Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(99,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("931.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.w (of order \(9\), 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: | \(7.43407242818\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 133) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 883.4 | ||
Character | \(\chi\) | \(=\) | 931.883 |
Dual form | 931.2.w.b.834.4 |
$q$-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 \(\left(\mathbb{Z}/931\mathbb{Z}\right)^\times\).
\(n\) | \(248\) | \(344\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.282479 | + | 1.60202i | 0.199743 | + | 1.13280i | 0.905501 | + | 0.424344i | \(0.139495\pi\) |
−0.705758 | + | 0.708453i | \(0.749394\pi\) | |||||||
\(3\) | −0.824180 | + | 0.691570i | −0.475841 | + | 0.399278i | −0.848920 | − | 0.528522i | \(-0.822747\pi\) |
0.373079 | + | 0.927800i | \(0.378302\pi\) | |||||||
\(4\) | −0.607278 | + | 0.221031i | −0.303639 | + | 0.110516i | ||||
\(5\) | 0.0661285 | + | 0.0240688i | 0.0295736 | + | 0.0107639i | 0.356765 | − | 0.934194i | \(-0.383880\pi\) |
−0.327191 | + | 0.944958i | \(0.606102\pi\) | |||||||
\(6\) | −1.34072 | − | 1.12500i | −0.547346 | − | 0.459278i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.10109 | + | 1.90715i | 0.389295 | + | 0.674278i | ||||
\(9\) | −0.319939 | + | 1.81447i | −0.106646 | + | 0.604822i | ||||
\(10\) | −0.0198787 | + | 0.112738i | −0.00628620 | + | 0.0356508i | ||||
\(11\) | −0.895617 | − | 1.55125i | −0.270039 | − | 0.467721i | 0.698833 | − | 0.715285i | \(-0.253703\pi\) |
−0.968871 | + | 0.247564i | \(0.920370\pi\) | |||||||
\(12\) | 0.347648 | − | 0.602145i | 0.100357 | − | 0.173824i | ||||
\(13\) | 2.27346 | + | 1.90766i | 0.630545 | + | 0.529090i | 0.901098 | − | 0.433615i | \(-0.142762\pi\) |
−0.270553 | + | 0.962705i | \(0.587207\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0711470 | + | 0.0258954i | −0.0183701 | + | 0.00668616i | ||||
\(16\) | −3.73436 | + | 3.13350i | −0.933590 | + | 0.783375i | ||||
\(17\) | 0.109331 | + | 0.620047i | 0.0265167 | + | 0.150383i | 0.995191 | − | 0.0979496i | \(-0.0312284\pi\) |
−0.968675 | + | 0.248333i | \(0.920117\pi\) | |||||||
\(18\) | −2.99718 | −0.706443 | ||||||||
\(19\) | 3.31609 | + | 2.82906i | 0.760762 | + | 0.649031i | ||||
\(20\) | −0.0454783 | −0.0101693 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.23214 | − | 1.87299i | 0.475894 | − | 0.399323i | ||||
\(23\) | 1.40979 | − | 0.513123i | 0.293963 | − | 0.106994i | −0.190829 | − | 0.981623i | \(-0.561118\pi\) |
0.484792 | + | 0.874630i | \(0.338895\pi\) | |||||||
\(24\) | −2.22642 | − | 0.810352i | −0.454467 | − | 0.165412i | ||||
\(25\) | −3.82643 | − | 3.21075i | −0.765286 | − | 0.642151i | ||||
\(26\) | −2.41390 | + | 4.18100i | −0.473405 | + | 0.819962i | ||||
\(27\) | −2.60498 | − | 4.51196i | −0.501328 | − | 0.868326i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.942253 | + | 5.34378i | −0.174972 | + | 0.992316i | 0.763204 | + | 0.646157i | \(0.223625\pi\) |
−0.938176 | + | 0.346158i | \(0.887486\pi\) | |||||||
\(30\) | −0.0615824 | − | 0.106664i | −0.0112434 | − | 0.0194741i | ||||
\(31\) | −3.26526 | + | 5.65559i | −0.586457 | + | 1.01577i | 0.408235 | + | 0.912877i | \(0.366144\pi\) |
−0.994692 | + | 0.102897i | \(0.967189\pi\) | |||||||
\(32\) | −2.70086 | − | 2.26629i | −0.477449 | − | 0.400627i | ||||
\(33\) | 1.81095 | + | 0.659132i | 0.315246 | + | 0.114740i | ||||
\(34\) | −0.962442 | + | 0.350300i | −0.165057 | + | 0.0600760i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.206761 | − | 1.17260i | −0.0344602 | − | 0.195434i | ||||
\(37\) | 0.691141 | 0.113623 | 0.0568115 | − | 0.998385i | \(-0.481907\pi\) | ||||
0.0568115 | + | 0.998385i | \(0.481907\pi\) | |||||||
\(38\) | −3.59548 | + | 6.11157i | −0.583263 | + | 0.991428i | ||||
\(39\) | −3.19303 | −0.511293 | ||||||||
\(40\) | 0.0269108 | + | 0.152619i | 0.00425497 | + | 0.0241311i | ||||
\(41\) | −5.15375 | + | 4.32451i | −0.804881 | + | 0.675376i | −0.949380 | − | 0.314129i | \(-0.898287\pi\) |
0.144499 | + | 0.989505i | \(0.453843\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.77256 | − | 0.645159i | −0.270313 | − | 0.0983859i | 0.203307 | − | 0.979115i | \(-0.434831\pi\) |
−0.473620 | + | 0.880729i | \(0.657053\pi\) | |||||||
\(44\) | 0.886764 | + | 0.744083i | 0.133685 | + | 0.112175i | ||||
\(45\) | −0.0648291 | + | 0.112287i | −0.00966416 | + | 0.0167388i | ||||
\(46\) | 1.22027 | + | 2.11357i | 0.179919 | + | 0.311629i | ||||
\(47\) | 0.241473 | − | 1.36946i | 0.0352225 | − | 0.199757i | −0.962119 | − | 0.272631i | \(-0.912106\pi\) |
0.997341 | + | 0.0728744i | \(0.0232172\pi\) | |||||||
\(48\) | 0.910754 | − | 5.16514i | 0.131456 | − | 0.745524i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.06280 | − | 7.03697i | 0.574566 | − | 0.995178i | ||||
\(51\) | −0.518914 | − | 0.435420i | −0.0726625 | − | 0.0609711i | ||||
\(52\) | −1.80228 | − | 0.655975i | −0.249931 | − | 0.0909674i | ||||
\(53\) | −6.93416 | + | 2.52383i | −0.952481 | + | 0.346675i | −0.771083 | − | 0.636735i | \(-0.780284\pi\) |
−0.181398 | + | 0.983410i | \(0.558062\pi\) | |||||||
\(54\) | 6.49238 | − | 5.44775i | 0.883501 | − | 0.741345i | ||||
\(55\) | −0.0218890 | − | 0.124138i | −0.00295151 | − | 0.0167388i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.68954 | − | 0.0383506i | −0.621145 | − | 0.00507966i | ||||
\(58\) | −8.82700 | −1.15904 | ||||||||
\(59\) | −2.40797 | − | 13.6563i | −0.313491 | − | 1.77790i | −0.580558 | − | 0.814219i | \(-0.697165\pi\) |
0.267066 | − | 0.963678i | \(-0.413946\pi\) | |||||||
\(60\) | 0.0374823 | − | 0.0314514i | 0.00483895 | − | 0.00406036i | ||||
\(61\) | −0.157948 | + | 0.0574884i | −0.0202232 | + | 0.00736064i | −0.352112 | − | 0.935958i | \(-0.614536\pi\) |
0.331889 | + | 0.943319i | \(0.392314\pi\) | |||||||
\(62\) | −9.98271 | − | 3.63341i | −1.26781 | − | 0.461444i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.00716 | + | 3.47651i | −0.250896 | + | 0.434564i | ||||
\(65\) | 0.104426 | + | 0.180870i | 0.0129524 | + | 0.0224342i | ||||
\(66\) | −0.544385 | + | 3.08736i | −0.0670092 | + | 0.380028i | ||||
\(67\) | −1.60409 | + | 9.09725i | −0.195971 | + | 1.11141i | 0.715059 | + | 0.699065i | \(0.246400\pi\) |
−0.911029 | + | 0.412341i | \(0.864711\pi\) | |||||||
\(68\) | −0.203444 | − | 0.352375i | −0.0246712 | − | 0.0427318i | ||||
\(69\) | −0.807065 | + | 1.39788i | −0.0971592 | + | 0.168285i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.0779 | + | 4.03202i | 1.31470 | + | 0.478513i | 0.901758 | − | 0.432242i | \(-0.142277\pi\) |
0.412947 | + | 0.910755i | \(0.364500\pi\) | |||||||
\(72\) | −3.81274 | + | 1.38772i | −0.449335 | + | 0.163545i | ||||
\(73\) | 8.59917 | − | 7.21556i | 1.00646 | − | 0.844517i | 0.0185909 | − | 0.999827i | \(-0.494082\pi\) |
0.987866 | + | 0.155310i | \(0.0496376\pi\) | |||||||
\(74\) | 0.195233 | + | 1.10722i | 0.0226953 | + | 0.128712i | ||||
\(75\) | 5.37413 | 0.620551 | ||||||||
\(76\) | −2.63910 | − | 0.985067i | −0.302725 | − | 0.112995i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.901962 | − | 5.11528i | −0.102127 | − | 0.579191i | ||||
\(79\) | 8.02843 | − | 6.73665i | 0.903269 | − | 0.757933i | −0.0675578 | − | 0.997715i | \(-0.521521\pi\) |
0.970827 | + | 0.239783i | \(0.0770762\pi\) | |||||||
\(80\) | −0.322367 | + | 0.117332i | −0.0360417 | + | 0.0131181i | ||||
\(81\) | 0.0732713 | + | 0.0266686i | 0.00814126 | + | 0.00296318i | ||||
\(82\) | −8.38377 | − | 7.03482i | −0.925832 | − | 0.776866i | ||||
\(83\) | −3.37852 | + | 5.85176i | −0.370840 | + | 0.642315i | −0.989695 | − | 0.143191i | \(-0.954264\pi\) |
0.618855 | + | 0.785506i | \(0.287597\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.00769389 | + | 0.0436342i | −0.000834519 | + | 0.00473279i | ||||
\(86\) | 0.532845 | − | 3.02192i | 0.0574582 | − | 0.325862i | ||||
\(87\) | −2.91901 | − | 5.05588i | −0.312951 | − | 0.542047i | ||||
\(88\) | 1.97231 | − | 3.41615i | 0.210249 | − | 0.364162i | ||||
\(89\) | 3.16208 | + | 2.65330i | 0.335180 | + | 0.281249i | 0.794806 | − | 0.606863i | \(-0.207572\pi\) |
−0.459627 | + | 0.888112i | \(0.652017\pi\) | |||||||
\(90\) | −0.198199 | − | 0.0721386i | −0.0208920 | − | 0.00760407i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.742721 | + | 0.623217i | −0.0774340 | + | 0.0649749i | ||||
\(93\) | −1.22007 | − | 6.91938i | −0.126516 | − | 0.717506i | ||||
\(94\) | 2.26212 | 0.233319 | ||||||||
\(95\) | 0.151196 | + | 0.266896i | 0.0155124 | + | 0.0273829i | ||||
\(96\) | 3.79329 | 0.387151 | ||||||||
\(97\) | 0.928436 | + | 5.26542i | 0.0942684 | + | 0.534623i | 0.994969 | + | 0.100182i | \(0.0319427\pi\) |
−0.900701 | + | 0.434440i | \(0.856946\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.10124 | − | 1.12876i | 0.311687 | − | 0.113445i | ||||
\(100\) | 3.03338 | + | 1.10406i | 0.303338 | + | 0.110406i | ||||
\(101\) | −3.82000 | − | 3.20536i | −0.380104 | − | 0.318945i | 0.432639 | − | 0.901567i | \(-0.357582\pi\) |
−0.812743 | + | 0.582622i | \(0.802027\pi\) | |||||||
\(102\) | 0.550969 | − | 0.954306i | 0.0545540 | − | 0.0944904i | ||||
\(103\) | −1.50069 | − | 2.59928i | −0.147868 | − | 0.256115i | 0.782571 | − | 0.622561i | \(-0.213908\pi\) |
−0.930439 | + | 0.366446i | \(0.880574\pi\) | |||||||
\(104\) | −1.13490 | + | 6.43634i | −0.111286 | + | 0.631135i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00197 | − | 10.3957i | −0.582963 | − | 1.00972i | ||||
\(107\) | 6.25942 | − | 10.8416i | 0.605121 | − | 1.04810i | −0.386912 | − | 0.922117i | \(-0.626458\pi\) |
0.992032 | − | 0.125983i | \(-0.0402086\pi\) | |||||||
\(108\) | 2.57923 | + | 2.16423i | 0.248186 | + | 0.208253i | ||||
\(109\) | 13.1915 | + | 4.80133i | 1.26352 | + | 0.459884i | 0.884949 | − | 0.465688i | \(-0.154193\pi\) |
0.378572 | + | 0.925572i | \(0.376415\pi\) | |||||||
\(110\) | 0.192689 | − | 0.0701330i | 0.0183722 | − | 0.00668692i | ||||
\(111\) | −0.569625 | + | 0.477972i | −0.0540664 | + | 0.0453671i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.420510 | −0.0395583 | −0.0197791 | − | 0.999804i | \(-0.506296\pi\) | ||||
−0.0197791 | + | 0.999804i | \(0.506296\pi\) | |||||||
\(114\) | −1.26326 | − | 7.52356i | −0.118315 | − | 0.704646i | ||||
\(115\) | 0.105578 | 0.00984518 | ||||||||
\(116\) | −0.608933 | − | 3.45343i | −0.0565380 | − | 0.320643i | ||||
\(117\) | −4.18876 | + | 3.51479i | −0.387251 | + | 0.324942i | ||||
\(118\) | 21.1974 | − | 7.71522i | 1.95138 | − | 0.710244i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.127726 | − | 0.107175i | −0.0116597 | − | 0.00978366i | ||||
\(121\) | 3.89574 | − | 6.74762i | 0.354158 | − | 0.613420i | ||||
\(122\) | −0.136714 | − | 0.236796i | −0.0123775 | − | 0.0214385i | ||||
\(123\) | 1.25692 | − | 7.12836i | 0.113333 | − | 0.642743i | ||||
\(124\) | 0.732857 | − | 4.15624i | 0.0658125 | − | 0.373241i | ||||
\(125\) | −0.351688 | − | 0.609141i | −0.0314559 | − | 0.0544833i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.45174 | + | 7.93095i | 0.838707 | + | 0.703758i | 0.957272 | − | 0.289188i | \(-0.0933852\pi\) |
−0.118566 | + | 0.992946i | \(0.537830\pi\) | |||||||
\(128\) | −12.7626 | − | 4.64520i | −1.12806 | − | 0.410582i | ||||
\(129\) | 1.90708 | − | 0.694121i | 0.167909 | − | 0.0611140i | ||||
\(130\) | −0.260259 | + | 0.218383i | −0.0228263 | + | 0.0191535i | ||||
\(131\) | −0.518798 | − | 2.94225i | −0.0453276 | − | 0.257066i | 0.953720 | − | 0.300696i | \(-0.0972188\pi\) |
−0.999048 | + | 0.0436300i | \(0.986108\pi\) | |||||||
\(132\) | −1.24544 | −0.108402 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −15.0271 | −1.29814 | ||||||||
\(135\) | −0.0636659 | − | 0.361067i | −0.00547949 | − | 0.0310757i | ||||
\(136\) | −1.06214 | + | 0.891239i | −0.0910775 | + | 0.0764231i | ||||
\(137\) | −20.0563 | + | 7.29991i | −1.71353 | + | 0.623673i | −0.997248 | − | 0.0741400i | \(-0.976379\pi\) |
−0.716280 | + | 0.697813i | \(0.754157\pi\) | |||||||
\(138\) | −2.46740 | − | 0.898061i | −0.210039 | − | 0.0764480i | ||||
\(139\) | 5.38233 | + | 4.51631i | 0.456523 | + | 0.383068i | 0.841850 | − | 0.539712i | \(-0.181467\pi\) |
−0.385327 | + | 0.922780i | \(0.625911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.748062 | + | 1.29568i | 0.0629982 | + | 0.109116i | ||||
\(142\) | −3.33010 | + | 18.8859i | −0.279456 | + | 1.58487i | ||||
\(143\) | 0.923117 | − | 5.23525i | 0.0771949 | − | 0.437794i | ||||
\(144\) | −4.49086 | − | 7.77841i | −0.374239 | − | 0.648200i | ||||
\(145\) | −0.190928 | + | 0.330697i | −0.0158557 | + | 0.0274629i | ||||
\(146\) | 13.9885 | + | 11.7378i | 1.15770 | + | 0.971425i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.419715 | + | 0.152764i | −0.0345003 | + | 0.0125571i | ||||
\(149\) | 6.17610 | − | 5.18236i | 0.505965 | − | 0.424555i | −0.353741 | − | 0.935343i | \(-0.615091\pi\) |
0.859707 | + | 0.510788i | \(0.170646\pi\) | |||||||
\(150\) | 1.51808 | + | 8.60944i | 0.123950 | + | 0.702958i | ||||
\(151\) | 20.2208 | 1.64555 | 0.822773 | − | 0.568369i | \(-0.192426\pi\) | ||||
0.822773 | + | 0.568369i | \(0.192426\pi\) | |||||||
\(152\) | −1.74411 | + | 9.43932i | −0.141466 | + | 0.765630i | ||||
\(153\) | −1.16003 | −0.0937832 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.352050 | + | 0.295405i | −0.0282773 | + | 0.0237275i | ||||
\(156\) | 1.93905 | − | 0.705758i | 0.155249 | − | 0.0565059i | ||||
\(157\) | 21.5853 | + | 7.85640i | 1.72269 | + | 0.627009i | 0.998068 | − | 0.0621344i | \(-0.0197907\pi\) |
0.724625 | + | 0.689143i | \(0.242013\pi\) | |||||||
\(158\) | 13.0601 | + | 10.9587i | 1.03900 | + | 0.871829i | ||||
\(159\) | 3.96960 | − | 6.87555i | 0.314810 | − | 0.545266i | ||||
\(160\) | −0.124057 | − | 0.214873i | −0.00980755 | − | 0.0169872i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.0220259 | + | 0.124915i | −0.00173052 | + | 0.00981426i | ||||
\(163\) | 9.01257 | + | 15.6102i | 0.705919 | + | 1.22269i | 0.966359 | + | 0.257198i | \(0.0827992\pi\) |
−0.260439 | + | 0.965490i | \(0.583867\pi\) | |||||||
\(164\) | 2.17391 | − | 3.76532i | 0.169754 | − | 0.294022i | ||||
\(165\) | 0.103891 | + | 0.0871748i | 0.00808789 | + | 0.00678655i | ||||
\(166\) | −10.3290 | − | 3.75944i | −0.801685 | − | 0.291789i | ||||
\(167\) | −3.45416 | + | 1.25721i | −0.267291 | + | 0.0972860i | −0.472189 | − | 0.881497i | \(-0.656536\pi\) |
0.204898 | + | 0.978783i | \(0.434314\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.727966 | − | 4.12850i | −0.0559974 | − | 0.317577i | ||||
\(170\) | −0.0720761 | −0.00552798 | ||||||||
\(171\) | −6.19418 | + | 5.11180i | −0.473681 | + | 0.390909i | ||||
\(172\) | 1.21904 | 0.0929507 | ||||||||
\(173\) | 1.87596 | + | 10.6391i | 0.142626 | + | 0.808874i | 0.969242 | + | 0.246108i | \(0.0791517\pi\) |
−0.826616 | + | 0.562766i | \(0.809737\pi\) | |||||||
\(174\) | 7.27504 | − | 6.10448i | 0.551519 | − | 0.462780i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.20541 | + | 2.98653i | 0.618506 | + | 0.225118i | ||||
\(177\) | 11.4289 | + | 9.58997i | 0.859047 | + | 0.720826i | ||||
\(178\) | −3.35741 | + | 5.81521i | −0.251649 | + | 0.435868i | ||||
\(179\) | 1.03576 | + | 1.79399i | 0.0774165 | + | 0.134089i | 0.902135 | − | 0.431455i | \(-0.142000\pi\) |
−0.824718 | + | 0.565544i | \(0.808666\pi\) | |||||||
\(180\) | 0.0145503 | − | 0.0825189i | 0.00108452 | − | 0.00615060i | ||||
\(181\) | −0.196089 | + | 1.11208i | −0.0145752 | + | 0.0826601i | −0.991228 | − | 0.132165i | \(-0.957807\pi\) |
0.976653 | + | 0.214825i | \(0.0689182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0904205 | − | 0.156613i | 0.00668408 | − | 0.0115772i | ||||
\(184\) | 2.53091 | + | 2.12369i | 0.186582 | + | 0.156560i | ||||
\(185\) | 0.0457041 | + | 0.0166349i | 0.00336023 | + | 0.00122302i | ||||
\(186\) | 10.7403 | − | 3.90915i | 0.787518 | − | 0.286633i | ||||
\(187\) | 0.863931 | − | 0.724925i | 0.0631769 | − | 0.0530117i | ||||
\(188\) | 0.156053 | + | 0.885019i | 0.0113813 | + | 0.0645466i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.384862 | + | 0.317610i | −0.0279208 | + | 0.0230419i | ||||
\(191\) | −0.301438 | −0.0218113 | −0.0109056 | − | 0.999941i | \(-0.503471\pi\) | ||||
−0.0109056 | + | 0.999941i | \(0.503471\pi\) | |||||||
\(192\) | −0.749983 | − | 4.25337i | −0.0541254 | − | 0.306960i | ||||
\(193\) | 2.36234 | − | 1.98224i | 0.170045 | − | 0.142684i | −0.553794 | − | 0.832654i | \(-0.686820\pi\) |
0.723839 | + | 0.689969i | \(0.242376\pi\) | |||||||
\(194\) | −8.17303 | + | 2.97474i | −0.586789 | + | 0.213574i | ||||
\(195\) | −0.211150 | − | 0.0768523i | −0.0151208 | − | 0.00550351i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.9602 | + | 24.1797i | −0.994620 | + | 1.72273i | −0.407595 | + | 0.913163i | \(0.633632\pi\) |
−0.587025 | + | 0.809569i | \(0.699701\pi\) | |||||||
\(198\) | 2.68433 | + | 4.64939i | 0.190767 | + | 0.330418i | ||||
\(199\) | 0.256896 | − | 1.45693i | 0.0182108 | − | 0.103279i | −0.974348 | − | 0.225049i | \(-0.927746\pi\) |
0.992558 | + | 0.121770i | \(0.0388570\pi\) | |||||||
\(200\) | 1.91013 | − | 10.8329i | 0.135067 | − | 0.766001i | ||||
\(201\) | −4.96932 | − | 8.60712i | −0.350509 | − | 0.607099i | ||||
\(202\) | 4.05597 | − | 7.02515i | 0.285377 | − | 0.494288i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.411367 | + | 0.149725i | 0.0288014 | + | 0.0104829i | ||||
\(205\) | −0.444896 | + | 0.161929i | −0.0310729 | + | 0.0113096i | ||||
\(206\) | 3.74018 | − | 3.13838i | 0.260590 | − | 0.218661i | ||||
\(207\) | 0.479996 | + | 2.72219i | 0.0333621 | + | 0.189206i | ||||
\(208\) | −14.4676 | −1.00315 | ||||||||
\(209\) | 1.41865 | − | 7.67785i | 0.0981298 | − | 0.531088i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.78998 | − | 27.1653i | −0.329756 | − | 1.87014i | −0.473894 | − | 0.880582i | \(-0.657152\pi\) |
0.144137 | − | 0.989558i | \(-0.453959\pi\) | |||||||
\(212\) | 3.65312 | − | 3.06533i | 0.250897 | − | 0.210528i | ||||
\(213\) | −11.9186 | + | 4.33802i | −0.816650 | + | 0.297236i | ||||
\(214\) | 19.1366 | + | 6.96516i | 1.30815 | + | 0.476129i | ||||
\(215\) | −0.101689 | − | 0.0853268i | −0.00693510 | − | 0.00581924i | ||||
\(216\) | 5.73664 | − | 9.93615i | 0.390329 | − | 0.676070i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.96548 | + | 22.4894i | −0.268576 | + | 1.52317i | ||||
\(219\) | −2.09721 | + | 11.8938i | −0.141716 | + | 0.803712i | ||||
\(220\) | 0.0407312 | + | 0.0705484i | 0.00274609 | + | 0.00475637i | ||||
\(221\) | −0.934280 | + | 1.61822i | −0.0628465 | + | 0.108853i | ||||
\(222\) | −0.926626 | − | 0.777532i | −0.0621911 | − | 0.0521845i | ||||
\(223\) | −8.38245 | − | 3.05096i | −0.561331 | − | 0.204308i | 0.0457430 | − | 0.998953i | \(-0.485434\pi\) |
−0.607074 | + | 0.794646i | \(0.707657\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.05003 | − | 5.91568i | 0.470002 | − | 0.394379i | ||||
\(226\) | −0.118785 | − | 0.673664i | −0.00790147 | − | 0.0448115i | ||||
\(227\) | 25.3449 | 1.68220 | 0.841101 | − | 0.540878i | \(-0.181908\pi\) | ||||
0.841101 | + | 0.540878i | \(0.181908\pi\) | |||||||
\(228\) | 2.85633 | − | 1.01325i | 0.189165 | − | 0.0671038i | ||||
\(229\) | −24.8429 | −1.64167 | −0.820834 | − | 0.571167i | \(-0.806491\pi\) | ||||
−0.820834 | + | 0.571167i | \(0.806491\pi\) | |||||||
\(230\) | 0.0298235 | + | 0.169137i | 0.00196650 | + | 0.0111526i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.2289 | + | 4.08698i | −0.737213 | + | 0.268323i | ||||
\(233\) | −14.8648 | − | 5.41034i | −0.973825 | − | 0.354443i | −0.194389 | − | 0.980925i | \(-0.562272\pi\) |
−0.779437 | + | 0.626481i | \(0.784495\pi\) | |||||||
\(234\) | −6.81399 | − | 5.71761i | −0.445444 | − | 0.373772i | ||||
\(235\) | 0.0489296 | − | 0.0847486i | 0.00319182 | − | 0.00552839i | ||||
\(236\) | 4.48077 | + | 7.76093i | 0.291674 | + | 0.505193i | ||||
\(237\) | −1.95801 | + | 11.1044i | −0.127186 | + | 0.721310i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.00385 | − | 3.47078i | −0.129619 | − | 0.224506i | 0.793910 | − | 0.608035i | \(-0.208042\pi\) |
−0.923529 | + | 0.383529i | \(0.874709\pi\) | |||||||
\(240\) | 0.184545 | − | 0.319642i | 0.0119124 | − | 0.0206328i | ||||
\(241\) | 17.3490 | + | 14.5575i | 1.11755 | + | 0.937733i | 0.998478 | − | 0.0551533i | \(-0.0175648\pi\) |
0.119068 | + | 0.992886i | \(0.462009\pi\) | |||||||
\(242\) | 11.9103 | + | 4.33498i | 0.765621 | + | 0.278663i | ||||
\(243\) | 14.6084 | − | 5.31704i | 0.937132 | − | 0.341088i | ||||
\(244\) | 0.0832117 | − | 0.0698229i | 0.00532708 | − | 0.00446995i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.7748 | 0.750734 | ||||||||
\(247\) | 2.14211 | + | 12.7577i | 0.136299 | + | 0.811755i | ||||
\(248\) | −14.3814 | −0.913219 | ||||||||
\(249\) | −1.26239 | − | 7.15939i | −0.0800009 | − | 0.453708i | ||||
\(250\) | 0.876510 | − | 0.735480i | 0.0554354 | − | 0.0465158i | ||||
\(251\) | 25.6565 | − | 9.33821i | 1.61942 | − | 0.589422i | 0.636152 | − | 0.771563i | \(-0.280525\pi\) |
0.983272 | + | 0.182141i | \(0.0583027\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.05862 | − | 1.72739i | −0.129424 | − | 0.108600i | ||||
\(254\) | −10.0356 | + | 17.3822i | −0.629690 | + | 1.09065i | ||||
\(255\) | −0.0238349 | − | 0.0412833i | −0.00149260 | − | 0.00258526i | ||||
\(256\) | 2.44237 | − | 13.8514i | 0.152648 | − | 0.865711i | ||||
\(257\) | −2.18071 | + | 12.3674i | −0.136029 | + | 0.771459i | 0.838109 | + | 0.545503i | \(0.183662\pi\) |
−0.974138 | + | 0.225956i | \(0.927450\pi\) | |||||||
\(258\) | 1.65070 | + | 2.85910i | 0.102768 | + | 0.178000i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.103393 | − | 0.0867573i | −0.00641218 | − | 0.00538046i | ||||
\(261\) | −9.39465 | − | 3.41937i | −0.581515 | − | 0.211654i | ||||
\(262\) | 4.56698 | − | 1.66225i | 0.282149 | − | 0.102694i | ||||
\(263\) | 12.6620 | − | 10.6247i | 0.780774 | − | 0.655147i | −0.162669 | − | 0.986681i | \(-0.552010\pi\) |
0.943443 | + | 0.331533i | \(0.107566\pi\) | |||||||
\(264\) | 0.736961 | + | 4.17951i | 0.0453568 | + | 0.257231i | ||||
\(265\) | −0.519291 | −0.0318998 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.44107 | −0.271789 | ||||||||
\(268\) | −1.03665 | − | 5.87911i | −0.0633233 | − | 0.359124i | ||||
\(269\) | 22.4497 | − | 18.8376i | 1.36879 | − | 1.14855i | 0.395627 | − | 0.918411i | \(-0.370527\pi\) |
0.973158 | − | 0.230136i | \(-0.0739171\pi\) | |||||||
\(270\) | 0.560452 | − | 0.203988i | 0.0341080 | − | 0.0124143i | ||||
\(271\) | 26.1830 | + | 9.52983i | 1.59050 | + | 0.578896i | 0.977454 | − | 0.211149i | \(-0.0677205\pi\) |
0.613049 | + | 0.790045i | \(0.289943\pi\) | |||||||
\(272\) | −2.35120 | − | 1.97289i | −0.142562 | − | 0.119624i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.3601 | − | 30.0685i | −1.04876 | − | 1.81650i | ||||
\(275\) | −1.55368 | + | 8.81137i | −0.0936906 | + | 0.531346i | ||||
\(276\) | 0.181138 | − | 1.02729i | 0.0109032 | − | 0.0618354i | ||||
\(277\) | −3.20279 | − | 5.54740i | −0.192437 | − | 0.333311i | 0.753620 | − | 0.657310i | \(-0.228306\pi\) |
−0.946057 | + | 0.323999i | \(0.894972\pi\) | |||||||
\(278\) | −5.71481 | + | 9.89834i | −0.342752 | + | 0.593663i | ||||
\(279\) | −9.21719 | − | 7.73414i | −0.551819 | − | 0.463031i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.456698 | + | 0.166224i | −0.0272443 | + | 0.00991612i | −0.355606 | − | 0.934636i | \(-0.615726\pi\) |
0.328362 | + | 0.944552i | \(0.393503\pi\) | |||||||
\(282\) | −1.86439 | + | 1.56441i | −0.111023 | + | 0.0931593i | ||||
\(283\) | 4.57468 | + | 25.9443i | 0.271936 | + | 1.54223i | 0.748528 | + | 0.663103i | \(0.230761\pi\) |
−0.476592 | + | 0.879125i | \(0.658128\pi\) | |||||||
\(284\) | −7.61856 | −0.452079 | ||||||||
\(285\) | −0.309189 | − | 0.115408i | −0.0183148 | − | 0.00683616i | ||||
\(286\) | 8.64773 | 0.511351 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.97622 | − | 4.17554i | 0.293226 | − | 0.246046i | ||||
\(289\) | 15.6023 | − | 5.67876i | 0.917781 | − | 0.334045i | ||||
\(290\) | −0.583716 | − | 0.212455i | −0.0342770 | − | 0.0124758i | ||||
\(291\) | −4.40660 | − | 3.69758i | −0.258320 | − | 0.216756i | ||||
\(292\) | −3.62722 | + | 6.28254i | −0.212267 | + | 0.367658i | ||||
\(293\) | −15.7393 | − | 27.2613i | −0.919500 | − | 1.59262i | −0.800176 | − | 0.599765i | \(-0.795261\pi\) |
−0.119324 | − | 0.992855i | \(-0.538073\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.169455 | − | 0.961026i | 0.00986605 | − | 0.0559531i | ||||
\(296\) | 0.761010 | + | 1.31811i | 0.0442328 | + | 0.0766135i | ||||
\(297\) | −4.66613 | + | 8.08197i | −0.270756 | + | 0.468963i | ||||
\(298\) | 10.0468 | + | 8.43030i | 0.581998 | + | 0.488354i | ||||
\(299\) | 4.18398 | + | 1.52285i | 0.241966 | + | 0.0880684i | ||||
\(300\) | −3.26359 | + | 1.18785i | −0.188423 | + | 0.0685805i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.71195 | + | 32.3941i | 0.328686 | + | 1.86407i | ||||
\(303\) | 5.36510 | 0.308217 | ||||||||
\(304\) | −21.2483 | − | 0.173766i | −1.21867 | − | 0.00996619i | ||||
\(305\) | −0.0118285 | −0.000677300 | ||||||||
\(306\) | −0.327685 | − | 1.85839i | −0.0187325 | − | 0.106237i | ||||
\(307\) | 13.1843 | − | 11.0629i | 0.752468 | − | 0.631395i | −0.183687 | − | 0.982985i | \(-0.558803\pi\) |
0.936154 | + | 0.351589i | \(0.114359\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.03443 | + | 1.10444i | 0.172622 | + | 0.0628294i | ||||
\(310\) | −0.572690 | − | 0.480544i | −0.0325266 | − | 0.0272930i | ||||
\(311\) | −14.3737 | + | 24.8960i | −0.815058 | + | 1.41172i | 0.0942276 | + | 0.995551i | \(0.469962\pi\) |
−0.909286 | + | 0.416172i | \(0.863371\pi\) | |||||||
\(312\) | −3.51581 | − | 6.08957i | −0.199044 | − | 0.344754i | ||||
\(313\) | 1.22739 | − | 6.96090i | 0.0693764 | − | 0.393453i | −0.930270 | − | 0.366875i | \(-0.880428\pi\) |
0.999647 | − | 0.0265784i | \(-0.00846115\pi\) | |||||||
\(314\) | −6.48870 | + | 36.7992i | −0.366179 | + | 2.07670i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.38648 | + | 5.86555i | −0.190504 | + | 0.329963i | ||||
\(317\) | −4.84236 | − | 4.06322i | −0.271974 | − | 0.228213i | 0.496592 | − | 0.867984i | \(-0.334585\pi\) |
−0.768565 | + | 0.639771i | \(0.779029\pi\) | |||||||
\(318\) | 12.1361 | + | 4.41717i | 0.680557 | + | 0.247702i | ||||
\(319\) | 9.13346 | − | 3.32431i | 0.511376 | − | 0.186126i | ||||
\(320\) | −0.216406 | + | 0.181586i | −0.0120975 | + | 0.0101510i | ||||
\(321\) | 2.33885 | + | 13.2643i | 0.130542 | + | 0.740340i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.39160 | + | 2.36543i | −0.0774306 | + | 0.131616i | ||||
\(324\) | −0.0503906 | −0.00279948 | ||||||||
\(325\) | −2.57421 | − | 14.5991i | −0.142791 | − | 0.809811i | ||||
\(326\) | −22.4620 | + | 18.8479i | −1.24406 | + | 1.04389i | ||||
\(327\) | −14.1927 | + | 5.16571i | −0.784857 | + | 0.285664i | ||||
\(328\) | −13.9222 | − | 5.06728i | −0.768727 | − | 0.279794i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.110308 | + | 0.191060i | −0.00607228 | + | 0.0105175i | ||||
\(331\) | −7.82141 | − | 13.5471i | −0.429904 | − | 0.744615i | 0.566960 | − | 0.823745i | \(-0.308119\pi\) |
−0.996864 | + | 0.0791297i | \(0.974786\pi\) | |||||||
\(332\) | 0.758277 | − | 4.30041i | 0.0416159 | − | 0.236015i | ||||
\(333\) | −0.221123 | + | 1.25405i | −0.0121175 | + | 0.0687217i | ||||
\(334\) | −2.98980 | − | 5.17849i | −0.163595 | − | 0.283354i | ||||
\(335\) | −0.325036 | + | 0.562979i | −0.0177586 | + | 0.0307588i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.04290 | − | 2.56341i | −0.383651 | − | 0.139638i | 0.142992 | − | 0.989724i | \(-0.454328\pi\) |
−0.526644 | + | 0.850086i | \(0.676550\pi\) | |||||||
\(338\) | 6.40829 | − | 2.33243i | 0.348565 | − | 0.126867i | ||||
\(339\) | 0.346576 | − | 0.290812i | 0.0188234 | − | 0.0157947i | ||||
\(340\) | −0.00497219 | − | 0.0281987i | −0.000269655 | − | 0.00152929i | ||||
\(341\) | 11.6977 | 0.633464 | ||||||||
\(342\) | −9.93892 | − | 8.47921i | −0.537435 | − | 0.458503i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.721338 | − | 4.09091i | −0.0388920 | − | 0.220567i | ||||
\(345\) | −0.0870152 | + | 0.0730144i | −0.00468474 | + | 0.00393096i | ||||
\(346\) | −16.5141 | + | 6.01062i | −0.887801 | + | 0.323133i | ||||
\(347\) | −7.98342 | − | 2.90573i | −0.428572 | − | 0.155988i | 0.118723 | − | 0.992927i | \(-0.462120\pi\) |
−0.547295 | + | 0.836940i | \(0.684342\pi\) | |||||||
\(348\) | 2.89016 | + | 2.42513i | 0.154929 | + | 0.130001i | ||||
\(349\) | 0.310773 | − | 0.538275i | 0.0166353 | − | 0.0288132i | −0.857588 | − | 0.514337i | \(-0.828038\pi\) |
0.874223 | + | 0.485524i | \(0.161371\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.68496 | − | 15.2272i | 0.143313 | − | 0.812767i | ||||
\(352\) | −1.09666 | + | 6.21944i | −0.0584520 | + | 0.331497i | ||||
\(353\) | −13.1627 | − | 22.7985i | −0.700580 | − | 1.21344i | −0.968263 | − | 0.249933i | \(-0.919591\pi\) |
0.267683 | − | 0.963507i | \(-0.413742\pi\) | |||||||
\(354\) | −12.1349 | + | 21.0182i | −0.644961 | + | 1.11711i | ||||
\(355\) | 0.635518 | + | 0.533263i | 0.0337298 | + | 0.0283027i | ||||
\(356\) | −2.50672 | − | 0.912373i | −0.132856 | − | 0.0483557i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.58142 | + | 2.16607i | −0.136433 | + | 0.114480i | ||||
\(359\) | −1.51662 | − | 8.60116i | −0.0800440 | − | 0.453952i | −0.998316 | − | 0.0580028i | \(-0.981527\pi\) |
0.918272 | − | 0.395949i | \(-0.129584\pi\) | |||||||
\(360\) | −0.285531 | −0.0150488 | ||||||||
\(361\) | 2.99286 | + | 18.7628i | 0.157519 | + | 0.987516i | ||||
\(362\) | −1.83696 | −0.0965484 | ||||||||
\(363\) | 1.45566 | + | 8.25543i | 0.0764021 | + | 0.433298i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.742320 | − | 0.270182i | 0.0388548 | − | 0.0141420i | ||||
\(366\) | 0.276438 | + | 0.100615i | 0.0144497 | + | 0.00525925i | ||||
\(367\) | −6.48617 | − | 5.44254i | −0.338575 | − | 0.284098i | 0.457608 | − | 0.889154i | \(-0.348706\pi\) |
−0.796183 | + | 0.605056i | \(0.793151\pi\) | |||||||
\(368\) | −3.65681 | + | 6.33378i | −0.190624 | + | 0.330171i | ||||
\(369\) | −6.19780 | − | 10.7349i | −0.322644 | − | 0.558837i | ||||
\(370\) | −0.0137390 | + | 0.0779178i | −0.000714257 | + | 0.00405075i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.27032 | + | 3.93231i | 0.117711 | + | 0.203881i | ||||
\(373\) | 11.8749 | − | 20.5679i | 0.614859 | − | 1.06497i | −0.375550 | − | 0.926802i | \(-0.622546\pi\) |
0.990409 | − | 0.138165i | \(-0.0441205\pi\) | |||||||
\(374\) | 1.40538 | + | 1.17926i | 0.0726707 | + | 0.0609779i | ||||
\(375\) | 0.711118 | + | 0.258826i | 0.0367220 | + | 0.0133657i | ||||
\(376\) | 2.87765 | − | 1.04738i | 0.148404 | − | 0.0540145i | ||||
\(377\) | −12.3363 | + | 10.3514i | −0.635352 | + | 0.533124i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.7476 | 0.962999 | 0.481500 | − | 0.876446i | \(-0.340092\pi\) | ||||
0.481500 | + | 0.876446i | \(0.340092\pi\) | |||||||
\(380\) | −0.150810 | − | 0.128661i | −0.00773639 | − | 0.00660016i | ||||
\(381\) | −13.2747 | −0.680086 | ||||||||
\(382\) | −0.0851498 | − | 0.482908i | −0.00435664 | − | 0.0247077i | ||||
\(383\) | 10.1179 | − | 8.48991i | 0.516999 | − | 0.433814i | −0.346585 | − | 0.938019i | \(-0.612659\pi\) |
0.863584 | + | 0.504205i | \(0.168214\pi\) | |||||||
\(384\) | 13.7312 | − | 4.99774i | 0.700716 | − | 0.255040i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.84288 | + | 3.22456i | 0.195598 | + | 0.164126i | ||||
\(387\) | 1.73773 | − | 3.00984i | 0.0883339 | − | 0.152999i | ||||
\(388\) | −1.72764 | − | 2.99236i | −0.0877077 | − | 0.151914i | ||||
\(389\) | 1.66371 | − | 9.43539i | 0.0843537 | − | 0.478393i | −0.913141 | − | 0.407645i | \(-0.866350\pi\) |
0.997494 | − | 0.0707485i | \(-0.0225388\pi\) | |||||||
\(390\) | 0.0634733 | − | 0.359975i | 0.00321409 | − | 0.0182280i | ||||
\(391\) | 0.472295 | + | 0.818038i | 0.0238850 | + | 0.0413700i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.46235 | + | 2.06616i | 0.124209 | + | 0.104224i | ||||
\(394\) | −42.6797 | − | 15.5341i | −2.15017 | − | 0.782599i | ||||
\(395\) | 0.693051 | − | 0.252250i | 0.0348712 | − | 0.0126921i | ||||
\(396\) | −1.63383 | + | 1.37094i | −0.0821028 | + | 0.0688924i | ||||
\(397\) | −2.89344 | − | 16.4095i | −0.145218 | − | 0.823571i | −0.967192 | − | 0.254046i | \(-0.918238\pi\) |
0.821974 | − | 0.569524i | \(-0.192873\pi\) | |||||||
\(398\) | 2.40659 | 0.120631 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24.3502 | 1.21751 | ||||||||
\(401\) | 3.48930 | + | 19.7888i | 0.174247 | + | 0.988206i | 0.939009 | + | 0.343893i | \(0.111746\pi\) |
−0.764761 | + | 0.644314i | \(0.777143\pi\) | |||||||
\(402\) | 12.3850 | − | 10.3923i | 0.617709 | − | 0.518319i | ||||
\(403\) | −18.2124 | + | 6.62877i | −0.907224 | + | 0.330202i | ||||
\(404\) | 3.02829 | + | 1.10221i | 0.150663 | + | 0.0548368i | ||||
\(405\) | 0.00420344 | + | 0.00352710i | 0.000208871 | + | 0.000175263i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.618998 | − | 1.07214i | −0.0306826 | − | 0.0531438i | ||||
\(408\) | 0.259039 | − | 1.46908i | 0.0128243 | − | 0.0727304i | ||||
\(409\) | 1.82074 | − | 10.3259i | 0.0900298 | − | 0.510585i | −0.906128 | − | 0.423004i | \(-0.860975\pi\) |
0.996157 | − | 0.0875802i | \(-0.0279134\pi\) | |||||||
\(410\) | −0.385086 | − | 0.666989i | −0.0190181 | − | 0.0329402i | ||||
\(411\) | 11.4816 | − | 19.8868i | 0.566348 | − | 0.980943i | ||||
\(412\) | 1.48586 | + | 1.24679i | 0.0732031 | + | 0.0614247i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.22541 | + | 1.53792i | −0.207668 | + | 0.0755849i | ||||
\(415\) | −0.364261 | + | 0.305651i | −0.0178809 | + | 0.0150038i | ||||
\(416\) | −1.81699 | − | 10.3047i | −0.0890852 | − | 0.505227i | ||||
\(417\) | −7.55935 | −0.370183 | ||||||||
\(418\) | 12.7008 | + | 0.103866i | 0.621215 | + | 0.00508023i | ||||
\(419\) | 13.0830 | 0.639145 | 0.319573 | − | 0.947562i | \(-0.396461\pi\) | ||||
0.319573 | + | 0.947562i | \(0.396461\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.1411 | − | 15.2222i | 0.884144 | − | 0.741885i | −0.0828825 | − | 0.996559i | \(-0.526413\pi\) |
0.967027 | + | 0.254674i | \(0.0819682\pi\) | |||||||
\(422\) | 42.1663 | − | 15.3473i | 2.05262 | − | 0.747093i | ||||
\(423\) | 2.40759 | + | 0.876291i | 0.117061 | + | 0.0426067i | ||||
\(424\) | −12.4485 | − | 10.4455i | −0.604551 | − | 0.507278i | ||||
\(425\) | 1.57247 | − | 2.72360i | 0.0762760 | − | 0.132114i | ||||
\(426\) | −10.3163 | − | 17.8684i | −0.499828 | − | 0.865727i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.40487 | + | 7.96741i | −0.0679069 | + | 0.385119i | ||||
\(429\) | 2.85973 | + | 4.95319i | 0.138069 | + | 0.239142i | ||||
\(430\) | 0.107970 | − | 0.187010i | 0.00520678 | − | 0.00901841i | ||||
\(431\) | −5.65367 | − | 4.74399i | −0.272328 | − | 0.228510i | 0.496388 | − | 0.868101i | \(-0.334659\pi\) |
−0.768716 | + | 0.639591i | \(0.779104\pi\) | |||||||
\(432\) | 23.8662 | + | 8.68657i | 1.14826 | + | 0.417933i | ||||
\(433\) | −32.5494 | + | 11.8470i | −1.56423 | + | 0.569331i | −0.971700 | − | 0.236220i | \(-0.924091\pi\) |
−0.592526 | + | 0.805551i | \(0.701869\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0713409 | − | 0.404594i | −0.00342053 | − | 0.0193988i | ||||
\(436\) | −9.07218 | −0.434479 | ||||||||
\(437\) | 6.12666 | + | 2.28683i | 0.293078 | + | 0.109394i | ||||
\(438\) | −19.6466 | −0.938749 | ||||||||
\(439\) | −5.60590 | − | 31.7926i | −0.267555 | − | 1.51738i | −0.761659 | − | 0.647978i | \(-0.775615\pi\) |
0.494104 | − | 0.869403i | \(-0.335496\pi\) | |||||||
\(440\) | 0.212649 | − | 0.178433i | 0.0101376 | − | 0.00850647i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.85633 | − | 1.03962i | −0.135862 | − | 0.0494496i | ||||
\(443\) | −12.6732 | − | 10.6341i | −0.602121 | − | 0.505239i | 0.290006 | − | 0.957025i | \(-0.406343\pi\) |
−0.892127 | + | 0.451786i | \(0.850787\pi\) | |||||||
\(444\) | 0.240274 | − | 0.416167i | 0.0114029 | − | 0.0197504i | ||||
\(445\) | 0.145242 | + | 0.251566i | 0.00688512 | + | 0.0119254i | ||||
\(446\) | 2.51983 | − | 14.2907i | 0.119317 | − | 0.676682i | ||||
\(447\) | −1.50626 | + | 8.54240i | −0.0712434 | + | 0.404042i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.1680 | + | 31.4678i | −0.857399 | + | 1.48506i | 0.0170021 | + | 0.999855i | \(0.494588\pi\) |
−0.874401 | + | 0.485204i | \(0.838746\pi\) | |||||||
\(450\) | 11.4685 | + | 9.62322i | 0.540631 | + | 0.453643i | ||||
\(451\) | 11.3242 | + | 4.12168i | 0.533236 | + | 0.194082i | ||||
\(452\) | 0.255367 | − | 0.0929458i | 0.0120114 | − | 0.00437180i | ||||
\(453\) | −16.6656 | + | 13.9841i | −0.783018 | + | 0.657030i | ||||
\(454\) | 7.15940 | + | 40.6030i | 0.336007 | + | 1.90559i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.09048 | − | 8.98588i | −0.238383 | − | 0.420802i | ||||
\(457\) | 26.6017 | 1.24438 | 0.622188 | − | 0.782868i | \(-0.286244\pi\) | ||||
0.622188 | + | 0.782868i | \(0.286244\pi\) | |||||||
\(458\) | −7.01760 | − | 39.7988i | −0.327911 | − | 1.85968i | ||||
\(459\) | 2.51282 | − | 2.10851i | 0.117288 | − | 0.0984166i | ||||
\(460\) | −0.0641151 | + | 0.0233360i | −0.00298938 | + | 0.00108805i | ||||
\(461\) | −0.0577102 | − | 0.0210048i | −0.00268783 | − | 0.000978292i | 0.340676 | − | 0.940181i | \(-0.389344\pi\) |
−0.343364 | + | 0.939203i | \(0.611566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.51380 | − | 11.2822i | 0.302722 | − | 0.524329i | −0.674030 | − | 0.738704i | \(-0.735438\pi\) |
0.976751 | + | 0.214375i | \(0.0687714\pi\) | |||||||
\(464\) | −13.2260 | − | 22.9082i | −0.614003 | − | 1.06349i | ||||
\(465\) | 0.0858595 | − | 0.486933i | 0.00398164 | − | 0.0225810i | ||||
\(466\) | 4.46847 | − | 25.3420i | 0.206998 | − | 1.17394i | ||||
\(467\) | 7.77568 | + | 13.4679i | 0.359815 | + | 0.623219i | 0.987930 | − | 0.154902i | \(-0.0495063\pi\) |
−0.628114 | + | 0.778121i | \(0.716173\pi\) | |||||||
\(468\) | 1.76687 | − | 3.06030i | 0.0816734 | − | 0.141462i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.149590 | + | 0.0544464i | 0.00690008 | + | 0.00251142i | ||||
\(471\) | −23.2234 | + | 8.45263i | −1.07008 | + | 0.389477i | ||||
\(472\) | 23.3931 | − | 19.6292i | 1.07676 | − | 0.903506i | ||||
\(473\) | 0.586729 | + | 3.32751i | 0.0269778 | + | 0.152999i | ||||
\(474\) | −18.3426 | −0.842503 | ||||||||
\(475\) | −3.60535 | − | 21.4723i | −0.165425 | − | 0.985218i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.36089 | − | 13.3893i | −0.108098 | − | 0.613053i | ||||
\(478\) | 4.99420 | − | 4.19063i | 0.228429 | − | 0.191675i | ||||
\(479\) | −28.2468 | + | 10.2810i | −1.29063 | + | 0.469751i | −0.893934 | − | 0.448199i | \(-0.852066\pi\) |
−0.396696 | + | 0.917950i | \(0.629843\pi\) | |||||||
\(480\) | 0.250845 | + | 0.0912999i | 0.0114494 | + | 0.00416725i | ||||
\(481\) | 1.57128 | + | 1.31846i | 0.0716444 | + | 0.0601168i | ||||
\(482\) | −18.4207 | + | 31.9056i | −0.839039 | + | 1.45326i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.874363 | + | 4.95876i | −0.0397438 | + | 0.225398i | ||||
\(485\) | −0.0653363 | + | 0.370541i | −0.00296677 | + | 0.0168254i | ||||
\(486\) | 12.6446 | + | 21.9010i | 0.573569 | + | 0.993451i | ||||
\(487\) | −6.20455 | + | 10.7466i | −0.281155 | + | 0.486975i | −0.971669 | − | 0.236344i | \(-0.924051\pi\) |
0.690515 | + | 0.723319i | \(0.257384\pi\) | |||||||
\(488\) | −0.283554 | − | 0.237930i | −0.0128359 | − | 0.0107706i | ||||
\(489\) | −18.2236 | − | 6.63283i | −0.824097 | − | 0.299947i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.3999 | − | 26.3477i | 1.41706 | − | 1.18905i | 0.464165 | − | 0.885749i | \(-0.346355\pi\) |
0.952894 | − | 0.303304i | \(-0.0980898\pi\) | |||||||
\(492\) | 0.812288 | + | 4.60672i | 0.0366208 | + | 0.207687i | ||||
\(493\) | −3.41641 | −0.153868 | ||||||||
\(494\) | −19.8330 | + | 7.03549i | −0.892329 | + | 0.316542i | ||||
\(495\) | 0.232248 | 0.0104388 | ||||||||
\(496\) | −5.52815 | − | 31.3517i | −0.248221 | − | 1.40773i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 11.1129 | − | 4.04475i | 0.497979 | − | 0.181250i | ||||
\(499\) | −6.97547 | − | 2.53886i | −0.312265 | − | 0.113655i | 0.181134 | − | 0.983459i | \(-0.442023\pi\) |
−0.493399 | + | 0.869803i | \(0.664246\pi\) | |||||||
\(500\) | 0.348212 | + | 0.292184i | 0.0155725 | + | 0.0130669i | ||||
\(501\) | 1.97740 | − | 3.42496i | 0.0883439 | − | 0.153016i | ||||
\(502\) | 22.2074 | + | 38.4643i | 0.991164 | + | 1.71675i | ||||
\(503\) | −3.81927 | + | 21.6602i | −0.170293 | + | 0.965779i | 0.773145 | + | 0.634229i | \(0.218682\pi\) |
−0.943438 | + | 0.331549i | \(0.892429\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.175462 | − | 0.303908i | −0.00780794 | − | 0.0135237i | ||||
\(506\) | 2.18579 | − | 3.78590i | 0.0971701 | − | 0.168304i | ||||
\(507\) | 3.45512 | + | 2.89919i | 0.153447 | + | 0.128757i | ||||
\(508\) | −7.49282 | − | 2.72716i | −0.332440 | − | 0.120998i | ||||
\(509\) | −3.22212 | + | 1.17276i | −0.142818 | + | 0.0519815i | −0.412440 | − | 0.910985i | \(-0.635323\pi\) |
0.269622 | + | 0.962966i | \(0.413101\pi\) | |||||||
\(510\) | 0.0594037 | − | 0.0498456i | 0.00263044 | − | 0.00220720i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −4.28328 | −0.189296 | ||||||||
\(513\) | 4.12625 | − | 22.3317i | 0.182179 | − | 0.985967i | ||||
\(514\) | −20.4288 | −0.901077 | ||||||||
\(515\) | −0.0366771 | − | 0.208006i | −0.00161619 | − | 0.00916585i | ||||
\(516\) | −1.00471 | + | 0.843049i | −0.0442298 | + | 0.0371132i | ||||
\(517\) | −2.34065 | + | 0.851929i | −0.102942 | + | 0.0374678i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.90378 | − | 7.47116i | −0.390833 | − | 0.327948i | ||||
\(520\) | −0.229964 | + | 0.398310i | −0.0100846 | + | 0.0174670i | ||||
\(521\) | −6.37820 | − | 11.0474i | −0.279434 | − | 0.483994i | 0.691810 | − | 0.722079i | \(-0.256814\pi\) |
−0.971244 | + | 0.238085i | \(0.923480\pi\) | |||||||
\(522\) | 2.82410 | − | 16.0163i | 0.123608 | − | 0.701014i | ||||
\(523\) | 3.26971 | − | 18.5435i | 0.142975 | − | 0.810849i | −0.825997 | − | 0.563675i | \(-0.809387\pi\) |
0.968971 | − | 0.247174i | \(-0.0795019\pi\) | |||||||
\(524\) | 0.965384 | + | 1.67209i | 0.0421730 | + | 0.0730457i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.5977 | + | 17.2835i | 0.898103 | + | 0.753597i | ||||
\(527\) | −3.86372 | − | 1.40628i | −0.168306 | − | 0.0612585i | ||||
\(528\) | −8.82813 | + | 3.21318i | −0.384195 | + | 0.139836i | ||||
\(529\) | −15.8948 | + | 13.3373i | −0.691078 | + | 0.579883i | ||||
\(530\) | −0.146689 | − | 0.831913i | −0.00637175 | − | 0.0361360i | ||||
\(531\) | 25.5493 | 1.10874 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.9666 | −0.864849 | ||||||||
\(534\) | −1.25451 | − | 7.11466i | −0.0542878 | − | 0.307882i | ||||
\(535\) | 0.674871 | − | 0.566284i | 0.0291772 | − | 0.0244826i | ||||
\(536\) | −19.1160 | + | 6.95767i | −0.825687 | + | 0.300526i | ||||
\(537\) | −2.09433 | − | 0.762272i | −0.0903768 | − | 0.0328945i | ||||
\(538\) | 36.5197 | + | 30.6437i | 1.57448 | + | 1.32114i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.118470 | + | 0.205196i | 0.00509814 | + | 0.00883024i | ||||
\(541\) | −5.35002 | + | 30.3415i | −0.230015 | + | 1.30448i | 0.622846 | + | 0.782345i | \(0.285976\pi\) |
−0.852861 | + | 0.522138i | \(0.825135\pi\) | |||||||
\(542\) | −7.87081 | + | 44.6376i | −0.338080 | + | 1.91735i | ||||
\(543\) | −0.607466 | − | 1.05216i | −0.0260689 | − | 0.0451526i | ||||
\(544\) | 1.10992 | − | 1.92243i | 0.0475873 | − | 0.0824237i | ||||
\(545\) | 0.756775 | + | 0.635009i | 0.0324167 | + | 0.0272008i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.70626 | + | 3.53279i | −0.415010 | + | 0.151051i | −0.541082 | − | 0.840970i | \(-0.681985\pi\) |
0.126072 | + | 0.992021i | \(0.459763\pi\) | |||||||
\(548\) | 10.5663 | − | 8.86615i | 0.451368 | − | 0.378743i | ||||
\(549\) | −0.0537770 | − | 0.304984i | −0.00229515 | − | 0.0130164i | ||||
\(550\) | −14.5548 | −0.620621 | ||||||||
\(551\) | −18.2425 | + | 15.0548i | −0.777155 | + | 0.641354i | ||||
\(552\) | −3.55461 | −0.151294 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.98230 | − | 6.69794i | 0.339135 | − | 0.284568i | ||||
\(555\) | −0.0491727 | + | 0.0178974i | −0.00208726 | + | 0.000759702i | ||||
\(556\) | −4.26681 | − | 1.55299i | −0.180953 | − | 0.0658616i | ||||
\(557\) | −15.9403 | − | 13.3755i | −0.675413 | − | 0.566739i | 0.239249 | − | 0.970958i | \(-0.423099\pi\) |
−0.914662 | + | 0.404220i | \(0.867543\pi\) | |||||||
\(558\) | 9.78657 | − | 16.9508i | 0.414298 | − | 0.717586i | ||||
\(559\) | −2.79911 | − | 4.84819i | −0.118390 | − | 0.205057i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.210700 | + | 1.19494i | −0.00889575 | + | 0.0504503i | ||||
\(562\) | −0.395302 | − | 0.684683i | −0.0166748 | − | 0.0288816i | ||||
\(563\) | −8.57899 | + | 14.8592i | −0.361561 | + | 0.626242i | −0.988218 | − | 0.153053i | \(-0.951089\pi\) |
0.626657 | + | 0.779295i | \(0.284423\pi\) | |||||||
\(564\) | −0.740667 | − | 0.621494i | −0.0311877 | − | 0.0261696i | ||||
\(565\) | −0.0278077 | − | 0.0101212i | −0.00116988 | − | 0.000425801i | ||||
\(566\) | −40.2709 | + | 14.6574i | −1.69271 | + | 0.616097i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.50812 | + | 25.5668i | 0.189156 | + | 1.07276i | ||||
\(569\) | −23.7998 | −0.997738 | −0.498869 | − | 0.866678i | \(-0.666251\pi\) | ||||
−0.498869 | + | 0.866678i | \(0.666251\pi\) | |||||||
\(570\) | 0.0975457 | − | 0.527927i | 0.00408574 | − | 0.0221124i | ||||
\(571\) | −10.6996 | −0.447766 | −0.223883 | − | 0.974616i | \(-0.571873\pi\) | ||||
−0.223883 | + | 0.974616i | \(0.571873\pi\) | |||||||
\(572\) | 0.596566 | + | 3.38329i | 0.0249437 | + | 0.141463i | ||||
\(573\) | 0.248439 | − | 0.208465i | 0.0103787 | − | 0.00870876i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.04199 | − | 2.56308i | −0.293671 | − | 0.106888i | ||||
\(576\) | −5.66584 | − | 4.75421i | −0.236077 | − | 0.198092i | ||||
\(577\) | −10.8671 | + | 18.8224i | −0.452404 | + | 0.783586i | −0.998535 | − | 0.0541136i | \(-0.982767\pi\) |
0.546131 | + | 0.837700i | \(0.316100\pi\) | |||||||
\(578\) | 13.5048 | + | 23.3910i | 0.561725 | + | 0.972936i | ||||
\(579\) | −0.576138 | + | 3.26744i | −0.0239435 | + | 0.135790i | ||||
\(580\) | 0.0428521 | − | 0.243026i | 0.00177934 | − | 0.0100911i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.67881 | − | 8.10394i | 0.193943 | − | 0.335919i | ||||
\(583\) | 10.1255 | + | 8.49627i | 0.419354 | + | 0.351879i | ||||
\(584\) | 23.2296 | + | 8.45489i | 0.961248 | + | 0.349866i | ||||
\(585\) | −0.361593 | + | 0.131609i | −0.0149500 | + | 0.00544137i | ||||
\(586\) | 39.2270 | − | 32.9154i | 1.62045 | − | 1.35972i | ||||
\(587\) | −4.64746 | − | 26.3570i | −0.191821 | − | 1.08787i | −0.916873 | − | 0.399178i | \(-0.869296\pi\) |
0.725052 | − | 0.688694i | \(-0.241816\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.8279 | + | 9.51682i | −1.10542 | + | 0.392134i | ||||
\(590\) | 1.58745 | 0.0653542 | ||||||||
\(591\) | −5.21625 | − | 29.5828i | −0.214568 | − | 1.21688i | ||||
\(592\) | −2.58097 | + | 2.16569i | −0.106077 | + | 0.0890094i | ||||
\(593\) | −31.7666 | + | 11.5621i | −1.30450 | + | 0.474798i | −0.898459 | − | 0.439058i | \(-0.855312\pi\) |
−0.406038 | + | 0.913856i | \(0.633090\pi\) | |||||||
\(594\) | −14.2655 | − | 5.19223i | −0.585322 | − | 0.213040i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.60514 | + | 4.51224i | −0.106711 | + | 0.184829i | ||||
\(597\) | 0.795838 | + | 1.37843i | 0.0325715 | + | 0.0564155i | ||||
\(598\) | −1.25774 | + | 7.13298i | −0.0514327 | + | 0.291689i | ||||
\(599\) | 0.481938 | − | 2.73321i | 0.0196915 | − | 0.111676i | −0.973378 | − | 0.229207i | \(-0.926387\pi\) |
0.993069 | + | 0.117531i | \(0.0374979\pi\) | |||||||
\(600\) | 5.91741 | + | 10.2493i | 0.241577 | + | 0.418424i | ||||
\(601\) | 18.6256 | − | 32.2605i | 0.759755 | − | 1.31594i | −0.183220 | − | 0.983072i | \(-0.558652\pi\) |
0.942975 | − | 0.332863i | \(-0.108015\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.9934 | − | 5.82114i | −0.651304 | − | 0.237055i | ||||
\(604\) | −12.2797 | + | 4.46943i | −0.499652 | + | 0.181859i | ||||
\(605\) | 0.420026 | − | 0.352444i | 0.0170765 | − | 0.0143289i | ||||
\(606\) | 1.51553 | + | 8.59498i | 0.0615641 | + | 0.349147i | ||||
\(607\) | 38.2873 | 1.55403 | 0.777016 | − | 0.629481i | \(-0.216732\pi\) | ||||
0.777016 | + | 0.629481i | \(0.216732\pi\) | |||||||
\(608\) | −2.54481 | − | 15.1561i | −0.103206 | − | 0.614661i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.00334131 | − | 0.0189495i | −0.000135286 | − | 0.000767244i | ||||
\(611\) | 3.16146 | − | 2.65278i | 0.127899 | − | 0.107320i | ||||
\(612\) | 0.704463 | − | 0.256404i | 0.0284762 | − | 0.0103645i | ||||
\(613\) | −17.9570 | − | 6.53583i | −0.725278 | − | 0.263980i | −0.0471132 | − | 0.998890i | \(-0.515002\pi\) |
−0.678165 | + | 0.734910i | \(0.737224\pi\) | |||||||
\(614\) | 21.4473 | + | 17.9964i | 0.865543 | + | 0.726277i | ||||
\(615\) | 0.254689 | − | 0.441135i | 0.0102701 | − | 0.0177883i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.242442 | + | 1.37496i | −0.00976036 | + | 0.0553538i | −0.989299 | − | 0.145903i | \(-0.953391\pi\) |
0.979539 | + | 0.201256i | \(0.0645025\pi\) | |||||||
\(618\) | −0.912172 | + | 5.17318i | −0.0366929 | + | 0.208096i | ||||
\(619\) | −18.1490 | − | 31.4350i | −0.729469 | − | 1.26348i | −0.957108 | − | 0.289732i | \(-0.906434\pi\) |
0.227638 | − | 0.973746i | \(-0.426900\pi\) | |||||||
\(620\) | 0.148498 | − | 0.257207i | 0.00596384 | − | 0.0103297i | ||||
\(621\) | −5.98768 | − | 5.02426i | −0.240277 | − | 0.201616i | ||||
\(622\) | −43.9441 | − | 15.9943i | −1.76200 | − | 0.641314i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.9239 | − | 10.0053i | 0.477338 | − | 0.400535i | ||||
\(625\) | 4.32831 | + | 24.5471i | 0.173132 | + | 0.981882i | ||||
\(626\) | 11.4982 | 0.459560 | ||||||||
\(627\) | 4.14054 | + | 7.30902i | 0.165357 | + | 0.291894i | ||||
\(628\) | −14.8448 | −0.592371 | ||||||||
\(629\) | 0.0755631 | + | 0.428540i | 0.00301290 | + | 0.0170870i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0984 | − | 5.49536i | 0.601057 | − | 0.218767i | −0.0235288 | − | 0.999723i | \(-0.507490\pi\) |
0.624586 | + | 0.780956i | \(0.285268\pi\) | |||||||
\(632\) | 21.6878 | + | 7.89372i | 0.862695 | + | 0.313995i | ||||
\(633\) | 22.7345 | + | 19.0765i | 0.903617 | + | 0.758225i | ||||
\(634\) | 5.14148 | − | 8.90531i | 0.204194 | − | 0.353675i | ||||
\(635\) | 0.434141 | + | 0.751954i | 0.0172284 | + | 0.0298404i | ||||
\(636\) | −0.890940 | + | 5.05277i | −0.0353281 | + | 0.200356i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.90561 | + | 13.6929i | 0.312986 | + | 0.542108i | ||||
\(639\) | −10.8602 | + | 18.8105i | −0.429624 | + | 0.744131i | ||||
\(640\) | −0.732166 | − | 0.614361i | −0.0289414 | − | 0.0242847i | ||||
\(641\) | 36.5569 | + | 13.3056i | 1.44391 | + | 0.525540i | 0.940883 | − | 0.338731i | \(-0.109998\pi\) |
0.503026 | + | 0.864271i | \(0.332220\pi\) | |||||||
\(642\) | −20.5889 | + | 7.49376i | −0.812580 | + | 0.295755i | ||||
\(643\) | 12.2408 | − | 10.2712i | 0.482729 | − | 0.405058i | −0.368683 | − | 0.929555i | \(-0.620191\pi\) |
0.851412 | + | 0.524498i | \(0.175747\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.142819 | 0.00562350 | ||||||||
\(646\) | −4.18256 | − | 1.56118i | −0.164561 | − | 0.0614237i | ||||
\(647\) | −1.82497 | −0.0717468 | −0.0358734 | − | 0.999356i | \(-0.511421\pi\) | ||||
−0.0358734 | + | 0.999356i | \(0.511421\pi\) | |||||||
\(648\) | 0.0298175 | + | 0.169104i | 0.00117134 | + | 0.00664302i | ||||
\(649\) | −19.0278 | + | 15.9662i | −0.746905 | + | 0.626727i | ||||
\(650\) | 22.6608 | − | 8.24785i | 0.888829 | − | 0.323507i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.92349 | − | 7.48769i | −0.349471 | − | 0.293241i | ||||
\(653\) | −10.8941 | + | 18.8692i | −0.426320 | + | 0.738407i | −0.996543 | − | 0.0830827i | \(-0.973523\pi\) |
0.570223 | + | 0.821490i | \(0.306857\pi\) | |||||||
\(654\) | −12.2847 | − | 21.2777i | −0.480369 | − | 0.832024i | ||||
\(655\) | 0.0365091 | − | 0.207053i | 0.00142653 | − | 0.00809024i | ||||
\(656\) | 5.69511 | − | 32.2986i | 0.222357 | − | 1.26105i | ||||
\(657\) | 10.3412 | + | 17.9115i | 0.403448 | + | 0.698792i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.3023 | + | 11.1620i | 0.518186 | + | 0.434810i | 0.863999 | − | 0.503494i | \(-0.167952\pi\) |
−0.345813 | + | 0.938303i | \(0.612397\pi\) | |||||||
\(660\) | −0.0823590 | − | 0.0299762i | −0.00320582 | − | 0.00116682i | ||||
\(661\) | −28.0558 | + | 10.2115i | −1.09124 | + | 0.397180i | −0.824082 | − | 0.566471i | \(-0.808308\pi\) |
−0.267162 | + | 0.963652i | \(0.586086\pi\) | |||||||
\(662\) | 19.4933 | − | 16.3568i | 0.757628 | − | 0.635725i | ||||
\(663\) | −0.349097 | − | 1.97983i | −0.0135578 | − | 0.0768900i | ||||
\(664\) | −14.8802 | −0.577465 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.07148 | −0.0802681 | ||||||||
\(667\) | 1.41364 | + | 8.01713i | 0.0547362 | + | 0.310425i | ||||
\(668\) | 1.81975 | − | 1.52696i | 0.0704084 | − | 0.0590797i | ||||
\(669\) | 9.01861 | − | 3.28250i | 0.348679 | − | 0.126909i | ||||
\(670\) | −0.993717 | − | 0.361683i | −0.0383906 | − | 0.0139731i | ||||
\(671\) | 0.230640 | + | 0.193530i | 0.00890376 | + | 0.00747114i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.12496 | + | 8.87669i | 0.197553 | + | 0.342171i | 0.947734 | − | 0.319061i | \(-0.103367\pi\) |
−0.750182 | + | 0.661232i | \(0.770034\pi\) | |||||||
\(674\) | 2.11715 | − | 12.0070i | 0.0815496 | − | 0.462491i | ||||
\(675\) | −4.51902 | + | 25.6286i | −0.173937 | + | 0.986446i | ||||
\(676\) | 1.35460 | + | 2.34624i | 0.0521002 | + | 0.0902401i | ||||
\(677\) | −13.9448 | + | 24.1531i | −0.535943 | + | 0.928280i | 0.463174 | + | 0.886267i | \(0.346710\pi\) |
−0.999117 | + | 0.0420130i | \(0.986623\pi\) | |||||||
\(678\) | 0.563786 | + | 0.473073i | 0.0216521 | + | 0.0181682i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.0916885 | + | 0.0333719i | −0.00351609 | + | 0.00127975i | ||||
\(681\) | −20.8888 | + | 17.5278i | −0.800460 | + | 0.671666i | ||||
\(682\) | 3.30434 | + | 18.7399i | 0.126530 | + | 0.717587i | ||||
\(683\) | 12.8899 | 0.493220 | 0.246610 | − | 0.969115i | \(-0.420683\pi\) | ||||
0.246610 | + | 0.969115i | \(0.420683\pi\) | |||||||
\(684\) | 2.63172 | − | 4.47339i | 0.100626 | − | 0.171044i | ||||
\(685\) | −1.50199 | −0.0573883 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.4751 | − | 17.1806i | 0.781172 | − | 0.655481i | ||||
\(688\) | 8.64099 | − | 3.14506i | 0.329435 | − | 0.119904i | ||||
\(689\) | −20.5792 | − | 7.49021i | −0.784005 | − | 0.285354i | ||||
\(690\) | −0.141550 | − | 0.118775i | −0.00538873 | − | 0.00452168i | ||||
\(691\) | −3.96995 | + | 6.87616i | −0.151024 | + | 0.261581i | −0.931604 | − | 0.363474i | \(-0.881590\pi\) |
0.780580 | + | 0.625056i | \(0.214924\pi\) | |||||||
\(692\) | −3.49079 | − | 6.04623i | −0.132700 | − | 0.229843i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.39988 | − | 13.6104i | 0.0910980 | − | 0.516643i | ||||
\(695\) | 0.247223 | + | 0.428203i | 0.00937770 | + | 0.0162427i | ||||
\(696\) | 6.42820 | − | 11.1340i | 0.243660 | − | 0.422032i | ||||
\(697\) | −3.24487 | − | 2.72277i | −0.122908 | − | 0.103132i | ||||
\(698\) | 0.950113 | + | 0.345813i | 0.0359623 | + | 0.0130892i | ||||
\(699\) | 15.9929 | − | 5.82094i | 0.604907 | − | 0.220168i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.73725 | + | 26.8663i | 0.178924 | + | 1.01473i | 0.933517 | + | 0.358533i | \(0.116723\pi\) |
−0.754593 | + | 0.656193i | \(0.772166\pi\) | |||||||
\(702\) | 25.1527 | 0.949326 | ||||||||
\(703\) | 2.29188 | + | 1.95528i | 0.0864400 | + | 0.0737447i | ||||
\(704\) | 7.19060 | 0.271006 | ||||||||
\(705\) | 0.0182827 | + | 0.103686i | 0.000688566 | + | 0.00390505i | ||||
\(706\) | 32.8053 | − | 27.5269i | 1.23464 | − | 1.03599i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.06019 | − | 3.29764i | −0.340503 | − | 0.123933i | ||||
\(709\) | −17.7443 | − | 14.8893i | −0.666402 | − | 0.559178i | 0.245596 | − | 0.969372i | \(-0.421016\pi\) |
−0.911998 | + | 0.410195i | \(0.865461\pi\) | |||||||
\(710\) | −0.674776 | + | 1.16875i | −0.0253239 | + | 0.0438623i | ||||
\(711\) | 9.65482 | + | 16.7226i | 0.362084 | + | 0.627148i | ||||
\(712\) | −1.57849 | + | 8.95208i | −0.0591565 | + | 0.335493i | ||||
\(713\) | −1.70133 | + | 9.64870i | −0.0637151 | + | 0.361347i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.187051 | − | 0.323981i | 0.00699529 | − | 0.0121162i | ||||
\(716\) | −1.02552 | − | 0.860516i | −0.0383256 | − | 0.0321590i | ||||
\(717\) | 4.05182 | + | 1.47474i | 0.151318 | + | 0.0550752i | ||||
\(718\) | 13.3508 | − | 4.85929i | 0.498247 | − | 0.181347i | ||||
\(719\) | −36.6562 | + | 30.7582i | −1.36705 | + | 1.14709i | −0.393311 | + | 0.919406i | \(0.628670\pi\) |
−0.973735 | + | 0.227682i | \(0.926885\pi\) | |||||||
\(720\) | −0.109757 | − | 0.622464i | −0.00409041 | − | 0.0231979i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −29.2129 | + | 10.0947i | −1.08719 | + | 0.375686i | ||||
\(723\) | −24.3662 | −0.906190 | ||||||||
\(724\) | −0.126723 | − | 0.718682i | −0.00470963 | − | 0.0267096i | ||||
\(725\) | 20.7630 | − | 17.4223i | 0.771120 | − | 0.647047i | ||||
\(726\) | −12.8141 | + | 4.66397i | −0.475578 | + | 0.173096i | ||||
\(727\) | −24.2763 | − | 8.83586i | −0.900359 | − | 0.327704i | −0.149963 | − | 0.988692i | \(-0.547915\pi\) |
−0.750397 | + | 0.660988i | \(0.770138\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.47985 | + | 14.6875i | −0.314069 | + | 0.543983i | ||||
\(730\) | 0.642526 | + | 1.11289i | 0.0237810 | + | 0.0411898i | ||||
\(731\) | 0.206233 | − | 1.16961i | 0.00762781 | − | 0.0432595i | ||||
\(732\) | −0.0202941 | + | 0.115093i | −0.000750090 | + | 0.00425397i | ||||
\(733\) | 12.6849 | + | 21.9708i | 0.468526 | + | 0.811511i | 0.999353 | − | 0.0359690i | \(-0.0114518\pi\) |
−0.530827 | + | 0.847480i | \(0.678118\pi\) | |||||||
\(734\) | 6.88684 | − | 11.9284i | 0.254198 | − | 0.440284i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.97054 | − | 1.80913i | −0.183217 | − | 0.0666854i | ||||
\(737\) | 15.5488 | − | 5.65930i | 0.572747 | − | 0.208463i | ||||
\(738\) | 15.4467 | − | 12.9614i | 0.568603 | − | 0.477114i | ||||
\(739\) | −5.90936 | − | 33.5136i | −0.217379 | − | 1.23282i | −0.876730 | − | 0.480983i | \(-0.840280\pi\) |
0.659350 | − | 0.751836i | \(-0.270831\pi\) | |||||||
\(740\) | −0.0314319 | −0.00115546 | ||||||||
\(741\) | −10.5883 | − | 9.03326i | −0.388973 | − | 0.331845i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.791920 | − | 4.49120i | −0.0290527 | − | 0.164766i | 0.966830 | − | 0.255423i | \(-0.0822146\pi\) |
−0.995882 | + | 0.0906564i | \(0.971103\pi\) | |||||||
\(744\) | 11.8529 | − | 9.94572i | 0.434547 | − | 0.364628i | ||||
\(745\) | 0.533149 | − | 0.194050i | 0.0195331 | − | 0.00710945i | ||||
\(746\) | 36.3046 | + | 13.2138i | 1.32921 | + | 0.483791i | ||||
\(747\) | −9.53691 | − | 8.00242i | −0.348937 | − | 0.292793i | ||||
\(748\) | −0.364416 | + | 0.631187i | −0.0133244 | + | 0.0230785i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.213768 | + | 1.21234i | −0.00780569 | + | 0.0442682i | ||||
\(751\) | −2.53555 | + | 14.3798i | −0.0925236 | + | 0.524727i | 0.902955 | + | 0.429736i | \(0.141393\pi\) |
−0.995478 | + | 0.0949911i | \(0.969718\pi\) | |||||||
\(752\) | 3.38947 | + | 5.87073i | 0.123601 | + | 0.214084i | ||||
\(753\) | −14.6876 | + | 25.4396i | −0.535245 | + | 0.927072i | ||||
\(754\) | −20.0679 | − | 16.8389i | −0.730828 | − | 0.613238i | ||||
\(755\) | 1.33717 | + | 0.486691i | 0.0486647 | + | 0.0177125i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.1043 | + | 16.0304i | −0.694358 | + | 0.582636i | −0.920162 | − | 0.391537i | \(-0.871943\pi\) |
0.225804 | + | 0.974173i | \(0.427499\pi\) | |||||||
\(758\) | 5.29580 | + | 30.0340i | 0.192352 | + | 1.09088i | ||||
\(759\) | 2.89128 | 0.104947 | ||||||||
\(760\) | −0.342529 | + | 0.582229i | −0.0124248 | + | 0.0211197i | ||||
\(761\) | 45.2806 | 1.64142 | 0.820711 | − | 0.571344i | \(-0.193578\pi\) | ||||
0.820711 | + | 0.571344i | \(0.193578\pi\) | |||||||
\(762\) | −3.74983 | − | 21.2664i | −0.135842 | − | 0.770399i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.183057 | − | 0.0666271i | 0.00662275 | − | 0.00241048i | ||||
\(765\) | −0.0767113 | − | 0.0279206i | −0.00277350 | − | 0.00100947i | ||||
\(766\) | 16.4591 | + | 13.8108i | 0.594690 | + | 0.499004i | ||||
\(767\) | 20.5772 | − | 35.6407i | 0.742998 | − | 1.28691i | ||||
\(768\) | 7.56624 | + | 13.1051i | 0.273023 | + | 0.472890i | ||||
\(769\) | −8.35448 | + | 47.3806i | −0.301270 | + | 1.70859i | 0.339291 | + | 0.940682i | \(0.389813\pi\) |
−0.640561 | + | 0.767907i | \(0.721298\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.75564 | − | 11.7011i | −0.243298 | − | 0.421405i | ||||
\(772\) | −0.996459 | + | 1.72592i | −0.0358634 | + | 0.0621171i | ||||
\(773\) | 18.8013 | + | 15.7762i | 0.676237 | + | 0.567430i | 0.914904 | − | 0.403671i | \(-0.132266\pi\) |
−0.238667 | + | 0.971101i | \(0.576710\pi\) | |||||||
\(774\) | 5.31269 | + | 1.93366i | 0.190961 | + | 0.0695040i | ||||
\(775\) | 30.6530 | − | 11.1568i | 1.10109 | − | 0.400763i | ||||
\(776\) | −9.01964 | + | 7.56838i | −0.323786 | + | 0.271689i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.5856 | 0.558772 | ||||||||
\(779\) | −29.3246 | − | 0.239813i | −1.05066 | − | 0.00859221i | ||||
\(780\) | 0.145213 | 0.00519948 | ||||||||
\(781\) | −3.66686 | − | 20.7958i | −0.131210 | − | 0.744131i | ||||
\(782\) | −1.17710 | + | 0.987703i | −0.0420929 | + | 0.0353202i | ||||
\(783\) | 26.5655 | − | 9.66904i | 0.949372 | − | 0.345543i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.23831 | + | 1.03906i | 0.0441971 | + | 0.0370858i | ||||
\(786\) | −2.61446 | + | 4.52838i | −0.0932547 | + | 0.161522i | ||||
\(787\) | 4.59751 | + | 7.96312i | 0.163884 | + | 0.283855i | 0.936258 | − | 0.351313i | \(-0.114265\pi\) |
−0.772375 | + | 0.635167i | \(0.780931\pi\) | |||||||
\(788\) | 3.13323 | − | 17.7694i | 0.111617 | − | 0.633010i | ||||
\(789\) | −3.08807 | + | 17.5133i | −0.109938 | + | 0.623492i | ||||
\(790\) | 0.599881 | + | 1.03902i | 0.0213428 | + | 0.0369668i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.56746 | + | 4.67166i | 0.197831 | + | 0.166000i | ||||
\(793\) | −0.468758 | − | 0.170614i | −0.0166461 | − | 0.00605868i | ||||
\(794\) | 25.4710 | − | 9.27069i | 0.903932 | − | 0.329004i | ||||
\(795\) | 0.427990 | − | 0.359126i | 0.0151792 | − | 0.0127369i | ||||
\(796\) | 0.166019 | + | 0.941542i | 0.00588439 | + | 0.0333721i | ||||
\(797\) | 50.7437 | 1.79743 | 0.898716 | − | 0.438530i | \(-0.144501\pi\) | ||||
0.898716 | + | 0.438530i | \(0.144501\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.875532 | 0.0309741 | ||||||||
\(800\) | 3.05814 | + | 17.3436i | 0.108122 | + | 0.613188i | ||||
\(801\) | −5.82600 | + | 4.88859i | −0.205852 | + | 0.172730i | ||||
\(802\) | −30.7164 | + | 11.1798i | −1.08463 | + | 0.394774i | ||||
\(803\) | −18.8947 | − | 6.87712i | −0.666781 | − | 0.242688i | ||||
\(804\) | 4.92020 | + | 4.12854i | 0.173522 | + | 0.145602i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.7640 | − | 27.3041i | −0.555264 | − | 0.961745i | ||||
\(807\) | −5.47515 | + | 31.0511i | −0.192734 | + | 1.09305i | ||||
\(808\) | 1.90692 | − | 10.8147i | 0.0670853 | − | 0.380460i | ||||
\(809\) | 1.11568 | + | 1.93241i | 0.0392252 | + | 0.0679400i | 0.884972 | − | 0.465645i | \(-0.154178\pi\) |
−0.845746 | + | 0.533585i | \(0.820844\pi\) | |||||||
\(810\) | −0.00446310 | + | 0.00773031i | −0.000156817 | + | 0.000271615i | ||||
\(811\) | 9.48231 | + | 7.95660i | 0.332969 | + | 0.279394i | 0.793908 | − | 0.608038i | \(-0.208043\pi\) |
−0.460939 | + | 0.887432i | \(0.652487\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.1700 | + | 10.2531i | −0.987967 | + | 0.359590i | ||||
\(814\) | 1.54273 | − | 1.29450i | 0.0540725 | − | 0.0453722i | ||||
\(815\) | 0.220268 | + | 1.24920i | 0.00771566 | + | 0.0437577i | ||||
\(816\) | 3.30220 | 0.115600 | ||||||||
\(817\) | −4.05277 | − | 7.15408i | −0.141788 | − | 0.250290i | ||||
\(818\) | 17.0566 | 0.596371 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.234384 | − | 0.196672i | 0.00818505 | − | 0.00686807i | ||||
\(821\) | 42.4324 | − | 15.4441i | 1.48090 | − | 0.539004i | 0.529865 | − | 0.848082i | \(-0.322242\pi\) |
0.951037 | + | 0.309077i | \(0.100020\pi\) | |||||||
\(822\) | 35.1023 | + | 12.7762i | 1.22433 | + | 0.445621i | ||||
\(823\) | −6.92579 | − | 5.81143i | −0.241418 | − | 0.202574i | 0.514048 | − | 0.857761i | \(-0.328145\pi\) |
−0.755466 | + | 0.655187i | \(0.772590\pi\) | |||||||
\(824\) | 3.30481 | − | 5.72409i | 0.115128 | − | 0.199408i | ||||
\(825\) | −4.81316 | − | 8.33664i | −0.167573 | − | 0.290244i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.71598 | + | 26.7457i | −0.163991 | + | 0.930037i | 0.786108 | + | 0.618089i | \(0.212093\pi\) |
−0.950099 | + | 0.311949i | \(0.899018\pi\) | |||||||
\(828\) | −0.893181 | − | 1.54703i | −0.0310402 | − | 0.0537632i | ||||
\(829\) | 12.3864 | − | 21.4539i | 0.430197 | − | 0.745123i | −0.566693 | − | 0.823929i | \(-0.691777\pi\) |
0.996890 | + | 0.0788058i | \(0.0251107\pi\) | |||||||
\(830\) | −0.592555 | − | 0.497212i | −0.0205679 | − | 0.0172585i | ||||
\(831\) | 6.47609 | + | 2.35710i | 0.224653 | + | 0.0817670i | ||||
\(832\) | −11.1952 | + | 4.07473i | −0.388125 | + | 0.141266i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.13536 | − | 12.1102i | −0.0739413 | − | 0.419342i | ||||
\(835\) | −0.258678 | −0.00895193 | ||||||||
\(836\) | 0.835531 | + | 4.97615i | 0.0288974 | + | 0.172104i | ||||
\(837\) | 34.0237 | 1.17603 | ||||||||
\(838\) | 3.69566 | + | 20.9591i | 0.127665 | + | 0.724022i | ||||
\(839\) | 23.9268 | − | 20.0769i | 0.826043 | − | 0.693133i | −0.128336 | − | 0.991731i | \(-0.540964\pi\) |
0.954379 | + | 0.298598i | \(0.0965191\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.417095 | − | 0.151810i | −0.0143826 | − | 0.00523483i | ||||
\(842\) | 29.5107 | + | 24.7624i | 1.01701 | + | 0.853370i | ||||
\(843\) | 0.261446 | − | 0.452837i | 0.00900467 | − | 0.0155965i | ||||
\(844\) | 8.91324 | + | 15.4382i | 0.306806 | + | 0.531404i | ||||
\(845\) | 0.0512287 | − | 0.290533i | 0.00176232 | − | 0.00999462i | ||||
\(846\) | −0.723740 | + | 4.10453i | −0.0248827 | + | 0.141117i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 17.9863 | − | 31.1531i | 0.617650 | − | 1.06980i | ||||
\(849\) | −21.7126 | − | 18.2191i | −0.745176 | − | 0.625277i | ||||
\(850\) | 4.80744 | + | 1.74977i | 0.164894 | + | 0.0600165i | ||||
\(851\) | 0.974367 | − | 0.354641i | 0.0334009 | − | 0.0121569i | ||||
\(852\) | 6.27907 | − | 5.26877i | 0.215117 | − | 0.180505i | ||||
\(853\) | 5.23367 | + | 29.6816i | 0.179197 | + | 1.01628i | 0.933187 | + | 0.359392i | \(0.117016\pi\) |
−0.753989 | + | 0.656887i | \(0.771873\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.532647 | + | 0.188949i | −0.0182161 | + | 0.00646193i | ||||
\(856\) | 27.5688 | 0.942281 | ||||||||
\(857\) | 4.54654 | + | 25.7847i | 0.155307 | + | 0.880789i | 0.958505 | + | 0.285077i | \(0.0920191\pi\) |
−0.803198 | + | 0.595713i | \(0.796870\pi\) | |||||||
\(858\) | −7.12729 | + | 5.98050i | −0.243322 | + | 0.204171i | ||||
\(859\) | −20.3489 | + | 7.40639i | −0.694295 | + | 0.252703i | −0.664973 | − | 0.746867i | \(-0.731557\pi\) |
−0.0293222 | + | 0.999570i | \(0.509335\pi\) | |||||||
\(860\) | 0.0806131 | + | 0.0293408i | 0.00274888 | + | 0.00100051i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.00291 | − | 10.3973i | 0.204460 | − | 0.354135i | ||||
\(863\) | −21.6234 | − | 37.4528i | −0.736068 | − | 1.27491i | −0.954253 | − | 0.299000i | \(-0.903347\pi\) |
0.218185 | − | 0.975907i | \(-0.429986\pi\) | |||||||
\(864\) | −3.18972 | + | 18.0898i | −0.108516 | + | 0.615427i | ||||
\(865\) | −0.132016 | + | 0.748698i | −0.00448866 | + | 0.0254565i | ||||
\(866\) | −28.1736 | − | 48.7982i | −0.957379 | − | 1.65823i | ||||
\(867\) | −8.93183 | + | 15.4704i | −0.303341 | + | 0.525402i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.6407 | − | 6.42067i | −0.598418 | − | 0.217806i | ||||
\(870\) | 0.628015 | − | 0.228579i | 0.0212917 | − | 0.00774954i | ||||
\(871\) | −21.0013 | + | 17.6222i | −0.711603 | + | 0.597106i | ||||
\(872\) | 5.36826 | + | 30.4449i | 0.181792 | + | 1.03100i | ||||
\(873\) | −9.85098 | −0.333405 | ||||||||
\(874\) | −1.93289 | + | 10.4610i | −0.0653810 | + | 0.353848i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.35532 | − | 7.68642i | −0.0457921 | − | 0.259700i | ||||
\(877\) | 14.3979 | − | 12.0813i | 0.486182 | − | 0.407956i | −0.366473 | − | 0.930429i | \(-0.619435\pi\) |
0.852656 | + | 0.522473i | \(0.174990\pi\) | |||||||
\(878\) | 49.3488 | − | 17.9615i | 1.66544 | − | 0.606171i | ||||
\(879\) | 31.8251 | + | 11.5834i | 1.07343 | + | 0.390698i | ||||
\(880\) | 0.470729 | + | 0.394989i | 0.0158683 | + | 0.0133151i | ||||
\(881\) | −4.57192 | + | 7.91881i | −0.154032 | + | 0.266791i | −0.932706 | − | 0.360637i | \(-0.882559\pi\) |
0.778674 | + | 0.627429i | \(0.215893\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.57800 | − | 20.2918i | 0.120409 | − | 0.682874i | −0.863520 | − | 0.504315i | \(-0.831745\pi\) |
0.983929 | − | 0.178560i | \(-0.0571437\pi\) | |||||||
\(884\) | 0.209691 | − | 1.18921i | 0.00705266 | − | 0.0399976i | ||||
\(885\) | 0.524955 | + | 0.909249i | 0.0176462 | + | 0.0305641i | ||||
\(886\) | 13.4560 | − | 23.3065i | 0.452064 | − | 0.782998i | ||||
\(887\) | −22.2337 | − | 18.6563i | −0.746534 | − | 0.626416i | 0.188050 | − | 0.982159i | \(-0.439783\pi\) |
−0.934584 | + | 0.355743i | \(0.884228\pi\) | |||||||
\(888\) | −1.53877 | − | 0.560067i | −0.0516378 | − | 0.0187946i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.361985 | + | 0.303742i | −0.0121338 | + | 0.0101814i | ||||
\(891\) | −0.0242533 | − | 0.137547i | −0.000812516 | − | 0.00460801i | ||||
\(892\) | 5.76484 | 0.193021 | ||||||||
\(893\) | 4.67504 | − | 3.85812i | 0.156444 | − | 0.129107i | ||||
\(894\) | −14.1106 | −0.471927 | ||||||||
\(895\) | 0.0253141 | + | 0.143564i | 0.000846158 | + | 0.00479880i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.50151 | + | 1.63842i | −0.150301 | + | 0.0547051i | ||||
\(898\) | −55.5441 | − | 20.2164i | −1.85353 | − | 0.674630i | ||||
\(899\) | −27.1455 | − | 22.7778i | −0.905354 | − | 0.759683i | ||||
\(900\) | −2.97378 | + | 5.15074i | −0.0991260 | + | 0.171691i | ||||
\(901\) | −2.32301 | − | 4.02357i | −0.0773907 | − | 0.134045i | ||||
\(902\) | −3.40414 | + | 19.3059i | −0.113346 | + | 0.642815i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.463020 | − | 0.801974i | −0.0153998 | − | 0.0266733i | ||||
\(905\) | −0.0397335 | + | 0.0688204i | −0.00132078 | + | 0.00228767i | ||||
\(906\) | −27.1104 | − | 22.7484i | −0.900684 | − | 0.755764i | ||||
\(907\) | −15.4723 | − | 5.63147i | −0.513750 | − | 0.186990i | 0.0721181 | − | 0.997396i | \(-0.477024\pi\) |
−0.585868 | + | 0.810406i | \(0.699246\pi\) | |||||||
\(908\) | −15.3914 | + | 5.60202i | −0.510782 | + | 0.185909i | ||||
\(909\) | 7.03819 | − | 5.90574i | 0.233442 | − | 0.195881i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.9644 | 0.959634 | 0.479817 | − | 0.877368i | \(-0.340703\pi\) | ||||
0.479817 | + | 0.877368i | \(0.340703\pi\) | |||||||
\(912\) | 17.6326 | − | 14.5515i | 0.583874 | − | 0.481848i | ||||
\(913\) | 12.1034 | 0.400565 | ||||||||
\(914\) | 7.51442 | + | 42.6164i | 0.248555 | + | 1.40963i | ||||
\(915\) | 0.00974885 | − | 0.00818026i | 0.000322287 | − | 0.000270431i | ||||
\(916\) | 15.0866 | − | 5.49106i | 0.498474 | − | 0.181430i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.08768 | + | 3.42997i | 0.134914 | + | 0.113206i | ||||
\(919\) | 10.8249 | − | 18.7493i | 0.357081 | − | 0.618482i | −0.630391 | − | 0.776278i | \(-0.717105\pi\) |
0.987472 | + | 0.157796i | \(0.0504387\pi\) | |||||||
\(920\) | 0.116251 | + | 0.201352i | 0.00383268 | + | 0.00663839i | ||||
\(921\) | −3.21545 | + | 18.2357i | −0.105953 | + | 0.600887i | ||||
\(922\) | 0.0173481 | − | 0.0983862i | 0.000571331 | − | 0.00324018i | ||||
\(923\) | 17.4934 | + | 30.2995i | 0.575804 | + | 0.997322i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.64460 | − | 2.21908i | −0.0869540 | − | 0.0729631i | ||||
\(926\) | 19.9143 | + | 7.24822i | 0.654425 | + | 0.238191i | ||||
\(927\) | 5.19644 | − | 1.89135i | 0.170673 | − | 0.0621201i | ||||
\(928\) | 14.6555 | − | 12.2974i | 0.481089 | − | 0.403681i | ||||
\(929\) | −2.99333 | − | 16.9760i | −0.0982081 | − | 0.556966i | −0.993717 | − | 0.111922i | \(-0.964299\pi\) |
0.895509 | − | 0.445044i | \(-0.146812\pi\) | |||||||
\(930\) | 0.804329 | 0.0263750 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 10.2229 | 0.334863 | ||||||||
\(933\) | −5.37078 | − | 30.4592i | −0.175831 | − | 0.997190i | ||||
\(934\) | −19.3793 | + | 16.2612i | −0.634110 | + | 0.532081i | ||||
\(935\) | 0.0745785 | − | 0.0271444i | 0.00243898 | − | 0.000887716i | ||||
\(936\) | −11.3154 | − | 4.11848i | −0.369856 | − | 0.134617i | ||||
\(937\) | −10.5786 | − | 8.87649i | −0.345588 | − | 0.289982i | 0.453428 | − | 0.891293i | \(-0.350201\pi\) |
−0.799015 | + | 0.601311i | \(0.794645\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.80235 | + | 6.58586i | 0.124085 | + | 0.214922i | ||||
\(940\) | −0.0109818 | + | 0.0622809i | −0.000358187 | + | 0.00203138i | ||||
\(941\) | 7.56796 | − | 42.9201i | 0.246709 | − | 1.39915i | −0.569782 | − | 0.821796i | \(-0.692972\pi\) |
0.816491 | − | 0.577358i | \(-0.195916\pi\) | |||||||
\(942\) | −20.1014 | − | 34.8166i | −0.654938 | − | 1.13439i | ||||
\(943\) | −5.04673 | + | 8.74119i | −0.164344 | + | 0.284652i | ||||
\(944\) | 51.7842 | + | 43.4521i | 1.68543 | + | 1.41425i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.16498 | + | 1.87990i | −0.167928 | + | 0.0611208i | ||||
\(947\) | 11.5267 | − | 9.67208i | 0.374569 | − | 0.314300i | −0.435997 | − | 0.899948i | \(-0.643604\pi\) |
0.810566 | + | 0.585648i | \(0.199160\pi\) | |||||||
\(948\) | −1.26537 | − | 7.17626i | −0.0410973 | − | 0.233074i | ||||
\(949\) | 33.3148 | 1.08144 | ||||||||
\(950\) | 33.3806 | − | 11.8413i | 1.08301 | − | 0.384183i | ||||
\(951\) | 6.80098 | 0.220537 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.9792 | + | 23.4774i | −0.906336 | + | 0.760506i | −0.971418 | − | 0.237374i | \(-0.923713\pi\) |
0.0650825 | + | 0.997880i | \(0.479269\pi\) | |||||||
\(954\) | 20.7830 | − | 7.56438i | 0.672873 | − | 0.244906i | ||||
\(955\) | −0.0199336 | − | 0.00725524i | −0.000645037 | − | 0.000234774i | ||||
\(956\) | 1.98405 | + | 1.66481i | 0.0641686 | + | 0.0538439i | ||||
\(957\) | −5.22863 | + | 9.05626i | −0.169018 | + | 0.292747i | ||||
\(958\) | −24.4495 | − | 42.3477i | −0.789926 | − | 1.36819i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.0527782 | − | 0.299320i | 0.00170341 | − | 0.00966050i | ||||
\(961\) | −5.82378 | − | 10.0871i | −0.187864 | − | 0.325390i | ||||
\(962\) | −1.66835 | + | 2.88966i | −0.0537897 | + | 0.0931664i | ||||
\(963\) | 17.6691 | + | 14.8262i | 0.569380 | + | 0.477767i | ||||
\(964\) | −13.7533 | − | 5.00580i | −0.442965 | − | 0.161226i | ||||
\(965\) | 0.203928 | − | 0.0742236i | 0.00656467 | − | 0.00238934i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.76506 | + | 15.6814i | 0.0889184 | + | 0.504281i | 0.996442 | + | 0.0842804i | \(0.0268592\pi\) |
−0.907524 | + | 0.420001i | \(0.862030\pi\) | |||||||
\(968\) | 17.1583 | 0.551488 | ||||||||
\(969\) | −0.488933 | − | 2.91193i | −0.0157068 | − | 0.0935447i | ||||
\(970\) | −0.612069 | −0.0196523 | ||||||||
\(971\) | 0.164226 | + | 0.931371i | 0.00527026 | + | 0.0298891i | 0.987329 | − | 0.158684i | \(-0.0507250\pi\) |
−0.982059 | + | 0.188573i | \(0.939614\pi\) | |||||||
\(972\) | −7.69616 | + | 6.45784i | −0.246854 | + | 0.207135i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18.9689 | − | 6.90411i | −0.607802 | − | 0.221222i | ||||
\(975\) | 12.2179 | + | 10.2520i | 0.391285 | + | 0.328327i | ||||
\(976\) | 0.409695 | − | 0.709613i | 0.0131140 | − | 0.0227142i | ||||
\(977\) | 1.32652 | + | 2.29761i | 0.0424392 | + | 0.0735069i | 0.886465 | − | 0.462796i | \(-0.153154\pi\) |
−0.844026 | + | 0.536303i | \(0.819820\pi\) | |||||||
\(978\) | 5.47814 | − | 31.0681i | 0.175172 | − | 0.993447i | ||||
\(979\) | 1.28393 | − | 7.28153i | 0.0410346 | − | 0.232719i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.9324 | + | 22.3995i | −0.412898 | + | 0.715161i | ||||
\(982\) | 51.0792 | + | 42.8605i | 1.63000 | + | 1.36773i | ||||
\(983\) | −31.5570 | − | 11.4858i | −1.00651 | − | 0.366340i | −0.214419 | − | 0.976742i | \(-0.568786\pi\) |
−0.792092 | + | 0.610402i | \(0.791008\pi\) | |||||||
\(984\) | 14.9788 | − | 5.45184i | 0.477507 | − | 0.173798i | ||||
\(985\) | −1.50514 | + | 1.26296i | −0.0479577 | + | 0.0402413i | ||||
\(986\) | −0.965064 | − | 5.47315i | −0.0307339 | − | 0.174301i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.12071 | − | 7.27402i | −0.131097 | − | 0.231417i | ||||
\(989\) | −2.82999 | −0.0899885 | ||||||||
\(990\) | 0.0656052 | + | 0.372066i | 0.00208507 | + | 0.0118250i | ||||
\(991\) | −24.2057 | + | 20.3110i | −0.768921 | + | 0.645201i | −0.940432 | − | 0.339981i | \(-0.889579\pi\) |
0.171511 | + | 0.985182i | \(0.445135\pi\) | |||||||
\(992\) | 21.6362 | − | 7.87493i | 0.686950 | − | 0.250029i | ||||
\(993\) | 15.8150 | + | 5.75619i | 0.501874 | + | 0.182667i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.0520546 | − | 0.0901612i | 0.00165024 | − | 0.00285830i | ||||
\(996\) | 2.34907 | + | 4.06871i | 0.0744332 | + | 0.128922i | ||||
\(997\) | 5.91647 | − | 33.5540i | 0.187376 | − | 1.06266i | −0.735488 | − | 0.677538i | \(-0.763047\pi\) |
0.922864 | − | 0.385126i | \(-0.125842\pi\) | |||||||
\(998\) | 2.09688 | − | 11.8920i | 0.0663756 | − | 0.376435i | ||||
\(999\) | −1.80041 | − | 3.11840i | −0.0569624 | − | 0.0986618i |
(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 | 931.2.w.b.883.4 | 30 | ||
7.2 | even | 3 | 931.2.x.d.655.4 | 30 | |||
7.3 | odd | 6 | 931.2.v.d.275.2 | 30 | |||
7.4 | even | 3 | 931.2.v.e.275.2 | 30 | |||
7.5 | odd | 6 | 931.2.x.e.655.4 | 30 | |||
7.6 | odd | 2 | 133.2.v.b.85.4 | yes | 30 | ||
19.17 | even | 9 | inner | 931.2.w.b.834.4 | 30 | ||
133.6 | odd | 18 | 2527.2.a.r.1.11 | 15 | |||
133.13 | even | 18 | 2527.2.a.s.1.5 | 15 | |||
133.17 | odd | 18 | 931.2.x.e.226.4 | 30 | |||
133.55 | odd | 18 | 133.2.v.b.36.4 | ✓ | 30 | ||
133.74 | even | 9 | 931.2.x.d.226.4 | 30 | |||
133.93 | even | 9 | 931.2.v.e.606.2 | 30 | |||
133.131 | odd | 18 | 931.2.v.d.606.2 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
133.2.v.b.36.4 | ✓ | 30 | 133.55 | odd | 18 | ||
133.2.v.b.85.4 | yes | 30 | 7.6 | odd | 2 | ||
931.2.v.d.275.2 | 30 | 7.3 | odd | 6 | |||
931.2.v.d.606.2 | 30 | 133.131 | odd | 18 | |||
931.2.v.e.275.2 | 30 | 7.4 | even | 3 | |||
931.2.v.e.606.2 | 30 | 133.93 | even | 9 | |||
931.2.w.b.834.4 | 30 | 19.17 | even | 9 | inner | ||
931.2.w.b.883.4 | 30 | 1.1 | even | 1 | trivial | ||
931.2.x.d.226.4 | 30 | 133.74 | even | 9 | |||
931.2.x.d.655.4 | 30 | 7.2 | even | 3 | |||
931.2.x.e.226.4 | 30 | 133.17 | odd | 18 | |||
931.2.x.e.655.4 | 30 | 7.5 | odd | 6 | |||
2527.2.a.r.1.11 | 15 | 133.6 | odd | 18 | |||
2527.2.a.s.1.5 | 15 | 133.13 | even | 18 |