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 | 331.3 | ||
Root | \(0.500000 + 2.43956i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.331 |
Dual form | 462.2.i.f.67.3 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(5\) | 1.60074 | − | 2.77256i | 0.715871 | − | 1.23992i | −0.246752 | − | 0.969079i | \(-0.579363\pi\) |
0.962623 | − | 0.270846i | \(-0.0873035\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.60074 | − | 2.10657i | 0.605021 | − | 0.796209i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.60074 | + | 2.77256i | 0.506197 | + | 0.876759i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | −6.40294 | −1.77586 | −0.887929 | − | 0.459981i | \(-0.847856\pi\) | ||||
−0.887929 | + | 0.459981i | \(0.847856\pi\) | |||||||
\(14\) | 1.02398 | + | 2.43956i | 0.273669 | + | 0.652001i | ||||
\(15\) | −3.20147 | −0.826617 | ||||||||
\(16\) | −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 | ||||
\(19\) | −0.576760 | + | 0.998977i | −0.132318 | + | 0.229181i | −0.924570 | − | 0.381013i | \(-0.875575\pi\) |
0.792252 | + | 0.610194i | \(0.208909\pi\) | |||||||
\(20\) | −3.20147 | −0.715871 | ||||||||
\(21\) | −2.62471 | − | 0.332992i | −0.572759 | − | 0.0726649i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −0.976024 | + | 1.69052i | −0.203515 | + | 0.352498i | −0.949659 | − | 0.313287i | \(-0.898570\pi\) |
0.746144 | + | 0.665785i | \(0.231903\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −2.62471 | − | 4.54614i | −0.524943 | − | 0.909227i | ||||
\(26\) | 3.20147 | − | 5.54511i | 0.627860 | − | 1.08749i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.62471 | − | 0.332992i | −0.496024 | − | 0.0629297i | ||||
\(29\) | 7.24943 | 1.34618 | 0.673092 | − | 0.739559i | \(-0.264966\pi\) | ||||
0.673092 | + | 0.739559i | \(0.264966\pi\) | |||||||
\(30\) | 1.60074 | − | 2.77256i | 0.292253 | − | 0.506197i | ||||
\(31\) | −5.24943 | − | 9.09227i | −0.942825 | − | 1.63302i | −0.760049 | − | 0.649865i | \(-0.774825\pi\) |
−0.182775 | − | 0.983155i | \(-0.558508\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −3.27823 | − | 7.81020i | −0.554122 | − | 1.32016i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.57676 | + | 4.46308i | −0.423617 | + | 0.733726i | −0.996290 | − | 0.0860579i | \(-0.972573\pi\) |
0.572673 | + | 0.819784i | \(0.305906\pi\) | |||||||
\(38\) | −0.576760 | − | 0.998977i | −0.0935628 | − | 0.162056i | ||||
\(39\) | 3.20147 | + | 5.54511i | 0.512646 | + | 0.887929i | ||||
\(40\) | 1.60074 | − | 2.77256i | 0.253099 | − | 0.438380i | ||||
\(41\) | 8.24943 | 1.28834 | 0.644172 | − | 0.764881i | \(-0.277202\pi\) | ||||
0.644172 | + | 0.764881i | \(0.277202\pi\) | |||||||
\(42\) | 1.60074 | − | 2.10657i | 0.246999 | − | 0.325051i | ||||
\(43\) | 5.15352 | 0.785904 | 0.392952 | − | 0.919559i | \(-0.371454\pi\) | ||||
0.392952 | + | 0.919559i | \(0.371454\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | 1.60074 | + | 2.77256i | 0.238624 | + | 0.413308i | ||||
\(46\) | −0.976024 | − | 1.69052i | −0.143907 | − | 0.249254i | ||||
\(47\) | 3.02398 | − | 5.23768i | 0.441092 | − | 0.763994i | −0.556679 | − | 0.830728i | \(-0.687924\pi\) |
0.997771 | + | 0.0667337i | \(0.0212578\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.87529 | − | 6.74413i | −0.267898 | − | 0.963447i | ||||
\(50\) | 5.24943 | 0.742381 | ||||||||
\(51\) | −0.500000 | + | 0.866025i | −0.0700140 | + | 0.121268i | ||||
\(52\) | 3.20147 | + | 5.54511i | 0.443964 | + | 0.768969i | ||||
\(53\) | 3.20147 | + | 5.54511i | 0.439756 | + | 0.761680i | 0.997670 | − | 0.0682187i | \(-0.0217316\pi\) |
−0.557914 | + | 0.829899i | \(0.688398\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −3.20147 | −0.431686 | ||||||||
\(56\) | 1.60074 | − | 2.10657i | 0.213907 | − | 0.281502i | ||||
\(57\) | 1.15352 | 0.152787 | ||||||||
\(58\) | −3.62471 | + | 6.27819i | −0.475948 | + | 0.824366i | ||||
\(59\) | −5.77823 | − | 10.0082i | −0.752262 | − | 1.30296i | −0.946724 | − | 0.322046i | \(-0.895630\pi\) |
0.194462 | − | 0.980910i | \(-0.437704\pi\) | |||||||
\(60\) | 1.60074 | + | 2.77256i | 0.206654 | + | 0.357935i | ||||
\(61\) | −4.85016 | + | 8.40073i | −0.621000 | + | 1.07560i | 0.368300 | + | 0.929707i | \(0.379940\pi\) |
−0.989300 | + | 0.145896i | \(0.953394\pi\) | |||||||
\(62\) | 10.4989 | 1.33336 | ||||||||
\(63\) | 1.02398 | + | 2.43956i | 0.129009 | + | 0.307356i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.2494 | + | 17.7525i | −1.27128 | + | 2.20193i | ||||
\(66\) | −0.500000 | − | 0.866025i | −0.0615457 | − | 0.106600i | ||||
\(67\) | −3.12471 | − | 5.41216i | −0.381744 | − | 0.661201i | 0.609567 | − | 0.792734i | \(-0.291343\pi\) |
−0.991312 | + | 0.131534i | \(0.958010\pi\) | |||||||
\(68\) | −0.500000 | + | 0.866025i | −0.0606339 | + | 0.105021i | ||||
\(69\) | 1.95205 | 0.234999 | ||||||||
\(70\) | 8.40294 | + | 1.06607i | 1.00434 | + | 0.127419i | ||||
\(71\) | 5.24943 | 0.622992 | 0.311496 | − | 0.950247i | \(-0.399170\pi\) | ||||
0.311496 | + | 0.950247i | \(0.399170\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 1.04795 | + | 1.81511i | 0.122654 | + | 0.212442i | 0.920813 | − | 0.390004i | \(-0.127526\pi\) |
−0.798160 | + | 0.602446i | \(0.794193\pi\) | |||||||
\(74\) | −2.57676 | − | 4.46308i | −0.299542 | − | 0.518822i | ||||
\(75\) | −2.62471 | + | 4.54614i | −0.303076 | + | 0.524943i | ||||
\(76\) | 1.15352 | 0.132318 | ||||||||
\(77\) | −2.62471 | − | 0.332992i | −0.299114 | − | 0.0379480i | ||||
\(78\) | −6.40294 | −0.724991 | ||||||||
\(79\) | 2.80221 | − | 4.85357i | 0.315273 | − | 0.546069i | −0.664222 | − | 0.747535i | \(-0.731237\pi\) |
0.979496 | + | 0.201466i | \(0.0645706\pi\) | |||||||
\(80\) | 1.60074 | + | 2.77256i | 0.178968 | + | 0.309981i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.12471 | + | 7.14421i | −0.455498 | + | 0.788946i | ||||
\(83\) | 6.55646 | 0.719665 | 0.359833 | − | 0.933017i | \(-0.382834\pi\) | ||||
0.359833 | + | 0.933017i | \(0.382834\pi\) | |||||||
\(84\) | 1.02398 | + | 2.43956i | 0.111725 | + | 0.266178i | ||||
\(85\) | −3.20147 | −0.347248 | ||||||||
\(86\) | −2.57676 | + | 4.46308i | −0.277859 | + | 0.481266i | ||||
\(87\) | −3.62471 | − | 6.27819i | −0.388610 | − | 0.673092i | ||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | 9.20147 | − | 15.9374i | 0.975354 | − | 1.68936i | 0.296593 | − | 0.955004i | \(-0.404150\pi\) |
0.678761 | − | 0.734359i | \(-0.262517\pi\) | |||||||
\(90\) | −3.20147 | −0.337465 | ||||||||
\(91\) | −10.2494 | + | 13.4883i | −1.07443 | + | 1.41395i | ||||
\(92\) | 1.95205 | 0.203515 | ||||||||
\(93\) | −5.24943 | + | 9.09227i | −0.544340 | + | 0.942825i | ||||
\(94\) | 3.02398 | + | 5.23768i | 0.311899 | + | 0.540226i | ||||
\(95\) | 1.84648 | + | 3.19820i | 0.189445 | + | 0.328128i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −5.49885 | −0.558324 | −0.279162 | − | 0.960244i | \(-0.590057\pi\) | ||||
−0.279162 | + | 0.960244i | \(0.590057\pi\) | |||||||
\(98\) | 6.77823 | + | 1.74802i | 0.684705 | + | 0.176577i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −2.62471 | + | 4.54614i | −0.262471 | + | 0.454614i | ||||
\(101\) | 9.97970 | + | 17.2854i | 0.993018 | + | 1.71996i | 0.598670 | + | 0.800996i | \(0.295696\pi\) |
0.394348 | + | 0.918961i | \(0.370971\pi\) | |||||||
\(102\) | −0.500000 | − | 0.866025i | −0.0495074 | − | 0.0857493i | ||||
\(103\) | −0.153520 | + | 0.265904i | −0.0151267 | + | 0.0262003i | −0.873490 | − | 0.486843i | \(-0.838149\pi\) |
0.858363 | + | 0.513043i | \(0.171482\pi\) | |||||||
\(104\) | −6.40294 | −0.627860 | ||||||||
\(105\) | −5.12471 | + | 6.74413i | −0.500121 | + | 0.658160i | ||||
\(106\) | −6.40294 | −0.621909 | ||||||||
\(107\) | 4.52766 | − | 7.84213i | 0.437705 | − | 0.758128i | −0.559807 | − | 0.828623i | \(-0.689125\pi\) |
0.997512 | + | 0.0704955i | \(0.0224580\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 4.85016 | + | 8.40073i | 0.464561 | + | 0.804644i | 0.999182 | − | 0.0404487i | \(-0.0128787\pi\) |
−0.534620 | + | 0.845092i | \(0.679545\pi\) | |||||||
\(110\) | 1.60074 | − | 2.77256i | 0.152624 | − | 0.264353i | ||||
\(111\) | 5.15352 | 0.489150 | ||||||||
\(112\) | 1.02398 | + | 2.43956i | 0.0967567 | + | 0.230517i | ||||
\(113\) | −12.4989 | −1.17579 | −0.587896 | − | 0.808936i | \(-0.700044\pi\) | ||||
−0.587896 | + | 0.808936i | \(0.700044\pi\) | |||||||
\(114\) | −0.576760 | + | 0.998977i | −0.0540185 | + | 0.0935628i | ||||
\(115\) | 3.12471 | + | 5.41216i | 0.291381 | + | 0.504687i | ||||
\(116\) | −3.62471 | − | 6.27819i | −0.336546 | − | 0.582915i | ||||
\(117\) | 3.20147 | − | 5.54511i | 0.295976 | − | 0.512646i | ||||
\(118\) | 11.5565 | 1.06386 | ||||||||
\(119\) | −2.62471 | − | 0.332992i | −0.240607 | − | 0.0305254i | ||||
\(120\) | −3.20147 | −0.292253 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −4.85016 | − | 8.40073i | −0.439113 | − | 0.760566i | ||||
\(123\) | −4.12471 | − | 7.14421i | −0.371913 | − | 0.644172i | ||||
\(124\) | −5.24943 | + | 9.09227i | −0.471412 | + | 0.816510i | ||||
\(125\) | −0.798528 | −0.0714225 | ||||||||
\(126\) | −2.62471 | − | 0.332992i | −0.233828 | − | 0.0296653i | ||||
\(127\) | 8.35499 | 0.741386 | 0.370693 | − | 0.928756i | \(-0.379120\pi\) | ||||
0.370693 | + | 0.928756i | \(0.379120\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −2.57676 | − | 4.46308i | −0.226871 | − | 0.392952i | ||||
\(130\) | −10.2494 | − | 17.7525i | −0.898934 | − | 1.55700i | ||||
\(131\) | −7.65237 | + | 13.2543i | −0.668591 | + | 1.15803i | 0.309708 | + | 0.950832i | \(0.399769\pi\) |
−0.978298 | + | 0.207201i | \(0.933565\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 1.18118 | + | 2.81408i | 0.102421 | + | 0.244012i | ||||
\(134\) | 6.24943 | 0.539868 | ||||||||
\(135\) | 1.60074 | − | 2.77256i | 0.137769 | − | 0.238624i | ||||
\(136\) | −0.500000 | − | 0.866025i | −0.0428746 | − | 0.0742611i | ||||
\(137\) | 3.20147 | + | 5.54511i | 0.273520 | + | 0.473751i | 0.969761 | − | 0.244058i | \(-0.0784786\pi\) |
−0.696240 | + | 0.717809i | \(0.745145\pi\) | |||||||
\(138\) | −0.976024 | + | 1.69052i | −0.0830846 | + | 0.143907i | ||||
\(139\) | 21.7483 | 1.84466 | 0.922332 | − | 0.386398i | \(-0.126281\pi\) | ||||
0.922332 | + | 0.386398i | \(0.126281\pi\) | |||||||
\(140\) | −5.12471 | + | 6.74413i | −0.433117 | + | 0.569983i | ||||
\(141\) | −6.04795 | −0.509330 | ||||||||
\(142\) | −2.62471 | + | 4.54614i | −0.220261 | + | 0.381503i | ||||
\(143\) | 3.20147 | + | 5.54511i | 0.267721 | + | 0.463706i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 11.6044 | − | 20.0994i | 0.963694 | − | 1.66917i | ||||
\(146\) | −2.09591 | −0.173458 | ||||||||
\(147\) | −4.90294 | + | 4.99611i | −0.404388 | + | 0.412072i | ||||
\(148\) | 5.15352 | 0.423617 | ||||||||
\(149\) | −3.42324 | + | 5.92923i | −0.280443 | + | 0.485741i | −0.971494 | − | 0.237065i | \(-0.923815\pi\) |
0.691051 | + | 0.722806i | \(0.257148\pi\) | |||||||
\(150\) | −2.62471 | − | 4.54614i | −0.214307 | − | 0.371190i | ||||
\(151\) | −7.42692 | − | 12.8638i | −0.604394 | − | 1.04684i | −0.992147 | − | 0.125078i | \(-0.960082\pi\) |
0.387753 | − | 0.921763i | \(-0.373251\pi\) | |||||||
\(152\) | −0.576760 | + | 0.998977i | −0.0467814 | + | 0.0810278i | ||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 1.60074 | − | 2.10657i | 0.128991 | − | 0.169752i | ||||
\(155\) | −33.6118 | −2.69976 | ||||||||
\(156\) | 3.20147 | − | 5.54511i | 0.256323 | − | 0.443964i | ||||
\(157\) | 4.73028 | + | 8.19308i | 0.377517 | + | 0.653879i | 0.990700 | − | 0.136062i | \(-0.0434445\pi\) |
−0.613183 | + | 0.789941i | \(0.710111\pi\) | |||||||
\(158\) | 2.80221 | + | 4.85357i | 0.222932 | + | 0.386129i | ||||
\(159\) | 3.20147 | − | 5.54511i | 0.253893 | − | 0.439756i | ||||
\(160\) | −3.20147 | −0.253099 | ||||||||
\(161\) | 1.99885 | + | 4.76214i | 0.157531 | + | 0.375310i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −6.52766 | + | 11.3062i | −0.511286 | + | 0.885573i | 0.488629 | + | 0.872492i | \(0.337497\pi\) |
−0.999914 | + | 0.0130809i | \(0.995836\pi\) | |||||||
\(164\) | −4.12471 | − | 7.14421i | −0.322086 | − | 0.557869i | ||||
\(165\) | 1.60074 | + | 2.77256i | 0.124617 | + | 0.215843i | ||||
\(166\) | −3.27823 | + | 5.67806i | −0.254440 | + | 0.440703i | ||||
\(167\) | −6.70998 | −0.519234 | −0.259617 | − | 0.965712i | \(-0.583596\pi\) | ||||
−0.259617 | + | 0.965712i | \(0.583596\pi\) | |||||||
\(168\) | −2.62471 | − | 0.332992i | −0.202501 | − | 0.0256909i | ||||
\(169\) | 27.9977 | 2.15367 | ||||||||
\(170\) | 1.60074 | − | 2.77256i | 0.122771 | − | 0.212645i | ||||
\(171\) | −0.576760 | − | 0.998977i | −0.0441059 | − | 0.0763937i | ||||
\(172\) | −2.57676 | − | 4.46308i | −0.196476 | − | 0.340307i | ||||
\(173\) | 2.75057 | − | 4.76414i | 0.209122 | − | 0.362211i | −0.742316 | − | 0.670050i | \(-0.766273\pi\) |
0.951438 | + | 0.307839i | \(0.0996060\pi\) | |||||||
\(174\) | 7.24943 | 0.549578 | ||||||||
\(175\) | −13.7782 | − | 1.74802i | −1.04154 | − | 0.132138i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −5.77823 | + | 10.0082i | −0.434319 | + | 0.752262i | ||||
\(178\) | 9.20147 | + | 15.9374i | 0.689680 | + | 1.19456i | ||||
\(179\) | −0.826185 | − | 1.43099i | −0.0617520 | − | 0.106958i | 0.833497 | − | 0.552525i | \(-0.186335\pi\) |
−0.895249 | + | 0.445567i | \(0.853002\pi\) | |||||||
\(180\) | 1.60074 | − | 2.77256i | 0.119312 | − | 0.206654i | ||||
\(181\) | 24.9018 | 1.85094 | 0.925468 | − | 0.378826i | \(-0.123672\pi\) | ||||
0.925468 | + | 0.378826i | \(0.123672\pi\) | |||||||
\(182\) | −6.55646 | − | 15.6204i | −0.485997 | − | 1.15786i | ||||
\(183\) | 9.70032 | 0.717068 | ||||||||
\(184\) | −0.976024 | + | 1.69052i | −0.0719534 | + | 0.124627i | ||||
\(185\) | 8.24943 | + | 14.2884i | 0.606510 | + | 1.05051i | ||||
\(186\) | −5.24943 | − | 9.09227i | −0.384907 | − | 0.666678i | ||||
\(187\) | −0.500000 | + | 0.866025i | −0.0365636 | + | 0.0633300i | ||||
\(188\) | −6.04795 | −0.441092 | ||||||||
\(189\) | 1.60074 | − | 2.10657i | 0.116436 | − | 0.153231i | ||||
\(190\) | −3.69296 | −0.267916 | ||||||||
\(191\) | 2.40294 | − | 4.16202i | 0.173871 | − | 0.301153i | −0.765899 | − | 0.642961i | \(-0.777706\pi\) |
0.939770 | + | 0.341808i | \(0.111039\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −4.35499 | − | 7.54307i | −0.313479 | − | 0.542962i | 0.665634 | − | 0.746278i | \(-0.268161\pi\) |
−0.979113 | + | 0.203317i | \(0.934828\pi\) | |||||||
\(194\) | 2.74943 | − | 4.76214i | 0.197397 | − | 0.341902i | ||||
\(195\) | 20.4989 | 1.46795 | ||||||||
\(196\) | −4.90294 | + | 4.99611i | −0.350210 | + | 0.356865i | ||||
\(197\) | 0.654669 | 0.0466433 | 0.0233216 | − | 0.999728i | \(-0.492576\pi\) | ||||
0.0233216 | + | 0.999728i | \(0.492576\pi\) | |||||||
\(198\) | −0.500000 | + | 0.866025i | −0.0355335 | + | 0.0615457i | ||||
\(199\) | 3.84648 | + | 6.66230i | 0.272670 | + | 0.472278i | 0.969545 | − | 0.244915i | \(-0.0787600\pi\) |
−0.696875 | + | 0.717193i | \(0.745427\pi\) | |||||||
\(200\) | −2.62471 | − | 4.54614i | −0.185595 | − | 0.321460i | ||||
\(201\) | −3.12471 | + | 5.41216i | −0.220400 | + | 0.381744i | ||||
\(202\) | −19.9594 | −1.40434 | ||||||||
\(203\) | 11.6044 | − | 15.2714i | 0.814470 | − | 1.07184i | ||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 13.2052 | − | 22.8720i | 0.922288 | − | 1.59745i | ||||
\(206\) | −0.153520 | − | 0.265904i | −0.0106962 | − | 0.0185264i | ||||
\(207\) | −0.976024 | − | 1.69052i | −0.0678383 | − | 0.117499i | ||||
\(208\) | 3.20147 | − | 5.54511i | 0.221982 | − | 0.384484i | ||||
\(209\) | 1.15352 | 0.0797906 | ||||||||
\(210\) | −3.27823 | − | 7.81020i | −0.226220 | − | 0.538955i | ||||
\(211\) | 14.5948 | 1.00474 | 0.502372 | − | 0.864651i | \(-0.332461\pi\) | ||||
0.502372 | + | 0.864651i | \(0.332461\pi\) | |||||||
\(212\) | 3.20147 | − | 5.54511i | 0.219878 | − | 0.380840i | ||||
\(213\) | −2.62471 | − | 4.54614i | −0.179842 | − | 0.311496i | ||||
\(214\) | 4.52766 | + | 7.84213i | 0.309504 | + | 0.536077i | ||||
\(215\) | 8.24943 | − | 14.2884i | 0.562606 | − | 0.974462i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −27.5565 | − | 3.49604i | −1.87065 | − | 0.237326i | ||||
\(218\) | −9.70032 | −0.656989 | ||||||||
\(219\) | 1.04795 | − | 1.81511i | 0.0708141 | − | 0.122654i | ||||
\(220\) | 1.60074 | + | 2.77256i | 0.107922 | + | 0.186926i | ||||
\(221\) | 3.20147 | + | 5.54511i | 0.215354 | + | 0.373005i | ||||
\(222\) | −2.57676 | + | 4.46308i | −0.172941 | + | 0.299542i | ||||
\(223\) | −14.9018 | −0.997898 | −0.498949 | − | 0.866631i | \(-0.666281\pi\) | ||||
−0.498949 | + | 0.866631i | \(0.666281\pi\) | |||||||
\(224\) | −2.62471 | − | 0.332992i | −0.175371 | − | 0.0222490i | ||||
\(225\) | 5.24943 | 0.349962 | ||||||||
\(226\) | 6.24943 | − | 10.8243i | 0.415706 | − | 0.720023i | ||||
\(227\) | 0.124713 | + | 0.216009i | 0.00827746 | + | 0.0143370i | 0.870134 | − | 0.492814i | \(-0.164032\pi\) |
−0.861857 | + | 0.507151i | \(0.830699\pi\) | |||||||
\(228\) | −0.576760 | − | 0.998977i | −0.0381968 | − | 0.0661589i | ||||
\(229\) | 2.04795 | − | 3.54716i | 0.135333 | − | 0.234403i | −0.790392 | − | 0.612602i | \(-0.790123\pi\) |
0.925724 | + | 0.378199i | \(0.123456\pi\) | |||||||
\(230\) | −6.24943 | −0.412075 | ||||||||
\(231\) | 1.02398 | + | 2.43956i | 0.0673727 | + | 0.160512i | ||||
\(232\) | 7.24943 | 0.475948 | ||||||||
\(233\) | −5.65352 | + | 9.79218i | −0.370374 | + | 0.641507i | −0.989623 | − | 0.143688i | \(-0.954104\pi\) |
0.619249 | + | 0.785195i | \(0.287437\pi\) | |||||||
\(234\) | 3.20147 | + | 5.54511i | 0.209287 | + | 0.362495i | ||||
\(235\) | −9.68118 | − | 16.7683i | −0.631530 | − | 1.09384i | ||||
\(236\) | −5.77823 | + | 10.0082i | −0.376131 | + | 0.651478i | ||||
\(237\) | −5.60442 | −0.364046 | ||||||||
\(238\) | 1.60074 | − | 2.10657i | 0.103760 | − | 0.136549i | ||||
\(239\) | 6.59476 | 0.426579 | 0.213290 | − | 0.976989i | \(-0.431582\pi\) | ||||
0.213290 | + | 0.976989i | \(0.431582\pi\) | |||||||
\(240\) | 1.60074 | − | 2.77256i | 0.103327 | − | 0.178968i | ||||
\(241\) | −8.55646 | − | 14.8202i | −0.551170 | − | 0.954655i | −0.998190 | − | 0.0601311i | \(-0.980848\pi\) |
0.447020 | − | 0.894524i | \(-0.352485\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 9.70032 | 0.621000 | ||||||||
\(245\) | −21.7003 | − | 5.59623i | −1.38638 | − | 0.357530i | ||||
\(246\) | 8.24943 | 0.525964 | ||||||||
\(247\) | 3.69296 | − | 6.39640i | 0.234977 | − | 0.406993i | ||||
\(248\) | −5.24943 | − | 9.09227i | −0.333339 | − | 0.577360i | ||||
\(249\) | −3.27823 | − | 5.67806i | −0.207750 | − | 0.359833i | ||||
\(250\) | 0.399264 | − | 0.691545i | 0.0252517 | − | 0.0437372i | ||||
\(251\) | 7.95941 | 0.502393 | 0.251197 | − | 0.967936i | \(-0.419176\pi\) | ||||
0.251197 | + | 0.967936i | \(0.419176\pi\) | |||||||
\(252\) | 1.60074 | − | 2.10657i | 0.100837 | − | 0.132702i | ||||
\(253\) | 1.95205 | 0.122724 | ||||||||
\(254\) | −4.17750 | + | 7.23564i | −0.262119 | + | 0.454004i | ||||
\(255\) | 1.60074 | + | 2.77256i | 0.100242 | + | 0.173624i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 11.2015 | − | 19.4015i | 0.698729 | − | 1.21023i | −0.270179 | − | 0.962810i | \(-0.587083\pi\) |
0.968907 | − | 0.247423i | \(-0.0795838\pi\) | |||||||
\(258\) | 5.15352 | 0.320844 | ||||||||
\(259\) | 5.27708 | + | 12.5723i | 0.327902 | + | 0.781207i | ||||
\(260\) | 20.4989 | 1.27128 | ||||||||
\(261\) | −3.62471 | + | 6.27819i | −0.224364 | + | 0.388610i | ||||
\(262\) | −7.65237 | − | 13.2543i | −0.472765 | − | 0.818853i | ||||
\(263\) | 12.5085 | + | 21.6654i | 0.771308 | + | 1.33594i | 0.936846 | + | 0.349741i | \(0.113730\pi\) |
−0.165539 | + | 0.986203i | \(0.552936\pi\) | |||||||
\(264\) | −0.500000 | + | 0.866025i | −0.0307729 | + | 0.0533002i | ||||
\(265\) | 20.4989 | 1.25923 | ||||||||
\(266\) | −3.02766 | − | 0.384113i | −0.185638 | − | 0.0235515i | ||||
\(267\) | −18.4029 | −1.12624 | ||||||||
\(268\) | −3.12471 | + | 5.41216i | −0.190872 | + | 0.330600i | ||||
\(269\) | −4.05163 | − | 7.01764i | −0.247032 | − | 0.427873i | 0.715669 | − | 0.698440i | \(-0.246122\pi\) |
−0.962701 | + | 0.270567i | \(0.912789\pi\) | |||||||
\(270\) | 1.60074 | + | 2.77256i | 0.0974177 | + | 0.168732i | ||||
\(271\) | 2.40294 | − | 4.16202i | 0.145968 | − | 0.252825i | −0.783765 | − | 0.621057i | \(-0.786704\pi\) |
0.929734 | + | 0.368232i | \(0.120037\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 16.8059 | + | 2.13213i | 1.01714 | + | 0.129042i | ||||
\(274\) | −6.40294 | −0.386816 | ||||||||
\(275\) | −2.62471 | + | 4.54614i | −0.158276 | + | 0.274142i | ||||
\(276\) | −0.976024 | − | 1.69052i | −0.0587497 | − | 0.101757i | ||||
\(277\) | 5.60442 | + | 9.70714i | 0.336737 | + | 0.583245i | 0.983817 | − | 0.179177i | \(-0.0573434\pi\) |
−0.647080 | + | 0.762422i | \(0.724010\pi\) | |||||||
\(278\) | −10.8741 | + | 18.8346i | −0.652187 | + | 1.12962i | ||||
\(279\) | 10.4989 | 0.628550 | ||||||||
\(280\) | −3.27823 | − | 7.81020i | −0.195912 | − | 0.466749i | ||||
\(281\) | −17.4989 | −1.04389 | −0.521947 | − | 0.852978i | \(-0.674794\pi\) | ||||
−0.521947 | + | 0.852978i | \(0.674794\pi\) | |||||||
\(282\) | 3.02398 | − | 5.23768i | 0.180075 | − | 0.311899i | ||||
\(283\) | −13.7003 | − | 23.7297i | −0.814400 | − | 1.41058i | −0.909758 | − | 0.415139i | \(-0.863733\pi\) |
0.0953585 | − | 0.995443i | \(-0.469600\pi\) | |||||||
\(284\) | −2.62471 | − | 4.54614i | −0.155748 | − | 0.269764i | ||||
\(285\) | 1.84648 | − | 3.19820i | 0.109376 | − | 0.189445i | ||||
\(286\) | −6.40294 | −0.378614 | ||||||||
\(287\) | 13.2052 | − | 17.3780i | 0.779476 | − | 1.02579i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 8.00000 | − | 13.8564i | 0.470588 | − | 0.815083i | ||||
\(290\) | 11.6044 | + | 20.0994i | 0.681435 | + | 1.18028i | ||||
\(291\) | 2.74943 | + | 4.76214i | 0.161174 | + | 0.279162i | ||||
\(292\) | 1.04795 | − | 1.81511i | 0.0613268 | − | 0.106221i | ||||
\(293\) | −19.7483 | −1.15371 | −0.576853 | − | 0.816848i | \(-0.695720\pi\) | ||||
−0.576853 | + | 0.816848i | \(0.695720\pi\) | |||||||
\(294\) | −1.87529 | − | 6.74413i | −0.109369 | − | 0.393326i | ||||
\(295\) | −36.9977 | −2.15409 | ||||||||
\(296\) | −2.57676 | + | 4.46308i | −0.149771 | + | 0.259411i | ||||
\(297\) | −0.500000 | − | 0.866025i | −0.0290129 | − | 0.0502519i | ||||
\(298\) | −3.42324 | − | 5.92923i | −0.198303 | − | 0.343471i | ||||
\(299\) | 6.24943 | − | 10.8243i | 0.361414 | − | 0.625987i | ||||
\(300\) | 5.24943 | 0.303076 | ||||||||
\(301\) | 8.24943 | − | 10.8563i | 0.475489 | − | 0.625744i | ||||
\(302\) | 14.8538 | 0.854743 | ||||||||
\(303\) | 9.97970 | − | 17.2854i | 0.573319 | − | 0.993018i | ||||
\(304\) | −0.576760 | − | 0.998977i | −0.0330794 | − | 0.0572953i | ||||
\(305\) | 15.5277 | + | 26.8947i | 0.889111 | + | 1.53999i | ||||
\(306\) | −0.500000 | + | 0.866025i | −0.0285831 | + | 0.0495074i | ||||
\(307\) | 4.30704 | 0.245816 | 0.122908 | − | 0.992418i | \(-0.460778\pi\) | ||||
0.122908 | + | 0.992418i | \(0.460778\pi\) | |||||||
\(308\) | 1.02398 | + | 2.43956i | 0.0583465 | + | 0.139007i | ||||
\(309\) | 0.307039 | 0.0174668 | ||||||||
\(310\) | 16.8059 | − | 29.1087i | 0.954510 | − | 1.65326i | ||||
\(311\) | 7.37897 | + | 12.7807i | 0.418423 | + | 0.724730i | 0.995781 | − | 0.0917613i | \(-0.0292497\pi\) |
−0.577358 | + | 0.816491i | \(0.695916\pi\) | |||||||
\(312\) | 3.20147 | + | 5.54511i | 0.181248 | + | 0.313930i | ||||
\(313\) | −10.3753 | + | 17.9705i | −0.586446 | + | 1.01575i | 0.408248 | + | 0.912871i | \(0.366140\pi\) |
−0.994693 | + | 0.102883i | \(0.967193\pi\) | |||||||
\(314\) | −9.46056 | −0.533890 | ||||||||
\(315\) | 8.40294 | + | 1.06607i | 0.473452 | + | 0.0600660i | ||||
\(316\) | −5.60442 | −0.315273 | ||||||||
\(317\) | −8.09959 | + | 14.0289i | −0.454918 | + | 0.787941i | −0.998683 | − | 0.0512960i | \(-0.983665\pi\) |
0.543765 | + | 0.839237i | \(0.316998\pi\) | |||||||
\(318\) | 3.20147 | + | 5.54511i | 0.179530 | + | 0.310954i | ||||
\(319\) | −3.62471 | − | 6.27819i | −0.202945 | − | 0.351511i | ||||
\(320\) | 1.60074 | − | 2.77256i | 0.0894839 | − | 0.154991i | ||||
\(321\) | −9.05531 | −0.505418 | ||||||||
\(322\) | −5.12356 | − | 0.650017i | −0.285525 | − | 0.0362240i | ||||
\(323\) | 1.15352 | 0.0641835 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 16.8059 | + | 29.1087i | 0.932223 | + | 1.61466i | ||||
\(326\) | −6.52766 | − | 11.3062i | −0.361533 | − | 0.626194i | ||||
\(327\) | 4.85016 | − | 8.40073i | 0.268215 | − | 0.464561i | ||||
\(328\) | 8.24943 | 0.455498 | ||||||||
\(329\) | −6.19296 | − | 14.7544i | −0.341429 | − | 0.813435i | ||||
\(330\) | −3.20147 | −0.176235 | ||||||||
\(331\) | −10.6236 | + | 18.4006i | −0.583924 | + | 1.01139i | 0.411085 | + | 0.911597i | \(0.365150\pi\) |
−0.995009 | + | 0.0997886i | \(0.968183\pi\) | |||||||
\(332\) | −3.27823 | − | 5.67806i | −0.179916 | − | 0.311624i | ||||
\(333\) | −2.57676 | − | 4.46308i | −0.141206 | − | 0.244575i | ||||
\(334\) | 3.35499 | − | 5.81102i | 0.183577 | − | 0.317965i | ||||
\(335\) | −20.0074 | −1.09312 | ||||||||
\(336\) | 1.60074 | − | 2.10657i | 0.0873273 | − | 0.114923i | ||||
\(337\) | −25.5159 | −1.38994 | −0.694969 | − | 0.719040i | \(-0.744582\pi\) | ||||
−0.694969 | + | 0.719040i | \(0.744582\pi\) | |||||||
\(338\) | −13.9989 | + | 24.2467i | −0.761437 | + | 1.31885i | ||||
\(339\) | 6.24943 | + | 10.8243i | 0.339422 | + | 0.587896i | ||||
\(340\) | 1.60074 | + | 2.77256i | 0.0868121 | + | 0.150363i | ||||
\(341\) | −5.24943 | + | 9.09227i | −0.284272 | + | 0.492374i | ||||
\(342\) | 1.15352 | 0.0623752 | ||||||||
\(343\) | −17.2088 | − | 6.84515i | −0.929190 | − | 0.369603i | ||||
\(344\) | 5.15352 | 0.277859 | ||||||||
\(345\) | 3.12471 | − | 5.41216i | 0.168229 | − | 0.291381i | ||||
\(346\) | 2.75057 | + | 4.76414i | 0.147872 | + | 0.256122i | ||||
\(347\) | −1.52766 | − | 2.64598i | −0.0820089 | − | 0.142044i | 0.822104 | − | 0.569338i | \(-0.192800\pi\) |
−0.904113 | + | 0.427294i | \(0.859467\pi\) | |||||||
\(348\) | −3.62471 | + | 6.27819i | −0.194305 | + | 0.336546i | ||||
\(349\) | −4.00736 | −0.214509 | −0.107255 | − | 0.994232i | \(-0.534206\pi\) | ||||
−0.107255 | + | 0.994232i | \(0.534206\pi\) | |||||||
\(350\) | 8.40294 | − | 11.0583i | 0.449156 | − | 0.591090i | ||||
\(351\) | −6.40294 | −0.341764 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | 0.549103 | + | 0.951073i | 0.0292258 | + | 0.0506205i | 0.880268 | − | 0.474476i | \(-0.157362\pi\) |
−0.851043 | + | 0.525097i | \(0.824029\pi\) | |||||||
\(354\) | −5.77823 | − | 10.0082i | −0.307110 | − | 0.531929i | ||||
\(355\) | 8.40294 | − | 14.5543i | 0.445982 | − | 0.772463i | ||||
\(356\) | −18.4029 | −0.975354 | ||||||||
\(357\) | 1.02398 | + | 2.43956i | 0.0541946 | + | 0.129115i | ||||
\(358\) | 1.65237 | 0.0873305 | ||||||||
\(359\) | −7.80589 | + | 13.5202i | −0.411979 | + | 0.713569i | −0.995106 | − | 0.0988123i | \(-0.968496\pi\) |
0.583127 | + | 0.812381i | \(0.301829\pi\) | |||||||
\(360\) | 1.60074 | + | 2.77256i | 0.0843662 | + | 0.146127i | ||||
\(361\) | 8.83470 | + | 15.3021i | 0.464984 | + | 0.805376i | ||||
\(362\) | −12.4509 | + | 21.5656i | −0.654405 | + | 1.13346i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 16.8059 | + | 2.13213i | 0.880868 | + | 0.111754i | ||||
\(365\) | 6.70998 | 0.351217 | ||||||||
\(366\) | −4.85016 | + | 8.40073i | −0.253522 | + | 0.439113i | ||||
\(367\) | −0.395583 | − | 0.685170i | −0.0206493 | − | 0.0357656i | 0.855516 | − | 0.517776i | \(-0.173240\pi\) |
−0.876165 | + | 0.482011i | \(0.839907\pi\) | |||||||
\(368\) | −0.976024 | − | 1.69052i | −0.0508787 | − | 0.0881246i | ||||
\(369\) | −4.12471 | + | 7.14421i | −0.214724 | + | 0.371913i | ||||
\(370\) | −16.4989 | −0.857734 | ||||||||
\(371\) | 16.8059 | + | 2.13213i | 0.872518 | + | 0.110695i | ||||
\(372\) | 10.4989 | 0.544340 | ||||||||
\(373\) | −7.95573 | + | 13.7797i | −0.411932 | + | 0.713487i | −0.995101 | − | 0.0988637i | \(-0.968479\pi\) |
0.583169 | + | 0.812351i | \(0.301813\pi\) | |||||||
\(374\) | −0.500000 | − | 0.866025i | −0.0258544 | − | 0.0447811i | ||||
\(375\) | 0.399264 | + | 0.691545i | 0.0206179 | + | 0.0357112i | ||||
\(376\) | 3.02398 | − | 5.23768i | 0.155950 | − | 0.270113i | ||||
\(377\) | −46.4177 | −2.39063 | ||||||||
\(378\) | 1.02398 | + | 2.43956i | 0.0526677 | + | 0.125478i | ||||
\(379\) | −17.0553 | −0.876073 | −0.438036 | − | 0.898957i | \(-0.644326\pi\) | ||||
−0.438036 | + | 0.898957i | \(0.644326\pi\) | |||||||
\(380\) | 1.84648 | − | 3.19820i | 0.0947224 | − | 0.164064i | ||||
\(381\) | −4.17750 | − | 7.23564i | −0.214020 | − | 0.370693i | ||||
\(382\) | 2.40294 | + | 4.16202i | 0.122945 | + | 0.212948i | ||||
\(383\) | −6.72062 | + | 11.6405i | −0.343408 | + | 0.594799i | −0.985063 | − | 0.172194i | \(-0.944915\pi\) |
0.641656 | + | 0.766993i | \(0.278248\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −5.12471 | + | 6.74413i | −0.261180 | + | 0.343713i | ||||
\(386\) | 8.70998 | 0.443327 | ||||||||
\(387\) | −2.57676 | + | 4.46308i | −0.130984 | + | 0.226871i | ||||
\(388\) | 2.74943 | + | 4.76214i | 0.139581 | + | 0.241761i | ||||
\(389\) | 3.60074 | + | 6.23666i | 0.182565 | + | 0.316211i | 0.942753 | − | 0.333491i | \(-0.108227\pi\) |
−0.760189 | + | 0.649702i | \(0.774893\pi\) | |||||||
\(390\) | −10.2494 | + | 17.7525i | −0.519000 | + | 0.898934i | ||||
\(391\) | 1.95205 | 0.0987193 | ||||||||
\(392\) | −1.87529 | − | 6.74413i | −0.0947163 | − | 0.340630i | ||||
\(393\) | 15.3047 | 0.772022 | ||||||||
\(394\) | −0.327335 | + | 0.566960i | −0.0164909 | + | 0.0285630i | ||||
\(395\) | −8.97119 | − | 15.5386i | −0.451390 | − | 0.781830i | ||||
\(396\) | −0.500000 | − | 0.866025i | −0.0251259 | − | 0.0435194i | ||||
\(397\) | −6.47119 | + | 11.2084i | −0.324780 | + | 0.562535i | −0.981468 | − | 0.191627i | \(-0.938624\pi\) |
0.656688 | + | 0.754162i | \(0.271957\pi\) | |||||||
\(398\) | −7.69296 | −0.385613 | ||||||||
\(399\) | 1.84648 | − | 2.42997i | 0.0924396 | − | 0.121651i | ||||
\(400\) | 5.24943 | 0.262471 | ||||||||
\(401\) | 8.45090 | − | 14.6374i | 0.422018 | − | 0.730956i | −0.574119 | − | 0.818772i | \(-0.694655\pi\) |
0.996137 | + | 0.0878158i | \(0.0279887\pi\) | |||||||
\(402\) | −3.12471 | − | 5.41216i | −0.155846 | − | 0.269934i | ||||
\(403\) | 33.6118 | + | 58.2173i | 1.67432 | + | 2.90001i | ||||
\(404\) | 9.97970 | − | 17.2854i | 0.496509 | − | 0.859979i | ||||
\(405\) | −3.20147 | −0.159082 | ||||||||
\(406\) | 7.42324 | + | 17.6854i | 0.368409 | + | 0.877713i | ||||
\(407\) | 5.15352 | 0.255450 | ||||||||
\(408\) | −0.500000 | + | 0.866025i | −0.0247537 | + | 0.0428746i | ||||
\(409\) | 18.5468 | + | 32.1240i | 0.917080 | + | 1.58843i | 0.803827 | + | 0.594864i | \(0.202794\pi\) |
0.113254 | + | 0.993566i | \(0.463873\pi\) | |||||||
\(410\) | 13.2052 | + | 22.8720i | 0.652156 | + | 1.12957i | ||||
\(411\) | 3.20147 | − | 5.54511i | 0.157917 | − | 0.273520i | ||||
\(412\) | 0.307039 | 0.0151267 | ||||||||
\(413\) | −30.3324 | − | 3.84821i | −1.49256 | − | 0.189358i | ||||
\(414\) | 1.95205 | 0.0959379 | ||||||||
\(415\) | 10.4952 | − | 18.1782i | 0.515188 | − | 0.892331i | ||||
\(416\) | 3.20147 | + | 5.54511i | 0.156965 | + | 0.271872i | ||||
\(417\) | −10.8741 | − | 18.8346i | −0.532509 | − | 0.922332i | ||||
\(418\) | −0.576760 | + | 0.998977i | −0.0282102 | + | 0.0488616i | ||||
\(419\) | 22.4583 | 1.09716 | 0.548579 | − | 0.836099i | \(-0.315169\pi\) | ||||
0.548579 | + | 0.836099i | \(0.315169\pi\) | |||||||
\(420\) | 8.40294 | + | 1.06607i | 0.410022 | + | 0.0520187i | ||||
\(421\) | −23.3453 | −1.13778 | −0.568891 | − | 0.822413i | \(-0.692627\pi\) | ||||
−0.568891 | + | 0.822413i | \(0.692627\pi\) | |||||||
\(422\) | −7.29738 | + | 12.6394i | −0.355231 | + | 0.615278i | ||||
\(423\) | 3.02398 | + | 5.23768i | 0.147031 | + | 0.254665i | ||||
\(424\) | 3.20147 | + | 5.54511i | 0.155477 | + | 0.269294i | ||||
\(425\) | −2.62471 | + | 4.54614i | −0.127317 | + | 0.220520i | ||||
\(426\) | 5.24943 | 0.254335 | ||||||||
\(427\) | 9.93290 | + | 23.6646i | 0.480687 | + | 1.14521i | ||||
\(428\) | −9.05531 | −0.437705 | ||||||||
\(429\) | 3.20147 | − | 5.54511i | 0.154569 | − | 0.267721i | ||||
\(430\) | 8.24943 | + | 14.2884i | 0.397823 | + | 0.689049i | ||||
\(431\) | −15.9115 | − | 27.5595i | −0.766428 | − | 1.32749i | −0.939488 | − | 0.342581i | \(-0.888699\pi\) |
0.173060 | − | 0.984911i | \(-0.444634\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 30.3047 | 1.45635 | 0.728176 | − | 0.685390i | \(-0.240368\pi\) | ||||
0.728176 | + | 0.685390i | \(0.240368\pi\) | |||||||
\(434\) | 16.8059 | − | 22.1166i | 0.806709 | − | 1.06163i | ||||
\(435\) | −23.2088 | −1.11278 | ||||||||
\(436\) | 4.85016 | − | 8.40073i | 0.232281 | − | 0.402322i | ||||
\(437\) | −1.12586 | − | 1.95005i | −0.0538573 | − | 0.0932836i | ||||
\(438\) | 1.04795 | + | 1.81511i | 0.0500731 | + | 0.0867292i | ||||
\(439\) | 5.33102 | − | 9.23359i | 0.254435 | − | 0.440695i | −0.710307 | − | 0.703892i | \(-0.751444\pi\) |
0.964742 | + | 0.263197i | \(0.0847770\pi\) | |||||||
\(440\) | −3.20147 | −0.152624 | ||||||||
\(441\) | 6.77823 | + | 1.74802i | 0.322773 | + | 0.0832390i | ||||
\(442\) | −6.40294 | −0.304557 | ||||||||
\(443\) | 18.0277 | − | 31.2248i | 0.856520 | − | 1.48354i | −0.0187080 | − | 0.999825i | \(-0.505955\pi\) |
0.875228 | − | 0.483711i | \(-0.160711\pi\) | |||||||
\(444\) | −2.57676 | − | 4.46308i | −0.122288 | − | 0.211808i | ||||
\(445\) | −29.4583 | − | 51.0232i | −1.39646 | − | 2.41873i | ||||
\(446\) | 7.45090 | − | 12.9053i | 0.352810 | − | 0.611085i | ||||
\(447\) | 6.84648 | 0.323827 | ||||||||
\(448\) | 1.60074 | − | 2.10657i | 0.0756277 | − | 0.0995262i | ||||
\(449\) | 23.4006 | 1.10434 | 0.552172 | − | 0.833730i | \(-0.313799\pi\) | ||||
0.552172 | + | 0.833730i | \(0.313799\pi\) | |||||||
\(450\) | −2.62471 | + | 4.54614i | −0.123730 | + | 0.214307i | ||||
\(451\) | −4.12471 | − | 7.14421i | −0.194225 | − | 0.336408i | ||||
\(452\) | 6.24943 | + | 10.8243i | 0.293948 | + | 0.509133i | ||||
\(453\) | −7.42692 | + | 12.8638i | −0.348947 | + | 0.604394i | ||||
\(454\) | −0.249425 | −0.0117061 | ||||||||
\(455\) | 20.9903 | + | 50.0083i | 0.984042 | + | 2.34442i | ||||
\(456\) | 1.15352 | 0.0540185 | ||||||||
\(457\) | 9.30704 | − | 16.1203i | 0.435365 | − | 0.754074i | −0.561960 | − | 0.827164i | \(-0.689953\pi\) |
0.997325 | + | 0.0730899i | \(0.0232860\pi\) | |||||||
\(458\) | 2.04795 | + | 3.54716i | 0.0956945 | + | 0.165748i | ||||
\(459\) | −0.500000 | − | 0.866025i | −0.0233380 | − | 0.0404226i | ||||
\(460\) | 3.12471 | − | 5.41216i | 0.145690 | − | 0.252343i | ||||
\(461\) | −31.4412 | −1.46436 | −0.732182 | − | 0.681109i | \(-0.761498\pi\) | ||||
−0.732182 | + | 0.681109i | \(0.761498\pi\) | |||||||
\(462\) | −2.62471 | − | 0.332992i | −0.122113 | − | 0.0154922i | ||||
\(463\) | −22.0959 | −1.02688 | −0.513442 | − | 0.858124i | \(-0.671630\pi\) | ||||
−0.513442 | + | 0.858124i | \(0.671630\pi\) | |||||||
\(464\) | −3.62471 | + | 6.27819i | −0.168273 | + | 0.291457i | ||||
\(465\) | 16.8059 | + | 29.1087i | 0.779354 | + | 1.34988i | ||||
\(466\) | −5.65352 | − | 9.79218i | −0.261894 | − | 0.453614i | ||||
\(467\) | −10.5288 | + | 18.2364i | −0.487215 | + | 0.843881i | −0.999892 | − | 0.0147004i | \(-0.995321\pi\) |
0.512677 | + | 0.858582i | \(0.328654\pi\) | |||||||
\(468\) | −6.40294 | −0.295976 | ||||||||
\(469\) | −16.4029 | − | 2.08101i | −0.757418 | − | 0.0960922i | ||||
\(470\) | 19.3624 | 0.893119 | ||||||||
\(471\) | 4.73028 | − | 8.19308i | 0.217960 | − | 0.377517i | ||||
\(472\) | −5.77823 | − | 10.0082i | −0.265965 | − | 0.460664i | ||||
\(473\) | −2.57676 | − | 4.46308i | −0.118480 | − | 0.205213i | ||||
\(474\) | 2.80221 | − | 4.85357i | 0.128710 | − | 0.222932i | ||||
\(475\) | 6.05531 | 0.277837 | ||||||||
\(476\) | 1.02398 | + | 2.43956i | 0.0469339 | + | 0.111817i | ||||
\(477\) | −6.40294 | −0.293171 | ||||||||
\(478\) | −3.29738 | + | 5.71123i | −0.150819 | + | 0.261225i | ||||
\(479\) | 10.6044 | + | 18.3674i | 0.484528 | + | 0.839227i | 0.999842 | − | 0.0177741i | \(-0.00565797\pi\) |
−0.515314 | + | 0.857002i | \(0.672325\pi\) | |||||||
\(480\) | 1.60074 | + | 2.77256i | 0.0730633 | + | 0.126549i | ||||
\(481\) | 16.4989 | − | 28.5768i | 0.752283 | − | 1.30299i | ||||
\(482\) | 17.1129 | 0.779473 | ||||||||
\(483\) | 3.12471 | − | 4.11213i | 0.142179 | − | 0.187108i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −8.80221 | + | 15.2459i | −0.399688 | + | 0.692279i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 19.3550 | + | 33.5238i | 0.877058 | + | 1.51911i | 0.854554 | + | 0.519363i | \(0.173831\pi\) |
0.0225047 | + | 0.999747i | \(0.492836\pi\) | |||||||
\(488\) | −4.85016 | + | 8.40073i | −0.219556 | + | 0.380283i | ||||
\(489\) | 13.0553 | 0.590382 | ||||||||
\(490\) | 15.6966 | − | 15.9949i | 0.709102 | − | 0.722577i | ||||
\(491\) | 19.1705 | 0.865154 | 0.432577 | − | 0.901597i | \(-0.357604\pi\) | ||||
0.432577 | + | 0.901597i | \(0.357604\pi\) | |||||||
\(492\) | −4.12471 | + | 7.14421i | −0.185956 | + | 0.322086i | ||||
\(493\) | −3.62471 | − | 6.27819i | −0.163249 | − | 0.282755i | ||||
\(494\) | 3.69296 | + | 6.39640i | 0.166154 | + | 0.287787i | ||||
\(495\) | 1.60074 | − | 2.77256i | 0.0719477 | − | 0.124617i | ||||
\(496\) | 10.4989 | 0.471412 | ||||||||
\(497\) | 8.40294 | − | 11.0583i | 0.376924 | − | 0.496032i | ||||
\(498\) | 6.55646 | 0.293802 | ||||||||
\(499\) | 13.9594 | − | 24.1784i | 0.624909 | − | 1.08237i | −0.363649 | − | 0.931536i | \(-0.618469\pi\) |
0.988558 | − | 0.150838i | \(-0.0481973\pi\) | |||||||
\(500\) | 0.399264 | + | 0.691545i | 0.0178556 | + | 0.0309268i | ||||
\(501\) | 3.35499 | + | 5.81102i | 0.149890 | + | 0.259617i | ||||
\(502\) | −3.97970 | + | 6.89305i | −0.177623 | + | 0.307652i | ||||
\(503\) | −8.70998 | −0.388359 | −0.194179 | − | 0.980966i | \(-0.562204\pi\) | ||||
−0.194179 | + | 0.980966i | \(0.562204\pi\) | |||||||
\(504\) | 1.02398 | + | 2.43956i | 0.0456115 | + | 0.108667i | ||||
\(505\) | 63.8995 | 2.84349 | ||||||||
\(506\) | −0.976024 | + | 1.69052i | −0.0433895 | + | 0.0751529i | ||||
\(507\) | −13.9989 | − | 24.2467i | −0.621711 | − | 1.07683i | ||||
\(508\) | −4.17750 | − | 7.23564i | −0.185346 | − | 0.321029i | ||||
\(509\) | 0.894433 | − | 1.54920i | 0.0396451 | − | 0.0686673i | −0.845522 | − | 0.533941i | \(-0.820711\pi\) |
0.885167 | + | 0.465273i | \(0.154044\pi\) | |||||||
\(510\) | −3.20147 | −0.141764 | ||||||||
\(511\) | 5.50115 | + | 0.697921i | 0.243357 | + | 0.0308742i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.576760 | + | 0.998977i | −0.0254646 | + | 0.0441059i | ||||
\(514\) | 11.2015 | + | 19.4015i | 0.494076 | + | 0.855764i | ||||
\(515\) | 0.491489 | + | 0.851283i | 0.0216576 | + | 0.0375120i | ||||
\(516\) | −2.57676 | + | 4.46308i | −0.113436 | + | 0.196476i | ||||
\(517\) | −6.04795 | −0.265989 | ||||||||
\(518\) | −13.5265 | − | 1.71608i | −0.594321 | − | 0.0754004i | ||||
\(519\) | −5.50115 | −0.241474 | ||||||||
\(520\) | −10.2494 | + | 17.7525i | −0.449467 | + | 0.778500i | ||||
\(521\) | −11.8059 | − | 20.4484i | −0.517225 | − | 0.895861i | −0.999800 | − | 0.0200057i | \(-0.993632\pi\) |
0.482574 | − | 0.875855i | \(-0.339702\pi\) | |||||||
\(522\) | −3.62471 | − | 6.27819i | −0.158649 | − | 0.274789i | ||||
\(523\) | −21.7003 | + | 37.5861i | −0.948889 | + | 1.64352i | −0.201118 | + | 0.979567i | \(0.564457\pi\) |
−0.747771 | + | 0.663957i | \(0.768876\pi\) | |||||||
\(524\) | 15.3047 | 0.668591 | ||||||||
\(525\) | 5.37529 | + | 12.8063i | 0.234597 | + | 0.558913i | ||||
\(526\) | −25.0170 | −1.09079 | ||||||||
\(527\) | −5.24943 | + | 9.09227i | −0.228669 | + | 0.396066i | ||||
\(528\) | −0.500000 | − | 0.866025i | −0.0217597 | − | 0.0376889i | ||||
\(529\) | 9.59476 | + | 16.6186i | 0.417163 | + | 0.722548i | ||||
\(530\) | −10.2494 | + | 17.7525i | −0.445207 | + | 0.771120i | ||||
\(531\) | 11.5565 | 0.501508 | ||||||||
\(532\) | 1.84648 | − | 2.42997i | 0.0800551 | − | 0.105353i | ||||
\(533\) | −52.8206 | −2.28791 | ||||||||
\(534\) | 9.20147 | − | 15.9374i | 0.398187 | − | 0.689680i | ||||
\(535\) | −14.4952 | − | 25.1064i | −0.626681 | − | 1.08544i | ||||
\(536\) | −3.12471 | − | 5.41216i | −0.134967 | − | 0.233770i | ||||
\(537\) | −0.826185 | + | 1.43099i | −0.0356525 | + | 0.0617520i | ||||
\(538\) | 8.10327 | 0.349357 | ||||||||
\(539\) | −4.90294 | + | 4.99611i | −0.211185 | + | 0.215198i | ||||
\(540\) | −3.20147 | −0.137769 | ||||||||
\(541\) | −8.49517 | + | 14.7141i | −0.365236 | + | 0.632607i | −0.988814 | − | 0.149154i | \(-0.952345\pi\) |
0.623578 | + | 0.781761i | \(0.285678\pi\) | |||||||
\(542\) | 2.40294 | + | 4.16202i | 0.103215 | + | 0.178774i | ||||
\(543\) | −12.4509 | − | 21.5656i | −0.534319 | − | 0.925468i | ||||
\(544\) | −0.500000 | + | 0.866025i | −0.0214373 | + | 0.0371305i | ||||
\(545\) | 31.0553 | 1.33026 | ||||||||
\(546\) | −10.2494 | + | 13.4883i | −0.438635 | + | 0.577244i | ||||
\(547\) | −1.34533 | −0.0575222 | −0.0287611 | − | 0.999586i | \(-0.509156\pi\) | ||||
−0.0287611 | + | 0.999586i | \(0.509156\pi\) | |||||||
\(548\) | 3.20147 | − | 5.54511i | 0.136760 | − | 0.236875i | ||||
\(549\) | −4.85016 | − | 8.40073i | −0.207000 | − | 0.358534i | ||||
\(550\) | −2.62471 | − | 4.54614i | −0.111918 | − | 0.193848i | ||||
\(551\) | −4.18118 | + | 7.24201i | −0.178124 | + | 0.308520i | ||||
\(552\) | 1.95205 | 0.0830846 | ||||||||
\(553\) | −5.73879 | − | 13.6723i | −0.244038 | − | 0.581407i | ||||
\(554\) | −11.2088 | −0.476218 | ||||||||
\(555\) | 8.24943 | − | 14.2884i | 0.350169 | − | 0.606510i | ||||
\(556\) | −10.8741 | − | 18.8346i | −0.461166 | − | 0.798763i | ||||
\(557\) | 8.32733 | + | 14.4234i | 0.352840 | + | 0.611138i | 0.986746 | − | 0.162273i | \(-0.0518825\pi\) |
−0.633905 | + | 0.773411i | \(0.718549\pi\) | |||||||
\(558\) | −5.24943 | + | 9.09227i | −0.222226 | + | 0.384907i | ||||
\(559\) | −32.9977 | −1.39565 | ||||||||
\(560\) | 8.40294 | + | 1.06607i | 0.355089 | + | 0.0450495i | ||||
\(561\) | 1.00000 | 0.0422200 | ||||||||
\(562\) | 8.74943 | − | 15.1544i | 0.369072 | − | 0.639252i | ||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 3.02398 | + | 5.23768i | 0.127332 | + | 0.220546i | ||||
\(565\) | −20.0074 | + | 34.6538i | −0.841716 | + | 1.45789i | ||||
\(566\) | 27.4006 | 1.15174 | ||||||||
\(567\) | −2.62471 | − | 0.332992i | −0.110228 | − | 0.0139844i | ||||
\(568\) | 5.24943 | 0.220261 | ||||||||
\(569\) | 5.27708 | − | 9.14017i | 0.221227 | − | 0.383176i | −0.733954 | − | 0.679199i | \(-0.762327\pi\) |
0.955181 | + | 0.296023i | \(0.0956606\pi\) | |||||||
\(570\) | 1.84648 | + | 3.19820i | 0.0773406 | + | 0.133958i | ||||
\(571\) | −2.37529 | − | 4.11412i | −0.0994027 | − | 0.172171i | 0.812035 | − | 0.583609i | \(-0.198360\pi\) |
−0.911438 | + | 0.411438i | \(0.865027\pi\) | |||||||
\(572\) | 3.20147 | − | 5.54511i | 0.133860 | − | 0.231853i | ||||
\(573\) | −4.80589 | −0.200769 | ||||||||
\(574\) | 8.44722 | + | 20.1250i | 0.352580 | + | 0.840001i | ||||
\(575\) | 10.2471 | 0.427335 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −18.7771 | − | 32.5229i | −0.781700 | − | 1.35394i | −0.930951 | − | 0.365145i | \(-0.881019\pi\) |
0.149250 | − | 0.988799i | \(-0.452314\pi\) | |||||||
\(578\) | 8.00000 | + | 13.8564i | 0.332756 | + | 0.576351i | ||||
\(579\) | −4.35499 | + | 7.54307i | −0.180987 | + | 0.313479i | ||||
\(580\) | −23.2088 | −0.963694 | ||||||||
\(581\) | 10.4952 | − | 13.8117i | 0.435413 | − | 0.573004i | ||||
\(582\) | −5.49885 | −0.227935 | ||||||||
\(583\) | 3.20147 | − | 5.54511i | 0.132591 | − | 0.229655i | ||||
\(584\) | 1.04795 | + | 1.81511i | 0.0433646 | + | 0.0751097i | ||||
\(585\) | −10.2494 | − | 17.7525i | −0.423762 | − | 0.733977i | ||||
\(586\) | 9.87414 | − | 17.1025i | 0.407897 | − | 0.706498i | ||||
\(587\) | −17.0982 | −0.705718 | −0.352859 | − | 0.935676i | \(-0.614791\pi\) | ||||
−0.352859 | + | 0.935676i | \(0.614791\pi\) | |||||||
\(588\) | 6.77823 | + | 1.74802i | 0.279530 | + | 0.0720871i | ||||
\(589\) | 12.1106 | 0.499010 | ||||||||
\(590\) | 18.4989 | − | 32.0409i | 0.761586 | − | 1.31910i | ||||
\(591\) | −0.327335 | − | 0.566960i | −0.0134647 | − | 0.0233216i | ||||
\(592\) | −2.57676 | − | 4.46308i | −0.105904 | − | 0.183431i | ||||
\(593\) | 16.1236 | − | 27.9268i | 0.662115 | − | 1.14682i | −0.317943 | − | 0.948110i | \(-0.602992\pi\) |
0.980059 | − | 0.198708i | \(-0.0636745\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | −5.12471 | + | 6.74413i | −0.210093 | + | 0.276482i | ||||
\(596\) | 6.84648 | 0.280443 | ||||||||
\(597\) | 3.84648 | − | 6.66230i | 0.157426 | − | 0.272670i | ||||
\(598\) | 6.24943 | + | 10.8243i | 0.255558 | + | 0.442639i | ||||
\(599\) | −1.69664 | − | 2.93867i | −0.0693229 | − | 0.120071i | 0.829281 | − | 0.558833i | \(-0.188751\pi\) |
−0.898603 | + | 0.438762i | \(0.855417\pi\) | |||||||
\(600\) | −2.62471 | + | 4.54614i | −0.107153 | + | 0.185595i | ||||
\(601\) | 30.4989 | 1.24407 | 0.622037 | − | 0.782988i | \(-0.286305\pi\) | ||||
0.622037 | + | 0.782988i | \(0.286305\pi\) | |||||||
\(602\) | 5.27708 | + | 12.5723i | 0.215078 | + | 0.512410i | ||||
\(603\) | 6.24943 | 0.254496 | ||||||||
\(604\) | −7.42692 | + | 12.8638i | −0.302197 | + | 0.523421i | ||||
\(605\) | 1.60074 | + | 2.77256i | 0.0650792 | + | 0.112720i | ||||
\(606\) | 9.97970 | + | 17.2854i | 0.405398 | + | 0.702170i | ||||
\(607\) | −6.49517 | + | 11.2500i | −0.263631 | + | 0.456622i | −0.967204 | − | 0.254001i | \(-0.918253\pi\) |
0.703573 | + | 0.710623i | \(0.251587\pi\) | |||||||
\(608\) | 1.15352 | 0.0467814 | ||||||||
\(609\) | −19.0277 | − | 2.41400i | −0.771040 | − | 0.0978204i | ||||
\(610\) | −31.0553 | −1.25739 | ||||||||
\(611\) | −19.3624 | + | 33.5366i | −0.783317 | + | 1.35674i | ||||
\(612\) | −0.500000 | − | 0.866025i | −0.0202113 | − | 0.0350070i | ||||
\(613\) | −10.0996 | − | 17.4930i | −0.407918 | − | 0.706535i | 0.586738 | − | 0.809777i | \(-0.300412\pi\) |
−0.994656 | + | 0.103241i | \(0.967079\pi\) | |||||||
\(614\) | −2.15352 | + | 3.73001i | −0.0869090 | + | 0.150531i | ||||
\(615\) | −26.4103 | −1.06497 | ||||||||
\(616\) | −2.62471 | − | 0.332992i | −0.105753 | − | 0.0134166i | ||||
\(617\) | 17.0936 | 0.688163 | 0.344081 | − | 0.938940i | \(-0.388190\pi\) | ||||
0.344081 | + | 0.938940i | \(0.388190\pi\) | |||||||
\(618\) | −0.153520 | + | 0.265904i | −0.00617546 | + | 0.0106962i | ||||
\(619\) | −20.8347 | − | 36.0868i | −0.837417 | − | 1.45045i | −0.892047 | − | 0.451942i | \(-0.850731\pi\) |
0.0546300 | − | 0.998507i | \(-0.482602\pi\) | |||||||
\(620\) | 16.8059 | + | 29.1087i | 0.674941 | + | 1.16903i | ||||
\(621\) | −0.976024 | + | 1.69052i | −0.0391665 | + | 0.0678383i | ||||
\(622\) | −14.7579 | −0.591739 | ||||||||
\(623\) | −18.8442 | − | 44.8952i | −0.754976 | − | 1.79869i | ||||
\(624\) | −6.40294 | −0.256323 | ||||||||
\(625\) | 11.8453 | − | 20.5167i | 0.473813 | − | 0.820669i | ||||
\(626\) | −10.3753 | − | 17.9705i | −0.414680 | − | 0.718247i | ||||
\(627\) | −0.576760 | − | 0.998977i | −0.0230336 | − | 0.0398953i | ||||
\(628\) | 4.73028 | − | 8.19308i | 0.188759 | − | 0.326940i | ||||
\(629\) | 5.15352 | 0.205484 | ||||||||
\(630\) | −5.12471 | + | 6.74413i | −0.204173 | + | 0.268693i | ||||
\(631\) | −23.8995 | −0.951424 | −0.475712 | − | 0.879601i | \(-0.657810\pi\) | ||||
−0.475712 | + | 0.879601i | \(0.657810\pi\) | |||||||
\(632\) | 2.80221 | − | 4.85357i | 0.111466 | − | 0.193065i | ||||
\(633\) | −7.29738 | − | 12.6394i | −0.290045 | − | 0.502372i | ||||
\(634\) | −8.09959 | − | 14.0289i | −0.321676 | − | 0.557159i | ||||
\(635\) | 13.3741 | − | 23.1647i | 0.530736 | − | 0.919263i | ||||
\(636\) | −6.40294 | −0.253893 | ||||||||
\(637\) | 12.0074 | + | 43.1823i | 0.475749 | + | 1.71094i | ||||
\(638\) | 7.24943 | 0.287007 | ||||||||
\(639\) | −2.62471 | + | 4.54614i | −0.103832 | + | 0.179842i | ||||
\(640\) | 1.60074 | + | 2.77256i | 0.0632747 | + | 0.109595i | ||||
\(641\) | 7.15352 | + | 12.3903i | 0.282547 | + | 0.489386i | 0.972011 | − | 0.234934i | \(-0.0754873\pi\) |
−0.689464 | + | 0.724320i | \(0.742154\pi\) | |||||||
\(642\) | 4.52766 | − | 7.84213i | 0.178692 | − | 0.309504i | ||||
\(643\) | −35.4966 | −1.39985 | −0.699924 | − | 0.714218i | \(-0.746783\pi\) | ||||
−0.699924 | + | 0.714218i | \(0.746783\pi\) | |||||||
\(644\) | 3.12471 | − | 4.11213i | 0.123131 | − | 0.162041i | ||||
\(645\) | −16.4989 | −0.649642 | ||||||||
\(646\) | −0.576760 | + | 0.998977i | −0.0226923 | + | 0.0393042i | ||||
\(647\) | −11.9078 | − | 20.6249i | −0.468143 | − | 0.810847i | 0.531194 | − | 0.847250i | \(-0.321743\pi\) |
−0.999337 | + | 0.0364027i | \(0.988410\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −5.77823 | + | 10.0082i | −0.226815 | + | 0.392856i | ||||
\(650\) | −33.6118 | −1.31836 | ||||||||
\(651\) | 10.7506 | + | 25.6126i | 0.421348 | + | 1.00384i | ||||
\(652\) | 13.0553 | 0.511286 | ||||||||
\(653\) | 6.89811 | − | 11.9479i | 0.269944 | − | 0.467557i | −0.698903 | − | 0.715216i | \(-0.746328\pi\) |
0.968847 | + | 0.247660i | \(0.0796615\pi\) | |||||||
\(654\) | 4.85016 | + | 8.40073i | 0.189656 | + | 0.328494i | ||||
\(655\) | 24.4989 | + | 42.4333i | 0.957249 | + | 1.65800i | ||||
\(656\) | −4.12471 | + | 7.14421i | −0.161043 | + | 0.278935i | ||||
\(657\) | −2.09591 | −0.0817691 | ||||||||
\(658\) | 15.8741 | + | 2.01392i | 0.618838 | + | 0.0785109i | ||||
\(659\) | 18.9447 | 0.737980 | 0.368990 | − | 0.929433i | \(-0.379704\pi\) | ||||
0.368990 | + | 0.929433i | \(0.379704\pi\) | |||||||
\(660\) | 1.60074 | − | 2.77256i | 0.0623086 | − | 0.107922i | ||||
\(661\) | −1.97970 | − | 3.42895i | −0.0770016 | − | 0.133371i | 0.824953 | − | 0.565201i | \(-0.191201\pi\) |
−0.901955 | + | 0.431830i | \(0.857868\pi\) | |||||||
\(662\) | −10.6236 | − | 18.4006i | −0.412896 | − | 0.715158i | ||||
\(663\) | 3.20147 | − | 5.54511i | 0.124335 | − | 0.215354i | ||||
\(664\) | 6.55646 | 0.254440 | ||||||||
\(665\) | 9.69296 | + | 1.22973i | 0.375877 | + | 0.0476868i | ||||
\(666\) | 5.15352 | 0.199695 | ||||||||
\(667\) | −7.07561 | + | 12.2553i | −0.273969 | + | 0.474528i | ||||
\(668\) | 3.35499 | + | 5.81102i | 0.129809 | + | 0.224835i | ||||
\(669\) | 7.45090 | + | 12.9053i | 0.288068 | + | 0.498949i | ||||
\(670\) | 10.0037 | − | 17.3269i | 0.386476 | − | 0.669396i | ||||
\(671\) | 9.70032 | 0.374477 | ||||||||
\(672\) | 1.02398 | + | 2.43956i | 0.0395007 | + | 0.0941082i | ||||
\(673\) | −8.69066 | −0.335000 | −0.167500 | − | 0.985872i | \(-0.553569\pi\) | ||||
−0.167500 | + | 0.985872i | \(0.553569\pi\) | |||||||
\(674\) | 12.7579 | − | 22.0974i | 0.491417 | − | 0.851160i | ||||
\(675\) | −2.62471 | − | 4.54614i | −0.101025 | − | 0.174981i | ||||
\(676\) | −13.9989 | − | 24.2467i | −0.538417 | − | 0.932566i | ||||
\(677\) | 15.7303 | − | 27.2456i | 0.604564 | − | 1.04714i | −0.387557 | − | 0.921846i | \(-0.626681\pi\) |
0.992120 | − | 0.125289i | \(-0.0399859\pi\) | |||||||
\(678\) | −12.4989 | −0.480015 | ||||||||
\(679\) | −8.80221 | + | 11.5837i | −0.337798 | + | 0.444542i | ||||
\(680\) | −3.20147 | −0.122771 | ||||||||
\(681\) | 0.124713 | − | 0.216009i | 0.00477900 | − | 0.00827746i | ||||
\(682\) | −5.24943 | − | 9.09227i | −0.201011 | − | 0.348161i | ||||
\(683\) | −12.3730 | − | 21.4306i | −0.473439 | − | 0.820021i | 0.526098 | − | 0.850424i | \(-0.323654\pi\) |
−0.999538 | + | 0.0304028i | \(0.990321\pi\) | |||||||
\(684\) | −0.576760 | + | 0.998977i | −0.0220530 | + | 0.0381968i | ||||
\(685\) | 20.4989 | 0.783221 | ||||||||
\(686\) | 14.5325 | − | 11.4807i | 0.554853 | − | 0.438336i | ||||
\(687\) | −4.09591 | −0.156269 | ||||||||
\(688\) | −2.57676 | + | 4.46308i | −0.0982380 | + | 0.170153i | ||||
\(689\) | −20.4989 | − | 35.5051i | −0.780944 | − | 1.35263i | ||||
\(690\) | 3.12471 | + | 5.41216i | 0.118956 | + | 0.206037i | ||||
\(691\) | −12.7771 | + | 22.1306i | −0.486063 | + | 0.841886i | −0.999872 | − | 0.0160188i | \(-0.994901\pi\) |
0.513809 | + | 0.857905i | \(0.328234\pi\) | |||||||
\(692\) | −5.50115 | −0.209122 | ||||||||
\(693\) | 1.60074 | − | 2.10657i | 0.0608069 | − | 0.0800220i | ||||
\(694\) | 3.05531 | 0.115978 | ||||||||
\(695\) | 34.8133 | − | 60.2983i | 1.32054 | − | 2.28725i | ||||
\(696\) | −3.62471 | − | 6.27819i | −0.137394 | − | 0.237974i | ||||
\(697\) | −4.12471 | − | 7.14421i | −0.156235 | − | 0.270606i | ||||
\(698\) | 2.00368 | − | 3.47048i | 0.0758404 | − | 0.131359i | ||||
\(699\) | 11.3070 | 0.427671 | ||||||||
\(700\) | 5.37529 | + | 12.8063i | 0.203167 | + | 0.484033i | ||||
\(701\) | −14.1512 | −0.534484 | −0.267242 | − | 0.963629i | \(-0.586112\pi\) | ||||
−0.267242 | + | 0.963629i | \(0.586112\pi\) | |||||||
\(702\) | 3.20147 | − | 5.54511i | 0.120832 | − | 0.209287i | ||||
\(703\) | −2.97234 | − | 5.14825i | −0.112104 | − | 0.194170i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | −9.68118 | + | 16.7683i | −0.364614 | + | 0.631530i | ||||
\(706\) | −1.09821 | −0.0413315 | ||||||||
\(707\) | 52.3877 | + | 6.64633i | 1.97024 | + | 0.249961i | ||||
\(708\) | 11.5565 | 0.434319 | ||||||||
\(709\) | 5.37529 | − | 9.31027i | 0.201873 | − | 0.349655i | −0.747259 | − | 0.664533i | \(-0.768630\pi\) |
0.949132 | + | 0.314879i | \(0.101964\pi\) | |||||||
\(710\) | 8.40294 | + | 14.5543i | 0.315357 | + | 0.546214i | ||||
\(711\) | 2.80221 | + | 4.85357i | 0.105091 | + | 0.182023i | ||||
\(712\) | 9.20147 | − | 15.9374i | 0.344840 | − | 0.597280i | ||||
\(713\) | 20.4943 | 0.767516 | ||||||||
\(714\) | −2.62471 | − | 0.332992i | −0.0982274 | − | 0.0124619i | ||||
\(715\) | 20.4989 | 0.766614 | ||||||||
\(716\) | −0.826185 | + | 1.43099i | −0.0308760 | + | 0.0534788i | ||||
\(717\) | −3.29738 | − | 5.71123i | −0.123143 | − | 0.213290i | ||||
\(718\) | −7.80589 | − | 13.5202i | −0.291313 | − | 0.504569i | ||||
\(719\) | −1.37897 | + | 2.38844i | −0.0514268 | + | 0.0890739i | −0.890593 | − | 0.454801i | \(-0.849710\pi\) |
0.839166 | + | 0.543875i | \(0.183044\pi\) | |||||||
\(720\) | −3.20147 | −0.119312 | ||||||||
\(721\) | 0.314401 | + | 0.749041i | 0.0117089 | + | 0.0278958i | ||||
\(722\) | −17.6694 | −0.657587 | ||||||||
\(723\) | −8.55646 | + | 14.8202i | −0.318218 | + | 0.551170i | ||||
\(724\) | −12.4509 | − | 21.5656i | −0.462734 | − | 0.801479i | ||||
\(725\) | −19.0277 | − | 32.9569i | −0.706669 | − | 1.22399i | ||||
\(726\) | −0.500000 | + | 0.866025i | −0.0185567 | + | 0.0321412i | ||||
\(727\) | 14.6141 | 0.542006 | 0.271003 | − | 0.962578i | \(-0.412645\pi\) | ||||
0.271003 | + | 0.962578i | \(0.412645\pi\) | |||||||
\(728\) | −10.2494 | + | 13.4883i | −0.379869 | + | 0.499908i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.35499 | + | 5.81102i | −0.124174 | + | 0.215075i | ||||
\(731\) | −2.57676 | − | 4.46308i | −0.0953049 | − | 0.165073i | ||||
\(732\) | −4.85016 | − | 8.40073i | −0.179267 | − | 0.310500i | ||||
\(733\) | −3.55278 | + | 6.15360i | −0.131225 | + | 0.227288i | −0.924149 | − | 0.382032i | \(-0.875224\pi\) |
0.792924 | + | 0.609321i | \(0.208558\pi\) | |||||||
\(734\) | 0.791166 | 0.0292025 | ||||||||
\(735\) | 6.00368 | + | 21.5911i | 0.221449 | + | 0.796401i | ||||
\(736\) | 1.95205 | 0.0719534 | ||||||||
\(737\) | −3.12471 | + | 5.41216i | −0.115100 | + | 0.199360i | ||||
\(738\) | −4.12471 | − | 7.14421i | −0.151833 | − | 0.262982i | ||||
\(739\) | 20.7483 | + | 35.9371i | 0.763238 | + | 1.32197i | 0.941173 | + | 0.337924i | \(0.109725\pi\) |
−0.177936 | + | 0.984042i | \(0.556942\pi\) | |||||||
\(740\) | 8.24943 | − | 14.2884i | 0.303255 | − | 0.525253i | ||||
\(741\) | −7.38592 | −0.271329 | ||||||||
\(742\) | −10.2494 | + | 13.4883i | −0.376268 | + | 0.495170i | ||||
\(743\) | −31.9041 | −1.17045 | −0.585224 | − | 0.810872i | \(-0.698993\pi\) | ||||
−0.585224 | + | 0.810872i | \(0.698993\pi\) | |||||||
\(744\) | −5.24943 | + | 9.09227i | −0.192453 | + | 0.333339i | ||||
\(745\) | 10.9594 | + | 18.9823i | 0.401522 | + | 0.695456i | ||||
\(746\) | −7.95573 | − | 13.7797i | −0.291280 | − | 0.504512i | ||||
\(747\) | −3.27823 | + | 5.67806i | −0.119944 | + | 0.207750i | ||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | −9.27243 | − | 22.0910i | −0.338807 | − | 0.807188i | ||||
\(750\) | −0.798528 | −0.0291581 | ||||||||
\(751\) | −6.75794 | + | 11.7051i | −0.246601 | + | 0.427125i | −0.962580 | − | 0.270996i | \(-0.912647\pi\) |
0.715980 | + | 0.698121i | \(0.245980\pi\) | |||||||
\(752\) | 3.02398 | + | 5.23768i | 0.110273 | + | 0.190999i | ||||
\(753\) | −3.97970 | − | 6.89305i | −0.145028 | − | 0.251197i | ||||
\(754\) | 23.2088 | − | 40.1989i | 0.845216 | − | 1.46396i | ||||
\(755\) | −47.5542 | −1.73067 | ||||||||
\(756\) | −2.62471 | − | 0.332992i | −0.0954599 | − | 0.0121108i | ||||
\(757\) | −18.5542 | −0.674363 | −0.337181 | − | 0.941440i | \(-0.609474\pi\) | ||||
−0.337181 | + | 0.941440i | \(0.609474\pi\) | |||||||
\(758\) | 8.52766 | − | 14.7703i | 0.309738 | − | 0.536483i | ||||
\(759\) | −0.976024 | − | 1.69052i | −0.0354274 | − | 0.0613621i | ||||
\(760\) | 1.84648 | + | 3.19820i | 0.0669789 | + | 0.116011i | ||||
\(761\) | −7.87529 | + | 13.6404i | −0.285479 | + | 0.494464i | −0.972725 | − | 0.231960i | \(-0.925486\pi\) |
0.687246 | + | 0.726425i | \(0.258819\pi\) | |||||||
\(762\) | 8.35499 | 0.302669 | ||||||||
\(763\) | 25.4606 | + | 3.23013i | 0.921734 | + | 0.116939i | ||||
\(764\) | −4.80589 | −0.173871 | ||||||||
\(765\) | 1.60074 | − | 2.77256i | 0.0578747 | − | 0.100242i | ||||
\(766\) | −6.72062 | − | 11.6405i | −0.242826 | − | 0.420587i | ||||
\(767\) | 36.9977 | + | 64.0819i | 1.33591 | + | 2.31386i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 41.2854 | 1.48879 | 0.744395 | − | 0.667739i | \(-0.232738\pi\) | ||||
0.744395 | + | 0.667739i | \(0.232738\pi\) | |||||||
\(770\) | −3.27823 | − | 7.81020i | −0.118139 | − | 0.281460i | ||||
\(771\) | −22.4029 | −0.806822 | ||||||||
\(772\) | −4.35499 | + | 7.54307i | −0.156740 | + | 0.271481i | ||||
\(773\) | −2.45458 | − | 4.25145i | −0.0882850 | − | 0.152914i | 0.818501 | − | 0.574505i | \(-0.194805\pi\) |
−0.906786 | + | 0.421591i | \(0.861472\pi\) | |||||||
\(774\) | −2.57676 | − | 4.46308i | −0.0926197 | − | 0.160422i | ||||
\(775\) | −27.5565 | + | 47.7292i | −0.989857 | + | 1.71448i | ||||
\(776\) | −5.49885 | −0.197397 | ||||||||
\(777\) | 8.24943 | − | 10.8563i | 0.295946 | − | 0.389466i | ||||
\(778\) | −7.20147 | −0.258185 | ||||||||
\(779\) | −4.75794 | + | 8.24099i | −0.170471 | + | 0.295264i | ||||
\(780\) | −10.2494 | − | 17.7525i | −0.366988 | − | 0.635642i | ||||
\(781\) | −2.62471 | − | 4.54614i | −0.0939196 | − | 0.162674i | ||||
\(782\) | −0.976024 | + | 1.69052i | −0.0349025 | + | 0.0604530i | ||||
\(783\) | 7.24943 | 0.259073 | ||||||||
\(784\) | 6.77823 | + | 1.74802i | 0.242080 | + | 0.0624292i | ||||
\(785\) | 30.2877 | 1.08101 | ||||||||
\(786\) | −7.65237 | + | 13.2543i | −0.272951 | + | 0.472765i | ||||
\(787\) | −0.384949 | − | 0.666751i | −0.0137219 | − | 0.0237671i | 0.859083 | − | 0.511836i | \(-0.171035\pi\) |
−0.872805 | + | 0.488069i | \(0.837701\pi\) | |||||||
\(788\) | −0.327335 | − | 0.566960i | −0.0116608 | − | 0.0201971i | ||||
\(789\) | 12.5085 | − | 21.6654i | 0.445315 | − | 0.771308i | ||||
\(790\) | 17.9424 | 0.638361 | ||||||||
\(791\) | −20.0074 | + | 26.3297i | −0.711380 | + | 0.936177i | ||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 31.0553 | − | 53.7894i | 1.10281 | − | 1.91012i | ||||
\(794\) | −6.47119 | − | 11.2084i | −0.229654 | − | 0.397772i | ||||
\(795\) | −10.2494 | − | 17.7525i | −0.363510 | − | 0.629617i | ||||
\(796\) | 3.84648 | − | 6.66230i | 0.136335 | − | 0.236139i | ||||
\(797\) | 28.9092 | 1.02401 | 0.512007 | − | 0.858981i | \(-0.328902\pi\) | ||||
0.512007 | + | 0.858981i | \(0.328902\pi\) | |||||||
\(798\) | 1.18118 | + | 2.81408i | 0.0418132 | + | 0.0996175i | ||||
\(799\) | −6.04795 | −0.213961 | ||||||||
\(800\) | −2.62471 | + | 4.54614i | −0.0927976 | + | 0.160730i | ||||
\(801\) | 9.20147 | + | 15.9374i | 0.325118 | + | 0.563121i | ||||
\(802\) | 8.45090 | + | 14.6374i | 0.298412 | + | 0.516864i | ||||
\(803\) | 1.04795 | − | 1.81511i | 0.0369815 | − | 0.0640538i | ||||
\(804\) | 6.24943 | 0.220400 | ||||||||
\(805\) | 16.4029 | + | 2.08101i | 0.578128 | + | 0.0733460i | ||||
\(806\) | −67.2236 | −2.36785 | ||||||||
\(807\) | −4.05163 | + | 7.01764i | −0.142624 | + | 0.247032i | ||||
\(808\) | 9.97970 | + | 17.2854i | 0.351085 | + | 0.608097i | ||||
\(809\) | 10.1247 | + | 17.5365i | 0.355966 | + | 0.616551i | 0.987283 | − | 0.158974i | \(-0.0508186\pi\) |
−0.631317 | + | 0.775525i | \(0.717485\pi\) | |||||||
\(810\) | 1.60074 | − | 2.77256i | 0.0562441 | − | 0.0974177i | ||||
\(811\) | −48.4989 | −1.70302 | −0.851512 | − | 0.524334i | \(-0.824314\pi\) | ||||
−0.851512 | + | 0.524334i | \(0.824314\pi\) | |||||||
\(812\) | −19.0277 | − | 2.41400i | −0.667740 | − | 0.0847149i | ||||
\(813\) | −4.80589 | −0.168550 | ||||||||
\(814\) | −2.57676 | + | 4.46308i | −0.0903154 | + | 0.156431i | ||||
\(815\) | 20.8981 | + | 36.1966i | 0.732029 | + | 1.26791i | ||||
\(816\) | −0.500000 | − | 0.866025i | −0.0175035 | − | 0.0303170i | ||||
\(817\) | −2.97234 | + | 5.14825i | −0.103989 | + | 0.180114i | ||||
\(818\) | −37.0936 | −1.29695 | ||||||||
\(819\) | −6.55646 | − | 15.6204i | −0.229101 | − | 0.545821i | ||||
\(820\) | −26.4103 | −0.922288 | ||||||||
\(821\) | −15.6524 | + | 27.1107i | −0.546271 | + | 0.946170i | 0.452254 | + | 0.891889i | \(0.350620\pi\) |
−0.998526 | + | 0.0542809i | \(0.982713\pi\) | |||||||
\(822\) | 3.20147 | + | 5.54511i | 0.111664 | + | 0.193408i | ||||
\(823\) | −0.143858 | − | 0.249170i | −0.00501459 | − | 0.00868552i | 0.863507 | − | 0.504336i | \(-0.168263\pi\) |
−0.868522 | + | 0.495651i | \(0.834930\pi\) | |||||||
\(824\) | −0.153520 | + | 0.265904i | −0.00534811 | + | 0.00926319i | ||||
\(825\) | 5.24943 | 0.182762 | ||||||||
\(826\) | 18.4989 | − | 24.3445i | 0.643657 | − | 0.847054i | ||||
\(827\) | 37.2471 | 1.29521 | 0.647605 | − | 0.761976i | \(-0.275771\pi\) | ||||
0.647605 | + | 0.761976i | \(0.275771\pi\) | |||||||
\(828\) | −0.976024 | + | 1.69052i | −0.0339192 | + | 0.0587497i | ||||
\(829\) | −24.5768 | − | 42.5682i | −0.853586 | − | 1.47845i | −0.877950 | − | 0.478751i | \(-0.841090\pi\) |
0.0243643 | − | 0.999703i | \(-0.492244\pi\) | |||||||
\(830\) | 10.4952 | + | 18.1782i | 0.364293 | + | 0.630973i | ||||
\(831\) | 5.60442 | − | 9.70714i | 0.194415 | − | 0.336737i | ||||
\(832\) | −6.40294 | −0.221982 | ||||||||
\(833\) | −4.90294 | + | 4.99611i | −0.169877 | + | 0.173105i | ||||
\(834\) | 21.7483 | 0.753081 | ||||||||
\(835\) | −10.7409 | + | 18.6038i | −0.371705 | + | 0.643811i | ||||
\(836\) | −0.576760 | − | 0.998977i | −0.0199477 | − | 0.0345503i | ||||
\(837\) | −5.24943 | − | 9.09227i | −0.181447 | − | 0.314275i | ||||
\(838\) | −11.2291 | + | 19.4494i | −0.387904 | + | 0.671869i | ||||
\(839\) | −2.81785 | −0.0972830 | −0.0486415 | − | 0.998816i | \(-0.515489\pi\) | ||||
−0.0486415 | + | 0.998816i | \(0.515489\pi\) | |||||||
\(840\) | −5.12471 | + | 6.74413i | −0.176819 | + | 0.232695i | ||||
\(841\) | 23.5542 | 0.812213 | ||||||||
\(842\) | 11.6727 | − | 20.2176i | 0.402267 | − | 0.696746i | ||||
\(843\) | 8.74943 | + | 15.1544i | 0.301346 | + | 0.521947i | ||||
\(844\) | −7.29738 | − | 12.6394i | −0.251186 | − | 0.435067i | ||||
\(845\) | 44.8169 | − | 77.6252i | 1.54175 | − | 2.67039i | ||||
\(846\) | −6.04795 | −0.207933 | ||||||||
\(847\) | 1.02398 | + | 2.43956i | 0.0351842 | + | 0.0838244i | ||||
\(848\) | −6.40294 | −0.219878 | ||||||||
\(849\) | −13.7003 | + | 23.7297i | −0.470194 | + | 0.814400i | ||||
\(850\) | −2.62471 | − | 4.54614i | −0.0900269 | − | 0.155931i | ||||
\(851\) | −5.02996 | − | 8.71214i | −0.172425 | − | 0.298648i | ||||
\(852\) | −2.62471 | + | 4.54614i | −0.0899212 | + | 0.155748i | ||||
\(853\) | 2.39558 | 0.0820232 | 0.0410116 | − | 0.999159i | \(-0.486942\pi\) | ||||
0.0410116 | + | 0.999159i | \(0.486942\pi\) | |||||||
\(854\) | −25.4606 | − | 3.23013i | −0.871242 | − | 0.110533i | ||||
\(855\) | −3.69296 | −0.126297 | ||||||||
\(856\) | 4.52766 | − | 7.84213i | 0.154752 | − | 0.268039i | ||||
\(857\) | −0.404094 | − | 0.699912i | −0.0138036 | − | 0.0239085i | 0.859041 | − | 0.511907i | \(-0.171061\pi\) |
−0.872845 | + | 0.487998i | \(0.837727\pi\) | |||||||
\(858\) | 3.20147 | + | 5.54511i | 0.109296 | + | 0.189307i | ||||
\(859\) | −3.27823 | + | 5.67806i | −0.111852 | + | 0.193733i | −0.916517 | − | 0.399996i | \(-0.869012\pi\) |
0.804665 | + | 0.593729i | \(0.202345\pi\) | |||||||
\(860\) | −16.4989 | −0.562606 | ||||||||
\(861\) | −21.6524 | − | 2.74700i | −0.737911 | − | 0.0936174i | ||||
\(862\) | 31.8229 | 1.08389 | ||||||||
\(863\) | 10.3034 | − | 17.8459i | 0.350730 | − | 0.607483i | −0.635647 | − | 0.771980i | \(-0.719267\pi\) |
0.986378 | + | 0.164497i | \(0.0526000\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −8.80589 | − | 15.2522i | −0.299409 | − | 0.518592i | ||||
\(866\) | −15.1524 | + | 26.2447i | −0.514898 | + | 0.891830i | ||||
\(867\) | −16.0000 | −0.543388 | ||||||||
\(868\) | 10.7506 | + | 25.6126i | 0.364898 | + | 0.869349i | ||||
\(869\) | −5.60442 | −0.190117 | ||||||||
\(870\) | 11.6044 | − | 20.0994i | 0.393427 | − | 0.681435i | ||||
\(871\) | 20.0074 | + | 34.6538i | 0.677924 | + | 1.17420i | ||||
\(872\) | 4.85016 | + | 8.40073i | 0.164247 | + | 0.284484i | ||||
\(873\) | 2.74943 | − | 4.76214i | 0.0930539 | − | 0.161174i | ||||
\(874\) | 2.25172 | 0.0761657 | ||||||||
\(875\) | −1.27823 | + | 1.68216i | −0.0432121 | + | 0.0568672i | ||||
\(876\) | −2.09591 | −0.0708141 | ||||||||
\(877\) | −13.3011 | + | 23.0381i | −0.449145 | + | 0.777942i | −0.998331 | − | 0.0577586i | \(-0.981605\pi\) |
0.549186 | + | 0.835700i | \(0.314938\pi\) | |||||||
\(878\) | 5.33102 | + | 9.23359i | 0.179913 | + | 0.311619i | ||||
\(879\) | 9.87414 | + | 17.1025i | 0.333046 | + | 0.576853i | ||||
\(880\) | 1.60074 | − | 2.77256i | 0.0539608 | − | 0.0934629i | ||||
\(881\) | −8.49885 | −0.286334 | −0.143167 | − | 0.989699i | \(-0.545729\pi\) | ||||
−0.143167 | + | 0.989699i | \(0.545729\pi\) | |||||||
\(882\) | −4.90294 | + | 4.99611i | −0.165091 | + | 0.168228i | ||||
\(883\) | 46.2448 | 1.55626 | 0.778131 | − | 0.628102i | \(-0.216168\pi\) | ||||
0.778131 | + | 0.628102i | \(0.216168\pi\) | |||||||
\(884\) | 3.20147 | − | 5.54511i | 0.107677 | − | 0.186502i | ||||
\(885\) | 18.4989 | + | 32.0409i | 0.621832 | + | 1.07704i | ||||
\(886\) | 18.0277 | + | 31.2248i | 0.605651 | + | 1.04902i | ||||
\(887\) | −9.14386 | + | 15.8376i | −0.307021 | + | 0.531775i | −0.977709 | − | 0.209964i | \(-0.932665\pi\) |
0.670688 | + | 0.741739i | \(0.265999\pi\) | |||||||
\(888\) | 5.15352 | 0.172941 | ||||||||
\(889\) | 13.3741 | − | 17.6004i | 0.448554 | − | 0.590298i | ||||
\(890\) | 58.9165 | 1.97489 | ||||||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | 7.45090 | + | 12.9053i | 0.249474 | + | 0.432103i | ||||
\(893\) | 3.48822 | + | 6.04177i | 0.116729 | + | 0.202180i | ||||
\(894\) | −3.42324 | + | 5.92923i | −0.114490 | + | 0.198303i | ||||
\(895\) | −5.29002 | −0.176826 | ||||||||
\(896\) | 1.02398 | + | 2.43956i | 0.0342087 | + | 0.0815001i | ||||
\(897\) | −12.4989 | −0.417324 | ||||||||
\(898\) | −11.7003 | + | 20.2656i | −0.390445 | + | 0.676270i | ||||
\(899\) | −38.0553 | − | 65.9137i | −1.26922 | − | 2.19835i | ||||
\(900\) | −2.62471 | − | 4.54614i | −0.0874904 | − | 0.151538i | ||||
\(901\) | 3.20147 | − | 5.54511i | 0.106657 | − | 0.184734i | ||||
\(902\) | 8.24943 | 0.274676 | ||||||||
\(903\) | −13.5265 | − | 1.71608i | −0.450134 | − | 0.0571077i | ||||
\(904\) | −12.4989 | −0.415706 | ||||||||
\(905\) | 39.8612 | − | 69.0416i | 1.32503 | − | 2.29502i | ||||
\(906\) | −7.42692 | − | 12.8638i | −0.246743 | − | 0.427371i | ||||
\(907\) | 15.8347 | + | 27.4265i | 0.525782 | + | 0.910682i | 0.999549 | + | 0.0300314i | \(0.00956074\pi\) |
−0.473766 | + | 0.880651i | \(0.657106\pi\) | |||||||
\(908\) | 0.124713 | − | 0.216009i | 0.00413873 | − | 0.00716849i | ||||
\(909\) | −19.9594 | −0.662012 | ||||||||
\(910\) | −53.8036 | − | 6.82596i | −1.78357 | − | 0.226278i | ||||
\(911\) | 58.7727 | 1.94723 | 0.973613 | − | 0.228207i | \(-0.0732864\pi\) | ||||
0.973613 | + | 0.228207i | \(0.0732864\pi\) | |||||||
\(912\) | −0.576760 | + | 0.998977i | −0.0190984 | + | 0.0330794i | ||||
\(913\) | −3.27823 | − | 5.67806i | −0.108494 | − | 0.187917i | ||||
\(914\) | 9.30704 | + | 16.1203i | 0.307849 | + | 0.533211i | ||||
\(915\) | 15.5277 | − | 26.8947i | 0.513329 | − | 0.889111i | ||||
\(916\) | −4.09591 | −0.135333 | ||||||||
\(917\) | 15.6717 | + | 37.3369i | 0.517525 | + | 1.23297i | ||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | 16.4845 | − | 28.5521i | 0.543775 | − | 0.941845i | −0.454908 | − | 0.890538i | \(-0.650328\pi\) |
0.998683 | − | 0.0513070i | \(-0.0163387\pi\) | |||||||
\(920\) | 3.12471 | + | 5.41216i | 0.103019 | + | 0.178434i | ||||
\(921\) | −2.15352 | − | 3.73001i | −0.0709609 | − | 0.122908i | ||||
\(922\) | 15.7206 | − | 27.2289i | 0.517731 | − | 0.896736i | ||||
\(923\) | −33.6118 | −1.10635 | ||||||||
\(924\) | 1.60074 | − | 2.10657i | 0.0526604 | − | 0.0693011i | ||||
\(925\) | 27.0530 | 0.889498 | ||||||||
\(926\) | 11.0480 | − | 19.1356i | 0.363058 | − | 0.628835i | ||||
\(927\) | −0.153520 | − | 0.265904i | −0.00504224 | − | 0.00873342i | ||||
\(928\) | −3.62471 | − | 6.27819i | −0.118987 | − | 0.206092i | ||||
\(929\) | −20.9497 | + | 36.2860i | −0.687339 | + | 1.19051i | 0.285357 | + | 0.958421i | \(0.407888\pi\) |
−0.972696 | + | 0.232085i | \(0.925445\pi\) | |||||||
\(930\) | −33.6118 | −1.10217 | ||||||||
\(931\) | 7.81882 | + | 2.01637i | 0.256252 | + | 0.0660840i | ||||
\(932\) | 11.3070 | 0.370374 | ||||||||
\(933\) | 7.37897 | − | 12.7807i | 0.241577 | − | 0.418423i | ||||
\(934\) | −10.5288 | − | 18.2364i | −0.344513 | − | 0.596714i | ||||
\(935\) | 1.60074 | + | 2.77256i | 0.0523497 | + | 0.0906723i | ||||
\(936\) | 3.20147 | − | 5.54511i | 0.104643 | − | 0.181248i | ||||
\(937\) | −33.4966 | −1.09428 | −0.547142 | − | 0.837040i | \(-0.684284\pi\) | ||||
−0.547142 | + | 0.837040i | \(0.684284\pi\) | |||||||
\(938\) | 10.0037 | − | 13.1649i | 0.326632 | − | 0.429848i | ||||
\(939\) | 20.7506 | 0.677169 | ||||||||
\(940\) | −9.68118 | + | 16.7683i | −0.315765 | + | 0.546921i | ||||
\(941\) | 22.8741 | + | 39.6192i | 0.745676 | + | 1.29155i | 0.949878 | + | 0.312619i | \(0.101206\pi\) |
−0.204203 | + | 0.978929i | \(0.565460\pi\) | |||||||
\(942\) | 4.73028 | + | 8.19308i | 0.154121 | + | 0.266945i | ||||
\(943\) | −8.05163 | + | 13.9458i | −0.262197 | + | 0.454139i | ||||
\(944\) | 11.5565 | 0.376131 | ||||||||
\(945\) | −3.27823 | − | 7.81020i | −0.106641 | − | 0.254066i | ||||
\(946\) | 5.15352 | 0.167555 | ||||||||
\(947\) | 22.5265 | − | 39.0171i | 0.732013 | − | 1.26788i | −0.224008 | − | 0.974587i | \(-0.571914\pi\) |
0.956021 | − | 0.293297i | \(-0.0947524\pi\) | |||||||
\(948\) | 2.80221 | + | 4.85357i | 0.0910115 | + | 0.157637i | ||||
\(949\) | −6.70998 | − | 11.6220i | −0.217815 | − | 0.377267i | ||||
\(950\) | −3.02766 | + | 5.24406i | −0.0982302 | + | 0.170140i | ||||
\(951\) | 16.1992 | 0.525294 | ||||||||
\(952\) | −2.62471 | − | 0.332992i | −0.0850674 | − | 0.0107923i | ||||
\(953\) | 37.1705 | 1.20407 | 0.602036 | − | 0.798469i | \(-0.294356\pi\) | ||||
0.602036 | + | 0.798469i | \(0.294356\pi\) | |||||||
\(954\) | 3.20147 | − | 5.54511i | 0.103651 | − | 0.179530i | ||||
\(955\) | −7.69296 | − | 13.3246i | −0.248938 | − | 0.431174i | ||||
\(956\) | −3.29738 | − | 5.71123i | −0.106645 | − | 0.184714i | ||||
\(957\) | −3.62471 | + | 6.27819i | −0.117170 | + | 0.202945i | ||||
\(958\) | −21.2088 | −0.685226 | ||||||||
\(959\) | 16.8059 | + | 2.13213i | 0.542690 | + | 0.0688501i | ||||
\(960\) | −3.20147 | −0.103327 | ||||||||
\(961\) | −39.6129 | + | 68.6116i | −1.27784 | + | 2.21328i | ||||
\(962\) | 16.4989 | + | 28.5768i | 0.531944 | + | 0.921355i | ||||
\(963\) | 4.52766 | + | 7.84213i | 0.145902 | + | 0.252709i | ||||
\(964\) | −8.55646 | + | 14.8202i | −0.275585 | + | 0.477327i | ||||
\(965\) | −27.8848 | −0.897643 | ||||||||
\(966\) | 1.99885 | + | 4.76214i | 0.0643120 | + | 0.153219i | ||||
\(967\) | 42.7579 | 1.37500 | 0.687501 | − | 0.726183i | \(-0.258708\pi\) | ||||
0.687501 | + | 0.726183i | \(0.258708\pi\) | |||||||
\(968\) | −0.500000 | + | 0.866025i | −0.0160706 | + | 0.0278351i | ||||
\(969\) | −0.576760 | − | 0.998977i | −0.0185282 | − | 0.0320918i | ||||
\(970\) | −8.80221 | − | 15.2459i | −0.282622 | − | 0.489515i | ||||
\(971\) | −0.345331 | + | 0.598130i | −0.0110822 | + | 0.0191949i | −0.871513 | − | 0.490372i | \(-0.836861\pi\) |
0.860431 | + | 0.509567i | \(0.170194\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 34.8133 | − | 45.8143i | 1.11606 | − | 1.46874i | ||||
\(974\) | −38.7100 | −1.24035 | ||||||||
\(975\) | 16.8059 | − | 29.1087i | 0.538219 | − | 0.932223i | ||||
\(976\) | −4.85016 | − | 8.40073i | −0.155250 | − | 0.268901i | ||||
\(977\) | 16.5948 | + | 28.7430i | 0.530913 | + | 0.919569i | 0.999349 | + | 0.0360713i | \(0.0114843\pi\) |
−0.468436 | + | 0.883497i | \(0.655182\pi\) | |||||||
\(978\) | −6.52766 | + | 11.3062i | −0.208731 | + | 0.361533i | ||||
\(979\) | −18.4029 | −0.588161 | ||||||||
\(980\) | 6.00368 | + | 21.5911i | 0.191781 | + | 0.689704i | ||||
\(981\) | −9.70032 | −0.309707 | ||||||||
\(982\) | −9.58527 | + | 16.6022i | −0.305878 | + | 0.529797i | ||||
\(983\) | 21.3310 | + | 36.9464i | 0.680354 | + | 1.17841i | 0.974873 | + | 0.222762i | \(0.0715072\pi\) |
−0.294519 | + | 0.955646i | \(0.595159\pi\) | |||||||
\(984\) | −4.12471 | − | 7.14421i | −0.131491 | − | 0.227749i | ||||
\(985\) | 1.04795 | − | 1.81511i | 0.0333906 | − | 0.0578341i | ||||
\(986\) | 7.24943 | 0.230869 | ||||||||
\(987\) | −9.68118 | + | 12.7404i | −0.308155 | + | 0.405533i | ||||
\(988\) | −7.38592 | −0.234977 | ||||||||
\(989\) | −5.02996 | + | 8.71214i | −0.159943 | + | 0.277030i | ||||
\(990\) | 1.60074 | + | 2.77256i | 0.0508747 | + | 0.0881176i | ||||
\(991\) | 12.0074 | + | 20.7974i | 0.381426 | + | 0.660650i | 0.991266 | − | 0.131875i | \(-0.0420996\pi\) |
−0.609840 | + | 0.792525i | \(0.708766\pi\) | |||||||
\(992\) | −5.24943 | + | 9.09227i | −0.166669 | + | 0.288680i | ||||
\(993\) | 21.2471 | 0.674257 | ||||||||
\(994\) | 5.37529 | + | 12.8063i | 0.170494 | + | 0.406191i | ||||
\(995\) | 24.6288 | 0.780785 | ||||||||
\(996\) | −3.27823 | + | 5.67806i | −0.103875 | + | 0.179916i | ||||
\(997\) | −16.7985 | − | 29.0959i | −0.532015 | − | 0.921477i | −0.999301 | − | 0.0373707i | \(-0.988102\pi\) |
0.467287 | − | 0.884106i | \(-0.345232\pi\) | |||||||
\(998\) | 13.9594 | + | 24.1784i | 0.441877 | + | 0.765354i | ||||
\(999\) | −2.57676 | + | 4.46308i | −0.0815251 | + | 0.141206i |
(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.331.3 | yes | 6 | |
3.2 | odd | 2 | 1386.2.k.w.793.1 | 6 | |||
7.2 | even | 3 | 3234.2.a.bi.1.1 | 3 | |||
7.4 | even | 3 | inner | 462.2.i.f.67.3 | ✓ | 6 | |
7.5 | odd | 6 | 3234.2.a.bg.1.3 | 3 | |||
21.2 | odd | 6 | 9702.2.a.dt.1.3 | 3 | |||
21.5 | even | 6 | 9702.2.a.du.1.1 | 3 | |||
21.11 | odd | 6 | 1386.2.k.w.991.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.f.67.3 | ✓ | 6 | 7.4 | even | 3 | inner | |
462.2.i.f.331.3 | yes | 6 | 1.1 | even | 1 | trivial | |
1386.2.k.w.793.1 | 6 | 3.2 | odd | 2 | |||
1386.2.k.w.991.1 | 6 | 21.11 | odd | 6 | |||
3234.2.a.bg.1.3 | 3 | 7.5 | odd | 6 | |||
3234.2.a.bi.1.1 | 3 | 7.2 | even | 3 | |||
9702.2.a.dt.1.3 | 3 | 21.2 | odd | 6 | |||
9702.2.a.du.1.1 | 3 | 21.5 | even | 6 |