Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(211,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("546.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.l (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(1.28078 - 2.21837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.211 |
Dual form | 546.2.l.i.295.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −3.56155 | −1.59277 | −0.796387 | − | 0.604787i | \(-0.793258\pi\) | ||||
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.78078 | + | 3.08440i | 0.563131 | + | 0.975371i | ||||
\(11\) | −1.28078 | − | 2.21837i | −0.386169 | − | 0.668864i | 0.605762 | − | 0.795646i | \(-0.292868\pi\) |
−0.991931 | + | 0.126782i | \(0.959535\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −0.500000 | + | 3.57071i | −0.138675 | + | 0.990338i | ||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 1.78078 | + | 3.08440i | 0.459794 | + | 0.796387i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.50000 | − | 4.33013i | 0.606339 | − | 1.05021i | −0.385499 | − | 0.922708i | \(-0.625971\pi\) |
0.991838 | − | 0.127502i | \(-0.0406959\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.84233 | + | 6.65511i | −0.881491 | + | 1.52679i | −0.0318071 | + | 0.999494i | \(0.510126\pi\) |
−0.849684 | + | 0.527293i | \(0.823207\pi\) | |||||||
\(20\) | 1.78078 | − | 3.08440i | 0.398194 | − | 0.689692i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −1.28078 | + | 2.21837i | −0.273062 | + | 0.472958i | ||||
\(23\) | 4.56155 | + | 7.90084i | 0.951150 | + | 1.64744i | 0.742943 | + | 0.669354i | \(0.233429\pi\) |
0.208206 | + | 0.978085i | \(0.433237\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 7.68466 | 1.53693 | ||||||||
\(26\) | 3.34233 | − | 1.35234i | 0.655485 | − | 0.265217i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.500000 | + | 0.866025i | 0.0944911 | + | 0.163663i | ||||
\(29\) | 0.500000 | + | 0.866025i | 0.0928477 | + | 0.160817i | 0.908708 | − | 0.417432i | \(-0.137070\pi\) |
−0.815861 | + | 0.578249i | \(0.803736\pi\) | |||||||
\(30\) | 1.78078 | − | 3.08440i | 0.325124 | − | 0.563131i | ||||
\(31\) | 5.12311 | 0.920137 | 0.460068 | − | 0.887883i | \(-0.347825\pi\) | ||||
0.460068 | + | 0.887883i | \(0.347825\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.28078 | + | 2.21837i | −0.222955 | + | 0.386169i | ||||
\(34\) | −5.00000 | −0.857493 | ||||||||
\(35\) | −1.78078 | + | 3.08440i | −0.301006 | + | 0.521358i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 4.90388 | + | 8.49377i | 0.806193 | + | 1.39637i | 0.915483 | + | 0.402358i | \(0.131809\pi\) |
−0.109289 | + | 0.994010i | \(0.534857\pi\) | |||||||
\(38\) | 7.68466 | 1.24662 | ||||||||
\(39\) | 3.34233 | − | 1.35234i | 0.535201 | − | 0.216548i | ||||
\(40\) | −3.56155 | −0.563131 | ||||||||
\(41\) | −2.06155 | − | 3.57071i | −0.321960 | − | 0.557652i | 0.658932 | − | 0.752202i | \(-0.271008\pi\) |
−0.980892 | + | 0.194551i | \(0.937675\pi\) | |||||||
\(42\) | 0.500000 | + | 0.866025i | 0.0771517 | + | 0.133631i | ||||
\(43\) | 1.43845 | − | 2.49146i | 0.219361 | − | 0.379945i | −0.735252 | − | 0.677794i | \(-0.762936\pi\) |
0.954613 | + | 0.297850i | \(0.0962694\pi\) | |||||||
\(44\) | 2.56155 | 0.386169 | ||||||||
\(45\) | 1.78078 | − | 3.08440i | 0.265462 | − | 0.459794i | ||||
\(46\) | 4.56155 | − | 7.90084i | 0.672564 | − | 1.16492i | ||||
\(47\) | −7.68466 | −1.12092 | −0.560461 | − | 0.828181i | \(-0.689376\pi\) | ||||
−0.560461 | + | 0.828181i | \(0.689376\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −3.84233 | − | 6.65511i | −0.543387 | − | 0.941175i | ||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | −2.84233 | − | 2.21837i | −0.394160 | − | 0.307633i | ||||
\(53\) | −3.87689 | −0.532532 | −0.266266 | − | 0.963900i | \(-0.585790\pi\) | ||||
−0.266266 | + | 0.963900i | \(0.585790\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 4.56155 | + | 7.90084i | 0.615080 | + | 1.06535i | ||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | 7.68466 | 1.01786 | ||||||||
\(58\) | 0.500000 | − | 0.866025i | 0.0656532 | − | 0.113715i | ||||
\(59\) | −6.56155 | + | 11.3649i | −0.854241 | + | 1.47959i | 0.0231056 | + | 0.999733i | \(0.492645\pi\) |
−0.877347 | + | 0.479857i | \(0.840689\pi\) | |||||||
\(60\) | −3.56155 | −0.459794 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | −2.56155 | − | 4.43674i | −0.325318 | − | 0.563466i | ||||
\(63\) | 0.500000 | + | 0.866025i | 0.0629941 | + | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.78078 | − | 12.7173i | 0.220878 | − | 1.57739i | ||||
\(66\) | 2.56155 | 0.315305 | ||||||||
\(67\) | −0.561553 | − | 0.972638i | −0.0686046 | − | 0.118827i | 0.829683 | − | 0.558235i | \(-0.188521\pi\) |
−0.898287 | + | 0.439409i | \(0.855188\pi\) | |||||||
\(68\) | 2.50000 | + | 4.33013i | 0.303170 | + | 0.525105i | ||||
\(69\) | 4.56155 | − | 7.90084i | 0.549146 | − | 0.951150i | ||||
\(70\) | 3.56155 | 0.425687 | ||||||||
\(71\) | 2.00000 | − | 3.46410i | 0.237356 | − | 0.411113i | −0.722599 | − | 0.691268i | \(-0.757052\pi\) |
0.959955 | + | 0.280155i | \(0.0903858\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −2.43845 | −0.285399 | −0.142699 | − | 0.989766i | \(-0.545578\pi\) | ||||
−0.142699 | + | 0.989766i | \(0.545578\pi\) | |||||||
\(74\) | 4.90388 | − | 8.49377i | 0.570065 | − | 0.987381i | ||||
\(75\) | −3.84233 | − | 6.65511i | −0.443674 | − | 0.768466i | ||||
\(76\) | −3.84233 | − | 6.65511i | −0.440745 | − | 0.763393i | ||||
\(77\) | −2.56155 | −0.291916 | ||||||||
\(78\) | −2.84233 | − | 2.21837i | −0.321830 | − | 0.251181i | ||||
\(79\) | 1.43845 | 0.161838 | 0.0809190 | − | 0.996721i | \(-0.474214\pi\) | ||||
0.0809190 | + | 0.996721i | \(0.474214\pi\) | |||||||
\(80\) | 1.78078 | + | 3.08440i | 0.199097 | + | 0.344846i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.06155 | + | 3.57071i | −0.227660 | + | 0.394319i | ||||
\(83\) | −10.2462 | −1.12467 | −0.562334 | − | 0.826910i | \(-0.690096\pi\) | ||||
−0.562334 | + | 0.826910i | \(0.690096\pi\) | |||||||
\(84\) | 0.500000 | − | 0.866025i | 0.0545545 | − | 0.0944911i | ||||
\(85\) | −8.90388 | + | 15.4220i | −0.965762 | + | 1.67275i | ||||
\(86\) | −2.87689 | −0.310223 | ||||||||
\(87\) | 0.500000 | − | 0.866025i | 0.0536056 | − | 0.0928477i | ||||
\(88\) | −1.28078 | − | 2.21837i | −0.136531 | − | 0.236479i | ||||
\(89\) | 4.84233 | + | 8.38716i | 0.513286 | + | 0.889037i | 0.999881 | + | 0.0154098i | \(0.00490527\pi\) |
−0.486595 | + | 0.873627i | \(0.661761\pi\) | |||||||
\(90\) | −3.56155 | −0.375421 | ||||||||
\(91\) | 2.84233 | + | 2.21837i | 0.297957 | + | 0.232548i | ||||
\(92\) | −9.12311 | −0.951150 | ||||||||
\(93\) | −2.56155 | − | 4.43674i | −0.265621 | − | 0.460068i | ||||
\(94\) | 3.84233 | + | 6.65511i | 0.396306 | + | 0.686422i | ||||
\(95\) | 13.6847 | − | 23.7025i | 1.40402 | − | 2.43183i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −6.12311 | + | 10.6055i | −0.621707 | + | 1.07683i | 0.367461 | + | 0.930039i | \(0.380227\pi\) |
−0.989168 | + | 0.146789i | \(0.953106\pi\) | |||||||
\(98\) | −0.500000 | + | 0.866025i | −0.0505076 | + | 0.0874818i | ||||
\(99\) | 2.56155 | 0.257446 | ||||||||
\(100\) | −3.84233 | + | 6.65511i | −0.384233 | + | 0.665511i | ||||
\(101\) | 9.78078 | + | 16.9408i | 0.973224 | + | 1.68567i | 0.685677 | + | 0.727906i | \(0.259506\pi\) |
0.287547 | + | 0.957767i | \(0.407160\pi\) | |||||||
\(102\) | 2.50000 | + | 4.33013i | 0.247537 | + | 0.428746i | ||||
\(103\) | −11.3693 | −1.12025 | −0.560126 | − | 0.828407i | \(-0.689247\pi\) | ||||
−0.560126 | + | 0.828407i | \(0.689247\pi\) | |||||||
\(104\) | −0.500000 | + | 3.57071i | −0.0490290 | + | 0.350137i | ||||
\(105\) | 3.56155 | 0.347572 | ||||||||
\(106\) | 1.93845 | + | 3.35749i | 0.188279 | + | 0.326108i | ||||
\(107\) | 4.71922 | + | 8.17394i | 0.456225 | + | 0.790204i | 0.998758 | − | 0.0498303i | \(-0.0158680\pi\) |
−0.542533 | + | 0.840034i | \(0.682535\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 0.876894 | 0.0839912 | 0.0419956 | − | 0.999118i | \(-0.486628\pi\) | ||||
0.0419956 | + | 0.999118i | \(0.486628\pi\) | |||||||
\(110\) | 4.56155 | − | 7.90084i | 0.434927 | − | 0.753316i | ||||
\(111\) | 4.90388 | − | 8.49377i | 0.465456 | − | 0.806193i | ||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −8.46543 | + | 14.6626i | −0.796361 | + | 1.37934i | 0.125610 | + | 0.992080i | \(0.459911\pi\) |
−0.921971 | + | 0.387258i | \(0.873422\pi\) | |||||||
\(114\) | −3.84233 | − | 6.65511i | −0.359867 | − | 0.623308i | ||||
\(115\) | −16.2462 | − | 28.1393i | −1.51497 | − | 2.62400i | ||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −2.84233 | − | 2.21837i | −0.262773 | − | 0.205088i | ||||
\(118\) | 13.1231 | 1.20808 | ||||||||
\(119\) | −2.50000 | − | 4.33013i | −0.229175 | − | 0.396942i | ||||
\(120\) | 1.78078 | + | 3.08440i | 0.162562 | + | 0.281565i | ||||
\(121\) | 2.21922 | − | 3.84381i | 0.201748 | − | 0.349437i | ||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | −2.06155 | + | 3.57071i | −0.185884 | + | 0.321960i | ||||
\(124\) | −2.56155 | + | 4.43674i | −0.230034 | + | 0.398431i | ||||
\(125\) | −9.56155 | −0.855211 | ||||||||
\(126\) | 0.500000 | − | 0.866025i | 0.0445435 | − | 0.0771517i | ||||
\(127\) | −1.12311 | − | 1.94528i | −0.0996595 | − | 0.172615i | 0.811884 | − | 0.583818i | \(-0.198442\pi\) |
−0.911544 | + | 0.411203i | \(0.865109\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −2.87689 | −0.253296 | ||||||||
\(130\) | −11.9039 | + | 4.81645i | −1.04404 | + | 0.422430i | ||||
\(131\) | −16.4924 | −1.44095 | −0.720475 | − | 0.693481i | \(-0.756076\pi\) | ||||
−0.720475 | + | 0.693481i | \(0.756076\pi\) | |||||||
\(132\) | −1.28078 | − | 2.21837i | −0.111477 | − | 0.193084i | ||||
\(133\) | 3.84233 | + | 6.65511i | 0.333172 | + | 0.577071i | ||||
\(134\) | −0.561553 | + | 0.972638i | −0.0485108 | + | 0.0840231i | ||||
\(135\) | −3.56155 | −0.306530 | ||||||||
\(136\) | 2.50000 | − | 4.33013i | 0.214373 | − | 0.371305i | ||||
\(137\) | 2.90388 | − | 5.02967i | 0.248095 | − | 0.429714i | −0.714902 | − | 0.699225i | \(-0.753529\pi\) |
0.962997 | + | 0.269511i | \(0.0868620\pi\) | |||||||
\(138\) | −9.12311 | −0.776610 | ||||||||
\(139\) | 3.84233 | − | 6.65511i | 0.325902 | − | 0.564479i | −0.655792 | − | 0.754941i | \(-0.727665\pi\) |
0.981695 | + | 0.190462i | \(0.0609987\pi\) | |||||||
\(140\) | −1.78078 | − | 3.08440i | −0.150503 | − | 0.260679i | ||||
\(141\) | 3.84233 | + | 6.65511i | 0.323582 | + | 0.560461i | ||||
\(142\) | −4.00000 | −0.335673 | ||||||||
\(143\) | 8.56155 | − | 3.46410i | 0.715953 | − | 0.289683i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.78078 | − | 3.08440i | −0.147885 | − | 0.256145i | ||||
\(146\) | 1.21922 | + | 2.11176i | 0.100904 | + | 0.174770i | ||||
\(147\) | −0.500000 | + | 0.866025i | −0.0412393 | + | 0.0714286i | ||||
\(148\) | −9.80776 | −0.806193 | ||||||||
\(149\) | 8.90388 | − | 15.4220i | 0.729434 | − | 1.26342i | −0.227688 | − | 0.973734i | \(-0.573117\pi\) |
0.957123 | − | 0.289683i | \(-0.0935500\pi\) | |||||||
\(150\) | −3.84233 | + | 6.65511i | −0.313725 | + | 0.543387i | ||||
\(151\) | −17.4384 | −1.41912 | −0.709560 | − | 0.704645i | \(-0.751106\pi\) | ||||
−0.709560 | + | 0.704645i | \(0.751106\pi\) | |||||||
\(152\) | −3.84233 | + | 6.65511i | −0.311654 | + | 0.539801i | ||||
\(153\) | 2.50000 | + | 4.33013i | 0.202113 | + | 0.350070i | ||||
\(154\) | 1.28078 | + | 2.21837i | 0.103208 | + | 0.178761i | ||||
\(155\) | −18.2462 | −1.46557 | ||||||||
\(156\) | −0.500000 | + | 3.57071i | −0.0400320 | + | 0.285886i | ||||
\(157\) | −5.80776 | −0.463510 | −0.231755 | − | 0.972774i | \(-0.574447\pi\) | ||||
−0.231755 | + | 0.972774i | \(0.574447\pi\) | |||||||
\(158\) | −0.719224 | − | 1.24573i | −0.0572184 | − | 0.0991051i | ||||
\(159\) | 1.93845 | + | 3.35749i | 0.153729 | + | 0.266266i | ||||
\(160\) | 1.78078 | − | 3.08440i | 0.140783 | − | 0.243843i | ||||
\(161\) | 9.12311 | 0.719001 | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | 0.561553 | − | 0.972638i | 0.0439842 | − | 0.0761829i | −0.843195 | − | 0.537608i | \(-0.819328\pi\) |
0.887179 | + | 0.461425i | \(0.152662\pi\) | |||||||
\(164\) | 4.12311 | 0.321960 | ||||||||
\(165\) | 4.56155 | − | 7.90084i | 0.355116 | − | 0.615080i | ||||
\(166\) | 5.12311 | + | 8.87348i | 0.397630 | + | 0.688716i | ||||
\(167\) | −10.2462 | − | 17.7470i | −0.792876 | − | 1.37330i | −0.924179 | − | 0.381959i | \(-0.875250\pi\) |
0.131304 | − | 0.991342i | \(-0.458084\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −12.5000 | − | 3.57071i | −0.961538 | − | 0.274670i | ||||
\(170\) | 17.8078 | 1.36579 | ||||||||
\(171\) | −3.84233 | − | 6.65511i | −0.293830 | − | 0.508929i | ||||
\(172\) | 1.43845 | + | 2.49146i | 0.109681 | + | 0.189972i | ||||
\(173\) | 2.43845 | − | 4.22351i | 0.185392 | − | 0.321108i | −0.758317 | − | 0.651886i | \(-0.773978\pi\) |
0.943708 | + | 0.330778i | \(0.107311\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | 3.84233 | − | 6.65511i | 0.290453 | − | 0.503079i | ||||
\(176\) | −1.28078 | + | 2.21837i | −0.0965422 | + | 0.167216i | ||||
\(177\) | 13.1231 | 0.986393 | ||||||||
\(178\) | 4.84233 | − | 8.38716i | 0.362948 | − | 0.628644i | ||||
\(179\) | 8.24621 | + | 14.2829i | 0.616351 | + | 1.06755i | 0.990146 | + | 0.140040i | \(0.0447230\pi\) |
−0.373795 | + | 0.927511i | \(0.621944\pi\) | |||||||
\(180\) | 1.78078 | + | 3.08440i | 0.132731 | + | 0.229897i | ||||
\(181\) | 13.2462 | 0.984583 | 0.492292 | − | 0.870430i | \(-0.336159\pi\) | ||||
0.492292 | + | 0.870430i | \(0.336159\pi\) | |||||||
\(182\) | 0.500000 | − | 3.57071i | 0.0370625 | − | 0.264679i | ||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 4.56155 | + | 7.90084i | 0.336282 | + | 0.582458i | ||||
\(185\) | −17.4654 | − | 30.2510i | −1.28408 | − | 2.22410i | ||||
\(186\) | −2.56155 | + | 4.43674i | −0.187822 | + | 0.325318i | ||||
\(187\) | −12.8078 | −0.936596 | ||||||||
\(188\) | 3.84233 | − | 6.65511i | 0.280231 | − | 0.485374i | ||||
\(189\) | 0.500000 | − | 0.866025i | 0.0363696 | − | 0.0629941i | ||||
\(190\) | −27.3693 | −1.98558 | ||||||||
\(191\) | −2.87689 | + | 4.98293i | −0.208165 | + | 0.360552i | −0.951136 | − | 0.308771i | \(-0.900082\pi\) |
0.742972 | + | 0.669323i | \(0.233416\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 10.1847 | + | 17.6403i | 0.733108 | + | 1.26978i | 0.955549 | + | 0.294834i | \(0.0952642\pi\) |
−0.222441 | + | 0.974946i | \(0.571402\pi\) | |||||||
\(194\) | 12.2462 | 0.879227 | ||||||||
\(195\) | −11.9039 | + | 4.81645i | −0.852455 | + | 0.344913i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 0.280776 | + | 0.486319i | 0.0200045 | + | 0.0346488i | 0.875854 | − | 0.482576i | \(-0.160299\pi\) |
−0.855850 | + | 0.517224i | \(0.826965\pi\) | |||||||
\(198\) | −1.28078 | − | 2.21837i | −0.0910208 | − | 0.157653i | ||||
\(199\) | 8.80776 | − | 15.2555i | 0.624366 | − | 1.08143i | −0.364297 | − | 0.931283i | \(-0.618691\pi\) |
0.988663 | − | 0.150151i | \(-0.0479759\pi\) | |||||||
\(200\) | 7.68466 | 0.543387 | ||||||||
\(201\) | −0.561553 | + | 0.972638i | −0.0396089 | + | 0.0686046i | ||||
\(202\) | 9.78078 | − | 16.9408i | 0.688173 | − | 1.19195i | ||||
\(203\) | 1.00000 | 0.0701862 | ||||||||
\(204\) | 2.50000 | − | 4.33013i | 0.175035 | − | 0.303170i | ||||
\(205\) | 7.34233 | + | 12.7173i | 0.512811 | + | 0.888214i | ||||
\(206\) | 5.68466 | + | 9.84612i | 0.396069 | + | 0.686011i | ||||
\(207\) | −9.12311 | −0.634100 | ||||||||
\(208\) | 3.34233 | − | 1.35234i | 0.231749 | − | 0.0937682i | ||||
\(209\) | 19.6847 | 1.36162 | ||||||||
\(210\) | −1.78078 | − | 3.08440i | −0.122885 | − | 0.212843i | ||||
\(211\) | 1.43845 | + | 2.49146i | 0.0990268 | + | 0.171519i | 0.911282 | − | 0.411783i | \(-0.135094\pi\) |
−0.812255 | + | 0.583302i | \(0.801760\pi\) | |||||||
\(212\) | 1.93845 | − | 3.35749i | 0.133133 | − | 0.230593i | ||||
\(213\) | −4.00000 | −0.274075 | ||||||||
\(214\) | 4.71922 | − | 8.17394i | 0.322599 | − | 0.558759i | ||||
\(215\) | −5.12311 | + | 8.87348i | −0.349393 | + | 0.605166i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.56155 | − | 4.43674i | 0.173890 | − | 0.301186i | ||||
\(218\) | −0.438447 | − | 0.759413i | −0.0296954 | − | 0.0514339i | ||||
\(219\) | 1.21922 | + | 2.11176i | 0.0823875 | + | 0.142699i | ||||
\(220\) | −9.12311 | −0.615080 | ||||||||
\(221\) | 14.2116 | + | 11.0918i | 0.955979 | + | 0.746119i | ||||
\(222\) | −9.80776 | −0.658254 | ||||||||
\(223\) | 8.24621 | + | 14.2829i | 0.552207 | + | 0.956451i | 0.998115 | + | 0.0613719i | \(0.0195476\pi\) |
−0.445908 | + | 0.895079i | \(0.647119\pi\) | |||||||
\(224\) | 0.500000 | + | 0.866025i | 0.0334077 | + | 0.0578638i | ||||
\(225\) | −3.84233 | + | 6.65511i | −0.256155 | + | 0.443674i | ||||
\(226\) | 16.9309 | 1.12622 | ||||||||
\(227\) | −6.56155 | + | 11.3649i | −0.435506 | + | 0.754318i | −0.997337 | − | 0.0729341i | \(-0.976764\pi\) |
0.561831 | + | 0.827252i | \(0.310097\pi\) | |||||||
\(228\) | −3.84233 | + | 6.65511i | −0.254464 | + | 0.440745i | ||||
\(229\) | 22.8078 | 1.50718 | 0.753590 | − | 0.657345i | \(-0.228321\pi\) | ||||
0.753590 | + | 0.657345i | \(0.228321\pi\) | |||||||
\(230\) | −16.2462 | + | 28.1393i | −1.07124 | + | 1.85545i | ||||
\(231\) | 1.28078 | + | 2.21837i | 0.0842689 | + | 0.145958i | ||||
\(232\) | 0.500000 | + | 0.866025i | 0.0328266 | + | 0.0568574i | ||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | −0.500000 | + | 3.57071i | −0.0326860 | + | 0.233425i | ||||
\(235\) | 27.3693 | 1.78538 | ||||||||
\(236\) | −6.56155 | − | 11.3649i | −0.427121 | − | 0.739795i | ||||
\(237\) | −0.719224 | − | 1.24573i | −0.0467186 | − | 0.0809190i | ||||
\(238\) | −2.50000 | + | 4.33013i | −0.162051 | + | 0.280680i | ||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | 1.78078 | − | 3.08440i | 0.114949 | − | 0.199097i | ||||
\(241\) | −5.65767 | + | 9.79937i | −0.364443 | + | 0.631233i | −0.988687 | − | 0.149996i | \(-0.952074\pi\) |
0.624244 | + | 0.781229i | \(0.285407\pi\) | |||||||
\(242\) | −4.43845 | −0.285314 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0.500000 | + | 0.866025i | 0.0320092 | + | 0.0554416i | ||||
\(245\) | 1.78078 | + | 3.08440i | 0.113770 | + | 0.197055i | ||||
\(246\) | 4.12311 | 0.262880 | ||||||||
\(247\) | −21.8423 | − | 17.0474i | −1.38979 | − | 1.08470i | ||||
\(248\) | 5.12311 | 0.325318 | ||||||||
\(249\) | 5.12311 | + | 8.87348i | 0.324664 | + | 0.562334i | ||||
\(250\) | 4.78078 | + | 8.28055i | 0.302363 | + | 0.523708i | ||||
\(251\) | −4.24621 | + | 7.35465i | −0.268018 | + | 0.464222i | −0.968350 | − | 0.249596i | \(-0.919702\pi\) |
0.700332 | + | 0.713818i | \(0.253035\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 11.6847 | − | 20.2384i | 0.734608 | − | 1.27238i | ||||
\(254\) | −1.12311 | + | 1.94528i | −0.0704699 | + | 0.122057i | ||||
\(255\) | 17.8078 | 1.11517 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 7.37689 | + | 12.7772i | 0.460158 | + | 0.797017i | 0.998968 | − | 0.0454100i | \(-0.0144594\pi\) |
−0.538810 | + | 0.842427i | \(0.681126\pi\) | |||||||
\(258\) | 1.43845 | + | 2.49146i | 0.0895538 | + | 0.155112i | ||||
\(259\) | 9.80776 | 0.609425 | ||||||||
\(260\) | 10.1231 | + | 7.90084i | 0.627808 | + | 0.489989i | ||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 8.24621 | + | 14.2829i | 0.509453 | + | 0.882398i | ||||
\(263\) | 10.2462 | + | 17.7470i | 0.631808 | + | 1.09432i | 0.987182 | + | 0.159600i | \(0.0510204\pi\) |
−0.355373 | + | 0.934724i | \(0.615646\pi\) | |||||||
\(264\) | −1.28078 | + | 2.21837i | −0.0788263 | + | 0.136531i | ||||
\(265\) | 13.8078 | 0.848204 | ||||||||
\(266\) | 3.84233 | − | 6.65511i | 0.235588 | − | 0.408051i | ||||
\(267\) | 4.84233 | − | 8.38716i | 0.296346 | − | 0.513286i | ||||
\(268\) | 1.12311 | 0.0686046 | ||||||||
\(269\) | 2.43845 | − | 4.22351i | 0.148675 | − | 0.257512i | −0.782063 | − | 0.623199i | \(-0.785833\pi\) |
0.930738 | + | 0.365687i | \(0.119166\pi\) | |||||||
\(270\) | 1.78078 | + | 3.08440i | 0.108375 | + | 0.187710i | ||||
\(271\) | −6.56155 | − | 11.3649i | −0.398586 | − | 0.690371i | 0.594966 | − | 0.803751i | \(-0.297166\pi\) |
−0.993552 | + | 0.113380i | \(0.963832\pi\) | |||||||
\(272\) | −5.00000 | −0.303170 | ||||||||
\(273\) | 0.500000 | − | 3.57071i | 0.0302614 | − | 0.216109i | ||||
\(274\) | −5.80776 | −0.350860 | ||||||||
\(275\) | −9.84233 | − | 17.0474i | −0.593515 | − | 1.02800i | ||||
\(276\) | 4.56155 | + | 7.90084i | 0.274573 | + | 0.475575i | ||||
\(277\) | 1.78078 | − | 3.08440i | 0.106996 | − | 0.185323i | −0.807556 | − | 0.589791i | \(-0.799210\pi\) |
0.914552 | + | 0.404468i | \(0.132543\pi\) | |||||||
\(278\) | −7.68466 | −0.460895 | ||||||||
\(279\) | −2.56155 | + | 4.43674i | −0.153356 | + | 0.265621i | ||||
\(280\) | −1.78078 | + | 3.08440i | −0.106422 | + | 0.184328i | ||||
\(281\) | 7.80776 | 0.465772 | 0.232886 | − | 0.972504i | \(-0.425183\pi\) | ||||
0.232886 | + | 0.972504i | \(0.425183\pi\) | |||||||
\(282\) | 3.84233 | − | 6.65511i | 0.228807 | − | 0.396306i | ||||
\(283\) | −4.24621 | − | 7.35465i | −0.252411 | − | 0.437189i | 0.711778 | − | 0.702404i | \(-0.247890\pi\) |
−0.964189 | + | 0.265216i | \(0.914557\pi\) | |||||||
\(284\) | 2.00000 | + | 3.46410i | 0.118678 | + | 0.205557i | ||||
\(285\) | −27.3693 | −1.62122 | ||||||||
\(286\) | −7.28078 | − | 5.68247i | −0.430521 | − | 0.336012i | ||||
\(287\) | −4.12311 | −0.243379 | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −4.00000 | − | 6.92820i | −0.235294 | − | 0.407541i | ||||
\(290\) | −1.78078 | + | 3.08440i | −0.104571 | + | 0.181122i | ||||
\(291\) | 12.2462 | 0.717886 | ||||||||
\(292\) | 1.21922 | − | 2.11176i | 0.0713497 | − | 0.123581i | ||||
\(293\) | 2.34233 | − | 4.05703i | 0.136840 | − | 0.237014i | −0.789459 | − | 0.613804i | \(-0.789639\pi\) |
0.926299 | + | 0.376789i | \(0.122972\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 23.3693 | − | 40.4768i | 1.36061 | − | 2.35665i | ||||
\(296\) | 4.90388 | + | 8.49377i | 0.285032 | + | 0.493691i | ||||
\(297\) | −1.28078 | − | 2.21837i | −0.0743182 | − | 0.128723i | ||||
\(298\) | −17.8078 | −1.03158 | ||||||||
\(299\) | −30.4924 | + | 12.3376i | −1.76342 | + | 0.713501i | ||||
\(300\) | 7.68466 | 0.443674 | ||||||||
\(301\) | −1.43845 | − | 2.49146i | −0.0829107 | − | 0.143606i | ||||
\(302\) | 8.71922 | + | 15.1021i | 0.501735 | + | 0.869030i | ||||
\(303\) | 9.78078 | − | 16.9408i | 0.561891 | − | 0.973224i | ||||
\(304\) | 7.68466 | 0.440745 | ||||||||
\(305\) | −1.78078 | + | 3.08440i | −0.101967 | + | 0.176612i | ||||
\(306\) | 2.50000 | − | 4.33013i | 0.142915 | − | 0.247537i | ||||
\(307\) | −33.9309 | −1.93654 | −0.968269 | − | 0.249912i | \(-0.919598\pi\) | ||||
−0.968269 | + | 0.249912i | \(0.919598\pi\) | |||||||
\(308\) | 1.28078 | − | 2.21837i | 0.0729790 | − | 0.126403i | ||||
\(309\) | 5.68466 | + | 9.84612i | 0.323389 | + | 0.560126i | ||||
\(310\) | 9.12311 | + | 15.8017i | 0.518158 | + | 0.897475i | ||||
\(311\) | 22.5616 | 1.27935 | 0.639674 | − | 0.768646i | \(-0.279069\pi\) | ||||
0.639674 | + | 0.768646i | \(0.279069\pi\) | |||||||
\(312\) | 3.34233 | − | 1.35234i | 0.189222 | − | 0.0765614i | ||||
\(313\) | 27.6155 | 1.56092 | 0.780461 | − | 0.625205i | \(-0.214984\pi\) | ||||
0.780461 | + | 0.625205i | \(0.214984\pi\) | |||||||
\(314\) | 2.90388 | + | 5.02967i | 0.163876 | + | 0.283841i | ||||
\(315\) | −1.78078 | − | 3.08440i | −0.100335 | − | 0.173786i | ||||
\(316\) | −0.719224 | + | 1.24573i | −0.0404595 | + | 0.0700779i | ||||
\(317\) | −11.5616 | −0.649362 | −0.324681 | − | 0.945824i | \(-0.605257\pi\) | ||||
−0.324681 | + | 0.945824i | \(0.605257\pi\) | |||||||
\(318\) | 1.93845 | − | 3.35749i | 0.108703 | − | 0.188279i | ||||
\(319\) | 1.28078 | − | 2.21837i | 0.0717097 | − | 0.124205i | ||||
\(320\) | −3.56155 | −0.199097 | ||||||||
\(321\) | 4.71922 | − | 8.17394i | 0.263401 | − | 0.456225i | ||||
\(322\) | −4.56155 | − | 7.90084i | −0.254205 | − | 0.440297i | ||||
\(323\) | 19.2116 | + | 33.2755i | 1.06896 | + | 1.85150i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.84233 | + | 27.4397i | −0.213134 | + | 1.52208i | ||||
\(326\) | −1.12311 | −0.0622031 | ||||||||
\(327\) | −0.438447 | − | 0.759413i | −0.0242462 | − | 0.0419956i | ||||
\(328\) | −2.06155 | − | 3.57071i | −0.113830 | − | 0.197160i | ||||
\(329\) | −3.84233 | + | 6.65511i | −0.211834 | + | 0.366908i | ||||
\(330\) | −9.12311 | −0.502210 | ||||||||
\(331\) | 17.6847 | − | 30.6307i | 0.972037 | − | 1.68362i | 0.282651 | − | 0.959223i | \(-0.408786\pi\) |
0.689386 | − | 0.724394i | \(-0.257880\pi\) | |||||||
\(332\) | 5.12311 | − | 8.87348i | 0.281167 | − | 0.486995i | ||||
\(333\) | −9.80776 | −0.537462 | ||||||||
\(334\) | −10.2462 | + | 17.7470i | −0.560648 | + | 0.971070i | ||||
\(335\) | 2.00000 | + | 3.46410i | 0.109272 | + | 0.189264i | ||||
\(336\) | 0.500000 | + | 0.866025i | 0.0272772 | + | 0.0472456i | ||||
\(337\) | −29.4924 | −1.60655 | −0.803277 | − | 0.595605i | \(-0.796912\pi\) | ||||
−0.803277 | + | 0.595605i | \(0.796912\pi\) | |||||||
\(338\) | 3.15767 | + | 12.6107i | 0.171755 | + | 0.685930i | ||||
\(339\) | 16.9309 | 0.919559 | ||||||||
\(340\) | −8.90388 | − | 15.4220i | −0.482881 | − | 0.836374i | ||||
\(341\) | −6.56155 | − | 11.3649i | −0.355328 | − | 0.615446i | ||||
\(342\) | −3.84233 | + | 6.65511i | −0.207769 | + | 0.359867i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 1.43845 | − | 2.49146i | 0.0775559 | − | 0.134331i | ||||
\(345\) | −16.2462 | + | 28.1393i | −0.874667 | + | 1.51497i | ||||
\(346\) | −4.87689 | −0.262183 | ||||||||
\(347\) | 0.157671 | − | 0.273094i | 0.00846421 | − | 0.0146604i | −0.861762 | − | 0.507312i | \(-0.830639\pi\) |
0.870226 | + | 0.492652i | \(0.163972\pi\) | |||||||
\(348\) | 0.500000 | + | 0.866025i | 0.0268028 | + | 0.0464238i | ||||
\(349\) | 3.24621 | + | 5.62260i | 0.173766 | + | 0.300971i | 0.939733 | − | 0.341908i | \(-0.111073\pi\) |
−0.765968 | + | 0.642879i | \(0.777740\pi\) | |||||||
\(350\) | −7.68466 | −0.410762 | ||||||||
\(351\) | −0.500000 | + | 3.57071i | −0.0266880 | + | 0.190591i | ||||
\(352\) | 2.56155 | 0.136531 | ||||||||
\(353\) | 4.90388 | + | 8.49377i | 0.261007 | + | 0.452078i | 0.966510 | − | 0.256629i | \(-0.0826120\pi\) |
−0.705503 | + | 0.708707i | \(0.749279\pi\) | |||||||
\(354\) | −6.56155 | − | 11.3649i | −0.348743 | − | 0.604040i | ||||
\(355\) | −7.12311 | + | 12.3376i | −0.378055 | + | 0.654811i | ||||
\(356\) | −9.68466 | −0.513286 | ||||||||
\(357\) | −2.50000 | + | 4.33013i | −0.132314 | + | 0.229175i | ||||
\(358\) | 8.24621 | − | 14.2829i | 0.435826 | − | 0.754872i | ||||
\(359\) | −4.63068 | −0.244398 | −0.122199 | − | 0.992506i | \(-0.538995\pi\) | ||||
−0.122199 | + | 0.992506i | \(0.538995\pi\) | |||||||
\(360\) | 1.78078 | − | 3.08440i | 0.0938552 | − | 0.162562i | ||||
\(361\) | −20.0270 | − | 34.6878i | −1.05405 | − | 1.82567i | ||||
\(362\) | −6.62311 | − | 11.4716i | −0.348103 | − | 0.602932i | ||||
\(363\) | −4.43845 | −0.232958 | ||||||||
\(364\) | −3.34233 | + | 1.35234i | −0.175186 | + | 0.0708821i | ||||
\(365\) | 8.68466 | 0.454576 | ||||||||
\(366\) | 0.500000 | + | 0.866025i | 0.0261354 | + | 0.0452679i | ||||
\(367\) | −5.68466 | − | 9.84612i | −0.296737 | − | 0.513963i | 0.678651 | − | 0.734461i | \(-0.262565\pi\) |
−0.975387 | + | 0.220498i | \(0.929232\pi\) | |||||||
\(368\) | 4.56155 | − | 7.90084i | 0.237787 | − | 0.411860i | ||||
\(369\) | 4.12311 | 0.214640 | ||||||||
\(370\) | −17.4654 | + | 30.2510i | −0.907985 | + | 1.57268i | ||||
\(371\) | −1.93845 | + | 3.35749i | −0.100639 | + | 0.174312i | ||||
\(372\) | 5.12311 | 0.265621 | ||||||||
\(373\) | −10.7808 | + | 18.6729i | −0.558207 | + | 0.966844i | 0.439439 | + | 0.898273i | \(0.355177\pi\) |
−0.997646 | + | 0.0685711i | \(0.978156\pi\) | |||||||
\(374\) | 6.40388 | + | 11.0918i | 0.331137 | + | 0.573546i | ||||
\(375\) | 4.78078 | + | 8.28055i | 0.246878 | + | 0.427606i | ||||
\(376\) | −7.68466 | −0.396306 | ||||||||
\(377\) | −3.34233 | + | 1.35234i | −0.172139 | + | 0.0696493i | ||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −0.246211 | − | 0.426450i | −0.0126470 | − | 0.0219053i | 0.859633 | − | 0.510913i | \(-0.170692\pi\) |
−0.872280 | + | 0.489007i | \(0.837359\pi\) | |||||||
\(380\) | 13.6847 | + | 23.7025i | 0.702008 | + | 1.21591i | ||||
\(381\) | −1.12311 | + | 1.94528i | −0.0575384 | + | 0.0996595i | ||||
\(382\) | 5.75379 | 0.294389 | ||||||||
\(383\) | −4.15767 | + | 7.20130i | −0.212447 | + | 0.367969i | −0.952480 | − | 0.304602i | \(-0.901477\pi\) |
0.740033 | + | 0.672571i | \(0.234810\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 9.12311 | 0.464957 | ||||||||
\(386\) | 10.1847 | − | 17.6403i | 0.518385 | − | 0.897870i | ||||
\(387\) | 1.43845 | + | 2.49146i | 0.0731204 | + | 0.126648i | ||||
\(388\) | −6.12311 | − | 10.6055i | −0.310854 | − | 0.538414i | ||||
\(389\) | 18.6847 | 0.947350 | 0.473675 | − | 0.880700i | \(-0.342927\pi\) | ||||
0.473675 | + | 0.880700i | \(0.342927\pi\) | |||||||
\(390\) | 10.1231 | + | 7.90084i | 0.512603 | + | 0.400075i | ||||
\(391\) | 45.6155 | 2.30688 | ||||||||
\(392\) | −0.500000 | − | 0.866025i | −0.0252538 | − | 0.0437409i | ||||
\(393\) | 8.24621 | + | 14.2829i | 0.415966 | + | 0.720475i | ||||
\(394\) | 0.280776 | − | 0.486319i | 0.0141453 | − | 0.0245004i | ||||
\(395\) | −5.12311 | −0.257771 | ||||||||
\(396\) | −1.28078 | + | 2.21837i | −0.0643614 | + | 0.111477i | ||||
\(397\) | −0.842329 | + | 1.45896i | −0.0422753 | + | 0.0732230i | −0.886389 | − | 0.462942i | \(-0.846794\pi\) |
0.844114 | + | 0.536164i | \(0.180127\pi\) | |||||||
\(398\) | −17.6155 | −0.882987 | ||||||||
\(399\) | 3.84233 | − | 6.65511i | 0.192357 | − | 0.333172i | ||||
\(400\) | −3.84233 | − | 6.65511i | −0.192116 | − | 0.332755i | ||||
\(401\) | −7.58854 | − | 13.1437i | −0.378954 | − | 0.656367i | 0.611957 | − | 0.790891i | \(-0.290383\pi\) |
−0.990910 | + | 0.134524i | \(0.957049\pi\) | |||||||
\(402\) | 1.12311 | 0.0560154 | ||||||||
\(403\) | −2.56155 | + | 18.2931i | −0.127600 | + | 0.911247i | ||||
\(404\) | −19.5616 | −0.973224 | ||||||||
\(405\) | 1.78078 | + | 3.08440i | 0.0884875 | + | 0.153265i | ||||
\(406\) | −0.500000 | − | 0.866025i | −0.0248146 | − | 0.0429801i | ||||
\(407\) | 12.5616 | − | 21.7572i | 0.622653 | − | 1.07847i | ||||
\(408\) | −5.00000 | −0.247537 | ||||||||
\(409\) | 15.2192 | − | 26.3605i | 0.752542 | − | 1.30344i | −0.194045 | − | 0.980993i | \(-0.562161\pi\) |
0.946587 | − | 0.322449i | \(-0.104506\pi\) | |||||||
\(410\) | 7.34233 | − | 12.7173i | 0.362612 | − | 0.628062i | ||||
\(411\) | −5.80776 | −0.286476 | ||||||||
\(412\) | 5.68466 | − | 9.84612i | 0.280063 | − | 0.485083i | ||||
\(413\) | 6.56155 | + | 11.3649i | 0.322873 | + | 0.559232i | ||||
\(414\) | 4.56155 | + | 7.90084i | 0.224188 | + | 0.388305i | ||||
\(415\) | 36.4924 | 1.79134 | ||||||||
\(416\) | −2.84233 | − | 2.21837i | −0.139357 | − | 0.108765i | ||||
\(417\) | −7.68466 | −0.376319 | ||||||||
\(418\) | −9.84233 | − | 17.0474i | −0.481404 | − | 0.833816i | ||||
\(419\) | −11.3693 | − | 19.6922i | −0.555427 | − | 0.962029i | −0.997870 | − | 0.0652318i | \(-0.979221\pi\) |
0.442443 | − | 0.896797i | \(-0.354112\pi\) | |||||||
\(420\) | −1.78078 | + | 3.08440i | −0.0868930 | + | 0.150503i | ||||
\(421\) | 8.43845 | 0.411265 | 0.205632 | − | 0.978629i | \(-0.434075\pi\) | ||||
0.205632 | + | 0.978629i | \(0.434075\pi\) | |||||||
\(422\) | 1.43845 | − | 2.49146i | 0.0700225 | − | 0.121283i | ||||
\(423\) | 3.84233 | − | 6.65511i | 0.186820 | − | 0.323582i | ||||
\(424\) | −3.87689 | −0.188279 | ||||||||
\(425\) | 19.2116 | − | 33.2755i | 0.931902 | − | 1.61410i | ||||
\(426\) | 2.00000 | + | 3.46410i | 0.0969003 | + | 0.167836i | ||||
\(427\) | −0.500000 | − | 0.866025i | −0.0241967 | − | 0.0419099i | ||||
\(428\) | −9.43845 | −0.456225 | ||||||||
\(429\) | −7.28078 | − | 5.68247i | −0.351519 | − | 0.274352i | ||||
\(430\) | 10.2462 | 0.494116 | ||||||||
\(431\) | 9.36932 | + | 16.2281i | 0.451304 | + | 0.781682i | 0.998467 | − | 0.0553443i | \(-0.0176256\pi\) |
−0.547163 | + | 0.837026i | \(0.684292\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 2.65767 | − | 4.60322i | 0.127720 | − | 0.221217i | −0.795073 | − | 0.606514i | \(-0.792568\pi\) |
0.922793 | + | 0.385297i | \(0.125901\pi\) | |||||||
\(434\) | −5.12311 | −0.245917 | ||||||||
\(435\) | −1.78078 | + | 3.08440i | −0.0853817 | + | 0.147885i | ||||
\(436\) | −0.438447 | + | 0.759413i | −0.0209978 | + | 0.0363693i | ||||
\(437\) | −70.1080 | −3.35372 | ||||||||
\(438\) | 1.21922 | − | 2.11176i | 0.0582568 | − | 0.100904i | ||||
\(439\) | 14.2462 | + | 24.6752i | 0.679935 | + | 1.17768i | 0.975000 | + | 0.222204i | \(0.0713252\pi\) |
−0.295066 | + | 0.955477i | \(0.595342\pi\) | |||||||
\(440\) | 4.56155 | + | 7.90084i | 0.217463 | + | 0.376658i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 2.50000 | − | 17.8536i | 0.118913 | − | 0.849208i | ||||
\(443\) | −34.4233 | −1.63550 | −0.817750 | − | 0.575574i | \(-0.804779\pi\) | ||||
−0.817750 | + | 0.575574i | \(0.804779\pi\) | |||||||
\(444\) | 4.90388 | + | 8.49377i | 0.232728 | + | 0.403097i | ||||
\(445\) | −17.2462 | − | 29.8713i | −0.817549 | − | 1.41604i | ||||
\(446\) | 8.24621 | − | 14.2829i | 0.390469 | − | 0.676313i | ||||
\(447\) | −17.8078 | −0.842278 | ||||||||
\(448\) | 0.500000 | − | 0.866025i | 0.0236228 | − | 0.0409159i | ||||
\(449\) | −9.00000 | + | 15.5885i | −0.424736 | + | 0.735665i | −0.996396 | − | 0.0848262i | \(-0.972967\pi\) |
0.571660 | + | 0.820491i | \(0.306300\pi\) | |||||||
\(450\) | 7.68466 | 0.362258 | ||||||||
\(451\) | −5.28078 | + | 9.14657i | −0.248662 | + | 0.430695i | ||||
\(452\) | −8.46543 | − | 14.6626i | −0.398181 | − | 0.689669i | ||||
\(453\) | 8.71922 | + | 15.1021i | 0.409665 | + | 0.709560i | ||||
\(454\) | 13.1231 | 0.615898 | ||||||||
\(455\) | −10.1231 | − | 7.90084i | −0.474579 | − | 0.370397i | ||||
\(456\) | 7.68466 | 0.359867 | ||||||||
\(457\) | 6.65767 | + | 11.5314i | 0.311433 | + | 0.539417i | 0.978673 | − | 0.205425i | \(-0.0658578\pi\) |
−0.667240 | + | 0.744843i | \(0.732524\pi\) | |||||||
\(458\) | −11.4039 | − | 19.7521i | −0.532868 | − | 0.922955i | ||||
\(459\) | 2.50000 | − | 4.33013i | 0.116690 | − | 0.202113i | ||||
\(460\) | 32.4924 | 1.51497 | ||||||||
\(461\) | −15.0270 | + | 26.0275i | −0.699877 | + | 1.21222i | 0.268632 | + | 0.963243i | \(0.413428\pi\) |
−0.968509 | + | 0.248979i | \(0.919905\pi\) | |||||||
\(462\) | 1.28078 | − | 2.21837i | 0.0595871 | − | 0.103208i | ||||
\(463\) | −11.6847 | −0.543032 | −0.271516 | − | 0.962434i | \(-0.587525\pi\) | ||||
−0.271516 | + | 0.962434i | \(0.587525\pi\) | |||||||
\(464\) | 0.500000 | − | 0.866025i | 0.0232119 | − | 0.0402042i | ||||
\(465\) | 9.12311 | + | 15.8017i | 0.423074 | + | 0.732785i | ||||
\(466\) | 3.00000 | + | 5.19615i | 0.138972 | + | 0.240707i | ||||
\(467\) | 28.0000 | 1.29569 | 0.647843 | − | 0.761774i | \(-0.275671\pi\) | ||||
0.647843 | + | 0.761774i | \(0.275671\pi\) | |||||||
\(468\) | 3.34233 | − | 1.35234i | 0.154499 | − | 0.0625121i | ||||
\(469\) | −1.12311 | −0.0518602 | ||||||||
\(470\) | −13.6847 | − | 23.7025i | −0.631226 | − | 1.09332i | ||||
\(471\) | 2.90388 | + | 5.02967i | 0.133804 | + | 0.231755i | ||||
\(472\) | −6.56155 | + | 11.3649i | −0.302020 | + | 0.523114i | ||||
\(473\) | −7.36932 | −0.338842 | ||||||||
\(474\) | −0.719224 | + | 1.24573i | −0.0330350 | + | 0.0572184i | ||||
\(475\) | −29.5270 | + | 51.1422i | −1.35479 | + | 2.34657i | ||||
\(476\) | 5.00000 | 0.229175 | ||||||||
\(477\) | 1.93845 | − | 3.35749i | 0.0887554 | − | 0.153729i | ||||
\(478\) | −2.00000 | − | 3.46410i | −0.0914779 | − | 0.158444i | ||||
\(479\) | 1.28078 | + | 2.21837i | 0.0585202 | + | 0.101360i | 0.893801 | − | 0.448463i | \(-0.148028\pi\) |
−0.835281 | + | 0.549823i | \(0.814695\pi\) | |||||||
\(480\) | −3.56155 | −0.162562 | ||||||||
\(481\) | −32.7808 | + | 13.2635i | −1.49467 | + | 0.604762i | ||||
\(482\) | 11.3153 | 0.515400 | ||||||||
\(483\) | −4.56155 | − | 7.90084i | −0.207558 | − | 0.359501i | ||||
\(484\) | 2.21922 | + | 3.84381i | 0.100874 | + | 0.174719i | ||||
\(485\) | 21.8078 | − | 37.7722i | 0.990240 | − | 1.71515i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −11.8423 | + | 20.5115i | −0.536627 | + | 0.929466i | 0.462456 | + | 0.886642i | \(0.346968\pi\) |
−0.999083 | + | 0.0428230i | \(0.986365\pi\) | |||||||
\(488\) | 0.500000 | − | 0.866025i | 0.0226339 | − | 0.0392031i | ||||
\(489\) | −1.12311 | −0.0507886 | ||||||||
\(490\) | 1.78078 | − | 3.08440i | 0.0804473 | − | 0.139339i | ||||
\(491\) | 0.876894 | + | 1.51883i | 0.0395737 | + | 0.0685436i | 0.885134 | − | 0.465337i | \(-0.154067\pi\) |
−0.845560 | + | 0.533880i | \(0.820733\pi\) | |||||||
\(492\) | −2.06155 | − | 3.57071i | −0.0929420 | − | 0.160980i | ||||
\(493\) | 5.00000 | 0.225189 | ||||||||
\(494\) | −3.84233 | + | 27.4397i | −0.172875 | + | 1.23457i | ||||
\(495\) | −9.12311 | −0.410053 | ||||||||
\(496\) | −2.56155 | − | 4.43674i | −0.115017 | − | 0.199215i | ||||
\(497\) | −2.00000 | − | 3.46410i | −0.0897123 | − | 0.155386i | ||||
\(498\) | 5.12311 | − | 8.87348i | 0.229572 | − | 0.397630i | ||||
\(499\) | −27.3693 | −1.22522 | −0.612609 | − | 0.790386i | \(-0.709880\pi\) | ||||
−0.612609 | + | 0.790386i | \(0.709880\pi\) | |||||||
\(500\) | 4.78078 | − | 8.28055i | 0.213803 | − | 0.370317i | ||||
\(501\) | −10.2462 | + | 17.7470i | −0.457767 | + | 0.792876i | ||||
\(502\) | 8.49242 | 0.379035 | ||||||||
\(503\) | −10.2462 | + | 17.7470i | −0.456856 | + | 0.791298i | −0.998793 | − | 0.0491215i | \(-0.984358\pi\) |
0.541937 | + | 0.840419i | \(0.317691\pi\) | |||||||
\(504\) | 0.500000 | + | 0.866025i | 0.0222718 | + | 0.0385758i | ||||
\(505\) | −34.8348 | − | 60.3356i | −1.55013 | − | 2.68490i | ||||
\(506\) | −23.3693 | −1.03889 | ||||||||
\(507\) | 3.15767 | + | 12.6107i | 0.140237 | + | 0.560060i | ||||
\(508\) | 2.24621 | 0.0996595 | ||||||||
\(509\) | −13.6577 | − | 23.6558i | −0.605366 | − | 1.04852i | −0.991994 | − | 0.126288i | \(-0.959694\pi\) |
0.386628 | − | 0.922236i | \(-0.373640\pi\) | |||||||
\(510\) | −8.90388 | − | 15.4220i | −0.394271 | − | 0.682897i | ||||
\(511\) | −1.21922 | + | 2.11176i | −0.0539353 | + | 0.0934186i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.84233 | + | 6.65511i | −0.169643 | + | 0.293830i | ||||
\(514\) | 7.37689 | − | 12.7772i | 0.325381 | − | 0.563576i | ||||
\(515\) | 40.4924 | 1.78431 | ||||||||
\(516\) | 1.43845 | − | 2.49146i | 0.0633241 | − | 0.109681i | ||||
\(517\) | 9.84233 | + | 17.0474i | 0.432865 | + | 0.749744i | ||||
\(518\) | −4.90388 | − | 8.49377i | −0.215464 | − | 0.373195i | ||||
\(519\) | −4.87689 | −0.214072 | ||||||||
\(520\) | 1.78078 | − | 12.7173i | 0.0780922 | − | 0.557690i | ||||
\(521\) | −17.0000 | −0.744784 | −0.372392 | − | 0.928076i | \(-0.621462\pi\) | ||||
−0.372392 | + | 0.928076i | \(0.621462\pi\) | |||||||
\(522\) | 0.500000 | + | 0.866025i | 0.0218844 | + | 0.0379049i | ||||
\(523\) | −7.59612 | − | 13.1569i | −0.332155 | − | 0.575309i | 0.650779 | − | 0.759267i | \(-0.274442\pi\) |
−0.982934 | + | 0.183958i | \(0.941109\pi\) | |||||||
\(524\) | 8.24621 | − | 14.2829i | 0.360237 | − | 0.623949i | ||||
\(525\) | −7.68466 | −0.335386 | ||||||||
\(526\) | 10.2462 | − | 17.7470i | 0.446756 | − | 0.773804i | ||||
\(527\) | 12.8078 | − | 22.1837i | 0.557915 | − | 0.966337i | ||||
\(528\) | 2.56155 | 0.111477 | ||||||||
\(529\) | −30.1155 | + | 52.1616i | −1.30937 | + | 2.26790i | ||||
\(530\) | −6.90388 | − | 11.9579i | −0.299885 | − | 0.519417i | ||||
\(531\) | −6.56155 | − | 11.3649i | −0.284747 | − | 0.493197i | ||||
\(532\) | −7.68466 | −0.333172 | ||||||||
\(533\) | 13.7808 | − | 5.57586i | 0.596912 | − | 0.241517i | ||||
\(534\) | −9.68466 | −0.419096 | ||||||||
\(535\) | −16.8078 | − | 29.1119i | −0.726663 | − | 1.25862i | ||||
\(536\) | −0.561553 | − | 0.972638i | −0.0242554 | − | 0.0420116i | ||||
\(537\) | 8.24621 | − | 14.2829i | 0.355850 | − | 0.616351i | ||||
\(538\) | −4.87689 | −0.210258 | ||||||||
\(539\) | −1.28078 | + | 2.21837i | −0.0551669 | + | 0.0955520i | ||||
\(540\) | 1.78078 | − | 3.08440i | 0.0766324 | − | 0.132731i | ||||
\(541\) | 1.56155 | 0.0671364 | 0.0335682 | − | 0.999436i | \(-0.489313\pi\) | ||||
0.0335682 | + | 0.999436i | \(0.489313\pi\) | |||||||
\(542\) | −6.56155 | + | 11.3649i | −0.281843 | + | 0.488166i | ||||
\(543\) | −6.62311 | − | 11.4716i | −0.284225 | − | 0.492292i | ||||
\(544\) | 2.50000 | + | 4.33013i | 0.107187 | + | 0.185653i | ||||
\(545\) | −3.12311 | −0.133779 | ||||||||
\(546\) | −3.34233 | + | 1.35234i | −0.143038 | + | 0.0578750i | ||||
\(547\) | −22.7386 | −0.972234 | −0.486117 | − | 0.873894i | \(-0.661587\pi\) | ||||
−0.486117 | + | 0.873894i | \(0.661587\pi\) | |||||||
\(548\) | 2.90388 | + | 5.02967i | 0.124048 | + | 0.214857i | ||||
\(549\) | 0.500000 | + | 0.866025i | 0.0213395 | + | 0.0369611i | ||||
\(550\) | −9.84233 | + | 17.0474i | −0.419678 | + | 0.726904i | ||||
\(551\) | −7.68466 | −0.327377 | ||||||||
\(552\) | 4.56155 | − | 7.90084i | 0.194153 | − | 0.336282i | ||||
\(553\) | 0.719224 | − | 1.24573i | 0.0305845 | − | 0.0529739i | ||||
\(554\) | −3.56155 | −0.151316 | ||||||||
\(555\) | −17.4654 | + | 30.2510i | −0.741366 | + | 1.28408i | ||||
\(556\) | 3.84233 | + | 6.65511i | 0.162951 | + | 0.282240i | ||||
\(557\) | −10.8693 | − | 18.8262i | −0.460548 | − | 0.797692i | 0.538441 | − | 0.842664i | \(-0.319014\pi\) |
−0.998988 | + | 0.0449714i | \(0.985680\pi\) | |||||||
\(558\) | 5.12311 | 0.216878 | ||||||||
\(559\) | 8.17708 | + | 6.38202i | 0.345854 | + | 0.269930i | ||||
\(560\) | 3.56155 | 0.150503 | ||||||||
\(561\) | 6.40388 | + | 11.0918i | 0.270372 | + | 0.468298i | ||||
\(562\) | −3.90388 | − | 6.76172i | −0.164675 | − | 0.285226i | ||||
\(563\) | 0.315342 | − | 0.546188i | 0.0132901 | − | 0.0230191i | −0.859304 | − | 0.511465i | \(-0.829103\pi\) |
0.872594 | + | 0.488446i | \(0.162436\pi\) | |||||||
\(564\) | −7.68466 | −0.323582 | ||||||||
\(565\) | 30.1501 | − | 52.2215i | 1.26842 | − | 2.19697i | ||||
\(566\) | −4.24621 | + | 7.35465i | −0.178482 | + | 0.309139i | ||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 2.00000 | − | 3.46410i | 0.0839181 | − | 0.145350i | ||||
\(569\) | −5.80776 | − | 10.0593i | −0.243474 | − | 0.421710i | 0.718227 | − | 0.695808i | \(-0.244954\pi\) |
−0.961702 | + | 0.274099i | \(0.911620\pi\) | |||||||
\(570\) | 13.6847 | + | 23.7025i | 0.573187 | + | 0.992789i | ||||
\(571\) | 13.7538 | 0.575578 | 0.287789 | − | 0.957694i | \(-0.407080\pi\) | ||||
0.287789 | + | 0.957694i | \(0.407080\pi\) | |||||||
\(572\) | −1.28078 | + | 9.14657i | −0.0535520 | + | 0.382437i | ||||
\(573\) | 5.75379 | 0.240368 | ||||||||
\(574\) | 2.06155 | + | 3.57071i | 0.0860476 | + | 0.149039i | ||||
\(575\) | 35.0540 | + | 60.7153i | 1.46185 | + | 2.53200i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 31.3153 | 1.30367 | 0.651837 | − | 0.758359i | \(-0.273998\pi\) | ||||
0.651837 | + | 0.758359i | \(0.273998\pi\) | |||||||
\(578\) | −4.00000 | + | 6.92820i | −0.166378 | + | 0.288175i | ||||
\(579\) | 10.1847 | − | 17.6403i | 0.423260 | − | 0.733108i | ||||
\(580\) | 3.56155 | 0.147885 | ||||||||
\(581\) | −5.12311 | + | 8.87348i | −0.212542 | + | 0.368134i | ||||
\(582\) | −6.12311 | − | 10.6055i | −0.253811 | − | 0.439613i | ||||
\(583\) | 4.96543 | + | 8.60039i | 0.205647 | + | 0.356192i | ||||
\(584\) | −2.43845 | −0.100904 | ||||||||
\(585\) | 10.1231 | + | 7.90084i | 0.418539 | + | 0.326660i | ||||
\(586\) | −4.68466 | −0.193521 | ||||||||
\(587\) | −15.6847 | − | 27.1666i | −0.647375 | − | 1.12129i | −0.983747 | − | 0.179558i | \(-0.942533\pi\) |
0.336372 | − | 0.941729i | \(-0.390800\pi\) | |||||||
\(588\) | −0.500000 | − | 0.866025i | −0.0206197 | − | 0.0357143i | ||||
\(589\) | −19.6847 | + | 34.0948i | −0.811092 | + | 1.40485i | ||||
\(590\) | −46.7386 | −1.92420 | ||||||||
\(591\) | 0.280776 | − | 0.486319i | 0.0115496 | − | 0.0200045i | ||||
\(592\) | 4.90388 | − | 8.49377i | 0.201548 | − | 0.349092i | ||||
\(593\) | 32.6155 | 1.33936 | 0.669680 | − | 0.742650i | \(-0.266431\pi\) | ||||
0.669680 | + | 0.742650i | \(0.266431\pi\) | |||||||
\(594\) | −1.28078 | + | 2.21837i | −0.0525509 | + | 0.0910208i | ||||
\(595\) | 8.90388 | + | 15.4220i | 0.365024 | + | 0.632239i | ||||
\(596\) | 8.90388 | + | 15.4220i | 0.364717 | + | 0.631709i | ||||
\(597\) | −17.6155 | −0.720956 | ||||||||
\(598\) | 25.9309 | + | 20.2384i | 1.06039 | + | 0.827611i | ||||
\(599\) | −22.8769 | −0.934725 | −0.467362 | − | 0.884066i | \(-0.654796\pi\) | ||||
−0.467362 | + | 0.884066i | \(0.654796\pi\) | |||||||
\(600\) | −3.84233 | − | 6.65511i | −0.156862 | − | 0.271694i | ||||
\(601\) | −18.4654 | − | 31.9831i | −0.753221 | − | 1.30462i | −0.946254 | − | 0.323424i | \(-0.895166\pi\) |
0.193033 | − | 0.981192i | \(-0.438167\pi\) | |||||||
\(602\) | −1.43845 | + | 2.49146i | −0.0586267 | + | 0.101544i | ||||
\(603\) | 1.12311 | 0.0457364 | ||||||||
\(604\) | 8.71922 | − | 15.1021i | 0.354780 | − | 0.614497i | ||||
\(605\) | −7.90388 | + | 13.6899i | −0.321339 | + | 0.556575i | ||||
\(606\) | −19.5616 | −0.794634 | ||||||||
\(607\) | −10.5616 | + | 18.2931i | −0.428680 | + | 0.742496i | −0.996756 | − | 0.0804802i | \(-0.974355\pi\) |
0.568076 | + | 0.822976i | \(0.307688\pi\) | |||||||
\(608\) | −3.84233 | − | 6.65511i | −0.155827 | − | 0.269900i | ||||
\(609\) | −0.500000 | − | 0.866025i | −0.0202610 | − | 0.0350931i | ||||
\(610\) | 3.56155 | 0.144203 | ||||||||
\(611\) | 3.84233 | − | 27.4397i | 0.155444 | − | 1.11009i | ||||
\(612\) | −5.00000 | −0.202113 | ||||||||
\(613\) | −18.1501 | − | 31.4369i | −0.733075 | − | 1.26972i | −0.955563 | − | 0.294788i | \(-0.904751\pi\) |
0.222487 | − | 0.974936i | \(-0.428582\pi\) | |||||||
\(614\) | 16.9654 | + | 29.3850i | 0.684669 | + | 1.18588i | ||||
\(615\) | 7.34233 | − | 12.7173i | 0.296071 | − | 0.512811i | ||||
\(616\) | −2.56155 | −0.103208 | ||||||||
\(617\) | 13.7116 | − | 23.7493i | 0.552010 | − | 0.956110i | −0.446119 | − | 0.894973i | \(-0.647194\pi\) |
0.998129 | − | 0.0611360i | \(-0.0194723\pi\) | |||||||
\(618\) | 5.68466 | − | 9.84612i | 0.228670 | − | 0.396069i | ||||
\(619\) | 4.31534 | 0.173448 | 0.0867241 | − | 0.996232i | \(-0.472360\pi\) | ||||
0.0867241 | + | 0.996232i | \(0.472360\pi\) | |||||||
\(620\) | 9.12311 | − | 15.8017i | 0.366393 | − | 0.634611i | ||||
\(621\) | 4.56155 | + | 7.90084i | 0.183049 | + | 0.317050i | ||||
\(622\) | −11.2808 | − | 19.5389i | −0.452318 | − | 0.783438i | ||||
\(623\) | 9.68466 | 0.388008 | ||||||||
\(624\) | −2.84233 | − | 2.21837i | −0.113784 | − | 0.0888059i | ||||
\(625\) | −4.36932 | −0.174773 | ||||||||
\(626\) | −13.8078 | − | 23.9157i | −0.551869 | − | 0.955866i | ||||
\(627\) | −9.84233 | − | 17.0474i | −0.393065 | − | 0.680808i | ||||
\(628\) | 2.90388 | − | 5.02967i | 0.115878 | − | 0.200706i | ||||
\(629\) | 49.0388 | 1.95531 | ||||||||
\(630\) | −1.78078 | + | 3.08440i | −0.0709478 | + | 0.122885i | ||||
\(631\) | −11.5961 | + | 20.0851i | −0.461634 | + | 0.799574i | −0.999043 | − | 0.0437483i | \(-0.986070\pi\) |
0.537408 | + | 0.843322i | \(0.319403\pi\) | |||||||
\(632\) | 1.43845 | 0.0572184 | ||||||||
\(633\) | 1.43845 | − | 2.49146i | 0.0571731 | − | 0.0990268i | ||||
\(634\) | 5.78078 | + | 10.0126i | 0.229584 | + | 0.397651i | ||||
\(635\) | 4.00000 | + | 6.92820i | 0.158735 | + | 0.274937i | ||||
\(636\) | −3.87689 | −0.153729 | ||||||||
\(637\) | 3.34233 | − | 1.35234i | 0.132428 | − | 0.0535818i | ||||
\(638\) | −2.56155 | −0.101413 | ||||||||
\(639\) | 2.00000 | + | 3.46410i | 0.0791188 | + | 0.137038i | ||||
\(640\) | 1.78078 | + | 3.08440i | 0.0703914 | + | 0.121921i | ||||
\(641\) | −18.4654 | + | 31.9831i | −0.729341 | + | 1.26326i | 0.227821 | + | 0.973703i | \(0.426840\pi\) |
−0.957162 | + | 0.289552i | \(0.906494\pi\) | |||||||
\(642\) | −9.43845 | −0.372506 | ||||||||
\(643\) | 13.2808 | − | 23.0030i | 0.523743 | − | 0.907149i | −0.475875 | − | 0.879513i | \(-0.657869\pi\) |
0.999618 | − | 0.0276362i | \(-0.00879800\pi\) | |||||||
\(644\) | −4.56155 | + | 7.90084i | −0.179750 | + | 0.311337i | ||||
\(645\) | 10.2462 | 0.403444 | ||||||||
\(646\) | 19.2116 | − | 33.2755i | 0.755872 | − | 1.30921i | ||||
\(647\) | 10.4039 | + | 18.0201i | 0.409019 | + | 0.708441i | 0.994780 | − | 0.102042i | \(-0.0325377\pi\) |
−0.585761 | + | 0.810484i | \(0.699204\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 33.6155 | 1.31952 | ||||||||
\(650\) | 25.6847 | − | 10.3923i | 1.00744 | − | 0.407620i | ||||
\(651\) | −5.12311 | −0.200790 | ||||||||
\(652\) | 0.561553 | + | 0.972638i | 0.0219921 | + | 0.0380914i | ||||
\(653\) | 9.40388 | + | 16.2880i | 0.368002 | + | 0.637399i | 0.989253 | − | 0.146213i | \(-0.0467085\pi\) |
−0.621251 | + | 0.783612i | \(0.713375\pi\) | |||||||
\(654\) | −0.438447 | + | 0.759413i | −0.0171446 | + | 0.0296954i | ||||
\(655\) | 58.7386 | 2.29511 | ||||||||
\(656\) | −2.06155 | + | 3.57071i | −0.0804901 | + | 0.139413i | ||||
\(657\) | 1.21922 | − | 2.11176i | 0.0475664 | − | 0.0823875i | ||||
\(658\) | 7.68466 | 0.299579 | ||||||||
\(659\) | 14.1577 | − | 24.5218i | 0.551505 | − | 0.955234i | −0.446662 | − | 0.894703i | \(-0.647387\pi\) |
0.998166 | − | 0.0605310i | \(-0.0192794\pi\) | |||||||
\(660\) | 4.56155 | + | 7.90084i | 0.177558 | + | 0.307540i | ||||
\(661\) | 4.90388 | + | 8.49377i | 0.190739 | + | 0.330369i | 0.945495 | − | 0.325636i | \(-0.105578\pi\) |
−0.754756 | + | 0.656005i | \(0.772245\pi\) | |||||||
\(662\) | −35.3693 | −1.37467 | ||||||||
\(663\) | 2.50000 | − | 17.8536i | 0.0970920 | − | 0.693375i | ||||
\(664\) | −10.2462 | −0.397630 | ||||||||
\(665\) | −13.6847 | − | 23.7025i | −0.530668 | − | 0.919144i | ||||
\(666\) | 4.90388 | + | 8.49377i | 0.190022 | + | 0.329127i | ||||
\(667\) | −4.56155 | + | 7.90084i | −0.176624 | + | 0.305922i | ||||
\(668\) | 20.4924 | 0.792876 | ||||||||
\(669\) | 8.24621 | − | 14.2829i | 0.318817 | − | 0.552207i | ||||
\(670\) | 2.00000 | − | 3.46410i | 0.0772667 | − | 0.133830i | ||||
\(671\) | −2.56155 | −0.0988876 | ||||||||
\(672\) | 0.500000 | − | 0.866025i | 0.0192879 | − | 0.0334077i | ||||
\(673\) | −4.37689 | − | 7.58100i | −0.168717 | − | 0.292226i | 0.769252 | − | 0.638945i | \(-0.220629\pi\) |
−0.937969 | + | 0.346719i | \(0.887296\pi\) | |||||||
\(674\) | 14.7462 | + | 25.5412i | 0.568003 | + | 0.983810i | ||||
\(675\) | 7.68466 | 0.295783 | ||||||||
\(676\) | 9.34233 | − | 9.03996i | 0.359320 | − | 0.347691i | ||||
\(677\) | −8.38447 | −0.322241 | −0.161121 | − | 0.986935i | \(-0.551511\pi\) | ||||
−0.161121 | + | 0.986935i | \(0.551511\pi\) | |||||||
\(678\) | −8.46543 | − | 14.6626i | −0.325113 | − | 0.563112i | ||||
\(679\) | 6.12311 | + | 10.6055i | 0.234983 | + | 0.407003i | ||||
\(680\) | −8.90388 | + | 15.4220i | −0.341448 | + | 0.591406i | ||||
\(681\) | 13.1231 | 0.502879 | ||||||||
\(682\) | −6.56155 | + | 11.3649i | −0.251255 | + | 0.435186i | ||||
\(683\) | −2.00000 | + | 3.46410i | −0.0765279 | + | 0.132550i | −0.901750 | − | 0.432259i | \(-0.857717\pi\) |
0.825222 | + | 0.564809i | \(0.191050\pi\) | |||||||
\(684\) | 7.68466 | 0.293830 | ||||||||
\(685\) | −10.3423 | + | 17.9134i | −0.395160 | + | 0.684437i | ||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | −11.4039 | − | 19.7521i | −0.435085 | − | 0.753590i | ||||
\(688\) | −2.87689 | −0.109681 | ||||||||
\(689\) | 1.93845 | − | 13.8433i | 0.0738490 | − | 0.527387i | ||||
\(690\) | 32.4924 | 1.23697 | ||||||||
\(691\) | 14.2462 | + | 24.6752i | 0.541951 | + | 0.938687i | 0.998792 | + | 0.0491388i | \(0.0156477\pi\) |
−0.456841 | + | 0.889549i | \(0.651019\pi\) | |||||||
\(692\) | 2.43845 | + | 4.22351i | 0.0926959 | + | 0.160554i | ||||
\(693\) | 1.28078 | − | 2.21837i | 0.0486527 | − | 0.0842689i | ||||
\(694\) | −0.315342 | −0.0119702 | ||||||||
\(695\) | −13.6847 | + | 23.7025i | −0.519089 | + | 0.899088i | ||||
\(696\) | 0.500000 | − | 0.866025i | 0.0189525 | − | 0.0328266i | ||||
\(697\) | −20.6155 | −0.780869 | ||||||||
\(698\) | 3.24621 | − | 5.62260i | 0.122871 | − | 0.212819i | ||||
\(699\) | 3.00000 | + | 5.19615i | 0.113470 | + | 0.196537i | ||||
\(700\) | 3.84233 | + | 6.65511i | 0.145226 | + | 0.251539i | ||||
\(701\) | 9.05398 | 0.341964 | 0.170982 | − | 0.985274i | \(-0.445306\pi\) | ||||
0.170982 | + | 0.985274i | \(0.445306\pi\) | |||||||
\(702\) | 3.34233 | − | 1.35234i | 0.126148 | − | 0.0510410i | ||||
\(703\) | −75.3693 | −2.84261 | ||||||||
\(704\) | −1.28078 | − | 2.21837i | −0.0482711 | − | 0.0836080i | ||||
\(705\) | −13.6847 | − | 23.7025i | −0.515394 | − | 0.892689i | ||||
\(706\) | 4.90388 | − | 8.49377i | 0.184560 | − | 0.319667i | ||||
\(707\) | 19.5616 | 0.735688 | ||||||||
\(708\) | −6.56155 | + | 11.3649i | −0.246598 | + | 0.427121i | ||||
\(709\) | −10.1501 | + | 17.5805i | −0.381195 | + | 0.660249i | −0.991233 | − | 0.132123i | \(-0.957821\pi\) |
0.610039 | + | 0.792372i | \(0.291154\pi\) | |||||||
\(710\) | 14.2462 | 0.534651 | ||||||||
\(711\) | −0.719224 | + | 1.24573i | −0.0269730 | + | 0.0467186i | ||||
\(712\) | 4.84233 | + | 8.38716i | 0.181474 | + | 0.314322i | ||||
\(713\) | 23.3693 | + | 40.4768i | 0.875188 | + | 1.51587i | ||||
\(714\) | 5.00000 | 0.187120 | ||||||||
\(715\) | −30.4924 | + | 12.3376i | −1.14035 | + | 0.461399i | ||||
\(716\) | −16.4924 | −0.616351 | ||||||||
\(717\) | −2.00000 | − | 3.46410i | −0.0746914 | − | 0.129369i | ||||
\(718\) | 2.31534 | + | 4.01029i | 0.0864078 | + | 0.149663i | ||||
\(719\) | −10.9654 | + | 18.9927i | −0.408942 | + | 0.708308i | −0.994771 | − | 0.102126i | \(-0.967435\pi\) |
0.585830 | + | 0.810434i | \(0.300769\pi\) | |||||||
\(720\) | −3.56155 | −0.132731 | ||||||||
\(721\) | −5.68466 | + | 9.84612i | −0.211708 | + | 0.366689i | ||||
\(722\) | −20.0270 | + | 34.6878i | −0.745327 | + | 1.29094i | ||||
\(723\) | 11.3153 | 0.420822 | ||||||||
\(724\) | −6.62311 | + | 11.4716i | −0.246146 | + | 0.426337i | ||||
\(725\) | 3.84233 | + | 6.65511i | 0.142701 | + | 0.247165i | ||||
\(726\) | 2.21922 | + | 3.84381i | 0.0823631 | + | 0.142657i | ||||
\(727\) | 50.2462 | 1.86353 | 0.931764 | − | 0.363063i | \(-0.118269\pi\) | ||||
0.931764 | + | 0.363063i | \(0.118269\pi\) | |||||||
\(728\) | 2.84233 | + | 2.21837i | 0.105344 | + | 0.0822183i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.34233 | − | 7.52113i | −0.160717 | − | 0.278370i | ||||
\(731\) | −7.19224 | − | 12.4573i | −0.266014 | − | 0.460751i | ||||
\(732\) | 0.500000 | − | 0.866025i | 0.0184805 | − | 0.0320092i | ||||
\(733\) | 32.6155 | 1.20468 | 0.602341 | − | 0.798239i | \(-0.294235\pi\) | ||||
0.602341 | + | 0.798239i | \(0.294235\pi\) | |||||||
\(734\) | −5.68466 | + | 9.84612i | −0.209825 | + | 0.363427i | ||||
\(735\) | 1.78078 | − | 3.08440i | 0.0656849 | − | 0.113770i | ||||
\(736\) | −9.12311 | −0.336282 | ||||||||
\(737\) | −1.43845 | + | 2.49146i | −0.0529859 | + | 0.0917742i | ||||
\(738\) | −2.06155 | − | 3.57071i | −0.0758868 | − | 0.131440i | ||||
\(739\) | −23.6847 | − | 41.0230i | −0.871254 | − | 1.50906i | −0.860700 | − | 0.509112i | \(-0.829974\pi\) |
−0.0105542 | − | 0.999944i | \(-0.503360\pi\) | |||||||
\(740\) | 34.9309 | 1.28408 | ||||||||
\(741\) | −3.84233 | + | 27.4397i | −0.141151 | + | 1.00802i | ||||
\(742\) | 3.87689 | 0.142325 | ||||||||
\(743\) | −4.31534 | − | 7.47439i | −0.158315 | − | 0.274209i | 0.775946 | − | 0.630799i | \(-0.217273\pi\) |
−0.934261 | + | 0.356590i | \(0.883939\pi\) | |||||||
\(744\) | −2.56155 | − | 4.43674i | −0.0939111 | − | 0.162659i | ||||
\(745\) | −31.7116 | + | 54.9262i | −1.16182 | + | 2.01234i | ||||
\(746\) | 21.5616 | 0.789425 | ||||||||
\(747\) | 5.12311 | − | 8.87348i | 0.187445 | − | 0.324664i | ||||
\(748\) | 6.40388 | − | 11.0918i | 0.234149 | − | 0.405558i | ||||
\(749\) | 9.43845 | 0.344873 | ||||||||
\(750\) | 4.78078 | − | 8.28055i | 0.174569 | − | 0.302363i | ||||
\(751\) | 0.403882 | + | 0.699544i | 0.0147379 | + | 0.0255267i | 0.873300 | − | 0.487182i | \(-0.161975\pi\) |
−0.858562 | + | 0.512709i | \(0.828642\pi\) | |||||||
\(752\) | 3.84233 | + | 6.65511i | 0.140115 | + | 0.242687i | ||||
\(753\) | 8.49242 | 0.309481 | ||||||||
\(754\) | 2.84233 | + | 2.21837i | 0.103512 | + | 0.0807883i | ||||
\(755\) | 62.1080 | 2.26034 | ||||||||
\(756\) | 0.500000 | + | 0.866025i | 0.0181848 | + | 0.0314970i | ||||
\(757\) | 3.56155 | + | 6.16879i | 0.129447 | + | 0.224209i | 0.923462 | − | 0.383689i | \(-0.125347\pi\) |
−0.794016 | + | 0.607897i | \(0.792013\pi\) | |||||||
\(758\) | −0.246211 | + | 0.426450i | −0.00894280 | + | 0.0154894i | ||||
\(759\) | −23.3693 | −0.848252 | ||||||||
\(760\) | 13.6847 | − | 23.7025i | 0.496395 | − | 0.859781i | ||||
\(761\) | 21.2462 | − | 36.7995i | 0.770175 | − | 1.33398i | −0.167292 | − | 0.985907i | \(-0.553502\pi\) |
0.937467 | − | 0.348074i | \(-0.113164\pi\) | |||||||
\(762\) | 2.24621 | 0.0813716 | ||||||||
\(763\) | 0.438447 | − | 0.759413i | 0.0158729 | − | 0.0274926i | ||||
\(764\) | −2.87689 | − | 4.98293i | −0.104082 | − | 0.180276i | ||||
\(765\) | −8.90388 | − | 15.4220i | −0.321921 | − | 0.557583i | ||||
\(766\) | 8.31534 | 0.300446 | ||||||||
\(767\) | −37.3002 | − | 29.1119i | −1.34683 | − | 1.05117i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 11.4924 | + | 19.9055i | 0.414427 | + | 0.717809i | 0.995368 | − | 0.0961366i | \(-0.0306486\pi\) |
−0.580941 | + | 0.813946i | \(0.697315\pi\) | |||||||
\(770\) | −4.56155 | − | 7.90084i | −0.164387 | − | 0.284727i | ||||
\(771\) | 7.37689 | − | 12.7772i | 0.265672 | − | 0.460158i | ||||
\(772\) | −20.3693 | −0.733108 | ||||||||
\(773\) | −13.2462 | + | 22.9431i | −0.476433 | + | 0.825206i | −0.999635 | − | 0.0270022i | \(-0.991404\pi\) |
0.523202 | + | 0.852209i | \(0.324737\pi\) | |||||||
\(774\) | 1.43845 | − | 2.49146i | 0.0517039 | − | 0.0895538i | ||||
\(775\) | 39.3693 | 1.41419 | ||||||||
\(776\) | −6.12311 | + | 10.6055i | −0.219807 | + | 0.380716i | ||||
\(777\) | −4.90388 | − | 8.49377i | −0.175926 | − | 0.304712i | ||||
\(778\) | −9.34233 | − | 16.1814i | −0.334939 | − | 0.580131i | ||||
\(779\) | 31.6847 | 1.13522 | ||||||||
\(780\) | 1.78078 | − | 12.7173i | 0.0637620 | − | 0.455352i | ||||
\(781\) | −10.2462 | −0.366638 | ||||||||
\(782\) | −22.8078 | − | 39.5042i | −0.815604 | − | 1.41267i | ||||
\(783\) | 0.500000 | + | 0.866025i | 0.0178685 | + | 0.0309492i | ||||
\(784\) | −0.500000 | + | 0.866025i | −0.0178571 | + | 0.0309295i | ||||
\(785\) | 20.6847 | 0.738267 | ||||||||
\(786\) | 8.24621 | − | 14.2829i | 0.294133 | − | 0.509453i | ||||
\(787\) | −0.403882 | + | 0.699544i | −0.0143968 | + | 0.0249361i | −0.873134 | − | 0.487480i | \(-0.837916\pi\) |
0.858737 | + | 0.512416i | \(0.171249\pi\) | |||||||
\(788\) | −0.561553 | −0.0200045 | ||||||||
\(789\) | 10.2462 | − | 17.7470i | 0.364775 | − | 0.631808i | ||||
\(790\) | 2.56155 | + | 4.43674i | 0.0911360 | + | 0.157852i | ||||
\(791\) | 8.46543 | + | 14.6626i | 0.300996 | + | 0.521341i | ||||
\(792\) | 2.56155 | 0.0910208 | ||||||||
\(793\) | 2.84233 | + | 2.21837i | 0.100934 | + | 0.0787766i | ||||
\(794\) | 1.68466 | 0.0597863 | ||||||||
\(795\) | −6.90388 | − | 11.9579i | −0.244855 | − | 0.424102i | ||||
\(796\) | 8.80776 | + | 15.2555i | 0.312183 | + | 0.540717i | ||||
\(797\) | 12.0540 | − | 20.8781i | 0.426974 | − | 0.739540i | −0.569629 | − | 0.821902i | \(-0.692913\pi\) |
0.996602 | + | 0.0823619i | \(0.0262463\pi\) | |||||||
\(798\) | −7.68466 | −0.272034 | ||||||||
\(799\) | −19.2116 | + | 33.2755i | −0.679659 | + | 1.17720i | ||||
\(800\) | −3.84233 | + | 6.65511i | −0.135847 | + | 0.235294i | ||||
\(801\) | −9.68466 | −0.342191 | ||||||||
\(802\) | −7.58854 | + | 13.1437i | −0.267961 | + | 0.464122i | ||||
\(803\) | 3.12311 | + | 5.40938i | 0.110212 | + | 0.190893i | ||||
\(804\) | −0.561553 | − | 0.972638i | −0.0198044 | − | 0.0343023i | ||||
\(805\) | −32.4924 | −1.14521 | ||||||||
\(806\) | 17.1231 | − | 6.92820i | 0.603136 | − | 0.244036i | ||||
\(807\) | −4.87689 | −0.171675 | ||||||||
\(808\) | 9.78078 | + | 16.9408i | 0.344087 | + | 0.595975i | ||||
\(809\) | 5.46543 | + | 9.46641i | 0.192154 | + | 0.332821i | 0.945964 | − | 0.324272i | \(-0.105119\pi\) |
−0.753810 | + | 0.657093i | \(0.771786\pi\) | |||||||
\(810\) | 1.78078 | − | 3.08440i | 0.0625701 | − | 0.108375i | ||||
\(811\) | 5.75379 | 0.202043 | 0.101021 | − | 0.994884i | \(-0.467789\pi\) | ||||
0.101021 | + | 0.994884i | \(0.467789\pi\) | |||||||
\(812\) | −0.500000 | + | 0.866025i | −0.0175466 | + | 0.0303915i | ||||
\(813\) | −6.56155 | + | 11.3649i | −0.230124 | + | 0.398586i | ||||
\(814\) | −25.1231 | −0.880564 | ||||||||
\(815\) | −2.00000 | + | 3.46410i | −0.0700569 | + | 0.121342i | ||||
\(816\) | 2.50000 | + | 4.33013i | 0.0875175 | + | 0.151585i | ||||
\(817\) | 11.0540 | + | 19.1460i | 0.386730 | + | 0.669835i | ||||
\(818\) | −30.4384 | −1.06426 | ||||||||
\(819\) | −3.34233 | + | 1.35234i | −0.116790 | + | 0.0472547i | ||||
\(820\) | −14.6847 | −0.512811 | ||||||||
\(821\) | 6.03457 | + | 10.4522i | 0.210608 | + | 0.364783i | 0.951905 | − | 0.306394i | \(-0.0991224\pi\) |
−0.741297 | + | 0.671177i | \(0.765789\pi\) | |||||||
\(822\) | 2.90388 | + | 5.02967i | 0.101285 | + | 0.175430i | ||||
\(823\) | −7.12311 | + | 12.3376i | −0.248296 | + | 0.430061i | −0.963053 | − | 0.269312i | \(-0.913204\pi\) |
0.714757 | + | 0.699373i | \(0.246537\pi\) | |||||||
\(824\) | −11.3693 | −0.396069 | ||||||||
\(825\) | −9.84233 | + | 17.0474i | −0.342666 | + | 0.593515i | ||||
\(826\) | 6.56155 | − | 11.3649i | 0.228306 | − | 0.395437i | ||||
\(827\) | −11.5076 | −0.400158 | −0.200079 | − | 0.979780i | \(-0.564120\pi\) | ||||
−0.200079 | + | 0.979780i | \(0.564120\pi\) | |||||||
\(828\) | 4.56155 | − | 7.90084i | 0.158525 | − | 0.274573i | ||||
\(829\) | −14.5540 | − | 25.2082i | −0.505480 | − | 0.875518i | −0.999980 | − | 0.00633989i | \(-0.997982\pi\) |
0.494499 | − | 0.869178i | \(-0.335351\pi\) | |||||||
\(830\) | −18.2462 | − | 31.6034i | −0.633335 | − | 1.09697i | ||||
\(831\) | −3.56155 | −0.123549 | ||||||||
\(832\) | −0.500000 | + | 3.57071i | −0.0173344 | + | 0.123792i | ||||
\(833\) | −5.00000 | −0.173240 | ||||||||
\(834\) | 3.84233 | + | 6.65511i | 0.133049 | + | 0.230448i | ||||
\(835\) | 36.4924 | + | 63.2067i | 1.26287 | + | 2.18736i | ||||
\(836\) | −9.84233 | + | 17.0474i | −0.340404 | + | 0.589597i | ||||
\(837\) | 5.12311 | 0.177080 | ||||||||
\(838\) | −11.3693 | + | 19.6922i | −0.392747 | + | 0.680257i | ||||
\(839\) | −4.00000 | + | 6.92820i | −0.138095 | + | 0.239188i | −0.926776 | − | 0.375615i | \(-0.877431\pi\) |
0.788680 | + | 0.614804i | \(0.210765\pi\) | |||||||
\(840\) | 3.56155 | 0.122885 | ||||||||
\(841\) | 14.0000 | − | 24.2487i | 0.482759 | − | 0.836162i | ||||
\(842\) | −4.21922 | − | 7.30791i | −0.145404 | − | 0.251847i | ||||
\(843\) | −3.90388 | − | 6.76172i | −0.134457 | − | 0.232886i | ||||
\(844\) | −2.87689 | −0.0990268 | ||||||||
\(845\) | 44.5194 | + | 12.7173i | 1.53151 | + | 0.437488i | ||||
\(846\) | −7.68466 | −0.264204 | ||||||||
\(847\) | −2.21922 | − | 3.84381i | −0.0762534 | − | 0.132075i | ||||
\(848\) | 1.93845 | + | 3.35749i | 0.0665665 | + | 0.115297i | ||||
\(849\) | −4.24621 | + | 7.35465i | −0.145730 | + | 0.252411i | ||||
\(850\) | −38.4233 | −1.31791 | ||||||||
\(851\) | −44.7386 | + | 77.4896i | −1.53362 | + | 2.65631i | ||||
\(852\) | 2.00000 | − | 3.46410i | 0.0685189 | − | 0.118678i | ||||
\(853\) | −0.369317 | −0.0126452 | −0.00632258 | − | 0.999980i | \(-0.502013\pi\) | ||||
−0.00632258 | + | 0.999980i | \(0.502013\pi\) | |||||||
\(854\) | −0.500000 | + | 0.866025i | −0.0171096 | + | 0.0296348i | ||||
\(855\) | 13.6847 | + | 23.7025i | 0.468005 | + | 0.810609i | ||||
\(856\) | 4.71922 | + | 8.17394i | 0.161300 | + | 0.279379i | ||||
\(857\) | −22.3002 | −0.761760 | −0.380880 | − | 0.924625i | \(-0.624379\pi\) | ||||
−0.380880 | + | 0.924625i | \(0.624379\pi\) | |||||||
\(858\) | −1.28078 | + | 9.14657i | −0.0437250 | + | 0.312259i | ||||
\(859\) | −36.8078 | −1.25586 | −0.627932 | − | 0.778268i | \(-0.716099\pi\) | ||||
−0.627932 | + | 0.778268i | \(0.716099\pi\) | |||||||
\(860\) | −5.12311 | − | 8.87348i | −0.174696 | − | 0.302583i | ||||
\(861\) | 2.06155 | + | 3.57071i | 0.0702575 | + | 0.121690i | ||||
\(862\) | 9.36932 | − | 16.2281i | 0.319120 | − | 0.552732i | ||||
\(863\) | 26.1080 | 0.888725 | 0.444362 | − | 0.895847i | \(-0.353430\pi\) | ||||
0.444362 | + | 0.895847i | \(0.353430\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −8.68466 | + | 15.0423i | −0.295287 | + | 0.511453i | ||||
\(866\) | −5.31534 | −0.180623 | ||||||||
\(867\) | −4.00000 | + | 6.92820i | −0.135847 | + | 0.235294i | ||||
\(868\) | 2.56155 | + | 4.43674i | 0.0869448 | + | 0.150593i | ||||
\(869\) | −1.84233 | − | 3.19101i | −0.0624967 | − | 0.108248i | ||||
\(870\) | 3.56155 | 0.120748 | ||||||||
\(871\) | 3.75379 | − | 1.51883i | 0.127192 | − | 0.0514634i | ||||
\(872\) | 0.876894 | 0.0296954 | ||||||||
\(873\) | −6.12311 | − | 10.6055i | −0.207236 | − | 0.358943i | ||||
\(874\) | 35.0540 | + | 60.7153i | 1.18572 | + | 2.05372i | ||||
\(875\) | −4.78078 | + | 8.28055i | −0.161620 | + | 0.279934i | ||||
\(876\) | −2.43845 | −0.0823875 | ||||||||
\(877\) | −4.15009 | + | 7.18817i | −0.140139 | + | 0.242727i | −0.927549 | − | 0.373702i | \(-0.878088\pi\) |
0.787410 | + | 0.616430i | \(0.211422\pi\) | |||||||
\(878\) | 14.2462 | − | 24.6752i | 0.480786 | − | 0.832746i | ||||
\(879\) | −4.68466 | −0.158010 | ||||||||
\(880\) | 4.56155 | − | 7.90084i | 0.153770 | − | 0.266337i | ||||
\(881\) | −23.5885 | − | 40.8566i | −0.794718 | − | 1.37649i | −0.923018 | − | 0.384757i | \(-0.874285\pi\) |
0.128300 | − | 0.991735i | \(-0.459048\pi\) | |||||||
\(882\) | −0.500000 | − | 0.866025i | −0.0168359 | − | 0.0291606i | ||||
\(883\) | 17.1231 | 0.576238 | 0.288119 | − | 0.957595i | \(-0.406970\pi\) | ||||
0.288119 | + | 0.957595i | \(0.406970\pi\) | |||||||
\(884\) | −16.7116 | + | 6.76172i | −0.562073 | + | 0.227421i | ||||
\(885\) | −46.7386 | −1.57110 | ||||||||
\(886\) | 17.2116 | + | 29.8114i | 0.578237 | + | 1.00154i | ||||
\(887\) | −2.71922 | − | 4.70983i | −0.0913026 | − | 0.158141i | 0.816757 | − | 0.576982i | \(-0.195770\pi\) |
−0.908059 | + | 0.418841i | \(0.862436\pi\) | |||||||
\(888\) | 4.90388 | − | 8.49377i | 0.164564 | − | 0.285032i | ||||
\(889\) | −2.24621 | −0.0753355 | ||||||||
\(890\) | −17.2462 | + | 29.8713i | −0.578094 | + | 1.00129i | ||||
\(891\) | −1.28078 | + | 2.21837i | −0.0429076 | + | 0.0743182i | ||||
\(892\) | −16.4924 | −0.552207 | ||||||||
\(893\) | 29.5270 | − | 51.1422i | 0.988083 | − | 1.71141i | ||||
\(894\) | 8.90388 | + | 15.4220i | 0.297790 | + | 0.515788i | ||||
\(895\) | −29.3693 | − | 50.8691i | −0.981708 | − | 1.70037i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 25.9309 | + | 20.2384i | 0.865807 | + | 0.675741i | ||||
\(898\) | 18.0000 | 0.600668 | ||||||||
\(899\) | 2.56155 | + | 4.43674i | 0.0854326 | + | 0.147974i | ||||
\(900\) | −3.84233 | − | 6.65511i | −0.128078 | − | 0.221837i | ||||
\(901\) | −9.69224 | + | 16.7874i | −0.322895 | + | 0.559271i | ||||
\(902\) | 10.5616 | 0.351661 | ||||||||
\(903\) | −1.43845 | + | 2.49146i | −0.0478685 | + | 0.0829107i | ||||
\(904\) | −8.46543 | + | 14.6626i | −0.281556 | + | 0.487670i | ||||
\(905\) | −47.1771 | −1.56822 | ||||||||
\(906\) | 8.71922 | − | 15.1021i | 0.289677 | − | 0.501735i | ||||
\(907\) | −11.4384 | − | 19.8120i | −0.379807 | − | 0.657846i | 0.611227 | − | 0.791456i | \(-0.290676\pi\) |
−0.991034 | + | 0.133610i | \(0.957343\pi\) | |||||||
\(908\) | −6.56155 | − | 11.3649i | −0.217753 | − | 0.377159i | ||||
\(909\) | −19.5616 | −0.648816 | ||||||||
\(910\) | −1.78078 | + | 12.7173i | −0.0590322 | + | 0.421574i | ||||
\(911\) | −5.26137 | −0.174317 | −0.0871584 | − | 0.996194i | \(-0.527779\pi\) | ||||
−0.0871584 | + | 0.996194i | \(0.527779\pi\) | |||||||
\(912\) | −3.84233 | − | 6.65511i | −0.127232 | − | 0.220373i | ||||
\(913\) | 13.1231 | + | 22.7299i | 0.434311 | + | 0.752249i | ||||
\(914\) | 6.65767 | − | 11.5314i | 0.220216 | − | 0.381426i | ||||
\(915\) | 3.56155 | 0.117741 | ||||||||
\(916\) | −11.4039 | + | 19.7521i | −0.376795 | + | 0.652628i | ||||
\(917\) | −8.24621 | + | 14.2829i | −0.272314 | + | 0.471661i | ||||
\(918\) | −5.00000 | −0.165025 | ||||||||
\(919\) | −3.28078 | + | 5.68247i | −0.108223 | + | 0.187447i | −0.915050 | − | 0.403340i | \(-0.867849\pi\) |
0.806828 | + | 0.590787i | \(0.201183\pi\) | |||||||
\(920\) | −16.2462 | − | 28.1393i | −0.535622 | − | 0.927724i | ||||
\(921\) | 16.9654 | + | 29.3850i | 0.559030 | + | 0.968269i | ||||
\(922\) | 30.0540 | 0.989775 | ||||||||
\(923\) | 11.3693 | + | 8.87348i | 0.374226 | + | 0.292074i | ||||
\(924\) | −2.56155 | −0.0842689 | ||||||||
\(925\) | 37.6847 | + | 65.2717i | 1.23906 | + | 2.14612i | ||||
\(926\) | 5.84233 | + | 10.1192i | 0.191991 | + | 0.332538i | ||||
\(927\) | 5.68466 | − | 9.84612i | 0.186709 | − | 0.323389i | ||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 3.30776 | − | 5.72922i | 0.108524 | − | 0.187969i | −0.806648 | − | 0.591032i | \(-0.798721\pi\) |
0.915173 | + | 0.403062i | \(0.132054\pi\) | |||||||
\(930\) | 9.12311 | − | 15.8017i | 0.299158 | − | 0.518158i | ||||
\(931\) | 7.68466 | 0.251855 | ||||||||
\(932\) | 3.00000 | − | 5.19615i | 0.0982683 | − | 0.170206i | ||||
\(933\) | −11.2808 | − | 19.5389i | −0.369316 | − | 0.639674i | ||||
\(934\) | −14.0000 | − | 24.2487i | −0.458094 | − | 0.793442i | ||||
\(935\) | 45.6155 | 1.49179 | ||||||||
\(936\) | −2.84233 | − | 2.21837i | −0.0929044 | − | 0.0725097i | ||||
\(937\) | 13.5616 | 0.443037 | 0.221518 | − | 0.975156i | \(-0.428899\pi\) | ||||
0.221518 | + | 0.975156i | \(0.428899\pi\) | |||||||
\(938\) | 0.561553 | + | 0.972638i | 0.0183353 | + | 0.0317578i | ||||
\(939\) | −13.8078 | − | 23.9157i | −0.450599 | − | 0.780461i | ||||
\(940\) | −13.6847 | + | 23.7025i | −0.446344 | + | 0.773091i | ||||
\(941\) | 53.3693 | 1.73979 | 0.869895 | − | 0.493237i | \(-0.164186\pi\) | ||||
0.869895 | + | 0.493237i | \(0.164186\pi\) | |||||||
\(942\) | 2.90388 | − | 5.02967i | 0.0946136 | − | 0.163876i | ||||
\(943\) | 18.8078 | − | 32.5760i | 0.612465 | − | 1.06082i | ||||
\(944\) | 13.1231 | 0.427121 | ||||||||
\(945\) | −1.78078 | + | 3.08440i | −0.0579287 | + | 0.100335i | ||||
\(946\) | 3.68466 | + | 6.38202i | 0.119799 | + | 0.207497i | ||||
\(947\) | 0.157671 | + | 0.273094i | 0.00512361 | + | 0.00887436i | 0.868576 | − | 0.495556i | \(-0.165036\pi\) |
−0.863452 | + | 0.504431i | \(0.831702\pi\) | |||||||
\(948\) | 1.43845 | 0.0467186 | ||||||||
\(949\) | 1.21922 | − | 8.70700i | 0.0395777 | − | 0.282641i | ||||
\(950\) | 59.0540 | 1.91596 | ||||||||
\(951\) | 5.78078 | + | 10.0126i | 0.187455 | + | 0.324681i | ||||
\(952\) | −2.50000 | − | 4.33013i | −0.0810255 | − | 0.140340i | ||||
\(953\) | 26.3693 | − | 45.6730i | 0.854186 | − | 1.47949i | −0.0232122 | − | 0.999731i | \(-0.507389\pi\) |
0.877398 | − | 0.479763i | \(-0.159277\pi\) | |||||||
\(954\) | −3.87689 | −0.125519 | ||||||||
\(955\) | 10.2462 | − | 17.7470i | 0.331560 | − | 0.574278i | ||||
\(956\) | −2.00000 | + | 3.46410i | −0.0646846 | + | 0.112037i | ||||
\(957\) | −2.56155 | −0.0828032 | ||||||||
\(958\) | 1.28078 | − | 2.21837i | 0.0413800 | − | 0.0716723i | ||||
\(959\) | −2.90388 | − | 5.02967i | −0.0937712 | − | 0.162417i | ||||
\(960\) | 1.78078 | + | 3.08440i | 0.0574743 | + | 0.0995484i | ||||
\(961\) | −4.75379 | −0.153348 | ||||||||
\(962\) | 27.8769 | + | 21.7572i | 0.898787 | + | 0.701482i | ||||
\(963\) | −9.43845 | −0.304150 | ||||||||
\(964\) | −5.65767 | − | 9.79937i | −0.182221 | − | 0.315617i | ||||
\(965\) | −36.2732 | − | 62.8270i | −1.16768 | − | 2.02247i | ||||
\(966\) | −4.56155 | + | 7.90084i | −0.146766 | + | 0.254205i | ||||
\(967\) | −4.49242 | −0.144467 | −0.0722333 | − | 0.997388i | \(-0.523013\pi\) | ||||
−0.0722333 | + | 0.997388i | \(0.523013\pi\) | |||||||
\(968\) | 2.21922 | − | 3.84381i | 0.0713285 | − | 0.123545i | ||||
\(969\) | 19.2116 | − | 33.2755i | 0.617167 | − | 1.06896i | ||||
\(970\) | −43.6155 | −1.40041 | ||||||||
\(971\) | 5.43845 | − | 9.41967i | 0.174528 | − | 0.302291i | −0.765470 | − | 0.643472i | \(-0.777493\pi\) |
0.939998 | + | 0.341180i | \(0.110827\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −3.84233 | − | 6.65511i | −0.123179 | − | 0.213353i | ||||
\(974\) | 23.6847 | 0.758905 | ||||||||
\(975\) | 25.6847 | − | 10.3923i | 0.822567 | − | 0.332820i | ||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | −1.02699 | − | 1.77879i | −0.0328562 | − | 0.0569087i | 0.849130 | − | 0.528184i | \(-0.177127\pi\) |
−0.881986 | + | 0.471276i | \(0.843794\pi\) | |||||||
\(978\) | 0.561553 | + | 0.972638i | 0.0179565 | + | 0.0311015i | ||||
\(979\) | 12.4039 | − | 21.4842i | 0.396430 | − | 0.686637i | ||||
\(980\) | −3.56155 | −0.113770 | ||||||||
\(981\) | −0.438447 | + | 0.759413i | −0.0139985 | + | 0.0242462i | ||||
\(982\) | 0.876894 | − | 1.51883i | 0.0279828 | − | 0.0484677i | ||||
\(983\) | 55.2311 | 1.76160 | 0.880799 | − | 0.473491i | \(-0.157006\pi\) | ||||
0.880799 | + | 0.473491i | \(0.157006\pi\) | |||||||
\(984\) | −2.06155 | + | 3.57071i | −0.0657199 | + | 0.113830i | ||||
\(985\) | −1.00000 | − | 1.73205i | −0.0318626 | − | 0.0551877i | ||||
\(986\) | −2.50000 | − | 4.33013i | −0.0796162 | − | 0.137899i | ||||
\(987\) | 7.68466 | 0.244605 | ||||||||
\(988\) | 25.6847 | − | 10.3923i | 0.817138 | − | 0.330623i | ||||
\(989\) | 26.2462 | 0.834581 | ||||||||
\(990\) | 4.56155 | + | 7.90084i | 0.144976 | + | 0.251105i | ||||
\(991\) | 0.719224 | + | 1.24573i | 0.0228469 | + | 0.0395720i | 0.877223 | − | 0.480084i | \(-0.159394\pi\) |
−0.854376 | + | 0.519655i | \(0.826060\pi\) | |||||||
\(992\) | −2.56155 | + | 4.43674i | −0.0813294 | + | 0.140867i | ||||
\(993\) | −35.3693 | −1.12241 | ||||||||
\(994\) | −2.00000 | + | 3.46410i | −0.0634361 | + | 0.109875i | ||||
\(995\) | −31.3693 | + | 54.3333i | −0.994474 | + | 1.72248i | ||||
\(996\) | −10.2462 | −0.324664 | ||||||||
\(997\) | 8.50000 | − | 14.7224i | 0.269198 | − | 0.466264i | −0.699457 | − | 0.714675i | \(-0.746575\pi\) |
0.968655 | + | 0.248410i | \(0.0799082\pi\) | |||||||
\(998\) | 13.6847 | + | 23.7025i | 0.433180 | + | 0.750290i | ||||
\(999\) | 4.90388 | + | 8.49377i | 0.155152 | + | 0.268731i |
(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 | 546.2.l.i.211.1 | ✓ | 4 | |
3.2 | odd | 2 | 1638.2.r.z.757.2 | 4 | |||
13.3 | even | 3 | 7098.2.a.bw.1.1 | 2 | |||
13.9 | even | 3 | inner | 546.2.l.i.295.1 | yes | 4 | |
13.10 | even | 6 | 7098.2.a.bq.1.2 | 2 | |||
39.35 | odd | 6 | 1638.2.r.z.1387.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.i.211.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
546.2.l.i.295.1 | yes | 4 | 13.9 | even | 3 | inner | |
1638.2.r.z.757.2 | 4 | 3.2 | odd | 2 | |||
1638.2.r.z.1387.2 | 4 | 39.35 | odd | 6 | |||
7098.2.a.bq.1.2 | 2 | 13.10 | even | 6 | |||
7098.2.a.bw.1.1 | 2 | 13.3 | even | 3 |