Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(5,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5, 15]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.ck (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 5.16 | ||
Character | \(\chi\) | \(=\) | 756.5 |
Dual form | 756.2.ck.a.605.16 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.727904 | − | 1.57167i | 0.420255 | − | 0.907406i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.591212 | + | 3.35293i | −0.264398 | + | 1.49948i | 0.506345 | + | 0.862331i | \(0.330996\pi\) |
−0.770743 | + | 0.637146i | \(0.780115\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.25160 | − | 2.33098i | −0.473062 | − | 0.881029i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.94031 | − | 2.28805i | −0.646771 | − | 0.762684i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.13559 | + | 0.905544i | −1.54844 | + | 0.273032i | −0.881538 | − | 0.472114i | \(-0.843491\pi\) |
−0.666902 | + | 0.745146i | \(0.732380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.56808 | − | 3.06052i | 0.712256 | − | 0.848834i | −0.281598 | − | 0.959533i | \(-0.590864\pi\) |
0.993854 | + | 0.110698i | \(0.0353088\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.83937 | + | 3.36980i | 1.24952 | + | 0.870080i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.67787 | −0.892015 | −0.446008 | − | 0.895029i | \(-0.647155\pi\) | ||||
−0.446008 | + | 0.895029i | \(0.647155\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.57664i | − | 1.73820i | −0.494635 | − | 0.869101i | \(-0.664698\pi\) | ||
0.494635 | − | 0.869101i | \(-0.335302\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.57459 | + | 0.270382i | −0.998258 | + | 0.0590022i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.17546 | − | 3.78437i | 0.662130 | − | 0.789096i | −0.325560 | − | 0.945521i | \(-0.605553\pi\) |
0.987690 | + | 0.156426i | \(0.0499972\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.19416 | − | 2.25449i | −1.23883 | − | 0.450898i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00843 | + | 1.38405i | −0.963873 | + | 0.266361i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.50806 | − | 6.56425i | −1.02282 | − | 1.21895i | −0.975484 | − | 0.220072i | \(-0.929371\pi\) |
−0.0473381 | − | 0.998879i | \(-0.515074\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.36807 | − | 3.75873i | −0.245712 | − | 0.675088i | −0.999832 | − | 0.0183509i | \(-0.994158\pi\) |
0.754120 | − | 0.656737i | \(-0.228064\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.31500 | + | 8.73062i | −0.402989 | + | 1.51981i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.55559 | − | 2.81844i | 1.44616 | − | 0.476403i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.11270 | + | 5.39136i | 0.511725 | + | 0.886334i | 0.999908 | + | 0.0135926i | \(0.00432679\pi\) |
−0.488182 | + | 0.872742i | \(0.662340\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.94082 | − | 6.26394i | −0.470908 | − | 1.00303i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.29135 | + | 2.76177i | 0.514022 | + | 0.431315i | 0.862542 | − | 0.505986i | \(-0.168871\pi\) |
−0.348520 | + | 0.937301i | \(0.613316\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.46720 | + | 3.08181i | 1.29124 | + | 0.469971i | 0.894132 | − | 0.447803i | \(-0.147793\pi\) |
0.397103 | + | 0.917774i | \(0.370015\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.81882 | − | 5.15301i | 1.31463 | − | 0.768165i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0867629 | + | 0.0315791i | 0.0126557 | + | 0.00460629i | 0.348340 | − | 0.937368i | \(-0.386745\pi\) |
−0.335685 | + | 0.941974i | \(0.608968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.86697 | + | 5.83494i | −0.552424 | + | 0.833563i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.67714 | + | 5.78041i | −0.374874 | + | 0.809420i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.822872 | + | 0.475085i | −0.113030 | + | 0.0652580i | −0.555449 | − | 0.831550i | \(-0.687454\pi\) |
0.442419 | + | 0.896808i | \(0.354120\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 17.7547i | − | 2.39404i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.9080 | − | 5.51507i | −1.57725 | − | 0.730488i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.157848 | + | 0.132450i | 0.0205500 | + | 0.0172435i | 0.653005 | − | 0.757354i | \(-0.273508\pi\) |
−0.632455 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.75967 | + | 10.3296i | −0.481376 | + | 1.32257i | 0.426938 | + | 0.904281i | \(0.359592\pi\) |
−0.908314 | + | 0.418289i | \(0.862630\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.90491 | + | 7.38658i | −0.365984 | + | 0.930621i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.74342 | + | 10.4200i | 1.08449 | + | 1.29244i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.114606 | − | 0.649962i | 0.0140013 | − | 0.0794055i | −0.977006 | − | 0.213210i | \(-0.931608\pi\) |
0.991008 | + | 0.133804i | \(0.0427193\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.63636 | − | 7.74545i | −0.437766 | − | 0.932442i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.63188 | − | 2.67422i | −0.549703 | − | 0.317371i | 0.199299 | − | 0.979939i | \(-0.436133\pi\) |
−0.749002 | + | 0.662568i | \(0.769467\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.35033 | − | 4.82106i | −0.977332 | − | 0.564263i | −0.0758684 | − | 0.997118i | \(-0.524173\pi\) |
−0.901464 | + | 0.432855i | \(0.857506\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.05207 | + | 8.09414i | −0.929773 | + | 0.934631i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.53854 | + | 10.8376i | 0.973057 | + | 1.23506i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.401358 | − | 2.27621i | −0.0451563 | − | 0.256094i | 0.953870 | − | 0.300221i | \(-0.0970605\pi\) |
−0.999026 | + | 0.0441271i | \(0.985949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.47037 | + | 8.87908i | −0.163375 | + | 0.986564i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.15096 | + | 4.32216i | −0.565391 | + | 0.474419i | −0.880113 | − | 0.474765i | \(-0.842533\pi\) |
0.314722 | + | 0.949184i | \(0.398089\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.17440 | − | 12.3317i | 0.235847 | − | 1.33756i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.3262 | + | 3.87873i | −1.53593 | + | 0.415844i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.57358 | 0.166799 | 0.0833997 | − | 0.996516i | \(-0.473422\pi\) | ||||
0.0833997 | + | 0.996516i | \(0.473422\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.3482 | − | 2.15559i | −1.08479 | − | 0.225967i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.90332 | − | 0.585841i | −0.715840 | − | 0.0607489i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 25.4040 | + | 4.47941i | 2.60639 | + | 0.459577i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.25237 | + | 3.44085i | −0.127159 | + | 0.349365i | −0.986893 | − | 0.161376i | \(-0.948407\pi\) |
0.859734 | + | 0.510741i | \(0.170629\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.0366 | + | 9.99347i | 1.20972 | + | 1.00438i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.45113 | − | 1.21764i | 0.144393 | − | 0.121160i | −0.567730 | − | 0.823215i | \(-0.692178\pi\) |
0.712123 | + | 0.702055i | \(0.247734\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.01468 | − | 0.884223i | −0.494111 | − | 0.0871251i | −0.0789603 | − | 0.996878i | \(-0.525160\pi\) |
−0.415151 | + | 0.909753i | \(0.636271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.79798 | − | 15.4981i | 0.175465 | − | 1.51246i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.57533 | + | 3.21892i | 0.538987 | + | 0.311184i | 0.744668 | − | 0.667435i | \(-0.232608\pi\) |
−0.205681 | + | 0.978619i | \(0.565941\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.33104 | − | 2.30543i | −0.127491 | − | 0.220820i | 0.795213 | − | 0.606330i | \(-0.207359\pi\) |
−0.922704 | + | 0.385510i | \(0.874026\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.7392 | − | 0.967761i | 1.01932 | − | 0.0918558i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.42760 | − | 3.92229i | −0.134297 | − | 0.368978i | 0.854256 | − | 0.519853i | \(-0.174013\pi\) |
−0.988553 | + | 0.150875i | \(0.951791\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.8114 | + | 12.8845i | 1.00816 | + | 1.20148i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.9855 | + | 0.0624590i | −1.10806 | + | 0.00577434i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.60324 | + | 8.57306i | 0.421979 | + | 0.785891i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2177 | − | 5.53878i | 1.38343 | − | 0.503526i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.73638 | − | 3.16262i | 0.607399 | − | 0.285164i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.70957 | − | 4.69311i | 0.242351 | − | 0.419765i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.14708 | − | 1.98680i | −0.101787 | − | 0.176300i | 0.810634 | − | 0.585553i | \(-0.199123\pi\) |
−0.912421 | + | 0.409253i | \(0.865789\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.0069 | − | 11.0644i | 0.969104 | − | 0.974167i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.4895 | + | 12.1582i | 1.26596 | + | 1.06226i | 0.995021 | + | 0.0996665i | \(0.0317776\pi\) |
0.270936 | + | 0.962597i | \(0.412667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.6610 | + | 9.48296i | −1.53141 | + | 0.822277i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.67959 | − | 17.6112i | −0.144556 | − | 1.51573i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.88509 | − | 18.9166i | 0.588233 | − | 1.61616i | −0.185499 | − | 0.982644i | \(-0.559390\pi\) |
0.773732 | − | 0.633513i | \(-0.218388\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.88650 | + | 1.56693i | 0.753743 | + | 0.132905i | 0.537302 | − | 0.843390i | \(-0.319444\pi\) |
0.216442 | + | 0.976296i | \(0.430555\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.112787 | − | 0.113376i | 0.00949838 | − | 0.00954801i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.4172 | + | 18.0431i | −0.871127 | + | 1.50884i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.2659 | − | 14.5873i | 2.09822 | − | 1.21141i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.35584 | + | 10.3249i | 0.524221 | + | 0.851582i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.94231 | − | 16.3264i | −0.486813 | − | 1.33751i | −0.903551 | − | 0.428482i | \(-0.859049\pi\) |
0.416737 | − | 0.909027i | \(-0.363174\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.04228 | − | 17.2537i | −0.247578 | − | 1.40408i | −0.814430 | − | 0.580262i | \(-0.802950\pi\) |
0.566852 | − | 0.823820i | \(-0.308161\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.13622 | + | 8.41517i | 0.576930 | + | 0.680326i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.4116 | − | 2.36482i | 1.07724 | − | 0.189947i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.4237 | + | 13.6142i | −0.911709 | + | 1.08653i | 0.0842255 | + | 0.996447i | \(0.473158\pi\) |
−0.995934 | + | 0.0900852i | \(0.971286\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.147707 | + | 1.63910i | 0.0117139 | + | 0.129989i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.7957 | − | 2.66542i | −1.00844 | − | 0.210064i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.26841 | − | 2.19695i | 0.0993497 | − | 0.172079i | −0.812066 | − | 0.583566i | \(-0.801657\pi\) |
0.911416 | + | 0.411487i | \(0.134990\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −27.9045 | − | 12.9237i | −2.17236 | − | 1.00611i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.64872 | + | 3.51185i | −0.746640 | + | 0.271755i | −0.687191 | − | 0.726477i | \(-0.741157\pi\) |
−0.0594489 | + | 0.998231i | \(0.518934\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.514306 | − | 2.91678i | −0.0395620 | − | 0.224367i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.3358 | + | 14.7011i | −1.32570 | + | 1.12422i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.4211 | − | 14.6180i | 1.32450 | − | 1.11139i | 0.339170 | − | 0.940725i | \(-0.389854\pi\) |
0.985330 | − | 0.170662i | \(-0.0545905\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.49746 | + | 17.2602i | 0.188790 | + | 1.30475i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.323066 | − | 0.151674i | 0.0242831 | − | 0.0114005i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.20144i | − | 0.613004i | −0.951870 | − | 0.306502i | \(-0.900841\pi\) | ||
0.951870 | − | 0.306502i | \(-0.0991586\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.4566 | − | 10.6559i | 1.37187 | − | 0.792050i | 0.380708 | − | 0.924695i | \(-0.375680\pi\) |
0.991164 | + | 0.132645i | \(0.0423471\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.4981 | + | 13.4279i | 0.997807 | + | 0.992621i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.9171 | + | 7.24924i | −1.46434 | + | 0.532975i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.8881 | − | 3.33047i | 1.38123 | − | 0.243548i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.49479 | + | 9.94228i | 0.690644 | + | 0.723195i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.4547 | − | 3.95937i | 1.62477 | − | 0.286490i | 0.714228 | − | 0.699913i | \(-0.246778\pi\) |
0.910539 | + | 0.413423i | \(0.135667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.1474 | − | 6.60512i | 1.30628 | − | 0.475447i | 0.407243 | − | 0.913320i | \(-0.366490\pi\) |
0.899037 | + | 0.437873i | \(0.144268\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 22.7412 | − | 6.15704i | 1.62853 | − | 0.440915i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.31379 | + | 0.758514i | −0.0936033 | + | 0.0540419i | −0.546071 | − | 0.837739i | \(-0.683877\pi\) |
0.452468 | + | 0.891781i | \(0.350544\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5673i | 0.749099i | 0.927207 | + | 0.374549i | \(0.122203\pi\) | ||||
−0.927207 | + | 0.374549i | \(0.877797\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.938106 | − | 0.653233i | −0.0661689 | − | 0.0460755i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.40725 | + | 21.0551i | −0.590073 | + | 1.47778i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.2059 | + | 9.40287i | −0.782654 | + | 0.656725i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.8202 | + | 0.0772315i | −1.03008 | + | 0.00536796i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.86098 | + | 38.9106i | 0.474584 | + | 2.69150i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.7963 | − | 4.29351i | 0.812093 | − | 0.295578i | 0.0976050 | − | 0.995225i | \(-0.468882\pi\) |
0.714488 | + | 0.699647i | \(0.246660\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.57456 | + | 5.33323i | −0.519000 | + | 0.365427i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.3390 | + | 26.5679i | −1.04611 | + | 1.81192i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.04926 | + | 7.89338i | −0.478535 | + | 0.535838i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.6554 | + | 9.61472i | −0.922744 | + | 0.649702i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.44506 | + | 11.2562i | −0.635344 | + | 0.757173i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.7911 | + | 3.13705i | −1.19138 | + | 0.210073i | −0.733970 | − | 0.679182i | \(-0.762335\pi\) |
−0.457412 | + | 0.889255i | \(0.651223\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.86021 | + | 18.5470i | 0.457347 | + | 1.23646i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.22816 | − | 23.9791i | −0.280633 | − | 1.59155i | −0.720481 | − | 0.693474i | \(-0.756079\pi\) |
0.439849 | − | 0.898072i | \(-0.355032\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.04053 | + | 8.35380i | 0.200924 | + | 0.552034i | 0.998703 | − | 0.0509157i | \(-0.0162140\pi\) |
−0.797779 | + | 0.602950i | \(0.793992\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.2484 | − | 5.53106i | 1.52963 | − | 0.363917i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.32605 | + | 1.92030i | −0.217897 | + | 0.125803i | −0.604976 | − | 0.796244i | \(-0.706817\pi\) |
0.387079 | + | 0.922046i | \(0.373484\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.157178 | + | 0.272240i | −0.0102532 | + | 0.0177590i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.86961 | − | 1.02606i | −0.251358 | − | 0.0666498i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.15316 | + | 0.555987i | 0.203961 | + | 0.0359638i | 0.274695 | − | 0.961531i | \(-0.411423\pi\) |
−0.0707342 | + | 0.997495i | \(0.522534\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.279960 | + | 0.769183i | −0.0180338 | + | 0.0495474i | −0.948383 | − | 0.317128i | \(-0.897282\pi\) |
0.930349 | + | 0.366675i | \(0.119504\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.8847 | + | 8.77406i | 0.826555 | + | 0.562856i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.2780 | − | 16.4154i | −1.10385 | − | 1.04874i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.1884 | − | 19.4574i | −1.47544 | − | 1.23805i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.04363 | + | 11.2417i | 0.192882 | + | 0.712416i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.58268 | − | 2.74129i | −0.0998981 | − | 0.173029i | 0.811744 | − | 0.584013i | \(-0.198518\pi\) |
−0.911642 | + | 0.410985i | \(0.865185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.8810 | + | 22.3105i | −0.809820 | + | 1.40265i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.7986 | − | 12.3937i | −1.11459 | − | 0.776124i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.10354 | + | 2.58548i | −0.443107 | + | 0.161278i | −0.553931 | − | 0.832562i | \(-0.686873\pi\) |
0.110825 | + | 0.993840i | \(0.464651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.67130 | − | 14.0035i | 0.538808 | − | 0.870136i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.33200 | + | 25.3394i | −0.268144 | + | 1.56847i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.3794 | − | 13.5615i | −0.701686 | − | 0.836237i | 0.291030 | − | 0.956714i | \(-0.406002\pi\) |
−0.992716 | + | 0.120477i | \(0.961558\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.10644 | − | 3.03991i | −0.0679678 | − | 0.186740i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.14542 | − | 2.47316i | 0.0700983 | − | 0.151355i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.49490 | + | 7.78539i | 0.274059 | + | 0.474683i | 0.969897 | − | 0.243515i | \(-0.0783004\pi\) |
−0.695839 | + | 0.718198i | \(0.744967\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.2099 | − | 16.2870i | −1.71363 | − | 0.989364i | −0.929545 | − | 0.368708i | \(-0.879800\pi\) |
−0.784083 | − | 0.620656i | \(-0.786866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.9204 | + | 14.6950i | −0.660932 | + | 0.889380i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 33.8522 | + | 5.96906i | 2.04136 | + | 0.359948i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.9194 | − | 19.2317i | 1.37709 | − | 1.15552i | 0.406819 | − | 0.913509i | \(-0.366638\pi\) |
0.970274 | − | 0.242009i | \(-0.0778064\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.94570 | + | 10.4233i | −0.355960 | + | 0.624028i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.56329 | + | 12.5375i | −0.272223 | + | 0.747926i | 0.725964 | + | 0.687733i | \(0.241394\pi\) |
−0.998187 | + | 0.0601934i | \(0.980828\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.2606 | + | 2.69085i | 0.907148 | + | 0.159955i | 0.607708 | − | 0.794160i | \(-0.292089\pi\) |
0.299440 | + | 0.954115i | \(0.403200\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 25.5318 | − | 36.6662i | 1.51237 | − | 2.17192i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.31817 | − | 11.1287i | 0.136837 | − | 0.656907i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.47325 | −0.204309 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.49629 | + | 4.47292i | 0.263577 | + | 0.262207i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.97923 | − | 11.2248i | 0.115628 | − | 0.655760i | −0.870809 | − | 0.491621i | \(-0.836405\pi\) |
0.986437 | − | 0.164138i | \(-0.0524844\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.537417 | + | 0.450946i | −0.0312896 | + | 0.0262551i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.4679 | − | 11.6433i | 1.41977 | − | 0.675612i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.42729 | − | 19.4371i | −0.198205 | − | 1.12408i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.41394 | − | 23.5941i | −0.196776 | − | 1.35994i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.857453 | − | 3.16703i | −0.0492594 | − | 0.181941i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −32.4117 | − | 18.7129i | −1.85589 | − | 1.07150i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.53824 | − | 1.46546i | −0.144865 | − | 0.0836380i | 0.425815 | − | 0.904810i | \(-0.359987\pi\) |
−0.570681 | + | 0.821172i | \(0.693321\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.03991 | + | 7.23781i | −0.286711 | + | 0.411744i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.51071 | − | 8.56764i | 0.0856643 | − | 0.485826i | −0.911547 | − | 0.411196i | \(-0.865111\pi\) |
0.997211 | − | 0.0746305i | \(-0.0237777\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.79403 | + | 4.52155i | 0.214451 | + | 0.255573i | 0.862537 | − | 0.505995i | \(-0.168874\pi\) |
−0.648085 | + | 0.761568i | \(0.724430\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −23.0493 | − | 14.1070i | −1.29868 | − | 0.794839i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.6009 | − | 31.8731i | 0.651569 | − | 1.79017i | 0.0396997 | − | 0.999212i | \(-0.487360\pi\) |
0.611869 | − | 0.790959i | \(-0.290418\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.2314 | + | 28.7235i | 1.91659 | + | 1.60821i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.11738 | − | 6.41953i | 0.508883 | − | 0.358303i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.8659i | 1.55050i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.8070 | + | 13.1676i | −1.26510 | + | 0.730408i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.59225 | + | 0.413830i | −0.253952 | + | 0.0228848i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.0349825 | − | 0.241767i | −0.00192865 | − | 0.0133291i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.4513 | − | 8.53558i | −1.28900 | − | 0.469158i | −0.395601 | − | 0.918422i | \(-0.629464\pi\) |
−0.893399 | + | 0.449265i | \(0.851686\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.29610 | − | 17.5830i | 0.345024 | − | 0.963540i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.11152 | + | 0.768531i | 0.115365 | + | 0.0419894i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.2082 | + | 11.9221i | 0.773968 | + | 0.649436i | 0.941722 | − | 0.336393i | \(-0.109207\pi\) |
−0.167754 | + | 0.985829i | \(0.553651\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.20371 | − | 0.611333i | −0.391252 | − | 0.0332031i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.4295 | + | 18.0645i | 0.564790 | + | 0.978246i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4411 | + | 1.71081i | 0.995724 | + | 0.0923748i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 28.1198 | − | 7.61327i | 1.51392 | − | 0.409885i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.00581 | + | 21.9958i | 0.429774 | + | 1.18080i | 0.945950 | + | 0.324313i | \(0.105133\pi\) |
−0.516175 | + | 0.856483i | \(0.672645\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0653 | − | 16.7624i | −0.752899 | − | 0.897270i | 0.244478 | − | 0.969655i | \(-0.421383\pi\) |
−0.997377 | + | 0.0723850i | \(0.976939\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.62612 | + | 18.8827i | −0.460428 | + | 1.00789i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.2118 | − | 7.72046i | −1.12899 | − | 0.410919i | −0.291064 | − | 0.956703i | \(-0.594009\pi\) |
−0.837925 | + | 0.545785i | \(0.816232\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.7049 | − | 13.9493i | 0.621231 | − | 0.740354i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.8248 | − | 0.994431i | 0.890461 | − | 0.0526309i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 26.0175i | − | 1.37315i | −0.727057 | − | 0.686577i | \(-0.759113\pi\) | ||
0.727057 | − | 0.686577i | \(-0.240887\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −38.4055 | −2.02134 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.37185 | − | 27.9489i | 0.124490 | − | 1.46694i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.1015 | − | 25.1478i | 1.10450 | − | 1.31630i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.7174 | + | 3.65303i | −1.08144 | + | 0.190687i | −0.685852 | − | 0.727741i | \(-0.740570\pi\) |
−0.395587 | + | 0.918428i | \(0.629459\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0671698 | − | 12.8895i | −0.00349672 | − | 0.670999i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.13733 | + | 1.32348i | 0.110964 | + | 0.0687117i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.91950 | − | 10.8860i | 0.0993881 | − | 0.563658i | −0.893926 | − | 0.448215i | \(-0.852060\pi\) |
0.993314 | − | 0.115443i | \(-0.0368288\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.40373 | − | 7.67469i | −0.279047 | − | 0.396319i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −34.2351 | −1.76320 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.1091 | 0.930203 | 0.465102 | − | 0.885257i | \(-0.346018\pi\) | ||||
0.465102 | + | 0.885257i | \(0.346018\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.95757 | + | 0.356635i | −0.202752 | + | 0.0182710i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.256321 | − | 1.45367i | 0.0130974 | − | 0.0742791i | −0.977558 | − | 0.210664i | \(-0.932437\pi\) |
0.990656 | + | 0.136385i | \(0.0435485\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −41.3858 | + | 22.2218i | −2.10922 | + | 1.13253i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.37767 | − | 25.3531i | −0.476694 | − | 1.28877i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.7473 | + | 2.07137i | −0.595614 | + | 0.105023i | −0.463325 | − | 0.886189i | \(-0.653344\pi\) |
−0.132289 | + | 0.991211i | \(0.542233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.6790 | + | 13.9184i | −0.590630 | + | 0.703886i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.6557 | − | 13.9228i | 1.49593 | − | 0.702315i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.86928 | 0.395946 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.36679i | 0.319540i | 0.987154 | + | 0.159770i | \(0.0510753\pi\) | ||||
−0.987154 | + | 0.159770i | \(0.948925\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.04859 | + | 34.6601i | 0.102558 | + | 1.73517i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.3873 | + | 19.5296i | −0.818341 | + | 0.975261i | −0.999967 | − | 0.00810645i | \(-0.997420\pi\) |
0.181626 | + | 0.983368i | \(0.441864\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.0170 | − | 5.46572i | −0.748048 | − | 0.272267i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −28.9016 | − | 10.1795i | −1.43613 | − | 0.505823i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.8677 | − | 24.8691i | −1.03437 | − | 1.23272i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.72474 | + | 18.4761i | 0.332517 | + | 0.913583i | 0.987455 | + | 0.157901i | \(0.0504726\pi\) |
−0.654938 | + | 0.755683i | \(0.727305\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.7191 | − | 24.5906i | −1.21930 | − | 1.21296i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.111176 | − | 0.533715i | 0.00547060 | − | 0.0262624i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.4466 | − | 19.8261i | −0.561892 | − | 0.973226i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.93122 | − | 12.8261i | 0.437364 | − | 0.628097i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.01894 | − | 4.21139i | −0.245191 | − | 0.205740i | 0.511907 | − | 0.859041i | \(-0.328939\pi\) |
−0.757098 | + | 0.653301i | \(0.773384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.0755 | + | 9.85467i | 1.31958 | + | 0.480287i | 0.903323 | − | 0.428960i | \(-0.141120\pi\) |
0.416255 | + | 0.909248i | \(0.363342\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.0960924 | − | 0.259791i | −0.00467217 | − | 0.0126315i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.7813 | + | 8.29172i | 1.10506 | + | 0.402208i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.7838 | − | 4.16486i | 1.39294 | − | 0.201552i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.7751 | + | 29.5060i | 1.00303 | + | 1.42456i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.0524 | − | 17.3507i | 1.44757 | − | 0.835756i | 0.449236 | − | 0.893413i | \(-0.351696\pi\) |
0.998336 | + | 0.0576573i | \(0.0183631\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.3944i | 1.07620i | 0.842880 | + | 0.538102i | \(0.180859\pi\) | ||||
−0.842880 | + | 0.538102i | \(0.819141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.53529 | − | 50.3279i | −0.217451 | − | 2.41304i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −28.6728 | − | 24.0594i | −1.37161 | − | 1.15092i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.41439 | + | 25.8658i | −0.449324 | + | 1.23451i | 0.483871 | + | 0.875139i | \(0.339230\pi\) |
−0.933195 | + | 0.359369i | \(0.882992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.8538 | − | 2.47378i | 0.993037 | − | 0.117799i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.01473 | − | 3.59281i | −0.143234 | − | 0.170700i | 0.689658 | − | 0.724135i | \(-0.257761\pi\) |
−0.832892 | + | 0.553436i | \(0.813316\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.930321 | + | 5.27611i | −0.0441014 | + | 0.250112i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −29.9852 | − | 2.54465i | −1.41825 | − | 0.120358i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.49280 | + | 0.861866i | 0.0704494 | + | 0.0406740i | 0.534811 | − | 0.844972i | \(-0.320383\pi\) |
−0.464362 | + | 0.885646i | \(0.653716\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.4039 | − | 11.2029i | −0.913694 | − | 0.527522i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −29.3316 | − | 7.77752i | −1.37812 | − | 0.365420i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.3455 | − | 33.4225i | 0.625649 | − | 1.56687i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.98772 | + | 11.2729i | 0.0929815 | + | 0.527324i | 0.995347 | + | 0.0963531i | \(0.0307178\pi\) |
−0.902366 | + | 0.430971i | \(0.858171\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.4204 | − | 5.09038i | 0.859790 | − | 0.237599i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.965463 | − | 0.810120i | 0.0449661 | − | 0.0377310i | −0.620028 | − | 0.784580i | \(-0.712879\pi\) |
0.664994 | + | 0.746849i | \(0.268434\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.39773 | + | 36.2833i | −0.297328 | + | 1.68623i | 0.360261 | + | 0.932851i | \(0.382687\pi\) |
−0.657589 | + | 0.753377i | \(0.728424\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.04561 | − | 22.8000i | 0.280358 | − | 1.05732i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.3672 | −0.942483 | −0.471242 | − | 0.882004i | \(-0.656194\pi\) | ||||
−0.471242 | + | 0.882004i | \(0.656194\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.65849 | + | 0.546351i | −0.0765821 | + | 0.0252282i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.0817 | + | 27.8641i | 0.602775 | + | 1.28391i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −46.2748 | − | 8.15950i | −2.12772 | − | 0.375174i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.0815 | + | 46.9309i | −0.783751 | + | 2.15334i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.68365 | + | 0.960960i | 0.122876 | + | 0.0439993i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.7978 | − | 18.2905i | 0.995968 | − | 0.835716i | 0.00954704 | − | 0.999954i | \(-0.496961\pi\) |
0.986421 | + | 0.164238i | \(0.0525166\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.4940 | + | 4.31895i | 1.11683 | + | 0.196927i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.5032 | + | 18.1705i | −0.614418 | + | 0.826788i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.7965 | − | 6.23337i | −0.490245 | − | 0.283043i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.199066 | + | 0.344792i | 0.00902053 | + | 0.0156240i | 0.870500 | − | 0.492168i | \(-0.163795\pi\) |
−0.861480 | + | 0.507792i | \(0.830462\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.52961 | − | 3.59270i | −0.114393 | − | 0.162468i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.68427 | + | 15.6174i | 0.256528 | + | 0.704804i | 0.999375 | + | 0.0353434i | \(0.0112525\pi\) |
−0.742848 | + | 0.669461i | \(0.766525\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.2580 | + | 24.1425i | 0.912373 | + | 1.08732i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −40.6236 | + | 34.4496i | −1.82590 | + | 1.54839i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.436273 | + | 14.1439i | −0.0195695 | + | 0.634441i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.1474 | + | 4.42128i | −0.543791 | + | 0.197924i | −0.599286 | − | 0.800535i | \(-0.704549\pi\) |
0.0554945 | + | 0.998459i | \(0.482326\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.50386 | + | 17.7209i | −0.0671876 | + | 0.791712i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.1104 | + | 22.7079i | −0.584565 | + | 1.01250i | 0.410365 | + | 0.911921i | \(0.365401\pi\) |
−0.994930 | + | 0.100574i | \(0.967932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.22474 | + | 5.58542i | 0.143499 | + | 0.248548i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.95858 | − | 1.31481i | −0.220218 | − | 0.0583928i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.78538 | + | 7.37181i | 0.389405 | + | 0.326750i | 0.816381 | − | 0.577513i | \(-0.195977\pi\) |
−0.426976 | + | 0.904263i | \(0.640421\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.786511 | + | 25.4985i | −0.0347932 | + | 1.12799i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.4865 | + | 37.9471i | 0.462990 | + | 1.67541i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.92948 | − | 16.2911i | 0.261284 | − | 0.717872i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.474175 | − | 0.0836099i | −0.0208542 | − | 0.00367716i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.2939 | − | 38.0207i | −0.451851 | − | 1.66892i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.75886 | + | 6.51053i | −0.164679 | + | 0.285232i | −0.936541 | − | 0.350558i | \(-0.885992\pi\) |
0.771863 | + | 0.635789i | \(0.219325\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.3709 | − | 17.5346i | 1.32803 | − | 0.766736i | 0.343031 | − | 0.939324i | \(-0.388546\pi\) |
0.984994 | + | 0.172588i | \(0.0552129\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 28.9453 | + | 8.63858i | 1.26328 | + | 0.377018i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.03157 | + | 13.8241i | 0.219179 | + | 0.602189i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.243980 | − | 1.38368i | −0.0106078 | − | 0.0601600i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.00322136 | − | 0.618158i | −0.000139795 | − | 0.0268258i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.9049 | − | 2.98078i | 0.732231 | − | 0.129112i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.0890 | + | 16.7906i | −0.609121 | + | 0.725922i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.8900 | − | 5.96986i | −0.556244 | − | 0.257618i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.5754 | − | 33.4676i | 0.627807 | − | 1.44155i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.21190 | − | 15.9555i | 0.396050 | − | 0.685979i | −0.597184 | − | 0.802104i | \(-0.703714\pi\) |
0.993235 | + | 0.116125i | \(0.0370472\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.31301 | − | 36.7643i | −0.142175 | − | 1.57771i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.51688 | − | 3.09989i | 0.364823 | − | 0.132785i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.17800 | − | 12.3520i | −0.0931245 | − | 0.528135i | −0.995306 | − | 0.0967786i | \(-0.969146\pi\) |
0.902181 | − | 0.431357i | \(-0.141965\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.9296 | − | 11.4403i | 1.32004 | − | 0.488262i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −49.7350 | + | 41.7326i | −2.11878 | + | 1.77787i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.80348 | + | 3.78448i | −0.204265 | + | 0.160932i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.10431 | + | 36.5800i | −0.131771 | + | 1.55273i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.2848i | 0.520524i | 0.965538 | + | 0.260262i | \(0.0838089\pi\) | ||||
−0.965538 | + | 0.260262i | \(0.916191\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.1763 | − | 17.9997i | 1.31862 | − | 0.761305i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.51427 | − | 32.1101i | 0.359473 | − | 1.35569i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.3440 | + | 9.95240i | −1.15241 | + | 0.419444i | −0.846381 | − | 0.532578i | \(-0.821223\pi\) |
−0.306031 | + | 0.952022i | \(0.599001\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.9952 | − | 2.46773i | 0.588781 | − | 0.103818i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.5373 | − | 7.68568i | 0.946478 | − | 0.322768i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.2725 | − | 2.34030i | 0.556412 | − | 0.0981104i | 0.111631 | − | 0.993750i | \(-0.464393\pi\) |
0.444781 | + | 0.895639i | \(0.353282\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.8860 | − | 4.69011i | 0.539261 | − | 0.196275i | −0.0580075 | − | 0.998316i | \(-0.518475\pi\) |
0.597269 | + | 0.802041i | \(0.296253\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.1220 | − | 38.1735i | 0.422854 | − | 1.59472i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.2011 | + | 16.2819i | −1.17607 | + | 0.679004i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 32.2107i | − | 1.34095i | −0.741932 | − | 0.670476i | \(-0.766090\pi\) | ||
0.741932 | − | 0.670476i | \(-0.233910\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.82848 | − | 33.3297i | 0.117548 | − | 1.38514i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.5219 | + | 6.59715i | 0.685442 | + | 0.273696i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.79572 | − | 3.18499i | 0.157203 | − | 0.131909i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.87655 | − | 40.2235i | 0.284310 | − | 1.66304i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.81253 | − | 27.2932i | −0.198634 | − | 1.12651i | −0.907147 | − | 0.420813i | \(-0.861745\pi\) |
0.708513 | − | 0.705698i | \(-0.249366\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.4786 | + | 10.3653i | −1.17344 | + | 0.427097i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.235827 | + | 2.61697i | 0.00970064 | + | 0.107648i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.73131 | + | 16.8551i | −0.399617 | + | 0.692157i | −0.993679 | − | 0.112262i | \(-0.964190\pi\) |
0.594061 | + | 0.804420i | \(0.297524\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −31.4664 | + | 10.3659i | −1.29000 | + | 0.424959i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.6084 | + | 7.69201i | 0.679737 | + | 0.314813i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.9010 | + | 17.7583i | −0.608839 | + | 0.725586i | −0.979108 | − | 0.203339i | \(-0.934821\pi\) |
0.370270 | + | 0.928924i | \(0.379265\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.4177 | − | 6.59776i | 1.52630 | − | 0.269128i | 0.653395 | − | 0.757017i | \(-0.273344\pi\) |
0.872906 | + | 0.487889i | \(0.162233\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.70952 | + | 0.998906i | −0.0696170 | + | 0.0406786i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.57428 | + | 54.2985i | 0.389250 | + | 2.20755i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.4714 | − | 34.2648i | −0.506197 | − | 1.39077i | −0.885131 | − | 0.465342i | \(-0.845931\pi\) |
0.378933 | − | 0.925424i | \(-0.376291\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26.9720 | + | 28.5395i | 1.09296 | + | 1.15648i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.319462 | − | 0.184442i | 0.0129241 | − | 0.00746171i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.58435 | − | 9.67238i | 0.225550 | − | 0.390664i | −0.730934 | − | 0.682448i | \(-0.760915\pi\) |
0.956484 | + | 0.291784i | \(0.0942488\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.62142 | + | 24.4564i | 0.267001 | + | 0.986177i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.5546 | + | 3.80066i | 0.867756 | + | 0.153009i | 0.589765 | − | 0.807575i | \(-0.299220\pi\) |
0.277991 | + | 0.960584i | \(0.410332\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.62741 | − | 26.4511i | 0.386958 | − | 1.06316i | −0.581405 | − | 0.813614i | \(-0.697497\pi\) |
0.968363 | − | 0.249545i | \(-0.0802810\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.6663 | + | 23.3488i | −0.428025 | + | 0.936954i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.96950 | − | 3.66799i | −0.0789064 | − | 0.146955i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.1139 | − | 9.32564i | −0.444555 | − | 0.373026i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 66.1488 | + | 17.5399i | 2.64173 | + | 0.700477i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.4481 | − | 19.8287i | −0.456467 | − | 0.790624i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.2798 | − | 24.7334i | 0.568472 | − | 0.984622i | −0.428246 | − | 0.903662i | \(-0.640868\pi\) |
0.996717 | − | 0.0809596i | \(-0.0257985\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.83859 | − | 21.6652i | 0.0730775 | − | 0.861116i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.33978 | − | 2.67146i | 0.291270 | − | 0.106014i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.92725 | + | 26.8195i | 0.314089 | + | 1.06263i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.86854 | + | 15.7868i | 0.113478 | + | 0.624516i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.54412 | − | 6.60722i | −0.218979 | − | 0.260969i | 0.645360 | − | 0.763879i | \(-0.276707\pi\) |
−0.864339 | + | 0.502909i | \(0.832263\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.28376 | + | 25.5069i | 0.366116 | + | 1.00589i | 0.976825 | + | 0.214040i | \(0.0686623\pi\) |
−0.610709 | + | 0.791855i | \(0.709116\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 30.5908 | + | 43.4468i | 1.20451 | + | 1.71072i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.4819 | − | 33.7436i | −0.765912 | − | 1.32660i | −0.939763 | − | 0.341827i | \(-0.888954\pi\) |
0.173850 | − | 0.984772i | \(-0.444379\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.930580 | − | 0.537271i | −0.0365285 | − | 0.0210897i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.27464 | + | 16.8248i | 0.285116 | + | 0.659414i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.30041 | + | 1.46359i | 0.324820 | + | 0.0572745i | 0.333681 | − | 0.942686i | \(-0.391709\pi\) |
−0.00886048 | + | 0.999961i | \(0.502820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −49.3319 | + | 41.3944i | −1.92756 | + | 1.61741i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.17140 | + | 28.4604i | 0.201755 | + | 1.11034i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.86933 | + | 21.6208i | −0.306546 | + | 0.842227i | 0.686778 | + | 0.726867i | \(0.259024\pi\) |
−0.993324 | + | 0.115360i | \(0.963198\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.02230 | − | 1.59088i | −0.350927 | − | 0.0618779i | −0.00459369 | − | 0.999989i | \(-0.501462\pi\) |
−0.346333 | + | 0.938112i | \(0.612573\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.8160 | + | 23.0380i | 0.420057 | + | 0.894721i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21.3543 | − | 64.8227i | −0.828085 | − | 2.51372i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −42.3322 | −1.63911 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.01980 | + | 30.2453i | −0.310063 | + | 1.16935i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.95422 | − | 56.4532i | 0.384278 | − | 2.17935i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.6890 | + | 30.7857i | −1.41426 | + | 1.18670i | −0.459923 | + | 0.887959i | \(0.652123\pi\) |
−0.954333 | + | 0.298743i | \(0.903433\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 34.1434 | + | 2.71840i | 1.31418 | + | 0.104631i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.43912 | − | 8.16168i | −0.0553101 | − | 0.313679i | 0.944583 | − | 0.328271i | \(-0.106466\pi\) |
−0.999894 | + | 0.0145924i | \(0.995355\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.58803 | − | 1.38734i | 0.367955 | − | 0.0532411i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −40.7649 | − | 10.8092i | −1.56212 | − | 0.414208i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.7981 | + | 12.0078i | 0.795818 | + | 0.459466i | 0.842007 | − | 0.539467i | \(-0.181374\pi\) |
−0.0461886 | + | 0.998933i | \(0.514708\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 59.3556 | + | 34.2690i | 2.26786 | + | 1.30935i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.3427 | + | 1.30203i | 0.585359 | + | 0.0496757i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.659192 | + | 3.73847i | −0.0251132 | + | 0.142424i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.68069 | − | 9.15348i | −0.292187 | − | 0.348215i | 0.599903 | − | 0.800073i | \(-0.295206\pi\) |
−0.892090 | + | 0.451858i | \(0.850761\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.22957 | − | 40.5650i | 0.312615 | − | 1.54094i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.5076 | + | 28.8694i | −0.398577 | + | 1.09508i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.1052 | − | 10.1574i | −0.458515 | − | 0.384740i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.597034 | + | 6.62526i | 0.0225819 | + | 0.250590i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0672i | 0.871236i | 0.900132 | + | 0.435618i | \(0.143470\pi\) | ||||
−0.900132 | + | 0.435618i | \(0.856530\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.8484 | − | 23.5838i | 1.54063 | − | 0.889482i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.313462 | + | 0.445197i | 0.0118057 | + | 0.0167671i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.65454 | − | 1.85855i | −0.175052 | − | 0.0698980i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.8202 | + | 12.3095i | 1.27014 | + | 0.462295i | 0.887161 | − | 0.461461i | \(-0.152674\pi\) |
0.382983 | + | 0.923755i | \(0.374897\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.42934 | + | 5.33489i | −0.166113 | + | 0.200074i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.5687 | − | 6.75844i | −0.695402 | − | 0.253106i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −54.3384 | − | 45.5953i | −2.03214 | − | 1.70517i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.16903 | − | 4.55103i | 0.118349 | − | 0.169961i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.8984 | + | 20.6086i | 0.443736 | + | 0.768573i | 0.997963 | − | 0.0637925i | \(-0.0203196\pi\) |
−0.554228 | + | 0.832365i | \(0.686986\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.21529 | + | 12.7958i | 0.156985 | + | 0.476542i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.00512 | + | 0.999896i | 0.0373808 | + | 0.0371865i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.3188 | + | 53.0779i | 0.717481 | + | 1.97126i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.48709 | − | 4.15575i | −0.129329 | − | 0.154128i | 0.697494 | − | 0.716591i | \(-0.254298\pi\) |
−0.826823 | + | 0.562463i | \(0.809854\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.1688 | − | 13.8639i | 0.858103 | − | 0.513477i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.1413 | − | 11.3345i | −1.15180 | − | 0.419222i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.72206 | − | 4.43578i | 0.137478 | − | 0.163839i | −0.692913 | − | 0.721021i | \(-0.743673\pi\) |
0.830390 | + | 0.557182i | \(0.188117\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −38.3763 | + | 15.2065i | −1.41553 | + | 0.560900i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.44172i | 0.126777i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.9316 | −0.622838 | −0.311419 | − | 0.950273i | \(-0.600804\pi\) | ||||
−0.311419 | + | 0.950273i | \(0.600804\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −47.4596 | + | 22.2815i | −1.74347 | + | 0.818532i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.8397 | − | 17.6852i | 0.544415 | − | 0.648808i | −0.421757 | − | 0.906709i | \(-0.638586\pi\) |
0.966171 | + | 0.257901i | \(0.0830308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 58.2544 | − | 10.2718i | 2.13428 | − | 0.376330i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.8838 | + | 3.39931i | 0.727510 | + | 0.124374i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.525136 | − | 17.0248i | 0.0191880 | − | 0.622073i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.05220 | − | 39.9950i | 0.257338 | − | 1.45944i | −0.532660 | − | 0.846329i | \(-0.678808\pi\) |
0.789999 | − | 0.613109i | \(-0.210081\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.46045 | + | 0.492067i | −0.198990 | + | 0.0179319i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 59.6490 | 2.17085 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.6945 | −0.643118 | −0.321559 | − | 0.946890i | \(-0.604207\pi\) | ||||
−0.321559 | + | 0.946890i | \(0.604207\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.6887 | + | 36.4846i | 0.932441 | + | 1.32431i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.35890 | + | 7.70670i | −0.0492601 | + | 0.279368i | −0.999481 | − | 0.0322086i | \(-0.989746\pi\) |
0.950221 | + | 0.311576i | \(0.100857\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.70798 | + | 5.98812i | −0.134238 | + | 0.216785i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −32.4345 | + | 18.9521i | −1.17267 | + | 0.685215i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.810730 | − | 0.142954i | 0.0292738 | − | 0.00516175i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.7523 | + | 33.0738i | −1.00077 | + | 1.19267i | −0.0195465 | + | 0.999809i | \(0.506222\pi\) |
−0.981225 | + | 0.192865i | \(0.938222\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.10717 | + | 13.0464i | −0.0398737 | + | 0.469856i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.416923 | −0.0149957 | −0.00749783 | − | 0.999972i | \(-0.502387\pi\) | ||||
−0.00749783 | + | 0.999972i | \(0.502387\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.3665i | 0.947111i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.6971 | − | 23.8217i | −0.563130 | − | 0.854597i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.9249 | − | 24.9374i | 0.749713 | − | 0.893473i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.2091 | + | 9.53932i | 0.937834 | + | 0.341344i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 36.6720 | + | 25.2532i | 1.31055 | + | 0.902474i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.8937 | − | 46.3517i | −1.38818 | − | 1.65436i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.9745 | + | 46.6370i | 0.605075 | + | 1.66243i | 0.740834 | + | 0.671688i | \(0.234431\pi\) |
−0.135759 | + | 0.990742i | \(0.543347\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.5973 | + | 8.01330i | −1.05369 | + | 0.285281i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.35600 | + | 8.23686i | −0.261549 | + | 0.292869i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.9588 | + | 38.0337i | 0.779779 | + | 1.35062i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.58312 | − | 0.473804i | −0.198013 | − | 0.0168041i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.06498 | − | 5.92823i | −0.250255 | − | 0.209989i | 0.509027 | − | 0.860750i | \(-0.330005\pi\) |
−0.759282 | + | 0.650762i | \(0.774450\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.319103 | − | 0.116144i | −0.0112890 | − | 0.00410888i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.05324 | − | 3.60044i | −0.107881 | − | 0.127215i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 47.2496 | + | 17.1974i | 1.66740 | + | 0.606884i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.5020 | − | 41.3274i | 0.581618 | − | 1.45660i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.5079 | − | 1.39749i | 0.545905 | − | 0.0491941i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.87854 | + | 4.54868i | −0.276995 | + | 0.159923i | −0.632062 | − | 0.774918i | \(-0.717791\pi\) |
0.355067 | + | 0.934841i | \(0.384458\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.06978i | − | 0.178024i | −0.996031 | − | 0.0890120i | \(-0.971629\pi\) | ||
0.996031 | − | 0.0890120i | \(-0.0283710\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −46.1319 | + | 32.4814i | −1.61792 | + | 1.13917i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.61634 | + | 5.55177i | 0.231760 | + | 0.194470i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.3498 | − | 64.1530i | 0.816905 | − | 2.24443i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.1467 | + | 27.8598i | 0.529268 | + | 0.973501i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1948 | + | 13.3415i | 0.390702 | + | 0.465621i | 0.925162 | − | 0.379573i | \(-0.123929\pi\) |
−0.534460 | + | 0.845194i | \(0.679485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.79691 | − | 27.2046i | 0.167210 | − | 0.948294i | −0.779547 | − | 0.626344i | \(-0.784551\pi\) |
0.946757 | − | 0.321950i | \(-0.104338\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 34.0225 | − | 48.8597i | 1.18451 | − | 1.70108i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.3776 | + | 8.30090i | 0.499957 | + | 0.288650i | 0.728696 | − | 0.684837i | \(-0.240127\pi\) |
−0.228739 | + | 0.973488i | \(0.573460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.5716 | − | 6.68085i | −0.401897 | − | 0.232035i | 0.285405 | − | 0.958407i | \(-0.407872\pi\) |
−0.687302 | + | 0.726372i | \(0.741205\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.5428 | − | 50.0206i | −0.469793 | − | 1.73519i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.2222 | − | 21.4602i | 0.492771 | − | 0.743551i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.07054 | − | 34.4277i | −0.210080 | − | 1.19142i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.0542 | + | 16.9319i | 0.416653 | + | 0.585251i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.63830 | − | 5.57020i | 0.229180 | − | 0.192305i | −0.520966 | − | 0.853578i | \(-0.674428\pi\) |
0.750145 | + | 0.661273i | \(0.229984\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.71487 | + | 43.7532i | −0.266030 | + | 1.50873i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.3833 | + | 16.2981i | 0.564270 | + | 0.561337i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.0838 | 0.346894 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.9573 | − | 28.5398i | −1.09807 | − | 0.980639i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.3374 | − | 22.0260i | 0.526378 | − | 0.755930i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.2872 | + | 5.34045i | 1.03823 | + | 0.183068i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.536334 | + | 1.47357i | −0.0183637 | + | 0.0504539i | −0.948536 | − | 0.316670i | \(-0.897435\pi\) |
0.930172 | + | 0.367124i | \(0.119657\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −39.0425 | − | 66.8171i | −1.33523 | − | 2.28510i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.54071 | − | 2.13191i | 0.0867889 | − | 0.0728246i | −0.598361 | − | 0.801227i | \(-0.704181\pi\) |
0.685150 | + | 0.728402i | \(0.259737\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.13266 | − | 0.728700i | −0.141005 | − | 0.0248629i | 0.102700 | − | 0.994712i | \(-0.467252\pi\) |
−0.243705 | + | 0.969849i | \(0.578363\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.8033 | − | 11.7440i | −0.538575 | − | 0.400236i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.0212 | − | 10.9819i | −0.647491 | − | 0.373829i | 0.140004 | − | 0.990151i | \(-0.455289\pi\) |
−0.787494 | + | 0.616322i | \(0.788622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38.7136 | + | 67.0540i | 1.31630 | + | 2.27990i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.52819 | + | 5.45881i | −0.0858618 | + | 0.185391i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.12242 | + | 11.3263i | 0.139844 | + | 0.384217i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.69490 | − | 2.01991i | −0.0574296 | − | 0.0684419i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.3028 | − | 3.81084i | 0.348698 | − | 0.128977i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.3309 | − | 0.442041i | −0.484472 | − | 0.0149437i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.4737 | + | 3.81213i | −0.353673 | + | 0.128726i | −0.512746 | − | 0.858540i | \(-0.671372\pi\) |
0.159073 | + | 0.987267i | \(0.449149\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.2010 | − | 11.2813i | −0.546447 | − | 0.380508i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.4795 | − | 28.5434i | 0.555209 | − | 0.961650i | −0.442678 | − | 0.896680i | \(-0.645972\pi\) |
0.997887 | − | 0.0649695i | \(-0.0206950\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.53887 | − | 6.12951i | −0.119093 | − | 0.206274i | 0.800316 | − | 0.599579i | \(-0.204665\pi\) |
−0.919408 | + | 0.393304i | \(0.871332\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.317552 | + | 1.17289i | 0.0106744 | + | 0.0394262i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.0443 | + | 13.4627i | 0.538713 | + | 0.452034i | 0.871098 | − | 0.491110i | \(-0.163409\pi\) |
−0.332384 | + | 0.943144i | \(0.607853\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.19551 | + | 5.16052i | −0.107174 | + | 0.173078i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.489147 | − | 46.9308i | −0.0163870 | − | 1.57224i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.239264 | − | 0.657371i | 0.00800665 | − | 0.0219981i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.4989 | + | 4.84879i | 0.919185 | + | 0.162077i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −33.0435 | − | 8.76177i | −1.10329 | − | 0.292547i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.1379 | + | 29.6837i | −0.571580 | + | 0.990005i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.02642 | − | 1.74730i | 0.100825 | − | 0.0582111i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −39.5673 | − | 11.8086i | −1.31672 | − | 0.392967i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.8169 | + | 68.1838i | 0.824941 | + | 2.26651i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.493825 | − | 2.80062i | −0.0163972 | − | 0.0929932i | 0.975511 | − | 0.219951i | \(-0.0705898\pi\) |
−0.991908 | + | 0.126958i | \(0.959479\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.60167 | − | 0.957654i | −0.185796 | − | 0.0317634i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.5632 | + | 4.33115i | −0.813814 | + | 0.143497i | −0.565039 | − | 0.825064i | \(-0.691139\pi\) |
−0.248775 | + | 0.968561i | \(0.580028\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.5393 | − | 26.8613i | 0.745942 | − | 0.888979i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −53.0032 | + | 37.3194i | −1.75223 | + | 1.23374i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.2053 | − | 48.9921i | 0.337009 | − | 1.61786i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.8003 | − | 25.6349i | 0.488218 | − | 0.845619i | −0.511690 | − | 0.859170i | \(-0.670980\pi\) |
0.999908 | + | 0.0135513i | \(0.00431366\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.15082 | + | 2.92258i | −0.136774 | + | 0.0963023i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.0795 | + | 7.30834i | −0.660925 | + | 0.240557i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.12581 | − | 40.4125i | −0.234295 | − | 1.32875i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.70689 | + | 13.1895i | 0.253128 | + | 0.433201i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.7619 | + | 12.3867i | −0.484322 | + | 0.406394i | −0.851986 | − | 0.523564i | \(-0.824602\pi\) |
0.367664 | + | 0.929959i | \(0.380158\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 44.2093 | + | 29.2987i | 1.44890 | + | 0.960225i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.3659 | − | 8.61076i | −0.404841 | − | 0.281903i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 65.2994i | 2.13552i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0886 | − | 12.7529i | 0.721604 | − | 0.416618i | −0.0937389 | − | 0.995597i | \(-0.529882\pi\) |
0.815343 | + | 0.578979i | \(0.196549\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.86809 | − | 2.67172i | 0.322033 | − | 0.0871884i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.8447 | + | 10.8626i | −0.972911 | + | 0.354111i | −0.779080 | − | 0.626924i | \(-0.784314\pi\) |
−0.193831 | + | 0.981035i | \(0.562091\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.9031 | − | 3.68578i | 0.680698 | − | 0.120025i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −38.9492 | + | 25.9574i | −1.26702 | + | 0.844393i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.9922 | + | 4.93578i | −0.909625 | + | 0.160391i | −0.608833 | − | 0.793298i | \(-0.708362\pi\) |
−0.300792 | + | 0.953690i | \(0.597251\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36.1992 | + | 13.1754i | −1.17508 | + | 0.427693i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −41.6498 | − | 41.4333i | −1.35059 | − | 1.34357i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.9982 | − | 24.2477i | 1.36046 | − | 0.785459i | 0.370771 | − | 0.928724i | \(-0.379093\pi\) |
0.989684 | + | 0.143265i | \(0.0457601\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 77.6300i | 2.51205i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 70.0612 | − | 32.8926i | 2.26476 | − | 1.06327i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −52.7118 | + | 7.62711i | −1.70215 | + | 0.246292i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.4909 | − | 9.64203i | 0.370675 | − | 0.311033i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.45282 | − | 19.0023i | −0.111266 | − | 0.612342i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.4175 | + | 64.7521i | 0.367544 | + | 2.08444i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.8353 | + | 11.5871i | −1.02375 | + | 0.372616i | −0.798699 | − | 0.601731i | \(-0.794478\pi\) |
−0.225054 | + | 0.974346i | \(0.572256\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 43.7961 | + | 20.2837i | 1.40693 | + | 0.651607i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.4445 | − | 30.2147i | 0.559820 | − | 0.969637i | −0.437691 | − | 0.899126i | \(-0.644204\pi\) |
0.997511 | − | 0.0705115i | \(-0.0224632\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.46990 | − | 22.6755i | −0.239474 | − | 0.726942i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.09390 | + | 45.4299i | 0.131110 | + | 1.45492i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.41030 | − | 8.83125i | 0.237077 | − | 0.282537i | −0.634368 | − | 0.773031i | \(-0.718739\pi\) |
0.871444 | + | 0.490495i | \(0.163184\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.08127 | + | 1.42495i | −0.258279 | + | 0.0455415i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.69231 | + | 7.51875i | −0.0859589 | + | 0.240055i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.78163 | − | 10.1041i | −0.0568252 | − | 0.322272i | 0.943123 | − | 0.332444i | \(-0.107873\pi\) |
−0.999948 | + | 0.0101720i | \(0.996762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.76652 | − | 4.85348i | −0.0562860 | − | 0.154645i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.405443 | − | 0.121002i | −0.0129054 | − | 0.00385155i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.5500 | − | 22.2568i | 1.22582 | − | 0.707727i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.77906 | − | 8.27757i | 0.151812 | − | 0.262946i | −0.780082 | − | 0.625678i | \(-0.784823\pi\) |
0.931894 | + | 0.362732i | \(0.118156\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.4854 | + | 30.6447i | −0.967426 | + | 0.972480i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35.4316 | − | 6.24754i | −1.12326 | − | 0.198060i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.1256 | + | 44.3048i | −0.510704 | + | 1.40315i | 0.369802 | + | 0.929111i | \(0.379426\pi\) |
−0.880505 | + | 0.474036i | \(0.842797\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.0517 | − | 22.6941i | −0.729324 | − | 0.718010i |
(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 | 756.2.ck.a.5.16 | yes | 144 | |
7.3 | odd | 6 | 756.2.ca.a.437.24 | yes | 144 | ||
27.11 | odd | 18 | 756.2.ca.a.173.24 | ✓ | 144 | ||
189.38 | even | 18 | inner | 756.2.ck.a.605.16 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.ca.a.173.24 | ✓ | 144 | 27.11 | odd | 18 | ||
756.2.ca.a.437.24 | yes | 144 | 7.3 | odd | 6 | ||
756.2.ck.a.5.16 | yes | 144 | 1.1 | even | 1 | trivial | |
756.2.ck.a.605.16 | yes | 144 | 189.38 | even | 18 | inner |