Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.i (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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.173309020416.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 5x^{6} - 28x^{5} - 4x^{4} + 70x^{3} + 51x^{2} + 406x + 841 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 415.3 | ||
Root | \(2.93560 + 0.167344i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.415 |
Dual form | 966.2.i.n.277.3 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.239514 | − | 0.414851i | 0.107114 | − | 0.185527i | −0.807486 | − | 0.589887i | \(-0.799172\pi\) |
0.914600 | + | 0.404360i | \(0.132506\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.32288 | + | 2.29129i | 0.500000 | + | 0.866025i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.239514 | − | 0.414851i | −0.0757411 | − | 0.131187i | ||||
\(11\) | 2.67511 | + | 4.63343i | 0.806577 | + | 1.39703i | 0.915221 | + | 0.402952i | \(0.132016\pi\) |
−0.108644 | + | 0.994081i | \(0.534651\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | −4.70448 | −1.30479 | −0.652394 | − | 0.757880i | \(-0.726235\pi\) | ||||
−0.652394 | + | 0.757880i | \(0.726235\pi\) | |||||||
\(14\) | 2.64575 | 0.707107 | ||||||||
\(15\) | 0.479029 | 0.123685 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.08336 | + | 1.87644i | 0.262754 | + | 0.455103i | 0.966973 | − | 0.254880i | \(-0.0820360\pi\) |
−0.704219 | + | 0.709983i | \(0.748703\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | 1.87321 | − | 3.24449i | 0.429744 | − | 0.744338i | −0.567106 | − | 0.823644i | \(-0.691937\pi\) |
0.996850 | + | 0.0793064i | \(0.0252705\pi\) | |||||||
\(20\) | −0.479029 | −0.107114 | ||||||||
\(21\) | −1.32288 | + | 2.29129i | −0.288675 | + | 0.500000i | ||||
\(22\) | 5.35023 | 1.14067 | ||||||||
\(23\) | −0.500000 | + | 0.866025i | −0.104257 | + | 0.180579i | ||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 2.38527 | + | 4.13140i | 0.477053 | + | 0.826280i | ||||
\(26\) | −2.35224 | + | 4.07420i | −0.461312 | + | 0.799016i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.32288 | − | 2.29129i | 0.250000 | − | 0.433013i | ||||
\(29\) | −4.74642 | −0.881388 | −0.440694 | − | 0.897657i | \(-0.645268\pi\) | ||||
−0.440694 | + | 0.897657i | \(0.645268\pi\) | |||||||
\(30\) | 0.239514 | − | 0.414851i | 0.0437291 | − | 0.0757411i | ||||
\(31\) | 4.88527 | + | 8.46153i | 0.877420 | + | 1.51974i | 0.854163 | + | 0.520006i | \(0.174070\pi\) |
0.0232569 | + | 0.999730i | \(0.492596\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −2.67511 | + | 4.63343i | −0.465678 | + | 0.806577i | ||||
\(34\) | 2.16672 | 0.371590 | ||||||||
\(35\) | 1.26739 | 0.214228 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.35224 | − | 2.34215i | 0.222307 | − | 0.385046i | −0.733201 | − | 0.680012i | \(-0.761975\pi\) |
0.955508 | + | 0.294965i | \(0.0953080\pi\) | |||||||
\(38\) | −1.87321 | − | 3.24449i | −0.303875 | − | 0.526327i | ||||
\(39\) | −2.35224 | − | 4.07420i | −0.376660 | − | 0.652394i | ||||
\(40\) | −0.239514 | + | 0.414851i | −0.0378706 | + | 0.0655937i | ||||
\(41\) | 0.253580 | 0.0396026 | 0.0198013 | − | 0.999804i | \(-0.493697\pi\) | ||||
0.0198013 | + | 0.999804i | \(0.493697\pi\) | |||||||
\(42\) | 1.32288 | + | 2.29129i | 0.204124 | + | 0.353553i | ||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 2.67511 | − | 4.63343i | 0.403289 | − | 0.698516i | ||||
\(45\) | 0.239514 | + | 0.414851i | 0.0357047 | + | 0.0618424i | ||||
\(46\) | 0.500000 | + | 0.866025i | 0.0737210 | + | 0.127688i | ||||
\(47\) | 4.96496 | − | 8.59957i | 0.724214 | − | 1.25438i | −0.235082 | − | 0.971975i | \(-0.575536\pi\) |
0.959297 | − | 0.282400i | \(-0.0911307\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −3.50000 | + | 6.06218i | −0.500000 | + | 0.866025i | ||||
\(50\) | 4.77053 | 0.674655 | ||||||||
\(51\) | −1.08336 | + | 1.87644i | −0.151701 | + | 0.262754i | ||||
\(52\) | 2.35224 | + | 4.07420i | 0.326197 | + | 0.564989i | ||||
\(53\) | −1.23951 | − | 2.14690i | −0.170260 | − | 0.294900i | 0.768250 | − | 0.640149i | \(-0.221128\pi\) |
−0.938511 | + | 0.345250i | \(0.887794\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 2.56291 | 0.345583 | ||||||||
\(56\) | −1.32288 | − | 2.29129i | −0.176777 | − | 0.306186i | ||||
\(57\) | 3.74642 | 0.496225 | ||||||||
\(58\) | −2.37321 | + | 4.11052i | −0.311618 | + | 0.539738i | ||||
\(59\) | −6.27945 | − | 10.8763i | −0.817514 | − | 1.41598i | −0.907508 | − | 0.420034i | \(-0.862018\pi\) |
0.0899940 | − | 0.995942i | \(-0.471315\pi\) | |||||||
\(60\) | −0.239514 | − | 0.414851i | −0.0309212 | − | 0.0535570i | ||||
\(61\) | 4.47903 | − | 7.75791i | 0.573481 | − | 0.993298i | −0.422724 | − | 0.906258i | \(-0.638926\pi\) |
0.996205 | − | 0.0870395i | \(-0.0277406\pi\) | |||||||
\(62\) | 9.77053 | 1.24086 | ||||||||
\(63\) | −2.64575 | −0.333333 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.12679 | + | 1.95166i | −0.139761 | + | 0.242073i | ||||
\(66\) | 2.67511 | + | 4.63343i | 0.329284 | + | 0.570336i | ||||
\(67\) | 3.35023 | + | 5.80277i | 0.409296 | + | 0.708921i | 0.994811 | − | 0.101741i | \(-0.0324412\pi\) |
−0.585515 | + | 0.810661i | \(0.699108\pi\) | |||||||
\(68\) | 1.08336 | − | 1.87644i | 0.131377 | − | 0.227551i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0.633696 | − | 1.09759i | 0.0757411 | − | 0.131187i | ||||
\(71\) | 0.774551 | 0.0919223 | 0.0459612 | − | 0.998943i | \(-0.485365\pi\) | ||||
0.0459612 | + | 0.998943i | \(0.485365\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 5.61071 | + | 9.71804i | 0.656684 | + | 1.13741i | 0.981469 | + | 0.191623i | \(0.0613750\pi\) |
−0.324784 | + | 0.945788i | \(0.605292\pi\) | |||||||
\(74\) | −1.35224 | − | 2.34215i | −0.157195 | − | 0.272269i | ||||
\(75\) | −2.38527 | + | 4.13140i | −0.275427 | + | 0.477053i | ||||
\(76\) | −3.74642 | −0.429744 | ||||||||
\(77\) | −7.07769 | + | 12.2589i | −0.806577 | + | 1.39703i | ||||
\(78\) | −4.70448 | −0.532677 | ||||||||
\(79\) | −0.423544 | + | 0.733600i | −0.0476524 | + | 0.0825365i | −0.888868 | − | 0.458164i | \(-0.848507\pi\) |
0.841215 | + | 0.540700i | \(0.181841\pi\) | |||||||
\(80\) | 0.239514 | + | 0.414851i | 0.0267785 | + | 0.0463818i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0.126790 | − | 0.219607i | 0.0140016 | − | 0.0242515i | ||||
\(83\) | 10.9299 | 1.19972 | 0.599858 | − | 0.800107i | \(-0.295224\pi\) | ||||
0.599858 | + | 0.800107i | \(0.295224\pi\) | |||||||
\(84\) | 2.64575 | 0.288675 | ||||||||
\(85\) | 1.03792 | 0.112578 | ||||||||
\(86\) | 1.00000 | − | 1.73205i | 0.107833 | − | 0.186772i | ||||
\(87\) | −2.37321 | − | 4.11052i | −0.254435 | − | 0.440694i | ||||
\(88\) | −2.67511 | − | 4.63343i | −0.285168 | − | 0.493926i | ||||
\(89\) | 1.60582 | − | 2.78136i | 0.170216 | − | 0.294824i | −0.768279 | − | 0.640115i | \(-0.778887\pi\) |
0.938495 | + | 0.345292i | \(0.112220\pi\) | |||||||
\(90\) | 0.479029 | 0.0504941 | ||||||||
\(91\) | −6.22344 | − | 10.7793i | −0.652394 | − | 1.12998i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −4.88527 | + | 8.46153i | −0.506578 | + | 0.877420i | ||||
\(94\) | −4.96496 | − | 8.59957i | −0.512097 | − | 0.886978i | ||||
\(95\) | −0.897321 | − | 1.55421i | −0.0920632 | − | 0.159458i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 13.0098 | 1.32094 | 0.660472 | − | 0.750851i | \(-0.270356\pi\) | ||||
0.660472 | + | 0.750851i | \(0.270356\pi\) | |||||||
\(98\) | 3.50000 | + | 6.06218i | 0.353553 | + | 0.612372i | ||||
\(99\) | −5.35023 | −0.537718 | ||||||||
\(100\) | 2.38527 | − | 4.13140i | 0.238527 | − | 0.413140i | ||||
\(101\) | −2.38527 | − | 4.13140i | −0.237343 | − | 0.411090i | 0.722608 | − | 0.691258i | \(-0.242943\pi\) |
−0.959951 | + | 0.280168i | \(0.909610\pi\) | |||||||
\(102\) | 1.08336 | + | 1.87644i | 0.107269 | + | 0.185795i | ||||
\(103\) | 3.68918 | − | 6.38985i | 0.363506 | − | 0.629610i | −0.625029 | − | 0.780601i | \(-0.714913\pi\) |
0.988535 | + | 0.150991i | \(0.0482464\pi\) | |||||||
\(104\) | 4.70448 | 0.461312 | ||||||||
\(105\) | 0.633696 | + | 1.09759i | 0.0618424 | + | 0.107114i | ||||
\(106\) | −2.47903 | −0.240785 | ||||||||
\(107\) | −7.46496 | + | 12.9297i | −0.721665 | + | 1.24996i | 0.238667 | + | 0.971102i | \(0.423290\pi\) |
−0.960332 | + | 0.278859i | \(0.910044\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −2.26888 | − | 3.92981i | −0.217319 | − | 0.376408i | 0.736668 | − | 0.676254i | \(-0.236398\pi\) |
−0.953987 | + | 0.299846i | \(0.903065\pi\) | |||||||
\(110\) | 1.28146 | − | 2.21955i | 0.122182 | − | 0.211626i | ||||
\(111\) | 2.70448 | 0.256698 | ||||||||
\(112\) | −2.64575 | −0.250000 | ||||||||
\(113\) | −14.2455 | −1.34011 | −0.670054 | − | 0.742312i | \(-0.733729\pi\) | ||||
−0.670054 | + | 0.742312i | \(0.733729\pi\) | |||||||
\(114\) | 1.87321 | − | 3.24449i | 0.175442 | − | 0.303875i | ||||
\(115\) | 0.239514 | + | 0.414851i | 0.0223348 | + | 0.0386851i | ||||
\(116\) | 2.37321 | + | 4.11052i | 0.220347 | + | 0.381652i | ||||
\(117\) | 2.35224 | − | 4.07420i | 0.217465 | − | 0.376660i | ||||
\(118\) | −12.5589 | −1.15614 | ||||||||
\(119\) | −2.86630 | + | 4.96458i | −0.262754 | + | 0.455103i | ||||
\(120\) | −0.479029 | −0.0437291 | ||||||||
\(121\) | −8.81247 | + | 15.2637i | −0.801134 | + | 1.38760i | ||||
\(122\) | −4.47903 | − | 7.75791i | −0.405512 | − | 0.702368i | ||||
\(123\) | 0.126790 | + | 0.219607i | 0.0114323 | + | 0.0198013i | ||||
\(124\) | 4.88527 | − | 8.46153i | 0.438710 | − | 0.759868i | ||||
\(125\) | 4.68037 | 0.418625 | ||||||||
\(126\) | −1.32288 | + | 2.29129i | −0.117851 | + | 0.204124i | ||||
\(127\) | −12.3053 | −1.09192 | −0.545960 | − | 0.837811i | \(-0.683835\pi\) | ||||
−0.545960 | + | 0.837811i | \(0.683835\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.00000 | + | 1.73205i | 0.0880451 | + | 0.152499i | ||||
\(130\) | 1.12679 | + | 1.95166i | 0.0988260 | + | 0.171172i | ||||
\(131\) | 4.65781 | − | 8.06756i | 0.406954 | − | 0.704866i | −0.587592 | − | 0.809157i | \(-0.699924\pi\) |
0.994547 | + | 0.104291i | \(0.0332574\pi\) | |||||||
\(132\) | 5.35023 | 0.465678 | ||||||||
\(133\) | 9.91210 | 0.859488 | ||||||||
\(134\) | 6.70046 | 0.578831 | ||||||||
\(135\) | −0.239514 | + | 0.414851i | −0.0206141 | + | 0.0357047i | ||||
\(136\) | −1.08336 | − | 1.87644i | −0.0928975 | − | 0.160903i | ||||
\(137\) | −6.60232 | − | 11.4356i | −0.564074 | − | 0.977006i | −0.997135 | − | 0.0756409i | \(-0.975900\pi\) |
0.433061 | − | 0.901365i | \(-0.357434\pi\) | |||||||
\(138\) | −0.500000 | + | 0.866025i | −0.0425628 | + | 0.0737210i | ||||
\(139\) | −5.92993 | −0.502970 | −0.251485 | − | 0.967861i | \(-0.580919\pi\) | ||||
−0.251485 | + | 0.967861i | \(0.580919\pi\) | |||||||
\(140\) | −0.633696 | − | 1.09759i | −0.0535570 | − | 0.0927635i | ||||
\(141\) | 9.92993 | 0.836251 | ||||||||
\(142\) | 0.387276 | − | 0.670781i | 0.0324995 | − | 0.0562907i | ||||
\(143\) | −12.5850 | − | 21.7979i | −1.05241 | − | 1.82283i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −1.13684 | + | 1.96906i | −0.0944091 | + | 0.163521i | ||||
\(146\) | 11.2214 | 0.928692 | ||||||||
\(147\) | −7.00000 | −0.577350 | ||||||||
\(148\) | −2.70448 | −0.222307 | ||||||||
\(149\) | 0.587025 | − | 1.01676i | 0.0480910 | − | 0.0832960i | −0.840978 | − | 0.541069i | \(-0.818020\pi\) |
0.889069 | + | 0.457773i | \(0.151353\pi\) | |||||||
\(150\) | 2.38527 | + | 4.13140i | 0.194756 | + | 0.337328i | ||||
\(151\) | −3.15266 | − | 5.46056i | −0.256560 | − | 0.444374i | 0.708758 | − | 0.705451i | \(-0.249256\pi\) |
−0.965318 | + | 0.261077i | \(0.915922\pi\) | |||||||
\(152\) | −1.87321 | + | 3.24449i | −0.151937 | + | 0.263163i | ||||
\(153\) | −2.16672 | −0.175169 | ||||||||
\(154\) | 7.07769 | + | 12.2589i | 0.570336 | + | 0.987851i | ||||
\(155\) | 4.68037 | 0.375936 | ||||||||
\(156\) | −2.35224 | + | 4.07420i | −0.188330 | + | 0.326197i | ||||
\(157\) | −1.14209 | − | 1.97815i | −0.0911485 | − | 0.157874i | 0.816846 | − | 0.576856i | \(-0.195720\pi\) |
−0.907995 | + | 0.418982i | \(0.862387\pi\) | |||||||
\(158\) | 0.423544 | + | 0.733600i | 0.0336954 | + | 0.0583621i | ||||
\(159\) | 1.23951 | − | 2.14690i | 0.0982999 | − | 0.170260i | ||||
\(160\) | 0.479029 | 0.0378706 | ||||||||
\(161\) | −2.64575 | −0.208514 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −2.38728 | + | 4.13488i | −0.186986 | + | 0.323869i | −0.944244 | − | 0.329247i | \(-0.893205\pi\) |
0.757258 | + | 0.653116i | \(0.226539\pi\) | |||||||
\(164\) | −0.126790 | − | 0.219607i | −0.00990064 | − | 0.0171484i | ||||
\(165\) | 1.28146 | + | 2.21955i | 0.0997613 | + | 0.172792i | ||||
\(166\) | 5.46496 | − | 9.46559i | 0.424163 | − | 0.734673i | ||||
\(167\) | −20.9500 | −1.62116 | −0.810581 | − | 0.585627i | \(-0.800848\pi\) | ||||
−0.810581 | + | 0.585627i | \(0.800848\pi\) | |||||||
\(168\) | 1.32288 | − | 2.29129i | 0.102062 | − | 0.176777i | ||||
\(169\) | 9.13211 | 0.702470 | ||||||||
\(170\) | 0.518961 | − | 0.898867i | 0.0398025 | − | 0.0689400i | ||||
\(171\) | 1.87321 | + | 3.24449i | 0.143248 | + | 0.248113i | ||||
\(172\) | −1.00000 | − | 1.73205i | −0.0762493 | − | 0.132068i | ||||
\(173\) | 8.61071 | − | 14.9142i | 0.654660 | − | 1.13391i | −0.327318 | − | 0.944914i | \(-0.606145\pi\) |
0.981979 | − | 0.188991i | \(-0.0605217\pi\) | |||||||
\(174\) | −4.74642 | −0.359825 | ||||||||
\(175\) | −6.31082 | + | 10.9307i | −0.477053 | + | 0.826280i | ||||
\(176\) | −5.35023 | −0.403289 | ||||||||
\(177\) | 6.27945 | − | 10.8763i | 0.471992 | − | 0.817514i | ||||
\(178\) | −1.60582 | − | 2.78136i | −0.120361 | − | 0.208472i | ||||
\(179\) | −12.2634 | − | 21.2408i | −0.916607 | − | 1.58761i | −0.804531 | − | 0.593911i | \(-0.797583\pi\) |
−0.112077 | − | 0.993700i | \(-0.535750\pi\) | |||||||
\(180\) | 0.239514 | − | 0.414851i | 0.0178523 | − | 0.0309212i | ||||
\(181\) | −20.4123 | −1.51723 | −0.758616 | − | 0.651538i | \(-0.774124\pi\) | ||||
−0.758616 | + | 0.651538i | \(0.774124\pi\) | |||||||
\(182\) | −12.4469 | −0.922624 | ||||||||
\(183\) | 8.95806 | 0.662199 | ||||||||
\(184\) | 0.500000 | − | 0.866025i | 0.0368605 | − | 0.0638442i | ||||
\(185\) | −0.647761 | − | 1.12196i | −0.0476244 | − | 0.0824878i | ||||
\(186\) | 4.88527 | + | 8.46153i | 0.358205 | + | 0.620429i | ||||
\(187\) | −5.79623 | + | 10.0394i | −0.423862 | + | 0.734151i | ||||
\(188\) | −9.92993 | −0.724214 | ||||||||
\(189\) | −1.32288 | − | 2.29129i | −0.0962250 | − | 0.166667i | ||||
\(190\) | −1.79464 | −0.130197 | ||||||||
\(191\) | 0.619630 | − | 1.07323i | 0.0448348 | − | 0.0776562i | −0.842737 | − | 0.538325i | \(-0.819057\pi\) |
0.887572 | + | 0.460669i | \(0.152391\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 5.58974 | + | 9.68172i | 0.402359 | + | 0.696905i | 0.994010 | − | 0.109288i | \(-0.0348572\pi\) |
−0.591652 | + | 0.806194i | \(0.701524\pi\) | |||||||
\(194\) | 6.50490 | − | 11.2668i | 0.467024 | − | 0.808910i | ||||
\(195\) | −2.25358 | −0.161382 | ||||||||
\(196\) | 7.00000 | 0.500000 | ||||||||
\(197\) | 22.0956 | 1.57425 | 0.787123 | − | 0.616796i | \(-0.211570\pi\) | ||||
0.787123 | + | 0.616796i | \(0.211570\pi\) | |||||||
\(198\) | −2.67511 | + | 4.63343i | −0.190112 | + | 0.329284i | ||||
\(199\) | −4.24807 | − | 7.35788i | −0.301138 | − | 0.521586i | 0.675256 | − | 0.737583i | \(-0.264033\pi\) |
−0.976394 | + | 0.215997i | \(0.930700\pi\) | |||||||
\(200\) | −2.38527 | − | 4.13140i | −0.168664 | − | 0.292134i | ||||
\(201\) | −3.35023 | + | 5.80277i | −0.236307 | + | 0.409296i | ||||
\(202\) | −4.77053 | −0.335653 | ||||||||
\(203\) | −6.27892 | − | 10.8754i | −0.440694 | − | 0.763304i | ||||
\(204\) | 2.16672 | 0.151701 | ||||||||
\(205\) | 0.0607361 | − | 0.105198i | 0.00424199 | − | 0.00734735i | ||||
\(206\) | −3.68918 | − | 6.38985i | −0.257037 | − | 0.445202i | ||||
\(207\) | −0.500000 | − | 0.866025i | −0.0347524 | − | 0.0601929i | ||||
\(208\) | 2.35224 | − | 4.07420i | 0.163098 | − | 0.282495i | ||||
\(209\) | 20.0442 | 1.38649 | ||||||||
\(210\) | 1.26739 | 0.0874583 | ||||||||
\(211\) | 20.3808 | 1.40307 | 0.701537 | − | 0.712633i | \(-0.252498\pi\) | ||||
0.701537 | + | 0.712633i | \(0.252498\pi\) | |||||||
\(212\) | −1.23951 | + | 2.14690i | −0.0851302 | + | 0.147450i | ||||
\(213\) | 0.387276 | + | 0.670781i | 0.0265357 | + | 0.0459612i | ||||
\(214\) | 7.46496 | + | 12.9297i | 0.510294 | + | 0.883856i | ||||
\(215\) | 0.479029 | − | 0.829702i | 0.0326695 | − | 0.0565852i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −12.9252 | + | 22.3871i | −0.877420 | + | 1.51974i | ||||
\(218\) | −4.53775 | −0.307336 | ||||||||
\(219\) | −5.61071 | + | 9.71804i | −0.379137 | + | 0.656684i | ||||
\(220\) | −1.28146 | − | 2.21955i | −0.0863958 | − | 0.149642i | ||||
\(221\) | −5.09665 | − | 8.82765i | −0.342838 | − | 0.593812i | ||||
\(222\) | 1.35224 | − | 2.34215i | 0.0907563 | − | 0.157195i | ||||
\(223\) | −3.18753 | −0.213453 | −0.106726 | − | 0.994288i | \(-0.534037\pi\) | ||||
−0.106726 | + | 0.994288i | \(0.534037\pi\) | |||||||
\(224\) | −1.32288 | + | 2.29129i | −0.0883883 | + | 0.153093i | ||||
\(225\) | −4.77053 | −0.318035 | ||||||||
\(226\) | −7.12277 | + | 12.3370i | −0.473800 | + | 0.820645i | ||||
\(227\) | −2.67913 | − | 4.64040i | −0.177820 | − | 0.307994i | 0.763313 | − | 0.646028i | \(-0.223571\pi\) |
−0.941134 | + | 0.338035i | \(0.890238\pi\) | |||||||
\(228\) | −1.87321 | − | 3.24449i | −0.124056 | − | 0.214872i | ||||
\(229\) | 11.7291 | − | 20.3154i | 0.775082 | − | 1.34248i | −0.159667 | − | 0.987171i | \(-0.551042\pi\) |
0.934749 | − | 0.355310i | \(-0.115625\pi\) | |||||||
\(230\) | 0.479029 | 0.0315862 | ||||||||
\(231\) | −14.1554 | −0.931355 | ||||||||
\(232\) | 4.74642 | 0.311618 | ||||||||
\(233\) | 12.3902 | − | 21.4604i | 0.811706 | − | 1.40592i | −0.0999624 | − | 0.994991i | \(-0.531872\pi\) |
0.911669 | − | 0.410926i | \(-0.134794\pi\) | |||||||
\(234\) | −2.35224 | − | 4.07420i | −0.153771 | − | 0.266339i | ||||
\(235\) | −2.37836 | − | 4.11944i | −0.155147 | − | 0.268723i | ||||
\(236\) | −6.27945 | + | 10.8763i | −0.408757 | + | 0.707988i | ||||
\(237\) | −0.847088 | −0.0550243 | ||||||||
\(238\) | 2.86630 | + | 4.96458i | 0.185795 | + | 0.321806i | ||||
\(239\) | 4.97187 | 0.321603 | 0.160802 | − | 0.986987i | \(-0.448592\pi\) | ||||
0.160802 | + | 0.986987i | \(0.448592\pi\) | |||||||
\(240\) | −0.239514 | + | 0.414851i | −0.0154606 | + | 0.0267785i | ||||
\(241\) | 3.74169 | + | 6.48080i | 0.241024 | + | 0.417465i | 0.961006 | − | 0.276527i | \(-0.0891836\pi\) |
−0.719983 | + | 0.693992i | \(0.755850\pi\) | |||||||
\(242\) | 8.81247 | + | 15.2637i | 0.566487 | + | 0.981185i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −8.95806 | −0.573481 | ||||||||
\(245\) | 1.67660 | + | 2.90396i | 0.107114 | + | 0.185527i | ||||
\(246\) | 0.253580 | 0.0161677 | ||||||||
\(247\) | −8.81247 | + | 15.2637i | −0.560724 | + | 0.971203i | ||||
\(248\) | −4.88527 | − | 8.46153i | −0.310215 | − | 0.537308i | ||||
\(249\) | 5.46496 | + | 9.46559i | 0.346328 | + | 0.599858i | ||||
\(250\) | 2.34018 | − | 4.05332i | 0.148006 | − | 0.256354i | ||||
\(251\) | −14.9752 | −0.945225 | −0.472612 | − | 0.881270i | \(-0.656689\pi\) | ||||
−0.472612 | + | 0.881270i | \(0.656689\pi\) | |||||||
\(252\) | 1.32288 | + | 2.29129i | 0.0833333 | + | 0.144338i | ||||
\(253\) | −5.35023 | −0.336366 | ||||||||
\(254\) | −6.15266 | + | 10.6567i | −0.386052 | + | 0.668662i | ||||
\(255\) | 0.518961 | + | 0.898867i | 0.0324986 | + | 0.0562892i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −0.251570 | + | 0.435732i | −0.0156925 | + | 0.0271802i | −0.873765 | − | 0.486348i | \(-0.838329\pi\) |
0.858073 | + | 0.513529i | \(0.171662\pi\) | |||||||
\(258\) | 2.00000 | 0.124515 | ||||||||
\(259\) | 7.15537 | 0.444613 | ||||||||
\(260\) | 2.25358 | 0.139761 | ||||||||
\(261\) | 2.37321 | − | 4.11052i | 0.146898 | − | 0.254435i | ||||
\(262\) | −4.65781 | − | 8.06756i | −0.287760 | − | 0.498415i | ||||
\(263\) | 2.49581 | + | 4.32287i | 0.153898 | + | 0.266560i | 0.932657 | − | 0.360763i | \(-0.117484\pi\) |
−0.778759 | + | 0.627323i | \(0.784150\pi\) | |||||||
\(264\) | 2.67511 | − | 4.63343i | 0.164642 | − | 0.285168i | ||||
\(265\) | −1.18753 | −0.0729492 | ||||||||
\(266\) | 4.95605 | − | 8.58413i | 0.303875 | − | 0.526327i | ||||
\(267\) | 3.21164 | 0.196549 | ||||||||
\(268\) | 3.35023 | − | 5.80277i | 0.204648 | − | 0.354460i | ||||
\(269\) | −2.06388 | − | 3.57474i | −0.125837 | − | 0.217956i | 0.796223 | − | 0.605003i | \(-0.206828\pi\) |
−0.922060 | + | 0.387048i | \(0.873495\pi\) | |||||||
\(270\) | 0.239514 | + | 0.414851i | 0.0145764 | + | 0.0252470i | ||||
\(271\) | 1.46898 | − | 2.54435i | 0.0892344 | − | 0.154558i | −0.817953 | − | 0.575285i | \(-0.804891\pi\) |
0.907188 | + | 0.420726i | \(0.138225\pi\) | |||||||
\(272\) | −2.16672 | −0.131377 | ||||||||
\(273\) | 6.22344 | − | 10.7793i | 0.376660 | − | 0.652394i | ||||
\(274\) | −13.2046 | −0.797722 | ||||||||
\(275\) | −12.7617 | + | 22.1039i | −0.769561 | + | 1.33292i | ||||
\(276\) | 0.500000 | + | 0.866025i | 0.0300965 | + | 0.0521286i | ||||
\(277\) | 14.3462 | + | 24.8484i | 0.861980 | + | 1.49299i | 0.870015 | + | 0.493026i | \(0.164109\pi\) |
−0.00803461 | + | 0.999968i | \(0.502558\pi\) | |||||||
\(278\) | −2.96496 | + | 5.13547i | −0.177827 | + | 0.308005i | ||||
\(279\) | −9.77053 | −0.584946 | ||||||||
\(280\) | −1.26739 | −0.0757411 | ||||||||
\(281\) | −14.7833 | −0.881897 | −0.440949 | − | 0.897532i | \(-0.645358\pi\) | ||||
−0.440949 | + | 0.897532i | \(0.645358\pi\) | |||||||
\(282\) | 4.96496 | − | 8.59957i | 0.295659 | − | 0.512097i | ||||
\(283\) | 6.55889 | + | 11.3603i | 0.389886 | + | 0.675302i | 0.992434 | − | 0.122781i | \(-0.0391812\pi\) |
−0.602548 | + | 0.798083i | \(0.705848\pi\) | |||||||
\(284\) | −0.387276 | − | 0.670781i | −0.0229806 | − | 0.0398035i | ||||
\(285\) | 0.897321 | − | 1.55421i | 0.0531527 | − | 0.0920632i | ||||
\(286\) | −25.1700 | −1.48834 | ||||||||
\(287\) | 0.335455 | + | 0.581025i | 0.0198013 | + | 0.0342968i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 6.15266 | − | 10.6567i | 0.361921 | − | 0.626866i | ||||
\(290\) | 1.13684 | + | 1.96906i | 0.0667573 | + | 0.115627i | ||||
\(291\) | 6.50490 | + | 11.2668i | 0.381324 | + | 0.660472i | ||||
\(292\) | 5.61071 | − | 9.71804i | 0.328342 | − | 0.568705i | ||||
\(293\) | −4.38920 | −0.256420 | −0.128210 | − | 0.991747i | \(-0.540923\pi\) | ||||
−0.128210 | + | 0.991747i | \(0.540923\pi\) | |||||||
\(294\) | −3.50000 | + | 6.06218i | −0.204124 | + | 0.353553i | ||||
\(295\) | −6.01607 | −0.350269 | ||||||||
\(296\) | −1.35224 | + | 2.34215i | −0.0785973 | + | 0.136134i | ||||
\(297\) | −2.67511 | − | 4.63343i | −0.155226 | − | 0.268859i | ||||
\(298\) | −0.587025 | − | 1.01676i | −0.0340055 | − | 0.0588992i | ||||
\(299\) | 2.35224 | − | 4.07420i | 0.136033 | − | 0.235617i | ||||
\(300\) | 4.77053 | 0.275427 | ||||||||
\(301\) | 2.64575 | + | 4.58258i | 0.152499 | + | 0.264135i | ||||
\(302\) | −6.30531 | −0.362830 | ||||||||
\(303\) | 2.38527 | − | 4.13140i | 0.137030 | − | 0.237343i | ||||
\(304\) | 1.87321 | + | 3.24449i | 0.107436 | + | 0.186085i | ||||
\(305\) | −2.14558 | − | 3.71626i | −0.122856 | − | 0.212792i | ||||
\(306\) | −1.08336 | + | 1.87644i | −0.0619316 | + | 0.107269i | ||||
\(307\) | 10.1755 | 0.580745 | 0.290372 | − | 0.956914i | \(-0.406221\pi\) | ||||
0.290372 | + | 0.956914i | \(0.406221\pi\) | |||||||
\(308\) | 14.1554 | 0.806577 | ||||||||
\(309\) | 7.37836 | 0.419740 | ||||||||
\(310\) | 2.34018 | − | 4.05332i | 0.132913 | − | 0.230213i | ||||
\(311\) | 6.27526 | + | 10.8691i | 0.355837 | + | 0.616328i | 0.987261 | − | 0.159110i | \(-0.0508624\pi\) |
−0.631424 | + | 0.775438i | \(0.717529\pi\) | |||||||
\(312\) | 2.35224 | + | 4.07420i | 0.133169 | + | 0.230656i | ||||
\(313\) | −7.94198 | + | 13.7559i | −0.448907 | + | 0.777530i | −0.998315 | − | 0.0580240i | \(-0.981520\pi\) |
0.549408 | + | 0.835554i | \(0.314853\pi\) | |||||||
\(314\) | −2.28417 | −0.128903 | ||||||||
\(315\) | −0.633696 | + | 1.09759i | −0.0357047 | + | 0.0618424i | ||||
\(316\) | 0.847088 | 0.0476524 | ||||||||
\(317\) | −15.2794 | + | 26.4648i | −0.858179 | + | 1.48641i | 0.0154847 | + | 0.999880i | \(0.495071\pi\) |
−0.873664 | + | 0.486530i | \(0.838262\pi\) | |||||||
\(318\) | −1.23951 | − | 2.14690i | −0.0695085 | − | 0.120392i | ||||
\(319\) | −12.6972 | − | 21.9922i | −0.710908 | − | 1.23133i | ||||
\(320\) | 0.239514 | − | 0.414851i | 0.0133893 | − | 0.0231909i | ||||
\(321\) | −14.9299 | −0.833307 | ||||||||
\(322\) | −1.32288 | + | 2.29129i | −0.0737210 | + | 0.127688i | ||||
\(323\) | 8.11745 | 0.451667 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −11.2214 | − | 19.4361i | −0.622453 | − | 1.07812i | ||||
\(326\) | 2.38728 | + | 4.13488i | 0.132219 | + | 0.229010i | ||||
\(327\) | 2.26888 | − | 3.92981i | 0.125469 | − | 0.217319i | ||||
\(328\) | −0.253580 | −0.0140016 | ||||||||
\(329\) | 26.2721 | 1.44843 | ||||||||
\(330\) | 2.56291 | 0.141084 | ||||||||
\(331\) | 17.1188 | − | 29.6505i | 0.940932 | − | 1.62974i | 0.177232 | − | 0.984169i | \(-0.443286\pi\) |
0.763699 | − | 0.645572i | \(-0.223381\pi\) | |||||||
\(332\) | −5.46496 | − | 9.46559i | −0.299929 | − | 0.519492i | ||||
\(333\) | 1.35224 | + | 2.34215i | 0.0741022 | + | 0.128349i | ||||
\(334\) | −10.4750 | + | 18.1432i | −0.573167 | + | 0.992754i | ||||
\(335\) | 3.20971 | 0.175365 | ||||||||
\(336\) | −1.32288 | − | 2.29129i | −0.0721688 | − | 0.125000i | ||||
\(337\) | −12.2590 | −0.667791 | −0.333896 | − | 0.942610i | \(-0.608363\pi\) | ||||
−0.333896 | + | 0.942610i | \(0.608363\pi\) | |||||||
\(338\) | 4.56605 | − | 7.90864i | 0.248361 | − | 0.430173i | ||||
\(339\) | −7.12277 | − | 12.3370i | −0.386856 | − | 0.670054i | ||||
\(340\) | −0.518961 | − | 0.898867i | −0.0281446 | − | 0.0487479i | ||||
\(341\) | −26.1373 | + | 45.2711i | −1.41541 | + | 2.45157i | ||||
\(342\) | 3.74642 | 0.202583 | ||||||||
\(343\) | −18.5203 | −1.00000 | ||||||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | −0.239514 | + | 0.414851i | −0.0128950 | + | 0.0223348i | ||||
\(346\) | −8.61071 | − | 14.9142i | −0.462915 | − | 0.801792i | ||||
\(347\) | 4.77053 | + | 8.26280i | 0.256096 | + | 0.443570i | 0.965193 | − | 0.261540i | \(-0.0842305\pi\) |
−0.709097 | + | 0.705111i | \(0.750897\pi\) | |||||||
\(348\) | −2.37321 | + | 4.11052i | −0.127217 | + | 0.220347i | ||||
\(349\) | −8.44688 | −0.452151 | −0.226075 | − | 0.974110i | \(-0.572590\pi\) | ||||
−0.226075 | + | 0.974110i | \(0.572590\pi\) | |||||||
\(350\) | 6.31082 | + | 10.9307i | 0.337328 | + | 0.584268i | ||||
\(351\) | 4.70448 | 0.251106 | ||||||||
\(352\) | −2.67511 | + | 4.63343i | −0.142584 | + | 0.246963i | ||||
\(353\) | −12.2402 | − | 21.2007i | −0.651481 | − | 1.12840i | −0.982764 | − | 0.184867i | \(-0.940815\pi\) |
0.331282 | − | 0.943532i | \(-0.392519\pi\) | |||||||
\(354\) | −6.27945 | − | 10.8763i | −0.333749 | − | 0.578070i | ||||
\(355\) | 0.185516 | − | 0.321323i | 0.00984618 | − | 0.0170541i | ||||
\(356\) | −3.21164 | −0.170216 | ||||||||
\(357\) | −5.73261 | −0.303402 | ||||||||
\(358\) | −24.5267 | −1.29628 | ||||||||
\(359\) | −10.1208 | + | 17.5297i | −0.534153 | + | 0.925181i | 0.465051 | + | 0.885284i | \(0.346036\pi\) |
−0.999204 | + | 0.0398965i | \(0.987297\pi\) | |||||||
\(360\) | −0.239514 | − | 0.414851i | −0.0126235 | − | 0.0218646i | ||||
\(361\) | 2.48217 | + | 4.29924i | 0.130640 | + | 0.226276i | ||||
\(362\) | −10.2061 | + | 17.6775i | −0.536422 | + | 0.929111i | ||||
\(363\) | −17.6249 | −0.925070 | ||||||||
\(364\) | −6.22344 | + | 10.7793i | −0.326197 | + | 0.564989i | ||||
\(365\) | 5.37539 | 0.281361 | ||||||||
\(366\) | 4.47903 | − | 7.75791i | 0.234123 | − | 0.405512i | ||||
\(367\) | −2.92520 | − | 5.06659i | −0.152694 | − | 0.264474i | 0.779523 | − | 0.626374i | \(-0.215462\pi\) |
−0.932217 | + | 0.361900i | \(0.882128\pi\) | |||||||
\(368\) | −0.500000 | − | 0.866025i | −0.0260643 | − | 0.0451447i | ||||
\(369\) | −0.126790 | + | 0.219607i | −0.00660043 | + | 0.0114323i | ||||
\(370\) | −1.29552 | −0.0673510 | ||||||||
\(371\) | 3.27945 | − | 5.68017i | 0.170260 | − | 0.294900i | ||||
\(372\) | 9.77053 | 0.506578 | ||||||||
\(373\) | −16.5772 | + | 28.7125i | −0.858333 | + | 1.48668i | 0.0151851 | + | 0.999885i | \(0.495166\pi\) |
−0.873518 | + | 0.486792i | \(0.838167\pi\) | |||||||
\(374\) | 5.79623 | + | 10.0394i | 0.299716 | + | 0.519123i | ||||
\(375\) | 2.34018 | + | 4.05332i | 0.120847 | + | 0.209312i | ||||
\(376\) | −4.96496 | + | 8.59957i | −0.256048 | + | 0.443489i | ||||
\(377\) | 22.3294 | 1.15002 | ||||||||
\(378\) | −2.64575 | −0.136083 | ||||||||
\(379\) | 29.1996 | 1.49988 | 0.749941 | − | 0.661505i | \(-0.230082\pi\) | ||||
0.749941 | + | 0.661505i | \(0.230082\pi\) | |||||||
\(380\) | −0.897321 | + | 1.55421i | −0.0460316 | + | 0.0797291i | ||||
\(381\) | −6.15266 | − | 10.6567i | −0.315210 | − | 0.545960i | ||||
\(382\) | −0.619630 | − | 1.07323i | −0.0317030 | − | 0.0549112i | ||||
\(383\) | 17.6116 | − | 30.5042i | 0.899910 | − | 1.55869i | 0.0723029 | − | 0.997383i | \(-0.476965\pi\) |
0.827607 | − | 0.561307i | \(-0.189701\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 3.39042 | + | 5.87237i | 0.172792 | + | 0.299284i | ||||
\(386\) | 11.1795 | 0.569021 | ||||||||
\(387\) | −1.00000 | + | 1.73205i | −0.0508329 | + | 0.0880451i | ||||
\(388\) | −6.50490 | − | 11.2668i | −0.330236 | − | 0.571986i | ||||
\(389\) | 15.3083 | + | 26.5147i | 0.776161 | + | 1.34435i | 0.934140 | + | 0.356908i | \(0.116169\pi\) |
−0.157979 | + | 0.987443i | \(0.550498\pi\) | |||||||
\(390\) | −1.12679 | + | 1.95166i | −0.0570572 | + | 0.0988260i | ||||
\(391\) | −2.16672 | −0.109576 | ||||||||
\(392\) | 3.50000 | − | 6.06218i | 0.176777 | − | 0.306186i | ||||
\(393\) | 9.31561 | 0.469911 | ||||||||
\(394\) | 11.0478 | − | 19.1354i | 0.556580 | − | 0.964025i | ||||
\(395\) | 0.202890 | + | 0.351416i | 0.0102085 | + | 0.0176816i | ||||
\(396\) | 2.67511 | + | 4.63343i | 0.134430 | + | 0.232839i | ||||
\(397\) | 8.45291 | − | 14.6409i | 0.424239 | − | 0.734804i | −0.572110 | − | 0.820177i | \(-0.693875\pi\) |
0.996349 | + | 0.0853731i | \(0.0272082\pi\) | |||||||
\(398\) | −8.49615 | −0.425873 | ||||||||
\(399\) | 4.95605 | + | 8.58413i | 0.248113 | + | 0.429744i | ||||
\(400\) | −4.77053 | −0.238527 | ||||||||
\(401\) | 16.2367 | − | 28.1228i | 0.810823 | − | 1.40439i | −0.101465 | − | 0.994839i | \(-0.532353\pi\) |
0.912288 | − | 0.409548i | \(-0.134314\pi\) | |||||||
\(402\) | 3.35023 | + | 5.80277i | 0.167094 | + | 0.289416i | ||||
\(403\) | −22.9826 | − | 39.8071i | −1.14485 | − | 1.98293i | ||||
\(404\) | −2.38527 | + | 4.13140i | −0.118671 | + | 0.205545i | ||||
\(405\) | −0.479029 | −0.0238031 | ||||||||
\(406\) | −12.5578 | −0.623235 | ||||||||
\(407\) | 14.4696 | 0.717230 | ||||||||
\(408\) | 1.08336 | − | 1.87644i | 0.0536344 | − | 0.0928975i | ||||
\(409\) | 13.5098 | + | 23.3996i | 0.668016 | + | 1.15704i | 0.978458 | + | 0.206446i | \(0.0661896\pi\) |
−0.310442 | + | 0.950592i | \(0.600477\pi\) | |||||||
\(410\) | −0.0607361 | − | 0.105198i | −0.00299954 | − | 0.00519536i | ||||
\(411\) | 6.60232 | − | 11.4356i | 0.325669 | − | 0.564074i | ||||
\(412\) | −7.37836 | −0.363506 | ||||||||
\(413\) | 16.6139 | − | 28.7760i | 0.817514 | − | 1.41598i | ||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 2.61787 | − | 4.53429i | 0.128506 | − | 0.222580i | ||||
\(416\) | −2.35224 | − | 4.07420i | −0.115328 | − | 0.199754i | ||||
\(417\) | −2.96496 | − | 5.13547i | −0.145195 | − | 0.251485i | ||||
\(418\) | 10.0221 | − | 17.3588i | 0.490197 | − | 0.849046i | ||||
\(419\) | 2.08686 | 0.101950 | 0.0509748 | − | 0.998700i | \(-0.483767\pi\) | ||||
0.0509748 | + | 0.998700i | \(0.483767\pi\) | |||||||
\(420\) | 0.633696 | − | 1.09759i | 0.0309212 | − | 0.0535570i | ||||
\(421\) | 23.2805 | 1.13462 | 0.567311 | − | 0.823504i | \(-0.307984\pi\) | ||||
0.567311 | + | 0.823504i | \(0.307984\pi\) | |||||||
\(422\) | 10.1904 | − | 17.6503i | 0.496061 | − | 0.859204i | ||||
\(423\) | 4.96496 | + | 8.59957i | 0.241405 | + | 0.418125i | ||||
\(424\) | 1.23951 | + | 2.14690i | 0.0601961 | + | 0.104263i | ||||
\(425\) | −5.16821 | + | 8.95160i | −0.250695 | + | 0.434216i | ||||
\(426\) | 0.774551 | 0.0375271 | ||||||||
\(427\) | 23.7008 | 1.14696 | ||||||||
\(428\) | 14.9299 | 0.721665 | ||||||||
\(429\) | 12.5850 | − | 21.7979i | 0.607610 | − | 1.05241i | ||||
\(430\) | −0.479029 | − | 0.829702i | −0.0231008 | − | 0.0400118i | ||||
\(431\) | 13.3053 | + | 23.0455i | 0.640894 | + | 1.11006i | 0.985233 | + | 0.171216i | \(0.0547697\pi\) |
−0.344339 | + | 0.938845i | \(0.611897\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 34.9354 | 1.67889 | 0.839443 | − | 0.543447i | \(-0.182881\pi\) | ||||
0.839443 | + | 0.543447i | \(0.182881\pi\) | |||||||
\(434\) | 12.9252 | + | 22.3871i | 0.620429 | + | 1.07462i | ||||
\(435\) | −2.27367 | −0.109014 | ||||||||
\(436\) | −2.26888 | + | 3.92981i | −0.108660 | + | 0.188204i | ||||
\(437\) | 1.87321 | + | 3.24449i | 0.0896078 | + | 0.155205i | ||||
\(438\) | 5.61071 | + | 9.71804i | 0.268090 | + | 0.464346i | ||||
\(439\) | 3.86848 | − | 6.70041i | 0.184633 | − | 0.319793i | −0.758820 | − | 0.651300i | \(-0.774224\pi\) |
0.943453 | + | 0.331507i | \(0.107557\pi\) | |||||||
\(440\) | −2.56291 | −0.122182 | ||||||||
\(441\) | −3.50000 | − | 6.06218i | −0.166667 | − | 0.288675i | ||||
\(442\) | −10.1933 | −0.484846 | ||||||||
\(443\) | −9.67162 | + | 16.7517i | −0.459512 | + | 0.795899i | −0.998935 | − | 0.0461362i | \(-0.985309\pi\) |
0.539423 | + | 0.842035i | \(0.318643\pi\) | |||||||
\(444\) | −1.35224 | − | 2.34215i | −0.0641744 | − | 0.111153i | ||||
\(445\) | −0.769233 | − | 1.33235i | −0.0364652 | − | 0.0631595i | ||||
\(446\) | −1.59376 | + | 2.76048i | −0.0754669 | + | 0.130712i | ||||
\(447\) | 1.17405 | 0.0555307 | ||||||||
\(448\) | 1.32288 | + | 2.29129i | 0.0625000 | + | 0.108253i | ||||
\(449\) | 16.0718 | 0.758476 | 0.379238 | − | 0.925299i | \(-0.376186\pi\) | ||||
0.379238 | + | 0.925299i | \(0.376186\pi\) | |||||||
\(450\) | −2.38527 | + | 4.13140i | −0.112443 | + | 0.194756i | ||||
\(451\) | 0.678356 | + | 1.17495i | 0.0319425 | + | 0.0553261i | ||||
\(452\) | 7.12277 | + | 12.3370i | 0.335027 | + | 0.580284i | ||||
\(453\) | 3.15266 | − | 5.46056i | 0.148125 | − | 0.256560i | ||||
\(454\) | −5.35827 | −0.251476 | ||||||||
\(455\) | −5.96241 | −0.279522 | ||||||||
\(456\) | −3.74642 | −0.175442 | ||||||||
\(457\) | −7.46697 | + | 12.9332i | −0.349290 | + | 0.604988i | −0.986124 | − | 0.166013i | \(-0.946911\pi\) |
0.636833 | + | 0.771002i | \(0.280244\pi\) | |||||||
\(458\) | −11.7291 | − | 20.3154i | −0.548065 | − | 0.949277i | ||||
\(459\) | −1.08336 | − | 1.87644i | −0.0505670 | − | 0.0875846i | ||||
\(460\) | 0.239514 | − | 0.414851i | 0.0111674 | − | 0.0193425i | ||||
\(461\) | 23.1660 | 1.07895 | 0.539474 | − | 0.842002i | \(-0.318623\pi\) | ||||
0.539474 | + | 0.842002i | \(0.318623\pi\) | |||||||
\(462\) | −7.07769 | + | 12.2589i | −0.329284 | + | 0.570336i | ||||
\(463\) | 40.4429 | 1.87954 | 0.939769 | − | 0.341809i | \(-0.111040\pi\) | ||||
0.939769 | + | 0.341809i | \(0.111040\pi\) | |||||||
\(464\) | 2.37321 | − | 4.11052i | 0.110174 | − | 0.190826i | ||||
\(465\) | 2.34018 | + | 4.05332i | 0.108523 | + | 0.187968i | ||||
\(466\) | −12.3902 | − | 21.4604i | −0.573963 | − | 0.994133i | ||||
\(467\) | −3.21015 | + | 5.56015i | −0.148548 | + | 0.257293i | −0.930691 | − | 0.365806i | \(-0.880793\pi\) |
0.782143 | + | 0.623099i | \(0.214127\pi\) | |||||||
\(468\) | −4.70448 | −0.217465 | ||||||||
\(469\) | −8.86387 | + | 15.3527i | −0.409296 | + | 0.708921i | ||||
\(470\) | −4.75672 | −0.219411 | ||||||||
\(471\) | 1.14209 | − | 1.97815i | 0.0526246 | − | 0.0911485i | ||||
\(472\) | 6.27945 | + | 10.8763i | 0.289035 | + | 0.500623i | ||||
\(473\) | 5.35023 | + | 9.26687i | 0.246004 | + | 0.426091i | ||||
\(474\) | −0.423544 | + | 0.733600i | −0.0194540 | + | 0.0336954i | ||||
\(475\) | 17.8724 | 0.820043 | ||||||||
\(476\) | 5.73261 | 0.262754 | ||||||||
\(477\) | 2.47903 | 0.113507 | ||||||||
\(478\) | 2.48593 | − | 4.30576i | 0.113704 | − | 0.196941i | ||||
\(479\) | −4.12679 | − | 7.14781i | −0.188558 | − | 0.326592i | 0.756212 | − | 0.654327i | \(-0.227048\pi\) |
−0.944770 | + | 0.327735i | \(0.893715\pi\) | |||||||
\(480\) | 0.239514 | + | 0.414851i | 0.0109323 | + | 0.0189353i | ||||
\(481\) | −6.36158 | + | 11.0186i | −0.290063 | + | 0.502404i | ||||
\(482\) | 7.48338 | 0.340859 | ||||||||
\(483\) | −1.32288 | − | 2.29129i | −0.0601929 | − | 0.104257i | ||||
\(484\) | 17.6249 | 0.801134 | ||||||||
\(485\) | 3.11603 | − | 5.39713i | 0.141492 | − | 0.245071i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −13.7145 | − | 23.7543i | −0.621464 | − | 1.07641i | −0.989213 | − | 0.146483i | \(-0.953205\pi\) |
0.367749 | − | 0.929925i | \(-0.380129\pi\) | |||||||
\(488\) | −4.47903 | + | 7.75791i | −0.202756 | + | 0.351184i | ||||
\(489\) | −4.77455 | −0.215913 | ||||||||
\(490\) | 3.35320 | 0.151482 | ||||||||
\(491\) | 15.9067 | 0.717857 | 0.358929 | − | 0.933365i | \(-0.383142\pi\) | ||||
0.358929 | + | 0.933365i | \(0.383142\pi\) | |||||||
\(492\) | 0.126790 | − | 0.219607i | 0.00571614 | − | 0.00990064i | ||||
\(493\) | −5.14209 | − | 8.90636i | −0.231588 | − | 0.401122i | ||||
\(494\) | 8.81247 | + | 15.2637i | 0.396492 | + | 0.686744i | ||||
\(495\) | −1.28146 | + | 2.21955i | −0.0575972 | + | 0.0997613i | ||||
\(496\) | −9.77053 | −0.438710 | ||||||||
\(497\) | 1.02464 | + | 1.77472i | 0.0459612 | + | 0.0796071i | ||||
\(498\) | 10.9299 | 0.489782 | ||||||||
\(499\) | 1.63587 | − | 2.83342i | 0.0732317 | − | 0.126841i | −0.827084 | − | 0.562078i | \(-0.810002\pi\) |
0.900316 | + | 0.435237i | \(0.143335\pi\) | |||||||
\(500\) | −2.34018 | − | 4.05332i | −0.104656 | − | 0.181270i | ||||
\(501\) | −10.4750 | − | 18.1432i | −0.467989 | − | 0.810581i | ||||
\(502\) | −7.48759 | + | 12.9689i | −0.334187 | + | 0.578830i | ||||
\(503\) | 1.58267 | 0.0705678 | 0.0352839 | − | 0.999377i | \(-0.488766\pi\) | ||||
0.0352839 | + | 0.999377i | \(0.488766\pi\) | |||||||
\(504\) | 2.64575 | 0.117851 | ||||||||
\(505\) | −2.28522 | −0.101691 | ||||||||
\(506\) | −2.67511 | + | 4.63343i | −0.118923 | + | 0.205981i | ||||
\(507\) | 4.56605 | + | 7.90864i | 0.202786 | + | 0.351235i | ||||
\(508\) | 6.15266 | + | 10.6567i | 0.272980 | + | 0.472815i | ||||
\(509\) | 8.47719 | − | 14.6829i | 0.375745 | − | 0.650809i | −0.614694 | − | 0.788766i | \(-0.710720\pi\) |
0.990438 | + | 0.137957i | \(0.0440536\pi\) | |||||||
\(510\) | 1.03792 | 0.0459600 | ||||||||
\(511\) | −14.8446 | + | 25.7115i | −0.656684 | + | 1.13741i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.87321 | + | 3.24449i | −0.0827042 | + | 0.143248i | ||||
\(514\) | 0.251570 | + | 0.435732i | 0.0110963 | + | 0.0192193i | ||||
\(515\) | −1.76722 | − | 3.06092i | −0.0778732 | − | 0.134880i | ||||
\(516\) | 1.00000 | − | 1.73205i | 0.0440225 | − | 0.0762493i | ||||
\(517\) | 53.1274 | 2.33654 | ||||||||
\(518\) | 3.57769 | − | 6.19674i | 0.157195 | − | 0.272269i | ||||
\(519\) | 17.2214 | 0.755937 | ||||||||
\(520\) | 1.12679 | − | 1.95166i | 0.0494130 | − | 0.0855859i | ||||
\(521\) | 3.77053 | + | 6.53075i | 0.165190 | + | 0.286117i | 0.936723 | − | 0.350072i | \(-0.113843\pi\) |
−0.771533 | + | 0.636190i | \(0.780510\pi\) | |||||||
\(522\) | −2.37321 | − | 4.11052i | −0.103873 | − | 0.179913i | ||||
\(523\) | −9.59648 | + | 16.6216i | −0.419625 | + | 0.726812i | −0.995902 | − | 0.0904431i | \(-0.971172\pi\) |
0.576277 | + | 0.817255i | \(0.304505\pi\) | |||||||
\(524\) | −9.31561 | −0.406954 | ||||||||
\(525\) | −12.6216 | −0.550854 | ||||||||
\(526\) | 4.99163 | 0.217645 | ||||||||
\(527\) | −10.5850 | + | 18.3338i | −0.461091 | + | 0.798632i | ||||
\(528\) | −2.67511 | − | 4.63343i | −0.116419 | − | 0.201644i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | −0.593763 | + | 1.02843i | −0.0257914 | + | 0.0446721i | ||||
\(531\) | 12.5589 | 0.545010 | ||||||||
\(532\) | −4.95605 | − | 8.58413i | −0.214872 | − | 0.372169i | ||||
\(533\) | −1.19296 | −0.0516729 | ||||||||
\(534\) | 1.60582 | − | 2.78136i | 0.0694906 | − | 0.120361i | ||||
\(535\) | 3.57593 | + | 6.19370i | 0.154601 | + | 0.267777i | ||||
\(536\) | −3.35023 | − | 5.80277i | −0.144708 | − | 0.250641i | ||||
\(537\) | 12.2634 | − | 21.2408i | 0.529204 | − | 0.916607i | ||||
\(538\) | −4.12775 | −0.177960 | ||||||||
\(539\) | −37.4516 | −1.61315 | ||||||||
\(540\) | 0.479029 | 0.0206141 | ||||||||
\(541\) | 14.8973 | − | 25.8029i | 0.640486 | − | 1.10935i | −0.344839 | − | 0.938662i | \(-0.612066\pi\) |
0.985324 | − | 0.170692i | \(-0.0546003\pi\) | |||||||
\(542\) | −1.46898 | − | 2.54435i | −0.0630982 | − | 0.109289i | ||||
\(543\) | −10.2061 | − | 17.6775i | −0.437987 | − | 0.758616i | ||||
\(544\) | −1.08336 | + | 1.87644i | −0.0464487 | + | 0.0804516i | ||||
\(545\) | −2.17372 | −0.0931117 | ||||||||
\(546\) | −6.22344 | − | 10.7793i | −0.266339 | − | 0.461312i | ||||
\(547\) | −16.6264 | −0.710892 | −0.355446 | − | 0.934697i | \(-0.615671\pi\) | ||||
−0.355446 | + | 0.934697i | \(0.615671\pi\) | |||||||
\(548\) | −6.60232 | + | 11.4356i | −0.282037 | + | 0.488503i | ||||
\(549\) | 4.47903 | + | 7.75791i | 0.191160 | + | 0.331099i | ||||
\(550\) | 12.7617 | + | 22.1039i | 0.544161 | + | 0.942515i | ||||
\(551\) | −8.89104 | + | 15.3997i | −0.378771 | + | 0.656051i | ||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | −2.24119 | −0.0953049 | ||||||||
\(554\) | 28.6924 | 1.21902 | ||||||||
\(555\) | 0.647761 | − | 1.12196i | 0.0274959 | − | 0.0476244i | ||||
\(556\) | 2.96496 | + | 5.13547i | 0.125742 | + | 0.217792i | ||||
\(557\) | −8.61490 | − | 14.9214i | −0.365025 | − | 0.632242i | 0.623755 | − | 0.781620i | \(-0.285606\pi\) |
−0.988780 | + | 0.149378i | \(0.952273\pi\) | |||||||
\(558\) | −4.88527 | + | 8.46153i | −0.206810 | + | 0.358205i | ||||
\(559\) | −9.40895 | −0.397956 | ||||||||
\(560\) | −0.633696 | + | 1.09759i | −0.0267785 | + | 0.0463818i | ||||
\(561\) | −11.5925 | −0.489434 | ||||||||
\(562\) | −7.39165 | + | 12.8027i | −0.311798 | + | 0.540050i | ||||
\(563\) | −14.9006 | − | 25.8085i | −0.627984 | − | 1.08770i | −0.987956 | − | 0.154737i | \(-0.950547\pi\) |
0.359972 | − | 0.932963i | \(-0.382786\pi\) | |||||||
\(564\) | −4.96496 | − | 8.59957i | −0.209063 | − | 0.362107i | ||||
\(565\) | −3.41201 | + | 5.90978i | −0.143544 | + | 0.248626i | ||||
\(566\) | 13.1178 | 0.551382 | ||||||||
\(567\) | 1.32288 | − | 2.29129i | 0.0555556 | − | 0.0962250i | ||||
\(568\) | −0.774551 | −0.0324995 | ||||||||
\(569\) | −8.32943 | + | 14.4270i | −0.349188 | + | 0.604811i | −0.986105 | − | 0.166121i | \(-0.946876\pi\) |
0.636918 | + | 0.770932i | \(0.280209\pi\) | |||||||
\(570\) | −0.897321 | − | 1.55421i | −0.0375847 | − | 0.0650985i | ||||
\(571\) | −20.7685 | − | 35.9721i | −0.869136 | − | 1.50539i | −0.862881 | − | 0.505407i | \(-0.831343\pi\) |
−0.00625421 | − | 0.999980i | \(-0.501991\pi\) | |||||||
\(572\) | −12.5850 | + | 21.7979i | −0.526206 | + | 0.911415i | ||||
\(573\) | 1.23926 | 0.0517708 | ||||||||
\(574\) | 0.670910 | 0.0280032 | ||||||||
\(575\) | −4.77053 | −0.198945 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 23.0129 | + | 39.8596i | 0.958041 | + | 1.65938i | 0.727251 | + | 0.686372i | \(0.240798\pi\) |
0.230790 | + | 0.973004i | \(0.425869\pi\) | |||||||
\(578\) | −6.15266 | − | 10.6567i | −0.255917 | − | 0.443261i | ||||
\(579\) | −5.58974 | + | 9.68172i | −0.232302 | + | 0.402359i | ||||
\(580\) | 2.27367 | 0.0944091 | ||||||||
\(581\) | 14.4589 | + | 25.0436i | 0.599858 | + | 1.03898i | ||||
\(582\) | 13.0098 | 0.539273 | ||||||||
\(583\) | 6.63169 | − | 11.4864i | 0.274656 | − | 0.475719i | ||||
\(584\) | −5.61071 | − | 9.71804i | −0.232173 | − | 0.402135i | ||||
\(585\) | −1.12679 | − | 1.95166i | −0.0465870 | − | 0.0806911i | ||||
\(586\) | −2.19460 | + | 3.80116i | −0.0906581 | + | 0.157024i | ||||
\(587\) | −10.5865 | −0.436952 | −0.218476 | − | 0.975842i | \(-0.570109\pi\) | ||||
−0.218476 | + | 0.975842i | \(0.570109\pi\) | |||||||
\(588\) | 3.50000 | + | 6.06218i | 0.144338 | + | 0.250000i | ||||
\(589\) | 36.6045 | 1.50826 | ||||||||
\(590\) | −3.00804 | + | 5.21007i | −0.123839 | + | 0.214495i | ||||
\(591\) | 11.0478 | + | 19.1354i | 0.454446 | + | 0.787123i | ||||
\(592\) | 1.35224 | + | 2.34215i | 0.0555767 | + | 0.0962616i | ||||
\(593\) | −20.8632 | + | 36.1361i | −0.856747 | + | 1.48393i | 0.0182672 | + | 0.999833i | \(0.494185\pi\) |
−0.875015 | + | 0.484097i | \(0.839148\pi\) | |||||||
\(594\) | −5.35023 | −0.219523 | ||||||||
\(595\) | 1.37304 | + | 2.37818i | 0.0562892 | + | 0.0974958i | ||||
\(596\) | −1.17405 | −0.0480910 | ||||||||
\(597\) | 4.24807 | − | 7.35788i | 0.173862 | − | 0.301138i | ||||
\(598\) | −2.35224 | − | 4.07420i | −0.0961902 | − | 0.166606i | ||||
\(599\) | −6.48690 | − | 11.2356i | −0.265047 | − | 0.459076i | 0.702529 | − | 0.711655i | \(-0.252054\pi\) |
−0.967576 | + | 0.252580i | \(0.918721\pi\) | |||||||
\(600\) | 2.38527 | − | 4.13140i | 0.0973781 | − | 0.168664i | ||||
\(601\) | 15.1795 | 0.619184 | 0.309592 | − | 0.950869i | \(-0.399808\pi\) | ||||
0.309592 | + | 0.950869i | \(0.399808\pi\) | |||||||
\(602\) | 5.29150 | 0.215666 | ||||||||
\(603\) | −6.70046 | −0.272864 | ||||||||
\(604\) | −3.15266 | + | 5.46056i | −0.128280 | + | 0.222187i | ||||
\(605\) | 4.22143 | + | 7.31173i | 0.171625 | + | 0.297264i | ||||
\(606\) | −2.38527 | − | 4.13140i | −0.0968948 | − | 0.167827i | ||||
\(607\) | 21.8393 | − | 37.8268i | 0.886430 | − | 1.53534i | 0.0423641 | − | 0.999102i | \(-0.486511\pi\) |
0.844066 | − | 0.536240i | \(-0.180156\pi\) | |||||||
\(608\) | 3.74642 | 0.151937 | ||||||||
\(609\) | 6.27892 | − | 10.8754i | 0.254435 | − | 0.440694i | ||||
\(610\) | −4.29117 | −0.173744 | ||||||||
\(611\) | −23.3576 | + | 40.4565i | −0.944946 | + | 1.63669i | ||||
\(612\) | 1.08336 | + | 1.87644i | 0.0437923 | + | 0.0758505i | ||||
\(613\) | −6.54657 | − | 11.3390i | −0.264413 | − | 0.457978i | 0.702996 | − | 0.711193i | \(-0.251845\pi\) |
−0.967410 | + | 0.253216i | \(0.918512\pi\) | |||||||
\(614\) | 5.08773 | − | 8.81221i | 0.205324 | − | 0.355632i | ||||
\(615\) | 0.121472 | 0.00489823 | ||||||||
\(616\) | 7.07769 | − | 12.2589i | 0.285168 | − | 0.493926i | ||||
\(617\) | −6.04525 | −0.243373 | −0.121686 | − | 0.992569i | \(-0.538830\pi\) | ||||
−0.121686 | + | 0.992569i | \(0.538830\pi\) | |||||||
\(618\) | 3.68918 | − | 6.38985i | 0.148401 | − | 0.257037i | ||||
\(619\) | −4.86919 | − | 8.43368i | −0.195709 | − | 0.338978i | 0.751424 | − | 0.659820i | \(-0.229368\pi\) |
−0.947133 | + | 0.320842i | \(0.896034\pi\) | |||||||
\(620\) | −2.34018 | − | 4.05332i | −0.0939840 | − | 0.162785i | ||||
\(621\) | 0.500000 | − | 0.866025i | 0.0200643 | − | 0.0347524i | ||||
\(622\) | 12.5505 | 0.503230 | ||||||||
\(623\) | 8.49719 | 0.340433 | ||||||||
\(624\) | 4.70448 | 0.188330 | ||||||||
\(625\) | −10.8053 | + | 18.7154i | −0.432213 | + | 0.748614i | ||||
\(626\) | 7.94198 | + | 13.7559i | 0.317425 | + | 0.549797i | ||||
\(627\) | 10.0221 | + | 17.3588i | 0.400244 | + | 0.693243i | ||||
\(628\) | −1.14209 | + | 1.97815i | −0.0455742 | + | 0.0789369i | ||||
\(629\) | 5.85985 | 0.233648 | ||||||||
\(630\) | 0.633696 | + | 1.09759i | 0.0252470 | + | 0.0437291i | ||||
\(631\) | −42.7282 | −1.70098 | −0.850492 | − | 0.525989i | \(-0.823695\pi\) | ||||
−0.850492 | + | 0.525989i | \(0.823695\pi\) | |||||||
\(632\) | 0.423544 | − | 0.733600i | 0.0168477 | − | 0.0291810i | ||||
\(633\) | 10.1904 | + | 17.6503i | 0.405033 | + | 0.701537i | ||||
\(634\) | 15.2794 | + | 26.4648i | 0.606824 | + | 1.05105i | ||||
\(635\) | −2.94730 | + | 5.10487i | −0.116960 | + | 0.202581i | ||||
\(636\) | −2.47903 | −0.0982999 | ||||||||
\(637\) | 16.4657 | − | 28.5194i | 0.652394 | − | 1.12998i | ||||
\(638\) | −25.3944 | −1.00538 | ||||||||
\(639\) | −0.387276 | + | 0.670781i | −0.0153204 | + | 0.0265357i | ||||
\(640\) | −0.239514 | − | 0.414851i | −0.00946764 | − | 0.0163984i | ||||
\(641\) | 7.10747 | + | 12.3105i | 0.280728 | + | 0.486236i | 0.971564 | − | 0.236776i | \(-0.0760907\pi\) |
−0.690836 | + | 0.723011i | \(0.742757\pi\) | |||||||
\(642\) | −7.46496 | + | 12.9297i | −0.294619 | + | 0.510294i | ||||
\(643\) | 29.3990 | 1.15938 | 0.579691 | − | 0.814836i | \(-0.303173\pi\) | ||||
0.579691 | + | 0.814836i | \(0.303173\pi\) | |||||||
\(644\) | 1.32288 | + | 2.29129i | 0.0521286 | + | 0.0902894i | ||||
\(645\) | 0.958058 | 0.0377235 | ||||||||
\(646\) | 4.05873 | − | 7.02992i | 0.159688 | − | 0.276588i | ||||
\(647\) | −17.5520 | − | 30.4009i | −0.690040 | − | 1.19518i | −0.971824 | − | 0.235706i | \(-0.924260\pi\) |
0.281784 | − | 0.959478i | \(-0.409074\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 33.5965 | − | 58.1908i | 1.31878 | − | 2.28419i | ||||
\(650\) | −22.4429 | −0.880281 | ||||||||
\(651\) | −25.8504 | −1.01316 | ||||||||
\(652\) | 4.77455 | 0.186986 | ||||||||
\(653\) | −7.66471 | + | 13.2757i | −0.299943 | + | 0.519517i | −0.976123 | − | 0.217220i | \(-0.930301\pi\) |
0.676179 | + | 0.736737i | \(0.263634\pi\) | |||||||
\(654\) | −2.26888 | − | 3.92981i | −0.0887201 | − | 0.153668i | ||||
\(655\) | −2.23122 | − | 3.86459i | −0.0871811 | − | 0.151002i | ||||
\(656\) | −0.126790 | + | 0.219607i | −0.00495032 | + | 0.00857421i | ||||
\(657\) | −11.2214 | −0.437790 | ||||||||
\(658\) | 13.1361 | − | 22.7523i | 0.512097 | − | 0.886978i | ||||
\(659\) | −6.98865 | −0.272239 | −0.136120 | − | 0.990692i | \(-0.543463\pi\) | ||||
−0.136120 | + | 0.990692i | \(0.543463\pi\) | |||||||
\(660\) | 1.28146 | − | 2.21955i | 0.0498806 | − | 0.0863958i | ||||
\(661\) | 7.10948 | + | 12.3140i | 0.276527 | + | 0.478959i | 0.970519 | − | 0.241024i | \(-0.0774832\pi\) |
−0.693992 | + | 0.719982i | \(0.744150\pi\) | |||||||
\(662\) | −17.1188 | − | 29.6505i | −0.665339 | − | 1.15240i | ||||
\(663\) | 5.09665 | − | 8.82765i | 0.197937 | − | 0.342838i | ||||
\(664\) | −10.9299 | −0.424163 | ||||||||
\(665\) | 2.37409 | − | 4.11204i | 0.0920632 | − | 0.159458i | ||||
\(666\) | 2.70448 | 0.104796 | ||||||||
\(667\) | 2.37321 | − | 4.11052i | 0.0918911 | − | 0.159160i | ||||
\(668\) | 10.4750 | + | 18.1432i | 0.405290 | + | 0.701983i | ||||
\(669\) | −1.59376 | − | 2.76048i | −0.0616184 | − | 0.106726i | ||||
\(670\) | 1.60486 | − | 2.77969i | 0.0620010 | − | 0.107389i | ||||
\(671\) | 47.9277 | 1.85023 | ||||||||
\(672\) | −2.64575 | −0.102062 | ||||||||
\(673\) | −14.0339 | −0.540967 | −0.270484 | − | 0.962725i | \(-0.587184\pi\) | ||||
−0.270484 | + | 0.962725i | \(0.587184\pi\) | |||||||
\(674\) | −6.12951 | + | 10.6166i | −0.236100 | + | 0.408937i | ||||
\(675\) | −2.38527 | − | 4.13140i | −0.0918089 | − | 0.159018i | ||||
\(676\) | −4.56605 | − | 7.90864i | −0.175617 | − | 0.304178i | ||||
\(677\) | 11.7353 | − | 20.3262i | 0.451025 | − | 0.781199i | −0.547425 | − | 0.836855i | \(-0.684392\pi\) |
0.998450 | + | 0.0556563i | \(0.0177251\pi\) | |||||||
\(678\) | −14.2455 | −0.547097 | ||||||||
\(679\) | 17.2103 | + | 29.8092i | 0.660472 | + | 1.14397i | ||||
\(680\) | −1.03792 | −0.0398025 | ||||||||
\(681\) | 2.67913 | − | 4.64040i | 0.102665 | − | 0.177820i | ||||
\(682\) | 26.1373 | + | 45.2711i | 1.00085 | + | 1.73352i | ||||
\(683\) | 11.9588 | + | 20.7132i | 0.457589 | + | 0.792568i | 0.998833 | − | 0.0482977i | \(-0.0153796\pi\) |
−0.541244 | + | 0.840866i | \(0.682046\pi\) | |||||||
\(684\) | 1.87321 | − | 3.24449i | 0.0716240 | − | 0.124056i | ||||
\(685\) | −6.32541 | −0.241681 | ||||||||
\(686\) | −9.26013 | + | 16.0390i | −0.353553 | + | 0.612372i | ||||
\(687\) | 23.4582 | 0.894987 | ||||||||
\(688\) | −1.00000 | + | 1.73205i | −0.0381246 | + | 0.0660338i | ||||
\(689\) | 5.83127 | + | 10.1001i | 0.222154 | + | 0.384781i | ||||
\(690\) | 0.239514 | + | 0.414851i | 0.00911816 | + | 0.0157931i | ||||
\(691\) | −7.34131 | + | 12.7155i | −0.279277 | + | 0.483721i | −0.971205 | − | 0.238245i | \(-0.923428\pi\) |
0.691928 | + | 0.721966i | \(0.256761\pi\) | |||||||
\(692\) | −17.2214 | −0.654660 | ||||||||
\(693\) | −7.07769 | − | 12.2589i | −0.268859 | − | 0.465678i | ||||
\(694\) | 9.54106 | 0.362174 | ||||||||
\(695\) | −1.42030 | + | 2.46004i | −0.0538752 | + | 0.0933145i | ||||
\(696\) | 2.37321 | + | 4.11052i | 0.0899563 | + | 0.155809i | ||||
\(697\) | 0.274719 | + | 0.475827i | 0.0104057 | + | 0.0180232i | ||||
\(698\) | −4.22344 | + | 7.31521i | −0.159860 | + | 0.276885i | ||||
\(699\) | 24.7803 | 0.937278 | ||||||||
\(700\) | 12.6216 | 0.477053 | ||||||||
\(701\) | −13.9383 | −0.526442 | −0.263221 | − | 0.964736i | \(-0.584785\pi\) | ||||
−0.263221 | + | 0.964736i | \(0.584785\pi\) | |||||||
\(702\) | 2.35224 | − | 4.07420i | 0.0887795 | − | 0.153771i | ||||
\(703\) | −5.06605 | − | 8.77466i | −0.191070 | − | 0.330943i | ||||
\(704\) | 2.67511 | + | 4.63343i | 0.100822 | + | 0.174629i | ||||
\(705\) | 2.37836 | − | 4.11944i | 0.0895742 | − | 0.155147i | ||||
\(706\) | −24.4804 | −0.921334 | ||||||||
\(707\) | 6.31082 | − | 10.9307i | 0.237343 | − | 0.411090i | ||||
\(708\) | −12.5589 | −0.471992 | ||||||||
\(709\) | −6.46172 | + | 11.1920i | −0.242675 | + | 0.420326i | −0.961475 | − | 0.274891i | \(-0.911358\pi\) |
0.718800 | + | 0.695217i | \(0.244692\pi\) | |||||||
\(710\) | −0.185516 | − | 0.321323i | −0.00696230 | − | 0.0120591i | ||||
\(711\) | −0.423544 | − | 0.733600i | −0.0158841 | − | 0.0275122i | ||||
\(712\) | −1.60582 | + | 2.78136i | −0.0601806 | + | 0.104236i | ||||
\(713\) | −9.77053 | −0.365909 | ||||||||
\(714\) | −2.86630 | + | 4.96458i | −0.107269 | + | 0.185795i | ||||
\(715\) | −12.0572 | −0.450913 | ||||||||
\(716\) | −12.2634 | + | 21.2408i | −0.458304 | + | 0.793805i | ||||
\(717\) | 2.48593 | + | 4.30576i | 0.0928389 | + | 0.160802i | ||||
\(718\) | 10.1208 | + | 17.5297i | 0.377703 | + | 0.654202i | ||||
\(719\) | −6.69100 | + | 11.5892i | −0.249532 | + | 0.432203i | −0.963396 | − | 0.268082i | \(-0.913610\pi\) |
0.713864 | + | 0.700285i | \(0.246944\pi\) | |||||||
\(720\) | −0.479029 | −0.0178523 | ||||||||
\(721\) | 19.5213 | 0.727011 | ||||||||
\(722\) | 4.96434 | 0.184754 | ||||||||
\(723\) | −3.74169 | + | 6.48080i | −0.139155 | + | 0.241024i | ||||
\(724\) | 10.2061 | + | 17.6775i | 0.379308 | + | 0.656981i | ||||
\(725\) | −11.3215 | − | 19.6094i | −0.420469 | − | 0.728274i | ||||
\(726\) | −8.81247 | + | 15.2637i | −0.327062 | + | 0.566487i | ||||
\(727\) | −47.9963 | −1.78009 | −0.890043 | − | 0.455877i | \(-0.849326\pi\) | ||||
−0.890043 | + | 0.455877i | \(0.849326\pi\) | |||||||
\(728\) | 6.22344 | + | 10.7793i | 0.230656 | + | 0.399508i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.68769 | − | 4.65522i | 0.0994760 | − | 0.172297i | ||||
\(731\) | 2.16672 | + | 3.75287i | 0.0801391 | + | 0.138805i | ||||
\(732\) | −4.47903 | − | 7.75791i | −0.165550 | − | 0.286740i | ||||
\(733\) | −12.7459 | + | 22.0765i | −0.470780 | + | 0.815416i | −0.999441 | − | 0.0334174i | \(-0.989361\pi\) |
0.528661 | + | 0.848833i | \(0.322694\pi\) | |||||||
\(734\) | −5.85040 | −0.215942 | ||||||||
\(735\) | −1.67660 | + | 2.90396i | −0.0618424 | + | 0.107114i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −17.9245 | + | 31.0461i | −0.660257 | + | 1.14360i | ||||
\(738\) | 0.126790 | + | 0.219607i | 0.00466721 | + | 0.00808384i | ||||
\(739\) | −12.3087 | − | 21.3193i | −0.452783 | − | 0.784243i | 0.545775 | − | 0.837932i | \(-0.316235\pi\) |
−0.998558 | + | 0.0536886i | \(0.982902\pi\) | |||||||
\(740\) | −0.647761 | + | 1.12196i | −0.0238122 | + | 0.0412439i | ||||
\(741\) | −17.6249 | −0.647469 | ||||||||
\(742\) | −3.27945 | − | 5.68017i | −0.120392 | − | 0.208526i | ||||
\(743\) | −2.89777 | −0.106309 | −0.0531545 | − | 0.998586i | \(-0.516928\pi\) | ||||
−0.0531545 | + | 0.998586i | \(0.516928\pi\) | |||||||
\(744\) | 4.88527 | − | 8.46153i | 0.179103 | − | 0.310215i | ||||
\(745\) | −0.281202 | − | 0.487056i | −0.0103024 | − | 0.0178444i | ||||
\(746\) | 16.5772 | + | 28.7125i | 0.606933 | + | 1.05124i | ||||
\(747\) | −5.46496 | + | 9.46559i | −0.199953 | + | 0.346328i | ||||
\(748\) | 11.5925 | 0.423862 | ||||||||
\(749\) | −39.5009 | −1.44333 | ||||||||
\(750\) | 4.68037 | 0.170903 | ||||||||
\(751\) | 18.4421 | − | 31.9427i | 0.672964 | − | 1.16561i | −0.304096 | − | 0.952641i | \(-0.598354\pi\) |
0.977060 | − | 0.212966i | \(-0.0683123\pi\) | |||||||
\(752\) | 4.96496 | + | 8.59957i | 0.181054 | + | 0.313594i | ||||
\(753\) | −7.48759 | − | 12.9689i | −0.272863 | − | 0.472612i | ||||
\(754\) | 11.1647 | − | 19.3378i | 0.406595 | − | 0.704243i | ||||
\(755\) | −3.02043 | −0.109925 | ||||||||
\(756\) | −1.32288 | + | 2.29129i | −0.0481125 | + | 0.0833333i | ||||
\(757\) | −46.4053 | −1.68663 | −0.843314 | − | 0.537421i | \(-0.819399\pi\) | ||||
−0.843314 | + | 0.537421i | \(0.819399\pi\) | |||||||
\(758\) | 14.5998 | − | 25.2876i | 0.530288 | − | 0.918486i | ||||
\(759\) | −2.67511 | − | 4.63343i | −0.0971005 | − | 0.168183i | ||||
\(760\) | 0.897321 | + | 1.55421i | 0.0325493 | + | 0.0563770i | ||||
\(761\) | 21.0738 | − | 36.5010i | 0.763926 | − | 1.32316i | −0.176887 | − | 0.984231i | \(-0.556603\pi\) |
0.940813 | − | 0.338927i | \(-0.110064\pi\) | |||||||
\(762\) | −12.3053 | −0.445774 | ||||||||
\(763\) | 6.00289 | − | 10.3973i | 0.217319 | − | 0.376408i | ||||
\(764\) | −1.23926 | −0.0448348 | ||||||||
\(765\) | −0.518961 | + | 0.898867i | −0.0187631 | + | 0.0324986i | ||||
\(766\) | −17.6116 | − | 30.5042i | −0.636333 | − | 1.10216i | ||||
\(767\) | 29.5415 | + | 51.1674i | 1.06668 | + | 1.84755i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | −38.8004 | −1.39918 | −0.699589 | − | 0.714545i | \(-0.746634\pi\) | ||||
−0.699589 | + | 0.714545i | \(0.746634\pi\) | |||||||
\(770\) | 6.78083 | 0.244364 | ||||||||
\(771\) | −0.503140 | −0.0181202 | ||||||||
\(772\) | 5.58974 | − | 9.68172i | 0.201179 | − | 0.348453i | ||||
\(773\) | −3.49284 | − | 6.04978i | −0.125629 | − | 0.217595i | 0.796350 | − | 0.604836i | \(-0.206761\pi\) |
−0.921979 | + | 0.387241i | \(0.873428\pi\) | |||||||
\(774\) | 1.00000 | + | 1.73205i | 0.0359443 | + | 0.0622573i | ||||
\(775\) | −23.3053 | + | 40.3660i | −0.837152 | + | 1.44999i | ||||
\(776\) | −13.0098 | −0.467024 | ||||||||
\(777\) | 3.57769 | + | 6.19674i | 0.128349 | + | 0.222307i | ||||
\(778\) | 30.6166 | 1.09766 | ||||||||
\(779\) | 0.475009 | − | 0.822739i | 0.0170190 | − | 0.0294777i | ||||
\(780\) | 1.12679 | + | 1.95166i | 0.0403456 | + | 0.0698806i | ||||
\(781\) | 2.07201 | + | 3.58883i | 0.0741425 | + | 0.128419i | ||||
\(782\) | −1.08336 | + | 1.87644i | −0.0387409 | + | 0.0671012i | ||||
\(783\) | 4.74642 | 0.169623 | ||||||||
\(784\) | −3.50000 | − | 6.06218i | −0.125000 | − | 0.216506i | ||||
\(785\) | −1.09419 | −0.0390532 | ||||||||
\(786\) | 4.65781 | − | 8.06756i | 0.166138 | − | 0.287760i | ||||
\(787\) | −15.7351 | − | 27.2539i | −0.560895 | − | 0.971498i | −0.997419 | − | 0.0718055i | \(-0.977124\pi\) |
0.436524 | − | 0.899693i | \(-0.356209\pi\) | |||||||
\(788\) | −11.0478 | − | 19.1354i | −0.393562 | − | 0.681669i | ||||
\(789\) | −2.49581 | + | 4.32287i | −0.0888533 | + | 0.153898i | ||||
\(790\) | 0.405780 | 0.0144370 | ||||||||
\(791\) | −18.8451 | − | 32.6406i | −0.670054 | − | 1.16057i | ||||
\(792\) | 5.35023 | 0.190112 | ||||||||
\(793\) | −21.0715 | + | 36.4969i | −0.748271 | + | 1.29604i | ||||
\(794\) | −8.45291 | − | 14.6409i | −0.299982 | − | 0.519585i | ||||
\(795\) | −0.593763 | − | 1.02843i | −0.0210586 | − | 0.0364746i | ||||
\(796\) | −4.24807 | + | 7.35788i | −0.150569 | + | 0.260793i | ||||
\(797\) | 8.98024 | 0.318097 | 0.159048 | − | 0.987271i | \(-0.449157\pi\) | ||||
0.159048 | + | 0.987271i | \(0.449157\pi\) | |||||||
\(798\) | 9.91210 | 0.350884 | ||||||||
\(799\) | 21.5154 | 0.761160 | ||||||||
\(800\) | −2.38527 | + | 4.13140i | −0.0843319 | + | 0.146067i | ||||
\(801\) | 1.60582 | + | 2.78136i | 0.0567388 | + | 0.0982745i | ||||
\(802\) | −16.2367 | − | 28.1228i | −0.573339 | − | 0.993052i | ||||
\(803\) | −30.0186 | + | 51.9937i | −1.05933 | + | 1.83482i | ||||
\(804\) | 6.70046 | 0.236307 | ||||||||
\(805\) | −0.633696 | + | 1.09759i | −0.0223348 | + | 0.0386851i | ||||
\(806\) | −45.9652 | −1.61906 | ||||||||
\(807\) | 2.06388 | − | 3.57474i | 0.0726519 | − | 0.125837i | ||||
\(808\) | 2.38527 | + | 4.13140i | 0.0839134 | + | 0.145342i | ||||
\(809\) | 16.7098 | + | 28.9422i | 0.587485 | + | 1.01755i | 0.994561 | + | 0.104160i | \(0.0332153\pi\) |
−0.407075 | + | 0.913395i | \(0.633451\pi\) | |||||||
\(810\) | −0.239514 | + | 0.414851i | −0.00841568 | + | 0.0145764i | ||||
\(811\) | −54.4130 | −1.91070 | −0.955349 | − | 0.295480i | \(-0.904520\pi\) | ||||
−0.955349 | + | 0.295480i | \(0.904520\pi\) | |||||||
\(812\) | −6.27892 | + | 10.8754i | −0.220347 | + | 0.381652i | ||||
\(813\) | 2.93797 | 0.103039 | ||||||||
\(814\) | 7.23479 | − | 12.5310i | 0.253579 | − | 0.439212i | ||||
\(815\) | 1.14357 | + | 1.98073i | 0.0400576 | + | 0.0693819i | ||||
\(816\) | −1.08336 | − | 1.87644i | −0.0379252 | − | 0.0656884i | ||||
\(817\) | 3.74642 | − | 6.48899i | 0.131071 | − | 0.227021i | ||||
\(818\) | 27.0196 | 0.944718 | ||||||||
\(819\) | 12.4469 | 0.434929 | ||||||||
\(820\) | −0.121472 | −0.00424199 | ||||||||
\(821\) | 2.54291 | − | 4.40444i | 0.0887480 | − | 0.153716i | −0.818234 | − | 0.574885i | \(-0.805047\pi\) |
0.906982 | + | 0.421169i | \(0.138380\pi\) | |||||||
\(822\) | −6.60232 | − | 11.4356i | −0.230282 | − | 0.398861i | ||||
\(823\) | 5.45421 | + | 9.44696i | 0.190122 | + | 0.329300i | 0.945290 | − | 0.326230i | \(-0.105778\pi\) |
−0.755169 | + | 0.655530i | \(0.772445\pi\) | |||||||
\(824\) | −3.68918 | + | 6.38985i | −0.128519 | + | 0.222601i | ||||
\(825\) | −25.5234 | −0.888612 | ||||||||
\(826\) | −16.6139 | − | 28.7760i | −0.578070 | − | 1.00125i | ||||
\(827\) | 50.5292 | 1.75707 | 0.878536 | − | 0.477676i | \(-0.158521\pi\) | ||||
0.878536 | + | 0.477676i | \(0.158521\pi\) | |||||||
\(828\) | −0.500000 | + | 0.866025i | −0.0173762 | + | 0.0300965i | ||||
\(829\) | −9.09996 | − | 15.7616i | −0.316055 | − | 0.547423i | 0.663607 | − | 0.748082i | \(-0.269025\pi\) |
−0.979661 | + | 0.200659i | \(0.935692\pi\) | |||||||
\(830\) | −2.61787 | − | 4.53429i | −0.0908678 | − | 0.157388i | ||||
\(831\) | −14.3462 | + | 24.8484i | −0.497664 | + | 0.861980i | ||||
\(832\) | −4.70448 | −0.163098 | ||||||||
\(833\) | −15.1671 | −0.525507 | ||||||||
\(834\) | −5.92993 | −0.205337 | ||||||||
\(835\) | −5.01783 | + | 8.69114i | −0.173649 | + | 0.300769i | ||||
\(836\) | −10.0221 | − | 17.3588i | −0.346622 | − | 0.600366i | ||||
\(837\) | −4.88527 | − | 8.46153i | −0.168859 | − | 0.292473i | ||||
\(838\) | 1.04343 | − | 1.80727i | 0.0360447 | − | 0.0624312i | ||||
\(839\) | 7.67057 | 0.264818 | 0.132409 | − | 0.991195i | \(-0.457729\pi\) | ||||
0.132409 | + | 0.991195i | \(0.457729\pi\) | |||||||
\(840\) | −0.633696 | − | 1.09759i | −0.0218646 | − | 0.0378706i | ||||
\(841\) | −6.47150 | −0.223155 | ||||||||
\(842\) | 11.6402 | − | 20.1615i | 0.401149 | − | 0.694811i | ||||
\(843\) | −7.39165 | − | 12.8027i | −0.254582 | − | 0.440949i | ||||
\(844\) | −10.1904 | − | 17.6503i | −0.350768 | − | 0.607549i | ||||
\(845\) | 2.18727 | − | 3.78847i | 0.0752444 | − | 0.130327i | ||||
\(846\) | 9.92993 | 0.341398 | ||||||||
\(847\) | −46.6312 | −1.60227 | ||||||||
\(848\) | 2.47903 | 0.0851302 | ||||||||
\(849\) | −6.55889 | + | 11.3603i | −0.225101 | + | 0.389886i | ||||
\(850\) | 5.16821 | + | 8.95160i | 0.177268 | + | 0.307037i | ||||
\(851\) | 1.35224 | + | 2.34215i | 0.0463541 | + | 0.0802877i | ||||
\(852\) | 0.387276 | − | 0.670781i | 0.0132678 | − | 0.0229806i | ||||
\(853\) | 30.6924 | 1.05089 | 0.525444 | − | 0.850828i | \(-0.323899\pi\) | ||||
0.525444 | + | 0.850828i | \(0.323899\pi\) | |||||||
\(854\) | 11.8504 | − | 20.5255i | 0.405512 | − | 0.702368i | ||||
\(855\) | 1.79464 | 0.0613755 | ||||||||
\(856\) | 7.46496 | − | 12.9297i | 0.255147 | − | 0.441928i | ||||
\(857\) | 15.4908 | + | 26.8309i | 0.529157 | + | 0.916526i | 0.999422 | + | 0.0340010i | \(0.0108250\pi\) |
−0.470265 | + | 0.882525i | \(0.655842\pi\) | |||||||
\(858\) | −12.5850 | − | 21.7979i | −0.429645 | − | 0.744168i | ||||
\(859\) | 21.6426 | − | 37.4861i | 0.738436 | − | 1.27901i | −0.214763 | − | 0.976666i | \(-0.568898\pi\) |
0.953199 | − | 0.302343i | \(-0.0977688\pi\) | |||||||
\(860\) | −0.958058 | −0.0326695 | ||||||||
\(861\) | −0.335455 | + | 0.581025i | −0.0114323 | + | 0.0198013i | ||||
\(862\) | 26.6106 | 0.906362 | ||||||||
\(863\) | −6.25517 | + | 10.8343i | −0.212928 | + | 0.368803i | −0.952630 | − | 0.304133i | \(-0.901633\pi\) |
0.739701 | + | 0.672935i | \(0.234967\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −4.12478 | − | 7.14433i | −0.140247 | − | 0.242914i | ||||
\(866\) | 17.4677 | − | 30.2549i | 0.593576 | − | 1.02810i | ||||
\(867\) | 12.3053 | 0.417910 | ||||||||
\(868\) | 25.8504 | 0.877420 | ||||||||
\(869\) | −4.53212 | −0.153742 | ||||||||
\(870\) | −1.13684 | + | 1.96906i | −0.0385423 | + | 0.0667573i | ||||
\(871\) | −15.7611 | − | 27.2990i | −0.534044 | − | 0.924991i | ||||
\(872\) | 2.26888 | + | 3.92981i | 0.0768339 | + | 0.133080i | ||||
\(873\) | −6.50490 | + | 11.2668i | −0.220157 | + | 0.381324i | ||||
\(874\) | 3.74642 | 0.126725 | ||||||||
\(875\) | 6.19154 | + | 10.7241i | 0.209312 | + | 0.362540i | ||||
\(876\) | 11.2214 | 0.379137 | ||||||||
\(877\) | −3.24022 | + | 5.61223i | −0.109415 | + | 0.189512i | −0.915533 | − | 0.402242i | \(-0.868231\pi\) |
0.806119 | + | 0.591754i | \(0.201564\pi\) | |||||||
\(878\) | −3.86848 | − | 6.70041i | −0.130555 | − | 0.226128i | ||||
\(879\) | −2.19460 | − | 3.80116i | −0.0740220 | − | 0.128210i | ||||
\(880\) | −1.28146 | + | 2.21955i | −0.0431979 | + | 0.0748210i | ||||
\(881\) | 7.96941 | 0.268496 | 0.134248 | − | 0.990948i | \(-0.457138\pi\) | ||||
0.134248 | + | 0.990948i | \(0.457138\pi\) | |||||||
\(882\) | −7.00000 | −0.235702 | ||||||||
\(883\) | 6.75270 | 0.227246 | 0.113623 | − | 0.993524i | \(-0.463754\pi\) | ||||
0.113623 | + | 0.993524i | \(0.463754\pi\) | |||||||
\(884\) | −5.09665 | + | 8.82765i | −0.171419 | + | 0.296906i | ||||
\(885\) | −3.00804 | − | 5.21007i | −0.101114 | − | 0.175135i | ||||
\(886\) | 9.67162 | + | 16.7517i | 0.324924 | + | 0.562786i | ||||
\(887\) | −27.7694 | + | 48.0980i | −0.932405 | + | 1.61497i | −0.153208 | + | 0.988194i | \(0.548960\pi\) |
−0.779197 | + | 0.626779i | \(0.784373\pi\) | |||||||
\(888\) | −2.70448 | −0.0907563 | ||||||||
\(889\) | −16.2784 | − | 28.1950i | −0.545960 | − | 0.945630i | ||||
\(890\) | −1.53847 | −0.0515695 | ||||||||
\(891\) | 2.67511 | − | 4.63343i | 0.0896197 | − | 0.155226i | ||||
\(892\) | 1.59376 | + | 2.76048i | 0.0533631 | + | 0.0924277i | ||||
\(893\) | −18.6008 | − | 32.2176i | −0.622453 | − | 1.07812i | ||||
\(894\) | 0.587025 | − | 1.01676i | 0.0196331 | − | 0.0340055i | ||||
\(895\) | −11.7490 | −0.392726 | ||||||||
\(896\) | 2.64575 | 0.0883883 | ||||||||
\(897\) | 4.70448 | 0.157078 | ||||||||
\(898\) | 8.03591 | − | 13.9186i | 0.268162 | − | 0.464470i | ||||
\(899\) | −23.1875 | − | 40.1620i | −0.773347 | − | 1.33948i | ||||
\(900\) | 2.38527 | + | 4.13140i | 0.0795089 | + | 0.137713i | ||||
\(901\) | 2.68568 | − | 4.65174i | 0.0894731 | − | 0.154972i | ||||
\(902\) | 1.35671 | 0.0451736 | ||||||||
\(903\) | −2.64575 | + | 4.58258i | −0.0880451 | + | 0.152499i | ||||
\(904\) | 14.2455 | 0.473800 | ||||||||
\(905\) | −4.88903 | + | 8.46805i | −0.162517 | + | 0.281487i | ||||
\(906\) | −3.15266 | − | 5.46056i | −0.104740 | − | 0.181415i | ||||
\(907\) | 24.8370 | + | 43.0190i | 0.824700 | + | 1.42842i | 0.902148 | + | 0.431426i | \(0.141990\pi\) |
−0.0774478 | + | 0.996996i | \(0.524677\pi\) | |||||||
\(908\) | −2.67913 | + | 4.64040i | −0.0889102 | + | 0.153997i | ||||
\(909\) | 4.77053 | 0.158229 | ||||||||
\(910\) | −2.98121 | + | 5.16360i | −0.0988260 | + | 0.171172i | ||||
\(911\) | −4.22403 | −0.139948 | −0.0699742 | − | 0.997549i | \(-0.522292\pi\) | ||||
−0.0699742 | + | 0.997549i | \(0.522292\pi\) | |||||||
\(912\) | −1.87321 | + | 3.24449i | −0.0620282 | + | 0.107436i | ||||
\(913\) | 29.2388 | + | 50.6431i | 0.967663 | + | 1.67604i | ||||
\(914\) | 7.46697 | + | 12.9332i | 0.246986 | + | 0.427791i | ||||
\(915\) | 2.14558 | − | 3.71626i | 0.0709308 | − | 0.122856i | ||||
\(916\) | −23.4582 | −0.775082 | ||||||||
\(917\) | 24.6468 | 0.813909 | ||||||||
\(918\) | −2.16672 | −0.0715125 | ||||||||
\(919\) | 16.8376 | − | 29.1635i | 0.555420 | − | 0.962016i | −0.442451 | − | 0.896793i | \(-0.645891\pi\) |
0.997871 | − | 0.0652228i | \(-0.0207758\pi\) | |||||||
\(920\) | −0.239514 | − | 0.414851i | −0.00789656 | − | 0.0136772i | ||||
\(921\) | 5.08773 | + | 8.81221i | 0.167647 | + | 0.290372i | ||||
\(922\) | 11.5830 | − | 20.0624i | 0.381466 | − | 0.660718i | ||||
\(923\) | −3.64386 | −0.119939 | ||||||||
\(924\) | 7.07769 | + | 12.2589i | 0.232839 | + | 0.403289i | ||||
\(925\) | 12.9018 | 0.424208 | ||||||||
\(926\) | 20.2214 | − | 35.0245i | 0.664517 | − | 1.15098i | ||||
\(927\) | 3.68918 | + | 6.38985i | 0.121169 | + | 0.209870i | ||||
\(928\) | −2.37321 | − | 4.11052i | −0.0779044 | − | 0.134934i | ||||
\(929\) | −14.1913 | + | 24.5800i | −0.465601 | + | 0.806445i | −0.999228 | − | 0.0392750i | \(-0.987495\pi\) |
0.533627 | + | 0.845720i | \(0.320828\pi\) | |||||||
\(930\) | 4.68037 | 0.153475 | ||||||||
\(931\) | 13.1125 | + | 22.7115i | 0.429744 | + | 0.744338i | ||||
\(932\) | −24.7803 | −0.811706 | ||||||||
\(933\) | −6.27526 | + | 10.8691i | −0.205443 | + | 0.355837i | ||||
\(934\) | 3.21015 | + | 5.56015i | 0.105039 | + | 0.181934i | ||||
\(935\) | 2.77656 | + | 4.80915i | 0.0908033 | + | 0.157276i | ||||
\(936\) | −2.35224 | + | 4.07420i | −0.0768853 | + | 0.133169i | ||||
\(937\) | −26.2115 | −0.856291 | −0.428146 | − | 0.903710i | \(-0.640833\pi\) | ||||
−0.428146 | + | 0.903710i | \(0.640833\pi\) | |||||||
\(938\) | 8.86387 | + | 15.3527i | 0.289416 | + | 0.501283i | ||||
\(939\) | −15.8840 | −0.518354 | ||||||||
\(940\) | −2.37836 | + | 4.11944i | −0.0775736 | + | 0.134361i | ||||
\(941\) | −19.2523 | − | 33.3459i | −0.627606 | − | 1.08705i | −0.988031 | − | 0.154258i | \(-0.950701\pi\) |
0.360424 | − | 0.932788i | \(-0.382632\pi\) | |||||||
\(942\) | −1.14209 | − | 1.97815i | −0.0372112 | − | 0.0644517i | ||||
\(943\) | −0.126790 | + | 0.219607i | −0.00412885 | + | 0.00715138i | ||||
\(944\) | 12.5589 | 0.408757 | ||||||||
\(945\) | −1.26739 | −0.0412282 | ||||||||
\(946\) | 10.7005 | 0.347902 | ||||||||
\(947\) | −7.23680 | + | 12.5345i | −0.235164 | + | 0.407316i | −0.959320 | − | 0.282320i | \(-0.908896\pi\) |
0.724156 | + | 0.689636i | \(0.242229\pi\) | |||||||
\(948\) | 0.423544 | + | 0.733600i | 0.0137561 | + | 0.0238262i | ||||
\(949\) | −26.3955 | − | 45.7183i | −0.856834 | − | 1.48408i | ||||
\(950\) | 8.93621 | − | 15.4780i | 0.289929 | − | 0.502171i | ||||
\(951\) | −30.5589 | −0.990940 | ||||||||
\(952\) | 2.86630 | − | 4.96458i | 0.0928975 | − | 0.160903i | ||||
\(953\) | −53.2578 | −1.72519 | −0.862595 | − | 0.505896i | \(-0.831162\pi\) | ||||
−0.862595 | + | 0.505896i | \(0.831162\pi\) | |||||||
\(954\) | 1.23951 | − | 2.14690i | 0.0401308 | − | 0.0695085i | ||||
\(955\) | −0.296821 | − | 0.514108i | −0.00960489 | − | 0.0166362i | ||||
\(956\) | −2.48593 | − | 4.30576i | −0.0804009 | − | 0.139258i | ||||
\(957\) | 12.6972 | − | 21.9922i | 0.410443 | − | 0.710908i | ||||
\(958\) | −8.25358 | −0.266661 | ||||||||
\(959\) | 17.4681 | − | 30.2556i | 0.564074 | − | 0.977006i | ||||
\(960\) | 0.479029 | 0.0154606 | ||||||||
\(961\) | −32.2316 | + | 55.8268i | −1.03973 | + | 1.80087i | ||||
\(962\) | 6.36158 | + | 11.0186i | 0.205105 | + | 0.355253i | ||||
\(963\) | −7.46496 | − | 12.9297i | −0.240555 | − | 0.416654i | ||||
\(964\) | 3.74169 | − | 6.48080i | 0.120512 | − | 0.208733i | ||||
\(965\) | 5.35530 | 0.172393 | ||||||||
\(966\) | −2.64575 | −0.0851257 | ||||||||
\(967\) | 52.5804 | 1.69087 | 0.845436 | − | 0.534077i | \(-0.179341\pi\) | ||||
0.845436 | + | 0.534077i | \(0.179341\pi\) | |||||||
\(968\) | 8.81247 | − | 15.2637i | 0.283244 | − | 0.490592i | ||||
\(969\) | 4.05873 | + | 7.02992i | 0.130385 | + | 0.225834i | ||||
\(970\) | −3.11603 | − | 5.39713i | −0.100050 | − | 0.173291i | ||||
\(971\) | 18.5601 | − | 32.1471i | 0.595623 | − | 1.03165i | −0.397836 | − | 0.917457i | \(-0.630239\pi\) |
0.993459 | − | 0.114192i | \(-0.0364280\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −7.84455 | − | 13.5872i | −0.251485 | − | 0.435585i | ||||
\(974\) | −27.4290 | −0.878883 | ||||||||
\(975\) | 11.2214 | − | 19.4361i | 0.359373 | − | 0.622453i | ||||
\(976\) | 4.47903 | + | 7.75791i | 0.143370 | + | 0.248325i | ||||
\(977\) | 1.10364 | + | 1.91156i | 0.0353086 | + | 0.0611563i | 0.883140 | − | 0.469110i | \(-0.155425\pi\) |
−0.847831 | + | 0.530266i | \(0.822092\pi\) | |||||||
\(978\) | −2.38728 | + | 4.13488i | −0.0763367 | + | 0.132219i | ||||
\(979\) | 17.1830 | 0.549171 | ||||||||
\(980\) | 1.67660 | − | 2.90396i | 0.0535570 | − | 0.0927635i | ||||
\(981\) | 4.53775 | 0.144879 | ||||||||
\(982\) | 7.95333 | − | 13.7756i | 0.253801 | − | 0.439596i | ||||
\(983\) | −0.0710368 | − | 0.123039i | −0.00226572 | − | 0.00392434i | 0.864890 | − | 0.501961i | \(-0.167388\pi\) |
−0.867156 | + | 0.498037i | \(0.834055\pi\) | |||||||
\(984\) | −0.126790 | − | 0.219607i | −0.00404192 | − | 0.00700081i | ||||
\(985\) | 5.29221 | − | 9.16638i | 0.168624 | − | 0.292065i | ||||
\(986\) | −10.2842 | −0.327515 | ||||||||
\(987\) | 13.1361 | + | 22.7523i | 0.418125 | + | 0.724214i | ||||
\(988\) | 17.6249 | 0.560724 | ||||||||
\(989\) | −1.00000 | + | 1.73205i | −0.0317982 | + | 0.0550760i | ||||
\(990\) | 1.28146 | + | 2.21955i | 0.0407274 | + | 0.0705419i | ||||
\(991\) | −24.1381 | − | 41.8085i | −0.766773 | − | 1.32809i | −0.939304 | − | 0.343086i | \(-0.888528\pi\) |
0.172531 | − | 0.985004i | \(-0.444806\pi\) | |||||||
\(992\) | −4.88527 | + | 8.46153i | −0.155107 | + | 0.268654i | ||||
\(993\) | 34.2375 | 1.08649 | ||||||||
\(994\) | 2.04927 | 0.0649989 | ||||||||
\(995\) | −4.06990 | −0.129024 | ||||||||
\(996\) | 5.46496 | − | 9.46559i | 0.173164 | − | 0.299929i | ||||
\(997\) | 17.2960 | + | 29.9575i | 0.547769 | + | 0.948764i | 0.998427 | + | 0.0560671i | \(0.0178561\pi\) |
−0.450658 | + | 0.892697i | \(0.648811\pi\) | |||||||
\(998\) | −1.63587 | − | 2.83342i | −0.0517827 | − | 0.0896902i | ||||
\(999\) | −1.35224 | + | 2.34215i | −0.0427829 | + | 0.0741022i |
(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 | 966.2.i.n.415.3 | yes | 8 | |
7.2 | even | 3 | 6762.2.a.cg.1.2 | 4 | |||
7.4 | even | 3 | inner | 966.2.i.n.277.3 | ✓ | 8 | |
7.5 | odd | 6 | 6762.2.a.ch.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.n.277.3 | ✓ | 8 | 7.4 | even | 3 | inner | |
966.2.i.n.415.3 | yes | 8 | 1.1 | even | 1 | trivial | |
6762.2.a.cg.1.2 | 4 | 7.2 | even | 3 | |||
6762.2.a.ch.1.3 | 4 | 7.5 | odd | 6 |