Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,3,Mod(10,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.10");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.f (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: | \(0.572208555157\) |
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 | 10.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.10 |
Dual form | 21.3.f.a.19.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50000 | − | 2.59808i | −0.750000 | − | 1.29904i | −0.947822 | − | 0.318800i | \(-0.896720\pi\) |
0.197822 | − | 0.980238i | \(-0.436613\pi\) | |||||||
\(3\) | −1.50000 | − | 0.866025i | −0.500000 | − | 0.288675i | ||||
\(4\) | −2.50000 | + | 4.33013i | −0.625000 | + | 1.08253i | ||||
\(5\) | 4.50000 | − | 2.59808i | 0.900000 | − | 0.519615i | 0.0227998 | − | 0.999740i | \(-0.492742\pi\) |
0.877200 | + | 0.480125i | \(0.159409\pi\) | |||||||
\(6\) | 5.19615i | 0.866025i | ||||||||
\(7\) | 6.50000 | + | 2.59808i | 0.928571 | + | 0.371154i | ||||
\(8\) | 3.00000 | 0.375000 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.166667 | + | 0.288675i | ||||
\(10\) | −13.5000 | − | 7.79423i | −1.35000 | − | 0.779423i | ||||
\(11\) | −7.50000 | + | 12.9904i | −0.681818 | + | 1.18094i | 0.292607 | + | 0.956233i | \(0.405477\pi\) |
−0.974425 | + | 0.224711i | \(0.927856\pi\) | |||||||
\(12\) | 7.50000 | − | 4.33013i | 0.625000 | − | 0.360844i | ||||
\(13\) | − | 13.8564i | − | 1.06588i | −0.846154 | − | 0.532939i | \(-0.821088\pi\) | ||
0.846154 | − | 0.532939i | \(-0.178912\pi\) | |||||||
\(14\) | −3.00000 | − | 20.7846i | −0.214286 | − | 1.48461i | ||||
\(15\) | −9.00000 | −0.600000 | ||||||||
\(16\) | 5.50000 | + | 9.52628i | 0.343750 | + | 0.595392i | ||||
\(17\) | 9.00000 | + | 5.19615i | 0.529412 | + | 0.305656i | 0.740777 | − | 0.671751i | \(-0.234458\pi\) |
−0.211365 | + | 0.977407i | \(0.567791\pi\) | |||||||
\(18\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(19\) | −9.00000 | + | 5.19615i | −0.473684 | + | 0.273482i | −0.717781 | − | 0.696269i | \(-0.754842\pi\) |
0.244096 | + | 0.969751i | \(0.421509\pi\) | |||||||
\(20\) | 25.9808i | 1.29904i | ||||||||
\(21\) | −7.50000 | − | 9.52628i | −0.357143 | − | 0.453632i | ||||
\(22\) | 45.0000 | 2.04545 | ||||||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | −4.50000 | − | 2.59808i | −0.187500 | − | 0.108253i | ||||
\(25\) | 1.00000 | − | 1.73205i | 0.0400000 | − | 0.0692820i | ||||
\(26\) | −36.0000 | + | 20.7846i | −1.38462 | + | 0.799408i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −27.5000 | + | 21.6506i | −0.982143 | + | 0.773237i | ||||
\(29\) | −9.00000 | −0.310345 | −0.155172 | − | 0.987887i | \(-0.549593\pi\) | ||||
−0.155172 | + | 0.987887i | \(0.549593\pi\) | |||||||
\(30\) | 13.5000 | + | 23.3827i | 0.450000 | + | 0.779423i | ||||
\(31\) | −10.5000 | − | 6.06218i | −0.338710 | − | 0.195554i | 0.320992 | − | 0.947082i | \(-0.395984\pi\) |
−0.659701 | + | 0.751528i | \(0.729317\pi\) | |||||||
\(32\) | 22.5000 | − | 38.9711i | 0.703125 | − | 1.21785i | ||||
\(33\) | 22.5000 | − | 12.9904i | 0.681818 | − | 0.393648i | ||||
\(34\) | − | 31.1769i | − | 0.916968i | ||||||
\(35\) | 36.0000 | − | 5.19615i | 1.02857 | − | 0.148461i | ||||
\(36\) | −15.0000 | −0.416667 | ||||||||
\(37\) | −5.00000 | − | 8.66025i | −0.135135 | − | 0.234061i | 0.790514 | − | 0.612444i | \(-0.209814\pi\) |
−0.925649 | + | 0.378383i | \(0.876480\pi\) | |||||||
\(38\) | 27.0000 | + | 15.5885i | 0.710526 | + | 0.410223i | ||||
\(39\) | −12.0000 | + | 20.7846i | −0.307692 | + | 0.532939i | ||||
\(40\) | 13.5000 | − | 7.79423i | 0.337500 | − | 0.194856i | ||||
\(41\) | − | 10.3923i | − | 0.253471i | −0.991937 | − | 0.126735i | \(-0.959550\pi\) | ||
0.991937 | − | 0.126735i | \(-0.0404499\pi\) | |||||||
\(42\) | −13.5000 | + | 33.7750i | −0.321429 | + | 0.804166i | ||||
\(43\) | −74.0000 | −1.72093 | −0.860465 | − | 0.509509i | \(-0.829827\pi\) | ||||
−0.860465 | + | 0.509509i | \(0.829827\pi\) | |||||||
\(44\) | −37.5000 | − | 64.9519i | −0.852273 | − | 1.47618i | ||||
\(45\) | 13.5000 | + | 7.79423i | 0.300000 | + | 0.173205i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | − | 19.0526i | − | 0.396928i | ||||||
\(49\) | 35.5000 | + | 33.7750i | 0.724490 | + | 0.689286i | ||||
\(50\) | −6.00000 | −0.120000 | ||||||||
\(51\) | −9.00000 | − | 15.5885i | −0.176471 | − | 0.305656i | ||||
\(52\) | 60.0000 | + | 34.6410i | 1.15385 | + | 0.666173i | ||||
\(53\) | −16.5000 | + | 28.5788i | −0.311321 | + | 0.539223i | −0.978649 | − | 0.205541i | \(-0.934105\pi\) |
0.667328 | + | 0.744764i | \(0.267438\pi\) | |||||||
\(54\) | −13.5000 | + | 7.79423i | −0.250000 | + | 0.144338i | ||||
\(55\) | 77.9423i | 1.41713i | ||||||||
\(56\) | 19.5000 | + | 7.79423i | 0.348214 | + | 0.139183i | ||||
\(57\) | 18.0000 | 0.315789 | ||||||||
\(58\) | 13.5000 | + | 23.3827i | 0.232759 | + | 0.403150i | ||||
\(59\) | 13.5000 | + | 7.79423i | 0.228814 | + | 0.132106i | 0.610025 | − | 0.792382i | \(-0.291160\pi\) |
−0.381211 | + | 0.924488i | \(0.624493\pi\) | |||||||
\(60\) | 22.5000 | − | 38.9711i | 0.375000 | − | 0.649519i | ||||
\(61\) | 78.0000 | − | 45.0333i | 1.27869 | − | 0.738251i | 0.302081 | − | 0.953282i | \(-0.402319\pi\) |
0.976607 | + | 0.215031i | \(0.0689853\pi\) | |||||||
\(62\) | 36.3731i | 0.586662i | ||||||||
\(63\) | 3.00000 | + | 20.7846i | 0.0476190 | + | 0.329914i | ||||
\(64\) | −91.0000 | −1.42188 | ||||||||
\(65\) | −36.0000 | − | 62.3538i | −0.553846 | − | 0.959290i | ||||
\(66\) | −67.5000 | − | 38.9711i | −1.02273 | − | 0.590472i | ||||
\(67\) | 38.0000 | − | 65.8179i | 0.567164 | − | 0.982357i | −0.429681 | − | 0.902981i | \(-0.641374\pi\) |
0.996845 | − | 0.0793762i | \(-0.0252928\pi\) | |||||||
\(68\) | −45.0000 | + | 25.9808i | −0.661765 | + | 0.382070i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −67.5000 | − | 85.7365i | −0.964286 | − | 1.22481i | ||||
\(71\) | 84.0000 | 1.18310 | 0.591549 | − | 0.806269i | \(-0.298517\pi\) | ||||
0.591549 | + | 0.806269i | \(0.298517\pi\) | |||||||
\(72\) | 4.50000 | + | 7.79423i | 0.0625000 | + | 0.108253i | ||||
\(73\) | −54.0000 | − | 31.1769i | −0.739726 | − | 0.427081i | 0.0822437 | − | 0.996612i | \(-0.473791\pi\) |
−0.821970 | + | 0.569531i | \(0.807125\pi\) | |||||||
\(74\) | −15.0000 | + | 25.9808i | −0.202703 | + | 0.351091i | ||||
\(75\) | −3.00000 | + | 1.73205i | −0.0400000 | + | 0.0230940i | ||||
\(76\) | − | 51.9615i | − | 0.683704i | ||||||
\(77\) | −82.5000 | + | 64.9519i | −1.07143 | + | 0.843531i | ||||
\(78\) | 72.0000 | 0.923077 | ||||||||
\(79\) | 21.5000 | + | 37.2391i | 0.272152 | + | 0.471381i | 0.969413 | − | 0.245437i | \(-0.0789313\pi\) |
−0.697261 | + | 0.716818i | \(0.745598\pi\) | |||||||
\(80\) | 49.5000 | + | 28.5788i | 0.618750 | + | 0.357235i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −27.0000 | + | 15.5885i | −0.329268 | + | 0.190103i | ||||
\(83\) | − | 119.512i | − | 1.43990i | −0.694027 | − | 0.719949i | \(-0.744165\pi\) | ||
0.694027 | − | 0.719949i | \(-0.255835\pi\) | |||||||
\(84\) | 60.0000 | − | 8.66025i | 0.714286 | − | 0.103098i | ||||
\(85\) | 54.0000 | 0.635294 | ||||||||
\(86\) | 111.000 | + | 192.258i | 1.29070 | + | 2.23555i | ||||
\(87\) | 13.5000 | + | 7.79423i | 0.155172 | + | 0.0895888i | ||||
\(88\) | −22.5000 | + | 38.9711i | −0.255682 | + | 0.442854i | ||||
\(89\) | −63.0000 | + | 36.3731i | −0.707865 | + | 0.408686i | −0.810270 | − | 0.586057i | \(-0.800680\pi\) |
0.102405 | + | 0.994743i | \(0.467346\pi\) | |||||||
\(90\) | − | 46.7654i | − | 0.519615i | ||||||
\(91\) | 36.0000 | − | 90.0666i | 0.395604 | − | 0.989743i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.5000 | + | 18.1865i | 0.112903 | + | 0.195554i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −27.0000 | + | 46.7654i | −0.284211 | + | 0.492267i | ||||
\(96\) | −67.5000 | + | 38.9711i | −0.703125 | + | 0.405949i | ||||
\(97\) | 185.329i | 1.91061i | 0.295618 | + | 0.955306i | \(0.404475\pi\) | ||||
−0.295618 | + | 0.955306i | \(0.595525\pi\) | |||||||
\(98\) | 34.5000 | − | 142.894i | 0.352041 | − | 1.45810i | ||||
\(99\) | −45.0000 | −0.454545 | ||||||||
\(100\) | 5.00000 | + | 8.66025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −126.000 | − | 72.7461i | −1.24752 | − | 0.720259i | −0.276910 | − | 0.960896i | \(-0.589310\pi\) |
−0.970615 | + | 0.240637i | \(0.922644\pi\) | |||||||
\(102\) | −27.0000 | + | 46.7654i | −0.264706 | + | 0.458484i | ||||
\(103\) | −60.0000 | + | 34.6410i | −0.582524 | + | 0.336321i | −0.762136 | − | 0.647417i | \(-0.775849\pi\) |
0.179612 | + | 0.983738i | \(0.442516\pi\) | |||||||
\(104\) | − | 41.5692i | − | 0.399704i | ||||||
\(105\) | −58.5000 | − | 23.3827i | −0.557143 | − | 0.222692i | ||||
\(106\) | 99.0000 | 0.933962 | ||||||||
\(107\) | −46.5000 | − | 80.5404i | −0.434579 | − | 0.752714i | 0.562682 | − | 0.826674i | \(-0.309770\pi\) |
−0.997261 | + | 0.0739599i | \(0.976436\pi\) | |||||||
\(108\) | 22.5000 | + | 12.9904i | 0.208333 | + | 0.120281i | ||||
\(109\) | 4.00000 | − | 6.92820i | 0.0366972 | − | 0.0635615i | −0.847093 | − | 0.531444i | \(-0.821650\pi\) |
0.883791 | + | 0.467882i | \(0.154983\pi\) | |||||||
\(110\) | 202.500 | − | 116.913i | 1.84091 | − | 1.06285i | ||||
\(111\) | 17.3205i | 0.156041i | ||||||||
\(112\) | 11.0000 | + | 76.2102i | 0.0982143 | + | 0.680449i | ||||
\(113\) | 42.0000 | 0.371681 | 0.185841 | − | 0.982580i | \(-0.440499\pi\) | ||||
0.185841 | + | 0.982580i | \(0.440499\pi\) | |||||||
\(114\) | −27.0000 | − | 46.7654i | −0.236842 | − | 0.410223i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 22.5000 | − | 38.9711i | 0.193966 | − | 0.335958i | ||||
\(117\) | 36.0000 | − | 20.7846i | 0.307692 | − | 0.177646i | ||||
\(118\) | − | 46.7654i | − | 0.396317i | ||||||
\(119\) | 45.0000 | + | 57.1577i | 0.378151 | + | 0.480317i | ||||
\(120\) | −27.0000 | −0.225000 | ||||||||
\(121\) | −52.0000 | − | 90.0666i | −0.429752 | − | 0.744352i | ||||
\(122\) | −234.000 | − | 135.100i | −1.91803 | − | 1.10738i | ||||
\(123\) | −9.00000 | + | 15.5885i | −0.0731707 | + | 0.126735i | ||||
\(124\) | 52.5000 | − | 30.3109i | 0.423387 | − | 0.244443i | ||||
\(125\) | 119.512i | 0.956092i | ||||||||
\(126\) | 49.5000 | − | 38.9711i | 0.392857 | − | 0.309295i | ||||
\(127\) | 35.0000 | 0.275591 | 0.137795 | − | 0.990461i | \(-0.455998\pi\) | ||||
0.137795 | + | 0.990461i | \(0.455998\pi\) | |||||||
\(128\) | 46.5000 | + | 80.5404i | 0.363281 | + | 0.629222i | ||||
\(129\) | 111.000 | + | 64.0859i | 0.860465 | + | 0.496790i | ||||
\(130\) | −108.000 | + | 187.061i | −0.830769 | + | 1.43893i | ||||
\(131\) | 148.500 | − | 85.7365i | 1.13359 | − | 0.654477i | 0.188753 | − | 0.982025i | \(-0.439555\pi\) |
0.944835 | + | 0.327547i | \(0.106222\pi\) | |||||||
\(132\) | 129.904i | 0.984120i | ||||||||
\(133\) | −72.0000 | + | 10.3923i | −0.541353 | + | 0.0781376i | ||||
\(134\) | −228.000 | −1.70149 | ||||||||
\(135\) | −13.5000 | − | 23.3827i | −0.100000 | − | 0.173205i | ||||
\(136\) | 27.0000 | + | 15.5885i | 0.198529 | + | 0.114621i | ||||
\(137\) | 48.0000 | − | 83.1384i | 0.350365 | − | 0.606850i | −0.635948 | − | 0.771732i | \(-0.719391\pi\) |
0.986313 | + | 0.164882i | \(0.0527242\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 183.597i | − | 1.32084i | −0.750894 | − | 0.660422i | \(-0.770377\pi\) | ||
0.750894 | − | 0.660422i | \(-0.229623\pi\) | |||||||
\(140\) | −67.5000 | + | 168.875i | −0.482143 | + | 1.20625i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −126.000 | − | 218.238i | −0.887324 | − | 1.53689i | ||||
\(143\) | 180.000 | + | 103.923i | 1.25874 | + | 0.726735i | ||||
\(144\) | −16.5000 | + | 28.5788i | −0.114583 | + | 0.198464i | ||||
\(145\) | −40.5000 | + | 23.3827i | −0.279310 | + | 0.161260i | ||||
\(146\) | 187.061i | 1.28124i | ||||||||
\(147\) | −24.0000 | − | 81.4064i | −0.163265 | − | 0.553785i | ||||
\(148\) | 50.0000 | 0.337838 | ||||||||
\(149\) | 93.0000 | + | 161.081i | 0.624161 | + | 1.08108i | 0.988702 | + | 0.149892i | \(0.0478924\pi\) |
−0.364541 | + | 0.931187i | \(0.618774\pi\) | |||||||
\(150\) | 9.00000 | + | 5.19615i | 0.0600000 | + | 0.0346410i | ||||
\(151\) | −39.5000 | + | 68.4160i | −0.261589 | + | 0.453086i | −0.966664 | − | 0.256047i | \(-0.917580\pi\) |
0.705075 | + | 0.709133i | \(0.250913\pi\) | |||||||
\(152\) | −27.0000 | + | 15.5885i | −0.177632 | + | 0.102556i | ||||
\(153\) | 31.1769i | 0.203771i | ||||||||
\(154\) | 292.500 | + | 116.913i | 1.89935 | + | 0.759178i | ||||
\(155\) | −63.0000 | −0.406452 | ||||||||
\(156\) | −60.0000 | − | 103.923i | −0.384615 | − | 0.666173i | ||||
\(157\) | −18.0000 | − | 10.3923i | −0.114650 | − | 0.0661930i | 0.441579 | − | 0.897223i | \(-0.354419\pi\) |
−0.556228 | + | 0.831030i | \(0.687752\pi\) | |||||||
\(158\) | 64.5000 | − | 111.717i | 0.408228 | − | 0.707071i | ||||
\(159\) | 49.5000 | − | 28.5788i | 0.311321 | − | 0.179741i | ||||
\(160\) | − | 233.827i | − | 1.46142i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 27.0000 | 0.166667 | ||||||||
\(163\) | 104.000 | + | 180.133i | 0.638037 | + | 1.10511i | 0.985863 | + | 0.167553i | \(0.0535866\pi\) |
−0.347826 | + | 0.937559i | \(0.613080\pi\) | |||||||
\(164\) | 45.0000 | + | 25.9808i | 0.274390 | + | 0.158419i | ||||
\(165\) | 67.5000 | − | 116.913i | 0.409091 | − | 0.708566i | ||||
\(166\) | −310.500 | + | 179.267i | −1.87048 | + | 1.07992i | ||||
\(167\) | − | 249.415i | − | 1.49350i | −0.665102 | − | 0.746752i | \(-0.731612\pi\) | ||
0.665102 | − | 0.746752i | \(-0.268388\pi\) | |||||||
\(168\) | −22.5000 | − | 28.5788i | −0.133929 | − | 0.170112i | ||||
\(169\) | −23.0000 | −0.136095 | ||||||||
\(170\) | −81.0000 | − | 140.296i | −0.476471 | − | 0.825271i | ||||
\(171\) | −27.0000 | − | 15.5885i | −0.157895 | − | 0.0911606i | ||||
\(172\) | 185.000 | − | 320.429i | 1.07558 | − | 1.86296i | ||||
\(173\) | −198.000 | + | 114.315i | −1.14451 | + | 0.660782i | −0.947543 | − | 0.319628i | \(-0.896442\pi\) |
−0.196966 | + | 0.980410i | \(0.563109\pi\) | |||||||
\(174\) | − | 46.7654i | − | 0.268767i | ||||||
\(175\) | 11.0000 | − | 8.66025i | 0.0628571 | − | 0.0494872i | ||||
\(176\) | −165.000 | −0.937500 | ||||||||
\(177\) | −13.5000 | − | 23.3827i | −0.0762712 | − | 0.132106i | ||||
\(178\) | 189.000 | + | 109.119i | 1.06180 | + | 0.613029i | ||||
\(179\) | −45.0000 | + | 77.9423i | −0.251397 | + | 0.435432i | −0.963911 | − | 0.266226i | \(-0.914223\pi\) |
0.712514 | + | 0.701658i | \(0.247557\pi\) | |||||||
\(180\) | −67.5000 | + | 38.9711i | −0.375000 | + | 0.216506i | ||||
\(181\) | − | 10.3923i | − | 0.0574160i | −0.999588 | − | 0.0287080i | \(-0.990861\pi\) | ||
0.999588 | − | 0.0287080i | \(-0.00913930\pi\) | |||||||
\(182\) | −288.000 | + | 41.5692i | −1.58242 | + | 0.228402i | ||||
\(183\) | −156.000 | −0.852459 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −45.0000 | − | 25.9808i | −0.243243 | − | 0.140437i | ||||
\(186\) | 31.5000 | − | 54.5596i | 0.169355 | − | 0.293331i | ||||
\(187\) | −135.000 | + | 77.9423i | −0.721925 | + | 0.416804i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.5000 | − | 33.7750i | 0.0714286 | − | 0.178704i | ||||
\(190\) | 162.000 | 0.852632 | ||||||||
\(191\) | 156.000 | + | 270.200i | 0.816754 | + | 1.41466i | 0.908062 | + | 0.418837i | \(0.137562\pi\) |
−0.0913077 | + | 0.995823i | \(0.529105\pi\) | |||||||
\(192\) | 136.500 | + | 78.8083i | 0.710938 | + | 0.410460i | ||||
\(193\) | 92.5000 | − | 160.215i | 0.479275 | − | 0.830128i | −0.520443 | − | 0.853896i | \(-0.674233\pi\) |
0.999717 | + | 0.0237685i | \(0.00756646\pi\) | |||||||
\(194\) | 481.500 | − | 277.994i | 2.48196 | − | 1.43296i | ||||
\(195\) | 124.708i | 0.639526i | ||||||||
\(196\) | −235.000 | + | 69.2820i | −1.19898 | + | 0.353480i | ||||
\(197\) | 330.000 | 1.67513 | 0.837563 | − | 0.546340i | \(-0.183979\pi\) | ||||
0.837563 | + | 0.546340i | \(0.183979\pi\) | |||||||
\(198\) | 67.5000 | + | 116.913i | 0.340909 | + | 0.590472i | ||||
\(199\) | 6.00000 | + | 3.46410i | 0.0301508 | + | 0.0174075i | 0.515000 | − | 0.857190i | \(-0.327792\pi\) |
−0.484849 | + | 0.874598i | \(0.661125\pi\) | |||||||
\(200\) | 3.00000 | − | 5.19615i | 0.0150000 | − | 0.0259808i | ||||
\(201\) | −114.000 | + | 65.8179i | −0.567164 | + | 0.327452i | ||||
\(202\) | 436.477i | 2.16078i | ||||||||
\(203\) | −58.5000 | − | 23.3827i | −0.288177 | − | 0.115186i | ||||
\(204\) | 90.0000 | 0.441176 | ||||||||
\(205\) | −27.0000 | − | 46.7654i | −0.131707 | − | 0.228124i | ||||
\(206\) | 180.000 | + | 103.923i | 0.873786 | + | 0.504481i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 132.000 | − | 76.2102i | 0.634615 | − | 0.366395i | ||||
\(209\) | − | 155.885i | − | 0.745859i | ||||||
\(210\) | 27.0000 | + | 187.061i | 0.128571 | + | 0.890769i | ||||
\(211\) | −248.000 | −1.17536 | −0.587678 | − | 0.809095i | \(-0.699958\pi\) | ||||
−0.587678 | + | 0.809095i | \(0.699958\pi\) | |||||||
\(212\) | −82.5000 | − | 142.894i | −0.389151 | − | 0.674029i | ||||
\(213\) | −126.000 | − | 72.7461i | −0.591549 | − | 0.341531i | ||||
\(214\) | −139.500 | + | 241.621i | −0.651869 | + | 1.12907i | ||||
\(215\) | −333.000 | + | 192.258i | −1.54884 | + | 0.894222i | ||||
\(216\) | − | 15.5885i | − | 0.0721688i | ||||||
\(217\) | −52.5000 | − | 66.6840i | −0.241935 | − | 0.307299i | ||||
\(218\) | −24.0000 | −0.110092 | ||||||||
\(219\) | 54.0000 | + | 93.5307i | 0.246575 | + | 0.427081i | ||||
\(220\) | −337.500 | − | 194.856i | −1.53409 | − | 0.885708i | ||||
\(221\) | 72.0000 | − | 124.708i | 0.325792 | − | 0.564288i | ||||
\(222\) | 45.0000 | − | 25.9808i | 0.202703 | − | 0.117030i | ||||
\(223\) | − | 192.258i | − | 0.862142i | −0.902318 | − | 0.431071i | \(-0.858136\pi\) | ||
0.902318 | − | 0.431071i | \(-0.141864\pi\) | |||||||
\(224\) | 247.500 | − | 194.856i | 1.10491 | − | 0.869892i | ||||
\(225\) | 6.00000 | 0.0266667 | ||||||||
\(226\) | −63.0000 | − | 109.119i | −0.278761 | − | 0.482828i | ||||
\(227\) | −76.5000 | − | 44.1673i | −0.337004 | − | 0.194570i | 0.321942 | − | 0.946759i | \(-0.395664\pi\) |
−0.658947 | + | 0.752190i | \(0.728998\pi\) | |||||||
\(228\) | −45.0000 | + | 77.9423i | −0.197368 | + | 0.341852i | ||||
\(229\) | 285.000 | − | 164.545i | 1.24454 | − | 0.718536i | 0.274526 | − | 0.961580i | \(-0.411479\pi\) |
0.970015 | + | 0.243043i | \(0.0781457\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 180.000 | − | 25.9808i | 0.779221 | − | 0.112471i | ||||
\(232\) | −27.0000 | −0.116379 | ||||||||
\(233\) | −135.000 | − | 233.827i | −0.579399 | − | 1.00355i | −0.995548 | − | 0.0942524i | \(-0.969954\pi\) |
0.416149 | − | 0.909296i | \(-0.363379\pi\) | |||||||
\(234\) | −108.000 | − | 62.3538i | −0.461538 | − | 0.266469i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −67.5000 | + | 38.9711i | −0.286017 | + | 0.165132i | ||||
\(237\) | − | 74.4782i | − | 0.314254i | ||||||
\(238\) | 81.0000 | − | 202.650i | 0.340336 | − | 0.851470i | ||||
\(239\) | −228.000 | −0.953975 | −0.476987 | − | 0.878910i | \(-0.658271\pi\) | ||||
−0.476987 | + | 0.878910i | \(0.658271\pi\) | |||||||
\(240\) | −49.5000 | − | 85.7365i | −0.206250 | − | 0.357235i | ||||
\(241\) | 385.500 | + | 222.569i | 1.59959 | + | 0.923521i | 0.991567 | + | 0.129598i | \(0.0413687\pi\) |
0.608018 | + | 0.793923i | \(0.291965\pi\) | |||||||
\(242\) | −156.000 | + | 270.200i | −0.644628 | + | 1.11653i | ||||
\(243\) | 13.5000 | − | 7.79423i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 450.333i | 1.84563i | ||||||||
\(245\) | 247.500 | + | 59.7558i | 1.01020 | + | 0.243901i | ||||
\(246\) | 54.0000 | 0.219512 | ||||||||
\(247\) | 72.0000 | + | 124.708i | 0.291498 | + | 0.504889i | ||||
\(248\) | −31.5000 | − | 18.1865i | −0.127016 | − | 0.0733328i | ||||
\(249\) | −103.500 | + | 179.267i | −0.415663 | + | 0.719949i | ||||
\(250\) | 310.500 | − | 179.267i | 1.24200 | − | 0.717069i | ||||
\(251\) | − | 5.19615i | − | 0.0207018i | −0.999946 | − | 0.0103509i | \(-0.996705\pi\) | ||
0.999946 | − | 0.0103509i | \(-0.00329485\pi\) | |||||||
\(252\) | −97.5000 | − | 38.9711i | −0.386905 | − | 0.154647i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −52.5000 | − | 90.9327i | −0.206693 | − | 0.358003i | ||||
\(255\) | −81.0000 | − | 46.7654i | −0.317647 | − | 0.183394i | ||||
\(256\) | −42.5000 | + | 73.6122i | −0.166016 | + | 0.287547i | ||||
\(257\) | 99.0000 | − | 57.1577i | 0.385214 | − | 0.222403i | −0.294870 | − | 0.955537i | \(-0.595276\pi\) |
0.680084 | + | 0.733134i | \(0.261943\pi\) | |||||||
\(258\) | − | 384.515i | − | 1.49037i | ||||||
\(259\) | −10.0000 | − | 69.2820i | −0.0386100 | − | 0.267498i | ||||
\(260\) | 360.000 | 1.38462 | ||||||||
\(261\) | −13.5000 | − | 23.3827i | −0.0517241 | − | 0.0895888i | ||||
\(262\) | −445.500 | − | 257.210i | −1.70038 | − | 0.981716i | ||||
\(263\) | −93.0000 | + | 161.081i | −0.353612 | + | 0.612474i | −0.986879 | − | 0.161459i | \(-0.948380\pi\) |
0.633267 | + | 0.773933i | \(0.281713\pi\) | |||||||
\(264\) | 67.5000 | − | 38.9711i | 0.255682 | − | 0.147618i | ||||
\(265\) | 171.473i | 0.647068i | ||||||||
\(266\) | 135.000 | + | 171.473i | 0.507519 | + | 0.644635i | ||||
\(267\) | 126.000 | 0.471910 | ||||||||
\(268\) | 190.000 | + | 329.090i | 0.708955 | + | 1.22795i | ||||
\(269\) | −292.500 | − | 168.875i | −1.08736 | − | 0.627788i | −0.154488 | − | 0.987995i | \(-0.549373\pi\) |
−0.932873 | + | 0.360207i | \(0.882706\pi\) | |||||||
\(270\) | −40.5000 | + | 70.1481i | −0.150000 | + | 0.259808i | ||||
\(271\) | 79.5000 | − | 45.8993i | 0.293358 | − | 0.169370i | −0.346097 | − | 0.938199i | \(-0.612493\pi\) |
0.639455 | + | 0.768828i | \(0.279160\pi\) | |||||||
\(272\) | 114.315i | 0.420277i | ||||||||
\(273\) | −132.000 | + | 103.923i | −0.483516 | + | 0.380671i | ||||
\(274\) | −288.000 | −1.05109 | ||||||||
\(275\) | 15.0000 | + | 25.9808i | 0.0545455 | + | 0.0944755i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −190.000 | + | 329.090i | −0.685921 | + | 1.18805i | 0.287226 | + | 0.957863i | \(0.407267\pi\) |
−0.973147 | + | 0.230186i | \(0.926066\pi\) | |||||||
\(278\) | −477.000 | + | 275.396i | −1.71583 | + | 0.990633i | ||||
\(279\) | − | 36.3731i | − | 0.130369i | ||||||
\(280\) | 108.000 | − | 15.5885i | 0.385714 | − | 0.0556731i | ||||
\(281\) | 300.000 | 1.06762 | 0.533808 | − | 0.845606i | \(-0.320761\pi\) | ||||
0.533808 | + | 0.845606i | \(0.320761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 177.000 | + | 102.191i | 0.625442 | + | 0.361099i | 0.778985 | − | 0.627043i | \(-0.215735\pi\) |
−0.153543 | + | 0.988142i | \(0.549068\pi\) | |||||||
\(284\) | −210.000 | + | 363.731i | −0.739437 | + | 1.28074i | ||||
\(285\) | 81.0000 | − | 46.7654i | 0.284211 | − | 0.164089i | ||||
\(286\) | − | 623.538i | − | 2.18020i | ||||||
\(287\) | 27.0000 | − | 67.5500i | 0.0940767 | − | 0.235366i | ||||
\(288\) | 135.000 | 0.468750 | ||||||||
\(289\) | −90.5000 | − | 156.751i | −0.313149 | − | 0.542390i | ||||
\(290\) | 121.500 | + | 70.1481i | 0.418966 | + | 0.241890i | ||||
\(291\) | 160.500 | − | 277.994i | 0.551546 | − | 0.955306i | ||||
\(292\) | 270.000 | − | 155.885i | 0.924658 | − | 0.533851i | ||||
\(293\) | 545.596i | 1.86210i | 0.364889 | + | 0.931051i | \(0.381107\pi\) | ||||
−0.364889 | + | 0.931051i | \(0.618893\pi\) | |||||||
\(294\) | −175.500 | + | 184.463i | −0.596939 | + | 0.627427i | ||||
\(295\) | 81.0000 | 0.274576 | ||||||||
\(296\) | −15.0000 | − | 25.9808i | −0.0506757 | − | 0.0877728i | ||||
\(297\) | 67.5000 | + | 38.9711i | 0.227273 | + | 0.131216i | ||||
\(298\) | 279.000 | − | 483.242i | 0.936242 | − | 1.62162i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | − | 17.3205i | − | 0.0577350i | ||||||
\(301\) | −481.000 | − | 192.258i | −1.59801 | − | 0.638730i | ||||
\(302\) | 237.000 | 0.784768 | ||||||||
\(303\) | 126.000 | + | 218.238i | 0.415842 | + | 0.720259i | ||||
\(304\) | −99.0000 | − | 57.1577i | −0.325658 | − | 0.188019i | ||||
\(305\) | 234.000 | − | 405.300i | 0.767213 | − | 1.32885i | ||||
\(306\) | 81.0000 | − | 46.7654i | 0.264706 | − | 0.152828i | ||||
\(307\) | 173.205i | 0.564186i | 0.959387 | + | 0.282093i | \(0.0910287\pi\) | ||||
−0.959387 | + | 0.282093i | \(0.908971\pi\) | |||||||
\(308\) | −75.0000 | − | 519.615i | −0.243506 | − | 1.68706i | ||||
\(309\) | 120.000 | 0.388350 | ||||||||
\(310\) | 94.5000 | + | 163.679i | 0.304839 | + | 0.527996i | ||||
\(311\) | −153.000 | − | 88.3346i | −0.491961 | − | 0.284034i | 0.233426 | − | 0.972374i | \(-0.425006\pi\) |
−0.725388 | + | 0.688340i | \(0.758340\pi\) | |||||||
\(312\) | −36.0000 | + | 62.3538i | −0.115385 | + | 0.199852i | ||||
\(313\) | −184.500 | + | 106.521i | −0.589457 | + | 0.340323i | −0.764883 | − | 0.644170i | \(-0.777203\pi\) |
0.175426 | + | 0.984493i | \(0.443870\pi\) | |||||||
\(314\) | 62.3538i | 0.198579i | ||||||||
\(315\) | 67.5000 | + | 85.7365i | 0.214286 | + | 0.272179i | ||||
\(316\) | −215.000 | −0.680380 | ||||||||
\(317\) | −58.5000 | − | 101.325i | −0.184543 | − | 0.319637i | 0.758880 | − | 0.651231i | \(-0.225747\pi\) |
−0.943422 | + | 0.331594i | \(0.892414\pi\) | |||||||
\(318\) | −148.500 | − | 85.7365i | −0.466981 | − | 0.269612i | ||||
\(319\) | 67.5000 | − | 116.913i | 0.211599 | − | 0.366500i | ||||
\(320\) | −409.500 | + | 236.425i | −1.27969 | + | 0.738828i | ||||
\(321\) | 161.081i | 0.501809i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −108.000 | −0.334365 | ||||||||
\(324\) | −22.5000 | − | 38.9711i | −0.0694444 | − | 0.120281i | ||||
\(325\) | −24.0000 | − | 13.8564i | −0.0738462 | − | 0.0426351i | ||||
\(326\) | 312.000 | − | 540.400i | 0.957055 | − | 1.65767i | ||||
\(327\) | −12.0000 | + | 6.92820i | −0.0366972 | + | 0.0211872i | ||||
\(328\) | − | 31.1769i | − | 0.0950516i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −405.000 | −1.22727 | ||||||||
\(331\) | −20.0000 | − | 34.6410i | −0.0604230 | − | 0.104656i | 0.834232 | − | 0.551414i | \(-0.185912\pi\) |
−0.894655 | + | 0.446759i | \(0.852578\pi\) | |||||||
\(332\) | 517.500 | + | 298.779i | 1.55873 | + | 0.899936i | ||||
\(333\) | 15.0000 | − | 25.9808i | 0.0450450 | − | 0.0780203i | ||||
\(334\) | −648.000 | + | 374.123i | −1.94012 | + | 1.12013i | ||||
\(335\) | − | 394.908i | − | 1.17883i | ||||||
\(336\) | 49.5000 | − | 123.842i | 0.147321 | − | 0.368576i | ||||
\(337\) | 91.0000 | 0.270030 | 0.135015 | − | 0.990844i | \(-0.456892\pi\) | ||||
0.135015 | + | 0.990844i | \(0.456892\pi\) | |||||||
\(338\) | 34.5000 | + | 59.7558i | 0.102071 | + | 0.176792i | ||||
\(339\) | −63.0000 | − | 36.3731i | −0.185841 | − | 0.107295i | ||||
\(340\) | −135.000 | + | 233.827i | −0.397059 | + | 0.687726i | ||||
\(341\) | 157.500 | − | 90.9327i | 0.461877 | − | 0.266665i | ||||
\(342\) | 93.5307i | 0.273482i | ||||||||
\(343\) | 143.000 | + | 311.769i | 0.416910 | + | 0.908948i | ||||
\(344\) | −222.000 | −0.645349 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 594.000 | + | 342.946i | 1.71676 | + | 0.991174i | ||||
\(347\) | −105.000 | + | 181.865i | −0.302594 | + | 0.524108i | −0.976723 | − | 0.214506i | \(-0.931186\pi\) |
0.674129 | + | 0.738614i | \(0.264519\pi\) | |||||||
\(348\) | −67.5000 | + | 38.9711i | −0.193966 | + | 0.111986i | ||||
\(349\) | − | 304.841i | − | 0.873470i | −0.899590 | − | 0.436735i | \(-0.856135\pi\) | ||
0.899590 | − | 0.436735i | \(-0.143865\pi\) | |||||||
\(350\) | −39.0000 | − | 15.5885i | −0.111429 | − | 0.0445384i | ||||
\(351\) | −72.0000 | −0.205128 | ||||||||
\(352\) | 337.500 | + | 584.567i | 0.958807 | + | 1.66070i | ||||
\(353\) | 342.000 | + | 197.454i | 0.968839 | + | 0.559359i | 0.898882 | − | 0.438191i | \(-0.144381\pi\) |
0.0699566 | + | 0.997550i | \(0.477714\pi\) | |||||||
\(354\) | −40.5000 | + | 70.1481i | −0.114407 | + | 0.198158i | ||||
\(355\) | 378.000 | − | 218.238i | 1.06479 | − | 0.614756i | ||||
\(356\) | − | 363.731i | − | 1.02172i | ||||||
\(357\) | −18.0000 | − | 124.708i | −0.0504202 | − | 0.349321i | ||||
\(358\) | 270.000 | 0.754190 | ||||||||
\(359\) | −246.000 | − | 426.084i | −0.685237 | − | 1.18686i | −0.973362 | − | 0.229272i | \(-0.926365\pi\) |
0.288126 | − | 0.957593i | \(-0.406968\pi\) | |||||||
\(360\) | 40.5000 | + | 23.3827i | 0.112500 | + | 0.0649519i | ||||
\(361\) | −126.500 | + | 219.104i | −0.350416 | + | 0.606937i | ||||
\(362\) | −27.0000 | + | 15.5885i | −0.0745856 | + | 0.0430620i | ||||
\(363\) | 180.133i | 0.496235i | ||||||||
\(364\) | 300.000 | + | 381.051i | 0.824176 | + | 1.04684i | ||||
\(365\) | −324.000 | −0.887671 | ||||||||
\(366\) | 234.000 | + | 405.300i | 0.639344 | + | 1.10738i | ||||
\(367\) | −283.500 | − | 163.679i | −0.772480 | − | 0.445991i | 0.0612789 | − | 0.998121i | \(-0.480482\pi\) |
−0.833758 | + | 0.552129i | \(0.813815\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 27.0000 | − | 15.5885i | 0.0731707 | − | 0.0422451i | ||||
\(370\) | 155.885i | 0.421310i | ||||||||
\(371\) | −181.500 | + | 142.894i | −0.489218 | + | 0.385160i | ||||
\(372\) | −105.000 | −0.282258 | ||||||||
\(373\) | −85.0000 | − | 147.224i | −0.227882 | − | 0.394703i | 0.729298 | − | 0.684196i | \(-0.239847\pi\) |
−0.957180 | + | 0.289493i | \(0.906513\pi\) | |||||||
\(374\) | 405.000 | + | 233.827i | 1.08289 | + | 0.625206i | ||||
\(375\) | 103.500 | − | 179.267i | 0.276000 | − | 0.478046i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 124.708i | 0.330790i | ||||||||
\(378\) | −108.000 | + | 15.5885i | −0.285714 | + | 0.0412393i | ||||
\(379\) | 82.0000 | 0.216359 | 0.108179 | − | 0.994131i | \(-0.465498\pi\) | ||||
0.108179 | + | 0.994131i | \(0.465498\pi\) | |||||||
\(380\) | −135.000 | − | 233.827i | −0.355263 | − | 0.615334i | ||||
\(381\) | −52.5000 | − | 30.3109i | −0.137795 | − | 0.0795561i | ||||
\(382\) | 468.000 | − | 810.600i | 1.22513 | − | 2.12199i | ||||
\(383\) | 189.000 | − | 109.119i | 0.493473 | − | 0.284907i | −0.232541 | − | 0.972587i | \(-0.574704\pi\) |
0.726014 | + | 0.687680i | \(0.241371\pi\) | |||||||
\(384\) | − | 161.081i | − | 0.419481i | ||||||
\(385\) | −202.500 | + | 506.625i | −0.525974 | + | 1.31591i | ||||
\(386\) | −555.000 | −1.43782 | ||||||||
\(387\) | −111.000 | − | 192.258i | −0.286822 | − | 0.496790i | ||||
\(388\) | −802.500 | − | 463.324i | −2.06830 | − | 1.19413i | ||||
\(389\) | −153.000 | + | 265.004i | −0.393316 | + | 0.681244i | −0.992885 | − | 0.119080i | \(-0.962006\pi\) |
0.599568 | + | 0.800323i | \(0.295339\pi\) | |||||||
\(390\) | 324.000 | − | 187.061i | 0.830769 | − | 0.479645i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 106.500 | + | 101.325i | 0.271684 | + | 0.258482i | ||||
\(393\) | −297.000 | −0.755725 | ||||||||
\(394\) | −495.000 | − | 857.365i | −1.25635 | − | 2.17605i | ||||
\(395\) | 193.500 | + | 111.717i | 0.489873 | + | 0.282829i | ||||
\(396\) | 112.500 | − | 194.856i | 0.284091 | − | 0.492060i | ||||
\(397\) | −222.000 | + | 128.172i | −0.559194 | + | 0.322851i | −0.752822 | − | 0.658224i | \(-0.771308\pi\) |
0.193628 | + | 0.981075i | \(0.437975\pi\) | |||||||
\(398\) | − | 20.7846i | − | 0.0522226i | ||||||
\(399\) | 117.000 | + | 46.7654i | 0.293233 | + | 0.117206i | ||||
\(400\) | 22.0000 | 0.0550000 | ||||||||
\(401\) | −66.0000 | − | 114.315i | −0.164589 | − | 0.285076i | 0.771921 | − | 0.635719i | \(-0.219296\pi\) |
−0.936509 | + | 0.350643i | \(0.885963\pi\) | |||||||
\(402\) | 342.000 | + | 197.454i | 0.850746 | + | 0.491179i | ||||
\(403\) | −84.0000 | + | 145.492i | −0.208437 | + | 0.361023i | ||||
\(404\) | 630.000 | − | 363.731i | 1.55941 | − | 0.900323i | ||||
\(405\) | 46.7654i | 0.115470i | ||||||||
\(406\) | 27.0000 | + | 187.061i | 0.0665025 | + | 0.460743i | ||||
\(407\) | 150.000 | 0.368550 | ||||||||
\(408\) | −27.0000 | − | 46.7654i | −0.0661765 | − | 0.114621i | ||||
\(409\) | −313.500 | − | 180.999i | −0.766504 | − | 0.442541i | 0.0651223 | − | 0.997877i | \(-0.479256\pi\) |
−0.831626 | + | 0.555336i | \(0.812590\pi\) | |||||||
\(410\) | −81.0000 | + | 140.296i | −0.197561 | + | 0.342186i | ||||
\(411\) | −144.000 | + | 83.1384i | −0.350365 | + | 0.202283i | ||||
\(412\) | − | 346.410i | − | 0.840801i | ||||||
\(413\) | 67.5000 | + | 85.7365i | 0.163438 | + | 0.207594i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −310.500 | − | 537.802i | −0.748193 | − | 1.29591i | ||||
\(416\) | −540.000 | − | 311.769i | −1.29808 | − | 0.749445i | ||||
\(417\) | −159.000 | + | 275.396i | −0.381295 | + | 0.660422i | ||||
\(418\) | −405.000 | + | 233.827i | −0.968900 | + | 0.559394i | ||||
\(419\) | 644.323i | 1.53776i | 0.639391 | + | 0.768882i | \(0.279187\pi\) | ||||
−0.639391 | + | 0.768882i | \(0.720813\pi\) | |||||||
\(420\) | 247.500 | − | 194.856i | 0.589286 | − | 0.463942i | ||||
\(421\) | 752.000 | 1.78622 | 0.893112 | − | 0.449835i | \(-0.148517\pi\) | ||||
0.893112 | + | 0.449835i | \(0.148517\pi\) | |||||||
\(422\) | 372.000 | + | 644.323i | 0.881517 | + | 1.52683i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −49.5000 | + | 85.7365i | −0.116745 | + | 0.202209i | ||||
\(425\) | 18.0000 | − | 10.3923i | 0.0423529 | − | 0.0244525i | ||||
\(426\) | 436.477i | 1.02459i | ||||||||
\(427\) | 624.000 | − | 90.0666i | 1.46136 | − | 0.210929i | ||||
\(428\) | 465.000 | 1.08645 | ||||||||
\(429\) | −180.000 | − | 311.769i | −0.419580 | − | 0.726735i | ||||
\(430\) | 999.000 | + | 576.773i | 2.32326 | + | 1.34133i | ||||
\(431\) | −81.0000 | + | 140.296i | −0.187935 | + | 0.325513i | −0.944562 | − | 0.328334i | \(-0.893513\pi\) |
0.756627 | + | 0.653847i | \(0.226846\pi\) | |||||||
\(432\) | 49.5000 | − | 28.5788i | 0.114583 | − | 0.0661547i | ||||
\(433\) | − | 339.482i | − | 0.784023i | −0.919960 | − | 0.392011i | \(-0.871779\pi\) | ||
0.919960 | − | 0.392011i | \(-0.128221\pi\) | |||||||
\(434\) | −94.5000 | + | 236.425i | −0.217742 | + | 0.544758i | ||||
\(435\) | 81.0000 | 0.186207 | ||||||||
\(436\) | 20.0000 | + | 34.6410i | 0.0458716 | + | 0.0794519i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 162.000 | − | 280.592i | 0.369863 | − | 0.640622i | ||||
\(439\) | 337.500 | − | 194.856i | 0.768793 | − | 0.443863i | −0.0636511 | − | 0.997972i | \(-0.520274\pi\) |
0.832444 | + | 0.554110i | \(0.186941\pi\) | |||||||
\(440\) | 233.827i | 0.531425i | ||||||||
\(441\) | −34.5000 | + | 142.894i | −0.0782313 | + | 0.324023i | ||||
\(442\) | −432.000 | −0.977376 | ||||||||
\(443\) | 148.500 | + | 257.210i | 0.335214 | + | 0.580608i | 0.983526 | − | 0.180767i | \(-0.0578579\pi\) |
−0.648312 | + | 0.761375i | \(0.724525\pi\) | |||||||
\(444\) | −75.0000 | − | 43.3013i | −0.168919 | − | 0.0975254i | ||||
\(445\) | −189.000 | + | 327.358i | −0.424719 | + | 0.735635i | ||||
\(446\) | −499.500 | + | 288.386i | −1.11996 | + | 0.646606i | ||||
\(447\) | − | 322.161i | − | 0.720719i | ||||||
\(448\) | −591.500 | − | 236.425i | −1.32031 | − | 0.527734i | ||||
\(449\) | −492.000 | −1.09577 | −0.547884 | − | 0.836554i | \(-0.684567\pi\) | ||||
−0.547884 | + | 0.836554i | \(0.684567\pi\) | |||||||
\(450\) | −9.00000 | − | 15.5885i | −0.0200000 | − | 0.0346410i | ||||
\(451\) | 135.000 | + | 77.9423i | 0.299335 | + | 0.172821i | ||||
\(452\) | −105.000 | + | 181.865i | −0.232301 | + | 0.402357i | ||||
\(453\) | 118.500 | − | 68.4160i | 0.261589 | − | 0.151029i | ||||
\(454\) | 265.004i | 0.583709i | ||||||||
\(455\) | −72.0000 | − | 498.831i | −0.158242 | − | 1.09633i | ||||
\(456\) | 54.0000 | 0.118421 | ||||||||
\(457\) | 221.500 | + | 383.649i | 0.484683 | + | 0.839495i | 0.999845 | − | 0.0175975i | \(-0.00560174\pi\) |
−0.515162 | + | 0.857093i | \(0.672268\pi\) | |||||||
\(458\) | −855.000 | − | 493.634i | −1.86681 | − | 1.07780i | ||||
\(459\) | 27.0000 | − | 46.7654i | 0.0588235 | − | 0.101885i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 415.692i | 0.901718i | 0.892595 | + | 0.450859i | \(0.148882\pi\) | ||||
−0.892595 | + | 0.450859i | \(0.851118\pi\) | |||||||
\(462\) | −337.500 | − | 428.683i | −0.730519 | − | 0.927884i | ||||
\(463\) | −82.0000 | −0.177106 | −0.0885529 | − | 0.996071i | \(-0.528224\pi\) | ||||
−0.0885529 | + | 0.996071i | \(0.528224\pi\) | |||||||
\(464\) | −49.5000 | − | 85.7365i | −0.106681 | − | 0.184777i | ||||
\(465\) | 94.5000 | + | 54.5596i | 0.203226 | + | 0.117332i | ||||
\(466\) | −405.000 | + | 701.481i | −0.869099 | + | 1.50532i | ||||
\(467\) | 234.000 | − | 135.100i | 0.501071 | − | 0.289293i | −0.228085 | − | 0.973641i | \(-0.573246\pi\) |
0.729156 | + | 0.684348i | \(0.239913\pi\) | |||||||
\(468\) | 207.846i | 0.444116i | ||||||||
\(469\) | 418.000 | − | 329.090i | 0.891258 | − | 0.701684i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.0000 | + | 31.1769i | 0.0382166 | + | 0.0661930i | ||||
\(472\) | 40.5000 | + | 23.3827i | 0.0858051 | + | 0.0495396i | ||||
\(473\) | 555.000 | − | 961.288i | 1.17336 | − | 2.03232i | ||||
\(474\) | −193.500 | + | 111.717i | −0.408228 | + | 0.235690i | ||||
\(475\) | 20.7846i | 0.0437571i | ||||||||
\(476\) | −360.000 | + | 51.9615i | −0.756303 | + | 0.109163i | ||||
\(477\) | −99.0000 | −0.207547 | ||||||||
\(478\) | 342.000 | + | 592.361i | 0.715481 | + | 1.23925i | ||||
\(479\) | 297.000 | + | 171.473i | 0.620042 | + | 0.357981i | 0.776885 | − | 0.629642i | \(-0.216798\pi\) |
−0.156844 | + | 0.987623i | \(0.550132\pi\) | |||||||
\(480\) | −202.500 | + | 350.740i | −0.421875 | + | 0.730709i | ||||
\(481\) | −120.000 | + | 69.2820i | −0.249480 | + | 0.144037i | ||||
\(482\) | − | 1335.41i | − | 2.77056i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 520.000 | 1.07438 | ||||||||
\(485\) | 481.500 | + | 833.982i | 0.992784 | + | 1.71955i | ||||
\(486\) | −40.5000 | − | 23.3827i | −0.0833333 | − | 0.0481125i | ||||
\(487\) | 158.500 | − | 274.530i | 0.325462 | − | 0.563717i | −0.656144 | − | 0.754636i | \(-0.727814\pi\) |
0.981606 | + | 0.190919i | \(0.0611468\pi\) | |||||||
\(488\) | 234.000 | − | 135.100i | 0.479508 | − | 0.276844i | ||||
\(489\) | − | 360.267i | − | 0.736741i | ||||||
\(490\) | −216.000 | − | 732.657i | −0.440816 | − | 1.49522i | ||||
\(491\) | 27.0000 | 0.0549898 | 0.0274949 | − | 0.999622i | \(-0.491247\pi\) | ||||
0.0274949 | + | 0.999622i | \(0.491247\pi\) | |||||||
\(492\) | −45.0000 | − | 77.9423i | −0.0914634 | − | 0.158419i | ||||
\(493\) | −81.0000 | − | 46.7654i | −0.164300 | − | 0.0948588i | ||||
\(494\) | 216.000 | − | 374.123i | 0.437247 | − | 0.757334i | ||||
\(495\) | −202.500 | + | 116.913i | −0.409091 | + | 0.236189i | ||||
\(496\) | − | 133.368i | − | 0.268887i | ||||||
\(497\) | 546.000 | + | 218.238i | 1.09859 | + | 0.439111i | ||||
\(498\) | 621.000 | 1.24699 | ||||||||
\(499\) | 223.000 | + | 386.247i | 0.446894 | + | 0.774043i | 0.998182 | − | 0.0602721i | \(-0.0191969\pi\) |
−0.551288 | + | 0.834315i | \(0.685864\pi\) | |||||||
\(500\) | −517.500 | − | 298.779i | −1.03500 | − | 0.597558i | ||||
\(501\) | −216.000 | + | 374.123i | −0.431138 | + | 0.746752i | ||||
\(502\) | −13.5000 | + | 7.79423i | −0.0268924 | + | 0.0155264i | ||||
\(503\) | − | 488.438i | − | 0.971050i | −0.874223 | − | 0.485525i | \(-0.838628\pi\) | ||
0.874223 | − | 0.485525i | \(-0.161372\pi\) | |||||||
\(504\) | 9.00000 | + | 62.3538i | 0.0178571 | + | 0.123718i | ||||
\(505\) | −756.000 | −1.49703 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 34.5000 | + | 19.9186i | 0.0680473 | + | 0.0392871i | ||||
\(508\) | −87.5000 | + | 151.554i | −0.172244 | + | 0.298336i | ||||
\(509\) | 85.5000 | − | 49.3634i | 0.167976 | − | 0.0969812i | −0.413655 | − | 0.910434i | \(-0.635748\pi\) |
0.581631 | + | 0.813453i | \(0.302415\pi\) | |||||||
\(510\) | 280.592i | 0.550181i | ||||||||
\(511\) | −270.000 | − | 342.946i | −0.528376 | − | 0.671127i | ||||
\(512\) | 627.000 | 1.22461 | ||||||||
\(513\) | 27.0000 | + | 46.7654i | 0.0526316 | + | 0.0911606i | ||||
\(514\) | −297.000 | − | 171.473i | −0.577821 | − | 0.333605i | ||||
\(515\) | −180.000 | + | 311.769i | −0.349515 | + | 0.605377i | ||||
\(516\) | −555.000 | + | 320.429i | −1.07558 | + | 0.620987i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −165.000 | + | 129.904i | −0.318533 | + | 0.250780i | ||||
\(519\) | 396.000 | 0.763006 | ||||||||
\(520\) | −108.000 | − | 187.061i | −0.207692 | − | 0.359734i | ||||
\(521\) | −783.000 | − | 452.065i | −1.50288 | − | 0.867688i | −0.999994 | − | 0.00333410i | \(-0.998939\pi\) |
−0.502885 | − | 0.864354i | \(-0.667728\pi\) | |||||||
\(522\) | −40.5000 | + | 70.1481i | −0.0775862 | + | 0.134383i | ||||
\(523\) | −606.000 | + | 349.874i | −1.15870 | + | 0.668976i | −0.950992 | − | 0.309215i | \(-0.899934\pi\) |
−0.207708 | + | 0.978191i | \(0.566600\pi\) | |||||||
\(524\) | 857.365i | 1.63619i | ||||||||
\(525\) | −24.0000 | + | 3.46410i | −0.0457143 | + | 0.00659829i | ||||
\(526\) | 558.000 | 1.06084 | ||||||||
\(527\) | −63.0000 | − | 109.119i | −0.119545 | − | 0.207057i | ||||
\(528\) | 247.500 | + | 142.894i | 0.468750 | + | 0.270633i | ||||
\(529\) | 264.500 | − | 458.127i | 0.500000 | − | 0.866025i | ||||
\(530\) | 445.500 | − | 257.210i | 0.840566 | − | 0.485301i | ||||
\(531\) | 46.7654i | 0.0880704i | ||||||||
\(532\) | 135.000 | − | 337.750i | 0.253759 | − | 0.634868i | ||||
\(533\) | −144.000 | −0.270169 | ||||||||
\(534\) | −189.000 | − | 327.358i | −0.353933 | − | 0.613029i | ||||
\(535\) | −418.500 | − | 241.621i | −0.782243 | − | 0.451628i | ||||
\(536\) | 114.000 | − | 197.454i | 0.212687 | − | 0.368384i | ||||
\(537\) | 135.000 | − | 77.9423i | 0.251397 | − | 0.145144i | ||||
\(538\) | 1013.25i | 1.88336i | ||||||||
\(539\) | −705.000 | + | 207.846i | −1.30798 | + | 0.385614i | ||||
\(540\) | 135.000 | 0.250000 | ||||||||
\(541\) | −37.0000 | − | 64.0859i | −0.0683919 | − | 0.118458i | 0.829802 | − | 0.558058i | \(-0.188453\pi\) |
−0.898194 | + | 0.439600i | \(0.855120\pi\) | |||||||
\(542\) | −238.500 | − | 137.698i | −0.440037 | − | 0.254055i | ||||
\(543\) | −9.00000 | + | 15.5885i | −0.0165746 | + | 0.0287080i | ||||
\(544\) | 405.000 | − | 233.827i | 0.744485 | − | 0.429829i | ||||
\(545\) | − | 41.5692i | − | 0.0762738i | ||||||
\(546\) | 468.000 | + | 187.061i | 0.857143 | + | 0.342603i | ||||
\(547\) | −934.000 | −1.70750 | −0.853748 | − | 0.520687i | \(-0.825676\pi\) | ||||
−0.853748 | + | 0.520687i | \(0.825676\pi\) | |||||||
\(548\) | 240.000 | + | 415.692i | 0.437956 | + | 0.758562i | ||||
\(549\) | 234.000 | + | 135.100i | 0.426230 | + | 0.246084i | ||||
\(550\) | 45.0000 | − | 77.9423i | 0.0818182 | − | 0.141713i | ||||
\(551\) | 81.0000 | − | 46.7654i | 0.147005 | − | 0.0848736i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.0000 | + | 297.913i | 0.0777577 | + | 0.538721i | ||||
\(554\) | 1140.00 | 2.05776 | ||||||||
\(555\) | 45.0000 | + | 77.9423i | 0.0810811 | + | 0.140437i | ||||
\(556\) | 795.000 | + | 458.993i | 1.42986 | + | 0.825528i | ||||
\(557\) | −421.500 | + | 730.059i | −0.756732 | + | 1.31070i | 0.187776 | + | 0.982212i | \(0.439872\pi\) |
−0.944508 | + | 0.328487i | \(0.893461\pi\) | |||||||
\(558\) | −94.5000 | + | 54.5596i | −0.169355 | + | 0.0977771i | ||||
\(559\) | 1025.37i | 1.83430i | ||||||||
\(560\) | 247.500 | + | 314.367i | 0.441964 | + | 0.561370i | ||||
\(561\) | 270.000 | 0.481283 | ||||||||
\(562\) | −450.000 | − | 779.423i | −0.800712 | − | 1.38687i | ||||
\(563\) | 823.500 | + | 475.448i | 1.46270 | + | 0.844490i | 0.999135 | − | 0.0415731i | \(-0.0132369\pi\) |
0.463564 | + | 0.886063i | \(0.346570\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 189.000 | − | 109.119i | 0.334513 | − | 0.193131i | ||||
\(566\) | − | 613.146i | − | 1.08330i | ||||||
\(567\) | −49.5000 | + | 38.9711i | −0.0873016 | + | 0.0687322i | ||||
\(568\) | 252.000 | 0.443662 | ||||||||
\(569\) | −111.000 | − | 192.258i | −0.195079 | − | 0.337887i | 0.751847 | − | 0.659337i | \(-0.229163\pi\) |
−0.946926 | + | 0.321450i | \(0.895830\pi\) | |||||||
\(570\) | −243.000 | − | 140.296i | −0.426316 | − | 0.246134i | ||||
\(571\) | −220.000 | + | 381.051i | −0.385289 | + | 0.667340i | −0.991809 | − | 0.127728i | \(-0.959232\pi\) |
0.606520 | + | 0.795068i | \(0.292565\pi\) | |||||||
\(572\) | −900.000 | + | 519.615i | −1.57343 | + | 0.908418i | ||||
\(573\) | − | 540.400i | − | 0.943106i | ||||||
\(574\) | −216.000 | + | 31.1769i | −0.376307 | + | 0.0543152i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −136.500 | − | 236.425i | −0.236979 | − | 0.410460i | ||||
\(577\) | 568.500 | + | 328.224i | 0.985269 | + | 0.568845i | 0.903857 | − | 0.427835i | \(-0.140724\pi\) |
0.0814120 | + | 0.996681i | \(0.474057\pi\) | |||||||
\(578\) | −271.500 | + | 470.252i | −0.469723 | + | 0.813584i | ||||
\(579\) | −277.500 | + | 160.215i | −0.479275 | + | 0.276709i | ||||
\(580\) | − | 233.827i | − | 0.403150i | ||||||
\(581\) | 310.500 | − | 776.825i | 0.534423 | − | 1.33705i | ||||
\(582\) | −963.000 | −1.65464 | ||||||||
\(583\) | −247.500 | − | 428.683i | −0.424528 | − | 0.735305i | ||||
\(584\) | −162.000 | − | 93.5307i | −0.277397 | − | 0.160155i | ||||
\(585\) | 108.000 | − | 187.061i | 0.184615 | − | 0.319763i | ||||
\(586\) | 1417.50 | − | 818.394i | 2.41894 | − | 1.39658i | ||||
\(587\) | − | 1054.82i | − | 1.79697i | −0.439008 | − | 0.898483i | \(-0.644670\pi\) | ||
0.439008 | − | 0.898483i | \(-0.355330\pi\) | |||||||
\(588\) | 412.500 | + | 99.5929i | 0.701531 | + | 0.169376i | ||||
\(589\) | 126.000 | 0.213922 | ||||||||
\(590\) | −121.500 | − | 210.444i | −0.205932 | − | 0.356685i | ||||
\(591\) | −495.000 | − | 285.788i | −0.837563 | − | 0.483567i | ||||
\(592\) | 55.0000 | − | 95.2628i | 0.0929054 | − | 0.160917i | ||||
\(593\) | 612.000 | − | 353.338i | 1.03204 | − | 0.595849i | 0.114472 | − | 0.993426i | \(-0.463482\pi\) |
0.917569 | + | 0.397578i | \(0.130149\pi\) | |||||||
\(594\) | − | 233.827i | − | 0.393648i | ||||||
\(595\) | 351.000 | + | 140.296i | 0.589916 | + | 0.235792i | ||||
\(596\) | −930.000 | −1.56040 | ||||||||
\(597\) | −6.00000 | − | 10.3923i | −0.0100503 | − | 0.0174075i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −258.000 | + | 446.869i | −0.430718 | + | 0.746025i | −0.996935 | − | 0.0782307i | \(-0.975073\pi\) |
0.566217 | + | 0.824256i | \(0.308406\pi\) | |||||||
\(600\) | −9.00000 | + | 5.19615i | −0.0150000 | + | 0.00866025i | ||||
\(601\) | − | 247.683i | − | 0.412119i | −0.978540 | − | 0.206059i | \(-0.933936\pi\) | ||
0.978540 | − | 0.206059i | \(-0.0660640\pi\) | |||||||
\(602\) | 222.000 | + | 1538.06i | 0.368771 | + | 2.55492i | ||||
\(603\) | 228.000 | 0.378109 | ||||||||
\(604\) | −197.500 | − | 342.080i | −0.326987 | − | 0.566358i | ||||
\(605\) | −468.000 | − | 270.200i | −0.773554 | − | 0.446611i | ||||
\(606\) | 378.000 | − | 654.715i | 0.623762 | − | 1.08039i | ||||
\(607\) | −562.500 | + | 324.760i | −0.926689 | + | 0.535024i | −0.885763 | − | 0.464138i | \(-0.846364\pi\) |
−0.0409259 | + | 0.999162i | \(0.513031\pi\) | |||||||
\(608\) | 467.654i | 0.769167i | ||||||||
\(609\) | 67.5000 | + | 85.7365i | 0.110837 | + | 0.140782i | ||||
\(610\) | −1404.00 | −2.30164 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −135.000 | − | 77.9423i | −0.220588 | − | 0.127357i | ||||
\(613\) | 446.000 | − | 772.495i | 0.727569 | − | 1.26019i | −0.230338 | − | 0.973111i | \(-0.573983\pi\) |
0.957908 | − | 0.287076i | \(-0.0926834\pi\) | |||||||
\(614\) | 450.000 | − | 259.808i | 0.732899 | − | 0.423139i | ||||
\(615\) | 93.5307i | 0.152083i | ||||||||
\(616\) | −247.500 | + | 194.856i | −0.401786 | + | 0.316324i | ||||
\(617\) | −1224.00 | −1.98379 | −0.991896 | − | 0.127050i | \(-0.959449\pi\) | ||||
−0.991896 | + | 0.127050i | \(0.959449\pi\) | |||||||
\(618\) | −180.000 | − | 311.769i | −0.291262 | − | 0.504481i | ||||
\(619\) | −348.000 | − | 200.918i | −0.562197 | − | 0.324585i | 0.191830 | − | 0.981428i | \(-0.438558\pi\) |
−0.754027 | + | 0.656844i | \(0.771891\pi\) | |||||||
\(620\) | 157.500 | − | 272.798i | 0.254032 | − | 0.439997i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 530.008i | 0.852102i | ||||||||
\(623\) | −504.000 | + | 72.7461i | −0.808989 | + | 0.116767i | ||||
\(624\) | −264.000 | −0.423077 | ||||||||
\(625\) | 335.500 | + | 581.103i | 0.536800 | + | 0.929765i | ||||
\(626\) | 553.500 | + | 319.563i | 0.884185 | + | 0.510485i | ||||
\(627\) | −135.000 | + | 233.827i | −0.215311 | + | 0.372930i | ||||
\(628\) | 90.0000 | − | 51.9615i | 0.143312 | − | 0.0827413i | ||||
\(629\) | − | 103.923i | − | 0.165219i | ||||||
\(630\) | 121.500 | − | 303.975i | 0.192857 | − | 0.482500i | ||||
\(631\) | 1115.00 | 1.76704 | 0.883518 | − | 0.468397i | \(-0.155168\pi\) | ||||
0.883518 | + | 0.468397i | \(0.155168\pi\) | |||||||
\(632\) | 64.5000 | + | 111.717i | 0.102057 | + | 0.176768i | ||||
\(633\) | 372.000 | + | 214.774i | 0.587678 | + | 0.339296i | ||||
\(634\) | −175.500 | + | 303.975i | −0.276814 | + | 0.479456i | ||||
\(635\) | 157.500 | − | 90.9327i | 0.248031 | − | 0.143201i | ||||
\(636\) | 285.788i | 0.449353i | ||||||||
\(637\) | 468.000 | − | 491.902i | 0.734694 | − | 0.772217i | ||||
\(638\) | −405.000 | −0.634796 | ||||||||
\(639\) | 126.000 | + | 218.238i | 0.197183 | + | 0.341531i | ||||
\(640\) | 418.500 | + | 241.621i | 0.653906 | + | 0.377533i | ||||
\(641\) | 192.000 | − | 332.554i | 0.299532 | − | 0.518805i | −0.676497 | − | 0.736445i | \(-0.736503\pi\) |
0.976029 | + | 0.217641i | \(0.0698361\pi\) | |||||||
\(642\) | 418.500 | − | 241.621i | 0.651869 | − | 0.376357i | ||||
\(643\) | − | 6.92820i | − | 0.0107748i | −0.999985 | − | 0.00538741i | \(-0.998285\pi\) | ||
0.999985 | − | 0.00538741i | \(-0.00171487\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 666.000 | 1.03256 | ||||||||
\(646\) | 162.000 | + | 280.592i | 0.250774 | + | 0.434353i | ||||
\(647\) | 774.000 | + | 446.869i | 1.19629 | + | 0.690679i | 0.959726 | − | 0.280937i | \(-0.0906452\pi\) |
0.236564 | + | 0.971616i | \(0.423979\pi\) | |||||||
\(648\) | −13.5000 | + | 23.3827i | −0.0208333 | + | 0.0360844i | ||||
\(649\) | −202.500 | + | 116.913i | −0.312018 | + | 0.180144i | ||||
\(650\) | 83.1384i | 0.127905i | ||||||||
\(651\) | 21.0000 | + | 145.492i | 0.0322581 | + | 0.223490i | ||||
\(652\) | −1040.00 | −1.59509 | ||||||||
\(653\) | −37.5000 | − | 64.9519i | −0.0574273 | − | 0.0994669i | 0.835883 | − | 0.548908i | \(-0.184956\pi\) |
−0.893310 | + | 0.449441i | \(0.851623\pi\) | |||||||
\(654\) | 36.0000 | + | 20.7846i | 0.0550459 | + | 0.0317807i | ||||
\(655\) | 445.500 | − | 771.629i | 0.680153 | − | 1.17806i | ||||
\(656\) | 99.0000 | − | 57.1577i | 0.150915 | − | 0.0871306i | ||||
\(657\) | − | 187.061i | − | 0.284721i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 642.000 | 0.974203 | 0.487102 | − | 0.873345i | \(-0.338054\pi\) | ||||
0.487102 | + | 0.873345i | \(0.338054\pi\) | |||||||
\(660\) | 337.500 | + | 584.567i | 0.511364 | + | 0.885708i | ||||
\(661\) | −243.000 | − | 140.296i | −0.367625 | − | 0.212248i | 0.304795 | − | 0.952418i | \(-0.401412\pi\) |
−0.672420 | + | 0.740170i | \(0.734745\pi\) | |||||||
\(662\) | −60.0000 | + | 103.923i | −0.0906344 | + | 0.156983i | ||||
\(663\) | −216.000 | + | 124.708i | −0.325792 | + | 0.188096i | ||||
\(664\) | − | 358.535i | − | 0.539962i | ||||||
\(665\) | −297.000 | + | 233.827i | −0.446617 | + | 0.351619i | ||||
\(666\) | −90.0000 | −0.135135 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1080.00 | + | 623.538i | 1.61677 | + | 0.933441i | ||||
\(669\) | −166.500 | + | 288.386i | −0.248879 | + | 0.431071i | ||||
\(670\) | −1026.00 | + | 592.361i | −1.53134 | + | 0.884121i | ||||
\(671\) | 1351.00i | 2.01341i | ||||||||
\(672\) | −540.000 | + | 77.9423i | −0.803571 | + | 0.115986i | ||||
\(673\) | 13.0000 | 0.0193165 | 0.00965825 | − | 0.999953i | \(-0.496926\pi\) | ||||
0.00965825 | + | 0.999953i | \(0.496926\pi\) | |||||||
\(674\) | −136.500 | − | 236.425i | −0.202522 | − | 0.350779i | ||||
\(675\) | −9.00000 | − | 5.19615i | −0.0133333 | − | 0.00769800i | ||||
\(676\) | 57.5000 | − | 99.5929i | 0.0850592 | − | 0.147327i | ||||
\(677\) | −1093.50 | + | 631.333i | −1.61521 | + | 0.932544i | −0.627079 | + | 0.778955i | \(0.715750\pi\) |
−0.988135 | + | 0.153589i | \(0.950917\pi\) | |||||||
\(678\) | 218.238i | 0.321886i | ||||||||
\(679\) | −481.500 | + | 1204.64i | −0.709131 | + | 1.77414i | ||||
\(680\) | 162.000 | 0.238235 | ||||||||
\(681\) | 76.5000 | + | 132.502i | 0.112335 | + | 0.194570i | ||||
\(682\) | −472.500 | − | 272.798i | −0.692815 | − | 0.399997i | ||||
\(683\) | 484.500 | − | 839.179i | 0.709370 | − | 1.22867i | −0.255721 | − | 0.966751i | \(-0.582313\pi\) |
0.965091 | − | 0.261915i | \(-0.0843540\pi\) | |||||||
\(684\) | 135.000 | − | 77.9423i | 0.197368 | − | 0.113951i | ||||
\(685\) | − | 498.831i | − | 0.728220i | ||||||
\(686\) | 595.500 | − | 839.179i | 0.868076 | − | 1.22329i | ||||
\(687\) | −570.000 | −0.829694 | ||||||||
\(688\) | −407.000 | − | 704.945i | −0.591570 | − | 1.02463i | ||||
\(689\) | 396.000 | + | 228.631i | 0.574746 | + | 0.331830i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −87.0000 | + | 50.2295i | −0.125904 | + | 0.0726910i | −0.561629 | − | 0.827389i | \(-0.689825\pi\) |
0.435725 | + | 0.900080i | \(0.356492\pi\) | |||||||
\(692\) | − | 1143.15i | − | 1.65196i | ||||||
\(693\) | −292.500 | − | 116.913i | −0.422078 | − | 0.168706i | ||||
\(694\) | 630.000 | 0.907781 | ||||||||
\(695\) | −477.000 | − | 826.188i | −0.686331 | − | 1.18876i | ||||
\(696\) | 40.5000 | + | 23.3827i | 0.0581897 | + | 0.0335958i | ||||
\(697\) | 54.0000 | − | 93.5307i | 0.0774749 | − | 0.134190i | ||||
\(698\) | −792.000 | + | 457.261i | −1.13467 | + | 0.655102i | ||||
\(699\) | 467.654i | 0.669033i | ||||||||
\(700\) | 10.0000 | + | 69.2820i | 0.0142857 | + | 0.0989743i | ||||
\(701\) | 597.000 | 0.851641 | 0.425820 | − | 0.904808i | \(-0.359986\pi\) | ||||
0.425820 | + | 0.904808i | \(0.359986\pi\) | |||||||
\(702\) | 108.000 | + | 187.061i | 0.153846 | + | 0.266469i | ||||
\(703\) | 90.0000 | + | 51.9615i | 0.128023 | + | 0.0739140i | ||||
\(704\) | 682.500 | − | 1182.12i | 0.969460 | − | 1.67915i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1184.72i | − | 1.67808i | ||||||
\(707\) | −630.000 | − | 800.207i | −0.891089 | − | 1.13184i | ||||
\(708\) | 135.000 | 0.190678 | ||||||||
\(709\) | 415.000 | + | 718.801i | 0.585331 | + | 1.01382i | 0.994834 | + | 0.101515i | \(0.0323689\pi\) |
−0.409503 | + | 0.912309i | \(0.634298\pi\) | |||||||
\(710\) | −1134.00 | − | 654.715i | −1.59718 | − | 0.922134i | ||||
\(711\) | −64.5000 | + | 111.717i | −0.0907173 | + | 0.157127i | ||||
\(712\) | −189.000 | + | 109.119i | −0.265449 | + | 0.153257i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −297.000 | + | 233.827i | −0.415966 | + | 0.327489i | ||||
\(715\) | 1080.00 | 1.51049 | ||||||||
\(716\) | −225.000 | − | 389.711i | −0.314246 | − | 0.544290i | ||||
\(717\) | 342.000 | + | 197.454i | 0.476987 | + | 0.275389i | ||||
\(718\) | −738.000 | + | 1278.25i | −1.02786 | + | 1.78030i | ||||
\(719\) | 297.000 | − | 171.473i | 0.413074 | − | 0.238488i | −0.279036 | − | 0.960281i | \(-0.590015\pi\) |
0.692110 | + | 0.721792i | \(0.256681\pi\) | |||||||
\(720\) | 171.473i | 0.238157i | ||||||||
\(721\) | −480.000 | + | 69.2820i | −0.665742 | + | 0.0960916i | ||||
\(722\) | 759.000 | 1.05125 | ||||||||
\(723\) | −385.500 | − | 667.706i | −0.533195 | − | 0.923521i | ||||
\(724\) | 45.0000 | + | 25.9808i | 0.0621547 | + | 0.0358850i | ||||
\(725\) | −9.00000 | + | 15.5885i | −0.0124138 | + | 0.0215013i | ||||
\(726\) | 468.000 | − | 270.200i | 0.644628 | − | 0.372176i | ||||
\(727\) | 50.2295i | 0.0690914i | 0.999403 | + | 0.0345457i | \(0.0109984\pi\) | ||||
−0.999403 | + | 0.0345457i | \(0.989002\pi\) | |||||||
\(728\) | 108.000 | − | 270.200i | 0.148352 | − | 0.371154i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 486.000 | + | 841.777i | 0.665753 | + | 1.15312i | ||||
\(731\) | −666.000 | − | 384.515i | −0.911081 | − | 0.526013i | ||||
\(732\) | 390.000 | − | 675.500i | 0.532787 | − | 0.922814i | ||||
\(733\) | −159.000 | + | 91.7987i | −0.216917 | + | 0.125237i | −0.604522 | − | 0.796589i | \(-0.706636\pi\) |
0.387605 | + | 0.921826i | \(0.373302\pi\) | |||||||
\(734\) | 982.073i | 1.33797i | ||||||||
\(735\) | −319.500 | − | 303.975i | −0.434694 | − | 0.413571i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 570.000 | + | 987.269i | 0.773406 | + | 1.33958i | ||||
\(738\) | −81.0000 | − | 46.7654i | −0.109756 | − | 0.0633677i | ||||
\(739\) | 167.000 | − | 289.252i | 0.225981 | − | 0.391411i | −0.730632 | − | 0.682771i | \(-0.760775\pi\) |
0.956613 | + | 0.291361i | \(0.0941079\pi\) | |||||||
\(740\) | 225.000 | − | 129.904i | 0.304054 | − | 0.175546i | ||||
\(741\) | − | 249.415i | − | 0.336593i | ||||||
\(742\) | 643.500 | + | 257.210i | 0.867251 | + | 0.346644i | ||||
\(743\) | 84.0000 | 0.113055 | 0.0565276 | − | 0.998401i | \(-0.481997\pi\) | ||||
0.0565276 | + | 0.998401i | \(0.481997\pi\) | |||||||
\(744\) | 31.5000 | + | 54.5596i | 0.0423387 | + | 0.0733328i | ||||
\(745\) | 837.000 | + | 483.242i | 1.12349 | + | 0.648647i | ||||
\(746\) | −255.000 | + | 441.673i | −0.341823 | + | 0.592055i | ||||
\(747\) | 310.500 | − | 179.267i | 0.415663 | − | 0.239983i | ||||
\(748\) | − | 779.423i | − | 1.04201i | ||||||
\(749\) | −93.0000 | − | 644.323i | −0.124166 | − | 0.860244i | ||||
\(750\) | −621.000 | −0.828000 | ||||||||
\(751\) | 179.500 | + | 310.903i | 0.239015 | + | 0.413986i | 0.960432 | − | 0.278515i | \(-0.0898423\pi\) |
−0.721417 | + | 0.692501i | \(0.756509\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.50000 | + | 7.79423i | −0.00597610 | + | 0.0103509i | ||||
\(754\) | 324.000 | − | 187.061i | 0.429708 | − | 0.248092i | ||||
\(755\) | 410.496i | 0.543703i | ||||||||
\(756\) | 112.500 | + | 142.894i | 0.148810 | + | 0.189013i | ||||
\(757\) | −80.0000 | −0.105680 | −0.0528402 | − | 0.998603i | \(-0.516827\pi\) | ||||
−0.0528402 | + | 0.998603i | \(0.516827\pi\) | |||||||
\(758\) | −123.000 | − | 213.042i | −0.162269 | − | 0.281058i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −81.0000 | + | 140.296i | −0.106579 | + | 0.184600i | ||||
\(761\) | −702.000 | + | 405.300i | −0.922470 | + | 0.532589i | −0.884422 | − | 0.466687i | \(-0.845447\pi\) |
−0.0380481 | + | 0.999276i | \(0.512114\pi\) | |||||||
\(762\) | 181.865i | 0.238668i | ||||||||
\(763\) | 44.0000 | − | 34.6410i | 0.0576671 | − | 0.0454011i | ||||
\(764\) | −1560.00 | −2.04188 | ||||||||
\(765\) | 81.0000 | + | 140.296i | 0.105882 | + | 0.183394i | ||||
\(766\) | −567.000 | − | 327.358i | −0.740209 | − | 0.427360i | ||||
\(767\) | 108.000 | − | 187.061i | 0.140808 | − | 0.243887i | ||||
\(768\) | 127.500 | − | 73.6122i | 0.166016 | − | 0.0958492i | ||||
\(769\) | − | 774.227i | − | 1.00680i | −0.864054 | − | 0.503398i | \(-0.832083\pi\) | ||
0.864054 | − | 0.503398i | \(-0.167917\pi\) | |||||||
\(770\) | 1620.00 | − | 233.827i | 2.10390 | − | 0.303671i | ||||
\(771\) | −198.000 | −0.256809 | ||||||||
\(772\) | 462.500 | + | 801.073i | 0.599093 | + | 1.03766i | ||||
\(773\) | −630.000 | − | 363.731i | −0.815006 | − | 0.470544i | 0.0336850 | − | 0.999433i | \(-0.489276\pi\) |
−0.848691 | + | 0.528888i | \(0.822609\pi\) | |||||||
\(774\) | −333.000 | + | 576.773i | −0.430233 | + | 0.745185i | ||||
\(775\) | −21.0000 | + | 12.1244i | −0.0270968 | + | 0.0156443i | ||||
\(776\) | 555.988i | 0.716480i | ||||||||
\(777\) | −45.0000 | + | 112.583i | −0.0579151 | + | 0.144895i | ||||
\(778\) | 918.000 | 1.17995 | ||||||||
\(779\) | 54.0000 | + | 93.5307i | 0.0693196 | + | 0.120065i | ||||
\(780\) | −540.000 | − | 311.769i | −0.692308 | − | 0.399704i | ||||
\(781\) | −630.000 | + | 1091.19i | −0.806658 | + | 1.39717i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 46.7654i | 0.0597259i | ||||||||
\(784\) | −126.500 | + | 523.945i | −0.161352 | + | 0.668298i | ||||
\(785\) | −108.000 | −0.137580 | ||||||||
\(786\) | 445.500 | + | 771.629i | 0.566794 | + | 0.981716i | ||||
\(787\) | −1236.00 | − | 713.605i | −1.57052 | − | 0.906741i | −0.996105 | − | 0.0881773i | \(-0.971896\pi\) |
−0.574416 | − | 0.818563i | \(-0.694771\pi\) | |||||||
\(788\) | −825.000 | + | 1428.94i | −1.04695 | + | 1.81338i | ||||
\(789\) | 279.000 | − | 161.081i | 0.353612 | − | 0.204158i | ||||
\(790\) | − | 670.304i | − | 0.848486i | ||||||
\(791\) | 273.000 | + | 109.119i | 0.345133 | + | 0.137951i | ||||
\(792\) | −135.000 | −0.170455 | ||||||||
\(793\) | −624.000 | − | 1080.80i | −0.786885 | − | 1.36293i | ||||
\(794\) | 666.000 | + | 384.515i | 0.838791 | + | 0.484276i | ||||
\(795\) | 148.500 | − | 257.210i | 0.186792 | − | 0.323534i | ||||
\(796\) | −30.0000 | + | 17.3205i | −0.0376884 | + | 0.0217594i | ||||
\(797\) | 607.950i | 0.762798i | 0.924411 | + | 0.381399i | \(0.124558\pi\) | ||||
−0.924411 | + | 0.381399i | \(0.875442\pi\) | |||||||
\(798\) | −54.0000 | − | 374.123i | −0.0676692 | − | 0.468826i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −45.0000 | − | 77.9423i | −0.0562500 | − | 0.0974279i | ||||
\(801\) | −189.000 | − | 109.119i | −0.235955 | − | 0.136229i | ||||
\(802\) | −198.000 | + | 342.946i | −0.246883 | + | 0.427614i | ||||
\(803\) | 810.000 | − | 467.654i | 1.00872 | − | 0.582383i | ||||
\(804\) | − | 658.179i | − | 0.818631i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 504.000 | 0.625310 | ||||||||
\(807\) | 292.500 | + | 506.625i | 0.362454 | + | 0.627788i | ||||
\(808\) | −378.000 | − | 218.238i | −0.467822 | − | 0.270097i | ||||
\(809\) | 84.0000 | − | 145.492i | 0.103832 | − | 0.179842i | −0.809428 | − | 0.587218i | \(-0.800223\pi\) |
0.913260 | + | 0.407376i | \(0.133556\pi\) | |||||||
\(810\) | 121.500 | − | 70.1481i | 0.150000 | − | 0.0866025i | ||||
\(811\) | 353.338i | 0.435682i | 0.975984 | + | 0.217841i | \(0.0699015\pi\) | ||||
−0.975984 | + | 0.217841i | \(0.930099\pi\) | |||||||
\(812\) | 247.500 | − | 194.856i | 0.304803 | − | 0.239970i | ||||
\(813\) | −159.000 | −0.195572 | ||||||||
\(814\) | −225.000 | − | 389.711i | −0.276413 | − | 0.478761i | ||||
\(815\) | 936.000 | + | 540.400i | 1.14847 | + | 0.663067i | ||||
\(816\) | 99.0000 | − | 171.473i | 0.121324 | − | 0.210139i | ||||
\(817\) | 666.000 | − | 384.515i | 0.815177 | − | 0.470643i | ||||
\(818\) | 1086.00i | 1.32762i | ||||||||
\(819\) | 288.000 | − | 41.5692i | 0.351648 | − | 0.0507561i | ||||
\(820\) | 270.000 | 0.329268 | ||||||||
\(821\) | −142.500 | − | 246.817i | −0.173569 | − | 0.300630i | 0.766096 | − | 0.642726i | \(-0.222197\pi\) |
−0.939665 | + | 0.342096i | \(0.888863\pi\) | |||||||
\(822\) | 432.000 | + | 249.415i | 0.525547 | + | 0.303425i | ||||
\(823\) | 137.000 | − | 237.291i | 0.166464 | − | 0.288324i | −0.770710 | − | 0.637186i | \(-0.780098\pi\) |
0.937174 | + | 0.348862i | \(0.113432\pi\) | |||||||
\(824\) | −180.000 | + | 103.923i | −0.218447 | + | 0.126120i | ||||
\(825\) | − | 51.9615i | − | 0.0629837i | ||||||
\(826\) | 121.500 | − | 303.975i | 0.147094 | − | 0.368008i | ||||
\(827\) | 429.000 | 0.518742 | 0.259371 | − | 0.965778i | \(-0.416485\pi\) | ||||
0.259371 | + | 0.965778i | \(0.416485\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −819.000 | − | 472.850i | −0.987937 | − | 0.570386i | −0.0832802 | − | 0.996526i | \(-0.526540\pi\) |
−0.904657 | + | 0.426140i | \(0.859873\pi\) | |||||||
\(830\) | −931.500 | + | 1613.41i | −1.12229 | + | 1.94386i | ||||
\(831\) | 570.000 | − | 329.090i | 0.685921 | − | 0.396016i | ||||
\(832\) | 1260.93i | 1.51554i | ||||||||
\(833\) | 144.000 | + | 488.438i | 0.172869 | + | 0.586361i | ||||
\(834\) | 954.000 | 1.14388 | ||||||||
\(835\) | −648.000 | − | 1122.37i | −0.776048 | − | 1.34415i | ||||
\(836\) | 675.000 | + | 389.711i | 0.807416 | + | 0.466162i | ||||
\(837\) | −31.5000 | + | 54.5596i | −0.0376344 | + | 0.0651847i | ||||
\(838\) | 1674.00 | − | 966.484i | 1.99761 | − | 1.15332i | ||||
\(839\) | 259.808i | 0.309663i | 0.987941 | + | 0.154832i | \(0.0494835\pi\) | ||||
−0.987941 | + | 0.154832i | \(0.950516\pi\) | |||||||
\(840\) | −175.500 | − | 70.1481i | −0.208929 | − | 0.0835096i | ||||
\(841\) | −760.000 | −0.903686 | ||||||||
\(842\) | −1128.00 | − | 1953.75i | −1.33967 | − | 2.32037i | ||||
\(843\) | −450.000 | − | 259.808i | −0.533808 | − | 0.308194i | ||||
\(844\) | 620.000 | − | 1073.87i | 0.734597 | − | 1.27236i | ||||
\(845\) | −103.500 | + | 59.7558i | −0.122485 | + | 0.0707169i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −104.000 | − | 720.533i | −0.122786 | − | 0.850688i | ||||
\(848\) | −363.000 | −0.428066 | ||||||||
\(849\) | −177.000 | − | 306.573i | −0.208481 | − | 0.361099i | ||||
\(850\) | −54.0000 | − | 31.1769i | −0.0635294 | − | 0.0366787i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 630.000 | − | 363.731i | 0.739437 | − | 0.426914i | ||||
\(853\) | 997.661i | 1.16959i | 0.811181 | + | 0.584796i | \(0.198825\pi\) | ||||
−0.811181 | + | 0.584796i | \(0.801175\pi\) | |||||||
\(854\) | −1170.00 | − | 1486.10i | −1.37002 | − | 1.74016i | ||||
\(855\) | −162.000 | −0.189474 | ||||||||
\(856\) | −139.500 | − | 241.621i | −0.162967 | − | 0.282268i | ||||
\(857\) | 378.000 | + | 218.238i | 0.441074 | + | 0.254654i | 0.704053 | − | 0.710148i | \(-0.251372\pi\) |
−0.262979 | + | 0.964801i | \(0.584705\pi\) | |||||||
\(858\) | −540.000 | + | 935.307i | −0.629371 | + | 1.09010i | ||||
\(859\) | −393.000 | + | 226.899i | −0.457509 | + | 0.264143i | −0.710996 | − | 0.703196i | \(-0.751756\pi\) |
0.253487 | + | 0.967339i | \(0.418422\pi\) | |||||||
\(860\) | − | 1922.58i | − | 2.23555i | ||||||
\(861\) | −99.0000 | + | 77.9423i | −0.114983 | + | 0.0905253i | ||||
\(862\) | 486.000 | 0.563805 | ||||||||
\(863\) | 195.000 | + | 337.750i | 0.225956 | + | 0.391367i | 0.956606 | − | 0.291385i | \(-0.0941161\pi\) |
−0.730650 | + | 0.682752i | \(0.760783\pi\) | |||||||
\(864\) | −202.500 | − | 116.913i | −0.234375 | − | 0.135316i | ||||
\(865\) | −594.000 | + | 1028.84i | −0.686705 | + | 1.18941i | ||||
\(866\) | −882.000 | + | 509.223i | −1.01848 | + | 0.588017i | ||||
\(867\) | 313.501i | 0.361593i | ||||||||
\(868\) | 420.000 | − | 60.6218i | 0.483871 | − | 0.0698408i | ||||
\(869\) | −645.000 | −0.742232 | ||||||||
\(870\) | −121.500 | − | 210.444i | −0.139655 | − | 0.241890i | ||||
\(871\) | −912.000 | − | 526.543i | −1.04707 | − | 0.604527i | ||||
\(872\) | 12.0000 | − | 20.7846i | 0.0137615 | − | 0.0238356i | ||||
\(873\) | −481.500 | + | 277.994i | −0.551546 | + | 0.318435i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −310.500 | + | 776.825i | −0.354857 | + | 0.887800i | ||||
\(876\) | −540.000 | −0.616438 | ||||||||
\(877\) | 272.000 | + | 471.118i | 0.310148 | + | 0.537192i | 0.978394 | − | 0.206748i | \(-0.0662880\pi\) |
−0.668246 | + | 0.743940i | \(0.732955\pi\) | |||||||
\(878\) | −1012.50 | − | 584.567i | −1.15319 | − | 0.665794i | ||||
\(879\) | 472.500 | − | 818.394i | 0.537543 | − | 0.931051i | ||||
\(880\) | −742.500 | + | 428.683i | −0.843750 | + | 0.487139i | ||||
\(881\) | − | 187.061i | − | 0.212329i | −0.994349 | − | 0.106164i | \(-0.966143\pi\) | ||
0.994349 | − | 0.106164i | \(-0.0338569\pi\) | |||||||
\(882\) | 423.000 | − | 124.708i | 0.479592 | − | 0.141392i | ||||
\(883\) | 322.000 | 0.364666 | 0.182333 | − | 0.983237i | \(-0.441635\pi\) | ||||
0.182333 | + | 0.983237i | \(0.441635\pi\) | |||||||
\(884\) | 360.000 | + | 623.538i | 0.407240 | + | 0.705360i | ||||
\(885\) | −121.500 | − | 70.1481i | −0.137288 | − | 0.0792633i | ||||
\(886\) | 445.500 | − | 771.629i | 0.502822 | − | 0.870913i | ||||
\(887\) | 612.000 | − | 353.338i | 0.689966 | − | 0.398352i | −0.113633 | − | 0.993523i | \(-0.536249\pi\) |
0.803599 | + | 0.595171i | \(0.202916\pi\) | |||||||
\(888\) | 51.9615i | 0.0585152i | ||||||||
\(889\) | 227.500 | + | 90.9327i | 0.255906 | + | 0.102286i | ||||
\(890\) | 1134.00 | 1.27416 | ||||||||
\(891\) | −67.5000 | − | 116.913i | −0.0757576 | − | 0.131216i | ||||
\(892\) | 832.500 | + | 480.644i | 0.933296 | + | 0.538839i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −837.000 | + | 483.242i | −0.936242 | + | 0.540539i | ||||
\(895\) | 467.654i | 0.522518i | ||||||||
\(896\) | 93.0000 | + | 644.323i | 0.103795 | + | 0.719110i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 738.000 | + | 1278.25i | 0.821826 | + | 1.42344i | ||||
\(899\) | 94.5000 | + | 54.5596i | 0.105117 | + | 0.0606892i | ||||
\(900\) | −15.0000 | + | 25.9808i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | −297.000 | + | 171.473i | −0.329634 | + | 0.190314i | ||||
\(902\) | − | 467.654i | − | 0.518463i | ||||||
\(903\) | 555.000 | + | 704.945i | 0.614618 | + | 0.780670i | ||||
\(904\) | 126.000 | 0.139381 | ||||||||
\(905\) | −27.0000 | − | 46.7654i | −0.0298343 | − | 0.0516744i | ||||
\(906\) | −355.500 | − | 205.248i | −0.392384 | − | 0.226543i | ||||
\(907\) | 550.000 | − | 952.628i | 0.606395 | − | 1.05031i | −0.385435 | − | 0.922735i | \(-0.625948\pi\) |
0.991829 | − | 0.127571i | \(-0.0407182\pi\) | |||||||
\(908\) | 382.500 | − | 220.836i | 0.421256 | − | 0.243212i | ||||
\(909\) | − | 436.477i | − | 0.480173i | ||||||
\(910\) | −1188.00 | + | 935.307i | −1.30549 | + | 1.02781i | ||||
\(911\) | 900.000 | 0.987925 | 0.493963 | − | 0.869483i | \(-0.335548\pi\) | ||||
0.493963 | + | 0.869483i | \(0.335548\pi\) | |||||||
\(912\) | 99.0000 | + | 171.473i | 0.108553 | + | 0.188019i | ||||
\(913\) | 1552.50 | + | 896.336i | 1.70044 | + | 0.981748i | ||||
\(914\) | 664.500 | − | 1150.95i | 0.727024 | − | 1.25924i | ||||
\(915\) | −702.000 | + | 405.300i | −0.767213 | + | 0.442951i | ||||
\(916\) | 1645.45i | 1.79634i | ||||||||
\(917\) | 1188.00 | − | 171.473i | 1.29553 | − | 0.186993i | ||||
\(918\) | −162.000 | −0.176471 | ||||||||
\(919\) | 859.000 | + | 1487.83i | 0.934712 | + | 1.61897i | 0.775147 | + | 0.631781i | \(0.217676\pi\) |
0.159564 | + | 0.987188i | \(0.448991\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 150.000 | − | 259.808i | 0.162866 | − | 0.282093i | ||||
\(922\) | 1080.00 | − | 623.538i | 1.17137 | − | 0.676289i | ||||
\(923\) | − | 1163.94i | − | 1.26104i | ||||||
\(924\) | −337.500 | + | 844.375i | −0.365260 | + | 0.913826i | ||||
\(925\) | −20.0000 | −0.0216216 | ||||||||
\(926\) | 123.000 | + | 213.042i | 0.132829 | + | 0.230067i | ||||
\(927\) | −180.000 | − | 103.923i | −0.194175 | − | 0.112107i | ||||
\(928\) | −202.500 | + | 350.740i | −0.218211 | + | 0.377953i | ||||
\(929\) | −1287.00 | + | 743.050i | −1.38536 | + | 0.799838i | −0.992788 | − | 0.119883i | \(-0.961748\pi\) |
−0.392573 | + | 0.919721i | \(0.628415\pi\) | |||||||
\(930\) | − | 327.358i | − | 0.351997i | ||||||
\(931\) | −495.000 | − | 119.512i | −0.531686 | − | 0.128369i | ||||
\(932\) | 1350.00 | 1.44850 | ||||||||
\(933\) | 153.000 | + | 265.004i | 0.163987 | + | 0.284034i | ||||
\(934\) | −702.000 | − | 405.300i | −0.751606 | − | 0.433940i | ||||
\(935\) | −405.000 | + | 701.481i | −0.433155 | + | 0.750247i | ||||
\(936\) | 108.000 | − | 62.3538i | 0.115385 | − | 0.0666173i | ||||
\(937\) | − | 957.824i | − | 1.02222i | −0.859514 | − | 0.511112i | \(-0.829234\pi\) | ||
0.859514 | − | 0.511112i | \(-0.170766\pi\) | |||||||
\(938\) | −1482.00 | − | 592.361i | −1.57996 | − | 0.631515i | ||||
\(939\) | 369.000 | 0.392971 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 310.500 | + | 179.267i | 0.329968 | + | 0.190507i | 0.655827 | − | 0.754911i | \(-0.272320\pi\) |
−0.325859 | + | 0.945418i | \(0.605653\pi\) | |||||||
\(942\) | 54.0000 | − | 93.5307i | 0.0573248 | − | 0.0992895i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 171.473i | 0.181645i | ||||||||
\(945\) | −27.0000 | − | 187.061i | −0.0285714 | − | 0.197949i | ||||
\(946\) | −3330.00 | −3.52008 | ||||||||
\(947\) | −81.0000 | − | 140.296i | −0.0855333 | − | 0.148148i | 0.820085 | − | 0.572242i | \(-0.193926\pi\) |
−0.905618 | + | 0.424094i | \(0.860593\pi\) | |||||||
\(948\) | 322.500 | + | 186.195i | 0.340190 | + | 0.196409i | ||||
\(949\) | −432.000 | + | 748.246i | −0.455216 | + | 0.788457i | ||||
\(950\) | 54.0000 | − | 31.1769i | 0.0568421 | − | 0.0328178i | ||||
\(951\) | 202.650i | 0.213091i | ||||||||
\(952\) | 135.000 | + | 171.473i | 0.141807 | + | 0.180119i | ||||
\(953\) | −954.000 | −1.00105 | −0.500525 | − | 0.865722i | \(-0.666860\pi\) | ||||
−0.500525 | + | 0.865722i | \(0.666860\pi\) | |||||||
\(954\) | 148.500 | + | 257.210i | 0.155660 | + | 0.269612i | ||||
\(955\) | 1404.00 | + | 810.600i | 1.47016 | + | 0.848796i | ||||
\(956\) | 570.000 | − | 987.269i | 0.596234 | − | 1.03271i | ||||
\(957\) | −202.500 | + | 116.913i | −0.211599 | + | 0.122167i | ||||
\(958\) | − | 1028.84i | − | 1.07394i | ||||||
\(959\) | 528.000 | − | 415.692i | 0.550574 | − | 0.433464i | ||||
\(960\) | 819.000 | 0.853125 | ||||||||
\(961\) | −407.000 | − | 704.945i | −0.423517 | − | 0.733553i | ||||
\(962\) | 360.000 | + | 207.846i | 0.374220 | + | 0.216056i | ||||
\(963\) | 139.500 | − | 241.621i | 0.144860 | − | 0.250905i | ||||
\(964\) | −1927.50 | + | 1112.84i | −1.99948 | + | 1.15440i | ||||
\(965\) | − | 961.288i | − | 0.996154i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −751.000 | −0.776629 | −0.388314 | − | 0.921527i | \(-0.626943\pi\) | ||||
−0.388314 | + | 0.921527i | \(0.626943\pi\) | |||||||
\(968\) | −156.000 | − | 270.200i | −0.161157 | − | 0.279132i | ||||
\(969\) | 162.000 | + | 93.5307i | 0.167183 | + | 0.0965230i | ||||
\(970\) | 1444.50 | − | 2501.95i | 1.48918 | − | 2.57933i | ||||
\(971\) | −247.500 | + | 142.894i | −0.254892 | + | 0.147162i | −0.622002 | − | 0.783016i | \(-0.713680\pi\) |
0.367110 | + | 0.930177i | \(0.380347\pi\) | |||||||
\(972\) | 77.9423i | 0.0801875i | ||||||||
\(973\) | 477.000 | − | 1193.38i | 0.490236 | − | 1.22650i | ||||
\(974\) | −951.000 | −0.976386 | ||||||||
\(975\) | 24.0000 | + | 41.5692i | 0.0246154 | + | 0.0426351i | ||||
\(976\) | 858.000 | + | 495.367i | 0.879098 | + | 0.507548i | ||||
\(977\) | 9.00000 | − | 15.5885i | 0.00921187 | − | 0.0159554i | −0.861383 | − | 0.507957i | \(-0.830401\pi\) |
0.870595 | + | 0.492001i | \(0.163734\pi\) | |||||||
\(978\) | −936.000 | + | 540.400i | −0.957055 | + | 0.552556i | ||||
\(979\) | − | 1091.19i | − | 1.11460i | ||||||
\(980\) | −877.500 | + | 922.317i | −0.895408 | + | 0.941140i | ||||
\(981\) | 24.0000 | 0.0244648 | ||||||||
\(982\) | −40.5000 | − | 70.1481i | −0.0412424 | − | 0.0714339i | ||||
\(983\) | −855.000 | − | 493.634i | −0.869786 | − | 0.502171i | −0.00250913 | − | 0.999997i | \(-0.500799\pi\) |
−0.867277 | + | 0.497825i | \(0.834132\pi\) | |||||||
\(984\) | −27.0000 | + | 46.7654i | −0.0274390 | + | 0.0475258i | ||||
\(985\) | 1485.00 | − | 857.365i | 1.50761 | − | 0.870421i | ||||
\(986\) | 280.592i | 0.284576i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −720.000 | −0.728745 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 607.500 | + | 350.740i | 0.613636 | + | 0.354283i | ||||
\(991\) | −351.500 | + | 608.816i | −0.354692 | + | 0.614345i | −0.987065 | − | 0.160319i | \(-0.948748\pi\) |
0.632373 | + | 0.774664i | \(0.282081\pi\) | |||||||
\(992\) | −472.500 | + | 272.798i | −0.476310 | + | 0.274998i | ||||
\(993\) | 69.2820i | 0.0697704i | ||||||||
\(994\) | −252.000 | − | 1745.91i | −0.253521 | − | 1.75645i | ||||
\(995\) | 36.0000 | 0.0361809 | ||||||||
\(996\) | −517.500 | − | 896.336i | −0.519578 | − | 0.899936i | ||||
\(997\) | 186.000 | + | 107.387i | 0.186560 | + | 0.107710i | 0.590371 | − | 0.807132i | \(-0.298981\pi\) |
−0.403811 | + | 0.914842i | \(0.632315\pi\) | |||||||
\(998\) | 669.000 | − | 1158.74i | 0.670341 | − | 1.16106i | ||||
\(999\) | −45.0000 | + | 25.9808i | −0.0450450 | + | 0.0260068i |
(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 | 21.3.f.a.10.1 | ✓ | 2 | |
3.2 | odd | 2 | 63.3.m.d.10.1 | 2 | |||
4.3 | odd | 2 | 336.3.bh.d.241.1 | 2 | |||
5.2 | odd | 4 | 525.3.s.e.199.2 | 4 | |||
5.3 | odd | 4 | 525.3.s.e.199.1 | 4 | |||
5.4 | even | 2 | 525.3.o.h.451.1 | 2 | |||
7.2 | even | 3 | 147.3.f.a.19.1 | 2 | |||
7.3 | odd | 6 | 147.3.d.c.97.1 | 2 | |||
7.4 | even | 3 | 147.3.d.c.97.2 | 2 | |||
7.5 | odd | 6 | inner | 21.3.f.a.19.1 | yes | 2 | |
7.6 | odd | 2 | 147.3.f.a.31.1 | 2 | |||
12.11 | even | 2 | 1008.3.cg.a.577.1 | 2 | |||
21.2 | odd | 6 | 441.3.m.g.19.1 | 2 | |||
21.5 | even | 6 | 63.3.m.d.19.1 | 2 | |||
21.11 | odd | 6 | 441.3.d.a.244.1 | 2 | |||
21.17 | even | 6 | 441.3.d.a.244.2 | 2 | |||
21.20 | even | 2 | 441.3.m.g.325.1 | 2 | |||
28.3 | even | 6 | 2352.3.f.a.97.2 | 2 | |||
28.11 | odd | 6 | 2352.3.f.a.97.1 | 2 | |||
28.19 | even | 6 | 336.3.bh.d.145.1 | 2 | |||
35.12 | even | 12 | 525.3.s.e.124.1 | 4 | |||
35.19 | odd | 6 | 525.3.o.h.376.1 | 2 | |||
35.33 | even | 12 | 525.3.s.e.124.2 | 4 | |||
84.47 | odd | 6 | 1008.3.cg.a.145.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.f.a.10.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
21.3.f.a.19.1 | yes | 2 | 7.5 | odd | 6 | inner | |
63.3.m.d.10.1 | 2 | 3.2 | odd | 2 | |||
63.3.m.d.19.1 | 2 | 21.5 | even | 6 | |||
147.3.d.c.97.1 | 2 | 7.3 | odd | 6 | |||
147.3.d.c.97.2 | 2 | 7.4 | even | 3 | |||
147.3.f.a.19.1 | 2 | 7.2 | even | 3 | |||
147.3.f.a.31.1 | 2 | 7.6 | odd | 2 | |||
336.3.bh.d.145.1 | 2 | 28.19 | even | 6 | |||
336.3.bh.d.241.1 | 2 | 4.3 | odd | 2 | |||
441.3.d.a.244.1 | 2 | 21.11 | odd | 6 | |||
441.3.d.a.244.2 | 2 | 21.17 | even | 6 | |||
441.3.m.g.19.1 | 2 | 21.2 | odd | 6 | |||
441.3.m.g.325.1 | 2 | 21.20 | even | 2 | |||
525.3.o.h.376.1 | 2 | 35.19 | odd | 6 | |||
525.3.o.h.451.1 | 2 | 5.4 | even | 2 | |||
525.3.s.e.124.1 | 4 | 35.12 | even | 12 | |||
525.3.s.e.124.2 | 4 | 35.33 | even | 12 | |||
525.3.s.e.199.1 | 4 | 5.3 | odd | 4 | |||
525.3.s.e.199.2 | 4 | 5.2 | odd | 4 | |||
1008.3.cg.a.145.1 | 2 | 84.47 | odd | 6 | |||
1008.3.cg.a.577.1 | 2 | 12.11 | even | 2 | |||
2352.3.f.a.97.1 | 2 | 28.11 | odd | 6 | |||
2352.3.f.a.97.2 | 2 | 28.3 | even | 6 |