Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [56,3,Mod(11,56)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(56, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("56.11");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 56 = 2^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 56.k (of order \(6\), 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: | \(1.52588948042\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 56.11 |
Dual form | 56.3.k.a.51.1 |
$q$-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 \(\left(\mathbb{Z}/56\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −1.00000 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | −0.937246 | − | 0.348669i | \(-0.886634\pi\) |
0.770579 | + | 0.637344i | \(0.219967\pi\) | |||||||
\(4\) | 4.00000 | 1.00000 | ||||||||
\(5\) | −4.50000 | + | 2.59808i | −0.900000 | + | 0.519615i | −0.877200 | − | 0.480125i | \(-0.840591\pi\) |
−0.0227998 | + | 0.999740i | \(0.507258\pi\) | |||||||
\(6\) | 1.00000 | − | 1.73205i | 0.166667 | − | 0.288675i | ||||
\(7\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(8\) | −8.00000 | −1.00000 | ||||||||
\(9\) | 4.00000 | + | 6.92820i | 0.444444 | + | 0.769800i | ||||
\(10\) | 9.00000 | − | 5.19615i | 0.900000 | − | 0.519615i | ||||
\(11\) | −8.50000 | + | 14.7224i | −0.772727 | + | 1.33840i | 0.163336 | + | 0.986571i | \(0.447775\pi\) |
−0.936063 | + | 0.351832i | \(0.885559\pi\) | |||||||
\(12\) | −2.00000 | + | 3.46410i | −0.166667 | + | 0.288675i | ||||
\(13\) | − | 13.8564i | − | 1.06588i | −0.846154 | − | 0.532939i | \(-0.821088\pi\) | ||
0.846154 | − | 0.532939i | \(-0.178912\pi\) | |||||||
\(14\) | 2.00000 | − | 13.8564i | 0.142857 | − | 0.989743i | ||||
\(15\) | − | 5.19615i | − | 0.346410i | ||||||
\(16\) | 16.0000 | 1.00000 | ||||||||
\(17\) | 12.5000 | − | 21.6506i | 0.735294 | − | 1.27357i | −0.219300 | − | 0.975657i | \(-0.570377\pi\) |
0.954594 | − | 0.297909i | \(-0.0962893\pi\) | |||||||
\(18\) | −8.00000 | − | 13.8564i | −0.444444 | − | 0.769800i | ||||
\(19\) | 3.50000 | + | 6.06218i | 0.184211 | + | 0.319062i | 0.943310 | − | 0.331912i | \(-0.107694\pi\) |
−0.759100 | + | 0.650974i | \(0.774361\pi\) | |||||||
\(20\) | −18.0000 | + | 10.3923i | −0.900000 | + | 0.519615i | ||||
\(21\) | −5.50000 | − | 4.33013i | −0.261905 | − | 0.206197i | ||||
\(22\) | 17.0000 | − | 29.4449i | 0.772727 | − | 1.33840i | ||||
\(23\) | 4.50000 | − | 2.59808i | 0.195652 | − | 0.112960i | −0.398974 | − | 0.916962i | \(-0.630634\pi\) |
0.594626 | + | 0.804003i | \(0.297300\pi\) | |||||||
\(24\) | 4.00000 | − | 6.92820i | 0.166667 | − | 0.288675i | ||||
\(25\) | 1.00000 | − | 1.73205i | 0.0400000 | − | 0.0692820i | ||||
\(26\) | 27.7128i | 1.06588i | ||||||||
\(27\) | −17.0000 | −0.629630 | ||||||||
\(28\) | −4.00000 | + | 27.7128i | −0.142857 | + | 0.989743i | ||||
\(29\) | 13.8564i | 0.477807i | 0.971043 | + | 0.238904i | \(0.0767880\pi\) | ||||
−0.971043 | + | 0.238904i | \(0.923212\pi\) | |||||||
\(30\) | 10.3923i | 0.346410i | ||||||||
\(31\) | 28.5000 | + | 16.4545i | 0.919355 | + | 0.530790i | 0.883429 | − | 0.468565i | \(-0.155229\pi\) |
0.0359257 | + | 0.999354i | \(0.488562\pi\) | |||||||
\(32\) | −32.0000 | −1.00000 | ||||||||
\(33\) | −8.50000 | − | 14.7224i | −0.257576 | − | 0.446134i | ||||
\(34\) | −25.0000 | + | 43.3013i | −0.735294 | + | 1.27357i | ||||
\(35\) | −13.5000 | − | 33.7750i | −0.385714 | − | 0.965000i | ||||
\(36\) | 16.0000 | + | 27.7128i | 0.444444 | + | 0.769800i | ||||
\(37\) | 7.50000 | − | 4.33013i | 0.202703 | − | 0.117030i | −0.395213 | − | 0.918590i | \(-0.629329\pi\) |
0.597916 | + | 0.801559i | \(0.295996\pi\) | |||||||
\(38\) | −7.00000 | − | 12.1244i | −0.184211 | − | 0.319062i | ||||
\(39\) | 12.0000 | + | 6.92820i | 0.307692 | + | 0.177646i | ||||
\(40\) | 36.0000 | − | 20.7846i | 0.900000 | − | 0.519615i | ||||
\(41\) | 26.0000 | 0.634146 | 0.317073 | − | 0.948401i | \(-0.397300\pi\) | ||||
0.317073 | + | 0.948401i | \(0.397300\pi\) | |||||||
\(42\) | 11.0000 | + | 8.66025i | 0.261905 | + | 0.206197i | ||||
\(43\) | 14.0000 | 0.325581 | 0.162791 | − | 0.986661i | \(-0.447950\pi\) | ||||
0.162791 | + | 0.986661i | \(0.447950\pi\) | |||||||
\(44\) | −34.0000 | + | 58.8897i | −0.772727 | + | 1.33840i | ||||
\(45\) | −36.0000 | − | 20.7846i | −0.800000 | − | 0.461880i | ||||
\(46\) | −9.00000 | + | 5.19615i | −0.195652 | + | 0.112960i | ||||
\(47\) | −43.5000 | + | 25.1147i | −0.925532 | + | 0.534356i | −0.885396 | − | 0.464838i | \(-0.846113\pi\) |
−0.0401362 | + | 0.999194i | \(0.512779\pi\) | |||||||
\(48\) | −8.00000 | + | 13.8564i | −0.166667 | + | 0.288675i | ||||
\(49\) | −47.0000 | − | 13.8564i | −0.959184 | − | 0.282784i | ||||
\(50\) | −2.00000 | + | 3.46410i | −0.0400000 | + | 0.0692820i | ||||
\(51\) | 12.5000 | + | 21.6506i | 0.245098 | + | 0.424522i | ||||
\(52\) | − | 55.4256i | − | 1.06588i | ||||||
\(53\) | 79.5000 | + | 45.8993i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 34.0000 | 0.629630 | ||||||||
\(55\) | − | 88.3346i | − | 1.60608i | ||||||
\(56\) | 8.00000 | − | 55.4256i | 0.142857 | − | 0.989743i | ||||
\(57\) | −7.00000 | −0.122807 | ||||||||
\(58\) | − | 27.7128i | − | 0.477807i | ||||||
\(59\) | 27.5000 | − | 47.6314i | 0.466102 | − | 0.807312i | −0.533149 | − | 0.846021i | \(-0.678991\pi\) |
0.999250 | + | 0.0387097i | \(0.0123247\pi\) | |||||||
\(60\) | − | 20.7846i | − | 0.346410i | ||||||
\(61\) | 19.5000 | − | 11.2583i | 0.319672 | − | 0.184563i | −0.331574 | − | 0.943429i | \(-0.607580\pi\) |
0.651246 | + | 0.758866i | \(0.274246\pi\) | |||||||
\(62\) | −57.0000 | − | 32.9090i | −0.919355 | − | 0.530790i | ||||
\(63\) | −52.0000 | + | 20.7846i | −0.825397 | + | 0.329914i | ||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | 36.0000 | + | 62.3538i | 0.553846 | + | 0.959290i | ||||
\(66\) | 17.0000 | + | 29.4449i | 0.257576 | + | 0.446134i | ||||
\(67\) | −8.50000 | + | 14.7224i | −0.126866 | + | 0.219738i | −0.922461 | − | 0.386091i | \(-0.873825\pi\) |
0.795595 | + | 0.605829i | \(0.207158\pi\) | |||||||
\(68\) | 50.0000 | − | 86.6025i | 0.735294 | − | 1.27357i | ||||
\(69\) | 5.19615i | 0.0753066i | ||||||||
\(70\) | 27.0000 | + | 67.5500i | 0.385714 | + | 0.965000i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | −32.0000 | − | 55.4256i | −0.444444 | − | 0.769800i | ||||
\(73\) | −59.5000 | + | 103.057i | −0.815068 | + | 1.41174i | 0.0942102 | + | 0.995552i | \(0.469967\pi\) |
−0.909279 | + | 0.416188i | \(0.863366\pi\) | |||||||
\(74\) | −15.0000 | + | 8.66025i | −0.202703 | + | 0.117030i | ||||
\(75\) | 1.00000 | + | 1.73205i | 0.0133333 | + | 0.0230940i | ||||
\(76\) | 14.0000 | + | 24.2487i | 0.184211 | + | 0.319062i | ||||
\(77\) | −93.5000 | − | 73.6122i | −1.21429 | − | 0.956002i | ||||
\(78\) | −24.0000 | − | 13.8564i | −0.307692 | − | 0.177646i | ||||
\(79\) | 64.5000 | − | 37.2391i | 0.816456 | − | 0.471381i | −0.0327370 | − | 0.999464i | \(-0.510422\pi\) |
0.849193 | + | 0.528083i | \(0.177089\pi\) | |||||||
\(80\) | −72.0000 | + | 41.5692i | −0.900000 | + | 0.519615i | ||||
\(81\) | −27.5000 | + | 47.6314i | −0.339506 | + | 0.588042i | ||||
\(82\) | −52.0000 | −0.634146 | ||||||||
\(83\) | 110.000 | 1.32530 | 0.662651 | − | 0.748929i | \(-0.269431\pi\) | ||||
0.662651 | + | 0.748929i | \(0.269431\pi\) | |||||||
\(84\) | −22.0000 | − | 17.3205i | −0.261905 | − | 0.206197i | ||||
\(85\) | 129.904i | 1.52828i | ||||||||
\(86\) | −28.0000 | −0.325581 | ||||||||
\(87\) | −12.0000 | − | 6.92820i | −0.137931 | − | 0.0796345i | ||||
\(88\) | 68.0000 | − | 117.779i | 0.772727 | − | 1.33840i | ||||
\(89\) | −35.5000 | − | 61.4878i | −0.398876 | − | 0.690874i | 0.594711 | − | 0.803939i | \(-0.297266\pi\) |
−0.993588 | + | 0.113065i | \(0.963933\pi\) | |||||||
\(90\) | 72.0000 | + | 41.5692i | 0.800000 | + | 0.461880i | ||||
\(91\) | 96.0000 | + | 13.8564i | 1.05495 | + | 0.152268i | ||||
\(92\) | 18.0000 | − | 10.3923i | 0.195652 | − | 0.112960i | ||||
\(93\) | −28.5000 | + | 16.4545i | −0.306452 | + | 0.176930i | ||||
\(94\) | 87.0000 | − | 50.2295i | 0.925532 | − | 0.534356i | ||||
\(95\) | −31.5000 | − | 18.1865i | −0.331579 | − | 0.191437i | ||||
\(96\) | 16.0000 | − | 27.7128i | 0.166667 | − | 0.288675i | ||||
\(97\) | −22.0000 | −0.226804 | −0.113402 | − | 0.993549i | \(-0.536175\pi\) | ||||
−0.113402 | + | 0.993549i | \(0.536175\pi\) | |||||||
\(98\) | 94.0000 | + | 27.7128i | 0.959184 | + | 0.282784i | ||||
\(99\) | −136.000 | −1.37374 | ||||||||
\(100\) | 4.00000 | − | 6.92820i | 0.0400000 | − | 0.0692820i | ||||
\(101\) | 67.5000 | + | 38.9711i | 0.668317 | + | 0.385853i | 0.795439 | − | 0.606034i | \(-0.207241\pi\) |
−0.127122 | + | 0.991887i | \(0.540574\pi\) | |||||||
\(102\) | −25.0000 | − | 43.3013i | −0.245098 | − | 0.424522i | ||||
\(103\) | −139.500 | + | 80.5404i | −1.35437 | + | 0.781945i | −0.988858 | − | 0.148862i | \(-0.952439\pi\) |
−0.365511 | + | 0.930807i | \(0.619106\pi\) | |||||||
\(104\) | 110.851i | 1.06588i | ||||||||
\(105\) | 36.0000 | + | 5.19615i | 0.342857 | + | 0.0494872i | ||||
\(106\) | −159.000 | − | 91.7987i | −1.50000 | − | 0.866025i | ||||
\(107\) | −32.5000 | − | 56.2917i | −0.303738 | − | 0.526090i | 0.673241 | − | 0.739423i | \(-0.264902\pi\) |
−0.976980 | + | 0.213333i | \(0.931568\pi\) | |||||||
\(108\) | −68.0000 | −0.629630 | ||||||||
\(109\) | 7.50000 | + | 4.33013i | 0.0688073 | + | 0.0397259i | 0.534009 | − | 0.845479i | \(-0.320685\pi\) |
−0.465202 | + | 0.885205i | \(0.654018\pi\) | |||||||
\(110\) | 176.669i | 1.60608i | ||||||||
\(111\) | 8.66025i | 0.0780203i | ||||||||
\(112\) | −16.0000 | + | 110.851i | −0.142857 | + | 0.989743i | ||||
\(113\) | 122.000 | 1.07965 | 0.539823 | − | 0.841779i | \(-0.318491\pi\) | ||||
0.539823 | + | 0.841779i | \(0.318491\pi\) | |||||||
\(114\) | 14.0000 | 0.122807 | ||||||||
\(115\) | −13.5000 | + | 23.3827i | −0.117391 | + | 0.203328i | ||||
\(116\) | 55.4256i | 0.477807i | ||||||||
\(117\) | 96.0000 | − | 55.4256i | 0.820513 | − | 0.473723i | ||||
\(118\) | −55.0000 | + | 95.2628i | −0.466102 | + | 0.807312i | ||||
\(119\) | 137.500 | + | 108.253i | 1.15546 | + | 0.909691i | ||||
\(120\) | 41.5692i | 0.346410i | ||||||||
\(121\) | −84.0000 | − | 145.492i | −0.694215 | − | 1.20242i | ||||
\(122\) | −39.0000 | + | 22.5167i | −0.319672 | + | 0.184563i | ||||
\(123\) | −13.0000 | + | 22.5167i | −0.105691 | + | 0.183062i | ||||
\(124\) | 114.000 | + | 65.8179i | 0.919355 | + | 0.530790i | ||||
\(125\) | − | 119.512i | − | 0.956092i | ||||||
\(126\) | 104.000 | − | 41.5692i | 0.825397 | − | 0.329914i | ||||
\(127\) | − | 166.277i | − | 1.30927i | −0.755947 | − | 0.654633i | \(-0.772823\pi\) | ||
0.755947 | − | 0.654633i | \(-0.227177\pi\) | |||||||
\(128\) | −128.000 | −1.00000 | ||||||||
\(129\) | −7.00000 | + | 12.1244i | −0.0542636 | + | 0.0939873i | ||||
\(130\) | −72.0000 | − | 124.708i | −0.553846 | − | 0.959290i | ||||
\(131\) | −8.50000 | − | 14.7224i | −0.0648855 | − | 0.112385i | 0.831758 | − | 0.555139i | \(-0.187335\pi\) |
−0.896643 | + | 0.442754i | \(0.854002\pi\) | |||||||
\(132\) | −34.0000 | − | 58.8897i | −0.257576 | − | 0.446134i | ||||
\(133\) | −45.5000 | + | 18.1865i | −0.342105 | + | 0.136741i | ||||
\(134\) | 17.0000 | − | 29.4449i | 0.126866 | − | 0.219738i | ||||
\(135\) | 76.5000 | − | 44.1673i | 0.566667 | − | 0.327165i | ||||
\(136\) | −100.000 | + | 173.205i | −0.735294 | + | 1.27357i | ||||
\(137\) | 72.5000 | − | 125.574i | 0.529197 | − | 0.916596i | −0.470223 | − | 0.882548i | \(-0.655827\pi\) |
0.999420 | − | 0.0340486i | \(-0.0108401\pi\) | |||||||
\(138\) | − | 10.3923i | − | 0.0753066i | ||||||
\(139\) | −82.0000 | −0.589928 | −0.294964 | − | 0.955508i | \(-0.595308\pi\) | ||||
−0.294964 | + | 0.955508i | \(0.595308\pi\) | |||||||
\(140\) | −54.0000 | − | 135.100i | −0.385714 | − | 0.965000i | ||||
\(141\) | − | 50.2295i | − | 0.356237i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 204.000 | + | 117.779i | 1.42657 | + | 0.823633i | ||||
\(144\) | 64.0000 | + | 110.851i | 0.444444 | + | 0.769800i | ||||
\(145\) | −36.0000 | − | 62.3538i | −0.248276 | − | 0.430026i | ||||
\(146\) | 119.000 | − | 206.114i | 0.815068 | − | 1.41174i | ||||
\(147\) | 35.5000 | − | 33.7750i | 0.241497 | − | 0.229762i | ||||
\(148\) | 30.0000 | − | 17.3205i | 0.202703 | − | 0.117030i | ||||
\(149\) | −4.50000 | + | 2.59808i | −0.0302013 | + | 0.0174368i | −0.515025 | − | 0.857175i | \(-0.672217\pi\) |
0.484823 | + | 0.874612i | \(0.338884\pi\) | |||||||
\(150\) | −2.00000 | − | 3.46410i | −0.0133333 | − | 0.0230940i | ||||
\(151\) | −31.5000 | − | 18.1865i | −0.208609 | − | 0.120441i | 0.392056 | − | 0.919942i | \(-0.371764\pi\) |
−0.600665 | + | 0.799501i | \(0.705097\pi\) | |||||||
\(152\) | −28.0000 | − | 48.4974i | −0.184211 | − | 0.319062i | ||||
\(153\) | 200.000 | 1.30719 | ||||||||
\(154\) | 187.000 | + | 147.224i | 1.21429 | + | 0.956002i | ||||
\(155\) | −171.000 | −1.10323 | ||||||||
\(156\) | 48.0000 | + | 27.7128i | 0.307692 | + | 0.177646i | ||||
\(157\) | −268.500 | − | 155.019i | −1.71019 | − | 0.987379i | −0.934282 | − | 0.356534i | \(-0.883958\pi\) |
−0.775909 | − | 0.630845i | \(-0.782708\pi\) | |||||||
\(158\) | −129.000 | + | 74.4782i | −0.816456 | + | 0.471381i | ||||
\(159\) | −79.5000 | + | 45.8993i | −0.500000 | + | 0.288675i | ||||
\(160\) | 144.000 | − | 83.1384i | 0.900000 | − | 0.519615i | ||||
\(161\) | 13.5000 | + | 33.7750i | 0.0838509 | + | 0.209783i | ||||
\(162\) | 55.0000 | − | 95.2628i | 0.339506 | − | 0.588042i | ||||
\(163\) | −8.50000 | − | 14.7224i | −0.0521472 | − | 0.0903217i | 0.838773 | − | 0.544481i | \(-0.183273\pi\) |
−0.890921 | + | 0.454159i | \(0.849940\pi\) | |||||||
\(164\) | 104.000 | 0.634146 | ||||||||
\(165\) | 76.5000 | + | 44.1673i | 0.463636 | + | 0.267681i | ||||
\(166\) | −220.000 | −1.32530 | ||||||||
\(167\) | − | 13.8564i | − | 0.0829725i | −0.999139 | − | 0.0414862i | \(-0.986791\pi\) | ||
0.999139 | − | 0.0414862i | \(-0.0132093\pi\) | |||||||
\(168\) | 44.0000 | + | 34.6410i | 0.261905 | + | 0.206197i | ||||
\(169\) | −23.0000 | −0.136095 | ||||||||
\(170\) | − | 259.808i | − | 1.52828i | ||||||
\(171\) | −28.0000 | + | 48.4974i | −0.163743 | + | 0.283611i | ||||
\(172\) | 56.0000 | 0.325581 | ||||||||
\(173\) | 91.5000 | − | 52.8275i | 0.528902 | − | 0.305362i | −0.211667 | − | 0.977342i | \(-0.567889\pi\) |
0.740569 | + | 0.671980i | \(0.234556\pi\) | |||||||
\(174\) | 24.0000 | + | 13.8564i | 0.137931 | + | 0.0796345i | ||||
\(175\) | 11.0000 | + | 8.66025i | 0.0628571 | + | 0.0494872i | ||||
\(176\) | −136.000 | + | 235.559i | −0.772727 | + | 1.33840i | ||||
\(177\) | 27.5000 | + | 47.6314i | 0.155367 | + | 0.269104i | ||||
\(178\) | 71.0000 | + | 122.976i | 0.398876 | + | 0.690874i | ||||
\(179\) | −44.5000 | + | 77.0763i | −0.248603 | + | 0.430594i | −0.963139 | − | 0.269006i | \(-0.913305\pi\) |
0.714535 | + | 0.699600i | \(0.246638\pi\) | |||||||
\(180\) | −144.000 | − | 83.1384i | −0.800000 | − | 0.461880i | ||||
\(181\) | 249.415i | 1.37799i | 0.724768 | + | 0.688993i | \(0.241947\pi\) | ||||
−0.724768 | + | 0.688993i | \(0.758053\pi\) | |||||||
\(182\) | −192.000 | − | 27.7128i | −1.05495 | − | 0.152268i | ||||
\(183\) | 22.5167i | 0.123042i | ||||||||
\(184\) | −36.0000 | + | 20.7846i | −0.195652 | + | 0.112960i | ||||
\(185\) | −22.5000 | + | 38.9711i | −0.121622 | + | 0.210655i | ||||
\(186\) | 57.0000 | − | 32.9090i | 0.306452 | − | 0.176930i | ||||
\(187\) | 212.500 | + | 368.061i | 1.13636 | + | 1.96824i | ||||
\(188\) | −174.000 | + | 100.459i | −0.925532 | + | 0.534356i | ||||
\(189\) | 17.0000 | − | 117.779i | 0.0899471 | − | 0.623172i | ||||
\(190\) | 63.0000 | + | 36.3731i | 0.331579 | + | 0.191437i | ||||
\(191\) | −187.500 | + | 108.253i | −0.981675 | + | 0.566771i | −0.902776 | − | 0.430112i | \(-0.858474\pi\) |
−0.0788999 | + | 0.996883i | \(0.525141\pi\) | |||||||
\(192\) | −32.0000 | + | 55.4256i | −0.166667 | + | 0.288675i | ||||
\(193\) | 36.5000 | − | 63.2199i | 0.189119 | − | 0.327564i | −0.755838 | − | 0.654759i | \(-0.772770\pi\) |
0.944957 | + | 0.327195i | \(0.106103\pi\) | |||||||
\(194\) | 44.0000 | 0.226804 | ||||||||
\(195\) | −72.0000 | −0.369231 | ||||||||
\(196\) | −188.000 | − | 55.4256i | −0.959184 | − | 0.282784i | ||||
\(197\) | 207.846i | 1.05506i | 0.849538 | + | 0.527528i | \(0.176881\pi\) | ||||
−0.849538 | + | 0.527528i | \(0.823119\pi\) | |||||||
\(198\) | 272.000 | 1.37374 | ||||||||
\(199\) | −55.5000 | − | 32.0429i | −0.278894 | − | 0.161020i | 0.354028 | − | 0.935235i | \(-0.384812\pi\) |
−0.632923 | + | 0.774215i | \(0.718145\pi\) | |||||||
\(200\) | −8.00000 | + | 13.8564i | −0.0400000 | + | 0.0692820i | ||||
\(201\) | −8.50000 | − | 14.7224i | −0.0422886 | − | 0.0732459i | ||||
\(202\) | −135.000 | − | 77.9423i | −0.668317 | − | 0.385853i | ||||
\(203\) | −96.0000 | − | 13.8564i | −0.472906 | − | 0.0682582i | ||||
\(204\) | 50.0000 | + | 86.6025i | 0.245098 | + | 0.424522i | ||||
\(205\) | −117.000 | + | 67.5500i | −0.570732 | + | 0.329512i | ||||
\(206\) | 279.000 | − | 161.081i | 1.35437 | − | 0.781945i | ||||
\(207\) | 36.0000 | + | 20.7846i | 0.173913 | + | 0.100409i | ||||
\(208\) | − | 221.703i | − | 1.06588i | ||||||
\(209\) | −119.000 | −0.569378 | ||||||||
\(210\) | −72.0000 | − | 10.3923i | −0.342857 | − | 0.0494872i | ||||
\(211\) | 302.000 | 1.43128 | 0.715640 | − | 0.698470i | \(-0.246135\pi\) | ||||
0.715640 | + | 0.698470i | \(0.246135\pi\) | |||||||
\(212\) | 318.000 | + | 183.597i | 1.50000 | + | 0.866025i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 65.0000 | + | 112.583i | 0.303738 | + | 0.526090i | ||||
\(215\) | −63.0000 | + | 36.3731i | −0.293023 | + | 0.169177i | ||||
\(216\) | 136.000 | 0.629630 | ||||||||
\(217\) | −142.500 | + | 180.999i | −0.656682 | + | 0.834098i | ||||
\(218\) | −15.0000 | − | 8.66025i | −0.0688073 | − | 0.0397259i | ||||
\(219\) | −59.5000 | − | 103.057i | −0.271689 | − | 0.470580i | ||||
\(220\) | − | 353.338i | − | 1.60608i | ||||||
\(221\) | −300.000 | − | 173.205i | −1.35747 | − | 0.783733i | ||||
\(222\) | − | 17.3205i | − | 0.0780203i | ||||||
\(223\) | 138.564i | 0.621364i | 0.950514 | + | 0.310682i | \(0.100557\pi\) | ||||
−0.950514 | + | 0.310682i | \(0.899443\pi\) | |||||||
\(224\) | 32.0000 | − | 221.703i | 0.142857 | − | 0.989743i | ||||
\(225\) | 16.0000 | 0.0711111 | ||||||||
\(226\) | −244.000 | −1.07965 | ||||||||
\(227\) | 27.5000 | − | 47.6314i | 0.121145 | − | 0.209830i | −0.799074 | − | 0.601232i | \(-0.794677\pi\) |
0.920220 | + | 0.391402i | \(0.128010\pi\) | |||||||
\(228\) | −28.0000 | −0.122807 | ||||||||
\(229\) | 283.500 | − | 163.679i | 1.23799 | − | 0.714755i | 0.269308 | − | 0.963054i | \(-0.413205\pi\) |
0.968683 | + | 0.248300i | \(0.0798717\pi\) | |||||||
\(230\) | 27.0000 | − | 46.7654i | 0.117391 | − | 0.203328i | ||||
\(231\) | 110.500 | − | 44.1673i | 0.478355 | − | 0.191200i | ||||
\(232\) | − | 110.851i | − | 0.477807i | ||||||
\(233\) | 192.500 | + | 333.420i | 0.826180 | + | 1.43099i | 0.901014 | + | 0.433790i | \(0.142824\pi\) |
−0.0748337 | + | 0.997196i | \(0.523843\pi\) | |||||||
\(234\) | −192.000 | + | 110.851i | −0.820513 | + | 0.473723i | ||||
\(235\) | 130.500 | − | 226.033i | 0.555319 | − | 0.961841i | ||||
\(236\) | 110.000 | − | 190.526i | 0.466102 | − | 0.807312i | ||||
\(237\) | 74.4782i | 0.314254i | ||||||||
\(238\) | −275.000 | − | 216.506i | −1.15546 | − | 0.909691i | ||||
\(239\) | − | 429.549i | − | 1.79727i | −0.438693 | − | 0.898637i | \(-0.644558\pi\) | ||
0.438693 | − | 0.898637i | \(-0.355442\pi\) | |||||||
\(240\) | − | 83.1384i | − | 0.346410i | ||||||
\(241\) | 72.5000 | − | 125.574i | 0.300830 | − | 0.521053i | −0.675494 | − | 0.737365i | \(-0.736070\pi\) |
0.976324 | + | 0.216313i | \(0.0694030\pi\) | |||||||
\(242\) | 168.000 | + | 290.985i | 0.694215 | + | 1.20242i | ||||
\(243\) | −104.000 | − | 180.133i | −0.427984 | − | 0.741289i | ||||
\(244\) | 78.0000 | − | 45.0333i | 0.319672 | − | 0.184563i | ||||
\(245\) | 247.500 | − | 59.7558i | 1.01020 | − | 0.243901i | ||||
\(246\) | 26.0000 | − | 45.0333i | 0.105691 | − | 0.183062i | ||||
\(247\) | 84.0000 | − | 48.4974i | 0.340081 | − | 0.196346i | ||||
\(248\) | −228.000 | − | 131.636i | −0.919355 | − | 0.530790i | ||||
\(249\) | −55.0000 | + | 95.2628i | −0.220884 | + | 0.382582i | ||||
\(250\) | 239.023i | 0.956092i | ||||||||
\(251\) | −58.0000 | −0.231076 | −0.115538 | − | 0.993303i | \(-0.536859\pi\) | ||||
−0.115538 | + | 0.993303i | \(0.536859\pi\) | |||||||
\(252\) | −208.000 | + | 83.1384i | −0.825397 | + | 0.329914i | ||||
\(253\) | 88.3346i | 0.349149i | ||||||||
\(254\) | 332.554i | 1.30927i | ||||||||
\(255\) | −112.500 | − | 64.9519i | −0.441176 | − | 0.254713i | ||||
\(256\) | 256.000 | 1.00000 | ||||||||
\(257\) | −59.5000 | − | 103.057i | −0.231518 | − | 0.401000i | 0.726737 | − | 0.686915i | \(-0.241036\pi\) |
−0.958255 | + | 0.285915i | \(0.907702\pi\) | |||||||
\(258\) | 14.0000 | − | 24.2487i | 0.0542636 | − | 0.0939873i | ||||
\(259\) | 22.5000 | + | 56.2917i | 0.0868726 | + | 0.217342i | ||||
\(260\) | 144.000 | + | 249.415i | 0.553846 | + | 0.959290i | ||||
\(261\) | −96.0000 | + | 55.4256i | −0.367816 | + | 0.212359i | ||||
\(262\) | 17.0000 | + | 29.4449i | 0.0648855 | + | 0.112385i | ||||
\(263\) | −283.500 | − | 163.679i | −1.07795 | − | 0.622353i | −0.147605 | − | 0.989046i | \(-0.547156\pi\) |
−0.930342 | + | 0.366694i | \(0.880490\pi\) | |||||||
\(264\) | 68.0000 | + | 117.779i | 0.257576 | + | 0.446134i | ||||
\(265\) | −477.000 | −1.80000 | ||||||||
\(266\) | 91.0000 | − | 36.3731i | 0.342105 | − | 0.136741i | ||||
\(267\) | 71.0000 | 0.265918 | ||||||||
\(268\) | −34.0000 | + | 58.8897i | −0.126866 | + | 0.219738i | ||||
\(269\) | 115.500 | + | 66.6840i | 0.429368 | + | 0.247896i | 0.699077 | − | 0.715046i | \(-0.253594\pi\) |
−0.269709 | + | 0.962942i | \(0.586928\pi\) | |||||||
\(270\) | −153.000 | + | 88.3346i | −0.566667 | + | 0.327165i | ||||
\(271\) | 376.500 | − | 217.372i | 1.38930 | − | 0.802112i | 0.396063 | − | 0.918223i | \(-0.370376\pi\) |
0.993236 | + | 0.116111i | \(0.0370430\pi\) | |||||||
\(272\) | 200.000 | − | 346.410i | 0.735294 | − | 1.27357i | ||||
\(273\) | −60.0000 | + | 76.2102i | −0.219780 | + | 0.279158i | ||||
\(274\) | −145.000 | + | 251.147i | −0.529197 | + | 0.916596i | ||||
\(275\) | 17.0000 | + | 29.4449i | 0.0618182 | + | 0.107072i | ||||
\(276\) | 20.7846i | 0.0753066i | ||||||||
\(277\) | 175.500 | + | 101.325i | 0.633574 | + | 0.365794i | 0.782135 | − | 0.623109i | \(-0.214131\pi\) |
−0.148561 | + | 0.988903i | \(0.547464\pi\) | |||||||
\(278\) | 164.000 | 0.589928 | ||||||||
\(279\) | 263.272i | 0.943626i | ||||||||
\(280\) | 108.000 | + | 270.200i | 0.385714 | + | 0.965000i | ||||
\(281\) | 74.0000 | 0.263345 | 0.131673 | − | 0.991293i | \(-0.457965\pi\) | ||||
0.131673 | + | 0.991293i | \(0.457965\pi\) | |||||||
\(282\) | 100.459i | 0.356237i | ||||||||
\(283\) | 231.500 | − | 400.970i | 0.818021 | − | 1.41685i | −0.0891169 | − | 0.996021i | \(-0.528404\pi\) |
0.907138 | − | 0.420833i | \(-0.138262\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 31.5000 | − | 18.1865i | 0.110526 | − | 0.0638124i | ||||
\(286\) | −408.000 | − | 235.559i | −1.42657 | − | 0.823633i | ||||
\(287\) | −26.0000 | + | 180.133i | −0.0905923 | + | 0.627642i | ||||
\(288\) | −128.000 | − | 221.703i | −0.444444 | − | 0.769800i | ||||
\(289\) | −168.000 | − | 290.985i | −0.581315 | − | 1.00687i | ||||
\(290\) | 72.0000 | + | 124.708i | 0.248276 | + | 0.430026i | ||||
\(291\) | 11.0000 | − | 19.0526i | 0.0378007 | − | 0.0654727i | ||||
\(292\) | −238.000 | + | 412.228i | −0.815068 | + | 1.41174i | ||||
\(293\) | 110.851i | 0.378332i | 0.981945 | + | 0.189166i | \(0.0605784\pi\) | ||||
−0.981945 | + | 0.189166i | \(0.939422\pi\) | |||||||
\(294\) | −71.0000 | + | 67.5500i | −0.241497 | + | 0.229762i | ||||
\(295\) | 285.788i | 0.968774i | ||||||||
\(296\) | −60.0000 | + | 34.6410i | −0.202703 | + | 0.117030i | ||||
\(297\) | 144.500 | − | 250.281i | 0.486532 | − | 0.842698i | ||||
\(298\) | 9.00000 | − | 5.19615i | 0.0302013 | − | 0.0174368i | ||||
\(299\) | −36.0000 | − | 62.3538i | −0.120401 | − | 0.208541i | ||||
\(300\) | 4.00000 | + | 6.92820i | 0.0133333 | + | 0.0230940i | ||||
\(301\) | −14.0000 | + | 96.9948i | −0.0465116 | + | 0.322242i | ||||
\(302\) | 63.0000 | + | 36.3731i | 0.208609 | + | 0.120441i | ||||
\(303\) | −67.5000 | + | 38.9711i | −0.222772 | + | 0.128618i | ||||
\(304\) | 56.0000 | + | 96.9948i | 0.184211 | + | 0.319062i | ||||
\(305\) | −58.5000 | + | 101.325i | −0.191803 | + | 0.332213i | ||||
\(306\) | −400.000 | −1.30719 | ||||||||
\(307\) | −274.000 | −0.892508 | −0.446254 | − | 0.894906i | \(-0.647242\pi\) | ||||
−0.446254 | + | 0.894906i | \(0.647242\pi\) | |||||||
\(308\) | −374.000 | − | 294.449i | −1.21429 | − | 0.956002i | ||||
\(309\) | − | 161.081i | − | 0.521297i | ||||||
\(310\) | 342.000 | 1.10323 | ||||||||
\(311\) | −43.5000 | − | 25.1147i | −0.139871 | − | 0.0807548i | 0.428431 | − | 0.903574i | \(-0.359066\pi\) |
−0.568303 | + | 0.822820i | \(0.692400\pi\) | |||||||
\(312\) | −96.0000 | − | 55.4256i | −0.307692 | − | 0.177646i | ||||
\(313\) | 204.500 | + | 354.204i | 0.653355 | + | 1.13164i | 0.982304 | + | 0.187296i | \(0.0599723\pi\) |
−0.328949 | + | 0.944348i | \(0.606694\pi\) | |||||||
\(314\) | 537.000 | + | 310.037i | 1.71019 | + | 0.987379i | ||||
\(315\) | 180.000 | − | 228.631i | 0.571429 | − | 0.725812i | ||||
\(316\) | 258.000 | − | 148.956i | 0.816456 | − | 0.471381i | ||||
\(317\) | 163.500 | − | 94.3968i | 0.515773 | − | 0.297782i | −0.219431 | − | 0.975628i | \(-0.570420\pi\) |
0.735203 | + | 0.677847i | \(0.237087\pi\) | |||||||
\(318\) | 159.000 | − | 91.7987i | 0.500000 | − | 0.288675i | ||||
\(319\) | −204.000 | − | 117.779i | −0.639498 | − | 0.369215i | ||||
\(320\) | −288.000 | + | 166.277i | −0.900000 | + | 0.519615i | ||||
\(321\) | 65.0000 | 0.202492 | ||||||||
\(322\) | −27.0000 | − | 67.5500i | −0.0838509 | − | 0.209783i | ||||
\(323\) | 175.000 | 0.541796 | ||||||||
\(324\) | −110.000 | + | 190.526i | −0.339506 | + | 0.588042i | ||||
\(325\) | −24.0000 | − | 13.8564i | −0.0738462 | − | 0.0426351i | ||||
\(326\) | 17.0000 | + | 29.4449i | 0.0521472 | + | 0.0903217i | ||||
\(327\) | −7.50000 | + | 4.33013i | −0.0229358 | + | 0.0132420i | ||||
\(328\) | −208.000 | −0.634146 | ||||||||
\(329\) | −130.500 | − | 326.492i | −0.396657 | − | 0.992376i | ||||
\(330\) | −153.000 | − | 88.3346i | −0.463636 | − | 0.267681i | ||||
\(331\) | 147.500 | + | 255.477i | 0.445619 | + | 0.771835i | 0.998095 | − | 0.0616936i | \(-0.0196502\pi\) |
−0.552476 | + | 0.833529i | \(0.686317\pi\) | |||||||
\(332\) | 440.000 | 1.32530 | ||||||||
\(333\) | 60.0000 | + | 34.6410i | 0.180180 | + | 0.104027i | ||||
\(334\) | 27.7128i | 0.0829725i | ||||||||
\(335\) | − | 88.3346i | − | 0.263685i | ||||||
\(336\) | −88.0000 | − | 69.2820i | −0.261905 | − | 0.206197i | ||||
\(337\) | 26.0000 | 0.0771513 | 0.0385757 | − | 0.999256i | \(-0.487718\pi\) | ||||
0.0385757 | + | 0.999256i | \(0.487718\pi\) | |||||||
\(338\) | 46.0000 | 0.136095 | ||||||||
\(339\) | −61.0000 | + | 105.655i | −0.179941 | + | 0.311667i | ||||
\(340\) | 519.615i | 1.52828i | ||||||||
\(341\) | −484.500 | + | 279.726i | −1.42082 | + | 0.820311i | ||||
\(342\) | 56.0000 | − | 96.9948i | 0.163743 | − | 0.283611i | ||||
\(343\) | 143.000 | − | 311.769i | 0.416910 | − | 0.908948i | ||||
\(344\) | −112.000 | −0.325581 | ||||||||
\(345\) | −13.5000 | − | 23.3827i | −0.0391304 | − | 0.0677759i | ||||
\(346\) | −183.000 | + | 105.655i | −0.528902 | + | 0.305362i | ||||
\(347\) | −188.500 | + | 326.492i | −0.543228 | + | 0.940898i | 0.455488 | + | 0.890242i | \(0.349465\pi\) |
−0.998716 | + | 0.0506562i | \(0.983869\pi\) | |||||||
\(348\) | −48.0000 | − | 27.7128i | −0.137931 | − | 0.0796345i | ||||
\(349\) | 96.9948i | 0.277922i | 0.990298 | + | 0.138961i | \(0.0443763\pi\) | ||||
−0.990298 | + | 0.138961i | \(0.955624\pi\) | |||||||
\(350\) | −22.0000 | − | 17.3205i | −0.0628571 | − | 0.0494872i | ||||
\(351\) | 235.559i | 0.671108i | ||||||||
\(352\) | 272.000 | − | 471.118i | 0.772727 | − | 1.33840i | ||||
\(353\) | −251.500 | + | 435.611i | −0.712465 | + | 1.23402i | 0.251465 | + | 0.967866i | \(0.419088\pi\) |
−0.963929 | + | 0.266158i | \(0.914246\pi\) | |||||||
\(354\) | −55.0000 | − | 95.2628i | −0.155367 | − | 0.269104i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −142.000 | − | 245.951i | −0.398876 | − | 0.690874i | ||||
\(357\) | −162.500 | + | 64.9519i | −0.455182 | + | 0.181938i | ||||
\(358\) | 89.0000 | − | 154.153i | 0.248603 | − | 0.430594i | ||||
\(359\) | 160.500 | − | 92.6647i | 0.447075 | − | 0.258119i | −0.259519 | − | 0.965738i | \(-0.583564\pi\) |
0.706594 | + | 0.707619i | \(0.250231\pi\) | |||||||
\(360\) | 288.000 | + | 166.277i | 0.800000 | + | 0.461880i | ||||
\(361\) | 156.000 | − | 270.200i | 0.432133 | − | 0.748476i | ||||
\(362\) | − | 498.831i | − | 1.37799i | ||||||
\(363\) | 168.000 | 0.462810 | ||||||||
\(364\) | 384.000 | + | 55.4256i | 1.05495 | + | 0.152268i | ||||
\(365\) | − | 618.342i | − | 1.69409i | ||||||
\(366\) | − | 45.0333i | − | 0.123042i | ||||||
\(367\) | 256.500 | + | 148.090i | 0.698910 | + | 0.403516i | 0.806941 | − | 0.590632i | \(-0.201121\pi\) |
−0.108031 | + | 0.994147i | \(0.534455\pi\) | |||||||
\(368\) | 72.0000 | − | 41.5692i | 0.195652 | − | 0.112960i | ||||
\(369\) | 104.000 | + | 180.133i | 0.281843 | + | 0.488166i | ||||
\(370\) | 45.0000 | − | 77.9423i | 0.121622 | − | 0.210655i | ||||
\(371\) | −397.500 | + | 504.893i | −1.07143 | + | 1.36090i | ||||
\(372\) | −114.000 | + | 65.8179i | −0.306452 | + | 0.176930i | ||||
\(373\) | 103.500 | − | 59.7558i | 0.277480 | − | 0.160203i | −0.354802 | − | 0.934941i | \(-0.615452\pi\) |
0.632282 | + | 0.774738i | \(0.282118\pi\) | |||||||
\(374\) | −425.000 | − | 736.122i | −1.13636 | − | 1.96824i | ||||
\(375\) | 103.500 | + | 59.7558i | 0.276000 | + | 0.159349i | ||||
\(376\) | 348.000 | − | 200.918i | 0.925532 | − | 0.534356i | ||||
\(377\) | 192.000 | 0.509284 | ||||||||
\(378\) | −34.0000 | + | 235.559i | −0.0899471 | + | 0.623172i | ||||
\(379\) | −634.000 | −1.67282 | −0.836412 | − | 0.548102i | \(-0.815351\pi\) | ||||
−0.836412 | + | 0.548102i | \(0.815351\pi\) | |||||||
\(380\) | −126.000 | − | 72.7461i | −0.331579 | − | 0.191437i | ||||
\(381\) | 144.000 | + | 83.1384i | 0.377953 | + | 0.218211i | ||||
\(382\) | 375.000 | − | 216.506i | 0.981675 | − | 0.566771i | ||||
\(383\) | −211.500 | + | 122.110i | −0.552219 | + | 0.318824i | −0.750017 | − | 0.661419i | \(-0.769955\pi\) |
0.197797 | + | 0.980243i | \(0.436621\pi\) | |||||||
\(384\) | 64.0000 | − | 110.851i | 0.166667 | − | 0.288675i | ||||
\(385\) | 612.000 | + | 88.3346i | 1.58961 | + | 0.229440i | ||||
\(386\) | −73.0000 | + | 126.440i | −0.189119 | + | 0.327564i | ||||
\(387\) | 56.0000 | + | 96.9948i | 0.144703 | + | 0.250633i | ||||
\(388\) | −88.0000 | −0.226804 | ||||||||
\(389\) | −508.500 | − | 293.583i | −1.30720 | − | 0.754711i | −0.325570 | − | 0.945518i | \(-0.605556\pi\) |
−0.981628 | + | 0.190807i | \(0.938890\pi\) | |||||||
\(390\) | 144.000 | 0.369231 | ||||||||
\(391\) | − | 129.904i | − | 0.332235i | ||||||
\(392\) | 376.000 | + | 110.851i | 0.959184 | + | 0.282784i | ||||
\(393\) | 17.0000 | 0.0432570 | ||||||||
\(394\) | − | 415.692i | − | 1.05506i | ||||||
\(395\) | −193.500 | + | 335.152i | −0.489873 | + | 0.848486i | ||||
\(396\) | −544.000 | −1.37374 | ||||||||
\(397\) | −208.500 | + | 120.378i | −0.525189 | + | 0.303218i | −0.739055 | − | 0.673645i | \(-0.764728\pi\) |
0.213866 | + | 0.976863i | \(0.431394\pi\) | |||||||
\(398\) | 111.000 | + | 64.0859i | 0.278894 | + | 0.161020i | ||||
\(399\) | 7.00000 | − | 48.4974i | 0.0175439 | − | 0.121547i | ||||
\(400\) | 16.0000 | − | 27.7128i | 0.0400000 | − | 0.0692820i | ||||
\(401\) | −59.5000 | − | 103.057i | −0.148379 | − | 0.257000i | 0.782249 | − | 0.622965i | \(-0.214072\pi\) |
−0.930629 | + | 0.365965i | \(0.880739\pi\) | |||||||
\(402\) | 17.0000 | + | 29.4449i | 0.0422886 | + | 0.0732459i | ||||
\(403\) | 228.000 | − | 394.908i | 0.565757 | − | 0.979920i | ||||
\(404\) | 270.000 | + | 155.885i | 0.668317 | + | 0.385853i | ||||
\(405\) | − | 285.788i | − | 0.705650i | ||||||
\(406\) | 192.000 | + | 27.7128i | 0.472906 | + | 0.0682582i | ||||
\(407\) | 147.224i | 0.361731i | ||||||||
\(408\) | −100.000 | − | 173.205i | −0.245098 | − | 0.424522i | ||||
\(409\) | 72.5000 | − | 125.574i | 0.177262 | − | 0.307026i | −0.763680 | − | 0.645595i | \(-0.776609\pi\) |
0.940942 | + | 0.338569i | \(0.109943\pi\) | |||||||
\(410\) | 234.000 | − | 135.100i | 0.570732 | − | 0.329512i | ||||
\(411\) | 72.5000 | + | 125.574i | 0.176399 | + | 0.305532i | ||||
\(412\) | −558.000 | + | 322.161i | −1.35437 | + | 0.781945i | ||||
\(413\) | 302.500 | + | 238.157i | 0.732446 | + | 0.576651i | ||||
\(414\) | −72.0000 | − | 41.5692i | −0.173913 | − | 0.100409i | ||||
\(415\) | −495.000 | + | 285.788i | −1.19277 | + | 0.688647i | ||||
\(416\) | 443.405i | 1.06588i | ||||||||
\(417\) | 41.0000 | − | 71.0141i | 0.0983213 | − | 0.170298i | ||||
\(418\) | 238.000 | 0.569378 | ||||||||
\(419\) | 302.000 | 0.720764 | 0.360382 | − | 0.932805i | \(-0.382646\pi\) | ||||
0.360382 | + | 0.932805i | \(0.382646\pi\) | |||||||
\(420\) | 144.000 | + | 20.7846i | 0.342857 | + | 0.0494872i | ||||
\(421\) | − | 401.836i | − | 0.954479i | −0.878773 | − | 0.477240i | \(-0.841637\pi\) | ||
0.878773 | − | 0.477240i | \(-0.158363\pi\) | |||||||
\(422\) | −604.000 | −1.43128 | ||||||||
\(423\) | −348.000 | − | 200.918i | −0.822695 | − | 0.474983i | ||||
\(424\) | −636.000 | − | 367.195i | −1.50000 | − | 0.866025i | ||||
\(425\) | −25.0000 | − | 43.3013i | −0.0588235 | − | 0.101885i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 58.5000 | + | 146.358i | 0.137002 | + | 0.342759i | ||||
\(428\) | −130.000 | − | 225.167i | −0.303738 | − | 0.526090i | ||||
\(429\) | −204.000 | + | 117.779i | −0.475524 | + | 0.274544i | ||||
\(430\) | 126.000 | − | 72.7461i | 0.293023 | − | 0.169177i | ||||
\(431\) | 700.500 | + | 404.434i | 1.62529 | + | 0.938362i | 0.985473 | + | 0.169835i | \(0.0543234\pi\) |
0.639817 | + | 0.768527i | \(0.279010\pi\) | |||||||
\(432\) | −272.000 | −0.629630 | ||||||||
\(433\) | 410.000 | 0.946882 | 0.473441 | − | 0.880825i | \(-0.343012\pi\) | ||||
0.473441 | + | 0.880825i | \(0.343012\pi\) | |||||||
\(434\) | 285.000 | − | 361.999i | 0.656682 | − | 0.834098i | ||||
\(435\) | 72.0000 | 0.165517 | ||||||||
\(436\) | 30.0000 | + | 17.3205i | 0.0688073 | + | 0.0397259i | ||||
\(437\) | 31.5000 | + | 18.1865i | 0.0720824 | + | 0.0416168i | ||||
\(438\) | 119.000 | + | 206.114i | 0.271689 | + | 0.470580i | ||||
\(439\) | 424.500 | − | 245.085i | 0.966970 | − | 0.558281i | 0.0686591 | − | 0.997640i | \(-0.478128\pi\) |
0.898311 | + | 0.439360i | \(0.144795\pi\) | |||||||
\(440\) | 706.677i | 1.60608i | ||||||||
\(441\) | −92.0000 | − | 381.051i | −0.208617 | − | 0.864062i | ||||
\(442\) | 600.000 | + | 346.410i | 1.35747 | + | 0.783733i | ||||
\(443\) | −200.500 | − | 347.276i | −0.452596 | − | 0.783919i | 0.545950 | − | 0.837817i | \(-0.316169\pi\) |
−0.998546 | + | 0.0538983i | \(0.982835\pi\) | |||||||
\(444\) | 34.6410i | 0.0780203i | ||||||||
\(445\) | 319.500 | + | 184.463i | 0.717978 | + | 0.414525i | ||||
\(446\) | − | 277.128i | − | 0.621364i | ||||||
\(447\) | − | 5.19615i | − | 0.0116245i | ||||||
\(448\) | −64.0000 | + | 443.405i | −0.142857 | + | 0.989743i | ||||
\(449\) | −310.000 | −0.690423 | −0.345212 | − | 0.938525i | \(-0.612193\pi\) | ||||
−0.345212 | + | 0.938525i | \(0.612193\pi\) | |||||||
\(450\) | −32.0000 | −0.0711111 | ||||||||
\(451\) | −221.000 | + | 382.783i | −0.490022 | + | 0.848743i | ||||
\(452\) | 488.000 | 1.07965 | ||||||||
\(453\) | 31.5000 | − | 18.1865i | 0.0695364 | − | 0.0401469i | ||||
\(454\) | −55.0000 | + | 95.2628i | −0.121145 | + | 0.209830i | ||||
\(455\) | −468.000 | + | 187.061i | −1.02857 | + | 0.411124i | ||||
\(456\) | 56.0000 | 0.122807 | ||||||||
\(457\) | −83.5000 | − | 144.626i | −0.182713 | − | 0.316469i | 0.760090 | − | 0.649818i | \(-0.225155\pi\) |
−0.942804 | + | 0.333349i | \(0.891821\pi\) | |||||||
\(458\) | −567.000 | + | 327.358i | −1.23799 | + | 0.714755i | ||||
\(459\) | −212.500 | + | 368.061i | −0.462963 | + | 0.801875i | ||||
\(460\) | −54.0000 | + | 93.5307i | −0.117391 | + | 0.203328i | ||||
\(461\) | 13.8564i | 0.0300573i | 0.999887 | + | 0.0150286i | \(0.00478394\pi\) | ||||
−0.999887 | + | 0.0150286i | \(0.995216\pi\) | |||||||
\(462\) | −221.000 | + | 88.3346i | −0.478355 | + | 0.191200i | ||||
\(463\) | 609.682i | 1.31681i | 0.752665 | + | 0.658404i | \(0.228768\pi\) | ||||
−0.752665 | + | 0.658404i | \(0.771232\pi\) | |||||||
\(464\) | 221.703i | 0.477807i | ||||||||
\(465\) | 85.5000 | − | 148.090i | 0.183871 | − | 0.318474i | ||||
\(466\) | −385.000 | − | 666.840i | −0.826180 | − | 1.43099i | ||||
\(467\) | −392.500 | − | 679.830i | −0.840471 | − | 1.45574i | −0.889497 | − | 0.456941i | \(-0.848945\pi\) |
0.0490258 | − | 0.998798i | \(-0.484388\pi\) | |||||||
\(468\) | 384.000 | − | 221.703i | 0.820513 | − | 0.473723i | ||||
\(469\) | −93.5000 | − | 73.6122i | −0.199360 | − | 0.156956i | ||||
\(470\) | −261.000 | + | 452.065i | −0.555319 | + | 0.961841i | ||||
\(471\) | 268.500 | − | 155.019i | 0.570064 | − | 0.329126i | ||||
\(472\) | −220.000 | + | 381.051i | −0.466102 | + | 0.807312i | ||||
\(473\) | −119.000 | + | 206.114i | −0.251586 | + | 0.435759i | ||||
\(474\) | − | 148.956i | − | 0.314254i | ||||||
\(475\) | 14.0000 | 0.0294737 | ||||||||
\(476\) | 550.000 | + | 433.013i | 1.15546 | + | 0.909691i | ||||
\(477\) | 734.390i | 1.53960i | ||||||||
\(478\) | 859.097i | 1.79727i | ||||||||
\(479\) | −535.500 | − | 309.171i | −1.11795 | − | 0.645451i | −0.177076 | − | 0.984197i | \(-0.556664\pi\) |
−0.940878 | + | 0.338746i | \(0.889997\pi\) | |||||||
\(480\) | 166.277i | 0.346410i | ||||||||
\(481\) | −60.0000 | − | 103.923i | −0.124740 | − | 0.216056i | ||||
\(482\) | −145.000 | + | 251.147i | −0.300830 | + | 0.521053i | ||||
\(483\) | −36.0000 | − | 5.19615i | −0.0745342 | − | 0.0107581i | ||||
\(484\) | −336.000 | − | 581.969i | −0.694215 | − | 1.20242i | ||||
\(485\) | 99.0000 | − | 57.1577i | 0.204124 | − | 0.117851i | ||||
\(486\) | 208.000 | + | 360.267i | 0.427984 | + | 0.741289i | ||||
\(487\) | 340.500 | + | 196.588i | 0.699179 | + | 0.403671i | 0.807041 | − | 0.590495i | \(-0.201067\pi\) |
−0.107863 | + | 0.994166i | \(0.534401\pi\) | |||||||
\(488\) | −156.000 | + | 90.0666i | −0.319672 | + | 0.184563i | ||||
\(489\) | 17.0000 | 0.0347648 | ||||||||
\(490\) | −495.000 | + | 119.512i | −1.01020 | + | 0.243901i | ||||
\(491\) | 422.000 | 0.859470 | 0.429735 | − | 0.902955i | \(-0.358607\pi\) | ||||
0.429735 | + | 0.902955i | \(0.358607\pi\) | |||||||
\(492\) | −52.0000 | + | 90.0666i | −0.105691 | + | 0.183062i | ||||
\(493\) | 300.000 | + | 173.205i | 0.608519 | + | 0.351329i | ||||
\(494\) | −168.000 | + | 96.9948i | −0.340081 | + | 0.196346i | ||||
\(495\) | 612.000 | − | 353.338i | 1.23636 | − | 0.713815i | ||||
\(496\) | 456.000 | + | 263.272i | 0.919355 | + | 0.530790i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 110.000 | − | 190.526i | 0.220884 | − | 0.382582i | ||||
\(499\) | −32.5000 | − | 56.2917i | −0.0651303 | − | 0.112809i | 0.831622 | − | 0.555343i | \(-0.187413\pi\) |
−0.896752 | + | 0.442534i | \(0.854080\pi\) | |||||||
\(500\) | − | 478.046i | − | 0.956092i | ||||||
\(501\) | 12.0000 | + | 6.92820i | 0.0239521 | + | 0.0138287i | ||||
\(502\) | 116.000 | 0.231076 | ||||||||
\(503\) | − | 249.415i | − | 0.495855i | −0.968779 | − | 0.247928i | \(-0.920250\pi\) | ||
0.968779 | − | 0.247928i | \(-0.0797496\pi\) | |||||||
\(504\) | 416.000 | − | 166.277i | 0.825397 | − | 0.329914i | ||||
\(505\) | −405.000 | −0.801980 | ||||||||
\(506\) | − | 176.669i | − | 0.349149i | ||||||
\(507\) | 11.5000 | − | 19.9186i | 0.0226824 | − | 0.0392871i | ||||
\(508\) | − | 665.108i | − | 1.30927i | ||||||
\(509\) | −472.500 | + | 272.798i | −0.928291 | + | 0.535949i | −0.886271 | − | 0.463168i | \(-0.846713\pi\) |
−0.0420202 | + | 0.999117i | \(0.513379\pi\) | |||||||
\(510\) | 225.000 | + | 129.904i | 0.441176 | + | 0.254713i | ||||
\(511\) | −654.500 | − | 515.285i | −1.28082 | − | 1.00839i | ||||
\(512\) | −512.000 | −1.00000 | ||||||||
\(513\) | −59.5000 | − | 103.057i | −0.115984 | − | 0.200891i | ||||
\(514\) | 119.000 | + | 206.114i | 0.231518 | + | 0.401000i | ||||
\(515\) | 418.500 | − | 724.863i | 0.812621 | − | 1.40750i | ||||
\(516\) | −28.0000 | + | 48.4974i | −0.0542636 | + | 0.0939873i | ||||
\(517\) | − | 853.901i | − | 1.65165i | ||||||
\(518\) | −45.0000 | − | 112.583i | −0.0868726 | − | 0.217342i | ||||
\(519\) | 105.655i | 0.203574i | ||||||||
\(520\) | −288.000 | − | 498.831i | −0.553846 | − | 0.959290i | ||||
\(521\) | 12.5000 | − | 21.6506i | 0.0239923 | − | 0.0415559i | −0.853780 | − | 0.520634i | \(-0.825696\pi\) |
0.877772 | + | 0.479078i | \(0.159029\pi\) | |||||||
\(522\) | 192.000 | − | 110.851i | 0.367816 | − | 0.212359i | ||||
\(523\) | −296.500 | − | 513.553i | −0.566922 | − | 0.981937i | −0.996868 | − | 0.0790826i | \(-0.974801\pi\) |
0.429946 | − | 0.902854i | \(-0.358532\pi\) | |||||||
\(524\) | −34.0000 | − | 58.8897i | −0.0648855 | − | 0.112385i | ||||
\(525\) | −13.0000 | + | 5.19615i | −0.0247619 | + | 0.00989743i | ||||
\(526\) | 567.000 | + | 327.358i | 1.07795 | + | 0.622353i | ||||
\(527\) | 712.500 | − | 411.362i | 1.35199 | − | 0.780573i | ||||
\(528\) | −136.000 | − | 235.559i | −0.257576 | − | 0.446134i | ||||
\(529\) | −251.000 | + | 434.745i | −0.474480 | + | 0.821824i | ||||
\(530\) | 954.000 | 1.80000 | ||||||||
\(531\) | 440.000 | 0.828625 | ||||||||
\(532\) | −182.000 | + | 72.7461i | −0.342105 | + | 0.136741i | ||||
\(533\) | − | 360.267i | − | 0.675922i | ||||||
\(534\) | −142.000 | −0.265918 | ||||||||
\(535\) | 292.500 | + | 168.875i | 0.546729 | + | 0.315654i | ||||
\(536\) | 68.0000 | − | 117.779i | 0.126866 | − | 0.219738i | ||||
\(537\) | −44.5000 | − | 77.0763i | −0.0828678 | − | 0.143531i | ||||
\(538\) | −231.000 | − | 133.368i | −0.429368 | − | 0.247896i | ||||
\(539\) | 603.500 | − | 574.175i | 1.11967 | − | 1.06526i | ||||
\(540\) | 306.000 | − | 176.669i | 0.566667 | − | 0.327165i | ||||
\(541\) | 655.500 | − | 378.453i | 1.21165 | − | 0.699544i | 0.248528 | − | 0.968625i | \(-0.420053\pi\) |
0.963117 | + | 0.269081i | \(0.0867200\pi\) | |||||||
\(542\) | −753.000 | + | 434.745i | −1.38930 | + | 0.802112i | ||||
\(543\) | −216.000 | − | 124.708i | −0.397790 | − | 0.229664i | ||||
\(544\) | −400.000 | + | 692.820i | −0.735294 | + | 1.27357i | ||||
\(545\) | −45.0000 | −0.0825688 | ||||||||
\(546\) | 120.000 | − | 152.420i | 0.219780 | − | 0.279158i | ||||
\(547\) | 662.000 | 1.21024 | 0.605119 | − | 0.796135i | \(-0.293126\pi\) | ||||
0.605119 | + | 0.796135i | \(0.293126\pi\) | |||||||
\(548\) | 290.000 | − | 502.295i | 0.529197 | − | 0.916596i | ||||
\(549\) | 156.000 | + | 90.0666i | 0.284153 | + | 0.164056i | ||||
\(550\) | −34.0000 | − | 58.8897i | −0.0618182 | − | 0.107072i | ||||
\(551\) | −84.0000 | + | 48.4974i | −0.152450 | + | 0.0880171i | ||||
\(552\) | − | 41.5692i | − | 0.0753066i | ||||||
\(553\) | 193.500 | + | 484.108i | 0.349910 | + | 0.875422i | ||||
\(554\) | −351.000 | − | 202.650i | −0.633574 | − | 0.365794i | ||||
\(555\) | −22.5000 | − | 38.9711i | −0.0405405 | − | 0.0702183i | ||||
\(556\) | −328.000 | −0.589928 | ||||||||
\(557\) | 511.500 | + | 295.315i | 0.918312 | + | 0.530188i | 0.883096 | − | 0.469192i | \(-0.155455\pi\) |
0.0352161 | + | 0.999380i | \(0.488788\pi\) | |||||||
\(558\) | − | 526.543i | − | 0.943626i | ||||||
\(559\) | − | 193.990i | − | 0.347030i | ||||||
\(560\) | −216.000 | − | 540.400i | −0.385714 | − | 0.965000i | ||||
\(561\) | −425.000 | −0.757576 | ||||||||
\(562\) | −148.000 | −0.263345 | ||||||||
\(563\) | −368.500 | + | 638.261i | −0.654529 | + | 1.13368i | 0.327482 | + | 0.944857i | \(0.393800\pi\) |
−0.982012 | + | 0.188821i | \(0.939534\pi\) | |||||||
\(564\) | − | 200.918i | − | 0.356237i | ||||||
\(565\) | −549.000 | + | 316.965i | −0.971681 | + | 0.561001i | ||||
\(566\) | −463.000 | + | 801.940i | −0.818021 | + | 1.41685i | ||||
\(567\) | −302.500 | − | 238.157i | −0.533510 | − | 0.420030i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 60.5000 | + | 104.789i | 0.106327 | + | 0.184164i | 0.914280 | − | 0.405084i | \(-0.132758\pi\) |
−0.807953 | + | 0.589247i | \(0.799424\pi\) | |||||||
\(570\) | −63.0000 | + | 36.3731i | −0.110526 | + | 0.0638124i | ||||
\(571\) | −368.500 | + | 638.261i | −0.645359 | + | 1.11779i | 0.338859 | + | 0.940837i | \(0.389959\pi\) |
−0.984218 | + | 0.176958i | \(0.943374\pi\) | |||||||
\(572\) | 816.000 | + | 471.118i | 1.42657 | + | 0.823633i | ||||
\(573\) | − | 216.506i | − | 0.377847i | ||||||
\(574\) | 52.0000 | − | 360.267i | 0.0905923 | − | 0.627642i | ||||
\(575\) | − | 10.3923i | − | 0.0180736i | ||||||
\(576\) | 256.000 | + | 443.405i | 0.444444 | + | 0.769800i | ||||
\(577\) | −23.5000 | + | 40.7032i | −0.0407279 | + | 0.0705428i | −0.885671 | − | 0.464314i | \(-0.846301\pi\) |
0.844943 | + | 0.534857i | \(0.179634\pi\) | |||||||
\(578\) | 336.000 | + | 581.969i | 0.581315 | + | 1.00687i | ||||
\(579\) | 36.5000 | + | 63.2199i | 0.0630397 | + | 0.109188i | ||||
\(580\) | −144.000 | − | 249.415i | −0.248276 | − | 0.430026i | ||||
\(581\) | −110.000 | + | 762.102i | −0.189329 | + | 1.31171i | ||||
\(582\) | −22.0000 | + | 38.1051i | −0.0378007 | + | 0.0654727i | ||||
\(583\) | −1351.50 | + | 780.289i | −2.31818 | + | 1.33840i | ||||
\(584\) | 476.000 | − | 824.456i | 0.815068 | − | 1.41174i | ||||
\(585\) | −288.000 | + | 498.831i | −0.492308 | + | 0.852702i | ||||
\(586\) | − | 221.703i | − | 0.378332i | ||||||
\(587\) | 446.000 | 0.759796 | 0.379898 | − | 0.925028i | \(-0.375959\pi\) | ||||
0.379898 | + | 0.925028i | \(0.375959\pi\) | |||||||
\(588\) | 142.000 | − | 135.100i | 0.241497 | − | 0.229762i | ||||
\(589\) | 230.363i | 0.391108i | ||||||||
\(590\) | − | 571.577i | − | 0.968774i | ||||||
\(591\) | −180.000 | − | 103.923i | −0.304569 | − | 0.175843i | ||||
\(592\) | 120.000 | − | 69.2820i | 0.202703 | − | 0.117030i | ||||
\(593\) | −107.500 | − | 186.195i | −0.181282 | − | 0.313989i | 0.761036 | − | 0.648710i | \(-0.224691\pi\) |
−0.942317 | + | 0.334721i | \(0.891358\pi\) | |||||||
\(594\) | −289.000 | + | 500.563i | −0.486532 | + | 0.842698i | ||||
\(595\) | −900.000 | − | 129.904i | −1.51261 | − | 0.218326i | ||||
\(596\) | −18.0000 | + | 10.3923i | −0.0302013 | + | 0.0174368i | ||||
\(597\) | 55.5000 | − | 32.0429i | 0.0929648 | − | 0.0536733i | ||||
\(598\) | 72.0000 | + | 124.708i | 0.120401 | + | 0.208541i | ||||
\(599\) | 244.500 | + | 141.162i | 0.408180 | + | 0.235663i | 0.690008 | − | 0.723802i | \(-0.257607\pi\) |
−0.281827 | + | 0.959465i | \(0.590941\pi\) | |||||||
\(600\) | −8.00000 | − | 13.8564i | −0.0133333 | − | 0.0230940i | ||||
\(601\) | 266.000 | 0.442596 | 0.221298 | − | 0.975206i | \(-0.428971\pi\) | ||||
0.221298 | + | 0.975206i | \(0.428971\pi\) | |||||||
\(602\) | 28.0000 | − | 193.990i | 0.0465116 | − | 0.322242i | ||||
\(603\) | −136.000 | −0.225539 | ||||||||
\(604\) | −126.000 | − | 72.7461i | −0.208609 | − | 0.120441i | ||||
\(605\) | 756.000 | + | 436.477i | 1.24959 | + | 0.721449i | ||||
\(606\) | 135.000 | − | 77.9423i | 0.222772 | − | 0.128618i | ||||
\(607\) | −571.500 | + | 329.956i | −0.941516 | + | 0.543584i | −0.890435 | − | 0.455110i | \(-0.849600\pi\) |
−0.0510805 | + | 0.998695i | \(0.516267\pi\) | |||||||
\(608\) | −112.000 | − | 193.990i | −0.184211 | − | 0.319062i | ||||
\(609\) | 60.0000 | − | 76.2102i | 0.0985222 | − | 0.125140i | ||||
\(610\) | 117.000 | − | 202.650i | 0.191803 | − | 0.332213i | ||||
\(611\) | 348.000 | + | 602.754i | 0.569558 | + | 0.986504i | ||||
\(612\) | 800.000 | 1.30719 | ||||||||
\(613\) | −604.500 | − | 349.008i | −0.986134 | − | 0.569345i | −0.0820174 | − | 0.996631i | \(-0.526136\pi\) |
−0.904116 | + | 0.427286i | \(0.859470\pi\) | |||||||
\(614\) | 548.000 | 0.892508 | ||||||||
\(615\) | − | 135.100i | − | 0.219675i | ||||||
\(616\) | 748.000 | + | 588.897i | 1.21429 | + | 0.956002i | ||||
\(617\) | −118.000 | −0.191248 | −0.0956240 | − | 0.995418i | \(-0.530485\pi\) | ||||
−0.0956240 | + | 0.995418i | \(0.530485\pi\) | |||||||
\(618\) | 322.161i | 0.521297i | ||||||||
\(619\) | 459.500 | − | 795.877i | 0.742326 | − | 1.28575i | −0.209107 | − | 0.977893i | \(-0.567056\pi\) |
0.951434 | − | 0.307854i | \(-0.0996109\pi\) | |||||||
\(620\) | −684.000 | −1.10323 | ||||||||
\(621\) | −76.5000 | + | 44.1673i | −0.123188 | + | 0.0711229i | ||||
\(622\) | 87.0000 | + | 50.2295i | 0.139871 | + | 0.0807548i | ||||
\(623\) | 461.500 | − | 184.463i | 0.740770 | − | 0.296089i | ||||
\(624\) | 192.000 | + | 110.851i | 0.307692 | + | 0.177646i | ||||
\(625\) | 335.500 | + | 581.103i | 0.536800 | + | 0.929765i | ||||
\(626\) | −409.000 | − | 708.409i | −0.653355 | − | 1.13164i | ||||
\(627\) | 59.5000 | − | 103.057i | 0.0948963 | − | 0.164365i | ||||
\(628\) | −1074.00 | − | 620.074i | −1.71019 | − | 0.987379i | ||||
\(629\) | − | 216.506i | − | 0.344207i | ||||||
\(630\) | −360.000 | + | 457.261i | −0.571429 | + | 0.725812i | ||||
\(631\) | − | 166.277i | − | 0.263513i | −0.991282 | − | 0.131757i | \(-0.957938\pi\) | ||
0.991282 | − | 0.131757i | \(-0.0420617\pi\) | |||||||
\(632\) | −516.000 | + | 297.913i | −0.816456 | + | 0.471381i | ||||
\(633\) | −151.000 | + | 261.540i | −0.238547 | + | 0.413175i | ||||
\(634\) | −327.000 | + | 188.794i | −0.515773 | + | 0.297782i | ||||
\(635\) | 432.000 | + | 748.246i | 0.680315 | + | 1.17834i | ||||
\(636\) | −318.000 | + | 183.597i | −0.500000 | + | 0.288675i | ||||
\(637\) | −192.000 | + | 651.251i | −0.301413 | + | 1.02237i | ||||
\(638\) | 408.000 | + | 235.559i | 0.639498 | + | 0.369215i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 576.000 | − | 332.554i | 0.900000 | − | 0.519615i | ||||
\(641\) | 0.500000 | − | 0.866025i | 0.000780031 | − | 0.00135105i | −0.865635 | − | 0.500675i | \(-0.833085\pi\) |
0.866415 | + | 0.499324i | \(0.166418\pi\) | |||||||
\(642\) | −130.000 | −0.202492 | ||||||||
\(643\) | −514.000 | −0.799378 | −0.399689 | − | 0.916651i | \(-0.630882\pi\) | ||||
−0.399689 | + | 0.916651i | \(0.630882\pi\) | |||||||
\(644\) | 54.0000 | + | 135.100i | 0.0838509 | + | 0.209783i | ||||
\(645\) | − | 72.7461i | − | 0.112785i | ||||||
\(646\) | −350.000 | −0.541796 | ||||||||
\(647\) | 52.5000 | + | 30.3109i | 0.0811437 | + | 0.0468484i | 0.540023 | − | 0.841650i | \(-0.318416\pi\) |
−0.458879 | + | 0.888499i | \(0.651749\pi\) | |||||||
\(648\) | 220.000 | − | 381.051i | 0.339506 | − | 0.588042i | ||||
\(649\) | 467.500 | + | 809.734i | 0.720339 | + | 1.24766i | ||||
\(650\) | 48.0000 | + | 27.7128i | 0.0738462 | + | 0.0426351i | ||||
\(651\) | −85.5000 | − | 213.908i | −0.131336 | − | 0.328584i | ||||
\(652\) | −34.0000 | − | 58.8897i | −0.0521472 | − | 0.0903217i | ||||
\(653\) | 283.500 | − | 163.679i | 0.434150 | − | 0.250657i | −0.266963 | − | 0.963707i | \(-0.586020\pi\) |
0.701113 | + | 0.713050i | \(0.252687\pi\) | |||||||
\(654\) | 15.0000 | − | 8.66025i | 0.0229358 | − | 0.0132420i | ||||
\(655\) | 76.5000 | + | 44.1673i | 0.116794 | + | 0.0674310i | ||||
\(656\) | 416.000 | 0.634146 | ||||||||
\(657\) | −952.000 | −1.44901 | ||||||||
\(658\) | 261.000 | + | 652.983i | 0.396657 | + | 0.992376i | ||||
\(659\) | 542.000 | 0.822458 | 0.411229 | − | 0.911532i | \(-0.365100\pi\) | ||||
0.411229 | + | 0.911532i | \(0.365100\pi\) | |||||||
\(660\) | 306.000 | + | 176.669i | 0.463636 | + | 0.267681i | ||||
\(661\) | −1024.50 | − | 591.495i | −1.54992 | − | 0.894849i | −0.998146 | − | 0.0608582i | \(-0.980616\pi\) |
−0.551778 | − | 0.833991i | \(-0.686050\pi\) | |||||||
\(662\) | −295.000 | − | 510.955i | −0.445619 | − | 0.771835i | ||||
\(663\) | 300.000 | − | 173.205i | 0.452489 | − | 0.261244i | ||||
\(664\) | −880.000 | −1.32530 | ||||||||
\(665\) | 157.500 | − | 200.052i | 0.236842 | − | 0.300830i | ||||
\(666\) | −120.000 | − | 69.2820i | −0.180180 | − | 0.104027i | ||||
\(667\) | 36.0000 | + | 62.3538i | 0.0539730 | + | 0.0934840i | ||||
\(668\) | − | 55.4256i | − | 0.0829725i | ||||||
\(669\) | −120.000 | − | 69.2820i | −0.179372 | − | 0.103561i | ||||
\(670\) | 176.669i | 0.263685i | ||||||||
\(671\) | 382.783i | 0.570467i | ||||||||
\(672\) | 176.000 | + | 138.564i | 0.261905 | + | 0.206197i | ||||
\(673\) | 218.000 | 0.323923 | 0.161961 | − | 0.986797i | \(-0.448218\pi\) | ||||
0.161961 | + | 0.986797i | \(0.448218\pi\) | |||||||
\(674\) | −52.0000 | −0.0771513 | ||||||||
\(675\) | −17.0000 | + | 29.4449i | −0.0251852 | + | 0.0436220i | ||||
\(676\) | −92.0000 | −0.136095 | ||||||||
\(677\) | −556.500 | + | 321.295i | −0.822009 | + | 0.474587i | −0.851109 | − | 0.524989i | \(-0.824069\pi\) |
0.0290999 | + | 0.999577i | \(0.490736\pi\) | |||||||
\(678\) | 122.000 | − | 211.310i | 0.179941 | − | 0.311667i | ||||
\(679\) | 22.0000 | − | 152.420i | 0.0324006 | − | 0.224478i | ||||
\(680\) | − | 1039.23i | − | 1.52828i | ||||||
\(681\) | 27.5000 | + | 47.6314i | 0.0403818 | + | 0.0699433i | ||||
\(682\) | 969.000 | − | 559.452i | 1.42082 | − | 0.820311i | ||||
\(683\) | 183.500 | − | 317.831i | 0.268668 | − | 0.465346i | −0.699850 | − | 0.714289i | \(-0.746750\pi\) |
0.968518 | + | 0.248943i | \(0.0800833\pi\) | |||||||
\(684\) | −112.000 | + | 193.990i | −0.163743 | + | 0.283611i | ||||
\(685\) | 753.442i | 1.09992i | ||||||||
\(686\) | −286.000 | + | 623.538i | −0.416910 | + | 0.908948i | ||||
\(687\) | 327.358i | 0.476503i | ||||||||
\(688\) | 224.000 | 0.325581 | ||||||||
\(689\) | 636.000 | − | 1101.58i | 0.923077 | − | 1.59882i | ||||
\(690\) | 27.0000 | + | 46.7654i | 0.0391304 | + | 0.0677759i | ||||
\(691\) | −248.500 | − | 430.415i | −0.359624 | − | 0.622887i | 0.628274 | − | 0.777992i | \(-0.283762\pi\) |
−0.987898 | + | 0.155105i | \(0.950428\pi\) | |||||||
\(692\) | 366.000 | − | 211.310i | 0.528902 | − | 0.305362i | ||||
\(693\) | 136.000 | − | 942.236i | 0.196248 | − | 1.35965i | ||||
\(694\) | 377.000 | − | 652.983i | 0.543228 | − | 0.940898i | ||||
\(695\) | 369.000 | − | 213.042i | 0.530935 | − | 0.306536i | ||||
\(696\) | 96.0000 | + | 55.4256i | 0.137931 | + | 0.0796345i | ||||
\(697\) | 325.000 | − | 562.917i | 0.466284 | − | 0.807628i | ||||
\(698\) | − | 193.990i | − | 0.277922i | ||||||
\(699\) | −385.000 | −0.550787 | ||||||||
\(700\) | 44.0000 | + | 34.6410i | 0.0628571 | + | 0.0494872i | ||||
\(701\) | − | 332.554i | − | 0.474399i | −0.971461 | − | 0.237200i | \(-0.923770\pi\) | ||
0.971461 | − | 0.237200i | \(-0.0762295\pi\) | |||||||
\(702\) | − | 471.118i | − | 0.671108i | ||||||
\(703\) | 52.5000 | + | 30.3109i | 0.0746799 | + | 0.0431165i | ||||
\(704\) | −544.000 | + | 942.236i | −0.772727 | + | 1.33840i | ||||
\(705\) | 130.500 | + | 226.033i | 0.185106 | + | 0.320614i | ||||
\(706\) | 503.000 | − | 871.222i | 0.712465 | − | 1.23402i | ||||
\(707\) | −337.500 | + | 428.683i | −0.477369 | + | 0.606340i | ||||
\(708\) | 110.000 | + | 190.526i | 0.155367 | + | 0.269104i | ||||
\(709\) | 343.500 | − | 198.320i | 0.484485 | − | 0.279718i | −0.237799 | − | 0.971314i | \(-0.576426\pi\) |
0.722284 | + | 0.691597i | \(0.243092\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 516.000 | + | 297.913i | 0.725738 | + | 0.419005i | ||||
\(712\) | 284.000 | + | 491.902i | 0.398876 | + | 0.690874i | ||||
\(713\) | 171.000 | 0.239832 | ||||||||
\(714\) | 325.000 | − | 129.904i | 0.455182 | − | 0.181938i | ||||
\(715\) | −1224.00 | −1.71189 | ||||||||
\(716\) | −178.000 | + | 308.305i | −0.248603 | + | 0.430594i | ||||
\(717\) | 372.000 | + | 214.774i | 0.518828 | + | 0.299546i | ||||
\(718\) | −321.000 | + | 185.329i | −0.447075 | + | 0.258119i | ||||
\(719\) | −55.5000 | + | 32.0429i | −0.0771905 | + | 0.0445660i | −0.538098 | − | 0.842882i | \(-0.680857\pi\) |
0.460908 | + | 0.887448i | \(0.347524\pi\) | |||||||
\(720\) | −576.000 | − | 332.554i | −0.800000 | − | 0.461880i | ||||
\(721\) | −418.500 | − | 1047.02i | −0.580444 | − | 1.45218i | ||||
\(722\) | −312.000 | + | 540.400i | −0.432133 | + | 0.748476i | ||||
\(723\) | 72.5000 | + | 125.574i | 0.100277 | + | 0.173684i | ||||
\(724\) | 997.661i | 1.37799i | ||||||||
\(725\) | 24.0000 | + | 13.8564i | 0.0331034 | + | 0.0191123i | ||||
\(726\) | −336.000 | −0.462810 | ||||||||
\(727\) | 55.4256i | 0.0762388i | 0.999273 | + | 0.0381194i | \(0.0121367\pi\) | ||||
−0.999273 | + | 0.0381194i | \(0.987863\pi\) | |||||||
\(728\) | −768.000 | − | 110.851i | −1.05495 | − | 0.152268i | ||||
\(729\) | −287.000 | −0.393690 | ||||||||
\(730\) | 1236.68i | 1.69409i | ||||||||
\(731\) | 175.000 | − | 303.109i | 0.239398 | − | 0.414650i | ||||
\(732\) | 90.0666i | 0.123042i | ||||||||
\(733\) | 715.500 | − | 413.094i | 0.976126 | − | 0.563566i | 0.0750273 | − | 0.997181i | \(-0.476096\pi\) |
0.901098 | + | 0.433615i | \(0.142762\pi\) | |||||||
\(734\) | −513.000 | − | 296.181i | −0.698910 | − | 0.403516i | ||||
\(735\) | −72.0000 | + | 244.219i | −0.0979592 | + | 0.332271i | ||||
\(736\) | −144.000 | + | 83.1384i | −0.195652 | + | 0.112960i | ||||
\(737\) | −144.500 | − | 250.281i | −0.196065 | − | 0.339595i | ||||
\(738\) | −208.000 | − | 360.267i | −0.281843 | − | 0.488166i | ||||
\(739\) | −356.500 | + | 617.476i | −0.482409 | + | 0.835556i | −0.999796 | − | 0.0201950i | \(-0.993571\pi\) |
0.517387 | + | 0.855751i | \(0.326905\pi\) | |||||||
\(740\) | −90.0000 | + | 155.885i | −0.121622 | + | 0.210655i | ||||
\(741\) | 96.9948i | 0.130897i | ||||||||
\(742\) | 795.000 | − | 1009.79i | 1.07143 | − | 1.36090i | ||||
\(743\) | − | 637.395i | − | 0.857866i | −0.903336 | − | 0.428933i | \(-0.858890\pi\) | ||
0.903336 | − | 0.428933i | \(-0.141110\pi\) | |||||||
\(744\) | 228.000 | − | 131.636i | 0.306452 | − | 0.176930i | ||||
\(745\) | 13.5000 | − | 23.3827i | 0.0181208 | − | 0.0313862i | ||||
\(746\) | −207.000 | + | 119.512i | −0.277480 | + | 0.160203i | ||||
\(747\) | 440.000 | + | 762.102i | 0.589023 | + | 1.02022i | ||||
\(748\) | 850.000 | + | 1472.24i | 1.13636 | + | 1.96824i | ||||
\(749\) | 422.500 | − | 168.875i | 0.564085 | − | 0.225467i | ||||
\(750\) | −207.000 | − | 119.512i | −0.276000 | − | 0.159349i | ||||
\(751\) | 1012.50 | − | 584.567i | 1.34820 | − | 0.778385i | 0.360208 | − | 0.932872i | \(-0.382706\pi\) |
0.987995 | + | 0.154487i | \(0.0493725\pi\) | |||||||
\(752\) | −696.000 | + | 401.836i | −0.925532 | + | 0.534356i | ||||
\(753\) | 29.0000 | − | 50.2295i | 0.0385126 | − | 0.0667058i | ||||
\(754\) | −384.000 | −0.509284 | ||||||||
\(755\) | 189.000 | 0.250331 | ||||||||
\(756\) | 68.0000 | − | 471.118i | 0.0899471 | − | 0.623172i | ||||
\(757\) | − | 1039.23i | − | 1.37283i | −0.727211 | − | 0.686414i | \(-0.759184\pi\) | ||
0.727211 | − | 0.686414i | \(-0.240816\pi\) | |||||||
\(758\) | 1268.00 | 1.67282 | ||||||||
\(759\) | −76.5000 | − | 44.1673i | −0.100791 | − | 0.0581914i | ||||
\(760\) | 252.000 | + | 145.492i | 0.331579 | + | 0.191437i | ||||
\(761\) | −431.500 | − | 747.380i | −0.567017 | − | 0.982102i | −0.996859 | − | 0.0791982i | \(-0.974764\pi\) |
0.429842 | − | 0.902904i | \(-0.358569\pi\) | |||||||
\(762\) | −288.000 | − | 166.277i | −0.377953 | − | 0.218211i | ||||
\(763\) | −37.5000 | + | 47.6314i | −0.0491481 | + | 0.0624265i | ||||
\(764\) | −750.000 | + | 433.013i | −0.981675 | + | 0.566771i | ||||
\(765\) | −900.000 | + | 519.615i | −1.17647 | + | 0.679236i | ||||
\(766\) | 423.000 | − | 244.219i | 0.552219 | − | 0.318824i | ||||
\(767\) | −660.000 | − | 381.051i | −0.860495 | − | 0.496807i | ||||
\(768\) | −128.000 | + | 221.703i | −0.166667 | + | 0.288675i | ||||
\(769\) | 410.000 | 0.533160 | 0.266580 | − | 0.963813i | \(-0.414106\pi\) | ||||
0.266580 | + | 0.963813i | \(0.414106\pi\) | |||||||
\(770\) | −1224.00 | − | 176.669i | −1.58961 | − | 0.229440i | ||||
\(771\) | 119.000 | 0.154345 | ||||||||
\(772\) | 146.000 | − | 252.879i | 0.189119 | − | 0.327564i | ||||
\(773\) | 691.500 | + | 399.238i | 0.894567 | + | 0.516478i | 0.875433 | − | 0.483339i | \(-0.160576\pi\) |
0.0191332 | + | 0.999817i | \(0.493909\pi\) | |||||||
\(774\) | −112.000 | − | 193.990i | −0.144703 | − | 0.250633i | ||||
\(775\) | 57.0000 | − | 32.9090i | 0.0735484 | − | 0.0424632i | ||||
\(776\) | 176.000 | 0.226804 | ||||||||
\(777\) | −60.0000 | − | 8.66025i | −0.0772201 | − | 0.0111458i | ||||
\(778\) | 1017.00 | + | 587.165i | 1.30720 | + | 0.754711i | ||||
\(779\) | 91.0000 | + | 157.617i | 0.116816 | + | 0.202332i | ||||
\(780\) | −288.000 | −0.369231 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 259.808i | 0.332235i | ||||||||
\(783\) | − | 235.559i | − | 0.300842i | ||||||
\(784\) | −752.000 | − | 221.703i | −0.959184 | − | 0.282784i | ||||
\(785\) | 1611.00 | 2.05223 | ||||||||
\(786\) | −34.0000 | −0.0432570 | ||||||||
\(787\) | 15.5000 | − | 26.8468i | 0.0196950 | − | 0.0341128i | −0.856010 | − | 0.516959i | \(-0.827064\pi\) |
0.875705 | + | 0.482847i | \(0.160397\pi\) | |||||||
\(788\) | 831.384i | 1.05506i | ||||||||
\(789\) | 283.500 | − | 163.679i | 0.359316 | − | 0.207451i | ||||
\(790\) | 387.000 | − | 670.304i | 0.489873 | − | 0.848486i | ||||
\(791\) | −122.000 | + | 845.241i | −0.154235 | + | 1.06857i | ||||
\(792\) | 1088.00 | 1.37374 | ||||||||
\(793\) | −156.000 | − | 270.200i | −0.196721 | − | 0.340731i | ||||
\(794\) | 417.000 | − | 240.755i | 0.525189 | − | 0.303218i | ||||
\(795\) | 238.500 | − | 413.094i | 0.300000 | − | 0.519615i | ||||
\(796\) | −222.000 | − | 128.172i | −0.278894 | − | 0.161020i | ||||
\(797\) | − | 595.825i | − | 0.747585i | −0.927512 | − | 0.373793i | \(-0.878057\pi\) | ||
0.927512 | − | 0.373793i | \(-0.121943\pi\) | |||||||
\(798\) | −14.0000 | + | 96.9948i | −0.0175439 | + | 0.121547i | ||||
\(799\) | 1255.74i | 1.57164i | ||||||||
\(800\) | −32.0000 | + | 55.4256i | −0.0400000 | + | 0.0692820i | ||||
\(801\) | 284.000 | − | 491.902i | 0.354557 | − | 0.614110i | ||||
\(802\) | 119.000 | + | 206.114i | 0.148379 | + | 0.257000i | ||||
\(803\) | −1011.50 | − | 1751.97i | −1.25965 | − | 2.18178i | ||||
\(804\) | −34.0000 | − | 58.8897i | −0.0422886 | − | 0.0732459i | ||||
\(805\) | −148.500 | − | 116.913i | −0.184472 | − | 0.145234i | ||||
\(806\) | −456.000 | + | 789.815i | −0.565757 | + | 0.979920i | ||||
\(807\) | −115.500 | + | 66.6840i | −0.143123 | + | 0.0826319i | ||||
\(808\) | −540.000 | − | 311.769i | −0.668317 | − | 0.385853i | ||||
\(809\) | 156.500 | − | 271.066i | 0.193449 | − | 0.335063i | −0.752942 | − | 0.658087i | \(-0.771366\pi\) |
0.946391 | + | 0.323024i | \(0.104699\pi\) | |||||||
\(810\) | 571.577i | 0.705650i | ||||||||
\(811\) | −1138.00 | −1.40321 | −0.701603 | − | 0.712568i | \(-0.747532\pi\) | ||||
−0.701603 | + | 0.712568i | \(0.747532\pi\) | |||||||
\(812\) | −384.000 | − | 55.4256i | −0.472906 | − | 0.0682582i | ||||
\(813\) | 434.745i | 0.534741i | ||||||||
\(814\) | − | 294.449i | − | 0.361731i | ||||||
\(815\) | 76.5000 | + | 44.1673i | 0.0938650 | + | 0.0541930i | ||||
\(816\) | 200.000 | + | 346.410i | 0.245098 | + | 0.424522i | ||||
\(817\) | 49.0000 | + | 84.8705i | 0.0599755 | + | 0.103881i | ||||
\(818\) | −145.000 | + | 251.147i | −0.177262 | + | 0.307026i | ||||
\(819\) | 288.000 | + | 720.533i | 0.351648 | + | 0.879772i | ||||
\(820\) | −468.000 | + | 270.200i | −0.570732 | + | 0.329512i | ||||
\(821\) | −1060.50 | + | 612.280i | −1.29172 | + | 0.745773i | −0.978959 | − | 0.204059i | \(-0.934587\pi\) |
−0.312759 | + | 0.949833i | \(0.601253\pi\) | |||||||
\(822\) | −145.000 | − | 251.147i | −0.176399 | − | 0.305532i | ||||
\(823\) | 100.500 | + | 58.0237i | 0.122114 | + | 0.0705027i | 0.559813 | − | 0.828619i | \(-0.310873\pi\) |
−0.437699 | + | 0.899122i | \(0.644206\pi\) | |||||||
\(824\) | 1116.00 | − | 644.323i | 1.35437 | − | 0.781945i | ||||
\(825\) | −34.0000 | −0.0412121 | ||||||||
\(826\) | −605.000 | − | 476.314i | −0.732446 | − | 0.576651i | ||||
\(827\) | −754.000 | −0.911729 | −0.455865 | − | 0.890049i | \(-0.650670\pi\) | ||||
−0.455865 | + | 0.890049i | \(0.650670\pi\) | |||||||
\(828\) | 144.000 | + | 83.1384i | 0.173913 | + | 0.100409i | ||||
\(829\) | −784.500 | − | 452.931i | −0.946321 | − | 0.546359i | −0.0543848 | − | 0.998520i | \(-0.517320\pi\) |
−0.891936 | + | 0.452161i | \(0.850653\pi\) | |||||||
\(830\) | 990.000 | − | 571.577i | 1.19277 | − | 0.688647i | ||||
\(831\) | −175.500 | + | 101.325i | −0.211191 | + | 0.121931i | ||||
\(832\) | − | 886.810i | − | 1.06588i | ||||||
\(833\) | −887.500 | + | 844.375i | −1.06543 | + | 1.01366i | ||||
\(834\) | −82.0000 | + | 142.028i | −0.0983213 | + | 0.170298i | ||||
\(835\) | 36.0000 | + | 62.3538i | 0.0431138 | + | 0.0746752i | ||||
\(836\) | −476.000 | −0.569378 | ||||||||
\(837\) | −484.500 | − | 279.726i | −0.578853 | − | 0.334201i | ||||
\(838\) | −604.000 | −0.720764 | ||||||||
\(839\) | 1053.09i | 1.25517i | 0.778548 | + | 0.627585i | \(0.215956\pi\) | ||||
−0.778548 | + | 0.627585i | \(0.784044\pi\) | |||||||
\(840\) | −288.000 | − | 41.5692i | −0.342857 | − | 0.0494872i | ||||
\(841\) | 649.000 | 0.771700 | ||||||||
\(842\) | 803.672i | 0.954479i | ||||||||
\(843\) | −37.0000 | + | 64.0859i | −0.0438909 | + | 0.0760212i | ||||
\(844\) | 1208.00 | 1.43128 | ||||||||
\(845\) | 103.500 | − | 59.7558i | 0.122485 | − | 0.0707169i | ||||
\(846\) | 696.000 | + | 401.836i | 0.822695 | + | 0.474983i | ||||
\(847\) | 1092.00 | − | 436.477i | 1.28926 | − | 0.515321i | ||||
\(848\) | 1272.00 | + | 734.390i | 1.50000 | + | 0.866025i | ||||
\(849\) | 231.500 | + | 400.970i | 0.272674 | + | 0.472285i | ||||
\(850\) | 50.0000 | + | 86.6025i | 0.0588235 | + | 0.101885i | ||||
\(851\) | 22.5000 | − | 38.9711i | 0.0264395 | − | 0.0457945i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 845.241i | 0.990904i | 0.868635 | + | 0.495452i | \(0.164997\pi\) | ||||
−0.868635 | + | 0.495452i | \(0.835003\pi\) | |||||||
\(854\) | −117.000 | − | 292.717i | −0.137002 | − | 0.342759i | ||||
\(855\) | − | 290.985i | − | 0.340333i | ||||||
\(856\) | 260.000 | + | 450.333i | 0.303738 | + | 0.526090i | ||||
\(857\) | −443.500 | + | 768.165i | −0.517503 | + | 0.896341i | 0.482290 | + | 0.876011i | \(0.339805\pi\) |
−0.999793 | + | 0.0203300i | \(0.993528\pi\) | |||||||
\(858\) | 408.000 | − | 235.559i | 0.475524 | − | 0.274544i | ||||
\(859\) | 831.500 | + | 1440.20i | 0.967986 | + | 1.67660i | 0.701369 | + | 0.712798i | \(0.252573\pi\) |
0.266617 | + | 0.963803i | \(0.414094\pi\) | |||||||
\(860\) | −252.000 | + | 145.492i | −0.293023 | + | 0.169177i | ||||
\(861\) | −143.000 | − | 112.583i | −0.166086 | − | 0.130759i | ||||
\(862\) | −1401.00 | − | 808.868i | −1.62529 | − | 0.938362i | ||||
\(863\) | −487.500 | + | 281.458i | −0.564890 | + | 0.326139i | −0.755106 | − | 0.655603i | \(-0.772415\pi\) |
0.190216 | + | 0.981742i | \(0.439081\pi\) | |||||||
\(864\) | 544.000 | 0.629630 | ||||||||
\(865\) | −274.500 | + | 475.448i | −0.317341 | + | 0.549651i | ||||
\(866\) | −820.000 | −0.946882 | ||||||||
\(867\) | 336.000 | 0.387543 | ||||||||
\(868\) | −570.000 | + | 723.997i | −0.656682 | + | 0.834098i | ||||
\(869\) | 1266.13i | 1.45700i | ||||||||
\(870\) | −144.000 | −0.165517 | ||||||||
\(871\) | 204.000 | + | 117.779i | 0.234214 | + | 0.135223i | ||||
\(872\) | −60.0000 | − | 34.6410i | −0.0688073 | − | 0.0397259i | ||||
\(873\) | −88.0000 | − | 152.420i | −0.100802 | − | 0.174594i | ||||
\(874\) | −63.0000 | − | 36.3731i | −0.0720824 | − | 0.0416168i | ||||
\(875\) | 828.000 | + | 119.512i | 0.946286 | + | 0.136585i | ||||
\(876\) | −238.000 | − | 412.228i | −0.271689 | − | 0.470580i | ||||
\(877\) | 103.500 | − | 59.7558i | 0.118016 | − | 0.0681365i | −0.439830 | − | 0.898081i | \(-0.644961\pi\) |
0.557846 | + | 0.829944i | \(0.311628\pi\) | |||||||
\(878\) | −849.000 | + | 490.170i | −0.966970 | + | 0.558281i | ||||
\(879\) | −96.0000 | − | 55.4256i | −0.109215 | − | 0.0630553i | ||||
\(880\) | − | 1413.35i | − | 1.60608i | ||||||
\(881\) | −574.000 | −0.651532 | −0.325766 | − | 0.945450i | \(-0.605622\pi\) | ||||
−0.325766 | + | 0.945450i | \(0.605622\pi\) | |||||||
\(882\) | 184.000 | + | 762.102i | 0.208617 | + | 0.864062i | ||||
\(883\) | 1166.00 | 1.32050 | 0.660249 | − | 0.751047i | \(-0.270451\pi\) | ||||
0.660249 | + | 0.751047i | \(0.270451\pi\) | |||||||
\(884\) | −1200.00 | − | 692.820i | −1.35747 | − | 0.783733i | ||||
\(885\) | −247.500 | − | 142.894i | −0.279661 | − | 0.161462i | ||||
\(886\) | 401.000 | + | 694.552i | 0.452596 | + | 0.783919i | ||||
\(887\) | 472.500 | − | 272.798i | 0.532694 | − | 0.307551i | −0.209419 | − | 0.977826i | \(-0.567157\pi\) |
0.742113 | + | 0.670275i | \(0.233824\pi\) | |||||||
\(888\) | − | 69.2820i | − | 0.0780203i | ||||||
\(889\) | 1152.00 | + | 166.277i | 1.29584 | + | 0.187038i | ||||
\(890\) | −639.000 | − | 368.927i | −0.717978 | − | 0.414525i | ||||
\(891\) | −467.500 | − | 809.734i | −0.524691 | − | 0.908792i | ||||
\(892\) | 554.256i | 0.621364i | ||||||||
\(893\) | −304.500 | − | 175.803i | −0.340985 | − | 0.196868i | ||||
\(894\) | 10.3923i | 0.0116245i | ||||||||
\(895\) | − | 462.458i | − | 0.516712i | ||||||
\(896\) | 128.000 | − | 886.810i | 0.142857 | − | 0.989743i | ||||
\(897\) | 72.0000 | 0.0802676 | ||||||||
\(898\) | 620.000 | 0.690423 | ||||||||
\(899\) | −228.000 | + | 394.908i | −0.253615 | + | 0.439274i | ||||
\(900\) | 64.0000 | 0.0711111 | ||||||||
\(901\) | 1987.50 | − | 1147.48i | 2.20588 | − | 1.27357i | ||||
\(902\) | 442.000 | − | 765.566i | 0.490022 | − | 0.848743i | ||||
\(903\) | −77.0000 | − | 60.6218i | −0.0852713 | − | 0.0671338i | ||||
\(904\) | −976.000 | −1.07965 | ||||||||
\(905\) | −648.000 | − | 1122.37i | −0.716022 | − | 1.24019i | ||||
\(906\) | −63.0000 | + | 36.3731i | −0.0695364 | + | 0.0401469i | ||||
\(907\) | −260.500 | + | 451.199i | −0.287211 | + | 0.497463i | −0.973143 | − | 0.230202i | \(-0.926061\pi\) |
0.685932 | + | 0.727665i | \(0.259395\pi\) | |||||||
\(908\) | 110.000 | − | 190.526i | 0.121145 | − | 0.209830i | ||||
\(909\) | 623.538i | 0.685961i | ||||||||
\(910\) | 936.000 | − | 374.123i | 1.02857 | − | 0.411124i | ||||
\(911\) | − | 1191.65i | − | 1.30807i | −0.756465 | − | 0.654035i | \(-0.773075\pi\) | ||
0.756465 | − | 0.654035i | \(-0.226925\pi\) | |||||||
\(912\) | −112.000 | −0.122807 | ||||||||
\(913\) | −935.000 | + | 1619.47i | −1.02410 | + | 1.77379i | ||||
\(914\) | 167.000 | + | 289.252i | 0.182713 | + | 0.316469i | ||||
\(915\) | −58.5000 | − | 101.325i | −0.0639344 | − | 0.110738i | ||||
\(916\) | 1134.00 | − | 654.715i | 1.23799 | − | 0.714755i | ||||
\(917\) | 110.500 | − | 44.1673i | 0.120502 | − | 0.0481650i | ||||
\(918\) | 425.000 | − | 736.122i | 0.462963 | − | 0.801875i | ||||
\(919\) | −1207.50 | + | 697.150i | −1.31393 | + | 0.758597i | −0.982744 | − | 0.184969i | \(-0.940781\pi\) |
−0.331184 | + | 0.943566i | \(0.607448\pi\) | |||||||
\(920\) | 108.000 | − | 187.061i | 0.117391 | − | 0.203328i | ||||
\(921\) | 137.000 | − | 237.291i | 0.148751 | − | 0.257645i | ||||
\(922\) | − | 27.7128i | − | 0.0300573i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 442.000 | − | 176.669i | 0.478355 | − | 0.191200i | ||||
\(925\) | − | 17.3205i | − | 0.0187249i | ||||||
\(926\) | − | 1219.36i | − | 1.31681i | ||||||
\(927\) | −1116.00 | − | 644.323i | −1.20388 | − | 0.695062i | ||||
\(928\) | − | 443.405i | − | 0.477807i | ||||||
\(929\) | 480.500 | + | 832.250i | 0.517223 | + | 0.895856i | 0.999800 | + | 0.0200027i | \(0.00636749\pi\) |
−0.482577 | + | 0.875853i | \(0.660299\pi\) | |||||||
\(930\) | −171.000 | + | 296.181i | −0.183871 | + | 0.318474i | ||||
\(931\) | −80.5000 | − | 333.420i | −0.0864662 | − | 0.358131i | ||||
\(932\) | 770.000 | + | 1333.68i | 0.826180 | + | 1.43099i | ||||
\(933\) | 43.5000 | − | 25.1147i | 0.0466238 | − | 0.0269183i | ||||
\(934\) | 785.000 | + | 1359.66i | 0.840471 | + | 1.45574i | ||||
\(935\) | −1912.50 | − | 1104.18i | −2.04545 | − | 1.18094i | ||||
\(936\) | −768.000 | + | 443.405i | −0.820513 | + | 0.473723i | ||||
\(937\) | −142.000 | −0.151547 | −0.0757737 | − | 0.997125i | \(-0.524143\pi\) | ||||
−0.0757737 | + | 0.997125i | \(0.524143\pi\) | |||||||
\(938\) | 187.000 | + | 147.224i | 0.199360 | + | 0.156956i | ||||
\(939\) | −409.000 | −0.435570 | ||||||||
\(940\) | 522.000 | − | 904.131i | 0.555319 | − | 0.961841i | ||||
\(941\) | −1060.50 | − | 612.280i | −1.12699 | − | 0.650669i | −0.183816 | − | 0.982961i | \(-0.558845\pi\) |
−0.943177 | + | 0.332291i | \(0.892178\pi\) | |||||||
\(942\) | −537.000 | + | 310.037i | −0.570064 | + | 0.329126i | ||||
\(943\) | 117.000 | − | 67.5500i | 0.124072 | − | 0.0716331i | ||||
\(944\) | 440.000 | − | 762.102i | 0.466102 | − | 0.807312i | ||||
\(945\) | 229.500 | + | 574.175i | 0.242857 | + | 0.607592i | ||||
\(946\) | 238.000 | − | 412.228i | 0.251586 | − | 0.435759i | ||||
\(947\) | 87.5000 | + | 151.554i | 0.0923970 | + | 0.160036i | 0.908519 | − | 0.417843i | \(-0.137214\pi\) |
−0.816122 | + | 0.577879i | \(0.803880\pi\) | |||||||
\(948\) | 297.913i | 0.314254i | ||||||||
\(949\) | 1428.00 | + | 824.456i | 1.50474 | + | 0.868763i | ||||
\(950\) | −28.0000 | −0.0294737 | ||||||||
\(951\) | 188.794i | 0.198521i | ||||||||
\(952\) | −1100.00 | − | 866.025i | −1.15546 | − | 0.909691i | ||||
\(953\) | −454.000 | −0.476390 | −0.238195 | − | 0.971217i | \(-0.576556\pi\) | ||||
−0.238195 | + | 0.971217i | \(0.576556\pi\) | |||||||
\(954\) | − | 1468.78i | − | 1.53960i | ||||||
\(955\) | 562.500 | − | 974.279i | 0.589005 | − | 1.02019i | ||||
\(956\) | − | 1718.19i | − | 1.79727i | ||||||
\(957\) | 204.000 | − | 117.779i | 0.213166 | − | 0.123072i | ||||
\(958\) | 1071.00 | + | 618.342i | 1.11795 | + | 0.645451i | ||||
\(959\) | 797.500 | + | 627.868i | 0.831595 | + | 0.654712i | ||||
\(960\) | − | 332.554i | − | 0.346410i | ||||||
\(961\) | 61.0000 | + | 105.655i | 0.0634755 | + | 0.109943i | ||||
\(962\) | 120.000 | + | 207.846i | 0.124740 | + | 0.216056i | ||||
\(963\) | 260.000 | − | 450.333i | 0.269990 | − | 0.467636i | ||||
\(964\) | 290.000 | − | 502.295i | 0.300830 | − | 0.521053i | ||||
\(965\) | 379.319i | 0.393077i | ||||||||
\(966\) | 72.0000 | + | 10.3923i | 0.0745342 | + | 0.0107581i | ||||
\(967\) | − | 720.533i | − | 0.745122i | −0.928008 | − | 0.372561i | \(-0.878480\pi\) | ||
0.928008 | − | 0.372561i | \(-0.121520\pi\) | |||||||
\(968\) | 672.000 | + | 1163.94i | 0.694215 | + | 1.20242i | ||||
\(969\) | −87.5000 | + | 151.554i | −0.0902993 | + | 0.156403i | ||||
\(970\) | −198.000 | + | 114.315i | −0.204124 | + | 0.117851i | ||||
\(971\) | 819.500 | + | 1419.42i | 0.843975 | + | 1.46181i | 0.886508 | + | 0.462713i | \(0.153124\pi\) |
−0.0425329 | + | 0.999095i | \(0.513543\pi\) | |||||||
\(972\) | −416.000 | − | 720.533i | −0.427984 | − | 0.741289i | ||||
\(973\) | 82.0000 | − | 568.113i | 0.0842754 | − | 0.583877i | ||||
\(974\) | −681.000 | − | 393.176i | −0.699179 | − | 0.403671i | ||||
\(975\) | 24.0000 | − | 13.8564i | 0.0246154 | − | 0.0142117i | ||||
\(976\) | 312.000 | − | 180.133i | 0.319672 | − | 0.184563i | ||||
\(977\) | 396.500 | − | 686.758i | 0.405834 | − | 0.702925i | −0.588584 | − | 0.808436i | \(-0.700314\pi\) |
0.994418 | + | 0.105511i | \(0.0336477\pi\) | |||||||
\(978\) | −34.0000 | −0.0347648 | ||||||||
\(979\) | 1207.00 | 1.23289 | ||||||||
\(980\) | 990.000 | − | 239.023i | 1.01020 | − | 0.243901i | ||||
\(981\) | 69.2820i | 0.0706239i | ||||||||
\(982\) | −844.000 | −0.859470 | ||||||||
\(983\) | 1336.50 | + | 771.629i | 1.35961 | + | 0.784973i | 0.989572 | − | 0.144042i | \(-0.0460100\pi\) |
0.370042 | + | 0.929015i | \(0.379343\pi\) | |||||||
\(984\) | 104.000 | − | 180.133i | 0.105691 | − | 0.183062i | ||||
\(985\) | −540.000 | − | 935.307i | −0.548223 | − | 0.949551i | ||||
\(986\) | −600.000 | − | 346.410i | −0.608519 | − | 0.351329i | ||||
\(987\) | 348.000 | + | 50.2295i | 0.352584 | + | 0.0508911i | ||||
\(988\) | 336.000 | − | 193.990i | 0.340081 | − | 0.196346i | ||||
\(989\) | 63.0000 | − | 36.3731i | 0.0637007 | − | 0.0367776i | ||||
\(990\) | −1224.00 | + | 706.677i | −1.23636 | + | 0.713815i | ||||
\(991\) | −775.500 | − | 447.735i | −0.782543 | − | 0.451801i | 0.0547878 | − | 0.998498i | \(-0.482552\pi\) |
−0.837331 | + | 0.546697i | \(0.815885\pi\) | |||||||
\(992\) | −912.000 | − | 526.543i | −0.919355 | − | 0.530790i | ||||
\(993\) | −295.000 | −0.297080 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 333.000 | 0.334673 | ||||||||
\(996\) | −220.000 | + | 381.051i | −0.220884 | + | 0.382582i | ||||
\(997\) | −688.500 | − | 397.506i | −0.690572 | − | 0.398702i | 0.113254 | − | 0.993566i | \(-0.463872\pi\) |
−0.803826 | + | 0.594864i | \(0.797206\pi\) | |||||||
\(998\) | 65.0000 | + | 112.583i | 0.0651303 | + | 0.112809i | ||||
\(999\) | −127.500 | + | 73.6122i | −0.127628 | + | 0.0736858i |
(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 | 56.3.k.a.11.1 | ✓ | 2 | |
4.3 | odd | 2 | 224.3.o.a.207.1 | 2 | |||
7.2 | even | 3 | 56.3.k.b.51.1 | yes | 2 | ||
7.3 | odd | 6 | 392.3.g.d.99.1 | 2 | |||
7.4 | even | 3 | 392.3.g.e.99.1 | 2 | |||
7.5 | odd | 6 | 392.3.k.c.275.1 | 2 | |||
7.6 | odd | 2 | 392.3.k.a.67.1 | 2 | |||
8.3 | odd | 2 | 56.3.k.b.11.1 | yes | 2 | ||
8.5 | even | 2 | 224.3.o.b.207.1 | 2 | |||
28.3 | even | 6 | 1568.3.g.f.687.2 | 2 | |||
28.11 | odd | 6 | 1568.3.g.c.687.1 | 2 | |||
28.23 | odd | 6 | 224.3.o.b.79.1 | 2 | |||
56.3 | even | 6 | 392.3.g.d.99.2 | 2 | |||
56.11 | odd | 6 | 392.3.g.e.99.2 | 2 | |||
56.19 | even | 6 | 392.3.k.a.275.1 | 2 | |||
56.27 | even | 2 | 392.3.k.c.67.1 | 2 | |||
56.37 | even | 6 | 224.3.o.a.79.1 | 2 | |||
56.45 | odd | 6 | 1568.3.g.f.687.1 | 2 | |||
56.51 | odd | 6 | inner | 56.3.k.a.51.1 | yes | 2 | |
56.53 | even | 6 | 1568.3.g.c.687.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.k.a.11.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
56.3.k.a.51.1 | yes | 2 | 56.51 | odd | 6 | inner | |
56.3.k.b.11.1 | yes | 2 | 8.3 | odd | 2 | ||
56.3.k.b.51.1 | yes | 2 | 7.2 | even | 3 | ||
224.3.o.a.79.1 | 2 | 56.37 | even | 6 | |||
224.3.o.a.207.1 | 2 | 4.3 | odd | 2 | |||
224.3.o.b.79.1 | 2 | 28.23 | odd | 6 | |||
224.3.o.b.207.1 | 2 | 8.5 | even | 2 | |||
392.3.g.d.99.1 | 2 | 7.3 | odd | 6 | |||
392.3.g.d.99.2 | 2 | 56.3 | even | 6 | |||
392.3.g.e.99.1 | 2 | 7.4 | even | 3 | |||
392.3.g.e.99.2 | 2 | 56.11 | odd | 6 | |||
392.3.k.a.67.1 | 2 | 7.6 | odd | 2 | |||
392.3.k.a.275.1 | 2 | 56.19 | even | 6 | |||
392.3.k.c.67.1 | 2 | 56.27 | even | 2 | |||
392.3.k.c.275.1 | 2 | 7.5 | odd | 6 | |||
1568.3.g.c.687.1 | 2 | 28.11 | odd | 6 | |||
1568.3.g.c.687.2 | 2 | 56.53 | even | 6 | |||
1568.3.g.f.687.1 | 2 | 56.45 | odd | 6 | |||
1568.3.g.f.687.2 | 2 | 28.3 | even | 6 |