Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,3,Mod(577,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.577");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.f (of order \(4\), 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: | \(27.6294988061\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 82x^{5} + 5053x^{4} - 6736x^{3} + 6728x^{2} + 275384x + 5635876 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(-5.39181 + 5.39181i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.577 |
Dual form | 1014.3.f.j.775.1 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | −4.02578 | + | 4.02578i | −0.805157 | + | 0.805157i | −0.983896 | − | 0.178740i | \(-0.942798\pi\) |
0.178740 | + | 0.983896i | \(0.442798\pi\) | |||||||
\(6\) | −1.73205 | + | 1.73205i | −0.288675 | + | 0.288675i | ||||
\(7\) | −3.65976 | − | 3.65976i | −0.522823 | − | 0.522823i | 0.395600 | − | 0.918423i | \(-0.370537\pi\) |
−0.918423 | + | 0.395600i | \(0.870537\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 8.05157i | 0.805157i | ||||||||
\(11\) | 9.31952 | + | 9.31952i | 0.847229 | + | 0.847229i | 0.989787 | − | 0.142558i | \(-0.0455326\pi\) |
−0.142558 | + | 0.989787i | \(0.545533\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −7.31952 | −0.522823 | ||||||||
\(15\) | 6.97286 | − | 6.97286i | 0.464858 | − | 0.464858i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 18.8551i | 1.10912i | 0.832143 | + | 0.554560i | \(0.187114\pi\) | ||||
−0.832143 | + | 0.554560i | \(0.812886\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | 21.4627 | − | 21.4627i | 1.12962 | − | 1.12962i | 0.139379 | − | 0.990239i | \(-0.455489\pi\) |
0.990239 | − | 0.139379i | \(-0.0445107\pi\) | |||||||
\(20\) | 8.05157 | + | 8.05157i | 0.402578 | + | 0.402578i | ||||
\(21\) | 6.33889 | + | 6.33889i | 0.301852 | + | 0.301852i | ||||
\(22\) | 18.6390 | 0.847229 | ||||||||
\(23\) | − | 12.1058i | − | 0.526341i | −0.964749 | − | 0.263170i | \(-0.915232\pi\) | ||
0.964749 | − | 0.263170i | \(-0.0847682\pi\) | |||||||
\(24\) | 3.46410 | + | 3.46410i | 0.144338 | + | 0.144338i | ||||
\(25\) | − | 7.41388i | − | 0.296555i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −7.31952 | + | 7.31952i | −0.261411 | + | 0.261411i | ||||
\(29\) | −36.9444 | −1.27394 | −0.636972 | − | 0.770887i | \(-0.719813\pi\) | ||||
−0.636972 | + | 0.770887i | \(0.719813\pi\) | |||||||
\(30\) | − | 13.9457i | − | 0.464858i | ||||||
\(31\) | 6.48248 | − | 6.48248i | 0.209112 | − | 0.209112i | −0.594778 | − | 0.803890i | \(-0.702760\pi\) |
0.803890 | + | 0.594778i | \(0.202760\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | −16.1419 | − | 16.1419i | −0.489148 | − | 0.489148i | ||||
\(34\) | 18.8551 | + | 18.8551i | 0.554560 | + | 0.554560i | ||||
\(35\) | 29.4668 | 0.841909 | ||||||||
\(36\) | − | 6.00000i | − | 0.166667i | ||||||
\(37\) | −37.1815 | − | 37.1815i | −1.00490 | − | 1.00490i | −0.999988 | − | 0.00491701i | \(-0.998435\pi\) |
−0.00491701 | − | 0.999988i | \(-0.501565\pi\) | |||||||
\(38\) | − | 42.9255i | − | 1.12962i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 16.1031 | 0.402578 | ||||||||
\(41\) | −4.67087 | + | 4.67087i | −0.113924 | + | 0.113924i | −0.761771 | − | 0.647847i | \(-0.775670\pi\) |
0.647847 | + | 0.761771i | \(0.275670\pi\) | |||||||
\(42\) | 12.6778 | 0.301852 | ||||||||
\(43\) | − | 13.6054i | − | 0.316404i | −0.987407 | − | 0.158202i | \(-0.949430\pi\) | ||
0.987407 | − | 0.158202i | \(-0.0505696\pi\) | |||||||
\(44\) | 18.6390 | − | 18.6390i | 0.423614 | − | 0.423614i | ||||
\(45\) | −12.0774 | + | 12.0774i | −0.268386 | + | 0.268386i | ||||
\(46\) | −12.1058 | − | 12.1058i | −0.263170 | − | 0.263170i | ||||
\(47\) | −61.6060 | − | 61.6060i | −1.31077 | − | 1.31077i | −0.920851 | − | 0.389914i | \(-0.872505\pi\) |
−0.389914 | − | 0.920851i | \(-0.627495\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | − | 22.2123i | − | 0.453313i | ||||||
\(50\) | −7.41388 | − | 7.41388i | −0.148278 | − | 0.148278i | ||||
\(51\) | − | 32.6579i | − | 0.640351i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.64409 | 0.0876244 | 0.0438122 | − | 0.999040i | \(-0.486050\pi\) | ||||
0.0438122 | + | 0.999040i | \(0.486050\pi\) | |||||||
\(54\) | −5.19615 | + | 5.19615i | −0.0962250 | + | 0.0962250i | ||||
\(55\) | −75.0367 | −1.36430 | ||||||||
\(56\) | 14.6390i | 0.261411i | ||||||||
\(57\) | −37.1746 | + | 37.1746i | −0.652185 | + | 0.652185i | ||||
\(58\) | −36.9444 | + | 36.9444i | −0.636972 | + | 0.636972i | ||||
\(59\) | 17.6437 | + | 17.6437i | 0.299046 | + | 0.299046i | 0.840640 | − | 0.541594i | \(-0.182179\pi\) |
−0.541594 | + | 0.840640i | \(0.682179\pi\) | |||||||
\(60\) | −13.9457 | − | 13.9457i | −0.232429 | − | 0.232429i | ||||
\(61\) | 38.5426 | 0.631845 | 0.315923 | − | 0.948785i | \(-0.397686\pi\) | ||||
0.315923 | + | 0.948785i | \(0.397686\pi\) | |||||||
\(62\) | − | 12.9650i | − | 0.209112i | ||||||
\(63\) | −10.9793 | − | 10.9793i | −0.174274 | − | 0.174274i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −32.2838 | −0.489148 | ||||||||
\(67\) | 67.2276 | − | 67.2276i | 1.00340 | − | 1.00340i | 0.00340321 | − | 0.999994i | \(-0.498917\pi\) |
0.999994 | − | 0.00340321i | \(-0.00108328\pi\) | |||||||
\(68\) | 37.7101 | 0.554560 | ||||||||
\(69\) | 20.9679i | 0.303883i | ||||||||
\(70\) | 29.4668 | − | 29.4668i | 0.420954 | − | 0.420954i | ||||
\(71\) | −28.7155 | + | 28.7155i | −0.404444 | + | 0.404444i | −0.879796 | − | 0.475352i | \(-0.842321\pi\) |
0.475352 | + | 0.879796i | \(0.342321\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | −60.4486 | − | 60.4486i | −0.828063 | − | 0.828063i | 0.159186 | − | 0.987249i | \(-0.449113\pi\) |
−0.987249 | + | 0.159186i | \(0.949113\pi\) | |||||||
\(74\) | −74.3630 | −1.00490 | ||||||||
\(75\) | 12.8412i | 0.171216i | ||||||||
\(76\) | −42.9255 | − | 42.9255i | −0.564809 | − | 0.564809i | ||||
\(77\) | − | 68.2144i | − | 0.885901i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −94.2854 | −1.19349 | −0.596743 | − | 0.802433i | \(-0.703539\pi\) | ||||
−0.596743 | + | 0.802433i | \(0.703539\pi\) | |||||||
\(80\) | 16.1031 | − | 16.1031i | 0.201289 | − | 0.201289i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 9.34174i | 0.113924i | ||||||||
\(83\) | 63.4890 | − | 63.4890i | 0.764928 | − | 0.764928i | −0.212281 | − | 0.977209i | \(-0.568089\pi\) |
0.977209 | + | 0.212281i | \(0.0680891\pi\) | |||||||
\(84\) | 12.6778 | − | 12.6778i | 0.150926 | − | 0.150926i | ||||
\(85\) | −75.9064 | − | 75.9064i | −0.893016 | − | 0.893016i | ||||
\(86\) | −13.6054 | − | 13.6054i | −0.158202 | − | 0.158202i | ||||
\(87\) | 63.9895 | 0.735512 | ||||||||
\(88\) | − | 37.2781i | − | 0.423614i | ||||||
\(89\) | −110.281 | − | 110.281i | −1.23911 | − | 1.23911i | −0.960366 | − | 0.278743i | \(-0.910082\pi\) |
−0.278743 | − | 0.960366i | \(-0.589918\pi\) | |||||||
\(90\) | 24.1547i | 0.268386i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −24.2117 | −0.263170 | ||||||||
\(93\) | −11.2280 | + | 11.2280i | −0.120731 | + | 0.120731i | ||||
\(94\) | −123.212 | −1.31077 | ||||||||
\(95\) | 172.809i | 1.81904i | ||||||||
\(96\) | 6.92820 | − | 6.92820i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | 107.297 | − | 107.297i | 1.10616 | − | 1.10616i | 0.112507 | − | 0.993651i | \(-0.464112\pi\) |
0.993651 | − | 0.112507i | \(-0.0358882\pi\) | |||||||
\(98\) | −22.2123 | − | 22.2123i | −0.226656 | − | 0.226656i | ||||
\(99\) | 27.9586 | + | 27.9586i | 0.282410 | + | 0.282410i | ||||
\(100\) | −14.8278 | −0.148278 | ||||||||
\(101\) | 45.9730i | 0.455178i | 0.973757 | + | 0.227589i | \(0.0730843\pi\) | ||||
−0.973757 | + | 0.227589i | \(0.926916\pi\) | |||||||
\(102\) | −32.6579 | − | 32.6579i | −0.320176 | − | 0.320176i | ||||
\(103\) | − | 92.8099i | − | 0.901067i | −0.892759 | − | 0.450534i | \(-0.851234\pi\) | ||
0.892759 | − | 0.450534i | \(-0.148766\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −51.0380 | −0.486076 | ||||||||
\(106\) | 4.64409 | − | 4.64409i | 0.0438122 | − | 0.0438122i | ||||
\(107\) | 75.2403 | 0.703181 | 0.351590 | − | 0.936154i | \(-0.385641\pi\) | ||||
0.351590 | + | 0.936154i | \(0.385641\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | 46.0551 | − | 46.0551i | 0.422524 | − | 0.422524i | −0.463548 | − | 0.886072i | \(-0.653424\pi\) |
0.886072 | + | 0.463548i | \(0.153424\pi\) | |||||||
\(110\) | −75.0367 | + | 75.0367i | −0.682152 | + | 0.682152i | ||||
\(111\) | 64.4002 | + | 64.4002i | 0.580182 | + | 0.580182i | ||||
\(112\) | 14.6390 | + | 14.6390i | 0.130706 | + | 0.130706i | ||||
\(113\) | 156.493 | 1.38490 | 0.692449 | − | 0.721467i | \(-0.256532\pi\) | ||||
0.692449 | + | 0.721467i | \(0.256532\pi\) | |||||||
\(114\) | 74.3491i | 0.652185i | ||||||||
\(115\) | 48.7355 | + | 48.7355i | 0.423787 | + | 0.423787i | ||||
\(116\) | 73.8888i | 0.636972i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 35.2875 | 0.299046 | ||||||||
\(119\) | 69.0050 | − | 69.0050i | 0.579874 | − | 0.579874i | ||||
\(120\) | −27.8915 | −0.232429 | ||||||||
\(121\) | 52.7068i | 0.435594i | ||||||||
\(122\) | 38.5426 | − | 38.5426i | 0.315923 | − | 0.315923i | ||||
\(123\) | 8.09018 | − | 8.09018i | 0.0657738 | − | 0.0657738i | ||||
\(124\) | −12.9650 | − | 12.9650i | −0.104556 | − | 0.104556i | ||||
\(125\) | −70.7979 | − | 70.7979i | −0.566383 | − | 0.566383i | ||||
\(126\) | −21.9586 | −0.174274 | ||||||||
\(127\) | 183.377i | 1.44391i | 0.691938 | + | 0.721957i | \(0.256757\pi\) | ||||
−0.691938 | + | 0.721957i | \(0.743243\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 23.5652i | 0.182676i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −151.996 | −1.16027 | −0.580137 | − | 0.814519i | \(-0.697001\pi\) | ||||
−0.580137 | + | 0.814519i | \(0.697001\pi\) | |||||||
\(132\) | −32.2838 | + | 32.2838i | −0.244574 | + | 0.244574i | ||||
\(133\) | −157.097 | −1.18118 | ||||||||
\(134\) | − | 134.455i | − | 1.00340i | ||||||
\(135\) | 20.9186 | − | 20.9186i | 0.154953 | − | 0.154953i | ||||
\(136\) | 37.7101 | − | 37.7101i | 0.277280 | − | 0.277280i | ||||
\(137\) | 170.039 | + | 170.039i | 1.24116 | + | 1.24116i | 0.959520 | + | 0.281642i | \(0.0908791\pi\) |
0.281642 | + | 0.959520i | \(0.409121\pi\) | |||||||
\(138\) | 20.9679 | + | 20.9679i | 0.151942 | + | 0.151942i | ||||
\(139\) | −185.463 | −1.33426 | −0.667132 | − | 0.744940i | \(-0.732478\pi\) | ||||
−0.667132 | + | 0.744940i | \(0.732478\pi\) | |||||||
\(140\) | − | 58.9336i | − | 0.420954i | ||||||
\(141\) | 106.705 | + | 106.705i | 0.756771 | + | 0.756771i | ||||
\(142\) | 57.4311i | 0.404444i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 148.730 | − | 148.730i | 1.02572 | − | 1.02572i | ||||
\(146\) | −120.897 | −0.828063 | ||||||||
\(147\) | 38.4729i | 0.261720i | ||||||||
\(148\) | −74.3630 | + | 74.3630i | −0.502452 | + | 0.502452i | ||||
\(149\) | 12.7760 | − | 12.7760i | 0.0857449 | − | 0.0857449i | −0.662933 | − | 0.748678i | \(-0.730689\pi\) |
0.748678 | + | 0.662933i | \(0.230689\pi\) | |||||||
\(150\) | 12.8412 | + | 12.8412i | 0.0856082 | + | 0.0856082i | ||||
\(151\) | 95.4196 | + | 95.4196i | 0.631918 | + | 0.631918i | 0.948549 | − | 0.316631i | \(-0.102552\pi\) |
−0.316631 | + | 0.948549i | \(0.602552\pi\) | |||||||
\(152\) | −85.8510 | −0.564809 | ||||||||
\(153\) | 56.5652i | 0.369707i | ||||||||
\(154\) | −68.2144 | − | 68.2144i | −0.442951 | − | 0.442951i | ||||
\(155\) | 52.1942i | 0.336736i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −195.116 | −1.24278 | −0.621389 | − | 0.783502i | \(-0.713431\pi\) | ||||
−0.621389 | + | 0.783502i | \(0.713431\pi\) | |||||||
\(158\) | −94.2854 | + | 94.2854i | −0.596743 | + | 0.596743i | ||||
\(159\) | −8.04381 | −0.0505900 | ||||||||
\(160\) | − | 32.2063i | − | 0.201289i | ||||||
\(161\) | −44.3045 | + | 44.3045i | −0.275183 | + | 0.275183i | ||||
\(162\) | 9.00000 | − | 9.00000i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −87.5027 | − | 87.5027i | −0.536826 | − | 0.536826i | 0.385769 | − | 0.922595i | \(-0.373936\pi\) |
−0.922595 | + | 0.385769i | \(0.873936\pi\) | |||||||
\(164\) | 9.34174 | + | 9.34174i | 0.0569618 | + | 0.0569618i | ||||
\(165\) | 129.967 | 0.787682 | ||||||||
\(166\) | − | 126.978i | − | 0.764928i | ||||||
\(167\) | −87.8436 | − | 87.8436i | −0.526010 | − | 0.526010i | 0.393371 | − | 0.919380i | \(-0.371309\pi\) |
−0.919380 | + | 0.393371i | \(0.871309\pi\) | |||||||
\(168\) | − | 25.3556i | − | 0.150926i | ||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −151.813 | −0.893016 | ||||||||
\(171\) | 64.3882 | − | 64.3882i | 0.376539 | − | 0.376539i | ||||
\(172\) | −27.2107 | −0.158202 | ||||||||
\(173\) | − | 119.181i | − | 0.688908i | −0.938803 | − | 0.344454i | \(-0.888064\pi\) | ||
0.938803 | − | 0.344454i | \(-0.111936\pi\) | |||||||
\(174\) | 63.9895 | − | 63.9895i | 0.367756 | − | 0.367756i | ||||
\(175\) | −27.1330 | + | 27.1330i | −0.155046 | + | 0.155046i | ||||
\(176\) | −37.2781 | − | 37.2781i | −0.211807 | − | 0.211807i | ||||
\(177\) | −30.5598 | − | 30.5598i | −0.172654 | − | 0.172654i | ||||
\(178\) | −220.561 | −1.23911 | ||||||||
\(179\) | − | 214.511i | − | 1.19838i | −0.800605 | − | 0.599192i | \(-0.795488\pi\) | ||
0.800605 | − | 0.599192i | \(-0.204512\pi\) | |||||||
\(180\) | 24.1547 | + | 24.1547i | 0.134193 | + | 0.134193i | ||||
\(181\) | 343.720i | 1.89901i | 0.313755 | + | 0.949504i | \(0.398413\pi\) | ||||
−0.313755 | + | 0.949504i | \(0.601587\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −66.7577 | −0.364796 | ||||||||
\(184\) | −24.2117 | + | 24.2117i | −0.131585 | + | 0.131585i | ||||
\(185\) | 299.369 | 1.61821 | ||||||||
\(186\) | 22.4560i | 0.120731i | ||||||||
\(187\) | −175.720 | + | 175.720i | −0.939679 | + | 0.939679i | ||||
\(188\) | −123.212 | + | 123.212i | −0.655383 | + | 0.655383i | ||||
\(189\) | 19.0167 | + | 19.0167i | 0.100617 | + | 0.100617i | ||||
\(190\) | 172.809 | + | 172.809i | 0.909520 | + | 0.909520i | ||||
\(191\) | 249.718 | 1.30742 | 0.653712 | − | 0.756743i | \(-0.273211\pi\) | ||||
0.653712 | + | 0.756743i | \(0.273211\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | −95.8199 | − | 95.8199i | −0.496476 | − | 0.496476i | 0.413863 | − | 0.910339i | \(-0.364179\pi\) |
−0.910339 | + | 0.413863i | \(0.864179\pi\) | |||||||
\(194\) | − | 214.595i | − | 1.10616i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −44.4246 | −0.226656 | ||||||||
\(197\) | −2.48643 | + | 2.48643i | −0.0126215 | + | 0.0126215i | −0.713389 | − | 0.700768i | \(-0.752841\pi\) |
0.700768 | + | 0.713389i | \(0.252841\pi\) | |||||||
\(198\) | 55.9171 | 0.282410 | ||||||||
\(199\) | 265.195i | 1.33264i | 0.745666 | + | 0.666319i | \(0.232131\pi\) | ||||
−0.745666 | + | 0.666319i | \(0.767869\pi\) | |||||||
\(200\) | −14.8278 | + | 14.8278i | −0.0741388 | + | 0.0741388i | ||||
\(201\) | −116.442 | + | 116.442i | −0.579312 | + | 0.579312i | ||||
\(202\) | 45.9730 | + | 45.9730i | 0.227589 | + | 0.227589i | ||||
\(203\) | 135.208 | + | 135.208i | 0.666047 | + | 0.666047i | ||||
\(204\) | −65.3158 | −0.320176 | ||||||||
\(205\) | − | 37.6078i | − | 0.183453i | ||||||
\(206\) | −92.8099 | − | 92.8099i | −0.450534 | − | 0.450534i | ||||
\(207\) | − | 36.3175i | − | 0.175447i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 400.045 | 1.91409 | ||||||||
\(210\) | −51.0380 | + | 51.0380i | −0.243038 | + | 0.243038i | ||||
\(211\) | −13.7413 | −0.0651248 | −0.0325624 | − | 0.999470i | \(-0.510367\pi\) | ||||
−0.0325624 | + | 0.999470i | \(0.510367\pi\) | |||||||
\(212\) | − | 9.28819i | − | 0.0438122i | ||||||
\(213\) | 49.7368 | − | 49.7368i | 0.233506 | − | 0.233506i | ||||
\(214\) | 75.2403 | − | 75.2403i | 0.351590 | − | 0.351590i | ||||
\(215\) | 54.7722 | + | 54.7722i | 0.254755 | + | 0.254755i | ||||
\(216\) | 10.3923 | + | 10.3923i | 0.0481125 | + | 0.0481125i | ||||
\(217\) | −47.4487 | −0.218657 | ||||||||
\(218\) | − | 92.1103i | − | 0.422524i | ||||||
\(219\) | 104.700 | + | 104.700i | 0.478082 | + | 0.478082i | ||||
\(220\) | 150.073i | 0.682152i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 128.800 | 0.580182 | ||||||||
\(223\) | 72.3147 | − | 72.3147i | 0.324281 | − | 0.324281i | −0.526126 | − | 0.850407i | \(-0.676356\pi\) |
0.850407 | + | 0.526126i | \(0.176356\pi\) | |||||||
\(224\) | 29.2781 | 0.130706 | ||||||||
\(225\) | − | 22.2417i | − | 0.0988518i | ||||||
\(226\) | 156.493 | − | 156.493i | 0.692449 | − | 0.692449i | ||||
\(227\) | 163.921 | − | 163.921i | 0.722119 | − | 0.722119i | −0.246917 | − | 0.969037i | \(-0.579418\pi\) |
0.969037 | + | 0.246917i | \(0.0794176\pi\) | |||||||
\(228\) | 74.3491 | + | 74.3491i | 0.326093 | + | 0.326093i | ||||
\(229\) | −306.032 | − | 306.032i | −1.33639 | − | 1.33639i | −0.899533 | − | 0.436854i | \(-0.856093\pi\) |
−0.436854 | − | 0.899533i | \(-0.643907\pi\) | |||||||
\(230\) | 97.4710 | 0.423787 | ||||||||
\(231\) | 118.151i | 0.511475i | ||||||||
\(232\) | 73.8888 | + | 73.8888i | 0.318486 | + | 0.318486i | ||||
\(233\) | − | 156.892i | − | 0.673356i | −0.941620 | − | 0.336678i | \(-0.890697\pi\) | ||
0.941620 | − | 0.336678i | \(-0.109303\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 496.025 | 2.11074 | ||||||||
\(236\) | 35.2875 | − | 35.2875i | 0.149523 | − | 0.149523i | ||||
\(237\) | 163.307 | 0.689059 | ||||||||
\(238\) | − | 138.010i | − | 0.579874i | ||||||
\(239\) | −10.5731 | + | 10.5731i | −0.0442390 | + | 0.0442390i | −0.728880 | − | 0.684641i | \(-0.759959\pi\) |
0.684641 | + | 0.728880i | \(0.259959\pi\) | |||||||
\(240\) | −27.8915 | + | 27.8915i | −0.116214 | + | 0.116214i | ||||
\(241\) | −166.546 | − | 166.546i | −0.691062 | − | 0.691062i | 0.271403 | − | 0.962466i | \(-0.412512\pi\) |
−0.962466 | + | 0.271403i | \(0.912512\pi\) | |||||||
\(242\) | 52.7068 | + | 52.7068i | 0.217797 | + | 0.217797i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − | 77.0851i | − | 0.315923i | ||||||
\(245\) | 89.4220 | + | 89.4220i | 0.364988 | + | 0.364988i | ||||
\(246\) | − | 16.1804i | − | 0.0657738i | ||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −25.9299 | −0.104556 | ||||||||
\(249\) | −109.966 | + | 109.966i | −0.441631 | + | 0.441631i | ||||
\(250\) | −141.596 | −0.566383 | ||||||||
\(251\) | − | 76.9248i | − | 0.306473i | −0.988190 | − | 0.153237i | \(-0.951030\pi\) | ||
0.988190 | − | 0.153237i | \(-0.0489697\pi\) | |||||||
\(252\) | −21.9586 | + | 21.9586i | −0.0871371 | + | 0.0871371i | ||||
\(253\) | 112.821 | − | 112.821i | 0.445931 | − | 0.445931i | ||||
\(254\) | 183.377 | + | 183.377i | 0.721957 | + | 0.721957i | ||||
\(255\) | 131.474 | + | 131.474i | 0.515583 | + | 0.515583i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 63.5214i | 0.247165i | 0.992334 | + | 0.123583i | \(0.0394384\pi\) | ||||
−0.992334 | + | 0.123583i | \(0.960562\pi\) | |||||||
\(258\) | 23.5652 | + | 23.5652i | 0.0913378 | + | 0.0913378i | ||||
\(259\) | 272.151i | 1.05077i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −110.833 | −0.424648 | ||||||||
\(262\) | −151.996 | + | 151.996i | −0.580137 | + | 0.580137i | ||||
\(263\) | 225.177 | 0.856188 | 0.428094 | − | 0.903734i | \(-0.359185\pi\) | ||||
0.428094 | + | 0.903734i | \(0.359185\pi\) | |||||||
\(264\) | 64.5675i | 0.244574i | ||||||||
\(265\) | −18.6961 | + | 18.6961i | −0.0705514 | + | 0.0705514i | ||||
\(266\) | −157.097 | + | 157.097i | −0.590590 | + | 0.590590i | ||||
\(267\) | 191.012 | + | 191.012i | 0.715400 | + | 0.715400i | ||||
\(268\) | −134.455 | − | 134.455i | −0.501699 | − | 0.501699i | ||||
\(269\) | 22.1441 | 0.0823200 | 0.0411600 | − | 0.999153i | \(-0.486895\pi\) | ||||
0.0411600 | + | 0.999153i | \(0.486895\pi\) | |||||||
\(270\) | − | 41.8372i | − | 0.154953i | ||||||
\(271\) | 105.317 | + | 105.317i | 0.388623 | + | 0.388623i | 0.874196 | − | 0.485573i | \(-0.161389\pi\) |
−0.485573 | + | 0.874196i | \(0.661389\pi\) | |||||||
\(272\) | − | 75.4202i | − | 0.277280i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 340.078 | 1.24116 | ||||||||
\(275\) | 69.0938 | − | 69.0938i | 0.251250 | − | 0.251250i | ||||
\(276\) | 41.9359 | 0.151942 | ||||||||
\(277\) | − | 202.590i | − | 0.731373i | −0.930738 | − | 0.365687i | \(-0.880834\pi\) | ||
0.930738 | − | 0.365687i | \(-0.119166\pi\) | |||||||
\(278\) | −185.463 | + | 185.463i | −0.667132 | + | 0.667132i | ||||
\(279\) | 19.4474 | − | 19.4474i | 0.0697041 | − | 0.0697041i | ||||
\(280\) | −58.9336 | − | 58.9336i | −0.210477 | − | 0.210477i | ||||
\(281\) | −44.0655 | − | 44.0655i | −0.156817 | − | 0.156817i | 0.624338 | − | 0.781154i | \(-0.285369\pi\) |
−0.781154 | + | 0.624338i | \(0.785369\pi\) | |||||||
\(282\) | 213.409 | 0.756771 | ||||||||
\(283\) | − | 140.882i | − | 0.497817i | −0.968527 | − | 0.248909i | \(-0.919928\pi\) | ||
0.968527 | − | 0.248909i | \(-0.0800719\pi\) | |||||||
\(284\) | 57.4311 | + | 57.4311i | 0.202222 | + | 0.202222i | ||||
\(285\) | − | 299.314i | − | 1.05022i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.1885 | 0.119124 | ||||||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | −66.5131 | −0.230149 | ||||||||
\(290\) | − | 297.460i | − | 1.02572i | ||||||
\(291\) | −185.844 | + | 185.844i | −0.638641 | + | 0.638641i | ||||
\(292\) | −120.897 | + | 120.897i | −0.414031 | + | 0.414031i | ||||
\(293\) | −121.000 | − | 121.000i | −0.412970 | − | 0.412970i | 0.469802 | − | 0.882772i | \(-0.344325\pi\) |
−0.882772 | + | 0.469802i | \(0.844325\pi\) | |||||||
\(294\) | 38.4729 | + | 38.4729i | 0.130860 | + | 0.130860i | ||||
\(295\) | −142.060 | −0.481558 | ||||||||
\(296\) | 148.726i | 0.502452i | ||||||||
\(297\) | −48.4256 | − | 48.4256i | −0.163049 | − | 0.163049i | ||||
\(298\) | − | 25.5520i | − | 0.0857449i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 25.6824 | 0.0856082 | ||||||||
\(301\) | −49.7923 | + | 49.7923i | −0.165423 | + | 0.165423i | ||||
\(302\) | 190.839 | 0.631918 | ||||||||
\(303\) | − | 79.6276i | − | 0.262797i | ||||||
\(304\) | −85.8510 | + | 85.8510i | −0.282405 | + | 0.282405i | ||||
\(305\) | −155.164 | + | 155.164i | −0.508735 | + | 0.508735i | ||||
\(306\) | 56.5652 | + | 56.5652i | 0.184853 | + | 0.184853i | ||||
\(307\) | 252.758 | + | 252.758i | 0.823317 | + | 0.823317i | 0.986582 | − | 0.163265i | \(-0.0522026\pi\) |
−0.163265 | + | 0.986582i | \(0.552203\pi\) | |||||||
\(308\) | −136.429 | −0.442951 | ||||||||
\(309\) | 160.752i | 0.520231i | ||||||||
\(310\) | 52.1942 | + | 52.1942i | 0.168368 | + | 0.168368i | ||||
\(311\) | 209.742i | 0.674411i | 0.941431 | + | 0.337206i | \(0.109482\pi\) | ||||
−0.941431 | + | 0.337206i | \(0.890518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 386.143 | 1.23368 | 0.616842 | − | 0.787087i | \(-0.288412\pi\) | ||||
0.616842 | + | 0.787087i | \(0.288412\pi\) | |||||||
\(314\) | −195.116 | + | 195.116i | −0.621389 | + | 0.621389i | ||||
\(315\) | 88.4004 | 0.280636 | ||||||||
\(316\) | 188.571i | 0.596743i | ||||||||
\(317\) | 114.759 | − | 114.759i | 0.362016 | − | 0.362016i | −0.502538 | − | 0.864555i | \(-0.667600\pi\) |
0.864555 | + | 0.502538i | \(0.167600\pi\) | |||||||
\(318\) | −8.04381 | + | 8.04381i | −0.0252950 | + | 0.0252950i | ||||
\(319\) | −344.304 | − | 344.304i | −1.07932 | − | 1.07932i | ||||
\(320\) | −32.2063 | − | 32.2063i | −0.100645 | − | 0.100645i | ||||
\(321\) | −130.320 | −0.405982 | ||||||||
\(322\) | 88.6089i | 0.275183i | ||||||||
\(323\) | 404.681 | + | 404.681i | 1.25288 | + | 1.25288i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −175.005 | −0.536826 | ||||||||
\(327\) | −79.7698 | + | 79.7698i | −0.243944 | + | 0.243944i | ||||
\(328\) | 18.6835 | 0.0569618 | ||||||||
\(329\) | 450.926i | 1.37060i | ||||||||
\(330\) | 129.967 | − | 129.967i | 0.393841 | − | 0.393841i | ||||
\(331\) | 258.146 | − | 258.146i | 0.779898 | − | 0.779898i | −0.199916 | − | 0.979813i | \(-0.564067\pi\) |
0.979813 | + | 0.199916i | \(0.0640668\pi\) | |||||||
\(332\) | −126.978 | − | 126.978i | −0.382464 | − | 0.382464i | ||||
\(333\) | −111.544 | − | 111.544i | −0.334968 | − | 0.334968i | ||||
\(334\) | −175.687 | −0.526010 | ||||||||
\(335\) | 541.288i | 1.61578i | ||||||||
\(336\) | −25.3556 | − | 25.3556i | −0.0754630 | − | 0.0754630i | ||||
\(337\) | − | 385.355i | − | 1.14349i | −0.820432 | − | 0.571744i | \(-0.806267\pi\) | ||
0.820432 | − | 0.571744i | \(-0.193733\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −271.055 | −0.799571 | ||||||||
\(340\) | −151.813 | + | 151.813i | −0.446508 | + | 0.446508i | ||||
\(341\) | 120.827 | 0.354332 | ||||||||
\(342\) | − | 128.776i | − | 0.376539i | ||||||
\(343\) | −260.620 | + | 260.620i | −0.759825 | + | 0.759825i | ||||
\(344\) | −27.2107 | + | 27.2107i | −0.0791009 | + | 0.0791009i | ||||
\(345\) | −84.4124 | − | 84.4124i | −0.244674 | − | 0.244674i | ||||
\(346\) | −119.181 | − | 119.181i | −0.344454 | − | 0.344454i | ||||
\(347\) | −23.8673 | −0.0687819 | −0.0343909 | − | 0.999408i | \(-0.510949\pi\) | ||||
−0.0343909 | + | 0.999408i | \(0.510949\pi\) | |||||||
\(348\) | − | 127.979i | − | 0.367756i | ||||||
\(349\) | 220.406 | + | 220.406i | 0.631536 | + | 0.631536i | 0.948453 | − | 0.316917i | \(-0.102648\pi\) |
−0.316917 | + | 0.948453i | \(0.602648\pi\) | |||||||
\(350\) | 54.2661i | 0.155046i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −74.5561 | −0.211807 | ||||||||
\(353\) | −400.332 | + | 400.332i | −1.13409 | + | 1.13409i | −0.144594 | + | 0.989491i | \(0.546188\pi\) |
−0.989491 | + | 0.144594i | \(0.953812\pi\) | |||||||
\(354\) | −61.1197 | −0.172654 | ||||||||
\(355\) | − | 231.205i | − | 0.651282i | ||||||
\(356\) | −220.561 | + | 220.561i | −0.619554 | + | 0.619554i | ||||
\(357\) | −119.520 | + | 119.520i | −0.334790 | + | 0.334790i | ||||
\(358\) | −214.511 | − | 214.511i | −0.599192 | − | 0.599192i | ||||
\(359\) | 30.3760 | + | 30.3760i | 0.0846129 | + | 0.0846129i | 0.748146 | − | 0.663534i | \(-0.230944\pi\) |
−0.663534 | + | 0.748146i | \(0.730944\pi\) | |||||||
\(360\) | 48.3094 | 0.134193 | ||||||||
\(361\) | − | 560.299i | − | 1.55208i | ||||||
\(362\) | 343.720 | + | 343.720i | 0.949504 | + | 0.949504i | ||||
\(363\) | − | 91.2909i | − | 0.251490i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 486.706 | 1.33344 | ||||||||
\(366\) | −66.7577 | + | 66.7577i | −0.182398 | + | 0.182398i | ||||
\(367\) | −453.012 | −1.23436 | −0.617182 | − | 0.786820i | \(-0.711726\pi\) | ||||
−0.617182 | + | 0.786820i | \(0.711726\pi\) | |||||||
\(368\) | 48.4234i | 0.131585i | ||||||||
\(369\) | −14.0126 | + | 14.0126i | −0.0379745 | + | 0.0379745i | ||||
\(370\) | 299.369 | − | 299.369i | 0.809106 | − | 0.809106i | ||||
\(371\) | −16.9963 | − | 16.9963i | −0.0458120 | − | 0.0458120i | ||||
\(372\) | 22.4560 | + | 22.4560i | 0.0603655 | + | 0.0603655i | ||||
\(373\) | −407.309 | −1.09198 | −0.545991 | − | 0.837791i | \(-0.683847\pi\) | ||||
−0.545991 | + | 0.837791i | \(0.683847\pi\) | |||||||
\(374\) | 351.440i | 0.939679i | ||||||||
\(375\) | 122.626 | + | 122.626i | 0.327002 | + | 0.327002i | ||||
\(376\) | 246.424i | 0.655383i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 38.0333 | 0.100617 | ||||||||
\(379\) | −7.46065 | + | 7.46065i | −0.0196851 | + | 0.0196851i | −0.716881 | − | 0.697196i | \(-0.754431\pi\) |
0.697196 | + | 0.716881i | \(0.254431\pi\) | |||||||
\(380\) | 345.618 | 0.909520 | ||||||||
\(381\) | − | 317.619i | − | 0.833644i | ||||||
\(382\) | 249.718 | − | 249.718i | 0.653712 | − | 0.653712i | ||||
\(383\) | 348.183 | − | 348.183i | 0.909093 | − | 0.909093i | −0.0871059 | − | 0.996199i | \(-0.527762\pi\) |
0.996199 | + | 0.0871059i | \(0.0277619\pi\) | |||||||
\(384\) | −13.8564 | − | 13.8564i | −0.0360844 | − | 0.0360844i | ||||
\(385\) | 274.616 | + | 274.616i | 0.713289 | + | 0.713289i | ||||
\(386\) | −191.640 | −0.496476 | ||||||||
\(387\) | − | 40.8161i | − | 0.105468i | ||||||
\(388\) | −214.595 | − | 214.595i | −0.553079 | − | 0.553079i | ||||
\(389\) | 61.5695i | 0.158276i | 0.996864 | + | 0.0791382i | \(0.0252168\pi\) | ||||
−0.996864 | + | 0.0791382i | \(0.974783\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 228.256 | 0.583776 | ||||||||
\(392\) | −44.4246 | + | 44.4246i | −0.113328 | + | 0.113328i | ||||
\(393\) | 263.265 | 0.669884 | ||||||||
\(394\) | 4.97285i | 0.0126215i | ||||||||
\(395\) | 379.573 | − | 379.573i | 0.960943 | − | 0.960943i | ||||
\(396\) | 55.9171 | − | 55.9171i | 0.141205 | − | 0.141205i | ||||
\(397\) | 143.539 | + | 143.539i | 0.361560 | + | 0.361560i | 0.864387 | − | 0.502827i | \(-0.167707\pi\) |
−0.502827 | + | 0.864387i | \(0.667707\pi\) | |||||||
\(398\) | 265.195 | + | 265.195i | 0.666319 | + | 0.666319i | ||||
\(399\) | 272.100 | 0.681955 | ||||||||
\(400\) | 29.6555i | 0.0741388i | ||||||||
\(401\) | 194.215 | + | 194.215i | 0.484326 | + | 0.484326i | 0.906510 | − | 0.422184i | \(-0.138736\pi\) |
−0.422184 | + | 0.906510i | \(0.638736\pi\) | |||||||
\(402\) | 232.883i | 0.579312i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 91.9460 | 0.227589 | ||||||||
\(405\) | −36.2321 | + | 36.2321i | −0.0894619 | + | 0.0894619i | ||||
\(406\) | 270.415 | 0.666047 | ||||||||
\(407\) | − | 693.027i | − | 1.70277i | ||||||
\(408\) | −65.3158 | + | 65.3158i | −0.160088 | + | 0.160088i | ||||
\(409\) | 154.552 | − | 154.552i | 0.377877 | − | 0.377877i | −0.492459 | − | 0.870336i | \(-0.663902\pi\) |
0.870336 | + | 0.492459i | \(0.163902\pi\) | |||||||
\(410\) | −37.6078 | − | 37.6078i | −0.0917264 | − | 0.0917264i | ||||
\(411\) | −294.516 | − | 294.516i | −0.716585 | − | 0.716585i | ||||
\(412\) | −185.620 | −0.450534 | ||||||||
\(413\) | − | 129.144i | − | 0.312696i | ||||||
\(414\) | −36.3175 | − | 36.3175i | −0.0877235 | − | 0.0877235i | ||||
\(415\) | 511.186i | 1.23177i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 321.231 | 0.770337 | ||||||||
\(418\) | 400.045 | − | 400.045i | 0.957045 | − | 0.957045i | ||||
\(419\) | −427.811 | −1.02103 | −0.510514 | − | 0.859869i | \(-0.670545\pi\) | ||||
−0.510514 | + | 0.859869i | \(0.670545\pi\) | |||||||
\(420\) | 102.076i | 0.243038i | ||||||||
\(421\) | −275.833 | + | 275.833i | −0.655185 | + | 0.655185i | −0.954237 | − | 0.299052i | \(-0.903330\pi\) |
0.299052 | + | 0.954237i | \(0.403330\pi\) | |||||||
\(422\) | −13.7413 | + | 13.7413i | −0.0325624 | + | 0.0325624i | ||||
\(423\) | −184.818 | − | 184.818i | −0.436922 | − | 0.436922i | ||||
\(424\) | −9.28819 | − | 9.28819i | −0.0219061 | − | 0.0219061i | ||||
\(425\) | 139.789 | 0.328916 | ||||||||
\(426\) | − | 99.4735i | − | 0.233506i | ||||||
\(427\) | −141.057 | − | 141.057i | −0.330343 | − | 0.330343i | ||||
\(428\) | − | 150.481i | − | 0.351590i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 109.544 | 0.254755 | ||||||||
\(431\) | −392.465 | + | 392.465i | −0.910591 | + | 0.910591i | −0.996319 | − | 0.0857274i | \(-0.972679\pi\) |
0.0857274 | + | 0.996319i | \(0.472679\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | − | 673.789i | − | 1.55610i | −0.628205 | − | 0.778048i | \(-0.716210\pi\) | ||
0.628205 | − | 0.778048i | \(-0.283790\pi\) | |||||||
\(434\) | −47.4487 | + | 47.4487i | −0.109329 | + | 0.109329i | ||||
\(435\) | −257.608 | + | 257.608i | −0.592203 | + | 0.592203i | ||||
\(436\) | −92.1103 | − | 92.1103i | −0.211262 | − | 0.211262i | ||||
\(437\) | −259.825 | − | 259.825i | −0.594564 | − | 0.594564i | ||||
\(438\) | 209.400 | 0.478082 | ||||||||
\(439\) | 574.138i | 1.30783i | 0.756567 | + | 0.653916i | \(0.226875\pi\) | ||||
−0.756567 | + | 0.653916i | \(0.773125\pi\) | |||||||
\(440\) | 150.073 | + | 150.073i | 0.341076 | + | 0.341076i | ||||
\(441\) | − | 66.6370i | − | 0.151104i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −365.652 | −0.825399 | −0.412700 | − | 0.910867i | \(-0.635414\pi\) | ||||
−0.412700 | + | 0.910867i | \(0.635414\pi\) | |||||||
\(444\) | 128.800 | − | 128.800i | 0.290091 | − | 0.290091i | ||||
\(445\) | 887.933 | 1.99535 | ||||||||
\(446\) | − | 144.629i | − | 0.324281i | ||||||
\(447\) | −22.1287 | + | 22.1287i | −0.0495048 | + | 0.0495048i | ||||
\(448\) | 29.2781 | − | 29.2781i | 0.0653528 | − | 0.0653528i | ||||
\(449\) | 580.110 | + | 580.110i | 1.29200 | + | 1.29200i | 0.933546 | + | 0.358458i | \(0.116697\pi\) |
0.358458 | + | 0.933546i | \(0.383303\pi\) | |||||||
\(450\) | −22.2417 | − | 22.2417i | −0.0494259 | − | 0.0494259i | ||||
\(451\) | −87.0605 | −0.193039 | ||||||||
\(452\) | − | 312.987i | − | 0.692449i | ||||||
\(453\) | −165.272 | − | 165.272i | −0.364838 | − | 0.364838i | ||||
\(454\) | − | 327.842i | − | 0.722119i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 148.698 | 0.326093 | ||||||||
\(457\) | 139.768 | − | 139.768i | 0.305838 | − | 0.305838i | −0.537455 | − | 0.843293i | \(-0.680614\pi\) |
0.843293 | + | 0.537455i | \(0.180614\pi\) | |||||||
\(458\) | −612.065 | −1.33639 | ||||||||
\(459\) | − | 97.9737i | − | 0.213450i | ||||||
\(460\) | 97.4710 | − | 97.4710i | 0.211894 | − | 0.211894i | ||||
\(461\) | 71.5746 | − | 71.5746i | 0.155259 | − | 0.155259i | −0.625203 | − | 0.780462i | \(-0.714984\pi\) |
0.780462 | + | 0.625203i | \(0.214984\pi\) | |||||||
\(462\) | 118.151 | + | 118.151i | 0.255738 | + | 0.255738i | ||||
\(463\) | −177.994 | − | 177.994i | −0.384435 | − | 0.384435i | 0.488262 | − | 0.872697i | \(-0.337631\pi\) |
−0.872697 | + | 0.488262i | \(0.837631\pi\) | |||||||
\(464\) | 147.778 | 0.318486 | ||||||||
\(465\) | − | 90.4029i | − | 0.194415i | ||||||
\(466\) | −156.892 | − | 156.892i | −0.336678 | − | 0.336678i | ||||
\(467\) | 104.162i | 0.223044i | 0.993762 | + | 0.111522i | \(0.0355726\pi\) | ||||
−0.993762 | + | 0.111522i | \(0.964427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −492.074 | −1.04920 | ||||||||
\(470\) | 496.025 | − | 496.025i | 1.05537 | − | 1.05537i | ||||
\(471\) | 337.951 | 0.717519 | ||||||||
\(472\) | − | 70.5749i | − | 0.149523i | ||||||
\(473\) | 126.795 | − | 126.795i | 0.268066 | − | 0.268066i | ||||
\(474\) | 163.307 | − | 163.307i | 0.344530 | − | 0.344530i | ||||
\(475\) | −159.122 | − | 159.122i | −0.334994 | − | 0.334994i | ||||
\(476\) | −138.010 | − | 138.010i | −0.289937 | − | 0.289937i | ||||
\(477\) | 13.9323 | 0.0292081 | ||||||||
\(478\) | 21.1462i | 0.0442390i | ||||||||
\(479\) | −52.2191 | − | 52.2191i | −0.109017 | − | 0.109017i | 0.650494 | − | 0.759511i | \(-0.274562\pi\) |
−0.759511 | + | 0.650494i | \(0.774562\pi\) | |||||||
\(480\) | 55.7829i | 0.116214i | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −333.092 | −0.691062 | ||||||||
\(483\) | 76.7376 | − | 76.7376i | 0.158877 | − | 0.158877i | ||||
\(484\) | 105.414 | 0.217797 | ||||||||
\(485\) | 863.912i | 1.78126i | ||||||||
\(486\) | −15.5885 | + | 15.5885i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | −464.187 | + | 464.187i | −0.953157 | + | 0.953157i | −0.998951 | − | 0.0457942i | \(-0.985418\pi\) |
0.0457942 | + | 0.998951i | \(0.485418\pi\) | |||||||
\(488\) | −77.0851 | − | 77.0851i | −0.157961 | − | 0.157961i | ||||
\(489\) | 151.559 | + | 151.559i | 0.309937 | + | 0.309937i | ||||
\(490\) | 178.844 | 0.364988 | ||||||||
\(491\) | 451.726i | 0.920012i | 0.887916 | + | 0.460006i | \(0.152153\pi\) | ||||
−0.887916 | + | 0.460006i | \(0.847847\pi\) | |||||||
\(492\) | −16.1804 | − | 16.1804i | −0.0328869 | − | 0.0328869i | ||||
\(493\) | − | 696.588i | − | 1.41296i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −225.110 | −0.454768 | ||||||||
\(496\) | −25.9299 | + | 25.9299i | −0.0522781 | + | 0.0522781i | ||||
\(497\) | 210.184 | 0.422905 | ||||||||
\(498\) | 219.932i | 0.441631i | ||||||||
\(499\) | 126.721 | − | 126.721i | 0.253950 | − | 0.253950i | −0.568638 | − | 0.822588i | \(-0.692529\pi\) |
0.822588 | + | 0.568638i | \(0.192529\pi\) | |||||||
\(500\) | −141.596 | + | 141.596i | −0.283192 | + | 0.283192i | ||||
\(501\) | 152.150 | + | 152.150i | 0.303692 | + | 0.303692i | ||||
\(502\) | −76.9248 | − | 76.9248i | −0.153237 | − | 0.153237i | ||||
\(503\) | −347.883 | −0.691616 | −0.345808 | − | 0.938305i | \(-0.612395\pi\) | ||||
−0.345808 | + | 0.938305i | \(0.612395\pi\) | |||||||
\(504\) | 43.9171i | 0.0871371i | ||||||||
\(505\) | −185.077 | − | 185.077i | −0.366490 | − | 0.366490i | ||||
\(506\) | − | 225.641i | − | 0.445931i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 366.754 | 0.721957 | ||||||||
\(509\) | −127.161 | + | 127.161i | −0.249826 | + | 0.249826i | −0.820899 | − | 0.571073i | \(-0.806527\pi\) |
0.571073 | + | 0.820899i | \(0.306527\pi\) | |||||||
\(510\) | 262.947 | 0.515583 | ||||||||
\(511\) | 442.454i | 0.865860i | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −111.524 | + | 111.524i | −0.217395 | + | 0.217395i | ||||
\(514\) | 63.5214 | + | 63.5214i | 0.123583 | + | 0.123583i | ||||
\(515\) | 373.633 | + | 373.633i | 0.725501 | + | 0.725501i | ||||
\(516\) | 47.1303 | 0.0913378 | ||||||||
\(517\) | − | 1148.28i | − | 2.22104i | ||||||
\(518\) | 272.151 | + | 272.151i | 0.525387 | + | 0.525387i | ||||
\(519\) | 206.428i | 0.397741i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −107.588 | −0.206503 | −0.103251 | − | 0.994655i | \(-0.532925\pi\) | ||||
−0.103251 | + | 0.994655i | \(0.532925\pi\) | |||||||
\(522\) | −110.833 | + | 110.833i | −0.212324 | + | 0.212324i | ||||
\(523\) | −601.633 | −1.15035 | −0.575175 | − | 0.818031i | \(-0.695066\pi\) | ||||
−0.575175 | + | 0.818031i | \(0.695066\pi\) | |||||||
\(524\) | 303.992i | 0.580137i | ||||||||
\(525\) | 46.9958 | − | 46.9958i | 0.0895158 | − | 0.0895158i | ||||
\(526\) | 225.177 | − | 225.177i | 0.428094 | − | 0.428094i | ||||
\(527\) | 122.228 | + | 122.228i | 0.231931 | + | 0.231931i | ||||
\(528\) | 64.5675 | + | 64.5675i | 0.122287 | + | 0.122287i | ||||
\(529\) | 382.449 | 0.722965 | ||||||||
\(530\) | 37.3923i | 0.0705514i | ||||||||
\(531\) | 52.9312 | + | 52.9312i | 0.0996821 | + | 0.0996821i | ||||
\(532\) | 314.194i | 0.590590i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 382.023 | 0.715400 | ||||||||
\(535\) | −302.901 | + | 302.901i | −0.566171 | + | 0.566171i | ||||
\(536\) | −268.911 | −0.501699 | ||||||||
\(537\) | 371.544i | 0.691888i | ||||||||
\(538\) | 22.1441 | − | 22.1441i | 0.0411600 | − | 0.0411600i | ||||
\(539\) | 207.008 | − | 207.008i | 0.384060 | − | 0.384060i | ||||
\(540\) | −41.8372 | − | 41.8372i | −0.0774763 | − | 0.0774763i | ||||
\(541\) | −212.291 | − | 212.291i | −0.392405 | − | 0.392405i | 0.483139 | − | 0.875544i | \(-0.339497\pi\) |
−0.875544 | + | 0.483139i | \(0.839497\pi\) | |||||||
\(542\) | 210.634 | 0.388623 | ||||||||
\(543\) | − | 595.341i | − | 1.09639i | ||||||
\(544\) | −75.4202 | − | 75.4202i | −0.138640 | − | 0.138640i | ||||
\(545\) | 370.816i | 0.680397i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −709.928 | −1.29786 | −0.648929 | − | 0.760849i | \(-0.724783\pi\) | ||||
−0.648929 | + | 0.760849i | \(0.724783\pi\) | |||||||
\(548\) | 340.078 | − | 340.078i | 0.620581 | − | 0.620581i | ||||
\(549\) | 115.628 | 0.210615 | ||||||||
\(550\) | − | 138.188i | − | 0.251250i | ||||||
\(551\) | −792.928 | + | 792.928i | −1.43907 | + | 1.43907i | ||||
\(552\) | 41.9359 | − | 41.9359i | 0.0759708 | − | 0.0759708i | ||||
\(553\) | 345.062 | + | 345.062i | 0.623982 | + | 0.623982i | ||||
\(554\) | −202.590 | − | 202.590i | −0.365687 | − | 0.365687i | ||||
\(555\) | −518.523 | −0.934275 | ||||||||
\(556\) | 370.925i | 0.667132i | ||||||||
\(557\) | −504.916 | − | 504.916i | −0.906492 | − | 0.906492i | 0.0894957 | − | 0.995987i | \(-0.471474\pi\) |
−0.995987 | + | 0.0894957i | \(0.971474\pi\) | |||||||
\(558\) | − | 38.8949i | − | 0.0697041i | ||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −117.867 | −0.210477 | ||||||||
\(561\) | 304.356 | − | 304.356i | 0.542524 | − | 0.542524i | ||||
\(562\) | −88.1310 | −0.156817 | ||||||||
\(563\) | 184.650i | 0.327975i | 0.986462 | + | 0.163988i | \(0.0524357\pi\) | ||||
−0.986462 | + | 0.163988i | \(0.947564\pi\) | |||||||
\(564\) | 213.409 | − | 213.409i | 0.378385 | − | 0.378385i | ||||
\(565\) | −630.009 | + | 630.009i | −1.11506 | + | 1.11506i | ||||
\(566\) | −140.882 | − | 140.882i | −0.248909 | − | 0.248909i | ||||
\(567\) | −32.9378 | − | 32.9378i | −0.0580914 | − | 0.0580914i | ||||
\(568\) | 114.862 | 0.202222 | ||||||||
\(569\) | − | 934.094i | − | 1.64164i | −0.571186 | − | 0.820820i | \(-0.693517\pi\) | ||
0.571186 | − | 0.820820i | \(-0.306483\pi\) | |||||||
\(570\) | −299.314 | − | 299.314i | −0.525112 | − | 0.525112i | ||||
\(571\) | − | 235.631i | − | 0.412664i | −0.978482 | − | 0.206332i | \(-0.933847\pi\) | ||
0.978482 | − | 0.206332i | \(-0.0661527\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −432.524 | −0.754842 | ||||||||
\(574\) | 34.1885 | − | 34.1885i | 0.0595619 | − | 0.0595619i | ||||
\(575\) | −89.7513 | −0.156089 | ||||||||
\(576\) | 24.0000i | 0.0416667i | ||||||||
\(577\) | 213.174 | − | 213.174i | 0.369452 | − | 0.369452i | −0.497826 | − | 0.867277i | \(-0.665868\pi\) |
0.867277 | + | 0.497826i | \(0.165868\pi\) | |||||||
\(578\) | −66.5131 | + | 66.5131i | −0.115075 | + | 0.115075i | ||||
\(579\) | 165.965 | + | 165.965i | 0.286641 | + | 0.286641i | ||||
\(580\) | −297.460 | − | 297.460i | −0.512862 | − | 0.512862i | ||||
\(581\) | −464.709 | −0.799844 | ||||||||
\(582\) | 371.689i | 0.638641i | ||||||||
\(583\) | 43.2807 | + | 43.2807i | 0.0742380 | + | 0.0742380i | ||||
\(584\) | 241.794i | 0.414031i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −242.001 | −0.412970 | ||||||||
\(587\) | −354.401 | + | 354.401i | −0.603750 | + | 0.603750i | −0.941305 | − | 0.337556i | \(-0.890400\pi\) |
0.337556 | + | 0.941305i | \(0.390400\pi\) | |||||||
\(588\) | 76.9457 | 0.130860 | ||||||||
\(589\) | − | 278.264i | − | 0.472434i | ||||||
\(590\) | −142.060 | + | 142.060i | −0.240779 | + | 0.240779i | ||||
\(591\) | 4.30662 | − | 4.30662i | 0.00728700 | − | 0.00728700i | ||||
\(592\) | 148.726 | + | 148.726i | 0.251226 | + | 0.251226i | ||||
\(593\) | 456.457 | + | 456.457i | 0.769743 | + | 0.769743i | 0.978061 | − | 0.208319i | \(-0.0667991\pi\) |
−0.208319 | + | 0.978061i | \(0.566799\pi\) | |||||||
\(594\) | −96.8513 | −0.163049 | ||||||||
\(595\) | 555.598i | 0.933779i | ||||||||
\(596\) | −25.5520 | − | 25.5520i | −0.0428724 | − | 0.0428724i | ||||
\(597\) | − | 459.331i | − | 0.769399i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 409.720 | 0.684007 | 0.342003 | − | 0.939699i | \(-0.388895\pi\) | ||||
0.342003 | + | 0.939699i | \(0.388895\pi\) | |||||||
\(600\) | 25.6824 | − | 25.6824i | 0.0428041 | − | 0.0428041i | ||||
\(601\) | −708.630 | −1.17909 | −0.589543 | − | 0.807737i | \(-0.700692\pi\) | ||||
−0.589543 | + | 0.807737i | \(0.700692\pi\) | |||||||
\(602\) | 99.5846i | 0.165423i | ||||||||
\(603\) | 201.683 | − | 201.683i | 0.334466 | − | 0.334466i | ||||
\(604\) | 190.839 | − | 190.839i | 0.315959 | − | 0.315959i | ||||
\(605\) | −212.186 | − | 212.186i | −0.350721 | − | 0.350721i | ||||
\(606\) | −79.6276 | − | 79.6276i | −0.131399 | − | 0.131399i | ||||
\(607\) | 467.364 | 0.769957 | 0.384978 | − | 0.922926i | \(-0.374209\pi\) | ||||
0.384978 | + | 0.922926i | \(0.374209\pi\) | |||||||
\(608\) | 171.702i | 0.282405i | ||||||||
\(609\) | −234.186 | − | 234.186i | −0.384542 | − | 0.384542i | ||||
\(610\) | 310.328i | 0.508735i | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 113.130 | 0.184853 | ||||||||
\(613\) | 704.485 | − | 704.485i | 1.14924 | − | 1.14924i | 0.162540 | − | 0.986702i | \(-0.448031\pi\) |
0.986702 | − | 0.162540i | \(-0.0519685\pi\) | |||||||
\(614\) | 505.517 | 0.823317 | ||||||||
\(615\) | 65.1387i | 0.105917i | ||||||||
\(616\) | −136.429 | + | 136.429i | −0.221475 | + | 0.221475i | ||||
\(617\) | −220.953 | + | 220.953i | −0.358108 | + | 0.358108i | −0.863115 | − | 0.505007i | \(-0.831490\pi\) |
0.505007 | + | 0.863115i | \(0.331490\pi\) | |||||||
\(618\) | 160.752 | + | 160.752i | 0.260116 | + | 0.260116i | ||||
\(619\) | 459.215 | + | 459.215i | 0.741865 | + | 0.741865i | 0.972937 | − | 0.231071i | \(-0.0742231\pi\) |
−0.231071 | + | 0.972937i | \(0.574223\pi\) | |||||||
\(620\) | 104.388 | 0.168368 | ||||||||
\(621\) | 62.9038i | 0.101294i | ||||||||
\(622\) | 209.742 | + | 209.742i | 0.337206 | + | 0.337206i | ||||
\(623\) | 807.201i | 1.29567i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 755.381 | 1.20861 | ||||||||
\(626\) | 386.143 | − | 386.143i | 0.616842 | − | 0.616842i | ||||
\(627\) | −692.898 | −1.10510 | ||||||||
\(628\) | 390.233i | 0.621389i | ||||||||
\(629\) | 701.059 | − | 701.059i | 1.11456 | − | 1.11456i | ||||
\(630\) | 88.4004 | − | 88.4004i | 0.140318 | − | 0.140318i | ||||
\(631\) | 189.565 | + | 189.565i | 0.300420 | + | 0.300420i | 0.841178 | − | 0.540758i | \(-0.181863\pi\) |
−0.540758 | + | 0.841178i | \(0.681863\pi\) | |||||||
\(632\) | 188.571 | + | 188.571i | 0.298371 | + | 0.298371i | ||||
\(633\) | 23.8007 | 0.0375998 | ||||||||
\(634\) | − | 229.518i | − | 0.362016i | ||||||
\(635\) | −738.237 | − | 738.237i | −1.16258 | − | 1.16258i | ||||
\(636\) | 16.0876i | 0.0252950i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −688.608 | −1.07932 | ||||||||
\(639\) | −86.1466 | + | 86.1466i | −0.134815 | + | 0.134815i | ||||
\(640\) | −64.4126 | −0.100645 | ||||||||
\(641\) | 172.486i | 0.269089i | 0.990908 | + | 0.134545i | \(0.0429572\pi\) | ||||
−0.990908 | + | 0.134545i | \(0.957043\pi\) | |||||||
\(642\) | −130.320 | + | 130.320i | −0.202991 | + | 0.202991i | ||||
\(643\) | −672.617 | + | 672.617i | −1.04606 | + | 1.04606i | −0.0471735 | + | 0.998887i | \(0.515021\pi\) |
−0.998887 | + | 0.0471735i | \(0.984979\pi\) | |||||||
\(644\) | 88.6089 | + | 88.6089i | 0.137592 | + | 0.137592i | ||||
\(645\) | −94.8683 | − | 94.8683i | −0.147083 | − | 0.147083i | ||||
\(646\) | 809.363 | 1.25288 | ||||||||
\(647\) | 739.211i | 1.14252i | 0.820769 | + | 0.571260i | \(0.193545\pi\) | ||||
−0.820769 | + | 0.571260i | \(0.806455\pi\) | |||||||
\(648\) | −18.0000 | − | 18.0000i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | 328.862i | 0.506721i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 82.1835 | 0.126242 | ||||||||
\(652\) | −175.005 | + | 175.005i | −0.268413 | + | 0.268413i | ||||
\(653\) | −1122.68 | −1.71926 | −0.859632 | − | 0.510914i | \(-0.829307\pi\) | ||||
−0.859632 | + | 0.510914i | \(0.829307\pi\) | |||||||
\(654\) | 159.540i | 0.243944i | ||||||||
\(655\) | 611.903 | − | 611.903i | 0.934202 | − | 0.934202i | ||||
\(656\) | 18.6835 | − | 18.6835i | 0.0284809 | − | 0.0284809i | ||||
\(657\) | −181.346 | − | 181.346i | −0.276021 | − | 0.276021i | ||||
\(658\) | 450.926 | + | 450.926i | 0.685298 | + | 0.685298i | ||||
\(659\) | 349.019 | 0.529619 | 0.264810 | − | 0.964301i | \(-0.414691\pi\) | ||||
0.264810 | + | 0.964301i | \(0.414691\pi\) | |||||||
\(660\) | − | 259.935i | − | 0.393841i | ||||||
\(661\) | −566.931 | − | 566.931i | −0.857686 | − | 0.857686i | 0.133379 | − | 0.991065i | \(-0.457417\pi\) |
−0.991065 | + | 0.133379i | \(0.957417\pi\) | |||||||
\(662\) | − | 516.292i | − | 0.779898i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −253.956 | −0.382464 | ||||||||
\(665\) | 632.439 | − | 632.439i | 0.951036 | − | 0.951036i | ||||
\(666\) | −223.089 | −0.334968 | ||||||||
\(667\) | 447.243i | 0.670529i | ||||||||
\(668\) | −175.687 | + | 175.687i | −0.263005 | + | 0.263005i | ||||
\(669\) | −125.253 | + | 125.253i | −0.187224 | + | 0.187224i | ||||
\(670\) | 541.288 | + | 541.288i | 0.807892 | + | 0.807892i | ||||
\(671\) | 359.198 | + | 359.198i | 0.535318 | + | 0.535318i | ||||
\(672\) | −50.7111 | −0.0754630 | ||||||||
\(673\) | 104.897i | 0.155865i | 0.996959 | + | 0.0779323i | \(0.0248318\pi\) | ||||
−0.996959 | + | 0.0779323i | \(0.975168\pi\) | |||||||
\(674\) | −385.355 | − | 385.355i | −0.571744 | − | 0.571744i | ||||
\(675\) | 38.5237i | 0.0570721i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −71.7517 | −0.105985 | −0.0529924 | − | 0.998595i | \(-0.516876\pi\) | ||||
−0.0529924 | + | 0.998595i | \(0.516876\pi\) | |||||||
\(678\) | −271.055 | + | 271.055i | −0.399785 | + | 0.399785i | ||||
\(679\) | −785.365 | −1.15665 | ||||||||
\(680\) | 303.626i | 0.446508i | ||||||||
\(681\) | −283.920 | + | 283.920i | −0.416916 | + | 0.416916i | ||||
\(682\) | 120.827 | − | 120.827i | 0.177166 | − | 0.177166i | ||||
\(683\) | −526.610 | − | 526.610i | −0.771024 | − | 0.771024i | 0.207261 | − | 0.978286i | \(-0.433545\pi\) |
−0.978286 | + | 0.207261i | \(0.933545\pi\) | |||||||
\(684\) | −128.776 | − | 128.776i | −0.188270 | − | 0.188270i | ||||
\(685\) | −1369.08 | −1.99866 | ||||||||
\(686\) | 521.240i | 0.759825i | ||||||||
\(687\) | 530.064 | + | 530.064i | 0.771563 | + | 0.771563i | ||||
\(688\) | 54.4214i | 0.0791009i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −168.825 | −0.244674 | ||||||||
\(691\) | −403.147 | + | 403.147i | −0.583425 | + | 0.583425i | −0.935843 | − | 0.352418i | \(-0.885360\pi\) |
0.352418 | + | 0.935843i | \(0.385360\pi\) | |||||||
\(692\) | −238.362 | −0.344454 | ||||||||
\(693\) | − | 204.643i | − | 0.295300i | ||||||
\(694\) | −23.8673 | + | 23.8673i | −0.0343909 | + | 0.0343909i | ||||
\(695\) | 746.632 | − | 746.632i | 1.07429 | − | 1.07429i | ||||
\(696\) | −127.979 | − | 127.979i | −0.183878 | − | 0.183878i | ||||
\(697\) | −88.0695 | − | 88.0695i | −0.126355 | − | 0.126355i | ||||
\(698\) | 440.812 | 0.631536 | ||||||||
\(699\) | 271.745i | 0.388762i | ||||||||
\(700\) | 54.2661 | + | 54.2661i | 0.0775229 | + | 0.0775229i | ||||
\(701\) | − | 234.275i | − | 0.334201i | −0.985940 | − | 0.167101i | \(-0.946559\pi\) | ||
0.985940 | − | 0.167101i | \(-0.0534405\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1596.03 | −2.27032 | ||||||||
\(704\) | −74.5561 | + | 74.5561i | −0.105904 | + | 0.105904i | ||||
\(705\) | −859.140 | −1.21864 | ||||||||
\(706\) | 800.664i | 1.13409i | ||||||||
\(707\) | 168.250 | − | 168.250i | 0.237978 | − | 0.237978i | ||||
\(708\) | −61.1197 | + | 61.1197i | −0.0863272 | + | 0.0863272i | ||||
\(709\) | 16.8626 | + | 16.8626i | 0.0237837 | + | 0.0237837i | 0.718899 | − | 0.695115i | \(-0.244647\pi\) |
−0.695115 | + | 0.718899i | \(0.744647\pi\) | |||||||
\(710\) | −231.205 | − | 231.205i | −0.325641 | − | 0.325641i | ||||
\(711\) | −282.856 | −0.397829 | ||||||||
\(712\) | 441.123i | 0.619554i | ||||||||
\(713\) | −78.4759 | − | 78.4759i | −0.110064 | − | 0.110064i | ||||
\(714\) | 239.040i | 0.334790i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −429.022 | −0.599192 | ||||||||
\(717\) | 18.3132 | − | 18.3132i | 0.0255414 | − | 0.0255414i | ||||
\(718\) | 60.7520 | 0.0846129 | ||||||||
\(719\) | − | 755.495i | − | 1.05076i | −0.850868 | − | 0.525379i | \(-0.823924\pi\) | ||
0.850868 | − | 0.525379i | \(-0.176076\pi\) | |||||||
\(720\) | 48.3094 | − | 48.3094i | 0.0670964 | − | 0.0670964i | ||||
\(721\) | −339.662 | + | 339.662i | −0.471098 | + | 0.471098i | ||||
\(722\) | −560.299 | − | 560.299i | −0.776038 | − | 0.776038i | ||||
\(723\) | 288.466 | + | 288.466i | 0.398985 | + | 0.398985i | ||||
\(724\) | 687.441 | 0.949504 | ||||||||
\(725\) | 273.901i | 0.377795i | ||||||||
\(726\) | −91.2909 | − | 91.2909i | −0.125745 | − | 0.125745i | ||||
\(727\) | − | 686.041i | − | 0.943660i | −0.881689 | − | 0.471830i | \(-0.843594\pi\) | ||
0.881689 | − | 0.471830i | \(-0.156406\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 486.706 | − | 486.706i | 0.666720 | − | 0.666720i | ||||
\(731\) | 256.530 | 0.350930 | ||||||||
\(732\) | 133.515i | 0.182398i | ||||||||
\(733\) | 173.245 | − | 173.245i | 0.236351 | − | 0.236351i | −0.578986 | − | 0.815337i | \(-0.696552\pi\) |
0.815337 | + | 0.578986i | \(0.196552\pi\) | |||||||
\(734\) | −453.012 | + | 453.012i | −0.617182 | + | 0.617182i | ||||
\(735\) | −154.884 | − | 154.884i | −0.210726 | − | 0.210726i | ||||
\(736\) | 48.4234 | + | 48.4234i | 0.0657926 | + | 0.0657926i | ||||
\(737\) | 1253.06 | 1.70021 | ||||||||
\(738\) | 28.0252i | 0.0379745i | ||||||||
\(739\) | 70.1524 | + | 70.1524i | 0.0949289 | + | 0.0949289i | 0.752976 | − | 0.658048i | \(-0.228617\pi\) |
−0.658048 | + | 0.752976i | \(0.728617\pi\) | |||||||
\(740\) | − | 598.739i | − | 0.809106i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −33.9925 | −0.0458120 | ||||||||
\(743\) | 882.457 | − | 882.457i | 1.18769 | − | 1.18769i | 0.209992 | − | 0.977703i | \(-0.432656\pi\) |
0.977703 | − | 0.209992i | \(-0.0673437\pi\) | |||||||
\(744\) | 44.9120 | 0.0603655 | ||||||||
\(745\) | 102.867i | 0.138076i | ||||||||
\(746\) | −407.309 | + | 407.309i | −0.545991 | + | 0.545991i | ||||
\(747\) | 190.467 | − | 190.467i | 0.254976 | − | 0.254976i | ||||
\(748\) | 351.440 | + | 351.440i | 0.469840 | + | 0.469840i | ||||
\(749\) | −275.361 | − | 275.361i | −0.367639 | − | 0.367639i | ||||
\(750\) | 245.251 | 0.327002 | ||||||||
\(751\) | 209.378i | 0.278798i | 0.990236 | + | 0.139399i | \(0.0445171\pi\) | ||||
−0.990236 | + | 0.139399i | \(0.955483\pi\) | |||||||
\(752\) | 246.424 | + | 246.424i | 0.327691 | + | 0.327691i | ||||
\(753\) | 133.238i | 0.176942i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −768.277 | −1.01759 | ||||||||
\(756\) | 38.0333 | − | 38.0333i | 0.0503086 | − | 0.0503086i | ||||
\(757\) | 1283.14 | 1.69503 | 0.847515 | − | 0.530771i | \(-0.178098\pi\) | ||||
0.847515 | + | 0.530771i | \(0.178098\pi\) | |||||||
\(758\) | 14.9213i | 0.0196851i | ||||||||
\(759\) | −195.411 | + | 195.411i | −0.257459 | + | 0.257459i | ||||
\(760\) | 345.618 | − | 345.618i | 0.454760 | − | 0.454760i | ||||
\(761\) | −328.989 | − | 328.989i | −0.432311 | − | 0.432311i | 0.457103 | − | 0.889414i | \(-0.348887\pi\) |
−0.889414 | + | 0.457103i | \(0.848887\pi\) | |||||||
\(762\) | −317.619 | − | 317.619i | −0.416822 | − | 0.416822i | ||||
\(763\) | −337.101 | −0.441811 | ||||||||
\(764\) | − | 499.436i | − | 0.653712i | ||||||
\(765\) | −227.719 | − | 227.719i | −0.297672 | − | 0.297672i | ||||
\(766\) | − | 696.365i | − | 0.909093i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | −591.777 | + | 591.777i | −0.769541 | + | 0.769541i | −0.978026 | − | 0.208485i | \(-0.933147\pi\) |
0.208485 | + | 0.978026i | \(0.433147\pi\) | |||||||
\(770\) | 549.233 | 0.713289 | ||||||||
\(771\) | − | 110.022i | − | 0.142701i | ||||||
\(772\) | −191.640 | + | 191.640i | −0.248238 | + | 0.248238i | ||||
\(773\) | −442.913 | + | 442.913i | −0.572979 | + | 0.572979i | −0.932960 | − | 0.359981i | \(-0.882783\pi\) |
0.359981 | + | 0.932960i | \(0.382783\pi\) | |||||||
\(774\) | −40.8161 | − | 40.8161i | −0.0527339 | − | 0.0527339i | ||||
\(775\) | −48.0604 | − | 48.0604i | −0.0620134 | − | 0.0620134i | ||||
\(776\) | −429.189 | −0.553079 | ||||||||
\(777\) | − | 471.379i | − | 0.606665i | ||||||
\(778\) | 61.5695 | + | 61.5695i | 0.0791382 | + | 0.0791382i | ||||
\(779\) | 200.499i | 0.257380i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −535.230 | −0.685313 | ||||||||
\(782\) | 228.256 | − | 228.256i | 0.291888 | − | 0.291888i | ||||
\(783\) | 191.969 | 0.245171 | ||||||||
\(784\) | 88.8493i | 0.113328i | ||||||||
\(785\) | 785.496 | − | 785.496i | 1.00063 | − | 1.00063i | ||||
\(786\) | 263.265 | − | 263.265i | 0.334942 | − | 0.334942i | ||||
\(787\) | −91.4093 | − | 91.4093i | −0.116149 | − | 0.116149i | 0.646643 | − | 0.762792i | \(-0.276172\pi\) |
−0.762792 | + | 0.646643i | \(0.776172\pi\) | |||||||
\(788\) | 4.97285 | + | 4.97285i | 0.00631073 | + | 0.00631073i | ||||
\(789\) | −390.019 | −0.494320 | ||||||||
\(790\) | − | 759.145i | − | 0.960943i | ||||||
\(791\) | −572.728 | − | 572.728i | −0.724056 | − | 0.724056i | ||||
\(792\) | − | 111.834i | − | 0.141205i | ||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 287.078 | 0.361560 | ||||||||
\(795\) | 32.3826 | − | 32.3826i | 0.0407329 | − | 0.0407329i | ||||
\(796\) | 530.390 | 0.666319 | ||||||||
\(797\) | − | 926.956i | − | 1.16306i | −0.813526 | − | 0.581528i | \(-0.802455\pi\) | ||
0.813526 | − | 0.581528i | \(-0.197545\pi\) | |||||||
\(798\) | 272.100 | − | 272.100i | 0.340977 | − | 0.340977i | ||||
\(799\) | 1161.58 | − | 1161.58i | 1.45380 | − | 1.45380i | ||||
\(800\) | 29.6555 | + | 29.6555i | 0.0370694 | + | 0.0370694i | ||||
\(801\) | −330.842 | − | 330.842i | −0.413036 | − | 0.413036i | ||||
\(802\) | 388.430 | 0.484326 | ||||||||
\(803\) | − | 1126.70i | − | 1.40312i | ||||||
\(804\) | 232.883 | + | 232.883i | 0.289656 | + | 0.289656i | ||||
\(805\) | − | 356.720i | − | 0.443131i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38.3547 | −0.0475275 | ||||||||
\(808\) | 91.9460 | − | 91.9460i | 0.113795 | − | 0.113795i | ||||
\(809\) | −754.553 | −0.932698 | −0.466349 | − | 0.884601i | \(-0.654431\pi\) | ||||
−0.466349 | + | 0.884601i | \(0.654431\pi\) | |||||||
\(810\) | 72.4641i | 0.0894619i | ||||||||
\(811\) | −398.188 | + | 398.188i | −0.490984 | + | 0.490984i | −0.908616 | − | 0.417632i | \(-0.862860\pi\) |
0.417632 | + | 0.908616i | \(0.362860\pi\) | |||||||
\(812\) | 270.415 | − | 270.415i | 0.333023 | − | 0.333023i | ||||
\(813\) | −182.414 | − | 182.414i | −0.224372 | − | 0.224372i | ||||
\(814\) | −693.027 | − | 693.027i | −0.851385 | − | 0.851385i | ||||
\(815\) | 704.534 | 0.864459 | ||||||||
\(816\) | 130.632i | 0.160088i | ||||||||
\(817\) | −292.008 | − | 292.008i | −0.357415 | − | 0.357415i | ||||
\(818\) | − | 309.104i | − | 0.377877i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −75.2156 | −0.0917264 | ||||||||
\(821\) | −497.803 | + | 497.803i | −0.606337 | + | 0.606337i | −0.941987 | − | 0.335650i | \(-0.891044\pi\) |
0.335650 | + | 0.941987i | \(0.391044\pi\) | |||||||
\(822\) | −589.033 | −0.716585 | ||||||||
\(823\) | 506.914i | 0.615934i | 0.951397 | + | 0.307967i | \(0.0996486\pi\) | ||||
−0.951397 | + | 0.307967i | \(0.900351\pi\) | |||||||
\(824\) | −185.620 | + | 185.620i | −0.225267 | + | 0.225267i | ||||
\(825\) | −119.674 | + | 119.674i | −0.145059 | + | 0.145059i | ||||
\(826\) | −129.144 | − | 129.144i | −0.156348 | − | 0.156348i | ||||
\(827\) | −31.7310 | − | 31.7310i | −0.0383689 | − | 0.0383689i | 0.687662 | − | 0.726031i | \(-0.258637\pi\) |
−0.726031 | + | 0.687662i | \(0.758637\pi\) | |||||||
\(828\) | −72.6351 | −0.0877235 | ||||||||
\(829\) | 150.237i | 0.181226i | 0.995886 | + | 0.0906131i | \(0.0288827\pi\) | ||||
−0.995886 | + | 0.0906131i | \(0.971117\pi\) | |||||||
\(830\) | 511.186 | + | 511.186i | 0.615887 | + | 0.615887i | ||||
\(831\) | 350.897i | 0.422259i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 418.815 | 0.502779 | ||||||||
\(834\) | 321.231 | − | 321.231i | 0.385169 | − | 0.385169i | ||||
\(835\) | 707.279 | 0.847040 | ||||||||
\(836\) | − | 800.090i | − | 0.957045i | ||||||
\(837\) | −33.6840 | + | 33.6840i | −0.0402437 | + | 0.0402437i | ||||
\(838\) | −427.811 | + | 427.811i | −0.510514 | + | 0.510514i | ||||
\(839\) | −150.327 | − | 150.327i | −0.179174 | − | 0.179174i | 0.611822 | − | 0.790996i | \(-0.290437\pi\) |
−0.790996 | + | 0.611822i | \(0.790437\pi\) | |||||||
\(840\) | 102.076 | + | 102.076i | 0.121519 | + | 0.121519i | ||||
\(841\) | 523.887 | 0.622933 | ||||||||
\(842\) | 551.666i | 0.655185i | ||||||||
\(843\) | 76.3237 | + | 76.3237i | 0.0905382 | + | 0.0905382i | ||||
\(844\) | 27.4826i | 0.0325624i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −369.636 | −0.436922 | ||||||||
\(847\) | 192.894 | − | 192.894i | 0.227738 | − | 0.227738i | ||||
\(848\) | −18.5764 | −0.0219061 | ||||||||
\(849\) | 244.015i | 0.287415i | ||||||||
\(850\) | 139.789 | − | 139.789i | 0.164458 | − | 0.164458i | ||||
\(851\) | −450.113 | + | 450.113i | −0.528923 | + | 0.528923i | ||||
\(852\) | −99.4735 | − | 99.4735i | −0.116753 | − | 0.116753i | ||||
\(853\) | −753.994 | − | 753.994i | −0.883932 | − | 0.883932i | 0.110000 | − | 0.993932i | \(-0.464915\pi\) |
−0.993932 | + | 0.110000i | \(0.964915\pi\) | |||||||
\(854\) | −282.113 | −0.330343 | ||||||||
\(855\) | 518.426i | 0.606347i | ||||||||
\(856\) | −150.481 | − | 150.481i | −0.175795 | − | 0.175795i | ||||
\(857\) | 844.995i | 0.985992i | 0.870031 | + | 0.492996i | \(0.164098\pi\) | ||||
−0.870031 | + | 0.492996i | \(0.835902\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 721.635 | 0.840087 | 0.420044 | − | 0.907504i | \(-0.362015\pi\) | ||||
0.420044 | + | 0.907504i | \(0.362015\pi\) | |||||||
\(860\) | 109.544 | − | 109.544i | 0.127377 | − | 0.127377i | ||||
\(861\) | −59.2162 | −0.0687761 | ||||||||
\(862\) | 784.930i | 0.910591i | ||||||||
\(863\) | −124.534 | + | 124.534i | −0.144304 | + | 0.144304i | −0.775568 | − | 0.631264i | \(-0.782536\pi\) |
0.631264 | + | 0.775568i | \(0.282536\pi\) | |||||||
\(864\) | 20.7846 | − | 20.7846i | 0.0240563 | − | 0.0240563i | ||||
\(865\) | 479.797 | + | 479.797i | 0.554679 | + | 0.554679i | ||||
\(866\) | −673.789 | − | 673.789i | −0.778048 | − | 0.778048i | ||||
\(867\) | 115.204 | 0.132877 | ||||||||
\(868\) | 94.8973i | 0.109329i | ||||||||
\(869\) | −878.694 | − | 878.694i | −1.01116 | − | 1.01116i | ||||
\(870\) | 515.216i | 0.592203i | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −184.221 | −0.211262 | ||||||||
\(873\) | 321.892 | − | 321.892i | 0.368719 | − | 0.368719i | ||||
\(874\) | −519.649 | −0.594564 | ||||||||
\(875\) | 518.207i | 0.592236i | ||||||||
\(876\) | 209.400 | − | 209.400i | 0.239041 | − | 0.239041i | ||||
\(877\) | 22.5917 | − | 22.5917i | 0.0257602 | − | 0.0257602i | −0.694109 | − | 0.719870i | \(-0.744202\pi\) |
0.719870 | + | 0.694109i | \(0.244202\pi\) | |||||||
\(878\) | 574.138 | + | 574.138i | 0.653916 | + | 0.653916i | ||||
\(879\) | 209.579 | + | 209.579i | 0.238428 | + | 0.238428i | ||||
\(880\) | 300.147 | 0.341076 | ||||||||
\(881\) | − | 1019.09i | − | 1.15674i | −0.815773 | − | 0.578372i | \(-0.803688\pi\) | ||
0.815773 | − | 0.578372i | \(-0.196312\pi\) | |||||||
\(882\) | −66.6370 | − | 66.6370i | −0.0755521 | − | 0.0755521i | ||||
\(883\) | − | 1092.31i | − | 1.23705i | −0.785767 | − | 0.618523i | \(-0.787732\pi\) | ||
0.785767 | − | 0.618523i | \(-0.212268\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 246.055 | 0.278028 | ||||||||
\(886\) | −365.652 | + | 365.652i | −0.412700 | + | 0.412700i | ||||
\(887\) | −677.300 | −0.763585 | −0.381792 | − | 0.924248i | \(-0.624693\pi\) | ||||
−0.381792 | + | 0.924248i | \(0.624693\pi\) | |||||||
\(888\) | − | 257.601i | − | 0.290091i | ||||||
\(889\) | 671.116 | − | 671.116i | 0.754911 | − | 0.754911i | ||||
\(890\) | 887.933 | − | 887.933i | 0.997677 | − | 0.997677i | ||||
\(891\) | 83.8757 | + | 83.8757i | 0.0941366 | + | 0.0941366i | ||||
\(892\) | −144.629 | − | 144.629i | −0.162141 | − | 0.162141i | ||||
\(893\) | −2644.47 | −2.96133 | ||||||||
\(894\) | 44.2573i | 0.0495048i | ||||||||
\(895\) | 863.574 | + | 863.574i | 0.964888 | + | 0.964888i | ||||
\(896\) | − | 58.5561i | − | 0.0653528i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1160.22 | 1.29200 | ||||||||
\(899\) | −239.491 | + | 239.491i | −0.266397 | + | 0.266397i | ||||
\(900\) | −44.4833 | −0.0494259 | ||||||||
\(901\) | 87.5647i | 0.0971861i | ||||||||
\(902\) | −87.0605 | + | 87.0605i | −0.0965194 | + | 0.0965194i | ||||
\(903\) | 86.2428 | − | 86.2428i | 0.0955070 | − | 0.0955070i | ||||
\(904\) | −312.987 | − | 312.987i | −0.346224 | − | 0.346224i | ||||
\(905\) | −1383.74 | − | 1383.74i | −1.52900 | − | 1.52900i | ||||
\(906\) | −330.543 | −0.364838 | ||||||||
\(907\) | 1105.90i | 1.21930i | 0.792672 | + | 0.609649i | \(0.208689\pi\) | ||||
−0.792672 | + | 0.609649i | \(0.791311\pi\) | |||||||
\(908\) | −327.842 | − | 327.842i | −0.361060 | − | 0.361060i | ||||
\(909\) | 137.919i | 0.151726i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1389.83 | 1.52560 | 0.762802 | − | 0.646632i | \(-0.223823\pi\) | ||||
0.762802 | + | 0.646632i | \(0.223823\pi\) | |||||||
\(912\) | 148.698 | − | 148.698i | 0.163046 | − | 0.163046i | ||||
\(913\) | 1183.37 | 1.29614 | ||||||||
\(914\) | − | 279.536i | − | 0.305838i | ||||||
\(915\) | 268.752 | − | 268.752i | 0.293718 | − | 0.293718i | ||||
\(916\) | −612.065 | + | 612.065i | −0.668193 | + | 0.668193i | ||||
\(917\) | 556.268 | + | 556.268i | 0.606617 | + | 0.606617i | ||||
\(918\) | −97.9737 | − | 97.9737i | −0.106725 | − | 0.106725i | ||||
\(919\) | 871.246 | 0.948037 | 0.474019 | − | 0.880515i | \(-0.342803\pi\) | ||||
0.474019 | + | 0.880515i | \(0.342803\pi\) | |||||||
\(920\) | − | 194.942i | − | 0.211894i | ||||||
\(921\) | −437.790 | − | 437.790i | −0.475342 | − | 0.475342i | ||||
\(922\) | − | 143.149i | − | 0.155259i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 236.302 | 0.255738 | ||||||||
\(925\) | −275.659 | + | 275.659i | −0.298010 | + | 0.298010i | ||||
\(926\) | −355.987 | −0.384435 | ||||||||
\(927\) | − | 278.430i | − | 0.300356i | ||||||
\(928\) | 147.778 | − | 147.778i | 0.159243 | − | 0.159243i | ||||
\(929\) | 425.936 | − | 425.936i | 0.458488 | − | 0.458488i | −0.439671 | − | 0.898159i | \(-0.644905\pi\) |
0.898159 | + | 0.439671i | \(0.144905\pi\) | |||||||
\(930\) | −90.4029 | − | 90.4029i | −0.0972075 | − | 0.0972075i | ||||
\(931\) | −476.738 | − | 476.738i | −0.512070 | − | 0.512070i | ||||
\(932\) | −313.784 | −0.336678 | ||||||||
\(933\) | − | 363.284i | − | 0.389372i | ||||||
\(934\) | 104.162 | + | 104.162i | 0.111522 | + | 0.111522i | ||||
\(935\) | − | 1414.82i | − | 1.51318i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −905.621 | −0.966511 | −0.483255 | − | 0.875479i | \(-0.660546\pi\) | ||||
−0.483255 | + | 0.875479i | \(0.660546\pi\) | |||||||
\(938\) | −492.074 | + | 492.074i | −0.524599 | + | 0.524599i | ||||
\(939\) | −668.819 | −0.712268 | ||||||||
\(940\) | − | 992.050i | − | 1.05537i | ||||||
\(941\) | 429.149 | − | 429.149i | 0.456057 | − | 0.456057i | −0.441302 | − | 0.897359i | \(-0.645483\pi\) |
0.897359 | + | 0.441302i | \(0.145483\pi\) | |||||||
\(942\) | 337.951 | − | 337.951i | 0.358759 | − | 0.358759i | ||||
\(943\) | 56.5448 | + | 56.5448i | 0.0599627 | + | 0.0599627i | ||||
\(944\) | −70.5749 | − | 70.5749i | −0.0747616 | − | 0.0747616i | ||||
\(945\) | −153.114 | −0.162025 | ||||||||
\(946\) | − | 253.591i | − | 0.268066i | ||||||
\(947\) | 719.464 | + | 719.464i | 0.759729 | + | 0.759729i | 0.976273 | − | 0.216544i | \(-0.0694784\pi\) |
−0.216544 | + | 0.976273i | \(0.569478\pi\) | |||||||
\(948\) | − | 326.614i | − | 0.344530i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −318.245 | −0.334994 | ||||||||
\(951\) | −198.769 | + | 198.769i | −0.209010 | + | 0.209010i | ||||
\(952\) | −276.020 | −0.289937 | ||||||||
\(953\) | 895.474i | 0.939637i | 0.882763 | + | 0.469819i | \(0.155681\pi\) | ||||
−0.882763 | + | 0.469819i | \(0.844319\pi\) | |||||||
\(954\) | 13.9323 | − | 13.9323i | 0.0146041 | − | 0.0146041i | ||||
\(955\) | −1005.31 | + | 1005.31i | −1.05268 | + | 1.05268i | ||||
\(956\) | 21.1462 | + | 21.1462i | 0.0221195 | + | 0.0221195i | ||||
\(957\) | 596.352 | + | 596.352i | 0.623147 | + | 0.623147i | ||||
\(958\) | −104.438 | −0.109017 | ||||||||
\(959\) | − | 1244.60i | − | 1.29782i | ||||||
\(960\) | 55.7829 | + | 55.7829i | 0.0581072 | + | 0.0581072i | ||||
\(961\) | 876.955i | 0.912544i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 225.721 | 0.234394 | ||||||||
\(964\) | −333.092 | + | 333.092i | −0.345531 | + | 0.345531i | ||||
\(965\) | 771.501 | 0.799483 | ||||||||
\(966\) | − | 153.475i | − | 0.158877i | ||||||
\(967\) | 299.780 | − | 299.780i | 0.310010 | − | 0.310010i | −0.534903 | − | 0.844913i | \(-0.679652\pi\) |
0.844913 | + | 0.534903i | \(0.179652\pi\) | |||||||
\(968\) | 105.414 | − | 105.414i | 0.108898 | − | 0.108898i | ||||
\(969\) | −700.929 | − | 700.929i | −0.723353 | − | 0.723353i | ||||
\(970\) | 863.912 | + | 863.912i | 0.890631 | + | 0.890631i | ||||
\(971\) | 645.587 | 0.664868 | 0.332434 | − | 0.943126i | \(-0.392130\pi\) | ||||
0.332434 | + | 0.943126i | \(0.392130\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 678.748 | + | 678.748i | 0.697583 | + | 0.697583i | ||||
\(974\) | 928.375i | 0.953157i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −154.170 | −0.157961 | ||||||||
\(977\) | −696.201 | + | 696.201i | −0.712591 | + | 0.712591i | −0.967076 | − | 0.254486i | \(-0.918094\pi\) |
0.254486 | + | 0.967076i | \(0.418094\pi\) | |||||||
\(978\) | 303.118 | 0.309937 | ||||||||
\(979\) | − | 2055.53i | − | 2.09962i | ||||||
\(980\) | 178.844 | − | 178.844i | 0.182494 | − | 0.182494i | ||||
\(981\) | 138.165 | − | 138.165i | 0.140841 | − | 0.140841i | ||||
\(982\) | 451.726 | + | 451.726i | 0.460006 | + | 0.460006i | ||||
\(983\) | 525.791 | + | 525.791i | 0.534884 | + | 0.534884i | 0.922022 | − | 0.387138i | \(-0.126536\pi\) |
−0.387138 | + | 0.922022i | \(0.626536\pi\) | |||||||
\(984\) | −32.3607 | −0.0328869 | ||||||||
\(985\) | − | 20.0196i | − | 0.0203245i | ||||||
\(986\) | −696.588 | − | 696.588i | −0.706479 | − | 0.706479i | ||||
\(987\) | − | 781.027i | − | 0.791314i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −164.704 | −0.166536 | ||||||||
\(990\) | −225.110 | + | 225.110i | −0.227384 | + | 0.227384i | ||||
\(991\) | 493.770 | 0.498255 | 0.249127 | − | 0.968471i | \(-0.419856\pi\) | ||||
0.249127 | + | 0.968471i | \(0.419856\pi\) | |||||||
\(992\) | 51.8599i | 0.0522781i | ||||||||
\(993\) | −447.122 | + | 447.122i | −0.450274 | + | 0.450274i | ||||
\(994\) | 210.184 | − | 210.184i | 0.211453 | − | 0.211453i | ||||
\(995\) | −1067.62 | − | 1067.62i | −1.07298 | − | 1.07298i | ||||
\(996\) | 219.932 | + | 219.932i | 0.220816 | + | 0.220816i | ||||
\(997\) | 1216.46 | 1.22012 | 0.610059 | − | 0.792356i | \(-0.291146\pi\) | ||||
0.610059 | + | 0.792356i | \(0.291146\pi\) | |||||||
\(998\) | − | 253.442i | − | 0.253950i | ||||||
\(999\) | 193.201 | + | 193.201i | 0.193394 | + | 0.193394i |
(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 | 1014.3.f.j.577.1 | 8 | ||
13.2 | odd | 12 | 78.3.l.c.7.2 | ✓ | 8 | ||
13.4 | even | 6 | 78.3.l.c.67.2 | yes | 8 | ||
13.5 | odd | 4 | 1014.3.f.h.775.2 | 8 | |||
13.8 | odd | 4 | inner | 1014.3.f.j.775.1 | 8 | ||
13.12 | even | 2 | 1014.3.f.h.577.2 | 8 | |||
39.2 | even | 12 | 234.3.bb.d.163.1 | 8 | |||
39.17 | odd | 6 | 234.3.bb.d.145.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.3.l.c.7.2 | ✓ | 8 | 13.2 | odd | 12 | ||
78.3.l.c.67.2 | yes | 8 | 13.4 | even | 6 | ||
234.3.bb.d.145.1 | 8 | 39.17 | odd | 6 | |||
234.3.bb.d.163.1 | 8 | 39.2 | even | 12 | |||
1014.3.f.h.577.2 | 8 | 13.12 | even | 2 | |||
1014.3.f.h.775.2 | 8 | 13.5 | odd | 4 | |||
1014.3.f.j.577.1 | 8 | 1.1 | even | 1 | trivial | ||
1014.3.f.j.775.1 | 8 | 13.8 | odd | 4 | inner |