Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(79,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.ci (of order \(18\), degree \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 319.1 | ||
Root | \(-0.766044 - 0.642788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.319 |
Dual form | 912.2.ci.b.223.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{11}{18}\right)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.173648 | − | 0.984808i | −0.100256 | − | 0.568579i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.93969 | + | 1.62760i | −0.867457 | + | 0.727883i | −0.963561 | − | 0.267489i | \(-0.913806\pi\) |
0.0961041 | + | 0.995371i | \(0.469362\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.386659 | + | 0.223238i | 0.146143 | + | 0.0843760i | 0.571289 | − | 0.820749i | \(-0.306444\pi\) |
−0.425145 | + | 0.905125i | \(0.639777\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.939693 | + | 0.342020i | −0.313231 | + | 0.114007i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.02094 | − | 1.16679i | 0.609338 | − | 0.351801i | −0.163369 | − | 0.986565i | \(-0.552236\pi\) |
0.772706 | + | 0.634764i | \(0.218903\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.358441 | + | 0.0632028i | 0.0994136 | + | 0.0175293i | 0.223134 | − | 0.974788i | \(-0.428371\pi\) |
−0.123720 | + | 0.992317i | \(0.539482\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.93969 | + | 1.62760i | 0.500826 | + | 0.420243i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.58512 | − | 2.03282i | −1.35459 | − | 0.493031i | −0.440213 | − | 0.897893i | \(-0.645097\pi\) |
−0.914378 | + | 0.404862i | \(0.867319\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.354570 | + | 4.34445i | 0.0813440 | + | 0.996686i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.152704 | − | 0.419550i | 0.0333227 | − | 0.0915533i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.14543 | + | 2.55682i | −0.447353 | + | 0.533135i | −0.941845 | − | 0.336048i | \(-0.890910\pi\) |
0.494492 | + | 0.869182i | \(0.335354\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.245100 | − | 1.39003i | 0.0490200 | − | 0.278006i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.500000 | + | 0.866025i | 0.0962250 | + | 0.166667i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.449493 | + | 1.23497i | 0.0834687 | + | 0.229328i | 0.974405 | − | 0.224800i | \(-0.0721729\pi\) |
−0.890936 | + | 0.454129i | \(0.849951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.35117 | + | 5.80439i | −0.601887 | + | 1.04250i | 0.390648 | + | 0.920540i | \(0.372251\pi\) |
−0.992535 | + | 0.121959i | \(0.961082\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50000 | − | 1.78763i | −0.261116 | − | 0.311187i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.11334 | + | 0.196312i | −0.188189 | + | 0.0331828i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.52974i | 1.23788i | 0.785438 | + | 0.618941i | \(0.212438\pi\) | ||||
−0.785438 | + | 0.618941i | \(0.787562\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.363970i | − | 0.0582819i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.2947 | + | 1.99157i | −1.76394 | + | 0.311030i | −0.959228 | − | 0.282634i | \(-0.908792\pi\) |
−0.804713 | + | 0.593664i | \(0.797681\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.52481 | + | 5.39246i | 0.690028 | + | 0.822343i | 0.991359 | − | 0.131176i | \(-0.0418754\pi\) |
−0.301331 | + | 0.953520i | \(0.597431\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.26604 | − | 2.19285i | 0.188731 | − | 0.326891i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.66978 | + | 7.33515i | 0.389427 | + | 1.06994i | 0.967260 | + | 0.253787i | \(0.0816763\pi\) |
−0.577833 | + | 0.816155i | \(0.696101\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.40033 | − | 5.88954i | −0.485761 | − | 0.841363i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.03209 | + | 5.85327i | −0.144521 | + | 0.819621i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.13176 | + | 1.34878i | −0.155459 | + | 0.185269i | −0.838152 | − | 0.545436i | \(-0.816364\pi\) |
0.682693 | + | 0.730705i | \(0.260808\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.02094 | + | 5.55250i | −0.272504 | + | 0.748699i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.21688 | − | 1.10359i | 0.558540 | − | 0.146174i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.69119 | − | 2.07142i | −0.740930 | − | 0.269676i | −0.0561458 | − | 0.998423i | \(-0.517881\pi\) |
−0.684784 | + | 0.728746i | \(0.740103\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.19459 | + | 4.35878i | 0.665099 | + | 0.558085i | 0.911610 | − | 0.411055i | \(-0.134840\pi\) |
−0.246511 | + | 0.969140i | \(0.579284\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.439693 | − | 0.0775297i | −0.0553961 | − | 0.00976782i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.798133 | + | 0.460802i | −0.0989963 | + | 0.0571555i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.71688 | − | 3.17269i | 1.06494 | − | 0.387605i | 0.250656 | − | 0.968076i | \(-0.419354\pi\) |
0.814281 | + | 0.580471i | \(0.197132\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.89053 | + | 1.66885i | 0.347979 | + | 0.200906i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.11334 | − | 3.45150i | 0.488164 | − | 0.409618i | −0.365204 | − | 0.930928i | \(-0.619001\pi\) |
0.853368 | + | 0.521310i | \(0.174556\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.591052 | − | 3.35202i | −0.0691774 | − | 0.392325i | −0.999662 | − | 0.0259938i | \(-0.991725\pi\) |
0.930485 | − | 0.366331i | \(-0.119386\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.41147 | −0.162983 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.04189 | 0.118734 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.442219 | + | 2.50795i | 0.0497535 | + | 0.282166i | 0.999526 | − | 0.0307739i | \(-0.00979720\pi\) |
−0.949773 | + | 0.312940i | \(0.898686\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.766044 | − | 0.642788i | 0.0851160 | − | 0.0714208i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.39053 | + | 0.802823i | 0.152630 | + | 0.0881212i | 0.574370 | − | 0.818596i | \(-0.305247\pi\) |
−0.421740 | + | 0.906717i | \(0.638580\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.1420 | − | 5.14728i | 1.53392 | − | 0.558301i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.13816 | − | 0.657115i | 0.122023 | − | 0.0704501i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.14930 | − | 1.08429i | −0.651825 | − | 0.114934i | −0.162049 | − | 0.986783i | \(-0.551810\pi\) |
−0.489776 | + | 0.871848i | \(0.662921\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.124485 | + | 0.104455i | 0.0130496 | + | 0.0109499i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.29813 | + | 2.29233i | 0.653086 | + | 0.237704i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.75877 | − | 7.84981i | −0.796033 | − | 0.805373i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.368241 | − | 1.01173i | 0.0373892 | − | 0.102726i | −0.919593 | − | 0.392872i | \(-0.871482\pi\) |
0.956982 | + | 0.290146i | \(0.0937038\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.50000 | + | 1.78763i | −0.150756 | + | 0.179664i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.84090 | + | 16.1115i | −0.282680 | + | 1.60316i | 0.430776 | + | 0.902459i | \(0.358240\pi\) |
−0.713456 | + | 0.700700i | \(0.752871\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.794263 | + | 1.37570i | 0.0782611 | + | 0.135552i | 0.902500 | − | 0.430690i | \(-0.141730\pi\) |
−0.824239 | + | 0.566243i | \(0.808397\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.386659 | + | 1.06234i | 0.0377341 | + | 0.103674i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000 | − | 5.19615i | 0.290021 | − | 0.502331i | −0.683793 | − | 0.729676i | \(-0.739671\pi\) |
0.973814 | + | 0.227345i | \(0.0730044\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.56418 | − | 11.3981i | −0.916082 | − | 1.09174i | −0.995487 | − | 0.0949016i | \(-0.969746\pi\) |
0.0794046 | − | 0.996842i | \(-0.474698\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.41534 | − | 1.30753i | 0.703833 | − | 0.124105i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.51860i | 0.801363i | 0.916217 | + | 0.400681i | \(0.131227\pi\) | ||||
−0.916217 | + | 0.400681i | \(0.868773\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.45134i | − | 0.788092i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.358441 | + | 0.0632028i | −0.0331379 | + | 0.00584310i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.70574 | − | 2.03282i | −0.156365 | − | 0.186348i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.77719 | + | 4.81023i | −0.252472 | + | 0.437294i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.92262 | + | 10.7773i | 0.353691 | + | 0.971757i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.54323 | − | 7.86911i | −0.406359 | − | 0.703835i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.28359 | − | 12.9509i | 0.202635 | − | 1.14920i | −0.698482 | − | 0.715628i | \(-0.746141\pi\) |
0.901117 | − | 0.433575i | \(-0.142748\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.52481 | − | 5.39246i | 0.398388 | − | 0.474780i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.52481 | − | 4.18939i | 0.133224 | − | 0.366029i | −0.855087 | − | 0.518485i | \(-0.826496\pi\) |
0.988310 | + | 0.152456i | \(0.0487183\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.832748 | + | 1.75898i | −0.0722084 | + | 0.152523i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.37939 | − | 0.866025i | −0.204785 | − | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.701867 | + | 0.588936i | 0.0599645 | + | 0.0503162i | 0.672277 | − | 0.740299i | \(-0.265316\pi\) |
−0.612313 | + | 0.790616i | \(0.709761\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0778 | − | 2.12965i | −1.02443 | − | 0.180635i | −0.363903 | − | 0.931437i | \(-0.618556\pi\) |
−0.660527 | + | 0.750802i | \(0.729667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.76011 | − | 3.90295i | 0.569304 | − | 0.328688i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.798133 | − | 0.290497i | 0.0667433 | − | 0.0242926i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.88191 | − | 1.66387i | −0.239330 | − | 0.138177i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.20961 | + | 4.37138i | −0.429681 | + | 0.360545i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.187319 | + | 1.06234i | 0.0153457 | + | 0.0870301i | 0.991519 | − | 0.129964i | \(-0.0414860\pi\) |
−0.976173 | + | 0.216994i | \(0.930375\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.0300 | −0.897611 | −0.448806 | − | 0.893629i | \(-0.648150\pi\) | ||||
−0.448806 | + | 0.893629i | \(0.648150\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.94356 | 0.480509 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.94697 | − | 16.7131i | −0.236706 | − | 1.34243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.06805 | − | 3.41350i | 0.324666 | − | 0.272427i | −0.465857 | − | 0.884860i | \(-0.654254\pi\) |
0.790522 | + | 0.612433i | \(0.209809\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.52481 | + | 0.880352i | 0.120926 | + | 0.0698165i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.40033 | + | 0.509678i | −0.110361 | + | 0.0401683i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.5201 | − | 6.65111i | 0.902321 | − | 0.520955i | 0.0243687 | − | 0.999703i | \(-0.492242\pi\) |
0.877953 | + | 0.478748i | \(0.158909\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.81908 | + | 1.02606i | 0.453015 | + | 0.0798787i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.87939 | − | 3.25519i | −0.300196 | − | 0.251894i | 0.480230 | − | 0.877143i | \(-0.340553\pi\) |
−0.780426 | + | 0.625248i | \(0.784998\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0915 | − | 4.40095i | −0.930117 | − | 0.338535i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.81908 | − | 3.96118i | −0.139108 | − | 0.302919i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.58765 | − | 12.6045i | 0.348792 | − | 0.958299i | −0.633959 | − | 0.773367i | \(-0.718571\pi\) |
0.982751 | − | 0.184933i | \(-0.0592067\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.405078 | − | 0.482753i | 0.0306210 | − | 0.0364927i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.05169 | + | 5.96443i | −0.0790498 | + | 0.448314i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.92855 | − | 10.2685i | −0.443121 | − | 0.767507i | 0.554799 | − | 0.831985i | \(-0.312795\pi\) |
−0.997919 | + | 0.0644774i | \(0.979462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.74170 | + | 18.5227i | 0.501106 | + | 1.37678i | 0.890196 | + | 0.455578i | \(0.150568\pi\) |
−0.389089 | + | 0.921200i | \(0.627210\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.39053 | − | 5.87257i | 0.250635 | − | 0.434113i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.2554 | − | 14.6054i | −0.901032 | − | 1.07381i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.6591 | + | 2.40847i | −0.998852 | + | 0.176125i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.446476i | 0.0324763i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.45545i | 0.684173i | 0.939669 | + | 0.342086i | \(0.111134\pi\) | ||||
−0.939669 | + | 0.342086i | \(0.888866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.93969 | − | 0.871001i | 0.355567 | − | 0.0626960i | 0.00698825 | − | 0.999976i | \(-0.497776\pi\) |
0.348579 | + | 0.937280i | \(0.386664\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.592396 | + | 0.705990i | 0.0424224 | + | 0.0505570i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.26651 | + | 14.3180i | −0.588965 | + | 1.02012i | 0.405404 | + | 0.914138i | \(0.367131\pi\) |
−0.994368 | + | 0.105979i | \(0.966202\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.35638 | + | 6.47410i | 0.167039 | + | 0.458937i | 0.994764 | − | 0.102197i | \(-0.0325873\pi\) |
−0.827725 | + | 0.561134i | \(0.810365\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.63816 | − | 8.03352i | −0.327150 | − | 0.566641i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.101892 | + | 0.577857i | −0.00715140 | + | 0.0405576i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.6668 | − | 22.2463i | 1.30375 | − | 1.55375i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.14156 | − | 3.13641i | 0.0793439 | − | 0.217995i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.78564 | + | 8.36619i | 0.400201 | + | 0.578701i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.7665 | + | 7.55839i | 1.42963 | + | 0.520341i | 0.936824 | − | 0.349801i | \(-0.113751\pi\) |
0.492801 | + | 0.870142i | \(0.335973\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.11334 | − | 3.45150i | −0.281841 | − | 0.236493i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.5535 | − | 3.09516i | −1.19714 | − | 0.211088i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.59152 | + | 1.49621i | −0.175924 | + | 0.101570i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.19846 | + | 1.16415i | −0.216132 | + | 0.0786657i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.87346 | − | 1.08164i | −0.126022 | − | 0.0727590i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.5797 | − | 14.7511i | 1.17722 | − | 0.987806i | 0.177228 | − | 0.984170i | \(-0.443287\pi\) |
0.999993 | − | 0.00363588i | \(-0.00115734\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.245100 | + | 1.39003i | 0.0163400 | + | 0.0926687i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.4338 | −0.891630 | −0.445815 | − | 0.895125i | \(-0.647086\pi\) | ||||
−0.445815 | + | 0.895125i | \(0.647086\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.5526 | 1.42424 | 0.712119 | − | 0.702059i | \(-0.247736\pi\) | ||||
0.712119 | + | 0.702059i | \(0.247736\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.180922 | − | 1.02606i | −0.0119038 | − | 0.0675098i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.5719 | + | 12.2273i | −0.954638 | + | 0.801036i | −0.980073 | − | 0.198640i | \(-0.936348\pi\) |
0.0254344 | + | 0.999676i | \(0.491903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.1172 | − | 9.88263i | −1.11660 | − | 0.644671i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.39306 | − | 0.871001i | 0.155446 | − | 0.0565776i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.3229 | − | 8.26936i | 0.926475 | − | 0.534900i | 0.0407797 | − | 0.999168i | \(-0.487016\pi\) |
0.885695 | + | 0.464268i | \(0.153682\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.1780 | + | 2.85262i | 1.04212 | + | 0.183753i | 0.668409 | − | 0.743794i | \(-0.266976\pi\) |
0.373707 | + | 0.927547i | \(0.378087\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.766044 | − | 0.642788i | −0.0491418 | − | 0.0412348i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.1814 | + | 5.88954i | 1.03379 | + | 0.376269i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.147489 | + | 1.57964i | −0.00938451 | + | 0.100510i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.549163 | − | 1.50881i | 0.0348018 | − | 0.0956171i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.0522 | − | 16.7467i | 0.886964 | − | 1.05704i | −0.111035 | − | 0.993816i | \(-0.535417\pi\) |
0.997999 | − | 0.0632263i | \(-0.0201390\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.35251 | + | 7.67047i | −0.0850316 | + | 0.482238i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.52481 | − | 13.0334i | −0.471222 | − | 0.816181i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.637222 | − | 1.75075i | −0.0397488 | − | 0.109209i | 0.918230 | − | 0.396047i | \(-0.129618\pi\) |
−0.957979 | + | 0.286838i | \(0.907396\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.68092 | + | 2.91144i | −0.104447 | + | 0.180908i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.844770 | − | 1.00676i | −0.0522900 | − | 0.0623167i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.4757 | − | 2.02347i | 0.707619 | − | 0.124772i | 0.191755 | − | 0.981443i | \(-0.438582\pi\) |
0.515864 | + | 0.856670i | \(0.327471\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.45826i | − | 0.273869i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.24416i | 0.382137i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.61856 | + | 0.990703i | −0.342569 | + | 0.0604042i | −0.342286 | − | 0.939596i | \(-0.611201\pi\) |
−0.000283157 | 1.00000i | \(0.500090\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.7306 | − | 19.9387i | −1.01631 | − | 1.21119i | −0.977280 | − | 0.211951i | \(-0.932018\pi\) |
−0.0390284 | − | 0.999238i | \(-0.512426\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0812519 | − | 0.140732i | 0.00491759 | − | 0.00851751i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.12654 | − | 3.09516i | −0.0679332 | − | 0.186645i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.28833 | + | 2.23146i | 0.0774084 | + | 0.134075i | 0.902131 | − | 0.431462i | \(-0.142002\pi\) |
−0.824723 | + | 0.565537i | \(0.808669\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.16385 | − | 6.60051i | 0.0696778 | − | 0.395162i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.4111 | − | 25.5167i | 1.27728 | − | 1.52220i | 0.551740 | − | 0.834016i | \(-0.313964\pi\) |
0.725537 | − | 0.688183i | \(-0.241592\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.91581 | + | 19.0010i | −0.411102 | + | 1.12949i | 0.545503 | + | 0.838109i | \(0.316339\pi\) |
−0.956606 | + | 0.291386i | \(0.905884\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.38326 | + | 9.00400i | −0.378111 | + | 0.533351i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.81180 | − | 1.75135i | −0.284032 | − | 0.103379i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.0385 | + | 11.7797i | 0.825793 | + | 0.692923i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.06031 | − | 0.186961i | −0.0621563 | − | 0.0109598i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.6964 | − | 6.75292i | 0.683311 | − | 0.394510i | −0.117790 | − | 0.993038i | \(-0.537581\pi\) |
0.801101 | + | 0.598529i | \(0.204248\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.4106 | − | 5.24503i | 0.839017 | − | 0.305377i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.02094 | + | 1.16679i | 0.117267 | + | 0.0677042i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.930608 | + | 0.780873i | −0.0538184 | + | 0.0451590i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.545759 | + | 3.09516i | 0.0314571 | + | 0.178402i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.3601 | 0.939863 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.1702 | −0.983165 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.54576 | + | 8.76644i | 0.0882212 | + | 0.500327i | 0.996615 | + | 0.0822113i | \(0.0261982\pi\) |
−0.908394 | + | 0.418116i | \(0.862691\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.21688 | − | 1.02108i | 0.0692260 | − | 0.0580875i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.62108 | − | 0.935932i | −0.0919231 | − | 0.0530718i | 0.453334 | − | 0.891341i | \(-0.350235\pi\) |
−0.545257 | + | 0.838269i | \(0.683568\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0881 | − | 5.12765i | 0.796307 | − | 0.289832i | 0.0883520 | − | 0.996089i | \(-0.471840\pi\) |
0.707955 | + | 0.706257i | \(0.249618\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.979055 | − | 0.565258i | 0.0551635 | − | 0.0318487i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.38460 | + | 1.47843i | 0.470926 | + | 0.0830370i | 0.404075 | − | 0.914726i | \(-0.367594\pi\) |
0.0668513 | + | 0.997763i | \(0.478705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.34936 | + | 1.97134i | 0.131539 | + | 0.110374i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.63816 | − | 2.05212i | −0.314691 | − | 0.114538i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.85117 | − | 24.9851i | 0.381209 | − | 1.39021i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.175708 | − | 0.482753i | 0.00974650 | − | 0.0267783i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.56418 | + | 11.3981i | −0.528900 | + | 0.630319i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.605189 | + | 3.43220i | −0.0333652 | + | 0.189223i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.1630 | + | 24.5310i | 0.778467 | + | 1.34834i | 0.932825 | + | 0.360330i | \(0.117336\pi\) |
−0.154358 | + | 0.988015i | \(0.549331\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.57532 | − | 7.07564i | −0.141127 | − | 0.387743i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.7442 | + | 20.3416i | −0.641655 | + | 1.11138i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.19506 | − | 9.76649i | −0.446413 | − | 0.532015i | 0.495169 | − | 0.868796i | \(-0.335106\pi\) |
−0.941583 | + | 0.336782i | \(0.890662\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.38919 | − | 1.47924i | 0.455638 | − | 0.0803413i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.6405i | 0.846979i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.16166i | − | 0.332698i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.32295 | + | 1.46756i | −0.448092 | + | 0.0790108i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.1147 | + | 21.5882i | 0.972447 | + | 1.15892i | 0.987274 | + | 0.159027i | \(0.0508358\pi\) |
−0.0148269 | + | 0.999890i | \(0.504720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.9067 | + | 22.3551i | −0.690881 | + | 1.19664i | 0.280668 | + | 0.959805i | \(0.409444\pi\) |
−0.971550 | + | 0.236837i | \(0.923889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.124485 | + | 0.342020i | 0.00664453 | + | 0.0182557i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.8464 | − | 18.7865i | −0.577297 | − | 0.999907i | −0.995788 | − | 0.0916863i | \(-0.970774\pi\) |
0.418491 | − | 0.908221i | \(-0.362559\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.36097 | + | 13.3897i | −0.125307 | + | 0.710652i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.70574 | + | 2.03282i | −0.0902772 | + | 0.107588i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.33527 | + | 20.1535i | −0.387141 | + | 1.06366i | 0.581141 | + | 0.813803i | \(0.302606\pi\) |
−0.968282 | + | 0.249859i | \(0.919616\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7486 | + | 3.08083i | −0.986766 | + | 0.162149i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.21941 | + | 1.89971i | 0.273948 | + | 0.0997089i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.60220 | + | 5.53990i | 0.345575 | + | 0.289972i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4500 | − | 2.37159i | −0.702082 | − | 0.123796i | −0.188800 | − | 0.982016i | \(-0.560460\pi\) |
−0.513283 | + | 0.858220i | \(0.671571\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.93242 | − | 5.73448i | 0.517061 | − | 0.298525i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.738703 | + | 0.268866i | −0.0383516 | + | 0.0139588i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.90848 | − | 4.56596i | −0.409486 | − | 0.236417i | 0.281083 | − | 0.959683i | \(-0.409306\pi\) |
−0.690569 | + | 0.723267i | \(0.742640\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.96064 | + | 5.84067i | −0.359446 | + | 0.301611i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0830629 | + | 0.471073i | 0.00427796 | + | 0.0242615i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.9154 | −1.84485 | −0.922425 | − | 0.386176i | \(-0.873796\pi\) | ||||
−0.922425 | + | 0.386176i | \(0.873796\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.1506 | −0.673728 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.95512 | + | 11.0880i | 0.0999019 | + | 0.566572i | 0.993135 | + | 0.116977i | \(0.0373204\pi\) |
−0.893233 | + | 0.449595i | \(0.851568\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.02094 | + | 1.69577i | −0.102997 | + | 0.0864246i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.09627 | − | 3.51968i | −0.309891 | − | 0.178915i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.3919 | − | 6.69409i | 0.932505 | − | 0.339404i | 0.169303 | − | 0.985564i | \(-0.445848\pi\) |
0.763202 | + | 0.646160i | \(0.223626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.1800 | − | 9.91890i | 0.868832 | − | 0.501621i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.39053 | − | 0.774169i | −0.221473 | − | 0.0390517i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.93969 | − | 4.14489i | −0.248543 | − | 0.208552i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.54963 | − | 3.11181i | −0.429094 | − | 0.156177i | 0.118440 | − | 0.992961i | \(-0.462211\pi\) |
−0.547533 | + | 0.836784i | \(0.684433\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.87686 | + | 0.514654i | 0.0939605 | + | 0.0257649i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.817734 | − | 2.24670i | 0.0408357 | − | 0.112195i | −0.917599 | − | 0.397508i | \(-0.869875\pi\) |
0.958435 | + | 0.285313i | \(0.0920974\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.56805 | + | 1.86873i | −0.0781100 | + | 0.0930879i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.439693 | + | 2.49362i | −0.0218485 | + | 0.123909i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.78564 | + | 15.2172i | 0.435488 | + | 0.754288i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.90420 | − | 27.2116i | −0.489731 | − | 1.34553i | −0.900924 | − | 0.433977i | \(-0.857110\pi\) |
0.411193 | − | 0.911548i | \(-0.365112\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.458111 | − | 0.793471i | 0.0225969 | − | 0.0391391i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.73813 | − | 2.07142i | −0.0855278 | − | 0.101928i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00387 | + | 0.705990i | −0.196542 | + | 0.0346557i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.2642i | 0.600579i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.56185i | 0.369420i | 0.982793 | + | 0.184710i | \(0.0591347\pi\) | ||||
−0.982793 | + | 0.184710i | \(0.940865\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.6969 | + | 6.47065i | −1.78850 | + | 0.315360i | −0.966985 | − | 0.254833i | \(-0.917980\pi\) |
−0.821511 | + | 0.570193i | \(0.806868\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.01754 | − | 5.97967i | −0.243961 | − | 0.290742i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.19459 | + | 7.26525i | −0.203468 | + | 0.352416i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.03549 | + | 2.84499i | 0.0501110 | + | 0.137679i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.424678 | − | 0.735564i | −0.0205036 | − | 0.0355133i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.28581 | + | 35.6486i | −0.302777 | + | 1.71713i | 0.331013 | + | 0.943626i | \(0.392610\pi\) |
−0.633790 | + | 0.773506i | \(0.718501\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.2335 | + | 28.8804i | −1.16459 | + | 1.38790i | −0.257865 | + | 0.966181i | \(0.583019\pi\) |
−0.906725 | + | 0.421723i | \(0.861425\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.13816 | + | 3.12706i | −0.0545704 | + | 0.149931i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.8687 | − | 8.41415i | −0.567757 | − | 0.402503i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.26130 | − | 0.459074i | −0.0601984 | − | 0.0219104i | 0.311745 | − | 0.950166i | \(-0.399086\pi\) |
−0.371944 | + | 0.928255i | \(0.621309\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.20961 | + | 4.37138i | 0.248077 | + | 0.208161i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.7802 | + | 5.60370i | 1.50992 | + | 0.266240i | 0.866463 | − | 0.499241i | \(-0.166388\pi\) |
0.643459 | + | 0.765481i | \(0.277499\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.6925 | − | 7.90539i | 0.649088 | − | 0.374751i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.01367 | − | 0.368946i | 0.0479450 | − | 0.0174505i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.34302 | − | 1.93009i | −0.157767 | − | 0.0910866i | 0.419038 | − | 0.907969i | \(-0.362367\pi\) |
−0.576805 | + | 0.816882i | \(0.695701\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.5023 | + | 17.2035i | −0.965415 | + | 0.810079i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.91534 | + | 10.8625i | 0.0899907 | + | 0.510363i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.411474 | −0.0192902 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.79055 | −0.270871 | −0.135435 | − | 0.990786i | \(-0.543243\pi\) | ||||
−0.135435 | + | 0.990786i | \(0.543243\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.03209 | − | 5.85327i | −0.0481738 | − | 0.273207i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.5517 | + | 14.7276i | −0.817464 | + | 0.685933i | −0.952377 | − | 0.304924i | \(-0.901369\pi\) |
0.134913 | + | 0.990857i | \(0.456924\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.3840 | + | 17.5422i | 1.41207 | + | 0.815256i | 0.995583 | − | 0.0938873i | \(-0.0299293\pi\) |
0.416483 | + | 0.909144i | \(0.363263\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.9474 | + | 5.80439i | −0.739545 | + | 0.269172i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.6352 | − | 6.71756i | 0.538411 | − | 0.310852i | −0.206024 | − | 0.978547i | \(-0.566052\pi\) |
0.744435 | + | 0.667695i | \(0.232719\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.07873 | + | 0.719189i | 0.188338 | + | 0.0332091i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.06805 | − | 3.41350i | −0.187446 | − | 0.157286i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.4363 | + | 5.61835i | 0.709761 | + | 0.258332i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.12583 | + | 0.571962i | 0.281072 | + | 0.0262434i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.602196 | − | 1.65452i | 0.0275727 | − | 0.0757553i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.1330 | + | 31.1441i | −1.19405 | + | 1.42301i | −0.313149 | + | 0.949704i | \(0.601384\pi\) |
−0.880898 | + | 0.473306i | \(0.843061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.475900 | + | 2.69896i | −0.0216992 | + | 0.123062i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.745100 | + | 1.29055i | 0.0339032 | + | 0.0587221i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.932419 | + | 2.56180i | 0.0423390 | + | 0.116325i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.8935 | − | 29.2604i | 0.765519 | − | 1.32592i | −0.174453 | − | 0.984665i | \(-0.555816\pi\) |
0.939972 | − | 0.341252i | \(-0.110851\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.55051 | − | 10.1901i | −0.386667 | − | 0.460812i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.48839 | + | 0.262443i | −0.0671700 | + | 0.0118439i | −0.207132 | − | 0.978313i | \(-0.566413\pi\) |
0.139962 | + | 0.990157i | \(0.455302\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.81120i | − | 0.351799i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 5.90885i | − | 0.265583i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.36097 | − | 0.416302i | 0.105904 | − | 0.0186737i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.2827 | − | 13.4462i | −0.505083 | − | 0.601935i | 0.451903 | − | 0.892067i | \(-0.350745\pi\) |
−0.956987 | + | 0.290132i | \(0.906301\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.53209 | + | 4.38571i | −0.113125 | + | 0.195939i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.82888 | + | 24.2571i | 0.393660 | + | 1.08157i | 0.965317 | + | 0.261080i | \(0.0840786\pi\) |
−0.571657 | + | 0.820493i | \(0.693699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.7126 | − | 35.8753i | −0.921699 | − | 1.59643i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.23442 | + | 12.6720i | −0.0992342 | + | 0.562785i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.24985 | − | 5.06477i | 0.188371 | − | 0.224492i | −0.663591 | − | 0.748096i | \(-0.730968\pi\) |
0.851962 | + | 0.523604i | \(0.175413\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.519762 | − | 1.42804i | 0.0229929 | − | 0.0631726i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.58512 | + | 2.47929i | −0.158287 | + | 0.109463i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.77972 | − | 1.37570i | −0.166554 | − | 0.0606208i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.9541 | + | 11.7089i | 0.613700 | + | 0.514955i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.2096 | − | 2.32921i | −0.579837 | − | 0.102241i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.8252 | − | 20.1064i | 1.52572 | − | 0.880875i | 0.526186 | − | 0.850369i | \(-0.323621\pi\) |
0.999535 | − | 0.0305060i | \(-0.00971187\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.5292 | − | 9.65582i | 1.16004 | − | 0.422220i | 0.310928 | − | 0.950434i | \(-0.399360\pi\) |
0.849111 | + | 0.528214i | \(0.177138\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.545759 | − | 0.315094i | −0.0238189 | − | 0.0137518i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.5159 | − | 25.6059i | 1.32930 | − | 1.11541i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.05943 | + | 11.6796i | 0.0895404 | + | 0.507809i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.05644 | 0.262827 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.17436 | −0.180812 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.63816 | + | 14.9617i | 0.114057 | + | 0.646852i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.08306 | + | 7.62159i | −0.391963 | + | 0.328896i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.7438 | − | 7.93496i | −0.591985 | − | 0.341783i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.2374 | + | 12.0974i | −1.42899 | + | 0.520109i | −0.936641 | − | 0.350290i | \(-0.886083\pi\) |
−0.492347 | + | 0.870399i | \(0.663861\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.0706 | − | 9.85570i | 0.732568 | − | 0.422949i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 37.1031 | + | 6.54228i | 1.58932 | + | 0.280241i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7044 | + | 13.1776i | 0.671471 | + | 0.563431i | 0.913500 | − | 0.406838i | \(-0.133369\pi\) |
−0.242029 | + | 0.970269i | \(0.577813\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.37211 | − | 2.31926i | −0.271955 | − | 0.0989836i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.20590 | + | 2.39068i | −0.221779 | + | 0.101847i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.388881 | + | 1.06844i | −0.0165369 | + | 0.0454347i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.2554 | + | 14.6054i | −0.520211 | + | 0.619964i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.71007 | − | 38.0547i | 0.284315 | − | 1.61243i | −0.423407 | − | 0.905939i | \(-0.639166\pi\) |
0.707722 | − | 0.706491i | \(-0.249723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.28106 | + | 2.21886i | 0.0541830 | + | 0.0938478i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.74376 | + | 13.0334i | 0.200282 | + | 0.550269i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.28833 | + | 9.15966i | −0.222877 | + | 0.386034i | −0.955680 | − | 0.294406i | \(-0.904878\pi\) |
0.732804 | + | 0.680440i | \(0.238211\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.8648 | − | 16.5235i | −0.583298 | − | 0.695148i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.439693 | − | 0.0775297i | 0.0184654 | − | 0.00325594i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.06920i | 0.254434i | 0.991875 | + | 0.127217i | \(0.0406045\pi\) | ||||
−0.991875 | + | 0.127217i | \(0.959396\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 38.8698i | − | 1.62665i | −0.581809 | − | 0.813326i | \(-0.697655\pi\) | ||
0.581809 | − | 0.813326i | \(-0.302345\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.31180 | − | 1.64192i | 0.389006 | − | 0.0685923i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.02822 | + | 3.60889i | 0.126285 | + | 0.150501i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.2319 | + | 38.5068i | −0.925526 | + | 1.60306i | −0.134813 | + | 0.990871i | \(0.543043\pi\) |
−0.790713 | + | 0.612187i | \(0.790290\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.71554 | − | 4.71340i | −0.0712953 | − | 0.195882i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.358441 | + | 0.620838i | 0.0148706 | + | 0.0257567i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.713478 | + | 4.04633i | −0.0295492 | + | 0.167582i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.592396 | − | 0.705990i | 0.0244926 | − | 0.0291891i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.10085 | − | 25.0044i | 0.375632 | − | 1.03204i | −0.597515 | − | 0.801858i | \(-0.703845\pi\) |
0.973147 | − | 0.230184i | \(-0.0739327\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.4051 | − | 12.5009i | −1.08800 | − | 0.515092i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.5360 | + | 5.65463i | 0.639064 | + | 0.232600i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.3730 | + | 30.5206i | 1.49366 | + | 1.25333i | 0.889891 | + | 0.456173i | \(0.150780\pi\) |
0.603771 | + | 0.797158i | \(0.293664\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.61721 | + | 1.16679i | 0.271279 | + | 0.0478338i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.96657 | − | 3.44480i | 0.244195 | − | 0.140986i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.8050 | + | 10.4842i | −1.17694 | + | 0.428371i | −0.855120 | − | 0.518430i | \(-0.826517\pi\) |
−0.321820 | + | 0.946801i | \(0.604295\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.9153 | + | 8.61138i | 0.608410 | + | 0.351265i | 0.772343 | − | 0.635206i | \(-0.219085\pi\) |
−0.163933 | + | 0.986471i | \(0.552418\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.10607 | + | 5.96270i | −0.289381 | + | 0.242820i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.44222 | − | 13.8505i | −0.0992903 | − | 0.563103i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.9659 | −0.688623 | −0.344311 | − | 0.938856i | \(-0.611888\pi\) | ||||
−0.344311 | + | 0.938856i | \(0.611888\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.586771 | 0.0237772 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.493355 | + | 2.79796i | 0.0199590 | + | 0.113193i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.5069 | + | 28.9547i | −1.39372 | + | 1.16947i | −0.429911 | + | 0.902871i | \(0.641455\pi\) |
−0.963808 | + | 0.266598i | \(0.914100\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −25.1498 | − | 14.5202i | −1.01414 | − | 0.585512i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.12314 | + | 0.408790i | −0.0452160 | + | 0.0164573i | −0.364529 | − | 0.931192i | \(-0.618770\pi\) |
0.319313 | + | 0.947649i | \(0.396548\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.5363 | + | 13.5887i | −0.946002 | + | 0.546175i | −0.891837 | − | 0.452357i | \(-0.850583\pi\) |
−0.0541655 | + | 0.998532i | \(0.517250\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.28699 | − | 0.579585i | −0.131902 | − | 0.0232579i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.13563 | − | 1.79201i | −0.0855622 | − | 0.0717952i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 28.2520 | + | 10.2829i | 1.13008 | + | 0.411315i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.23442 | − | 7.15052i | 0.288915 | − | 0.285564i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.3066 | − | 42.0545i | 0.610314 | − | 1.67682i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.1001 | − | 12.0369i | 0.402080 | − | 0.479180i | −0.526573 | − | 0.850130i | \(-0.676523\pi\) |
0.928653 | + | 0.370950i | \(0.120968\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.83750 | − | 21.7635i | 0.152527 | − | 0.865022i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.6493 | + | 28.8374i | 0.660707 | + | 1.14438i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.846581 | − | 2.32596i | −0.0335428 | − | 0.0921580i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.68479 | + | 4.65020i | −0.106209 | + | 0.183959i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.1802 | + | 26.4333i | 0.876066 | + | 1.04405i | 0.998668 | + | 0.0515983i | \(0.0164316\pi\) |
−0.122602 | + | 0.992456i | \(0.539124\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.89646 | + | 1.39236i | −0.311406 | + | 0.0549093i | −0.327167 | − | 0.944967i | \(-0.606094\pi\) |
0.0157611 | + | 0.999876i | \(0.494983\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.8243i | 0.701831i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 47.3299i | 1.86073i | 0.366633 | + | 0.930366i | \(0.380510\pi\) | ||||
−0.366633 | + | 0.930366i | \(0.619490\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.9185 | + | 2.45421i | −0.546349 | + | 0.0963361i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.92350 | + | 2.29233i | 0.0753877 | + | 0.0898436i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.95723 | + | 12.0503i | −0.272258 | + | 0.471564i | −0.969440 | − | 0.245330i | \(-0.921104\pi\) |
0.697182 | + | 0.716894i | \(0.254437\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.86097 | + | 10.6079i | 0.150860 | + | 0.414486i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.70187 | + | 2.94772i | 0.0663961 | + | 0.115001i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.23854 | + | 35.3805i | −0.243019 | + | 1.37823i | 0.582029 | + | 0.813168i | \(0.302259\pi\) |
−0.825049 | + | 0.565062i | \(0.808852\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.82682 | − | 9.32764i | 0.304428 | − | 0.362803i | −0.592042 | − | 0.805907i | \(-0.701678\pi\) |
0.896470 | + | 0.443104i | \(0.146123\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.739885 | + | 2.03282i | −0.0287348 | + | 0.0789481i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.24763 | − | 4.76725i | −0.0483809 | − | 0.184866i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.12196 | − | 1.50027i | −0.159603 | − | 0.0580907i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.5797 | − | 14.7511i | −0.679669 | − | 0.570310i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.5838 | + | 2.74784i | 0.601605 | + | 0.106079i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.4029 | − | 10.6249i | 0.709378 | − | 0.409560i | −0.101453 | − | 0.994840i | \(-0.532349\pi\) |
0.810831 | + | 0.585281i | \(0.199016\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.32635 | − | 0.482753i | 0.0510513 | − | 0.0185812i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.71806 | − | 5.61073i | −0.373496 | − | 0.215638i | 0.301489 | − | 0.953470i | \(-0.402516\pi\) |
−0.674984 | + | 0.737832i | \(0.735850\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.368241 | − | 0.308991i | 0.0141318 | − | 0.0118580i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.33275 | + | 13.2297i | 0.0893911 | + | 0.506962i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.4867 | 1.39612 | 0.698062 | − | 0.716037i | \(-0.254046\pi\) | ||||
0.698062 | + | 0.716037i | \(0.254046\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.31996 | −0.0886409 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.74257 | − | 21.2252i | −0.142788 | − | 0.809792i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.490915 | + | 0.411927i | −0.0187024 | + | 0.0156932i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.74990 | − | 5.62911i | −0.370904 | − | 0.214141i | 0.302949 | − | 0.953007i | \(-0.402029\pi\) |
−0.673853 | + | 0.738865i | \(0.735362\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.979055 | + | 0.356347i | −0.0371912 | + | 0.0135365i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.8935 | − | 15.5270i | 1.02013 | − | 0.588972i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 67.1309 | + | 11.8370i | 2.54277 | + | 0.448358i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.5719 | + | 12.2273i | 0.551161 | + | 0.462479i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.0120217 | + | 0.00437554i | 0.000454053 | + | 0.000165262i | 0.342247 | − | 0.939610i | \(-0.388812\pi\) |
−0.341793 | + | 0.939775i | \(0.611034\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.7126 | + | 2.66982i | −1.23378 | + | 0.100694i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.76011 | + | 18.5733i | −0.254601 | + | 0.699510i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.69517 | + | 5.59548i | −0.176580 | + | 0.210440i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.64694 | − | 32.0254i | 0.212075 | − | 1.20274i | −0.673835 | − | 0.738882i | \(-0.735354\pi\) |
0.885910 | − | 0.463856i | \(-0.153535\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.27332 | − | 2.20545i | −0.0477532 | − | 0.0827109i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.65111 | − | 21.0213i | −0.286536 | − | 0.787252i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.07532 | + | 1.86251i | −0.0402148 | + | 0.0696540i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.6309 | − | 12.6694i | −0.397018 | − | 0.473147i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.9876 | + | 8.99048i | −1.90152 | + | 0.335288i | −0.996025 | − | 0.0890776i | \(-0.971608\pi\) |
−0.905491 | + | 0.424366i | \(0.860497\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.709238i | 0.0264134i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 16.4276i | − | 0.610947i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.82682 | − | 0.322117i | 0.0678463 | − | 0.0119631i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.8025 | − | 21.2162i | −0.660257 | − | 0.786864i | 0.327165 | − | 0.944967i | \(-0.393907\pi\) |
−0.987423 | + | 0.158103i | \(0.949462\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.500000 | + | 0.866025i | −0.0185185 | + | 0.0320750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.3097 | − | 39.3157i | −0.529265 | − | 1.45414i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0608 | − | 38.2104i | −0.814833 | − | 1.41133i | −0.909448 | − | 0.415819i | \(-0.863495\pi\) |
0.0946143 | − | 0.995514i | \(-0.469838\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.99020 | − | 16.9583i | 0.110295 | − | 0.625515i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.9145 | − | 16.5826i | 0.512546 | − | 0.610829i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.90436 | − | 7.97967i | 0.106839 | − | 0.293537i | −0.874741 | − | 0.484591i | \(-0.838968\pi\) |
0.981579 | + | 0.191054i | \(0.0611906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.58125 | − | 0.129053i | 0.0580887 | − | 0.00474088i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.31908 | − | 0.480105i | −0.0483923 | − | 0.0176133i | 0.317711 | − | 0.948188i | \(-0.397086\pi\) |
−0.366103 | + | 0.930574i | \(0.619308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.09240 | − | 1.75573i | −0.0766595 | − | 0.0643249i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.58125 | − | 0.278817i | −0.0578550 | − | 0.0102014i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.31996 | − | 1.33943i | 0.0847693 | − | 0.0489416i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.12196 | + | 3.32012i | −0.332865 | + | 0.121153i | −0.503045 | − | 0.864260i | \(-0.667787\pi\) |
0.170180 | + | 0.985413i | \(0.445565\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.9324 | − | 10.9306i | −0.689936 | − | 0.398335i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.3949 | − | 17.9524i | 0.778639 | − | 0.653356i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.14858 | + | 34.8704i | 0.223474 | + | 1.26738i | 0.865581 | + | 0.500769i | \(0.166950\pi\) |
−0.642107 | + | 0.766615i | \(0.721939\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.78880 | 0.282716 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.28817 | 0.119196 | 0.0595981 | − | 0.998222i | \(-0.481018\pi\) | ||||
0.0595981 | + | 0.998222i | \(0.481018\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.15358 | − | 6.54228i | −0.0417624 | − | 0.236847i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.5287 | + | 9.67372i | −0.416820 | + | 0.349754i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.90903 | − | 1.10218i | −0.0689312 | − | 0.0397975i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.9443 | − | 7.98708i | 0.791333 | − | 0.288022i | 0.0854429 | − | 0.996343i | \(-0.472769\pi\) |
0.705890 | + | 0.708321i | \(0.250547\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.61350 | + | 0.931556i | −0.0581089 | + | 0.0335492i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.6550 | + | 4.17101i | 0.850811 | + | 0.150021i | 0.582017 | − | 0.813177i | \(-0.302264\pi\) |
0.268794 | + | 0.963198i | \(0.413375\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.24691 | + | 6.08088i | 0.260317 | + | 0.218432i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.15910 | + | 1.14982i | 0.113332 | + | 0.0412495i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.6570 | − | 48.3633i | −0.453486 | − | 1.73279i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.28564 | − | 11.7747i | 0.153352 | − | 0.421332i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.844770 | + | 1.00676i | −0.0301896 | + | 0.0359786i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.33497 | + | 13.2423i | −0.0833387 | + | 0.472637i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.58765 | + | 16.6063i | 0.341763 | + | 0.591950i | 0.984760 | − | 0.173918i | \(-0.0556427\pi\) |
−0.642997 | + | 0.765868i | \(0.722309\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.98545 | − | 10.9499i | −0.141886 | − | 0.389828i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.90167 | + | 3.29380i | −0.0676157 | + | 0.117114i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.58647 | + | 1.89068i | 0.0563371 | + | 0.0671399i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.39053 | + | 0.774169i | −0.155716 | + | 0.0274569i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 7.63624i | − | 0.270490i | −0.990812 | − | 0.135245i | \(-0.956818\pi\) | ||
0.990812 | − | 0.135245i | \(-0.0431821\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 46.3949i | − | 1.64133i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.14930 | − | 1.08429i | 0.217275 | − | 0.0383114i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.10560 | − | 6.08462i | −0.180173 | − | 0.214721i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.88666 | − | 3.26779i | 0.0664960 | − | 0.115174i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.95130 | + | 5.36116i | 0.0686891 | + | 0.188722i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.65389 | − | 8.06077i | −0.163622 | − | 0.283401i | 0.772543 | − | 0.634962i | \(-0.218984\pi\) |
−0.936165 | + | 0.351561i | \(0.885651\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.22962 | + | 18.3161i | −0.113407 | + | 0.643164i | 0.874119 | + | 0.485711i | \(0.161439\pi\) |
−0.987526 | + | 0.157453i | \(0.949672\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.7306 | + | 19.9387i | −0.586766 | + | 0.699281i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.5201 | + | 31.6511i | −0.403530 | + | 1.10869i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.8229 | + | 21.5699i | −0.763488 | + | 0.754634i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.152704 | − | 0.0555796i | −0.00533590 | − | 0.00194211i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.56212 | − | 4.66717i | −0.194119 | − | 0.162885i | 0.540548 | − | 0.841313i | \(-0.318217\pi\) |
−0.734667 | + | 0.678428i | \(0.762662\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.18732 | + | 0.562010i | 0.111103 | + | 0.0195904i | 0.228923 | − | 0.973444i | \(-0.426480\pi\) |
−0.117820 | + | 0.993035i | \(0.537591\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.85251 | + | 1.64690i | −0.0993117 | + | 0.0573376i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.1207 | − | 16.4226i | 1.56900 | − | 0.571069i | 0.596224 | − | 0.802818i | \(-0.296667\pi\) |
0.972776 | + | 0.231749i | \(0.0744448\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.1279 | − | 5.84737i | −0.351758 | − | 0.203088i | 0.313701 | − | 0.949522i | \(-0.398431\pi\) |
−0.665459 | + | 0.746434i | \(0.731764\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.97384 | − | 1.65625i | 0.0684718 | − | 0.0574546i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.01889 | + | 39.8061i | 0.243190 | + | 1.37920i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.8229 | 0.443756 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.70233 | −0.231667 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.04307 | − | 39.9432i | −0.243154 | − | 1.37899i | −0.824741 | − | 0.565510i | \(-0.808679\pi\) |
0.581588 | − | 0.813484i | \(-0.302432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.8922 | − | 17.5306i | 0.720420 | − | 0.604504i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.8470 | − | 16.6549i | −0.993545 | − | 0.573624i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.6168 | − | 11.1436i | 1.05325 | − | 0.383352i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.14765 | + | 1.23995i | −0.0737942 | + | 0.0426051i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.9133 | + | 3.51125i | 0.683422 | + | 0.120506i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.2522 | − | 16.1545i | −0.659957 | − | 0.553770i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.9950 | + | 16.0129i | 1.50636 | + | 0.548270i | 0.957698 | − | 0.287774i | \(-0.0929152\pi\) |
0.548662 | + | 0.836044i | \(0.315137\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.97565 | + | 4.72275i | 0.341160 | + | 0.161515i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.5483 | − | 39.9711i | 0.496960 | − | 1.36539i | −0.397238 | − | 0.917715i | \(-0.630031\pi\) |
0.894198 | − | 0.447671i | \(-0.147746\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.523938 | − | 0.624404i | 0.0178765 | − | 0.0213044i | −0.757032 | − | 0.653378i | \(-0.773351\pi\) |
0.774909 | + | 0.632073i | \(0.217796\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.889185 | + | 5.04282i | −0.0303034 | + | 0.171859i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.92649 | − | 3.33678i | −0.0655784 | − | 0.113585i | 0.831372 | − | 0.555716i | \(-0.187556\pi\) |
−0.896950 | + | 0.442131i | \(0.854223\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.6163 | + | 31.9156i | 0.394967 | + | 1.08516i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.16297 | − | 15.8707i | 0.311191 | − | 0.538998i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.81996 | + | 4.55245i | 0.129583 | + | 0.154431i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.32501 | − | 0.586289i | 0.112664 | − | 0.0198656i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.07666i | 0.0364396i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 4.05689i | − | 0.137148i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.12196 | − | 0.726813i | 0.139189 | − | 0.0245427i | −0.103620 | − | 0.994617i | \(-0.533042\pi\) |
0.242808 | + | 0.970074i | \(0.421931\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.68139 | − | 10.3461i | −0.292816 | − | 0.348964i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.5287 | + | 35.5567i | −0.691629 | + | 1.19794i | 0.279675 | + | 0.960095i | \(0.409773\pi\) |
−0.971304 | + | 0.237842i | \(0.923560\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.0651 | − | 41.3909i | −0.506979 | − | 1.39291i | −0.884338 | − | 0.466847i | \(-0.845390\pi\) |
0.377358 | − | 0.926067i | \(-0.376832\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.66772 | − | 13.2809i | −0.257748 | − | 0.446432i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.16668 | − | 34.9730i | 0.207057 | − | 1.17428i | −0.687113 | − | 0.726550i | \(-0.741122\pi\) |
0.894170 | − | 0.447727i | \(-0.147766\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.77409 | − | 4.49779i | 0.126579 | − | 0.150851i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.798133 | − | 2.19285i | 0.0267385 | − | 0.0734633i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.9206 | + | 14.1996i | −1.03472 | + | 0.475170i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.2126 | + | 10.2685i | 0.943043 | + | 0.343240i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.930608 | + | 0.780873i | 0.0310721 | + | 0.0260726i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.67458 | − | 1.52956i | −0.289314 | − | 0.0510138i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.06283 | − | 5.23243i | 0.301927 | − | 0.174317i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.95336 | − | 1.07494i | 0.0982818 | − | 0.0357716i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −43.2242 | − | 24.9555i | −1.43682 | − | 0.829549i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.3746 | + | 13.7400i | −0.543711 | + | 0.456228i | −0.872805 | − | 0.488070i | \(-0.837701\pi\) |
0.329094 | + | 0.944297i | \(0.393257\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.84090 | − | 16.1115i | −0.0942267 | − | 0.534386i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.9932 | 0.397352 | 0.198676 | − | 0.980065i | \(-0.436336\pi\) | ||||
0.198676 | + | 0.980065i | \(0.436336\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.74691 | 0.124005 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.98158 | + | 16.9094i | 0.0985681 | + | 0.559007i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.52481 | − | 1.27947i | 0.0503538 | − | 0.0422519i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.3219 | − | 13.4649i | −0.769319 | − | 0.444166i | 0.0633128 | − | 0.997994i | \(-0.479833\pi\) |
−0.832632 | + | 0.553827i | \(0.813167\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.36484 | − | 3.04455i | 0.275631 | − | 0.100321i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.69253 | − | 0.977185i | 0.0557104 | − | 0.0321644i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.4666 | + | 1.84554i | 0.344139 | + | 0.0606809i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.21688 | − | 1.02108i | −0.0399676 | − | 0.0335368i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.8192 | + | 8.30552i | 0.748675 | + | 0.272495i | 0.688048 | − | 0.725665i | \(-0.258468\pi\) |
0.0606269 | + | 0.998160i | \(0.480690\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.3812 | − | 16.8608i | 0.799061 | − | 0.552591i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.640215 | + | 1.75898i | −0.0209597 | + | 0.0575863i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.5744 | − | 26.9032i | 0.738263 | − | 0.879828i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.48235 | + | 48.1058i | −0.277106 | + | 1.57155i | 0.455084 | + | 0.890449i | \(0.349609\pi\) |
−0.732190 | + | 0.681100i | \(0.761502\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.49613 | − | 12.9837i | −0.244627 | − | 0.423706i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.48111 | − | 26.0491i | −0.309076 | − | 0.849178i | −0.992837 | − | 0.119473i | \(-0.961880\pi\) |
0.683762 | − | 0.729705i | \(-0.260343\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.1400 | − | 33.1514i | 0.623283 | − | 1.07956i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.726682 | − | 0.866025i | −0.0236390 | − | 0.0281718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.5042 | + | 5.55504i | −1.02375 | + | 0.180514i | −0.660223 | − | 0.751070i | \(-0.729538\pi\) |
−0.363525 | + | 0.931584i | \(0.618427\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.23886i | − | 0.0402150i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 8.51395i | − | 0.276084i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.3683 | − | 8.17598i | 1.50202 | − | 0.264846i | 0.638679 | − | 0.769473i | \(-0.279481\pi\) |
0.863337 | + | 0.504627i | \(0.168370\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.3897 | − | 18.3407i | −0.497997 | − | 0.593490i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.53343 | − | 2.65598i | 0.0495689 | − | 0.0858558i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.139910 | + | 0.384401i | 0.00451794 | + | 0.0124129i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.96064 | − | 12.0562i | −0.224537 | − | 0.388909i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.04189 | + | 5.90885i | −0.0335744 | + | 0.190410i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.16385 | + | 9.72930i | −0.262804 | + | 0.313197i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.58284 | + | 4.34883i | −0.0509008 | + | 0.139849i | −0.962538 | − | 0.271147i | \(-0.912597\pi\) |
0.911637 | + | 0.410996i | \(0.134819\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −25.7952 | − | 2.40847i | −0.828661 | − | 0.0773711i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.8824 | − | 7.96453i | −0.702239 | − | 0.255594i | −0.0338724 | − | 0.999426i | \(-0.510784\pi\) |
−0.668367 | + | 0.743832i | \(0.733006\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.19459 | − | 3.51968i | −0.134472 | − | 0.112836i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.505930 | − | 0.0892091i | −0.0162027 | − | 0.00285698i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.3717 | − | 21.5766i | 1.19563 | − | 0.690295i | 0.236049 | − | 0.971741i | \(-0.424147\pi\) |
0.959577 | + | 0.281446i | \(0.0908139\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.6925 | + | 4.98367i | −0.437615 | + | 0.159279i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.8858 | + | 7.43961i | 0.411411 | + | 0.237528i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.0390 | − | 31.9185i | 1.21325 | − | 1.01804i | 0.214104 | − | 0.976811i | \(-0.431317\pi\) |
0.999150 | − | 0.0412304i | \(-0.0131278\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.26945 | − | 41.2271i | −0.231624 | − | 1.31360i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.48515 | 0.110933 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.4953 | −0.747106 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.01290 | − | 28.4296i | −0.159240 | − | 0.903095i | −0.954806 | − | 0.297228i | \(-0.903938\pi\) |
0.795566 | − | 0.605866i | \(-0.207173\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.6989 | − | 18.2076i | 0.688595 | − | 0.577800i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.1079 | − | 8.72254i | −0.478952 | − | 0.276523i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.8999 | + | 9.42680i | −0.820259 | + | 0.298550i | −0.717855 | − | 0.696193i | \(-0.754876\pi\) |
−0.102404 | + | 0.994743i | \(0.532653\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.52094 | + | 3.76487i | −0.206314 | + | 0.119115i |
(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 | 912.2.ci.b.319.1 | yes | 6 | |
4.3 | odd | 2 | 912.2.ci.a.319.1 | yes | 6 | ||
19.14 | odd | 18 | 912.2.ci.a.223.1 | ✓ | 6 | ||
76.71 | even | 18 | inner | 912.2.ci.b.223.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.ci.a.223.1 | ✓ | 6 | 19.14 | odd | 18 | ||
912.2.ci.a.319.1 | yes | 6 | 4.3 | odd | 2 | ||
912.2.ci.b.223.1 | yes | 6 | 76.71 | even | 18 | inner | |
912.2.ci.b.319.1 | yes | 6 | 1.1 | even | 1 | trivial |