Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(67,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, 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("462.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1156923.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 331.1 | ||
Root | \(0.500000 - 0.0585812i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.331 |
Dual form | 462.2.i.f.67.1 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(5\) | −1.37328 | + | 2.37860i | −0.614151 | + | 1.06374i | 0.376381 | + | 0.926465i | \(0.377168\pi\) |
−0.990533 | + | 0.137277i | \(0.956165\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.37328 | − | 2.26144i | −0.519053 | − | 0.854742i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −1.37328 | − | 2.37860i | −0.434271 | − | 0.752179i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 5.49314 | 1.52352 | 0.761761 | − | 0.647858i | \(-0.224335\pi\) | ||||
0.761761 | + | 0.647858i | \(0.224335\pi\) | |||||||
\(14\) | 2.64510 | − | 0.0585812i | 0.706933 | − | 0.0156565i | ||||
\(15\) | 2.74657 | 0.709161 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.500000 | − | 0.866025i | −0.121268 | − | 0.210042i | 0.799000 | − | 0.601331i | \(-0.205363\pi\) |
−0.920268 | + | 0.391289i | \(0.872029\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | 4.01839 | − | 6.96005i | 0.921881 | − | 1.59675i | 0.125379 | − | 0.992109i | \(-0.459985\pi\) |
0.796502 | − | 0.604636i | \(-0.206681\pi\) | |||||||
\(20\) | 2.74657 | 0.614151 | ||||||||
\(21\) | −1.27182 | + | 2.32002i | −0.277534 | + | 0.506269i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 0.645103 | − | 1.11735i | 0.134513 | − | 0.232984i | −0.790898 | − | 0.611948i | \(-0.790386\pi\) |
0.925411 | + | 0.378964i | \(0.123720\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −1.27182 | − | 2.20285i | −0.254364 | − | 0.440571i | ||||
\(26\) | −2.74657 | + | 4.75720i | −0.538646 | + | 0.932963i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.27182 | + | 2.32002i | −0.240351 | + | 0.438442i | ||||
\(29\) | 4.54364 | 0.843732 | 0.421866 | − | 0.906658i | \(-0.361375\pi\) | ||||
0.421866 | + | 0.906658i | \(0.361375\pi\) | |||||||
\(30\) | −1.37328 | + | 2.37860i | −0.250726 | + | 0.434271i | ||||
\(31\) | −2.54364 | − | 4.40571i | −0.456851 | − | 0.791289i | 0.541942 | − | 0.840416i | \(-0.317689\pi\) |
−0.998793 | + | 0.0491274i | \(0.984356\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 7.26496 | − | 0.160897i | 1.22800 | − | 0.0271966i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.01839 | − | 3.49595i | 0.331821 | − | 0.574730i | −0.651048 | − | 0.759036i | \(-0.725670\pi\) |
0.982869 | + | 0.184306i | \(0.0590038\pi\) | |||||||
\(38\) | 4.01839 | + | 6.96005i | 0.651868 | + | 1.12907i | ||||
\(39\) | −2.74657 | − | 4.75720i | −0.439803 | − | 0.761761i | ||||
\(40\) | −1.37328 | + | 2.37860i | −0.217135 | + | 0.376089i | ||||
\(41\) | 5.54364 | 0.865771 | 0.432885 | − | 0.901449i | \(-0.357495\pi\) | ||||
0.432885 | + | 0.901449i | \(0.357495\pi\) | |||||||
\(42\) | −1.37328 | − | 2.26144i | −0.211902 | − | 0.348947i | ||||
\(43\) | −4.03677 | −0.615602 | −0.307801 | − | 0.951451i | \(-0.599593\pi\) | ||||
−0.307801 | + | 0.951451i | \(0.599593\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | −1.37328 | − | 2.37860i | −0.204717 | − | 0.354580i | ||||
\(46\) | 0.645103 | + | 1.11735i | 0.0951152 | + | 0.164744i | ||||
\(47\) | 4.64510 | − | 8.04555i | 0.677558 | − | 1.17356i | −0.298156 | − | 0.954517i | \(-0.596372\pi\) |
0.975714 | − | 0.219048i | \(-0.0702950\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −3.22818 | + | 6.21119i | −0.461169 | + | 0.887312i | ||||
\(50\) | 2.54364 | 0.359725 | ||||||||
\(51\) | −0.500000 | + | 0.866025i | −0.0700140 | + | 0.121268i | ||||
\(52\) | −2.74657 | − | 4.75720i | −0.380880 | − | 0.659704i | ||||
\(53\) | −2.74657 | − | 4.75720i | −0.377270 | − | 0.653451i | 0.613394 | − | 0.789777i | \(-0.289804\pi\) |
−0.990664 | + | 0.136326i | \(0.956471\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 2.74657 | 0.370347 | ||||||||
\(56\) | −1.37328 | − | 2.26144i | −0.183513 | − | 0.302197i | ||||
\(57\) | −8.03677 | −1.06450 | ||||||||
\(58\) | −2.27182 | + | 3.93491i | −0.298304 | + | 0.516678i | ||||
\(59\) | 4.76496 | + | 8.25314i | 0.620344 | + | 1.07447i | 0.989422 | + | 0.145069i | \(0.0463405\pi\) |
−0.369077 | + | 0.929399i | \(0.620326\pi\) | |||||||
\(60\) | −1.37328 | − | 2.37860i | −0.177290 | − | 0.307076i | ||||
\(61\) | 0.829647 | − | 1.43699i | 0.106225 | − | 0.183988i | −0.808013 | − | 0.589165i | \(-0.799457\pi\) |
0.914238 | + | 0.405177i | \(0.132790\pi\) | |||||||
\(62\) | 5.08727 | 0.646084 | ||||||||
\(63\) | 2.64510 | − | 0.0585812i | 0.333252 | − | 0.00738053i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.54364 | + | 13.0660i | −0.935673 | + | 1.62063i | ||||
\(66\) | −0.500000 | − | 0.866025i | −0.0615457 | − | 0.106600i | ||||
\(67\) | −1.77182 | − | 3.06888i | −0.216462 | − | 0.374923i | 0.737262 | − | 0.675607i | \(-0.236118\pi\) |
−0.953724 | + | 0.300684i | \(0.902785\pi\) | |||||||
\(68\) | −0.500000 | + | 0.866025i | −0.0606339 | + | 0.105021i | ||||
\(69\) | −1.29021 | −0.155322 | ||||||||
\(70\) | −3.49314 | + | 6.37208i | −0.417510 | + | 0.761610i | ||||
\(71\) | 2.54364 | 0.301874 | 0.150937 | − | 0.988543i | \(-0.451771\pi\) | ||||
0.150937 | + | 0.988543i | \(0.451771\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 4.29021 | + | 7.43085i | 0.502131 | + | 0.869716i | 0.999997 | + | 0.00246191i | \(0.000783650\pi\) |
−0.497866 | + | 0.867254i | \(0.665883\pi\) | |||||||
\(74\) | 2.01839 | + | 3.49595i | 0.234633 | + | 0.406396i | ||||
\(75\) | −1.27182 | + | 2.20285i | −0.146857 | + | 0.254364i | ||||
\(76\) | −8.03677 | −0.921881 | ||||||||
\(77\) | −1.27182 | + | 2.32002i | −0.144937 | + | 0.264390i | ||||
\(78\) | 5.49314 | 0.621975 | ||||||||
\(79\) | −6.11985 | + | 10.5999i | −0.688537 | + | 1.19258i | 0.283774 | + | 0.958891i | \(0.408413\pi\) |
−0.972311 | + | 0.233690i | \(0.924920\pi\) | |||||||
\(80\) | −1.37328 | − | 2.37860i | −0.153538 | − | 0.265935i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.77182 | + | 4.80093i | −0.306096 | + | 0.530174i | ||||
\(83\) | −14.5299 | −1.59486 | −0.797432 | − | 0.603408i | \(-0.793809\pi\) | ||||
−0.797432 | + | 0.603408i | \(0.793809\pi\) | |||||||
\(84\) | 2.64510 | − | 0.0585812i | 0.288604 | − | 0.00639173i | ||||
\(85\) | 2.74657 | 0.297907 | ||||||||
\(86\) | 2.01839 | − | 3.49595i | 0.217648 | − | 0.376978i | ||||
\(87\) | −2.27182 | − | 3.93491i | −0.243565 | − | 0.421866i | ||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | 3.25343 | − | 5.63511i | 0.344863 | − | 0.597320i | −0.640466 | − | 0.767987i | \(-0.721259\pi\) |
0.985329 | + | 0.170666i | \(0.0545920\pi\) | |||||||
\(90\) | 2.74657 | 0.289514 | ||||||||
\(91\) | −7.54364 | − | 12.4224i | −0.790788 | − | 1.30222i | ||||
\(92\) | −1.29021 | −0.134513 | ||||||||
\(93\) | −2.54364 | + | 4.40571i | −0.263763 | + | 0.456851i | ||||
\(94\) | 4.64510 | + | 8.04555i | 0.479106 | + | 0.829836i | ||||
\(95\) | 11.0368 | + | 19.1163i | 1.13235 | + | 1.96129i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −0.0872743 | −0.00886136 | −0.00443068 | − | 0.999990i | \(-0.501410\pi\) | ||||
−0.00443068 | + | 0.999990i | \(0.501410\pi\) | |||||||
\(98\) | −3.76496 | − | 5.90128i | −0.380318 | − | 0.596119i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −1.27182 | + | 2.20285i | −0.127182 | + | 0.220285i | ||||
\(101\) | −6.51152 | − | 11.2783i | −0.647921 | − | 1.12223i | −0.983619 | − | 0.180262i | \(-0.942305\pi\) |
0.335698 | − | 0.941970i | \(-0.391028\pi\) | |||||||
\(102\) | −0.500000 | − | 0.866025i | −0.0495074 | − | 0.0857493i | ||||
\(103\) | 9.03677 | − | 15.6522i | 0.890420 | − | 1.54225i | 0.0510469 | − | 0.998696i | \(-0.483744\pi\) |
0.839373 | − | 0.543556i | \(-0.182922\pi\) | |||||||
\(104\) | 5.49314 | 0.538646 | ||||||||
\(105\) | −3.77182 | − | 6.21119i | −0.368092 | − | 0.606150i | ||||
\(106\) | 5.49314 | 0.533541 | ||||||||
\(107\) | −8.72132 | + | 15.1058i | −0.843122 | + | 1.46033i | 0.0441209 | + | 0.999026i | \(0.485951\pi\) |
−0.887243 | + | 0.461303i | \(0.847382\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −0.829647 | − | 1.43699i | −0.0794658 | − | 0.137639i | 0.823554 | − | 0.567238i | \(-0.191988\pi\) |
−0.903020 | + | 0.429599i | \(0.858655\pi\) | |||||||
\(110\) | −1.37328 | + | 2.37860i | −0.130938 | + | 0.226790i | ||||
\(111\) | −4.03677 | −0.383154 | ||||||||
\(112\) | 2.64510 | − | 0.0585812i | 0.249939 | − | 0.00553540i | ||||
\(113\) | −7.08727 | −0.666715 | −0.333357 | − | 0.942801i | \(-0.608182\pi\) | ||||
−0.333357 | + | 0.942801i | \(0.608182\pi\) | |||||||
\(114\) | 4.01839 | − | 6.96005i | 0.376356 | − | 0.651868i | ||||
\(115\) | 1.77182 | + | 3.06888i | 0.165223 | + | 0.286175i | ||||
\(116\) | −2.27182 | − | 3.93491i | −0.210933 | − | 0.365347i | ||||
\(117\) | −2.74657 | + | 4.75720i | −0.253920 | + | 0.439803i | ||||
\(118\) | −9.52991 | −0.877299 | ||||||||
\(119\) | −1.27182 | + | 2.32002i | −0.116587 | + | 0.212676i | ||||
\(120\) | 2.74657 | 0.250726 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 0.829647 | + | 1.43699i | 0.0751127 | + | 0.130099i | ||||
\(123\) | −2.77182 | − | 4.80093i | −0.249926 | − | 0.432885i | ||||
\(124\) | −2.54364 | + | 4.40571i | −0.228425 | + | 0.395644i | ||||
\(125\) | −6.74657 | −0.603431 | ||||||||
\(126\) | −1.27182 | + | 2.32002i | −0.113303 | + | 0.206684i | ||||
\(127\) | −6.78334 | −0.601924 | −0.300962 | − | 0.953636i | \(-0.597308\pi\) | ||||
−0.300962 | + | 0.953636i | \(0.597308\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.01839 | + | 3.49595i | 0.177709 | + | 0.307801i | ||||
\(130\) | −7.54364 | − | 13.0660i | −0.661621 | − | 1.14596i | ||||
\(131\) | 6.94950 | − | 12.0369i | 0.607181 | − | 1.05167i | −0.384522 | − | 0.923116i | \(-0.625634\pi\) |
0.991703 | − | 0.128552i | \(-0.0410329\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −21.2581 | + | 0.470804i | −1.84331 | + | 0.0408238i | ||||
\(134\) | 3.54364 | 0.306124 | ||||||||
\(135\) | −1.37328 | + | 2.37860i | −0.118193 | + | 0.204717i | ||||
\(136\) | −0.500000 | − | 0.866025i | −0.0428746 | − | 0.0742611i | ||||
\(137\) | −2.74657 | − | 4.75720i | −0.234655 | − | 0.406435i | 0.724517 | − | 0.689257i | \(-0.242063\pi\) |
−0.959172 | + | 0.282822i | \(0.908729\pi\) | |||||||
\(138\) | 0.645103 | − | 1.11735i | 0.0549148 | − | 0.0951152i | ||||
\(139\) | 13.6309 | 1.15616 | 0.578079 | − | 0.815981i | \(-0.303802\pi\) | ||||
0.578079 | + | 0.815981i | \(0.303802\pi\) | |||||||
\(140\) | −3.77182 | − | 6.21119i | −0.318777 | − | 0.524941i | ||||
\(141\) | −9.29021 | −0.782376 | ||||||||
\(142\) | −1.27182 | + | 2.20285i | −0.106729 | + | 0.184859i | ||||
\(143\) | −2.74657 | − | 4.75720i | −0.229680 | − | 0.397817i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −6.23970 | + | 10.8075i | −0.518179 | + | 0.897513i | ||||
\(146\) | −8.58041 | −0.710120 | ||||||||
\(147\) | 6.99314 | − | 0.309906i | 0.576784 | − | 0.0255606i | ||||
\(148\) | −4.03677 | −0.331821 | ||||||||
\(149\) | −8.01839 | + | 13.8883i | −0.656892 | + | 1.13777i | 0.324524 | + | 0.945877i | \(0.394796\pi\) |
−0.981416 | + | 0.191893i | \(0.938537\pi\) | |||||||
\(150\) | −1.27182 | − | 2.20285i | −0.103844 | − | 0.179862i | ||||
\(151\) | 2.84803 | + | 4.93294i | 0.231770 | + | 0.401437i | 0.958329 | − | 0.285667i | \(-0.0922151\pi\) |
−0.726559 | + | 0.687104i | \(0.758882\pi\) | |||||||
\(152\) | 4.01839 | − | 6.96005i | 0.325934 | − | 0.564535i | ||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −1.37328 | − | 2.26144i | −0.110662 | − | 0.182232i | ||||
\(155\) | 13.9725 | 1.12230 | ||||||||
\(156\) | −2.74657 | + | 4.75720i | −0.219901 | + | 0.380880i | ||||
\(157\) | −9.05516 | − | 15.6840i | −0.722680 | − | 1.25172i | −0.959922 | − | 0.280269i | \(-0.909576\pi\) |
0.237241 | − | 0.971451i | \(-0.423757\pi\) | |||||||
\(158\) | −6.11985 | − | 10.5999i | −0.486869 | − | 0.843282i | ||||
\(159\) | −2.74657 | + | 4.75720i | −0.217817 | + | 0.377270i | ||||
\(160\) | 2.74657 | 0.217135 | ||||||||
\(161\) | −3.41273 | + | 0.0755817i | −0.268960 | + | 0.00595668i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 6.72132 | − | 11.6417i | 0.526454 | − | 0.911846i | −0.473071 | − | 0.881024i | \(-0.656854\pi\) |
0.999525 | − | 0.0308210i | \(-0.00981219\pi\) | |||||||
\(164\) | −2.77182 | − | 4.80093i | −0.216443 | − | 0.374890i | ||||
\(165\) | −1.37328 | − | 2.37860i | −0.106910 | − | 0.185174i | ||||
\(166\) | 7.26496 | − | 12.5833i | 0.563870 | − | 0.976651i | ||||
\(167\) | 23.5667 | 1.82364 | 0.911822 | − | 0.410585i | \(-0.134675\pi\) | ||||
0.911822 | + | 0.410585i | \(0.134675\pi\) | |||||||
\(168\) | −1.27182 | + | 2.32002i | −0.0981229 | + | 0.178993i | ||||
\(169\) | 17.1745 | 1.32112 | ||||||||
\(170\) | −1.37328 | + | 2.37860i | −0.105326 | + | 0.182430i | ||||
\(171\) | 4.01839 | + | 6.96005i | 0.307294 | + | 0.532248i | ||||
\(172\) | 2.01839 | + | 3.49595i | 0.153901 | + | 0.266564i | ||||
\(173\) | 5.45636 | − | 9.45070i | 0.414840 | − | 0.718523i | −0.580572 | − | 0.814209i | \(-0.697171\pi\) |
0.995412 | + | 0.0956857i | \(0.0305044\pi\) | |||||||
\(174\) | 4.54364 | 0.344452 | ||||||||
\(175\) | −3.23504 | + | 5.90128i | −0.244546 | + | 0.446095i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 4.76496 | − | 8.25314i | 0.358156 | − | 0.620344i | ||||
\(178\) | 3.25343 | + | 5.63511i | 0.243855 | + | 0.422369i | ||||
\(179\) | 6.47475 | + | 11.2146i | 0.483946 | + | 0.838218i | 0.999830 | − | 0.0184400i | \(-0.00586995\pi\) |
−0.515884 | + | 0.856658i | \(0.672537\pi\) | |||||||
\(180\) | −1.37328 | + | 2.37860i | −0.102359 | + | 0.177290i | ||||
\(181\) | 7.59414 | 0.564468 | 0.282234 | − | 0.959346i | \(-0.408925\pi\) | ||||
0.282234 | + | 0.959346i | \(0.408925\pi\) | |||||||
\(182\) | 14.5299 | − | 0.321794i | 1.07703 | − | 0.0238530i | ||||
\(183\) | −1.65929 | −0.122659 | ||||||||
\(184\) | 0.645103 | − | 1.11735i | 0.0475576 | − | 0.0823722i | ||||
\(185\) | 5.54364 | + | 9.60186i | 0.407576 | + | 0.705943i | ||||
\(186\) | −2.54364 | − | 4.40571i | −0.186509 | − | 0.323042i | ||||
\(187\) | −0.500000 | + | 0.866025i | −0.0365636 | + | 0.0633300i | ||||
\(188\) | −9.29021 | −0.677558 | ||||||||
\(189\) | −1.37328 | − | 2.26144i | −0.0998917 | − | 0.164495i | ||||
\(190\) | −22.0735 | −1.60138 | ||||||||
\(191\) | −9.49314 | + | 16.4426i | −0.686899 | + | 1.18974i | 0.285937 | + | 0.958249i | \(0.407695\pi\) |
−0.972836 | + | 0.231496i | \(0.925638\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 10.7833 | + | 18.6773i | 0.776202 | + | 1.34442i | 0.934116 | + | 0.356968i | \(0.116190\pi\) |
−0.157915 | + | 0.987453i | \(0.550477\pi\) | |||||||
\(194\) | 0.0436371 | − | 0.0755817i | 0.00313296 | − | 0.00542645i | ||||
\(195\) | 15.0873 | 1.08042 | ||||||||
\(196\) | 6.99314 | − | 0.309906i | 0.499510 | − | 0.0221362i | ||||
\(197\) | −3.12405 | −0.222579 | −0.111290 | − | 0.993788i | \(-0.535498\pi\) | ||||
−0.111290 | + | 0.993788i | \(0.535498\pi\) | |||||||
\(198\) | −0.500000 | + | 0.866025i | −0.0355335 | + | 0.0615457i | ||||
\(199\) | 13.0368 | + | 22.5804i | 0.924152 | + | 1.60068i | 0.792919 | + | 0.609327i | \(0.208560\pi\) |
0.131234 | + | 0.991351i | \(0.458106\pi\) | |||||||
\(200\) | −1.27182 | − | 2.20285i | −0.0899312 | − | 0.155765i | ||||
\(201\) | −1.77182 | + | 3.06888i | −0.124974 | + | 0.216462i | ||||
\(202\) | 13.0230 | 0.916298 | ||||||||
\(203\) | −6.23970 | − | 10.2751i | −0.437941 | − | 0.721174i | ||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −7.61299 | + | 13.1861i | −0.531714 | + | 0.920956i | ||||
\(206\) | 9.03677 | + | 15.6522i | 0.629622 | + | 1.09054i | ||||
\(207\) | 0.645103 | + | 1.11735i | 0.0448377 | + | 0.0776612i | ||||
\(208\) | −2.74657 | + | 4.75720i | −0.190440 | + | 0.329852i | ||||
\(209\) | −8.03677 | −0.555915 | ||||||||
\(210\) | 7.26496 | − | 0.160897i | 0.501330 | − | 0.0111030i | ||||
\(211\) | 15.6677 | 1.07861 | 0.539304 | − | 0.842111i | \(-0.318687\pi\) | ||||
0.539304 | + | 0.842111i | \(0.318687\pi\) | |||||||
\(212\) | −2.74657 | + | 4.75720i | −0.188635 | + | 0.326726i | ||||
\(213\) | −1.27182 | − | 2.20285i | −0.0871436 | − | 0.150937i | ||||
\(214\) | −8.72132 | − | 15.1058i | −0.596177 | − | 1.03261i | ||||
\(215\) | 5.54364 | − | 9.60186i | 0.378073 | − | 0.654841i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −6.47009 | + | 11.8026i | −0.439218 | + | 0.801210i | ||||
\(218\) | 1.65929 | 0.112382 | ||||||||
\(219\) | 4.29021 | − | 7.43085i | 0.289905 | − | 0.502131i | ||||
\(220\) | −1.37328 | − | 2.37860i | −0.0925868 | − | 0.160365i | ||||
\(221\) | −2.74657 | − | 4.75720i | −0.184754 | − | 0.320004i | ||||
\(222\) | 2.01839 | − | 3.49595i | 0.135465 | − | 0.234633i | ||||
\(223\) | 2.40586 | 0.161108 | 0.0805542 | − | 0.996750i | \(-0.474331\pi\) | ||||
0.0805542 | + | 0.996750i | \(0.474331\pi\) | |||||||
\(224\) | −1.27182 | + | 2.32002i | −0.0849770 | + | 0.155013i | ||||
\(225\) | 2.54364 | 0.169576 | ||||||||
\(226\) | 3.54364 | − | 6.13776i | 0.235719 | − | 0.408278i | ||||
\(227\) | −1.22818 | − | 2.12727i | −0.0815173 | − | 0.141192i | 0.822385 | − | 0.568932i | \(-0.192643\pi\) |
−0.903902 | + | 0.427740i | \(0.859310\pi\) | |||||||
\(228\) | 4.01839 | + | 6.96005i | 0.266124 | + | 0.460941i | ||||
\(229\) | 5.29021 | − | 9.16290i | 0.349587 | − | 0.605502i | −0.636589 | − | 0.771203i | \(-0.719655\pi\) |
0.986176 | + | 0.165701i | \(0.0529887\pi\) | |||||||
\(230\) | −3.54364 | −0.233661 | ||||||||
\(231\) | 2.64510 | − | 0.0585812i | 0.174035 | − | 0.00385436i | ||||
\(232\) | 4.54364 | 0.298304 | ||||||||
\(233\) | 3.53677 | − | 6.12587i | 0.231702 | − | 0.401319i | −0.726607 | − | 0.687053i | \(-0.758904\pi\) |
0.958309 | + | 0.285734i | \(0.0922373\pi\) | |||||||
\(234\) | −2.74657 | − | 4.75720i | −0.179549 | − | 0.310988i | ||||
\(235\) | 12.7581 | + | 22.0977i | 0.832246 | + | 1.44149i | ||||
\(236\) | 4.76496 | − | 8.25314i | 0.310172 | − | 0.537234i | ||||
\(237\) | 12.2397 | 0.795054 | ||||||||
\(238\) | −1.37328 | − | 2.26144i | −0.0890168 | − | 0.146587i | ||||
\(239\) | 7.66769 | 0.495981 | 0.247991 | − | 0.968762i | \(-0.420230\pi\) | ||||
0.247991 | + | 0.968762i | \(0.420230\pi\) | |||||||
\(240\) | −1.37328 | + | 2.37860i | −0.0886451 | + | 0.153538i | ||||
\(241\) | 12.5299 | + | 21.7024i | 0.807122 | + | 1.39798i | 0.914849 | + | 0.403797i | \(0.132310\pi\) |
−0.107726 | + | 0.994181i | \(0.534357\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −1.65929 | −0.106225 | ||||||||
\(245\) | −10.3407 | − | 16.2083i | −0.660643 | − | 1.03551i | ||||
\(246\) | 5.54364 | 0.353449 | ||||||||
\(247\) | 22.0735 | − | 38.2325i | 1.40451 | − | 2.43268i | ||||
\(248\) | −2.54364 | − | 4.40571i | −0.161521 | − | 0.279763i | ||||
\(249\) | 7.26496 | + | 12.5833i | 0.460398 | + | 0.797432i | ||||
\(250\) | 3.37328 | − | 5.84270i | 0.213345 | − | 0.369525i | ||||
\(251\) | −25.0230 | −1.57944 | −0.789720 | − | 0.613467i | \(-0.789774\pi\) | ||||
−0.789720 | + | 0.613467i | \(0.789774\pi\) | |||||||
\(252\) | −1.37328 | − | 2.26144i | −0.0865088 | − | 0.142457i | ||||
\(253\) | −1.29021 | −0.0811145 | ||||||||
\(254\) | 3.39167 | − | 5.87455i | 0.212812 | − | 0.368602i | ||||
\(255\) | −1.37328 | − | 2.37860i | −0.0859984 | − | 0.148954i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 5.25343 | − | 9.09921i | 0.327700 | − | 0.567593i | −0.654355 | − | 0.756187i | \(-0.727060\pi\) |
0.982055 | + | 0.188594i | \(0.0603931\pi\) | |||||||
\(258\) | −4.03677 | −0.251319 | ||||||||
\(259\) | −10.6777 | + | 0.236479i | −0.663479 | + | 0.0146941i | ||||
\(260\) | 15.0873 | 0.935673 | ||||||||
\(261\) | −2.27182 | + | 3.93491i | −0.140622 | + | 0.243565i | ||||
\(262\) | 6.94950 | + | 12.0369i | 0.429342 | + | 0.743641i | ||||
\(263\) | −11.8201 | − | 20.4730i | −0.728860 | − | 1.26242i | −0.957366 | − | 0.288879i | \(-0.906717\pi\) |
0.228506 | − | 0.973543i | \(-0.426616\pi\) | |||||||
\(264\) | −0.500000 | + | 0.866025i | −0.0307729 | + | 0.0533002i | ||||
\(265\) | 15.0873 | 0.926804 | ||||||||
\(266\) | 10.2213 | − | 18.6454i | 0.626709 | − | 1.14323i | ||||
\(267\) | −6.50686 | −0.398214 | ||||||||
\(268\) | −1.77182 | + | 3.06888i | −0.108231 | + | 0.187462i | ||||
\(269\) | 7.57622 | + | 13.1224i | 0.461930 | + | 0.800086i | 0.999057 | − | 0.0434151i | \(-0.0138238\pi\) |
−0.537127 | + | 0.843501i | \(0.680490\pi\) | |||||||
\(270\) | −1.37328 | − | 2.37860i | −0.0835754 | − | 0.144757i | ||||
\(271\) | −9.49314 | + | 16.4426i | −0.576667 | + | 0.998816i | 0.419191 | + | 0.907898i | \(0.362314\pi\) |
−0.995858 | + | 0.0909186i | \(0.971020\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −6.98627 | + | 12.7442i | −0.422828 | + | 0.771312i | ||||
\(274\) | 5.49314 | 0.331853 | ||||||||
\(275\) | −1.27182 | + | 2.20285i | −0.0766935 | + | 0.132837i | ||||
\(276\) | 0.645103 | + | 1.11735i | 0.0388306 | + | 0.0672566i | ||||
\(277\) | −12.2397 | − | 21.1998i | −0.735413 | − | 1.27377i | −0.954542 | − | 0.298076i | \(-0.903655\pi\) |
0.219130 | − | 0.975696i | \(-0.429678\pi\) | |||||||
\(278\) | −6.81546 | + | 11.8047i | −0.408764 | + | 0.708000i | ||||
\(279\) | 5.08727 | 0.304567 | ||||||||
\(280\) | 7.26496 | − | 0.160897i | 0.434164 | − | 0.00961545i | ||||
\(281\) | −12.0873 | −0.721066 | −0.360533 | − | 0.932746i | \(-0.617405\pi\) | ||||
−0.360533 | + | 0.932746i | \(0.617405\pi\) | |||||||
\(282\) | 4.64510 | − | 8.04555i | 0.276612 | − | 0.479106i | ||||
\(283\) | −2.34071 | − | 4.05422i | −0.139141 | − | 0.240998i | 0.788031 | − | 0.615636i | \(-0.211101\pi\) |
−0.927172 | + | 0.374637i | \(0.877767\pi\) | |||||||
\(284\) | −1.27182 | − | 2.20285i | −0.0754685 | − | 0.130715i | ||||
\(285\) | 11.0368 | − | 19.1163i | 0.653762 | − | 1.13235i | ||||
\(286\) | 5.49314 | 0.324816 | ||||||||
\(287\) | −7.61299 | − | 12.5366i | −0.449381 | − | 0.740011i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 8.00000 | − | 13.8564i | 0.470588 | − | 0.815083i | ||||
\(290\) | −6.23970 | − | 10.8075i | −0.366408 | − | 0.634637i | ||||
\(291\) | 0.0436371 | + | 0.0755817i | 0.00255805 | + | 0.00443068i | ||||
\(292\) | 4.29021 | − | 7.43085i | 0.251065 | − | 0.434858i | ||||
\(293\) | −11.6309 | −0.679485 | −0.339743 | − | 0.940518i | \(-0.610340\pi\) | ||||
−0.339743 | + | 0.940518i | \(0.610340\pi\) | |||||||
\(294\) | −3.22818 | + | 6.21119i | −0.188271 | + | 0.362244i | ||||
\(295\) | −26.1745 | −1.52394 | ||||||||
\(296\) | 2.01839 | − | 3.49595i | 0.117316 | − | 0.203198i | ||||
\(297\) | −0.500000 | − | 0.866025i | −0.0290129 | − | 0.0502519i | ||||
\(298\) | −8.01839 | − | 13.8883i | −0.464493 | − | 0.804525i | ||||
\(299\) | 3.54364 | − | 6.13776i | 0.204934 | − | 0.354956i | ||||
\(300\) | 2.54364 | 0.146857 | ||||||||
\(301\) | 5.54364 | + | 9.12890i | 0.319530 | + | 0.526181i | ||||
\(302\) | −5.69607 | −0.327772 | ||||||||
\(303\) | −6.51152 | + | 11.2783i | −0.374077 | + | 0.647921i | ||||
\(304\) | 4.01839 | + | 6.96005i | 0.230470 | + | 0.399186i | ||||
\(305\) | 2.27868 | + | 3.94679i | 0.130477 | + | 0.225993i | ||||
\(306\) | −0.500000 | + | 0.866025i | −0.0285831 | + | 0.0495074i | ||||
\(307\) | −14.0735 | −0.803220 | −0.401610 | − | 0.915811i | \(-0.631549\pi\) | ||||
−0.401610 | + | 0.915811i | \(0.631549\pi\) | |||||||
\(308\) | 2.64510 | − | 0.0585812i | 0.150719 | − | 0.00333797i | ||||
\(309\) | −18.0735 | −1.02817 | ||||||||
\(310\) | −6.98627 | + | 12.1006i | −0.396794 | + | 0.687267i | ||||
\(311\) | −6.13824 | − | 10.6317i | −0.348068 | − | 0.602871i | 0.637839 | − | 0.770170i | \(-0.279829\pi\) |
−0.985906 | + | 0.167299i | \(0.946495\pi\) | |||||||
\(312\) | −2.74657 | − | 4.75720i | −0.155494 | − | 0.269323i | ||||
\(313\) | −11.7282 | + | 20.3138i | −0.662916 | + | 1.14820i | 0.316930 | + | 0.948449i | \(0.397348\pi\) |
−0.979846 | + | 0.199755i | \(0.935985\pi\) | |||||||
\(314\) | 18.1103 | 1.02202 | ||||||||
\(315\) | −3.49314 | + | 6.37208i | −0.196816 | + | 0.359026i | ||||
\(316\) | 12.2397 | 0.688537 | ||||||||
\(317\) | 0.286010 | − | 0.495384i | 0.0160639 | − | 0.0278235i | −0.857882 | − | 0.513847i | \(-0.828220\pi\) |
0.873946 | + | 0.486024i | \(0.161553\pi\) | |||||||
\(318\) | −2.74657 | − | 4.75720i | −0.154020 | − | 0.266770i | ||||
\(319\) | −2.27182 | − | 3.93491i | −0.127197 | − | 0.220312i | ||||
\(320\) | −1.37328 | + | 2.37860i | −0.0767689 | + | 0.132968i | ||||
\(321\) | 17.4426 | 0.973553 | ||||||||
\(322\) | 1.64091 | − | 2.99330i | 0.0914442 | − | 0.166810i | ||||
\(323\) | −8.03677 | −0.447178 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −6.98627 | − | 12.1006i | −0.387529 | − | 0.671219i | ||||
\(326\) | 6.72132 | + | 11.6417i | 0.372259 | + | 0.644772i | ||||
\(327\) | −0.829647 | + | 1.43699i | −0.0458796 | + | 0.0794658i | ||||
\(328\) | 5.54364 | 0.306096 | ||||||||
\(329\) | −24.5735 | + | 0.544231i | −1.35478 | + | 0.0300044i | ||||
\(330\) | 2.74657 | 0.151194 | ||||||||
\(331\) | −3.85909 | + | 6.68414i | −0.212115 | + | 0.367394i | −0.952376 | − | 0.304925i | \(-0.901368\pi\) |
0.740261 | + | 0.672319i | \(0.234702\pi\) | |||||||
\(332\) | 7.26496 | + | 12.5833i | 0.398716 | + | 0.690597i | ||||
\(333\) | 2.01839 | + | 3.49595i | 0.110607 | + | 0.191577i | ||||
\(334\) | −11.7833 | + | 20.4093i | −0.644756 | + | 1.11675i | ||||
\(335\) | 9.73284 | 0.531762 | ||||||||
\(336\) | −1.37328 | − | 2.26144i | −0.0749188 | − | 0.123371i | ||||
\(337\) | 28.5530 | 1.55538 | 0.777689 | − | 0.628649i | \(-0.216392\pi\) | ||||
0.777689 | + | 0.628649i | \(0.216392\pi\) | |||||||
\(338\) | −8.58727 | + | 14.8736i | −0.467086 | + | 0.809017i | ||||
\(339\) | 3.54364 | + | 6.13776i | 0.192464 | + | 0.333357i | ||||
\(340\) | −1.37328 | − | 2.37860i | −0.0744768 | − | 0.128998i | ||||
\(341\) | −2.54364 | + | 4.40571i | −0.137746 | + | 0.238583i | ||||
\(342\) | −8.03677 | −0.434579 | ||||||||
\(343\) | 18.4794 | − | 1.22940i | 0.997794 | − | 0.0663814i | ||||
\(344\) | −4.03677 | −0.217648 | ||||||||
\(345\) | 1.77182 | − | 3.06888i | 0.0953915 | − | 0.165223i | ||||
\(346\) | 5.45636 | + | 9.45070i | 0.293336 | + | 0.508073i | ||||
\(347\) | 11.7213 | + | 20.3019i | 0.629233 | + | 1.08986i | 0.987706 | + | 0.156324i | \(0.0499643\pi\) |
−0.358473 | + | 0.933540i | \(0.616702\pi\) | |||||||
\(348\) | −2.27182 | + | 3.93491i | −0.121782 | + | 0.210933i | ||||
\(349\) | 25.7328 | 1.37745 | 0.688724 | − | 0.725024i | \(-0.258171\pi\) | ||||
0.688724 | + | 0.725024i | \(0.258171\pi\) | |||||||
\(350\) | −3.49314 | − | 5.75227i | −0.186716 | − | 0.307472i | ||||
\(351\) | 5.49314 | 0.293202 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | 9.20293 | + | 15.9399i | 0.489823 | + | 0.848398i | 0.999931 | − | 0.0117122i | \(-0.00372821\pi\) |
−0.510109 | + | 0.860110i | \(0.670395\pi\) | |||||||
\(354\) | 4.76496 | + | 8.25314i | 0.253255 | + | 0.438650i | ||||
\(355\) | −3.49314 | + | 6.05029i | −0.185396 | + | 0.321116i | ||||
\(356\) | −6.50686 | −0.344863 | ||||||||
\(357\) | 2.64510 | − | 0.0585812i | 0.139994 | − | 0.00310044i | ||||
\(358\) | −12.9495 | −0.684402 | ||||||||
\(359\) | 15.9863 | − | 27.6890i | 0.843723 | − | 1.46137i | −0.0430022 | − | 0.999075i | \(-0.513692\pi\) |
0.886725 | − | 0.462297i | \(-0.152974\pi\) | |||||||
\(360\) | −1.37328 | − | 2.37860i | −0.0723784 | − | 0.125363i | ||||
\(361\) | −22.7949 | − | 39.4819i | −1.19973 | − | 2.07799i | ||||
\(362\) | −3.79707 | + | 6.57672i | −0.199570 | + | 0.345665i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −6.98627 | + | 12.7442i | −0.366180 | + | 0.667976i | ||||
\(365\) | −23.5667 | −1.23354 | ||||||||
\(366\) | 0.829647 | − | 1.43699i | 0.0433663 | − | 0.0751127i | ||||
\(367\) | −18.2397 | − | 31.5921i | −0.952105 | − | 1.64909i | −0.740859 | − | 0.671661i | \(-0.765581\pi\) |
−0.211246 | − | 0.977433i | \(-0.567752\pi\) | |||||||
\(368\) | 0.645103 | + | 1.11735i | 0.0336283 | + | 0.0582459i | ||||
\(369\) | −2.77182 | + | 4.80093i | −0.144295 | + | 0.249926i | ||||
\(370\) | −11.0873 | −0.576400 | ||||||||
\(371\) | −6.98627 | + | 12.7442i | −0.362709 | + | 0.661644i | ||||
\(372\) | 5.08727 | 0.263763 | ||||||||
\(373\) | 10.1566 | − | 17.5918i | 0.525890 | − | 0.910868i | −0.473655 | − | 0.880710i | \(-0.657066\pi\) |
0.999545 | − | 0.0301580i | \(-0.00960104\pi\) | |||||||
\(374\) | −0.500000 | − | 0.866025i | −0.0258544 | − | 0.0447811i | ||||
\(375\) | 3.37328 | + | 5.84270i | 0.174196 | + | 0.301716i | ||||
\(376\) | 4.64510 | − | 8.04555i | 0.239553 | − | 0.414918i | ||||
\(377\) | 24.9588 | 1.28544 | ||||||||
\(378\) | 2.64510 | − | 0.0585812i | 0.136049 | − | 0.00301309i | ||||
\(379\) | 9.44264 | 0.485036 | 0.242518 | − | 0.970147i | \(-0.422027\pi\) | ||||
0.242518 | + | 0.970147i | \(0.422027\pi\) | |||||||
\(380\) | 11.0368 | − | 19.1163i | 0.566175 | − | 0.980643i | ||||
\(381\) | 3.39167 | + | 5.87455i | 0.173761 | + | 0.300962i | ||||
\(382\) | −9.49314 | − | 16.4426i | −0.485711 | − | 0.841276i | ||||
\(383\) | −11.8522 | + | 20.5287i | −0.605621 | + | 1.04897i | 0.386332 | + | 0.922360i | \(0.373742\pi\) |
−0.991953 | + | 0.126606i | \(0.959592\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −3.77182 | − | 6.21119i | −0.192230 | − | 0.316551i | ||||
\(386\) | −21.5667 | −1.09772 | ||||||||
\(387\) | 2.01839 | − | 3.49595i | 0.102600 | − | 0.177709i | ||||
\(388\) | 0.0436371 | + | 0.0755817i | 0.00221534 | + | 0.00383708i | ||||
\(389\) | 0.626716 | + | 1.08550i | 0.0317758 | + | 0.0550372i | 0.881476 | − | 0.472229i | \(-0.156550\pi\) |
−0.849700 | + | 0.527266i | \(0.823217\pi\) | |||||||
\(390\) | −7.54364 | + | 13.0660i | −0.381987 | + | 0.661621i | ||||
\(391\) | −1.29021 | −0.0652485 | ||||||||
\(392\) | −3.22818 | + | 6.21119i | −0.163048 | + | 0.313712i | ||||
\(393\) | −13.8990 | −0.701112 | ||||||||
\(394\) | 1.56202 | − | 2.70550i | 0.0786936 | − | 0.136301i | ||||
\(395\) | −16.8086 | − | 29.1133i | −0.845732 | − | 1.46485i | ||||
\(396\) | −0.500000 | − | 0.866025i | −0.0251259 | − | 0.0435194i | ||||
\(397\) | −14.3086 | + | 24.7832i | −0.718128 | + | 1.24383i | 0.243613 | + | 0.969872i | \(0.421667\pi\) |
−0.961741 | + | 0.273961i | \(0.911666\pi\) | |||||||
\(398\) | −26.0735 | −1.30695 | ||||||||
\(399\) | 11.0368 | + | 18.1746i | 0.552530 | + | 0.909870i | ||||
\(400\) | 2.54364 | 0.127182 | ||||||||
\(401\) | −0.202931 | + | 0.351487i | −0.0101339 | + | 0.0175524i | −0.871048 | − | 0.491198i | \(-0.836559\pi\) |
0.860914 | + | 0.508751i | \(0.169892\pi\) | |||||||
\(402\) | −1.77182 | − | 3.06888i | −0.0883703 | − | 0.153062i | ||||
\(403\) | −13.9725 | − | 24.2012i | −0.696022 | − | 1.20555i | ||||
\(404\) | −6.51152 | + | 11.2783i | −0.323960 | + | 0.561116i | ||||
\(405\) | 2.74657 | 0.136478 | ||||||||
\(406\) | 12.0184 | − | 0.266172i | 0.596463 | − | 0.0132099i | ||||
\(407\) | −4.03677 | −0.200095 | ||||||||
\(408\) | −0.500000 | + | 0.866025i | −0.0247537 | + | 0.0428746i | ||||
\(409\) | 16.3775 | + | 28.3666i | 0.809814 | + | 1.40264i | 0.912992 | + | 0.407977i | \(0.133765\pi\) |
−0.103178 | + | 0.994663i | \(0.532901\pi\) | |||||||
\(410\) | −7.61299 | − | 13.1861i | −0.375979 | − | 0.651214i | ||||
\(411\) | −2.74657 | + | 4.75720i | −0.135478 | + | 0.234655i | ||||
\(412\) | −18.0735 | −0.890420 | ||||||||
\(413\) | 12.1203 | − | 22.1096i | 0.596402 | − | 1.08794i | ||||
\(414\) | −1.29021 | −0.0634101 | ||||||||
\(415\) | 19.9537 | − | 34.5608i | 0.979488 | − | 1.69652i | ||||
\(416\) | −2.74657 | − | 4.75720i | −0.134662 | − | 0.233241i | ||||
\(417\) | −6.81546 | − | 11.8047i | −0.333754 | − | 0.578079i | ||||
\(418\) | 4.01839 | − | 6.96005i | 0.196546 | − | 0.340427i | ||||
\(419\) | −15.9358 | −0.778513 | −0.389257 | − | 0.921129i | \(-0.627268\pi\) | ||||
−0.389257 | + | 0.921129i | \(0.627268\pi\) | |||||||
\(420\) | −3.49314 | + | 6.37208i | −0.170448 | + | 0.310926i | ||||
\(421\) | −27.1240 | −1.32195 | −0.660973 | − | 0.750410i | \(-0.729856\pi\) | ||||
−0.660973 | + | 0.750410i | \(0.729856\pi\) | |||||||
\(422\) | −7.83384 | + | 13.5686i | −0.381345 | + | 0.660510i | ||||
\(423\) | 4.64510 | + | 8.04555i | 0.225853 | + | 0.391188i | ||||
\(424\) | −2.74657 | − | 4.75720i | −0.133385 | − | 0.231030i | ||||
\(425\) | −1.27182 | + | 2.20285i | −0.0616923 | + | 0.106854i | ||||
\(426\) | 2.54364 | 0.123240 | ||||||||
\(427\) | −4.38900 | + | 0.0972034i | −0.212399 | + | 0.00470400i | ||||
\(428\) | 17.4426 | 0.843122 | ||||||||
\(429\) | −2.74657 | + | 4.75720i | −0.132606 | + | 0.229680i | ||||
\(430\) | 5.54364 | + | 9.60186i | 0.267338 | + | 0.463043i | ||||
\(431\) | 20.3133 | + | 35.1836i | 0.978455 | + | 1.69473i | 0.668028 | + | 0.744137i | \(0.267139\pi\) |
0.310427 | + | 0.950597i | \(0.399528\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 1.10100 | 0.0529107 | 0.0264554 | − | 0.999650i | \(-0.491578\pi\) | ||||
0.0264554 | + | 0.999650i | \(0.491578\pi\) | |||||||
\(434\) | −6.98627 | − | 11.5045i | −0.335352 | − | 0.552236i | ||||
\(435\) | 12.4794 | 0.598342 | ||||||||
\(436\) | −0.829647 | + | 1.43699i | −0.0397329 | + | 0.0688194i | ||||
\(437\) | −5.18454 | − | 8.97989i | −0.248010 | − | 0.429567i | ||||
\(438\) | 4.29021 | + | 7.43085i | 0.204994 | + | 0.355060i | ||||
\(439\) | −11.4284 | + | 19.7946i | −0.545450 | + | 0.944747i | 0.453129 | + | 0.891445i | \(0.350308\pi\) |
−0.998578 | + | 0.0533018i | \(0.983025\pi\) | |||||||
\(440\) | 2.74657 | 0.130938 | ||||||||
\(441\) | −3.76496 | − | 5.90128i | −0.179284 | − | 0.281013i | ||||
\(442\) | 5.49314 | 0.261282 | ||||||||
\(443\) | 4.77868 | − | 8.27692i | 0.227042 | − | 0.393248i | −0.729888 | − | 0.683567i | \(-0.760428\pi\) |
0.956930 | + | 0.290318i | \(0.0937612\pi\) | |||||||
\(444\) | 2.01839 | + | 3.49595i | 0.0957884 | + | 0.165910i | ||||
\(445\) | 8.93577 | + | 15.4772i | 0.423596 | + | 0.733690i | ||||
\(446\) | −1.20293 | + | 2.08354i | −0.0569604 | + | 0.0986584i | ||||
\(447\) | 16.0368 | 0.758513 | ||||||||
\(448\) | −1.37328 | − | 2.26144i | −0.0648816 | − | 0.106843i | ||||
\(449\) | 0.681412 | 0.0321578 | 0.0160789 | − | 0.999871i | \(-0.494882\pi\) | ||||
0.0160789 | + | 0.999871i | \(0.494882\pi\) | |||||||
\(450\) | −1.27182 | + | 2.20285i | −0.0599541 | + | 0.103844i | ||||
\(451\) | −2.77182 | − | 4.80093i | −0.130520 | − | 0.226067i | ||||
\(452\) | 3.54364 | + | 6.13776i | 0.166679 | + | 0.288696i | ||||
\(453\) | 2.84803 | − | 4.93294i | 0.133812 | − | 0.231770i | ||||
\(454\) | 2.45636 | 0.115283 | ||||||||
\(455\) | 39.9074 | − | 0.883830i | 1.87089 | − | 0.0414346i | ||||
\(456\) | −8.03677 | −0.376356 | ||||||||
\(457\) | −9.07355 | + | 15.7158i | −0.424443 | + | 0.735156i | −0.996368 | − | 0.0851493i | \(-0.972863\pi\) |
0.571926 | + | 0.820306i | \(0.306197\pi\) | |||||||
\(458\) | 5.29021 | + | 9.16290i | 0.247195 | + | 0.428154i | ||||
\(459\) | −0.500000 | − | 0.866025i | −0.0233380 | − | 0.0404226i | ||||
\(460\) | 1.77182 | − | 3.06888i | 0.0826115 | − | 0.143087i | ||||
\(461\) | −41.7045 | −1.94237 | −0.971185 | − | 0.238326i | \(-0.923401\pi\) | ||||
−0.971185 | + | 0.238326i | \(0.923401\pi\) | |||||||
\(462\) | −1.27182 | + | 2.32002i | −0.0591704 | + | 0.107937i | ||||
\(463\) | −28.5804 | −1.32824 | −0.664122 | − | 0.747624i | \(-0.731195\pi\) | ||||
−0.664122 | + | 0.747624i | \(0.731195\pi\) | |||||||
\(464\) | −2.27182 | + | 3.93491i | −0.105467 | + | 0.182673i | ||||
\(465\) | −6.98627 | − | 12.1006i | −0.323981 | − | 0.561151i | ||||
\(466\) | 3.53677 | + | 6.12587i | 0.163838 | + | 0.283776i | ||||
\(467\) | −2.69141 | + | 4.66166i | −0.124544 | + | 0.215716i | −0.921554 | − | 0.388249i | \(-0.873080\pi\) |
0.797011 | + | 0.603965i | \(0.206413\pi\) | |||||||
\(468\) | 5.49314 | 0.253920 | ||||||||
\(469\) | −4.50686 | + | 8.22130i | −0.208108 | + | 0.379624i | ||||
\(470\) | −25.5162 | −1.17697 | ||||||||
\(471\) | −9.05516 | + | 15.6840i | −0.417240 | + | 0.722680i | ||||
\(472\) | 4.76496 | + | 8.25314i | 0.219325 | + | 0.379882i | ||||
\(473\) | 2.01839 | + | 3.49595i | 0.0928055 | + | 0.160744i | ||||
\(474\) | −6.11985 | + | 10.5999i | −0.281094 | + | 0.486869i | ||||
\(475\) | −20.4426 | −0.937972 | ||||||||
\(476\) | 2.64510 | − | 0.0585812i | 0.121238 | − | 0.00268506i | ||||
\(477\) | 5.49314 | 0.251513 | ||||||||
\(478\) | −3.83384 | + | 6.64041i | −0.175356 | + | 0.303725i | ||||
\(479\) | −7.23970 | − | 12.5395i | −0.330791 | − | 0.572946i | 0.651877 | − | 0.758325i | \(-0.273982\pi\) |
−0.982667 | + | 0.185379i | \(0.940649\pi\) | |||||||
\(480\) | −1.37328 | − | 2.37860i | −0.0626816 | − | 0.108568i | ||||
\(481\) | 11.0873 | − | 19.2037i | 0.505536 | − | 0.875614i | ||||
\(482\) | −25.0598 | −1.14144 | ||||||||
\(483\) | 1.77182 | + | 2.91772i | 0.0806205 | + | 0.132761i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0.119852 | − | 0.207590i | 0.00544222 | − | 0.00942619i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 4.21666 | + | 7.30347i | 0.191075 | + | 0.330952i | 0.945607 | − | 0.325312i | \(-0.105469\pi\) |
−0.754532 | + | 0.656264i | \(0.772136\pi\) | |||||||
\(488\) | 0.829647 | − | 1.43699i | 0.0375564 | − | 0.0650495i | ||||
\(489\) | −13.4426 | −0.607897 | ||||||||
\(490\) | 19.2071 | − | 0.851179i | 0.867690 | − | 0.0384524i | ||||
\(491\) | −38.6770 | −1.74547 | −0.872734 | − | 0.488195i | \(-0.837655\pi\) | ||||
−0.872734 | + | 0.488195i | \(0.837655\pi\) | |||||||
\(492\) | −2.77182 | + | 4.80093i | −0.124963 | + | 0.216443i | ||||
\(493\) | −2.27182 | − | 3.93491i | −0.102318 | − | 0.177219i | ||||
\(494\) | 22.0735 | + | 38.2325i | 0.993136 | + | 1.72016i | ||||
\(495\) | −1.37328 | + | 2.37860i | −0.0617245 | + | 0.106910i | ||||
\(496\) | 5.08727 | 0.228425 | ||||||||
\(497\) | −3.49314 | − | 5.75227i | −0.156689 | − | 0.258025i | ||||
\(498\) | −14.5299 | −0.651101 | ||||||||
\(499\) | −19.0230 | + | 32.9489i | −0.851589 | + | 1.47499i | 0.0281856 | + | 0.999603i | \(0.491027\pi\) |
−0.879774 | + | 0.475392i | \(0.842306\pi\) | |||||||
\(500\) | 3.37328 | + | 5.84270i | 0.150858 | + | 0.261293i | ||||
\(501\) | −11.7833 | − | 20.4093i | −0.526441 | − | 0.911822i | ||||
\(502\) | 12.5115 | − | 21.6706i | 0.558417 | − | 0.967206i | ||||
\(503\) | 21.5667 | 0.961611 | 0.480805 | − | 0.876827i | \(-0.340344\pi\) | ||||
0.480805 | + | 0.876827i | \(0.340344\pi\) | |||||||
\(504\) | 2.64510 | − | 0.0585812i | 0.117822 | − | 0.00260941i | ||||
\(505\) | 35.7687 | 1.59169 | ||||||||
\(506\) | 0.645103 | − | 1.11735i | 0.0286783 | − | 0.0496723i | ||||
\(507\) | −8.58727 | − | 14.8736i | −0.381374 | − | 0.660560i | ||||
\(508\) | 3.39167 | + | 5.87455i | 0.150481 | + | 0.260641i | ||||
\(509\) | 13.3270 | − | 23.0830i | 0.590708 | − | 1.02314i | −0.403429 | − | 0.915011i | \(-0.632182\pi\) |
0.994137 | − | 0.108125i | \(-0.0344848\pi\) | |||||||
\(510\) | 2.74657 | 0.121620 | ||||||||
\(511\) | 10.9127 | − | 19.9067i | 0.482751 | − | 0.880620i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.01839 | − | 6.96005i | 0.177416 | − | 0.307294i | ||||
\(514\) | 5.25343 | + | 9.09921i | 0.231719 | + | 0.401349i | ||||
\(515\) | 24.8201 | + | 42.9897i | 1.09370 | + | 1.89435i | ||||
\(516\) | 2.01839 | − | 3.49595i | 0.0888545 | − | 0.153901i | ||||
\(517\) | −9.29021 | −0.408583 | ||||||||
\(518\) | 5.13404 | − | 9.36538i | 0.225577 | − | 0.411491i | ||||
\(519\) | −10.9127 | −0.479015 | ||||||||
\(520\) | −7.54364 | + | 13.0660i | −0.330810 | + | 0.572980i | ||||
\(521\) | 11.9863 | + | 20.7608i | 0.525128 | + | 0.909549i | 0.999572 | + | 0.0292627i | \(0.00931595\pi\) |
−0.474444 | + | 0.880286i | \(0.657351\pi\) | |||||||
\(522\) | −2.27182 | − | 3.93491i | −0.0994348 | − | 0.172226i | ||||
\(523\) | −10.3407 | + | 17.9106i | −0.452168 | + | 0.783177i | −0.998520 | − | 0.0543780i | \(-0.982682\pi\) |
0.546353 | + | 0.837555i | \(0.316016\pi\) | |||||||
\(524\) | −13.8990 | −0.607181 | ||||||||
\(525\) | 6.72818 | − | 0.149009i | 0.293642 | − | 0.00650330i | ||||
\(526\) | 23.6402 | 1.03076 | ||||||||
\(527\) | −2.54364 | + | 4.40571i | −0.110803 | + | 0.191916i | ||||
\(528\) | −0.500000 | − | 0.866025i | −0.0217597 | − | 0.0376889i | ||||
\(529\) | 10.6677 | + | 18.4770i | 0.463812 | + | 0.803347i | ||||
\(530\) | −7.54364 | + | 13.0660i | −0.327675 | + | 0.567549i | ||||
\(531\) | −9.52991 | −0.413563 | ||||||||
\(532\) | 11.0368 | + | 18.1746i | 0.478505 | + | 0.787971i | ||||
\(533\) | 30.4520 | 1.31902 | ||||||||
\(534\) | 3.25343 | − | 5.63511i | 0.140790 | − | 0.243855i | ||||
\(535\) | −23.9537 | − | 41.4890i | −1.03561 | − | 1.79373i | ||||
\(536\) | −1.77182 | − | 3.06888i | −0.0765309 | − | 0.132555i | ||||
\(537\) | 6.47475 | − | 11.2146i | 0.279406 | − | 0.483946i | ||||
\(538\) | −15.1524 | −0.653268 | ||||||||
\(539\) | 6.99314 | − | 0.309906i | 0.301216 | − | 0.0133486i | ||||
\(540\) | 2.74657 | 0.118193 | ||||||||
\(541\) | −17.9537 | + | 31.0967i | −0.771890 | + | 1.33695i | 0.164637 | + | 0.986354i | \(0.447355\pi\) |
−0.936526 | + | 0.350598i | \(0.885978\pi\) | |||||||
\(542\) | −9.49314 | − | 16.4426i | −0.407765 | − | 0.706270i | ||||
\(543\) | −3.79707 | − | 6.57672i | −0.162948 | − | 0.282234i | ||||
\(544\) | −0.500000 | + | 0.866025i | −0.0214373 | + | 0.0371305i | ||||
\(545\) | 4.55736 | 0.195216 | ||||||||
\(546\) | −7.54364 | − | 12.4224i | −0.322838 | − | 0.531629i | ||||
\(547\) | −5.12405 | −0.219088 | −0.109544 | − | 0.993982i | \(-0.534939\pi\) | ||||
−0.109544 | + | 0.993982i | \(0.534939\pi\) | |||||||
\(548\) | −2.74657 | + | 4.75720i | −0.117328 | + | 0.203217i | ||||
\(549\) | 0.829647 | + | 1.43699i | 0.0354085 | + | 0.0613293i | ||||
\(550\) | −1.27182 | − | 2.20285i | −0.0542305 | − | 0.0939300i | ||||
\(551\) | 18.2581 | − | 31.6239i | 0.777821 | − | 1.34723i | ||||
\(552\) | −1.29021 | −0.0549148 | ||||||||
\(553\) | 32.3753 | − | 0.717016i | 1.37674 | − | 0.0304906i | ||||
\(554\) | 24.4794 | 1.04003 | ||||||||
\(555\) | 5.54364 | − | 9.60186i | 0.235314 | − | 0.407576i | ||||
\(556\) | −6.81546 | − | 11.8047i | −0.289040 | − | 0.500631i | ||||
\(557\) | 6.43798 | + | 11.1509i | 0.272786 | + | 0.472479i | 0.969574 | − | 0.244798i | \(-0.0787216\pi\) |
−0.696788 | + | 0.717277i | \(0.745388\pi\) | |||||||
\(558\) | −2.54364 | + | 4.40571i | −0.107681 | + | 0.186509i | ||||
\(559\) | −22.1745 | −0.937883 | ||||||||
\(560\) | −3.49314 | + | 6.37208i | −0.147612 | + | 0.269270i | ||||
\(561\) | 1.00000 | 0.0422200 | ||||||||
\(562\) | 6.04364 | − | 10.4679i | 0.254935 | − | 0.441561i | ||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 4.64510 | + | 8.04555i | 0.195594 | + | 0.338779i | ||||
\(565\) | 9.73284 | − | 16.8578i | 0.409464 | − | 0.709212i | ||||
\(566\) | 4.68141 | 0.196774 | ||||||||
\(567\) | −1.27182 | + | 2.32002i | −0.0534114 | + | 0.0974315i | ||||
\(568\) | 2.54364 | 0.106729 | ||||||||
\(569\) | −10.6777 | + | 18.4943i | −0.447632 | + | 0.775321i | −0.998231 | − | 0.0594486i | \(-0.981066\pi\) |
0.550600 | + | 0.834769i | \(0.314399\pi\) | |||||||
\(570\) | 11.0368 | + | 19.1163i | 0.462280 | + | 0.800692i | ||||
\(571\) | −3.72818 | − | 6.45740i | −0.156020 | − | 0.270234i | 0.777410 | − | 0.628994i | \(-0.216533\pi\) |
−0.933430 | + | 0.358760i | \(0.883200\pi\) | |||||||
\(572\) | −2.74657 | + | 4.75720i | −0.114840 | + | 0.198908i | ||||
\(573\) | 18.9863 | 0.793163 | ||||||||
\(574\) | 14.6635 | − | 0.324753i | 0.612042 | − | 0.0135549i | ||||
\(575\) | −3.28181 | −0.136861 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −2.82232 | − | 4.88840i | −0.117495 | − | 0.203507i | 0.801280 | − | 0.598290i | \(-0.204153\pi\) |
−0.918774 | + | 0.394783i | \(0.870820\pi\) | |||||||
\(578\) | 8.00000 | + | 13.8564i | 0.332756 | + | 0.576351i | ||||
\(579\) | 10.7833 | − | 18.6773i | 0.448140 | − | 0.776202i | ||||
\(580\) | 12.4794 | 0.518179 | ||||||||
\(581\) | 19.9537 | + | 32.8585i | 0.827819 | + | 1.36320i | ||||
\(582\) | −0.0872743 | −0.00361763 | ||||||||
\(583\) | −2.74657 | + | 4.75720i | −0.113751 | + | 0.197023i | ||||
\(584\) | 4.29021 | + | 7.43085i | 0.177530 | + | 0.307491i | ||||
\(585\) | −7.54364 | − | 13.0660i | −0.311891 | − | 0.540211i | ||||
\(586\) | 5.81546 | − | 10.0727i | 0.240234 | − | 0.416098i | ||||
\(587\) | −34.4059 | −1.42008 | −0.710041 | − | 0.704160i | \(-0.751324\pi\) | ||||
−0.710041 | + | 0.704160i | \(0.751324\pi\) | |||||||
\(588\) | −3.76496 | − | 5.90128i | −0.155264 | − | 0.243365i | ||||
\(589\) | −40.8853 | −1.68465 | ||||||||
\(590\) | 13.0873 | − | 22.6678i | 0.538795 | − | 0.933220i | ||||
\(591\) | 1.56202 | + | 2.70550i | 0.0642531 | + | 0.111290i | ||||
\(592\) | 2.01839 | + | 3.49595i | 0.0829552 | + | 0.143683i | ||||
\(593\) | 9.35909 | − | 16.2104i | 0.384332 | − | 0.665682i | −0.607344 | − | 0.794439i | \(-0.707765\pi\) |
0.991676 | + | 0.128756i | \(0.0410985\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | −3.77182 | − | 6.21119i | −0.154629 | − | 0.254634i | ||||
\(596\) | 16.0368 | 0.656892 | ||||||||
\(597\) | 13.0368 | − | 22.5804i | 0.533560 | − | 0.924152i | ||||
\(598\) | 3.54364 | + | 6.13776i | 0.144910 | + | 0.250992i | ||||
\(599\) | −5.20713 | − | 9.01901i | −0.212757 | − | 0.368507i | 0.739819 | − | 0.672806i | \(-0.234911\pi\) |
−0.952577 | + | 0.304299i | \(0.901578\pi\) | |||||||
\(600\) | −1.27182 | + | 2.20285i | −0.0519218 | + | 0.0899312i | ||||
\(601\) | 25.0873 | 1.02333 | 0.511666 | − | 0.859185i | \(-0.329029\pi\) | ||||
0.511666 | + | 0.859185i | \(0.329029\pi\) | |||||||
\(602\) | −10.6777 | + | 0.236479i | −0.435190 | + | 0.00963816i | ||||
\(603\) | 3.54364 | 0.144308 | ||||||||
\(604\) | 2.84803 | − | 4.93294i | 0.115885 | − | 0.200718i | ||||
\(605\) | −1.37328 | − | 2.37860i | −0.0558319 | − | 0.0967038i | ||||
\(606\) | −6.51152 | − | 11.2783i | −0.264513 | − | 0.458149i | ||||
\(607\) | −15.9537 | + | 27.6326i | −0.647541 | + | 1.12157i | 0.336168 | + | 0.941802i | \(0.390869\pi\) |
−0.983708 | + | 0.179771i | \(0.942464\pi\) | |||||||
\(608\) | −8.03677 | −0.325934 | ||||||||
\(609\) | −5.77868 | + | 10.5413i | −0.234164 | + | 0.427156i | ||||
\(610\) | −4.55736 | −0.184522 | ||||||||
\(611\) | 25.5162 | − | 44.1953i | 1.03227 | − | 1.78795i | ||||
\(612\) | −0.500000 | − | 0.866025i | −0.0202113 | − | 0.0350070i | ||||
\(613\) | −1.71399 | − | 2.96872i | −0.0692274 | − | 0.119905i | 0.829334 | − | 0.558753i | \(-0.188720\pi\) |
−0.898561 | + | 0.438848i | \(0.855387\pi\) | |||||||
\(614\) | 7.03677 | − | 12.1880i | 0.283981 | − | 0.491870i | ||||
\(615\) | 15.2260 | 0.613971 | ||||||||
\(616\) | −1.27182 | + | 2.32002i | −0.0512430 | + | 0.0934761i | ||||
\(617\) | 12.7550 | 0.513495 | 0.256748 | − | 0.966478i | \(-0.417349\pi\) | ||||
0.256748 | + | 0.966478i | \(0.417349\pi\) | |||||||
\(618\) | 9.03677 | − | 15.6522i | 0.363512 | − | 0.629622i | ||||
\(619\) | 10.7949 | + | 18.6973i | 0.433882 | + | 0.751506i | 0.997204 | − | 0.0747317i | \(-0.0238100\pi\) |
−0.563321 | + | 0.826238i | \(0.690477\pi\) | |||||||
\(620\) | −6.98627 | − | 12.1006i | −0.280575 | − | 0.485971i | ||||
\(621\) | 0.645103 | − | 1.11735i | 0.0258871 | − | 0.0448377i | ||||
\(622\) | 12.2765 | 0.492242 | ||||||||
\(623\) | −17.2113 | + | 0.381180i | −0.689557 | + | 0.0152716i | ||||
\(624\) | 5.49314 | 0.219901 | ||||||||
\(625\) | 15.6240 | − | 27.0616i | 0.624962 | − | 1.08247i | ||||
\(626\) | −11.7282 | − | 20.3138i | −0.468752 | − | 0.811903i | ||||
\(627\) | 4.01839 | + | 6.96005i | 0.160479 | + | 0.277958i | ||||
\(628\) | −9.05516 | + | 15.6840i | −0.361340 | + | 0.625860i | ||||
\(629\) | −4.03677 | −0.160957 | ||||||||
\(630\) | −3.77182 | − | 6.21119i | −0.150273 | − | 0.247460i | ||||
\(631\) | 4.23131 | 0.168446 | 0.0842230 | − | 0.996447i | \(-0.473159\pi\) | ||||
0.0842230 | + | 0.996447i | \(0.473159\pi\) | |||||||
\(632\) | −6.11985 | + | 10.5999i | −0.243435 | + | 0.421641i | ||||
\(633\) | −7.83384 | − | 13.5686i | −0.311367 | − | 0.539304i | ||||
\(634\) | 0.286010 | + | 0.495384i | 0.0113589 | + | 0.0196742i | ||||
\(635\) | 9.31546 | − | 16.1348i | 0.369673 | − | 0.640292i | ||||
\(636\) | 5.49314 | 0.217817 | ||||||||
\(637\) | −17.7328 | + | 34.1189i | −0.702601 | + | 1.35184i | ||||
\(638\) | 4.54364 | 0.179884 | ||||||||
\(639\) | −1.27182 | + | 2.20285i | −0.0503124 | + | 0.0871436i | ||||
\(640\) | −1.37328 | − | 2.37860i | −0.0542838 | − | 0.0940223i | ||||
\(641\) | −2.03677 | − | 3.52780i | −0.0804477 | − | 0.139340i | 0.822995 | − | 0.568049i | \(-0.192302\pi\) |
−0.903442 | + | 0.428710i | \(0.858968\pi\) | |||||||
\(642\) | −8.72132 | + | 15.1058i | −0.344203 | + | 0.596177i | ||||
\(643\) | −19.2618 | −0.759612 | −0.379806 | − | 0.925066i | \(-0.624009\pi\) | ||||
−0.379806 | + | 0.925066i | \(0.624009\pi\) | |||||||
\(644\) | 1.77182 | + | 2.91772i | 0.0698194 | + | 0.114974i | ||||
\(645\) | −11.0873 | −0.436561 | ||||||||
\(646\) | 4.01839 | − | 6.96005i | 0.158101 | − | 0.273840i | ||||
\(647\) | 9.44683 | + | 16.3624i | 0.371393 | + | 0.643272i | 0.989780 | − | 0.142602i | \(-0.0455468\pi\) |
−0.618387 | + | 0.785874i | \(0.712214\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 4.76496 | − | 8.25314i | 0.187041 | − | 0.323964i | ||||
\(650\) | 13.9725 | 0.548048 | ||||||||
\(651\) | 13.4564 | − | 0.298018i | 0.527396 | − | 0.0116803i | ||||
\(652\) | −13.4426 | −0.526454 | ||||||||
\(653\) | 4.46056 | − | 7.72591i | 0.174555 | − | 0.302338i | −0.765452 | − | 0.643493i | \(-0.777485\pi\) |
0.940007 | + | 0.341155i | \(0.110818\pi\) | |||||||
\(654\) | −0.829647 | − | 1.43699i | −0.0324418 | − | 0.0561908i | ||||
\(655\) | 19.0873 | + | 33.0601i | 0.745802 | + | 1.29177i | ||||
\(656\) | −2.77182 | + | 4.80093i | −0.108221 | + | 0.187445i | ||||
\(657\) | −8.58041 | −0.334754 | ||||||||
\(658\) | 11.8155 | − | 21.5534i | 0.460614 | − | 0.840240i | ||||
\(659\) | 45.4426 | 1.77019 | 0.885097 | − | 0.465407i | \(-0.154092\pi\) | ||||
0.885097 | + | 0.465407i | \(0.154092\pi\) | |||||||
\(660\) | −1.37328 | + | 2.37860i | −0.0534550 | + | 0.0925868i | ||||
\(661\) | 14.5115 | + | 25.1347i | 0.564433 | + | 0.977626i | 0.997102 | + | 0.0760737i | \(0.0242384\pi\) |
−0.432669 | + | 0.901553i | \(0.642428\pi\) | |||||||
\(662\) | −3.85909 | − | 6.68414i | −0.149988 | − | 0.259787i | ||||
\(663\) | −2.74657 | + | 4.75720i | −0.106668 | + | 0.184754i | ||||
\(664\) | −14.5299 | −0.563870 | ||||||||
\(665\) | 28.0735 | − | 51.2110i | 1.08865 | − | 1.98588i | ||||
\(666\) | −4.03677 | −0.156422 | ||||||||
\(667\) | 2.93111 | − | 5.07684i | 0.113493 | − | 0.196576i | ||||
\(668\) | −11.7833 | − | 20.4093i | −0.455911 | − | 0.789661i | ||||
\(669\) | −1.20293 | − | 2.08354i | −0.0465080 | − | 0.0805542i | ||||
\(670\) | −4.86642 | + | 8.42889i | −0.188006 | + | 0.325636i | ||||
\(671\) | −1.65929 | −0.0640563 | ||||||||
\(672\) | 2.64510 | − | 0.0585812i | 0.102037 | − | 0.00225982i | ||||
\(673\) | −16.2481 | −0.626318 | −0.313159 | − | 0.949701i | \(-0.601387\pi\) | ||||
−0.313159 | + | 0.949701i | \(0.601387\pi\) | |||||||
\(674\) | −14.2765 | + | 24.7276i | −0.549909 | + | 0.952471i | ||||
\(675\) | −1.27182 | − | 2.20285i | −0.0489523 | − | 0.0847879i | ||||
\(676\) | −8.58727 | − | 14.8736i | −0.330280 | − | 0.572061i | ||||
\(677\) | 1.94484 | − | 3.36856i | 0.0747463 | − | 0.129464i | −0.826230 | − | 0.563333i | \(-0.809519\pi\) |
0.900976 | + | 0.433869i | \(0.142852\pi\) | |||||||
\(678\) | −7.08727 | −0.272185 | ||||||||
\(679\) | 0.119852 | + | 0.197365i | 0.00459951 | + | 0.00757418i | ||||
\(680\) | 2.74657 | 0.105326 | ||||||||
\(681\) | −1.22818 | + | 2.12727i | −0.0470640 | + | 0.0815173i | ||||
\(682\) | −2.54364 | − | 4.40571i | −0.0974009 | − | 0.168703i | ||||
\(683\) | −2.90273 | − | 5.02768i | −0.111070 | − | 0.192379i | 0.805132 | − | 0.593096i | \(-0.202094\pi\) |
−0.916202 | + | 0.400717i | \(0.868761\pi\) | |||||||
\(684\) | 4.01839 | − | 6.96005i | 0.153647 | − | 0.266124i | ||||
\(685\) | 15.0873 | 0.576455 | ||||||||
\(686\) | −8.17501 | + | 16.6183i | −0.312123 | + | 0.634491i | ||||
\(687\) | −10.5804 | −0.403668 | ||||||||
\(688\) | 2.01839 | − | 3.49595i | 0.0769503 | − | 0.133282i | ||||
\(689\) | −15.0873 | − | 26.1319i | −0.574779 | − | 0.995547i | ||||
\(690\) | 1.77182 | + | 3.06888i | 0.0674520 | + | 0.116830i | ||||
\(691\) | 3.17768 | − | 5.50390i | 0.120885 | − | 0.209378i | −0.799232 | − | 0.601022i | \(-0.794760\pi\) |
0.920117 | + | 0.391644i | \(0.128094\pi\) | |||||||
\(692\) | −10.9127 | −0.414840 | ||||||||
\(693\) | −1.37328 | − | 2.26144i | −0.0521668 | − | 0.0859048i | ||||
\(694\) | −23.4426 | −0.889870 | ||||||||
\(695\) | −18.7191 | + | 32.4225i | −0.710056 | + | 1.22985i | ||||
\(696\) | −2.27182 | − | 3.93491i | −0.0861131 | − | 0.149152i | ||||
\(697\) | −2.77182 | − | 4.80093i | −0.104990 | − | 0.181848i | ||||
\(698\) | −12.8664 | + | 22.2853i | −0.487001 | + | 0.843511i | ||||
\(699\) | −7.07355 | −0.267546 | ||||||||
\(700\) | 6.72818 | − | 0.149009i | 0.254301 | − | 0.00563202i | ||||
\(701\) | 5.86223 | 0.221413 | 0.110707 | − | 0.993853i | \(-0.464689\pi\) | ||||
0.110707 | + | 0.993853i | \(0.464689\pi\) | |||||||
\(702\) | −2.74657 | + | 4.75720i | −0.103663 | + | 0.179549i | ||||
\(703\) | −16.2213 | − | 28.0961i | −0.611799 | − | 1.05967i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | 12.7581 | − | 22.0977i | 0.480498 | − | 0.832246i | ||||
\(706\) | −18.4059 | −0.692714 | ||||||||
\(707\) | −16.5630 | + | 30.2137i | −0.622914 | + | 1.13630i | ||||
\(708\) | −9.52991 | −0.358156 | ||||||||
\(709\) | 6.72818 | − | 11.6536i | 0.252682 | − | 0.437658i | −0.711581 | − | 0.702604i | \(-0.752021\pi\) |
0.964263 | + | 0.264946i | \(0.0853540\pi\) | |||||||
\(710\) | −3.49314 | − | 6.05029i | −0.131095 | − | 0.227063i | ||||
\(711\) | −6.11985 | − | 10.5999i | −0.229512 | − | 0.397527i | ||||
\(712\) | 3.25343 | − | 5.63511i | 0.121928 | − | 0.211185i | ||||
\(713\) | −6.56363 | −0.245810 | ||||||||
\(714\) | −1.27182 | + | 2.32002i | −0.0475966 | + | 0.0868244i | ||||
\(715\) | 15.0873 | 0.564232 | ||||||||
\(716\) | 6.47475 | − | 11.2146i | 0.241973 | − | 0.419109i | ||||
\(717\) | −3.83384 | − | 6.64041i | −0.143177 | − | 0.247991i | ||||
\(718\) | 15.9863 | + | 27.6890i | 0.596602 | + | 1.03335i | ||||
\(719\) | 12.1382 | − | 21.0240i | 0.452680 | − | 0.784065i | −0.545872 | − | 0.837869i | \(-0.683801\pi\) |
0.998552 | + | 0.0538042i | \(0.0171347\pi\) | |||||||
\(720\) | 2.74657 | 0.102359 | ||||||||
\(721\) | −47.8064 | + | 1.05877i | −1.78040 | + | 0.0394306i | ||||
\(722\) | 45.5897 | 1.69667 | ||||||||
\(723\) | 12.5299 | − | 21.7024i | 0.465992 | − | 0.807122i | ||||
\(724\) | −3.79707 | − | 6.57672i | −0.141117 | − | 0.244422i | ||||
\(725\) | −5.77868 | − | 10.0090i | −0.214615 | − | 0.371724i | ||||
\(726\) | −0.500000 | + | 0.866025i | −0.0185567 | + | 0.0321412i | ||||
\(727\) | −22.1471 | −0.821390 | −0.410695 | − | 0.911773i | \(-0.634714\pi\) | ||||
−0.410695 | + | 0.911773i | \(0.634714\pi\) | |||||||
\(728\) | −7.54364 | − | 12.4224i | −0.279586 | − | 0.460404i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.7833 | − | 20.4093i | 0.436121 | − | 0.755384i | ||||
\(731\) | 2.01839 | + | 3.49595i | 0.0746527 | + | 0.129302i | ||||
\(732\) | 0.829647 | + | 1.43699i | 0.0306646 | + | 0.0531127i | ||||
\(733\) | 2.66349 | − | 4.61330i | 0.0983782 | − | 0.170396i | −0.812635 | − | 0.582773i | \(-0.801968\pi\) |
0.911014 | + | 0.412377i | \(0.135301\pi\) | |||||||
\(734\) | 36.4794 | 1.34648 | ||||||||
\(735\) | −8.86642 | + | 17.0594i | −0.327043 | + | 0.629247i | ||||
\(736\) | −1.29021 | −0.0475576 | ||||||||
\(737\) | −1.77182 | + | 3.06888i | −0.0652658 | + | 0.113044i | ||||
\(738\) | −2.77182 | − | 4.80093i | −0.102032 | − | 0.176725i | ||||
\(739\) | 12.6309 | + | 21.8774i | 0.464636 | + | 0.804772i | 0.999185 | − | 0.0403648i | \(-0.0128520\pi\) |
−0.534549 | + | 0.845137i | \(0.679519\pi\) | |||||||
\(740\) | 5.54364 | − | 9.60186i | 0.203788 | − | 0.352971i | ||||
\(741\) | −44.1471 | −1.62178 | ||||||||
\(742\) | −7.54364 | − | 12.4224i | −0.276936 | − | 0.456040i | ||||
\(743\) | −25.4196 | −0.932554 | −0.466277 | − | 0.884639i | \(-0.654405\pi\) | ||||
−0.466277 | + | 0.884639i | \(0.654405\pi\) | |||||||
\(744\) | −2.54364 | + | 4.40571i | −0.0932543 | + | 0.161521i | ||||
\(745\) | −22.0230 | − | 38.1450i | −0.806862 | − | 1.39753i | ||||
\(746\) | 10.1566 | + | 17.5918i | 0.371860 | + | 0.644081i | ||||
\(747\) | 7.26496 | − | 12.5833i | 0.265811 | − | 0.460398i | ||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | 46.1376 | − | 1.02181i | 1.68583 | − | 0.0373361i | ||||
\(750\) | −6.74657 | −0.246350 | ||||||||
\(751\) | 20.2765 | − | 35.1199i | 0.739899 | − | 1.28154i | −0.212641 | − | 0.977130i | \(-0.568206\pi\) |
0.952540 | − | 0.304413i | \(-0.0984602\pi\) | |||||||
\(752\) | 4.64510 | + | 8.04555i | 0.169389 | + | 0.293391i | ||||
\(753\) | 12.5115 | + | 21.6706i | 0.455945 | + | 0.789720i | ||||
\(754\) | −12.4794 | + | 21.6150i | −0.454473 | + | 0.787171i | ||||
\(755\) | −15.6446 | −0.569367 | ||||||||
\(756\) | −1.27182 | + | 2.32002i | −0.0462556 | + | 0.0843782i | ||||
\(757\) | 13.3554 | 0.485409 | 0.242704 | − | 0.970100i | \(-0.421965\pi\) | ||||
0.242704 | + | 0.970100i | \(0.421965\pi\) | |||||||
\(758\) | −4.72132 | + | 8.17756i | −0.171486 | + | 0.297022i | ||||
\(759\) | 0.645103 | + | 1.11735i | 0.0234157 | + | 0.0405573i | ||||
\(760\) | 11.0368 | + | 19.1163i | 0.400346 | + | 0.693419i | ||||
\(761\) | −9.22818 | + | 15.9837i | −0.334521 | + | 0.579408i | −0.983393 | − | 0.181490i | \(-0.941908\pi\) |
0.648871 | + | 0.760898i | \(0.275241\pi\) | |||||||
\(762\) | −6.78334 | −0.245735 | ||||||||
\(763\) | −2.11032 | + | 3.84959i | −0.0763987 | + | 0.139365i | ||||
\(764\) | 18.9863 | 0.686899 | ||||||||
\(765\) | −1.37328 | + | 2.37860i | −0.0496512 | + | 0.0859984i | ||||
\(766\) | −11.8522 | − | 20.5287i | −0.428238 | − | 0.741731i | ||||
\(767\) | 26.1745 | + | 45.3356i | 0.945108 | + | 1.63698i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 49.9158 | 1.80001 | 0.900005 | − | 0.435881i | \(-0.143563\pi\) | ||||
0.900005 | + | 0.435881i | \(0.143563\pi\) | |||||||
\(770\) | 7.26496 | − | 0.160897i | 0.261811 | − | 0.00579833i | ||||
\(771\) | −10.5069 | −0.378395 | ||||||||
\(772\) | 10.7833 | − | 18.6773i | 0.388101 | − | 0.672211i | ||||
\(773\) | 21.0694 | + | 36.4932i | 0.757812 | + | 1.31257i | 0.943964 | + | 0.330048i | \(0.107065\pi\) |
−0.186152 | + | 0.982521i | \(0.559602\pi\) | |||||||
\(774\) | 2.01839 | + | 3.49595i | 0.0725494 | + | 0.125659i | ||||
\(775\) | −6.47009 | + | 11.2065i | −0.232412 | + | 0.402550i | ||||
\(776\) | −0.0872743 | −0.00313296 | ||||||||
\(777\) | 5.54364 | + | 9.12890i | 0.198877 | + | 0.327498i | ||||
\(778\) | −1.25343 | −0.0449377 | ||||||||
\(779\) | 22.2765 | − | 38.5840i | 0.798138 | − | 1.38241i | ||||
\(780\) | −7.54364 | − | 13.0660i | −0.270106 | − | 0.467837i | ||||
\(781\) | −1.27182 | − | 2.20285i | −0.0455092 | − | 0.0788243i | ||||
\(782\) | 0.645103 | − | 1.11735i | 0.0230688 | − | 0.0399564i | ||||
\(783\) | 4.54364 | 0.162376 | ||||||||
\(784\) | −3.76496 | − | 5.90128i | −0.134463 | − | 0.210760i | ||||
\(785\) | 49.7412 | 1.77534 | ||||||||
\(786\) | 6.94950 | − | 12.0369i | 0.247880 | − | 0.429342i | ||||
\(787\) | 17.1792 | + | 29.7553i | 0.612373 | + | 1.06066i | 0.990839 | + | 0.135046i | \(0.0431181\pi\) |
−0.378467 | + | 0.925615i | \(0.623549\pi\) | |||||||
\(788\) | 1.56202 | + | 2.70550i | 0.0556448 | + | 0.0963796i | ||||
\(789\) | −11.8201 | + | 20.4730i | −0.420807 | + | 0.728860i | ||||
\(790\) | 33.6172 | 1.19605 | ||||||||
\(791\) | 9.73284 | + | 16.0274i | 0.346060 | + | 0.569869i | ||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 4.55736 | − | 7.89359i | 0.161837 | − | 0.280309i | ||||
\(794\) | −14.3086 | − | 24.7832i | −0.507793 | − | 0.879523i | ||||
\(795\) | −7.54364 | − | 13.0660i | −0.267545 | − | 0.463402i | ||||
\(796\) | 13.0368 | − | 22.5804i | 0.462076 | − | 0.800339i | ||||
\(797\) | −18.1387 | −0.642506 | −0.321253 | − | 0.946993i | \(-0.604104\pi\) | ||||
−0.321253 | + | 0.946993i | \(0.604104\pi\) | |||||||
\(798\) | −21.2581 | + | 0.470804i | −0.752528 | + | 0.0166663i | ||||
\(799\) | −9.29021 | −0.328664 | ||||||||
\(800\) | −1.27182 | + | 2.20285i | −0.0449656 | + | 0.0778827i | ||||
\(801\) | 3.25343 | + | 5.63511i | 0.114954 | + | 0.199107i | ||||
\(802\) | −0.202931 | − | 0.351487i | −0.00716575 | − | 0.0124114i | ||||
\(803\) | 4.29021 | − | 7.43085i | 0.151398 | − | 0.262229i | ||||
\(804\) | 3.54364 | 0.124974 | ||||||||
\(805\) | 4.50686 | − | 8.22130i | 0.158846 | − | 0.289763i | ||||
\(806\) | 27.9451 | 0.984324 | ||||||||
\(807\) | 7.57622 | − | 13.1224i | 0.266695 | − | 0.461930i | ||||
\(808\) | −6.51152 | − | 11.2783i | −0.229075 | − | 0.396769i | ||||
\(809\) | 8.77182 | + | 15.1932i | 0.308401 | + | 0.534166i | 0.978013 | − | 0.208545i | \(-0.0668729\pi\) |
−0.669612 | + | 0.742711i | \(0.733540\pi\) | |||||||
\(810\) | −1.37328 | + | 2.37860i | −0.0482523 | + | 0.0835754i | ||||
\(811\) | −43.0873 | −1.51300 | −0.756499 | − | 0.653994i | \(-0.773092\pi\) | ||||
−0.756499 | + | 0.653994i | \(0.773092\pi\) | |||||||
\(812\) | −5.77868 | + | 10.5413i | −0.202792 | + | 0.369928i | ||||
\(813\) | 18.9863 | 0.665878 | ||||||||
\(814\) | 2.01839 | − | 3.49595i | 0.0707444 | − | 0.122533i | ||||
\(815\) | 18.4606 | + | 31.9746i | 0.646645 | + | 1.12002i | ||||
\(816\) | −0.500000 | − | 0.866025i | −0.0175035 | − | 0.0303170i | ||||
\(817\) | −16.2213 | + | 28.0961i | −0.567512 | + | 0.982960i | ||||
\(818\) | −32.7550 | −1.14525 | ||||||||
\(819\) | 14.5299 | − | 0.321794i | 0.507716 | − | 0.0112444i | ||||
\(820\) | 15.2260 | 0.531714 | ||||||||
\(821\) | −1.05050 | + | 1.81952i | −0.0366627 | + | 0.0635017i | −0.883775 | − | 0.467913i | \(-0.845006\pi\) |
0.847112 | + | 0.531415i | \(0.178339\pi\) | |||||||
\(822\) | −2.74657 | − | 4.75720i | −0.0957976 | − | 0.165926i | ||||
\(823\) | −9.87062 | − | 17.0964i | −0.344068 | − | 0.595943i | 0.641116 | − | 0.767444i | \(-0.278472\pi\) |
−0.985184 | + | 0.171501i | \(0.945138\pi\) | |||||||
\(824\) | 9.03677 | − | 15.6522i | 0.314811 | − | 0.545269i | ||||
\(825\) | 2.54364 | 0.0885581 | ||||||||
\(826\) | 13.0873 | + | 21.5513i | 0.455365 | + | 0.749865i | ||||
\(827\) | 23.7182 | 0.824762 | 0.412381 | − | 0.911011i | \(-0.364697\pi\) | ||||
0.412381 | + | 0.911011i | \(0.364697\pi\) | |||||||
\(828\) | 0.645103 | − | 1.11735i | 0.0224189 | − | 0.0388306i | ||||
\(829\) | −19.9816 | − | 34.6092i | −0.693990 | − | 1.20203i | −0.970520 | − | 0.241021i | \(-0.922518\pi\) |
0.276530 | − | 0.961005i | \(-0.410816\pi\) | |||||||
\(830\) | 19.9537 | + | 34.5608i | 0.692603 | + | 1.19962i | ||||
\(831\) | −12.2397 | + | 21.1998i | −0.424591 | + | 0.735413i | ||||
\(832\) | 5.49314 | 0.190440 | ||||||||
\(833\) | 6.99314 | − | 0.309906i | 0.242298 | − | 0.0107376i | ||||
\(834\) | 13.6309 | 0.472000 | ||||||||
\(835\) | −32.3638 | + | 56.0557i | −1.11999 | + | 1.93989i | ||||
\(836\) | 4.01839 | + | 6.96005i | 0.138979 | + | 0.240718i | ||||
\(837\) | −2.54364 | − | 4.40571i | −0.0879210 | − | 0.152284i | ||||
\(838\) | 7.96789 | − | 13.8008i | 0.275246 | − | 0.476740i | ||||
\(839\) | 29.0682 | 1.00355 | 0.501773 | − | 0.864999i | \(-0.332681\pi\) | ||||
0.501773 | + | 0.864999i | \(0.332681\pi\) | |||||||
\(840\) | −3.77182 | − | 6.21119i | −0.130140 | − | 0.214306i | ||||
\(841\) | −8.35536 | −0.288116 | ||||||||
\(842\) | 13.5620 | − | 23.4901i | 0.467378 | − | 0.809523i | ||||
\(843\) | 6.04364 | + | 10.4679i | 0.208154 | + | 0.360533i | ||||
\(844\) | −7.83384 | − | 13.5686i | −0.269652 | − | 0.467051i | ||||
\(845\) | −23.5855 | + | 40.8513i | −0.811367 | + | 1.40533i | ||||
\(846\) | −9.29021 | −0.319404 | ||||||||
\(847\) | 2.64510 | − | 0.0585812i | 0.0908868 | − | 0.00201287i | ||||
\(848\) | 5.49314 | 0.188635 | ||||||||
\(849\) | −2.34071 | + | 4.05422i | −0.0803328 | + | 0.139141i | ||||
\(850\) | −1.27182 | − | 2.20285i | −0.0436230 | − | 0.0755573i | ||||
\(851\) | −2.60413 | − | 4.51049i | −0.0892685 | − | 0.154618i | ||||
\(852\) | −1.27182 | + | 2.20285i | −0.0435718 | + | 0.0754685i | ||||
\(853\) | 20.2397 | 0.692994 | 0.346497 | − | 0.938051i | \(-0.387371\pi\) | ||||
0.346497 | + | 0.938051i | \(0.387371\pi\) | |||||||
\(854\) | 2.11032 | − | 3.84959i | 0.0722137 | − | 0.131730i | ||||
\(855\) | −22.0735 | −0.754899 | ||||||||
\(856\) | −8.72132 | + | 15.1058i | −0.298089 | + | 0.516304i | ||||
\(857\) | 6.08041 | + | 10.5316i | 0.207703 | + | 0.359752i | 0.950991 | − | 0.309220i | \(-0.100068\pi\) |
−0.743288 | + | 0.668972i | \(0.766735\pi\) | |||||||
\(858\) | −2.74657 | − | 4.75720i | −0.0937663 | − | 0.162408i | ||||
\(859\) | 7.26496 | − | 12.5833i | 0.247877 | − | 0.429336i | −0.715060 | − | 0.699064i | \(-0.753600\pi\) |
0.962937 | + | 0.269728i | \(0.0869338\pi\) | |||||||
\(860\) | −11.0873 | −0.378073 | ||||||||
\(861\) | −7.05050 | + | 12.8613i | −0.240280 | + | 0.438313i | ||||
\(862\) | −40.6265 | −1.38374 | ||||||||
\(863\) | 6.79287 | − | 11.7656i | 0.231232 | − | 0.400506i | −0.726939 | − | 0.686702i | \(-0.759058\pi\) |
0.958171 | + | 0.286196i | \(0.0923910\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 14.9863 | + | 25.9570i | 0.509549 | + | 0.882564i | ||||
\(866\) | −0.550501 | + | 0.953495i | −0.0187068 | + | 0.0324011i | ||||
\(867\) | −16.0000 | −0.543388 | ||||||||
\(868\) | 13.4564 | − | 0.298018i | 0.456739 | − | 0.0101154i | ||||
\(869\) | 12.2397 | 0.415204 | ||||||||
\(870\) | −6.23970 | + | 10.8075i | −0.211546 | + | 0.366408i | ||||
\(871\) | −9.73284 | − | 16.8578i | −0.329785 | − | 0.571204i | ||||
\(872\) | −0.829647 | − | 1.43699i | −0.0280954 | − | 0.0486626i | ||||
\(873\) | 0.0436371 | − | 0.0755817i | 0.00147689 | − | 0.00255805i | ||||
\(874\) | 10.3691 | 0.350740 | ||||||||
\(875\) | 9.26496 | + | 15.2569i | 0.313213 | + | 0.515778i | ||||
\(876\) | −8.58041 | −0.289905 | ||||||||
\(877\) | 1.03258 | − | 1.78848i | 0.0348677 | − | 0.0603926i | −0.848065 | − | 0.529892i | \(-0.822232\pi\) |
0.882933 | + | 0.469500i | \(0.155566\pi\) | |||||||
\(878\) | −11.4284 | − | 19.7946i | −0.385691 | − | 0.668037i | ||||
\(879\) | 5.81546 | + | 10.0727i | 0.196150 | + | 0.339743i | ||||
\(880\) | −1.37328 | + | 2.37860i | −0.0462934 | + | 0.0801825i | ||||
\(881\) | −3.08727 | −0.104013 | −0.0520065 | − | 0.998647i | \(-0.516562\pi\) | ||||
−0.0520065 | + | 0.998647i | \(0.516562\pi\) | |||||||
\(882\) | 6.99314 | − | 0.309906i | 0.235471 | − | 0.0104351i | ||||
\(883\) | 21.8927 | 0.736749 | 0.368375 | − | 0.929677i | \(-0.379914\pi\) | ||||
0.368375 | + | 0.929677i | \(0.379914\pi\) | |||||||
\(884\) | −2.74657 | + | 4.75720i | −0.0923771 | + | 0.160002i | ||||
\(885\) | 13.0873 | + | 22.6678i | 0.439924 | + | 0.761971i | ||||
\(886\) | 4.77868 | + | 8.27692i | 0.160543 | + | 0.278069i | ||||
\(887\) | −18.8706 | + | 32.6849i | −0.633613 | + | 1.09745i | 0.353194 | + | 0.935550i | \(0.385096\pi\) |
−0.986807 | + | 0.161900i | \(0.948238\pi\) | |||||||
\(888\) | −4.03677 | −0.135465 | ||||||||
\(889\) | 9.31546 | + | 15.3401i | 0.312430 | + | 0.514490i | ||||
\(890\) | −17.8715 | −0.599056 | ||||||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | −1.20293 | − | 2.08354i | −0.0402771 | − | 0.0697620i | ||||
\(893\) | −37.3316 | − | 64.6603i | −1.24926 | − | 2.16377i | ||||
\(894\) | −8.01839 | + | 13.8883i | −0.268175 | + | 0.464493i | ||||
\(895\) | −35.5667 | −1.18886 | ||||||||
\(896\) | 2.64510 | − | 0.0585812i | 0.0883667 | − | 0.00195706i | ||||
\(897\) | −7.08727 | −0.236637 | ||||||||
\(898\) | −0.340706 | + | 0.590120i | −0.0113695 | + | 0.0196926i | ||||
\(899\) | −11.5574 | − | 20.0179i | −0.385460 | − | 0.667636i | ||||
\(900\) | −1.27182 | − | 2.20285i | −0.0423940 | − | 0.0734285i | ||||
\(901\) | −2.74657 | + | 4.75720i | −0.0915015 | + | 0.158485i | ||||
\(902\) | 5.54364 | 0.184583 | ||||||||
\(903\) | 5.13404 | − | 9.36538i | 0.170850 | − | 0.311660i | ||||
\(904\) | −7.08727 | −0.235719 | ||||||||
\(905\) | −10.4289 | + | 18.0634i | −0.346669 | + | 0.600448i | ||||
\(906\) | 2.84803 | + | 4.93294i | 0.0946196 | + | 0.163886i | ||||
\(907\) | −15.7949 | − | 27.3575i | −0.524460 | − | 0.908391i | −0.999594 | − | 0.0284780i | \(-0.990934\pi\) |
0.475135 | − | 0.879913i | \(-0.342399\pi\) | |||||||
\(908\) | −1.22818 | + | 2.12727i | −0.0407586 | + | 0.0705960i | ||||
\(909\) | 13.0230 | 0.431947 | ||||||||
\(910\) | −19.1883 | + | 35.0027i | −0.636085 | + | 1.16033i | ||||
\(911\) | −27.7422 | −0.919139 | −0.459569 | − | 0.888142i | \(-0.651996\pi\) | ||||
−0.459569 | + | 0.888142i | \(0.651996\pi\) | |||||||
\(912\) | 4.01839 | − | 6.96005i | 0.133062 | − | 0.230470i | ||||
\(913\) | 7.26496 | + | 12.5833i | 0.240435 | + | 0.416445i | ||||
\(914\) | −9.07355 | − | 15.7158i | −0.300126 | − | 0.519834i | ||||
\(915\) | 2.27868 | − | 3.94679i | 0.0753309 | − | 0.130477i | ||||
\(916\) | −10.5804 | −0.349587 | ||||||||
\(917\) | −36.7643 | + | 0.814220i | −1.21406 | + | 0.0268879i | ||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −9.46522 | + | 16.3942i | −0.312229 | + | 0.540796i | −0.978845 | − | 0.204605i | \(-0.934409\pi\) |
0.666616 | + | 0.745401i | \(0.267742\pi\) | |||||||
\(920\) | 1.77182 | + | 3.06888i | 0.0584151 | + | 0.101178i | ||||
\(921\) | 7.03677 | + | 12.1880i | 0.231870 | + | 0.401610i | ||||
\(922\) | 20.8522 | − | 36.1171i | 0.686732 | − | 1.18945i | ||||
\(923\) | 13.9725 | 0.459912 | ||||||||
\(924\) | −1.37328 | − | 2.26144i | −0.0451777 | − | 0.0743958i | ||||
\(925\) | −10.2681 | −0.337613 | ||||||||
\(926\) | 14.2902 | − | 24.7514i | 0.469605 | − | 0.813380i | ||||
\(927\) | 9.03677 | + | 15.6522i | 0.296807 | + | 0.514084i | ||||
\(928\) | −2.27182 | − | 3.93491i | −0.0745761 | − | 0.129170i | ||||
\(929\) | −6.88434 | + | 11.9240i | −0.225868 | + | 0.391215i | −0.956579 | − | 0.291472i | \(-0.905855\pi\) |
0.730712 | + | 0.682686i | \(0.239188\pi\) | |||||||
\(930\) | 13.9725 | 0.458178 | ||||||||
\(931\) | 30.2581 | + | 47.4273i | 0.991669 | + | 1.55437i | ||||
\(932\) | −7.07355 | −0.231702 | ||||||||
\(933\) | −6.13824 | + | 10.6317i | −0.200957 | + | 0.348068i | ||||
\(934\) | −2.69141 | − | 4.66166i | −0.0880656 | − | 0.152534i | ||||
\(935\) | −1.37328 | − | 2.37860i | −0.0449112 | − | 0.0777885i | ||||
\(936\) | −2.74657 | + | 4.75720i | −0.0897744 | + | 0.155494i | ||||
\(937\) | −17.2618 | −0.563919 | −0.281960 | − | 0.959426i | \(-0.590984\pi\) | ||||
−0.281960 | + | 0.959426i | \(0.590984\pi\) | |||||||
\(938\) | −4.86642 | − | 8.01371i | −0.158894 | − | 0.261657i | ||||
\(939\) | 23.4564 | 0.765469 | ||||||||
\(940\) | 12.7581 | − | 22.0977i | 0.416123 | − | 0.720746i | ||||
\(941\) | 18.8155 | + | 32.5893i | 0.613366 | + | 1.06238i | 0.990669 | + | 0.136292i | \(0.0435184\pi\) |
−0.377302 | + | 0.926090i | \(0.623148\pi\) | |||||||
\(942\) | −9.05516 | − | 15.6840i | −0.295033 | − | 0.511012i | ||||
\(943\) | 3.57622 | − | 6.19419i | 0.116458 | − | 0.201710i | ||||
\(944\) | −9.52991 | −0.310172 | ||||||||
\(945\) | 7.26496 | − | 0.160897i | 0.236329 | − | 0.00523399i | ||||
\(946\) | −4.03677 | −0.131247 | ||||||||
\(947\) | 3.86596 | − | 6.69603i | 0.125627 | − | 0.217592i | −0.796351 | − | 0.604835i | \(-0.793239\pi\) |
0.921978 | + | 0.387243i | \(0.126573\pi\) | |||||||
\(948\) | −6.11985 | − | 10.5999i | −0.198764 | − | 0.344269i | ||||
\(949\) | 23.5667 | + | 40.8187i | 0.765007 | + | 1.32503i | ||||
\(950\) | 10.2213 | − | 17.7038i | 0.331623 | − | 0.574388i | ||||
\(951\) | −0.572020 | −0.0185490 | ||||||||
\(952\) | −1.27182 | + | 2.32002i | −0.0412199 | + | 0.0751922i | ||||
\(953\) | −20.6770 | −0.669794 | −0.334897 | − | 0.942255i | \(-0.608702\pi\) | ||||
−0.334897 | + | 0.942255i | \(0.608702\pi\) | |||||||
\(954\) | −2.74657 | + | 4.75720i | −0.0889234 | + | 0.154020i | ||||
\(955\) | −26.0735 | − | 45.1607i | −0.843720 | − | 1.46137i | ||||
\(956\) | −3.83384 | − | 6.64041i | −0.123995 | − | 0.214766i | ||||
\(957\) | −2.27182 | + | 3.93491i | −0.0734375 | + | 0.127197i | ||||
\(958\) | 14.4794 | 0.467808 | ||||||||
\(959\) | −6.98627 | + | 12.7442i | −0.225599 | + | 0.411531i | ||||
\(960\) | 2.74657 | 0.0886451 | ||||||||
\(961\) | 2.55982 | − | 4.43374i | 0.0825748 | − | 0.143024i | ||||
\(962\) | 11.0873 | + | 19.2037i | 0.357468 | + | 0.619153i | ||||
\(963\) | −8.72132 | − | 15.1058i | −0.281041 | − | 0.486776i | ||||
\(964\) | 12.5299 | − | 21.7024i | 0.403561 | − | 0.698989i | ||||
\(965\) | −59.2344 | −1.90682 | ||||||||
\(966\) | −3.41273 | + | 0.0755817i | −0.109803 | + | 0.00243180i | ||||
\(967\) | 15.7235 | 0.505634 | 0.252817 | − | 0.967514i | \(-0.418643\pi\) | ||||
0.252817 | + | 0.967514i | \(0.418643\pi\) | |||||||
\(968\) | −0.500000 | + | 0.866025i | −0.0160706 | + | 0.0278351i | ||||
\(969\) | 4.01839 | + | 6.96005i | 0.129089 | + | 0.223589i | ||||
\(970\) | 0.119852 | + | 0.207590i | 0.00384823 | + | 0.00666533i | ||||
\(971\) | −4.12405 | + | 7.14306i | −0.132347 | + | 0.229232i | −0.924581 | − | 0.380986i | \(-0.875585\pi\) |
0.792234 | + | 0.610218i | \(0.208918\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −18.7191 | − | 30.8254i | −0.600107 | − | 0.988218i | ||||
\(974\) | −8.43332 | −0.270221 | ||||||||
\(975\) | −6.98627 | + | 12.1006i | −0.223740 | + | 0.387529i | ||||
\(976\) | 0.829647 | + | 1.43699i | 0.0265564 | + | 0.0459970i | ||||
\(977\) | 17.6677 | + | 30.6013i | 0.565239 | + | 0.979023i | 0.997027 | + | 0.0770481i | \(0.0245495\pi\) |
−0.431788 | + | 0.901975i | \(0.642117\pi\) | |||||||
\(978\) | 6.72132 | − | 11.6417i | 0.214924 | − | 0.372259i | ||||
\(979\) | −6.50686 | −0.207960 | ||||||||
\(980\) | −8.86642 | + | 17.0594i | −0.283227 | + | 0.544944i | ||||
\(981\) | 1.65929 | 0.0529772 | ||||||||
\(982\) | 19.3385 | − | 33.4953i | 0.617116 | − | 1.06888i | ||||
\(983\) | 4.57156 | + | 7.91817i | 0.145810 | + | 0.252550i | 0.929675 | − | 0.368381i | \(-0.120088\pi\) |
−0.783865 | + | 0.620931i | \(0.786755\pi\) | |||||||
\(984\) | −2.77182 | − | 4.80093i | −0.0883623 | − | 0.153048i | ||||
\(985\) | 4.29021 | − | 7.43085i | 0.136697 | − | 0.236767i | ||||
\(986\) | 4.54364 | 0.144699 | ||||||||
\(987\) | 12.7581 | + | 21.0092i | 0.406095 | + | 0.668730i | ||||
\(988\) | −44.1471 | −1.40451 | ||||||||
\(989\) | −2.60413 | + | 4.51049i | −0.0828066 | + | 0.143425i | ||||
\(990\) | −1.37328 | − | 2.37860i | −0.0436458 | − | 0.0755968i | ||||
\(991\) | −17.7328 | − | 30.7142i | −0.563302 | − | 0.975668i | −0.997205 | − | 0.0747086i | \(-0.976197\pi\) |
0.433903 | − | 0.900960i | \(-0.357136\pi\) | |||||||
\(992\) | −2.54364 | + | 4.40571i | −0.0807606 | + | 0.139881i | ||||
\(993\) | 7.71819 | 0.244929 | ||||||||
\(994\) | 6.72818 | − | 0.149009i | 0.213405 | − | 0.00472629i | ||||
\(995\) | −71.6128 | −2.27028 | ||||||||
\(996\) | 7.26496 | − | 12.5833i | 0.230199 | − | 0.398716i | ||||
\(997\) | −22.7466 | − | 39.3982i | −0.720391 | − | 1.24775i | −0.960843 | − | 0.277093i | \(-0.910629\pi\) |
0.240452 | − | 0.970661i | \(-0.422704\pi\) | |||||||
\(998\) | −19.0230 | − | 32.9489i | −0.602164 | − | 1.04298i | ||||
\(999\) | 2.01839 | − | 3.49595i | 0.0638589 | − | 0.110607i |
(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 | 462.2.i.f.331.1 | yes | 6 | |
3.2 | odd | 2 | 1386.2.k.w.793.3 | 6 | |||
7.2 | even | 3 | 3234.2.a.bi.1.3 | 3 | |||
7.4 | even | 3 | inner | 462.2.i.f.67.1 | ✓ | 6 | |
7.5 | odd | 6 | 3234.2.a.bg.1.1 | 3 | |||
21.2 | odd | 6 | 9702.2.a.dt.1.1 | 3 | |||
21.5 | even | 6 | 9702.2.a.du.1.3 | 3 | |||
21.11 | odd | 6 | 1386.2.k.w.991.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.f.67.1 | ✓ | 6 | 7.4 | even | 3 | inner | |
462.2.i.f.331.1 | yes | 6 | 1.1 | even | 1 | trivial | |
1386.2.k.w.793.3 | 6 | 3.2 | odd | 2 | |||
1386.2.k.w.991.3 | 6 | 21.11 | odd | 6 | |||
3234.2.a.bg.1.1 | 3 | 7.5 | odd | 6 | |||
3234.2.a.bi.1.3 | 3 | 7.2 | even | 3 | |||
9702.2.a.dt.1.1 | 3 | 21.2 | odd | 6 | |||
9702.2.a.du.1.3 | 3 | 21.5 | even | 6 |