Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(379,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.f (of order \(3\), degree \(2\), not 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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 757.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.757 |
Dual form | 1134.2.f.q.379.2 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.866025 | − | 1.50000i | 0.387298 | − | 0.670820i | −0.604787 | − | 0.796387i | \(-0.706742\pi\) |
0.992085 | + | 0.125567i | \(0.0400750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.73205 | −0.547723 | ||||||||
\(11\) | −2.36603 | − | 4.09808i | −0.713384 | − | 1.23562i | −0.963580 | − | 0.267421i | \(-0.913828\pi\) |
0.250196 | − | 0.968195i | \(-0.419505\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | −0.500000 | + | 0.866025i | −0.133631 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 6.46410 | 1.56777 | 0.783887 | − | 0.620903i | \(-0.213234\pi\) | ||||
0.783887 | + | 0.620903i | \(0.213234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.19615 | −1.42149 | −0.710747 | − | 0.703447i | \(-0.751643\pi\) | ||||
−0.710747 | + | 0.703447i | \(0.751643\pi\) | |||||||
\(20\) | 0.866025 | + | 1.50000i | 0.193649 | + | 0.335410i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.36603 | + | 4.09808i | −0.504438 | + | 0.873713i | ||||
\(23\) | −0.633975 | + | 1.09808i | −0.132193 | + | 0.228965i | −0.924522 | − | 0.381130i | \(-0.875535\pi\) |
0.792329 | + | 0.610094i | \(0.208868\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | + | 1.73205i | 0.200000 | + | 0.346410i | ||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −3.23205 | − | 5.59808i | −0.600177 | − | 1.03954i | −0.992794 | − | 0.119835i | \(-0.961764\pi\) |
0.392617 | − | 0.919702i | \(-0.371570\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.09808 | + | 3.63397i | −0.376826 | + | 0.652681i | −0.990598 | − | 0.136802i | \(-0.956318\pi\) |
0.613773 | + | 0.789483i | \(0.289651\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.23205 | − | 5.59808i | −0.554292 | − | 0.960062i | ||||
\(35\) | −1.73205 | −0.292770 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.19615 | −0.525444 | −0.262722 | − | 0.964872i | \(-0.584620\pi\) | ||||
−0.262722 | + | 0.964872i | \(0.584620\pi\) | |||||||
\(38\) | 3.09808 | + | 5.36603i | 0.502574 | + | 0.870484i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.866025 | − | 1.50000i | 0.136931 | − | 0.237171i | ||||
\(41\) | −1.26795 | + | 2.19615i | −0.198020 | + | 0.342981i | −0.947886 | − | 0.318608i | \(-0.896785\pi\) |
0.749866 | + | 0.661590i | \(0.230118\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.19615 | − | 10.7321i | −0.944904 | − | 1.63662i | −0.755943 | − | 0.654638i | \(-0.772821\pi\) |
−0.188962 | − | 0.981984i | \(-0.560512\pi\) | |||||||
\(44\) | 4.73205 | 0.713384 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.26795 | 0.186949 | ||||||||
\(47\) | −1.09808 | − | 1.90192i | −0.160171 | − | 0.277424i | 0.774759 | − | 0.632257i | \(-0.217871\pi\) |
−0.934930 | + | 0.354833i | \(0.884538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 1.00000 | − | 1.73205i | 0.141421 | − | 0.244949i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.500000 | + | 0.866025i | 0.0693375 | + | 0.120096i | ||||
\(53\) | 9.46410 | 1.29999 | 0.649997 | − | 0.759937i | \(-0.274770\pi\) | ||||
0.649997 | + | 0.759937i | \(0.274770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.19615 | −1.10517 | ||||||||
\(56\) | −0.500000 | − | 0.866025i | −0.0668153 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.23205 | + | 5.59808i | −0.424389 | + | 0.735063i | ||||
\(59\) | 4.09808 | − | 7.09808i | 0.533524 | − | 0.924091i | −0.465709 | − | 0.884938i | \(-0.654201\pi\) |
0.999233 | − | 0.0391530i | \(-0.0124660\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.69615 | − | 8.13397i | −0.601281 | − | 1.04145i | −0.992627 | − | 0.121205i | \(-0.961324\pi\) |
0.391347 | − | 0.920243i | \(-0.372009\pi\) | |||||||
\(62\) | 4.19615 | 0.532912 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.866025 | − | 1.50000i | −0.107417 | − | 0.186052i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.09808 | + | 3.63397i | −0.256321 | + | 0.443961i | −0.965253 | − | 0.261316i | \(-0.915844\pi\) |
0.708933 | + | 0.705276i | \(0.249177\pi\) | |||||||
\(68\) | −3.23205 | + | 5.59808i | −0.391944 | + | 0.678866i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.866025 | + | 1.50000i | 0.103510 | + | 0.179284i | ||||
\(71\) | −4.39230 | −0.521271 | −0.260635 | − | 0.965437i | \(-0.583932\pi\) | ||||
−0.260635 | + | 0.965437i | \(0.583932\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.19615 | −1.07633 | −0.538164 | − | 0.842840i | \(-0.680882\pi\) | ||||
−0.538164 | + | 0.842840i | \(0.680882\pi\) | |||||||
\(74\) | 1.59808 | + | 2.76795i | 0.185773 | + | 0.321768i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.09808 | − | 5.36603i | 0.355374 | − | 0.615525i | ||||
\(77\) | −2.36603 | + | 4.09808i | −0.269634 | + | 0.467019i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.09808 | + | 5.36603i | 0.348561 | + | 0.603725i | 0.985994 | − | 0.166781i | \(-0.0533372\pi\) |
−0.637433 | + | 0.770506i | \(0.720004\pi\) | |||||||
\(80\) | −1.73205 | −0.193649 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.53590 | 0.280043 | ||||||||
\(83\) | −0.633975 | − | 1.09808i | −0.0695878 | − | 0.120530i | 0.829132 | − | 0.559053i | \(-0.188835\pi\) |
−0.898720 | + | 0.438523i | \(0.855502\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.59808 | − | 9.69615i | 0.607197 | − | 1.05170i | ||||
\(86\) | −6.19615 | + | 10.7321i | −0.668148 | + | 1.15727i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.36603 | − | 4.09808i | −0.252219 | − | 0.436856i | ||||
\(89\) | −12.4641 | −1.32119 | −0.660596 | − | 0.750742i | \(-0.729696\pi\) | ||||
−0.660596 | + | 0.750742i | \(0.729696\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | −0.633975 | − | 1.09808i | −0.0660964 | − | 0.114482i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.09808 | + | 1.90192i | −0.113258 | + | 0.196168i | ||||
\(95\) | −5.36603 | + | 9.29423i | −0.550543 | + | 0.953568i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000 | + | 13.8564i | 0.812277 | + | 1.40690i | 0.911267 | + | 0.411816i | \(0.135106\pi\) |
−0.0989899 | + | 0.995088i | \(0.531561\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | −6.46410 | − | 11.1962i | −0.643202 | − | 1.11406i | −0.984714 | − | 0.174181i | \(-0.944272\pi\) |
0.341511 | − | 0.939878i | \(-0.389061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.19615 | − | 7.26795i | 0.413459 | − | 0.716132i | −0.581806 | − | 0.813327i | \(-0.697654\pi\) |
0.995265 | + | 0.0971952i | \(0.0309871\pi\) | |||||||
\(104\) | 0.500000 | − | 0.866025i | 0.0490290 | − | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.73205 | − | 8.19615i | −0.459617 | − | 0.796081i | ||||
\(107\) | −13.8564 | −1.33955 | −0.669775 | − | 0.742564i | \(-0.733609\pi\) | ||||
−0.669775 | + | 0.742564i | \(0.733609\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.80385 | −0.460125 | −0.230063 | − | 0.973176i | \(-0.573893\pi\) | ||||
−0.230063 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(110\) | 4.09808 | + | 7.09808i | 0.390736 | + | 0.676775i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.500000 | + | 0.866025i | −0.0472456 | + | 0.0818317i | ||||
\(113\) | 5.13397 | − | 8.89230i | 0.482964 | − | 0.836518i | −0.516845 | − | 0.856079i | \(-0.672894\pi\) |
0.999809 | + | 0.0195613i | \(0.00622697\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.09808 | + | 1.90192i | 0.102396 | + | 0.177355i | ||||
\(116\) | 6.46410 | 0.600177 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.19615 | −0.754517 | ||||||||
\(119\) | −3.23205 | − | 5.59808i | −0.296282 | − | 0.513175i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.69615 | + | 9.86603i | −0.517832 | + | 0.896911i | ||||
\(122\) | −4.69615 | + | 8.13397i | −0.425170 | + | 0.736415i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.09808 | − | 3.63397i | −0.188413 | − | 0.326341i | ||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.866025 | + | 1.50000i | −0.0759555 | + | 0.131559i | ||||
\(131\) | 1.26795 | − | 2.19615i | 0.110781 | − | 0.191879i | −0.805304 | − | 0.592862i | \(-0.797998\pi\) |
0.916085 | + | 0.400983i | \(0.131331\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.09808 | + | 5.36603i | 0.268637 | + | 0.465293i | ||||
\(134\) | 4.19615 | 0.362492 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.46410 | 0.554292 | ||||||||
\(137\) | 1.33013 | + | 2.30385i | 0.113640 | + | 0.196831i | 0.917235 | − | 0.398345i | \(-0.130415\pi\) |
−0.803595 | + | 0.595176i | \(0.797082\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.09808 | − | 15.7583i | 0.771689 | − | 1.33660i | −0.164948 | − | 0.986302i | \(-0.552746\pi\) |
0.936637 | − | 0.350302i | \(-0.113921\pi\) | |||||||
\(140\) | 0.866025 | − | 1.50000i | 0.0731925 | − | 0.126773i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.19615 | + | 3.80385i | 0.184297 | + | 0.319212i | ||||
\(143\) | −4.73205 | −0.395714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.1962 | −0.929790 | ||||||||
\(146\) | 4.59808 | + | 7.96410i | 0.380539 | + | 0.659114i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.59808 | − | 2.76795i | 0.131361 | − | 0.227524i | ||||
\(149\) | 1.96410 | − | 3.40192i | 0.160905 | − | 0.278696i | −0.774288 | − | 0.632833i | \(-0.781892\pi\) |
0.935194 | + | 0.354137i | \(0.115225\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2942 | + | 19.5622i | 0.919111 | + | 1.59195i | 0.800768 | + | 0.598975i | \(0.204425\pi\) |
0.118343 | + | 0.992973i | \(0.462242\pi\) | |||||||
\(152\) | −6.19615 | −0.502574 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.73205 | 0.381320 | ||||||||
\(155\) | 3.63397 | + | 6.29423i | 0.291888 | + | 0.505565i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.69615 | + | 13.3301i | −0.614220 | + | 1.06386i | 0.376301 | + | 0.926497i | \(0.377196\pi\) |
−0.990521 | + | 0.137362i | \(0.956137\pi\) | |||||||
\(158\) | 3.09808 | − | 5.36603i | 0.246470 | − | 0.426898i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.866025 | + | 1.50000i | 0.0684653 | + | 0.118585i | ||||
\(161\) | 1.26795 | 0.0999284 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.3923 | 1.91055 | 0.955276 | − | 0.295714i | \(-0.0955577\pi\) | ||||
0.955276 | + | 0.295714i | \(0.0955577\pi\) | |||||||
\(164\) | −1.26795 | − | 2.19615i | −0.0990102 | − | 0.171491i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.633975 | + | 1.09808i | −0.0492060 | + | 0.0852272i | ||||
\(167\) | 3.63397 | − | 6.29423i | 0.281205 | − | 0.487062i | −0.690477 | − | 0.723355i | \(-0.742599\pi\) |
0.971682 | + | 0.236293i | \(0.0759324\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | −11.1962 | −0.858706 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.3923 | 0.944904 | ||||||||
\(173\) | 6.40192 | + | 11.0885i | 0.486729 | + | 0.843040i | 0.999884 | − | 0.0152565i | \(-0.00485650\pi\) |
−0.513154 | + | 0.858296i | \(0.671523\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | − | 1.73205i | 0.0755929 | − | 0.130931i | ||||
\(176\) | −2.36603 | + | 4.09808i | −0.178346 | + | 0.308904i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.23205 | + | 10.7942i | 0.467112 | + | 0.809062i | ||||
\(179\) | 7.26795 | 0.543232 | 0.271616 | − | 0.962406i | \(-0.412442\pi\) | ||||
0.271616 | + | 0.962406i | \(0.412442\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.392305 | 0.0291598 | 0.0145799 | − | 0.999894i | \(-0.495359\pi\) | ||||
0.0145799 | + | 0.999894i | \(0.495359\pi\) | |||||||
\(182\) | 0.500000 | + | 0.866025i | 0.0370625 | + | 0.0641941i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.633975 | + | 1.09808i | −0.0467372 | + | 0.0809513i | ||||
\(185\) | −2.76795 | + | 4.79423i | −0.203504 | + | 0.352479i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.2942 | − | 26.4904i | −1.11842 | − | 1.93717i | ||||
\(188\) | 2.19615 | 0.160171 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.7321 | 0.778585 | ||||||||
\(191\) | −12.2942 | − | 21.2942i | −0.889579 | − | 1.54080i | −0.840374 | − | 0.542008i | \(-0.817664\pi\) |
−0.0492056 | − | 0.998789i | \(-0.515669\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.50000 | − | 16.4545i | 0.683825 | − | 1.18442i | −0.289980 | − | 0.957033i | \(-0.593649\pi\) |
0.973805 | − | 0.227387i | \(-0.0730182\pi\) | |||||||
\(194\) | 8.00000 | − | 13.8564i | 0.574367 | − | 0.994832i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.500000 | − | 0.866025i | −0.0357143 | − | 0.0618590i | ||||
\(197\) | −15.0000 | −1.06871 | −0.534353 | − | 0.845262i | \(-0.679445\pi\) | ||||
−0.534353 | + | 0.845262i | \(0.679445\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.5885 | 1.45948 | 0.729739 | − | 0.683726i | \(-0.239642\pi\) | ||||
0.729739 | + | 0.683726i | \(0.239642\pi\) | |||||||
\(200\) | 1.00000 | + | 1.73205i | 0.0707107 | + | 0.122474i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.46410 | + | 11.1962i | −0.454813 | + | 0.787759i | ||||
\(203\) | −3.23205 | + | 5.59808i | −0.226845 | + | 0.392908i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.19615 | + | 3.80385i | 0.153386 | + | 0.265672i | ||||
\(206\) | −8.39230 | −0.584720 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 14.6603 | + | 25.3923i | 1.01407 | + | 1.75642i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.90192 | + | 10.2224i | −0.406305 | + | 0.703741i | −0.994472 | − | 0.104998i | \(-0.966516\pi\) |
0.588167 | + | 0.808739i | \(0.299850\pi\) | |||||||
\(212\) | −4.73205 | + | 8.19615i | −0.324999 | + | 0.562914i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.92820 | + | 12.0000i | 0.473602 | + | 0.820303i | ||||
\(215\) | −21.4641 | −1.46384 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.19615 | 0.284853 | ||||||||
\(218\) | 2.40192 | + | 4.16025i | 0.162679 | + | 0.281768i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.09808 | − | 7.09808i | 0.276292 | − | 0.478552i | ||||
\(221\) | 3.23205 | − | 5.59808i | 0.217411 | − | 0.376567i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.19615 | − | 10.7321i | −0.414925 | − | 0.718671i | 0.580496 | − | 0.814263i | \(-0.302859\pi\) |
−0.995421 | + | 0.0955922i | \(0.969526\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.2679 | −0.683014 | ||||||||
\(227\) | 2.53590 | + | 4.39230i | 0.168313 | + | 0.291528i | 0.937827 | − | 0.347103i | \(-0.112835\pi\) |
−0.769514 | + | 0.638631i | \(0.779501\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.8923 | − | 18.8660i | 0.719784 | − | 1.24670i | −0.241302 | − | 0.970450i | \(-0.577574\pi\) |
0.961085 | − | 0.276252i | \(-0.0890924\pi\) | |||||||
\(230\) | 1.09808 | − | 1.90192i | 0.0724050 | − | 0.125409i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.23205 | − | 5.59808i | −0.212195 | − | 0.367532i | ||||
\(233\) | 13.7321 | 0.899617 | 0.449808 | − | 0.893125i | \(-0.351492\pi\) | ||||
0.449808 | + | 0.893125i | \(0.351492\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.80385 | −0.248136 | ||||||||
\(236\) | 4.09808 | + | 7.09808i | 0.266762 | + | 0.462045i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.23205 | + | 5.59808i | −0.209503 | + | 0.362869i | ||||
\(239\) | −7.56218 | + | 13.0981i | −0.489157 | + | 0.847244i | −0.999922 | − | 0.0124759i | \(-0.996029\pi\) |
0.510766 | + | 0.859720i | \(0.329362\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.79423 | + | 11.7679i | 0.437655 | + | 0.758040i | 0.997508 | − | 0.0705514i | \(-0.0224759\pi\) |
−0.559853 | + | 0.828592i | \(0.689143\pi\) | |||||||
\(242\) | 11.3923 | 0.732325 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.39230 | 0.601281 | ||||||||
\(245\) | 0.866025 | + | 1.50000i | 0.0553283 | + | 0.0958315i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.09808 | + | 5.36603i | −0.197126 | + | 0.341432i | ||||
\(248\) | −2.09808 | + | 3.63397i | −0.133228 | + | 0.230758i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.06218 | − | 10.5000i | −0.383406 | − | 0.664078i | ||||
\(251\) | −3.80385 | −0.240097 | −0.120048 | − | 0.992768i | \(-0.538305\pi\) | ||||
−0.120048 | + | 0.992768i | \(0.538305\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | 2.00000 | + | 3.46410i | 0.125491 | + | 0.217357i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 13.9641 | − | 24.1865i | 0.871057 | − | 1.50871i | 0.0101519 | − | 0.999948i | \(-0.496768\pi\) |
0.860905 | − | 0.508766i | \(-0.169898\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.59808 | + | 2.76795i | 0.0992996 | + | 0.171992i | ||||
\(260\) | 1.73205 | 0.107417 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.53590 | −0.156668 | ||||||||
\(263\) | −7.56218 | − | 13.0981i | −0.466304 | − | 0.807662i | 0.532955 | − | 0.846143i | \(-0.321081\pi\) |
−0.999259 | + | 0.0384813i | \(0.987748\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.19615 | − | 14.1962i | 0.503486 | − | 0.872063i | ||||
\(266\) | 3.09808 | − | 5.36603i | 0.189955 | − | 0.329012i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.09808 | − | 3.63397i | −0.128160 | − | 0.221980i | ||||
\(269\) | 29.4449 | 1.79529 | 0.897643 | − | 0.440724i | \(-0.145278\pi\) | ||||
0.897643 | + | 0.440724i | \(0.145278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.1962 | 1.71279 | 0.856397 | − | 0.516318i | \(-0.172698\pi\) | ||||
0.856397 | + | 0.516318i | \(0.172698\pi\) | |||||||
\(272\) | −3.23205 | − | 5.59808i | −0.195972 | − | 0.339433i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.33013 | − | 2.30385i | 0.0803559 | − | 0.139181i | ||||
\(275\) | 4.73205 | − | 8.19615i | 0.285353 | − | 0.494247i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.39230 | + | 16.2679i | 0.564329 | + | 0.977446i | 0.997112 | + | 0.0759481i | \(0.0241983\pi\) |
−0.432783 | + | 0.901498i | \(0.642468\pi\) | |||||||
\(278\) | −18.1962 | −1.09133 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.73205 | −0.103510 | ||||||||
\(281\) | 6.86603 | + | 11.8923i | 0.409593 | + | 0.709435i | 0.994844 | − | 0.101417i | \(-0.0323375\pi\) |
−0.585251 | + | 0.810852i | \(0.699004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.80385 | + | 3.12436i | −0.107228 | + | 0.185724i | −0.914646 | − | 0.404255i | \(-0.867531\pi\) |
0.807419 | + | 0.589979i | \(0.200864\pi\) | |||||||
\(284\) | 2.19615 | − | 3.80385i | 0.130318 | − | 0.225717i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.36603 | + | 4.09808i | 0.139906 | + | 0.242324i | ||||
\(287\) | 2.53590 | 0.149689 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.7846 | 1.45792 | ||||||||
\(290\) | 5.59808 | + | 9.69615i | 0.328730 | + | 0.569378i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.59808 | − | 7.96410i | 0.269082 | − | 0.466064i | ||||
\(293\) | 13.3301 | − | 23.0885i | 0.778754 | − | 1.34884i | −0.153906 | − | 0.988086i | \(-0.549185\pi\) |
0.932660 | − | 0.360757i | \(-0.117481\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.09808 | − | 12.2942i | −0.413266 | − | 0.715798i | ||||
\(296\) | −3.19615 | −0.185773 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.92820 | −0.227555 | ||||||||
\(299\) | 0.633975 | + | 1.09808i | 0.0366637 | + | 0.0635034i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.19615 | + | 10.7321i | −0.357140 | + | 0.618585i | ||||
\(302\) | 11.2942 | − | 19.5622i | 0.649910 | − | 1.12568i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.09808 | + | 5.36603i | 0.177687 | + | 0.307763i | ||||
\(305\) | −16.2679 | −0.931500 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | −2.36603 | − | 4.09808i | −0.134817 | − | 0.233510i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.63397 | − | 6.29423i | 0.206396 | − | 0.357488i | ||||
\(311\) | 11.4904 | − | 19.9019i | 0.651560 | − | 1.12853i | −0.331185 | − | 0.943566i | \(-0.607448\pi\) |
0.982744 | − | 0.184969i | \(-0.0592183\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.9904 | − | 19.0359i | −0.621213 | − | 1.07597i | −0.989260 | − | 0.146165i | \(-0.953307\pi\) |
0.368047 | − | 0.929807i | \(-0.380027\pi\) | |||||||
\(314\) | 15.3923 | 0.868638 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.19615 | −0.348561 | ||||||||
\(317\) | 0.696152 | + | 1.20577i | 0.0390998 | + | 0.0677229i | 0.884913 | − | 0.465756i | \(-0.154218\pi\) |
−0.845813 | + | 0.533479i | \(0.820884\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.2942 | + | 26.4904i | −0.856312 | + | 1.48318i | ||||
\(320\) | 0.866025 | − | 1.50000i | 0.0484123 | − | 0.0838525i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.633975 | − | 1.09808i | −0.0353300 | − | 0.0611934i | ||||
\(323\) | −40.0526 | −2.22858 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | −12.1962 | − | 21.1244i | −0.675482 | − | 1.16997i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.26795 | + | 2.19615i | −0.0700108 | + | 0.121262i | ||||
\(329\) | −1.09808 | + | 1.90192i | −0.0605389 | + | 0.104856i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5885 | + | 25.2679i | 0.801854 | + | 1.38885i | 0.918394 | + | 0.395666i | \(0.129486\pi\) |
−0.116540 | + | 0.993186i | \(0.537180\pi\) | |||||||
\(332\) | 1.26795 | 0.0695878 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.26795 | −0.397684 | ||||||||
\(335\) | 3.63397 | + | 6.29423i | 0.198545 | + | 0.343890i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.1962 | − | 28.0526i | 0.882261 | − | 1.52812i | 0.0334391 | − | 0.999441i | \(-0.489354\pi\) |
0.848822 | − | 0.528679i | \(-0.177313\pi\) | |||||||
\(338\) | 6.00000 | − | 10.3923i | 0.326357 | − | 0.565267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.59808 | + | 9.69615i | 0.303598 | + | 0.525848i | ||||
\(341\) | 19.8564 | 1.07528 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −6.19615 | − | 10.7321i | −0.334074 | − | 0.578633i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.40192 | − | 11.0885i | 0.344170 | − | 0.596119i | ||||
\(347\) | −8.19615 | + | 14.1962i | −0.439993 | + | 0.762089i | −0.997688 | − | 0.0679560i | \(-0.978352\pi\) |
0.557696 | + | 0.830045i | \(0.311686\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.19615 | − | 10.7321i | −0.331672 | − | 0.574474i | 0.651167 | − | 0.758934i | \(-0.274280\pi\) |
−0.982840 | + | 0.184461i | \(0.940946\pi\) | |||||||
\(350\) | −2.00000 | −0.106904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.73205 | 0.252219 | ||||||||
\(353\) | −2.07180 | − | 3.58846i | −0.110271 | − | 0.190994i | 0.805609 | − | 0.592448i | \(-0.201838\pi\) |
−0.915879 | + | 0.401454i | \(0.868505\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.80385 | + | 6.58846i | −0.201887 | + | 0.349679i | ||||
\(356\) | 6.23205 | − | 10.7942i | 0.330298 | − | 0.572093i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.63397 | − | 6.29423i | −0.192062 | − | 0.332660i | ||||
\(359\) | 18.9282 | 0.998992 | 0.499496 | − | 0.866316i | \(-0.333518\pi\) | ||||
0.499496 | + | 0.866316i | \(0.333518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.3923 | 1.02065 | ||||||||
\(362\) | −0.196152 | − | 0.339746i | −0.0103095 | − | 0.0178567i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.500000 | − | 0.866025i | 0.0262071 | − | 0.0453921i | ||||
\(365\) | −7.96410 | + | 13.7942i | −0.416860 | + | 0.722023i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.29423 | + | 3.97372i | 0.119758 | + | 0.207427i | 0.919672 | − | 0.392688i | \(-0.128455\pi\) |
−0.799914 | + | 0.600115i | \(0.795122\pi\) | |||||||
\(368\) | 1.26795 | 0.0660964 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.53590 | 0.287798 | ||||||||
\(371\) | −4.73205 | − | 8.19615i | −0.245676 | − | 0.425523i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | + | 17.3205i | −0.517780 | + | 0.896822i | 0.482006 | + | 0.876168i | \(0.339908\pi\) |
−0.999787 | + | 0.0206542i | \(0.993425\pi\) | |||||||
\(374\) | −15.2942 | + | 26.4904i | −0.790846 | + | 1.36978i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.09808 | − | 1.90192i | −0.0566290 | − | 0.0980842i | ||||
\(377\) | −6.46410 | −0.332918 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.5885 | −0.852092 | −0.426046 | − | 0.904702i | \(-0.640094\pi\) | ||||
−0.426046 | + | 0.904702i | \(0.640094\pi\) | |||||||
\(380\) | −5.36603 | − | 9.29423i | −0.275271 | − | 0.476784i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.2942 | + | 21.2942i | −0.629027 | + | 1.08951i | ||||
\(383\) | 5.07180 | − | 8.78461i | 0.259157 | − | 0.448873i | −0.706860 | − | 0.707354i | \(-0.749889\pi\) |
0.966016 | + | 0.258481i | \(0.0832221\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.09808 | + | 7.09808i | 0.208857 | + | 0.361751i | ||||
\(386\) | −19.0000 | −0.967075 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.0000 | −0.812277 | ||||||||
\(389\) | 15.1244 | + | 26.1962i | 0.766835 | + | 1.32820i | 0.939271 | + | 0.343177i | \(0.111503\pi\) |
−0.172436 | + | 0.985021i | \(0.555164\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.09808 | + | 7.09808i | −0.207249 | + | 0.358965i | ||||
\(392\) | −0.500000 | + | 0.866025i | −0.0252538 | + | 0.0437409i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.50000 | + | 12.9904i | 0.377845 | + | 0.654446i | ||||
\(395\) | 10.7321 | 0.539988 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.3923 | −1.47516 | −0.737579 | − | 0.675261i | \(-0.764031\pi\) | ||||
−0.737579 | + | 0.675261i | \(0.764031\pi\) | |||||||
\(398\) | −10.2942 | − | 17.8301i | −0.516003 | − | 0.893744i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | − | 1.73205i | 0.0500000 | − | 0.0866025i | ||||
\(401\) | −11.1340 | + | 19.2846i | −0.556004 | + | 0.963027i | 0.441820 | + | 0.897103i | \(0.354333\pi\) |
−0.997825 | + | 0.0659240i | \(0.979001\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.09808 | + | 3.63397i | 0.104513 | + | 0.181021i | ||||
\(404\) | 12.9282 | 0.643202 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.46410 | 0.320808 | ||||||||
\(407\) | 7.56218 | + | 13.0981i | 0.374843 | + | 0.649248i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.5981 | − | 18.3564i | 0.524041 | − | 0.907666i | −0.475567 | − | 0.879679i | \(-0.657757\pi\) |
0.999608 | − | 0.0279865i | \(-0.00890953\pi\) | |||||||
\(410\) | 2.19615 | − | 3.80385i | 0.108460 | − | 0.187859i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.19615 | + | 7.26795i | 0.206730 | + | 0.358066i | ||||
\(413\) | −8.19615 | −0.403306 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.19615 | −0.107805 | ||||||||
\(416\) | 0.500000 | + | 0.866025i | 0.0245145 | + | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.6603 | − | 25.3923i | 0.717056 | − | 1.24198i | ||||
\(419\) | −11.6603 | + | 20.1962i | −0.569641 | + | 0.986647i | 0.426961 | + | 0.904270i | \(0.359584\pi\) |
−0.996601 | + | 0.0823764i | \(0.973749\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.59808 | − | 11.4282i | −0.321571 | − | 0.556977i | 0.659242 | − | 0.751931i | \(-0.270877\pi\) |
−0.980812 | + | 0.194955i | \(0.937544\pi\) | |||||||
\(422\) | 11.8038 | 0.574602 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.46410 | 0.459617 | ||||||||
\(425\) | 6.46410 | + | 11.1962i | 0.313555 | + | 0.543093i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.69615 | + | 8.13397i | −0.227263 | + | 0.393631i | ||||
\(428\) | 6.92820 | − | 12.0000i | 0.334887 | − | 0.580042i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.7321 | + | 18.5885i | 0.517545 | + | 0.896415i | ||||
\(431\) | 0.679492 | 0.0327300 | 0.0163650 | − | 0.999866i | \(-0.494791\pi\) | ||||
0.0163650 | + | 0.999866i | \(0.494791\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.5885 | −1.51804 | −0.759022 | − | 0.651065i | \(-0.774323\pi\) | ||||
−0.759022 | + | 0.651065i | \(0.774323\pi\) | |||||||
\(434\) | −2.09808 | − | 3.63397i | −0.100711 | − | 0.174436i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.40192 | − | 4.16025i | 0.115031 | − | 0.199240i | ||||
\(437\) | 3.92820 | − | 6.80385i | 0.187911 | − | 0.325472i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.5885 | − | 18.3397i | −0.505359 | − | 0.875308i | −0.999981 | − | 0.00619971i | \(-0.998027\pi\) |
0.494621 | − | 0.869109i | \(-0.335307\pi\) | |||||||
\(440\) | −8.19615 | −0.390736 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.46410 | −0.307466 | ||||||||
\(443\) | −1.09808 | − | 1.90192i | −0.0521712 | − | 0.0903631i | 0.838760 | − | 0.544501i | \(-0.183281\pi\) |
−0.890932 | + | 0.454138i | \(0.849947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.7942 | + | 18.6962i | −0.511696 | + | 0.886283i | ||||
\(446\) | −6.19615 | + | 10.7321i | −0.293396 | + | 0.508177i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.500000 | − | 0.866025i | −0.0236228 | − | 0.0409159i | ||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | 0.565058 | ||||||||
\(452\) | 5.13397 | + | 8.89230i | 0.241482 | + | 0.418259i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.53590 | − | 4.39230i | 0.119016 | − | 0.206141i | ||||
\(455\) | −0.866025 | + | 1.50000i | −0.0405999 | + | 0.0703211i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.500000 | + | 0.866025i | 0.0233890 | + | 0.0405110i | 0.877483 | − | 0.479608i | \(-0.159221\pi\) |
−0.854094 | + | 0.520119i | \(0.825888\pi\) | |||||||
\(458\) | −21.7846 | −1.01793 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.19615 | −0.102396 | ||||||||
\(461\) | −5.53590 | − | 9.58846i | −0.257832 | − | 0.446579i | 0.707829 | − | 0.706384i | \(-0.249675\pi\) |
−0.965661 | + | 0.259805i | \(0.916342\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.90192 | + | 5.02628i | −0.134864 | + | 0.233591i | −0.925545 | − | 0.378637i | \(-0.876393\pi\) |
0.790682 | + | 0.612228i | \(0.209726\pi\) | |||||||
\(464\) | −3.23205 | + | 5.59808i | −0.150044 | + | 0.259884i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.86603 | − | 11.8923i | −0.318062 | − | 0.550900i | ||||
\(467\) | −1.26795 | −0.0586737 | −0.0293368 | − | 0.999570i | \(-0.509340\pi\) | ||||
−0.0293368 | + | 0.999570i | \(0.509340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.19615 | 0.193760 | ||||||||
\(470\) | 1.90192 | + | 3.29423i | 0.0877292 | + | 0.151951i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.09808 | − | 7.09808i | 0.188629 | − | 0.326715i | ||||
\(473\) | −29.3205 | + | 50.7846i | −1.34816 | + | 2.33508i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.19615 | − | 10.7321i | −0.284299 | − | 0.492420i | ||||
\(476\) | 6.46410 | 0.296282 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.1244 | 0.691772 | ||||||||
\(479\) | −8.36603 | − | 14.4904i | −0.382253 | − | 0.662082i | 0.609131 | − | 0.793070i | \(-0.291519\pi\) |
−0.991384 | + | 0.130988i | \(0.958185\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.59808 | + | 2.76795i | −0.0728660 | + | 0.126208i | ||||
\(482\) | 6.79423 | − | 11.7679i | 0.309469 | − | 0.536015i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.69615 | − | 9.86603i | −0.258916 | − | 0.448456i | ||||
\(485\) | 27.7128 | 1.25837 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.19615 | −0.280774 | −0.140387 | − | 0.990097i | \(-0.544835\pi\) | ||||
−0.140387 | + | 0.990097i | \(0.544835\pi\) | |||||||
\(488\) | −4.69615 | − | 8.13397i | −0.212585 | − | 0.368208i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.866025 | − | 1.50000i | 0.0391230 | − | 0.0677631i | ||||
\(491\) | −5.66025 | + | 9.80385i | −0.255444 | + | 0.442441i | −0.965016 | − | 0.262191i | \(-0.915555\pi\) |
0.709572 | + | 0.704633i | \(0.248888\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.8923 | − | 36.1865i | −0.940942 | − | 1.62976i | ||||
\(494\) | 6.19615 | 0.278778 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.19615 | 0.188413 | ||||||||
\(497\) | 2.19615 | + | 3.80385i | 0.0985109 | + | 0.170626i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.2942 | + | 17.8301i | −0.460833 | + | 0.798186i | −0.999003 | − | 0.0446504i | \(-0.985783\pi\) |
0.538170 | + | 0.842836i | \(0.319116\pi\) | |||||||
\(500\) | −6.06218 | + | 10.5000i | −0.271109 | + | 0.469574i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.90192 | + | 3.29423i | 0.0848870 | + | 0.147029i | ||||
\(503\) | −22.9808 | −1.02466 | −0.512331 | − | 0.858788i | \(-0.671218\pi\) | ||||
−0.512331 | + | 0.858788i | \(0.671218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.3923 | −0.996444 | ||||||||
\(506\) | −3.00000 | − | 5.19615i | −0.133366 | − | 0.230997i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.00000 | − | 3.46410i | 0.0887357 | − | 0.153695i | ||||
\(509\) | 10.8564 | − | 18.8038i | 0.481202 | − | 0.833466i | −0.518566 | − | 0.855038i | \(-0.673534\pi\) |
0.999767 | + | 0.0215720i | \(0.00686711\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.59808 | + | 7.96410i | 0.203407 | + | 0.352311i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.9282 | −1.23186 | ||||||||
\(515\) | −7.26795 | − | 12.5885i | −0.320264 | − | 0.554714i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.19615 | + | 9.00000i | −0.228527 | + | 0.395820i | ||||
\(518\) | 1.59808 | − | 2.76795i | 0.0702154 | − | 0.121617i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.866025 | − | 1.50000i | −0.0379777 | − | 0.0657794i | ||||
\(521\) | 43.8564 | 1.92138 | 0.960692 | − | 0.277616i | \(-0.0895444\pi\) | ||||
0.960692 | + | 0.277616i | \(0.0895444\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6077 | 0.682477 | 0.341238 | − | 0.939977i | \(-0.389154\pi\) | ||||
0.341238 | + | 0.939977i | \(0.389154\pi\) | |||||||
\(524\) | 1.26795 | + | 2.19615i | 0.0553906 | + | 0.0959394i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.56218 | + | 13.0981i | −0.329727 | + | 0.571103i | ||||
\(527\) | −13.5622 | + | 23.4904i | −0.590778 | + | 1.02326i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6962 | + | 18.5263i | 0.465050 | + | 0.805490i | ||||
\(530\) | −16.3923 | −0.712036 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.19615 | −0.268637 | ||||||||
\(533\) | 1.26795 | + | 2.19615i | 0.0549210 | + | 0.0951259i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0000 | + | 20.7846i | −0.518805 | + | 0.898597i | ||||
\(536\) | −2.09808 | + | 3.63397i | −0.0906231 | + | 0.156964i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.7224 | − | 25.5000i | −0.634729 | − | 1.09938i | ||||
\(539\) | 4.73205 | 0.203824 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.5885 | −1.35809 | −0.679047 | − | 0.734095i | \(-0.737607\pi\) | ||||
−0.679047 | + | 0.734095i | \(0.737607\pi\) | |||||||
\(542\) | −14.0981 | − | 24.4186i | −0.605564 | − | 1.04887i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.23205 | + | 5.59808i | −0.138573 | + | 0.240016i | ||||
\(545\) | −4.16025 | + | 7.20577i | −0.178206 | + | 0.308661i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.90192 | + | 17.1506i | 0.423376 | + | 0.733308i | 0.996267 | − | 0.0863230i | \(-0.0275117\pi\) |
−0.572892 | + | 0.819631i | \(0.694178\pi\) | |||||||
\(548\) | −2.66025 | −0.113640 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.46410 | −0.403551 | ||||||||
\(551\) | 20.0263 | + | 34.6865i | 0.853148 | + | 1.47770i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.09808 | − | 5.36603i | 0.131744 | − | 0.228187i | ||||
\(554\) | 9.39230 | − | 16.2679i | 0.399041 | − | 0.691159i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.09808 | + | 15.7583i | 0.385844 | + | 0.668302i | ||||
\(557\) | 40.8564 | 1.73114 | 0.865571 | − | 0.500787i | \(-0.166956\pi\) | ||||
0.865571 | + | 0.500787i | \(0.166956\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.3923 | −0.524139 | ||||||||
\(560\) | 0.866025 | + | 1.50000i | 0.0365963 | + | 0.0633866i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.86603 | − | 11.8923i | 0.289626 | − | 0.501647i | ||||
\(563\) | −12.0000 | + | 20.7846i | −0.505740 | + | 0.875967i | 0.494238 | + | 0.869326i | \(0.335447\pi\) |
−0.999978 | + | 0.00664037i | \(0.997886\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.89230 | − | 15.4019i | −0.374102 | − | 0.647964i | ||||
\(566\) | 3.60770 | 0.151643 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.39230 | −0.184297 | ||||||||
\(569\) | 3.99038 | + | 6.91154i | 0.167285 | + | 0.289747i | 0.937465 | − | 0.348081i | \(-0.113167\pi\) |
−0.770179 | + | 0.637828i | \(0.779833\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.90192 | − | 17.1506i | 0.414383 | − | 0.717732i | −0.580981 | − | 0.813917i | \(-0.697331\pi\) |
0.995363 | + | 0.0961855i | \(0.0306642\pi\) | |||||||
\(572\) | 2.36603 | − | 4.09808i | 0.0989285 | − | 0.171349i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.26795 | − | 2.19615i | −0.0529232 | − | 0.0916656i | ||||
\(575\) | −2.53590 | −0.105754 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.1962 | 1.29871 | 0.649356 | − | 0.760484i | \(-0.275038\pi\) | ||||
0.649356 | + | 0.760484i | \(0.275038\pi\) | |||||||
\(578\) | −12.3923 | − | 21.4641i | −0.515452 | − | 0.892789i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.59808 | − | 9.69615i | 0.232447 | − | 0.402611i | ||||
\(581\) | −0.633975 | + | 1.09808i | −0.0263017 | + | 0.0455559i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.3923 | − | 38.7846i | −0.927395 | − | 1.60629i | ||||
\(584\) | −9.19615 | −0.380539 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.6603 | −1.10132 | ||||||||
\(587\) | 5.36603 | + | 9.29423i | 0.221480 | + | 0.383614i | 0.955257 | − | 0.295776i | \(-0.0955781\pi\) |
−0.733778 | + | 0.679389i | \(0.762245\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.0000 | − | 22.5167i | 0.535656 | − | 0.927783i | ||||
\(590\) | −7.09808 | + | 12.2942i | −0.292223 | + | 0.506145i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.59808 | + | 2.76795i | 0.0656805 | + | 0.113762i | ||||
\(593\) | −40.8564 | −1.67777 | −0.838886 | − | 0.544308i | \(-0.816792\pi\) | ||||
−0.838886 | + | 0.544308i | \(0.816792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.1962 | −0.458997 | ||||||||
\(596\) | 1.96410 | + | 3.40192i | 0.0804527 | + | 0.139348i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.633975 | − | 1.09808i | 0.0259251 | − | 0.0449037i | ||||
\(599\) | 1.90192 | − | 3.29423i | 0.0777105 | − | 0.134599i | −0.824551 | − | 0.565787i | \(-0.808572\pi\) |
0.902262 | + | 0.431189i | \(0.141906\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.59808 | + | 7.96410i | 0.187559 | + | 0.324862i | 0.944436 | − | 0.328695i | \(-0.106609\pi\) |
−0.756877 | + | 0.653558i | \(0.773276\pi\) | |||||||
\(602\) | 12.3923 | 0.505073 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −22.5885 | −0.919111 | ||||||||
\(605\) | 9.86603 | + | 17.0885i | 0.401111 | + | 0.694745i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.2942 | − | 24.7583i | 0.580185 | − | 1.00491i | −0.415272 | − | 0.909697i | \(-0.636314\pi\) |
0.995457 | − | 0.0952124i | \(-0.0303530\pi\) | |||||||
\(608\) | 3.09808 | − | 5.36603i | 0.125644 | − | 0.217621i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.13397 | + | 14.0885i | 0.329335 | + | 0.570425i | ||||
\(611\) | −2.19615 | −0.0888468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.78461 | −0.274028 | −0.137014 | − | 0.990569i | \(-0.543751\pi\) | ||||
−0.137014 | + | 0.990569i | \(0.543751\pi\) | |||||||
\(614\) | −4.00000 | − | 6.92820i | −0.161427 | − | 0.279600i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.36603 | + | 4.09808i | −0.0953299 | + | 0.165116i | ||||
\(617\) | −8.25833 | + | 14.3038i | −0.332468 | + | 0.575851i | −0.982995 | − | 0.183632i | \(-0.941215\pi\) |
0.650527 | + | 0.759483i | \(0.274548\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.00000 | + | 3.46410i | 0.0803868 | + | 0.139234i | 0.903416 | − | 0.428765i | \(-0.141051\pi\) |
−0.823029 | + | 0.567999i | \(0.807718\pi\) | |||||||
\(620\) | −7.26795 | −0.291888 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.9808 | −0.921445 | ||||||||
\(623\) | 6.23205 | + | 10.7942i | 0.249682 | + | 0.432462i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | −10.9904 | + | 19.0359i | −0.439264 | + | 0.760828i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.69615 | − | 13.3301i | −0.307110 | − | 0.531930i | ||||
\(629\) | −20.6603 | −0.823778 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.5885 | −0.899232 | −0.449616 | − | 0.893222i | \(-0.648439\pi\) | ||||
−0.449616 | + | 0.893222i | \(0.648439\pi\) | |||||||
\(632\) | 3.09808 | + | 5.36603i | 0.123235 | + | 0.213449i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.696152 | − | 1.20577i | 0.0276477 | − | 0.0478873i | ||||
\(635\) | −3.46410 | + | 6.00000i | −0.137469 | + | 0.238103i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.500000 | + | 0.866025i | 0.0198107 | + | 0.0343132i | ||||
\(638\) | 30.5885 | 1.21101 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.73205 | −0.0684653 | ||||||||
\(641\) | −4.66987 | − | 8.08846i | −0.184449 | − | 0.319475i | 0.758942 | − | 0.651158i | \(-0.225717\pi\) |
−0.943391 | + | 0.331684i | \(0.892383\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.90192 | + | 15.4186i | −0.351058 | + | 0.608050i | −0.986435 | − | 0.164152i | \(-0.947511\pi\) |
0.635377 | + | 0.772202i | \(0.280845\pi\) | |||||||
\(644\) | −0.633975 | + | 1.09808i | −0.0249821 | + | 0.0432703i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.0263 | + | 34.6865i | 0.787923 | + | 1.36472i | ||||
\(647\) | −23.3205 | −0.916824 | −0.458412 | − | 0.888740i | \(-0.651582\pi\) | ||||
−0.458412 | + | 0.888740i | \(0.651582\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −38.7846 | −1.52243 | ||||||||
\(650\) | −1.00000 | − | 1.73205i | −0.0392232 | − | 0.0679366i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.1962 | + | 21.1244i | −0.477638 | + | 0.827294i | ||||
\(653\) | 17.6603 | − | 30.5885i | 0.691099 | − | 1.19702i | −0.280379 | − | 0.959889i | \(-0.590460\pi\) |
0.971478 | − | 0.237129i | \(-0.0762065\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.19615 | − | 3.80385i | −0.0858108 | − | 0.148629i | ||||
\(656\) | 2.53590 | 0.0990102 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.19615 | 0.0856149 | ||||||||
\(659\) | −0.339746 | − | 0.588457i | −0.0132346 | − | 0.0229230i | 0.859332 | − | 0.511418i | \(-0.170880\pi\) |
−0.872567 | + | 0.488495i | \(0.837546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.6962 | + | 28.9186i | −0.649405 | + | 1.12480i | 0.333860 | + | 0.942623i | \(0.391649\pi\) |
−0.983265 | + | 0.182180i | \(0.941685\pi\) | |||||||
\(662\) | 14.5885 | − | 25.2679i | 0.566996 | − | 0.982067i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.633975 | − | 1.09808i | −0.0246030 | − | 0.0426136i | ||||
\(665\) | 10.7321 | 0.416171 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.19615 | 0.317356 | ||||||||
\(668\) | 3.63397 | + | 6.29423i | 0.140603 | + | 0.243531i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.63397 | − | 6.29423i | 0.140393 | − | 0.243167i | ||||
\(671\) | −22.2224 | + | 38.4904i | −0.857887 | + | 1.48590i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.08846 | − | 15.7417i | −0.350334 | − | 0.606797i | 0.635974 | − | 0.771711i | \(-0.280599\pi\) |
−0.986308 | + | 0.164914i | \(0.947265\pi\) | |||||||
\(674\) | −32.3923 | −1.24770 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | −22.3923 | − | 38.7846i | −0.860606 | − | 1.49061i | −0.871345 | − | 0.490671i | \(-0.836752\pi\) |
0.0107386 | − | 0.999942i | \(-0.496582\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.00000 | − | 13.8564i | 0.307012 | − | 0.531760i | ||||
\(680\) | 5.59808 | − | 9.69615i | 0.214676 | − | 0.371830i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.92820 | − | 17.1962i | −0.380171 | − | 0.658475i | ||||
\(683\) | −39.7128 | −1.51957 | −0.759784 | − | 0.650175i | \(-0.774695\pi\) | ||||
−0.759784 | + | 0.650175i | \(0.774695\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.60770 | 0.176051 | ||||||||
\(686\) | −0.500000 | − | 0.866025i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.19615 | + | 10.7321i | −0.236226 | + | 0.409156i | ||||
\(689\) | 4.73205 | − | 8.19615i | 0.180277 | − | 0.312249i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0000 | − | 38.1051i | −0.836919 | − | 1.44959i | −0.892458 | − | 0.451130i | \(-0.851021\pi\) |
0.0555386 | − | 0.998457i | \(-0.482312\pi\) | |||||||
\(692\) | −12.8038 | −0.486729 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.3923 | 0.622243 | ||||||||
\(695\) | −15.7583 | − | 27.2942i | −0.597748 | − | 1.03533i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.19615 | + | 14.1962i | −0.310451 | + | 0.537718i | ||||
\(698\) | −6.19615 | + | 10.7321i | −0.234528 | + | 0.406214i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | + | 1.73205i | 0.0377964 | + | 0.0654654i | ||||
\(701\) | 46.1769 | 1.74408 | 0.872039 | − | 0.489436i | \(-0.162797\pi\) | ||||
0.872039 | + | 0.489436i | \(0.162797\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.8038 | 0.746916 | ||||||||
\(704\) | −2.36603 | − | 4.09808i | −0.0891729 | − | 0.154452i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.07180 | + | 3.58846i | −0.0779731 | + | 0.135053i | ||||
\(707\) | −6.46410 | + | 11.1962i | −0.243108 | + | 0.421075i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.79423 | + | 6.57180i | 0.142495 | + | 0.246809i | 0.928436 | − | 0.371493i | \(-0.121154\pi\) |
−0.785940 | + | 0.618302i | \(0.787821\pi\) | |||||||
\(710\) | 7.60770 | 0.285512 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.4641 | −0.467112 | ||||||||
\(713\) | −2.66025 | − | 4.60770i | −0.0996273 | − | 0.172560i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.09808 | + | 7.09808i | −0.153259 | + | 0.265453i | ||||
\(716\) | −3.63397 | + | 6.29423i | −0.135808 | + | 0.235226i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.46410 | − | 16.3923i | −0.353197 | − | 0.611755i | ||||
\(719\) | 23.3205 | 0.869708 | 0.434854 | − | 0.900501i | \(-0.356800\pi\) | ||||
0.434854 | + | 0.900501i | \(0.356800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.39230 | −0.312546 | ||||||||
\(722\) | −9.69615 | − | 16.7942i | −0.360853 | − | 0.625016i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.196152 | + | 0.339746i | −0.00728995 | + | 0.0126266i | ||||
\(725\) | 6.46410 | − | 11.1962i | 0.240071 | − | 0.415815i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.80385 | − | 13.5167i | −0.289429 | − | 0.501305i | 0.684245 | − | 0.729252i | \(-0.260132\pi\) |
−0.973673 | + | 0.227947i | \(0.926799\pi\) | |||||||
\(728\) | −1.00000 | −0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.9282 | 0.589529 | ||||||||
\(731\) | −40.0526 | − | 69.3731i | −1.48140 | − | 2.56586i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.5885 | − | 25.2679i | 0.538837 | − | 0.933293i | −0.460130 | − | 0.887852i | \(-0.652197\pi\) |
0.998967 | − | 0.0454415i | \(-0.0144694\pi\) | |||||||
\(734\) | 2.29423 | − | 3.97372i | 0.0846815 | − | 0.146673i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.633975 | − | 1.09808i | −0.0233686 | − | 0.0404756i | ||||
\(737\) | 19.8564 | 0.731420 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.1962 | −0.890070 | −0.445035 | − | 0.895513i | \(-0.646809\pi\) | ||||
−0.445035 | + | 0.895513i | \(0.646809\pi\) | |||||||
\(740\) | −2.76795 | − | 4.79423i | −0.101752 | − | 0.176239i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.73205 | + | 8.19615i | −0.173719 | + | 0.300890i | ||||
\(743\) | 10.7321 | − | 18.5885i | 0.393721 | − | 0.681944i | −0.599216 | − | 0.800587i | \(-0.704521\pi\) |
0.992937 | + | 0.118643i | \(0.0378544\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.40192 | − | 5.89230i | −0.124637 | − | 0.215877i | ||||
\(746\) | 20.0000 | 0.732252 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 30.5885 | 1.11842 | ||||||||
\(749\) | 6.92820 | + | 12.0000i | 0.253151 | + | 0.438470i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | − | 3.46410i | 0.0729810 | − | 0.126407i | −0.827225 | − | 0.561870i | \(-0.810082\pi\) |
0.900207 | + | 0.435463i | \(0.143415\pi\) | |||||||
\(752\) | −1.09808 | + | 1.90192i | −0.0400427 | + | 0.0693560i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.23205 | + | 5.59808i | 0.117704 | + | 0.203870i | ||||
\(755\) | 39.1244 | 1.42388 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.78461 | 0.173900 | 0.0869498 | − | 0.996213i | \(-0.472288\pi\) | ||||
0.0869498 | + | 0.996213i | \(0.472288\pi\) | |||||||
\(758\) | 8.29423 | + | 14.3660i | 0.301260 | + | 0.521798i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.36603 | + | 9.29423i | −0.194646 | + | 0.337137i | ||||
\(761\) | 4.16025 | − | 7.20577i | 0.150809 | − | 0.261209i | −0.780716 | − | 0.624886i | \(-0.785145\pi\) |
0.931525 | + | 0.363677i | \(0.118479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.40192 | + | 4.16025i | 0.0869555 | + | 0.150611i | ||||
\(764\) | 24.5885 | 0.889579 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.1436 | −0.366503 | ||||||||
\(767\) | −4.09808 | − | 7.09808i | −0.147973 | − | 0.256297i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.59808 | + | 6.23205i | −0.129750 | + | 0.224733i | −0.923580 | − | 0.383407i | \(-0.874751\pi\) |
0.793830 | + | 0.608140i | \(0.208084\pi\) | |||||||
\(770\) | 4.09808 | − | 7.09808i | 0.147684 | − | 0.255797i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.50000 | + | 16.4545i | 0.341912 | + | 0.592210i | ||||
\(773\) | −21.3397 | −0.767537 | −0.383769 | − | 0.923429i | \(-0.625374\pi\) | ||||
−0.383769 | + | 0.923429i | \(0.625374\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.39230 | −0.301460 | ||||||||
\(776\) | 8.00000 | + | 13.8564i | 0.287183 | + | 0.497416i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.1244 | − | 26.1962i | 0.542234 | − | 0.939178i | ||||
\(779\) | 7.85641 | − | 13.6077i | 0.281485 | − | 0.487546i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.3923 | + | 18.0000i | 0.371866 | + | 0.644091i | ||||
\(782\) | 8.19615 | 0.293094 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 13.3301 | + | 23.0885i | 0.475773 | + | 0.824062i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.5885 | + | 39.1244i | −0.805192 | + | 1.39463i | 0.110970 | + | 0.993824i | \(0.464604\pi\) |
−0.916162 | + | 0.400809i | \(0.868729\pi\) | |||||||
\(788\) | 7.50000 | − | 12.9904i | 0.267176 | − | 0.462763i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.36603 | − | 9.29423i | −0.190915 | − | 0.330674i | ||||
\(791\) | −10.2679 | −0.365086 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.39230 | −0.333531 | ||||||||
\(794\) | 14.6962 | + | 25.4545i | 0.521547 | + | 0.903346i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.2942 | + | 17.8301i | −0.364869 | + | 0.631972i | ||||
\(797\) | −10.6699 | + | 18.4808i | −0.377946 | + | 0.654622i | −0.990763 | − | 0.135603i | \(-0.956703\pi\) |
0.612817 | + | 0.790225i | \(0.290036\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.09808 | − | 12.2942i | −0.251112 | − | 0.434939i | ||||
\(800\) | −2.00000 | −0.0707107 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.2679 | 0.786309 | ||||||||
\(803\) | 21.7583 | + | 37.6865i | 0.767835 | + | 1.32993i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.09808 | − | 1.90192i | 0.0387021 | − | 0.0670340i | ||||
\(806\) | 2.09808 | − | 3.63397i | 0.0739016 | − | 0.128001i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.46410 | − | 11.1962i | −0.227406 | − | 0.393879i | ||||
\(809\) | −0.124356 | −0.00437211 | −0.00218606 | − | 0.999998i | \(-0.500696\pi\) | ||||
−0.00218606 | + | 0.999998i | \(0.500696\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.9808 | 1.93064 | 0.965318 | − | 0.261078i | \(-0.0840778\pi\) | ||||
0.965318 | + | 0.261078i | \(0.0840778\pi\) | |||||||
\(812\) | −3.23205 | − | 5.59808i | −0.113423 | − | 0.196454i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.56218 | − | 13.0981i | 0.265054 | − | 0.459087i | ||||
\(815\) | 21.1244 | − | 36.5885i | 0.739954 | − | 1.28164i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.3923 | + | 66.4974i | 1.34318 | + | 2.32645i | ||||
\(818\) | −21.1962 | −0.741106 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.39230 | −0.153386 | ||||||||
\(821\) | 7.50000 | + | 12.9904i | 0.261752 | + | 0.453367i | 0.966708 | − | 0.255884i | \(-0.0823665\pi\) |
−0.704956 | + | 0.709251i | \(0.749033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.3923 | − | 21.4641i | 0.431969 | − | 0.748192i | −0.565074 | − | 0.825040i | \(-0.691152\pi\) |
0.997043 | + | 0.0768486i | \(0.0244858\pi\) | |||||||
\(824\) | 4.19615 | − | 7.26795i | 0.146180 | − | 0.253191i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.09808 | + | 7.09808i | 0.142590 | + | 0.246974i | ||||
\(827\) | 19.6077 | 0.681826 | 0.340913 | − | 0.940095i | \(-0.389264\pi\) | ||||
0.340913 | + | 0.940095i | \(0.389264\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.0000 | 0.903017 | 0.451509 | − | 0.892267i | \(-0.350886\pi\) | ||||
0.451509 | + | 0.892267i | \(0.350886\pi\) | |||||||
\(830\) | 1.09808 | + | 1.90192i | 0.0381148 | + | 0.0660167i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.500000 | − | 0.866025i | 0.0173344 | − | 0.0300240i | ||||
\(833\) | −3.23205 | + | 5.59808i | −0.111984 | + | 0.193962i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.29423 | − | 10.9019i | −0.217821 | − | 0.377277i | ||||
\(836\) | −29.3205 | −1.01407 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23.3205 | 0.805594 | ||||||||
\(839\) | −21.1244 | − | 36.5885i | −0.729294 | − | 1.26317i | −0.957182 | − | 0.289487i | \(-0.906515\pi\) |
0.227888 | − | 0.973687i | \(-0.426818\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.39230 | + | 11.0718i | −0.220424 | + | 0.381786i | ||||
\(842\) | −6.59808 | + | 11.4282i | −0.227385 | + | 0.393842i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.90192 | − | 10.2224i | −0.203153 | − | 0.351871i | ||||
\(845\) | 20.7846 | 0.715012 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.3923 | 0.391444 | ||||||||
\(848\) | −4.73205 | − | 8.19615i | −0.162499 | − | 0.281457i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.46410 | − | 11.1962i | 0.221717 | − | 0.384025i | ||||
\(851\) | 2.02628 | − | 3.50962i | 0.0694600 | − | 0.120308i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.00000 | − | 1.73205i | −0.0342393 | − | 0.0593043i | 0.848398 | − | 0.529359i | \(-0.177568\pi\) |
−0.882637 | + | 0.470055i | \(0.844234\pi\) | |||||||
\(854\) | 9.39230 | 0.321398 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.8564 | −0.473602 | ||||||||
\(857\) | 9.23205 | + | 15.9904i | 0.315361 | + | 0.546221i | 0.979514 | − | 0.201375i | \(-0.0645411\pi\) |
−0.664153 | + | 0.747596i | \(0.731208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.196152 | + | 0.339746i | −0.00669263 | + | 0.0115920i | −0.869352 | − | 0.494193i | \(-0.835464\pi\) |
0.862660 | + | 0.505785i | \(0.168797\pi\) | |||||||
\(860\) | 10.7321 | − | 18.5885i | 0.365960 | − | 0.633861i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.339746 | − | 0.588457i | −0.0115718 | − | 0.0200429i | ||||
\(863\) | 23.9090 | 0.813871 | 0.406935 | − | 0.913457i | \(-0.366597\pi\) | ||||
0.406935 | + | 0.913457i | \(0.366597\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.1769 | 0.754038 | ||||||||
\(866\) | 15.7942 | + | 27.3564i | 0.536710 | + | 0.929609i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.09808 | + | 3.63397i | −0.0712133 | + | 0.123345i | ||||
\(869\) | 14.6603 | − | 25.3923i | 0.497315 | − | 0.861375i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.09808 | + | 3.63397i | 0.0710906 | + | 0.123133i | ||||
\(872\) | −4.80385 | −0.162679 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.85641 | −0.265747 | ||||||||
\(875\) | −6.06218 | − | 10.5000i | −0.204939 | − | 0.354965i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.5981 | + | 27.0167i | −0.526710 | + | 0.912288i | 0.472806 | + | 0.881167i | \(0.343241\pi\) |
−0.999516 | + | 0.0311213i | \(0.990092\pi\) | |||||||
\(878\) | −10.5885 | + | 18.3397i | −0.357343 | + | 0.618936i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.09808 | + | 7.09808i | 0.138146 | + | 0.239276i | ||||
\(881\) | −25.1769 | −0.848232 | −0.424116 | − | 0.905608i | \(-0.639415\pi\) | ||||
−0.424116 | + | 0.905608i | \(0.639415\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.9808 | 0.436837 | 0.218419 | − | 0.975855i | \(-0.429910\pi\) | ||||
0.218419 | + | 0.975855i | \(0.429910\pi\) | |||||||
\(884\) | 3.23205 | + | 5.59808i | 0.108706 | + | 0.188284i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.09808 | + | 1.90192i | −0.0368906 | + | 0.0638964i | ||||
\(887\) | −17.8301 | + | 30.8827i | −0.598677 | + | 1.03694i | 0.394340 | + | 0.918965i | \(0.370973\pi\) |
−0.993017 | + | 0.117974i | \(0.962360\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.00000 | + | 3.46410i | 0.0670778 | + | 0.116182i | ||||
\(890\) | 21.5885 | 0.723647 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.3923 | 0.414925 | ||||||||
\(893\) | 6.80385 | + | 11.7846i | 0.227682 | + | 0.394357i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.29423 | − | 10.9019i | 0.210393 | − | 0.364411i | ||||
\(896\) | −0.500000 | + | 0.866025i | −0.0167038 | + | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.00000 | − | 5.19615i | −0.100111 | − | 0.173398i | ||||
\(899\) | 27.1244 | 0.904648 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61.1769 | 2.03810 | ||||||||
\(902\) | −6.00000 | − | 10.3923i | −0.199778 | − | 0.346026i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.13397 | − | 8.89230i | 0.170753 | − | 0.295754i | ||||
\(905\) | 0.339746 | − | 0.588457i | 0.0112935 | − | 0.0195610i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0000 | − | 17.3205i | −0.332045 | − | 0.575118i | 0.650868 | − | 0.759191i | \(-0.274405\pi\) |
−0.982913 | + | 0.184073i | \(0.941072\pi\) | |||||||
\(908\) | −5.07180 | −0.168313 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.73205 | 0.0574169 | ||||||||
\(911\) | 16.0526 | + | 27.8038i | 0.531845 | + | 0.921183i | 0.999309 | + | 0.0371704i | \(0.0118344\pi\) |
−0.467464 | + | 0.884012i | \(0.654832\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.00000 | + | 5.19615i | −0.0992855 | + | 0.171968i | ||||
\(914\) | 0.500000 | − | 0.866025i | 0.0165385 | − | 0.0286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.8923 | + | 18.8660i | 0.359892 | + | 0.623351i | ||||
\(917\) | −2.53590 | −0.0837427 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.8038 | −1.24703 | −0.623517 | − | 0.781810i | \(-0.714297\pi\) | ||||
−0.623517 | + | 0.781810i | \(0.714297\pi\) | |||||||
\(920\) | 1.09808 | + | 1.90192i | 0.0362025 | + | 0.0627046i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.53590 | + | 9.58846i | −0.182315 | + | 0.315779i | ||||
\(923\) | −2.19615 | + | 3.80385i | −0.0722872 | + | 0.125205i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.19615 | − | 5.53590i | −0.105089 | − | 0.182019i | ||||
\(926\) | 5.80385 | 0.190726 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.46410 | 0.212195 | ||||||||
\(929\) | −3.69615 | − | 6.40192i | −0.121267 | − | 0.210040i | 0.799001 | − | 0.601330i | \(-0.205362\pi\) |
−0.920268 | + | 0.391290i | \(0.872029\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.09808 | − | 5.36603i | 0.101535 | − | 0.175864i | ||||
\(932\) | −6.86603 | + | 11.8923i | −0.224904 | + | 0.389545i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.633975 | + | 1.09808i | 0.0207443 | + | 0.0359302i | ||||
\(935\) | −52.9808 | −1.73266 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.8038 | −0.744969 | −0.372485 | − | 0.928038i | \(-0.621494\pi\) | ||||
−0.372485 | + | 0.928038i | \(0.621494\pi\) | |||||||
\(938\) | −2.09808 | − | 3.63397i | −0.0685046 | − | 0.118653i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.90192 | − | 3.29423i | 0.0620339 | − | 0.107446i | ||||
\(941\) | 23.3827 | − | 40.5000i | 0.762254 | − | 1.32026i | −0.179433 | − | 0.983770i | \(-0.557426\pi\) |
0.941686 | − | 0.336492i | \(-0.109241\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.60770 | − | 2.78461i | −0.0523538 | − | 0.0906794i | ||||
\(944\) | −8.19615 | −0.266762 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 58.6410 | 1.90658 | ||||||||
\(947\) | 3.80385 | + | 6.58846i | 0.123608 | + | 0.214096i | 0.921188 | − | 0.389117i | \(-0.127220\pi\) |
−0.797580 | + | 0.603214i | \(0.793887\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.59808 | + | 7.96410i | −0.149260 | + | 0.258526i | ||||
\(950\) | −6.19615 | + | 10.7321i | −0.201030 | + | 0.348194i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.23205 | − | 5.59808i | −0.104751 | − | 0.181435i | ||||
\(953\) | −55.9808 | −1.81339 | −0.906697 | − | 0.421782i | \(-0.861405\pi\) | ||||
−0.906697 | + | 0.421782i | \(0.861405\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.5885 | −1.37813 | ||||||||
\(956\) | −7.56218 | − | 13.0981i | −0.244578 | − | 0.423622i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.36603 | + | 14.4904i | −0.270294 | + | 0.468163i | ||||
\(959\) | 1.33013 | − | 2.30385i | 0.0429520 | − | 0.0743951i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.69615 | + | 11.5981i | 0.216005 | + | 0.374131i | ||||
\(962\) | 3.19615 | 0.103048 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.5885 | −0.437655 | ||||||||
\(965\) | −16.4545 | − | 28.5000i | −0.529689 | − | 0.917447i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.2942 | − | 19.5622i | 0.363198 | − | 0.629077i | −0.625287 | − | 0.780395i | \(-0.715018\pi\) |
0.988485 | + | 0.151317i | \(0.0483516\pi\) | |||||||
\(968\) | −5.69615 | + | 9.86603i | −0.183081 | + | 0.317106i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.8564 | − | 24.0000i | −0.444902 | − | 0.770594i | ||||
\(971\) | 3.12436 | 0.100265 | 0.0501327 | − | 0.998743i | \(-0.484036\pi\) | ||||
0.0501327 | + | 0.998743i | \(0.484036\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.1962 | −0.583342 | ||||||||
\(974\) | 3.09808 | + | 5.36603i | 0.0992688 | + | 0.171939i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.69615 | + | 8.13397i | −0.150320 | + | 0.260362i | ||||
\(977\) | −17.7846 | + | 30.8038i | −0.568980 | + | 0.985502i | 0.427687 | + | 0.903927i | \(0.359329\pi\) |
−0.996667 | + | 0.0815755i | \(0.974005\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.4904 | + | 51.0788i | 0.942517 | + | 1.63249i | ||||
\(980\) | −1.73205 | −0.0553283 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.3205 | 0.361252 | ||||||||
\(983\) | 20.5359 | + | 35.5692i | 0.654993 | + | 1.13448i | 0.981895 | + | 0.189424i | \(0.0606620\pi\) |
−0.326902 | + | 0.945058i | \(0.606005\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.9904 | + | 22.5000i | −0.413908 | + | 0.716910i | ||||
\(986\) | −20.8923 | + | 36.1865i | −0.665347 | + | 1.15241i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.09808 | − | 5.36603i | −0.0985629 | − | 0.170716i | ||||
\(989\) | 15.7128 | 0.499638 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.9808 | 1.36533 | 0.682664 | − | 0.730732i | \(-0.260821\pi\) | ||||
0.682664 | + | 0.730732i | \(0.260821\pi\) | |||||||
\(992\) | −2.09808 | − | 3.63397i | −0.0666140 | − | 0.115379i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.19615 | − | 3.80385i | 0.0696577 | − | 0.120651i | ||||
\(995\) | 17.8301 | − | 30.8827i | 0.565253 | − | 0.979047i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.8923 | + | 18.8660i | 0.344963 | + | 0.597493i | 0.985347 | − | 0.170562i | \(-0.0545582\pi\) |
−0.640384 | + | 0.768055i | \(0.721225\pi\) | |||||||
\(998\) | 20.5885 | 0.651716 | ||||||||
\(999\) | 0 | 0 |
(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 | 1134.2.f.q.757.2 | 4 | ||
3.2 | odd | 2 | 1134.2.f.t.757.1 | 4 | |||
9.2 | odd | 6 | 1134.2.f.t.379.1 | 4 | |||
9.4 | even | 3 | 1134.2.a.o.1.1 | yes | 2 | ||
9.5 | odd | 6 | 1134.2.a.j.1.2 | ✓ | 2 | ||
9.7 | even | 3 | inner | 1134.2.f.q.379.2 | 4 | ||
36.23 | even | 6 | 9072.2.a.bi.1.2 | 2 | |||
36.31 | odd | 6 | 9072.2.a.bf.1.1 | 2 | |||
63.13 | odd | 6 | 7938.2.a.br.1.2 | 2 | |||
63.41 | even | 6 | 7938.2.a.bi.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.a.j.1.2 | ✓ | 2 | 9.5 | odd | 6 | ||
1134.2.a.o.1.1 | yes | 2 | 9.4 | even | 3 | ||
1134.2.f.q.379.2 | 4 | 9.7 | even | 3 | inner | ||
1134.2.f.q.757.2 | 4 | 1.1 | even | 1 | trivial | ||
1134.2.f.t.379.1 | 4 | 9.2 | odd | 6 | |||
1134.2.f.t.757.1 | 4 | 3.2 | odd | 2 | |||
7938.2.a.bi.1.1 | 2 | 63.41 | even | 6 | |||
7938.2.a.br.1.2 | 2 | 63.13 | odd | 6 | |||
9072.2.a.bf.1.1 | 2 | 36.31 | odd | 6 | |||
9072.2.a.bi.1.2 | 2 | 36.23 | even | 6 |