Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(124,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.124");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.e (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: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.58140625.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 374.1 | ||
Root | \(1.17421 - 0.0566033i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.374 |
Dual form | 625.2.e.i.249.1 |
$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.107666 | − | 0.148189i | −0.0761313 | − | 0.104786i | 0.769253 | − | 0.638944i | \(-0.220629\pi\) |
−0.845384 | + | 0.534159i | \(0.820629\pi\) | |||||||
\(3\) | −1.39991 | − | 0.454857i | −0.808237 | − | 0.262612i | −0.124386 | − | 0.992234i | \(-0.539696\pi\) |
−0.683851 | + | 0.729622i | \(0.739696\pi\) | |||||||
\(4\) | 0.607666 | − | 1.87020i | 0.303833 | − | 0.935102i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0833172 | + | 0.256424i | 0.0340141 | + | 0.104685i | ||||
\(7\) | 3.26086i | 1.23249i | 0.787555 | + | 0.616244i | \(0.211346\pi\) | ||||
−0.787555 | + | 0.616244i | \(0.788654\pi\) | |||||||
\(8\) | −0.690983 | + | 0.224514i | −0.244299 | + | 0.0793777i | ||||
\(9\) | −0.674207 | − | 0.489840i | −0.224736 | − | 0.163280i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.61803 | + | 1.17557i | −0.487856 | + | 0.354448i | −0.804359 | − | 0.594144i | \(-0.797491\pi\) |
0.316503 | + | 0.948591i | \(0.397491\pi\) | |||||||
\(12\) | −1.70135 | + | 2.34171i | −0.491138 | + | 0.675993i | ||||
\(13\) | −0.174207 | + | 0.239775i | −0.0483163 | + | 0.0665017i | −0.832492 | − | 0.554038i | \(-0.813086\pi\) |
0.784175 | + | 0.620539i | \(0.213086\pi\) | |||||||
\(14\) | 0.483224 | − | 0.351083i | 0.129147 | − | 0.0938308i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.07411 | − | 2.23347i | −0.768528 | − | 0.558369i | ||||
\(17\) | −4.91027 | + | 1.59545i | −1.19092 | + | 0.386952i | −0.836412 | − | 0.548102i | \(-0.815351\pi\) |
−0.354505 | + | 0.935054i | \(0.615351\pi\) | |||||||
\(18\) | 0.152649i | 0.0359798i | ||||||||
\(19\) | −0.534717 | − | 1.64569i | −0.122672 | − | 0.377547i | 0.870797 | − | 0.491642i | \(-0.163603\pi\) |
−0.993470 | + | 0.114095i | \(0.963603\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.48322 | − | 4.56489i | 0.323666 | − | 0.996142i | ||||
\(22\) | 0.348414 | + | 0.113207i | 0.0742821 | + | 0.0241357i | ||||
\(23\) | −0.516776 | − | 0.711281i | −0.107755 | − | 0.148312i | 0.751734 | − | 0.659467i | \(-0.229218\pi\) |
−0.859489 | + | 0.511155i | \(0.829218\pi\) | |||||||
\(24\) | 1.06943 | 0.218297 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.0542883 | 0.0106468 | ||||||||
\(27\) | 3.31659 | + | 4.56489i | 0.638278 | + | 0.878514i | ||||
\(28\) | 6.09846 | + | 1.98151i | 1.15250 | + | 0.374470i | ||||
\(29\) | −1.82696 | + | 5.62280i | −0.339258 | + | 1.04413i | 0.625329 | + | 0.780361i | \(0.284965\pi\) |
−0.964587 | + | 0.263766i | \(0.915035\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.88486 | + | 5.80100i | 0.338531 | + | 1.04189i | 0.964957 | + | 0.262409i | \(0.0845170\pi\) |
−0.626426 | + | 0.779481i | \(0.715483\pi\) | |||||||
\(32\) | 2.14910i | 0.379912i | ||||||||
\(33\) | 2.79981 | − | 0.909715i | 0.487385 | − | 0.158361i | ||||
\(34\) | 0.765097 | + | 0.555875i | 0.131213 | + | 0.0953318i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.32579 | + | 0.963245i | −0.220965 | + | 0.160541i | ||||
\(37\) | −4.75401 | + | 6.54333i | −0.781554 | + | 1.07572i | 0.213554 | + | 0.976931i | \(0.431496\pi\) |
−0.995109 | + | 0.0987860i | \(0.968504\pi\) | |||||||
\(38\) | −0.186303 | + | 0.256424i | −0.0302223 | + | 0.0415974i | ||||
\(39\) | 0.352937 | − | 0.256424i | 0.0565152 | − | 0.0410607i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.821270 | + | 0.596687i | 0.128261 | + | 0.0931869i | 0.650066 | − | 0.759878i | \(-0.274741\pi\) |
−0.521805 | + | 0.853065i | \(0.674741\pi\) | |||||||
\(42\) | −0.836161 | + | 0.271685i | −0.129022 | + | 0.0419219i | ||||
\(43\) | − | 3.24199i | − | 0.494399i | −0.968965 | − | 0.247200i | \(-0.920490\pi\) | ||
0.968965 | − | 0.247200i | \(-0.0795103\pi\) | |||||||
\(44\) | 1.21533 | + | 3.74041i | 0.183218 | + | 0.563887i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.0497651 | + | 0.153161i | −0.00733747 | + | 0.0225824i | ||||
\(47\) | −4.01342 | − | 1.30404i | −0.585417 | − | 0.190214i | 0.00130878 | − | 0.999999i | \(-0.499583\pi\) |
−0.586726 | + | 0.809786i | \(0.699583\pi\) | |||||||
\(48\) | 3.28756 | + | 4.52494i | 0.474519 | + | 0.653119i | ||||
\(49\) | −3.63318 | −0.519026 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.59963 | 1.06416 | ||||||||
\(52\) | 0.342569 | + | 0.471506i | 0.0475058 | + | 0.0653861i | ||||
\(53\) | −7.70424 | − | 2.50326i | −1.05826 | − | 0.343849i | −0.272355 | − | 0.962197i | \(-0.587802\pi\) |
−0.785905 | + | 0.618348i | \(0.787802\pi\) | |||||||
\(54\) | 0.319385 | − | 0.982966i | 0.0434628 | − | 0.133765i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.732108 | − | 2.25320i | −0.0978320 | − | 0.301096i | ||||
\(57\) | 2.54703i | 0.337363i | ||||||||
\(58\) | 1.02994 | − | 0.334648i | 0.135238 | − | 0.0439414i | ||||
\(59\) | 4.80261 | + | 3.48930i | 0.625246 | + | 0.454268i | 0.854750 | − | 0.519040i | \(-0.173710\pi\) |
−0.229504 | + | 0.973308i | \(0.573710\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.740748 | + | 0.538185i | −0.0948431 | + | 0.0689075i | −0.634196 | − | 0.773172i | \(-0.718669\pi\) |
0.539353 | + | 0.842080i | \(0.318669\pi\) | |||||||
\(62\) | 0.656711 | − | 0.903885i | 0.0834024 | − | 0.114794i | ||||
\(63\) | 1.59730 | − | 2.19849i | 0.201241 | − | 0.276984i | ||||
\(64\) | −5.82975 | + | 4.23556i | −0.728719 | + | 0.529445i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.436254 | − | 0.316957i | −0.0536992 | − | 0.0390147i | ||||
\(67\) | 6.55093 | − | 2.12853i | 0.800323 | − | 0.260041i | 0.119829 | − | 0.992794i | \(-0.461765\pi\) |
0.680494 | + | 0.732754i | \(0.261765\pi\) | |||||||
\(68\) | 10.1527i | 1.23120i | ||||||||
\(69\) | 0.399907 | + | 1.23079i | 0.0481431 | + | 0.148169i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.84445 | + | 5.67664i | −0.218896 | + | 0.673694i | 0.779958 | + | 0.625832i | \(0.215241\pi\) |
−0.998854 | + | 0.0478614i | \(0.984759\pi\) | |||||||
\(72\) | 0.575842 | + | 0.187102i | 0.0678636 | + | 0.0220502i | ||||
\(73\) | −5.19215 | − | 7.14638i | −0.607695 | − | 0.836420i | 0.388690 | − | 0.921368i | \(-0.372928\pi\) |
−0.996385 | + | 0.0849481i | \(0.972928\pi\) | |||||||
\(74\) | 1.48150 | 0.172220 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.40270 | −0.390317 | ||||||||
\(77\) | −3.83337 | − | 5.27618i | −0.436853 | − | 0.601276i | ||||
\(78\) | −0.0759986 | − | 0.0246934i | −0.00860514 | − | 0.00279598i | ||||
\(79\) | 2.39818 | − | 7.38084i | 0.269816 | − | 0.830409i | −0.720728 | − | 0.693218i | \(-0.756192\pi\) |
0.990545 | − | 0.137191i | \(-0.0438075\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.79397 | − | 5.52127i | −0.199330 | − | 0.613474i | ||||
\(82\) | − | 0.185946i | − | 0.0205343i | ||||||
\(83\) | −13.8049 | + | 4.48550i | −1.51529 | + | 0.492347i | −0.944433 | − | 0.328703i | \(-0.893388\pi\) |
−0.570856 | + | 0.821050i | \(0.693388\pi\) | |||||||
\(84\) | −7.63597 | − | 5.54786i | −0.833153 | − | 0.605321i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.480429 | + | 0.349052i | −0.0518059 | + | 0.0376392i | ||||
\(87\) | 5.11514 | − | 7.04039i | 0.548401 | − | 0.754809i | ||||
\(88\) | 0.854102 | − | 1.17557i | 0.0910476 | − | 0.125316i | ||||
\(89\) | 6.08901 | − | 4.42392i | 0.645433 | − | 0.468935i | −0.216279 | − | 0.976332i | \(-0.569392\pi\) |
0.861713 | + | 0.507397i | \(0.169392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.781873 | − | 0.568064i | −0.0819625 | − | 0.0595493i | ||||
\(92\) | −1.64427 | + | 0.534255i | −0.171427 | + | 0.0556999i | ||||
\(93\) | − | 8.97820i | − | 0.930996i | ||||||
\(94\) | 0.238863 | + | 0.735146i | 0.0246369 | + | 0.0758245i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.977536 | − | 3.00855i | 0.0997694 | − | 0.307058i | ||||
\(97\) | 6.39727 | + | 2.07860i | 0.649544 | + | 0.211050i | 0.615213 | − | 0.788361i | \(-0.289070\pi\) |
0.0343310 | + | 0.999411i | \(0.489070\pi\) | |||||||
\(98\) | 0.391169 | + | 0.538398i | 0.0395141 | + | 0.0543865i | ||||
\(99\) | 1.66673 | 0.167513 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.1955 | −1.21350 | −0.606748 | − | 0.794894i | \(-0.707526\pi\) | ||||
−0.606748 | + | 0.794894i | \(0.707526\pi\) | |||||||
\(102\) | −0.818220 | − | 1.12618i | −0.0810159 | − | 0.111509i | ||||
\(103\) | 1.31379 | + | 0.426878i | 0.129452 | + | 0.0420615i | 0.373027 | − | 0.927821i | \(-0.378320\pi\) |
−0.243575 | + | 0.969882i | \(0.578320\pi\) | |||||||
\(104\) | 0.0665412 | − | 0.204793i | 0.00652490 | − | 0.0200816i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.458527 | + | 1.41120i | 0.0445361 | + | 0.137068i | ||||
\(107\) | − | 15.8285i | − | 1.53020i | −0.643911 | − | 0.765101i | \(-0.722689\pi\) | ||
0.643911 | − | 0.765101i | \(-0.277311\pi\) | |||||||
\(108\) | 10.5527 | − | 3.42877i | 1.01543 | − | 0.329933i | ||||
\(109\) | −1.62108 | − | 1.17779i | −0.155272 | − | 0.112811i | 0.507437 | − | 0.861689i | \(-0.330593\pi\) |
−0.662708 | + | 0.748878i | \(0.730593\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.63145 | − | 6.99766i | 0.914177 | − | 0.664188i | ||||
\(112\) | 7.28304 | − | 10.0242i | 0.688182 | − | 0.947202i | ||||
\(113\) | −6.12912 | + | 8.43601i | −0.576579 | + | 0.793593i | −0.993315 | − | 0.115434i | \(-0.963174\pi\) |
0.416736 | + | 0.909028i | \(0.363174\pi\) | |||||||
\(114\) | 0.377443 | − | 0.274228i | 0.0353508 | − | 0.0256838i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.40559 | + | 6.83356i | 0.873288 | + | 0.634481i | ||||
\(117\) | 0.234903 | − | 0.0763247i | 0.0217168 | − | 0.00705622i | ||||
\(118\) | − | 1.08737i | − | 0.100101i | ||||||
\(119\) | −5.20252 | − | 16.0117i | −0.476914 | − | 1.46779i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.16312 | + | 6.65740i | −0.196647 | + | 0.605218i | ||||
\(122\) | 0.159507 | + | 0.0518268i | 0.0144410 | + | 0.00469218i | ||||
\(123\) | −0.878294 | − | 1.20887i | −0.0791931 | − | 0.109000i | ||||
\(124\) | 11.9944 | 1.07713 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.497767 | −0.0443446 | ||||||||
\(127\) | −3.43858 | − | 4.73280i | −0.305125 | − | 0.419969i | 0.628728 | − | 0.777625i | \(-0.283576\pi\) |
−0.933853 | + | 0.357657i | \(0.883576\pi\) | |||||||
\(128\) | 5.34317 | + | 1.73610i | 0.472274 | + | 0.153451i | ||||
\(129\) | −1.47464 | + | 4.53849i | −0.129835 | + | 0.399591i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.462488 | − | 1.42339i | −0.0404077 | − | 0.124362i | 0.928818 | − | 0.370537i | \(-0.120826\pi\) |
−0.969225 | + | 0.246175i | \(0.920826\pi\) | |||||||
\(132\) | − | 5.78902i | − | 0.503870i | ||||||
\(133\) | 5.36635 | − | 1.74363i | 0.465322 | − | 0.151192i | ||||
\(134\) | −1.02074 | − | 0.741608i | −0.0881782 | − | 0.0640652i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.03472 | − | 2.20485i | 0.260225 | − | 0.189064i | ||||
\(137\) | 4.61345 | − | 6.34987i | 0.394154 | − | 0.542506i | −0.565111 | − | 0.825015i | \(-0.691167\pi\) |
0.959265 | + | 0.282509i | \(0.0911667\pi\) | |||||||
\(138\) | 0.139333 | − | 0.191776i | 0.0118608 | − | 0.0163250i | ||||
\(139\) | 4.36183 | − | 3.16906i | 0.369966 | − | 0.268796i | −0.387231 | − | 0.921983i | \(-0.626568\pi\) |
0.757197 | + | 0.653187i | \(0.226568\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.02526 | + | 3.65106i | 0.423203 | + | 0.307475i | ||||
\(142\) | 1.03980 | − | 0.337852i | 0.0872583 | − | 0.0283519i | ||||
\(143\) | − | 0.592757i | − | 0.0495689i | ||||||
\(144\) | 0.978544 | + | 3.01165i | 0.0815453 | + | 0.250971i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.500000 | + | 1.53884i | −0.0413803 | + | 0.127355i | ||||
\(147\) | 5.08611 | + | 1.65258i | 0.419495 | + | 0.136302i | ||||
\(148\) | 9.34851 | + | 12.8671i | 0.768443 | + | 1.05767i | ||||
\(149\) | −18.8229 | −1.54203 | −0.771015 | − | 0.636817i | \(-0.780251\pi\) | ||||
−0.771015 | + | 0.636817i | \(0.780251\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.88797 | −0.316398 | −0.158199 | − | 0.987407i | \(-0.550569\pi\) | ||||
−0.158199 | + | 0.987407i | \(0.550569\pi\) | |||||||
\(152\) | 0.738960 | + | 1.01709i | 0.0599376 | + | 0.0824970i | ||||
\(153\) | 4.09205 | + | 1.32959i | 0.330823 | + | 0.107491i | ||||
\(154\) | −0.369150 | + | 1.13613i | −0.0297470 | + | 0.0915518i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.265097 | − | 0.815884i | −0.0212247 | − | 0.0653230i | ||||
\(157\) | − | 4.28378i | − | 0.341883i | −0.985281 | − | 0.170941i | \(-0.945319\pi\) | ||
0.985281 | − | 0.170941i | \(-0.0546808\pi\) | |||||||
\(158\) | −1.35196 | + | 0.439279i | −0.107556 | + | 0.0349472i | ||||
\(159\) | 9.64660 | + | 7.00866i | 0.765025 | + | 0.555823i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.31939 | − | 1.68513i | 0.182793 | − | 0.132807i | ||||
\(162\) | −0.625044 | + | 0.860299i | −0.0491081 | + | 0.0675915i | ||||
\(163\) | 9.24370 | − | 12.7229i | 0.724023 | − | 0.996531i | −0.275358 | − | 0.961342i | \(-0.588796\pi\) |
0.999381 | − | 0.0351898i | \(-0.0112036\pi\) | |||||||
\(164\) | 1.61498 | − | 1.17335i | 0.126109 | − | 0.0916236i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.15102 | + | 1.56281i | 0.166952 | + | 0.121298i | ||||
\(167\) | 20.0036 | − | 6.49956i | 1.54792 | − | 0.502951i | 0.594375 | − | 0.804188i | \(-0.297399\pi\) |
0.953549 | + | 0.301237i | \(0.0973995\pi\) | |||||||
\(168\) | 3.48727i | 0.269049i | ||||||||
\(169\) | 3.99008 | + | 12.2802i | 0.306929 | + | 0.944630i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.445615 | + | 1.37146i | −0.0340770 | + | 0.104878i | ||||
\(172\) | −6.06318 | − | 1.97005i | −0.462313 | − | 0.150215i | ||||
\(173\) | −4.21244 | − | 5.79793i | −0.320266 | − | 0.440808i | 0.618283 | − | 0.785956i | \(-0.287829\pi\) |
−0.938548 | + | 0.345148i | \(0.887829\pi\) | |||||||
\(174\) | −1.59404 | −0.120844 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.59963 | 0.572843 | ||||||||
\(177\) | −5.13607 | − | 7.06920i | −0.386051 | − | 0.531353i | ||||
\(178\) | −1.31116 | − | 0.426020i | −0.0982753 | − | 0.0319316i | ||||
\(179\) | −2.48429 | + | 7.64586i | −0.185685 | + | 0.571479i | −0.999959 | − | 0.00900088i | \(-0.997135\pi\) |
0.814275 | + | 0.580480i | \(0.197135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.37104 | − | 19.6080i | −0.473555 | − | 1.45745i | −0.847896 | − | 0.530162i | \(-0.822131\pi\) |
0.374341 | − | 0.927291i | \(-0.377869\pi\) | |||||||
\(182\) | 0.177026i | 0.0131221i | ||||||||
\(183\) | 1.28178 | − | 0.416474i | 0.0947516 | − | 0.0307867i | ||||
\(184\) | 0.516776 | + | 0.375460i | 0.0380972 | + | 0.0276793i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.33047 | + | 0.966645i | −0.0975550 | + | 0.0708779i | ||||
\(187\) | 6.06943 | − | 8.35386i | 0.443841 | − | 0.610895i | ||||
\(188\) | −4.87763 | + | 6.71349i | −0.355738 | + | 0.489631i | ||||
\(189\) | −14.8855 | + | 10.8149i | −1.08276 | + | 0.786670i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.5868 | − | 10.5979i | −1.05546 | − | 0.766840i | −0.0822207 | − | 0.996614i | \(-0.526201\pi\) |
−0.973244 | + | 0.229774i | \(0.926201\pi\) | |||||||
\(192\) | 10.0877 | − | 3.27769i | 0.728016 | − | 0.236547i | ||||
\(193\) | 6.78859i | 0.488653i | 0.969693 | + | 0.244327i | \(0.0785669\pi\) | ||||
−0.969693 | + | 0.244327i | \(0.921433\pi\) | |||||||
\(194\) | −0.380741 | − | 1.17180i | −0.0273356 | − | 0.0841304i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.20776 | + | 6.79478i | −0.157697 | + | 0.485342i | ||||
\(197\) | −7.60405 | − | 2.47071i | −0.541766 | − | 0.176031i | 0.0253343 | − | 0.999679i | \(-0.491935\pi\) |
−0.567101 | + | 0.823648i | \(0.691935\pi\) | |||||||
\(198\) | −0.179450 | − | 0.246992i | −0.0127530 | − | 0.0175529i | ||||
\(199\) | 5.20485 | 0.368962 | 0.184481 | − | 0.982836i | \(-0.440940\pi\) | ||||
0.184481 | + | 0.982836i | \(0.440940\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.1389 | −0.715141 | ||||||||
\(202\) | 1.31304 | + | 1.80724i | 0.0923850 | + | 0.127157i | ||||
\(203\) | −18.3351 | − | 5.95745i | −1.28687 | − | 0.418131i | ||||
\(204\) | 4.61803 | − | 14.2128i | 0.323327 | − | 0.995098i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.0781921 | − | 0.240650i | −0.00544790 | − | 0.0167669i | ||||
\(207\) | 0.732688i | 0.0509254i | ||||||||
\(208\) | 1.07106 | − | 0.348010i | 0.0742649 | − | 0.0241301i | ||||
\(209\) | 2.79981 | + | 2.03418i | 0.193667 | + | 0.140707i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4313 | + | 9.75839i | −0.924646 | + | 0.671795i | −0.944676 | − | 0.328004i | \(-0.893624\pi\) |
0.0200297 | + | 0.999799i | \(0.493624\pi\) | |||||||
\(212\) | −9.36321 | + | 12.8874i | −0.643068 | + | 0.885107i | ||||
\(213\) | 5.16413 | − | 7.10781i | 0.353840 | − | 0.487019i | ||||
\(214\) | −2.34562 | + | 1.70419i | −0.160343 | + | 0.116496i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.31659 | − | 2.40964i | −0.225665 | − | 0.163955i | ||||
\(217\) | −18.9162 | + | 6.14625i | −1.28412 | + | 0.417235i | ||||
\(218\) | 0.367035i | 0.0248587i | ||||||||
\(219\) | 4.01794 | + | 12.3660i | 0.271507 | + | 0.835613i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.472856 | − | 1.45530i | 0.0318077 | − | 0.0978941i | ||||
\(222\) | −2.07396 | − | 0.673869i | −0.139195 | − | 0.0452272i | ||||
\(223\) | −3.89589 | − | 5.36223i | −0.260888 | − | 0.359082i | 0.658399 | − | 0.752669i | \(-0.271234\pi\) |
−0.919287 | + | 0.393587i | \(0.871234\pi\) | |||||||
\(224\) | −7.00792 | −0.468236 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.91002 | 0.127053 | ||||||||
\(227\) | 7.87158 | + | 10.8343i | 0.522455 | + | 0.719097i | 0.985957 | − | 0.166998i | \(-0.0534074\pi\) |
−0.463502 | + | 0.886096i | \(0.653407\pi\) | |||||||
\(228\) | 4.76347 | + | 1.54774i | 0.315468 | + | 0.102502i | ||||
\(229\) | −3.11697 | + | 9.59304i | −0.205975 | + | 0.633926i | 0.793697 | + | 0.608313i | \(0.208154\pi\) |
−0.999672 | + | 0.0256124i | \(0.991846\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.96645 | + | 9.12979i | 0.195178 | + | 0.600696i | ||||
\(232\) | − | 4.29544i | − | 0.282009i | ||||||
\(233\) | −20.9285 | + | 6.80007i | −1.37107 | + | 0.445488i | −0.899723 | − | 0.436461i | \(-0.856232\pi\) |
−0.471346 | + | 0.881948i | \(0.656232\pi\) | |||||||
\(234\) | −0.0366015 | − | 0.0265926i | −0.00239272 | − | 0.00173841i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.44408 | − | 6.86153i | 0.614757 | − | 0.446647i | ||||
\(237\) | −6.71445 | + | 9.24165i | −0.436151 | + | 0.600310i | ||||
\(238\) | −1.81263 | + | 2.49487i | −0.117495 | + | 0.161718i | ||||
\(239\) | 6.11640 | − | 4.44383i | 0.395637 | − | 0.287447i | −0.372124 | − | 0.928183i | \(-0.621371\pi\) |
0.767762 | + | 0.640736i | \(0.221371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.4995 | + | 11.9876i | 1.06283 | + | 0.772190i | 0.974610 | − | 0.223911i | \(-0.0718825\pi\) |
0.0882188 | + | 0.996101i | \(0.471883\pi\) | |||||||
\(242\) | 1.21945 | − | 0.396223i | 0.0783892 | − | 0.0254702i | ||||
\(243\) | − | 8.38230i | − | 0.537725i | ||||||
\(244\) | 0.556388 | + | 1.71239i | 0.0356191 | + | 0.109624i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0845790 | + | 0.260307i | −0.00539256 | + | 0.0165966i | ||||
\(247\) | 0.487747 | + | 0.158479i | 0.0310346 | + | 0.0100838i | ||||
\(248\) | −2.60481 | − | 3.58521i | −0.165406 | − | 0.227661i | ||||
\(249\) | 21.3659 | 1.35401 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5717 | 0.667278 | 0.333639 | − | 0.942701i | \(-0.391723\pi\) | ||||
0.333639 | + | 0.942701i | \(0.391723\pi\) | |||||||
\(252\) | −3.14100 | − | 4.32322i | −0.197865 | − | 0.272337i | ||||
\(253\) | 1.67232 | + | 0.543370i | 0.105138 | + | 0.0341614i | ||||
\(254\) | −0.331133 | + | 1.01912i | −0.0207771 | + | 0.0639455i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.13553 | + | 12.7279i | 0.258471 | + | 0.795491i | ||||
\(257\) | 20.2700i | 1.26441i | 0.774801 | + | 0.632205i | \(0.217850\pi\) | ||||
−0.774801 | + | 0.632205i | \(0.782150\pi\) | |||||||
\(258\) | 0.831324 | − | 0.270114i | 0.0517560 | − | 0.0168165i | ||||
\(259\) | −21.3369 | − | 15.5021i | −1.32581 | − | 0.963256i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.98602 | − | 2.89601i | 0.246728 | − | 0.179259i | ||||
\(262\) | −0.161137 | + | 0.221786i | −0.00995509 | + | 0.0137020i | ||||
\(263\) | −16.5114 | + | 22.7260i | −1.01814 | + | 1.40135i | −0.104636 | + | 0.994511i | \(0.533368\pi\) |
−0.913501 | + | 0.406835i | \(0.866632\pi\) | |||||||
\(264\) | −1.73038 | + | 1.25719i | −0.106498 | + | 0.0773750i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.836161 | − | 0.607507i | −0.0512683 | − | 0.0372486i | ||||
\(267\) | −10.5363 | + | 3.42345i | −0.644811 | + | 0.209512i | ||||
\(268\) | − | 13.5450i | − | 0.827393i | ||||||
\(269\) | −6.28015 | − | 19.3283i | −0.382907 | − | 1.17847i | −0.937987 | − | 0.346670i | \(-0.887312\pi\) |
0.555080 | − | 0.831797i | \(-0.312688\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.71756 | − | 29.9076i | 0.590300 | − | 1.81676i | 0.0134456 | − | 0.999910i | \(-0.495720\pi\) |
0.576854 | − | 0.816847i | \(-0.304280\pi\) | |||||||
\(272\) | 18.6581 | + | 6.06239i | 1.13132 | + | 0.367587i | ||||
\(273\) | 0.836161 | + | 1.15088i | 0.0506068 | + | 0.0696542i | ||||
\(274\) | −1.43769 | −0.0868543 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.54483 | 0.153181 | ||||||||
\(277\) | 8.18813 | + | 11.2700i | 0.491977 | + | 0.677148i | 0.980751 | − | 0.195262i | \(-0.0625558\pi\) |
−0.488774 | + | 0.872410i | \(0.662556\pi\) | |||||||
\(278\) | −0.939241 | − | 0.305178i | −0.0563319 | − | 0.0183033i | ||||
\(279\) | 1.57078 | − | 4.83435i | 0.0940399 | − | 0.289425i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.99664 | + | 24.6111i | 0.477040 | + | 1.46818i | 0.843187 | + | 0.537620i | \(0.180677\pi\) |
−0.366147 | + | 0.930557i | \(0.619323\pi\) | |||||||
\(282\) | − | 1.13778i | − | 0.0677541i | ||||||
\(283\) | 22.5701 | − | 7.33348i | 1.34166 | − | 0.435930i | 0.451778 | − | 0.892130i | \(-0.350790\pi\) |
0.889877 | + | 0.456200i | \(0.150790\pi\) | |||||||
\(284\) | 9.49567 | + | 6.89901i | 0.563464 | + | 0.409381i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0878403 | + | 0.0638197i | −0.00519411 | + | 0.00377374i | ||||
\(287\) | −1.94571 | + | 2.67804i | −0.114852 | + | 0.158080i | ||||
\(288\) | 1.05272 | − | 1.44894i | 0.0620320 | − | 0.0853797i | ||||
\(289\) | 7.81207 | − | 5.67580i | 0.459533 | − | 0.333871i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.01011 | − | 5.81969i | −0.469561 | − | 0.341156i | ||||
\(292\) | −16.5203 | + | 5.36776i | −0.966776 | + | 0.314124i | ||||
\(293\) | 12.3029i | 0.718742i | 0.933195 | + | 0.359371i | \(0.117009\pi\) | ||||
−0.933195 | + | 0.359371i | \(0.882991\pi\) | |||||||
\(294\) | −0.302706 | − | 0.931634i | −0.0176542 | − | 0.0543340i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.81587 | − | 5.58867i | 0.105545 | − | 0.324835i | ||||
\(297\) | −10.7327 | − | 3.48727i | −0.622775 | − | 0.202352i | ||||
\(298\) | 2.02658 | + | 2.78935i | 0.117397 | + | 0.161583i | ||||
\(299\) | 0.260574 | 0.0150694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.5717 | 0.609341 | ||||||||
\(302\) | 0.418601 | + | 0.576155i | 0.0240878 | + | 0.0331540i | ||||
\(303\) | 17.0725 | + | 5.54721i | 0.980792 | + | 0.318679i | ||||
\(304\) | −2.03182 | + | 6.25331i | −0.116533 | + | 0.358652i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.243544 | − | 0.749550i | −0.0139225 | − | 0.0428489i | ||||
\(307\) | 4.28249i | 0.244415i | 0.992505 | + | 0.122207i | \(0.0389973\pi\) | ||||
−0.992505 | + | 0.122207i | \(0.961003\pi\) | |||||||
\(308\) | −12.1969 | + | 3.96302i | −0.694984 | + | 0.225814i | ||||
\(309\) | −1.64502 | − | 1.19518i | −0.0935820 | − | 0.0679913i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.7486 | + | 15.0747i | −1.17655 | + | 0.854810i | −0.991778 | − | 0.127972i | \(-0.959153\pi\) |
−0.184768 | + | 0.982782i | \(0.559153\pi\) | |||||||
\(312\) | −0.186303 | + | 0.256424i | −0.0105473 | + | 0.0145171i | ||||
\(313\) | 13.1377 | − | 18.0825i | 0.742589 | − | 1.02209i | −0.255876 | − | 0.966709i | \(-0.582364\pi\) |
0.998466 | − | 0.0553767i | \(-0.0176360\pi\) | |||||||
\(314\) | −0.634810 | + | 0.461216i | −0.0358244 | + | 0.0260280i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.3464 | − | 8.97016i | −0.694538 | − | 0.504611i | ||||
\(317\) | −20.8499 | + | 6.77453i | −1.17105 | + | 0.380496i | −0.829033 | − | 0.559200i | \(-0.811108\pi\) |
−0.342012 | + | 0.939695i | \(0.611108\pi\) | |||||||
\(318\) | − | 2.18412i | − | 0.122479i | ||||||
\(319\) | −3.65392 | − | 11.2456i | −0.204580 | − | 0.629632i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.19972 | + | 22.1585i | −0.401849 | + | 1.23676i | ||||
\(322\) | −0.499437 | − | 0.162277i | −0.0278325 | − | 0.00904334i | ||||
\(323\) | 5.25121 | + | 7.22768i | 0.292185 | + | 0.402159i | ||||
\(324\) | −11.4160 | −0.634224 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.88062 | −0.159543 | ||||||||
\(327\) | 1.73364 | + | 2.38615i | 0.0958706 | + | 0.131955i | ||||
\(328\) | −0.701448 | − | 0.227914i | −0.0387310 | − | 0.0125845i | ||||
\(329\) | 4.25228 | − | 13.0872i | 0.234436 | − | 0.721519i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.76972 | − | 8.52431i | −0.152237 | − | 0.468539i | 0.845633 | − | 0.533765i | \(-0.179223\pi\) |
−0.997871 | + | 0.0652260i | \(0.979223\pi\) | |||||||
\(332\) | 28.5437i | 1.56654i | ||||||||
\(333\) | 6.41037 | − | 2.08286i | 0.351286 | − | 0.114140i | ||||
\(334\) | −3.11687 | − | 2.26454i | −0.170547 | − | 0.123910i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −14.7552 | + | 10.7203i | −0.804961 | + | 0.584838i | ||||
\(337\) | −17.0949 | + | 23.5291i | −0.931218 | + | 1.28171i | 0.0281648 | + | 0.999603i | \(0.491034\pi\) |
−0.959383 | + | 0.282108i | \(0.908966\pi\) | |||||||
\(338\) | 1.39020 | − | 1.91344i | 0.0756168 | − | 0.104078i | ||||
\(339\) | 12.4174 | − | 9.02176i | 0.674420 | − | 0.489995i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.86925 | − | 7.17043i | −0.534450 | − | 0.388300i | ||||
\(342\) | 0.251213 | − | 0.0816242i | 0.0135841 | − | 0.00441373i | ||||
\(343\) | 10.9787i | 0.592795i | ||||||||
\(344\) | 0.727872 | + | 2.24016i | 0.0392443 | + | 0.120781i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.405655 | + | 1.24848i | −0.0218081 | + | 0.0671185i | ||||
\(347\) | 13.5974 | + | 4.41807i | 0.729948 | + | 0.237175i | 0.650331 | − | 0.759651i | \(-0.274630\pi\) |
0.0796174 | + | 0.996825i | \(0.474630\pi\) | |||||||
\(348\) | −10.0587 | − | 13.8446i | −0.539201 | − | 0.742146i | ||||
\(349\) | −5.62382 | −0.301036 | −0.150518 | − | 0.988607i | \(-0.548094\pi\) | ||||
−0.150518 | + | 0.988607i | \(0.548094\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.67232 | −0.0892620 | ||||||||
\(352\) | −2.52642 | − | 3.47732i | −0.134659 | − | 0.185342i | ||||
\(353\) | −1.81649 | − | 0.590214i | −0.0966821 | − | 0.0314139i | 0.260276 | − | 0.965534i | \(-0.416186\pi\) |
−0.356959 | + | 0.934120i | \(0.616186\pi\) | |||||||
\(354\) | −0.494600 | + | 1.52222i | −0.0262877 | + | 0.0809052i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.57355 | − | 14.0759i | −0.242398 | − | 0.746023i | ||||
\(357\) | 24.7813i | 1.31156i | ||||||||
\(358\) | 1.40051 | − | 0.455053i | 0.0740192 | − | 0.0240503i | ||||
\(359\) | 17.9639 | + | 13.0516i | 0.948101 | + | 0.688835i | 0.950357 | − | 0.311162i | \(-0.100718\pi\) |
−0.00225634 | + | 0.999997i | \(0.500718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.9490 | − | 9.40796i | 0.681524 | − | 0.495156i | ||||
\(362\) | −2.21976 | + | 3.05523i | −0.116668 | + | 0.160580i | ||||
\(363\) | 6.05633 | − | 8.33582i | 0.317875 | − | 0.437517i | ||||
\(364\) | −1.53751 | + | 1.11707i | −0.0805875 | + | 0.0585503i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.199721 | − | 0.145105i | −0.0104396 | − | 0.00758478i | ||||
\(367\) | 20.3954 | − | 6.62686i | 1.06463 | − | 0.345919i | 0.276236 | − | 0.961090i | \(-0.410913\pi\) |
0.788394 | + | 0.615170i | \(0.210913\pi\) | |||||||
\(368\) | 3.34077i | 0.174149i | ||||||||
\(369\) | −0.261424 | − | 0.804582i | −0.0136092 | − | 0.0418849i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.16277 | − | 25.1224i | 0.423790 | − | 1.30429i | ||||
\(372\) | −16.7911 | − | 5.45574i | −0.870576 | − | 0.282867i | ||||
\(373\) | 13.6013 | + | 18.7206i | 0.704248 | + | 0.969315i | 0.999902 | + | 0.0140195i | \(0.00446270\pi\) |
−0.295653 | + | 0.955295i | \(0.595537\pi\) | |||||||
\(374\) | −1.89142 | −0.0978032 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.06598 | 0.158116 | ||||||||
\(377\) | −1.02994 | − | 1.41759i | −0.0530446 | − | 0.0730096i | ||||
\(378\) | 3.20531 | + | 1.04147i | 0.164863 | + | 0.0535674i | ||||
\(379\) | 6.69026 | − | 20.5905i | 0.343656 | − | 1.05766i | −0.618644 | − | 0.785672i | \(-0.712318\pi\) |
0.962300 | − | 0.271992i | \(-0.0876824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.66095 | + | 8.18955i | 0.136324 | + | 0.419563i | ||||
\(382\) | 3.30265i | 0.168978i | ||||||||
\(383\) | 5.37804 | − | 1.74743i | 0.274805 | − | 0.0892896i | −0.168372 | − | 0.985723i | \(-0.553851\pi\) |
0.443178 | + | 0.896434i | \(0.353851\pi\) | |||||||
\(384\) | −6.69026 | − | 4.86076i | −0.341411 | − | 0.248050i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.00600 | − | 0.730899i | 0.0512039 | − | 0.0372018i | ||||
\(387\) | −1.58806 | + | 2.18577i | −0.0807255 | + | 0.111109i | ||||
\(388\) | 7.77480 | − | 10.7011i | 0.394706 | − | 0.543266i | ||||
\(389\) | −6.57411 | + | 4.77637i | −0.333321 | + | 0.242172i | −0.741838 | − | 0.670579i | \(-0.766046\pi\) |
0.408518 | + | 0.912750i | \(0.366046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.67232 | + | 2.66810i | 0.185717 | + | 0.134932i | ||||
\(392\) | 2.51047 | − | 0.815700i | 0.126798 | − | 0.0411991i | ||||
\(393\) | 2.20298i | 0.111126i | ||||||||
\(394\) | 0.452564 | + | 1.39285i | 0.0227999 | + | 0.0701708i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.01282 | − | 3.11713i | 0.0508959 | − | 0.156641i | ||||
\(397\) | −19.7524 | − | 6.41794i | −0.991343 | − | 0.322107i | −0.231942 | − | 0.972730i | \(-0.574508\pi\) |
−0.759401 | + | 0.650623i | \(0.774508\pi\) | |||||||
\(398\) | −0.560384 | − | 0.771303i | −0.0280895 | − | 0.0386619i | ||||
\(399\) | −8.30550 | −0.415795 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.1195 | 1.50410 | 0.752049 | − | 0.659107i | \(-0.229066\pi\) | ||||
0.752049 | + | 0.659107i | \(0.229066\pi\) | |||||||
\(402\) | 1.09161 | + | 1.50247i | 0.0544445 | + | 0.0749365i | ||||
\(403\) | −1.71929 | − | 0.558632i | −0.0856440 | − | 0.0278274i | ||||
\(404\) | −7.41078 | + | 22.8080i | −0.368700 | + | 1.13474i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.09124 | + | 3.35848i | 0.0541572 | + | 0.166679i | ||||
\(407\) | − | 16.1760i | − | 0.801815i | ||||||
\(408\) | −5.25121 | + | 1.70622i | −0.259974 | + | 0.0844706i | ||||
\(409\) | 8.93579 | + | 6.49223i | 0.441846 | + | 0.321020i | 0.786368 | − | 0.617758i | \(-0.211959\pi\) |
−0.344522 | + | 0.938778i | \(0.611959\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.34669 | + | 6.79077i | −0.461038 | + | 0.334964i | ||||
\(412\) | 1.59670 | − | 2.19766i | 0.0786636 | − | 0.108271i | ||||
\(413\) | −11.3781 | + | 15.6606i | −0.559880 | + | 0.770608i | ||||
\(414\) | 0.108577 | − | 0.0788855i | 0.00533625 | − | 0.00387701i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.515302 | − | 0.374389i | −0.0252648 | − | 0.0183559i | ||||
\(417\) | −7.54763 | + | 2.45237i | −0.369609 | + | 0.120093i | ||||
\(418\) | − | 0.633915i | − | 0.0310058i | ||||||
\(419\) | 10.1732 | + | 31.3099i | 0.496993 | + | 1.52959i | 0.813827 | + | 0.581107i | \(0.197380\pi\) |
−0.316834 | + | 0.948481i | \(0.602620\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.26214 | + | 19.2729i | −0.305198 | + | 0.939304i | 0.674405 | + | 0.738362i | \(0.264400\pi\) |
−0.979603 | + | 0.200942i | \(0.935600\pi\) | |||||||
\(422\) | 2.89218 | + | 0.939725i | 0.140789 | + | 0.0457451i | ||||
\(423\) | 2.06710 | + | 2.84512i | 0.100506 | + | 0.138335i | ||||
\(424\) | 5.88552 | 0.285826 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.60930 | −0.0779709 | ||||||||
\(427\) | −1.75494 | − | 2.41547i | −0.0849277 | − | 0.116893i | ||||
\(428\) | −29.6026 | − | 9.61845i | −1.43089 | − | 0.464926i | ||||
\(429\) | −0.269620 | + | 0.829805i | −0.0130174 | + | 0.0400634i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.21110 | + | 6.80506i | 0.106505 | + | 0.327788i | 0.990081 | − | 0.140500i | \(-0.0448710\pi\) |
−0.883576 | + | 0.468288i | \(0.844871\pi\) | |||||||
\(432\) | − | 21.4405i | − | 1.03156i | ||||||
\(433\) | −5.21430 | + | 1.69423i | −0.250583 | + | 0.0814195i | −0.431615 | − | 0.902058i | \(-0.642056\pi\) |
0.181032 | + | 0.983477i | \(0.442056\pi\) | |||||||
\(434\) | 2.94744 | + | 2.14144i | 0.141482 | + | 0.102792i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.18778 | + | 2.31606i | −0.152667 | + | 0.110919i | ||||
\(437\) | −0.894219 | + | 1.23079i | −0.0427763 | + | 0.0588765i | ||||
\(438\) | 1.39991 | − | 1.92681i | 0.0668901 | − | 0.0920664i | ||||
\(439\) | −24.8822 | + | 18.0780i | −1.18756 | + | 0.862815i | −0.993005 | − | 0.118076i | \(-0.962327\pi\) |
−0.194558 | + | 0.980891i | \(0.562327\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.44951 | + | 1.77968i | 0.116644 | + | 0.0847465i | ||||
\(442\) | −0.266570 | + | 0.0866140i | −0.0126795 | + | 0.00411981i | ||||
\(443\) | − | 11.3527i | − | 0.539381i | −0.962947 | − | 0.269691i | \(-0.913079\pi\) | ||
0.962947 | − | 0.269691i | \(-0.0869214\pi\) | |||||||
\(444\) | −7.23434 | − | 22.2650i | −0.343327 | − | 1.05665i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.375171 | + | 1.15466i | −0.0177649 | + | 0.0546747i | ||||
\(447\) | 26.3503 | + | 8.56172i | 1.24633 | + | 0.404956i | ||||
\(448\) | −13.8116 | − | 19.0100i | −0.652535 | − | 0.898137i | ||||
\(449\) | 15.7661 | 0.744050 | 0.372025 | − | 0.928223i | \(-0.378664\pi\) | ||||
0.372025 | + | 0.928223i | \(0.378664\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.03029 | −0.0956027 | ||||||||
\(452\) | 12.0526 | + | 16.5890i | 0.566907 | + | 0.780280i | ||||
\(453\) | 5.44279 | + | 1.76847i | 0.255725 | + | 0.0830900i | ||||
\(454\) | 0.758027 | − | 2.33297i | 0.0355760 | − | 0.109492i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.571844 | − | 1.75996i | −0.0267791 | − | 0.0824175i | ||||
\(457\) | − | 4.16714i | − | 0.194931i | −0.995239 | − | 0.0974653i | \(-0.968926\pi\) | ||
0.995239 | − | 0.0974653i | \(-0.0310735\pi\) | |||||||
\(458\) | 1.75718 | − | 0.570941i | 0.0821075 | − | 0.0266783i | ||||
\(459\) | −23.5684 | − | 17.1234i | −1.10008 | − | 0.799254i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.3933 | − | 14.0900i | 0.903235 | − | 0.656239i | −0.0360595 | − | 0.999350i | \(-0.511481\pi\) |
0.939295 | + | 0.343111i | \(0.111481\pi\) | |||||||
\(462\) | 1.03355 | − | 1.42256i | 0.0480852 | − | 0.0661836i | ||||
\(463\) | −24.2900 | + | 33.4324i | −1.12885 | + | 1.55373i | −0.338624 | + | 0.940922i | \(0.609962\pi\) |
−0.790229 | + | 0.612812i | \(0.790038\pi\) | |||||||
\(464\) | 18.1747 | − | 13.2047i | 0.843737 | − | 0.613011i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.26098 | + | 2.36924i | 0.151062 | + | 0.109753i | ||||
\(467\) | 9.88775 | − | 3.21272i | 0.457550 | − | 0.148667i | −0.0711682 | − | 0.997464i | \(-0.522673\pi\) |
0.528719 | + | 0.848797i | \(0.322673\pi\) | |||||||
\(468\) | − | 0.485697i | − | 0.0224513i | ||||||
\(469\) | 6.94082 | + | 21.3616i | 0.320497 | + | 0.986389i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.94851 | + | 5.99689i | −0.0897825 | + | 0.276322i | ||||
\(472\) | −4.10192 | − | 1.33279i | −0.188806 | − | 0.0613468i | ||||
\(473\) | 3.81119 | + | 5.24565i | 0.175239 | + | 0.241195i | ||||
\(474\) | 2.09243 | 0.0961086 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −33.1065 | −1.51743 | ||||||||
\(477\) | 3.96806 | + | 5.46156i | 0.181685 | + | 0.250068i | ||||
\(478\) | −1.31706 | − | 0.427937i | −0.0602407 | − | 0.0195734i | ||||
\(479\) | −11.1271 | + | 34.2458i | −0.508411 | + | 1.56473i | 0.286548 | + | 0.958066i | \(0.407492\pi\) |
−0.794959 | + | 0.606663i | \(0.792508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.740748 | − | 2.27979i | −0.0337752 | − | 0.103949i | ||||
\(482\) | − | 3.73571i | − | 0.170157i | ||||||
\(483\) | −4.01342 | + | 1.30404i | −0.182617 | + | 0.0593358i | ||||
\(484\) | 11.1362 | + | 8.09094i | 0.506192 | + | 0.367770i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.24217 | + | 0.902487i | −0.0563458 | + | 0.0409377i | ||||
\(487\) | 6.25275 | − | 8.60617i | 0.283339 | − | 0.389983i | −0.643497 | − | 0.765448i | \(-0.722517\pi\) |
0.926836 | + | 0.375466i | \(0.122517\pi\) | |||||||
\(488\) | 0.391014 | − | 0.538185i | 0.0177004 | − | 0.0243625i | ||||
\(489\) | −18.7274 | + | 13.6063i | −0.846883 | + | 0.615296i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2947 | + | 10.3857i | 0.645112 | + | 0.468701i | 0.861603 | − | 0.507583i | \(-0.169461\pi\) |
−0.216491 | + | 0.976285i | \(0.569461\pi\) | |||||||
\(492\) | −2.79454 | + | 0.908000i | −0.125987 | + | 0.0409358i | ||||
\(493\) | − | 30.5243i | − | 1.37475i | ||||||
\(494\) | −0.0290289 | − | 0.0893417i | −0.00130607 | − | 0.00401967i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.16211 | − | 22.0427i | 0.321588 | − | 0.989747i | ||||
\(497\) | −18.5107 | − | 6.01450i | −0.830319 | − | 0.269787i | ||||
\(498\) | −2.30038 | − | 3.16620i | −0.103082 | − | 0.141881i | ||||
\(499\) | 9.41734 | 0.421578 | 0.210789 | − | 0.977532i | \(-0.432397\pi\) | ||||
0.210789 | + | 0.977532i | \(0.432397\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.9595 | −1.38317 | ||||||||
\(502\) | −1.13821 | − | 1.56661i | −0.0508007 | − | 0.0699211i | ||||
\(503\) | 17.1316 | + | 5.56641i | 0.763862 | + | 0.248194i | 0.664935 | − | 0.746901i | \(-0.268459\pi\) |
0.0989268 | + | 0.995095i | \(0.468459\pi\) | |||||||
\(504\) | −0.610113 | + | 1.87774i | −0.0271766 | + | 0.0836410i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.0995303 | − | 0.306323i | −0.00442466 | − | 0.0136177i | ||||
\(507\) | − | 19.0060i | − | 0.844088i | ||||||
\(508\) | −10.9408 | + | 3.55489i | −0.485420 | + | 0.157723i | ||||
\(509\) | −12.9835 | − | 9.43307i | −0.575484 | − | 0.418114i | 0.261609 | − | 0.965174i | \(-0.415747\pi\) |
−0.837093 | + | 0.547060i | \(0.815747\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.3033 | − | 16.9308i | 1.03088 | − | 0.748976i | ||||
\(512\) | 8.04540 | − | 11.0735i | 0.355560 | − | 0.489386i | ||||
\(513\) | 5.73896 | − | 7.89900i | 0.253381 | − | 0.348749i | ||||
\(514\) | 3.00380 | − | 2.18239i | 0.132492 | − | 0.0962611i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.59180 | + | 5.51577i | 0.334210 | + | 0.242818i | ||||
\(517\) | 8.02684 | − | 2.60808i | 0.353020 | − | 0.114703i | ||||
\(518\) | 4.83095i | 0.212260i | ||||||||
\(519\) | 3.25979 | + | 10.0326i | 0.143089 | + | 0.440383i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.680052 | + | 2.09298i | −0.0297936 | + | 0.0916953i | −0.964848 | − | 0.262810i | \(-0.915351\pi\) |
0.935054 | + | 0.354505i | \(0.115351\pi\) | |||||||
\(522\) | −0.858316 | − | 0.278884i | −0.0375675 | − | 0.0122064i | ||||
\(523\) | −4.37070 | − | 6.01575i | −0.191117 | − | 0.263050i | 0.702695 | − | 0.711491i | \(-0.251980\pi\) |
−0.893813 | + | 0.448440i | \(0.851980\pi\) | |||||||
\(524\) | −2.94307 | −0.128569 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.14547 | 0.224353 | ||||||||
\(527\) | −18.5103 | − | 25.4773i | −0.806323 | − | 1.10981i | ||||
\(528\) | −10.6388 | − | 3.45675i | −0.462993 | − | 0.150436i | ||||
\(529\) | 6.86853 | − | 21.1392i | 0.298632 | − | 0.919094i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.52875 | − | 4.70502i | −0.0663423 | − | 0.204181i | ||||
\(532\) | − | 11.0957i | − | 0.481061i | ||||||
\(533\) | −0.286142 | + | 0.0929731i | −0.0123942 | + | 0.00402711i | ||||
\(534\) | 1.64172 | + | 1.19278i | 0.0710441 | + | 0.0516165i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.04870 | + | 2.94155i | −0.174877 | + | 0.127056i | ||||
\(537\) | 6.95555 | − | 9.57350i | 0.300154 | − | 0.413127i | ||||
\(538\) | −2.18809 | + | 3.01165i | −0.0943353 | + | 0.129841i | ||||
\(539\) | 5.87861 | − | 4.27106i | 0.253210 | − | 0.183968i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.7041 | − | 12.1362i | −0.718165 | − | 0.521777i | 0.167632 | − | 0.985850i | \(-0.446388\pi\) |
−0.885797 | + | 0.464072i | \(0.846388\pi\) | |||||||
\(542\) | −5.47824 | + | 1.77999i | −0.235310 | + | 0.0764570i | ||||
\(543\) | 30.3473i | 1.30233i | ||||||||
\(544\) | −3.42878 | − | 10.5527i | −0.147008 | − | 0.452443i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.0805217 | − | 0.247820i | 0.00344601 | − | 0.0106057i | ||||
\(547\) | 29.8405 | + | 9.69577i | 1.27589 | + | 0.414561i | 0.867130 | − | 0.498082i | \(-0.165962\pi\) |
0.408758 | + | 0.912643i | \(0.365962\pi\) | |||||||
\(548\) | −9.07211 | − | 12.4867i | −0.387541 | − | 0.533405i | ||||
\(549\) | 0.763042 | 0.0325658 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.2303 | 0.435825 | ||||||||
\(552\) | −0.552658 | − | 0.760668i | −0.0235227 | − | 0.0323762i | ||||
\(553\) | 24.0678 | + | 7.82012i | 1.02347 | + | 0.332545i | ||||
\(554\) | 0.788511 | − | 2.42679i | 0.0335006 | − | 0.103104i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.27624 | − | 10.0832i | −0.138944 | − | 0.427625i | ||||
\(557\) | − | 22.3515i | − | 0.947064i | −0.880776 | − | 0.473532i | \(-0.842979\pi\) | ||
0.880776 | − | 0.473532i | \(-0.157021\pi\) | |||||||
\(558\) | −0.885518 | + | 0.287722i | −0.0374870 | + | 0.0121803i | ||||
\(559\) | 0.777350 | + | 0.564778i | 0.0328784 | + | 0.0238875i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.2965 | + | 8.93390i | −0.519157 | + | 0.377189i | ||||
\(562\) | 2.78614 | − | 3.83480i | 0.117526 | − | 0.161761i | ||||
\(563\) | 20.2000 | − | 27.8029i | 0.851329 | − | 1.17175i | −0.132240 | − | 0.991218i | \(-0.542217\pi\) |
0.983568 | − | 0.180536i | \(-0.0577832\pi\) | |||||||
\(564\) | 9.88191 | − | 7.17963i | 0.416104 | − | 0.302317i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.51678 | − | 2.55509i | −0.147821 | − | 0.107398i | ||||
\(567\) | 18.0041 | − | 5.84987i | 0.756099 | − | 0.245672i | ||||
\(568\) | − | 4.33657i | − | 0.181958i | ||||||
\(569\) | −9.93991 | − | 30.5919i | −0.416703 | − | 1.28248i | −0.910719 | − | 0.413026i | \(-0.864472\pi\) |
0.494017 | − | 0.869452i | \(-0.335528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.39501 | + | 25.8372i | −0.351320 | + | 1.08125i | 0.606792 | + | 0.794861i | \(0.292456\pi\) |
−0.958112 | + | 0.286392i | \(0.907544\pi\) | |||||||
\(572\) | −1.10858 | − | 0.360198i | −0.0463519 | − | 0.0150607i | ||||
\(573\) | 15.5996 | + | 21.4710i | 0.651684 | + | 0.896966i | ||||
\(574\) | 0.606344 | 0.0253083 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.00521 | 0.250217 | ||||||||
\(577\) | −8.14100 | − | 11.2051i | −0.338914 | − | 0.466476i | 0.605210 | − | 0.796066i | \(-0.293089\pi\) |
−0.944124 | + | 0.329591i | \(0.893089\pi\) | |||||||
\(578\) | −1.68219 | − | 0.546575i | −0.0699697 | − | 0.0227345i | ||||
\(579\) | 3.08784 | − | 9.50340i | 0.128326 | − | 0.394948i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.6266 | − | 45.0159i | −0.606812 | − | 1.86757i | ||||
\(582\) | 1.81360i | 0.0751759i | ||||||||
\(583\) | 15.4085 | − | 5.00652i | 0.638154 | − | 0.207349i | ||||
\(584\) | 5.19215 | + | 3.77232i | 0.214853 | + | 0.156100i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.82315 | − | 1.32460i | 0.0753138 | − | 0.0547187i | ||||
\(587\) | 25.9507 | − | 35.7180i | 1.07110 | − | 1.47424i | 0.202139 | − | 0.979357i | \(-0.435211\pi\) |
0.868959 | − | 0.494884i | \(-0.164789\pi\) | |||||||
\(588\) | 6.18131 | − | 8.50785i | 0.254913 | − | 0.350858i | ||||
\(589\) | 8.53877 | − | 6.20378i | 0.351834 | − | 0.255622i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.52115 | + | 6.91752i | 0.391648 | + | 0.284549i | ||||
\(592\) | 29.2287 | − | 9.49699i | 1.20129 | − | 0.390324i | ||||
\(593\) | 16.2531i | 0.667437i | 0.942673 | + | 0.333718i | \(0.108303\pi\) | ||||
−0.942673 | + | 0.333718i | \(0.891697\pi\) | |||||||
\(594\) | 0.638770 | + | 1.96593i | 0.0262091 | + | 0.0806632i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.4380 | + | 35.2026i | −0.468520 | + | 1.44196i | ||||
\(597\) | −7.28630 | − | 2.36746i | −0.298208 | − | 0.0968938i | ||||
\(598\) | −0.0280549 | − | 0.0386142i | −0.00114725 | − | 0.00157905i | ||||
\(599\) | −30.4822 | −1.24547 | −0.622734 | − | 0.782433i | \(-0.713978\pi\) | ||||
−0.622734 | + | 0.782433i | \(0.713978\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.9162 | −1.17952 | −0.589758 | − | 0.807580i | \(-0.700777\pi\) | ||||
−0.589758 | + | 0.807580i | \(0.700777\pi\) | |||||||
\(602\) | −1.13821 | − | 1.56661i | −0.0463899 | − | 0.0638502i | ||||
\(603\) | −5.45932 | − | 1.77384i | −0.222321 | − | 0.0722364i | ||||
\(604\) | −2.36259 | + | 7.27129i | −0.0961322 | + | 0.295865i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.01609 | − | 3.12721i | −0.0412760 | − | 0.127034i | ||||
\(607\) | 8.23276i | 0.334157i | 0.985944 | + | 0.167079i | \(0.0534334\pi\) | ||||
−0.985944 | + | 0.167079i | \(0.946567\pi\) | |||||||
\(608\) | 3.53676 | − | 1.14916i | 0.143435 | − | 0.0466047i | ||||
\(609\) | 22.9577 | + | 16.6797i | 0.930293 | + | 0.675897i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.01184 | − | 0.735146i | 0.0409347 | − | 0.0297408i | ||||
\(612\) | 4.97320 | − | 6.84503i | 0.201030 | − | 0.276694i | ||||
\(613\) | −2.82026 | + | 3.88175i | −0.113909 | + | 0.156783i | −0.862165 | − | 0.506628i | \(-0.830892\pi\) |
0.748256 | + | 0.663411i | \(0.230892\pi\) | |||||||
\(614\) | 0.634619 | − | 0.461078i | 0.0256111 | − | 0.0186076i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.83337 | + | 2.78510i | 0.154451 | + | 0.112215i | ||||
\(617\) | 1.93239 | − | 0.627872i | 0.0777951 | − | 0.0252772i | −0.269861 | − | 0.962899i | \(-0.586978\pi\) |
0.347656 | + | 0.937622i | \(0.386978\pi\) | |||||||
\(618\) | 0.372454i | 0.0149823i | ||||||||
\(619\) | −2.51571 | − | 7.74255i | −0.101115 | − | 0.311200i | 0.887684 | − | 0.460453i | \(-0.152313\pi\) |
−0.988799 | + | 0.149253i | \(0.952313\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.53299 | − | 4.71806i | 0.0615167 | − | 0.189329i | ||||
\(622\) | 4.46783 | + | 1.45169i | 0.179144 | + | 0.0582073i | ||||
\(623\) | 14.4258 | + | 19.8554i | 0.577956 | + | 0.795488i | ||||
\(624\) | −1.65769 | −0.0663605 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.09413 | −0.163634 | ||||||||
\(627\) | −2.99421 | − | 4.12118i | −0.119577 | − | 0.164584i | ||||
\(628\) | −8.01153 | − | 2.60310i | −0.319695 | − | 0.103875i | ||||
\(629\) | 12.9040 | − | 39.7143i | 0.514515 | − | 1.58351i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.2855 | + | 31.6557i | 0.409461 | + | 1.26019i | 0.917112 | + | 0.398629i | \(0.130514\pi\) |
−0.507651 | + | 0.861563i | \(0.669486\pi\) | |||||||
\(632\) | 5.63846i | 0.224286i | ||||||||
\(633\) | 23.2412 | − | 7.55152i | 0.923754 | − | 0.300146i | ||||
\(634\) | 3.24873 | + | 2.36034i | 0.129024 | + | 0.0937412i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 18.9695 | − | 13.7822i | 0.752191 | − | 0.546499i | ||||
\(637\) | 0.632925 | − | 0.871147i | 0.0250774 | − | 0.0345161i | ||||
\(638\) | −1.27308 | + | 1.75224i | −0.0504015 | + | 0.0693718i | ||||
\(639\) | 4.02419 | − | 2.92375i | 0.159195 | − | 0.115662i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.3996 | + | 23.5397i | 1.27971 | + | 0.929761i | 0.999544 | − | 0.0301916i | \(-0.00961174\pi\) |
0.280162 | + | 0.959953i | \(0.409612\pi\) | |||||||
\(642\) | 4.05881 | − | 1.31879i | 0.160189 | − | 0.0520484i | ||||
\(643\) | 11.6870i | 0.460890i | 0.973085 | + | 0.230445i | \(0.0740182\pi\) | ||||
−0.973085 | + | 0.230445i | \(0.925982\pi\) | |||||||
\(644\) | −1.74213 | − | 5.36172i | −0.0686495 | − | 0.211281i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.505688 | − | 1.55635i | 0.0198960 | − | 0.0612337i | ||||
\(647\) | −7.56029 | − | 2.45649i | −0.297226 | − | 0.0965745i | 0.156608 | − | 0.987661i | \(-0.449944\pi\) |
−0.453834 | + | 0.891086i | \(0.649944\pi\) | |||||||
\(648\) | 2.47920 | + | 3.41233i | 0.0973923 | + | 0.134049i | ||||
\(649\) | −11.8727 | −0.466044 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.2766 | 1.14744 | ||||||||
\(652\) | −18.1773 | − | 25.0188i | −0.711876 | − | 0.979814i | ||||
\(653\) | −3.17402 | − | 1.03130i | −0.124209 | − | 0.0403579i | 0.246253 | − | 0.969206i | \(-0.420801\pi\) |
−0.370462 | + | 0.928848i | \(0.620801\pi\) | |||||||
\(654\) | 0.166948 | − | 0.513814i | 0.00652820 | − | 0.0200917i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.19199 | − | 3.66857i | −0.0465394 | − | 0.143234i | ||||
\(657\) | 7.36146i | 0.287198i | ||||||||
\(658\) | −2.39721 | + | 0.778899i | −0.0934528 | + | 0.0303647i | ||||
\(659\) | −24.3116 | − | 17.6634i | −0.947046 | − | 0.688069i | 0.00306074 | − | 0.999995i | \(-0.499026\pi\) |
−0.950106 | + | 0.311926i | \(0.899026\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.32670 | − | 3.87008i | 0.207185 | − | 0.150529i | −0.479354 | − | 0.877621i | \(-0.659129\pi\) |
0.686539 | + | 0.727093i | \(0.259129\pi\) | |||||||
\(662\) | −0.965008 | + | 1.32822i | −0.0375061 | + | 0.0516227i | ||||
\(663\) | −1.32391 | + | 1.82220i | −0.0514163 | + | 0.0707685i | ||||
\(664\) | 8.53192 | − | 6.19880i | 0.331103 | − | 0.240560i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.998835 | − | 0.725696i | −0.0387041 | − | 0.0281202i | ||||
\(667\) | 4.94352 | − | 1.60625i | 0.191414 | − | 0.0621941i | ||||
\(668\) | − | 41.3603i | − | 1.60028i | ||||||
\(669\) | 3.01483 | + | 9.27870i | 0.116560 | + | 0.358735i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.565881 | − | 1.74160i | 0.0218456 | − | 0.0672339i | ||||
\(672\) | 9.81044 | + | 3.18760i | 0.378446 | + | 0.122964i | ||||
\(673\) | 3.95662 | + | 5.44582i | 0.152516 | + | 0.209921i | 0.878438 | − | 0.477857i | \(-0.158586\pi\) |
−0.725921 | + | 0.687778i | \(0.758586\pi\) | |||||||
\(674\) | 5.32730 | 0.205200 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.3911 | 0.976580 | ||||||||
\(677\) | −8.02200 | − | 11.0413i | −0.308310 | − | 0.424353i | 0.626543 | − | 0.779387i | \(-0.284469\pi\) |
−0.934853 | + | 0.355034i | \(0.884469\pi\) | |||||||
\(678\) | −2.67386 | − | 0.868788i | −0.102689 | − | 0.0333656i | ||||
\(679\) | −6.77801 | + | 20.8606i | −0.260116 | + | 0.800555i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.09142 | − | 18.7474i | −0.233424 | − | 0.718404i | ||||
\(682\) | 2.23453i | 0.0855645i | ||||||||
\(683\) | 1.11483 | − | 0.362229i | 0.0426577 | − | 0.0138603i | −0.287610 | − | 0.957747i | \(-0.592861\pi\) |
0.330268 | + | 0.943887i | \(0.392861\pi\) | |||||||
\(684\) | 2.29413 | + | 1.66678i | 0.0877181 | + | 0.0637309i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.62693 | − | 1.18203i | 0.0621164 | − | 0.0451302i | ||||
\(687\) | 8.72692 | − | 12.0116i | 0.332953 | − | 0.458270i | ||||
\(688\) | −7.24091 | + | 9.96625i | −0.276057 | + | 0.379960i | ||||
\(689\) | 1.94235 | − | 1.41120i | 0.0739978 | − | 0.0537625i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.92451 | − | 7.21058i | −0.377546 | − | 0.274303i | 0.382787 | − | 0.923837i | \(-0.374964\pi\) |
−0.760333 | + | 0.649533i | \(0.774964\pi\) | |||||||
\(692\) | −13.4031 | + | 4.35492i | −0.509508 | + | 0.165549i | ||||
\(693\) | 5.43497i | 0.206457i | ||||||||
\(694\) | −0.809268 | − | 2.49067i | −0.0307194 | − | 0.0945445i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.95381 | + | 6.01321i | −0.0740590 | + | 0.227930i | ||||
\(697\) | −4.98464 | − | 1.61961i | −0.188807 | − | 0.0613471i | ||||
\(698\) | 0.605493 | + | 0.833390i | 0.0229183 | + | 0.0315443i | ||||
\(699\) | 32.3910 | 1.22514 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.0271 | −0.756415 | −0.378207 | − | 0.925721i | \(-0.623459\pi\) | ||||
−0.378207 | + | 0.925721i | \(0.623459\pi\) | |||||||
\(702\) | 0.180052 | + | 0.247820i | 0.00679562 | + | 0.00935337i | ||||
\(703\) | 13.3103 | + | 4.32479i | 0.502009 | + | 0.163113i | ||||
\(704\) | 4.45354 | − | 13.7066i | 0.167849 | − | 0.516586i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.108111 | + | 0.332731i | 0.00406880 | + | 0.0125225i | ||||
\(707\) | − | 39.7677i | − | 1.49562i | ||||||
\(708\) | −16.3418 | + | 5.30979i | −0.614164 | + | 0.199554i | ||||
\(709\) | −3.55571 | − | 2.58337i | −0.133537 | − | 0.0970206i | 0.519011 | − | 0.854767i | \(-0.326300\pi\) |
−0.652549 | + | 0.757747i | \(0.726300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.23230 | + | 3.80149i | −0.196227 | + | 0.142567i | ||||
\(712\) | −3.21417 | + | 4.42392i | −0.120456 | + | 0.165793i | ||||
\(713\) | 3.15209 | − | 4.33848i | 0.118047 | − | 0.162477i | ||||
\(714\) | 3.67232 | − | 2.66810i | 0.137433 | − | 0.0998511i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.7897 | + | 9.29226i | 0.477974 | + | 0.347268i | ||||
\(717\) | −10.5837 | + | 3.43885i | −0.395256 | + | 0.128426i | ||||
\(718\) | − | 4.06727i | − | 0.151789i | ||||||
\(719\) | 3.37704 | + | 10.3934i | 0.125942 | + | 0.387610i | 0.994072 | − | 0.108728i | \(-0.0346777\pi\) |
−0.868129 | + | 0.496338i | \(0.834678\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.39199 | + | 4.28409i | −0.0518403 | + | 0.159548i | ||||
\(722\) | −2.78832 | − | 0.905980i | −0.103771 | − | 0.0337171i | ||||
\(723\) | −17.6452 | − | 24.2865i | −0.656230 | − | 0.903224i | ||||
\(724\) | −40.5425 | −1.50675 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.88734 | −0.0700458 | ||||||||
\(727\) | 19.3400 | + | 26.6193i | 0.717282 | + | 0.987254i | 0.999610 | + | 0.0279359i | \(0.00889342\pi\) |
−0.282328 | + | 0.959318i | \(0.591107\pi\) | |||||||
\(728\) | 0.667799 | + | 0.216981i | 0.0247503 | + | 0.00804185i | ||||
\(729\) | −9.19466 | + | 28.2982i | −0.340543 | + | 1.04808i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.17242 | + | 15.9191i | 0.191309 | + | 0.588788i | ||||
\(732\) | − | 2.65026i | − | 0.0979564i | ||||||
\(733\) | −13.0768 | + | 4.24891i | −0.483002 | + | 0.156937i | −0.540389 | − | 0.841415i | \(-0.681723\pi\) |
0.0573871 | + | 0.998352i | \(0.481723\pi\) | |||||||
\(734\) | −3.17792 | − | 2.30889i | −0.117299 | − | 0.0852227i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.52862 | − | 1.11061i | 0.0563456 | − | 0.0409375i | ||||
\(737\) | −8.09739 | + | 11.1451i | −0.298271 | + | 0.410535i | ||||
\(738\) | −0.0910839 | + | 0.125366i | −0.00335285 | + | 0.00461480i | ||||
\(739\) | −34.9409 | + | 25.3860i | −1.28532 | + | 0.933840i | −0.999700 | − | 0.0245030i | \(-0.992200\pi\) |
−0.285621 | + | 0.958343i | \(0.592200\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.610715 | − | 0.443711i | −0.0224352 | − | 0.0163001i | ||||
\(742\) | −4.60173 | + | 1.49519i | −0.168935 | + | 0.0548902i | ||||
\(743\) | 31.8479i | 1.16838i | 0.811615 | + | 0.584192i | \(0.198589\pi\) | ||||
−0.811615 | + | 0.584192i | \(0.801411\pi\) | |||||||
\(744\) | 2.01573 | + | 6.20378i | 0.0739003 | + | 0.227442i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.30979 | − | 4.03113i | 0.0479550 | − | 0.147590i | ||||
\(747\) | 11.5046 | + | 3.73806i | 0.420930 | + | 0.136768i | ||||
\(748\) | −11.9352 | − | 16.4274i | −0.436395 | − | 0.600646i | ||||
\(749\) | 51.6145 | 1.88595 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.5952 | −1.07995 | −0.539973 | − | 0.841682i | \(-0.681565\pi\) | ||||
−0.539973 | + | 0.841682i | \(0.681565\pi\) | |||||||
\(752\) | 9.42517 | + | 12.9726i | 0.343700 | + | 0.473063i | ||||
\(753\) | −14.7993 | − | 4.80860i | −0.539318 | − | 0.175235i | ||||
\(754\) | −0.0991824 | + | 0.305252i | −0.00361201 | + | 0.0111166i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 11.1807 | + | 34.4107i | 0.406639 | + | 1.25150i | ||||
\(757\) | 0.0984401i | 0.00357786i | 0.999998 | + | 0.00178893i | \(0.000569435\pi\) | ||||
−0.999998 | + | 0.00178893i | \(0.999431\pi\) | |||||||
\(758\) | −3.77161 | + | 1.22547i | −0.136991 | + | 0.0445111i | ||||
\(759\) | −2.09394 | − | 1.52134i | −0.0760052 | − | 0.0552210i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.86717 | − | 2.08312i | 0.103935 | − | 0.0755131i | −0.534604 | − | 0.845103i | \(-0.679539\pi\) |
0.638539 | + | 0.769590i | \(0.279539\pi\) | |||||||
\(762\) | 0.927111 | − | 1.27606i | 0.0335857 | − | 0.0462267i | ||||
\(763\) | 3.84059 | − | 5.28612i | 0.139039 | − | 0.191370i | ||||
\(764\) | −28.6842 | + | 20.8403i | −1.03776 | + | 0.753975i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.837983 | − | 0.608830i | −0.0302775 | − | 0.0219979i | ||||
\(767\) | −1.67330 | + | 0.543687i | −0.0604192 | + | 0.0196314i | ||||
\(768\) | − | 19.6989i | − | 0.710822i | ||||||
\(769\) | −0.441149 | − | 1.35772i | −0.0159083 | − | 0.0489606i | 0.942787 | − | 0.333395i | \(-0.108194\pi\) |
−0.958696 | + | 0.284434i | \(0.908194\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.21997 | − | 28.3762i | 0.332049 | − | 1.02194i | ||||
\(772\) | 12.6960 | + | 4.12520i | 0.456941 | + | 0.148469i | ||||
\(773\) | −19.8558 | − | 27.3292i | −0.714163 | − | 0.982962i | −0.999698 | − | 0.0245930i | \(-0.992171\pi\) |
0.285534 | − | 0.958369i | \(-0.407829\pi\) | |||||||
\(774\) | 0.494888 | 0.0177884 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.88708 | −0.175436 | ||||||||
\(777\) | 22.8184 | + | 31.4068i | 0.818604 | + | 1.12671i | ||||
\(778\) | 1.41562 | + | 0.459961i | 0.0507523 | + | 0.0164904i | ||||
\(779\) | 0.542815 | − | 1.67061i | 0.0194484 | − | 0.0598559i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.68891 | − | 11.3533i | −0.131999 | − | 0.406253i | ||||
\(782\) | − | 0.831462i | − | 0.0297330i | ||||||
\(783\) | −31.7267 | + | 10.3086i | −1.13382 | + | 0.368401i | ||||
\(784\) | 11.1688 | + | 8.11461i | 0.398886 | + | 0.289808i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.326458 | − | 0.237186i | 0.0116444 | − | 0.00846014i | ||||
\(787\) | −1.28155 | + | 1.76390i | −0.0456822 | + | 0.0628761i | −0.831247 | − | 0.555903i | \(-0.812373\pi\) |
0.785565 | + | 0.618779i | \(0.212373\pi\) | |||||||
\(788\) | −9.24145 | + | 12.7198i | −0.329213 | + | 0.453123i | ||||
\(789\) | 33.4515 | − | 24.3040i | 1.19091 | − | 0.865244i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.5086 | − | 19.9862i | −0.978094 | − | 0.710627i | ||||
\(792\) | −1.15168 | + | 0.374205i | −0.0409233 | + | 0.0132968i | ||||
\(793\) | − | 0.271369i | − | 0.00963659i | ||||||
\(794\) | 1.17559 | + | 3.61808i | 0.0417200 | + | 0.128401i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.16281 | − | 9.73412i | 0.112103 | − | 0.345017i | ||||
\(797\) | −22.3421 | − | 7.25938i | −0.791397 | − | 0.257141i | −0.114698 | − | 0.993400i | \(-0.536590\pi\) |
−0.676699 | + | 0.736260i | \(0.736590\pi\) | |||||||
\(798\) | 0.894219 | + | 1.23079i | 0.0316550 | + | 0.0435694i | ||||
\(799\) | 21.7875 | 0.770787 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.27226 | −0.221620 | ||||||||
\(802\) | −3.24284 | − | 4.46339i | −0.114509 | − | 0.157608i | ||||
\(803\) | 16.8021 | + | 5.45935i | 0.592935 | + | 0.192656i | ||||
\(804\) | −6.16104 | + | 18.9617i | −0.217283 | + | 0.668729i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.102326 | + | 0.314926i | 0.00360427 | + | 0.0110928i | ||||
\(807\) | 29.9144i | 1.05304i | ||||||||
\(808\) | 8.42687 | − | 2.73806i | 0.296456 | − | 0.0963245i | ||||
\(809\) | −30.8648 | − | 22.4246i | −1.08515 | − | 0.788406i | −0.106574 | − | 0.994305i | \(-0.533988\pi\) |
−0.978573 | + | 0.205899i | \(0.933988\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.7575 | + | 28.1590i | −1.36096 | + | 0.988795i | −0.362577 | + | 0.931954i | \(0.618103\pi\) |
−0.998383 | + | 0.0568414i | \(0.981897\pi\) | |||||||
\(812\) | −22.2833 | + | 30.6703i | −0.781989 | + | 1.07632i | ||||
\(813\) | −27.2074 | + | 37.4477i | −0.954204 | + | 1.31335i | ||||
\(814\) | −2.39711 | + | 1.74160i | −0.0840187 | + | 0.0610432i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −23.3621 | − | 16.9736i | −0.817838 | − | 0.594194i | ||||
\(817\) | −5.33531 | + | 1.73355i | −0.186659 | + | 0.0606491i | ||||
\(818\) | − | 2.02318i | − | 0.0707388i | ||||||
\(819\) | 0.248884 | + | 0.765985i | 0.00869670 | + | 0.0267657i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.86538 | − | 18.0518i | 0.204703 | − | 0.630012i | −0.795022 | − | 0.606580i | \(-0.792541\pi\) |
0.999725 | − | 0.0234316i | \(-0.00745919\pi\) | |||||||
\(822\) | 2.01264 | + | 0.653946i | 0.0701988 | + | 0.0228090i | ||||
\(823\) | 13.0301 | + | 17.9344i | 0.454201 | + | 0.625154i | 0.973293 | − | 0.229564i | \(-0.0737301\pi\) |
−0.519093 | + | 0.854718i | \(0.673730\pi\) | |||||||
\(824\) | −1.00365 | −0.0349638 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.54577 | 0.123373 | ||||||||
\(827\) | −2.77986 | − | 3.82615i | −0.0966651 | − | 0.133048i | 0.757945 | − | 0.652319i | \(-0.226204\pi\) |
−0.854610 | + | 0.519271i | \(0.826204\pi\) | |||||||
\(828\) | 1.37028 | + | 0.445230i | 0.0476204 | + | 0.0154728i | ||||
\(829\) | −5.08025 | + | 15.6354i | −0.176444 | + | 0.543040i | −0.999696 | − | 0.0246362i | \(-0.992157\pi\) |
0.823252 | + | 0.567676i | \(0.192157\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.33638 | − | 19.5014i | −0.219807 | − | 0.676495i | ||||
\(832\) | − | 2.13570i | − | 0.0740419i | ||||||
\(833\) | 17.8399 | − | 5.79654i | 0.618116 | − | 0.200838i | ||||
\(834\) | 1.17604 | + | 0.854441i | 0.0407228 | + | 0.0295869i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.50569 | − | 4.00012i | 0.190418 | − | 0.138347i | ||||
\(837\) | −20.2296 | + | 27.8437i | −0.699239 | + | 0.962419i | ||||
\(838\) | 3.54449 | − | 4.87857i | 0.122442 | − | 0.168527i | ||||
\(839\) | −4.53117 | + | 3.29209i | −0.156433 | + | 0.113655i | −0.663248 | − | 0.748399i | \(-0.730823\pi\) |
0.506815 | + | 0.862055i | \(0.330823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.81659 | − | 3.49946i | −0.166089 | − | 0.120671i | ||||
\(842\) | 3.53026 | − | 1.14705i | 0.121661 | − | 0.0395300i | ||||
\(843\) | − | 38.0906i | − | 1.31191i | ||||||
\(844\) | 10.0884 | + | 31.0490i | 0.347259 | + | 1.06875i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.199061 | − | 0.612646i | 0.00684384 | − | 0.0210632i | ||||
\(847\) | −21.7088 | − | 7.05362i | −0.745923 | − | 0.242365i | ||||
\(848\) | 18.0928 | + | 24.9025i | 0.621308 | + | 0.855157i | ||||
\(849\) | −34.9318 | −1.19886 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.11091 | 0.243759 | ||||||||
\(852\) | −10.1550 | − | 13.9771i | −0.347904 | − | 0.478849i | ||||
\(853\) | −17.0149 | − | 5.52847i | −0.582578 | − | 0.189291i | 0.00287712 | − | 0.999996i | \(-0.499084\pi\) |
−0.585455 | + | 0.810705i | \(0.699084\pi\) | |||||||
\(854\) | −0.169000 | + | 0.520128i | −0.00578305 | + | 0.0177984i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.55373 | + | 10.9372i | 0.121464 | + | 0.373827i | ||||
\(857\) | − | 3.19536i | − | 0.109151i | −0.998510 | − | 0.0545757i | \(-0.982619\pi\) | ||
0.998510 | − | 0.0545757i | \(-0.0173806\pi\) | |||||||
\(858\) | 0.151997 | − | 0.0493869i | 0.00518910 | − | 0.00168604i | ||||
\(859\) | 35.1272 | + | 25.5214i | 1.19852 | + | 0.870778i | 0.994139 | − | 0.108113i | \(-0.0344807\pi\) |
0.204385 | + | 0.978891i | \(0.434481\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.94194 | − | 2.86399i | 0.134341 | − | 0.0976045i | ||||
\(862\) | 0.770377 | − | 1.06033i | 0.0262391 | − | 0.0361151i | ||||
\(863\) | 25.4349 | − | 35.0081i | 0.865813 | − | 1.19169i | −0.114339 | − | 0.993442i | \(-0.536475\pi\) |
0.980152 | − | 0.198247i | \(-0.0635248\pi\) | |||||||
\(864\) | −9.81044 | + | 7.12770i | −0.333758 | + | 0.242489i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.812469 | + | 0.590293i | 0.0276088 | + | 0.0200590i | ||||
\(867\) | −13.5178 | + | 4.39221i | −0.459090 | + | 0.149167i | ||||
\(868\) | 39.1120i | 1.32755i | ||||||||
\(869\) | 4.79636 | + | 14.7617i | 0.162705 | + | 0.500755i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.630850 | + | 1.94156i | −0.0213755 | + | 0.0657871i | ||||
\(872\) | 1.38457 | + | 0.449874i | 0.0468875 | + | 0.0152347i | ||||
\(873\) | −3.29490 | − | 4.53504i | −0.111516 | − | 0.153488i | ||||
\(874\) | 0.278666 | 0.00942603 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 25.5684 | 0.863876 | ||||||||
\(877\) | 20.1222 | + | 27.6958i | 0.679478 | + | 0.935221i | 0.999927 | − | 0.0120443i | \(-0.00383391\pi\) |
−0.320449 | + | 0.947266i | \(0.603834\pi\) | |||||||
\(878\) | 5.35793 | + | 1.74090i | 0.180821 | + | 0.0587524i | ||||
\(879\) | 5.59605 | − | 17.2229i | 0.188750 | − | 0.580913i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.53722 | + | 26.2749i | 0.287626 | + | 0.885223i | 0.985599 | + | 0.169099i | \(0.0540857\pi\) |
−0.697973 | + | 0.716124i | \(0.745914\pi\) | |||||||
\(882\) | − | 0.554602i | − | 0.0186744i | ||||||
\(883\) | −24.6314 | + | 8.00324i | −0.828913 | + | 0.269330i | −0.692588 | − | 0.721334i | \(-0.743529\pi\) |
−0.136326 | + | 0.990664i | \(0.543529\pi\) | |||||||
\(884\) | −2.43437 | − | 1.76867i | −0.0818767 | − | 0.0594869i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.68234 | + | 1.22229i | −0.0565194 | + | 0.0410638i | ||||
\(887\) | −10.1363 | + | 13.9514i | −0.340344 | + | 0.468443i | −0.944542 | − | 0.328391i | \(-0.893494\pi\) |
0.604198 | + | 0.796834i | \(0.293494\pi\) | |||||||
\(888\) | −5.08410 | + | 6.99766i | −0.170611 | + | 0.234826i | ||||
\(889\) | 15.4330 | − | 11.2127i | 0.517606 | − | 0.376063i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.39334 | + | 6.82466i | 0.314689 | + | 0.228635i | ||||
\(892\) | −12.3959 | + | 4.02766i | −0.415044 | + | 0.134856i | ||||
\(893\) | 7.30213i | 0.244356i | ||||||||
\(894\) | −1.56827 | − | 4.82664i | −0.0524508 | − | 0.161427i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.66118 | + | 17.4233i | −0.189127 | + | 0.582072i | ||||
\(897\) | −0.364779 | − | 0.118524i | −0.0121796 | − | 0.00395740i | ||||
\(898\) | −1.69748 | − | 2.33637i | −0.0566455 | − | 0.0779658i | ||||
\(899\) | −36.0614 | −1.20271 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.8238 | 1.39335 | ||||||||
\(902\) | 0.218593 | + | 0.300867i | 0.00727835 | + | 0.0100178i | ||||
\(903\) | −14.7993 | − | 4.80860i | −0.492491 | − | 0.160020i | ||||
\(904\) | 2.34112 | − | 7.20522i | 0.0778644 | − | 0.239642i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.323934 | − | 0.996968i | −0.0107620 | − | 0.0331220i | ||||
\(907\) | 57.0465i | 1.89420i | 0.320940 | + | 0.947099i | \(0.396001\pi\) | ||||
−0.320940 | + | 0.947099i | \(0.603999\pi\) | |||||||
\(908\) | 25.0456 | − | 8.13782i | 0.831168 | − | 0.270063i | ||||
\(909\) | 8.22228 | + | 5.97384i | 0.272716 | + | 0.198140i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0738 | + | 11.6783i | −0.532549 | + | 0.386919i | −0.821310 | − | 0.570482i | \(-0.806757\pi\) |
0.288761 | + | 0.957401i | \(0.406757\pi\) | |||||||
\(912\) | 5.68873 | − | 7.82986i | 0.188373 | − | 0.259273i | ||||
\(913\) | 17.0638 | − | 23.4864i | 0.564731 | − | 0.777285i | ||||
\(914\) | −0.617526 | + | 0.448659i | −0.0204259 | + | 0.0148403i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.0469 | + | 11.6587i | 0.530203 | + | 0.385215i | ||||
\(917\) | 4.64147 | − | 1.50811i | 0.153275 | − | 0.0498020i | ||||
\(918\) | 5.33620i | 0.176121i | ||||||||
\(919\) | −8.64582 | − | 26.6091i | −0.285199 | − | 0.877753i | −0.986339 | − | 0.164729i | \(-0.947325\pi\) |
0.701140 | − | 0.713024i | \(-0.252675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.94792 | − | 5.99509i | 0.0641862 | − | 0.197545i | ||||
\(922\) | −4.17599 | − | 1.35686i | −0.137529 | − | 0.0446858i | ||||
\(923\) | −1.03980 | − | 1.43117i | −0.0342255 | − | 0.0471074i | ||||
\(924\) | 18.8772 | 0.621013 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.56952 | 0.248750 | ||||||||
\(927\) | −0.676668 | − | 0.931353i | −0.0222247 | − | 0.0305896i | ||||
\(928\) | −12.0840 | − | 3.92632i | −0.396676 | − | 0.128888i | ||||
\(929\) | 4.36484 | − | 13.4336i | 0.143206 | − | 0.440742i | −0.853570 | − | 0.520978i | \(-0.825567\pi\) |
0.996776 | + | 0.0802358i | \(0.0255673\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.94272 | + | 5.97908i | 0.0636701 | + | 0.195957i | ||||
\(932\) | 43.2727i | 1.41744i | ||||||||
\(933\) | 35.9030 | − | 11.6656i | 1.17541 | − | 0.381914i | ||||
\(934\) | −1.54066 | − | 1.11936i | −0.0504121 | − | 0.0366265i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.145178 | + | 0.105478i | −0.00474530 | + | 0.00344766i | ||||
\(937\) | −21.1336 | + | 29.0879i | −0.690404 | + | 0.950260i | −1.00000 | 0.000608458i | \(-0.999806\pi\) | |
0.309596 | + | 0.950868i | \(0.399806\pi\) | |||||||
\(938\) | 2.41828 | − | 3.32847i | 0.0789596 | − | 0.108679i | ||||
\(939\) | −26.6166 | + | 19.3381i | −0.868600 | + | 0.631075i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.5991 | − | 15.6926i | −0.704109 | − | 0.511565i | 0.177159 | − | 0.984182i | \(-0.443309\pi\) |
−0.881268 | + | 0.472617i | \(0.843309\pi\) | |||||||
\(942\) | 1.09846 | − | 0.356912i | 0.0357898 | − | 0.0116288i | ||||
\(943\) | − | 0.892508i | − | 0.0290640i | ||||||
\(944\) | −6.97051 | − | 21.4530i | −0.226871 | − | 0.698236i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.367015 | − | 1.12956i | 0.0119327 | − | 0.0367250i | ||||
\(947\) | −16.4630 | − | 5.34914i | −0.534975 | − | 0.173824i | 0.0290558 | − | 0.999578i | \(-0.490750\pi\) |
−0.564030 | + | 0.825754i | \(0.690750\pi\) | |||||||
\(948\) | 13.2036 | + | 18.1732i | 0.428834 | + | 0.590239i | ||||
\(949\) | 2.61803 | 0.0849850 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.2693 | 1.04640 | ||||||||
\(952\) | 7.18970 | + | 9.89577i | 0.233020 | + | 0.320724i | ||||
\(953\) | 23.0748 | + | 7.49744i | 0.747465 | + | 0.242866i | 0.657890 | − | 0.753114i | \(-0.271449\pi\) |
0.0895748 | + | 0.995980i | \(0.471449\pi\) | |||||||
\(954\) | 0.382121 | − | 1.17605i | 0.0123716 | − | 0.0380759i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.59413 | − | 14.1393i | −0.148585 | − | 0.457297i | ||||
\(957\) | 17.4048i | 0.562617i | ||||||||
\(958\) | 6.27287 | − | 2.03818i | 0.202667 | − | 0.0658505i | ||||
\(959\) | 20.7060 | + | 15.0438i | 0.668632 | + | 0.485790i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.01936 | + | 3.64678i | −0.161915 | + | 0.117638i | ||||
\(962\) | −0.258087 | + | 0.355226i | −0.00832106 | + | 0.0114530i | ||||
\(963\) | −7.75345 | + | 10.6717i | −0.249851 | + | 0.343891i | ||||
\(964\) | 32.4455 | − | 23.5730i | 1.04500 | − | 0.759236i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.625353 | + | 0.454345i | 0.0201204 | + | 0.0146183i | ||||
\(967\) | −29.5915 | + | 9.61485i | −0.951598 | + | 0.309193i | −0.743365 | − | 0.668886i | \(-0.766771\pi\) |
−0.208233 | + | 0.978079i | \(0.566771\pi\) | |||||||
\(968\) | − | 5.08580i | − | 0.163464i | ||||||
\(969\) | −4.06365 | − | 12.5066i | −0.130543 | − | 0.401771i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.36828 | + | 16.5219i | −0.172276 | + | 0.530212i | −0.999499 | − | 0.0316630i | \(-0.989920\pi\) |
0.827222 | + | 0.561875i | \(0.189920\pi\) | |||||||
\(972\) | −15.6766 | − | 5.09364i | −0.502827 | − | 0.163378i | ||||
\(973\) | 10.3338 | + | 14.2233i | 0.331288 | + | 0.455978i | ||||
\(974\) | −1.94855 | −0.0624356 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.47917 | 0.111365 | ||||||||
\(977\) | −25.2118 | − | 34.7011i | −0.806598 | − | 1.11019i | −0.991839 | − | 0.127494i | \(-0.959307\pi\) |
0.185241 | − | 0.982693i | \(-0.440693\pi\) | |||||||
\(978\) | 4.03260 | + | 1.31027i | 0.128948 | + | 0.0418979i | ||||
\(979\) | −4.65159 | + | 14.3161i | −0.148665 | + | 0.457545i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.516019 | + | 1.58814i | 0.0164752 | + | 0.0507055i | ||||
\(982\) | − | 3.23651i | − | 0.103281i | ||||||
\(983\) | 35.6202 | − | 11.5737i | 1.13611 | − | 0.369144i | 0.320214 | − | 0.947345i | \(-0.396245\pi\) |
0.815894 | + | 0.578202i | \(0.196245\pi\) | |||||||
\(984\) | 0.878294 | + | 0.638118i | 0.0279990 | + | 0.0203424i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.52337 | + | 3.28642i | −0.144054 | + | 0.104661i | ||||
\(987\) | −11.9056 | + | 16.3866i | −0.378959 | + | 0.521593i | ||||
\(988\) | 0.592775 | − | 0.815884i | 0.0188587 | − | 0.0259567i | ||||
\(989\) | −2.30597 | + | 1.67538i | −0.0733255 | + | 0.0532741i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.5611 | − | 9.85271i | −0.430782 | − | 0.312982i | 0.351179 | − | 0.936308i | \(-0.385781\pi\) |
−0.781962 | + | 0.623327i | \(0.785781\pi\) | |||||||
\(992\) | −12.4670 | + | 4.05076i | −0.395826 | + | 0.128612i | ||||
\(993\) | 13.1931i | 0.418669i | ||||||||
\(994\) | 1.10169 | + | 3.39065i | 0.0349434 | + | 0.107545i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 12.9833 | − | 39.9586i | 0.411392 | − | 1.26614i | ||||
\(997\) | 56.9297 | + | 18.4976i | 1.80298 | + | 0.585825i | 0.999949 | − | 0.0101082i | \(-0.00321760\pi\) |
0.803034 | + | 0.595933i | \(0.203218\pi\) | |||||||
\(998\) | −1.01393 | − | 1.39555i | −0.0320953 | − | 0.0441753i | ||||
\(999\) | −45.6367 | −1.44388 |
(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 | 625.2.e.i.374.1 | 8 | ||
5.2 | odd | 4 | 625.2.d.o.251.3 | 16 | |||
5.3 | odd | 4 | 625.2.d.o.251.2 | 16 | |||
5.4 | even | 2 | 625.2.e.a.374.2 | 8 | |||
25.2 | odd | 20 | 125.2.d.b.26.2 | 16 | |||
25.3 | odd | 20 | 625.2.a.f.1.5 | 8 | |||
25.4 | even | 10 | 625.2.b.c.624.4 | 8 | |||
25.6 | even | 5 | 25.2.e.a.4.2 | ✓ | 8 | ||
25.8 | odd | 20 | 125.2.d.b.101.3 | 16 | |||
25.9 | even | 10 | inner | 625.2.e.i.249.1 | 8 | ||
25.11 | even | 5 | 125.2.e.b.99.1 | 8 | |||
25.12 | odd | 20 | 625.2.d.o.376.3 | 16 | |||
25.13 | odd | 20 | 625.2.d.o.376.2 | 16 | |||
25.14 | even | 10 | 25.2.e.a.19.2 | yes | 8 | ||
25.16 | even | 5 | 625.2.e.a.249.2 | 8 | |||
25.17 | odd | 20 | 125.2.d.b.101.2 | 16 | |||
25.19 | even | 10 | 125.2.e.b.24.1 | 8 | |||
25.21 | even | 5 | 625.2.b.c.624.5 | 8 | |||
25.22 | odd | 20 | 625.2.a.f.1.4 | 8 | |||
25.23 | odd | 20 | 125.2.d.b.26.3 | 16 | |||
75.14 | odd | 10 | 225.2.m.a.19.1 | 8 | |||
75.47 | even | 20 | 5625.2.a.x.1.5 | 8 | |||
75.53 | even | 20 | 5625.2.a.x.1.4 | 8 | |||
75.56 | odd | 10 | 225.2.m.a.154.1 | 8 | |||
100.3 | even | 20 | 10000.2.a.bj.1.3 | 8 | |||
100.31 | odd | 10 | 400.2.y.c.129.2 | 8 | |||
100.39 | odd | 10 | 400.2.y.c.369.2 | 8 | |||
100.47 | even | 20 | 10000.2.a.bj.1.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.e.a.4.2 | ✓ | 8 | 25.6 | even | 5 | ||
25.2.e.a.19.2 | yes | 8 | 25.14 | even | 10 | ||
125.2.d.b.26.2 | 16 | 25.2 | odd | 20 | |||
125.2.d.b.26.3 | 16 | 25.23 | odd | 20 | |||
125.2.d.b.101.2 | 16 | 25.17 | odd | 20 | |||
125.2.d.b.101.3 | 16 | 25.8 | odd | 20 | |||
125.2.e.b.24.1 | 8 | 25.19 | even | 10 | |||
125.2.e.b.99.1 | 8 | 25.11 | even | 5 | |||
225.2.m.a.19.1 | 8 | 75.14 | odd | 10 | |||
225.2.m.a.154.1 | 8 | 75.56 | odd | 10 | |||
400.2.y.c.129.2 | 8 | 100.31 | odd | 10 | |||
400.2.y.c.369.2 | 8 | 100.39 | odd | 10 | |||
625.2.a.f.1.4 | 8 | 25.22 | odd | 20 | |||
625.2.a.f.1.5 | 8 | 25.3 | odd | 20 | |||
625.2.b.c.624.4 | 8 | 25.4 | even | 10 | |||
625.2.b.c.624.5 | 8 | 25.21 | even | 5 | |||
625.2.d.o.251.2 | 16 | 5.3 | odd | 4 | |||
625.2.d.o.251.3 | 16 | 5.2 | odd | 4 | |||
625.2.d.o.376.2 | 16 | 25.13 | odd | 20 | |||
625.2.d.o.376.3 | 16 | 25.12 | odd | 20 | |||
625.2.e.a.249.2 | 8 | 25.16 | even | 5 | |||
625.2.e.a.374.2 | 8 | 5.4 | even | 2 | |||
625.2.e.i.249.1 | 8 | 25.9 | even | 10 | inner | ||
625.2.e.i.374.1 | 8 | 1.1 | even | 1 | trivial | ||
5625.2.a.x.1.4 | 8 | 75.53 | even | 20 | |||
5625.2.a.x.1.5 | 8 | 75.47 | even | 20 | |||
10000.2.a.bj.1.3 | 8 | 100.3 | even | 20 | |||
10000.2.a.bj.1.6 | 8 | 100.47 | even | 20 |