | − | 0.547372i | ||||
\(463\) | − | 40.2561i | − | 1.87086i | −0.353511 | − | 0.935430i | \(-0.615012\pi\) | ||
0.353511 | − | 0.935430i | \(-0.384988\pi\) | |||||||
\(464\) | −36.4393 | − | 26.4747i | −1.69165 | − | 1.22906i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.43639 | − | 13.6538i | −0.205512 | − | 0.632501i | ||||
\(467\) | 8.88502 | + | 12.2292i | 0.411150 | + | 0.565899i | 0.963498 | − | 0.267714i | \(-0.0862683\pi\) |
−0.552349 | + | 0.833613i | \(0.686268\pi\) | |||||||
\(468\) | 1.45610 | + | 2.00415i | 0.0673081 | + | 0.0926417i | ||||
\(469\) | −1.73876 | − | 5.35135i | −0.0802885 | − | 0.247102i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.3421 | − | 11.8732i | −0.753005 | − | 0.547090i | ||||
\(472\) | − | 40.2110i | − | 1.85086i | ||||||
\(473\) | 23.2152 | − | 0.736752i | 1.06744 | − | 0.0338759i | ||||
\(474\) | 30.1360 | 1.38419 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −20.0067 | + | 61.5743i | −0.917005 | + | 2.82225i | ||||
\(477\) | −10.3081 | + | 3.34932i | −0.471977 | + | 0.153355i | ||||
\(478\) | −17.6517 | − | 24.2955i | −0.807370 | − | 1.11125i | ||||
\(479\) | −23.3033 | + | 16.9308i | −1.06476 | + | 0.773590i | −0.974962 | − | 0.222370i | \(-0.928621\pi\) |
−0.0897931 | + | 0.995960i | \(0.528621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.19332 | − | 3.67267i | 0.0544108 | − | 0.167459i | ||||
\(482\) | 4.83180 | − | 6.65040i | 0.220083 | − | 0.302918i | ||||
\(483\) | 1.92641i | 0.0876548i | ||||||||
\(484\) | 23.0575 | + | 58.1316i | 1.04807 | + | 2.64234i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.24278 | − | 1.62947i | −0.101734 | − | 0.0739143i | ||||
\(487\) | −27.4404 | − | 8.91592i | −1.24344 | − | 0.404019i | −0.387876 | − | 0.921712i | \(-0.626791\pi\) |
−0.855567 | + | 0.517693i | \(0.826791\pi\) | |||||||
\(488\) | −28.8134 | + | 9.36204i | −1.30432 | + | 0.423799i | ||||
\(489\) | −7.92498 | + | 5.75784i | −0.358380 | + | 0.260378i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.61569 | − | 14.2056i | −0.208303 | − | 0.641092i | −0.999562 | − | 0.0296097i | \(-0.990574\pi\) |
0.791258 | − | 0.611482i | \(-0.209426\pi\) | |||||||
\(492\) | 23.2184 | + | 7.54413i | 1.04677 | + | 0.340116i | ||||
\(493\) | −7.80906 | + | 10.7482i | −0.351702 | + | 0.484076i | ||||
\(494\) | 5.67253 | 0.255219 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −79.1260 | −3.55286 | ||||||||
\(497\) | −15.1464 | + | 20.8473i | −0.679410 | + | 0.935128i | ||||
\(498\) | −15.6096 | − | 5.07188i | −0.699484 | − | 0.227276i | ||||
\(499\) | −6.85987 | − | 21.1125i | −0.307090 | − | 0.945125i | −0.978889 | − | 0.204392i | \(-0.934478\pi\) |
0.671799 | − | 0.740733i | \(-0.265522\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.6927 | + | 15.0341i | −0.924483 | + | 0.671676i | ||||
\(502\) | −46.4411 | + | 15.0896i | −2.07277 | + | 0.673484i | ||||
\(503\) | 0.147752 | + | 0.0480077i | 0.00658795 | + | 0.00214056i | 0.312309 | − | 0.949981i | \(-0.398898\pi\) |
−0.305721 | + | 0.952121i | \(0.598898\pi\) | |||||||
\(504\) | −18.8246 | − | 13.6768i | −0.838513 | − | 0.609215i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.36919 | − | 6.43335i | 0.194234 | − | 0.285997i | ||||
\(507\) | 12.8101i | 0.568918i | ||||||||
\(508\) | −1.68325 | + | 2.31680i | −0.0746822 | + | 0.102791i | ||||
\(509\) | 5.75932 | − | 17.7254i | 0.255277 | − | 0.785663i | −0.738498 | − | 0.674256i | \(-0.764464\pi\) |
0.993775 | − | 0.111407i | \(-0.0355356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.5315 | − | 11.2843i | 0.687075 | − | 0.499189i | ||||
\(512\) | 61.0550 | + | 84.0350i | 2.69828 | + | 3.71386i | ||||
\(513\) | −4.46612 | + | 1.45113i | −0.197184 | + | 0.0640690i | ||||
\(514\) | −17.9597 | + | 55.2743i | −0.792169 | + | 2.43804i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 39.8145 | 1.75274 | ||||||||
\(517\) | −0.432749 | + | 1.49125i | −0.0190323 | + | 0.0655852i | ||||
\(518\) | 55.9571i | 2.45861i | ||||||||
\(519\) | −5.46415 | − | 3.96994i | −0.239850 | − | 0.174261i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.69969 | + | 29.8526i | 0.424951 | + | 1.30786i | 0.903041 | + | 0.429554i | \(0.141329\pi\) |
−0.478090 | + | 0.878311i | \(0.658671\pi\) | |||||||
\(522\) | −4.32969 | − | 5.95930i | −0.189505 | − | 0.260832i | ||||
\(523\) | 14.0975 | + | 19.4036i | 0.616442 | + | 0.848459i | 0.997088 | − | 0.0762616i | \(-0.0242984\pi\) |
−0.380646 | + | 0.924721i | \(0.624298\pi\) | |||||||
\(524\) | −33.5727 | − | 103.326i | −1.46663 | − | 4.51382i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.9172 | − | 13.7441i | −0.824828 | − | 0.599272i | ||||
\(527\) | 23.3392i | 1.01667i | ||||||||
\(528\) | 19.0606 | + | 52.8914i | 0.829504 | + | 2.30180i | ||||
\(529\) | 22.2846 | 0.968896 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.21629 | − | 3.74334i | 0.0527823 | − | 0.162447i | ||||
\(532\) | −57.8300 | + | 18.7901i | −2.50725 | + | 0.814655i | ||||
\(533\) | −1.09982 | − | 1.51378i | −0.0476386 | − | 0.0655689i | ||||
\(534\) | 13.2314 | − | 9.61320i | 0.572580 | − | 0.416004i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.79929 | + | 24.0038i | −0.336878 | + | 1.03680i | ||||
\(537\) | −3.83351 | + | 5.27637i | −0.165428 | + | 0.227692i | ||||
\(538\) | 26.7338i | 1.15258i | ||||||||
\(539\) | 3.68605 | + | 4.74899i | 0.158769 | + | 0.204554i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.06851 | − | 5.86211i | −0.346892 | − | 0.252032i | 0.400672 | − | 0.916222i | \(-0.368777\pi\) |
−0.747564 | + | 0.664190i | \(0.768777\pi\) | |||||||
\(542\) | −26.9660 | − | 8.76177i | −1.15829 | − | 0.376350i | ||||
\(543\) | −13.0791 | + | 4.24966i | −0.561278 | + | 0.182370i | ||||
\(544\) | 107.438 | − | 78.0586i | 4.60638 | − | 3.34673i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.850179 | + | 2.61658i | 0.0363843 | + | 0.111979i | ||||
\(547\) | 38.0582 | + | 12.3659i | 1.62725 | + | 0.528726i | 0.973637 | − | 0.228103i | \(-0.0732522\pi\) |
0.653614 | + | 0.756829i | \(0.273252\pi\) | |||||||
\(548\) | 41.2524 | − | 56.7791i | 1.76222 | − | 2.42548i | ||||
\(549\) | −2.96549 | −0.126564 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.4777 | −0.531567 | ||||||||
\(552\) | 5.07906 | − | 6.99073i | 0.216179 | − | 0.297545i | ||||
\(553\) | 23.5472 | + | 7.65094i | 1.00133 | + | 0.325351i | ||||
\(554\) | 5.00209 | + | 15.3948i | 0.212518 | + | 0.654064i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 35.5645 | − | 25.8391i | 1.50827 | − | 1.09582i | ||||
\(557\) | −7.38064 | + | 2.39812i | −0.312728 | + | 0.101611i | −0.461176 | − | 0.887309i | \(-0.652572\pi\) |
0.148448 | + | 0.988920i | \(0.452572\pi\) | |||||||
\(558\) | −12.3070 | − | 3.99878i | −0.520996 | − | 0.169282i | ||||
\(559\) | −2.46875 | − | 1.79365i | −0.104417 | − | 0.0758633i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.6010 | − | 5.62216i | 0.658675 | − | 0.237368i | ||||
\(562\) | − | 39.9584i | − | 1.68554i | ||||||
\(563\) | 10.8361 | − | 14.9146i | 0.456688 | − | 0.628577i | −0.517130 | − | 0.855907i | \(-0.673000\pi\) |
0.973818 | + | 0.227330i | \(0.0729996\pi\) | |||||||
\(564\) | −0.822511 | + | 2.53143i | −0.0346340 | + | 0.106592i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 23.8484 | − | 17.3269i | 1.00242 | − | 0.728304i | ||||
\(567\) | −1.33873 | − | 1.84261i | −0.0562216 | − | 0.0773823i | ||||
\(568\) | 109.929 | − | 35.7182i | 4.61253 | − | 1.49870i | ||||
\(569\) | −3.40658 | + | 10.4844i | −0.142811 | + | 0.439528i | −0.996723 | − | 0.0808896i | \(-0.974224\pi\) |
0.853912 | + | 0.520418i | \(0.174224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.1338 | −1.59585 | −0.797926 | − | 0.602756i | \(-0.794069\pi\) | ||||
−0.797926 | + | 0.602756i | \(0.794069\pi\) | |||||||
\(572\) | 2.28979 | − | 7.89062i | 0.0957410 | − | 0.329923i | ||||
\(573\) | − | 19.4360i | − | 0.811952i | ||||||
\(574\) | 21.9352 | + | 15.9368i | 0.915556 | + | 0.665191i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.2767 | + | 37.7839i | 0.511530 | + | 1.57433i | ||||
\(577\) | 6.47284 | + | 8.90910i | 0.269468 | + | 0.370891i | 0.922210 | − | 0.386690i | \(-0.126382\pi\) |
−0.652742 | + | 0.757580i | \(0.726382\pi\) | |||||||
\(578\) | −13.0358 | − | 17.9422i | −0.542217 | − | 0.746297i | ||||
\(579\) | −6.98760 | − | 21.5056i | −0.290395 | − | 0.893743i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9092 | − | 7.92597i | −0.452589 | − | 0.328825i | ||||
\(582\) | 23.9743i | 0.993765i | ||||||||
\(583\) | 29.7378 | + | 20.1964i | 1.23162 | + | 0.836448i | ||||
\(584\) | −86.1138 | −3.56341 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.19234 | + | 22.1358i | −0.297113 | + | 0.914420i | ||||
\(587\) | 11.2643 | − | 3.65999i | 0.464927 | − | 0.151064i | −0.0671803 | − | 0.997741i | \(-0.521400\pi\) |
0.532107 | + | 0.846677i | \(0.321400\pi\) | |||||||
\(588\) | 6.05707 | + | 8.33685i | 0.249790 | + | 0.343806i | ||||
\(589\) | −17.7337 | + | 12.8843i | −0.730703 | + | 0.530887i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.11666 | − | 21.9028i | 0.292740 | − | 0.900962i | ||||
\(592\) | 88.3024 | − | 121.538i | 3.62920 | − | 4.99517i | ||||
\(593\) | 9.25062i | 0.379877i | 0.981796 | + | 0.189939i | \(0.0608289\pi\) | ||||
−0.981796 | + | 0.189939i | \(0.939171\pi\) | |||||||
\(594\) | 0.291645 | + | 9.18980i | 0.0119663 | + | 0.377062i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −34.9969 | − | 25.4267i | −1.43353 | − | 1.04152i | ||||
\(597\) | 18.6612 | + | 6.06340i | 0.763753 | + | 0.248158i | ||||
\(598\) | −0.971700 | + | 0.315724i | −0.0397358 | + | 0.0129109i | ||||
\(599\) | 19.1603 | − | 13.9208i | 0.782868 | − | 0.568787i | −0.122971 | − | 0.992410i | \(-0.539242\pi\) |
0.905838 | + | 0.423624i | \(0.139242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.2090 | + | 34.4978i | 0.457225 | + | 1.40719i | 0.868503 | + | 0.495684i | \(0.165083\pi\) |
−0.411278 | + | 0.911510i | \(0.634917\pi\) | |||||||
\(602\) | 42.0537 | + | 13.6641i | 1.71398 | + | 0.556907i | ||||
\(603\) | −1.45211 | + | 1.99866i | −0.0591346 | + | 0.0813918i | ||||
\(604\) | 15.2037 | 0.618630 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.7497 | −0.639789 | ||||||||
\(607\) | 14.4047 | − | 19.8264i | 0.584669 | − | 0.804728i | −0.409528 | − | 0.912297i | \(-0.634307\pi\) |
0.994198 | + | 0.107569i | \(0.0343067\pi\) | |||||||
\(608\) | 118.621 | + | 38.5424i | 4.81072 | + | 1.56310i | ||||
\(609\) | −1.87011 | − | 5.75562i | −0.0757808 | − | 0.233229i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.165042 | − | 0.119910i | 0.00667688 | − | 0.00485103i | ||||
\(612\) | 27.0348 | − | 8.78415i | 1.09282 | − | 0.355078i | ||||
\(613\) | 4.41763 | + | 1.43538i | 0.178427 | + | 0.0579743i | 0.396868 | − | 0.917876i | \(-0.370097\pi\) |
−0.218441 | + | 0.975850i | \(0.570097\pi\) | |||||||
\(614\) | 10.1351 | + | 7.36361i | 0.409021 | + | 0.297171i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.44790 | + | 77.1339i | 0.0986288 | + | 3.10781i | ||||
\(617\) | − | 41.7419i | − | 1.68047i | −0.542226 | − | 0.840233i | \(-0.682418\pi\) | ||
0.542226 | − | 0.840233i | \(-0.317582\pi\) | |||||||
\(618\) | −2.11201 | + | 2.90693i | −0.0849574 | + | 0.116934i | ||||
\(619\) | 13.6592 | − | 42.0385i | 0.549008 | − | 1.68967i | −0.162258 | − | 0.986748i | \(-0.551878\pi\) |
0.711266 | − | 0.702923i | \(-0.248122\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.684276 | − | 0.497155i | 0.0274590 | − | 0.0199502i | ||||
\(622\) | 39.1024 | + | 53.8199i | 1.56786 | + | 2.15798i | ||||
\(623\) | 12.7792 | − | 4.15221i | 0.511987 | − | 0.166355i | ||||
\(624\) | 2.28249 | − | 7.02479i | 0.0913728 | − | 0.281217i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −71.7136 | −2.86625 | ||||||||
\(627\) | 12.8843 | + | 8.75031i | 0.514548 | + | 0.349454i | ||||
\(628\) | 114.841i | 4.58267i | ||||||||
\(629\) | −35.8491 | − | 26.0459i | −1.42940 | − | 1.03852i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.98015 | − | 15.3273i | −0.198257 | − | 0.610171i | −0.999923 | − | 0.0123995i | \(-0.996053\pi\) |
0.801667 | − | 0.597771i | \(-0.203947\pi\) | |||||||
\(632\) | −65.2780 | − | 89.8475i | −2.59662 | − | 3.57394i | ||||
\(633\) | −0.0293453 | − | 0.0403903i | −0.00116637 | − | 0.00160537i | ||||
\(634\) | −2.48706 | − | 7.65439i | −0.0987739 | − | 0.303995i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 49.8516 | + | 36.2193i | 1.97674 | + | 1.43619i | ||||
\(637\) | − | 0.789807i | − | 0.0312933i | ||||||
\(638\) | −6.80867 | + | 23.4627i | −0.269558 | + | 0.928896i | ||||
\(639\) | 11.3140 | 0.447575 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.84600 | + | 8.75909i | −0.112410 | + | 0.345963i | −0.991398 | − | 0.130881i | \(-0.958219\pi\) |
0.878988 | + | 0.476844i | \(0.158219\pi\) | |||||||
\(642\) | −32.1678 | + | 10.4520i | −1.26956 | + | 0.412506i | ||||
\(643\) | −2.36014 | − | 3.24845i | −0.0930747 | − | 0.128106i | 0.759940 | − | 0.649993i | \(-0.225228\pi\) |
−0.853015 | + | 0.521887i | \(0.825228\pi\) | |||||||
\(644\) | 8.86041 | − | 6.43747i | 0.349149 | − | 0.253672i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.1143 | − | 61.9054i | 0.791386 | − | 2.43564i | ||||
\(647\) | −8.38728 | + | 11.5441i | −0.329738 | + | 0.453846i | −0.941409 | − | 0.337267i | \(-0.890498\pi\) |
0.611671 | + | 0.791112i | \(0.290498\pi\) | |||||||
\(648\) | 10.2163i | 0.401332i | ||||||||
\(649\) | −12.2811 | + | 4.42574i | −0.482073 | + | 0.173726i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.60102 | − | 6.24901i | −0.337101 | − | 0.244918i | ||||
\(652\) | 52.9656 | + | 17.2096i | 2.07429 | + | 0.673979i | ||||
\(653\) | 6.20252 | − | 2.01532i | 0.242723 | − | 0.0788656i | −0.185129 | − | 0.982714i | \(-0.559270\pi\) |
0.427852 | + | 0.903849i | \(0.359270\pi\) | |||||||
\(654\) | −27.2819 | + | 19.8215i | −1.06681 | + | 0.775082i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −22.4939 | − | 69.2291i | −0.878239 | − | 2.70294i | ||||
\(657\) | −8.01655 | − | 2.60474i | −0.312755 | − | 0.101620i | ||||
\(658\) | −1.73754 | + | 2.39152i | −0.0677363 | + | 0.0932311i | ||||
\(659\) | −6.74928 | −0.262915 | −0.131457 | − | 0.991322i | \(-0.541966\pi\) | ||||
−0.131457 | + | 0.991322i | \(0.541966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.65248 | 0.375438 | 0.187719 | − | 0.982223i | \(-0.439891\pi\) | ||||
0.187719 | + | 0.982223i | \(0.439891\pi\) | |||||||
\(662\) | −17.8977 | + | 24.6340i | −0.695613 | + | 0.957429i | ||||
\(663\) | −2.07205 | − | 0.673251i | −0.0804718 | − | 0.0261469i | ||||
\(664\) | 18.6910 | + | 57.5249i | 0.725351 | + | 2.23240i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 19.8764 | − | 14.4410i | 0.770193 | − | 0.559578i | ||||
\(667\) | 2.13742 | − | 0.694489i | 0.0827612 | − | 0.0268907i | ||||
\(668\) | 138.297 | + | 44.9355i | 5.35088 | + | 1.73861i | ||||
\(669\) | 0.610777 | + | 0.443756i | 0.0236140 | + | 0.0171566i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.03060 | + | 7.76964i | 0.232809 | + | 0.299944i | ||||
\(672\) | 60.4934i | 2.33358i | ||||||||
\(673\) | −16.6693 | + | 22.9433i | −0.642553 | + | 0.884398i | −0.998749 | − | 0.0500135i | \(-0.984074\pi\) |
0.356196 | + | 0.934411i | \(0.384074\pi\) | |||||||
\(674\) | −11.0048 | + | 33.8694i | −0.423891 | + | 1.30460i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 58.9194 | − | 42.8075i | 2.26613 | − | 1.64644i | ||||
\(677\) | −2.99004 | − | 4.11544i | −0.114917 | − | 0.158169i | 0.747684 | − | 0.664055i | \(-0.231166\pi\) |
−0.862601 | + | 0.505885i | \(0.831166\pi\) | |||||||
\(678\) | −0.374527 | + | 0.121691i | −0.0143836 | + | 0.00467352i | ||||
\(679\) | −6.08661 | + | 18.7327i | −0.233583 | + | 0.718893i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.28399 | 0.317443 | ||||||||
\(682\) | 14.5505 | + | 40.3764i | 0.557167 | + | 1.54609i | ||||
\(683\) | 17.3612i | 0.664310i | 0.943225 | + | 0.332155i | \(0.107776\pi\) | ||||
−0.943225 | + | 0.332155i | \(0.892224\pi\) | |||||||
\(684\) | 21.5988 | + | 15.6924i | 0.825849 | + | 0.600015i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.1945 | + | 52.9192i | 0.656489 | + | 2.02046i | ||||
\(687\) | −1.69060 | − | 2.32691i | −0.0645004 | − | 0.0887772i | ||||
\(688\) | −69.7776 | − | 96.0406i | −2.66024 | − | 3.66151i | ||||
\(689\) | −1.45942 | − | 4.49164i | −0.0555995 | − | 0.171118i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.7708 | + | 25.2625i | 1.32274 | + | 0.961029i | 0.999894 | + | 0.0145791i | \(0.00464085\pi\) |
0.322850 | + | 0.946450i | \(0.395359\pi\) | |||||||
\(692\) | 38.3983i | 1.45969i | ||||||||
\(693\) | −2.10523 | + | 7.25463i | −0.0799712 | + | 0.275581i | ||||
\(694\) | 5.23870 | 0.198858 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.38849 | + | 25.8171i | −0.317965 | + | 0.978595i | ||||
\(697\) | −20.4200 | + | 6.63486i | −0.773463 | + | 0.251313i | ||||
\(698\) | −38.7467 | − | 53.3302i | −1.46658 | − | 2.01858i | ||||
\(699\) | −4.18964 | + | 3.04395i | −0.158467 | + | 0.115133i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.44621 | + | 13.6840i | −0.167931 | + | 0.516838i | −0.999240 | − | 0.0389718i | \(-0.987592\pi\) |
0.831309 | + | 0.555810i | \(0.187592\pi\) | |||||||
\(702\) | 0.710021 | − | 0.977260i | 0.0267980 | − | 0.0368843i | ||||
\(703\) | − | 41.6174i | − | 1.56963i | ||||||
\(704\) | 74.0286 | − | 109.002i | 2.79006 | − | 4.10818i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 45.3701 | + | 32.9633i | 1.70753 | + | 1.24059i | ||||
\(707\) | −12.3063 | − | 3.99855i | −0.462825 | − | 0.150381i | ||||
\(708\) | −21.2817 | + | 6.91485i | −0.799816 | + | 0.259876i | ||||
\(709\) | 41.4016 | − | 30.0800i | 1.55487 | − | 1.12968i | 0.614805 | − | 0.788680i | \(-0.289235\pi\) |
0.940064 | − | 0.340998i | \(-0.110765\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.35923 | − | 10.3386i | −0.125981 | − | 0.387729i | ||||
\(712\) | −57.3217 | − | 18.6250i | −2.14822 | − | 0.698000i | ||||
\(713\) | 2.32065 | − | 3.19409i | 0.0869088 | − | 0.119620i | ||||
\(714\) | 31.5700 | 1.18148 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 37.0787 | 1.38570 | ||||||||
\(717\) | −6.36734 | + | 8.76390i | −0.237793 | + | 0.327294i | ||||
\(718\) | −49.0126 | − | 15.9252i | −1.82913 | − | 0.594322i | ||||
\(719\) | −16.0803 | − | 49.4902i | −0.599696 | − | 1.84567i | −0.529806 | − | 0.848119i | \(-0.677735\pi\) |
−0.0698891 | − | 0.997555i | \(-0.522265\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.38826 | + | 1.73517i | −0.0889435 | + | 0.0646213i | ||||
\(722\) | 8.04673 | − | 2.61454i | 0.299468 | − | 0.0973032i | ||||
\(723\) | −2.82013 | − | 0.916315i | −0.104882 | − | 0.0340781i | ||||
\(724\) | 63.2523 | + | 45.9555i | 2.35075 | + | 1.70792i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 23.4844 | − | 19.4524i | 0.871586 | − | 0.721947i | ||||
\(727\) | 18.2951i | 0.678528i | 0.940691 | + | 0.339264i | \(0.110178\pi\) | ||||
−0.940691 | + | 0.339264i | \(0.889822\pi\) | |||||||
\(728\) | 5.95951 | − | 8.20256i | 0.220874 | − | 0.304007i | ||||
\(729\) | −0.309017 | + | 0.951057i | −0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.3284 | + | 20.5818i | −1.04776 | + | 0.761245i | ||||
\(732\) | 9.90974 | + | 13.6396i | 0.366275 | + | 0.504134i | ||||
\(733\) | −35.6792 | + | 11.5929i | −1.31784 | + | 0.428192i | −0.881753 | − | 0.471712i | \(-0.843636\pi\) |
−0.436088 | + | 0.899904i | \(0.643636\pi\) | |||||||
\(734\) | −5.06126 | + | 15.5770i | −0.186815 | + | 0.574956i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22.4649 | −0.828069 | ||||||||
\(737\) | 8.18953 | − | 0.259901i | 0.301665 | − | 0.00957358i | ||||
\(738\) | − | 11.9044i | − | 0.438207i | ||||||
\(739\) | −22.0973 | − | 16.0546i | −0.812863 | − | 0.590579i | 0.101796 | − | 0.994805i | \(-0.467541\pi\) |
−0.914659 | + | 0.404226i | \(0.867541\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.632311 | − | 1.94605i | −0.0232285 | − | 0.0714900i | ||||
\(742\) | 40.2250 | + | 55.3650i | 1.47671 | + | 2.03251i | ||||
\(743\) | −11.0641 | − | 15.2284i | −0.405902 | − | 0.558677i | 0.556311 | − | 0.830974i | \(-0.312216\pi\) |
−0.962213 | + | 0.272298i | \(0.912216\pi\) | |||||||
\(744\) | 14.7364 | + | 45.3539i | 0.540262 | + | 1.66275i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.74525 | + | 2.72108i | 0.137123 | + | 0.0996259i | ||||
\(747\) | 5.92050i | 0.216620i | ||||||||
\(748\) | −77.9925 | − | 52.9684i | −2.85169 | − | 1.93672i | ||||
\(749\) | −27.7884 | −1.01536 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.78395 | + | 23.9565i | −0.284040 | + | 0.874186i | 0.702644 | + | 0.711541i | \(0.252003\pi\) |
−0.986685 | + | 0.162645i | \(0.947997\pi\) | |||||||
\(752\) | 7.54781 | − | 2.45243i | 0.275240 | − | 0.0894310i | ||||
\(753\) | 10.3535 | + | 14.2504i | 0.377302 | + | 0.519312i | ||||
\(754\) | 2.59669 | − | 1.88660i | 0.0945658 | − | 0.0687061i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.00134 | + | 12.3149i | −0.145527 | + | 0.447887i | ||||
\(757\) | −26.9170 | + | 37.0481i | −0.978315 | + | 1.34653i | −0.0405820 | + | 0.999176i | \(0.512921\pi\) |
−0.937733 | + | 0.347358i | \(0.887079\pi\) | |||||||
\(758\) | 23.3842i | 0.849352i | ||||||||
\(759\) | −2.69409 | − | 0.781804i | −0.0977894 | − | 0.0283777i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.48664 | − | 4.71282i | −0.235141 | − | 0.170840i | 0.463975 | − | 0.885848i | \(-0.346423\pi\) |
−0.699116 | + | 0.715009i | \(0.746423\pi\) | |||||||
\(762\) | 1.32806 | + | 0.431513i | 0.0481105 | + | 0.0156321i | ||||
\(763\) | −26.3495 | + | 8.56146i | −0.953914 | + | 0.309946i | ||||
\(764\) | −89.3949 | + | 64.9492i | −3.23419 | + | 2.34978i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.7451 | + | 57.6916i | 0.677289 | + | 2.08448i | ||||
\(767\) | 1.63111 | + | 0.529980i | 0.0588960 | + | 0.0191365i | ||||
\(768\) | 46.2014 | − | 63.5907i | 1.66715 | − | 2.29463i | ||||
\(769\) | −40.0439 | −1.44402 | −0.722010 | − | 0.691883i | \(-0.756782\pi\) | ||||
−0.722010 | + | 0.691883i | \(0.756782\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.9647 | 0.755025 | ||||||||
\(772\) | −75.5634 | + | 104.004i | −2.71959 | + | 3.74319i | ||||
\(773\) | −22.6589 | − | 7.36232i | −0.814984 | − | 0.264804i | −0.128277 | − | 0.991738i | \(-0.540945\pi\) |
−0.686707 | + | 0.726934i | \(0.740945\pi\) | |||||||
\(774\) | −5.99936 | − | 18.4641i | −0.215643 | − | 0.663680i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 71.4770 | − | 51.9311i | 2.56588 | − | 1.86422i | ||||
\(777\) | 19.1970 | − | 6.23748i | 0.688688 | − | 0.223768i | ||||
\(778\) | −1.03377 | − | 0.335891i | −0.0370624 | − | 0.0120423i | ||||
\(779\) | −16.3140 | − | 11.8528i | −0.584511 | − | 0.424672i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.0081 | − | 29.6429i | −0.823293 | − | 1.06071i | ||||
\(782\) | 11.7239i | 0.419245i | ||||||||
\(783\) | −1.56181 | + | 2.14965i | −0.0558146 | + | 0.0768222i | ||||
\(784\) | 9.49471 | − | 29.2217i | 0.339097 | − | 1.04363i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −42.8590 | + | 31.1389i | −1.52873 | + | 1.11069i | ||||
\(787\) | −5.57737 | − | 7.67659i | −0.198812 | − | 0.273641i | 0.697958 | − | 0.716139i | \(-0.254092\pi\) |
−0.896769 | + | 0.442498i | \(0.854092\pi\) | |||||||
\(788\) | −124.522 | + | 40.4598i | −4.43593 | + | 1.44132i | ||||
\(789\) | −2.60647 | + | 8.02189i | −0.0927928 | + | 0.285587i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.323537 | −0.0115037 | ||||||||
\(792\) | 26.7668 | − | 20.7757i | 0.951116 | − | 0.738232i | ||||
\(793\) | − | 1.29217i | − | 0.0458864i | ||||||
\(794\) | 80.2517 | + | 58.3063i | 2.84803 | + | 2.06921i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −34.4718 | − | 106.093i | −1.22182 | − | 3.76037i | ||||
\(797\) | −13.9680 | − | 19.2254i | −0.494774 | − | 0.680998i | 0.486486 | − | 0.873688i | \(-0.338279\pi\) |
−0.981259 | + | 0.192691i | \(0.938279\pi\) | |||||||
\(798\) | 17.4280 | + | 23.9875i | 0.616943 | + | 0.849149i | ||||
\(799\) | −0.723376 | − | 2.22632i | −0.0255912 | − | 0.0787617i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.77286 | − | 3.46769i | −0.168641 | − | 0.122525i | ||||
\(802\) | − | 84.3212i | − | 2.97749i | ||||||
\(803\) | 9.47795 | + | 26.3005i | 0.334469 | + | 0.928124i | ||||
\(804\) | 14.0452 | 0.495337 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.74241 | − | 5.36260i | 0.0613739 | − | 0.188890i | ||||
\(807\) | 9.17148 | − | 2.97999i | 0.322851 | − | 0.104901i | ||||
\(808\) | 34.1158 | + | 46.9563i | 1.20019 | + | 1.65192i | ||||
\(809\) | −14.8963 | + | 10.8228i | −0.523726 | + | 0.380509i | −0.818006 | − | 0.575210i | \(-0.804920\pi\) |
0.294280 | + | 0.955719i | \(0.404920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.30675 | − | 22.4879i | 0.256575 | − | 0.789656i | −0.736941 | − | 0.675957i | \(-0.763730\pi\) |
0.993515 | − | 0.113698i | \(-0.0362697\pi\) | |||||||
\(812\) | −20.2233 | + | 27.8350i | −0.709698 | + | 0.976815i | ||||
\(813\) | 10.2278i | 0.358704i | ||||||||
\(814\) | −78.2562 | − | 22.7093i | −2.74288 | − | 0.795960i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −68.5694 | − | 49.8186i | −2.40041 | − | 1.74400i | ||||
\(817\) | −31.2770 | − | 10.1625i | −1.09424 | − | 0.355541i | ||||
\(818\) | 42.8958 | − | 13.9377i | 1.49982 | − | 0.487320i | ||||
\(819\) | 0.802893 | − | 0.583336i | 0.0280554 | − | 0.0203834i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.13186 | + | 25.0273i | 0.283804 | + | 0.873459i | 0.986755 | + | 0.162220i | \(0.0518654\pi\) |
−0.702951 | + | 0.711239i | \(0.748135\pi\) | |||||||
\(822\) | −32.5475 | − | 10.5753i | −1.13522 | − | 0.368857i | ||||
\(823\) | 23.7652 | − | 32.7100i | 0.828403 | − | 1.14020i | −0.159816 | − | 0.987147i | \(-0.551090\pi\) |
0.988218 | − | 0.153051i | \(-0.0489100\pi\) | |||||||
\(824\) | 13.2416 | 0.461293 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.8517 | −0.864703 | ||||||||
\(827\) | −9.75293 | + | 13.4238i | −0.339143 | + | 0.466790i | −0.944191 | − | 0.329399i | \(-0.893154\pi\) |
0.605048 | + | 0.796189i | \(0.293154\pi\) | |||||||
\(828\) | −4.57327 | − | 1.48595i | −0.158932 | − | 0.0516402i | ||||
\(829\) | 10.6015 | + | 32.6281i | 0.368206 | + | 1.13322i | 0.947949 | + | 0.318422i | \(0.103153\pi\) |
−0.579743 | + | 0.814800i | \(0.696847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.72388 | − | 3.43210i | 0.163869 | − | 0.119058i | ||||
\(832\) | −16.4638 | + | 5.34942i | −0.570781 | + | 0.185458i | ||||
\(833\) | −8.61932 | − | 2.80059i | −0.298642 | − | 0.0970346i | ||||
\(834\) | −17.3419 | − | 12.5997i | −0.600502 | − | 0.436290i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.80865 | − | 88.5012i | −0.0971393 | − | 3.06088i | ||||
\(837\) | 4.66785i | 0.161344i | ||||||||
\(838\) | −65.2934 | + | 89.8686i | −2.25552 | + | 3.10446i | ||||
\(839\) | 1.04698 | − | 3.22229i | 0.0361459 | − | 0.111246i | −0.931356 | − | 0.364111i | \(-0.881373\pi\) |
0.967502 | + | 0.252865i | \(0.0813729\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.7496 | − | 12.8959i | 0.612056 | − | 0.444685i | ||||
\(842\) | −31.6024 | − | 43.4970i | −1.08909 | − | 1.49901i | ||||
\(843\) | −13.7084 | + | 4.45412i | −0.472142 | + | 0.153408i | ||||
\(844\) | −0.0877101 | + | 0.269944i | −0.00301910 | + | 0.00929185i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.29790 | 0.0446226 | ||||||||
\(847\) | 23.2884 | − | 9.23721i | 0.800201 | − | 0.317394i | ||||
\(848\) | − | 183.729i | − | 6.30926i | ||||||
\(849\) | −8.60264 | − | 6.25018i | −0.295242 | − | 0.214506i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.31636 | + | 7.12903i | 0.0794039 | + | 0.244380i | ||||
\(852\) | −37.8078 | − | 52.0380i | −1.29527 | − | 1.78279i | ||||
\(853\) | −9.64323 | − | 13.2728i | −0.330178 | − | 0.454451i | 0.611363 | − | 0.791351i | \(-0.290622\pi\) |
−0.941541 | + | 0.336900i | \(0.890622\pi\) | |||||||
\(854\) | 5.78606 | + | 17.8076i | 0.197995 | + | 0.609365i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 100.841 | + | 73.2651i | 3.44667 | + | 2.50415i | ||||
\(857\) | 3.37817i | 0.115396i | 0.998334 | + | 0.0576981i | \(0.0183761\pi\) | ||||
−0.998334 | + | 0.0576981i | \(0.981624\pi\) | |||||||
\(858\) | −4.00433 | + | 0.127081i | −0.136706 | + | 0.00433846i | ||||
\(859\) | 2.32376 | 0.0792855 | 0.0396428 | − | 0.999214i | \(-0.487378\pi\) | ||||
0.0396428 | + | 0.999214i | \(0.487378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.02230 | − | 9.30168i | 0.103000 | − | 0.317001i | ||||
\(862\) | 89.4959 | − | 29.0790i | 3.04824 | − | 0.990434i | ||||
\(863\) | 11.9116 | + | 16.3949i | 0.405476 | + | 0.558090i | 0.962108 | − | 0.272670i | \(-0.0879066\pi\) |
−0.556632 | + | 0.830759i | \(0.687907\pi\) | |||||||
\(864\) | 21.4877 | − | 15.6117i | 0.731026 | − | 0.531121i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.2356 | + | 34.5795i | −0.381800 | + | 1.17506i | ||||
\(867\) | −4.70228 | + | 6.47214i | −0.159698 | + | 0.219805i | ||||
\(868\) | 60.4421i | 2.05154i | ||||||||
\(869\) | −20.2561 | + | 29.8258i | −0.687142 | + | 1.01177i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.870890 | − | 0.632739i | −0.0295090 | − | 0.0214395i | ||||
\(872\) | 118.192 | + | 38.4029i | 4.00248 | + | 1.30048i | ||||
\(873\) | 8.22477 | − | 2.67239i | 0.278366 | − | 0.0904466i | ||||
\(874\) | −8.90806 | + | 6.47209i | −0.301320 | + | 0.218922i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.8085 | + | 45.5759i | 0.500333 | + | 1.53987i | ||||
\(877\) | 15.8073 | + | 5.13611i | 0.533775 | + | 0.173434i | 0.563488 | − | 0.826125i | \(-0.309459\pi\) |
−0.0297127 | + | 0.999558i | \(0.509459\pi\) | |||||||
\(878\) | −15.7200 | + | 21.6367i | −0.530525 | + | 0.730205i | ||||
\(879\) | 8.39576 | 0.283182 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.8895 | −1.00700 | −0.503502 | − | 0.863994i | \(-0.667955\pi\) | ||||
−0.503502 | + | 0.863994i | \(0.667955\pi\) | |||||||
\(882\) | 2.95355 | − | 4.06521i | 0.0994511 | − | 0.136883i | ||||
\(883\) | 13.3277 | + | 4.33042i | 0.448511 | + | 0.145730i | 0.524559 | − | 0.851374i | \(-0.324230\pi\) |
−0.0760479 | + | 0.997104i | \(0.524230\pi\) | |||||||
\(884\) | 3.82758 | + | 11.7801i | 0.128735 | + | 0.396207i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.9923 | − | 14.5253i | 0.671655 | − | 0.487986i | ||||
\(887\) | 27.2079 | − | 8.84040i | 0.913553 | − | 0.296831i | 0.185734 | − | 0.982600i | \(-0.440534\pi\) |
0.727820 | + | 0.685769i | \(0.240534\pi\) | |||||||
\(888\) | −86.1091 | − | 27.9785i | −2.88963 | − | 0.938898i | ||||
\(889\) | 0.928146 | + | 0.674338i | 0.0311290 | + | 0.0226166i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.12020 | − | 1.12443i | 0.104531 | − | 0.0376699i | ||||
\(892\) | − | 4.29213i | − | 0.143711i | ||||||
\(893\) | 1.29227 | − | 1.77866i | 0.0432443 | − | 0.0595207i | ||||
\(894\) | −6.51832 | + | 20.0613i | −0.218005 | + | 0.670951i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 105.057 | − | 76.3284i | 3.50971 | − | 2.54995i | ||||
\(897\) | 0.216629 | + | 0.298164i | 0.00723303 | + | 0.00995541i | ||||
\(898\) | 32.7902 | − | 10.6542i | 1.09422 | − | 0.355535i | ||||
\(899\) | −3.83274 | + | 11.7959i | −0.127829 | + | 0.393417i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54.1931 | −1.80543 | ||||||||
\(902\) | −31.1898 | + | 24.2087i | −1.03851 | + | 0.806062i | ||||
\(903\) | − | 15.9504i | − | 0.530794i | ||||||
\(904\) | 1.17408 | + | 0.853019i | 0.0390493 | + | 0.0283710i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.29093 | − | 7.05077i | −0.0761112 | − | 0.234246i | ||||
\(907\) | 15.8521 | + | 21.8186i | 0.526361 | + | 0.724474i | 0.986570 | − | 0.163336i | \(-0.0522256\pi\) |
−0.460209 | + | 0.887811i | \(0.652226\pi\) | |||||||
\(908\) | −27.6825 | − | 38.1017i | −0.918677 | − | 1.26445i | ||||
\(909\) | 1.75561 | + | 5.40320i | 0.0582298 | + | 0.179213i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.77363 | − | 4.19479i | −0.191289 | − | 0.138980i | 0.488019 | − | 0.872833i | \(-0.337720\pi\) |
−0.679308 | + | 0.733854i | \(0.737720\pi\) | |||||||
\(912\) | − | 79.6025i | − | 2.63590i | ||||||
\(913\) | 15.5118 | − | 12.0399i | 0.513366 | − | 0.398462i | ||||
\(914\) | 105.783 | 3.49900 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.05303 | + | 15.5516i | −0.166957 | + | 0.513840i | ||||
\(917\) | −41.3941 | + | 13.4498i | −1.36695 | + | 0.444150i | ||||
\(918\) | −8.14736 | − | 11.2139i | −0.268903 | − | 0.370113i | ||||
\(919\) | −5.57755 | + | 4.05233i | −0.183987 | + | 0.133674i | −0.675966 | − | 0.736933i | \(-0.736273\pi\) |
0.491980 | + | 0.870607i | \(0.336273\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.39645 | − | 4.29784i | 0.0460147 | − | 0.141619i | ||||
\(922\) | −56.0288 | + | 77.1171i | −1.84521 | + | 2.53971i | ||||
\(923\) | 4.92992i | 0.162270i | ||||||||
\(924\) | 40.4023 | − | 14.5598i | 1.32914 | − | 0.478983i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 90.2854 | + | 65.5962i | 2.96696 | + | 2.15563i | ||||
\(927\) | 1.23269 | + | 0.400526i | 0.0404869 | + | 0.0131550i | ||||
\(928\) | 67.1194 | − | 21.8084i | 2.20330 | − | 0.715896i | ||||
\(929\) | −29.4333 | + | 21.3846i | −0.965676 | + | 0.701605i | −0.954462 | − | 0.298332i | \(-0.903570\pi\) |
−0.0112141 | + | 0.999937i | \(0.503570\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.63029 | − | 8.09519i | −0.0862042 | − | 0.265309i | ||||
\(932\) | 28.0010 | + | 9.09807i | 0.917202 | + | 0.298017i | ||||
\(933\) | 14.1051 | − | 19.4140i | 0.461780 | − | 0.635585i | ||||
\(934\) | −41.9052 | −1.37118 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.45160 | −0.145505 | ||||||||
\(937\) | −30.9724 | + | 42.6299i | −1.01183 | + | 1.39266i | −0.0940454 | + | 0.995568i | \(0.529980\pi\) |
−0.917780 | + | 0.397090i | \(0.870020\pi\) | |||||||
\(938\) | 14.8351 | + | 4.82023i | 0.484385 | + | 0.157386i | ||||
\(939\) | 7.99384 | + | 24.6025i | 0.260869 | + | 0.802873i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.4217 | − | 11.9311i | 0.535334 | − | 0.388943i | −0.287015 | − | 0.957926i | \(-0.592663\pi\) |
0.822349 | + | 0.568983i | \(0.192663\pi\) | |||||||
\(942\) | 53.2581 | − | 17.3046i | 1.73524 | − | 0.563814i | ||||
\(943\) | 3.45429 | + | 1.12237i | 0.112487 | + | 0.0365493i | ||||
\(944\) | 53.9776 | + | 39.2170i | 1.75682 | + | 1.27640i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.1761 | + | 53.2670i | −1.17619 | + | 1.73186i | ||||
\(947\) | − | 14.5680i | − | 0.473395i | −0.971583 | − | 0.236698i | \(-0.923935\pi\) | ||
0.971583 | − | 0.236698i | \(-0.0760651\pi\) | |||||||
\(948\) | −36.3264 | + | 49.9991i | −1.17983 | + | 1.62389i | ||||
\(949\) | 1.13498 | − | 3.49311i | 0.0368430 | − | 0.113391i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.34873 | + | 1.70645i | −0.0761629 | + | 0.0553356i | ||||
\(952\) | −68.3842 | − | 94.1228i | −2.21635 | − | 3.05054i | ||||
\(953\) | 37.5718 | − | 12.2078i | 1.21707 | − | 0.395450i | 0.371056 | − | 0.928610i | \(-0.378996\pi\) |
0.846014 | + | 0.533160i | \(0.178996\pi\) | |||||||
\(954\) | 9.28505 | − | 28.5765i | 0.300615 | − | 0.925197i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 61.5867 | 1.99186 | ||||||||
\(957\) | 8.80821 | − | 0.279535i | 0.284729 | − | 0.00903609i | ||||
\(958\) | − | 79.8524i | − | 2.57991i | ||||||
\(959\) | −22.7466 | − | 16.5264i | −0.734526 | − | 0.533665i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.84642 | − | 8.76037i | −0.0918199 | − | 0.282592i | ||||
\(962\) | 6.29248 | + | 8.66086i | 0.202878 | + | 0.279237i | ||||
\(963\) | 7.17143 | + | 9.87063i | 0.231096 | + | 0.318077i | ||||
\(964\) | 5.20945 | + | 16.0330i | 0.167785 | + | 0.516389i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.32051 | − | 3.13903i | −0.139010 | − | 0.100997i | ||||
\(967\) | 44.8051i | 1.44083i | 0.693541 | + | 0.720417i | \(0.256050\pi\) | ||||
−0.693541 | + | 0.720417i | \(0.743950\pi\) | |||||||
\(968\) | −108.865 | − | 27.8801i | −3.49907 | − | 0.896102i | ||||
\(969\) | −23.4798 | −0.754279 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.60723 | − | 17.2573i | 0.179945 | − | 0.553812i | −0.819880 | − | 0.572535i | \(-0.805960\pi\) |
0.999825 | + | 0.0187228i | \(0.00596000\pi\) | |||||||
\(972\) | 5.40697 | − | 1.75683i | 0.173428 | − | 0.0563503i | ||||
\(973\) | −10.3516 | − | 14.2477i | −0.331856 | − | 0.456761i | ||||
\(974\) | 64.7097 | − | 47.0144i | 2.07343 | − | 1.50644i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.5339 | − | 47.8085i | 0.497229 | − | 1.53031i | ||||
\(977\) | −30.5629 | + | 42.0662i | −0.977794 | + | 1.34582i | −0.0397838 | + | 0.999208i | \(0.512667\pi\) |
−0.938010 | + | 0.346609i | \(0.887333\pi\) | |||||||
\(978\) | − | 27.1562i | − | 0.868359i | ||||||
\(979\) | 0.620652 | + | 19.5569i | 0.0198361 | + | 0.625040i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.84118 | + | 7.15004i | 0.314205 | + | 0.228283i | ||||
\(982\) | 39.3812 | + | 12.7957i | 1.25671 | + | 0.408328i | ||||
\(983\) | −42.1625 | + | 13.6994i | −1.34477 | + | 0.436943i | −0.890931 | − | 0.454139i | \(-0.849947\pi\) |
−0.453842 | + | 0.891082i | \(0.649947\pi\) | |||||||
\(984\) | −35.4919 | + | 25.7863i | −1.13144 | + | 0.822039i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11.3813 | − | 35.0279i | −0.362453 | − | 1.11552i | ||||
\(987\) | 1.01413 | + | 0.329511i | 0.0322801 | + | 0.0104885i | ||||
\(988\) | −6.83777 | + | 9.41138i | −0.217538 | + | 0.299416i | ||||
\(989\) | 5.92336 | 0.188352 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.4084 | 0.330635 | 0.165317 | − | 0.986240i | \(-0.447135\pi\) | ||||
0.165317 | + | 0.986240i | \(0.447135\pi\) | |||||||
\(992\) | 72.8731 | − | 100.301i | 2.31372 | − | 3.18457i | ||||
\(993\) | 10.4461 | + | 3.39416i | 0.331498 | + | 0.107710i | ||||
\(994\) | −22.0751 | − | 67.9401i | −0.700179 | − | 2.15493i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 27.2310 | − | 19.7845i | 0.862846 | − | 0.626895i | ||||
\(997\) | 6.20281 | − | 2.01541i | 0.196445 | − | 0.0638288i | −0.209142 | − | 0.977885i | \(-0.567067\pi\) |
0.405587 | + | 0.914056i | \(0.367067\pi\) | |||||||
\(998\) | 58.5286 | + | 19.0171i | 1.85269 | + | 0.601975i | ||||
\(999\) | −7.16983 | − | 5.20918i | −0.226843 | − | 0.164811i |
(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 | 825.2.bx.h.499.1 | 16 | ||
5.2 | odd | 4 | 165.2.m.a.136.1 | yes | 8 | ||
5.3 | odd | 4 | 825.2.n.k.301.2 | 8 | |||
5.4 | even | 2 | inner | 825.2.bx.h.499.4 | 16 | ||
11.3 | even | 5 | inner | 825.2.bx.h.124.4 | 16 | ||
15.2 | even | 4 | 495.2.n.d.136.2 | 8 | |||
55.3 | odd | 20 | 825.2.n.k.751.2 | 8 | |||
55.14 | even | 10 | inner | 825.2.bx.h.124.1 | 16 | ||
55.17 | even | 20 | 1815.2.a.o.1.1 | 4 | |||
55.27 | odd | 20 | 1815.2.a.x.1.4 | 4 | |||
55.28 | even | 20 | 9075.2.a.dj.1.4 | 4 | |||
55.38 | odd | 20 | 9075.2.a.cl.1.1 | 4 | |||
55.47 | odd | 20 | 165.2.m.a.91.1 | ✓ | 8 | ||
165.17 | odd | 20 | 5445.2.a.bv.1.4 | 4 | |||
165.47 | even | 20 | 495.2.n.d.91.2 | 8 | |||
165.137 | even | 20 | 5445.2.a.be.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.a.91.1 | ✓ | 8 | 55.47 | odd | 20 | ||
165.2.m.a.136.1 | yes | 8 | 5.2 | odd | 4 | ||
495.2.n.d.91.2 | 8 | 165.47 | even | 20 | |||
495.2.n.d.136.2 | 8 | 15.2 | even | 4 | |||
825.2.n.k.301.2 | 8 | 5.3 | odd | 4 | |||
825.2.n.k.751.2 | 8 | 55.3 | odd | 20 | |||
825.2.bx.h.124.1 | 16 | 55.14 | even | 10 | inner | ||
825.2.bx.h.124.4 | 16 | 11.3 | even | 5 | inner | ||
825.2.bx.h.499.1 | 16 | 1.1 | even | 1 | trivial | ||
825.2.bx.h.499.4 | 16 | 5.4 | even | 2 | inner | ||
1815.2.a.o.1.1 | 4 | 55.17 | even | 20 | |||
1815.2.a.x.1.4 | 4 | 55.27 | odd | 20 | |||
5445.2.a.be.1.1 | 4 | 165.137 | even | 20 | |||
5445.2.a.bv.1.4 | 4 | 165.17 | odd | 20 | |||
9075.2.a.cl.1.1 | 4 | 55.38 | odd | 20 | |||
9075.2.a.dj.1.4 | 4 | 55.28 | even | 20 |