Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [798,2,Mod(457,798)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(798, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("798.457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 798.j (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: | \(6.37206208130\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 457.2 | ||
Root | \(2.33086i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 798.457 |
Dual form | 798.2.j.l.571.2 |
$q$-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 \(\left(\mathbb{Z}/798\mathbb{Z}\right)^\times\).
\(n\) | \(115\) | \(211\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.05903 | + | 1.83430i | −0.473613 | + | 0.820322i | −0.999544 | − | 0.0302055i | \(-0.990384\pi\) |
0.525931 | + | 0.850528i | \(0.323717\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.11699 | − | 2.39840i | −0.422181 | − | 0.906512i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.05903 | + | 1.83430i | 0.334895 | + | 0.580055i | ||||
\(11\) | −1.67602 | − | 2.90295i | −0.505338 | − | 0.875271i | −0.999981 | − | 0.00617477i | \(-0.998034\pi\) |
0.494643 | − | 0.869096i | \(-0.335299\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | −4.23612 | −1.17489 | −0.587445 | − | 0.809264i | \(-0.699866\pi\) | ||||
−0.587445 | + | 0.809264i | \(0.699866\pi\) | |||||||
\(14\) | −2.63557 | − | 0.231865i | −0.704386 | − | 0.0619684i | ||||
\(15\) | −2.11806 | −0.546881 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.47814 | − | 6.02432i | −0.843573 | − | 1.46111i | −0.886854 | − | 0.462049i | \(-0.847114\pi\) |
0.0432811 | − | 0.999063i | \(-0.486219\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | ||||
\(20\) | 2.11806 | 0.473613 | ||||||||
\(21\) | 1.51859 | − | 2.16654i | 0.331383 | − | 0.472778i | ||||
\(22\) | −3.35203 | −0.714656 | ||||||||
\(23\) | 3.59035 | − | 6.21867i | 0.748640 | − | 1.29668i | −0.199834 | − | 0.979830i | \(-0.564040\pi\) |
0.948475 | − | 0.316853i | \(-0.102626\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0.256906 | + | 0.444974i | 0.0513812 | + | 0.0889948i | ||||
\(26\) | −2.11806 | + | 3.66859i | −0.415386 | + | 0.719470i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.51859 | + | 2.16654i | −0.286986 | + | 0.409438i | ||||
\(29\) | 7.29877 | 1.35535 | 0.677673 | − | 0.735363i | \(-0.262988\pi\) | ||||
0.677673 | + | 0.735363i | \(0.262988\pi\) | |||||||
\(30\) | −1.05903 | + | 1.83430i | −0.193352 | + | 0.334895i | ||||
\(31\) | −2.27442 | − | 3.93940i | −0.408497 | − | 0.707538i | 0.586225 | − | 0.810149i | \(-0.300614\pi\) |
−0.994722 | + | 0.102611i | \(0.967280\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 1.67602 | − | 2.90295i | 0.291757 | − | 0.505338i | ||||
\(34\) | −6.95628 | −1.19299 | ||||||||
\(35\) | 5.58231 | + | 0.491104i | 0.943582 | + | 0.0830117i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.126109 | − | 0.218427i | 0.0207322 | − | 0.0359092i | −0.855473 | − | 0.517847i | \(-0.826734\pi\) |
0.876205 | + | 0.481938i | \(0.160067\pi\) | |||||||
\(38\) | 0.500000 | + | 0.866025i | 0.0811107 | + | 0.140488i | ||||
\(39\) | −2.11806 | − | 3.66859i | −0.339161 | − | 0.587445i | ||||
\(40\) | 1.05903 | − | 1.83430i | 0.167448 | − | 0.290028i | ||||
\(41\) | −10.3359 | −1.61420 | −0.807101 | − | 0.590413i | \(-0.798965\pi\) | ||||
−0.807101 | + | 0.590413i | \(0.798965\pi\) | |||||||
\(42\) | −1.11699 | − | 2.39840i | −0.172355 | − | 0.370082i | ||||
\(43\) | 3.17133 | 0.483623 | 0.241812 | − | 0.970323i | \(-0.422258\pi\) | ||||
0.241812 | + | 0.970323i | \(0.422258\pi\) | |||||||
\(44\) | −1.67602 | + | 2.90295i | −0.252669 | + | 0.437636i | ||||
\(45\) | −1.05903 | − | 1.83430i | −0.157871 | − | 0.273441i | ||||
\(46\) | −3.59035 | − | 6.21867i | −0.529369 | − | 0.916893i | ||||
\(47\) | −3.57762 | + | 6.19662i | −0.521849 | + | 0.903869i | 0.477828 | + | 0.878454i | \(0.341424\pi\) |
−0.999677 | + | 0.0254158i | \(0.991909\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −4.50469 | + | 5.35796i | −0.643527 | + | 0.765424i | ||||
\(50\) | 0.513812 | 0.0726639 | ||||||||
\(51\) | 3.47814 | − | 6.02432i | 0.487037 | − | 0.843573i | ||||
\(52\) | 2.11806 | + | 3.66859i | 0.293722 | + | 0.508742i | ||||
\(53\) | −0.878666 | − | 1.52189i | −0.120694 | − | 0.209048i | 0.799348 | − | 0.600869i | \(-0.205179\pi\) |
−0.920042 | + | 0.391821i | \(0.871845\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 7.09982 | 0.957339 | ||||||||
\(56\) | 1.11699 | + | 2.39840i | 0.149263 | + | 0.320500i | ||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 3.64938 | − | 6.32092i | 0.479188 | − | 0.829977i | ||||
\(59\) | −6.52327 | − | 11.2986i | −0.849258 | − | 1.47096i | −0.881871 | − | 0.471490i | \(-0.843716\pi\) |
0.0326134 | − | 0.999468i | \(-0.489617\pi\) | |||||||
\(60\) | 1.05903 | + | 1.83430i | 0.136720 | + | 0.236807i | ||||
\(61\) | −3.45956 | + | 5.99213i | −0.442951 | + | 0.767213i | −0.997907 | − | 0.0646665i | \(-0.979402\pi\) |
0.554956 | + | 0.831880i | \(0.312735\pi\) | |||||||
\(62\) | −4.54883 | −0.577702 | ||||||||
\(63\) | 2.63557 | + | 0.231865i | 0.332051 | + | 0.0292122i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.48619 | − | 7.77031i | 0.556443 | − | 0.963788i | ||||
\(66\) | −1.67602 | − | 2.90295i | −0.206303 | − | 0.357328i | ||||
\(67\) | 2.15308 | + | 3.72925i | 0.263041 | + | 0.455600i | 0.967048 | − | 0.254592i | \(-0.0819413\pi\) |
−0.704008 | + | 0.710192i | \(0.748608\pi\) | |||||||
\(68\) | −3.47814 | + | 6.02432i | −0.421787 | + | 0.730556i | ||||
\(69\) | 7.18070 | 0.864455 | ||||||||
\(70\) | 3.21646 | − | 4.58887i | 0.384441 | − | 0.548474i | ||||
\(71\) | −10.4518 | −1.24041 | −0.620203 | − | 0.784441i | \(-0.712950\pi\) | ||||
−0.620203 | + | 0.784441i | \(0.712950\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 6.38335 | + | 11.0563i | 0.747115 | + | 1.29404i | 0.949200 | + | 0.314673i | \(0.101895\pi\) |
−0.202085 | + | 0.979368i | \(0.564772\pi\) | |||||||
\(74\) | −0.126109 | − | 0.218427i | −0.0146599 | − | 0.0253916i | ||||
\(75\) | −0.256906 | + | 0.444974i | −0.0296649 | + | 0.0513812i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −5.09035 | + | 7.26231i | −0.580099 | + | 0.827617i | ||||
\(78\) | −4.23612 | −0.479647 | ||||||||
\(79\) | −1.13557 | + | 1.96687i | −0.127762 | + | 0.221290i | −0.922809 | − | 0.385257i | \(-0.874113\pi\) |
0.795047 | + | 0.606547i | \(0.207446\pi\) | |||||||
\(80\) | −1.05903 | − | 1.83430i | −0.118403 | − | 0.205081i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −5.16797 | + | 8.95119i | −0.570707 | + | 0.988493i | ||||
\(83\) | 16.5699 | 1.81878 | 0.909392 | − | 0.415940i | \(-0.136547\pi\) | ||||
0.909392 | + | 0.415940i | \(0.136547\pi\) | |||||||
\(84\) | −2.63557 | − | 0.231865i | −0.287564 | − | 0.0252985i | ||||
\(85\) | 14.7338 | 1.59811 | ||||||||
\(86\) | 1.58566 | − | 2.74645i | 0.170987 | − | 0.296157i | ||||
\(87\) | 3.64938 | + | 6.32092i | 0.391255 | + | 0.677673i | ||||
\(88\) | 1.67602 | + | 2.90295i | 0.178664 | + | 0.309455i | ||||
\(89\) | −1.89683 | + | 3.28540i | −0.201063 | + | 0.348252i | −0.948871 | − | 0.315663i | \(-0.897773\pi\) |
0.747808 | + | 0.663915i | \(0.231106\pi\) | |||||||
\(90\) | −2.11806 | −0.223263 | ||||||||
\(91\) | 4.73169 | + | 10.1599i | 0.496016 | + | 1.06505i | ||||
\(92\) | −7.18070 | −0.748640 | ||||||||
\(93\) | 2.27442 | − | 3.93940i | 0.235846 | − | 0.408497i | ||||
\(94\) | 3.57762 | + | 6.19662i | 0.369003 | + | 0.639132i | ||||
\(95\) | −1.05903 | − | 1.83430i | −0.108654 | − | 0.188195i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −6.18070 | −0.627555 | −0.313778 | − | 0.949496i | \(-0.601595\pi\) | ||||
−0.313778 | + | 0.949496i | \(0.601595\pi\) | |||||||
\(98\) | 2.38779 | + | 6.58016i | 0.241203 | + | 0.664696i | ||||
\(99\) | 3.35203 | 0.336892 | ||||||||
\(100\) | 0.256906 | − | 0.444974i | 0.0256906 | − | 0.0444974i | ||||
\(101\) | −6.61479 | − | 11.4572i | −0.658196 | − | 1.14003i | −0.981082 | − | 0.193592i | \(-0.937986\pi\) |
0.322886 | − | 0.946438i | \(-0.395347\pi\) | |||||||
\(102\) | −3.47814 | − | 6.02432i | −0.344387 | − | 0.596496i | ||||
\(103\) | 3.72700 | − | 6.45536i | 0.367232 | − | 0.636065i | −0.621899 | − | 0.783097i | \(-0.713639\pi\) |
0.989132 | + | 0.147032i | \(0.0469721\pi\) | |||||||
\(104\) | 4.23612 | 0.415386 | ||||||||
\(105\) | 2.36584 | + | 5.07997i | 0.230883 | + | 0.495754i | ||||
\(106\) | −1.75733 | −0.170687 | ||||||||
\(107\) | −4.30354 | + | 7.45395i | −0.416039 | + | 0.720601i | −0.995537 | − | 0.0943730i | \(-0.969915\pi\) |
0.579498 | + | 0.814974i | \(0.303249\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −3.15373 | − | 5.46242i | −0.302073 | − | 0.523205i | 0.674533 | − | 0.738245i | \(-0.264345\pi\) |
−0.976605 | + | 0.215040i | \(0.931012\pi\) | |||||||
\(110\) | 3.54991 | − | 6.14862i | 0.338470 | − | 0.586248i | ||||
\(111\) | 0.252218 | 0.0239395 | ||||||||
\(112\) | 2.63557 | + | 0.231865i | 0.249038 | + | 0.0219091i | ||||
\(113\) | 1.97453 | 0.185748 | 0.0928741 | − | 0.995678i | \(-0.470395\pi\) | ||||
0.0928741 | + | 0.995678i | \(0.470395\pi\) | |||||||
\(114\) | −0.500000 | + | 0.866025i | −0.0468293 | + | 0.0811107i | ||||
\(115\) | 7.60459 | + | 13.1715i | 0.709132 | + | 1.22825i | ||||
\(116\) | −3.64938 | − | 6.32092i | −0.338837 | − | 0.586882i | ||||
\(117\) | 2.11806 | − | 3.66859i | 0.195815 | − | 0.339161i | ||||
\(118\) | −13.0465 | −1.20103 | ||||||||
\(119\) | −10.5637 | + | 15.0711i | −0.968375 | + | 1.38156i | ||||
\(120\) | 2.11806 | 0.193352 | ||||||||
\(121\) | −0.118062 | + | 0.204490i | −0.0107329 | + | 0.0185900i | ||||
\(122\) | 3.45956 | + | 5.99213i | 0.313213 | + | 0.542502i | ||||
\(123\) | −5.16797 | − | 8.95119i | −0.465980 | − | 0.807101i | ||||
\(124\) | −2.27442 | + | 3.93940i | −0.204249 | + | 0.353769i | ||||
\(125\) | −11.6786 | −1.04457 | ||||||||
\(126\) | 1.51859 | − | 2.16654i | 0.135286 | − | 0.193011i | ||||
\(127\) | 12.2296 | 1.08520 | 0.542600 | − | 0.839991i | \(-0.317440\pi\) | ||||
0.542600 | + | 0.839991i | \(0.317440\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.58566 | + | 2.74645i | 0.139610 | + | 0.241812i | ||||
\(130\) | −4.48619 | − | 7.77031i | −0.393465 | − | 0.681501i | ||||
\(131\) | 0.510540 | − | 0.884281i | 0.0446061 | − | 0.0772600i | −0.842860 | − | 0.538132i | \(-0.819130\pi\) |
0.887466 | + | 0.460872i | \(0.152463\pi\) | |||||||
\(132\) | −3.35203 | −0.291757 | ||||||||
\(133\) | 2.63557 | + | 0.231865i | 0.228533 | + | 0.0201052i | ||||
\(134\) | 4.30616 | 0.371996 | ||||||||
\(135\) | 1.05903 | − | 1.83430i | 0.0911469 | − | 0.157871i | ||||
\(136\) | 3.47814 | + | 6.02432i | 0.298248 | + | 0.516581i | ||||
\(137\) | 3.06381 | + | 5.30667i | 0.261759 | + | 0.453379i | 0.966709 | − | 0.255877i | \(-0.0823642\pi\) |
−0.704951 | + | 0.709256i | \(0.749031\pi\) | |||||||
\(138\) | 3.59035 | − | 6.21867i | 0.305631 | − | 0.529369i | ||||
\(139\) | 18.3476 | 1.55623 | 0.778113 | − | 0.628124i | \(-0.216177\pi\) | ||||
0.778113 | + | 0.628124i | \(0.216177\pi\) | |||||||
\(140\) | −2.36584 | − | 5.07997i | −0.199950 | − | 0.429336i | ||||
\(141\) | −7.15524 | −0.602580 | ||||||||
\(142\) | −5.22592 | + | 9.05157i | −0.438550 | + | 0.759591i | ||||
\(143\) | 7.09982 | + | 12.2972i | 0.593716 | + | 1.02835i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −7.72962 | + | 13.3881i | −0.641910 | + | 1.11182i | ||||
\(146\) | 12.7667 | 1.05658 | ||||||||
\(147\) | −6.89248 | − | 1.22219i | −0.568482 | − | 0.100805i | ||||
\(148\) | −0.252218 | −0.0207322 | ||||||||
\(149\) | 10.9551 | − | 18.9748i | 0.897478 | − | 1.55448i | 0.0667713 | − | 0.997768i | \(-0.478730\pi\) |
0.830707 | − | 0.556710i | \(-0.187936\pi\) | |||||||
\(150\) | 0.256906 | + | 0.444974i | 0.0209763 | + | 0.0363320i | ||||
\(151\) | −0.174600 | − | 0.302416i | −0.0142088 | − | 0.0246103i | 0.858834 | − | 0.512255i | \(-0.171190\pi\) |
−0.873042 | + | 0.487644i | \(0.837856\pi\) | |||||||
\(152\) | 0.500000 | − | 0.866025i | 0.0405554 | − | 0.0702439i | ||||
\(153\) | 6.95628 | 0.562382 | ||||||||
\(154\) | 3.74417 | + | 8.03953i | 0.301714 | + | 0.647844i | ||||
\(155\) | 9.63471 | 0.773878 | ||||||||
\(156\) | −2.11806 | + | 3.66859i | −0.169581 | + | 0.293722i | ||||
\(157\) | −6.52435 | − | 11.3005i | −0.520700 | − | 0.901879i | −0.999710 | − | 0.0240695i | \(-0.992338\pi\) |
0.479010 | − | 0.877809i | \(-0.340996\pi\) | |||||||
\(158\) | 1.13557 | + | 1.96687i | 0.0903412 | + | 0.156476i | ||||
\(159\) | 0.878666 | − | 1.52189i | 0.0696827 | − | 0.120694i | ||||
\(160\) | −2.11806 | −0.167448 | ||||||||
\(161\) | −18.9253 | − | 1.66495i | −1.49152 | − | 0.131217i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −7.73070 | + | 13.3900i | −0.605515 | + | 1.04878i | 0.386455 | + | 0.922308i | \(0.373700\pi\) |
−0.991970 | + | 0.126475i | \(0.959634\pi\) | |||||||
\(164\) | 5.16797 | + | 8.95119i | 0.403551 | + | 0.698970i | ||||
\(165\) | 3.54991 | + | 6.14862i | 0.276360 | + | 0.478669i | ||||
\(166\) | 8.28496 | − | 14.3500i | 0.643037 | − | 1.11377i | ||||
\(167\) | −4.68797 | −0.362766 | −0.181383 | − | 0.983413i | \(-0.558057\pi\) | ||||
−0.181383 | + | 0.983413i | \(0.558057\pi\) | |||||||
\(168\) | −1.51859 | + | 2.16654i | −0.117161 | + | 0.167152i | ||||
\(169\) | 4.94475 | 0.380366 | ||||||||
\(170\) | 7.36692 | − | 12.7599i | 0.565017 | − | 0.978638i | ||||
\(171\) | −0.500000 | − | 0.866025i | −0.0382360 | − | 0.0662266i | ||||
\(172\) | −1.58566 | − | 2.74645i | −0.120906 | − | 0.209415i | ||||
\(173\) | 10.7642 | − | 18.6441i | 0.818385 | − | 1.41748i | −0.0884866 | − | 0.996077i | \(-0.528203\pi\) |
0.906872 | − | 0.421407i | \(-0.138464\pi\) | |||||||
\(174\) | 7.29877 | 0.553318 | ||||||||
\(175\) | 0.780267 | − | 1.11319i | 0.0589827 | − | 0.0841495i | ||||
\(176\) | 3.35203 | 0.252669 | ||||||||
\(177\) | 6.52327 | − | 11.2986i | 0.490319 | − | 0.849258i | ||||
\(178\) | 1.89683 | + | 3.28540i | 0.142173 | + | 0.246251i | ||||
\(179\) | −0.919111 | − | 1.59195i | −0.0686976 | − | 0.118988i | 0.829631 | − | 0.558313i | \(-0.188551\pi\) |
−0.898328 | + | 0.439325i | \(0.855218\pi\) | |||||||
\(180\) | −1.05903 | + | 1.83430i | −0.0789355 | + | 0.136720i | ||||
\(181\) | 20.3848 | 1.51519 | 0.757596 | − | 0.652724i | \(-0.226374\pi\) | ||||
0.757596 | + | 0.652724i | \(0.226374\pi\) | |||||||
\(182\) | 11.1646 | + | 0.982207i | 0.827576 | + | 0.0728061i | ||||
\(183\) | −6.91911 | −0.511475 | ||||||||
\(184\) | −3.59035 | + | 6.21867i | −0.264684 | + | 0.458447i | ||||
\(185\) | 0.267107 | + | 0.462642i | 0.0196381 | + | 0.0340141i | ||||
\(186\) | −2.27442 | − | 3.93940i | −0.166768 | − | 0.288851i | ||||
\(187\) | −11.6588 | + | 20.1937i | −0.852579 | + | 1.47671i | ||||
\(188\) | 7.15524 | 0.521849 | ||||||||
\(189\) | 1.11699 | + | 2.39840i | 0.0812487 | + | 0.174458i | ||||
\(190\) | −2.11806 | −0.153660 | ||||||||
\(191\) | 2.74895 | − | 4.76131i | 0.198907 | − | 0.344517i | −0.749267 | − | 0.662268i | \(-0.769594\pi\) |
0.948174 | + | 0.317751i | \(0.102928\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −3.94935 | − | 6.84048i | −0.284281 | − | 0.492389i | 0.688154 | − | 0.725565i | \(-0.258421\pi\) |
−0.972435 | + | 0.233176i | \(0.925088\pi\) | |||||||
\(194\) | −3.09035 | + | 5.35265i | −0.221874 | + | 0.384298i | ||||
\(195\) | 8.97238 | 0.642525 | ||||||||
\(196\) | 6.89248 | + | 1.22219i | 0.492320 | + | 0.0872994i | ||||
\(197\) | −1.93736 | −0.138031 | −0.0690155 | − | 0.997616i | \(-0.521986\pi\) | ||||
−0.0690155 | + | 0.997616i | \(0.521986\pi\) | |||||||
\(198\) | 1.67602 | − | 2.90295i | 0.119109 | − | 0.206303i | ||||
\(199\) | −4.36912 | − | 7.56753i | −0.309718 | − | 0.536448i | 0.668582 | − | 0.743638i | \(-0.266901\pi\) |
−0.978301 | + | 0.207190i | \(0.933568\pi\) | |||||||
\(200\) | −0.256906 | − | 0.444974i | −0.0181660 | − | 0.0314644i | ||||
\(201\) | −2.15308 | + | 3.72925i | −0.151867 | + | 0.263041i | ||||
\(202\) | −13.2296 | −0.930830 | ||||||||
\(203\) | −8.15261 | − | 17.5054i | −0.572201 | − | 1.22864i | ||||
\(204\) | −6.95628 | −0.487037 | ||||||||
\(205\) | 10.9461 | − | 18.9592i | 0.764508 | − | 1.32417i | ||||
\(206\) | −3.72700 | − | 6.45536i | −0.259672 | − | 0.449766i | ||||
\(207\) | 3.59035 | + | 6.21867i | 0.249547 | + | 0.432228i | ||||
\(208\) | 2.11806 | − | 3.66859i | 0.146861 | − | 0.254371i | ||||
\(209\) | 3.35203 | 0.231865 | ||||||||
\(210\) | 5.58231 | + | 0.491104i | 0.385216 | + | 0.0338894i | ||||
\(211\) | −23.3870 | −1.61003 | −0.805013 | − | 0.593257i | \(-0.797842\pi\) | ||||
−0.805013 | + | 0.593257i | \(0.797842\pi\) | |||||||
\(212\) | −0.878666 | + | 1.52189i | −0.0603470 | + | 0.104524i | ||||
\(213\) | −5.22592 | − | 9.05157i | −0.358074 | − | 0.620203i | ||||
\(214\) | 4.30354 | + | 7.45395i | 0.294184 | + | 0.509542i | ||||
\(215\) | −3.35854 | + | 5.81715i | −0.229050 | + | 0.396727i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −6.90779 | + | 9.85522i | −0.468932 | + | 0.669016i | ||||
\(218\) | −6.30746 | −0.427195 | ||||||||
\(219\) | −6.38335 | + | 11.0563i | −0.431347 | + | 0.747115i | ||||
\(220\) | −3.54991 | − | 6.14862i | −0.239335 | − | 0.414540i | ||||
\(221\) | 14.7338 | + | 25.5198i | 0.991106 | + | 1.71665i | ||||
\(222\) | 0.126109 | − | 0.218427i | 0.00846388 | − | 0.0146599i | ||||
\(223\) | 9.80320 | 0.656471 | 0.328236 | − | 0.944596i | \(-0.393546\pi\) | ||||
0.328236 | + | 0.944596i | \(0.393546\pi\) | |||||||
\(224\) | 1.51859 | − | 2.16654i | 0.101465 | − | 0.144758i | ||||
\(225\) | −0.513812 | −0.0342541 | ||||||||
\(226\) | 0.987266 | − | 1.70999i | 0.0656719 | − | 0.113747i | ||||
\(227\) | 9.14176 | + | 15.8340i | 0.606760 | + | 1.05094i | 0.991771 | + | 0.128027i | \(0.0408645\pi\) |
−0.385011 | + | 0.922912i | \(0.625802\pi\) | |||||||
\(228\) | 0.500000 | + | 0.866025i | 0.0331133 | + | 0.0573539i | ||||
\(229\) | 0.722313 | − | 1.25108i | 0.0477318 | − | 0.0826739i | −0.841172 | − | 0.540767i | \(-0.818134\pi\) |
0.888904 | + | 0.458093i | \(0.151467\pi\) | |||||||
\(230\) | 15.2092 | 1.00286 | ||||||||
\(231\) | −8.83452 | − | 0.777218i | −0.581269 | − | 0.0511372i | ||||
\(232\) | −7.29877 | −0.479188 | ||||||||
\(233\) | 7.84038 | − | 13.5799i | 0.513640 | − | 0.889651i | −0.486235 | − | 0.873828i | \(-0.661630\pi\) |
0.999875 | − | 0.0158225i | \(-0.00503667\pi\) | |||||||
\(234\) | −2.11806 | − | 3.66859i | −0.138462 | − | 0.239823i | ||||
\(235\) | −7.57762 | − | 13.1248i | −0.494309 | − | 0.856169i | ||||
\(236\) | −6.52327 | + | 11.2986i | −0.424629 | + | 0.735479i | ||||
\(237\) | −2.27114 | −0.147527 | ||||||||
\(238\) | 7.77007 | + | 16.6840i | 0.503659 | + | 1.08146i | ||||
\(239\) | 3.76818 | 0.243744 | 0.121872 | − | 0.992546i | \(-0.461110\pi\) | ||||
0.121872 | + | 0.992546i | \(0.461110\pi\) | |||||||
\(240\) | 1.05903 | − | 1.83430i | 0.0683602 | − | 0.118403i | ||||
\(241\) | −1.49781 | − | 2.59428i | −0.0964821 | − | 0.167112i | 0.813744 | − | 0.581223i | \(-0.197426\pi\) |
−0.910226 | + | 0.414111i | \(0.864092\pi\) | |||||||
\(242\) | 0.118062 | + | 0.204490i | 0.00758934 | + | 0.0131451i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 6.91911 | 0.442951 | ||||||||
\(245\) | −5.05749 | − | 13.9372i | −0.323111 | − | 0.890414i | ||||
\(246\) | −10.3359 | −0.658995 | ||||||||
\(247\) | 2.11806 | − | 3.66859i | 0.134769 | − | 0.233427i | ||||
\(248\) | 2.27442 | + | 3.93940i | 0.144426 | + | 0.250152i | ||||
\(249\) | 8.28496 | + | 14.3500i | 0.525038 | + | 0.909392i | ||||
\(250\) | −5.83930 | + | 10.1140i | −0.369310 | + | 0.639663i | ||||
\(251\) | 26.2922 | 1.65955 | 0.829775 | − | 0.558098i | \(-0.188469\pi\) | ||||
0.829775 | + | 0.558098i | \(0.188469\pi\) | |||||||
\(252\) | −1.11699 | − | 2.39840i | −0.0703635 | − | 0.151085i | ||||
\(253\) | −24.0700 | −1.51327 | ||||||||
\(254\) | 6.11479 | − | 10.5911i | 0.383676 | − | 0.664547i | ||||
\(255\) | 7.36692 | + | 12.7599i | 0.461335 | + | 0.799055i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 9.86584 | − | 17.0881i | 0.615414 | − | 1.06593i | −0.374897 | − | 0.927066i | \(-0.622322\pi\) |
0.990312 | − | 0.138863i | \(-0.0443447\pi\) | |||||||
\(258\) | 3.17133 | 0.197438 | ||||||||
\(259\) | −0.664738 | − | 0.0584804i | −0.0413048 | − | 0.00363380i | ||||
\(260\) | −8.97238 | −0.556443 | ||||||||
\(261\) | −3.64938 | + | 6.32092i | −0.225891 | + | 0.391255i | ||||
\(262\) | −0.510540 | − | 0.884281i | −0.0315413 | − | 0.0546311i | ||||
\(263\) | 2.22124 | + | 3.84729i | 0.136967 | + | 0.237234i | 0.926347 | − | 0.376671i | \(-0.122931\pi\) |
−0.789380 | + | 0.613905i | \(0.789598\pi\) | |||||||
\(264\) | −1.67602 | + | 2.90295i | −0.103152 | + | 0.178664i | ||||
\(265\) | 3.72214 | 0.228649 | ||||||||
\(266\) | 1.51859 | − | 2.16654i | 0.0931105 | − | 0.132839i | ||||
\(267\) | −3.79365 | −0.232168 | ||||||||
\(268\) | 2.15308 | − | 3.72925i | 0.131520 | − | 0.227800i | ||||
\(269\) | −9.73982 | − | 16.8699i | −0.593847 | − | 1.02857i | −0.993708 | − | 0.111998i | \(-0.964275\pi\) |
0.399861 | − | 0.916576i | \(-0.369058\pi\) | |||||||
\(270\) | −1.05903 | − | 1.83430i | −0.0644506 | − | 0.111632i | ||||
\(271\) | −0.787888 | + | 1.36466i | −0.0478608 | + | 0.0828973i | −0.888963 | − | 0.457978i | \(-0.848574\pi\) |
0.841103 | + | 0.540876i | \(0.181907\pi\) | |||||||
\(272\) | 6.95628 | 0.421787 | ||||||||
\(273\) | −6.43292 | + | 9.17773i | −0.389338 | + | 0.555462i | ||||
\(274\) | 6.12761 | 0.370183 | ||||||||
\(275\) | 0.861157 | − | 1.49157i | 0.0519297 | − | 0.0899449i | ||||
\(276\) | −3.59035 | − | 6.21867i | −0.216114 | − | 0.374320i | ||||
\(277\) | −4.90306 | − | 8.49234i | −0.294596 | − | 0.510256i | 0.680295 | − | 0.732939i | \(-0.261852\pi\) |
−0.974891 | + | 0.222683i | \(0.928518\pi\) | |||||||
\(278\) | 9.17382 | − | 15.8895i | 0.550209 | − | 0.952990i | ||||
\(279\) | 4.54883 | 0.272331 | ||||||||
\(280\) | −5.58231 | − | 0.491104i | −0.333607 | − | 0.0293491i | ||||
\(281\) | −3.60641 | −0.215140 | −0.107570 | − | 0.994198i | \(-0.534307\pi\) | ||||
−0.107570 | + | 0.994198i | \(0.534307\pi\) | |||||||
\(282\) | −3.57762 | + | 6.19662i | −0.213044 | + | 0.369003i | ||||
\(283\) | 10.7664 | + | 18.6479i | 0.639994 | + | 1.10850i | 0.985433 | + | 0.170061i | \(0.0543966\pi\) |
−0.345439 | + | 0.938441i | \(0.612270\pi\) | |||||||
\(284\) | 5.22592 | + | 9.05157i | 0.310102 | + | 0.537112i | ||||
\(285\) | 1.05903 | − | 1.83430i | 0.0627316 | − | 0.108654i | ||||
\(286\) | 14.1996 | 0.839642 | ||||||||
\(287\) | 11.5451 | + | 24.7898i | 0.681485 | + | 1.46329i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −15.6949 | + | 27.1844i | −0.923232 | + | 1.59908i | ||||
\(290\) | 7.72962 | + | 13.3881i | 0.453899 | + | 0.786176i | ||||
\(291\) | −3.09035 | − | 5.35265i | −0.181160 | − | 0.313778i | ||||
\(292\) | 6.38335 | − | 11.0563i | 0.373558 | − | 0.647021i | ||||
\(293\) | −24.2946 | −1.41930 | −0.709651 | − | 0.704553i | \(-0.751148\pi\) | ||||
−0.709651 | + | 0.704553i | \(0.751148\pi\) | |||||||
\(294\) | −4.50469 | + | 5.35796i | −0.262719 | + | 0.312483i | ||||
\(295\) | 27.6334 | 1.60888 | ||||||||
\(296\) | −0.126109 | + | 0.218427i | −0.00732993 | + | 0.0126958i | ||||
\(297\) | 1.67602 | + | 2.90295i | 0.0972523 | + | 0.168446i | ||||
\(298\) | −10.9551 | − | 18.9748i | −0.634613 | − | 1.09918i | ||||
\(299\) | −15.2092 | + | 26.3431i | −0.879570 | + | 1.52346i | ||||
\(300\) | 0.513812 | 0.0296649 | ||||||||
\(301\) | −3.54233 | − | 7.60613i | −0.204176 | − | 0.438410i | ||||
\(302\) | −0.349200 | −0.0200942 | ||||||||
\(303\) | 6.61479 | − | 11.4572i | 0.380010 | − | 0.658196i | ||||
\(304\) | −0.500000 | − | 0.866025i | −0.0286770 | − | 0.0496700i | ||||
\(305\) | −7.32755 | − | 12.6917i | −0.419575 | − | 0.726724i | ||||
\(306\) | 3.47814 | − | 6.02432i | 0.198832 | − | 0.344387i | ||||
\(307\) | 5.79365 | 0.330661 | 0.165331 | − | 0.986238i | \(-0.447131\pi\) | ||||
0.165331 | + | 0.986238i | \(0.447131\pi\) | |||||||
\(308\) | 8.83452 | + | 0.777218i | 0.503394 | + | 0.0442861i | ||||
\(309\) | 7.45400 | 0.424043 | ||||||||
\(310\) | 4.81735 | − | 8.34390i | 0.273607 | − | 0.473902i | ||||
\(311\) | −9.33930 | − | 16.1761i | −0.529583 | − | 0.917265i | −0.999405 | − | 0.0345033i | \(-0.989015\pi\) |
0.469822 | − | 0.882761i | \(-0.344318\pi\) | |||||||
\(312\) | 2.11806 | + | 3.66859i | 0.119912 | + | 0.207693i | ||||
\(313\) | −12.8684 | + | 22.2888i | −0.727366 | + | 1.25984i | 0.230626 | + | 0.973042i | \(0.425923\pi\) |
−0.957993 | + | 0.286793i | \(0.907411\pi\) | |||||||
\(314\) | −13.0487 | −0.736381 | ||||||||
\(315\) | −3.21646 | + | 4.58887i | −0.181227 | + | 0.258553i | ||||
\(316\) | 2.27114 | 0.127762 | ||||||||
\(317\) | 10.3764 | − | 17.9724i | 0.582796 | − | 1.00943i | −0.412350 | − | 0.911025i | \(-0.635292\pi\) |
0.995146 | − | 0.0984067i | \(-0.0313746\pi\) | |||||||
\(318\) | −0.878666 | − | 1.52189i | −0.0492731 | − | 0.0853436i | ||||
\(319\) | −12.2329 | − | 21.1879i | −0.684908 | − | 1.18630i | ||||
\(320\) | −1.05903 | + | 1.83430i | −0.0592016 | + | 0.102540i | ||||
\(321\) | −8.60708 | −0.480401 | ||||||||
\(322\) | −10.9045 | + | 15.5573i | −0.607685 | + | 0.866973i | ||||
\(323\) | 6.95628 | 0.387058 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −1.08828 | − | 1.88496i | −0.0603672 | − | 0.104559i | ||||
\(326\) | 7.73070 | + | 13.3900i | 0.428164 | + | 0.741601i | ||||
\(327\) | 3.15373 | − | 5.46242i | 0.174402 | − | 0.302073i | ||||
\(328\) | 10.3359 | 0.570707 | ||||||||
\(329\) | 18.8581 | + | 1.65905i | 1.03968 | + | 0.0914662i | ||||
\(330\) | 7.09982 | 0.390832 | ||||||||
\(331\) | 17.5018 | − | 30.3139i | 0.961983 | − | 1.66620i | 0.244474 | − | 0.969656i | \(-0.421385\pi\) |
0.717510 | − | 0.696548i | \(-0.245282\pi\) | |||||||
\(332\) | −8.28496 | − | 14.3500i | −0.454696 | − | 0.787557i | ||||
\(333\) | 0.126109 | + | 0.218427i | 0.00691073 | + | 0.0119697i | ||||
\(334\) | −2.34399 | + | 4.05990i | −0.128257 | + | 0.222148i | ||||
\(335\) | −9.12072 | −0.498318 | ||||||||
\(336\) | 1.11699 | + | 2.39840i | 0.0609365 | + | 0.130844i | ||||
\(337\) | −9.06565 | −0.493837 | −0.246919 | − | 0.969036i | \(-0.579418\pi\) | ||||
−0.246919 | + | 0.969036i | \(0.579418\pi\) | |||||||
\(338\) | 2.47238 | − | 4.28228i | 0.134480 | − | 0.232925i | ||||
\(339\) | 0.987266 | + | 1.70999i | 0.0536209 | + | 0.0928741i | ||||
\(340\) | −7.36692 | − | 12.7599i | −0.399527 | − | 0.692002i | ||||
\(341\) | −7.62391 | + | 13.2050i | −0.412858 | + | 0.715091i | ||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 17.8822 | + | 4.81930i | 0.965550 | + | 0.260218i | ||||
\(344\) | −3.17133 | −0.170987 | ||||||||
\(345\) | −7.60459 | + | 13.1715i | −0.409417 | + | 0.709132i | ||||
\(346\) | −10.7642 | − | 18.6441i | −0.578686 | − | 1.00231i | ||||
\(347\) | 8.82798 | + | 15.2905i | 0.473911 | + | 0.820838i | 0.999554 | − | 0.0298676i | \(-0.00950857\pi\) |
−0.525643 | + | 0.850705i | \(0.676175\pi\) | |||||||
\(348\) | 3.64938 | − | 6.32092i | 0.195627 | − | 0.338837i | ||||
\(349\) | 19.9745 | 1.06921 | 0.534606 | − | 0.845101i | \(-0.320460\pi\) | ||||
0.534606 | + | 0.845101i | \(0.320460\pi\) | |||||||
\(350\) | −0.573920 | − | 1.23233i | −0.0306773 | − | 0.0658707i | ||||
\(351\) | 4.23612 | 0.226108 | ||||||||
\(352\) | 1.67602 | − | 2.90295i | 0.0893320 | − | 0.154728i | ||||
\(353\) | −11.2514 | − | 19.4880i | −0.598851 | − | 1.03724i | −0.992991 | − | 0.118190i | \(-0.962291\pi\) |
0.394140 | − | 0.919051i | \(-0.371043\pi\) | |||||||
\(354\) | −6.52327 | − | 11.2986i | −0.346708 | − | 0.600516i | ||||
\(355\) | 11.0688 | − | 19.1718i | 0.587473 | − | 1.01753i | ||||
\(356\) | 3.79365 | 0.201063 | ||||||||
\(357\) | −18.3338 | − | 1.61292i | −0.970327 | − | 0.0853646i | ||||
\(358\) | −1.83822 | −0.0971530 | ||||||||
\(359\) | 4.91795 | − | 8.51813i | 0.259559 | − | 0.449570i | −0.706565 | − | 0.707649i | \(-0.749756\pi\) |
0.966124 | + | 0.258079i | \(0.0830894\pi\) | |||||||
\(360\) | 1.05903 | + | 1.83430i | 0.0558158 | + | 0.0966759i | ||||
\(361\) | −0.500000 | − | 0.866025i | −0.0263158 | − | 0.0455803i | ||||
\(362\) | 10.1924 | − | 17.6538i | 0.535701 | − | 0.927862i | ||||
\(363\) | −0.236125 | −0.0123933 | ||||||||
\(364\) | 6.43292 | − | 9.17773i | 0.337177 | − | 0.481044i | ||||
\(365\) | −27.0407 | −1.41537 | ||||||||
\(366\) | −3.45956 | + | 5.99213i | −0.180834 | + | 0.313213i | ||||
\(367\) | −17.6673 | − | 30.6006i | −0.922224 | − | 1.59734i | −0.795965 | − | 0.605342i | \(-0.793036\pi\) |
−0.126259 | − | 0.991997i | \(-0.540297\pi\) | |||||||
\(368\) | 3.59035 | + | 6.21867i | 0.187160 | + | 0.324171i | ||||
\(369\) | 5.16797 | − | 8.95119i | 0.269034 | − | 0.465980i | ||||
\(370\) | 0.534213 | 0.0277724 | ||||||||
\(371\) | −2.66866 | + | 3.80733i | −0.138550 | + | 0.197667i | ||||
\(372\) | −4.54883 | −0.235846 | ||||||||
\(373\) | −16.9147 | + | 29.2972i | −0.875811 | + | 1.51695i | −0.0199149 | + | 0.999802i | \(0.506340\pi\) |
−0.855896 | + | 0.517148i | \(0.826994\pi\) | |||||||
\(374\) | 11.6588 | + | 20.1937i | 0.602865 | + | 1.04419i | ||||
\(375\) | −5.83930 | − | 10.1140i | −0.301540 | − | 0.522283i | ||||
\(376\) | 3.57762 | − | 6.19662i | 0.184502 | − | 0.319566i | ||||
\(377\) | −30.9185 | −1.59238 | ||||||||
\(378\) | 2.63557 | + | 0.231865i | 0.135559 | + | 0.0119258i | ||||
\(379\) | 25.4999 | 1.30984 | 0.654920 | − | 0.755698i | \(-0.272702\pi\) | ||||
0.654920 | + | 0.755698i | \(0.272702\pi\) | |||||||
\(380\) | −1.05903 | + | 1.83430i | −0.0543272 | + | 0.0940974i | ||||
\(381\) | 6.11479 | + | 10.5911i | 0.313270 | + | 0.542600i | ||||
\(382\) | −2.74895 | − | 4.76131i | −0.140648 | − | 0.243610i | ||||
\(383\) | −17.8593 | + | 30.9332i | −0.912568 | + | 1.58061i | −0.102144 | + | 0.994770i | \(0.532570\pi\) |
−0.810424 | + | 0.585844i | \(0.800763\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −7.93039 | − | 17.0282i | −0.404170 | − | 0.867839i | ||||
\(386\) | −7.89871 | −0.402034 | ||||||||
\(387\) | −1.58566 | + | 2.74645i | −0.0806038 | + | 0.139610i | ||||
\(388\) | 3.09035 | + | 5.35265i | 0.156889 | + | 0.271739i | ||||
\(389\) | −11.0124 | − | 19.0740i | −0.558350 | − | 0.967091i | −0.997634 | − | 0.0687425i | \(-0.978101\pi\) |
0.439284 | − | 0.898348i | \(-0.355232\pi\) | |||||||
\(390\) | 4.48619 | − | 7.77031i | 0.227167 | − | 0.393465i | ||||
\(391\) | −49.9510 | −2.52613 | ||||||||
\(392\) | 4.50469 | − | 5.35796i | 0.227521 | − | 0.270618i | ||||
\(393\) | 1.02108 | 0.0515067 | ||||||||
\(394\) | −0.968679 | + | 1.67780i | −0.0488013 | + | 0.0845264i | ||||
\(395\) | −2.40521 | − | 4.16595i | −0.121019 | − | 0.209612i | ||||
\(396\) | −1.67602 | − | 2.90295i | −0.0842230 | − | 0.145879i | ||||
\(397\) | −9.86584 | + | 17.0881i | −0.495153 | + | 0.857629i | −0.999984 | − | 0.00558835i | \(-0.998221\pi\) |
0.504832 | + | 0.863218i | \(0.331554\pi\) | |||||||
\(398\) | −8.73823 | −0.438008 | ||||||||
\(399\) | 1.11699 | + | 2.39840i | 0.0559192 | + | 0.120070i | ||||
\(400\) | −0.513812 | −0.0256906 | ||||||||
\(401\) | −7.42638 | + | 12.8629i | −0.370856 | + | 0.642341i | −0.989697 | − | 0.143175i | \(-0.954269\pi\) |
0.618842 | + | 0.785516i | \(0.287602\pi\) | |||||||
\(402\) | 2.15308 | + | 3.72925i | 0.107386 | + | 0.185998i | ||||
\(403\) | 9.63471 | + | 16.6878i | 0.479939 | + | 0.831279i | ||||
\(404\) | −6.61479 | + | 11.4572i | −0.329098 | + | 0.570015i | ||||
\(405\) | 2.11806 | 0.105247 | ||||||||
\(406\) | −19.2364 | − | 1.69233i | −0.954688 | − | 0.0839887i | ||||
\(407\) | −0.845443 | −0.0419070 | ||||||||
\(408\) | −3.47814 | + | 6.02432i | −0.172194 | + | 0.298248i | ||||
\(409\) | −3.01816 | − | 5.22761i | −0.149238 | − | 0.258489i | 0.781708 | − | 0.623645i | \(-0.214349\pi\) |
−0.930946 | + | 0.365156i | \(0.881016\pi\) | |||||||
\(410\) | −10.9461 | − | 18.9592i | −0.540589 | − | 0.936327i | ||||
\(411\) | −3.06381 | + | 5.30667i | −0.151126 | + | 0.261759i | ||||
\(412\) | −7.45400 | −0.367232 | ||||||||
\(413\) | −19.8123 | + | 28.2659i | −0.974900 | + | 1.39087i | ||||
\(414\) | 7.18070 | 0.352912 | ||||||||
\(415\) | −17.5481 | + | 30.3941i | −0.861400 | + | 1.49199i | ||||
\(416\) | −2.11806 | − | 3.66859i | −0.103847 | − | 0.179868i | ||||
\(417\) | 9.17382 | + | 15.8895i | 0.449244 | + | 0.778113i | ||||
\(418\) | 1.67602 | − | 2.90295i | 0.0819766 | − | 0.141988i | ||||
\(419\) | 14.1370 | 0.690637 | 0.345319 | − | 0.938486i | \(-0.387771\pi\) | ||||
0.345319 | + | 0.938486i | \(0.387771\pi\) | |||||||
\(420\) | 3.21646 | − | 4.58887i | 0.156947 | − | 0.223914i | ||||
\(421\) | −35.7565 | −1.74266 | −0.871331 | − | 0.490695i | \(-0.836743\pi\) | ||||
−0.871331 | + | 0.490695i | \(0.836743\pi\) | |||||||
\(422\) | −11.6935 | + | 20.2537i | −0.569230 | + | 0.985935i | ||||
\(423\) | −3.57762 | − | 6.19662i | −0.173950 | − | 0.301290i | ||||
\(424\) | 0.878666 | + | 1.52189i | 0.0426718 | + | 0.0739097i | ||||
\(425\) | 1.78711 | − | 3.09536i | 0.0866875 | − | 0.150147i | ||||
\(426\) | −10.4518 | −0.506394 | ||||||||
\(427\) | 18.2358 | + | 1.60430i | 0.882493 | + | 0.0776374i | ||||
\(428\) | 8.60708 | 0.416039 | ||||||||
\(429\) | −7.09982 | + | 12.2972i | −0.342782 | + | 0.593716i | ||||
\(430\) | 3.35854 | + | 5.81715i | 0.161963 | + | 0.280528i | ||||
\(431\) | −8.71211 | − | 15.0898i | −0.419648 | − | 0.726851i | 0.576256 | − | 0.817269i | \(-0.304513\pi\) |
−0.995904 | + | 0.0904180i | \(0.971180\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −0.745628 | −0.0358326 | −0.0179163 | − | 0.999839i | \(-0.505703\pi\) | ||||
−0.0179163 | + | 0.999839i | \(0.505703\pi\) | |||||||
\(434\) | 5.08098 | + | 10.9099i | 0.243895 | + | 0.523694i | ||||
\(435\) | −15.4592 | −0.741214 | ||||||||
\(436\) | −3.15373 | + | 5.46242i | −0.151036 | + | 0.261603i | ||||
\(437\) | 3.59035 | + | 6.21867i | 0.171750 | + | 0.297479i | ||||
\(438\) | 6.38335 | + | 11.0563i | 0.305008 | + | 0.528290i | ||||
\(439\) | −5.86443 | + | 10.1575i | −0.279894 | + | 0.484790i | −0.971358 | − | 0.237620i | \(-0.923633\pi\) |
0.691464 | + | 0.722411i | \(0.256966\pi\) | |||||||
\(440\) | −7.09982 | −0.338470 | ||||||||
\(441\) | −2.38779 | − | 6.58016i | −0.113704 | − | 0.313341i | ||||
\(442\) | 29.4677 | 1.40163 | ||||||||
\(443\) | −3.47805 | + | 6.02417i | −0.165247 | + | 0.286217i | −0.936743 | − | 0.350018i | \(-0.886176\pi\) |
0.771496 | + | 0.636234i | \(0.219509\pi\) | |||||||
\(444\) | −0.126109 | − | 0.218427i | −0.00598487 | − | 0.0103661i | ||||
\(445\) | −4.01760 | − | 6.95868i | −0.190452 | − | 0.329873i | ||||
\(446\) | 4.90160 | − | 8.48982i | 0.232098 | − | 0.402005i | ||||
\(447\) | 21.9102 | 1.03632 | ||||||||
\(448\) | −1.11699 | − | 2.39840i | −0.0527726 | − | 0.113314i | ||||
\(449\) | −27.5823 | −1.30169 | −0.650844 | − | 0.759211i | \(-0.725585\pi\) | ||||
−0.650844 | + | 0.759211i | \(0.725585\pi\) | |||||||
\(450\) | −0.256906 | + | 0.444974i | −0.0121107 | + | 0.0209763i | ||||
\(451\) | 17.3232 | + | 30.0047i | 0.815718 | + | 1.41286i | ||||
\(452\) | −0.987266 | − | 1.70999i | −0.0464371 | − | 0.0804314i | ||||
\(453\) | 0.174600 | − | 0.302416i | 0.00820343 | − | 0.0142088i | ||||
\(454\) | 18.2835 | 0.858088 | ||||||||
\(455\) | −23.6473 | − | 2.08038i | −1.10860 | − | 0.0975296i | ||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | −10.3866 | + | 17.9902i | −0.485866 | + | 0.841544i | −0.999868 | − | 0.0162445i | \(-0.994829\pi\) |
0.514002 | + | 0.857789i | \(0.328162\pi\) | |||||||
\(458\) | −0.722313 | − | 1.25108i | −0.0337515 | − | 0.0584593i | ||||
\(459\) | 3.47814 | + | 6.02432i | 0.162346 | + | 0.281191i | ||||
\(460\) | 7.60459 | − | 13.1715i | 0.354566 | − | 0.614126i | ||||
\(461\) | 33.6610 | 1.56775 | 0.783875 | − | 0.620918i | \(-0.213240\pi\) | ||||
0.783875 | + | 0.620918i | \(0.213240\pi\) | |||||||
\(462\) | −5.09035 | + | 7.26231i | −0.236825 | + | 0.337873i | ||||
\(463\) | −18.4933 | −0.859458 | −0.429729 | − | 0.902958i | \(-0.641391\pi\) | ||||
−0.429729 | + | 0.902958i | \(0.641391\pi\) | |||||||
\(464\) | −3.64938 | + | 6.32092i | −0.169418 | + | 0.293441i | ||||
\(465\) | 4.81735 | + | 8.34390i | 0.223399 | + | 0.386939i | ||||
\(466\) | −7.84038 | − | 13.5799i | −0.363198 | − | 0.629078i | ||||
\(467\) | 6.71646 | − | 11.6333i | 0.310801 | − | 0.538323i | −0.667735 | − | 0.744399i | \(-0.732736\pi\) |
0.978536 | + | 0.206076i | \(0.0660695\pi\) | |||||||
\(468\) | −4.23612 | −0.195815 | ||||||||
\(469\) | 6.53928 | − | 9.32947i | 0.301956 | − | 0.430795i | ||||
\(470\) | −15.1552 | −0.699059 | ||||||||
\(471\) | 6.52435 | − | 11.3005i | 0.300626 | − | 0.520700i | ||||
\(472\) | 6.52327 | + | 11.2986i | 0.300258 | + | 0.520062i | ||||
\(473\) | −5.31520 | − | 9.20619i | −0.244393 | − | 0.423301i | ||||
\(474\) | −1.13557 | + | 1.96687i | −0.0521585 | + | 0.0903412i | ||||
\(475\) | −0.513812 | −0.0235753 | ||||||||
\(476\) | 18.3338 | + | 1.61292i | 0.840328 | + | 0.0739279i | ||||
\(477\) | 1.75733 | 0.0804627 | ||||||||
\(478\) | 1.88409 | − | 3.26334i | 0.0861764 | − | 0.149262i | ||||
\(479\) | 2.02947 | + | 3.51514i | 0.0927287 | + | 0.160611i | 0.908658 | − | 0.417540i | \(-0.137108\pi\) |
−0.815930 | + | 0.578151i | \(0.803774\pi\) | |||||||
\(480\) | −1.05903 | − | 1.83430i | −0.0483379 | − | 0.0837238i | ||||
\(481\) | −0.534213 | + | 0.925285i | −0.0243580 | + | 0.0421893i | ||||
\(482\) | −2.99561 | −0.136446 | ||||||||
\(483\) | −8.02074 | − | 17.2222i | −0.364956 | − | 0.783639i | ||||
\(484\) | 0.236125 | 0.0107329 | ||||||||
\(485\) | 6.54556 | − | 11.3372i | 0.297219 | − | 0.514798i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −18.7539 | − | 32.4827i | −0.849820 | − | 1.47193i | −0.881369 | − | 0.472429i | \(-0.843377\pi\) |
0.0315492 | − | 0.999502i | \(-0.489956\pi\) | |||||||
\(488\) | 3.45956 | − | 5.99213i | 0.156607 | − | 0.271251i | ||||
\(489\) | −15.4614 | −0.699189 | ||||||||
\(490\) | −14.5987 | − | 2.58868i | −0.659502 | − | 0.116945i | ||||
\(491\) | −27.2230 | −1.22856 | −0.614279 | − | 0.789089i | \(-0.710553\pi\) | ||||
−0.614279 | + | 0.789089i | \(0.710553\pi\) | |||||||
\(492\) | −5.16797 | + | 8.95119i | −0.232990 | + | 0.403551i | ||||
\(493\) | −25.3861 | − | 43.9701i | −1.14333 | − | 1.98031i | ||||
\(494\) | −2.11806 | − | 3.66859i | −0.0952961 | − | 0.165058i | ||||
\(495\) | −3.54991 | + | 6.14862i | −0.159556 | + | 0.276360i | ||||
\(496\) | 4.54883 | 0.204249 | ||||||||
\(497\) | 11.6746 | + | 25.0678i | 0.523676 | + | 1.12444i | ||||
\(498\) | 16.5699 | 0.742515 | ||||||||
\(499\) | −3.46825 | + | 6.00719i | −0.155260 | + | 0.268919i | −0.933154 | − | 0.359477i | \(-0.882955\pi\) |
0.777893 | + | 0.628396i | \(0.216288\pi\) | |||||||
\(500\) | 5.83930 | + | 10.1140i | 0.261141 | + | 0.452310i | ||||
\(501\) | −2.34399 | − | 4.05990i | −0.104722 | − | 0.181383i | ||||
\(502\) | 13.1461 | − | 22.7697i | 0.586740 | − | 1.01626i | ||||
\(503\) | 24.0509 | 1.07237 | 0.536187 | − | 0.844099i | \(-0.319864\pi\) | ||||
0.536187 | + | 0.844099i | \(0.319864\pi\) | |||||||
\(504\) | −2.63557 | − | 0.231865i | −0.117398 | − | 0.0103281i | ||||
\(505\) | 28.0211 | 1.24692 | ||||||||
\(506\) | −12.0350 | + | 20.8452i | −0.535020 | + | 0.926682i | ||||
\(507\) | 2.47238 | + | 4.28228i | 0.109802 | + | 0.190183i | ||||
\(508\) | −6.11479 | − | 10.5911i | −0.271300 | − | 0.469905i | ||||
\(509\) | −16.1843 | + | 28.0320i | −0.717355 | + | 1.24250i | 0.244689 | + | 0.969602i | \(0.421314\pi\) |
−0.962044 | + | 0.272894i | \(0.912019\pi\) | |||||||
\(510\) | 14.7338 | 0.652426 | ||||||||
\(511\) | 19.3874 | − | 27.6596i | 0.857646 | − | 1.22359i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.500000 | − | 0.866025i | 0.0220755 | − | 0.0382360i | ||||
\(514\) | −9.86584 | − | 17.0881i | −0.435164 | − | 0.753726i | ||||
\(515\) | 7.89402 | + | 13.6728i | 0.347852 | + | 0.602498i | ||||
\(516\) | 1.58566 | − | 2.74645i | 0.0698050 | − | 0.120906i | ||||
\(517\) | 23.9846 | 1.05484 | ||||||||
\(518\) | −0.383015 | + | 0.546440i | −0.0168287 | + | 0.0240092i | ||||
\(519\) | 21.5283 | 0.944990 | ||||||||
\(520\) | −4.48619 | + | 7.77031i | −0.196732 | + | 0.340750i | ||||
\(521\) | −6.25728 | − | 10.8379i | −0.274137 | − | 0.474819i | 0.695780 | − | 0.718255i | \(-0.255059\pi\) |
−0.969917 | + | 0.243436i | \(0.921725\pi\) | |||||||
\(522\) | 3.64938 | + | 6.32092i | 0.159729 | + | 0.276659i | ||||
\(523\) | 7.98288 | − | 13.8267i | 0.349067 | − | 0.604601i | −0.637017 | − | 0.770850i | \(-0.719832\pi\) |
0.986084 | + | 0.166248i | \(0.0531653\pi\) | |||||||
\(524\) | −1.02108 | −0.0446061 | ||||||||
\(525\) | 1.35419 | + | 0.119135i | 0.0591016 | + | 0.00519947i | ||||
\(526\) | 4.44247 | 0.193701 | ||||||||
\(527\) | −15.8215 | + | 27.4036i | −0.689194 | + | 1.19372i | ||||
\(528\) | 1.67602 | + | 2.90295i | 0.0729393 | + | 0.126334i | ||||
\(529\) | −14.2813 | − | 24.7359i | −0.620924 | − | 1.07547i | ||||
\(530\) | 1.86107 | − | 3.22347i | 0.0808397 | − | 0.140018i | ||||
\(531\) | 13.0465 | 0.566172 | ||||||||
\(532\) | −1.11699 | − | 2.39840i | −0.0484275 | − | 0.103984i | ||||
\(533\) | 43.7843 | 1.89651 | ||||||||
\(534\) | −1.89683 | + | 3.28540i | −0.0820837 | + | 0.142173i | ||||
\(535\) | −9.11517 | − | 15.7879i | −0.394083 | − | 0.682572i | ||||
\(536\) | −2.15308 | − | 3.72925i | −0.0929989 | − | 0.161079i | ||||
\(537\) | 0.919111 | − | 1.59195i | 0.0396626 | − | 0.0686976i | ||||
\(538\) | −19.4796 | −0.839827 | ||||||||
\(539\) | 23.1038 | + | 4.09683i | 0.995152 | + | 0.176463i | ||||
\(540\) | −2.11806 | −0.0911469 | ||||||||
\(541\) | 20.1348 | − | 34.8745i | 0.865662 | − | 1.49937i | −0.000725557 | − | 1.00000i | \(-0.500231\pi\) |
0.866388 | − | 0.499372i | \(-0.166436\pi\) | |||||||
\(542\) | 0.787888 | + | 1.36466i | 0.0338427 | + | 0.0586172i | ||||
\(543\) | 10.1924 | + | 17.6538i | 0.437398 | + | 0.757596i | ||||
\(544\) | 3.47814 | − | 6.02432i | 0.149124 | − | 0.258291i | ||||
\(545\) | 13.3596 | 0.572263 | ||||||||
\(546\) | 4.73169 | + | 10.1599i | 0.202498 | + | 0.434805i | ||||
\(547\) | 7.22088 | 0.308743 | 0.154371 | − | 0.988013i | \(-0.450665\pi\) | ||||
0.154371 | + | 0.988013i | \(0.450665\pi\) | |||||||
\(548\) | 3.06381 | − | 5.30667i | 0.130879 | − | 0.226690i | ||||
\(549\) | −3.45956 | − | 5.99213i | −0.147650 | − | 0.255738i | ||||
\(550\) | −0.861157 | − | 1.49157i | −0.0367198 | − | 0.0636006i | ||||
\(551\) | −3.64938 | + | 6.32092i | −0.155469 | + | 0.269280i | ||||
\(552\) | −7.18070 | −0.305631 | ||||||||
\(553\) | 5.98576 | + | 0.526598i | 0.254540 | + | 0.0223932i | ||||
\(554\) | −9.80612 | −0.416622 | ||||||||
\(555\) | −0.267107 | + | 0.462642i | −0.0113380 | + | 0.0196381i | ||||
\(556\) | −9.17382 | − | 15.8895i | −0.389057 | − | 0.673866i | ||||
\(557\) | −1.36266 | − | 2.36020i | −0.0577378 | − | 0.100005i | 0.835712 | − | 0.549168i | \(-0.185055\pi\) |
−0.893450 | + | 0.449164i | \(0.851722\pi\) | |||||||
\(558\) | 2.27442 | − | 3.93940i | 0.0962837 | − | 0.166768i | ||||
\(559\) | −13.4341 | −0.568204 | ||||||||
\(560\) | −3.21646 | + | 4.58887i | −0.135920 | + | 0.193915i | ||||
\(561\) | −23.3177 | −0.984474 | ||||||||
\(562\) | −1.80320 | + | 3.12324i | −0.0760635 | + | 0.131746i | ||||
\(563\) | −9.17340 | − | 15.8888i | −0.386613 | − | 0.669633i | 0.605379 | − | 0.795937i | \(-0.293022\pi\) |
−0.991991 | + | 0.126305i | \(0.959688\pi\) | |||||||
\(564\) | 3.57762 | + | 6.19662i | 0.150645 | + | 0.260925i | ||||
\(565\) | −2.09109 | + | 3.62187i | −0.0879728 | + | 0.152373i | ||||
\(566\) | 21.5327 | 0.905088 | ||||||||
\(567\) | −1.51859 | + | 2.16654i | −0.0637746 | + | 0.0909861i | ||||
\(568\) | 10.4518 | 0.438550 | ||||||||
\(569\) | −18.1465 | + | 31.4307i | −0.760742 | + | 1.31764i | 0.181726 | + | 0.983349i | \(0.441832\pi\) |
−0.942468 | + | 0.334295i | \(0.891502\pi\) | |||||||
\(570\) | −1.05903 | − | 1.83430i | −0.0443579 | − | 0.0768302i | ||||
\(571\) | −22.9055 | − | 39.6735i | −0.958566 | − | 1.66028i | −0.725989 | − | 0.687707i | \(-0.758617\pi\) |
−0.232577 | − | 0.972578i | \(-0.574716\pi\) | |||||||
\(572\) | 7.09982 | − | 12.2972i | 0.296858 | − | 0.514173i | ||||
\(573\) | 5.49789 | 0.229678 | ||||||||
\(574\) | 27.2411 | + | 2.39654i | 1.13702 | + | 0.100030i | ||||
\(575\) | 3.68953 | 0.153864 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 7.94463 | + | 13.7605i | 0.330739 | + | 0.572857i | 0.982657 | − | 0.185433i | \(-0.0593686\pi\) |
−0.651918 | + | 0.758290i | \(0.726035\pi\) | |||||||
\(578\) | 15.6949 | + | 27.1844i | 0.652824 | + | 1.13072i | ||||
\(579\) | 3.94935 | − | 6.84048i | 0.164130 | − | 0.284281i | ||||
\(580\) | 15.4592 | 0.641910 | ||||||||
\(581\) | −18.5083 | − | 39.7413i | −0.767856 | − | 1.64875i | ||||
\(582\) | −6.18070 | −0.256198 | ||||||||
\(583\) | −2.94532 | + | 5.10144i | −0.121983 | + | 0.211280i | ||||
\(584\) | −6.38335 | − | 11.0563i | −0.264145 | − | 0.457513i | ||||
\(585\) | 4.48619 | + | 7.77031i | 0.185481 | + | 0.321263i | ||||
\(586\) | −12.1473 | + | 21.0397i | −0.501799 | + | 0.869142i | ||||
\(587\) | −4.19680 | −0.173220 | −0.0866102 | − | 0.996242i | \(-0.527603\pi\) | ||||
−0.0866102 | + | 0.996242i | \(0.527603\pi\) | |||||||
\(588\) | 2.38779 | + | 6.58016i | 0.0984708 | + | 0.271361i | ||||
\(589\) | 4.54883 | 0.187431 | ||||||||
\(590\) | 13.8167 | − | 23.9312i | 0.568825 | − | 0.985233i | ||||
\(591\) | −0.968679 | − | 1.67780i | −0.0398461 | − | 0.0690155i | ||||
\(592\) | 0.126109 | + | 0.218427i | 0.00518305 | + | 0.00897730i | ||||
\(593\) | 12.3647 | − | 21.4163i | 0.507758 | − | 0.879464i | −0.492201 | − | 0.870481i | \(-0.663808\pi\) |
0.999960 | − | 0.00898203i | \(-0.00285911\pi\) | |||||||
\(594\) | 3.35203 | 0.137536 | ||||||||
\(595\) | −16.4575 | − | 35.3377i | −0.674691 | − | 1.44871i | ||||
\(596\) | −21.9102 | −0.897478 | ||||||||
\(597\) | 4.36912 | − | 7.56753i | 0.178816 | − | 0.309718i | ||||
\(598\) | 15.2092 | + | 26.3431i | 0.621950 | + | 1.07725i | ||||
\(599\) | 2.26964 | + | 3.93113i | 0.0927350 | + | 0.160622i | 0.908661 | − | 0.417535i | \(-0.137106\pi\) |
−0.815926 | + | 0.578156i | \(0.803772\pi\) | |||||||
\(600\) | 0.256906 | − | 0.444974i | 0.0104881 | − | 0.0181660i | ||||
\(601\) | 9.37441 | 0.382390 | 0.191195 | − | 0.981552i | \(-0.438764\pi\) | ||||
0.191195 | + | 0.981552i | \(0.438764\pi\) | |||||||
\(602\) | −8.35826 | − | 0.735319i | −0.340657 | − | 0.0299694i | ||||
\(603\) | −4.30616 | −0.175360 | ||||||||
\(604\) | −0.174600 | + | 0.302416i | −0.00710438 | + | 0.0123051i | ||||
\(605\) | −0.250064 | − | 0.433123i | −0.0101665 | − | 0.0176089i | ||||
\(606\) | −6.61479 | − | 11.4572i | −0.268708 | − | 0.465415i | ||||
\(607\) | −10.3804 | + | 17.9794i | −0.421327 | + | 0.729760i | −0.996070 | − | 0.0885743i | \(-0.971769\pi\) |
0.574742 | + | 0.818334i | \(0.305102\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 11.0838 | − | 15.8131i | 0.449139 | − | 0.640778i | ||||
\(610\) | −14.6551 | −0.593368 | ||||||||
\(611\) | 15.1552 | − | 26.2496i | 0.613115 | − | 1.06195i | ||||
\(612\) | −3.47814 | − | 6.02432i | −0.140596 | − | 0.243519i | ||||
\(613\) | −1.62869 | − | 2.82097i | −0.0657822 | − | 0.113938i | 0.831259 | − | 0.555886i | \(-0.187621\pi\) |
−0.897041 | + | 0.441948i | \(0.854288\pi\) | |||||||
\(614\) | 2.89683 | − | 5.01745i | 0.116906 | − | 0.202488i | ||||
\(615\) | 21.8922 | 0.882777 | ||||||||
\(616\) | 5.09035 | − | 7.26231i | 0.205096 | − | 0.292607i | ||||
\(617\) | −9.82446 | −0.395518 | −0.197759 | − | 0.980251i | \(-0.563366\pi\) | ||||
−0.197759 | + | 0.980251i | \(0.563366\pi\) | |||||||
\(618\) | 3.72700 | − | 6.45536i | 0.149922 | − | 0.259672i | ||||
\(619\) | 6.88508 | + | 11.9253i | 0.276735 | + | 0.479319i | 0.970571 | − | 0.240814i | \(-0.0774143\pi\) |
−0.693837 | + | 0.720133i | \(0.744081\pi\) | |||||||
\(620\) | −4.81735 | − | 8.34390i | −0.193470 | − | 0.335099i | ||||
\(621\) | −3.59035 | + | 6.21867i | −0.144076 | + | 0.249547i | ||||
\(622\) | −18.6786 | −0.748944 | ||||||||
\(623\) | 9.99844 | + | 0.879614i | 0.400579 | + | 0.0352410i | ||||
\(624\) | 4.23612 | 0.169581 | ||||||||
\(625\) | 11.0835 | − | 19.1971i | 0.443339 | − | 0.767885i | ||||
\(626\) | 12.8684 | + | 22.2888i | 0.514326 | + | 0.890838i | ||||
\(627\) | 1.67602 | + | 2.90295i | 0.0669337 | + | 0.115932i | ||||
\(628\) | −6.52435 | + | 11.3005i | −0.260350 | + | 0.450939i | ||||
\(629\) | −1.75450 | −0.0699565 | ||||||||
\(630\) | 2.36584 | + | 5.07997i | 0.0942575 | + | 0.202391i | ||||
\(631\) | 45.3832 | 1.80668 | 0.903338 | − | 0.428930i | \(-0.141109\pi\) | ||||
0.903338 | + | 0.428930i | \(0.141109\pi\) | |||||||
\(632\) | 1.13557 | − | 1.96687i | 0.0451706 | − | 0.0782378i | ||||
\(633\) | −11.6935 | − | 20.2537i | −0.464774 | − | 0.805013i | ||||
\(634\) | −10.3764 | − | 17.9724i | −0.412099 | − | 0.713776i | ||||
\(635\) | −12.9515 | + | 22.4327i | −0.513965 | + | 0.890213i | ||||
\(636\) | −1.75733 | −0.0696827 | ||||||||
\(637\) | 19.0824 | − | 22.6970i | 0.756073 | − | 0.899288i | ||||
\(638\) | −24.4657 | −0.968607 | ||||||||
\(639\) | 5.22592 | − | 9.05157i | 0.206734 | − | 0.358074i | ||||
\(640\) | 1.05903 | + | 1.83430i | 0.0418619 | + | 0.0725069i | ||||
\(641\) | 10.5389 | + | 18.2540i | 0.416263 | + | 0.720988i | 0.995560 | − | 0.0941282i | \(-0.0300064\pi\) |
−0.579297 | + | 0.815116i | \(0.696673\pi\) | |||||||
\(642\) | −4.30354 | + | 7.45395i | −0.169847 | + | 0.294184i | ||||
\(643\) | 28.6923 | 1.13151 | 0.565757 | − | 0.824572i | \(-0.308584\pi\) | ||||
0.565757 | + | 0.824572i | \(0.308584\pi\) | |||||||
\(644\) | 8.02074 | + | 17.2222i | 0.316061 | + | 0.678651i | ||||
\(645\) | −6.71707 | −0.264484 | ||||||||
\(646\) | 3.47814 | − | 6.02432i | 0.136846 | − | 0.237024i | ||||
\(647\) | −0.425741 | − | 0.737405i | −0.0167376 | − | 0.0289904i | 0.857535 | − | 0.514425i | \(-0.171995\pi\) |
−0.874273 | + | 0.485435i | \(0.838661\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −21.8662 | + | 37.8734i | −0.858325 | + | 1.48666i | ||||
\(650\) | −2.17657 | −0.0853721 | ||||||||
\(651\) | −11.9888 | − | 1.05471i | −0.469877 | − | 0.0413375i | ||||
\(652\) | 15.4614 | 0.605515 | ||||||||
\(653\) | 0.507356 | − | 0.878766i | 0.0198544 | − | 0.0343888i | −0.855928 | − | 0.517096i | \(-0.827013\pi\) |
0.875782 | + | 0.482707i | \(0.160346\pi\) | |||||||
\(654\) | −3.15373 | − | 5.46242i | −0.123321 | − | 0.213598i | ||||
\(655\) | 1.08136 | + | 1.87296i | 0.0422521 | + | 0.0731827i | ||||
\(656\) | 5.16797 | − | 8.95119i | 0.201775 | − | 0.349485i | ||||
\(657\) | −12.7667 | −0.498077 | ||||||||
\(658\) | 10.8658 | − | 15.5021i | 0.423595 | − | 0.604335i | ||||
\(659\) | 10.9687 | 0.427279 | 0.213639 | − | 0.976913i | \(-0.431468\pi\) | ||||
0.213639 | + | 0.976913i | \(0.431468\pi\) | |||||||
\(660\) | 3.54991 | − | 6.14862i | 0.138180 | − | 0.239335i | ||||
\(661\) | 10.1333 | + | 17.5514i | 0.394141 | + | 0.682672i | 0.992991 | − | 0.118189i | \(-0.0377089\pi\) |
−0.598850 | + | 0.800861i | \(0.704376\pi\) | |||||||
\(662\) | −17.5018 | − | 30.3139i | −0.680225 | − | 1.17818i | ||||
\(663\) | −14.7338 | + | 25.5198i | −0.572215 | + | 0.991106i | ||||
\(664\) | −16.5699 | −0.643037 | ||||||||
\(665\) | −3.21646 | + | 4.58887i | −0.124729 | + | 0.177949i | ||||
\(666\) | 0.252218 | 0.00977325 | ||||||||
\(667\) | 26.2051 | − | 45.3886i | 1.01467 | − | 1.75746i | ||||
\(668\) | 2.34399 | + | 4.05990i | 0.0906916 | + | 0.157082i | ||||
\(669\) | 4.90160 | + | 8.48982i | 0.189507 | + | 0.328236i | ||||
\(670\) | −4.56036 | + | 7.89878i | −0.176182 | + | 0.305156i | ||||
\(671\) | 23.1931 | 0.895359 | ||||||||
\(672\) | 2.63557 | + | 0.231865i | 0.101669 | + | 0.00894437i | ||||
\(673\) | 40.5792 | 1.56421 | 0.782107 | − | 0.623145i | \(-0.214145\pi\) | ||||
0.782107 | + | 0.623145i | \(0.214145\pi\) | |||||||
\(674\) | −4.53282 | + | 7.85108i | −0.174598 | + | 0.302412i | ||||
\(675\) | −0.256906 | − | 0.444974i | −0.00988831 | − | 0.0171271i | ||||
\(676\) | −2.47238 | − | 4.28228i | −0.0950914 | − | 0.164703i | ||||
\(677\) | 4.55641 | − | 7.89193i | 0.175117 | − | 0.303312i | −0.765085 | − | 0.643930i | \(-0.777303\pi\) |
0.940202 | + | 0.340618i | \(0.110636\pi\) | |||||||
\(678\) | 1.97453 | 0.0758314 | ||||||||
\(679\) | 6.90376 | + | 14.8238i | 0.264942 | + | 0.568886i | ||||
\(680\) | −14.7338 | −0.565017 | ||||||||
\(681\) | −9.14176 | + | 15.8340i | −0.350313 | + | 0.606760i | ||||
\(682\) | 7.62391 | + | 13.2050i | 0.291935 | + | 0.505646i | ||||
\(683\) | 2.03979 | + | 3.53303i | 0.0780505 | + | 0.135188i | 0.902409 | − | 0.430881i | \(-0.141797\pi\) |
−0.824358 | + | 0.566068i | \(0.808464\pi\) | |||||||
\(684\) | −0.500000 | + | 0.866025i | −0.0191180 | + | 0.0331133i | ||||
\(685\) | −12.9787 | −0.495889 | ||||||||
\(686\) | 13.1148 | − | 13.0768i | 0.500724 | − | 0.499275i | ||||
\(687\) | 1.44463 | 0.0551159 | ||||||||
\(688\) | −1.58566 | + | 2.74645i | −0.0604529 | + | 0.104707i | ||||
\(689\) | 3.72214 | + | 6.44693i | 0.141802 | + | 0.245609i | ||||
\(690\) | 7.60459 | + | 13.1715i | 0.289502 | + | 0.501432i | ||||
\(691\) | 0.733192 | − | 1.26993i | 0.0278920 | − | 0.0483103i | −0.851742 | − | 0.523961i | \(-0.824454\pi\) |
0.879634 | + | 0.475650i | \(0.157787\pi\) | |||||||
\(692\) | −21.5283 | −0.818385 | ||||||||
\(693\) | −3.74417 | − | 8.03953i | −0.142229 | − | 0.305397i | ||||
\(694\) | 17.6560 | 0.670211 | ||||||||
\(695\) | −19.4307 | + | 33.6550i | −0.737050 | + | 1.27661i | ||||
\(696\) | −3.64938 | − | 6.32092i | −0.138330 | − | 0.239594i | ||||
\(697\) | 35.9499 | + | 62.2670i | 1.36170 | + | 2.35853i | ||||
\(698\) | 9.98727 | − | 17.2985i | 0.378024 | − | 0.654756i | ||||
\(699\) | 15.6808 | 0.593100 | ||||||||
\(700\) | −1.35419 | − | 0.119135i | −0.0511835 | − | 0.00450287i | ||||
\(701\) | 18.9890 | 0.717204 | 0.358602 | − | 0.933491i | \(-0.383254\pi\) | ||||
0.358602 | + | 0.933491i | \(0.383254\pi\) | |||||||
\(702\) | 2.11806 | − | 3.66859i | 0.0799411 | − | 0.138462i | ||||
\(703\) | 0.126109 | + | 0.218427i | 0.00475629 | + | 0.00823814i | ||||
\(704\) | −1.67602 | − | 2.90295i | −0.0631672 | − | 0.109409i | ||||
\(705\) | 7.57762 | − | 13.1248i | 0.285390 | − | 0.494309i | ||||
\(706\) | −22.5028 | −0.846904 | ||||||||
\(707\) | −20.0903 | + | 28.6624i | −0.755572 | + | 1.07796i | ||||
\(708\) | −13.0465 | −0.490319 | ||||||||
\(709\) | 10.3040 | − | 17.8470i | 0.386974 | − | 0.670258i | −0.605067 | − | 0.796174i | \(-0.706854\pi\) |
0.992041 | + | 0.125916i | \(0.0401871\pi\) | |||||||
\(710\) | −11.0688 | − | 19.1718i | −0.415406 | − | 0.719504i | ||||
\(711\) | −1.13557 | − | 1.96687i | −0.0425873 | − | 0.0737633i | ||||
\(712\) | 1.89683 | − | 3.28540i | 0.0710866 | − | 0.123126i | ||||
\(713\) | −32.6638 | −1.22327 | ||||||||
\(714\) | −10.5637 | + | 15.0711i | −0.395337 | + | 0.564020i | ||||
\(715\) | −30.0757 | −1.12477 | ||||||||
\(716\) | −0.919111 | + | 1.59195i | −0.0343488 | + | 0.0594938i | ||||
\(717\) | 1.88409 | + | 3.26334i | 0.0703627 | + | 0.121872i | ||||
\(718\) | −4.91795 | − | 8.51813i | −0.183536 | − | 0.317894i | ||||
\(719\) | −2.51399 | + | 4.35435i | −0.0937559 | + | 0.162390i | −0.909089 | − | 0.416603i | \(-0.863221\pi\) |
0.815333 | + | 0.578993i | \(0.196554\pi\) | |||||||
\(720\) | 2.11806 | 0.0789355 | ||||||||
\(721\) | −19.6456 | − | 1.72832i | −0.731639 | − | 0.0643660i | ||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 1.49781 | − | 2.59428i | 0.0557040 | − | 0.0964821i | ||||
\(724\) | −10.1924 | − | 17.6538i | −0.378798 | − | 0.656097i | ||||
\(725\) | 1.87510 | + | 3.24776i | 0.0696393 | + | 0.120619i | ||||
\(726\) | −0.118062 | + | 0.204490i | −0.00438171 | + | 0.00758934i | ||||
\(727\) | −12.6690 | −0.469866 | −0.234933 | − | 0.972012i | \(-0.575487\pi\) | ||||
−0.234933 | + | 0.972012i | \(0.575487\pi\) | |||||||
\(728\) | −4.73169 | − | 10.1599i | −0.175368 | − | 0.376552i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −13.5203 | + | 23.4179i | −0.500410 | + | 0.866736i | ||||
\(731\) | −11.0303 | − | 19.1051i | −0.407972 | − | 0.706627i | ||||
\(732\) | 3.45956 | + | 5.99213i | 0.127869 | + | 0.221475i | ||||
\(733\) | −1.65416 | + | 2.86509i | −0.0610977 | + | 0.105824i | −0.894956 | − | 0.446154i | \(-0.852793\pi\) |
0.833859 | + | 0.551978i | \(0.186127\pi\) | |||||||
\(734\) | −35.3346 | −1.30422 | ||||||||
\(735\) | 9.54121 | − | 11.3485i | 0.351933 | − | 0.418596i | ||||
\(736\) | 7.18070 | 0.264684 | ||||||||
\(737\) | 7.21720 | − | 12.5006i | 0.265849 | − | 0.460464i | ||||
\(738\) | −5.16797 | − | 8.95119i | −0.190236 | − | 0.329498i | ||||
\(739\) | 10.2448 | + | 17.7446i | 0.376863 | + | 0.652746i | 0.990604 | − | 0.136762i | \(-0.0436695\pi\) |
−0.613741 | + | 0.789507i | \(0.710336\pi\) | |||||||
\(740\) | 0.267107 | − | 0.462642i | 0.00981904 | − | 0.0170071i | ||||
\(741\) | 4.23612 | 0.155618 | ||||||||
\(742\) | 1.96291 | + | 4.21479i | 0.0720608 | + | 0.154730i | ||||
\(743\) | 13.7973 | 0.506172 | 0.253086 | − | 0.967444i | \(-0.418554\pi\) | ||||
0.253086 | + | 0.967444i | \(0.418554\pi\) | |||||||
\(744\) | −2.27442 | + | 3.93940i | −0.0833841 | + | 0.144426i | ||||
\(745\) | 23.2036 | + | 40.1899i | 0.850115 | + | 1.47244i | ||||
\(746\) | 16.9147 | + | 29.2972i | 0.619292 | + | 1.07265i | ||||
\(747\) | −8.28496 | + | 14.3500i | −0.303131 | + | 0.525038i | ||||
\(748\) | 23.3177 | 0.852579 | ||||||||
\(749\) | 22.6846 | + | 1.99568i | 0.828877 | + | 0.0729205i | ||||
\(750\) | −11.6786 | −0.426442 | ||||||||
\(751\) | 4.40672 | − | 7.63266i | 0.160803 | − | 0.278520i | −0.774354 | − | 0.632753i | \(-0.781925\pi\) |
0.935157 | + | 0.354233i | \(0.115258\pi\) | |||||||
\(752\) | −3.57762 | − | 6.19662i | −0.130462 | − | 0.225967i | ||||
\(753\) | 13.1461 | + | 22.7697i | 0.479071 | + | 0.829775i | ||||
\(754\) | −15.4592 | + | 26.7762i | −0.562992 | + | 0.975132i | ||||
\(755\) | 0.739628 | 0.0269178 | ||||||||
\(756\) | 1.51859 | − | 2.16654i | 0.0552305 | − | 0.0787963i | ||||
\(757\) | −16.4445 | −0.597684 | −0.298842 | − | 0.954303i | \(-0.596600\pi\) | ||||
−0.298842 | + | 0.954303i | \(0.596600\pi\) | |||||||
\(758\) | 12.7499 | − | 22.0835i | 0.463099 | − | 0.802110i | ||||
\(759\) | −12.0350 | − | 20.8452i | −0.436842 | − | 0.756633i | ||||
\(760\) | 1.05903 | + | 1.83430i | 0.0384151 | + | 0.0665369i | ||||
\(761\) | 13.8327 | − | 23.9589i | 0.501434 | − | 0.868509i | −0.498565 | − | 0.866852i | \(-0.666139\pi\) |
0.999999 | − | 0.00165644i | \(-0.000527262\pi\) | |||||||
\(762\) | 12.2296 | 0.443031 | ||||||||
\(763\) | −9.57843 | + | 13.6654i | −0.346762 | + | 0.494720i | ||||
\(764\) | −5.49789 | −0.198907 | ||||||||
\(765\) | −7.36692 | + | 12.7599i | −0.266352 | + | 0.461335i | ||||
\(766\) | 17.8593 | + | 30.9332i | 0.645283 | + | 1.11766i | ||||
\(767\) | 27.6334 | + | 47.8625i | 0.997784 | + | 1.72821i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | −6.46278 | −0.233054 | −0.116527 | − | 0.993188i | \(-0.537176\pi\) | ||||
−0.116527 | + | 0.993188i | \(0.537176\pi\) | |||||||
\(770\) | −18.7121 | − | 1.64620i | −0.674336 | − | 0.0593248i | ||||
\(771\) | 19.7317 | 0.710619 | ||||||||
\(772\) | −3.94935 | + | 6.84048i | −0.142140 | + | 0.246194i | ||||
\(773\) | 12.2665 | + | 21.2461i | 0.441194 | + | 0.764170i | 0.997778 | − | 0.0666209i | \(-0.0212218\pi\) |
−0.556585 | + | 0.830791i | \(0.687888\pi\) | |||||||
\(774\) | 1.58566 | + | 2.74645i | 0.0569955 | + | 0.0987191i | ||||
\(775\) | 1.16862 | − | 2.02411i | 0.0419781 | − | 0.0727082i | ||||
\(776\) | 6.18070 | 0.221874 | ||||||||
\(777\) | −0.281724 | − | 0.604921i | −0.0101068 | − | 0.0217014i | ||||
\(778\) | −22.0248 | −0.789626 | ||||||||
\(779\) | 5.16797 | − | 8.95119i | 0.185162 | − | 0.320710i | ||||
\(780\) | −4.48619 | − | 7.77031i | −0.160631 | − | 0.278222i | ||||
\(781\) | 17.5175 | + | 30.3411i | 0.626824 | + | 1.08569i | ||||
\(782\) | −24.9755 | + | 43.2588i | −0.893122 | + | 1.54693i | ||||
\(783\) | −7.29877 | −0.260837 | ||||||||
\(784\) | −2.38779 | − | 6.58016i | −0.0852782 | − | 0.235006i | ||||
\(785\) | 27.6380 | 0.986441 | ||||||||
\(786\) | 0.510540 | − | 0.884281i | 0.0182104 | − | 0.0315413i | ||||
\(787\) | −0.606405 | − | 1.05032i | −0.0216160 | − | 0.0374400i | 0.855015 | − | 0.518603i | \(-0.173548\pi\) |
−0.876631 | + | 0.481163i | \(0.840214\pi\) | |||||||
\(788\) | 0.968679 | + | 1.67780i | 0.0345078 | + | 0.0597692i | ||||
\(789\) | −2.22124 | + | 3.84729i | −0.0790781 | + | 0.136967i | ||||
\(790\) | −4.81042 | −0.171147 | ||||||||
\(791\) | −2.20552 | − | 4.73572i | −0.0784193 | − | 0.168383i | ||||
\(792\) | −3.35203 | −0.119109 | ||||||||
\(793\) | 14.6551 | − | 25.3834i | 0.520418 | − | 0.901391i | ||||
\(794\) | 9.86584 | + | 17.0881i | 0.350126 | + | 0.606436i | ||||
\(795\) | 1.86107 | + | 3.22347i | 0.0660053 | + | 0.114325i | ||||
\(796\) | −4.36912 | + | 7.56753i | −0.154859 | + | 0.268224i | ||||
\(797\) | 3.35867 | 0.118970 | 0.0594851 | − | 0.998229i | \(-0.481054\pi\) | ||||
0.0594851 | + | 0.998229i | \(0.481054\pi\) | |||||||
\(798\) | 2.63557 | + | 0.231865i | 0.0932982 | + | 0.00820792i | ||||
\(799\) | 49.7738 | 1.76087 | ||||||||
\(800\) | −0.256906 | + | 0.444974i | −0.00908299 | + | 0.0157322i | ||||
\(801\) | −1.89683 | − | 3.28540i | −0.0670211 | − | 0.116084i | ||||
\(802\) | 7.42638 | + | 12.8629i | 0.262235 | + | 0.454204i | ||||
\(803\) | 21.3972 | − | 37.0611i | 0.755091 | − | 1.30786i | ||||
\(804\) | 4.30616 | 0.151867 | ||||||||
\(805\) | 23.0965 | − | 32.9513i | 0.814043 | − | 1.16138i | ||||
\(806\) | 19.2694 | 0.678736 | ||||||||
\(807\) | 9.73982 | − | 16.8699i | 0.342858 | − | 0.593847i | ||||
\(808\) | 6.61479 | + | 11.4572i | 0.232708 | + | 0.403061i | ||||
\(809\) | 5.94424 | + | 10.2957i | 0.208988 | + | 0.361978i | 0.951396 | − | 0.307970i | \(-0.0996496\pi\) |
−0.742408 | + | 0.669948i | \(0.766316\pi\) | |||||||
\(810\) | 1.05903 | − | 1.83430i | 0.0372106 | − | 0.0644506i | ||||
\(811\) | −27.5357 | −0.966908 | −0.483454 | − | 0.875370i | \(-0.660618\pi\) | ||||
−0.483454 | + | 0.875370i | \(0.660618\pi\) | |||||||
\(812\) | −11.0838 | + | 15.8131i | −0.388965 | + | 0.554930i | ||||
\(813\) | −1.57578 | −0.0552648 | ||||||||
\(814\) | −0.422721 | + | 0.732175i | −0.0148164 | + | 0.0256627i | ||||
\(815\) | −16.3741 | − | 28.3608i | −0.573560 | − | 0.993435i | ||||
\(816\) | 3.47814 | + | 6.02432i | 0.121759 | + | 0.210893i | ||||
\(817\) | −1.58566 | + | 2.74645i | −0.0554754 | + | 0.0960862i | ||||
\(818\) | −6.03632 | −0.211055 | ||||||||
\(819\) | −11.1646 | − | 0.982207i | −0.390123 | − | 0.0343211i | ||||
\(820\) | −21.8922 | −0.764508 | ||||||||
\(821\) | −19.3370 | + | 33.4927i | −0.674867 | + | 1.16890i | 0.301641 | + | 0.953421i | \(0.402465\pi\) |
−0.976508 | + | 0.215482i | \(0.930868\pi\) | |||||||
\(822\) | 3.06381 | + | 5.30667i | 0.106863 | + | 0.185091i | ||||
\(823\) | −17.5783 | − | 30.4465i | −0.612741 | − | 1.06130i | −0.990776 | − | 0.135507i | \(-0.956734\pi\) |
0.378035 | − | 0.925791i | \(-0.376600\pi\) | |||||||
\(824\) | −3.72700 | + | 6.45536i | −0.129836 | + | 0.224883i | ||||
\(825\) | 1.72231 | 0.0599633 | ||||||||
\(826\) | 14.5728 | + | 31.2909i | 0.507053 | + | 1.08875i | ||||
\(827\) | 0.861710 | 0.0299646 | 0.0149823 | − | 0.999888i | \(-0.495231\pi\) | ||||
0.0149823 | + | 0.999888i | \(0.495231\pi\) | |||||||
\(828\) | 3.59035 | − | 6.21867i | 0.124773 | − | 0.216114i | ||||
\(829\) | −1.92565 | − | 3.33533i | −0.0668807 | − | 0.115841i | 0.830646 | − | 0.556801i | \(-0.187971\pi\) |
−0.897527 | + | 0.440960i | \(0.854638\pi\) | |||||||
\(830\) | 17.5481 | + | 30.3941i | 0.609102 | + | 1.05500i | ||||
\(831\) | 4.90306 | − | 8.49234i | 0.170085 | − | 0.294596i | ||||
\(832\) | −4.23612 | −0.146861 | ||||||||
\(833\) | 47.9460 | + | 8.50191i | 1.66123 | + | 0.294574i | ||||
\(834\) | 18.3476 | 0.635327 | ||||||||
\(835\) | 4.96471 | − | 8.59913i | 0.171811 | − | 0.297585i | ||||
\(836\) | −1.67602 | − | 2.90295i | −0.0579662 | − | 0.100400i | ||||
\(837\) | 2.27442 | + | 3.93940i | 0.0786153 | + | 0.136166i | ||||
\(838\) | 7.06849 | − | 12.2430i | 0.244177 | − | 0.422927i | ||||
\(839\) | −14.4709 | −0.499593 | −0.249796 | − | 0.968298i | \(-0.580364\pi\) | ||||
−0.249796 | + | 0.968298i | \(0.580364\pi\) | |||||||
\(840\) | −2.36584 | − | 5.07997i | −0.0816294 | − | 0.175276i | ||||
\(841\) | 24.2720 | 0.836965 | ||||||||
\(842\) | −17.8782 | + | 30.9660i | −0.616124 | + | 1.06716i | ||||
\(843\) | −1.80320 | − | 3.12324i | −0.0621056 | − | 0.107570i | ||||
\(844\) | 11.6935 | + | 20.2537i | 0.402506 | + | 0.697162i | ||||
\(845\) | −5.23665 | + | 9.07014i | −0.180146 | + | 0.312022i | ||||
\(846\) | −7.15524 | −0.246002 | ||||||||
\(847\) | 0.622324 | + | 0.0547490i | 0.0213833 | + | 0.00188120i | ||||
\(848\) | 1.75733 | 0.0603470 | ||||||||
\(849\) | −10.7664 | + | 18.6479i | −0.369501 | + | 0.639994i | ||||
\(850\) | −1.78711 | − | 3.09536i | −0.0612974 | − | 0.106170i | ||||
\(851\) | −0.905551 | − | 1.56846i | −0.0310419 | − | 0.0537661i | ||||
\(852\) | −5.22592 | + | 9.05157i | −0.179037 | + | 0.310102i | ||||
\(853\) | −22.3323 | −0.764642 | −0.382321 | − | 0.924030i | \(-0.624875\pi\) | ||||
−0.382321 | + | 0.924030i | \(0.624875\pi\) | |||||||
\(854\) | 10.5073 | − | 14.9905i | 0.359551 | − | 0.512965i | ||||
\(855\) | 2.11806 | 0.0724362 | ||||||||
\(856\) | 4.30354 | − | 7.45395i | 0.147092 | − | 0.254771i | ||||
\(857\) | 15.8047 | + | 27.3746i | 0.539879 | + | 0.935099i | 0.998910 | + | 0.0466781i | \(0.0148635\pi\) |
−0.459031 | + | 0.888420i | \(0.651803\pi\) | |||||||
\(858\) | 7.09982 | + | 12.2972i | 0.242384 | + | 0.419821i | ||||
\(859\) | −11.8560 | + | 20.5352i | −0.404521 | + | 0.700651i | −0.994266 | − | 0.106939i | \(-0.965895\pi\) |
0.589745 | + | 0.807590i | \(0.299228\pi\) | |||||||
\(860\) | 6.71707 | 0.229050 | ||||||||
\(861\) | −15.6960 | + | 22.3932i | −0.534919 | + | 0.763159i | ||||
\(862\) | −17.4242 | −0.593471 | ||||||||
\(863\) | 13.9643 | − | 24.1869i | 0.475351 | − | 0.823333i | −0.524250 | − | 0.851564i | \(-0.675654\pi\) |
0.999601 | + | 0.0282317i | \(0.00898762\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 22.7992 | + | 39.4894i | 0.775196 | + | 1.34268i | ||||
\(866\) | −0.372814 | + | 0.645733i | −0.0126687 | + | 0.0219429i | ||||
\(867\) | −31.3899 | −1.06606 | ||||||||
\(868\) | 11.9888 | + | 1.05471i | 0.406925 | + | 0.0357993i | ||||
\(869\) | 7.61295 | 0.258252 | ||||||||
\(870\) | −7.72962 | + | 13.3881i | −0.262059 | + | 0.453899i | ||||
\(871\) | −9.12072 | − | 15.7976i | −0.309044 | − | 0.535280i | ||||
\(872\) | 3.15373 | + | 5.46242i | 0.106799 | + | 0.184981i | ||||
\(873\) | 3.09035 | − | 5.35265i | 0.104593 | − | 0.181160i | ||||
\(874\) | 7.18070 | 0.242891 | ||||||||
\(875\) | 13.0448 | + | 28.0100i | 0.440995 | + | 0.946911i | ||||
\(876\) | 12.7667 | 0.431347 | ||||||||
\(877\) | 6.14418 | − | 10.6420i | 0.207474 | − | 0.359356i | −0.743444 | − | 0.668798i | \(-0.766809\pi\) |
0.950918 | + | 0.309442i | \(0.100142\pi\) | |||||||
\(878\) | 5.86443 | + | 10.1575i | 0.197915 | + | 0.342799i | ||||
\(879\) | −12.1473 | − | 21.0397i | −0.409717 | − | 0.709651i | ||||
\(880\) | −3.54991 | + | 6.14862i | −0.119667 | + | 0.207270i | ||||
\(881\) | −20.8380 | −0.702049 | −0.351024 | − | 0.936366i | \(-0.614167\pi\) | ||||
−0.351024 | + | 0.936366i | \(0.614167\pi\) | |||||||
\(882\) | −6.89248 | − | 1.22219i | −0.232082 | − | 0.0411533i | ||||
\(883\) | −43.9662 | −1.47958 | −0.739790 | − | 0.672838i | \(-0.765075\pi\) | ||||
−0.739790 | + | 0.672838i | \(0.765075\pi\) | |||||||
\(884\) | 14.7338 | − | 25.5198i | 0.495553 | − | 0.858323i | ||||
\(885\) | 13.8167 | + | 23.9312i | 0.464443 | + | 0.804440i | ||||
\(886\) | 3.47805 | + | 6.02417i | 0.116848 | + | 0.202386i | ||||
\(887\) | −0.105707 | + | 0.183090i | −0.00354930 | + | 0.00614757i | −0.867795 | − | 0.496923i | \(-0.834463\pi\) |
0.864245 | + | 0.503071i | \(0.167796\pi\) | |||||||
\(888\) | −0.252218 | −0.00846388 | ||||||||
\(889\) | −13.6603 | − | 29.3315i | −0.458151 | − | 0.983746i | ||||
\(890\) | −8.03519 | −0.269340 | ||||||||
\(891\) | −1.67602 | + | 2.90295i | −0.0561487 | + | 0.0972523i | ||||
\(892\) | −4.90160 | − | 8.48982i | −0.164118 | − | 0.284260i | ||||
\(893\) | −3.57762 | − | 6.19662i | −0.119720 | − | 0.207362i | ||||
\(894\) | 10.9551 | − | 18.9748i | 0.366394 | − | 0.634613i | ||||
\(895\) | 3.89347 | 0.130144 | ||||||||
\(896\) | −2.63557 | − | 0.231865i | −0.0880483 | − | 0.00774605i | ||||
\(897\) | −30.4184 | −1.01564 | ||||||||
\(898\) | −13.7911 | + | 23.8870i | −0.460217 | + | 0.797118i | ||||
\(899\) | −16.6004 | − | 28.7528i | −0.553655 | − | 0.958959i | ||||
\(900\) | 0.256906 | + | 0.444974i | 0.00856353 | + | 0.0148325i | ||||
\(901\) | −6.11225 | + | 10.5867i | −0.203629 | + | 0.352695i | ||||
\(902\) | 34.6464 | 1.15360 | ||||||||
\(903\) | 4.81594 | − | 6.87081i | 0.160264 | − | 0.228646i | ||||
\(904\) | −1.97453 | −0.0656719 | ||||||||
\(905\) | −21.5882 | + | 37.3918i | −0.717615 | + | 1.24295i | ||||
\(906\) | −0.174600 | − | 0.302416i | −0.00580070 | − | 0.0100471i | ||||
\(907\) | −14.9938 | − | 25.9700i | −0.497861 | − | 0.862321i | 0.502136 | − | 0.864789i | \(-0.332548\pi\) |
−0.999997 | + | 0.00246786i | \(0.999214\pi\) | |||||||
\(908\) | 9.14176 | − | 15.8340i | 0.303380 | − | 0.525470i | ||||
\(909\) | 13.2296 | 0.438798 | ||||||||
\(910\) | −13.6253 | + | 19.4390i | −0.451675 | + | 0.644397i | ||||
\(911\) | 36.8337 | 1.22035 | 0.610177 | − | 0.792265i | \(-0.291098\pi\) | ||||
0.610177 | + | 0.792265i | \(0.291098\pi\) | |||||||
\(912\) | 0.500000 | − | 0.866025i | 0.0165567 | − | 0.0286770i | ||||
\(913\) | −27.7714 | − | 48.1015i | −0.919101 | − | 1.59193i | ||||
\(914\) | 10.3866 | + | 17.9902i | 0.343559 | + | 0.595062i | ||||
\(915\) | 7.32755 | − | 12.6917i | 0.242241 | − | 0.419575i | ||||
\(916\) | −1.44463 | −0.0477318 | ||||||||
\(917\) | −2.69113 | − | 0.236752i | −0.0888689 | − | 0.00781825i | ||||
\(918\) | 6.95628 | 0.229592 | ||||||||
\(919\) | −10.3368 | + | 17.9039i | −0.340980 | + | 0.590594i | −0.984615 | − | 0.174738i | \(-0.944092\pi\) |
0.643635 | + | 0.765332i | \(0.277425\pi\) | |||||||
\(920\) | −7.60459 | − | 13.1715i | −0.250716 | − | 0.434253i | ||||
\(921\) | 2.89683 | + | 5.01745i | 0.0954537 | + | 0.165331i | ||||
\(922\) | 16.8305 | − | 29.1513i | 0.554283 | − | 0.960047i | ||||
\(923\) | 44.2753 | 1.45734 | ||||||||
\(924\) | 3.74417 | + | 8.03953i | 0.123174 | + | 0.264481i | ||||
\(925\) | 0.129592 | 0.00426097 | ||||||||
\(926\) | −9.24666 | + | 16.0157i | −0.303864 | + | 0.526308i | ||||
\(927\) | 3.72700 | + | 6.45536i | 0.122411 | + | 0.212022i | ||||
\(928\) | 3.64938 | + | 6.32092i | 0.119797 | + | 0.207494i | ||||
\(929\) | 26.2416 | − | 45.4518i | 0.860960 | − | 1.49123i | −0.0100438 | − | 0.999950i | \(-0.503197\pi\) |
0.871004 | − | 0.491277i | \(-0.163470\pi\) | |||||||
\(930\) | 9.63471 | 0.315934 | ||||||||
\(931\) | −2.38779 | − | 6.58016i | −0.0782566 | − | 0.215656i | ||||
\(932\) | −15.6808 | −0.513640 | ||||||||
\(933\) | 9.33930 | − | 16.1761i | 0.305755 | − | 0.529583i | ||||
\(934\) | −6.71646 | − | 11.6333i | −0.219769 | − | 0.380652i | ||||
\(935\) | −24.6942 | − | 42.7715i | −0.807586 | − | 1.39878i | ||||
\(936\) | −2.11806 | + | 3.66859i | −0.0692310 | + | 0.119912i | ||||
\(937\) | 8.21848 | 0.268486 | 0.134243 | − | 0.990948i | \(-0.457140\pi\) | ||||
0.134243 | + | 0.990948i | \(0.457140\pi\) | |||||||
\(938\) | −4.80992 | − | 10.3279i | −0.157049 | − | 0.337219i | ||||
\(939\) | −25.7369 | −0.839890 | ||||||||
\(940\) | −7.57762 | + | 13.1248i | −0.247155 | + | 0.428084i | ||||
\(941\) | −10.5412 | − | 18.2578i | −0.343632 | − | 0.595189i | 0.641472 | − | 0.767146i | \(-0.278324\pi\) |
−0.985104 | + | 0.171958i | \(0.944991\pi\) | |||||||
\(942\) | −6.52435 | − | 11.3005i | −0.212575 | − | 0.368190i | ||||
\(943\) | −37.1097 | + | 64.2758i | −1.20846 | + | 2.09311i | ||||
\(944\) | 13.0465 | 0.424629 | ||||||||
\(945\) | −5.58231 | − | 0.491104i | −0.181592 | − | 0.0159756i | ||||
\(946\) | −10.6304 | −0.345624 | ||||||||
\(947\) | −27.0863 | + | 46.9148i | −0.880185 | + | 1.52453i | −0.0290503 | + | 0.999578i | \(0.509248\pi\) |
−0.851135 | + | 0.524947i | \(0.824085\pi\) | |||||||
\(948\) | 1.13557 | + | 1.96687i | 0.0368817 | + | 0.0638809i | ||||
\(949\) | −27.0407 | − | 46.8358i | −0.877778 | − | 1.52036i | ||||
\(950\) | −0.256906 | + | 0.444974i | −0.00833512 | + | 0.0144369i | ||||
\(951\) | 20.7528 | 0.672955 | ||||||||
\(952\) | 10.5637 | − | 15.0711i | 0.342372 | − | 0.488456i | ||||
\(953\) | 21.4081 | 0.693477 | 0.346739 | − | 0.937962i | \(-0.387289\pi\) | ||||
0.346739 | + | 0.937962i | \(0.387289\pi\) | |||||||
\(954\) | 0.878666 | − | 1.52189i | 0.0284479 | − | 0.0492731i | ||||
\(955\) | 5.82244 | + | 10.0848i | 0.188410 | + | 0.326335i | ||||
\(956\) | −1.88409 | − | 3.26334i | −0.0609359 | − | 0.105544i | ||||
\(957\) | 12.2329 | − | 21.1879i | 0.395432 | − | 0.684908i | ||||
\(958\) | 4.05893 | 0.131138 | ||||||||
\(959\) | 9.30531 | − | 13.2757i | 0.300484 | − | 0.428695i | ||||
\(960\) | −2.11806 | −0.0683602 | ||||||||
\(961\) | 5.15407 | − | 8.92711i | 0.166260 | − | 0.287971i | ||||
\(962\) | 0.534213 | + | 0.925285i | 0.0172237 | + | 0.0298324i | ||||
\(963\) | −4.30354 | − | 7.45395i | −0.138680 | − | 0.240200i | ||||
\(964\) | −1.49781 | + | 2.59428i | −0.0482411 | + | 0.0835560i | ||||
\(965\) | 16.7300 | 0.538556 | ||||||||
\(966\) | −18.9253 | − | 1.66495i | −0.608910 | − | 0.0535689i | ||||
\(967\) | 41.4314 | 1.33234 | 0.666171 | − | 0.745799i | \(-0.267932\pi\) | ||||
0.666171 | + | 0.745799i | \(0.267932\pi\) | |||||||
\(968\) | 0.118062 | − | 0.204490i | 0.00379467 | − | 0.00657256i | ||||
\(969\) | 3.47814 | + | 6.02432i | 0.111734 | + | 0.193529i | ||||
\(970\) | −6.54556 | − | 11.3372i | −0.210165 | − | 0.364017i | ||||
\(971\) | −8.87315 | + | 15.3688i | −0.284753 | + | 0.493207i | −0.972549 | − | 0.232697i | \(-0.925245\pi\) |
0.687796 | + | 0.725904i | \(0.258578\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −20.4940 | − | 44.0051i | −0.657009 | − | 1.41074i | ||||
\(974\) | −37.5078 | −1.20183 | ||||||||
\(975\) | 1.08828 | − | 1.88496i | 0.0348530 | − | 0.0603672i | ||||
\(976\) | −3.45956 | − | 5.99213i | −0.110738 | − | 0.191803i | ||||
\(977\) | 16.3988 | + | 28.4035i | 0.524643 | + | 0.908708i | 0.999588 | + | 0.0286926i | \(0.00913440\pi\) |
−0.474946 | + | 0.880015i | \(0.657532\pi\) | |||||||
\(978\) | −7.73070 | + | 13.3900i | −0.247200 | + | 0.428164i | ||||
\(979\) | 12.7164 | 0.406419 | ||||||||
\(980\) | −9.54121 | + | 11.3485i | −0.304783 | + | 0.362515i | ||||
\(981\) | 6.30746 | 0.201382 | ||||||||
\(982\) | −13.6115 | + | 23.5758i | −0.434361 | + | 0.752335i | ||||
\(983\) | 10.0285 | + | 17.3698i | 0.319859 | + | 0.554012i | 0.980458 | − | 0.196727i | \(-0.0630312\pi\) |
−0.660600 | + | 0.750738i | \(0.729698\pi\) | |||||||
\(984\) | 5.16797 | + | 8.95119i | 0.164749 | + | 0.285353i | ||||
\(985\) | 2.05172 | − | 3.55369i | 0.0653733 | − | 0.113230i | ||||
\(986\) | −50.7723 | −1.61692 | ||||||||
\(987\) | 7.99229 | + | 17.1611i | 0.254397 | + | 0.546245i | ||||
\(988\) | −4.23612 | −0.134769 | ||||||||
\(989\) | 11.3862 | − | 19.7215i | 0.362060 | − | 0.627106i | ||||
\(990\) | 3.54991 | + | 6.14862i | 0.112823 | + | 0.195416i | ||||
\(991\) | −10.1783 | − | 17.6293i | −0.323324 | − | 0.560013i | 0.657848 | − | 0.753151i | \(-0.271467\pi\) |
−0.981172 | + | 0.193137i | \(0.938134\pi\) | |||||||
\(992\) | 2.27442 | − | 3.93940i | 0.0722128 | − | 0.125076i | ||||
\(993\) | 35.0035 | 1.11080 | ||||||||
\(994\) | 27.5466 | + | 2.42341i | 0.873725 | + | 0.0768660i | ||||
\(995\) | 18.5081 | 0.586747 | ||||||||
\(996\) | 8.28496 | − | 14.3500i | 0.262519 | − | 0.454696i | ||||
\(997\) | −0.131921 | − | 0.228494i | −0.00417798 | − | 0.00723648i | 0.863929 | − | 0.503614i | \(-0.167997\pi\) |
−0.868107 | + | 0.496377i | \(0.834663\pi\) | |||||||
\(998\) | 3.46825 | + | 6.00719i | 0.109786 | + | 0.190154i | ||||
\(999\) | −0.126109 | + | 0.218427i | −0.00398991 | + | 0.00691073i |
(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 | 798.2.j.l.457.2 | ✓ | 8 | |
7.2 | even | 3 | 5586.2.a.bw.1.3 | 4 | |||
7.4 | even | 3 | inner | 798.2.j.l.571.2 | yes | 8 | |
7.5 | odd | 6 | 5586.2.a.bz.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.j.l.457.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
798.2.j.l.571.2 | yes | 8 | 7.4 | even | 3 | inner | |
5586.2.a.bw.1.3 | 4 | 7.2 | even | 3 | |||
5586.2.a.bz.1.2 | 4 | 7.5 | odd | 6 |