Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [670,2,Mod(171,670)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(670, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("670.171");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 670 = 2 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 670.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.34997693543\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{193})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 49x^{2} + 48x + 2304 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 431.1 | ||
Root | \(-3.22311 + 5.58259i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 670.431 |
Dual form | 670.2.e.e.171.1 |
$q$-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 \(\left(\mathbb{Z}/670\mathbb{Z}\right)^\times\).
\(n\) | \(471\) | \(537\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | −1.00000 | − | 1.73205i | −0.377964 | − | 0.654654i | 0.612801 | − | 0.790237i | \(-0.290043\pi\) |
−0.990766 | + | 0.135583i | \(0.956709\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | −1.00000 | + | 1.73205i | −0.277350 | + | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.22311 | + | 5.58259i | −0.781719 | + | 1.35398i | 0.149220 | + | 0.988804i | \(0.452324\pi\) |
−0.930939 | + | 0.365173i | \(0.881010\pi\) | |||||||
\(18\) | 1.00000 | − | 1.73205i | 0.235702 | − | 0.408248i | ||||
\(19\) | −4.22311 | + | 7.31464i | −0.968848 | + | 1.67809i | −0.269948 | + | 0.962875i | \(0.587006\pi\) |
−0.698900 | + | 0.715219i | \(0.746327\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | −1.00000 | − | 1.73205i | −0.218218 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.00000 | − | 1.73205i | −0.196116 | − | 0.339683i | ||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | −1.00000 | + | 1.73205i | −0.188982 | + | 0.327327i | ||||
\(29\) | −3.00000 | − | 5.19615i | −0.557086 | − | 0.964901i | −0.997738 | − | 0.0672232i | \(-0.978586\pi\) |
0.440652 | − | 0.897678i | \(-0.354747\pi\) | |||||||
\(30\) | 0.500000 | − | 0.866025i | 0.0912871 | − | 0.158114i | ||||
\(31\) | 3.72311 | + | 6.44862i | 0.668690 | + | 1.15821i | 0.978271 | + | 0.207332i | \(0.0664782\pi\) |
−0.309580 | + | 0.950873i | \(0.600188\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.22311 | − | 5.58259i | −0.552759 | − | 0.957407i | ||||
\(35\) | 1.00000 | + | 1.73205i | 0.169031 | + | 0.292770i | ||||
\(36\) | 1.00000 | + | 1.73205i | 0.166667 | + | 0.288675i | ||||
\(37\) | −2.72311 | + | 4.71657i | −0.447677 | + | 0.775399i | −0.998234 | − | 0.0593984i | \(-0.981082\pi\) |
0.550558 | + | 0.834797i | \(0.314415\pi\) | |||||||
\(38\) | −4.22311 | − | 7.31464i | −0.685079 | − | 1.18659i | ||||
\(39\) | −1.00000 | + | 1.73205i | −0.160128 | + | 0.277350i | ||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −4.72311 | − | 8.18067i | −0.737626 | − | 1.27761i | −0.953562 | − | 0.301198i | \(-0.902613\pi\) |
0.215936 | − | 0.976408i | \(-0.430720\pi\) | |||||||
\(42\) | 2.00000 | 0.308607 | ||||||||
\(43\) | 2.44622 | 0.373045 | 0.186523 | − | 0.982451i | \(-0.440278\pi\) | ||||
0.186523 | + | 0.982451i | \(0.440278\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | 0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | −3.22311 | + | 5.58259i | −0.451326 | + | 0.781719i | ||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 9.44622 | 1.29754 | 0.648769 | − | 0.760985i | \(-0.275284\pi\) | ||||
0.648769 | + | 0.760985i | \(0.275284\pi\) | |||||||
\(54\) | 2.50000 | − | 4.33013i | 0.340207 | − | 0.589256i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | − | 1.73205i | −0.133631 | − | 0.231455i | ||||
\(57\) | −4.22311 | + | 7.31464i | −0.559365 | + | 0.968848i | ||||
\(58\) | 6.00000 | 0.787839 | ||||||||
\(59\) | −0.446222 | −0.0580932 | −0.0290466 | − | 0.999578i | \(-0.509247\pi\) | ||||
−0.0290466 | + | 0.999578i | \(0.509247\pi\) | |||||||
\(60\) | 0.500000 | + | 0.866025i | 0.0645497 | + | 0.111803i | ||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | −7.44622 | −0.945671 | ||||||||
\(63\) | 2.00000 | + | 3.46410i | 0.251976 | + | 0.436436i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | − | 1.73205i | 0.124035 | − | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.276889 | − | 8.18067i | −0.0338274 | − | 0.999428i | ||||
\(68\) | 6.44622 | 0.781719 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | −4.72311 | − | 8.18067i | −0.560530 | − | 0.970867i | −0.997450 | − | 0.0713663i | \(-0.977264\pi\) |
0.436920 | − | 0.899500i | \(-0.356069\pi\) | |||||||
\(72\) | −2.00000 | −0.235702 | ||||||||
\(73\) | −0.776889 | + | 1.34561i | −0.0909280 | + | 0.157492i | −0.907902 | − | 0.419183i | \(-0.862317\pi\) |
0.816974 | + | 0.576675i | \(0.195650\pi\) | |||||||
\(74\) | −2.72311 | − | 4.71657i | −0.316555 | − | 0.548290i | ||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 8.44622 | 0.968848 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.00000 | − | 1.73205i | −0.113228 | − | 0.196116i | ||||
\(79\) | −4.00000 | − | 6.92820i | −0.450035 | − | 0.779484i | 0.548352 | − | 0.836247i | \(-0.315255\pi\) |
−0.998388 | + | 0.0567635i | \(0.981922\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.44622 | 1.04316 | ||||||||
\(83\) | −1.72311 | + | 2.98452i | −0.189136 | + | 0.327593i | −0.944962 | − | 0.327179i | \(-0.893902\pi\) |
0.755826 | + | 0.654772i | \(0.227235\pi\) | |||||||
\(84\) | −1.00000 | + | 1.73205i | −0.109109 | + | 0.188982i | ||||
\(85\) | 3.22311 | − | 5.58259i | 0.349595 | − | 0.605517i | ||||
\(86\) | −1.22311 | + | 2.11849i | −0.131891 | + | 0.228443i | ||||
\(87\) | −3.00000 | − | 5.19615i | −0.321634 | − | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.8924 | −1.68460 | −0.842298 | − | 0.539012i | \(-0.818798\pi\) | ||||
−0.842298 | + | 0.539012i | \(0.818798\pi\) | |||||||
\(90\) | −1.00000 | + | 1.73205i | −0.105409 | + | 0.182574i | ||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.72311 | + | 6.44862i | 0.386069 | + | 0.668690i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.22311 | − | 7.31464i | 0.433282 | − | 0.750467i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 2.22311 | − | 3.85054i | 0.225723 | − | 0.390963i | −0.730813 | − | 0.682577i | \(-0.760859\pi\) |
0.956536 | + | 0.291614i | \(0.0941923\pi\) | |||||||
\(98\) | 1.50000 | + | 2.59808i | 0.151523 | + | 0.262445i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −3.00000 | − | 5.19615i | −0.298511 | − | 0.517036i | 0.677284 | − | 0.735721i | \(-0.263157\pi\) |
−0.975796 | + | 0.218685i | \(0.929823\pi\) | |||||||
\(102\) | −3.22311 | − | 5.58259i | −0.319136 | − | 0.552759i | ||||
\(103\) | 2.00000 | + | 3.46410i | 0.197066 | + | 0.341328i | 0.947576 | − | 0.319531i | \(-0.103525\pi\) |
−0.750510 | + | 0.660859i | \(0.770192\pi\) | |||||||
\(104\) | −1.00000 | + | 1.73205i | −0.0980581 | + | 0.169842i | ||||
\(105\) | 1.00000 | + | 1.73205i | 0.0975900 | + | 0.169031i | ||||
\(106\) | −4.72311 | + | 8.18067i | −0.458749 | + | 0.794577i | ||||
\(107\) | −3.44622 | −0.333159 | −0.166579 | − | 0.986028i | \(-0.553272\pi\) | ||||
−0.166579 | + | 0.986028i | \(0.553272\pi\) | |||||||
\(108\) | 2.50000 | + | 4.33013i | 0.240563 | + | 0.416667i | ||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.72311 | + | 4.71657i | −0.258466 | + | 0.447677i | ||||
\(112\) | 2.00000 | 0.188982 | ||||||||
\(113\) | 9.22311 | + | 15.9749i | 0.867637 | + | 1.50279i | 0.864404 | + | 0.502797i | \(0.167696\pi\) |
0.00323284 | + | 0.999995i | \(0.498971\pi\) | |||||||
\(114\) | −4.22311 | − | 7.31464i | −0.395531 | − | 0.685079i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.00000 | + | 5.19615i | −0.278543 | + | 0.482451i | ||||
\(117\) | 2.00000 | − | 3.46410i | 0.184900 | − | 0.320256i | ||||
\(118\) | 0.223111 | − | 0.386440i | 0.0205390 | − | 0.0355746i | ||||
\(119\) | 12.8924 | 1.18185 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | −4.00000 | − | 6.92820i | −0.362143 | − | 0.627250i | ||||
\(123\) | −4.72311 | − | 8.18067i | −0.425869 | − | 0.737626i | ||||
\(124\) | 3.72311 | − | 6.44862i | 0.334345 | − | 0.579103i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −4.00000 | −0.356348 | ||||||||
\(127\) | 5.00000 | + | 8.66025i | 0.443678 | + | 0.768473i | 0.997959 | − | 0.0638564i | \(-0.0203400\pi\) |
−0.554281 | + | 0.832330i | \(0.687007\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.44622 | 0.215378 | ||||||||
\(130\) | 1.00000 | + | 1.73205i | 0.0877058 | + | 0.151911i | ||||
\(131\) | −18.8924 | −1.65064 | −0.825320 | − | 0.564665i | \(-0.809005\pi\) | ||||
−0.825320 | + | 0.564665i | \(0.809005\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.8924 | 1.46476 | ||||||||
\(134\) | 7.22311 | + | 3.85054i | 0.623982 | + | 0.332636i | ||||
\(135\) | 5.00000 | 0.430331 | ||||||||
\(136\) | −3.22311 | + | 5.58259i | −0.276379 | + | 0.478703i | ||||
\(137\) | 6.44622 | 0.550738 | 0.275369 | − | 0.961339i | \(-0.411200\pi\) | ||||
0.275369 | + | 0.961339i | \(0.411200\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.4462 | −1.90386 | −0.951932 | − | 0.306310i | \(-0.900906\pi\) | ||||
−0.951932 | + | 0.306310i | \(0.900906\pi\) | |||||||
\(140\) | 1.00000 | − | 1.73205i | 0.0845154 | − | 0.146385i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.44622 | 0.792709 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | − | 1.73205i | 0.0833333 | − | 0.144338i | ||||
\(145\) | 3.00000 | + | 5.19615i | 0.249136 | + | 0.431517i | ||||
\(146\) | −0.776889 | − | 1.34561i | −0.0642958 | − | 0.111364i | ||||
\(147\) | 1.50000 | − | 2.59808i | 0.123718 | − | 0.214286i | ||||
\(148\) | 5.44622 | 0.447677 | ||||||||
\(149\) | −12.0000 | −0.983078 | −0.491539 | − | 0.870855i | \(-0.663566\pi\) | ||||
−0.491539 | + | 0.870855i | \(0.663566\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | −2.27689 | + | 3.94369i | −0.185291 | + | 0.320933i | −0.943674 | − | 0.330876i | \(-0.892656\pi\) |
0.758384 | + | 0.651808i | \(0.225989\pi\) | |||||||
\(152\) | −4.22311 | + | 7.31464i | −0.342540 | + | 0.593296i | ||||
\(153\) | 6.44622 | − | 11.1652i | 0.521146 | − | 0.902652i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.72311 | − | 6.44862i | −0.299047 | − | 0.517965i | ||||
\(156\) | 2.00000 | 0.160128 | ||||||||
\(157\) | −7.00000 | + | 12.1244i | −0.558661 | + | 0.967629i | 0.438948 | + | 0.898513i | \(0.355351\pi\) |
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | 8.00000 | 0.636446 | ||||||||
\(159\) | 9.44622 | 0.749134 | ||||||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | 3.94622 | + | 6.83506i | 0.309092 | + | 0.535363i | 0.978164 | − | 0.207835i | \(-0.0666416\pi\) |
−0.669072 | + | 0.743198i | \(0.733308\pi\) | |||||||
\(164\) | −4.72311 | + | 8.18067i | −0.368813 | + | 0.638803i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.72311 | − | 2.98452i | −0.133739 | − | 0.231643i | ||||
\(167\) | 9.44622 | + | 16.3613i | 0.730971 | + | 1.26608i | 0.956469 | + | 0.291835i | \(0.0942657\pi\) |
−0.225498 | + | 0.974244i | \(0.572401\pi\) | |||||||
\(168\) | −1.00000 | − | 1.73205i | −0.0771517 | − | 0.133631i | ||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 3.22311 | + | 5.58259i | 0.247201 | + | 0.428165i | ||||
\(171\) | 8.44622 | − | 14.6293i | 0.645899 | − | 1.11873i | ||||
\(172\) | −1.22311 | − | 2.11849i | −0.0932613 | − | 0.161533i | ||||
\(173\) | 8.16933 | − | 14.1497i | 0.621103 | − | 1.07578i | −0.368178 | − | 0.929755i | \(-0.620018\pi\) |
0.989281 | − | 0.146026i | \(-0.0466484\pi\) | |||||||
\(174\) | 6.00000 | 0.454859 | ||||||||
\(175\) | −1.00000 | − | 1.73205i | −0.0755929 | − | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.446222 | −0.0335401 | ||||||||
\(178\) | 7.94622 | − | 13.7633i | 0.595595 | − | 1.03160i | ||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | −1.00000 | − | 1.73205i | −0.0745356 | − | 0.129099i | ||||
\(181\) | 11.4462 | + | 19.8254i | 0.850791 | + | 1.47361i | 0.880496 | + | 0.474054i | \(0.157210\pi\) |
−0.0297045 | + | 0.999559i | \(0.509457\pi\) | |||||||
\(182\) | −2.00000 | + | 3.46410i | −0.148250 | + | 0.256776i | ||||
\(183\) | −4.00000 | + | 6.92820i | −0.295689 | + | 0.512148i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.72311 | − | 4.71657i | 0.200207 | − | 0.346769i | ||||
\(186\) | −7.44622 | −0.545983 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.00000 | + | 8.66025i | 0.363696 | + | 0.629941i | ||||
\(190\) | 4.22311 | + | 7.31464i | 0.306377 | + | 0.530660i | ||||
\(191\) | −1.72311 | + | 2.98452i | −0.124680 | + | 0.215952i | −0.921608 | − | 0.388123i | \(-0.873124\pi\) |
0.796928 | + | 0.604074i | \(0.206457\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 20.8924 | 1.50387 | 0.751936 | − | 0.659237i | \(-0.229120\pi\) | ||||
0.751936 | + | 0.659237i | \(0.229120\pi\) | |||||||
\(194\) | 2.22311 | + | 3.85054i | 0.159610 | + | 0.276453i | ||||
\(195\) | 1.00000 | − | 1.73205i | 0.0716115 | − | 0.124035i | ||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 3.44622 | + | 5.96903i | 0.245533 | + | 0.425276i | 0.962281 | − | 0.272056i | \(-0.0877036\pi\) |
−0.716748 | + | 0.697332i | \(0.754370\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.72311 | + | 4.71657i | −0.193036 | + | 0.334349i | −0.946255 | − | 0.323422i | \(-0.895167\pi\) |
0.753219 | + | 0.657770i | \(0.228500\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −0.276889 | − | 8.18067i | −0.0195302 | − | 0.577020i | ||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | −6.00000 | + | 10.3923i | −0.421117 | + | 0.729397i | ||||
\(204\) | 6.44622 | 0.451326 | ||||||||
\(205\) | 4.72311 | + | 8.18067i | 0.329876 | + | 0.571363i | ||||
\(206\) | −4.00000 | −0.278693 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | − | 1.73205i | −0.0693375 | − | 0.120096i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.00000 | −0.138013 | ||||||||
\(211\) | 4.77689 | − | 8.27381i | 0.328855 | − | 0.569593i | −0.653430 | − | 0.756987i | \(-0.726671\pi\) |
0.982285 | + | 0.187394i | \(0.0600041\pi\) | |||||||
\(212\) | −4.72311 | − | 8.18067i | −0.324385 | − | 0.561851i | ||||
\(213\) | −4.72311 | − | 8.18067i | −0.323622 | − | 0.560530i | ||||
\(214\) | 1.72311 | − | 2.98452i | 0.117789 | − | 0.204017i | ||||
\(215\) | −2.44622 | −0.166831 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 7.44622 | − | 12.8972i | 0.505482 | − | 0.875521i | ||||
\(218\) | −7.00000 | + | 12.1244i | −0.474100 | + | 0.821165i | ||||
\(219\) | −0.776889 | + | 1.34561i | −0.0524973 | + | 0.0909280i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.44622 | − | 11.1652i | −0.433620 | − | 0.751052i | ||||
\(222\) | −2.72311 | − | 4.71657i | −0.182763 | − | 0.316555i | ||||
\(223\) | 2.00000 | 0.133930 | 0.0669650 | − | 0.997755i | \(-0.478668\pi\) | ||||
0.0669650 | + | 0.997755i | \(0.478668\pi\) | |||||||
\(224\) | −1.00000 | + | 1.73205i | −0.0668153 | + | 0.115728i | ||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | −18.4462 | −1.22702 | ||||||||
\(227\) | −4.50000 | − | 7.79423i | −0.298675 | − | 0.517321i | 0.677158 | − | 0.735838i | \(-0.263211\pi\) |
−0.975833 | + | 0.218517i | \(0.929878\pi\) | |||||||
\(228\) | 8.44622 | 0.559365 | ||||||||
\(229\) | −4.00000 | + | 6.92820i | −0.264327 | + | 0.457829i | −0.967387 | − | 0.253302i | \(-0.918483\pi\) |
0.703060 | + | 0.711131i | \(0.251817\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.00000 | − | 5.19615i | −0.196960 | − | 0.341144i | ||||
\(233\) | −9.66933 | − | 16.7478i | −0.633459 | − | 1.09718i | −0.986839 | − | 0.161704i | \(-0.948301\pi\) |
0.353380 | − | 0.935480i | \(-0.385032\pi\) | |||||||
\(234\) | 2.00000 | + | 3.46410i | 0.130744 | + | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.223111 | + | 0.386440i | 0.0145233 | + | 0.0251551i | ||||
\(237\) | −4.00000 | − | 6.92820i | −0.259828 | − | 0.450035i | ||||
\(238\) | −6.44622 | + | 11.1652i | −0.417847 | + | 0.723731i | ||||
\(239\) | 6.44622 | + | 11.1652i | 0.416971 | + | 0.722216i | 0.995633 | − | 0.0933519i | \(-0.0297582\pi\) |
−0.578662 | + | 0.815568i | \(0.696425\pi\) | |||||||
\(240\) | 0.500000 | − | 0.866025i | 0.0322749 | − | 0.0559017i | ||||
\(241\) | 17.4462 | 1.12381 | 0.561905 | − | 0.827202i | \(-0.310069\pi\) | ||||
0.561905 | + | 0.827202i | \(0.310069\pi\) | |||||||
\(242\) | 5.50000 | + | 9.52628i | 0.353553 | + | 0.612372i | ||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | −1.50000 | + | 2.59808i | −0.0958315 | + | 0.165985i | ||||
\(246\) | 9.44622 | 0.602269 | ||||||||
\(247\) | −8.44622 | − | 14.6293i | −0.537420 | − | 0.930839i | ||||
\(248\) | 3.72311 | + | 6.44862i | 0.236418 | + | 0.409488i | ||||
\(249\) | −1.72311 | + | 2.98452i | −0.109198 | + | 0.189136i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 2.77689 | − | 4.80971i | 0.175276 | − | 0.303586i | −0.764981 | − | 0.644053i | \(-0.777252\pi\) |
0.940257 | + | 0.340467i | \(0.110585\pi\) | |||||||
\(252\) | 2.00000 | − | 3.46410i | 0.125988 | − | 0.218218i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −10.0000 | −0.627456 | ||||||||
\(255\) | 3.22311 | − | 5.58259i | 0.201839 | − | 0.349595i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −9.00000 | − | 15.5885i | −0.561405 | − | 0.972381i | −0.997374 | − | 0.0724199i | \(-0.976928\pi\) |
0.435970 | − | 0.899961i | \(-0.356405\pi\) | |||||||
\(258\) | −1.22311 | + | 2.11849i | −0.0761476 | + | 0.131891i | ||||
\(259\) | 10.8924 | 0.676824 | ||||||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | 6.00000 | + | 10.3923i | 0.371391 | + | 0.643268i | ||||
\(262\) | 9.44622 | − | 16.3613i | 0.583590 | − | 1.01081i | ||||
\(263\) | −6.89244 | −0.425006 | −0.212503 | − | 0.977160i | \(-0.568162\pi\) | ||||
−0.212503 | + | 0.977160i | \(0.568162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.44622 | −0.580277 | ||||||||
\(266\) | −8.44622 | + | 14.6293i | −0.517871 | + | 0.896979i | ||||
\(267\) | −15.8924 | −0.972602 | ||||||||
\(268\) | −6.94622 | + | 4.33013i | −0.424308 | + | 0.264505i | ||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | −2.50000 | + | 4.33013i | −0.152145 | + | 0.263523i | ||||
\(271\) | −25.4462 | −1.54575 | −0.772874 | − | 0.634560i | \(-0.781182\pi\) | ||||
−0.772874 | + | 0.634560i | \(0.781182\pi\) | |||||||
\(272\) | −3.22311 | − | 5.58259i | −0.195430 | − | 0.338494i | ||||
\(273\) | 4.00000 | 0.242091 | ||||||||
\(274\) | −3.22311 | + | 5.58259i | −0.194715 | + | 0.337257i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.55378 | 0.273610 | 0.136805 | − | 0.990598i | \(-0.456317\pi\) | ||||
0.136805 | + | 0.990598i | \(0.456317\pi\) | |||||||
\(278\) | 11.2231 | − | 19.4390i | 0.673117 | − | 1.16587i | ||||
\(279\) | −7.44622 | − | 12.8972i | −0.445794 | − | 0.772137i | ||||
\(280\) | 1.00000 | + | 1.73205i | 0.0597614 | + | 0.103510i | ||||
\(281\) | −4.94622 | + | 8.56711i | −0.295067 | + | 0.511071i | −0.975000 | − | 0.222203i | \(-0.928675\pi\) |
0.679934 | + | 0.733274i | \(0.262009\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.3387 | −1.38734 | −0.693670 | − | 0.720293i | \(-0.744007\pi\) | ||||
−0.693670 | + | 0.720293i | \(0.744007\pi\) | |||||||
\(284\) | −4.72311 | + | 8.18067i | −0.280265 | + | 0.485433i | ||||
\(285\) | 4.22311 | − | 7.31464i | 0.250156 | − | 0.433282i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.44622 | + | 16.3613i | −0.557593 | + | 0.965779i | ||||
\(288\) | 1.00000 | + | 1.73205i | 0.0589256 | + | 0.102062i | ||||
\(289\) | −12.2769 | − | 21.2642i | −0.722170 | − | 1.25084i | ||||
\(290\) | −6.00000 | −0.352332 | ||||||||
\(291\) | 2.22311 | − | 3.85054i | 0.130321 | − | 0.225723i | ||||
\(292\) | 1.55378 | 0.0909280 | ||||||||
\(293\) | 2.55378 | 0.149193 | 0.0745967 | − | 0.997214i | \(-0.476233\pi\) | ||||
0.0745967 | + | 0.997214i | \(0.476233\pi\) | |||||||
\(294\) | 1.50000 | + | 2.59808i | 0.0874818 | + | 0.151523i | ||||
\(295\) | 0.446222 | 0.0259800 | ||||||||
\(296\) | −2.72311 | + | 4.71657i | −0.158278 | + | 0.274145i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | − | 10.3923i | 0.347571 | − | 0.602010i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.500000 | − | 0.866025i | −0.0288675 | − | 0.0500000i | ||||
\(301\) | −2.44622 | − | 4.23698i | −0.140998 | − | 0.244216i | ||||
\(302\) | −2.27689 | − | 3.94369i | −0.131020 | − | 0.226934i | ||||
\(303\) | −3.00000 | − | 5.19615i | −0.172345 | − | 0.298511i | ||||
\(304\) | −4.22311 | − | 7.31464i | −0.242212 | − | 0.419524i | ||||
\(305\) | 4.00000 | − | 6.92820i | 0.229039 | − | 0.396708i | ||||
\(306\) | 6.44622 | + | 11.1652i | 0.368506 | + | 0.638271i | ||||
\(307\) | −8.94622 | + | 15.4953i | −0.510588 | + | 0.884364i | 0.489337 | + | 0.872095i | \(0.337239\pi\) |
−0.999925 | + | 0.0122693i | \(0.996094\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.00000 | + | 3.46410i | 0.113776 | + | 0.197066i | ||||
\(310\) | 7.44622 | 0.422917 | ||||||||
\(311\) | −22.3387 | −1.26671 | −0.633355 | − | 0.773862i | \(-0.718323\pi\) | ||||
−0.633355 | + | 0.773862i | \(0.718323\pi\) | |||||||
\(312\) | −1.00000 | + | 1.73205i | −0.0566139 | + | 0.0980581i | ||||
\(313\) | 19.5538 | 1.10524 | 0.552622 | − | 0.833432i | \(-0.313627\pi\) | ||||
0.552622 | + | 0.833432i | \(0.313627\pi\) | |||||||
\(314\) | −7.00000 | − | 12.1244i | −0.395033 | − | 0.684217i | ||||
\(315\) | −2.00000 | − | 3.46410i | −0.112687 | − | 0.195180i | ||||
\(316\) | −4.00000 | + | 6.92820i | −0.225018 | + | 0.389742i | ||||
\(317\) | −16.7231 | + | 28.9653i | −0.939263 | + | 1.62685i | −0.172415 | + | 0.985024i | \(0.555157\pi\) |
−0.766849 | + | 0.641828i | \(0.778176\pi\) | |||||||
\(318\) | −4.72311 | + | 8.18067i | −0.264859 | + | 0.458749i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −3.44622 | −0.192349 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.2231 | − | 47.1518i | −1.51473 | − | 2.62360i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −1.00000 | + | 1.73205i | −0.0554700 | + | 0.0960769i | ||||
\(326\) | −7.89244 | −0.437122 | ||||||||
\(327\) | 14.0000 | 0.774202 | ||||||||
\(328\) | −4.72311 | − | 8.18067i | −0.260790 | − | 0.451702i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.2231 | − | 17.7069i | −0.561913 | − | 0.973262i | −0.997330 | − | 0.0730328i | \(-0.976732\pi\) |
0.435417 | − | 0.900229i | \(-0.356601\pi\) | |||||||
\(332\) | 3.44622 | 0.189136 | ||||||||
\(333\) | 5.44622 | − | 9.43313i | 0.298451 | − | 0.516933i | ||||
\(334\) | −18.8924 | −1.03375 | ||||||||
\(335\) | 0.276889 | + | 8.18067i | 0.0151281 | + | 0.446958i | ||||
\(336\) | 2.00000 | 0.109109 | ||||||||
\(337\) | 2.44622 | − | 4.23698i | 0.133254 | − | 0.230803i | −0.791675 | − | 0.610942i | \(-0.790791\pi\) |
0.924929 | + | 0.380139i | \(0.124124\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | 9.22311 | + | 15.9749i | 0.500931 | + | 0.867637i | ||||
\(340\) | −6.44622 | −0.349595 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 8.44622 | + | 14.6293i | 0.456719 | + | 0.791061i | ||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 2.44622 | 0.131891 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.16933 | + | 14.1497i | 0.439186 | + | 0.760693i | ||||
\(347\) | −2.77689 | − | 4.80971i | −0.149071 | − | 0.258199i | 0.781813 | − | 0.623513i | \(-0.214295\pi\) |
−0.930884 | + | 0.365314i | \(0.880962\pi\) | |||||||
\(348\) | −3.00000 | + | 5.19615i | −0.160817 | + | 0.278543i | ||||
\(349\) | 8.00000 | 0.428230 | 0.214115 | − | 0.976808i | \(-0.431313\pi\) | ||||
0.214115 | + | 0.976808i | \(0.431313\pi\) | |||||||
\(350\) | 2.00000 | 0.106904 | ||||||||
\(351\) | 5.00000 | − | 8.66025i | 0.266880 | − | 0.462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.44622 | + | 11.1652i | −0.343098 | + | 0.594263i | −0.985006 | − | 0.172518i | \(-0.944810\pi\) |
0.641909 | + | 0.766781i | \(0.278143\pi\) | |||||||
\(354\) | 0.223111 | − | 0.386440i | 0.0118582 | − | 0.0205390i | ||||
\(355\) | 4.72311 | + | 8.18067i | 0.250677 | + | 0.434185i | ||||
\(356\) | 7.94622 | + | 13.7633i | 0.421149 | + | 0.729451i | ||||
\(357\) | 12.8924 | 0.682340 | ||||||||
\(358\) | −6.00000 | + | 10.3923i | −0.317110 | + | 0.549250i | ||||
\(359\) | −28.3387 | −1.49566 | −0.747829 | − | 0.663892i | \(-0.768904\pi\) | ||||
−0.747829 | + | 0.663892i | \(0.768904\pi\) | |||||||
\(360\) | 2.00000 | 0.105409 | ||||||||
\(361\) | −26.1693 | − | 45.3266i | −1.37733 | − | 2.38561i | ||||
\(362\) | −22.8924 | −1.20320 | ||||||||
\(363\) | 5.50000 | − | 9.52628i | 0.288675 | − | 0.500000i | ||||
\(364\) | −2.00000 | − | 3.46410i | −0.104828 | − | 0.181568i | ||||
\(365\) | 0.776889 | − | 1.34561i | 0.0406642 | − | 0.0704325i | ||||
\(366\) | −4.00000 | − | 6.92820i | −0.209083 | − | 0.362143i | ||||
\(367\) | 17.8924 | + | 30.9906i | 0.933978 | + | 1.61770i | 0.776446 | + | 0.630183i | \(0.217020\pi\) |
0.157532 | + | 0.987514i | \(0.449646\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.44622 | + | 16.3613i | 0.491751 | + | 0.851737i | ||||
\(370\) | 2.72311 | + | 4.71657i | 0.141568 | + | 0.245203i | ||||
\(371\) | −9.44622 | − | 16.3613i | −0.490423 | − | 0.849438i | ||||
\(372\) | 3.72311 | − | 6.44862i | 0.193034 | − | 0.334345i | ||||
\(373\) | 12.7231 | + | 22.0371i | 0.658778 | + | 1.14104i | 0.980932 | + | 0.194349i | \(0.0622596\pi\) |
−0.322155 | + | 0.946687i | \(0.604407\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | −10.0000 | −0.514344 | ||||||||
\(379\) | −16.8924 | + | 29.2586i | −0.867707 | + | 1.50291i | −0.00337217 | + | 0.999994i | \(0.501073\pi\) |
−0.864334 | + | 0.502918i | \(0.832260\pi\) | |||||||
\(380\) | −8.44622 | −0.433282 | ||||||||
\(381\) | 5.00000 | + | 8.66025i | 0.256158 | + | 0.443678i | ||||
\(382\) | −1.72311 | − | 2.98452i | −0.0881620 | − | 0.152701i | ||||
\(383\) | 3.00000 | − | 5.19615i | 0.153293 | − | 0.265511i | −0.779143 | − | 0.626846i | \(-0.784346\pi\) |
0.932436 | + | 0.361335i | \(0.117679\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.4462 | + | 18.0934i | −0.531699 | + | 0.920929i | ||||
\(387\) | −4.89244 | −0.248697 | ||||||||
\(388\) | −4.44622 | −0.225723 | ||||||||
\(389\) | 9.44622 | − | 16.3613i | 0.478942 | − | 0.829553i | −0.520766 | − | 0.853699i | \(-0.674354\pi\) |
0.999708 | + | 0.0241468i | \(0.00768691\pi\) | |||||||
\(390\) | 1.00000 | + | 1.73205i | 0.0506370 | + | 0.0877058i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.50000 | − | 2.59808i | 0.0757614 | − | 0.131223i | ||||
\(393\) | −18.8924 | −0.952998 | ||||||||
\(394\) | −6.89244 | −0.347236 | ||||||||
\(395\) | 4.00000 | + | 6.92820i | 0.201262 | + | 0.348596i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.33867 | 0.318129 | 0.159064 | − | 0.987268i | \(-0.449152\pi\) | ||||
0.159064 | + | 0.987268i | \(0.449152\pi\) | |||||||
\(398\) | −2.72311 | − | 4.71657i | −0.136497 | − | 0.236420i | ||||
\(399\) | 16.8924 | 0.845680 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 18.0000 | 0.898877 | 0.449439 | − | 0.893311i | \(-0.351624\pi\) | ||||
0.449439 | + | 0.893311i | \(0.351624\pi\) | |||||||
\(402\) | 7.22311 | + | 3.85054i | 0.360256 | + | 0.192048i | ||||
\(403\) | −14.8924 | −0.741845 | ||||||||
\(404\) | −3.00000 | + | 5.19615i | −0.149256 | + | 0.258518i | ||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −6.00000 | − | 10.3923i | −0.297775 | − | 0.515761i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −3.22311 | + | 5.58259i | −0.159568 | + | 0.276379i | ||||
\(409\) | 0.723111 | + | 1.25246i | 0.0357555 | + | 0.0619304i | 0.883349 | − | 0.468715i | \(-0.155283\pi\) |
−0.847594 | + | 0.530645i | \(0.821950\pi\) | |||||||
\(410\) | −9.44622 | −0.466516 | ||||||||
\(411\) | 6.44622 | 0.317969 | ||||||||
\(412\) | 2.00000 | − | 3.46410i | 0.0985329 | − | 0.170664i | ||||
\(413\) | 0.446222 | + | 0.772879i | 0.0219571 | + | 0.0380309i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.72311 | − | 2.98452i | 0.0845842 | − | 0.146504i | ||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | −22.4462 | −1.09920 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.77689 | + | 4.80971i | −0.135660 | + | 0.234970i | −0.925849 | − | 0.377893i | \(-0.876649\pi\) |
0.790189 | + | 0.612863i | \(0.209982\pi\) | |||||||
\(420\) | 1.00000 | − | 1.73205i | 0.0487950 | − | 0.0845154i | ||||
\(421\) | −0.553778 | + | 0.959172i | −0.0269895 | + | 0.0467472i | −0.879205 | − | 0.476444i | \(-0.841925\pi\) |
0.852215 | + | 0.523191i | \(0.175259\pi\) | |||||||
\(422\) | 4.77689 | + | 8.27381i | 0.232535 | + | 0.402763i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.44622 | 0.458749 | ||||||||
\(425\) | −3.22311 | + | 5.58259i | −0.156344 | + | 0.270795i | ||||
\(426\) | 9.44622 | 0.457671 | ||||||||
\(427\) | 16.0000 | 0.774294 | ||||||||
\(428\) | 1.72311 | + | 2.98452i | 0.0832897 | + | 0.144262i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.22311 | − | 2.11849i | 0.0589836 | − | 0.102163i | ||||
\(431\) | −8.16933 | − | 14.1497i | −0.393503 | − | 0.681567i | 0.599406 | − | 0.800445i | \(-0.295404\pi\) |
−0.992909 | + | 0.118878i | \(0.962070\pi\) | |||||||
\(432\) | 2.50000 | − | 4.33013i | 0.120281 | − | 0.208333i | ||||
\(433\) | −10.6693 | − | 18.4798i | −0.512735 | − | 0.888084i | −0.999891 | − | 0.0147686i | \(-0.995299\pi\) |
0.487156 | − | 0.873315i | \(-0.338034\pi\) | |||||||
\(434\) | 7.44622 | + | 12.8972i | 0.357430 | + | 0.619087i | ||||
\(435\) | 3.00000 | + | 5.19615i | 0.143839 | + | 0.249136i | ||||
\(436\) | −7.00000 | − | 12.1244i | −0.335239 | − | 0.580651i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.776889 | − | 1.34561i | −0.0371212 | − | 0.0642958i | ||||
\(439\) | 15.7231 | − | 27.2332i | 0.750423 | − | 1.29977i | −0.197195 | − | 0.980364i | \(-0.563183\pi\) |
0.947618 | − | 0.319407i | \(-0.103484\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | + | 5.19615i | −0.142857 | + | 0.247436i | ||||
\(442\) | 12.8924 | 0.613231 | ||||||||
\(443\) | 10.9462 | + | 18.9594i | 0.520071 | + | 0.900789i | 0.999728 | + | 0.0233328i | \(0.00742775\pi\) |
−0.479657 | + | 0.877456i | \(0.659239\pi\) | |||||||
\(444\) | 5.44622 | 0.258466 | ||||||||
\(445\) | 15.8924 | 0.753374 | ||||||||
\(446\) | −1.00000 | + | 1.73205i | −0.0473514 | + | 0.0820150i | ||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | −1.00000 | − | 1.73205i | −0.0472456 | − | 0.0818317i | ||||
\(449\) | −8.16933 | − | 14.1497i | −0.385535 | − | 0.667766i | 0.606309 | − | 0.795229i | \(-0.292650\pi\) |
−0.991843 | + | 0.127464i | \(0.959316\pi\) | |||||||
\(450\) | 1.00000 | − | 1.73205i | 0.0471405 | − | 0.0816497i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.22311 | − | 15.9749i | 0.433819 | − | 0.751396i | ||||
\(453\) | −2.27689 | + | 3.94369i | −0.106978 | + | 0.185291i | ||||
\(454\) | 9.00000 | 0.422391 | ||||||||
\(455\) | −4.00000 | −0.187523 | ||||||||
\(456\) | −4.22311 | + | 7.31464i | −0.197765 | + | 0.342540i | ||||
\(457\) | −13.2231 | − | 22.9031i | −0.618551 | − | 1.07136i | −0.989750 | − | 0.142809i | \(-0.954387\pi\) |
0.371199 | − | 0.928553i | \(-0.378947\pi\) | |||||||
\(458\) | −4.00000 | − | 6.92820i | −0.186908 | − | 0.323734i | ||||
\(459\) | 16.1156 | − | 27.9130i | 0.752210 | − | 1.30287i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.8924 | 1.71825 | 0.859126 | − | 0.511764i | \(-0.171008\pi\) | ||||
0.859126 | + | 0.511764i | \(0.171008\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8924 | + | 24.0624i | −0.645637 | + | 1.11828i | 0.338517 | + | 0.940960i | \(0.390075\pi\) |
−0.984154 | + | 0.177315i | \(0.943259\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | −3.72311 | − | 6.44862i | −0.172655 | − | 0.299047i | ||||
\(466\) | 19.3387 | 0.895846 | ||||||||
\(467\) | 1.72311 | − | 2.98452i | 0.0797361 | − | 0.138107i | −0.823400 | − | 0.567461i | \(-0.807926\pi\) |
0.903136 | + | 0.429355i | \(0.141259\pi\) | |||||||
\(468\) | −4.00000 | −0.184900 | ||||||||
\(469\) | −13.8924 | + | 8.66025i | −0.641493 | + | 0.399893i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.00000 | + | 12.1244i | −0.322543 | + | 0.558661i | ||||
\(472\) | −0.446222 | −0.0205390 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 8.00000 | 0.367452 | ||||||||
\(475\) | −4.22311 | + | 7.31464i | −0.193770 | + | 0.335619i | ||||
\(476\) | −6.44622 | − | 11.1652i | −0.295462 | − | 0.511755i | ||||
\(477\) | −18.8924 | −0.865026 | ||||||||
\(478\) | −12.8924 | −0.589687 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0.500000 | + | 0.866025i | 0.0228218 | + | 0.0395285i | ||||
\(481\) | −5.44622 | − | 9.43313i | −0.248326 | − | 0.430114i | ||||
\(482\) | −8.72311 | + | 15.1089i | −0.397327 | + | 0.688190i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | −2.22311 | + | 3.85054i | −0.100946 | + | 0.174844i | ||||
\(486\) | −8.00000 | + | 13.8564i | −0.362887 | + | 0.628539i | ||||
\(487\) | 8.00000 | − | 13.8564i | 0.362515 | − | 0.627894i | −0.625859 | − | 0.779936i | \(-0.715252\pi\) |
0.988374 | + | 0.152042i | \(0.0485850\pi\) | |||||||
\(488\) | −4.00000 | + | 6.92820i | −0.181071 | + | 0.313625i | ||||
\(489\) | 3.94622 | + | 6.83506i | 0.178454 | + | 0.309092i | ||||
\(490\) | −1.50000 | − | 2.59808i | −0.0677631 | − | 0.117369i | ||||
\(491\) | 37.3387 | 1.68507 | 0.842535 | − | 0.538641i | \(-0.181062\pi\) | ||||
0.842535 | + | 0.538641i | \(0.181062\pi\) | |||||||
\(492\) | −4.72311 | + | 8.18067i | −0.212934 | + | 0.368813i | ||||
\(493\) | 38.6773 | 1.74194 | ||||||||
\(494\) | 16.8924 | 0.760027 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.44622 | −0.334345 | ||||||||
\(497\) | −9.44622 | + | 16.3613i | −0.423721 | + | 0.733906i | ||||
\(498\) | −1.72311 | − | 2.98452i | −0.0772145 | − | 0.133739i | ||||
\(499\) | −13.2231 | + | 22.9031i | −0.591948 | + | 1.02528i | 0.402022 | + | 0.915630i | \(0.368307\pi\) |
−0.993970 | + | 0.109654i | \(0.965026\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 9.44622 | + | 16.3613i | 0.422026 | + | 0.730971i | ||||
\(502\) | 2.77689 | + | 4.80971i | 0.123939 | + | 0.214668i | ||||
\(503\) | −12.4462 | − | 21.5575i | −0.554950 | − | 0.961201i | −0.997907 | − | 0.0646585i | \(-0.979404\pi\) |
0.442958 | − | 0.896542i | \(-0.353929\pi\) | |||||||
\(504\) | 2.00000 | + | 3.46410i | 0.0890871 | + | 0.154303i | ||||
\(505\) | 3.00000 | + | 5.19615i | 0.133498 | + | 0.231226i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.50000 | + | 7.79423i | 0.199852 | + | 0.346154i | ||||
\(508\) | 5.00000 | − | 8.66025i | 0.221839 | − | 0.384237i | ||||
\(509\) | 18.0000 | 0.797836 | 0.398918 | − | 0.916987i | \(-0.369386\pi\) | ||||
0.398918 | + | 0.916987i | \(0.369386\pi\) | |||||||
\(510\) | 3.22311 | + | 5.58259i | 0.142722 | + | 0.247201i | ||||
\(511\) | 3.10756 | 0.137470 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 21.1156 | − | 36.5732i | 0.932275 | − | 1.61475i | ||||
\(514\) | 18.0000 | 0.793946 | ||||||||
\(515\) | −2.00000 | − | 3.46410i | −0.0881305 | − | 0.152647i | ||||
\(516\) | −1.22311 | − | 2.11849i | −0.0538445 | − | 0.0932613i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −5.44622 | + | 9.43313i | −0.239293 | + | 0.414468i | ||||
\(519\) | 8.16933 | − | 14.1497i | 0.358594 | − | 0.621103i | ||||
\(520\) | 1.00000 | − | 1.73205i | 0.0438529 | − | 0.0759555i | ||||
\(521\) | −13.3387 | −0.584378 | −0.292189 | − | 0.956361i | \(-0.594384\pi\) | ||||
−0.292189 | + | 0.956361i | \(0.594384\pi\) | |||||||
\(522\) | −12.0000 | −0.525226 | ||||||||
\(523\) | −9.39244 | + | 16.2682i | −0.410703 | + | 0.711358i | −0.994967 | − | 0.100205i | \(-0.968050\pi\) |
0.584264 | + | 0.811564i | \(0.301383\pi\) | |||||||
\(524\) | 9.44622 | + | 16.3613i | 0.412660 | + | 0.714748i | ||||
\(525\) | −1.00000 | − | 1.73205i | −0.0436436 | − | 0.0755929i | ||||
\(526\) | 3.44622 | − | 5.96903i | 0.150262 | − | 0.260262i | ||||
\(527\) | −48.0000 | −2.09091 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 4.72311 | − | 8.18067i | 0.205159 | − | 0.355346i | ||||
\(531\) | 0.892444 | 0.0387288 | ||||||||
\(532\) | −8.44622 | − | 14.6293i | −0.366190 | − | 0.634260i | ||||
\(533\) | 18.8924 | 0.818323 | ||||||||
\(534\) | 7.94622 | − | 13.7633i | 0.343867 | − | 0.595595i | ||||
\(535\) | 3.44622 | 0.148993 | ||||||||
\(536\) | −0.276889 | − | 8.18067i | −0.0119598 | − | 0.353351i | ||||
\(537\) | 12.0000 | 0.517838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.50000 | − | 4.33013i | −0.107583 | − | 0.186339i | ||||
\(541\) | 40.6773 | 1.74886 | 0.874428 | − | 0.485156i | \(-0.161237\pi\) | ||||
0.874428 | + | 0.485156i | \(0.161237\pi\) | |||||||
\(542\) | 12.7231 | − | 22.0371i | 0.546504 | − | 0.946573i | ||||
\(543\) | 11.4462 | + | 19.8254i | 0.491204 | + | 0.850791i | ||||
\(544\) | 6.44622 | 0.276379 | ||||||||
\(545\) | −14.0000 | −0.599694 | ||||||||
\(546\) | −2.00000 | + | 3.46410i | −0.0855921 | + | 0.148250i | ||||
\(547\) | 9.72311 | + | 16.8409i | 0.415730 | + | 0.720066i | 0.995505 | − | 0.0947111i | \(-0.0301927\pi\) |
−0.579775 | + | 0.814777i | \(0.696859\pi\) | |||||||
\(548\) | −3.22311 | − | 5.58259i | −0.137684 | − | 0.238477i | ||||
\(549\) | 8.00000 | − | 13.8564i | 0.341432 | − | 0.591377i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 50.6773 | 2.15893 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | + | 13.8564i | −0.340195 | + | 0.589234i | ||||
\(554\) | −2.27689 | + | 3.94369i | −0.0967357 | + | 0.167551i | ||||
\(555\) | 2.72311 | − | 4.71657i | 0.115590 | − | 0.200207i | ||||
\(556\) | 11.2231 | + | 19.4390i | 0.475966 | + | 0.824397i | ||||
\(557\) | 11.1693 | + | 19.3459i | 0.473260 | + | 0.819710i | 0.999532 | − | 0.0306064i | \(-0.00974384\pi\) |
−0.526272 | + | 0.850316i | \(0.676411\pi\) | |||||||
\(558\) | 14.8924 | 0.630447 | ||||||||
\(559\) | −2.44622 | + | 4.23698i | −0.103464 | + | 0.179205i | ||||
\(560\) | −2.00000 | −0.0845154 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.94622 | − | 8.56711i | −0.208644 | − | 0.361382i | ||||
\(563\) | −27.8924 | −1.17553 | −0.587763 | − | 0.809033i | \(-0.699991\pi\) | ||||
−0.587763 | + | 0.809033i | \(0.699991\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.22311 | − | 15.9749i | −0.388019 | − | 0.672069i | ||||
\(566\) | 11.6693 | − | 20.2119i | 0.490499 | − | 0.849569i | ||||
\(567\) | −1.00000 | − | 1.73205i | −0.0419961 | − | 0.0727393i | ||||
\(568\) | −4.72311 | − | 8.18067i | −0.198177 | − | 0.343253i | ||||
\(569\) | 7.50000 | + | 12.9904i | 0.314416 | + | 0.544585i | 0.979313 | − | 0.202350i | \(-0.0648579\pi\) |
−0.664897 | + | 0.746935i | \(0.731525\pi\) | |||||||
\(570\) | 4.22311 | + | 7.31464i | 0.176887 | + | 0.306377i | ||||
\(571\) | 13.7769 | + | 23.8623i | 0.576545 | + | 0.998605i | 0.995872 | + | 0.0907697i | \(0.0289327\pi\) |
−0.419327 | + | 0.907835i | \(0.637734\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.72311 | + | 2.98452i | −0.0719840 | + | 0.124680i | ||||
\(574\) | −9.44622 | − | 16.3613i | −0.394278 | − | 0.682909i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.00000 | −0.0833333 | ||||||||
\(577\) | 5.22311 | + | 9.04669i | 0.217441 | + | 0.376619i | 0.954025 | − | 0.299727i | \(-0.0968957\pi\) |
−0.736584 | + | 0.676346i | \(0.763562\pi\) | |||||||
\(578\) | 24.5538 | 1.02130 | ||||||||
\(579\) | 20.8924 | 0.868260 | ||||||||
\(580\) | 3.00000 | − | 5.19615i | 0.124568 | − | 0.215758i | ||||
\(581\) | 6.89244 | 0.285947 | ||||||||
\(582\) | 2.22311 | + | 3.85054i | 0.0921509 | + | 0.159610i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.776889 | + | 1.34561i | −0.0321479 | + | 0.0556818i | ||||
\(585\) | −2.00000 | + | 3.46410i | −0.0826898 | + | 0.143223i | ||||
\(586\) | −1.27689 | + | 2.21164i | −0.0527478 | + | 0.0913619i | ||||
\(587\) | 4.50000 | − | 7.79423i | 0.185735 | − | 0.321702i | −0.758089 | − | 0.652151i | \(-0.773867\pi\) |
0.943824 | + | 0.330449i | \(0.107200\pi\) | |||||||
\(588\) | −3.00000 | −0.123718 | ||||||||
\(589\) | −62.8924 | −2.59144 | ||||||||
\(590\) | −0.223111 | + | 0.386440i | −0.00918533 | + | 0.0159095i | ||||
\(591\) | 3.44622 | + | 5.96903i | 0.141759 | + | 0.245533i | ||||
\(592\) | −2.72311 | − | 4.71657i | −0.111919 | − | 0.193850i | ||||
\(593\) | −21.6693 | + | 37.5324i | −0.889853 | + | 1.54127i | −0.0498044 | + | 0.998759i | \(0.515860\pi\) |
−0.840048 | + | 0.542511i | \(0.817474\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.8924 | −0.528539 | ||||||||
\(596\) | 6.00000 | + | 10.3923i | 0.245770 | + | 0.425685i | ||||
\(597\) | −2.72311 | + | 4.71657i | −0.111450 | + | 0.193036i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.446222 | − | 0.772879i | −0.0182321 | − | 0.0315790i | 0.856765 | − | 0.515706i | \(-0.172470\pi\) |
−0.874998 | + | 0.484127i | \(0.839137\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 2.22311 | − | 3.85054i | 0.0906826 | − | 0.157067i | −0.817116 | − | 0.576473i | \(-0.804428\pi\) |
0.907799 | + | 0.419406i | \(0.137762\pi\) | |||||||
\(602\) | 4.89244 | 0.199401 | ||||||||
\(603\) | 0.553778 | + | 16.3613i | 0.0225516 | + | 0.666285i | ||||
\(604\) | 4.55378 | 0.185291 | ||||||||
\(605\) | −5.50000 | + | 9.52628i | −0.223607 | + | 0.387298i | ||||
\(606\) | 6.00000 | 0.243733 | ||||||||
\(607\) | −0.553778 | − | 0.959172i | −0.0224772 | − | 0.0389316i | 0.854568 | − | 0.519339i | \(-0.173822\pi\) |
−0.877045 | + | 0.480408i | \(0.840489\pi\) | |||||||
\(608\) | 8.44622 | 0.342540 | ||||||||
\(609\) | −6.00000 | + | 10.3923i | −0.243132 | + | 0.421117i | ||||
\(610\) | 4.00000 | + | 6.92820i | 0.161955 | + | 0.280515i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −12.8924 | −0.521146 | ||||||||
\(613\) | −2.72311 | + | 4.71657i | −0.109985 | + | 0.190500i | −0.915764 | − | 0.401716i | \(-0.868414\pi\) |
0.805779 | + | 0.592217i | \(0.201747\pi\) | |||||||
\(614\) | −8.94622 | − | 15.4953i | −0.361040 | − | 0.625340i | ||||
\(615\) | 4.72311 | + | 8.18067i | 0.190454 | + | 0.329876i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | −4.00000 | −0.160904 | ||||||||
\(619\) | 14.6693 | − | 25.4080i | 0.589610 | − | 1.02123i | −0.404673 | − | 0.914461i | \(-0.632615\pi\) |
0.994283 | − | 0.106774i | \(-0.0340520\pi\) | |||||||
\(620\) | −3.72311 | + | 6.44862i | −0.149524 | + | 0.258983i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.1693 | − | 19.3459i | 0.447849 | − | 0.775698i | ||||
\(623\) | 15.8924 | + | 27.5265i | 0.636717 | + | 1.10283i | ||||
\(624\) | −1.00000 | − | 1.73205i | −0.0400320 | − | 0.0693375i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.77689 | + | 16.9341i | −0.390763 | + | 0.676821i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | −17.5538 | − | 30.4040i | −0.699915 | − | 1.21229i | ||||
\(630\) | 4.00000 | 0.159364 | ||||||||
\(631\) | 1.55378 | − | 2.69122i | 0.0618549 | − | 0.107136i | −0.833440 | − | 0.552611i | \(-0.813632\pi\) |
0.895295 | + | 0.445475i | \(0.146965\pi\) | |||||||
\(632\) | −4.00000 | − | 6.92820i | −0.159111 | − | 0.275589i | ||||
\(633\) | 4.77689 | − | 8.27381i | 0.189864 | − | 0.328855i | ||||
\(634\) | −16.7231 | − | 28.9653i | −0.664160 | − | 1.15036i | ||||
\(635\) | −5.00000 | − | 8.66025i | −0.198419 | − | 0.343672i | ||||
\(636\) | −4.72311 | − | 8.18067i | −0.187284 | − | 0.324385i | ||||
\(637\) | 3.00000 | + | 5.19615i | 0.118864 | + | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.44622 | + | 16.3613i | 0.373687 | + | 0.647244i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −19.1156 | − | 33.1091i | −0.755019 | − | 1.30773i | −0.945365 | − | 0.326014i | \(-0.894294\pi\) |
0.190346 | − | 0.981717i | \(-0.439039\pi\) | |||||||
\(642\) | 1.72311 | − | 2.98452i | 0.0680058 | − | 0.117789i | ||||
\(643\) | −44.7849 | −1.76614 | −0.883072 | − | 0.469238i | \(-0.844529\pi\) | ||||
−0.883072 | + | 0.469238i | \(0.844529\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.44622 | −0.0963199 | ||||||||
\(646\) | 54.4462 | 2.14216 | ||||||||
\(647\) | −3.00000 | + | 5.19615i | −0.117942 | + | 0.204282i | −0.918952 | − | 0.394369i | \(-0.870963\pi\) |
0.801010 | + | 0.598651i | \(0.204296\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.00000 | − | 1.73205i | −0.0392232 | − | 0.0679366i | ||||
\(651\) | 7.44622 | − | 12.8972i | 0.291840 | − | 0.505482i | ||||
\(652\) | 3.94622 | − | 6.83506i | 0.154546 | − | 0.267681i | ||||
\(653\) | −1.27689 | + | 2.21164i | −0.0499685 | + | 0.0865480i | −0.889928 | − | 0.456101i | \(-0.849245\pi\) |
0.839959 | + | 0.542649i | \(0.182579\pi\) | |||||||
\(654\) | −7.00000 | + | 12.1244i | −0.273722 | + | 0.474100i | ||||
\(655\) | 18.8924 | 0.738189 | ||||||||
\(656\) | 9.44622 | 0.368813 | ||||||||
\(657\) | 1.55378 | − | 2.69122i | 0.0606187 | − | 0.104995i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.66933 | + | 6.35547i | 0.142937 | + | 0.247574i | 0.928601 | − | 0.371079i | \(-0.121012\pi\) |
−0.785664 | + | 0.618653i | \(0.787679\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.78489 | 0.380588 | 0.190294 | − | 0.981727i | \(-0.439056\pi\) | ||||
0.190294 | + | 0.981727i | \(0.439056\pi\) | |||||||
\(662\) | 20.4462 | 0.794665 | ||||||||
\(663\) | −6.44622 | − | 11.1652i | −0.250351 | − | 0.433620i | ||||
\(664\) | −1.72311 | + | 2.98452i | −0.0668697 | + | 0.115822i | ||||
\(665\) | −16.8924 | −0.655061 | ||||||||
\(666\) | 5.44622 | + | 9.43313i | 0.211037 | + | 0.365526i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 9.44622 | − | 16.3613i | 0.365485 | − | 0.633039i | ||||
\(669\) | 2.00000 | 0.0773245 | ||||||||
\(670\) | −7.22311 | − | 3.85054i | −0.279053 | − | 0.148759i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.00000 | + | 1.73205i | −0.0385758 | + | 0.0668153i | ||||
\(673\) | −42.2311 | −1.62789 | −0.813945 | − | 0.580942i | \(-0.802684\pi\) | ||||
−0.813945 | + | 0.580942i | \(0.802684\pi\) | |||||||
\(674\) | 2.44622 | + | 4.23698i | 0.0942250 | + | 0.163202i | ||||
\(675\) | −5.00000 | −0.192450 | ||||||||
\(676\) | 4.50000 | − | 7.79423i | 0.173077 | − | 0.299778i | ||||
\(677\) | −2.16933 | − | 3.75739i | −0.0833742 | − | 0.144408i | 0.821323 | − | 0.570463i | \(-0.193236\pi\) |
−0.904697 | + | 0.426055i | \(0.859903\pi\) | |||||||
\(678\) | −18.4462 | −0.708423 | ||||||||
\(679\) | −8.89244 | −0.341261 | ||||||||
\(680\) | 3.22311 | − | 5.58259i | 0.123601 | − | 0.214083i | ||||
\(681\) | −4.50000 | − | 7.79423i | −0.172440 | − | 0.298675i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.05378 | + | 7.02135i | −0.155114 | + | 0.268664i | −0.933100 | − | 0.359616i | \(-0.882908\pi\) |
0.777987 | + | 0.628281i | \(0.216241\pi\) | |||||||
\(684\) | −16.8924 | −0.645899 | ||||||||
\(685\) | −6.44622 | −0.246297 | ||||||||
\(686\) | 10.0000 | − | 17.3205i | 0.381802 | − | 0.661300i | ||||
\(687\) | −4.00000 | + | 6.92820i | −0.152610 | + | 0.264327i | ||||
\(688\) | −1.22311 | + | 2.11849i | −0.0466307 | + | 0.0807667i | ||||
\(689\) | −9.44622 | + | 16.3613i | −0.359872 | + | 0.623317i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.5538 | + | 18.2797i | 0.401485 | + | 0.695392i | 0.993905 | − | 0.110237i | \(-0.0351610\pi\) |
−0.592421 | + | 0.805629i | \(0.701828\pi\) | |||||||
\(692\) | −16.3387 | −0.621103 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.55378 | 0.210819 | ||||||||
\(695\) | 22.4462 | 0.851434 | ||||||||
\(696\) | −3.00000 | − | 5.19615i | −0.113715 | − | 0.196960i | ||||
\(697\) | 60.8924 | 2.30647 | ||||||||
\(698\) | −4.00000 | + | 6.92820i | −0.151402 | + | 0.262236i | ||||
\(699\) | −9.66933 | − | 16.7478i | −0.365728 | − | 0.633459i | ||||
\(700\) | −1.00000 | + | 1.73205i | −0.0377964 | + | 0.0654654i | ||||
\(701\) | 12.4462 | + | 21.5575i | 0.470087 | + | 0.814215i | 0.999415 | − | 0.0342024i | \(-0.0108891\pi\) |
−0.529328 | + | 0.848418i | \(0.677556\pi\) | |||||||
\(702\) | 5.00000 | + | 8.66025i | 0.188713 | + | 0.326860i | ||||
\(703\) | −23.0000 | − | 39.8372i | −0.867461 | − | 1.50249i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.44622 | − | 11.1652i | −0.242607 | − | 0.420207i | ||||
\(707\) | −6.00000 | + | 10.3923i | −0.225653 | + | 0.390843i | ||||
\(708\) | 0.223111 | + | 0.386440i | 0.00838502 | + | 0.0145233i | ||||
\(709\) | −16.8924 | + | 29.2586i | −0.634409 | + | 1.09883i | 0.352231 | + | 0.935913i | \(0.385423\pi\) |
−0.986640 | + | 0.162916i | \(0.947910\pi\) | |||||||
\(710\) | −9.44622 | −0.354510 | ||||||||
\(711\) | 8.00000 | + | 13.8564i | 0.300023 | + | 0.519656i | ||||
\(712\) | −15.8924 | −0.595595 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −6.44622 | + | 11.1652i | −0.241244 | + | 0.417847i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.00000 | − | 10.3923i | −0.224231 | − | 0.388379i | ||||
\(717\) | 6.44622 | + | 11.1652i | 0.240739 | + | 0.416971i | ||||
\(718\) | 14.1693 | − | 24.5420i | 0.528795 | − | 0.915899i | ||||
\(719\) | 17.6156 | − | 30.5110i | 0.656949 | − | 1.13787i | −0.324452 | − | 0.945902i | \(-0.605180\pi\) |
0.981401 | − | 0.191967i | \(-0.0614868\pi\) | |||||||
\(720\) | −1.00000 | + | 1.73205i | −0.0372678 | + | 0.0645497i | ||||
\(721\) | 4.00000 | − | 6.92820i | 0.148968 | − | 0.258020i | ||||
\(722\) | 52.3387 | 1.94784 | ||||||||
\(723\) | 17.4462 | 0.648832 | ||||||||
\(724\) | 11.4462 | − | 19.8254i | 0.425395 | − | 0.736807i | ||||
\(725\) | −3.00000 | − | 5.19615i | −0.111417 | − | 0.192980i | ||||
\(726\) | 5.50000 | + | 9.52628i | 0.204124 | + | 0.353553i | ||||
\(727\) | 11.8924 | − | 20.5983i | 0.441066 | − | 0.763949i | −0.556703 | − | 0.830712i | \(-0.687934\pi\) |
0.997769 | + | 0.0667626i | \(0.0212670\pi\) | |||||||
\(728\) | 4.00000 | 0.148250 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0.776889 | + | 1.34561i | 0.0287540 | + | 0.0498033i | ||||
\(731\) | −7.88445 | + | 13.6563i | −0.291617 | + | 0.505095i | ||||
\(732\) | 8.00000 | 0.295689 | ||||||||
\(733\) | −14.2769 | − | 24.7283i | −0.527329 | − | 0.913360i | −0.999493 | − | 0.0318496i | \(-0.989860\pi\) |
0.472164 | − | 0.881511i | \(-0.343473\pi\) | |||||||
\(734\) | −35.7849 | −1.32084 | ||||||||
\(735\) | −1.50000 | + | 2.59808i | −0.0553283 | + | 0.0958315i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −18.8924 | −0.695440 | ||||||||
\(739\) | −10.2231 | + | 17.7069i | −0.376063 | + | 0.651361i | −0.990486 | − | 0.137617i | \(-0.956056\pi\) |
0.614422 | + | 0.788977i | \(0.289389\pi\) | |||||||
\(740\) | −5.44622 | −0.200207 | ||||||||
\(741\) | −8.44622 | − | 14.6293i | −0.310280 | − | 0.537420i | ||||
\(742\) | 18.8924 | 0.693563 | ||||||||
\(743\) | −0.446222 | + | 0.772879i | −0.0163703 | + | 0.0283542i | −0.874095 | − | 0.485756i | \(-0.838544\pi\) |
0.857724 | + | 0.514110i | \(0.171878\pi\) | |||||||
\(744\) | 3.72311 | + | 6.44862i | 0.136496 | + | 0.236418i | ||||
\(745\) | 12.0000 | 0.439646 | ||||||||
\(746\) | −25.4462 | −0.931652 | ||||||||
\(747\) | 3.44622 | − | 5.96903i | 0.126091 | − | 0.218395i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.44622 | + | 5.96903i | 0.125922 | + | 0.218104i | ||||
\(750\) | 0.500000 | − | 0.866025i | 0.0182574 | − | 0.0316228i | ||||
\(751\) | 17.4462 | 0.636622 | 0.318311 | − | 0.947986i | \(-0.396884\pi\) | ||||
0.318311 | + | 0.947986i | \(0.396884\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.77689 | − | 4.80971i | 0.101195 | − | 0.175276i | ||||
\(754\) | −6.00000 | + | 10.3923i | −0.218507 | + | 0.378465i | ||||
\(755\) | 2.27689 | − | 3.94369i | 0.0828645 | − | 0.143525i | ||||
\(756\) | 5.00000 | − | 8.66025i | 0.181848 | − | 0.314970i | ||||
\(757\) | −2.72311 | − | 4.71657i | −0.0989732 | − | 0.171427i | 0.812287 | − | 0.583258i | \(-0.198222\pi\) |
−0.911260 | + | 0.411832i | \(0.864889\pi\) | |||||||
\(758\) | −16.8924 | − | 29.2586i | −0.613561 | − | 1.06272i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.22311 | − | 7.31464i | 0.153188 | − | 0.265330i | ||||
\(761\) | −33.4462 | −1.21242 | −0.606212 | − | 0.795303i | \(-0.707312\pi\) | ||||
−0.606212 | + | 0.795303i | \(0.707312\pi\) | |||||||
\(762\) | −10.0000 | −0.362262 | ||||||||
\(763\) | −14.0000 | − | 24.2487i | −0.506834 | − | 0.877862i | ||||
\(764\) | 3.44622 | 0.124680 | ||||||||
\(765\) | −6.44622 | + | 11.1652i | −0.233064 | + | 0.403678i | ||||
\(766\) | 3.00000 | + | 5.19615i | 0.108394 | + | 0.187745i | ||||
\(767\) | 0.446222 | − | 0.772879i | 0.0161121 | − | 0.0279070i | ||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | 2.66933 | + | 4.62342i | 0.0962586 | + | 0.166725i | 0.910133 | − | 0.414316i | \(-0.135979\pi\) |
−0.813875 | + | 0.581041i | \(0.802646\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.00000 | − | 15.5885i | −0.324127 | − | 0.561405i | ||||
\(772\) | −10.4462 | − | 18.0934i | −0.375968 | − | 0.651195i | ||||
\(773\) | 20.1693 | + | 34.9343i | 0.725440 | + | 1.25650i | 0.958792 | + | 0.284107i | \(0.0916972\pi\) |
−0.233352 | + | 0.972392i | \(0.574969\pi\) | |||||||
\(774\) | 2.44622 | − | 4.23698i | 0.0879276 | − | 0.152295i | ||||
\(775\) | 3.72311 | + | 6.44862i | 0.133738 | + | 0.231641i | ||||
\(776\) | 2.22311 | − | 3.85054i | 0.0798050 | − | 0.138226i | ||||
\(777\) | 10.8924 | 0.390764 | ||||||||
\(778\) | 9.44622 | + | 16.3613i | 0.338663 | + | 0.586582i | ||||
\(779\) | 79.7849 | 2.85859 | ||||||||
\(780\) | −2.00000 | −0.0716115 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.0000 | + | 25.9808i | 0.536056 | + | 0.928477i | ||||
\(784\) | 1.50000 | + | 2.59808i | 0.0535714 | + | 0.0927884i | ||||
\(785\) | 7.00000 | − | 12.1244i | 0.249841 | − | 0.432737i | ||||
\(786\) | 9.44622 | − | 16.3613i | 0.336936 | − | 0.583590i | ||||
\(787\) | −5.72311 | + | 9.91272i | −0.204007 | + | 0.353350i | −0.949816 | − | 0.312810i | \(-0.898730\pi\) |
0.745809 | + | 0.666160i | \(0.232063\pi\) | |||||||
\(788\) | 3.44622 | − | 5.96903i | 0.122767 | − | 0.212638i | ||||
\(789\) | −6.89244 | −0.245378 | ||||||||
\(790\) | −8.00000 | −0.284627 | ||||||||
\(791\) | 18.4462 | − | 31.9498i | 0.655872 | − | 1.13600i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | − | 13.8564i | −0.284088 | − | 0.492055i | ||||
\(794\) | −3.16933 | + | 5.48945i | −0.112475 | + | 0.194813i | ||||
\(795\) | −9.44622 | −0.335023 | ||||||||
\(796\) | 5.44622 | 0.193036 | ||||||||
\(797\) | 13.7231 | + | 23.7691i | 0.486098 | + | 0.841946i | 0.999872 | − | 0.0159795i | \(-0.00508664\pi\) |
−0.513775 | + | 0.857925i | \(0.671753\pi\) | |||||||
\(798\) | −8.44622 | + | 14.6293i | −0.298993 | + | 0.517871i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 31.7849 | 1.12306 | ||||||||
\(802\) | −9.00000 | + | 15.5885i | −0.317801 | + | 0.550448i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −6.94622 | + | 4.33013i | −0.244974 | + | 0.152712i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.44622 | − | 12.8972i | 0.262282 | − | 0.454286i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.00000 | − | 5.19615i | −0.105540 | − | 0.182800i | ||||
\(809\) | −19.7849 | −0.695600 | −0.347800 | − | 0.937569i | \(-0.613071\pi\) | ||||
−0.347800 | + | 0.937569i | \(0.613071\pi\) | |||||||
\(810\) | 0.500000 | − | 0.866025i | 0.0175682 | − | 0.0304290i | ||||
\(811\) | 11.4462 | + | 19.8254i | 0.401931 | + | 0.696165i | 0.993959 | − | 0.109752i | \(-0.0350058\pi\) |
−0.592028 | + | 0.805918i | \(0.701672\pi\) | |||||||
\(812\) | 12.0000 | 0.421117 | ||||||||
\(813\) | −25.4462 | −0.892438 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.94622 | − | 6.83506i | −0.138230 | − | 0.239422i | ||||
\(816\) | −3.22311 | − | 5.58259i | −0.112831 | − | 0.195430i | ||||
\(817\) | −10.3307 | + | 17.8932i | −0.361424 | + | 0.626005i | ||||
\(818\) | −1.44622 | −0.0505660 | ||||||||
\(819\) | −8.00000 | −0.279543 | ||||||||
\(820\) | 4.72311 | − | 8.18067i | 0.164938 | − | 0.285681i | ||||
\(821\) | −19.3387 | + | 33.4956i | −0.674924 | + | 1.16900i | 0.301567 | + | 0.953445i | \(0.402490\pi\) |
−0.976491 | + | 0.215558i | \(0.930843\pi\) | |||||||
\(822\) | −3.22311 | + | 5.58259i | −0.112419 | + | 0.194715i | ||||
\(823\) | 5.44622 | − | 9.43313i | 0.189843 | − | 0.328818i | −0.755355 | − | 0.655316i | \(-0.772535\pi\) |
0.945198 | + | 0.326498i | \(0.105869\pi\) | |||||||
\(824\) | 2.00000 | + | 3.46410i | 0.0696733 | + | 0.120678i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.892444 | −0.0310521 | ||||||||
\(827\) | 18.8924 | − | 32.7227i | 0.656955 | − | 1.13788i | −0.324445 | − | 0.945904i | \(-0.605178\pi\) |
0.981400 | − | 0.191974i | \(-0.0614890\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.7849 | −1.24286 | −0.621430 | − | 0.783469i | \(-0.713448\pi\) | ||||
−0.621430 | + | 0.783469i | \(0.713448\pi\) | |||||||
\(830\) | 1.72311 | + | 2.98452i | 0.0598101 | + | 0.103594i | ||||
\(831\) | 4.55378 | 0.157969 | ||||||||
\(832\) | −1.00000 | + | 1.73205i | −0.0346688 | + | 0.0600481i | ||||
\(833\) | 9.66933 | + | 16.7478i | 0.335023 | + | 0.580276i | ||||
\(834\) | 11.2231 | − | 19.4390i | 0.388625 | − | 0.673117i | ||||
\(835\) | −9.44622 | − | 16.3613i | −0.326900 | − | 0.566207i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.6156 | − | 32.2431i | −0.643448 | − | 1.11448i | ||||
\(838\) | −2.77689 | − | 4.80971i | −0.0959260 | − | 0.166149i | ||||
\(839\) | 22.7231 | + | 39.3576i | 0.784489 | + | 1.35877i | 0.929304 | + | 0.369316i | \(0.120408\pi\) |
−0.144815 | + | 0.989459i | \(0.546259\pi\) | |||||||
\(840\) | 1.00000 | + | 1.73205i | 0.0345033 | + | 0.0597614i | ||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | −0.553778 | − | 0.959172i | −0.0190845 | − | 0.0330552i | ||||
\(843\) | −4.94622 | + | 8.56711i | −0.170357 | + | 0.295067i | ||||
\(844\) | −9.55378 | −0.328855 | ||||||||
\(845\) | −4.50000 | − | 7.79423i | −0.154805 | − | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.0000 | −0.755929 | ||||||||
\(848\) | −4.72311 | + | 8.18067i | −0.162192 | + | 0.280925i | ||||
\(849\) | −23.3387 | −0.800981 | ||||||||
\(850\) | −3.22311 | − | 5.58259i | −0.110552 | − | 0.191481i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −4.72311 | + | 8.18067i | −0.161811 | + | 0.280265i | ||||
\(853\) | −8.72311 | + | 15.1089i | −0.298674 | + | 0.517318i | −0.975833 | − | 0.218519i | \(-0.929878\pi\) |
0.677159 | + | 0.735837i | \(0.263211\pi\) | |||||||
\(854\) | −8.00000 | + | 13.8564i | −0.273754 | + | 0.474156i | ||||
\(855\) | −8.44622 | + | 14.6293i | −0.288855 | + | 0.500311i | ||||
\(856\) | −3.44622 | −0.117789 | ||||||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.7769 | − | 27.3264i | −0.538301 | − | 0.932364i | −0.998996 | − | 0.0448054i | \(-0.985733\pi\) |
0.460695 | − | 0.887558i | \(-0.347600\pi\) | |||||||
\(860\) | 1.22311 | + | 2.11849i | 0.0417077 | + | 0.0722399i | ||||
\(861\) | −9.44622 | + | 16.3613i | −0.321926 | + | 0.557593i | ||||
\(862\) | 16.3387 | 0.556497 | ||||||||
\(863\) | −49.7849 | −1.69470 | −0.847349 | − | 0.531037i | \(-0.821803\pi\) | ||||
−0.847349 | + | 0.531037i | \(0.821803\pi\) | |||||||
\(864\) | 2.50000 | + | 4.33013i | 0.0850517 | + | 0.147314i | ||||
\(865\) | −8.16933 | + | 14.1497i | −0.277766 | + | 0.481104i | ||||
\(866\) | 21.3387 | 0.725117 | ||||||||
\(867\) | −12.2769 | − | 21.2642i | −0.416945 | − | 0.722170i | ||||
\(868\) | −14.8924 | −0.505482 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −6.00000 | −0.203419 | ||||||||
\(871\) | 14.4462 | + | 7.70108i | 0.489492 | + | 0.260941i | ||||
\(872\) | 14.0000 | 0.474100 | ||||||||
\(873\) | −4.44622 | + | 7.70108i | −0.150482 | + | 0.260642i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | + | 1.73205i | 0.0338062 | + | 0.0585540i | ||||
\(876\) | 1.55378 | 0.0524973 | ||||||||
\(877\) | 23.4462 | − | 40.6100i | 0.791723 | − | 1.37130i | −0.133177 | − | 0.991092i | \(-0.542518\pi\) |
0.924900 | − | 0.380212i | \(-0.124149\pi\) | |||||||
\(878\) | 15.7231 | + | 27.2332i | 0.530629 | + | 0.919077i | ||||
\(879\) | 2.55378 | 0.0861368 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.7231 | − | 28.9653i | 0.563416 | − | 0.975865i | −0.433779 | − | 0.901019i | \(-0.642820\pi\) |
0.997195 | − | 0.0748458i | \(-0.0238465\pi\) | |||||||
\(882\) | −3.00000 | − | 5.19615i | −0.101015 | − | 0.174964i | ||||
\(883\) | 2.00000 | + | 3.46410i | 0.0673054 | + | 0.116576i | 0.897714 | − | 0.440578i | \(-0.145226\pi\) |
−0.830409 | + | 0.557154i | \(0.811893\pi\) | |||||||
\(884\) | −6.44622 | + | 11.1652i | −0.216810 | + | 0.375526i | ||||
\(885\) | 0.446222 | 0.0149996 | ||||||||
\(886\) | −21.8924 | −0.735491 | ||||||||
\(887\) | 14.5538 | − | 25.2079i | 0.488668 | − | 0.846398i | −0.511247 | − | 0.859434i | \(-0.670816\pi\) |
0.999915 | + | 0.0130360i | \(0.00414959\pi\) | |||||||
\(888\) | −2.72311 | + | 4.71657i | −0.0913816 | + | 0.158278i | ||||
\(889\) | 10.0000 | − | 17.3205i | 0.335389 | − | 0.580911i | ||||
\(890\) | −7.94622 | + | 13.7633i | −0.266358 | + | 0.461346i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | − | 1.73205i | −0.0334825 | − | 0.0579934i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 6.00000 | − | 10.3923i | 0.200670 | − | 0.347571i | ||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 2.00000 | 0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.3387 | 0.545228 | ||||||||
\(899\) | 22.3387 | − | 38.6917i | 0.745036 | − | 1.29044i | ||||
\(900\) | 1.00000 | + | 1.73205i | 0.0333333 | + | 0.0577350i | ||||
\(901\) | −30.4462 | + | 52.7344i | −1.01431 | + | 1.75684i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.44622 | − | 4.23698i | −0.0814052 | − | 0.140998i | ||||
\(904\) | 9.22311 | + | 15.9749i | 0.306756 | + | 0.531317i | ||||
\(905\) | −11.4462 | − | 19.8254i | −0.380485 | − | 0.659020i | ||||
\(906\) | −2.27689 | − | 3.94369i | −0.0756446 | − | 0.131020i | ||||
\(907\) | −9.16933 | − | 15.8818i | −0.304463 | − | 0.527345i | 0.672679 | − | 0.739935i | \(-0.265144\pi\) |
−0.977142 | + | 0.212590i | \(0.931810\pi\) | |||||||
\(908\) | −4.50000 | + | 7.79423i | −0.149338 | + | 0.258661i | ||||
\(909\) | 6.00000 | + | 10.3923i | 0.199007 | + | 0.344691i | ||||
\(910\) | 2.00000 | − | 3.46410i | 0.0662994 | − | 0.114834i | ||||
\(911\) | −7.66133 | −0.253831 | −0.126916 | − | 0.991914i | \(-0.540508\pi\) | ||||
−0.126916 | + | 0.991914i | \(0.540508\pi\) | |||||||
\(912\) | −4.22311 | − | 7.31464i | −0.139841 | − | 0.242212i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 26.4462 | 0.874763 | ||||||||
\(915\) | 4.00000 | − | 6.92820i | 0.132236 | − | 0.229039i | ||||
\(916\) | 8.00000 | 0.264327 | ||||||||
\(917\) | 18.8924 | + | 32.7227i | 0.623883 | + | 1.08060i | ||||
\(918\) | 16.1156 | + | 27.9130i | 0.531893 | + | 0.921265i | ||||
\(919\) | −20.7231 | + | 35.8935i | −0.683592 | + | 1.18402i | 0.290285 | + | 0.956940i | \(0.406250\pi\) |
−0.973877 | + | 0.227076i | \(0.927083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.94622 | + | 15.4953i | −0.294788 | + | 0.510588i | ||||
\(922\) | −18.4462 | + | 31.9498i | −0.607494 | + | 1.05221i | ||||
\(923\) | 18.8924 | 0.621852 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.72311 | + | 4.71657i | −0.0895353 | + | 0.155080i | ||||
\(926\) | −13.8924 | − | 24.0624i | −0.456534 | − | 0.790740i | ||||
\(927\) | −4.00000 | − | 6.92820i | −0.131377 | − | 0.227552i | ||||
\(928\) | −3.00000 | + | 5.19615i | −0.0984798 | + | 0.170572i | ||||
\(929\) | −49.3387 | −1.61875 | −0.809375 | − | 0.587293i | \(-0.800194\pi\) | ||||
−0.809375 | + | 0.587293i | \(0.800194\pi\) | |||||||
\(930\) | 7.44622 | 0.244171 | ||||||||
\(931\) | 12.6693 | + | 21.9439i | 0.415221 | + | 0.719183i | ||||
\(932\) | −9.66933 | + | 16.7478i | −0.316730 | + | 0.548592i | ||||
\(933\) | −22.3387 | −0.731335 | ||||||||
\(934\) | 1.72311 | + | 2.98452i | 0.0563819 | + | 0.0976563i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | − | 3.46410i | 0.0653720 | − | 0.113228i | ||||
\(937\) | −4.89244 | −0.159829 | −0.0799146 | − | 0.996802i | \(-0.525465\pi\) | ||||
−0.0799146 | + | 0.996802i | \(0.525465\pi\) | |||||||
\(938\) | −0.553778 | − | 16.3613i | −0.0180815 | − | 0.534217i | ||||
\(939\) | 19.5538 | 0.638113 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.7849 | 0.840563 | 0.420282 | − | 0.907394i | \(-0.361931\pi\) | ||||
0.420282 | + | 0.907394i | \(0.361931\pi\) | |||||||
\(942\) | −7.00000 | − | 12.1244i | −0.228072 | − | 0.395033i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.223111 | − | 0.386440i | 0.00726164 | − | 0.0125775i | ||||
\(945\) | −5.00000 | − | 8.66025i | −0.162650 | − | 0.281718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.3387 | 1.40832 | 0.704159 | − | 0.710043i | \(-0.251324\pi\) | ||||
0.704159 | + | 0.710043i | \(0.251324\pi\) | |||||||
\(948\) | −4.00000 | + | 6.92820i | −0.129914 | + | 0.225018i | ||||
\(949\) | −1.55378 | − | 2.69122i | −0.0504378 | − | 0.0873608i | ||||
\(950\) | −4.22311 | − | 7.31464i | −0.137016 | − | 0.237318i | ||||
\(951\) | −16.7231 | + | 28.9653i | −0.542284 | + | 0.939263i | ||||
\(952\) | 12.8924 | 0.417847 | ||||||||
\(953\) | −0.446222 | −0.0144545 | −0.00722727 | − | 0.999974i | \(-0.502301\pi\) | ||||
−0.00722727 | + | 0.999974i | \(0.502301\pi\) | |||||||
\(954\) | 9.44622 | − | 16.3613i | 0.305833 | − | 0.529718i | ||||
\(955\) | 1.72311 | − | 2.98452i | 0.0557586 | − | 0.0965767i | ||||
\(956\) | 6.44622 | − | 11.1652i | 0.208486 | − | 0.361108i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.44622 | − | 11.1652i | −0.208159 | − | 0.360543i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −12.2231 | + | 21.1710i | −0.394294 | + | 0.682937i | ||||
\(962\) | 10.8924 | 0.351186 | ||||||||
\(963\) | 6.89244 | 0.222106 | ||||||||
\(964\) | −8.72311 | − | 15.1089i | −0.280952 | − | 0.486624i | ||||
\(965\) | −20.8924 | −0.672552 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.0000 | + | 19.0526i | 0.353736 | + | 0.612689i | 0.986901 | − | 0.161328i | \(-0.0515777\pi\) |
−0.633165 | + | 0.774017i | \(0.718244\pi\) | |||||||
\(968\) | 5.50000 | − | 9.52628i | 0.176777 | − | 0.306186i | ||||
\(969\) | −27.2231 | − | 47.1518i | −0.874532 | − | 1.51473i | ||||
\(970\) | −2.22311 | − | 3.85054i | −0.0713798 | − | 0.123633i | ||||
\(971\) | 21.6693 | + | 37.5324i | 0.695402 | + | 1.20447i | 0.970045 | + | 0.242925i | \(0.0781070\pi\) |
−0.274643 | + | 0.961546i | \(0.588560\pi\) | |||||||
\(972\) | −8.00000 | − | 13.8564i | −0.256600 | − | 0.444444i | ||||
\(973\) | 22.4462 | + | 38.8780i | 0.719593 | + | 1.24637i | ||||
\(974\) | 8.00000 | + | 13.8564i | 0.256337 | + | 0.443988i | ||||
\(975\) | −1.00000 | + | 1.73205i | −0.0320256 | + | 0.0554700i | ||||
\(976\) | −4.00000 | − | 6.92820i | −0.128037 | − | 0.221766i | ||||
\(977\) | 0.446222 | − | 0.772879i | 0.0142759 | − | 0.0247266i | −0.858799 | − | 0.512312i | \(-0.828789\pi\) |
0.873075 | + | 0.487586i | \(0.162122\pi\) | |||||||
\(978\) | −7.89244 | −0.252373 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | −28.0000 | −0.893971 | ||||||||
\(982\) | −18.6693 | + | 32.3362i | −0.595762 | + | 1.03189i | ||||
\(983\) | 29.1076 | 0.928387 | 0.464193 | − | 0.885734i | \(-0.346344\pi\) | ||||
0.464193 | + | 0.885734i | \(0.346344\pi\) | |||||||
\(984\) | −4.72311 | − | 8.18067i | −0.150567 | − | 0.260790i | ||||
\(985\) | −3.44622 | − | 5.96903i | −0.109806 | − | 0.190189i | ||||
\(986\) | −19.3387 | + | 33.4956i | −0.615869 | + | 1.06672i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.44622 | + | 14.6293i | −0.268710 | + | 0.465420i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.66133 | 0.116306 | 0.0581531 | − | 0.998308i | \(-0.481479\pi\) | ||||
0.0581531 | + | 0.998308i | \(0.481479\pi\) | |||||||
\(992\) | 3.72311 | − | 6.44862i | 0.118209 | − | 0.204744i | ||||
\(993\) | −10.2231 | − | 17.7069i | −0.324421 | − | 0.561913i | ||||
\(994\) | −9.44622 | − | 16.3613i | −0.299616 | − | 0.518950i | ||||
\(995\) | 2.72311 | − | 4.71657i | 0.0863284 | − | 0.149525i | ||||
\(996\) | 3.44622 | 0.109198 | ||||||||
\(997\) | 47.4462 | 1.50264 | 0.751318 | − | 0.659940i | \(-0.229418\pi\) | ||||
0.751318 | + | 0.659940i | \(0.229418\pi\) | |||||||
\(998\) | −13.2231 | − | 22.9031i | −0.418570 | − | 0.724985i | ||||
\(999\) | 13.6156 | − | 23.5828i | 0.430777 | − | 0.746128i |
(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 | 670.2.e.e.431.1 | yes | 4 | |
67.37 | even | 3 | inner | 670.2.e.e.171.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
670.2.e.e.171.1 | ✓ | 4 | 67.37 | even | 3 | inner | |
670.2.e.e.431.1 | yes | 4 | 1.1 | even | 1 | trivial |