Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(316,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, 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("945.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.54586299101\) |
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: | \( 3 \) |
Twist minimal: | no (minimal twist has level 315) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 631.4 | ||
Root | \(0.818235 - 1.15347i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 945.631 |
Dual form | 945.2.i.d.316.4 |
$q$-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 \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).
\(n\) | \(136\) | \(596\) | \(757\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.875400 | + | 1.51624i | 0.619001 | + | 1.07214i | 0.989668 | + | 0.143376i | \(0.0457958\pi\) |
−0.370667 | + | 0.928766i | \(0.620871\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.532651 | + | 0.922579i | −0.266326 | + | 0.461289i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | 1.63647 | 0.578579 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.75080 | 0.553652 | ||||||||
\(11\) | −3.05503 | − | 5.29147i | −0.921127 | − | 1.59544i | −0.797674 | − | 0.603089i | \(-0.793936\pi\) |
−0.123453 | − | 0.992350i | \(-0.539397\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 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 | 0 | ||||||||
\(16\) | 2.49787 | + | 4.32643i | 0.624467 | + | 1.08161i | ||||
\(17\) | −4.73907 | −1.14939 | −0.574697 | − | 0.818367i | \(-0.694880\pi\) | ||||
−0.574697 | + | 0.818367i | \(0.694880\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 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 | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.34875 | − | 9.26431i | 1.14036 | − | 1.97516i | ||||
\(23\) | −0.500000 | + | 0.866025i | −0.104257 | + | 0.180579i | −0.913434 | − | 0.406986i | \(-0.866580\pi\) |
0.809177 | + | 0.587565i | \(0.199913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 10.1828 | 1.99702 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.06530 | 0.201323 | ||||||||
\(29\) | −0.839016 | − | 1.45322i | −0.155801 | − | 0.269856i | 0.777549 | − | 0.628822i | \(-0.216463\pi\) |
−0.933351 | + | 0.358966i | \(0.883129\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 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 | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.14858 | − | 7.18556i | −0.711476 | − | 1.23231i | ||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −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 | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.818235 | − | 1.41722i | 0.129374 | − | 0.224083i | ||||
\(41\) | −1.98736 | + | 3.44220i | −0.310373 | + | 0.537581i | −0.978443 | − | 0.206517i | \(-0.933787\pi\) |
0.668070 | + | 0.744098i | \(0.267121\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 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 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.75080 | −0.258141 | ||||||||
\(47\) | 2.08768 | + | 3.61598i | 0.304520 | + | 0.527444i | 0.977154 | − | 0.212531i | \(-0.0681706\pi\) |
−0.672634 | + | 0.739975i | \(0.734837\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0.875400 | − | 1.51624i | 0.123800 | − | 0.214428i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.09795 | + | 5.36581i | 0.429609 | + | 0.744104i | ||||
\(53\) | 8.30597 | 1.14091 | 0.570457 | − | 0.821328i | \(-0.306766\pi\) | ||||
0.570457 | + | 0.821328i | \(0.306766\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.11007 | −0.823881 | ||||||||
\(56\) | −0.818235 | − | 1.41722i | −0.109341 | − | 0.189385i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.46895 | − | 2.54430i | 0.192883 | − | 0.334082i | ||||
\(59\) | 0.418564 | − | 0.724974i | 0.0544924 | − | 0.0943836i | −0.837492 | − | 0.546449i | \(-0.815979\pi\) |
0.891985 | + | 0.452065i | \(0.149313\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.408295 | 0.0510369 | ||||||||
\(65\) | −2.90805 | − | 5.03689i | −0.360699 | − | 0.624750i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −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 | 0 | ||||||||
\(70\) | −0.875400 | − | 1.51624i | −0.104630 | − | 0.181225i | ||||
\(71\) | −10.3667 | −1.23030 | −0.615152 | − | 0.788408i | \(-0.710906\pi\) | ||||
−0.615152 | + | 0.788408i | \(0.710906\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 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 | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.96081 | + | 3.39623i | −0.224921 | + | 0.389574i | ||||
\(77\) | −3.05503 | + | 5.29147i | −0.348153 | + | 0.603019i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.95892 | −0.768485 | ||||||||
\(83\) | −3.17072 | − | 5.49185i | −0.348032 | − | 0.602809i | 0.637868 | − | 0.770146i | \(-0.279817\pi\) |
−0.985900 | + | 0.167337i | \(0.946483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.36954 | + | 4.10416i | −0.257012 | + | 0.445158i | ||||
\(86\) | −9.91566 | + | 17.1744i | −1.06923 | + | 1.85197i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.99947 | − | 8.65933i | −0.532945 | − | 0.923088i | ||||
\(89\) | 9.66496 | 1.02448 | 0.512242 | − | 0.858841i | \(-0.328815\pi\) | ||||
0.512242 | + | 0.858841i | \(0.328815\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.81610 | −0.609693 | ||||||||
\(92\) | −0.532651 | − | 0.922579i | −0.0555327 | − | 0.0961855i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.65512 | + | 6.33085i | −0.376997 | + | 0.652977i | ||||
\(95\) | 1.84062 | − | 3.18804i | 0.188843 | − | 0.327086i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.06530 | 0.106530 | ||||||||
\(101\) | 6.06599 | + | 10.5066i | 0.603588 | + | 1.04545i | 0.992273 | + | 0.124075i | \(0.0395963\pi\) |
−0.388684 | + | 0.921371i | \(0.627070\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 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 | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.27105 | + | 12.5938i | 0.706227 | + | 1.22322i | ||||
\(107\) | 0.484840 | 0.0468713 | 0.0234356 | − | 0.999725i | \(-0.492540\pi\) | ||||
0.0234356 | + | 0.999725i | \(0.492540\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −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 | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.49787 | − | 4.32643i | 0.236026 | − | 0.408810i | ||||
\(113\) | −0.559298 | + | 0.968732i | −0.0526143 | + | 0.0911306i | −0.891133 | − | 0.453742i | \(-0.850089\pi\) |
0.838519 | + | 0.544873i | \(0.183422\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.500000 | + | 0.866025i | 0.0466252 | + | 0.0807573i | ||||
\(116\) | 1.78761 | 0.165976 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.46564 | 0.134923 | ||||||||
\(119\) | 2.36954 | + | 4.10416i | 0.217215 | + | 0.376227i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.1665 | + | 22.8050i | −1.19695 | + | 2.07318i | ||||
\(122\) | −8.10329 | + | 14.0353i | −0.733637 | + | 1.27070i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.70642 | + | 6.41971i | 0.332846 | + | 0.576507i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −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 | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.09142 | − | 8.81859i | 0.446547 | − | 0.773442i | ||||
\(131\) | −0.485084 | + | 0.840190i | −0.0423820 | + | 0.0734077i | −0.886438 | − | 0.462847i | \(-0.846828\pi\) |
0.844056 | + | 0.536255i | \(0.180161\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.84062 | − | 3.18804i | −0.159602 | − | 0.276438i | ||||
\(134\) | −7.90990 | −0.683311 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.75534 | −0.665015 | ||||||||
\(137\) | 5.38354 | + | 9.32456i | 0.459947 | + | 0.796651i | 0.998958 | − | 0.0456479i | \(-0.0145352\pi\) |
−0.539011 | + | 0.842299i | \(0.681202\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 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 | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.07504 | − | 15.7184i | −0.761560 | − | 1.31906i | ||||
\(143\) | −35.5368 | −2.97173 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.67803 | −0.139353 | ||||||||
\(146\) | 10.7102 | + | 18.5505i | 0.886378 | + | 1.53525i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.39381 | − | 4.14619i | 0.196770 | − | 0.340815i | ||||
\(149\) | −6.90752 | + | 11.9642i | −0.565886 | + | 0.980143i | 0.431081 | + | 0.902313i | \(0.358132\pi\) |
−0.996967 | + | 0.0778300i | \(0.975201\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.6975 | −0.862030 | ||||||||
\(155\) | −3.47922 | − | 6.02618i | −0.279458 | − | 0.484035i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 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 | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.73680 | + | 4.74027i | 0.216363 | + | 0.374752i | ||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 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 | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.55130 | − | 9.61513i | 0.430864 | − | 0.746279i | ||||
\(167\) | 11.8200 | − | 20.4728i | 0.914657 | − | 1.58423i | 0.107255 | − | 0.994232i | \(-0.465794\pi\) |
0.807403 | − | 0.590001i | \(-0.200873\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4135 | − | 18.0368i | −0.801040 | − | 1.38744i | ||||
\(170\) | −8.29717 | −0.636364 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.0667 | −0.920075 | ||||||||
\(173\) | −1.54452 | − | 2.67519i | −0.117428 | − | 0.203391i | 0.801320 | − | 0.598236i | \(-0.204132\pi\) |
−0.918748 | + | 0.394845i | \(0.870798\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.500000 | + | 0.866025i | −0.0377964 | + | 0.0654654i | ||||
\(176\) | 15.2621 | − | 26.4348i | 1.15043 | − | 1.99260i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.46071 | + | 14.6544i | 0.634157 | + | 1.09839i | ||||
\(179\) | −22.9526 | −1.71556 | −0.857780 | − | 0.514017i | \(-0.828157\pi\) | ||||
−0.857780 | + | 0.514017i | \(0.828157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −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 | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.818235 | + | 1.41722i | −0.0603211 | + | 0.104479i | ||||
\(185\) | −2.24707 | + | 3.89203i | −0.165208 | + | 0.286148i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.4780 | + | 25.0767i | 1.05874 | + | 1.83379i | ||||
\(188\) | −4.44803 | −0.324406 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.44511 | 0.467577 | ||||||||
\(191\) | −4.36740 | − | 7.56456i | −0.316014 | − | 0.547353i | 0.663638 | − | 0.748054i | \(-0.269011\pi\) |
−0.979653 | + | 0.200701i | \(0.935678\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 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 | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.532651 | − | 0.922579i | −0.0380465 | − | 0.0658985i | ||||
\(197\) | 0.418652 | 0.0298278 | 0.0149139 | − | 0.999889i | \(-0.495253\pi\) | ||||
0.0149139 | + | 0.999889i | \(0.495253\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −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 | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.6203 | + | 18.3950i | −0.747244 | + | 1.29426i | ||||
\(203\) | −0.839016 | + | 1.45322i | −0.0588874 | + | 0.101996i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.98736 | + | 3.44220i | 0.138803 | + | 0.240414i | ||||
\(206\) | 2.44376 | 0.170265 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 29.0557 | 2.01465 | ||||||||
\(209\) | −11.2463 | − | 19.4791i | −0.777922 | − | 1.34740i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −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 | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.424429 | + | 0.735133i | 0.0290134 | + | 0.0502526i | ||||
\(215\) | 11.3270 | 0.772495 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.95844 | −0.472369 | ||||||||
\(218\) | −9.39701 | − | 16.2761i | −0.636446 | − | 1.10236i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.25453 | − | 5.63702i | 0.219421 | − | 0.380048i | ||||
\(221\) | −13.7815 | + | 23.8702i | −0.927041 | + | 1.60568i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 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 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.95844 | −0.130273 | ||||||||
\(227\) | 9.88422 | + | 17.1200i | 0.656039 | + | 1.13629i | 0.981632 | + | 0.190783i | \(0.0611026\pi\) |
−0.325593 | + | 0.945510i | \(0.605564\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 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 | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.37302 | − | 2.37815i | −0.0901435 | − | 0.156133i | ||||
\(233\) | 6.48609 | 0.424918 | 0.212459 | − | 0.977170i | \(-0.431853\pi\) | ||||
0.212459 | + | 0.977170i | \(0.431853\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.17537 | 0.272371 | ||||||||
\(236\) | 0.445897 | + | 0.772316i | 0.0290254 | + | 0.0502735i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.14858 | + | 7.18556i | −0.268913 | + | 0.465770i | ||||
\(239\) | 7.89928 | − | 13.6820i | 0.510962 | − | 0.885012i | −0.488957 | − | 0.872308i | \(-0.662623\pi\) |
0.999919 | − | 0.0127043i | \(-0.00404400\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.86115 | −0.631295 | ||||||||
\(245\) | 0.500000 | + | 0.866025i | 0.0319438 | + | 0.0553283i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.7052 | − | 18.5420i | 0.681157 | − | 1.17980i | ||||
\(248\) | 5.69363 | − | 9.86166i | 0.361546 | − | 0.626216i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.875400 | − | 1.51624i | −0.0553652 | − | 0.0958953i | ||||
\(251\) | −4.15861 | −0.262489 | −0.131245 | − | 0.991350i | \(-0.541897\pi\) | ||||
−0.131245 | + | 0.991350i | \(0.541897\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.11007 | 0.384137 | ||||||||
\(254\) | −10.2918 | − | 17.8260i | −0.645767 | − | 1.11850i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.80066 | + | 16.9752i | −0.612541 | + | 1.06095i | ||||
\(257\) | 5.87404 | − | 10.1741i | 0.366413 | − | 0.634645i | −0.622589 | − | 0.782549i | \(-0.713919\pi\) |
0.989002 | + | 0.147903i | \(0.0472525\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.24707 | + | 3.89203i | 0.139626 | + | 0.241839i | ||||
\(260\) | 6.19591 | 0.384254 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.69857 | −0.104938 | ||||||||
\(263\) | −6.19926 | − | 10.7374i | −0.382263 | − | 0.662098i | 0.609123 | − | 0.793076i | \(-0.291522\pi\) |
−0.991385 | + | 0.130978i | \(0.958188\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.15299 | − | 7.19318i | 0.255116 | − | 0.441874i | ||||
\(266\) | 3.22255 | − | 5.58163i | 0.197587 | − | 0.342231i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.40645 | − | 4.16809i | −0.146997 | − | 0.254607i | ||||
\(269\) | 18.8491 | 1.14925 | 0.574626 | − | 0.818416i | \(-0.305148\pi\) | ||||
0.574626 | + | 0.818416i | \(0.305148\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −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 | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.42550 | + | 16.3254i | −0.569415 | + | 0.986256i | ||||
\(275\) | −3.05503 | + | 5.29147i | −0.184225 | + | 0.319088i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.63647 | −0.0977978 | ||||||||
\(281\) | 8.81421 | + | 15.2667i | 0.525812 | + | 0.910733i | 0.999548 | + | 0.0300661i | \(0.00957177\pi\) |
−0.473736 | + | 0.880667i | \(0.657095\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 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 | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −31.1089 | − | 53.8822i | −1.83951 | − | 3.18612i | ||||
\(287\) | 3.97471 | 0.234620 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.45878 | 0.321105 | ||||||||
\(290\) | −1.46895 | − | 2.54430i | −0.0862597 | − | 0.149406i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.51676 | + | 11.2874i | −0.381365 | + | 0.660543i | ||||
\(293\) | −4.03730 | + | 6.99281i | −0.235861 | + | 0.408524i | −0.959523 | − | 0.281631i | \(-0.909125\pi\) |
0.723661 | + | 0.690155i | \(0.242458\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.418564 | − | 0.724974i | −0.0243697 | − | 0.0422096i | ||||
\(296\) | −7.35451 | −0.427472 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.1874 | −1.40114 | ||||||||
\(299\) | 2.90805 | + | 5.03689i | 0.168177 | + | 0.291291i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.66350 | − | 9.80947i | 0.326439 | − | 0.565408i | ||||
\(302\) | 9.48944 | − | 16.4362i | 0.546056 | − | 0.945797i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.19524 | + | 15.9266i | 0.527383 | + | 0.913454i | ||||
\(305\) | 9.25667 | 0.530035 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −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 | 0 | ||||||||
\(310\) | 6.09142 | − | 10.5506i | 0.345969 | − | 0.599236i | ||||
\(311\) | 4.14471 | − | 7.17885i | 0.235025 | − | 0.407075i | −0.724255 | − | 0.689532i | \(-0.757816\pi\) |
0.959280 | + | 0.282457i | \(0.0911495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −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 | 0 | ||||||||
\(316\) | 9.40967 | 0.529335 | ||||||||
\(317\) | 10.3821 | + | 17.9823i | 0.583116 | + | 1.00999i | 0.995107 | + | 0.0987992i | \(0.0315002\pi\) |
−0.411991 | + | 0.911188i | \(0.635167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.12644 | + | 8.87926i | −0.287026 | + | 0.497143i | ||||
\(320\) | 0.204148 | − | 0.353594i | 0.0114122 | − | 0.0197665i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.875400 | + | 1.51624i | 0.0487841 | + | 0.0844966i | ||||
\(323\) | −17.4456 | −0.970701 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.81610 | −0.322619 | ||||||||
\(326\) | 9.81024 | + | 16.9918i | 0.543339 | + | 0.941090i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.25225 | + | 5.63306i | −0.179575 | + | 0.311033i | ||||
\(329\) | 2.08768 | − | 3.61598i | 0.115098 | − | 0.199355i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 41.3888 | 2.26470 | ||||||||
\(335\) | 2.25894 | + | 3.91259i | 0.123419 | + | 0.213768i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −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 | 0 | ||||||||
\(340\) | −2.52427 | − | 4.37217i | −0.136898 | − | 0.237114i | ||||
\(341\) | −42.5165 | −2.30240 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.26814 | + | 16.0529i | 0.499705 | + | 0.865514i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.70415 | − | 4.68372i | 0.145376 | − | 0.251798i | ||||
\(347\) | 9.75254 | − | 16.8919i | 0.523544 | − | 0.906804i | −0.476081 | − | 0.879402i | \(-0.657943\pi\) |
0.999624 | − | 0.0274029i | \(-0.00872369\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 33.4440 | 1.78257 | ||||||||
\(353\) | 8.20857 | + | 14.2177i | 0.436898 | + | 0.756729i | 0.997448 | − | 0.0713908i | \(-0.0227438\pi\) |
−0.560550 | + | 0.828120i | \(0.689410\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.18337 | + | 8.97785i | −0.275105 | + | 0.476495i | ||||
\(356\) | −5.14805 | + | 8.91669i | −0.272846 | + | 0.472583i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.0927 | − | 34.8016i | −1.06193 | − | 1.83932i | ||||
\(359\) | 13.2324 | 0.698381 | 0.349191 | − | 0.937052i | \(-0.386457\pi\) | ||||
0.349191 | + | 0.937052i | \(0.386457\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.44852 | −0.286764 | ||||||||
\(362\) | −3.58939 | − | 6.21701i | −0.188654 | − | 0.326759i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.09795 | − | 5.36581i | 0.162377 | − | 0.281245i | ||||
\(365\) | 6.11729 | − | 10.5955i | 0.320194 | − | 0.554591i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 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 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.86833 | −0.409055 | ||||||||
\(371\) | −4.15299 | − | 7.19318i | −0.215612 | − | 0.373451i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −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 | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.41643 | + | 5.91743i | 0.176189 | + | 0.305168i | ||||
\(377\) | −9.75961 | −0.502645 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −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 | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.64645 | − | 13.2440i | 0.391226 | − | 0.677624i | ||||
\(383\) | 3.04757 | − | 5.27854i | 0.155723 | − | 0.269721i | −0.777599 | − | 0.628761i | \(-0.783562\pi\) |
0.933322 | + | 0.359040i | \(0.116896\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.05503 | + | 5.29147i | 0.155699 | + | 0.269678i | ||||
\(386\) | 28.3329 | 1.44211 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.70729 | −0.442046 | ||||||||
\(389\) | 6.77943 | + | 11.7423i | 0.343731 | + | 0.595359i | 0.985122 | − | 0.171855i | \(-0.0549759\pi\) |
−0.641392 | + | 0.767214i | \(0.721643\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.36954 | − | 4.10416i | 0.119833 | − | 0.207556i | ||||
\(392\) | −0.818235 | + | 1.41722i | −0.0413271 | + | 0.0715806i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.366488 | + | 0.634777i | 0.0184634 | + | 0.0319796i | ||||
\(395\) | −8.83286 | −0.444430 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −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 | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.49787 | − | 4.32643i | 0.124893 | − | 0.216322i | ||||
\(401\) | −1.75042 | + | 3.03181i | −0.0874117 | + | 0.151401i | −0.906416 | − | 0.422385i | \(-0.861193\pi\) |
0.819005 | + | 0.573787i | \(0.194526\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.2355 | − | 35.0489i | −1.00800 | − | 1.74591i | ||||
\(404\) | −12.9242 | −0.643004 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.93790 | −0.145806 | ||||||||
\(407\) | 13.7297 | + | 23.7806i | 0.680558 | + | 1.17876i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −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 | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.743474 | + | 1.28773i | 0.0366283 | + | 0.0634421i | ||||
\(413\) | −0.837128 | −0.0411924 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.34144 | −0.311289 | ||||||||
\(416\) | 15.9175 | + | 27.5699i | 0.780420 | + | 1.35173i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 19.6900 | − | 34.1041i | 0.963070 | − | 1.66809i | ||||
\(419\) | −15.1142 | + | 26.1785i | −0.738376 | + | 1.27890i | 0.214850 | + | 0.976647i | \(0.431074\pi\) |
−0.953226 | + | 0.302258i | \(0.902260\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.5925 | 0.660109 | ||||||||
\(425\) | 2.36954 | + | 4.10416i | 0.114939 | + | 0.199081i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.62833 | − | 8.01651i | 0.223981 | − | 0.387946i | ||||
\(428\) | −0.258251 | + | 0.447303i | −0.0124830 | + | 0.0216212i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.91566 | + | 17.1744i | 0.478175 | + | 0.828224i | ||||
\(431\) | 6.84759 | 0.329837 | 0.164918 | − | 0.986307i | \(-0.447264\pi\) | ||||
0.164918 | + | 0.986307i | \(0.447264\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −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 | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.71776 | − | 9.90345i | 0.273831 | − | 0.474289i | ||||
\(437\) | −1.84062 | + | 3.18804i | −0.0880487 | + | 0.152505i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −48.2572 | −2.29536 | ||||||||
\(443\) | 5.16965 | + | 8.95410i | 0.245618 | + | 0.425422i | 0.962305 | − | 0.271972i | \(-0.0876759\pi\) |
−0.716687 | + | 0.697394i | \(0.754343\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.83248 | − | 8.37010i | 0.229082 | − | 0.396781i | ||||
\(446\) | −20.3456 | + | 35.2395i | −0.963390 | + | 1.66864i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.204148 | − | 0.353594i | −0.00964506 | − | 0.0167057i | ||||
\(449\) | −24.4414 | −1.15346 | −0.576731 | − | 0.816934i | \(-0.695672\pi\) | ||||
−0.576731 | + | 0.816934i | \(0.695672\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.2857 | 1.14357 | ||||||||
\(452\) | −0.595821 | − | 1.03199i | −0.0280251 | − | 0.0485408i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.3053 | + | 29.9737i | −0.812178 | + | 1.40673i | ||||
\(455\) | −2.90805 | + | 5.03689i | −0.136332 | + | 0.236133i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 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 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.06530 | −0.0496700 | ||||||||
\(461\) | −7.58273 | − | 13.1337i | −0.353163 | − | 0.611696i | 0.633639 | − | 0.773629i | \(-0.281561\pi\) |
−0.986802 | + | 0.161933i | \(0.948227\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −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 | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.67793 | + | 9.83446i | 0.263025 | + | 0.455573i | ||||
\(467\) | 27.5899 | 1.27671 | 0.638353 | − | 0.769744i | \(-0.279616\pi\) | ||||
0.638353 | + | 0.769744i | \(0.279616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.51787 | 0.208616 | ||||||||
\(470\) | 3.65512 | + | 6.33085i | 0.168598 | + | 0.292020i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.684967 | − | 1.18640i | 0.0315282 | − | 0.0546084i | ||||
\(473\) | 34.6044 | − | 59.9365i | 1.59111 | − | 2.75588i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.84062 | − | 3.18804i | −0.0844533 | − | 0.146277i | ||||
\(476\) | −5.04854 | −0.231400 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.6601 | 1.26514 | ||||||||
\(479\) | 10.7444 | + | 18.6099i | 0.490924 | + | 0.850306i | 0.999945 | − | 0.0104482i | \(-0.00332581\pi\) |
−0.509021 | + | 0.860754i | \(0.669992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.0692 | + | 22.6365i | −0.595903 | + | 1.03213i | ||||
\(482\) | −5.61831 | + | 9.73119i | −0.255907 | + | 0.443244i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.0263 | − | 24.2942i | −0.637557 | − | 1.10428i | ||||
\(485\) | 8.17354 | 0.371141 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 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 | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.875400 | + | 1.51624i | −0.0395466 | + | 0.0684966i | ||||
\(491\) | 17.3701 | − | 30.0860i | 0.783903 | − | 1.35776i | −0.145749 | − | 0.989322i | \(-0.546559\pi\) |
0.929652 | − | 0.368438i | \(-0.120107\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.97616 | + | 6.88690i | 0.179077 | + | 0.310171i | ||||
\(494\) | 37.4854 | 1.68655 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 34.7625 | 1.56088 | ||||||||
\(497\) | 5.18337 | + | 8.97785i | 0.232506 | + | 0.402712i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 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 | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.64045 | − | 6.30544i | −0.162481 | − | 0.281425i | ||||
\(503\) | 3.40995 | 0.152042 | 0.0760210 | − | 0.997106i | \(-0.475778\pi\) | ||||
0.0760210 | + | 0.997106i | \(0.475778\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1320 | 0.539866 | ||||||||
\(506\) | 5.34875 | + | 9.26431i | 0.237781 | + | 0.411849i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.26223 | − | 10.8465i | 0.277841 | − | 0.481235i | ||||
\(509\) | −15.6708 | + | 27.1427i | −0.694597 | + | 1.20308i | 0.275719 | + | 0.961238i | \(0.411084\pi\) |
−0.970316 | + | 0.241839i | \(0.922249\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.11729 | − | 10.5955i | −0.270613 | − | 0.468715i | ||||
\(512\) | −10.9939 | −0.485867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.5686 | 0.907240 | ||||||||
\(515\) | −0.697899 | − | 1.20880i | −0.0307531 | − | 0.0532660i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.7559 | − | 22.0939i | 0.561003 | − | 0.971686i | ||||
\(518\) | −3.93417 | + | 6.81418i | −0.172857 | + | 0.299398i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.75894 | − | 8.24272i | −0.208693 | − | 0.361467i | ||||
\(521\) | 11.9819 | 0.524936 | 0.262468 | − | 0.964941i | \(-0.415464\pi\) | ||||
0.262468 | + | 0.964941i | \(0.415464\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −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 | 0 | ||||||||
\(526\) | 10.8537 | − | 18.7991i | 0.473242 | − | 0.819679i | ||||
\(527\) | −16.4883 | + | 28.5585i | −0.718240 | + | 1.24403i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | 14.5421 | 0.631669 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.92163 | 0.170024 | ||||||||
\(533\) | 11.5587 | + | 20.0202i | 0.500661 | + | 0.867171i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.242420 | − | 0.419884i | 0.0104807 | − | 0.0181532i | ||||
\(536\) | −3.69668 | + | 6.40284i | −0.159672 | + | 0.276561i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.5005 | + | 28.5798i | 0.711389 | + | 1.23216i | ||||
\(539\) | 6.11007 | 0.263179 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.9699 | − | 22.4645i | 0.556079 | − | 0.963157i | ||||
\(545\) | −5.36726 | + | 9.29637i | −0.229908 | + | 0.398213i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.6975 | −0.456143 | ||||||||
\(551\) | −3.08861 | − | 5.34964i | −0.131579 | − | 0.227902i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.41643 | + | 7.64948i | −0.187806 | + | 0.325289i | ||||
\(554\) | −16.1926 | + | 28.0464i | −0.687956 | + | 1.19158i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.76616 | + | 9.98728i | 0.244540 | + | 0.423555i | ||||
\(557\) | 10.2775 | 0.435472 | 0.217736 | − | 0.976008i | \(-0.430133\pi\) | ||||
0.217736 | + | 0.976008i | \(0.430133\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 65.8790 | 2.78638 | ||||||||
\(560\) | −2.49787 | − | 4.32643i | −0.105554 | − | 0.182825i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.4319 | + | 26.7289i | −0.650957 | + | 1.12749i | ||||
\(563\) | −4.49496 | + | 7.78550i | −0.189440 | + | 0.328120i | −0.945064 | − | 0.326886i | \(-0.894001\pi\) |
0.755624 | + | 0.655006i | \(0.227334\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.559298 | + | 0.968732i | 0.0235298 | + | 0.0407549i | ||||
\(566\) | 6.63882 | 0.279050 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16.9648 | −0.711829 | ||||||||
\(569\) | 3.97112 | + | 6.87818i | 0.166478 | + | 0.288348i | 0.937179 | − | 0.348849i | \(-0.113427\pi\) |
−0.770701 | + | 0.637197i | \(0.780094\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −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 | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.47946 | + | 6.02661i | 0.145230 | + | 0.251546i | ||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 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 | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.893806 | − | 1.54812i | 0.0371133 | − | 0.0642821i | ||||
\(581\) | −3.17072 | + | 5.49185i | −0.131544 | + | 0.227840i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.3750 | − | 43.9508i | −1.05093 | − | 1.82026i | ||||
\(584\) | 20.0215 | 0.828496 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.1370 | −0.583994 | ||||||||
\(587\) | 1.00014 | + | 1.73229i | 0.0412802 | + | 0.0714993i | 0.885927 | − | 0.463824i | \(-0.153523\pi\) |
−0.844647 | + | 0.535323i | \(0.820190\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.8078 | − | 22.1838i | 0.527737 | − | 0.914067i | ||||
\(590\) | 0.732822 | − | 1.26928i | 0.0301698 | − | 0.0522556i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.2258 | − | 19.4436i | −0.461376 | − | 0.799126i | ||||
\(593\) | −18.6458 | −0.765690 | −0.382845 | − | 0.923813i | \(-0.625056\pi\) | ||||
−0.382845 | + | 0.923813i | \(0.625056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.73907 | 0.194283 | ||||||||
\(596\) | −7.35860 | − | 12.7455i | −0.301420 | − | 0.522074i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.09142 | + | 8.81859i | −0.208204 | + | 0.360619i | ||||
\(599\) | 14.0200 | − | 24.2833i | 0.572840 | − | 0.992188i | −0.423432 | − | 0.905928i | \(-0.639175\pi\) |
0.996273 | − | 0.0862606i | \(-0.0274918\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.5480 | 0.469882 | ||||||||
\(605\) | 13.1665 | + | 22.8050i | 0.535293 | + | 0.927154i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −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 | 0 | ||||||||
\(610\) | 8.10329 | + | 14.0353i | 0.328093 | + | 0.568273i | ||||
\(611\) | 24.2844 | 0.982441 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 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 | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.99947 | + | 8.65933i | −0.201434 | + | 0.348894i | ||||
\(617\) | −15.8000 | + | 27.3664i | −0.636085 | + | 1.10173i | 0.350199 | + | 0.936675i | \(0.386114\pi\) |
−0.986284 | + | 0.165056i | \(0.947220\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −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 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.5131 | 0.581923 | ||||||||
\(623\) | −4.83248 | − | 8.37010i | −0.193609 | − | 0.335341i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 17.5686 | − | 30.4298i | 0.702184 | − | 1.21622i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.89648 | + | 10.2130i | 0.235295 | + | 0.407543i | ||||
\(629\) | 21.2980 | 0.849208 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.1770 | + | 31.4834i | −0.721900 | + | 1.25037i | ||||
\(635\) | −5.87836 | + | 10.1816i | −0.233276 | + | 0.404045i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.90805 | + | 5.03689i | 0.115221 | + | 0.199569i | ||||
\(638\) | −17.9508 | −0.710677 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.6620 | 0.460983 | ||||||||
\(641\) | −20.6415 | − | 35.7522i | −0.815291 | − | 1.41213i | −0.909119 | − | 0.416537i | \(-0.863244\pi\) |
0.0938280 | − | 0.995588i | \(-0.470090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −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 | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.2719 | − | 26.4517i | −0.600865 | − | 1.04073i | ||||
\(647\) | 4.79934 | 0.188682 | 0.0943408 | − | 0.995540i | \(-0.469926\pi\) | ||||
0.0943408 | + | 0.995540i | \(0.469926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.11491 | −0.200778 | ||||||||
\(650\) | −5.09142 | − | 8.81859i | −0.199702 | − | 0.345894i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.96919 | + | 10.3389i | −0.233772 | + | 0.404904i | ||||
\(653\) | 7.23824 | − | 12.5370i | 0.283254 | − | 0.490611i | −0.688930 | − | 0.724828i | \(-0.741919\pi\) |
0.972184 | + | 0.234217i | \(0.0752526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.485084 | + | 0.840190i | 0.0189538 | + | 0.0328289i | ||||
\(656\) | −19.8566 | −0.775270 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.31024 | 0.284983 | ||||||||
\(659\) | −14.0086 | − | 24.2636i | −0.545696 | − | 0.945174i | −0.998563 | − | 0.0535955i | \(-0.982932\pi\) |
0.452866 | − | 0.891578i | \(-0.350401\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 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 | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.18879 | − | 8.98725i | −0.201364 | − | 0.348773i | ||||
\(665\) | −3.68123 | −0.142752 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.67803 | 0.0649737 | ||||||||
\(668\) | 12.5918 | + | 21.8097i | 0.487193 | + | 0.843843i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.95495 | + | 6.85017i | −0.152793 | + | 0.264645i | ||||
\(671\) | 28.2794 | − | 48.9814i | 1.09171 | − | 1.89091i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 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 | 0 | ||||||||
\(676\) | 22.1871 | 0.853350 | ||||||||
\(677\) | −14.2219 | − | 24.6331i | −0.546593 | − | 0.946727i | −0.998505 | − | 0.0546646i | \(-0.982591\pi\) |
0.451911 | − | 0.892063i | \(-0.350742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.08677 | − | 7.07849i | 0.156836 | − | 0.271648i | ||||
\(680\) | −3.87767 | + | 6.71632i | −0.148702 | + | 0.257559i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −37.2190 | − | 64.4651i | −1.42519 | − | 2.46850i | ||||
\(683\) | 41.1926 | 1.57619 | 0.788096 | − | 0.615553i | \(-0.211067\pi\) | ||||
0.788096 | + | 0.615553i | \(0.211067\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.7671 | 0.411389 | ||||||||
\(686\) | 0.875400 | + | 1.51624i | 0.0334229 | + | 0.0578902i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −28.2933 | + | 49.0055i | −1.07867 | + | 1.86832i | ||||
\(689\) | 24.1542 | − | 41.8363i | 0.920202 | − | 1.59384i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 34.1495 | 1.29630 | ||||||||
\(695\) | −5.41270 | − | 9.37507i | −0.205315 | − | 0.355617i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.41822 | − | 16.3128i | 0.356740 | − | 0.617892i | ||||
\(698\) | −11.0197 | + | 19.0867i | −0.417103 | + | 0.722443i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.532651 | − | 0.922579i | −0.0201323 | − | 0.0348702i | ||||
\(701\) | 2.61012 | 0.0985828 | 0.0492914 | − | 0.998784i | \(-0.484304\pi\) | ||||
0.0492914 | + | 0.998784i | \(0.484304\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.5440 | −0.623967 | ||||||||
\(704\) | −1.24735 | − | 2.16048i | −0.0470115 | − | 0.0814262i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.3716 | + | 24.8923i | −0.540881 | + | 0.936833i | ||||
\(707\) | 6.06599 | − | 10.5066i | 0.228135 | − | 0.395141i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.8164 | 0.592745 | ||||||||
\(713\) | 3.47922 | + | 6.02618i | 0.130298 | + | 0.225682i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.7684 | + | 30.7757i | −0.664500 | + | 1.15095i | ||||
\(716\) | 12.2257 | − | 21.1756i | 0.456897 | − | 0.791369i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.5837 | + | 20.0635i | 0.432299 | + | 0.748764i | ||||
\(719\) | −8.13828 | −0.303507 | −0.151753 | − | 0.988418i | \(-0.548492\pi\) | ||||
−0.151753 | + | 0.988418i | \(0.548492\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.39580 | −0.0519823 | ||||||||
\(722\) | −4.76963 | − | 8.26125i | −0.177507 | − | 0.307452i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.18402 | − | 3.78283i | 0.0811685 | − | 0.140588i | ||||
\(725\) | −0.839016 | + | 1.45322i | −0.0311603 | + | 0.0539712i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21.4203 | 0.792801 | ||||||||
\(731\) | −26.8397 | − | 46.4878i | −0.992703 | − | 1.71941i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 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 | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.73680 | − | 4.74027i | −0.100880 | − | 0.174729i | ||||
\(737\) | 27.6045 | 1.01683 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −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 | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.27105 | − | 12.5938i | 0.266929 | − | 0.462334i | ||||
\(743\) | 4.65459 | − | 8.06198i | 0.170760 | − | 0.295765i | −0.767926 | − | 0.640539i | \(-0.778711\pi\) |
0.938686 | + | 0.344774i | \(0.112044\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.90752 | + | 11.9642i | 0.253072 | + | 0.438333i | ||||
\(746\) | −52.9630 | −1.93911 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −30.8469 | −1.12788 | ||||||||
\(749\) | −0.242420 | − | 0.419884i | −0.00885783 | − | 0.0153422i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 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 | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.54356 | − | 14.7979i | −0.311138 | − | 0.538907i | ||||
\(755\) | −10.8401 | −0.394512 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −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 | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.01211 | − | 5.21713i | 0.109261 | − | 0.189245i | ||||
\(761\) | −21.0958 | + | 36.5391i | −0.764723 | + | 1.32454i | 0.175669 | + | 0.984449i | \(0.443791\pi\) |
−0.940393 | + | 0.340091i | \(0.889542\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.36726 | + | 9.29637i | 0.194308 | + | 0.336551i | ||||
\(764\) | 9.30521 | 0.336651 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.6714 | 0.385572 | ||||||||
\(767\) | −2.43441 | − | 4.21652i | −0.0879015 | − | 0.152250i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −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 | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.61980 | + | 14.9299i | 0.310234 | + | 0.537340i | ||||
\(773\) | −20.9848 | −0.754770 | −0.377385 | − | 0.926056i | \(-0.623177\pi\) | ||||
−0.377385 | + | 0.926056i | \(0.623177\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.95844 | −0.249954 | ||||||||
\(776\) | 6.68787 | + | 11.5837i | 0.240081 | + | 0.415832i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.8694 | + | 20.5585i | −0.425540 | + | 0.737056i | ||||
\(779\) | −7.31592 | + | 12.6715i | −0.262120 | + | 0.454005i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.6707 | + | 54.8553i | 1.13327 | + | 1.96288i | ||||
\(782\) | 8.29717 | 0.296706 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.99574 | −0.178419 | ||||||||
\(785\) | −5.53503 | − | 9.58695i | −0.197554 | − | 0.342173i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 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 | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.73229 | − | 13.3927i | −0.275103 | − | 0.476492i | ||||
\(791\) | 1.11860 | 0.0397727 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53.8377 | 1.91183 | ||||||||
\(794\) | −14.3661 | − | 24.8828i | −0.509834 | − | 0.883058i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.98778 | − | 6.90704i | 0.141343 | − | 0.244814i | ||||
\(797\) | 24.8167 | − | 42.9839i | 0.879054 | − | 1.52257i | 0.0266739 | − | 0.999644i | \(-0.491508\pi\) |
0.852380 | − | 0.522922i | \(-0.175158\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.89368 | − | 17.1364i | −0.350013 | − | 0.606241i | ||||
\(800\) | 5.47360 | 0.193521 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.12926 | −0.216432 | ||||||||
\(803\) | −37.3770 | − | 64.7389i | −1.31901 | − | 2.28459i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.500000 | − | 0.866025i | 0.0176227 | − | 0.0305234i | ||||
\(806\) | 35.4283 | − | 61.3636i | 1.24791 | − | 2.16144i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.92681 | + | 17.1937i | 0.349224 | + | 0.604873i | ||||
\(809\) | 55.4296 | 1.94880 | 0.974401 | − | 0.224818i | \(-0.0721789\pi\) | ||||
0.974401 | + | 0.224818i | \(0.0721789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −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 | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −24.0380 | + | 41.6351i | −0.842532 | + | 1.45931i | ||||
\(815\) | 5.60329 | − | 9.70518i | 0.196275 | − | 0.339958i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.8487 | + | 36.1109i | 0.729402 | + | 1.26336i | ||||
\(818\) | −11.8305 | −0.413642 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.23427 | −0.147867 | ||||||||
\(821\) | 2.55717 | + | 4.42914i | 0.0892457 | + | 0.154578i | 0.907192 | − | 0.420716i | \(-0.138221\pi\) |
−0.817947 | + | 0.575294i | \(0.804888\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 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 | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.732822 | − | 1.26928i | −0.0254981 | − | 0.0441641i | ||||
\(827\) | −23.9366 | −0.832356 | −0.416178 | − | 0.909283i | \(-0.636631\pi\) | ||||
−0.416178 | + | 0.909283i | \(0.636631\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −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 | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.18734 | − | 2.05654i | 0.0411637 | − | 0.0712976i | ||||
\(833\) | 2.36954 | − | 4.10416i | 0.0820995 | − | 0.142201i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.8200 | − | 20.4728i | −0.409047 | − | 0.708490i | ||||
\(836\) | 23.9614 | 0.828722 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −52.9238 | −1.82822 | ||||||||
\(839\) | −18.9639 | − | 32.8465i | −0.654707 | − | 1.13399i | −0.981967 | − | 0.189051i | \(-0.939459\pi\) |
0.327260 | − | 0.944934i | \(-0.393875\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0921 | − | 22.6762i | 0.451452 | − | 0.781938i | ||||
\(842\) | −1.13909 | + | 1.97296i | −0.0392556 | + | 0.0679927i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.33407 | − | 5.77477i | −0.114763 | − | 0.198776i | ||||
\(845\) | −20.8270 | −0.716472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.3329 | 0.904810 | ||||||||
\(848\) | 20.7472 | + | 35.9352i | 0.712463 | + | 1.23402i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.14858 | + | 7.18556i | −0.142295 | + | 0.246463i | ||||
\(851\) | 2.24707 | − | 3.89203i | 0.0770285 | − | 0.133417i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −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 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.793426 | 0.0271187 | ||||||||
\(857\) | 11.8587 | + | 20.5399i | 0.405087 | + | 0.701631i | 0.994332 | − | 0.106324i | \(-0.0339080\pi\) |
−0.589245 | + | 0.807954i | \(0.700575\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −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 | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.99438 | + | 10.3826i | 0.204169 | + | 0.353632i | ||||
\(863\) | 5.54957 | 0.188909 | 0.0944547 | − | 0.995529i | \(-0.469889\pi\) | ||||
0.0944547 | + | 0.995529i | \(0.469889\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.08904 | −0.105031 | ||||||||
\(866\) | −5.02356 | − | 8.70105i | −0.170707 | − | 0.295674i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.70642 | − | 6.41971i | 0.125804 | − | 0.217899i | ||||
\(869\) | −26.9847 | + | 46.7389i | −0.915393 | + | 1.58551i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.1382 | + | 22.7560i | 0.445171 | + | 0.771059i | ||||
\(872\) | −17.5667 | −0.594884 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.44511 | −0.218009 | ||||||||
\(875\) | 0.500000 | + | 0.866025i | 0.0169031 | + | 0.0292770i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −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 | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15.2621 | − | 26.4348i | −0.514487 | − | 0.891117i | ||||
\(881\) | −8.12987 | −0.273902 | −0.136951 | − | 0.990578i | \(-0.543730\pi\) | ||||
−0.136951 | + | 0.990578i | \(0.543730\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −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 | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.05103 | + | 15.6768i | −0.304075 | + | 0.526674i | ||||
\(887\) | −25.7749 | + | 44.6434i | −0.865435 | + | 1.49898i | 0.00117920 | + | 0.999999i | \(0.499625\pi\) |
−0.866614 | + | 0.498978i | \(0.833709\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.87836 | + | 10.1816i | 0.197154 | + | 0.341480i | ||||
\(890\) | 16.9214 | 0.567207 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.7592 | −0.828998 | ||||||||
\(893\) | 7.68525 | + | 13.3113i | 0.257177 | + | 0.445444i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.4763 | + | 19.8776i | −0.383611 | + | 0.664433i | ||||
\(896\) | 5.83102 | − | 10.0996i | 0.194801 | − | 0.337405i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21.3960 | − | 37.0590i | −0.713995 | − | 1.23668i | ||||
\(899\) | −11.6765 | −0.389432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.3626 | −1.31136 | ||||||||
\(902\) | 21.2597 | + | 36.8230i | 0.707872 | + | 1.22607i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.915274 | + | 1.58530i | −0.0304415 | + | 0.0527263i | ||||
\(905\) | −2.05014 | + | 3.55095i | −0.0681490 | + | 0.118038i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 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 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.1828 | −0.337558 | ||||||||
\(911\) | 17.1698 | + | 29.7389i | 0.568860 | + | 0.985295i | 0.996679 | + | 0.0814303i | \(0.0259488\pi\) |
−0.427819 | + | 0.903865i | \(0.640718\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.3733 | + | 33.5556i | −0.641163 | + | 1.11053i | ||||
\(914\) | −34.9771 | + | 60.5821i | −1.15694 | + | 2.00388i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.00551690 | + | 0.00955555i | 0.000182283 | + | 0.000315724i | ||||
\(917\) | 0.970168 | 0.0320378 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 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 | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.2759 | − | 22.9945i | 0.437217 | − | 0.757282i | ||||
\(923\) | −30.1470 | + | 52.2161i | −0.992300 | + | 1.71871i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.24707 | + | 3.89203i | 0.0738831 | + | 0.127969i | ||||
\(926\) | −18.2583 | −0.600006 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.18487 | 0.301508 | ||||||||
\(929\) | −5.84648 | − | 10.1264i | −0.191817 | − | 0.332237i | 0.754036 | − | 0.656834i | \(-0.228105\pi\) |
−0.945852 | + | 0.324597i | \(0.894771\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.84062 | + | 3.18804i | −0.0603238 | + | 0.104484i | ||||
\(932\) | −3.45482 | + | 5.98393i | −0.113167 | + | 0.196010i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 24.1522 | + | 41.8328i | 0.790283 | + | 1.36881i | ||||
\(935\) | 28.9560 | 0.946964 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 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 | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.22401 | + | 3.85211i | −0.0725394 | + | 0.125642i | ||||
\(941\) | −2.79192 | + | 4.83575i | −0.0910140 | + | 0.157641i | −0.907938 | − | 0.419104i | \(-0.862344\pi\) |
0.816924 | + | 0.576745i | \(0.195677\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.98736 | − | 3.44220i | −0.0647172 | − | 0.112093i | ||||
\(944\) | 4.18207 | 0.136115 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 121.171 | 3.93960 | ||||||||
\(947\) | −12.6053 | − | 21.8331i | −0.409618 | − | 0.709480i | 0.585229 | − | 0.810868i | \(-0.301005\pi\) |
−0.994847 | + | 0.101389i | \(0.967671\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.5788 | − | 61.6243i | 1.15494 | − | 2.00041i | ||||
\(950\) | 3.22255 | − | 5.58163i | 0.104553 | − | 0.181092i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.87767 | + | 6.71632i | 0.125676 | + | 0.217677i | ||||
\(953\) | −32.3742 | −1.04870 | −0.524351 | − | 0.851502i | \(-0.675692\pi\) | ||||
−0.524351 | + | 0.851502i | \(0.675692\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.73481 | −0.282652 | ||||||||
\(956\) | 8.41512 | + | 14.5754i | 0.272164 | + | 0.471403i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.8113 | + | 32.5821i | −0.607766 | + | 1.05268i | ||||
\(959\) | 5.38354 | − | 9.32456i | 0.173843 | − | 0.301106i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.70992 | − | 15.0860i | −0.280965 | − | 0.486646i | ||||
\(962\) | −45.7630 | −1.47546 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.83710 | −0.220208 | ||||||||
\(965\) | −8.09142 | − | 14.0147i | −0.260472 | − | 0.451151i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −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 | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.15512 | + | 12.3930i | 0.229737 | + | 0.397916i | ||||
\(971\) | −16.6145 | −0.533185 | −0.266592 | − | 0.963809i | \(-0.585898\pi\) | ||||
−0.266592 | + | 0.963809i | \(0.585898\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.8254 | −0.347046 | ||||||||
\(974\) | 10.1702 | + | 17.6153i | 0.325874 | + | 0.564430i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −23.1219 | + | 40.0484i | −0.740115 | + | 1.28192i | ||||
\(977\) | −30.5289 | + | 52.8776i | −0.976707 | + | 1.69171i | −0.302523 | + | 0.953142i | \(0.597829\pi\) |
−0.674183 | + | 0.738564i | \(0.735504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.5268 | − | 51.1419i | −0.943680 | − | 1.63450i | ||||
\(980\) | −1.06530 | −0.0340298 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 60.8233 | 1.94095 | ||||||||
\(983\) | 3.51023 | + | 6.07990i | 0.111959 | + | 0.193919i | 0.916560 | − | 0.399897i | \(-0.130954\pi\) |
−0.804601 | + | 0.593816i | \(0.797621\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.209326 | − | 0.362564i | 0.00666969 | − | 0.0115522i | ||||
\(986\) | −6.96146 | + | 12.0576i | −0.221698 | + | 0.383992i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.4043 | + | 19.7528i | 0.362819 | + | 0.628421i | ||||
\(989\) | −11.3270 | −0.360178 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.07504 | + | 15.7184i | −0.287843 | + | 0.498558i | ||||
\(995\) | −3.74333 | + | 6.48365i | −0.118672 | + | 0.205545i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −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 | ||||||||
\(999\) | 0 | 0 |
(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 | 945.2.i.d.631.4 | 8 | ||
3.2 | odd | 2 | 315.2.i.c.211.1 | yes | 8 | ||
9.2 | odd | 6 | 315.2.i.c.106.1 | ✓ | 8 | ||
9.4 | even | 3 | 2835.2.a.p.1.1 | 4 | |||
9.5 | odd | 6 | 2835.2.a.m.1.4 | 4 | |||
9.7 | even | 3 | inner | 945.2.i.d.316.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.i.c.106.1 | ✓ | 8 | 9.2 | odd | 6 | ||
315.2.i.c.211.1 | yes | 8 | 3.2 | odd | 2 | ||
945.2.i.d.316.4 | 8 | 9.7 | even | 3 | inner | ||
945.2.i.d.631.4 | 8 | 1.1 | even | 1 | trivial | ||
2835.2.a.m.1.4 | 4 | 9.5 | odd | 6 | |||
2835.2.a.p.1.1 | 4 | 9.4 | even | 3 |