Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(106,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.i (of order \(3\), degree \(2\), 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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.142635249.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 3x^{6} + 3x^{5} - 11x^{4} + 6x^{3} + 12x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(0.818235 - 1.15347i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.211 |
Dual form | 315.2.i.c.106.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.875400 | − | 1.51624i | −0.619001 | − | 1.07214i | −0.989668 | − | 0.143376i | \(-0.954204\pi\) |
0.370667 | − | 0.928766i | \(-0.379129\pi\) | |||||||
\(3\) | −1.16098 | + | 1.28535i | −0.670294 | + | 0.742095i | ||||
\(4\) | −0.532651 | + | 0.922579i | −0.266326 | + | 0.461289i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 2.96522 | + | 0.635135i | 1.21054 | + | 0.259293i | ||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | −1.63647 | −0.578579 | ||||||||
\(9\) | −0.304233 | − | 2.98453i | −0.101411 | − | 0.994845i | ||||
\(10\) | 1.75080 | 0.553652 | ||||||||
\(11\) | 3.05503 | + | 5.29147i | 0.921127 | + | 1.59544i | 0.797674 | + | 0.603089i | \(0.206064\pi\) |
0.123453 | + | 0.992350i | \(0.460603\pi\) | |||||||
\(12\) | −0.567434 | − | 1.75574i | −0.163804 | − | 0.506839i | ||||
\(13\) | 2.90805 | − | 5.03689i | 0.806548 | − | 1.39698i | −0.108693 | − | 0.994075i | \(-0.534666\pi\) |
0.915241 | − | 0.402907i | \(-0.132000\pi\) | |||||||
\(14\) | −0.875400 | + | 1.51624i | −0.233961 | + | 0.405232i | ||||
\(15\) | −0.532651 | − | 1.64811i | −0.137530 | − | 0.425541i | ||||
\(16\) | 2.49787 | + | 4.32643i | 0.624467 | + | 1.08161i | ||||
\(17\) | 4.73907 | 1.14939 | 0.574697 | − | 0.818367i | \(-0.305120\pi\) | ||||
0.574697 | + | 0.818367i | \(0.305120\pi\) | |||||||
\(18\) | −4.25894 | + | 3.07395i | −1.00384 | + | 0.724537i | ||||
\(19\) | 3.68123 | 0.844533 | 0.422266 | − | 0.906472i | \(-0.361235\pi\) | ||||
0.422266 | + | 0.906472i | \(0.361235\pi\) | |||||||
\(20\) | −0.532651 | − | 0.922579i | −0.119104 | − | 0.206295i | ||||
\(21\) | 1.69363 | + | 0.362768i | 0.369581 | + | 0.0791625i | ||||
\(22\) | 5.34875 | − | 9.26431i | 1.14036 | − | 1.97516i | ||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | −0.809177 | − | 0.587565i | \(-0.800087\pi\) |
0.913434 | + | 0.406986i | \(0.133420\pi\) | |||||||
\(24\) | 1.89991 | − | 2.10343i | 0.387818 | − | 0.429361i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −10.1828 | −1.99702 | ||||||||
\(27\) | 4.18937 | + | 3.07395i | 0.806245 | + | 0.591582i | ||||
\(28\) | 1.06530 | 0.201323 | ||||||||
\(29\) | 0.839016 | + | 1.45322i | 0.155801 | + | 0.269856i | 0.933351 | − | 0.358966i | \(-0.116871\pi\) |
−0.777549 | + | 0.628822i | \(0.783537\pi\) | |||||||
\(30\) | −2.03265 | + | 2.25039i | −0.371110 | + | 0.410862i | ||||
\(31\) | 3.47922 | − | 6.02618i | 0.624886 | − | 1.08233i | −0.363677 | − | 0.931525i | \(-0.618479\pi\) |
0.988563 | − | 0.150809i | \(-0.0481879\pi\) | |||||||
\(32\) | 2.73680 | − | 4.74027i | 0.483802 | − | 0.837970i | ||||
\(33\) | −10.3482 | − | 2.21654i | −1.80139 | − | 0.385850i | ||||
\(34\) | −4.14858 | − | 7.18556i | −0.711476 | − | 1.23231i | ||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 2.91552 | + | 1.30904i | 0.485920 | + | 0.218173i | ||||
\(37\) | −4.49413 | −0.738831 | −0.369416 | − | 0.929264i | \(-0.620442\pi\) | ||||
−0.369416 | + | 0.929264i | \(0.620442\pi\) | |||||||
\(38\) | −3.22255 | − | 5.58163i | −0.522767 | − | 0.905459i | ||||
\(39\) | 3.09795 | + | 9.58561i | 0.496070 | + | 1.53493i | ||||
\(40\) | 0.818235 | − | 1.41722i | 0.129374 | − | 0.224083i | ||||
\(41\) | 1.98736 | − | 3.44220i | 0.310373 | − | 0.537581i | −0.668070 | − | 0.744098i | \(-0.732879\pi\) |
0.978443 | + | 0.206517i | \(0.0662128\pi\) | |||||||
\(42\) | −0.932566 | − | 2.88552i | −0.143898 | − | 0.445245i | ||||
\(43\) | 5.66350 | + | 9.80947i | 0.863676 | + | 1.49593i | 0.868356 | + | 0.495941i | \(0.165177\pi\) |
−0.00468081 | + | 0.999989i | \(0.501490\pi\) | |||||||
\(44\) | −6.50907 | −0.981279 | ||||||||
\(45\) | 2.73680 | + | 1.22879i | 0.407978 | + | 0.183178i | ||||
\(46\) | −1.75080 | −0.258141 | ||||||||
\(47\) | −2.08768 | − | 3.61598i | −0.304520 | − | 0.527444i | 0.672634 | − | 0.739975i | \(-0.265163\pi\) |
−0.977154 | + | 0.212531i | \(0.931829\pi\) | |||||||
\(48\) | −8.46095 | − | 1.81229i | −1.22123 | − | 0.261582i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −0.875400 | + | 1.51624i | −0.123800 | + | 0.214428i | ||||
\(51\) | −5.50198 | + | 6.09135i | −0.770432 | + | 0.852959i | ||||
\(52\) | 3.09795 | + | 5.36581i | 0.429609 | + | 0.744104i | ||||
\(53\) | −8.30597 | −1.14091 | −0.570457 | − | 0.821328i | \(-0.693234\pi\) | ||||
−0.570457 | + | 0.821328i | \(0.693234\pi\) | |||||||
\(54\) | 0.993464 | − | 9.04302i | 0.135193 | − | 1.23060i | ||||
\(55\) | −6.11007 | −0.823881 | ||||||||
\(56\) | 0.818235 | + | 1.41722i | 0.109341 | + | 0.189385i | ||||
\(57\) | −4.27385 | + | 4.73166i | −0.566086 | + | 0.626724i | ||||
\(58\) | 1.46895 | − | 2.54430i | 0.192883 | − | 0.334082i | ||||
\(59\) | −0.418564 | + | 0.724974i | −0.0544924 | + | 0.0943836i | −0.891985 | − | 0.452065i | \(-0.850687\pi\) |
0.837492 | + | 0.546449i | \(0.184021\pi\) | |||||||
\(60\) | 1.80423 | + | 0.386458i | 0.232925 | + | 0.0498915i | ||||
\(61\) | 4.62833 | + | 8.01651i | 0.592597 | + | 1.02641i | 0.993881 | + | 0.110455i | \(0.0352308\pi\) |
−0.401284 | + | 0.915954i | \(0.631436\pi\) | |||||||
\(62\) | −12.1828 | −1.54722 | ||||||||
\(63\) | −2.43257 | + | 1.75574i | −0.306474 | + | 0.221202i | ||||
\(64\) | 0.408295 | 0.0510369 | ||||||||
\(65\) | 2.90805 | + | 5.03689i | 0.360699 | + | 0.624750i | ||||
\(66\) | 5.69804 | + | 17.6307i | 0.701380 | + | 2.17019i | ||||
\(67\) | −2.25894 | + | 3.91259i | −0.275973 | + | 0.477999i | −0.970380 | − | 0.241583i | \(-0.922333\pi\) |
0.694407 | + | 0.719582i | \(0.255667\pi\) | |||||||
\(68\) | −2.52427 | + | 4.37217i | −0.306113 | + | 0.530203i | ||||
\(69\) | 0.532651 | + | 1.64811i | 0.0641237 | + | 0.198410i | ||||
\(70\) | −0.875400 | − | 1.51624i | −0.104630 | − | 0.181225i | ||||
\(71\) | 10.3667 | 1.23030 | 0.615152 | − | 0.788408i | \(-0.289094\pi\) | ||||
0.615152 | + | 0.788408i | \(0.289094\pi\) | |||||||
\(72\) | 0.497868 | + | 4.88410i | 0.0586743 | + | 0.575597i | ||||
\(73\) | 12.2346 | 1.43195 | 0.715975 | − | 0.698126i | \(-0.245983\pi\) | ||||
0.715975 | + | 0.698126i | \(0.245983\pi\) | |||||||
\(74\) | 3.93417 | + | 6.81418i | 0.457338 | + | 0.792132i | ||||
\(75\) | 1.69363 | + | 0.362768i | 0.195564 | + | 0.0418889i | ||||
\(76\) | −1.96081 | + | 3.39623i | −0.224921 | + | 0.389574i | ||||
\(77\) | 3.05503 | − | 5.29147i | 0.348153 | − | 0.603019i | ||||
\(78\) | 11.8221 | − | 13.0885i | 1.33859 | − | 1.48198i | ||||
\(79\) | −4.41643 | − | 7.64948i | −0.496887 | − | 0.860634i | 0.503106 | − | 0.864225i | \(-0.332190\pi\) |
−0.999994 | + | 0.00359042i | \(0.998857\pi\) | |||||||
\(80\) | −4.99574 | −0.558540 | ||||||||
\(81\) | −8.81488 | + | 1.81599i | −0.979432 | + | 0.201776i | ||||
\(82\) | −6.95892 | −0.768485 | ||||||||
\(83\) | 3.17072 | + | 5.49185i | 0.348032 | + | 0.602809i | 0.985900 | − | 0.167337i | \(-0.0535168\pi\) |
−0.637868 | + | 0.770146i | \(0.720183\pi\) | |||||||
\(84\) | −1.23680 | + | 1.36928i | −0.134946 | + | 0.149401i | ||||
\(85\) | −2.36954 | + | 4.10416i | −0.257012 | + | 0.445158i | ||||
\(86\) | 9.91566 | − | 17.1744i | 1.06923 | − | 1.85197i | ||||
\(87\) | −2.84197 | − | 0.608737i | −0.304692 | − | 0.0652634i | ||||
\(88\) | −4.99947 | − | 8.65933i | −0.532945 | − | 0.923088i | ||||
\(89\) | −9.66496 | −1.02448 | −0.512242 | − | 0.858841i | \(-0.671185\pi\) | ||||
−0.512242 | + | 0.858841i | \(0.671185\pi\) | |||||||
\(90\) | −0.532651 | − | 5.22532i | −0.0561464 | − | 0.550797i | ||||
\(91\) | −5.81610 | −0.609693 | ||||||||
\(92\) | 0.532651 | + | 0.922579i | 0.0555327 | + | 0.0961855i | ||||
\(93\) | 3.70642 | + | 11.4683i | 0.384338 | + | 1.18921i | ||||
\(94\) | −3.65512 | + | 6.33085i | −0.376997 | + | 0.652977i | ||||
\(95\) | −1.84062 | + | 3.18804i | −0.188843 | + | 0.327086i | ||||
\(96\) | 2.91552 | + | 9.02112i | 0.297564 | + | 0.920714i | ||||
\(97\) | 4.08677 | + | 7.07849i | 0.414949 | + | 0.718712i | 0.995423 | − | 0.0955664i | \(-0.0304662\pi\) |
−0.580474 | + | 0.814278i | \(0.697133\pi\) | |||||||
\(98\) | 1.75080 | 0.176858 | ||||||||
\(99\) | 14.8631 | − | 10.7277i | 1.49380 | − | 1.07817i | ||||
\(100\) | 1.06530 | 0.106530 | ||||||||
\(101\) | −6.06599 | − | 10.5066i | −0.603588 | − | 1.04545i | −0.992273 | − | 0.124075i | \(-0.960404\pi\) |
0.388684 | − | 0.921371i | \(-0.372930\pi\) | |||||||
\(102\) | 14.0524 | + | 3.00995i | 1.39139 | + | 0.298029i | ||||
\(103\) | 0.697899 | − | 1.20880i | 0.0687661 | − | 0.119106i | −0.829592 | − | 0.558370i | \(-0.811427\pi\) |
0.898358 | + | 0.439263i | \(0.144760\pi\) | |||||||
\(104\) | −4.75894 | + | 8.24272i | −0.466652 | + | 0.808265i | ||||
\(105\) | −1.16098 | + | 1.28535i | −0.113300 | + | 0.125437i | ||||
\(106\) | 7.27105 | + | 12.5938i | 0.706227 | + | 1.22322i | ||||
\(107\) | −0.484840 | −0.0468713 | −0.0234356 | − | 0.999725i | \(-0.507460\pi\) | ||||
−0.0234356 | + | 0.999725i | \(0.507460\pi\) | |||||||
\(108\) | −5.06743 | + | 2.22768i | −0.487614 | + | 0.214359i | ||||
\(109\) | −10.7345 | −1.02818 | −0.514091 | − | 0.857736i | \(-0.671870\pi\) | ||||
−0.514091 | + | 0.857736i | \(0.671870\pi\) | |||||||
\(110\) | 5.34875 | + | 9.26431i | 0.509984 | + | 0.883318i | ||||
\(111\) | 5.21762 | − | 5.77652i | 0.495234 | − | 0.548283i | ||||
\(112\) | 2.49787 | − | 4.32643i | 0.236026 | − | 0.408810i | ||||
\(113\) | 0.559298 | − | 0.968732i | 0.0526143 | − | 0.0911306i | −0.838519 | − | 0.544873i | \(-0.816578\pi\) |
0.891133 | + | 0.453742i | \(0.149911\pi\) | |||||||
\(114\) | 10.9157 | + | 2.33808i | 1.02234 | + | 0.218981i | ||||
\(115\) | 0.500000 | + | 0.866025i | 0.0466252 | + | 0.0807573i | ||||
\(116\) | −1.78761 | −0.165976 | ||||||||
\(117\) | −15.9175 | − | 7.14679i | −1.47157 | − | 0.660721i | ||||
\(118\) | 1.46564 | 0.134923 | ||||||||
\(119\) | −2.36954 | − | 4.10416i | −0.217215 | − | 0.376227i | ||||
\(120\) | 0.871667 | + | 2.69709i | 0.0795720 | + | 0.246209i | ||||
\(121\) | −13.1665 | + | 22.8050i | −1.19695 | + | 2.07318i | ||||
\(122\) | 8.10329 | − | 14.0353i | 0.733637 | − | 1.27070i | ||||
\(123\) | 2.11713 | + | 6.55078i | 0.190896 | + | 0.590664i | ||||
\(124\) | 3.70642 | + | 6.41971i | 0.332846 | + | 0.576507i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 4.79159 | + | 2.15137i | 0.426869 | + | 0.191659i | ||||
\(127\) | −11.7567 | −1.04324 | −0.521620 | − | 0.853178i | \(-0.674672\pi\) | ||||
−0.521620 | + | 0.853178i | \(0.674672\pi\) | |||||||
\(128\) | −5.83102 | − | 10.0996i | −0.515394 | − | 0.892689i | ||||
\(129\) | −19.1838 | − | 4.10907i | −1.68904 | − | 0.361784i | ||||
\(130\) | 5.09142 | − | 8.81859i | 0.446547 | − | 0.773442i | ||||
\(131\) | 0.485084 | − | 0.840190i | 0.0423820 | − | 0.0734077i | −0.844056 | − | 0.536255i | \(-0.819839\pi\) |
0.886438 | + | 0.462847i | \(0.153172\pi\) | |||||||
\(132\) | 7.55692 | − | 8.36641i | 0.657746 | − | 0.728202i | ||||
\(133\) | −1.84062 | − | 3.18804i | −0.159602 | − | 0.276438i | ||||
\(134\) | 7.90990 | 0.683311 | ||||||||
\(135\) | −4.75680 | + | 2.09113i | −0.409401 | + | 0.179975i | ||||
\(136\) | −7.75534 | −0.665015 | ||||||||
\(137\) | −5.38354 | − | 9.32456i | −0.459947 | − | 0.796651i | 0.539011 | − | 0.842299i | \(-0.318798\pi\) |
−0.998958 | + | 0.0456479i | \(0.985465\pi\) | |||||||
\(138\) | 2.03265 | − | 2.25039i | 0.173031 | − | 0.191566i | ||||
\(139\) | 5.41270 | − | 9.37507i | 0.459099 | − | 0.795183i | −0.539814 | − | 0.841784i | \(-0.681506\pi\) |
0.998914 | + | 0.0466010i | \(0.0148389\pi\) | |||||||
\(140\) | −0.532651 | + | 0.922579i | −0.0450172 | + | 0.0779721i | ||||
\(141\) | 7.07155 | + | 1.51469i | 0.595532 | + | 0.127560i | ||||
\(142\) | −9.07504 | − | 15.7184i | −0.761560 | − | 1.31906i | ||||
\(143\) | 35.5368 | 2.97173 | ||||||||
\(144\) | 12.1525 | − | 8.77121i | 1.01270 | − | 0.730935i | ||||
\(145\) | −1.67803 | −0.139353 | ||||||||
\(146\) | −10.7102 | − | 18.5505i | −0.886378 | − | 1.53525i | ||||
\(147\) | −0.532651 | − | 1.64811i | −0.0439323 | − | 0.135934i | ||||
\(148\) | 2.39381 | − | 4.14619i | 0.196770 | − | 0.340815i | ||||
\(149\) | 6.90752 | − | 11.9642i | 0.565886 | − | 0.980143i | −0.431081 | − | 0.902313i | \(-0.641868\pi\) |
0.996967 | − | 0.0778300i | \(-0.0247991\pi\) | |||||||
\(150\) | −0.932566 | − | 2.88552i | −0.0761437 | − | 0.235602i | ||||
\(151\) | −5.42006 | − | 9.38782i | −0.441078 | − | 0.763970i | 0.556692 | − | 0.830719i | \(-0.312071\pi\) |
−0.997770 | + | 0.0667494i | \(0.978737\pi\) | |||||||
\(152\) | −6.02423 | −0.488629 | ||||||||
\(153\) | −1.44178 | − | 14.1439i | −0.116561 | − | 1.14347i | ||||
\(154\) | −10.6975 | −0.862030 | ||||||||
\(155\) | 3.47922 | + | 6.02618i | 0.279458 | + | 0.484035i | ||||
\(156\) | −10.4936 | − | 2.24768i | −0.840161 | − | 0.179958i | ||||
\(157\) | 5.53503 | − | 9.58695i | 0.441743 | − | 0.765122i | −0.556076 | − | 0.831132i | \(-0.687694\pi\) |
0.997819 | + | 0.0660099i | \(0.0210269\pi\) | |||||||
\(158\) | −7.73229 | + | 13.3927i | −0.615148 | + | 1.06547i | ||||
\(159\) | 9.64310 | − | 10.6761i | 0.764748 | − | 0.846666i | ||||
\(160\) | 2.73680 | + | 4.74027i | 0.216363 | + | 0.374752i | ||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 10.4700 | + | 11.7757i | 0.822602 | + | 0.925190i | ||||
\(163\) | 11.2066 | 0.877767 | 0.438883 | − | 0.898544i | \(-0.355374\pi\) | ||||
0.438883 | + | 0.898544i | \(0.355374\pi\) | |||||||
\(164\) | 2.11713 | + | 3.66698i | 0.165320 | + | 0.286343i | ||||
\(165\) | 7.09369 | − | 7.85355i | 0.552243 | − | 0.611398i | ||||
\(166\) | 5.55130 | − | 9.61513i | 0.430864 | − | 0.746279i | ||||
\(167\) | −11.8200 | + | 20.4728i | −0.914657 | + | 1.58423i | −0.107255 | + | 0.994232i | \(0.534206\pi\) |
−0.807403 | + | 0.590001i | \(0.799127\pi\) | |||||||
\(168\) | −2.77158 | − | 0.593659i | −0.213832 | − | 0.0458018i | ||||
\(169\) | −10.4135 | − | 18.0368i | −0.801040 | − | 1.38744i | ||||
\(170\) | 8.29717 | 0.636364 | ||||||||
\(171\) | −1.11995 | − | 10.9868i | −0.0856449 | − | 0.840179i | ||||
\(172\) | −12.0667 | −0.920075 | ||||||||
\(173\) | 1.54452 | + | 2.67519i | 0.117428 | + | 0.203391i | 0.918748 | − | 0.394845i | \(-0.129202\pi\) |
−0.801320 | + | 0.598236i | \(0.795868\pi\) | |||||||
\(174\) | 1.56488 | + | 4.84200i | 0.118633 | + | 0.367071i | ||||
\(175\) | −0.500000 | + | 0.866025i | −0.0377964 | + | 0.0654654i | ||||
\(176\) | −15.2621 | + | 26.4348i | −1.15043 | + | 1.99260i | ||||
\(177\) | −0.445897 | − | 1.37968i | −0.0335157 | − | 0.103703i | ||||
\(178\) | 8.46071 | + | 14.6544i | 0.634157 | + | 1.09839i | ||||
\(179\) | 22.9526 | 1.71556 | 0.857780 | − | 0.514017i | \(-0.171843\pi\) | ||||
0.857780 | + | 0.514017i | \(0.171843\pi\) | |||||||
\(180\) | −2.59142 | + | 1.87039i | −0.193153 | + | 0.139411i | ||||
\(181\) | −4.10028 | −0.304772 | −0.152386 | − | 0.988321i | \(-0.548696\pi\) | ||||
−0.152386 | + | 0.988321i | \(0.548696\pi\) | |||||||
\(182\) | 5.09142 | + | 8.81859i | 0.377401 | + | 0.653678i | ||||
\(183\) | −15.6774 | − | 3.35802i | −1.15891 | − | 0.248232i | ||||
\(184\) | −0.818235 | + | 1.41722i | −0.0603211 | + | 0.104479i | ||||
\(185\) | 2.24707 | − | 3.89203i | 0.165208 | − | 0.286148i | ||||
\(186\) | 14.1441 | − | 15.6592i | 1.03709 | − | 1.14819i | ||||
\(187\) | 14.4780 | + | 25.0767i | 1.05874 | + | 1.83379i | ||||
\(188\) | 4.44803 | 0.324406 | ||||||||
\(189\) | 0.567434 | − | 5.16508i | 0.0412748 | − | 0.375704i | ||||
\(190\) | 6.44511 | 0.467577 | ||||||||
\(191\) | 4.36740 | + | 7.56456i | 0.316014 | + | 0.547353i | 0.979653 | − | 0.200701i | \(-0.0643219\pi\) |
−0.663638 | + | 0.748054i | \(0.730989\pi\) | |||||||
\(192\) | −0.474024 | + | 0.524801i | −0.0342097 | + | 0.0378742i | ||||
\(193\) | 8.09142 | − | 14.0147i | 0.582433 | − | 1.00880i | −0.412757 | − | 0.910841i | \(-0.635434\pi\) |
0.995190 | − | 0.0979624i | \(-0.0312325\pi\) | |||||||
\(194\) | 7.15512 | − | 12.3930i | 0.513708 | − | 0.889768i | ||||
\(195\) | −9.85035 | − | 2.10990i | −0.705399 | − | 0.151093i | ||||
\(196\) | −0.532651 | − | 0.922579i | −0.0380465 | − | 0.0658985i | ||||
\(197\) | −0.418652 | −0.0298278 | −0.0149139 | − | 0.999889i | \(-0.504747\pi\) | ||||
−0.0149139 | + | 0.999889i | \(0.504747\pi\) | |||||||
\(198\) | −29.2769 | − | 13.1450i | −2.08062 | − | 0.934176i | ||||
\(199\) | −7.48667 | −0.530716 | −0.265358 | − | 0.964150i | \(-0.585490\pi\) | ||||
−0.265358 | + | 0.964150i | \(0.585490\pi\) | |||||||
\(200\) | 0.818235 | + | 1.41722i | 0.0578579 | + | 0.100213i | ||||
\(201\) | −2.40645 | − | 7.44598i | −0.169738 | − | 0.525199i | ||||
\(202\) | −10.6203 | + | 18.3950i | −0.747244 | + | 1.29426i | ||||
\(203\) | 0.839016 | − | 1.45322i | 0.0588874 | − | 0.101996i | ||||
\(204\) | −2.68911 | − | 8.32058i | −0.188275 | − | 0.582557i | ||||
\(205\) | 1.98736 | + | 3.44220i | 0.138803 | + | 0.240414i | ||||
\(206\) | −2.44376 | −0.170265 | ||||||||
\(207\) | −2.73680 | − | 1.22879i | −0.190221 | − | 0.0854071i | ||||
\(208\) | 29.0557 | 2.01465 | ||||||||
\(209\) | 11.2463 | + | 19.4791i | 0.777922 | + | 1.34740i | ||||
\(210\) | 2.96522 | + | 0.635135i | 0.204619 | + | 0.0438284i | ||||
\(211\) | −3.12969 | + | 5.42078i | −0.215457 | + | 0.373182i | −0.953414 | − | 0.301666i | \(-0.902457\pi\) |
0.737957 | + | 0.674848i | \(0.235791\pi\) | |||||||
\(212\) | 4.42419 | − | 7.66291i | 0.303854 | − | 0.526291i | ||||
\(213\) | −12.0356 | + | 13.3248i | −0.824666 | + | 0.913003i | ||||
\(214\) | 0.424429 | + | 0.735133i | 0.0290134 | + | 0.0502526i | ||||
\(215\) | −11.3270 | −0.772495 | ||||||||
\(216\) | −6.85578 | − | 5.03043i | −0.466477 | − | 0.342277i | ||||
\(217\) | −6.95844 | −0.472369 | ||||||||
\(218\) | 9.39701 | + | 16.2761i | 0.636446 | + | 1.10236i | ||||
\(219\) | −14.2041 | + | 15.7257i | −0.959827 | + | 1.06264i | ||||
\(220\) | 3.25453 | − | 5.63702i | 0.219421 | − | 0.380048i | ||||
\(221\) | 13.7815 | − | 23.8702i | 0.927041 | − | 1.60568i | ||||
\(222\) | −13.3261 | − | 2.85438i | −0.894388 | − | 0.191573i | ||||
\(223\) | 11.6207 | + | 20.1277i | 0.778181 | + | 1.34785i | 0.932989 | + | 0.359904i | \(0.117191\pi\) |
−0.154808 | + | 0.987945i | \(0.549476\pi\) | |||||||
\(224\) | −5.47360 | −0.365720 | ||||||||
\(225\) | −2.43257 | + | 1.75574i | −0.162171 | + | 0.117049i | ||||
\(226\) | −1.95844 | −0.130273 | ||||||||
\(227\) | −9.88422 | − | 17.1200i | −0.656039 | − | 1.13629i | −0.981632 | − | 0.190783i | \(-0.938897\pi\) |
0.325593 | − | 0.945510i | \(-0.394436\pi\) | |||||||
\(228\) | −2.08886 | − | 6.46329i | −0.138338 | − | 0.428042i | ||||
\(229\) | 0.00517872 | − | 0.00896980i | 0.000342219 | − | 0.000592741i | −0.865854 | − | 0.500296i | \(-0.833224\pi\) |
0.866196 | + | 0.499704i | \(0.166558\pi\) | |||||||
\(230\) | 0.875400 | − | 1.51624i | 0.0577222 | − | 0.0999777i | ||||
\(231\) | 3.25453 | + | 10.0701i | 0.214133 | + | 0.662563i | ||||
\(232\) | −1.37302 | − | 2.37815i | −0.0901435 | − | 0.156133i | ||||
\(233\) | −6.48609 | −0.424918 | −0.212459 | − | 0.977170i | \(-0.568147\pi\) | ||||
−0.212459 | + | 0.977170i | \(0.568147\pi\) | |||||||
\(234\) | 3.09795 | + | 30.3910i | 0.202520 | + | 1.98672i | ||||
\(235\) | 4.17537 | 0.272371 | ||||||||
\(236\) | −0.445897 | − | 0.772316i | −0.0290254 | − | 0.0502735i | ||||
\(237\) | 14.9596 | + | 3.20428i | 0.971733 | + | 0.208140i | ||||
\(238\) | −4.14858 | + | 7.18556i | −0.268913 | + | 0.465770i | ||||
\(239\) | −7.89928 | + | 13.6820i | −0.510962 | + | 0.885012i | 0.488957 | + | 0.872308i | \(0.337377\pi\) |
−0.999919 | + | 0.0127043i | \(0.995956\pi\) | |||||||
\(240\) | 5.79997 | − | 6.42125i | 0.374386 | − | 0.414490i | ||||
\(241\) | 3.20899 | + | 5.55814i | 0.206709 | + | 0.358031i | 0.950676 | − | 0.310186i | \(-0.100391\pi\) |
−0.743967 | + | 0.668217i | \(0.767058\pi\) | |||||||
\(242\) | 46.1037 | 2.96366 | ||||||||
\(243\) | 7.89977 | − | 13.4385i | 0.506770 | − | 0.862081i | ||||
\(244\) | −9.86115 | −0.631295 | ||||||||
\(245\) | −0.500000 | − | 0.866025i | −0.0319438 | − | 0.0553283i | ||||
\(246\) | 8.07920 | − | 8.94463i | 0.515111 | − | 0.570289i | ||||
\(247\) | 10.7052 | − | 18.5420i | 0.681157 | − | 1.17980i | ||||
\(248\) | −5.69363 | + | 9.86166i | −0.361546 | + | 0.626216i | ||||
\(249\) | −10.7401 | − | 2.30047i | −0.680625 | − | 0.145787i | ||||
\(250\) | −0.875400 | − | 1.51624i | −0.0553652 | − | 0.0958953i | ||||
\(251\) | 4.15861 | 0.262489 | 0.131245 | − | 0.991350i | \(-0.458103\pi\) | ||||
0.131245 | + | 0.991350i | \(0.458103\pi\) | |||||||
\(252\) | −0.324100 | − | 3.17943i | −0.0204164 | − | 0.200285i | ||||
\(253\) | 6.11007 | 0.384137 | ||||||||
\(254\) | 10.2918 | + | 17.8260i | 0.645767 | + | 1.11850i | ||||
\(255\) | −2.52427 | − | 7.81053i | −0.158076 | − | 0.489114i | ||||
\(256\) | −9.80066 | + | 16.9752i | −0.612541 | + | 1.06095i | ||||
\(257\) | −5.87404 | + | 10.1741i | −0.366413 | + | 0.634645i | −0.989002 | − | 0.147903i | \(-0.952748\pi\) |
0.622589 | + | 0.782549i | \(0.286081\pi\) | |||||||
\(258\) | 10.5632 | + | 32.6843i | 0.657634 | + | 2.03483i | ||||
\(259\) | 2.24707 | + | 3.89203i | 0.139626 | + | 0.241839i | ||||
\(260\) | −6.19591 | −0.384254 | ||||||||
\(261\) | 4.08192 | − | 2.94619i | 0.252665 | − | 0.182365i | ||||
\(262\) | −1.69857 | −0.104938 | ||||||||
\(263\) | 6.19926 | + | 10.7374i | 0.382263 | + | 0.662098i | 0.991385 | − | 0.130978i | \(-0.0418117\pi\) |
−0.609123 | + | 0.793076i | \(0.708478\pi\) | |||||||
\(264\) | 16.9345 | + | 3.62730i | 1.04225 | + | 0.223245i | ||||
\(265\) | 4.15299 | − | 7.19318i | 0.255116 | − | 0.441874i | ||||
\(266\) | −3.22255 | + | 5.58163i | −0.197587 | + | 0.342231i | ||||
\(267\) | 11.2209 | − | 12.4228i | 0.686706 | − | 0.760265i | ||||
\(268\) | −2.40645 | − | 4.16809i | −0.146997 | − | 0.254607i | ||||
\(269\) | −18.8491 | −1.14925 | −0.574626 | − | 0.818416i | \(-0.694852\pi\) | ||||
−0.574626 | + | 0.818416i | \(0.694852\pi\) | |||||||
\(270\) | 7.33475 | + | 5.38187i | 0.446379 | + | 0.327530i | ||||
\(271\) | −21.0866 | −1.28092 | −0.640461 | − | 0.767991i | \(-0.721257\pi\) | ||||
−0.640461 | + | 0.767991i | \(0.721257\pi\) | |||||||
\(272\) | 11.8376 | + | 20.5033i | 0.717758 | + | 1.24319i | ||||
\(273\) | 6.75240 | − | 7.47571i | 0.408674 | − | 0.452450i | ||||
\(274\) | −9.42550 | + | 16.3254i | −0.569415 | + | 0.986256i | ||||
\(275\) | 3.05503 | − | 5.29147i | 0.184225 | − | 0.319088i | ||||
\(276\) | −1.80423 | − | 0.386458i | −0.108602 | − | 0.0232620i | ||||
\(277\) | 9.24867 | + | 16.0192i | 0.555699 | + | 0.962498i | 0.997849 | + | 0.0655572i | \(0.0208825\pi\) |
−0.442150 | + | 0.896941i | \(0.645784\pi\) | |||||||
\(278\) | −18.9531 | −1.13673 | ||||||||
\(279\) | −19.0438 | − | 8.55048i | −1.14012 | − | 0.511904i | ||||
\(280\) | −1.63647 | −0.0977978 | ||||||||
\(281\) | −8.81421 | − | 15.2667i | −0.525812 | − | 0.910733i | −0.999548 | − | 0.0300661i | \(-0.990428\pi\) |
0.473736 | − | 0.880667i | \(-0.342905\pi\) | |||||||
\(282\) | −3.89381 | − | 12.0481i | −0.231873 | − | 0.717455i | ||||
\(283\) | 1.89594 | − | 3.28386i | 0.112702 | − | 0.195205i | −0.804157 | − | 0.594417i | \(-0.797383\pi\) |
0.916859 | + | 0.399212i | \(0.130716\pi\) | |||||||
\(284\) | −5.52185 | + | 9.56413i | −0.327662 | + | 0.567526i | ||||
\(285\) | −1.96081 | − | 6.06710i | −0.116149 | − | 0.359384i | ||||
\(286\) | −31.1089 | − | 53.8822i | −1.83951 | − | 3.18612i | ||||
\(287\) | −3.97471 | −0.234620 | ||||||||
\(288\) | −14.9801 | − | 6.72592i | −0.882713 | − | 0.396329i | ||||
\(289\) | 5.45878 | 0.321105 | ||||||||
\(290\) | 1.46895 | + | 2.54430i | 0.0862597 | + | 0.149406i | ||||
\(291\) | −13.8430 | − | 2.96510i | −0.811491 | − | 0.173817i | ||||
\(292\) | −6.51676 | + | 11.2874i | −0.381365 | + | 0.660543i | ||||
\(293\) | 4.03730 | − | 6.99281i | 0.235861 | − | 0.408524i | −0.723661 | − | 0.690155i | \(-0.757542\pi\) |
0.959523 | + | 0.281631i | \(0.0908755\pi\) | |||||||
\(294\) | −2.03265 | + | 2.25039i | −0.118547 | + | 0.131245i | ||||
\(295\) | −0.418564 | − | 0.724974i | −0.0243697 | − | 0.0422096i | ||||
\(296\) | 7.35451 | 0.427472 | ||||||||
\(297\) | −3.46706 | + | 31.5590i | −0.201179 | + | 1.83124i | ||||
\(298\) | −24.1874 | −1.40114 | ||||||||
\(299\) | −2.90805 | − | 5.03689i | −0.168177 | − | 0.291291i | ||||
\(300\) | −1.23680 | + | 1.36928i | −0.0714066 | + | 0.0790556i | ||||
\(301\) | 5.66350 | − | 9.80947i | 0.326439 | − | 0.565408i | ||||
\(302\) | −9.48944 | + | 16.4362i | −0.546056 | + | 0.945797i | ||||
\(303\) | 20.5471 | + | 4.40109i | 1.18040 | + | 0.252836i | ||||
\(304\) | 9.19524 | + | 15.9266i | 0.527383 | + | 0.913454i | ||||
\(305\) | −9.25667 | −0.530035 | ||||||||
\(306\) | −20.1834 | + | 14.5677i | −1.15381 | + | 0.832778i | ||||
\(307\) | −1.03255 | −0.0589305 | −0.0294653 | − | 0.999566i | \(-0.509380\pi\) | ||||
−0.0294653 | + | 0.999566i | \(0.509380\pi\) | |||||||
\(308\) | 3.25453 | + | 5.63702i | 0.185444 | + | 0.321199i | ||||
\(309\) | 0.743474 | + | 2.30044i | 0.0422947 | + | 0.130867i | ||||
\(310\) | 6.09142 | − | 10.5506i | 0.345969 | − | 0.599236i | ||||
\(311\) | −4.14471 | + | 7.17885i | −0.235025 | + | 0.407075i | −0.959280 | − | 0.282457i | \(-0.908851\pi\) |
0.724255 | + | 0.689532i | \(0.242184\pi\) | |||||||
\(312\) | −5.06971 | − | 15.6866i | −0.287016 | − | 0.888076i | ||||
\(313\) | −10.0346 | − | 17.3805i | −0.567191 | − | 0.982404i | −0.996842 | − | 0.0794088i | \(-0.974697\pi\) |
0.429651 | − | 0.902995i | \(-0.358637\pi\) | |||||||
\(314\) | −19.3815 | −1.09376 | ||||||||
\(315\) | −0.304233 | − | 2.98453i | −0.0171416 | − | 0.168159i | ||||
\(316\) | 9.40967 | 0.529335 | ||||||||
\(317\) | −10.3821 | − | 17.9823i | −0.583116 | − | 1.00999i | −0.995107 | − | 0.0987992i | \(-0.968500\pi\) |
0.411991 | − | 0.911188i | \(-0.364833\pi\) | |||||||
\(318\) | −24.6290 | − | 5.27541i | −1.38113 | − | 0.295830i | ||||
\(319\) | −5.12644 | + | 8.87926i | −0.287026 | + | 0.497143i | ||||
\(320\) | −0.204148 | + | 0.353594i | −0.0114122 | + | 0.0197665i | ||||
\(321\) | 0.562891 | − | 0.623188i | 0.0314175 | − | 0.0347829i | ||||
\(322\) | 0.875400 | + | 1.51624i | 0.0487841 | + | 0.0844966i | ||||
\(323\) | 17.4456 | 0.970701 | ||||||||
\(324\) | 3.01987 | − | 9.09971i | 0.167770 | − | 0.505540i | ||||
\(325\) | −5.81610 | −0.322619 | ||||||||
\(326\) | −9.81024 | − | 16.9918i | −0.543339 | − | 0.941090i | ||||
\(327\) | 12.4626 | − | 13.7976i | 0.689184 | − | 0.763008i | ||||
\(328\) | −3.25225 | + | 5.63306i | −0.179575 | + | 0.311033i | ||||
\(329\) | −2.08768 | + | 3.61598i | −0.115098 | + | 0.199355i | ||||
\(330\) | −18.1177 | − | 3.88071i | −0.997345 | − | 0.213626i | ||||
\(331\) | 5.58158 | + | 9.66757i | 0.306791 | + | 0.531378i | 0.977659 | − | 0.210200i | \(-0.0674114\pi\) |
−0.670867 | + | 0.741577i | \(0.734078\pi\) | |||||||
\(332\) | −6.75555 | −0.370759 | ||||||||
\(333\) | 1.36726 | + | 13.4129i | 0.0749256 | + | 0.735022i | ||||
\(334\) | 41.3888 | 2.26470 | ||||||||
\(335\) | −2.25894 | − | 3.91259i | −0.123419 | − | 0.213768i | ||||
\(336\) | 2.66098 | + | 8.23355i | 0.145169 | + | 0.449177i | ||||
\(337\) | −3.03624 | + | 5.25893i | −0.165395 | + | 0.286472i | −0.936795 | − | 0.349878i | \(-0.886223\pi\) |
0.771401 | + | 0.636350i | \(0.219556\pi\) | |||||||
\(338\) | −18.2320 | + | 31.5788i | −0.991690 | + | 1.71766i | ||||
\(339\) | 0.595821 | + | 1.84357i | 0.0323606 | + | 0.100129i | ||||
\(340\) | −2.52427 | − | 4.37217i | −0.136898 | − | 0.237114i | ||||
\(341\) | 42.5165 | 2.30240 | ||||||||
\(342\) | −15.6781 | + | 11.3159i | −0.847777 | + | 0.611896i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −9.26814 | − | 16.0529i | −0.499705 | − | 0.865514i | ||||
\(345\) | −1.69363 | − | 0.362768i | −0.0911822 | − | 0.0195308i | ||||
\(346\) | 2.70415 | − | 4.68372i | 0.145376 | − | 0.251798i | ||||
\(347\) | −9.75254 | + | 16.8919i | −0.523544 | + | 0.906804i | 0.476081 | + | 0.879402i | \(0.342057\pi\) |
−0.999624 | + | 0.0274029i | \(0.991276\pi\) | |||||||
\(348\) | 2.07539 | − | 2.29770i | 0.111252 | − | 0.123170i | ||||
\(349\) | 6.29410 | + | 10.9017i | 0.336916 | + | 0.583555i | 0.983851 | − | 0.178990i | \(-0.0572830\pi\) |
−0.646935 | + | 0.762545i | \(0.723950\pi\) | |||||||
\(350\) | 1.75080 | 0.0935842 | ||||||||
\(351\) | 27.6661 | − | 12.1622i | 1.47671 | − | 0.649170i | ||||
\(352\) | 33.4440 | 1.78257 | ||||||||
\(353\) | −8.20857 | − | 14.2177i | −0.436898 | − | 0.756729i | 0.560550 | − | 0.828120i | \(-0.310590\pi\) |
−0.997448 | + | 0.0713908i | \(0.977256\pi\) | |||||||
\(354\) | −1.70159 | + | 1.88386i | −0.0904384 | + | 0.100126i | ||||
\(355\) | −5.18337 | + | 8.97785i | −0.275105 | + | 0.476495i | ||||
\(356\) | 5.14805 | − | 8.91669i | 0.272846 | − | 0.472583i | ||||
\(357\) | 8.02625 | + | 1.71918i | 0.424794 | + | 0.0909888i | ||||
\(358\) | −20.0927 | − | 34.8016i | −1.06193 | − | 1.83932i | ||||
\(359\) | −13.2324 | −0.698381 | −0.349191 | − | 0.937052i | \(-0.613543\pi\) | ||||
−0.349191 | + | 0.937052i | \(0.613543\pi\) | |||||||
\(360\) | −4.47869 | − | 2.01088i | −0.236048 | − | 0.105983i | ||||
\(361\) | −5.44852 | −0.286764 | ||||||||
\(362\) | 3.58939 | + | 6.21701i | 0.188654 | + | 0.326759i | ||||
\(363\) | −14.0263 | − | 43.3997i | −0.736187 | − | 2.27789i | ||||
\(364\) | 3.09795 | − | 5.36581i | 0.162377 | − | 0.281245i | ||||
\(365\) | −6.11729 | + | 10.5955i | −0.320194 | + | 0.554591i | ||||
\(366\) | 8.63245 | + | 26.7103i | 0.451225 | + | 1.39617i | ||||
\(367\) | 10.1362 | + | 17.5564i | 0.529104 | + | 0.916436i | 0.999424 | + | 0.0339395i | \(0.0108053\pi\) |
−0.470320 | + | 0.882496i | \(0.655861\pi\) | |||||||
\(368\) | 4.99574 | 0.260421 | ||||||||
\(369\) | −10.8780 | − | 4.88410i | −0.566285 | − | 0.254256i | ||||
\(370\) | −7.86833 | −0.409055 | ||||||||
\(371\) | 4.15299 | + | 7.19318i | 0.215612 | + | 0.373451i | ||||
\(372\) | −12.5546 | − | 2.68914i | −0.650928 | − | 0.139425i | ||||
\(373\) | −15.1254 | + | 26.1979i | −0.783162 | + | 1.35648i | 0.146929 | + | 0.989147i | \(0.453061\pi\) |
−0.930091 | + | 0.367329i | \(0.880272\pi\) | |||||||
\(374\) | 25.3481 | − | 43.9042i | 1.31072 | − | 2.27023i | ||||
\(375\) | −1.16098 | + | 1.28535i | −0.0599529 | + | 0.0663750i | ||||
\(376\) | 3.41643 | + | 5.91743i | 0.176189 | + | 0.305168i | ||||
\(377\) | 9.75961 | 0.502645 | ||||||||
\(378\) | −8.32822 | + | 3.66114i | −0.428357 | + | 0.188309i | ||||
\(379\) | −0.698602 | −0.0358848 | −0.0179424 | − | 0.999839i | \(-0.505712\pi\) | ||||
−0.0179424 | + | 0.999839i | \(0.505712\pi\) | |||||||
\(380\) | −1.96081 | − | 3.39623i | −0.100588 | − | 0.174223i | ||||
\(381\) | 13.6494 | − | 15.1115i | 0.699278 | − | 0.774183i | ||||
\(382\) | 7.64645 | − | 13.2440i | 0.391226 | − | 0.677624i | ||||
\(383\) | −3.04757 | + | 5.27854i | −0.155723 | + | 0.269721i | −0.933322 | − | 0.359040i | \(-0.883104\pi\) |
0.777599 | + | 0.628761i | \(0.216438\pi\) | |||||||
\(384\) | 19.7512 | + | 4.23062i | 1.00793 | + | 0.215893i | ||||
\(385\) | 3.05503 | + | 5.29147i | 0.155699 | + | 0.269678i | ||||
\(386\) | −28.3329 | −1.44211 | ||||||||
\(387\) | 27.5537 | − | 19.8873i | 1.40063 | − | 1.01093i | ||||
\(388\) | −8.70729 | −0.442046 | ||||||||
\(389\) | −6.77943 | − | 11.7423i | −0.343731 | − | 0.595359i | 0.641392 | − | 0.767214i | \(-0.278357\pi\) |
−0.985122 | + | 0.171855i | \(0.945024\pi\) | |||||||
\(390\) | 5.42390 | + | 16.7825i | 0.274650 | + | 0.849814i | ||||
\(391\) | 2.36954 | − | 4.10416i | 0.119833 | − | 0.207556i | ||||
\(392\) | 0.818235 | − | 1.41722i | 0.0413271 | − | 0.0715806i | ||||
\(393\) | 0.516761 | + | 1.59895i | 0.0260671 | + | 0.0806562i | ||||
\(394\) | 0.366488 | + | 0.634777i | 0.0184634 | + | 0.0319796i | ||||
\(395\) | 8.83286 | 0.444430 | ||||||||
\(396\) | 1.98027 | + | 19.4265i | 0.0995124 | + | 0.976220i | ||||
\(397\) | −16.4109 | −0.823639 | −0.411819 | − | 0.911265i | \(-0.635107\pi\) | ||||
−0.411819 | + | 0.911265i | \(0.635107\pi\) | |||||||
\(398\) | 6.55383 | + | 11.3516i | 0.328514 | + | 0.569003i | ||||
\(399\) | 6.23467 | + | 1.33543i | 0.312124 | + | 0.0668553i | ||||
\(400\) | 2.49787 | − | 4.32643i | 0.124893 | − | 0.216322i | ||||
\(401\) | 1.75042 | − | 3.03181i | 0.0874117 | − | 0.151401i | −0.819005 | − | 0.573787i | \(-0.805474\pi\) |
0.906416 | + | 0.422385i | \(0.138807\pi\) | |||||||
\(402\) | −9.18326 | + | 10.1670i | −0.458019 | + | 0.507082i | ||||
\(403\) | −20.2355 | − | 35.0489i | −1.00800 | − | 1.74591i | ||||
\(404\) | 12.9242 | 0.643004 | ||||||||
\(405\) | 2.83475 | − | 8.54191i | 0.140860 | − | 0.424451i | ||||
\(406\) | −2.93790 | −0.145806 | ||||||||
\(407\) | −13.7297 | − | 23.7806i | −0.680558 | − | 1.17876i | ||||
\(408\) | 9.00383 | − | 9.96831i | 0.445756 | − | 0.493505i | ||||
\(409\) | −3.37859 | + | 5.85188i | −0.167060 | + | 0.289357i | −0.937385 | − | 0.348295i | \(-0.886761\pi\) |
0.770325 | + | 0.637652i | \(0.220094\pi\) | |||||||
\(410\) | 3.47946 | − | 6.02661i | 0.171838 | − | 0.297633i | ||||
\(411\) | 18.2355 | + | 3.90595i | 0.899490 | + | 0.192666i | ||||
\(412\) | 0.743474 | + | 1.28773i | 0.0366283 | + | 0.0634421i | ||||
\(413\) | 0.837128 | 0.0411924 | ||||||||
\(414\) | 0.532651 | + | 5.22532i | 0.0261784 | + | 0.256811i | ||||
\(415\) | −6.34144 | −0.311289 | ||||||||
\(416\) | −15.9175 | − | 27.5699i | −0.780420 | − | 1.35173i | ||||
\(417\) | 5.76616 | + | 17.8415i | 0.282370 | + | 0.873702i | ||||
\(418\) | 19.6900 | − | 34.1041i | 0.963070 | − | 1.66809i | ||||
\(419\) | 15.1142 | − | 26.1785i | 0.738376 | − | 1.27890i | −0.214850 | − | 0.976647i | \(-0.568926\pi\) |
0.953226 | − | 0.302258i | \(-0.0977404\pi\) | |||||||
\(420\) | −0.567434 | − | 1.75574i | −0.0276880 | − | 0.0856714i | ||||
\(421\) | 0.650611 | + | 1.12689i | 0.0317088 | + | 0.0549213i | 0.881444 | − | 0.472288i | \(-0.156572\pi\) |
−0.849736 | + | 0.527209i | \(0.823238\pi\) | |||||||
\(422\) | 10.9589 | 0.533472 | ||||||||
\(423\) | −10.1569 | + | 7.33086i | −0.493843 | + | 0.356439i | ||||
\(424\) | 13.5925 | 0.660109 | ||||||||
\(425\) | −2.36954 | − | 4.10416i | −0.114939 | − | 0.199081i | ||||
\(426\) | 30.7396 | + | 6.58427i | 1.48934 | + | 0.319009i | ||||
\(427\) | 4.62833 | − | 8.01651i | 0.223981 | − | 0.387946i | ||||
\(428\) | 0.258251 | − | 0.447303i | 0.0124830 | − | 0.0216212i | ||||
\(429\) | −41.2576 | + | 45.6771i | −1.99194 | + | 2.20531i | ||||
\(430\) | 9.91566 | + | 17.1744i | 0.478175 | + | 0.828224i | ||||
\(431\) | −6.84759 | −0.329837 | −0.164918 | − | 0.986307i | \(-0.552736\pi\) | ||||
−0.164918 | + | 0.986307i | \(0.552736\pi\) | |||||||
\(432\) | −2.83475 | + | 25.8034i | −0.136387 | + | 1.24146i | ||||
\(433\) | −5.73858 | −0.275779 | −0.137889 | − | 0.990448i | \(-0.544032\pi\) | ||||
−0.137889 | + | 0.990448i | \(0.544032\pi\) | |||||||
\(434\) | 6.09142 | + | 10.5506i | 0.292397 | + | 0.506447i | ||||
\(435\) | 1.94817 | − | 2.15685i | 0.0934075 | − | 0.103413i | ||||
\(436\) | 5.71776 | − | 9.90345i | 0.273831 | − | 0.474289i | ||||
\(437\) | 1.84062 | − | 3.18804i | 0.0880487 | − | 0.152505i | ||||
\(438\) | 36.2782 | + | 7.77060i | 1.73344 | + | 0.371294i | ||||
\(439\) | −6.16981 | − | 10.6864i | −0.294469 | − | 0.510035i | 0.680392 | − | 0.732848i | \(-0.261809\pi\) |
−0.974861 | + | 0.222813i | \(0.928476\pi\) | |||||||
\(440\) | 9.99894 | 0.476681 | ||||||||
\(441\) | 2.73680 | + | 1.22879i | 0.130324 | + | 0.0585140i | ||||
\(442\) | −48.2572 | −2.29536 | ||||||||
\(443\) | −5.16965 | − | 8.95410i | −0.245618 | − | 0.425422i | 0.716687 | − | 0.697394i | \(-0.245657\pi\) |
−0.962305 | + | 0.271972i | \(0.912324\pi\) | |||||||
\(444\) | 2.55013 | + | 7.89053i | 0.121024 | + | 0.374468i | ||||
\(445\) | 4.83248 | − | 8.37010i | 0.229082 | − | 0.396781i | ||||
\(446\) | 20.3456 | − | 35.2395i | 0.963390 | − | 1.66864i | ||||
\(447\) | 7.35860 | + | 22.7688i | 0.348050 | + | 1.07693i | ||||
\(448\) | −0.204148 | − | 0.353594i | −0.00964506 | − | 0.0167057i | ||||
\(449\) | 24.4414 | 1.15346 | 0.576731 | − | 0.816934i | \(-0.304328\pi\) | ||||
0.576731 | + | 0.816934i | \(0.304328\pi\) | |||||||
\(450\) | 4.79159 | + | 2.15137i | 0.225878 | + | 0.101417i | ||||
\(451\) | 24.2857 | 1.14357 | ||||||||
\(452\) | 0.595821 | + | 1.03199i | 0.0280251 | + | 0.0485408i | ||||
\(453\) | 18.3592 | + | 3.93245i | 0.862591 | + | 0.184763i | ||||
\(454\) | −17.3053 | + | 29.9737i | −0.812178 | + | 1.40673i | ||||
\(455\) | 2.90805 | − | 5.03689i | 0.136332 | − | 0.236133i | ||||
\(456\) | 6.99403 | − | 7.74322i | 0.327525 | − | 0.362610i | ||||
\(457\) | 19.9778 | + | 34.6025i | 0.934520 | + | 1.61864i | 0.775487 | + | 0.631364i | \(0.217504\pi\) |
0.159033 | + | 0.987273i | \(0.449162\pi\) | |||||||
\(458\) | −0.0181338 | −0.000847337 | ||||||||
\(459\) | 19.8537 | + | 14.5677i | 0.926692 | + | 0.679961i | ||||
\(460\) | −1.06530 | −0.0496700 | ||||||||
\(461\) | 7.58273 | + | 13.1337i | 0.353163 | + | 0.611696i | 0.986802 | − | 0.161933i | \(-0.0517727\pi\) |
−0.633639 | + | 0.773629i | \(0.718439\pi\) | |||||||
\(462\) | 12.4196 | − | 13.7500i | 0.577814 | − | 0.639708i | ||||
\(463\) | −5.21428 | + | 9.03139i | −0.242328 | + | 0.419724i | −0.961377 | − | 0.275235i | \(-0.911244\pi\) |
0.719049 | + | 0.694959i | \(0.244578\pi\) | |||||||
\(464\) | −4.19150 | + | 7.25990i | −0.194586 | + | 0.337032i | ||||
\(465\) | −11.7851 | − | 2.52430i | −0.546519 | − | 0.117062i | ||||
\(466\) | 5.67793 | + | 9.83446i | 0.263025 | + | 0.455573i | ||||
\(467\) | −27.5899 | −1.27671 | −0.638353 | − | 0.769744i | \(-0.720384\pi\) | ||||
−0.638353 | + | 0.769744i | \(0.720384\pi\) | |||||||
\(468\) | 15.0719 | − | 10.8784i | 0.696701 | − | 0.502854i | ||||
\(469\) | 4.51787 | 0.208616 | ||||||||
\(470\) | −3.65512 | − | 6.33085i | −0.168598 | − | 0.292020i | ||||
\(471\) | 5.89648 | + | 18.2447i | 0.271695 | + | 0.840672i | ||||
\(472\) | 0.684967 | − | 1.18640i | 0.0315282 | − | 0.0546084i | ||||
\(473\) | −34.6044 | + | 59.9365i | −1.59111 | + | 2.75588i | ||||
\(474\) | −8.23723 | − | 25.4874i | −0.378348 | − | 1.17068i | ||||
\(475\) | −1.84062 | − | 3.18804i | −0.0844533 | − | 0.146277i | ||||
\(476\) | 5.04854 | 0.231400 | ||||||||
\(477\) | 2.52695 | + | 24.7895i | 0.115701 | + | 1.13503i | ||||
\(478\) | 27.6601 | 1.26514 | ||||||||
\(479\) | −10.7444 | − | 18.6099i | −0.490924 | − | 0.850306i | 0.509021 | − | 0.860754i | \(-0.330008\pi\) |
−0.999945 | + | 0.0104482i | \(0.996674\pi\) | |||||||
\(480\) | −9.27028 | − | 1.98565i | −0.423128 | − | 0.0906320i | ||||
\(481\) | −13.0692 | + | 22.6365i | −0.595903 | + | 1.03213i | ||||
\(482\) | 5.61831 | − | 9.73119i | 0.255907 | − | 0.443244i | ||||
\(483\) | 1.16098 | − | 1.28535i | 0.0528266 | − | 0.0584853i | ||||
\(484\) | −14.0263 | − | 24.2942i | −0.637557 | − | 1.10428i | ||||
\(485\) | −8.17354 | −0.371141 | ||||||||
\(486\) | −27.2914 | − | 0.213844i | −1.23796 | − | 0.00970016i | ||||
\(487\) | 11.6178 | 0.526451 | 0.263225 | − | 0.964734i | \(-0.415214\pi\) | ||||
0.263225 | + | 0.964734i | \(0.415214\pi\) | |||||||
\(488\) | −7.57413 | − | 13.1188i | −0.342865 | − | 0.593859i | ||||
\(489\) | −13.0107 | + | 14.4043i | −0.588362 | + | 0.651387i | ||||
\(490\) | −0.875400 | + | 1.51624i | −0.0395466 | + | 0.0684966i | ||||
\(491\) | −17.3701 | + | 30.0860i | −0.783903 | + | 1.35776i | 0.145749 | + | 0.989322i | \(0.453441\pi\) |
−0.929652 | + | 0.368438i | \(0.879893\pi\) | |||||||
\(492\) | −7.17130 | − | 1.53606i | −0.323307 | − | 0.0692508i | ||||
\(493\) | 3.97616 | + | 6.88690i | 0.179077 | + | 0.310171i | ||||
\(494\) | −37.4854 | −1.68655 | ||||||||
\(495\) | 1.85888 | + | 18.2357i | 0.0835506 | + | 0.819634i | ||||
\(496\) | 34.7625 | 1.56088 | ||||||||
\(497\) | −5.18337 | − | 8.97785i | −0.232506 | − | 0.402712i | ||||
\(498\) | 5.91381 | + | 18.2984i | 0.265004 | + | 0.819969i | ||||
\(499\) | 1.51854 | − | 2.63020i | 0.0679794 | − | 0.117744i | −0.830032 | − | 0.557715i | \(-0.811678\pi\) |
0.898012 | + | 0.439971i | \(0.145011\pi\) | |||||||
\(500\) | −0.532651 | + | 0.922579i | −0.0238209 | + | 0.0412590i | ||||
\(501\) | −12.5918 | − | 38.9614i | −0.562562 | − | 1.74066i | ||||
\(502\) | −3.64045 | − | 6.30544i | −0.162481 | − | 0.281425i | ||||
\(503\) | −3.40995 | −0.152042 | −0.0760210 | − | 0.997106i | \(-0.524222\pi\) | ||||
−0.0760210 | + | 0.997106i | \(0.524222\pi\) | |||||||
\(504\) | 3.98082 | − | 2.87322i | 0.177320 | − | 0.127983i | ||||
\(505\) | 12.1320 | 0.539866 | ||||||||
\(506\) | −5.34875 | − | 9.26431i | −0.237781 | − | 0.411849i | ||||
\(507\) | 35.2734 | + | 7.55539i | 1.56655 | + | 0.335547i | ||||
\(508\) | 6.26223 | − | 10.8465i | 0.277841 | − | 0.481235i | ||||
\(509\) | 15.6708 | − | 27.1427i | 0.694597 | − | 1.20308i | −0.275719 | − | 0.961238i | \(-0.588916\pi\) |
0.970316 | − | 0.241839i | \(-0.0777507\pi\) | |||||||
\(510\) | −9.63288 | + | 10.6647i | −0.426551 | + | 0.472242i | ||||
\(511\) | −6.11729 | − | 10.5955i | −0.270613 | − | 0.468715i | ||||
\(512\) | 10.9939 | 0.485867 | ||||||||
\(513\) | 15.4221 | + | 11.3159i | 0.680900 | + | 0.499611i | ||||
\(514\) | 20.5686 | 0.907240 | ||||||||
\(515\) | 0.697899 | + | 1.20880i | 0.0307531 | + | 0.0532660i | ||||
\(516\) | 14.0092 | − | 15.5099i | 0.616721 | − | 0.682784i | ||||
\(517\) | 12.7559 | − | 22.0939i | 0.561003 | − | 0.971686i | ||||
\(518\) | 3.93417 | − | 6.81418i | 0.172857 | − | 0.299398i | ||||
\(519\) | −5.23171 | − | 1.12061i | −0.229647 | − | 0.0491891i | ||||
\(520\) | −4.75894 | − | 8.24272i | −0.208693 | − | 0.361467i | ||||
\(521\) | −11.9819 | −0.524936 | −0.262468 | − | 0.964941i | \(-0.584536\pi\) | ||||
−0.262468 | + | 0.964941i | \(0.584536\pi\) | |||||||
\(522\) | −8.04044 | − | 3.61007i | −0.351920 | − | 0.158009i | ||||
\(523\) | −23.4259 | −1.02434 | −0.512172 | − | 0.858883i | \(-0.671159\pi\) | ||||
−0.512172 | + | 0.858883i | \(0.671159\pi\) | |||||||
\(524\) | 0.516761 | + | 0.895056i | 0.0225748 | + | 0.0391007i | ||||
\(525\) | −0.532651 | − | 1.64811i | −0.0232468 | − | 0.0719296i | ||||
\(526\) | 10.8537 | − | 18.7991i | 0.473242 | − | 0.819679i | ||||
\(527\) | 16.4883 | − | 28.5585i | 0.718240 | − | 1.24403i | ||||
\(528\) | −16.2588 | − | 50.3075i | −0.707573 | − | 2.18935i | ||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | −14.5421 | −0.631669 | ||||||||
\(531\) | 2.29105 | + | 1.02866i | 0.0994231 | + | 0.0446399i | ||||
\(532\) | 3.92163 | 0.170024 | ||||||||
\(533\) | −11.5587 | − | 20.0202i | −0.500661 | − | 0.867171i | ||||
\(534\) | −28.6587 | − | 6.13855i | −1.24018 | − | 0.265641i | ||||
\(535\) | 0.242420 | − | 0.419884i | 0.0104807 | − | 0.0181532i | ||||
\(536\) | 3.69668 | − | 6.40284i | 0.159672 | − | 0.276561i | ||||
\(537\) | −26.6476 | + | 29.5021i | −1.14993 | + | 1.27311i | ||||
\(538\) | 16.5005 | + | 28.5798i | 0.711389 | + | 1.23216i | ||||
\(539\) | −6.11007 | −0.263179 | ||||||||
\(540\) | 0.604489 | − | 5.50237i | 0.0260131 | − | 0.236784i | ||||
\(541\) | 7.62446 | 0.327801 | 0.163901 | − | 0.986477i | \(-0.447592\pi\) | ||||
0.163901 | + | 0.986477i | \(0.447592\pi\) | |||||||
\(542\) | 18.4592 | + | 31.9724i | 0.792893 | + | 1.37333i | ||||
\(543\) | 4.76036 | − | 5.27029i | 0.204287 | − | 0.226170i | ||||
\(544\) | 12.9699 | − | 22.4645i | 0.556079 | − | 0.963157i | ||||
\(545\) | 5.36726 | − | 9.29637i | 0.229908 | − | 0.398213i | ||||
\(546\) | −17.2460 | − | 3.69401i | −0.738061 | − | 0.158089i | ||||
\(547\) | −20.6792 | − | 35.8175i | −0.884180 | − | 1.53145i | −0.846650 | − | 0.532150i | \(-0.821384\pi\) |
−0.0375304 | − | 0.999295i | \(-0.511949\pi\) | |||||||
\(548\) | 11.4702 | 0.489982 | ||||||||
\(549\) | 22.5174 | − | 16.2523i | 0.961021 | − | 0.693631i | ||||
\(550\) | −10.6975 | −0.456143 | ||||||||
\(551\) | 3.08861 | + | 5.34964i | 0.131579 | + | 0.227902i | ||||
\(552\) | −0.871667 | − | 2.69709i | −0.0371006 | − | 0.114796i | ||||
\(553\) | −4.41643 | + | 7.64948i | −0.187806 | + | 0.325289i | ||||
\(554\) | 16.1926 | − | 28.0464i | 0.687956 | − | 1.19158i | ||||
\(555\) | 2.39381 | + | 7.40685i | 0.101611 | + | 0.314403i | ||||
\(556\) | 5.76616 | + | 9.98728i | 0.244540 | + | 0.423555i | ||||
\(557\) | −10.2775 | −0.435472 | −0.217736 | − | 0.976008i | \(-0.569867\pi\) | ||||
−0.217736 | + | 0.976008i | \(0.569867\pi\) | |||||||
\(558\) | 3.70642 | + | 36.3601i | 0.156905 | + | 1.53925i | ||||
\(559\) | 65.8790 | 2.78638 | ||||||||
\(560\) | 2.49787 | + | 4.32643i | 0.105554 | + | 0.182825i | ||||
\(561\) | −49.0409 | − | 10.5043i | −2.07051 | − | 0.443493i | ||||
\(562\) | −15.4319 | + | 26.7289i | −0.650957 | + | 1.12749i | ||||
\(563\) | 4.49496 | − | 7.78550i | 0.189440 | − | 0.328120i | −0.755624 | − | 0.655006i | \(-0.772666\pi\) |
0.945064 | + | 0.326886i | \(0.105999\pi\) | |||||||
\(564\) | −5.16409 | + | 5.71726i | −0.217447 | + | 0.240740i | ||||
\(565\) | 0.559298 | + | 0.968732i | 0.0235298 | + | 0.0407549i | ||||
\(566\) | −6.63882 | −0.279050 | ||||||||
\(567\) | 5.98013 | + | 6.72592i | 0.251142 | + | 0.282462i | ||||
\(568\) | −16.9648 | −0.711829 | ||||||||
\(569\) | −3.97112 | − | 6.87818i | −0.166478 | − | 0.288348i | 0.770701 | − | 0.637197i | \(-0.219906\pi\) |
−0.937179 | + | 0.348849i | \(0.886573\pi\) | |||||||
\(570\) | −7.48266 | + | 8.28420i | −0.313414 | + | 0.346987i | ||||
\(571\) | −19.5862 | + | 33.9243i | −0.819656 | + | 1.41969i | 0.0862797 | + | 0.996271i | \(0.472502\pi\) |
−0.905936 | + | 0.423415i | \(0.860831\pi\) | |||||||
\(572\) | −18.9287 | + | 32.7855i | −0.791449 | + | 1.37083i | ||||
\(573\) | −14.7936 | − | 3.16871i | −0.618010 | − | 0.132375i | ||||
\(574\) | 3.47946 | + | 6.02661i | 0.145230 | + | 0.251546i | ||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | −0.124217 | − | 1.21857i | −0.00517570 | − | 0.0507738i | ||||
\(577\) | 5.80815 | 0.241796 | 0.120898 | − | 0.992665i | \(-0.461423\pi\) | ||||
0.120898 | + | 0.992665i | \(0.461423\pi\) | |||||||
\(578\) | −4.77862 | − | 8.27681i | −0.198764 | − | 0.344270i | ||||
\(579\) | 8.61980 | + | 26.6712i | 0.358227 | + | 1.10842i | ||||
\(580\) | 0.893806 | − | 1.54812i | 0.0371133 | − | 0.0642821i | ||||
\(581\) | 3.17072 | − | 5.49185i | 0.131544 | − | 0.227840i | ||||
\(582\) | 7.62236 | + | 23.5849i | 0.315957 | + | 0.977626i | ||||
\(583\) | −25.3750 | − | 43.9508i | −1.05093 | − | 1.82026i | ||||
\(584\) | −20.0215 | −0.828496 | ||||||||
\(585\) | 14.1481 | − | 10.2116i | 0.584950 | − | 0.422196i | ||||
\(586\) | −14.1370 | −0.583994 | ||||||||
\(587\) | −1.00014 | − | 1.73229i | −0.0412802 | − | 0.0714993i | 0.844647 | − | 0.535323i | \(-0.179810\pi\) |
−0.885927 | + | 0.463824i | \(0.846477\pi\) | |||||||
\(588\) | 1.80423 | + | 0.386458i | 0.0744053 | + | 0.0159372i | ||||
\(589\) | 12.8078 | − | 22.1838i | 0.527737 | − | 0.914067i | ||||
\(590\) | −0.732822 | + | 1.26928i | −0.0301698 | + | 0.0522556i | ||||
\(591\) | 0.486049 | − | 0.538114i | 0.0199934 | − | 0.0221350i | ||||
\(592\) | −11.2258 | − | 19.4436i | −0.461376 | − | 0.799126i | ||||
\(593\) | 18.6458 | 0.765690 | 0.382845 | − | 0.923813i | \(-0.374944\pi\) | ||||
0.382845 | + | 0.923813i | \(0.374944\pi\) | |||||||
\(594\) | 50.8860 | − | 22.3698i | 2.08788 | − | 0.917845i | ||||
\(595\) | 4.73907 | 0.194283 | ||||||||
\(596\) | 7.35860 | + | 12.7455i | 0.301420 | + | 0.522074i | ||||
\(597\) | 8.69190 | − | 9.62297i | 0.355736 | − | 0.393842i | ||||
\(598\) | −5.09142 | + | 8.81859i | −0.208204 | + | 0.360619i | ||||
\(599\) | −14.0200 | + | 24.2833i | −0.572840 | + | 0.992188i | 0.423432 | + | 0.905928i | \(0.360825\pi\) |
−0.996273 | + | 0.0862606i | \(0.972508\pi\) | |||||||
\(600\) | −2.77158 | − | 0.593659i | −0.113149 | − | 0.0242360i | ||||
\(601\) | −14.9532 | − | 25.8996i | −0.609952 | − | 1.05647i | −0.991248 | − | 0.132015i | \(-0.957855\pi\) |
0.381296 | − | 0.924453i | \(-0.375478\pi\) | |||||||
\(602\) | −19.8313 | −0.808264 | ||||||||
\(603\) | 12.3645 | + | 5.55153i | 0.503522 | + | 0.226076i | ||||
\(604\) | 11.5480 | 0.469882 | ||||||||
\(605\) | −13.1665 | − | 22.8050i | −0.535293 | − | 0.927154i | ||||
\(606\) | −11.3139 | − | 35.0071i | −0.459594 | − | 1.42206i | ||||
\(607\) | −7.62634 | + | 13.2092i | −0.309544 | + | 0.536145i | −0.978263 | − | 0.207370i | \(-0.933510\pi\) |
0.668719 | + | 0.743515i | \(0.266843\pi\) | |||||||
\(608\) | 10.0748 | − | 17.4501i | 0.408587 | − | 0.707693i | ||||
\(609\) | 0.893806 | + | 2.76559i | 0.0362188 | + | 0.112067i | ||||
\(610\) | 8.10329 | + | 14.0353i | 0.328093 | + | 0.568273i | ||||
\(611\) | −24.2844 | −0.982441 | ||||||||
\(612\) | 13.8168 | + | 6.20361i | 0.558513 | + | 0.250766i | ||||
\(613\) | 21.4518 | 0.866431 | 0.433215 | − | 0.901290i | \(-0.357379\pi\) | ||||
0.433215 | + | 0.901290i | \(0.357379\pi\) | |||||||
\(614\) | 0.903891 | + | 1.56559i | 0.0364781 | + | 0.0631819i | ||||
\(615\) | −6.73171 | − | 1.44190i | −0.271449 | − | 0.0581429i | ||||
\(616\) | −4.99947 | + | 8.65933i | −0.201434 | + | 0.348894i | ||||
\(617\) | 15.8000 | − | 27.3664i | 0.636085 | − | 1.10173i | −0.350199 | − | 0.936675i | \(-0.613886\pi\) |
0.986284 | − | 0.165056i | \(-0.0527805\pi\) | |||||||
\(618\) | 2.83717 | − | 3.14109i | 0.114128 | − | 0.126353i | ||||
\(619\) | −9.37249 | − | 16.2336i | −0.376712 | − | 0.652485i | 0.613869 | − | 0.789408i | \(-0.289612\pi\) |
−0.990582 | + | 0.136923i | \(0.956279\pi\) | |||||||
\(620\) | −7.41284 | −0.297707 | ||||||||
\(621\) | 4.75680 | − | 2.09113i | 0.190884 | − | 0.0839140i | ||||
\(622\) | 14.5131 | 0.581923 | ||||||||
\(623\) | 4.83248 | + | 8.37010i | 0.193609 | + | 0.335341i | ||||
\(624\) | −33.7332 | + | 37.3467i | −1.35041 | + | 1.49506i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −17.5686 | + | 30.4298i | −0.702184 | + | 1.21622i | ||||
\(627\) | −38.0942 | − | 8.15959i | −1.52134 | − | 0.325863i | ||||
\(628\) | 5.89648 | + | 10.2130i | 0.235295 | + | 0.407543i | ||||
\(629\) | −21.2980 | −0.849208 | ||||||||
\(630\) | −4.25894 | + | 3.07395i | −0.169680 | + | 0.122469i | ||||
\(631\) | −34.9978 | −1.39324 | −0.696619 | − | 0.717441i | \(-0.745313\pi\) | ||||
−0.696619 | + | 0.717441i | \(0.745313\pi\) | |||||||
\(632\) | 7.22736 | + | 12.5181i | 0.287489 | + | 0.497945i | ||||
\(633\) | −3.33407 | − | 10.3162i | −0.132517 | − | 0.410031i | ||||
\(634\) | −18.1770 | + | 31.4834i | −0.721900 | + | 1.25037i | ||||
\(635\) | 5.87836 | − | 10.1816i | 0.233276 | − | 0.404045i | ||||
\(636\) | 4.71309 | + | 14.5831i | 0.186886 | + | 0.578259i | ||||
\(637\) | 2.90805 | + | 5.03689i | 0.115221 | + | 0.199569i | ||||
\(638\) | 17.9508 | 0.710677 | ||||||||
\(639\) | −3.15390 | − | 30.9399i | −0.124766 | − | 1.22396i | ||||
\(640\) | 11.6620 | 0.460983 | ||||||||
\(641\) | 20.6415 | + | 35.7522i | 0.815291 | + | 1.41213i | 0.909119 | + | 0.416537i | \(0.136756\pi\) |
−0.0938280 | + | 0.995588i | \(0.529910\pi\) | |||||||
\(642\) | −1.43766 | − | 0.307939i | −0.0567397 | − | 0.0121534i | ||||
\(643\) | −2.63091 | + | 4.55687i | −0.103753 | + | 0.179705i | −0.913228 | − | 0.407449i | \(-0.866418\pi\) |
0.809475 | + | 0.587154i | \(0.199752\pi\) | |||||||
\(644\) | 0.532651 | − | 0.922579i | 0.0209894 | − | 0.0363547i | ||||
\(645\) | 13.1505 | − | 14.5591i | 0.517799 | − | 0.573265i | ||||
\(646\) | −15.2719 | − | 26.4517i | −0.600865 | − | 1.04073i | ||||
\(647\) | −4.79934 | −0.188682 | −0.0943408 | − | 0.995540i | \(-0.530074\pi\) | ||||
−0.0943408 | + | 0.995540i | \(0.530074\pi\) | |||||||
\(648\) | 14.4253 | − | 2.97181i | 0.566679 | − | 0.116744i | ||||
\(649\) | −5.11491 | −0.200778 | ||||||||
\(650\) | 5.09142 | + | 8.81859i | 0.199702 | + | 0.345894i | ||||
\(651\) | 8.07863 | − | 8.94401i | 0.316627 | − | 0.350543i | ||||
\(652\) | −5.96919 | + | 10.3389i | −0.233772 | + | 0.404904i | ||||
\(653\) | −7.23824 | + | 12.5370i | −0.283254 | + | 0.490611i | −0.972184 | − | 0.234217i | \(-0.924747\pi\) |
0.688930 | + | 0.724828i | \(0.258081\pi\) | |||||||
\(654\) | −31.8302 | − | 6.81787i | −1.24466 | − | 0.266600i | ||||
\(655\) | 0.485084 | + | 0.840190i | 0.0189538 | + | 0.0328289i | ||||
\(656\) | 19.8566 | 0.775270 | ||||||||
\(657\) | −3.72216 | − | 36.5145i | −0.145215 | − | 1.42457i | ||||
\(658\) | 7.31024 | 0.284983 | ||||||||
\(659\) | 14.0086 | + | 24.2636i | 0.545696 | + | 0.945174i | 0.998563 | + | 0.0535955i | \(0.0170682\pi\) |
−0.452866 | + | 0.891578i | \(0.649599\pi\) | |||||||
\(660\) | 3.46706 | + | 10.7277i | 0.134955 | + | 0.417575i | ||||
\(661\) | 24.2168 | − | 41.9448i | 0.941926 | − | 1.63146i | 0.180134 | − | 0.983642i | \(-0.442347\pi\) |
0.761792 | − | 0.647822i | \(-0.224320\pi\) | |||||||
\(662\) | 9.77222 | − | 16.9260i | 0.379808 | − | 0.657847i | ||||
\(663\) | 14.6814 | + | 45.4269i | 0.570179 | + | 1.76423i | ||||
\(664\) | −5.18879 | − | 8.98725i | −0.201364 | − | 0.348773i | ||||
\(665\) | 3.68123 | 0.142752 | ||||||||
\(666\) | 19.1402 | − | 13.8147i | 0.741669 | − | 0.535311i | ||||
\(667\) | 1.67803 | 0.0649737 | ||||||||
\(668\) | −12.5918 | − | 21.8097i | −0.487193 | − | 0.843843i | ||||
\(669\) | −39.3625 | − | 8.43125i | −1.52184 | − | 0.325971i | ||||
\(670\) | −3.95495 | + | 6.85017i | −0.152793 | + | 0.264645i | ||||
\(671\) | −28.2794 | + | 48.9814i | −1.09171 | + | 1.89091i | ||||
\(672\) | 6.35476 | − | 7.03547i | 0.245140 | − | 0.271399i | ||||
\(673\) | 17.9700 | + | 31.1250i | 0.692693 | + | 1.19978i | 0.970952 | + | 0.239274i | \(0.0769094\pi\) |
−0.278259 | + | 0.960506i | \(0.589757\pi\) | |||||||
\(674\) | 10.6317 | 0.409518 | ||||||||
\(675\) | 0.567434 | − | 5.16508i | 0.0218406 | − | 0.198804i | ||||
\(676\) | 22.1871 | 0.853350 | ||||||||
\(677\) | 14.2219 | + | 24.6331i | 0.546593 | + | 0.946727i | 0.998505 | + | 0.0546646i | \(0.0174089\pi\) |
−0.451911 | + | 0.892063i | \(0.649258\pi\) | |||||||
\(678\) | 2.27371 | − | 2.51727i | 0.0873215 | − | 0.0966752i | ||||
\(679\) | 4.08677 | − | 7.07849i | 0.156836 | − | 0.271648i | ||||
\(680\) | 3.87767 | − | 6.71632i | 0.148702 | − | 0.257559i | ||||
\(681\) | 33.4805 | + | 7.17136i | 1.28298 | + | 0.274807i | ||||
\(682\) | −37.2190 | − | 64.4651i | −1.42519 | − | 2.46850i | ||||
\(683\) | −41.1926 | −1.57619 | −0.788096 | − | 0.615553i | \(-0.788933\pi\) | ||||
−0.788096 | + | 0.615553i | \(0.788933\pi\) | |||||||
\(684\) | 10.7327 | + | 4.81887i | 0.410375 | + | 0.184254i | ||||
\(685\) | 10.7671 | 0.411389 | ||||||||
\(686\) | −0.875400 | − | 1.51624i | −0.0334229 | − | 0.0578902i | ||||
\(687\) | 0.00551690 | + | 0.0170702i | 0.000210483 | + | 0.000651270i | ||||
\(688\) | −28.2933 | + | 49.0055i | −1.07867 | + | 1.86832i | ||||
\(689\) | −24.1542 | + | 41.8363i | −0.920202 | + | 1.59384i | ||||
\(690\) | 0.932566 | + | 2.88552i | 0.0355022 | + | 0.109850i | ||||
\(691\) | 3.28345 | + | 5.68710i | 0.124908 | + | 0.216348i | 0.921697 | − | 0.387910i | \(-0.126803\pi\) |
−0.796789 | + | 0.604258i | \(0.793470\pi\) | |||||||
\(692\) | −3.29076 | −0.125096 | ||||||||
\(693\) | −16.7220 | − | 7.50801i | −0.635217 | − | 0.285206i | ||||
\(694\) | 34.1495 | 1.29630 | ||||||||
\(695\) | 5.41270 | + | 9.37507i | 0.205315 | + | 0.355617i | ||||
\(696\) | 4.65080 | + | 0.996179i | 0.176288 | + | 0.0377601i | ||||
\(697\) | 9.41822 | − | 16.3128i | 0.356740 | − | 0.617892i | ||||
\(698\) | 11.0197 | − | 19.0867i | 0.417103 | − | 0.722443i | ||||
\(699\) | 7.53025 | − | 8.33688i | 0.284820 | − | 0.315330i | ||||
\(700\) | −0.532651 | − | 0.922579i | −0.0201323 | − | 0.0348702i | ||||
\(701\) | −2.61012 | −0.0985828 | −0.0492914 | − | 0.998784i | \(-0.515696\pi\) | ||||
−0.0492914 | + | 0.998784i | \(0.515696\pi\) | |||||||
\(702\) | −42.6597 | − | 31.3015i | −1.61009 | − | 1.18140i | ||||
\(703\) | −16.5440 | −0.623967 | ||||||||
\(704\) | 1.24735 | + | 2.16048i | 0.0470115 | + | 0.0814262i | ||||
\(705\) | −4.84754 | + | 5.36680i | −0.182569 | + | 0.202125i | ||||
\(706\) | −14.3716 | + | 24.8923i | −0.540881 | + | 0.936833i | ||||
\(707\) | −6.06599 | + | 10.5066i | −0.228135 | + | 0.395141i | ||||
\(708\) | 1.51037 | + | 0.323514i | 0.0567633 | + | 0.0121584i | ||||
\(709\) | 6.45282 | + | 11.1766i | 0.242341 | + | 0.419746i | 0.961381 | − | 0.275223i | \(-0.0887515\pi\) |
−0.719040 | + | 0.694969i | \(0.755418\pi\) | |||||||
\(710\) | 18.1501 | 0.681160 | ||||||||
\(711\) | −21.4865 | + | 15.5082i | −0.805807 | + | 0.581603i | ||||
\(712\) | 15.8164 | 0.592745 | ||||||||
\(713\) | −3.47922 | − | 6.02618i | −0.130298 | − | 0.225682i | ||||
\(714\) | −4.41949 | − | 13.6747i | −0.165395 | − | 0.511762i | ||||
\(715\) | −17.7684 | + | 30.7757i | −0.664500 | + | 1.15095i | ||||
\(716\) | −12.2257 | + | 21.1756i | −0.456897 | + | 0.791369i | ||||
\(717\) | −8.41512 | − | 26.0378i | −0.314268 | − | 0.972401i | ||||
\(718\) | 11.5837 | + | 20.0635i | 0.432299 | + | 0.748764i | ||||
\(719\) | 8.13828 | 0.303507 | 0.151753 | − | 0.988418i | \(-0.451508\pi\) | ||||
0.151753 | + | 0.988418i | \(0.451508\pi\) | |||||||
\(720\) | 1.51987 | + | 14.9099i | 0.0566421 | + | 0.555661i | ||||
\(721\) | −1.39580 | −0.0519823 | ||||||||
\(722\) | 4.76963 | + | 8.26125i | 0.177507 | + | 0.307452i | ||||
\(723\) | −10.8697 | − | 2.32824i | −0.404250 | − | 0.0865882i | ||||
\(724\) | 2.18402 | − | 3.78283i | 0.0811685 | − | 0.140588i | ||||
\(725\) | 0.839016 | − | 1.45322i | 0.0311603 | − | 0.0539712i | ||||
\(726\) | −53.5256 | + | 59.2592i | −1.98652 | + | 2.19932i | ||||
\(727\) | −14.2624 | − | 24.7031i | −0.528962 | − | 0.916189i | −0.999430 | − | 0.0337717i | \(-0.989248\pi\) |
0.470468 | − | 0.882417i | \(-0.344085\pi\) | |||||||
\(728\) | 9.51787 | 0.352756 | ||||||||
\(729\) | 8.10165 | + | 25.7558i | 0.300061 | + | 0.953920i | ||||
\(730\) | 21.4203 | 0.792801 | ||||||||
\(731\) | 26.8397 | + | 46.4878i | 0.992703 | + | 1.71941i | ||||
\(732\) | 11.4486 | − | 12.6750i | 0.423154 | − | 0.468481i | ||||
\(733\) | 18.9040 | − | 32.7427i | 0.698236 | − | 1.20938i | −0.270841 | − | 0.962624i | \(-0.587302\pi\) |
0.969077 | − | 0.246757i | \(-0.0793649\pi\) | |||||||
\(734\) | 17.7464 | − | 30.7377i | 0.655033 | − | 1.13455i | ||||
\(735\) | 1.69363 | + | 0.362768i | 0.0624707 | + | 0.0133809i | ||||
\(736\) | −2.73680 | − | 4.74027i | −0.100880 | − | 0.174729i | ||||
\(737\) | −27.6045 | −1.01683 | ||||||||
\(738\) | 2.11713 | + | 20.7691i | 0.0779328 | + | 0.764523i | ||||
\(739\) | −39.0949 | −1.43813 | −0.719065 | − | 0.694943i | \(-0.755430\pi\) | ||||
−0.719065 | + | 0.694943i | \(0.755430\pi\) | |||||||
\(740\) | 2.39381 | + | 4.14619i | 0.0879980 | + | 0.152417i | ||||
\(741\) | 11.4043 | + | 35.2869i | 0.418947 | + | 1.29630i | ||||
\(742\) | 7.27105 | − | 12.5938i | 0.266929 | − | 0.462334i | ||||
\(743\) | −4.65459 | + | 8.06198i | −0.170760 | + | 0.295765i | −0.938686 | − | 0.344774i | \(-0.887956\pi\) |
0.767926 | + | 0.640539i | \(0.221289\pi\) | |||||||
\(744\) | −6.06544 | − | 18.7675i | −0.222370 | − | 0.688051i | ||||
\(745\) | 6.90752 | + | 11.9642i | 0.253072 | + | 0.438333i | ||||
\(746\) | 52.9630 | 1.93911 | ||||||||
\(747\) | 15.4260 | − | 11.1339i | 0.564407 | − | 0.407369i | ||||
\(748\) | −30.8469 | −1.12788 | ||||||||
\(749\) | 0.242420 | + | 0.419884i | 0.00885783 | + | 0.0153422i | ||||
\(750\) | 2.96522 | + | 0.635135i | 0.108274 | + | 0.0231918i | ||||
\(751\) | 8.88756 | − | 15.3937i | 0.324312 | − | 0.561725i | −0.657061 | − | 0.753837i | \(-0.728201\pi\) |
0.981373 | + | 0.192113i | \(0.0615340\pi\) | |||||||
\(752\) | 10.4295 | − | 18.0645i | 0.380325 | − | 0.658743i | ||||
\(753\) | −4.82808 | + | 5.34525i | −0.175945 | + | 0.194792i | ||||
\(754\) | −8.54356 | − | 14.7979i | −0.311138 | − | 0.538907i | ||||
\(755\) | 10.8401 | 0.394512 | ||||||||
\(756\) | 4.46295 | + | 3.27469i | 0.162316 | + | 0.119099i | ||||
\(757\) | −11.2184 | −0.407739 | −0.203870 | − | 0.978998i | \(-0.565352\pi\) | ||||
−0.203870 | + | 0.978998i | \(0.565352\pi\) | |||||||
\(758\) | 0.611556 | + | 1.05925i | 0.0222127 | + | 0.0384736i | ||||
\(759\) | −7.09369 | + | 7.85355i | −0.257485 | + | 0.285066i | ||||
\(760\) | 3.01211 | − | 5.21713i | 0.109261 | − | 0.189245i | ||||
\(761\) | 21.0958 | − | 36.5391i | 0.764723 | − | 1.32454i | −0.175669 | − | 0.984449i | \(-0.556209\pi\) |
0.940393 | − | 0.340091i | \(-0.110458\pi\) | |||||||
\(762\) | −34.8612 | − | 7.46710i | −1.26289 | − | 0.270504i | ||||
\(763\) | 5.36726 | + | 9.29637i | 0.194308 | + | 0.336551i | ||||
\(764\) | −9.30521 | −0.336651 | ||||||||
\(765\) | 12.9699 | + | 5.82334i | 0.468927 | + | 0.210543i | ||||
\(766\) | 10.6714 | 0.385572 | ||||||||
\(767\) | 2.43441 | + | 4.21652i | 0.0879015 | + | 0.152250i | ||||
\(768\) | −10.4407 | − | 32.3052i | −0.376745 | − | 1.16571i | ||||
\(769\) | −1.72091 | + | 2.98070i | −0.0620575 | + | 0.107487i | −0.895385 | − | 0.445293i | \(-0.853100\pi\) |
0.833327 | + | 0.552780i | \(0.186433\pi\) | |||||||
\(770\) | 5.34875 | − | 9.26431i | 0.192756 | − | 0.333863i | ||||
\(771\) | −6.25763 | − | 19.3622i | −0.225363 | − | 0.697312i | ||||
\(772\) | 8.61980 | + | 14.9299i | 0.310234 | + | 0.537340i | ||||
\(773\) | 20.9848 | 0.754770 | 0.377385 | − | 0.926056i | \(-0.376823\pi\) | ||||
0.377385 | + | 0.926056i | \(0.376823\pi\) | |||||||
\(774\) | −54.2743 | − | 24.3686i | −1.95085 | − | 0.875911i | ||||
\(775\) | −6.95844 | −0.249954 | ||||||||
\(776\) | −6.68787 | − | 11.5837i | −0.240081 | − | 0.415832i | ||||
\(777\) | −7.61142 | − | 1.63033i | −0.273058 | − | 0.0584877i | ||||
\(778\) | −11.8694 | + | 20.5585i | −0.425540 | + | 0.737056i | ||||
\(779\) | 7.31592 | − | 12.6715i | 0.262120 | − | 0.454005i | ||||
\(780\) | 7.19335 | − | 7.96389i | 0.257563 | − | 0.285153i | ||||
\(781\) | 31.6707 | + | 54.8553i | 1.13327 | + | 1.96288i | ||||
\(782\) | −8.29717 | −0.296706 | ||||||||
\(783\) | −0.952173 | + | 8.66717i | −0.0340279 | + | 0.309739i | ||||
\(784\) | −4.99574 | −0.178419 | ||||||||
\(785\) | 5.53503 | + | 9.58695i | 0.197554 | + | 0.342173i | ||||
\(786\) | 1.97201 | − | 2.18325i | 0.0703393 | − | 0.0778740i | ||||
\(787\) | 13.3900 | − | 23.1922i | 0.477303 | − | 0.826713i | −0.522359 | − | 0.852726i | \(-0.674948\pi\) |
0.999662 | + | 0.0260129i | \(0.00828109\pi\) | |||||||
\(788\) | 0.222996 | − | 0.386240i | 0.00794389 | − | 0.0137592i | ||||
\(789\) | −20.9986 | − | 4.49779i | −0.747568 | − | 0.160125i | ||||
\(790\) | −7.73229 | − | 13.3927i | −0.275103 | − | 0.476492i | ||||
\(791\) | −1.11860 | −0.0397727 | ||||||||
\(792\) | −24.3231 | + | 17.5555i | −0.864283 | + | 0.623809i | ||||
\(793\) | 53.8377 | 1.91183 | ||||||||
\(794\) | 14.3661 | + | 24.8828i | 0.509834 | + | 0.883058i | ||||
\(795\) | 4.42419 | + | 13.6892i | 0.156910 | + | 0.485506i | ||||
\(796\) | 3.98778 | − | 6.90704i | 0.141343 | − | 0.244814i | ||||
\(797\) | −24.8167 | + | 42.9839i | −0.879054 | + | 1.52257i | −0.0266739 | + | 0.999644i | \(0.508492\pi\) |
−0.852380 | + | 0.522922i | \(0.824842\pi\) | |||||||
\(798\) | −3.43299 | − | 10.6223i | −0.121527 | − | 0.376024i | ||||
\(799\) | −9.89368 | − | 17.1364i | −0.350013 | − | 0.606241i | ||||
\(800\) | −5.47360 | −0.193521 | ||||||||
\(801\) | 2.94040 | + | 28.8454i | 0.103894 | + | 1.01920i | ||||
\(802\) | −6.12926 | −0.216432 | ||||||||
\(803\) | 37.3770 | + | 64.7389i | 1.31901 | + | 2.28459i | ||||
\(804\) | 8.15130 | + | 1.74597i | 0.287474 | + | 0.0615755i | ||||
\(805\) | 0.500000 | − | 0.866025i | 0.0176227 | − | 0.0305234i | ||||
\(806\) | −35.4283 | + | 61.3636i | −1.24791 | + | 2.16144i | ||||
\(807\) | 21.8835 | − | 24.2277i | 0.770337 | − | 0.852855i | ||||
\(808\) | 9.92681 | + | 17.1937i | 0.349224 | + | 0.604873i | ||||
\(809\) | −55.4296 | −1.94880 | −0.974401 | − | 0.224818i | \(-0.927821\pi\) | ||||
−0.974401 | + | 0.224818i | \(0.927821\pi\) | |||||||
\(810\) | −15.4331 | + | 3.17943i | −0.542264 | + | 0.111714i | ||||
\(811\) | −51.0851 | −1.79384 | −0.896920 | − | 0.442193i | \(-0.854200\pi\) | ||||
−0.896920 | + | 0.442193i | \(0.854200\pi\) | |||||||
\(812\) | 0.893806 | + | 1.54812i | 0.0313664 | + | 0.0543282i | ||||
\(813\) | 24.4812 | − | 27.1036i | 0.858595 | − | 0.950566i | ||||
\(814\) | −24.0380 | + | 41.6351i | −0.842532 | + | 1.45931i | ||||
\(815\) | −5.60329 | + | 9.70518i | −0.196275 | + | 0.339958i | ||||
\(816\) | −40.0970 | − | 8.58859i | −1.40368 | − | 0.300661i | ||||
\(817\) | 20.8487 | + | 36.1109i | 0.729402 | + | 1.26336i | ||||
\(818\) | 11.8305 | 0.413642 | ||||||||
\(819\) | 1.76945 | + | 17.3584i | 0.0618296 | + | 0.606550i | ||||
\(820\) | −4.23427 | −0.147867 | ||||||||
\(821\) | −2.55717 | − | 4.42914i | −0.0892457 | − | 0.154578i | 0.817947 | − | 0.575294i | \(-0.195112\pi\) |
−0.907192 | + | 0.420716i | \(0.861779\pi\) | |||||||
\(822\) | −10.0410 | − | 31.0686i | −0.350220 | − | 1.08364i | ||||
\(823\) | 18.6307 | − | 32.2693i | 0.649425 | − | 1.12484i | −0.333835 | − | 0.942632i | \(-0.608343\pi\) |
0.983260 | − | 0.182206i | \(-0.0583238\pi\) | |||||||
\(824\) | −1.14209 | + | 1.97816i | −0.0397866 | + | 0.0689124i | ||||
\(825\) | 3.25453 | + | 10.0701i | 0.113308 | + | 0.350596i | ||||
\(826\) | −0.732822 | − | 1.26928i | −0.0254981 | − | 0.0441641i | ||||
\(827\) | 23.9366 | 0.832356 | 0.416178 | − | 0.909283i | \(-0.363369\pi\) | ||||
0.416178 | + | 0.909283i | \(0.363369\pi\) | |||||||
\(828\) | 2.59142 | − | 1.87039i | 0.0900580 | − | 0.0650007i | ||||
\(829\) | −11.3556 | −0.394397 | −0.197198 | − | 0.980364i | \(-0.563184\pi\) | ||||
−0.197198 | + | 0.980364i | \(0.563184\pi\) | |||||||
\(830\) | 5.55130 | + | 9.61513i | 0.192688 | + | 0.333746i | ||||
\(831\) | −31.3277 | − | 6.71024i | −1.08675 | − | 0.232776i | ||||
\(832\) | 1.18734 | − | 2.05654i | 0.0411637 | − | 0.0712976i | ||||
\(833\) | −2.36954 | + | 4.10416i | −0.0820995 | + | 0.142201i | ||||
\(834\) | 22.0043 | − | 24.3613i | 0.761945 | − | 0.843564i | ||||
\(835\) | −11.8200 | − | 20.4728i | −0.409047 | − | 0.708490i | ||||
\(836\) | −23.9614 | −0.828722 | ||||||||
\(837\) | 33.0999 | − | 14.5510i | 1.14410 | − | 0.502955i | ||||
\(838\) | −52.9238 | −1.82822 | ||||||||
\(839\) | 18.9639 | + | 32.8465i | 0.654707 | + | 1.13399i | 0.981967 | + | 0.189051i | \(0.0605413\pi\) |
−0.327260 | + | 0.944934i | \(0.606125\pi\) | |||||||
\(840\) | 1.89991 | − | 2.10343i | 0.0655533 | − | 0.0725753i | ||||
\(841\) | 13.0921 | − | 22.6762i | 0.451452 | − | 0.781938i | ||||
\(842\) | 1.13909 | − | 1.97296i | 0.0392556 | − | 0.0679927i | ||||
\(843\) | 29.8561 | + | 6.39503i | 1.02830 | + | 0.220257i | ||||
\(844\) | −3.33407 | − | 5.77477i | −0.114763 | − | 0.198776i | ||||
\(845\) | 20.8270 | 0.716472 | ||||||||
\(846\) | 20.0066 | + | 8.98277i | 0.687843 | + | 0.308834i | ||||
\(847\) | 26.3329 | 0.904810 | ||||||||
\(848\) | −20.7472 | − | 35.9352i | −0.712463 | − | 1.23402i | ||||
\(849\) | 2.01975 | + | 6.24945i | 0.0693175 | + | 0.214480i | ||||
\(850\) | −4.14858 | + | 7.18556i | −0.142295 | + | 0.246463i | ||||
\(851\) | −2.24707 | + | 3.89203i | −0.0770285 | + | 0.133417i | ||||
\(852\) | −5.88244 | − | 18.2013i | −0.201529 | − | 0.623566i | ||||
\(853\) | −19.5193 | − | 33.8085i | −0.668329 | − | 1.15758i | −0.978371 | − | 0.206857i | \(-0.933677\pi\) |
0.310042 | − | 0.950723i | \(-0.399657\pi\) | |||||||
\(854\) | −16.2066 | −0.554578 | ||||||||
\(855\) | 10.0748 | + | 4.52348i | 0.344551 | + | 0.154700i | ||||
\(856\) | 0.793426 | 0.0271187 | ||||||||
\(857\) | −11.8587 | − | 20.5399i | −0.405087 | − | 0.701631i | 0.589245 | − | 0.807954i | \(-0.299425\pi\) |
−0.994332 | + | 0.106324i | \(0.966092\pi\) | |||||||
\(858\) | 105.374 | + | 22.5706i | 3.59742 | + | 0.770549i | ||||
\(859\) | −22.8542 | + | 39.5847i | −0.779777 | + | 1.35061i | 0.152294 | + | 0.988335i | \(0.451334\pi\) |
−0.932070 | + | 0.362278i | \(0.881999\pi\) | |||||||
\(860\) | 6.03334 | − | 10.4500i | 0.205735 | − | 0.356344i | ||||
\(861\) | 4.61457 | − | 5.10888i | 0.157264 | − | 0.174110i | ||||
\(862\) | 5.99438 | + | 10.3826i | 0.204169 | + | 0.353632i | ||||
\(863\) | −5.54957 | −0.188909 | −0.0944547 | − | 0.995529i | \(-0.530111\pi\) | ||||
−0.0944547 | + | 0.995529i | \(0.530111\pi\) | |||||||
\(864\) | 26.0368 | − | 11.4460i | 0.885791 | − | 0.389400i | ||||
\(865\) | −3.08904 | −0.105031 | ||||||||
\(866\) | 5.02356 | + | 8.70105i | 0.170707 | + | 0.295674i | ||||
\(867\) | −6.33756 | + | 7.01643i | −0.215235 | + | 0.238290i | ||||
\(868\) | 3.70642 | − | 6.41971i | 0.125804 | − | 0.217899i | ||||
\(869\) | 26.9847 | − | 46.7389i | 0.915393 | − | 1.58551i | ||||
\(870\) | −4.97573 | − | 1.06578i | −0.168693 | − | 0.0361332i | ||||
\(871\) | 13.1382 | + | 22.7560i | 0.445171 | + | 0.771059i | ||||
\(872\) | 17.5667 | 0.594884 | ||||||||
\(873\) | 19.8827 | − | 14.3506i | 0.672927 | − | 0.485695i | ||||
\(874\) | −6.44511 | −0.218009 | ||||||||
\(875\) | −0.500000 | − | 0.866025i | −0.0169031 | − | 0.0292770i | ||||
\(876\) | −6.94232 | − | 21.4807i | −0.234559 | − | 0.725767i | ||||
\(877\) | −10.6589 | + | 18.4617i | −0.359924 | + | 0.623406i | −0.987948 | − | 0.154788i | \(-0.950531\pi\) |
0.628024 | + | 0.778194i | \(0.283864\pi\) | |||||||
\(878\) | −10.8021 | + | 18.7098i | −0.364553 | + | 0.631425i | ||||
\(879\) | 4.30094 | + | 13.3079i | 0.145067 | + | 0.448863i | ||||
\(880\) | −15.2621 | − | 26.4348i | −0.514487 | − | 0.891117i | ||||
\(881\) | 8.12987 | 0.273902 | 0.136951 | − | 0.990578i | \(-0.456270\pi\) | ||||
0.136951 | + | 0.990578i | \(0.456270\pi\) | |||||||
\(882\) | −0.532651 | − | 5.22532i | −0.0179353 | − | 0.175946i | ||||
\(883\) | −4.24853 | −0.142975 | −0.0714873 | − | 0.997442i | \(-0.522775\pi\) | ||||
−0.0714873 | + | 0.997442i | \(0.522775\pi\) | |||||||
\(884\) | 14.6814 | + | 25.4290i | 0.493789 | + | 0.855268i | ||||
\(885\) | 1.41779 | + | 0.303683i | 0.0476584 | + | 0.0102082i | ||||
\(886\) | −9.05103 | + | 15.6768i | −0.304075 | + | 0.526674i | ||||
\(887\) | 25.7749 | − | 44.6434i | 0.865435 | − | 1.49898i | −0.00117920 | − | 0.999999i | \(-0.500375\pi\) |
0.866614 | − | 0.498978i | \(-0.166291\pi\) | |||||||
\(888\) | −8.53847 | + | 9.45310i | −0.286532 | + | 0.317225i | ||||
\(889\) | 5.87836 | + | 10.1816i | 0.197154 | + | 0.341480i | ||||
\(890\) | −16.9214 | −0.567207 | ||||||||
\(891\) | −36.5390 | − | 41.0958i | −1.22410 | − | 1.37676i | ||||
\(892\) | −24.7592 | −0.828998 | ||||||||
\(893\) | −7.68525 | − | 13.3113i | −0.257177 | − | 0.445444i | ||||
\(894\) | 28.0812 | − | 31.0892i | 0.939174 | − | 1.03978i | ||||
\(895\) | −11.4763 | + | 19.8776i | −0.383611 | + | 0.664433i | ||||
\(896\) | −5.83102 | + | 10.0996i | −0.194801 | + | 0.337405i | ||||
\(897\) | 9.85035 | + | 2.10990i | 0.328894 | + | 0.0704474i | ||||
\(898\) | −21.3960 | − | 37.0590i | −0.713995 | − | 1.23668i | ||||
\(899\) | 11.6765 | 0.389432 | ||||||||
\(900\) | −0.324100 | − | 3.17943i | −0.0108033 | − | 0.105981i | ||||
\(901\) | −39.3626 | −1.31136 | ||||||||
\(902\) | −21.2597 | − | 36.8230i | −0.707872 | − | 1.22607i | ||||
\(903\) | 6.03334 | + | 18.6682i | 0.200777 | + | 0.621239i | ||||
\(904\) | −0.915274 | + | 1.58530i | −0.0304415 | + | 0.0527263i | ||||
\(905\) | 2.05014 | − | 3.55095i | 0.0681490 | − | 0.118038i | ||||
\(906\) | −10.1091 | − | 31.2794i | −0.335853 | − | 1.03919i | ||||
\(907\) | 1.07275 | + | 1.85806i | 0.0356202 | + | 0.0616959i | 0.883286 | − | 0.468835i | \(-0.155326\pi\) |
−0.847666 | + | 0.530531i | \(0.821993\pi\) | |||||||
\(908\) | 21.0594 | 0.698880 | ||||||||
\(909\) | −29.5118 | + | 21.3006i | −0.978846 | + | 0.706496i | ||||
\(910\) | −10.1828 | −0.337558 | ||||||||
\(911\) | −17.1698 | − | 29.7389i | −0.568860 | − | 0.985295i | −0.996679 | − | 0.0814303i | \(-0.974051\pi\) |
0.427819 | − | 0.903865i | \(-0.359282\pi\) | |||||||
\(912\) | −31.1467 | − | 6.67148i | −1.03137 | − | 0.220915i | ||||
\(913\) | −19.3733 | + | 33.5556i | −0.641163 | + | 1.11053i | ||||
\(914\) | 34.9771 | − | 60.5821i | 1.15694 | − | 2.00388i | ||||
\(915\) | 10.7468 | − | 11.8980i | 0.355280 | − | 0.393337i | ||||
\(916\) | 0.00551690 | + | 0.00955555i | 0.000182283 | + | 0.000315724i | ||||
\(917\) | −0.970168 | −0.0320378 | ||||||||
\(918\) | 4.70810 | − | 42.8555i | 0.155390 | − | 1.41444i | ||||
\(919\) | 2.02313 | 0.0667370 | 0.0333685 | − | 0.999443i | \(-0.489377\pi\) | ||||
0.0333685 | + | 0.999443i | \(0.489377\pi\) | |||||||
\(920\) | −0.818235 | − | 1.41722i | −0.0269764 | − | 0.0467245i | ||||
\(921\) | 1.19877 | − | 1.32718i | 0.0395008 | − | 0.0437321i | ||||
\(922\) | 13.2759 | − | 22.9945i | 0.437217 | − | 0.757282i | ||||
\(923\) | 30.1470 | − | 52.2161i | 0.992300 | − | 1.71871i | ||||
\(924\) | −11.0240 | − | 2.36128i | −0.362662 | − | 0.0776805i | ||||
\(925\) | 2.24707 | + | 3.89203i | 0.0738831 | + | 0.127969i | ||||
\(926\) | 18.2583 | 0.600006 | ||||||||
\(927\) | −3.82002 | − | 1.71515i | −0.125466 | − | 0.0563329i | ||||
\(928\) | 9.18487 | 0.301508 | ||||||||
\(929\) | 5.84648 | + | 10.1264i | 0.191817 | + | 0.332237i | 0.945852 | − | 0.324597i | \(-0.105229\pi\) |
−0.754036 | + | 0.656834i | \(0.771895\pi\) | |||||||
\(930\) | 6.48920 | + | 20.0787i | 0.212789 | + | 0.658407i | ||||
\(931\) | −1.84062 | + | 3.18804i | −0.0603238 | + | 0.104484i | ||||
\(932\) | 3.45482 | − | 5.98393i | 0.113167 | − | 0.196010i | ||||
\(933\) | −4.41537 | − | 13.6619i | −0.144553 | − | 0.447271i | ||||
\(934\) | 24.1522 | + | 41.8328i | 0.790283 | + | 1.36881i | ||||
\(935\) | −28.9560 | −0.946964 | ||||||||
\(936\) | 26.0485 | + | 11.6955i | 0.851422 | + | 0.382279i | ||||
\(937\) | 13.5123 | 0.441427 | 0.220713 | − | 0.975339i | \(-0.429161\pi\) | ||||
0.220713 | + | 0.975339i | \(0.429161\pi\) | |||||||
\(938\) | −3.95495 | − | 6.85017i | −0.129134 | − | 0.223666i | ||||
\(939\) | 33.9900 | + | 7.28049i | 1.10922 | + | 0.237590i | ||||
\(940\) | −2.22401 | + | 3.85211i | −0.0725394 | + | 0.125642i | ||||
\(941\) | 2.79192 | − | 4.83575i | 0.0910140 | − | 0.157641i | −0.816924 | − | 0.576745i | \(-0.804323\pi\) |
0.907938 | + | 0.419104i | \(0.137656\pi\) | |||||||
\(942\) | 22.5016 | − | 24.9119i | 0.733140 | − | 0.811673i | ||||
\(943\) | −1.98736 | − | 3.44220i | −0.0647172 | − | 0.112093i | ||||
\(944\) | −4.18207 | −0.136115 | ||||||||
\(945\) | 4.18937 | + | 3.07395i | 0.136280 | + | 0.0999956i | ||||
\(946\) | 121.171 | 3.93960 | ||||||||
\(947\) | 12.6053 | + | 21.8331i | 0.409618 | + | 0.709480i | 0.994847 | − | 0.101389i | \(-0.0323286\pi\) |
−0.585229 | + | 0.810868i | \(0.698995\pi\) | |||||||
\(948\) | −10.9245 | + | 12.0947i | −0.354810 | + | 0.392817i | ||||
\(949\) | 35.5788 | − | 61.6243i | 1.15494 | − | 2.00041i | ||||
\(950\) | −3.22255 | + | 5.58163i | −0.104553 | + | 0.181092i | ||||
\(951\) | 35.1669 | + | 7.53258i | 1.14037 | + | 0.244261i | ||||
\(952\) | 3.87767 | + | 6.71632i | 0.125676 | + | 0.217677i | ||||
\(953\) | 32.3742 | 1.04870 | 0.524351 | − | 0.851502i | \(-0.324308\pi\) | ||||
0.524351 | + | 0.851502i | \(0.324308\pi\) | |||||||
\(954\) | 35.3746 | − | 25.5322i | 1.14530 | − | 0.826634i | ||||
\(955\) | −8.73481 | −0.282652 | ||||||||
\(956\) | −8.41512 | − | 14.5754i | −0.272164 | − | 0.471403i | ||||
\(957\) | −5.46121 | − | 16.8979i | −0.176536 | − | 0.546233i | ||||
\(958\) | −18.8113 | + | 32.5821i | −0.607766 | + | 1.05268i | ||||
\(959\) | −5.38354 | + | 9.32456i | −0.173843 | + | 0.301106i | ||||
\(960\) | −0.217479 | − | 0.672917i | −0.00701910 | − | 0.0217183i | ||||
\(961\) | −8.70992 | − | 15.0860i | −0.280965 | − | 0.486646i | ||||
\(962\) | 45.7630 | 1.47546 | ||||||||
\(963\) | 0.147504 | + | 1.44702i | 0.00475326 | + | 0.0466296i | ||||
\(964\) | −6.83710 | −0.220208 | ||||||||
\(965\) | 8.09142 | + | 14.0147i | 0.260472 | + | 0.451151i | ||||
\(966\) | −2.96522 | − | 0.635135i | −0.0954043 | − | 0.0204351i | ||||
\(967\) | −13.7076 | + | 23.7423i | −0.440808 | + | 0.763502i | −0.997750 | − | 0.0670499i | \(-0.978641\pi\) |
0.556942 | + | 0.830552i | \(0.311975\pi\) | |||||||
\(968\) | 21.5465 | − | 37.3196i | 0.692531 | − | 1.19950i | ||||
\(969\) | −20.2541 | + | 22.4237i | −0.650655 | + | 0.720352i | ||||
\(970\) | 7.15512 | + | 12.3930i | 0.229737 | + | 0.397916i | ||||
\(971\) | 16.6145 | 0.533185 | 0.266592 | − | 0.963809i | \(-0.414102\pi\) | ||||
0.266592 | + | 0.963809i | \(0.414102\pi\) | |||||||
\(972\) | 8.19027 | + | 14.4462i | 0.262703 | + | 0.463362i | ||||
\(973\) | −10.8254 | −0.347046 | ||||||||
\(974\) | −10.1702 | − | 17.6153i | −0.325874 | − | 0.564430i | ||||
\(975\) | 6.75240 | − | 7.47571i | 0.216250 | − | 0.239414i | ||||
\(976\) | −23.1219 | + | 40.0484i | −0.740115 | + | 1.28192i | ||||
\(977\) | 30.5289 | − | 52.8776i | 0.976707 | − | 1.69171i | 0.302523 | − | 0.953142i | \(-0.402171\pi\) |
0.674183 | − | 0.738564i | \(-0.264496\pi\) | |||||||
\(978\) | 33.2299 | + | 7.11768i | 1.06258 | + | 0.227598i | ||||
\(979\) | −29.5268 | − | 51.1419i | −0.943680 | − | 1.63450i | ||||
\(980\) | 1.06530 | 0.0340298 | ||||||||
\(981\) | 3.26580 | + | 32.0376i | 0.104269 | + | 1.02288i | ||||
\(982\) | 60.8233 | 1.94095 | ||||||||
\(983\) | −3.51023 | − | 6.07990i | −0.111959 | − | 0.193919i | 0.804601 | − | 0.593816i | \(-0.202379\pi\) |
−0.916560 | + | 0.399897i | \(0.869046\pi\) | |||||||
\(984\) | −3.46462 | − | 10.7202i | −0.110448 | − | 0.341746i | ||||
\(985\) | 0.209326 | − | 0.362564i | 0.00666969 | − | 0.0115522i | ||||
\(986\) | 6.96146 | − | 12.0576i | 0.221698 | − | 0.383992i | ||||
\(987\) | −2.22401 | − | 6.88149i | −0.0707912 | − | 0.219040i | ||||
\(988\) | 11.4043 | + | 19.7528i | 0.362819 | + | 0.628421i | ||||
\(989\) | 11.3270 | 0.360178 | ||||||||
\(990\) | 26.0224 | − | 18.7820i | 0.827046 | − | 0.596933i | ||||
\(991\) | 60.0698 | 1.90818 | 0.954090 | − | 0.299522i | \(-0.0968270\pi\) | ||||
0.954090 | + | 0.299522i | \(0.0968270\pi\) | |||||||
\(992\) | −19.0438 | − | 32.9849i | −0.604643 | − | 1.04727i | ||||
\(993\) | −18.9063 | − | 4.04964i | −0.599973 | − | 0.128511i | ||||
\(994\) | −9.07504 | + | 15.7184i | −0.287843 | + | 0.498558i | ||||
\(995\) | 3.74333 | − | 6.48365i | 0.118672 | − | 0.205545i | ||||
\(996\) | 7.84309 | − | 8.68323i | 0.248518 | − | 0.275139i | ||||
\(997\) | −7.44502 | − | 12.8951i | −0.235786 | − | 0.408393i | 0.723715 | − | 0.690099i | \(-0.242433\pi\) |
−0.959501 | + | 0.281706i | \(0.909100\pi\) | |||||||
\(998\) | −5.31734 | −0.168317 | ||||||||
\(999\) | −18.8276 | − | 13.8147i | −0.595679 | − | 0.437079i |
(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 | 315.2.i.c.211.1 | yes | 8 | |
3.2 | odd | 2 | 945.2.i.d.631.4 | 8 | |||
9.2 | odd | 6 | 945.2.i.d.316.4 | 8 | |||
9.4 | even | 3 | 2835.2.a.m.1.4 | 4 | |||
9.5 | odd | 6 | 2835.2.a.p.1.1 | 4 | |||
9.7 | even | 3 | inner | 315.2.i.c.106.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.i.c.106.1 | ✓ | 8 | 9.7 | even | 3 | inner | |
315.2.i.c.211.1 | yes | 8 | 1.1 | even | 1 | trivial | |
945.2.i.d.316.4 | 8 | 9.2 | odd | 6 | |||
945.2.i.d.631.4 | 8 | 3.2 | odd | 2 | |||
2835.2.a.m.1.4 | 4 | 9.4 | even | 3 | |||
2835.2.a.p.1.1 | 4 | 9.5 | odd | 6 |