Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(211,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 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("630.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(1.71903 + 0.211943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.211 |
Dual form | 630.2.j.i.421.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.71903 | + | 0.211943i | −0.992485 | + | 0.122365i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 1.04307 | + | 1.38276i | 0.425830 | + | 0.564508i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.91016 | − | 0.728674i | 0.970054 | − | 0.242891i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −0.0430651 | − | 0.0745909i | −0.0129846 | − | 0.0224900i | 0.859460 | − | 0.511203i | \(-0.170800\pi\) |
−0.872445 | + | 0.488713i | \(0.837467\pi\) | |||||||
\(12\) | 0.675970 | − | 1.59470i | 0.195136 | − | 0.460350i | ||||
\(13\) | 1.89500 | − | 3.28224i | 0.525580 | − | 0.910331i | −0.473976 | − | 0.880538i | \(-0.657182\pi\) |
0.999556 | − | 0.0297931i | \(-0.00948484\pi\) | |||||||
\(14\) | 0.500000 | − | 0.866025i | 0.133631 | − | 0.231455i | ||||
\(15\) | 0.675970 | − | 1.59470i | 0.174535 | − | 0.411750i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −5.82032 | −1.41164 | −0.705818 | − | 0.708394i | \(-0.749420\pi\) | ||||
−0.705818 | + | 0.708394i | \(0.749420\pi\) | |||||||
\(18\) | −2.08613 | − | 2.15594i | −0.491706 | − | 0.508159i | ||||
\(19\) | −1.64806 | −0.378091 | −0.189046 | − | 0.981968i | \(-0.560539\pi\) | ||||
−0.189046 | + | 0.981968i | \(0.560539\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | −1.04307 | − | 1.38276i | −0.227615 | − | 0.301742i | ||||
\(22\) | −0.0430651 | + | 0.0745909i | −0.00918151 | + | 0.0159028i | ||||
\(23\) | −3.98113 | + | 6.89553i | −0.830124 | + | 1.43782i | 0.0678156 | + | 0.997698i | \(0.478397\pi\) |
−0.897939 | + | 0.440119i | \(0.854936\pi\) | |||||||
\(24\) | −1.71903 | + | 0.211943i | −0.350896 | + | 0.0432626i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −3.79001 | −0.743282 | ||||||||
\(27\) | −4.84823 | + | 1.86940i | −0.933042 | + | 0.359767i | ||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 4.54307 | + | 7.86882i | 0.843626 | + | 1.46120i | 0.886809 | + | 0.462136i | \(0.152917\pi\) |
−0.0431831 | + | 0.999067i | \(0.513750\pi\) | |||||||
\(30\) | −1.71903 | + | 0.211943i | −0.313851 | + | 0.0386953i | ||||
\(31\) | −1.08613 | + | 1.88123i | −0.195075 | + | 0.337879i | −0.946925 | − | 0.321455i | \(-0.895828\pi\) |
0.751850 | + | 0.659334i | \(0.229162\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0.0898394 | + | 0.119097i | 0.0156390 | + | 0.0207321i | ||||
\(34\) | 2.91016 | + | 5.04055i | 0.499088 | + | 0.864447i | ||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −0.824030 | + | 2.88461i | −0.137338 | + | 0.480768i | ||||
\(37\) | −4.43807 | −0.729614 | −0.364807 | − | 0.931083i | \(-0.618865\pi\) | ||||
−0.364807 | + | 0.931083i | \(0.618865\pi\) | |||||||
\(38\) | 0.824030 | + | 1.42726i | 0.133675 | + | 0.231533i | ||||
\(39\) | −2.56193 | + | 6.04392i | −0.410237 | + | 0.967802i | ||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | 1.69113 | − | 2.92912i | 0.264109 | − | 0.457451i | −0.703220 | − | 0.710972i | \(-0.748255\pi\) |
0.967330 | + | 0.253521i | \(0.0815886\pi\) | |||||||
\(42\) | −0.675970 | + | 1.59470i | −0.104304 | + | 0.246067i | ||||
\(43\) | 4.23419 | + | 7.33383i | 0.645708 | + | 1.11840i | 0.984137 | + | 0.177407i | \(0.0567710\pi\) |
−0.338429 | + | 0.940992i | \(0.609896\pi\) | |||||||
\(44\) | 0.0861302 | 0.0129846 | ||||||||
\(45\) | −0.824030 | + | 2.88461i | −0.122839 | + | 0.430012i | ||||
\(46\) | 7.96227 | 1.17397 | ||||||||
\(47\) | −5.17226 | − | 8.95862i | −0.754452 | − | 1.30675i | −0.945646 | − | 0.325197i | \(-0.894570\pi\) |
0.191195 | − | 0.981552i | \(-0.438764\pi\) | |||||||
\(48\) | 1.04307 | + | 1.38276i | 0.150553 | + | 0.199584i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | 10.0053 | − | 1.23357i | 1.40103 | − | 0.172735i | ||||
\(52\) | 1.89500 | + | 3.28224i | 0.262790 | + | 0.455165i | ||||
\(53\) | −12.7826 | −1.75582 | −0.877912 | − | 0.478822i | \(-0.841064\pi\) | ||||
−0.877912 | + | 0.478822i | \(0.841064\pi\) | |||||||
\(54\) | 4.04307 | + | 3.26399i | 0.550191 | + | 0.444173i | ||||
\(55\) | 0.0861302 | 0.0116138 | ||||||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 2.83307 | − | 0.349294i | 0.375250 | − | 0.0462652i | ||||
\(58\) | 4.54307 | − | 7.86882i | 0.596534 | − | 1.03323i | ||||
\(59\) | −6.43436 | + | 11.1446i | −0.837682 | + | 1.45091i | 0.0541453 | + | 0.998533i | \(0.482757\pi\) |
−0.891828 | + | 0.452375i | \(0.850577\pi\) | |||||||
\(60\) | 1.04307 | + | 1.38276i | 0.134659 | + | 0.178513i | ||||
\(61\) | −0.219035 | − | 0.379379i | −0.0280445 | − | 0.0485745i | 0.851663 | − | 0.524091i | \(-0.175595\pi\) |
−0.879707 | + | 0.475516i | \(0.842261\pi\) | |||||||
\(62\) | 2.17226 | 0.275877 | ||||||||
\(63\) | 2.08613 | + | 2.15594i | 0.262828 | + | 0.271622i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.89500 | + | 3.28224i | 0.235046 | + | 0.407112i | ||||
\(66\) | 0.0582214 | − | 0.137352i | 0.00716656 | − | 0.0169068i | ||||
\(67\) | 0.527909 | − | 0.914365i | 0.0644943 | − | 0.111707i | −0.831975 | − | 0.554813i | \(-0.812790\pi\) |
0.896470 | + | 0.443105i | \(0.146123\pi\) | |||||||
\(68\) | 2.91016 | − | 5.04055i | 0.352909 | − | 0.611256i | ||||
\(69\) | 5.38225 | − | 12.6974i | 0.647947 | − | 1.52859i | ||||
\(70\) | 0.500000 | + | 0.866025i | 0.0597614 | + | 0.103510i | ||||
\(71\) | −16.0181 | −1.90100 | −0.950499 | − | 0.310729i | \(-0.899427\pi\) | ||||
−0.950499 | + | 0.310729i | \(0.899427\pi\) | |||||||
\(72\) | 2.91016 | − | 0.728674i | 0.342966 | − | 0.0858750i | ||||
\(73\) | −7.17226 | −0.839450 | −0.419725 | − | 0.907651i | \(-0.637873\pi\) | ||||
−0.419725 | + | 0.907651i | \(0.637873\pi\) | |||||||
\(74\) | 2.21903 | + | 3.84348i | 0.257958 | + | 0.446796i | ||||
\(75\) | 1.04307 | + | 1.38276i | 0.120443 | + | 0.159667i | ||||
\(76\) | 0.824030 | − | 1.42726i | 0.0945228 | − | 0.163718i | ||||
\(77\) | 0.0430651 | − | 0.0745909i | 0.00490772 | − | 0.00850043i | ||||
\(78\) | 6.51516 | − | 0.803265i | 0.737696 | − | 0.0909518i | ||||
\(79\) | 6.52420 | + | 11.3002i | 0.734030 | + | 1.27138i | 0.955148 | + | 0.296130i | \(0.0956961\pi\) |
−0.221118 | + | 0.975247i | \(0.570971\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 7.93807 | − | 4.24111i | 0.882008 | − | 0.471235i | ||||
\(82\) | −3.38225 | −0.373507 | ||||||||
\(83\) | 4.43807 | + | 7.68696i | 0.487141 | + | 0.843754i | 0.999891 | − | 0.0147847i | \(-0.00470630\pi\) |
−0.512749 | + | 0.858538i | \(0.671373\pi\) | |||||||
\(84\) | 1.71903 | − | 0.211943i | 0.187562 | − | 0.0231248i | ||||
\(85\) | 2.91016 | − | 5.04055i | 0.315651 | − | 0.546724i | ||||
\(86\) | 4.23419 | − | 7.33383i | 0.456585 | − | 0.790828i | ||||
\(87\) | −9.47743 | − | 12.5639i | −1.01609 | − | 1.34699i | ||||
\(88\) | −0.0430651 | − | 0.0745909i | −0.00459075 | − | 0.00795142i | ||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 2.91016 | − | 0.728674i | 0.306758 | − | 0.0768089i | ||||
\(91\) | 3.79001 | 0.397301 | ||||||||
\(92\) | −3.98113 | − | 6.89553i | −0.415062 | − | 0.718908i | ||||
\(93\) | 1.46838 | − | 3.46410i | 0.152264 | − | 0.359211i | ||||
\(94\) | −5.17226 | + | 8.95862i | −0.533478 | + | 0.924011i | ||||
\(95\) | 0.824030 | − | 1.42726i | 0.0845437 | − | 0.146434i | ||||
\(96\) | 0.675970 | − | 1.59470i | 0.0689909 | − | 0.162758i | ||||
\(97\) | −3.96838 | − | 6.87344i | −0.402928 | − | 0.697892i | 0.591150 | − | 0.806562i | \(-0.298674\pi\) |
−0.994078 | + | 0.108670i | \(0.965341\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −0.179679 | − | 0.185691i | −0.0180584 | − | 0.0186627i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −0.734191 | − | 1.27166i | −0.0730547 | − | 0.126535i | 0.827184 | − | 0.561931i | \(-0.189941\pi\) |
−0.900239 | + | 0.435397i | \(0.856608\pi\) | |||||||
\(102\) | −6.07097 | − | 8.04809i | −0.601116 | − | 0.796879i | ||||
\(103\) | −3.74323 | + | 6.48347i | −0.368832 | + | 0.638835i | −0.989383 | − | 0.145330i | \(-0.953576\pi\) |
0.620551 | + | 0.784166i | \(0.286909\pi\) | |||||||
\(104\) | 1.89500 | − | 3.28224i | 0.185820 | − | 0.321850i | ||||
\(105\) | 1.71903 | − | 0.211943i | 0.167761 | − | 0.0206835i | ||||
\(106\) | 6.39130 | + | 11.0700i | 0.620777 | + | 1.07522i | ||||
\(107\) | −0.351939 | −0.0340232 | −0.0170116 | − | 0.999855i | \(-0.505415\pi\) | ||||
−0.0170116 | + | 0.999855i | \(0.505415\pi\) | |||||||
\(108\) | 0.805165 | − | 5.13339i | 0.0774770 | − | 0.493961i | ||||
\(109\) | 8.38225 | 0.802874 | 0.401437 | − | 0.915887i | \(-0.368511\pi\) | ||||
0.401437 | + | 0.915887i | \(0.368511\pi\) | |||||||
\(110\) | −0.0430651 | − | 0.0745909i | −0.00410610 | − | 0.00711197i | ||||
\(111\) | 7.62920 | − | 0.940616i | 0.724131 | − | 0.0892794i | ||||
\(112\) | 0.500000 | − | 0.866025i | 0.0472456 | − | 0.0818317i | ||||
\(113\) | 2.76210 | − | 4.78410i | 0.259836 | − | 0.450050i | −0.706361 | − | 0.707851i | \(-0.749665\pi\) |
0.966198 | + | 0.257801i | \(0.0829980\pi\) | |||||||
\(114\) | −1.71903 | − | 2.27887i | −0.161002 | − | 0.213435i | ||||
\(115\) | −3.98113 | − | 6.89553i | −0.371243 | − | 0.643011i | ||||
\(116\) | −9.08613 | −0.843626 | ||||||||
\(117\) | 3.12308 | − | 10.9327i | 0.288729 | − | 1.01073i | ||||
\(118\) | 12.8687 | 1.18466 | ||||||||
\(119\) | −2.91016 | − | 5.04055i | −0.266774 | − | 0.462066i | ||||
\(120\) | 0.675970 | − | 1.59470i | 0.0617073 | − | 0.145575i | ||||
\(121\) | 5.49629 | − | 9.51985i | 0.499663 | − | 0.865441i | ||||
\(122\) | −0.219035 | + | 0.379379i | −0.0198305 | + | 0.0343474i | ||||
\(123\) | −2.28630 | + | 5.39367i | −0.206149 | + | 0.486331i | ||||
\(124\) | −1.08613 | − | 1.88123i | −0.0975374 | − | 0.168940i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.824030 | − | 2.88461i | 0.0734105 | − | 0.256981i | ||||
\(127\) | −5.85063 | −0.519160 | −0.259580 | − | 0.965722i | \(-0.583584\pi\) | ||||
−0.259580 | + | 0.965722i | \(0.583584\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −8.83307 | − | 11.7097i | −0.777709 | − | 1.03098i | ||||
\(130\) | 1.89500 | − | 3.28224i | 0.166203 | − | 0.287872i | ||||
\(131\) | −3.02791 | + | 5.24449i | −0.264550 | + | 0.458213i | −0.967446 | − | 0.253079i | \(-0.918557\pi\) |
0.702896 | + | 0.711293i | \(0.251890\pi\) | |||||||
\(132\) | −0.148061 | + | 0.0182547i | −0.0128870 | + | 0.00158886i | ||||
\(133\) | −0.824030 | − | 1.42726i | −0.0714525 | − | 0.123759i | ||||
\(134\) | −1.05582 | −0.0912087 | ||||||||
\(135\) | 0.805165 | − | 5.13339i | 0.0692976 | − | 0.441812i | ||||
\(136\) | −5.82032 | −0.499088 | ||||||||
\(137\) | 3.98484 | + | 6.90195i | 0.340448 | + | 0.589674i | 0.984516 | − | 0.175295i | \(-0.0560879\pi\) |
−0.644068 | + | 0.764968i | \(0.722755\pi\) | |||||||
\(138\) | −13.6874 | + | 1.68754i | −1.16515 | + | 0.143653i | ||||
\(139\) | 3.50000 | − | 6.06218i | 0.296866 | − | 0.514187i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) |
0.975417 | + | 0.220366i | \(0.0707252\pi\) | |||||||
\(140\) | 0.500000 | − | 0.866025i | 0.0422577 | − | 0.0731925i | ||||
\(141\) | 10.7900 | + | 14.3040i | 0.908683 | + | 1.20461i | ||||
\(142\) | 8.00904 | + | 13.8721i | 0.672104 | + | 1.16412i | ||||
\(143\) | −0.326434 | −0.0272978 | ||||||||
\(144\) | −2.08613 | − | 2.15594i | −0.173844 | − | 0.179661i | ||||
\(145\) | −9.08613 | −0.754562 | ||||||||
\(146\) | 3.58613 | + | 6.21136i | 0.296790 | + | 0.514056i | ||||
\(147\) | 0.675970 | − | 1.59470i | 0.0557530 | − | 0.131529i | ||||
\(148\) | 2.21903 | − | 3.84348i | 0.182404 | − | 0.315932i | ||||
\(149\) | 5.38225 | − | 9.32233i | 0.440931 | − | 0.763715i | −0.556828 | − | 0.830628i | \(-0.687982\pi\) |
0.997759 | + | 0.0669128i | \(0.0213149\pi\) | |||||||
\(150\) | 0.675970 | − | 1.59470i | 0.0551927 | − | 0.130207i | ||||
\(151\) | −2.70388 | − | 4.68325i | −0.220039 | − | 0.381118i | 0.734781 | − | 0.678305i | \(-0.237285\pi\) |
−0.954819 | + | 0.297187i | \(0.903952\pi\) | |||||||
\(152\) | −1.64806 | −0.133675 | ||||||||
\(153\) | −16.9381 | + | 4.24111i | −1.36936 | + | 0.342874i | ||||
\(154\) | −0.0861302 | −0.00694057 | ||||||||
\(155\) | −1.08613 | − | 1.88123i | −0.0872401 | − | 0.151104i | ||||
\(156\) | −3.95323 | − | 5.24066i | −0.316511 | − | 0.419588i | ||||
\(157\) | −5.80887 | + | 10.0613i | −0.463599 | + | 0.802976i | −0.999137 | − | 0.0415345i | \(-0.986775\pi\) |
0.535538 | + | 0.844511i | \(0.320109\pi\) | |||||||
\(158\) | 6.52420 | − | 11.3002i | 0.519037 | − | 0.898999i | ||||
\(159\) | 21.9737 | − | 2.70918i | 1.74263 | − | 0.214852i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | −7.96227 | −0.627515 | ||||||||
\(162\) | −7.64195 | − | 4.75401i | −0.600408 | − | 0.373510i | ||||
\(163\) | 5.86872 | 0.459674 | 0.229837 | − | 0.973229i | \(-0.426181\pi\) | ||||
0.229837 | + | 0.973229i | \(0.426181\pi\) | |||||||
\(164\) | 1.69113 | + | 2.92912i | 0.132055 | + | 0.228726i | ||||
\(165\) | −0.148061 | + | 0.0182547i | −0.0115265 | + | 0.00142112i | ||||
\(166\) | 4.43807 | − | 7.68696i | 0.344461 | − | 0.596624i | ||||
\(167\) | 8.00904 | − | 13.8721i | 0.619758 | − | 1.07345i | −0.369771 | − | 0.929123i | \(-0.620564\pi\) |
0.989530 | − | 0.144330i | \(-0.0461027\pi\) | |||||||
\(168\) | −1.04307 | − | 1.38276i | −0.0804742 | − | 0.106682i | ||||
\(169\) | −0.682083 | − | 1.18140i | −0.0524679 | − | 0.0908771i | ||||
\(170\) | −5.82032 | −0.446398 | ||||||||
\(171\) | −4.79612 | + | 1.20090i | −0.366769 | + | 0.0918350i | ||||
\(172\) | −8.46838 | −0.645708 | ||||||||
\(173\) | 3.25839 | + | 5.64370i | 0.247731 | + | 0.429082i | 0.962896 | − | 0.269873i | \(-0.0869818\pi\) |
−0.715165 | + | 0.698956i | \(0.753648\pi\) | |||||||
\(174\) | −6.14195 | + | 14.4896i | −0.465620 | + | 1.09846i | ||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | −0.0430651 | + | 0.0745909i | −0.00324615 | + | 0.00562250i | ||||
\(177\) | 8.69886 | − | 20.5217i | 0.653847 | − | 1.54251i | ||||
\(178\) | 1.00000 | + | 1.73205i | 0.0749532 | + | 0.129823i | ||||
\(179\) | −1.00742 | −0.0752980 | −0.0376490 | − | 0.999291i | \(-0.511987\pi\) | ||||
−0.0376490 | + | 0.999291i | \(0.511987\pi\) | |||||||
\(180\) | −2.08613 | − | 2.15594i | −0.155491 | − | 0.160694i | ||||
\(181\) | 19.9852 | 1.48549 | 0.742743 | − | 0.669577i | \(-0.233525\pi\) | ||||
0.742743 | + | 0.669577i | \(0.233525\pi\) | |||||||
\(182\) | −1.89500 | − | 3.28224i | −0.140467 | − | 0.243296i | ||||
\(183\) | 0.456935 | + | 0.605743i | 0.0337776 | + | 0.0447778i | ||||
\(184\) | −3.98113 | + | 6.89553i | −0.293493 | + | 0.508345i | ||||
\(185\) | 2.21903 | − | 3.84348i | 0.163147 | − | 0.282578i | ||||
\(186\) | −3.73419 | + | 0.460395i | −0.273804 | + | 0.0337578i | ||||
\(187\) | 0.250653 | + | 0.434143i | 0.0183295 | + | 0.0317477i | ||||
\(188\) | 10.3445 | 0.754452 | ||||||||
\(189\) | −4.04307 | − | 3.26399i | −0.294090 | − | 0.237420i | ||||
\(190\) | −1.64806 | −0.119563 | ||||||||
\(191\) | −1.61033 | − | 2.78917i | −0.116519 | − | 0.201817i | 0.801867 | − | 0.597503i | \(-0.203840\pi\) |
−0.918386 | + | 0.395685i | \(0.870507\pi\) | |||||||
\(192\) | −1.71903 | + | 0.211943i | −0.124061 | + | 0.0152956i | ||||
\(193\) | 7.50904 | − | 13.0060i | 0.540513 | − | 0.936196i | −0.458362 | − | 0.888766i | \(-0.651564\pi\) |
0.998875 | − | 0.0474299i | \(-0.0151031\pi\) | |||||||
\(194\) | −3.96838 | + | 6.87344i | −0.284913 | + | 0.493484i | ||||
\(195\) | −3.95323 | − | 5.24066i | −0.283096 | − | 0.375291i | ||||
\(196\) | −0.500000 | − | 0.866025i | −0.0357143 | − | 0.0618590i | ||||
\(197\) | 3.48647 | 0.248401 | 0.124200 | − | 0.992257i | \(-0.460363\pi\) | ||||
0.124200 | + | 0.992257i | \(0.460363\pi\) | |||||||
\(198\) | −0.0709739 | + | 0.248452i | −0.00504390 | + | 0.0176567i | ||||
\(199\) | −8.30679 | −0.588853 | −0.294426 | − | 0.955674i | \(-0.595129\pi\) | ||||
−0.294426 | + | 0.955674i | \(0.595129\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | −0.713701 | + | 1.68371i | −0.0503406 | + | 0.118760i | ||||
\(202\) | −0.734191 | + | 1.27166i | −0.0516575 | + | 0.0894734i | ||||
\(203\) | −4.54307 | + | 7.86882i | −0.318861 | + | 0.552283i | ||||
\(204\) | −3.93436 | + | 9.28166i | −0.275460 | + | 0.649846i | ||||
\(205\) | 1.69113 | + | 2.92912i | 0.118113 | + | 0.204578i | ||||
\(206\) | 7.48647 | 0.521607 | ||||||||
\(207\) | −6.56115 | + | 22.9680i | −0.456032 | + | 1.59639i | ||||
\(208\) | −3.79001 | −0.262790 | ||||||||
\(209\) | 0.0709739 | + | 0.122930i | 0.00490937 | + | 0.00850327i | ||||
\(210\) | −1.04307 | − | 1.38276i | −0.0719783 | − | 0.0954193i | ||||
\(211\) | −14.1723 | + | 24.5471i | −0.975659 | + | 1.68989i | −0.297914 | + | 0.954593i | \(0.596291\pi\) |
−0.677744 | + | 0.735298i | \(0.737042\pi\) | |||||||
\(212\) | 6.39130 | − | 11.0700i | 0.438956 | − | 0.760294i | ||||
\(213\) | 27.5356 | − | 3.39492i | 1.88671 | − | 0.232616i | ||||
\(214\) | 0.175970 | + | 0.304788i | 0.0120290 | + | 0.0208349i | ||||
\(215\) | −8.46838 | −0.577539 | ||||||||
\(216\) | −4.84823 | + | 1.86940i | −0.329880 | + | 0.127197i | ||||
\(217\) | −2.17226 | −0.147463 | ||||||||
\(218\) | −4.19113 | − | 7.25924i | −0.283859 | − | 0.491658i | ||||
\(219\) | 12.3294 | − | 1.52011i | 0.833141 | − | 0.102719i | ||||
\(220\) | −0.0430651 | + | 0.0745909i | −0.00290345 | + | 0.00502892i | ||||
\(221\) | −11.0295 | + | 19.1037i | −0.741927 | + | 1.28505i | ||||
\(222\) | −4.62920 | − | 6.13677i | −0.310691 | − | 0.411873i | ||||
\(223\) | 1.24935 | + | 2.16393i | 0.0836625 | + | 0.144908i | 0.904820 | − | 0.425793i | \(-0.140005\pi\) |
−0.821158 | + | 0.570701i | \(0.806672\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.08613 | − | 2.15594i | −0.139075 | − | 0.143729i | ||||
\(226\) | −5.52420 | −0.367464 | ||||||||
\(227\) | 7.62549 | + | 13.2077i | 0.506121 | + | 0.876628i | 0.999975 | + | 0.00708274i | \(0.00225452\pi\) |
−0.493854 | + | 0.869545i | \(0.664412\pi\) | |||||||
\(228\) | −1.11404 | + | 2.62816i | −0.0737790 | + | 0.174054i | ||||
\(229\) | −12.4471 | + | 21.5590i | −0.822528 | + | 1.42466i | 0.0812653 | + | 0.996693i | \(0.474104\pi\) |
−0.903794 | + | 0.427968i | \(0.859229\pi\) | |||||||
\(230\) | −3.98113 | + | 6.89553i | −0.262508 | + | 0.454678i | ||||
\(231\) | −0.0582214 | + | 0.137352i | −0.00383069 | + | 0.00903708i | ||||
\(232\) | 4.54307 | + | 7.86882i | 0.298267 | + | 0.516613i | ||||
\(233\) | 28.9474 | 1.89641 | 0.948205 | − | 0.317660i | \(-0.102897\pi\) | ||||
0.948205 | + | 0.317660i | \(0.102897\pi\) | |||||||
\(234\) | −11.0295 | + | 2.76168i | −0.721023 | + | 0.180537i | ||||
\(235\) | 10.3445 | 0.674802 | ||||||||
\(236\) | −6.43436 | − | 11.1446i | −0.418841 | − | 0.725454i | ||||
\(237\) | −13.6103 | − | 18.0428i | −0.884086 | − | 1.17200i | ||||
\(238\) | −2.91016 | + | 5.04055i | −0.188638 | + | 0.326730i | ||||
\(239\) | 15.2584 | − | 26.4283i | 0.986983 | − | 1.70951i | 0.354215 | − | 0.935164i | \(-0.384748\pi\) |
0.632769 | − | 0.774341i | \(-0.281918\pi\) | |||||||
\(240\) | −1.71903 | + | 0.211943i | −0.110963 | + | 0.0136808i | ||||
\(241\) | −10.8913 | − | 18.8643i | −0.701570 | − | 1.21515i | −0.967915 | − | 0.251277i | \(-0.919149\pi\) |
0.266345 | − | 0.963878i | \(-0.414184\pi\) | |||||||
\(242\) | −10.9926 | −0.706630 | ||||||||
\(243\) | −12.7469 | + | 8.97304i | −0.817717 | + | 0.575621i | ||||
\(244\) | 0.438069 | 0.0280445 | ||||||||
\(245\) | −0.500000 | − | 0.866025i | −0.0319438 | − | 0.0553283i | ||||
\(246\) | 5.81421 | − | 0.716844i | 0.370700 | − | 0.0457043i | ||||
\(247\) | −3.12308 | + | 5.40934i | −0.198717 | + | 0.344188i | ||||
\(248\) | −1.08613 | + | 1.88123i | −0.0689693 | + | 0.119458i | ||||
\(249\) | −9.25839 | − | 12.2735i | −0.586727 | − | 0.777804i | ||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | −5.17226 | −0.326470 | −0.163235 | − | 0.986587i | \(-0.552193\pi\) | ||||
−0.163235 | + | 0.986587i | \(0.552193\pi\) | |||||||
\(252\) | −2.91016 | + | 0.728674i | −0.183323 | + | 0.0459021i | ||||
\(253\) | 0.685792 | 0.0431154 | ||||||||
\(254\) | 2.92532 | + | 5.06680i | 0.183551 | + | 0.317919i | ||||
\(255\) | −3.93436 | + | 9.28166i | −0.246379 | + | 0.581240i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 8.72808 | − | 15.1175i | 0.544443 | − | 0.943002i | −0.454199 | − | 0.890900i | \(-0.650075\pi\) |
0.998642 | − | 0.0521020i | \(-0.0165921\pi\) | |||||||
\(258\) | −5.72437 | + | 13.5045i | −0.356384 | + | 0.840755i | ||||
\(259\) | −2.21903 | − | 3.84348i | −0.137884 | − | 0.238822i | ||||
\(260\) | −3.79001 | −0.235046 | ||||||||
\(261\) | 18.9549 | + | 19.5891i | 1.17328 | + | 1.21254i | ||||
\(262\) | 6.05582 | 0.374130 | ||||||||
\(263\) | 13.0114 | + | 22.5365i | 0.802320 | + | 1.38966i | 0.918085 | + | 0.396383i | \(0.129735\pi\) |
−0.115765 | + | 0.993277i | \(0.536932\pi\) | |||||||
\(264\) | 0.0898394 | + | 0.119097i | 0.00552923 | + | 0.00732992i | ||||
\(265\) | 6.39130 | − | 11.0700i | 0.392614 | − | 0.680028i | ||||
\(266\) | −0.824030 | + | 1.42726i | −0.0505245 | + | 0.0875111i | ||||
\(267\) | 3.43807 | − | 0.423885i | 0.210406 | − | 0.0259414i | ||||
\(268\) | 0.527909 | + | 0.914365i | 0.0322472 | + | 0.0558537i | ||||
\(269\) | 22.1297 | 1.34927 | 0.674636 | − | 0.738150i | \(-0.264300\pi\) | ||||
0.674636 | + | 0.738150i | \(0.264300\pi\) | |||||||
\(270\) | −4.84823 | + | 1.86940i | −0.295054 | + | 0.113768i | ||||
\(271\) | −2.13453 | −0.129663 | −0.0648317 | − | 0.997896i | \(-0.520651\pi\) | ||||
−0.0648317 | + | 0.997896i | \(0.520651\pi\) | |||||||
\(272\) | 2.91016 | + | 5.04055i | 0.176454 | + | 0.305628i | ||||
\(273\) | −6.51516 | + | 0.803265i | −0.394315 | + | 0.0486158i | ||||
\(274\) | 3.98484 | − | 6.90195i | 0.240733 | − | 0.416962i | ||||
\(275\) | −0.0430651 | + | 0.0745909i | −0.00259692 | + | 0.00449800i | ||||
\(276\) | 8.30516 | + | 11.0099i | 0.499912 | + | 0.662717i | ||||
\(277\) | −0.883557 | − | 1.53037i | −0.0530878 | − | 0.0919508i | 0.838260 | − | 0.545270i | \(-0.183573\pi\) |
−0.891348 | + | 0.453320i | \(0.850240\pi\) | |||||||
\(278\) | −7.00000 | −0.419832 | ||||||||
\(279\) | −1.79001 | + | 6.26612i | −0.107165 | + | 0.375143i | ||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −9.11404 | − | 15.7860i | −0.543698 | − | 0.941713i | −0.998688 | − | 0.0512158i | \(-0.983690\pi\) |
0.454990 | − | 0.890497i | \(-0.349643\pi\) | |||||||
\(282\) | 6.99258 | − | 16.4964i | 0.416402 | − | 0.982346i | ||||
\(283\) | 6.78259 | − | 11.7478i | 0.403183 | − | 0.698334i | −0.590925 | − | 0.806726i | \(-0.701237\pi\) |
0.994108 | + | 0.108393i | \(0.0345704\pi\) | |||||||
\(284\) | 8.00904 | − | 13.8721i | 0.475249 | − | 0.823156i | ||||
\(285\) | −1.11404 | + | 2.62816i | −0.0659900 | + | 0.155679i | ||||
\(286\) | 0.163217 | + | 0.282700i | 0.00965123 | + | 0.0167164i | ||||
\(287\) | 3.38225 | 0.199648 | ||||||||
\(288\) | −0.824030 | + | 2.88461i | −0.0485565 | + | 0.169977i | ||||
\(289\) | 16.8761 | 0.992714 | ||||||||
\(290\) | 4.54307 | + | 7.86882i | 0.266778 | + | 0.462073i | ||||
\(291\) | 8.27856 | + | 10.9746i | 0.485298 | + | 0.643343i | ||||
\(292\) | 3.58613 | − | 6.21136i | 0.209862 | − | 0.363492i | ||||
\(293\) | −11.6218 | + | 20.1295i | −0.678951 | + | 1.17598i | 0.296346 | + | 0.955081i | \(0.404232\pi\) |
−0.975297 | + | 0.220898i | \(0.929101\pi\) | |||||||
\(294\) | −1.71903 | + | 0.211943i | −0.100256 | + | 0.0123607i | ||||
\(295\) | −6.43436 | − | 11.1446i | −0.374623 | − | 0.648866i | ||||
\(296\) | −4.43807 | −0.257958 | ||||||||
\(297\) | 0.348230 | + | 0.281128i | 0.0202064 | + | 0.0163127i | ||||
\(298\) | −10.7645 | −0.623571 | ||||||||
\(299\) | 15.0885 | + | 26.1341i | 0.872592 | + | 1.51137i | ||||
\(300\) | −1.71903 | + | 0.211943i | −0.0992485 | + | 0.0122365i | ||||
\(301\) | −4.23419 | + | 7.33383i | −0.244055 | + | 0.422715i | ||||
\(302\) | −2.70388 | + | 4.68325i | −0.155591 | + | 0.269491i | ||||
\(303\) | 1.53162 | + | 2.03041i | 0.0879892 | + | 0.116644i | ||||
\(304\) | 0.824030 | + | 1.42726i | 0.0472614 | + | 0.0818591i | ||||
\(305\) | 0.438069 | 0.0250838 | ||||||||
\(306\) | 12.1419 | + | 12.5482i | 0.694109 | + | 0.717335i | ||||
\(307\) | −12.3700 | −0.705995 | −0.352997 | − | 0.935624i | \(-0.614838\pi\) | ||||
−0.352997 | + | 0.935624i | \(0.614838\pi\) | |||||||
\(308\) | 0.0430651 | + | 0.0745909i | 0.00245386 | + | 0.00425021i | ||||
\(309\) | 5.06063 | − | 11.9387i | 0.287889 | − | 0.679167i | ||||
\(310\) | −1.08613 | + | 1.88123i | −0.0616880 | + | 0.106847i | ||||
\(311\) | −4.64806 | + | 8.05068i | −0.263567 | + | 0.456512i | −0.967187 | − | 0.254064i | \(-0.918232\pi\) |
0.703620 | + | 0.710577i | \(0.251566\pi\) | |||||||
\(312\) | −2.56193 | + | 6.04392i | −0.145041 | + | 0.342170i | ||||
\(313\) | 10.2621 | + | 17.7745i | 0.580048 | + | 1.00467i | 0.995473 | + | 0.0950454i | \(0.0302996\pi\) |
−0.415425 | + | 0.909628i | \(0.636367\pi\) | |||||||
\(314\) | 11.6177 | 0.655627 | ||||||||
\(315\) | −2.91016 | + | 0.728674i | −0.163969 | + | 0.0410561i | ||||
\(316\) | −13.0484 | −0.734030 | ||||||||
\(317\) | 12.7358 | + | 22.0591i | 0.715315 | + | 1.23896i | 0.962838 | + | 0.270079i | \(0.0870500\pi\) |
−0.247523 | + | 0.968882i | \(0.579617\pi\) | |||||||
\(318\) | −13.3331 | − | 17.6752i | −0.747682 | − | 0.991176i | ||||
\(319\) | 0.391295 | − | 0.677743i | 0.0219083 | − | 0.0379463i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | 0.604996 | − | 0.0745909i | 0.0337676 | − | 0.00416326i | ||||
\(322\) | 3.98113 | + | 6.89553i | 0.221860 | + | 0.384273i | ||||
\(323\) | 9.59224 | 0.533727 | ||||||||
\(324\) | −0.296122 | + | 8.99513i | −0.0164512 | + | 0.499729i | ||||
\(325\) | −3.79001 | −0.210232 | ||||||||
\(326\) | −2.93436 | − | 5.08246i | −0.162519 | − | 0.281491i | ||||
\(327\) | −14.4094 | + | 1.77656i | −0.796841 | + | 0.0982438i | ||||
\(328\) | 1.69113 | − | 2.92912i | 0.0933768 | − | 0.161733i | ||||
\(329\) | 5.17226 | − | 8.95862i | 0.285156 | − | 0.493905i | ||||
\(330\) | 0.0898394 | + | 0.119097i | 0.00494550 | + | 0.00655608i | ||||
\(331\) | −4.43807 | − | 7.68696i | −0.243938 | − | 0.422514i | 0.717894 | − | 0.696152i | \(-0.245106\pi\) |
−0.961833 | + | 0.273639i | \(0.911773\pi\) | |||||||
\(332\) | −8.87614 | −0.487141 | ||||||||
\(333\) | −12.9155 | + | 3.23390i | −0.707765 | + | 0.177217i | ||||
\(334\) | −16.0181 | −0.876471 | ||||||||
\(335\) | 0.527909 | + | 0.914365i | 0.0288427 | + | 0.0499571i | ||||
\(336\) | −0.675970 | + | 1.59470i | −0.0368772 | + | 0.0869980i | ||||
\(337\) | −6.21292 | + | 10.7611i | −0.338439 | + | 0.586194i | −0.984139 | − | 0.177397i | \(-0.943232\pi\) |
0.645700 | + | 0.763591i | \(0.276566\pi\) | |||||||
\(338\) | −0.682083 | + | 1.18140i | −0.0371004 | + | 0.0642598i | ||||
\(339\) | −3.73419 | + | 8.80944i | −0.202813 | + | 0.478463i | ||||
\(340\) | 2.91016 | + | 5.04055i | 0.157826 | + | 0.273362i | ||||
\(341\) | 0.187097 | 0.0101319 | ||||||||
\(342\) | 3.43807 | + | 3.55311i | 0.185910 | + | 0.192130i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 4.23419 | + | 7.33383i | 0.228292 | + | 0.395414i | ||||
\(345\) | 8.30516 | + | 11.0099i | 0.447135 | + | 0.592752i | ||||
\(346\) | 3.25839 | − | 5.64370i | 0.175172 | − | 0.303407i | ||||
\(347\) | 6.35565 | − | 11.0083i | 0.341189 | − | 0.590957i | −0.643465 | − | 0.765476i | \(-0.722504\pi\) |
0.984654 | + | 0.174519i | \(0.0558370\pi\) | |||||||
\(348\) | 15.6194 | − | 1.92574i | 0.837286 | − | 0.103230i | ||||
\(349\) | −12.7991 | − | 22.1686i | −0.685118 | − | 1.18666i | −0.973400 | − | 0.229113i | \(-0.926417\pi\) |
0.288282 | − | 0.957545i | \(-0.406916\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −3.05158 | + | 19.4556i | −0.162881 | + | 1.03846i | ||||
\(352\) | 0.0861302 | 0.00459075 | ||||||||
\(353\) | 3.90776 | + | 6.76843i | 0.207989 | + | 0.360247i | 0.951081 | − | 0.308942i | \(-0.0999749\pi\) |
−0.743092 | + | 0.669189i | \(0.766642\pi\) | |||||||
\(354\) | −22.1218 | + | 2.72743i | −1.17576 | + | 0.144961i | ||||
\(355\) | 8.00904 | − | 13.8721i | 0.425076 | − | 0.736253i | ||||
\(356\) | 1.00000 | − | 1.73205i | 0.0529999 | − | 0.0917985i | ||||
\(357\) | 6.07097 | + | 8.04809i | 0.321310 | + | 0.425950i | ||||
\(358\) | 0.503709 | + | 0.872450i | 0.0266219 | + | 0.0461104i | ||||
\(359\) | −35.5981 | −1.87880 | −0.939398 | − | 0.342828i | \(-0.888615\pi\) | ||||
−0.939398 | + | 0.342828i | \(0.888615\pi\) | |||||||
\(360\) | −0.824030 | + | 2.88461i | −0.0434302 | + | 0.152032i | ||||
\(361\) | −16.2839 | −0.857047 | ||||||||
\(362\) | −9.99258 | − | 17.3077i | −0.525198 | − | 0.909670i | ||||
\(363\) | −7.43065 | + | 17.5299i | −0.390008 | + | 0.920079i | ||||
\(364\) | −1.89500 | + | 3.28224i | −0.0993252 | + | 0.172036i | ||||
\(365\) | 3.58613 | − | 6.21136i | 0.187707 | − | 0.325117i | ||||
\(366\) | 0.296122 | − | 0.698589i | 0.0154785 | − | 0.0365158i | ||||
\(367\) | −3.13290 | − | 5.42635i | −0.163536 | − | 0.283253i | 0.772598 | − | 0.634895i | \(-0.218957\pi\) |
−0.936135 | + | 0.351642i | \(0.885623\pi\) | |||||||
\(368\) | 7.96227 | 0.415062 | ||||||||
\(369\) | 2.78708 | − | 9.75648i | 0.145090 | − | 0.507902i | ||||
\(370\) | −4.43807 | −0.230724 | ||||||||
\(371\) | −6.39130 | − | 11.0700i | −0.331820 | − | 0.574728i | ||||
\(372\) | 2.26581 | + | 3.00371i | 0.117477 | + | 0.155735i | ||||
\(373\) | −8.66615 | + | 15.0102i | −0.448716 | + | 0.777199i | −0.998303 | − | 0.0582376i | \(-0.981452\pi\) |
0.549587 | + | 0.835437i | \(0.314785\pi\) | |||||||
\(374\) | 0.250653 | − | 0.434143i | 0.0129609 | − | 0.0224490i | ||||
\(375\) | −1.71903 | + | 0.211943i | −0.0887706 | + | 0.0109447i | ||||
\(376\) | −5.17226 | − | 8.95862i | −0.266739 | − | 0.462005i | ||||
\(377\) | 34.4365 | 1.77357 | ||||||||
\(378\) | −0.805165 | + | 5.13339i | −0.0414132 | + | 0.264033i | ||||
\(379\) | 17.9549 | 0.922279 | 0.461139 | − | 0.887328i | \(-0.347441\pi\) | ||||
0.461139 | + | 0.887328i | \(0.347441\pi\) | |||||||
\(380\) | 0.824030 | + | 1.42726i | 0.0422719 | + | 0.0732170i | ||||
\(381\) | 10.0574 | − | 1.24000i | 0.515258 | − | 0.0635271i | ||||
\(382\) | −1.61033 | + | 2.78917i | −0.0823916 | + | 0.142707i | ||||
\(383\) | 3.26581 | − | 5.65655i | 0.166875 | − | 0.289036i | −0.770445 | − | 0.637507i | \(-0.779966\pi\) |
0.937320 | + | 0.348471i | \(0.113299\pi\) | |||||||
\(384\) | 1.04307 | + | 1.38276i | 0.0532287 | + | 0.0705635i | ||||
\(385\) | 0.0430651 | + | 0.0745909i | 0.00219480 | + | 0.00380151i | ||||
\(386\) | −15.0181 | −0.764400 | ||||||||
\(387\) | 17.6661 | + | 18.2573i | 0.898021 | + | 0.928070i | ||||
\(388\) | 7.93676 | 0.402928 | ||||||||
\(389\) | 4.22808 | + | 7.32325i | 0.214372 | + | 0.371303i | 0.953078 | − | 0.302724i | \(-0.0978962\pi\) |
−0.738706 | + | 0.674028i | \(0.764563\pi\) | |||||||
\(390\) | −2.56193 | + | 6.04392i | −0.129728 | + | 0.306046i | ||||
\(391\) | 23.1715 | − | 40.1342i | 1.17183 | − | 2.02967i | ||||
\(392\) | −0.500000 | + | 0.866025i | −0.0252538 | + | 0.0437409i | ||||
\(393\) | 4.09355 | − | 9.65721i | 0.206492 | − | 0.487142i | ||||
\(394\) | −1.74323 | − | 3.01937i | −0.0878229 | − | 0.152114i | ||||
\(395\) | −13.0484 | −0.656536 | ||||||||
\(396\) | 0.250653 | − | 0.0627608i | 0.0125958 | − | 0.00315385i | ||||
\(397\) | −22.4791 | −1.12819 | −0.564096 | − | 0.825709i | \(-0.690775\pi\) | ||||
−0.564096 | + | 0.825709i | \(0.690775\pi\) | |||||||
\(398\) | 4.15339 | + | 7.19389i | 0.208191 | + | 0.360597i | ||||
\(399\) | 1.71903 | + | 2.27887i | 0.0860594 | + | 0.114086i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −7.90776 | + | 13.6966i | −0.394895 | + | 0.683977i | −0.993088 | − | 0.117375i | \(-0.962552\pi\) |
0.598193 | + | 0.801352i | \(0.295886\pi\) | |||||||
\(402\) | 1.81499 | − | 0.223773i | 0.0905233 | − | 0.0111608i | ||||
\(403\) | 4.11644 | + | 7.12989i | 0.205055 | + | 0.355165i | ||||
\(404\) | 1.46838 | 0.0730547 | ||||||||
\(405\) | −0.296122 | + | 8.99513i | −0.0147144 | + | 0.446971i | ||||
\(406\) | 9.08613 | 0.450937 | ||||||||
\(407\) | 0.191126 | + | 0.331040i | 0.00947376 | + | 0.0164090i | ||||
\(408\) | 10.0053 | − | 1.23357i | 0.495338 | − | 0.0610710i | ||||
\(409\) | −8.95693 | + | 15.5139i | −0.442892 | + | 0.767111i | −0.997903 | − | 0.0647318i | \(-0.979381\pi\) |
0.555011 | + | 0.831843i | \(0.312714\pi\) | |||||||
\(410\) | 1.69113 | − | 2.92912i | 0.0835188 | − | 0.144659i | ||||
\(411\) | −8.31290 | − | 11.0201i | −0.410045 | − | 0.543583i | ||||
\(412\) | −3.74323 | − | 6.48347i | −0.184416 | − | 0.319418i | ||||
\(413\) | −12.8687 | −0.633228 | ||||||||
\(414\) | 23.1715 | − | 5.80190i | 1.13882 | − | 0.285148i | ||||
\(415\) | −8.87614 | −0.435713 | ||||||||
\(416\) | 1.89500 | + | 3.28224i | 0.0929102 | + | 0.160925i | ||||
\(417\) | −4.73179 | + | 11.1629i | −0.231717 | + | 0.546649i | ||||
\(418\) | 0.0709739 | − | 0.122930i | 0.00347145 | − | 0.00601272i | ||||
\(419\) | −3.02791 | + | 5.24449i | −0.147923 | + | 0.256210i | −0.930460 | − | 0.366394i | \(-0.880592\pi\) |
0.782537 | + | 0.622605i | \(0.213925\pi\) | |||||||
\(420\) | −0.675970 | + | 1.59470i | −0.0329839 | + | 0.0778133i | ||||
\(421\) | −7.10500 | − | 12.3062i | −0.346276 | − | 0.599768i | 0.639308 | − | 0.768950i | \(-0.279221\pi\) |
−0.985585 | + | 0.169182i | \(0.945887\pi\) | |||||||
\(422\) | 28.3445 | 1.37979 | ||||||||
\(423\) | −21.5800 | − | 22.3021i | −1.04926 | − | 1.08437i | ||||
\(424\) | −12.7826 | −0.620777 | ||||||||
\(425\) | 2.91016 | + | 5.04055i | 0.141164 | + | 0.244502i | ||||
\(426\) | −16.7079 | − | 22.1491i | −0.809501 | − | 1.07313i | ||||
\(427\) | 0.219035 | − | 0.379379i | 0.0105998 | − | 0.0183594i | ||||
\(428\) | 0.175970 | − | 0.304788i | 0.00850581 | − | 0.0147325i | ||||
\(429\) | 0.561152 | − | 0.0691853i | 0.0270927 | − | 0.00334030i | ||||
\(430\) | 4.23419 | + | 7.33383i | 0.204191 | + | 0.353669i | ||||
\(431\) | −15.5800 | −0.750463 | −0.375232 | − | 0.926931i | \(-0.622437\pi\) | ||||
−0.375232 | + | 0.926931i | \(0.622437\pi\) | |||||||
\(432\) | 4.04307 | + | 3.26399i | 0.194522 | + | 0.157039i | ||||
\(433\) | −36.6768 | −1.76258 | −0.881288 | − | 0.472580i | \(-0.843323\pi\) | ||||
−0.881288 | + | 0.472580i | \(0.843323\pi\) | |||||||
\(434\) | 1.08613 | + | 1.88123i | 0.0521359 | + | 0.0903021i | ||||
\(435\) | 15.6194 | − | 1.92574i | 0.748892 | − | 0.0923321i | ||||
\(436\) | −4.19113 | + | 7.25924i | −0.200719 | + | 0.347655i | ||||
\(437\) | 6.56115 | − | 11.3642i | 0.313862 | − | 0.543626i | ||||
\(438\) | −7.48113 | − | 9.91749i | −0.357462 | − | 0.473876i | ||||
\(439\) | 8.85727 | + | 15.3412i | 0.422735 | + | 0.732198i | 0.996206 | − | 0.0870279i | \(-0.0277369\pi\) |
−0.573471 | + | 0.819226i | \(0.694404\pi\) | |||||||
\(440\) | 0.0861302 | 0.00410610 | ||||||||
\(441\) | −0.824030 | + | 2.88461i | −0.0392395 | + | 0.137362i | ||||
\(442\) | 22.0591 | 1.04924 | ||||||||
\(443\) | −18.9307 | − | 32.7888i | −0.899422 | − | 1.55785i | −0.828234 | − | 0.560382i | \(-0.810654\pi\) |
−0.0711883 | − | 0.997463i | \(-0.522679\pi\) | |||||||
\(444\) | −3.00000 | + | 7.07739i | −0.142374 | + | 0.335878i | ||||
\(445\) | 1.00000 | − | 1.73205i | 0.0474045 | − | 0.0821071i | ||||
\(446\) | 1.24935 | − | 2.16393i | 0.0591583 | − | 0.102465i | ||||
\(447\) | −7.27648 | + | 17.1661i | −0.344166 | + | 0.811931i | ||||
\(448\) | 0.500000 | + | 0.866025i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | −38.6965 | −1.82620 | −0.913099 | − | 0.407737i | \(-0.866318\pi\) | ||||
−0.913099 | + | 0.407737i | \(0.866318\pi\) | |||||||
\(450\) | −0.824030 | + | 2.88461i | −0.0388452 | + | 0.135982i | ||||
\(451\) | −0.291314 | −0.0137174 | ||||||||
\(452\) | 2.76210 | + | 4.78410i | 0.129918 | + | 0.225025i | ||||
\(453\) | 5.64064 | + | 7.47761i | 0.265020 | + | 0.351329i | ||||
\(454\) | 7.62549 | − | 13.2077i | 0.357882 | − | 0.619869i | ||||
\(455\) | −1.89500 | + | 3.28224i | −0.0888392 | + | 0.153874i | ||||
\(456\) | 2.83307 | − | 0.349294i | 0.132671 | − | 0.0163572i | ||||
\(457\) | 0.488553 | + | 0.846198i | 0.0228535 | + | 0.0395835i | 0.877226 | − | 0.480078i | \(-0.159392\pi\) |
−0.854372 | + | 0.519661i | \(0.826058\pi\) | |||||||
\(458\) | 24.8942 | 1.16323 | ||||||||
\(459\) | 28.2183 | − | 10.8805i | 1.31712 | − | 0.507859i | ||||
\(460\) | 7.96227 | 0.371243 | ||||||||
\(461\) | 12.6194 | + | 21.8574i | 0.587743 | + | 1.01800i | 0.994527 | + | 0.104476i | \(0.0333166\pi\) |
−0.406785 | + | 0.913524i | \(0.633350\pi\) | |||||||
\(462\) | 0.148061 | − | 0.0182547i | 0.00688841 | − | 0.000849284i | ||||
\(463\) | 8.61775 | − | 14.9264i | 0.400501 | − | 0.693688i | −0.593286 | − | 0.804992i | \(-0.702170\pi\) |
0.993786 | + | 0.111304i | \(0.0355029\pi\) | |||||||
\(464\) | 4.54307 | − | 7.86882i | 0.210907 | − | 0.365301i | ||||
\(465\) | 2.26581 | + | 3.00371i | 0.105074 | + | 0.139294i | ||||
\(466\) | −14.4737 | − | 25.0692i | −0.670482 | − | 1.16131i | ||||
\(467\) | 8.71935 | 0.403484 | 0.201742 | − | 0.979439i | \(-0.435340\pi\) | ||||
0.201742 | + | 0.979439i | \(0.435340\pi\) | |||||||
\(468\) | 7.90645 | + | 8.17102i | 0.365476 | + | 0.377705i | ||||
\(469\) | 1.05582 | 0.0487531 | ||||||||
\(470\) | −5.17226 | − | 8.95862i | −0.238579 | − | 0.413230i | ||||
\(471\) | 7.85324 | − | 18.5268i | 0.361858 | − | 0.853670i | ||||
\(472\) | −6.43436 | + | 11.1446i | −0.296165 | + | 0.512974i | ||||
\(473\) | 0.364692 | − | 0.631665i | 0.0167685 | − | 0.0290440i | ||||
\(474\) | −8.82032 | + | 20.8083i | −0.405131 | + | 0.955755i | ||||
\(475\) | 0.824030 | + | 1.42726i | 0.0378091 | + | 0.0654873i | ||||
\(476\) | 5.82032 | 0.266774 | ||||||||
\(477\) | −37.1994 | + | 9.31434i | −1.70324 | + | 0.426474i | ||||
\(478\) | −30.5168 | −1.39581 | ||||||||
\(479\) | 2.89500 | + | 5.01429i | 0.132276 | + | 0.229109i | 0.924554 | − | 0.381052i | \(-0.124438\pi\) |
−0.792277 | + | 0.610161i | \(0.791105\pi\) | |||||||
\(480\) | 1.04307 | + | 1.38276i | 0.0476092 | + | 0.0631139i | ||||
\(481\) | −8.41016 | + | 14.5668i | −0.383470 | + | 0.664190i | ||||
\(482\) | −10.8913 | + | 18.8643i | −0.496085 | + | 0.859244i | ||||
\(483\) | 13.6874 | − | 1.68754i | 0.622799 | − | 0.0767859i | ||||
\(484\) | 5.49629 | + | 9.51985i | 0.249831 | + | 0.432721i | ||||
\(485\) | 7.93676 | 0.360390 | ||||||||
\(486\) | 14.1444 | + | 6.55266i | 0.641601 | + | 0.297235i | ||||
\(487\) | 38.1574 | 1.72908 | 0.864539 | − | 0.502566i | \(-0.167611\pi\) | ||||
0.864539 | + | 0.502566i | \(0.167611\pi\) | |||||||
\(488\) | −0.219035 | − | 0.379379i | −0.00991523 | − | 0.0171737i | ||||
\(489\) | −10.0885 | + | 1.24383i | −0.456219 | + | 0.0562480i | ||||
\(490\) | −0.500000 | + | 0.866025i | −0.0225877 | + | 0.0391230i | ||||
\(491\) | 2.06356 | − | 3.57418i | 0.0931270 | − | 0.161301i | −0.815698 | − | 0.578477i | \(-0.803647\pi\) |
0.908825 | + | 0.417177i | \(0.136980\pi\) | |||||||
\(492\) | −3.52791 | − | 4.67683i | −0.159050 | − | 0.210848i | ||||
\(493\) | −26.4421 | − | 45.7991i | −1.19089 | − | 2.06269i | ||||
\(494\) | 6.24616 | 0.281028 | ||||||||
\(495\) | 0.250653 | − | 0.0627608i | 0.0112660 | − | 0.00282089i | ||||
\(496\) | 2.17226 | 0.0975374 | ||||||||
\(497\) | −8.00904 | − | 13.8721i | −0.359255 | − | 0.622247i | ||||
\(498\) | −6.00000 | + | 14.1548i | −0.268866 | + | 0.634290i | ||||
\(499\) | −8.68371 | + | 15.0406i | −0.388736 | + | 0.673311i | −0.992280 | − | 0.124019i | \(-0.960422\pi\) |
0.603544 | + | 0.797330i | \(0.293755\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | −10.8277 | + | 25.5440i | −0.483748 | + | 1.14122i | ||||
\(502\) | 2.58613 | + | 4.47931i | 0.115425 | + | 0.199921i | ||||
\(503\) | 2.47099 | 0.110176 | 0.0550881 | − | 0.998481i | \(-0.482456\pi\) | ||||
0.0550881 | + | 0.998481i | \(0.482456\pi\) | |||||||
\(504\) | 2.08613 | + | 2.15594i | 0.0929236 | + | 0.0960330i | ||||
\(505\) | 1.46838 | 0.0653421 | ||||||||
\(506\) | −0.342896 | − | 0.593913i | −0.0152436 | − | 0.0264027i | ||||
\(507\) | 1.42291 | + | 1.88631i | 0.0631938 | + | 0.0837739i | ||||
\(508\) | 2.92532 | − | 5.06680i | 0.129790 | − | 0.224803i | ||||
\(509\) | 11.5710 | − | 20.0415i | 0.512874 | − | 0.888325i | −0.487014 | − | 0.873394i | \(-0.661914\pi\) |
0.999889 | − | 0.0149304i | \(-0.00475268\pi\) | |||||||
\(510\) | 10.0053 | − | 1.23357i | 0.443044 | − | 0.0546236i | ||||
\(511\) | −3.58613 | − | 6.21136i | −0.158641 | − | 0.274774i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 7.99018 | − | 3.08089i | 0.352775 | − | 0.136025i | ||||
\(514\) | −17.4562 | −0.769958 | ||||||||
\(515\) | −3.74323 | − | 6.48347i | −0.164947 | − | 0.285696i | ||||
\(516\) | 14.5574 | − | 1.79481i | 0.640856 | − | 0.0790122i | ||||
\(517\) | −0.445488 | + | 0.771608i | −0.0195925 | + | 0.0339353i | ||||
\(518\) | −2.21903 | + | 3.84348i | −0.0974988 | + | 0.168873i | ||||
\(519\) | −6.79743 | − | 9.01112i | −0.298374 | − | 0.395544i | ||||
\(520\) | 1.89500 | + | 3.28224i | 0.0831014 | + | 0.143936i | ||||
\(521\) | −0.425843 | −0.0186565 | −0.00932827 | − | 0.999956i | \(-0.502969\pi\) | ||||
−0.00932827 | + | 0.999956i | \(0.502969\pi\) | |||||||
\(522\) | 7.48725 | − | 26.2099i | 0.327708 | − | 1.14718i | ||||
\(523\) | 13.8081 | 0.603786 | 0.301893 | − | 0.953342i | \(-0.402381\pi\) | ||||
0.301893 | + | 0.953342i | \(0.402381\pi\) | |||||||
\(524\) | −3.02791 | − | 5.24449i | −0.132275 | − | 0.229107i | ||||
\(525\) | −0.675970 | + | 1.59470i | −0.0295017 | + | 0.0695984i | ||||
\(526\) | 13.0114 | − | 22.5365i | 0.567326 | − | 0.982638i | ||||
\(527\) | 6.32163 | − | 10.9494i | 0.275374 | − | 0.476962i | ||||
\(528\) | 0.0582214 | − | 0.137352i | 0.00253376 | − | 0.00597747i | ||||
\(529\) | −20.1989 | − | 34.9855i | −0.878211 | − | 1.52111i | ||||
\(530\) | −12.7826 | −0.555240 | ||||||||
\(531\) | −10.6042 | + | 37.1212i | −0.460184 | + | 1.61092i | ||||
\(532\) | 1.64806 | 0.0714525 | ||||||||
\(533\) | −6.40938 | − | 11.1014i | −0.277621 | − | 0.480854i | ||||
\(534\) | −2.08613 | − | 2.76551i | −0.0902757 | − | 0.119675i | ||||
\(535\) | 0.175970 | − | 0.304788i | 0.00760783 | − | 0.0131771i | ||||
\(536\) | 0.527909 | − | 0.914365i | 0.0228022 | − | 0.0394945i | ||||
\(537\) | 1.73179 | − | 0.213515i | 0.0747321 | − | 0.00921385i | ||||
\(538\) | −11.0649 | − | 19.1649i | −0.477040 | − | 0.826258i | ||||
\(539\) | 0.0861302 | 0.00370989 | ||||||||
\(540\) | 4.04307 | + | 3.26399i | 0.173986 | + | 0.140460i | ||||
\(541\) | 25.0484 | 1.07691 | 0.538457 | − | 0.842653i | \(-0.319007\pi\) | ||||
0.538457 | + | 0.842653i | \(0.319007\pi\) | |||||||
\(542\) | 1.06726 | + | 1.84856i | 0.0458429 | + | 0.0794023i | ||||
\(543\) | −34.3552 | + | 4.23571i | −1.47432 | + | 0.181772i | ||||
\(544\) | 2.91016 | − | 5.04055i | 0.124772 | − | 0.216112i | ||||
\(545\) | −4.19113 | + | 7.25924i | −0.179528 | + | 0.310952i | ||||
\(546\) | 3.95323 | + | 5.24066i | 0.169182 | + | 0.224279i | ||||
\(547\) | −4.85194 | − | 8.40381i | −0.207454 | − | 0.359321i | 0.743458 | − | 0.668783i | \(-0.233184\pi\) |
−0.950912 | + | 0.309462i | \(0.899851\pi\) | |||||||
\(548\) | −7.96969 | −0.340448 | ||||||||
\(549\) | −0.913870 | − | 0.944450i | −0.0390030 | − | 0.0403081i | ||||
\(550\) | 0.0861302 | 0.00367260 | ||||||||
\(551\) | −7.48725 | − | 12.9683i | −0.318967 | − | 0.552468i | ||||
\(552\) | 5.38225 | − | 12.6974i | 0.229084 | − | 0.540438i | ||||
\(553\) | −6.52420 | + | 11.3002i | −0.277437 | + | 0.480535i | ||||
\(554\) | −0.883557 | + | 1.53037i | −0.0375387 | + | 0.0650190i | ||||
\(555\) | −3.00000 | + | 7.07739i | −0.127343 | + | 0.300418i | ||||
\(556\) | 3.50000 | + | 6.06218i | 0.148433 | + | 0.257094i | ||||
\(557\) | 16.0968 | 0.682043 | 0.341022 | − | 0.940055i | \(-0.389227\pi\) | ||||
0.341022 | + | 0.940055i | \(0.389227\pi\) | |||||||
\(558\) | 6.32163 | − | 1.58287i | 0.267616 | − | 0.0670082i | ||||
\(559\) | 32.0952 | 1.35748 | ||||||||
\(560\) | 0.500000 | + | 0.866025i | 0.0211289 | + | 0.0365963i | ||||
\(561\) | −0.522894 | − | 0.693183i | −0.0220766 | − | 0.0292662i | ||||
\(562\) | −9.11404 | + | 15.7860i | −0.384453 | + | 0.665891i | ||||
\(563\) | 11.5418 | − | 19.9909i | 0.486427 | − | 0.842517i | −0.513451 | − | 0.858119i | \(-0.671633\pi\) |
0.999878 | + | 0.0156023i | \(0.00496656\pi\) | |||||||
\(564\) | −17.7826 | + | 2.19245i | −0.748782 | + | 0.0923186i | ||||
\(565\) | 2.76210 | + | 4.78410i | 0.116202 | + | 0.201268i | ||||
\(566\) | −13.5652 | −0.570187 | ||||||||
\(567\) | 7.64195 | + | 4.75401i | 0.320932 | + | 0.199650i | ||||
\(568\) | −16.0181 | −0.672104 | ||||||||
\(569\) | −14.6550 | − | 25.3832i | −0.614370 | − | 1.06412i | −0.990495 | − | 0.137551i | \(-0.956077\pi\) |
0.376124 | − | 0.926569i | \(-0.377257\pi\) | |||||||
\(570\) | 2.83307 | − | 0.349294i | 0.118664 | − | 0.0146303i | ||||
\(571\) | 10.1497 | − | 17.5798i | 0.424751 | − | 0.735691i | −0.571646 | − | 0.820500i | \(-0.693695\pi\) |
0.996397 | + | 0.0848098i | \(0.0270283\pi\) | |||||||
\(572\) | 0.163217 | − | 0.282700i | 0.00682445 | − | 0.0118203i | ||||
\(573\) | 3.35936 | + | 4.45339i | 0.140339 | + | 0.186043i | ||||
\(574\) | −1.69113 | − | 2.92912i | −0.0705862 | − | 0.122259i | ||||
\(575\) | 7.96227 | 0.332050 | ||||||||
\(576\) | 2.91016 | − | 0.728674i | 0.121257 | − | 0.0303614i | ||||
\(577\) | 35.5726 | 1.48091 | 0.740453 | − | 0.672108i | \(-0.234611\pi\) | ||||
0.740453 | + | 0.672108i | \(0.234611\pi\) | |||||||
\(578\) | −8.43807 | − | 14.6152i | −0.350977 | − | 0.607911i | ||||
\(579\) | −10.1518 | + | 23.9493i | −0.421893 | + | 0.995300i | ||||
\(580\) | 4.54307 | − | 7.86882i | 0.188641 | − | 0.326735i | ||||
\(581\) | −4.43807 | + | 7.68696i | −0.184122 | + | 0.318909i | ||||
\(582\) | 5.36501 | − | 12.6568i | 0.222387 | − | 0.524639i | ||||
\(583\) | 0.550484 | + | 0.953465i | 0.0227987 | + | 0.0394885i | ||||
\(584\) | −7.17226 | −0.296790 | ||||||||
\(585\) | 7.90645 | + | 8.17102i | 0.326892 | + | 0.337830i | ||||
\(586\) | 23.2436 | 0.960182 | ||||||||
\(587\) | 2.80757 | + | 4.86285i | 0.115881 | + | 0.200711i | 0.918131 | − | 0.396276i | \(-0.129698\pi\) |
−0.802251 | + | 0.596987i | \(0.796364\pi\) | |||||||
\(588\) | 1.04307 | + | 1.38276i | 0.0430153 | + | 0.0570239i | ||||
\(589\) | 1.79001 | − | 3.10039i | 0.0737560 | − | 0.127749i | ||||
\(590\) | −6.43436 | + | 11.1446i | −0.264898 | + | 0.458818i | ||||
\(591\) | −5.99336 | + | 0.738932i | −0.246534 | + | 0.0303956i | ||||
\(592\) | 2.21903 | + | 3.84348i | 0.0912018 | + | 0.157966i | ||||
\(593\) | 3.86872 | 0.158869 | 0.0794347 | − | 0.996840i | \(-0.474688\pi\) | ||||
0.0794347 | + | 0.996840i | \(0.474688\pi\) | |||||||
\(594\) | 0.0693490 | − | 0.442140i | 0.00284542 | − | 0.0181412i | ||||
\(595\) | 5.82032 | 0.238610 | ||||||||
\(596\) | 5.38225 | + | 9.32233i | 0.220466 | + | 0.381858i | ||||
\(597\) | 14.2797 | − | 1.76056i | 0.584428 | − | 0.0720551i | ||||
\(598\) | 15.0885 | − | 26.1341i | 0.617016 | − | 1.06870i | ||||
\(599\) | 21.1648 | − | 36.6586i | 0.864772 | − | 1.49783i | −0.00250139 | − | 0.999997i | \(-0.500796\pi\) |
0.867273 | − | 0.497832i | \(-0.165870\pi\) | |||||||
\(600\) | 1.04307 | + | 1.38276i | 0.0425830 | + | 0.0564508i | ||||
\(601\) | −4.71663 | − | 8.16944i | −0.192395 | − | 0.333239i | 0.753648 | − | 0.657278i | \(-0.228292\pi\) |
−0.946044 | + | 0.324039i | \(0.894959\pi\) | |||||||
\(602\) | 8.46838 | 0.345145 | ||||||||
\(603\) | 0.870026 | − | 3.04562i | 0.0354302 | − | 0.124027i | ||||
\(604\) | 5.40776 | 0.220039 | ||||||||
\(605\) | 5.49629 | + | 9.51985i | 0.223456 | + | 0.387037i | ||||
\(606\) | 0.992582 | − | 2.34163i | 0.0403209 | − | 0.0951221i | ||||
\(607\) | −18.3445 | + | 31.7736i | −0.744581 | + | 1.28965i | 0.205809 | + | 0.978592i | \(0.434017\pi\) |
−0.950390 | + | 0.311060i | \(0.899316\pi\) | |||||||
\(608\) | 0.824030 | − | 1.42726i | 0.0334188 | − | 0.0578831i | ||||
\(609\) | 6.14195 | − | 14.4896i | 0.248884 | − | 0.587150i | ||||
\(610\) | −0.219035 | − | 0.379379i | −0.00886846 | − | 0.0153606i | ||||
\(611\) | −39.2058 | −1.58610 | ||||||||
\(612\) | 4.79612 | − | 16.7894i | 0.193872 | − | 0.678669i | ||||
\(613\) | 6.70388 | 0.270767 | 0.135384 | − | 0.990793i | \(-0.456773\pi\) | ||||
0.135384 | + | 0.990793i | \(0.456773\pi\) | |||||||
\(614\) | 6.18501 | + | 10.7128i | 0.249607 | + | 0.432332i | ||||
\(615\) | −3.52791 | − | 4.67683i | −0.142259 | − | 0.188588i | ||||
\(616\) | 0.0430651 | − | 0.0745909i | 0.00173514 | − | 0.00300535i | ||||
\(617\) | 2.10870 | − | 3.65238i | 0.0848933 | − | 0.147039i | −0.820452 | − | 0.571715i | \(-0.806278\pi\) |
0.905346 | + | 0.424675i | \(0.139612\pi\) | |||||||
\(618\) | −12.8695 | + | 1.58670i | −0.517687 | + | 0.0638265i | ||||
\(619\) | 1.96838 | + | 3.40934i | 0.0791160 | + | 0.137033i | 0.902869 | − | 0.429916i | \(-0.141457\pi\) |
−0.823753 | + | 0.566949i | \(0.808124\pi\) | |||||||
\(620\) | 2.17226 | 0.0872401 | ||||||||
\(621\) | 6.41094 | − | 40.8734i | 0.257262 | − | 1.64019i | ||||
\(622\) | 9.29612 | 0.372741 | ||||||||
\(623\) | −1.00000 | − | 1.73205i | −0.0400642 | − | 0.0693932i | ||||
\(624\) | 6.51516 | − | 0.803265i | 0.260815 | − | 0.0321563i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 10.2621 | − | 17.7745i | 0.410156 | − | 0.710411i | ||||
\(627\) | −0.148061 | − | 0.196279i | −0.00591298 | − | 0.00783864i | ||||
\(628\) | −5.80887 | − | 10.0613i | −0.231799 | − | 0.401488i | ||||
\(629\) | 25.8310 | 1.02995 | ||||||||
\(630\) | 2.08613 | + | 2.15594i | 0.0831134 | + | 0.0858946i | ||||
\(631\) | 6.62517 | 0.263744 | 0.131872 | − | 0.991267i | \(-0.457901\pi\) | ||||
0.131872 | + | 0.991267i | \(0.457901\pi\) | |||||||
\(632\) | 6.52420 | + | 11.3002i | 0.259519 | + | 0.449500i | ||||
\(633\) | 19.1600 | − | 45.2010i | 0.761543 | − | 1.79658i | ||||
\(634\) | 12.7358 | − | 22.0591i | 0.505804 | − | 0.876078i | ||||
\(635\) | 2.92532 | − | 5.06680i | 0.116088 | − | 0.201070i | ||||
\(636\) | −8.64064 | + | 20.3844i | −0.342624 | + | 0.808293i | ||||
\(637\) | 1.89500 | + | 3.28224i | 0.0750828 | + | 0.130047i | ||||
\(638\) | −0.782590 | −0.0309830 | ||||||||
\(639\) | −46.6152 | + | 11.6720i | −1.84407 | + | 0.461736i | ||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 17.1382 | + | 29.6843i | 0.676920 | + | 1.17246i | 0.975904 | + | 0.218201i | \(0.0700189\pi\) |
−0.298984 | + | 0.954258i | \(0.596648\pi\) | |||||||
\(642\) | −0.367095 | − | 0.486646i | −0.0144881 | − | 0.0192064i | ||||
\(643\) | 5.21292 | − | 9.02905i | 0.205578 | − | 0.356071i | −0.744739 | − | 0.667356i | \(-0.767426\pi\) |
0.950317 | + | 0.311285i | \(0.100759\pi\) | |||||||
\(644\) | 3.98113 | − | 6.89553i | 0.156879 | − | 0.271722i | ||||
\(645\) | 14.5574 | − | 1.79481i | 0.573199 | − | 0.0706706i | ||||
\(646\) | −4.79612 | − | 8.30713i | −0.188701 | − | 0.326840i | ||||
\(647\) | 35.0155 | 1.37660 | 0.688300 | − | 0.725426i | \(-0.258357\pi\) | ||||
0.688300 | + | 0.725426i | \(0.258357\pi\) | |||||||
\(648\) | 7.93807 | − | 4.24111i | 0.311837 | − | 0.166607i | ||||
\(649\) | 1.10839 | 0.0435079 | ||||||||
\(650\) | 1.89500 | + | 3.28224i | 0.0743282 | + | 0.128740i | ||||
\(651\) | 3.73419 | − | 0.460395i | 0.146354 | − | 0.0180443i | ||||
\(652\) | −2.93436 | + | 5.08246i | −0.114918 | + | 0.199045i | ||||
\(653\) | 17.5168 | − | 30.3400i | 0.685485 | − | 1.18729i | −0.287800 | − | 0.957691i | \(-0.592924\pi\) |
0.973284 | − | 0.229604i | \(-0.0737430\pi\) | |||||||
\(654\) | 8.74323 | + | 11.5906i | 0.341888 | + | 0.453229i | ||||
\(655\) | −3.02791 | − | 5.24449i | −0.118310 | − | 0.204919i | ||||
\(656\) | −3.38225 | −0.132055 | ||||||||
\(657\) | −20.8724 | + | 5.22624i | −0.814311 | + | 0.203895i | ||||
\(658\) | −10.3445 | −0.403271 | ||||||||
\(659\) | −14.4610 | − | 25.0471i | −0.563319 | − | 0.975697i | −0.997204 | − | 0.0747290i | \(-0.976191\pi\) |
0.433885 | − | 0.900968i | \(-0.357143\pi\) | |||||||
\(660\) | 0.0582214 | − | 0.137352i | 0.00226626 | − | 0.00534641i | ||||
\(661\) | −3.61775 | + | 6.26612i | −0.140714 | + | 0.243724i | −0.927766 | − | 0.373163i | \(-0.878273\pi\) |
0.787052 | + | 0.616887i | \(0.211607\pi\) | |||||||
\(662\) | −4.43807 | + | 7.68696i | −0.172490 | + | 0.298762i | ||||
\(663\) | 14.9113 | − | 35.1776i | 0.579105 | − | 1.36618i | ||||
\(664\) | 4.43807 | + | 7.68696i | 0.172230 | + | 0.298312i | ||||
\(665\) | 1.64806 | 0.0639091 | ||||||||
\(666\) | 9.25839 | + | 9.56819i | 0.358755 | + | 0.370760i | ||||
\(667\) | −72.3462 | −2.80126 | ||||||||
\(668\) | 8.00904 | + | 13.8721i | 0.309879 | + | 0.536726i | ||||
\(669\) | −2.60630 | − | 3.45509i | −0.100765 | − | 0.133581i | ||||
\(670\) | 0.527909 | − | 0.914365i | 0.0203949 | − | 0.0353250i | ||||
\(671\) | −0.0188655 | + | 0.0326760i | −0.000728295 | + | 0.00126144i | ||||
\(672\) | 1.71903 | − | 0.211943i | 0.0663132 | − | 0.00817587i | ||||
\(673\) | 11.4939 | + | 19.9080i | 0.443057 | + | 0.767397i | 0.997915 | − | 0.0645483i | \(-0.0205607\pi\) |
−0.554858 | + | 0.831945i | \(0.687227\pi\) | |||||||
\(674\) | 12.4258 | 0.478626 | ||||||||
\(675\) | 4.04307 | + | 3.26399i | 0.155618 | + | 0.125631i | ||||
\(676\) | 1.36417 | 0.0524679 | ||||||||
\(677\) | 5.78337 | + | 10.0171i | 0.222273 | + | 0.384988i | 0.955498 | − | 0.294998i | \(-0.0953191\pi\) |
−0.733225 | + | 0.679986i | \(0.761986\pi\) | |||||||
\(678\) | 9.49629 | − | 1.17081i | 0.364703 | − | 0.0449648i | ||||
\(679\) | 3.96838 | − | 6.87344i | 0.152293 | − | 0.263778i | ||||
\(680\) | 2.91016 | − | 5.04055i | 0.111600 | − | 0.193296i | ||||
\(681\) | −15.9078 | − | 21.0884i | −0.609587 | − | 0.808108i | ||||
\(682\) | −0.0935486 | − | 0.162031i | −0.00358216 | − | 0.00620449i | ||||
\(683\) | −2.06804 | −0.0791315 | −0.0395657 | − | 0.999217i | \(-0.512597\pi\) | ||||
−0.0395657 | + | 0.999217i | \(0.512597\pi\) | |||||||
\(684\) | 1.35805 | − | 4.75401i | 0.0519264 | − | 0.181774i | ||||
\(685\) | −7.96969 | −0.304506 | ||||||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | 16.8277 | − | 39.6988i | 0.642018 | − | 1.51460i | ||||
\(688\) | 4.23419 | − | 7.33383i | 0.161427 | − | 0.279600i | ||||
\(689\) | −24.2231 | + | 41.9556i | −0.922825 | + | 1.59838i | ||||
\(690\) | 5.38225 | − | 12.6974i | 0.204899 | − | 0.483383i | ||||
\(691\) | −10.5316 | − | 18.2413i | −0.400642 | − | 0.693932i | 0.593162 | − | 0.805083i | \(-0.297879\pi\) |
−0.993803 | + | 0.111152i | \(0.964546\pi\) | |||||||
\(692\) | −6.51678 | −0.247731 | ||||||||
\(693\) | 0.0709739 | − | 0.248452i | 0.00269608 | − | 0.00943791i | ||||
\(694\) | −12.7113 | −0.482514 | ||||||||
\(695\) | 3.50000 | + | 6.06218i | 0.132763 | + | 0.229952i | ||||
\(696\) | −9.47743 | − | 12.5639i | −0.359241 | − | 0.476234i | ||||
\(697\) | −9.84290 | + | 17.0484i | −0.372826 | + | 0.645754i | ||||
\(698\) | −12.7991 | + | 22.1686i | −0.484451 | + | 0.839094i | ||||
\(699\) | −49.7616 | + | 6.13520i | −1.88216 | + | 0.232054i | ||||
\(700\) | 0.500000 | + | 0.866025i | 0.0188982 | + | 0.0327327i | ||||
\(701\) | 26.3068 | 0.993594 | 0.496797 | − | 0.867867i | \(-0.334509\pi\) | ||||
0.496797 | + | 0.867867i | \(0.334509\pi\) | |||||||
\(702\) | 18.3748 | − | 7.08505i | 0.693513 | − | 0.267408i | ||||
\(703\) | 7.31421 | 0.275861 | ||||||||
\(704\) | −0.0430651 | − | 0.0745909i | −0.00162308 | − | 0.00281125i | ||||
\(705\) | −17.7826 | + | 2.19245i | −0.669731 | + | 0.0825723i | ||||
\(706\) | 3.90776 | − | 6.76843i | 0.147070 | − | 0.254733i | ||||
\(707\) | 0.734191 | − | 1.27166i | 0.0276121 | − | 0.0478256i | ||||
\(708\) | 13.4229 | + | 17.7943i | 0.504464 | + | 0.668751i | ||||
\(709\) | 2.85727 | + | 4.94894i | 0.107307 | + | 0.185861i | 0.914678 | − | 0.404182i | \(-0.132444\pi\) |
−0.807371 | + | 0.590044i | \(0.799111\pi\) | |||||||
\(710\) | −16.0181 | −0.601148 | ||||||||
\(711\) | 27.2207 | + | 28.1315i | 1.02085 | + | 1.05501i | ||||
\(712\) | −2.00000 | −0.0749532 | ||||||||
\(713\) | −8.64806 | − | 14.9789i | −0.323872 | − | 0.560963i | ||||
\(714\) | 3.93436 | − | 9.28166i | 0.147240 | − | 0.347357i | ||||
\(715\) | 0.163217 | − | 0.282700i | 0.00610397 | − | 0.0105724i | ||||
\(716\) | 0.503709 | − | 0.872450i | 0.0188245 | − | 0.0326050i | ||||
\(717\) | −20.6284 | + | 48.6651i | −0.770382 | + | 1.81743i | ||||
\(718\) | 17.7991 | + | 30.8289i | 0.664255 | + | 1.15052i | ||||
\(719\) | 5.07129 | 0.189127 | 0.0945637 | − | 0.995519i | \(-0.469854\pi\) | ||||
0.0945637 | + | 0.995519i | \(0.469854\pi\) | |||||||
\(720\) | 2.91016 | − | 0.728674i | 0.108455 | − | 0.0271561i | ||||
\(721\) | −7.48647 | −0.278811 | ||||||||
\(722\) | 8.14195 | + | 14.1023i | 0.303012 | + | 0.524832i | ||||
\(723\) | 22.7207 | + | 30.1200i | 0.844990 | + | 1.12018i | ||||
\(724\) | −9.99258 | + | 17.3077i | −0.371371 | + | 0.643234i | ||||
\(725\) | 4.54307 | − | 7.86882i | 0.168725 | − | 0.292241i | ||||
\(726\) | 18.8966 | − | 2.32980i | 0.701320 | − | 0.0864669i | ||||
\(727\) | 13.8597 | + | 24.0057i | 0.514027 | + | 0.890321i | 0.999868 | + | 0.0162734i | \(0.00518021\pi\) |
−0.485841 | + | 0.874047i | \(0.661486\pi\) | |||||||
\(728\) | 3.79001 | 0.140467 | ||||||||
\(729\) | 20.0107 | − | 18.1266i | 0.741136 | − | 0.671355i | ||||
\(730\) | −7.17226 | −0.265457 | ||||||||
\(731\) | −24.6444 | − | 42.6853i | −0.911504 | − | 1.57877i | ||||
\(732\) | −0.753056 | + | 0.0928456i | −0.0278338 | + | 0.00343167i | ||||
\(733\) | −19.0854 | + | 33.0568i | −0.704934 | + | 1.22098i | 0.261782 | + | 0.965127i | \(0.415690\pi\) |
−0.966716 | + | 0.255854i | \(0.917643\pi\) | |||||||
\(734\) | −3.13290 | + | 5.42635i | −0.115638 | + | 0.200290i | ||||
\(735\) | 1.04307 | + | 1.38276i | 0.0384740 | + | 0.0510037i | ||||
\(736\) | −3.98113 | − | 6.89553i | −0.146747 | − | 0.254173i | ||||
\(737\) | −0.0909378 | −0.00334974 | ||||||||
\(738\) | −9.84290 | + | 2.46456i | −0.362322 | + | 0.0907216i | ||||
\(739\) | 31.3068 | 1.15164 | 0.575819 | − | 0.817577i | \(-0.304683\pi\) | ||||
0.575819 | + | 0.817577i | \(0.304683\pi\) | |||||||
\(740\) | 2.21903 | + | 3.84348i | 0.0815733 | + | 0.141289i | ||||
\(741\) | 4.22222 | − | 9.96075i | 0.155107 | − | 0.365917i | ||||
\(742\) | −6.39130 | + | 11.0700i | −0.234632 | + | 0.406394i | ||||
\(743\) | −20.7523 | + | 35.9440i | −0.761327 | + | 1.31866i | 0.180839 | + | 0.983513i | \(0.442119\pi\) |
−0.942167 | + | 0.335145i | \(0.891215\pi\) | |||||||
\(744\) | 1.46838 | − | 3.46410i | 0.0538335 | − | 0.127000i | ||||
\(745\) | 5.38225 | + | 9.32233i | 0.197190 | + | 0.341544i | ||||
\(746\) | 17.3323 | 0.634580 | ||||||||
\(747\) | 18.5168 | + | 19.1364i | 0.677494 | + | 0.700164i | ||||
\(748\) | −0.501305 | −0.0183295 | ||||||||
\(749\) | −0.175970 | − | 0.304788i | −0.00642979 | − | 0.0111367i | ||||
\(750\) | 1.04307 | + | 1.38276i | 0.0380874 | + | 0.0504911i | ||||
\(751\) | 5.61937 | − | 9.73304i | 0.205054 | − | 0.355164i | −0.745096 | − | 0.666957i | \(-0.767596\pi\) |
0.950150 | + | 0.311794i | \(0.100930\pi\) | |||||||
\(752\) | −5.17226 | + | 8.95862i | −0.188613 | + | 0.326687i | ||||
\(753\) | 8.89130 | − | 1.09622i | 0.324017 | − | 0.0399486i | ||||
\(754\) | −17.2183 | − | 29.8229i | −0.627052 | − | 1.08609i | ||||
\(755\) | 5.40776 | 0.196808 | ||||||||
\(756\) | 4.84823 | − | 1.86940i | 0.176328 | − | 0.0679895i | ||||
\(757\) | 7.61294 | 0.276697 | 0.138349 | − | 0.990384i | \(-0.455821\pi\) | ||||
0.138349 | + | 0.990384i | \(0.455821\pi\) | |||||||
\(758\) | −8.97743 | − | 15.5494i | −0.326075 | − | 0.564778i | ||||
\(759\) | −1.17890 | + | 0.145349i | −0.0427914 | + | 0.00527582i | ||||
\(760\) | 0.824030 | − | 1.42726i | 0.0298907 | − | 0.0517723i | ||||
\(761\) | −20.1648 | + | 34.9265i | −0.730975 | + | 1.26609i | 0.225492 | + | 0.974245i | \(0.427601\pi\) |
−0.956467 | + | 0.291841i | \(0.905732\pi\) | |||||||
\(762\) | −6.10259 | − | 8.09000i | −0.221074 | − | 0.293070i | ||||
\(763\) | 4.19113 | + | 7.25924i | 0.151729 | + | 0.262802i | ||||
\(764\) | 3.22066 | 0.116519 | ||||||||
\(765\) | 4.79612 | − | 16.7894i | 0.173404 | − | 0.607020i | ||||
\(766\) | −6.53162 | −0.235997 | ||||||||
\(767\) | 24.3863 | + | 42.2383i | 0.880538 | + | 1.52514i | ||||
\(768\) | 0.675970 | − | 1.59470i | 0.0243920 | − | 0.0575437i | ||||
\(769\) | 12.2863 | − | 21.2805i | 0.443055 | − | 0.767394i | −0.554859 | − | 0.831944i | \(-0.687228\pi\) |
0.997914 | + | 0.0645500i | \(0.0205612\pi\) | |||||||
\(770\) | 0.0430651 | − | 0.0745909i | 0.00155196 | − | 0.00268807i | ||||
\(771\) | −11.7998 | + | 27.8373i | −0.424961 | + | 1.00254i | ||||
\(772\) | 7.50904 | + | 13.0060i | 0.270256 | + | 0.468098i | ||||
\(773\) | −11.4455 | −0.411666 | −0.205833 | − | 0.978587i | \(-0.565990\pi\) | ||||
−0.205833 | + | 0.978587i | \(0.565990\pi\) | |||||||
\(774\) | 6.97820 | − | 24.4280i | 0.250826 | − | 0.878046i | ||||
\(775\) | 2.17226 | 0.0780299 | ||||||||
\(776\) | −3.96838 | − | 6.87344i | −0.142457 | − | 0.246742i | ||||
\(777\) | 4.62920 | + | 6.13677i | 0.166071 | + | 0.220155i | ||||
\(778\) | 4.22808 | − | 7.32325i | 0.151584 | − | 0.262551i | ||||
\(779\) | −2.78708 | + | 4.82736i | −0.0998574 | + | 0.172958i | ||||
\(780\) | 6.51516 | − | 0.803265i | 0.233280 | − | 0.0287615i | ||||
\(781\) | 0.689820 | + | 1.19480i | 0.0246837 | + | 0.0427535i | ||||
\(782\) | −46.3430 | −1.65722 | ||||||||
\(783\) | −36.7358 | − | 29.6570i | −1.31283 | − | 1.05986i | ||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −5.80887 | − | 10.0613i | −0.207328 | − | 0.359102i | ||||
\(786\) | −10.4102 | + | 1.28349i | −0.371318 | + | 0.0457804i | ||||
\(787\) | 19.1419 | − | 33.1548i | 0.682337 | − | 1.18184i | −0.291929 | − | 0.956440i | \(-0.594297\pi\) |
0.974266 | − | 0.225402i | \(-0.0723695\pi\) | |||||||
\(788\) | −1.74323 | + | 3.01937i | −0.0621002 | + | 0.107561i | ||||
\(789\) | −27.1436 | − | 35.9833i | −0.966337 | − | 1.28104i | ||||
\(790\) | 6.52420 | + | 11.3002i | 0.232121 | + | 0.402045i | ||||
\(791\) | 5.52420 | 0.196418 | ||||||||
\(792\) | −0.179679 | − | 0.185691i | −0.00638461 | − | 0.00659825i | ||||
\(793\) | −1.66029 | −0.0589585 | ||||||||
\(794\) | 11.2395 | + | 19.4674i | 0.398876 | + | 0.690873i | ||||
\(795\) | −8.64064 | + | 20.3844i | −0.306452 | + | 0.722960i | ||||
\(796\) | 4.15339 | − | 7.19389i | 0.147213 | − | 0.254981i | ||||
\(797\) | −7.72677 | + | 13.3832i | −0.273696 | + | 0.474056i | −0.969805 | − | 0.243880i | \(-0.921580\pi\) |
0.696109 | + | 0.717936i | \(0.254913\pi\) | |||||||
\(798\) | 1.11404 | − | 2.62816i | 0.0394366 | − | 0.0930359i | ||||
\(799\) | 30.1042 | + | 52.1420i | 1.06501 | + | 1.84465i | ||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −5.82032 | + | 1.45735i | −0.205651 | + | 0.0514928i | ||||
\(802\) | 15.8155 | 0.558465 | ||||||||
\(803\) | 0.308874 | + | 0.534986i | 0.0108999 | + | 0.0188792i | ||||
\(804\) | −1.10129 | − | 1.45994i | −0.0388394 | − | 0.0514881i | ||||
\(805\) | 3.98113 | − | 6.89553i | 0.140317 | − | 0.243035i | ||||
\(806\) | 4.11644 | − | 7.12989i | 0.144996 | − | 0.251140i | ||||
\(807\) | −38.0418 | + | 4.69023i | −1.33913 | + | 0.165104i | ||||
\(808\) | −0.734191 | − | 1.27166i | −0.0258287 | − | 0.0447367i | ||||
\(809\) | −30.8539 | −1.08476 | −0.542382 | − | 0.840132i | \(-0.682478\pi\) | ||||
−0.542382 | + | 0.840132i | \(0.682478\pi\) | |||||||
\(810\) | 7.93807 | − | 4.24111i | 0.278915 | − | 0.149018i | ||||
\(811\) | 18.9804 | 0.666490 | 0.333245 | − | 0.942840i | \(-0.391856\pi\) | ||||
0.333245 | + | 0.942840i | \(0.391856\pi\) | |||||||
\(812\) | −4.54307 | − | 7.86882i | −0.159430 | − | 0.276141i | ||||
\(813\) | 3.66933 | − | 0.452398i | 0.128689 | − | 0.0158663i | ||||
\(814\) | 0.191126 | − | 0.331040i | 0.00669896 | − | 0.0116029i | ||||
\(815\) | −2.93436 | + | 5.08246i | −0.102786 | + | 0.178031i | ||||
\(816\) | −6.07097 | − | 8.04809i | −0.212527 | − | 0.281739i | ||||
\(817\) | −6.97820 | − | 12.0866i | −0.244136 | − | 0.422857i | ||||
\(818\) | 17.9139 | 0.626344 | ||||||||
\(819\) | 11.0295 | − | 2.76168i | 0.385403 | − | 0.0965009i | ||||
\(820\) | −3.38225 | −0.118113 | ||||||||
\(821\) | −3.59888 | − | 6.23345i | −0.125602 | − | 0.217549i | 0.796366 | − | 0.604815i | \(-0.206753\pi\) |
−0.921968 | + | 0.387266i | \(0.873420\pi\) | |||||||
\(822\) | −5.38727 | + | 12.7093i | −0.187902 | + | 0.443286i | ||||
\(823\) | −14.1460 | + | 24.5015i | −0.493098 | + | 0.854070i | −0.999968 | − | 0.00795179i | \(-0.997469\pi\) |
0.506871 | + | 0.862022i | \(0.330802\pi\) | |||||||
\(824\) | −3.74323 | + | 6.48347i | −0.130402 | + | 0.225862i | ||||
\(825\) | 0.0582214 | − | 0.137352i | 0.00202701 | − | 0.00478197i | ||||
\(826\) | 6.43436 | + | 11.1446i | 0.223880 | + | 0.387772i | ||||
\(827\) | −4.46096 | −0.155123 | −0.0775615 | − | 0.996988i | \(-0.524713\pi\) | ||||
−0.0775615 | + | 0.996988i | \(0.524713\pi\) | |||||||
\(828\) | −16.6103 | − | 17.1661i | −0.577249 | − | 0.596565i | ||||
\(829\) | −10.8613 | −0.377229 | −0.188614 | − | 0.982051i | \(-0.560400\pi\) | ||||
−0.188614 | + | 0.982051i | \(0.560400\pi\) | |||||||
\(830\) | 4.43807 | + | 7.68696i | 0.154048 | + | 0.266818i | ||||
\(831\) | 1.84322 | + | 2.44349i | 0.0639404 | + | 0.0847637i | ||||
\(832\) | 1.89500 | − | 3.28224i | 0.0656975 | − | 0.113791i | ||||
\(833\) | 2.91016 | − | 5.04055i | 0.100831 | − | 0.174645i | ||||
\(834\) | 12.0332 | − | 1.48360i | 0.416677 | − | 0.0513728i | ||||
\(835\) | 8.00904 | + | 13.8721i | 0.277164 | + | 0.480063i | ||||
\(836\) | −0.141948 | −0.00490937 | ||||||||
\(837\) | 1.74903 | − | 11.1511i | 0.0604552 | − | 0.385437i | ||||
\(838\) | 6.05582 | 0.209195 | ||||||||
\(839\) | 0.981134 | + | 1.69937i | 0.0338725 | + | 0.0586689i | 0.882465 | − | 0.470379i | \(-0.155883\pi\) |
−0.848592 | + | 0.529048i | \(0.822549\pi\) | |||||||
\(840\) | 1.71903 | − | 0.211943i | 0.0593123 | − | 0.00731272i | ||||
\(841\) | −26.7789 | + | 46.3824i | −0.923410 | + | 1.59939i | ||||
\(842\) | −7.10500 | + | 12.3062i | −0.244854 | + | 0.424100i | ||||
\(843\) | 19.0131 | + | 25.2050i | 0.654845 | + | 0.868106i | ||||
\(844\) | −14.1723 | − | 24.5471i | −0.487829 | − | 0.844945i | ||||
\(845\) | 1.36417 | 0.0469287 | ||||||||
\(846\) | −8.52420 | + | 29.8399i | −0.293068 | + | 1.02592i | ||||
\(847\) | 10.9926 | 0.377710 | ||||||||
\(848\) | 6.39130 | + | 11.0700i | 0.219478 | + | 0.380147i | ||||
\(849\) | −9.16965 | + | 21.6324i | −0.314702 | + | 0.742421i | ||||
\(850\) | 2.91016 | − | 5.04055i | 0.0998177 | − | 0.172889i | ||||
\(851\) | 17.6686 | − | 30.6028i | 0.605670 | − | 1.04905i | ||||
\(852\) | −10.8277 | + | 25.5440i | −0.370952 | + | 0.875124i | ||||
\(853\) | 10.3216 | + | 17.8776i | 0.353406 | + | 0.612117i | 0.986844 | − | 0.161677i | \(-0.0516902\pi\) |
−0.633438 | + | 0.773793i | \(0.718357\pi\) | |||||||
\(854\) | −0.438069 | −0.0149904 | ||||||||
\(855\) | 1.35805 | − | 4.75401i | 0.0464444 | − | 0.162584i | ||||
\(856\) | −0.351939 | −0.0120290 | ||||||||
\(857\) | −11.2305 | − | 19.4518i | −0.383626 | − | 0.664460i | 0.607952 | − | 0.793974i | \(-0.291991\pi\) |
−0.991578 | + | 0.129514i | \(0.958658\pi\) | |||||||
\(858\) | −0.340492 | − | 0.451379i | −0.0116242 | − | 0.0154098i | ||||
\(859\) | −13.0070 | + | 22.5287i | −0.443792 | + | 0.768670i | −0.997967 | − | 0.0637301i | \(-0.979700\pi\) |
0.554175 | + | 0.832400i | \(0.313034\pi\) | |||||||
\(860\) | 4.23419 | − | 7.33383i | 0.144385 | − | 0.250082i | ||||
\(861\) | −5.81421 | + | 0.716844i | −0.198148 | + | 0.0244300i | ||||
\(862\) | 7.79001 | + | 13.4927i | 0.265329 | + | 0.459563i | ||||
\(863\) | −56.3052 | −1.91665 | −0.958326 | − | 0.285676i | \(-0.907782\pi\) | ||||
−0.958326 | + | 0.285676i | \(0.907782\pi\) | |||||||
\(864\) | 0.805165 | − | 5.13339i | 0.0273923 | − | 0.174642i | ||||
\(865\) | −6.51678 | −0.221577 | ||||||||
\(866\) | 18.3384 | + | 31.7631i | 0.623164 | + | 1.07935i | ||||
\(867\) | −29.0107 | + | 3.57677i | −0.985254 | + | 0.121474i | ||||
\(868\) | 1.08613 | − | 1.88123i | 0.0368657 | − | 0.0638532i | ||||
\(869\) | 0.561931 | − | 0.973292i | 0.0190622 | − | 0.0330167i | ||||
\(870\) | −9.47743 | − | 12.5639i | −0.321315 | − | 0.425956i | ||||
\(871\) | −2.00078 | − | 3.46545i | −0.0677938 | − | 0.117422i | ||||
\(872\) | 8.38225 | 0.283859 | ||||||||
\(873\) | −16.5571 | − | 17.1112i | −0.560374 | − | 0.579125i | ||||
\(874\) | −13.1223 | −0.443869 | ||||||||
\(875\) | 0.500000 | + | 0.866025i | 0.0169031 | + | 0.0292770i | ||||
\(876\) | −4.84823 | + | 11.4376i | −0.163807 | + | 0.386441i | ||||
\(877\) | −21.2297 | + | 36.7709i | −0.716876 | + | 1.24167i | 0.245355 | + | 0.969433i | \(0.421095\pi\) |
−0.962231 | + | 0.272233i | \(0.912238\pi\) | |||||||
\(878\) | 8.85727 | − | 15.3412i | 0.298918 | − | 0.517742i | ||||
\(879\) | 15.7119 | − | 37.0665i | 0.529950 | − | 1.25022i | ||||
\(880\) | −0.0430651 | − | 0.0745909i | −0.00145172 | − | 0.00251446i | ||||
\(881\) | 45.6358 | 1.53751 | 0.768755 | − | 0.639543i | \(-0.220876\pi\) | ||||
0.768755 | + | 0.639543i | \(0.220876\pi\) | |||||||
\(882\) | 2.91016 | − | 0.728674i | 0.0979902 | − | 0.0245357i | ||||
\(883\) | −3.19190 | −0.107416 | −0.0537081 | − | 0.998557i | \(-0.517104\pi\) | ||||
−0.0537081 | + | 0.998557i | \(0.517104\pi\) | |||||||
\(884\) | −11.0295 | − | 19.1037i | −0.370963 | − | 0.642527i | ||||
\(885\) | 13.4229 | + | 17.7943i | 0.451206 | + | 0.598149i | ||||
\(886\) | −18.9307 | + | 32.7888i | −0.635988 | + | 1.10156i | ||||
\(887\) | 24.4487 | − | 42.3465i | 0.820908 | − | 1.42185i | −0.0840984 | − | 0.996457i | \(-0.526801\pi\) |
0.905007 | − | 0.425397i | \(-0.139866\pi\) | |||||||
\(888\) | 7.62920 | − | 0.940616i | 0.256019 | − | 0.0315650i | ||||
\(889\) | −2.92532 | − | 5.06680i | −0.0981120 | − | 0.169935i | ||||
\(890\) | −2.00000 | −0.0670402 | ||||||||
\(891\) | −0.658202 | − | 0.409464i | −0.0220506 | − | 0.0137176i | ||||
\(892\) | −2.49869 | −0.0836625 | ||||||||
\(893\) | 8.52420 | + | 14.7643i | 0.285251 | + | 0.494070i | ||||
\(894\) | 18.5046 | − | 2.28146i | 0.618885 | − | 0.0763034i | ||||
\(895\) | 0.503709 | − | 0.872450i | 0.0168371 | − | 0.0291628i | ||||
\(896\) | 0.500000 | − | 0.866025i | 0.0167038 | − | 0.0289319i | ||||
\(897\) | −31.4766 | − | 41.7275i | −1.05097 | − | 1.39324i | ||||
\(898\) | 19.3482 | + | 33.5121i | 0.645659 | + | 1.11831i | ||||
\(899\) | −19.7374 | −0.658281 | ||||||||
\(900\) | 2.91016 | − | 0.728674i | 0.0970054 | − | 0.0242891i | ||||
\(901\) | 74.3988 | 2.47858 | ||||||||
\(902\) | 0.145657 | + | 0.252285i | 0.00484985 | + | 0.00840018i | ||||
\(903\) | 5.72437 | − | 13.5045i | 0.190495 | − | 0.449402i | ||||
\(904\) | 2.76210 | − | 4.78410i | 0.0918661 | − | 0.159117i | ||||
\(905\) | −9.99258 | + | 17.3077i | −0.332165 | + | 0.575326i | ||||
\(906\) | 3.65548 | − | 8.62374i | 0.121445 | − | 0.286505i | ||||
\(907\) | −3.35565 | − | 5.81215i | −0.111422 | − | 0.192989i | 0.804922 | − | 0.593381i | \(-0.202207\pi\) |
−0.916344 | + | 0.400392i | \(0.868874\pi\) | |||||||
\(908\) | −15.2510 | −0.506121 | ||||||||
\(909\) | −3.06324 | − | 3.16574i | −0.101601 | − | 0.105001i | ||||
\(910\) | 3.79001 | 0.125638 | ||||||||
\(911\) | −13.5029 | − | 23.3878i | −0.447372 | − | 0.774871i | 0.550842 | − | 0.834610i | \(-0.314307\pi\) |
−0.998214 | + | 0.0597384i | \(0.980973\pi\) | |||||||
\(912\) | −1.71903 | − | 2.27887i | −0.0569229 | − | 0.0754608i | ||||
\(913\) | 0.382252 | − | 0.662080i | 0.0126507 | − | 0.0219116i | ||||
\(914\) | 0.488553 | − | 0.846198i | 0.0161599 | − | 0.0279898i | ||||
\(915\) | −0.753056 | + | 0.0928456i | −0.0248953 | + | 0.00306938i | ||||
\(916\) | −12.4471 | − | 21.5590i | −0.411264 | − | 0.712330i | ||||
\(917\) | −6.05582 | −0.199981 | ||||||||
\(918\) | −23.5319 | − | 18.9975i | −0.776670 | − | 0.627010i | ||||
\(919\) | −46.7167 | −1.54104 | −0.770522 | − | 0.637414i | \(-0.780004\pi\) | ||||
−0.770522 | + | 0.637414i | \(0.780004\pi\) | |||||||
\(920\) | −3.98113 | − | 6.89553i | −0.131254 | − | 0.227339i | ||||
\(921\) | 21.2645 | − | 2.62174i | 0.700689 | − | 0.0863892i | ||||
\(922\) | 12.6194 | − | 21.8574i | 0.415597 | − | 0.719835i | ||||
\(923\) | −30.3543 | + | 52.5753i | −0.999125 | + | 1.73054i | ||||
\(924\) | −0.0898394 | − | 0.119097i | −0.00295550 | − | 0.00391801i | ||||
\(925\) | 2.21903 | + | 3.84348i | 0.0729614 | + | 0.126373i | ||||
\(926\) | −17.2355 | −0.566394 | ||||||||
\(927\) | −6.16908 | + | 21.5955i | −0.202619 | + | 0.709291i | ||||
\(928\) | −9.08613 | −0.298267 | ||||||||
\(929\) | −5.38225 | − | 9.32233i | −0.176586 | − | 0.305856i | 0.764123 | − | 0.645071i | \(-0.223172\pi\) |
−0.940709 | + | 0.339215i | \(0.889839\pi\) | |||||||
\(930\) | 1.46838 | − | 3.46410i | 0.0481501 | − | 0.113592i | ||||
\(931\) | 0.824030 | − | 1.42726i | 0.0270065 | − | 0.0467766i | ||||
\(932\) | −14.4737 | + | 25.0692i | −0.474102 | + | 0.821169i | ||||
\(933\) | 6.28390 | − | 14.8245i | 0.205726 | − | 0.485333i | ||||
\(934\) | −4.35968 | − | 7.55118i | −0.142653 | − | 0.247082i | ||||
\(935\) | −0.501305 | −0.0163944 | ||||||||
\(936\) | 3.12308 | − | 10.9327i | 0.102081 | − | 0.357346i | ||||
\(937\) | −20.7449 | −0.677705 | −0.338853 | − | 0.940840i | \(-0.610039\pi\) | ||||
−0.338853 | + | 0.940840i | \(0.610039\pi\) | |||||||
\(938\) | −0.527909 | − | 0.914365i | −0.0172368 | − | 0.0298551i | ||||
\(939\) | −21.4081 | − | 28.3800i | −0.698626 | − | 0.926145i | ||||
\(940\) | −5.17226 | + | 8.95862i | −0.168701 | + | 0.292198i | ||||
\(941\) | −19.3142 | + | 33.4532i | −0.629625 | + | 1.09054i | 0.358002 | + | 0.933721i | \(0.383458\pi\) |
−0.987627 | + | 0.156822i | \(0.949875\pi\) | |||||||
\(942\) | −19.9713 | + | 2.46230i | −0.650701 | + | 0.0802260i | ||||
\(943\) | 13.4652 | + | 23.3224i | 0.438487 | + | 0.759482i | ||||
\(944\) | 12.8687 | 0.418841 | ||||||||
\(945\) | 4.84823 | − | 1.86940i | 0.157713 | − | 0.0608117i | ||||
\(946\) | −0.729383 | −0.0237143 | ||||||||
\(947\) | 6.93807 | + | 12.0171i | 0.225457 | + | 0.390503i | 0.956456 | − | 0.291875i | \(-0.0942792\pi\) |
−0.730999 | + | 0.682378i | \(0.760946\pi\) | |||||||
\(948\) | 22.4307 | − | 2.76551i | 0.728514 | − | 0.0898197i | ||||
\(949\) | −13.5915 | + | 23.5411i | −0.441198 | + | 0.764177i | ||||
\(950\) | 0.824030 | − | 1.42726i | 0.0267351 | − | 0.0463065i | ||||
\(951\) | −26.5686 | − | 35.2211i | −0.861545 | − | 1.14212i | ||||
\(952\) | −2.91016 | − | 5.04055i | −0.0943188 | − | 0.163365i | ||||
\(953\) | −15.9500 | −0.516673 | −0.258336 | − | 0.966055i | \(-0.583174\pi\) | ||||
−0.258336 | + | 0.966055i | \(0.583174\pi\) | |||||||
\(954\) | 26.6661 | + | 27.5584i | 0.863348 | + | 0.892238i | ||||
\(955\) | 3.22066 | 0.104218 | ||||||||
\(956\) | 15.2584 | + | 26.4283i | 0.493492 | + | 0.854753i | ||||
\(957\) | −0.529007 | + | 1.24800i | −0.0171004 | + | 0.0403420i | ||||
\(958\) | 2.89500 | − | 5.01429i | 0.0935333 | − | 0.162005i | ||||
\(959\) | −3.98484 | + | 6.90195i | −0.128677 | + | 0.222876i | ||||
\(960\) | 0.675970 | − | 1.59470i | 0.0218168 | − | 0.0514687i | ||||
\(961\) | 13.1406 | + | 22.7603i | 0.423892 | + | 0.734202i | ||||
\(962\) | 16.8203 | 0.542309 | ||||||||
\(963\) | −1.02420 | + | 0.256449i | −0.0330044 | + | 0.00826395i | ||||
\(964\) | 21.7826 | 0.701570 | ||||||||
\(965\) | 7.50904 | + | 13.0060i | 0.241725 | + | 0.418679i | ||||
\(966\) | −8.30516 | − | 11.0099i | −0.267214 | − | 0.354237i | ||||
\(967\) | −24.7268 | + | 42.8280i | −0.795159 | + | 1.37726i | 0.127579 | + | 0.991828i | \(0.459280\pi\) |
−0.922738 | + | 0.385428i | \(0.874054\pi\) | |||||||
\(968\) | 5.49629 | − | 9.51985i | 0.176657 | − | 0.305980i | ||||
\(969\) | −16.4894 | + | 2.03301i | −0.529716 | + | 0.0653096i | ||||
\(970\) | −3.96838 | − | 6.87344i | −0.127417 | − | 0.220693i | ||||
\(971\) | 10.2477 | 0.328865 | 0.164433 | − | 0.986388i | \(-0.447421\pi\) | ||||
0.164433 | + | 0.986388i | \(0.447421\pi\) | |||||||
\(972\) | −1.39741 | − | 15.5257i | −0.0448219 | − | 0.497987i | ||||
\(973\) | 7.00000 | 0.224410 | ||||||||
\(974\) | −19.0787 | − | 33.0453i | −0.611321 | − | 1.05884i | ||||
\(975\) | 6.51516 | − | 0.803265i | 0.208652 | − | 0.0257251i | ||||
\(976\) | −0.219035 | + | 0.379379i | −0.00701113 | + | 0.0121436i | ||||
\(977\) | −3.21292 | + | 5.56494i | −0.102790 | + | 0.178038i | −0.912833 | − | 0.408332i | \(-0.866110\pi\) |
0.810043 | + | 0.586371i | \(0.199444\pi\) | |||||||
\(978\) | 6.12146 | + | 8.11501i | 0.195743 | + | 0.259489i | ||||
\(979\) | 0.0861302 | + | 0.149182i | 0.00275273 | + | 0.00476787i | ||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 24.3937 | − | 6.10793i | 0.778831 | − | 0.195011i | ||||
\(982\) | −4.12711 | −0.131701 | ||||||||
\(983\) | −20.1723 | − | 34.9394i | −0.643395 | − | 1.11439i | −0.984670 | − | 0.174429i | \(-0.944192\pi\) |
0.341274 | − | 0.939964i | \(-0.389141\pi\) | |||||||
\(984\) | −2.28630 | + | 5.39367i | −0.0728846 | + | 0.171944i | ||||
\(985\) | −1.74323 | + | 3.01937i | −0.0555441 | + | 0.0962051i | ||||
\(986\) | −26.4421 | + | 45.7991i | −0.842088 | + | 1.45854i | ||||
\(987\) | −6.99258 | + | 16.4964i | −0.222576 | + | 0.525086i | ||||
\(988\) | −3.12308 | − | 5.40934i | −0.0993585 | − | 0.172094i | ||||
\(989\) | −67.4275 | −2.14407 | ||||||||
\(990\) | −0.179679 | − | 0.185691i | −0.00571057 | − | 0.00590165i | ||||
\(991\) | 16.5168 | 0.524673 | 0.262336 | − | 0.964976i | \(-0.415507\pi\) | ||||
0.262336 | + | 0.964976i | \(0.415507\pi\) | |||||||
\(992\) | −1.08613 | − | 1.88123i | −0.0344847 | − | 0.0597292i | ||||
\(993\) | 9.25839 | + | 12.2735i | 0.293806 | + | 0.389489i | ||||
\(994\) | −8.00904 | + | 13.8721i | −0.254031 | + | 0.439995i | ||||
\(995\) | 4.15339 | − | 7.19389i | 0.131671 | − | 0.228062i | ||||
\(996\) | 15.2584 | − | 1.88123i | 0.483481 | − | 0.0596091i | ||||
\(997\) | −3.72938 | − | 6.45948i | −0.118111 | − | 0.204574i | 0.800908 | − | 0.598787i | \(-0.204350\pi\) |
−0.919019 | + | 0.394213i | \(0.871017\pi\) | |||||||
\(998\) | 17.3674 | 0.549756 | ||||||||
\(999\) | 21.5168 | − | 8.29654i | 0.680761 | − | 0.262491i |
(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 | 630.2.j.i.211.1 | ✓ | 6 | |
3.2 | odd | 2 | 1890.2.j.k.631.3 | 6 | |||
9.2 | odd | 6 | 1890.2.j.k.1261.3 | 6 | |||
9.4 | even | 3 | 5670.2.a.bs.1.3 | 3 | |||
9.5 | odd | 6 | 5670.2.a.bo.1.1 | 3 | |||
9.7 | even | 3 | inner | 630.2.j.i.421.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.j.i.211.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
630.2.j.i.421.1 | yes | 6 | 9.7 | even | 3 | inner | |
1890.2.j.k.631.3 | 6 | 3.2 | odd | 2 | |||
1890.2.j.k.1261.3 | 6 | 9.2 | odd | 6 | |||
5670.2.a.bo.1.1 | 3 | 9.5 | odd | 6 | |||
5670.2.a.bs.1.3 | 3 | 9.4 | even | 3 |