Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(289,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.j (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.6498455769.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.3 | ||
Root | \(1.33821 + 2.31784i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.529 |
Dual form | 546.2.j.b.289.3 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.651388 | + | 1.12824i | 0.291309 | + | 0.504563i | 0.974120 | − | 0.226033i | \(-0.0725757\pi\) |
−0.682810 | + | 0.730596i | \(0.739242\pi\) | |||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | −2.36323 | + | 1.18960i | −0.893216 | + | 0.449628i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.651388 | − | 1.12824i | −0.205987 | − | 0.356780i | ||||
\(11\) | −1.05939 | − | 1.83493i | −0.319419 | − | 0.553251i | 0.660948 | − | 0.750432i | \(-0.270155\pi\) |
−0.980367 | + | 0.197181i | \(0.936821\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | 0.0315412 | − | 3.60541i | 0.00874794 | − | 0.999962i | ||||
\(14\) | 2.36323 | − | 1.18960i | 0.631599 | − | 0.317935i | ||||
\(15\) | 0.651388 | − | 1.12824i | 0.168188 | − | 0.291309i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.486762 | −0.118057 | −0.0590286 | − | 0.998256i | \(-0.518800\pi\) | ||||
−0.0590286 | + | 0.998256i | \(0.518800\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | 3.13815 | − | 5.43544i | 0.719941 | − | 1.24697i | −0.241082 | − | 0.970505i | \(-0.577502\pi\) |
0.961023 | − | 0.276470i | \(-0.0891645\pi\) | |||||||
\(20\) | 0.651388 | + | 1.12824i | 0.145655 | + | 0.252281i | ||||
\(21\) | 2.21184 | + | 1.45181i | 0.482663 | + | 0.316812i | ||||
\(22\) | 1.05939 | + | 1.83493i | 0.225864 | + | 0.391207i | ||||
\(23\) | −4.78954 | −0.998688 | −0.499344 | − | 0.866404i | \(-0.666426\pi\) | ||||
−0.499344 | + | 0.866404i | \(0.666426\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 1.65139 | − | 2.86029i | 0.330278 | − | 0.572058i | ||||
\(26\) | −0.0315412 | + | 3.60541i | −0.00618573 | + | 0.707080i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.36323 | + | 1.18960i | −0.446608 | + | 0.224814i | ||||
\(29\) | 1.74338 | − | 3.01962i | 0.323738 | − | 0.560730i | −0.657518 | − | 0.753439i | \(-0.728394\pi\) |
0.981256 | + | 0.192708i | \(0.0617271\pi\) | |||||||
\(30\) | −0.651388 | + | 1.12824i | −0.118927 | + | 0.205987i | ||||
\(31\) | 2.24338 | − | 3.88565i | 0.402923 | − | 0.697883i | −0.591154 | − | 0.806559i | \(-0.701328\pi\) |
0.994077 | + | 0.108675i | \(0.0346609\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.05939 | + | 1.83493i | −0.184417 | + | 0.319419i | ||||
\(34\) | 0.486762 | 0.0834790 | ||||||||
\(35\) | −2.88153 | − | 1.89139i | −0.487068 | − | 0.319703i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −1.15751 | −0.190294 | −0.0951468 | − | 0.995463i | \(-0.530332\pi\) | ||||
−0.0951468 | + | 0.995463i | \(0.530332\pi\) | |||||||
\(38\) | −3.13815 | + | 5.43544i | −0.509075 | + | 0.881744i | ||||
\(39\) | −3.13815 | + | 1.77539i | −0.502506 | + | 0.284290i | ||||
\(40\) | −0.651388 | − | 1.12824i | −0.102993 | − | 0.178390i | ||||
\(41\) | −6.31845 | + | 10.9439i | −0.986776 | + | 1.70915i | −0.353014 | + | 0.935618i | \(0.614843\pi\) |
−0.633762 | + | 0.773528i | \(0.718490\pi\) | |||||||
\(42\) | −2.21184 | − | 1.45181i | −0.341294 | − | 0.224020i | ||||
\(43\) | −4.01356 | − | 6.95169i | −0.612062 | − | 1.06012i | −0.990892 | − | 0.134656i | \(-0.957007\pi\) |
0.378831 | − | 0.925466i | \(-0.376326\pi\) | |||||||
\(44\) | −1.05939 | − | 1.83493i | −0.159710 | − | 0.276625i | ||||
\(45\) | −1.30278 | −0.194206 | ||||||||
\(46\) | 4.78954 | 0.706179 | ||||||||
\(47\) | −3.98570 | − | 6.90344i | −0.581375 | − | 1.00697i | −0.995317 | − | 0.0966674i | \(-0.969182\pi\) |
0.413942 | − | 0.910303i | \(-0.364152\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | 4.16969 | − | 5.62260i | 0.595670 | − | 0.803229i | ||||
\(50\) | −1.65139 | + | 2.86029i | −0.233542 | + | 0.404506i | ||||
\(51\) | 0.243381 | + | 0.421549i | 0.0340802 | + | 0.0590286i | ||||
\(52\) | 0.0315412 | − | 3.60541i | 0.00437397 | − | 0.499981i | ||||
\(53\) | 4.29060 | − | 7.43153i | 0.589359 | − | 1.02080i | −0.404958 | − | 0.914335i | \(-0.632714\pi\) |
0.994317 | − | 0.106464i | \(-0.0339528\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 1.38015 | − | 2.39050i | 0.186100 | − | 0.322334i | ||||
\(56\) | 2.36323 | − | 1.18960i | 0.315800 | − | 0.158967i | ||||
\(57\) | −6.27630 | −0.831316 | ||||||||
\(58\) | −1.74338 | + | 3.01962i | −0.228917 | + | 0.396496i | ||||
\(59\) | −9.15014 | −1.19125 | −0.595623 | − | 0.803264i | \(-0.703095\pi\) | ||||
−0.595623 | + | 0.803264i | \(0.703095\pi\) | |||||||
\(60\) | 0.651388 | − | 1.12824i | 0.0840938 | − | 0.145655i | ||||
\(61\) | 5.09231 | − | 8.82015i | 0.652004 | − | 1.12930i | −0.330632 | − | 0.943760i | \(-0.607262\pi\) |
0.982636 | − | 0.185544i | \(-0.0594048\pi\) | |||||||
\(62\) | −2.24338 | + | 3.88565i | −0.284910 | + | 0.493478i | ||||
\(63\) | 0.151388 | − | 2.64142i | 0.0190731 | − | 0.332787i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.08831 | − | 2.31294i | 0.507092 | − | 0.286884i | ||||
\(66\) | 1.05939 | − | 1.83493i | 0.130402 | − | 0.225864i | ||||
\(67\) | 1.67924 | + | 2.90853i | 0.205152 | + | 0.355334i | 0.950181 | − | 0.311698i | \(-0.100898\pi\) |
−0.745029 | + | 0.667032i | \(0.767564\pi\) | |||||||
\(68\) | −0.486762 | −0.0590286 | ||||||||
\(69\) | 2.39477 | + | 4.14786i | 0.288296 | + | 0.499344i | ||||
\(70\) | 2.88153 | + | 1.89139i | 0.344409 | + | 0.226064i | ||||
\(71\) | 1.46740 | + | 2.54161i | 0.174148 | + | 0.301634i | 0.939866 | − | 0.341543i | \(-0.110949\pi\) |
−0.765718 | + | 0.643177i | \(0.777616\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −8.09337 | + | 14.0181i | −0.947257 | + | 1.64070i | −0.196090 | + | 0.980586i | \(0.562825\pi\) |
−0.751167 | + | 0.660112i | \(0.770509\pi\) | |||||||
\(74\) | 1.15751 | 0.134558 | ||||||||
\(75\) | −3.30278 | −0.381372 | ||||||||
\(76\) | 3.13815 | − | 5.43544i | 0.359971 | − | 0.623487i | ||||
\(77\) | 4.68642 | + | 3.07609i | 0.534067 | + | 0.350553i | ||||
\(78\) | 3.13815 | − | 1.77539i | 0.355326 | − | 0.201023i | ||||
\(79\) | −7.16738 | − | 12.4143i | −0.806393 | − | 1.39671i | −0.915346 | − | 0.402667i | \(-0.868083\pi\) |
0.108953 | − | 0.994047i | \(-0.465250\pi\) | |||||||
\(80\) | 0.651388 | + | 1.12824i | 0.0728274 | + | 0.126141i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 6.31845 | − | 10.9439i | 0.697756 | − | 1.20855i | ||||
\(83\) | 3.48676 | 0.382722 | 0.191361 | − | 0.981520i | \(-0.438710\pi\) | ||||
0.191361 | + | 0.981520i | \(0.438710\pi\) | |||||||
\(84\) | 2.21184 | + | 1.45181i | 0.241332 | + | 0.158406i | ||||
\(85\) | −0.317071 | − | 0.549183i | −0.0343912 | − | 0.0595673i | ||||
\(86\) | 4.01356 | + | 6.95169i | 0.432793 | + | 0.749620i | ||||
\(87\) | −3.48676 | −0.373820 | ||||||||
\(88\) | 1.05939 | + | 1.83493i | 0.112932 | + | 0.195604i | ||||
\(89\) | 9.39720 | 0.996102 | 0.498051 | − | 0.867148i | \(-0.334049\pi\) | ||||
0.498051 | + | 0.867148i | \(0.334049\pi\) | |||||||
\(90\) | 1.30278 | 0.137325 | ||||||||
\(91\) | 4.21447 | + | 8.55793i | 0.441797 | + | 0.897115i | ||||
\(92\) | −4.78954 | −0.499344 | ||||||||
\(93\) | −4.48676 | −0.465256 | ||||||||
\(94\) | 3.98570 | + | 6.90344i | 0.411094 | + | 0.712036i | ||||
\(95\) | 8.17661 | 0.838903 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 0.698602 | + | 1.21001i | 0.0709323 | + | 0.122858i | 0.899310 | − | 0.437311i | \(-0.144069\pi\) |
−0.828378 | + | 0.560170i | \(0.810736\pi\) | |||||||
\(98\) | −4.16969 | + | 5.62260i | −0.421202 | + | 0.567969i | ||||
\(99\) | 2.11879 | 0.212946 | ||||||||
\(100\) | 1.65139 | − | 2.86029i | 0.165139 | − | 0.286029i | ||||
\(101\) | 3.01725 | + | 5.22602i | 0.300227 | + | 0.520009i | 0.976187 | − | 0.216930i | \(-0.0696042\pi\) |
−0.675960 | + | 0.736938i | \(0.736271\pi\) | |||||||
\(102\) | −0.243381 | − | 0.421549i | −0.0240983 | − | 0.0417395i | ||||
\(103\) | 5.64770 | + | 9.78210i | 0.556484 | + | 0.963859i | 0.997786 | + | 0.0665006i | \(0.0211834\pi\) |
−0.441302 | + | 0.897359i | \(0.645483\pi\) | |||||||
\(104\) | −0.0315412 | + | 3.60541i | −0.00309287 | + | 0.353540i | ||||
\(105\) | −0.197224 | + | 3.44117i | −0.0192471 | + | 0.335824i | ||||
\(106\) | −4.29060 | + | 7.43153i | −0.416739 | + | 0.721814i | ||||
\(107\) | −14.0292 | −1.35626 | −0.678128 | − | 0.734943i | \(-0.737209\pi\) | ||||
−0.678128 | + | 0.734943i | \(0.737209\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −5.50000 | + | 9.52628i | −0.526804 | + | 0.912452i | 0.472708 | + | 0.881219i | \(0.343277\pi\) |
−0.999512 | + | 0.0312328i | \(0.990057\pi\) | |||||||
\(110\) | −1.38015 | + | 2.39050i | −0.131592 | + | 0.227925i | ||||
\(111\) | 0.578756 | + | 1.00243i | 0.0549331 | + | 0.0951468i | ||||
\(112\) | −2.36323 | + | 1.18960i | −0.223304 | + | 0.112407i | ||||
\(113\) | 3.56552 | + | 6.17566i | 0.335416 | + | 0.580957i | 0.983565 | − | 0.180557i | \(-0.0577899\pi\) |
−0.648149 | + | 0.761514i | \(0.724457\pi\) | |||||||
\(114\) | 6.27630 | 0.587829 | ||||||||
\(115\) | −3.11985 | − | 5.40373i | −0.290927 | − | 0.503901i | ||||
\(116\) | 1.74338 | − | 3.01962i | 0.161869 | − | 0.280365i | ||||
\(117\) | 3.10661 | + | 1.83002i | 0.287206 | + | 0.169186i | ||||
\(118\) | 9.15014 | 0.842338 | ||||||||
\(119\) | 1.15033 | − | 0.579054i | 0.105451 | − | 0.0530818i | ||||
\(120\) | −0.651388 | + | 1.12824i | −0.0594633 | + | 0.102993i | ||||
\(121\) | 3.25537 | − | 5.63846i | 0.295942 | − | 0.512587i | ||||
\(122\) | −5.09231 | + | 8.82015i | −0.461036 | + | 0.798538i | ||||
\(123\) | 12.6369 | 1.13943 | ||||||||
\(124\) | 2.24338 | − | 3.88565i | 0.201462 | − | 0.348942i | ||||
\(125\) | 10.8167 | 0.967471 | ||||||||
\(126\) | −0.151388 | + | 2.64142i | −0.0134867 | + | 0.235316i | ||||
\(127\) | 2.59305 | − | 4.49130i | 0.230096 | − | 0.398538i | −0.727740 | − | 0.685853i | \(-0.759429\pi\) |
0.957836 | + | 0.287315i | \(0.0927626\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.01356 | + | 6.95169i | −0.353374 | + | 0.612062i | ||||
\(130\) | −4.08831 | + | 2.31294i | −0.358568 | + | 0.202858i | ||||
\(131\) | 4.03186 | + | 6.98339i | 0.352265 | + | 0.610142i | 0.986646 | − | 0.162879i | \(-0.0520781\pi\) |
−0.634381 | + | 0.773021i | \(0.718745\pi\) | |||||||
\(132\) | −1.05939 | + | 1.83493i | −0.0922085 | + | 0.159710i | ||||
\(133\) | −0.950155 | + | 16.5783i | −0.0823889 | + | 1.43752i | ||||
\(134\) | −1.67924 | − | 2.90853i | −0.145064 | − | 0.251259i | ||||
\(135\) | 0.651388 | + | 1.12824i | 0.0560625 | + | 0.0971032i | ||||
\(136\) | 0.486762 | 0.0417395 | ||||||||
\(137\) | −6.79165 | −0.580250 | −0.290125 | − | 0.956989i | \(-0.593697\pi\) | ||||
−0.290125 | + | 0.956989i | \(0.593697\pi\) | |||||||
\(138\) | −2.39477 | − | 4.14786i | −0.203856 | − | 0.353089i | ||||
\(139\) | 6.45522 | + | 11.1808i | 0.547525 | + | 0.948341i | 0.998443 | + | 0.0557755i | \(0.0177631\pi\) |
−0.450919 | + | 0.892565i | \(0.648904\pi\) | |||||||
\(140\) | −2.88153 | − | 1.89139i | −0.243534 | − | 0.159851i | ||||
\(141\) | −3.98570 | + | 6.90344i | −0.335657 | + | 0.581375i | ||||
\(142\) | −1.46740 | − | 2.54161i | −0.123142 | − | 0.213287i | ||||
\(143\) | −6.64908 | + | 3.76168i | −0.556024 | + | 0.314567i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 4.54247 | 0.377232 | ||||||||
\(146\) | 8.09337 | − | 14.0181i | 0.669812 | − | 1.16015i | ||||
\(147\) | −6.95416 | − | 0.799757i | −0.573570 | − | 0.0659628i | ||||
\(148\) | −1.15751 | −0.0951468 | ||||||||
\(149\) | 11.6820 | − | 20.2338i | 0.957026 | − | 1.65762i | 0.227365 | − | 0.973810i | \(-0.426989\pi\) |
0.729661 | − | 0.683809i | \(-0.239678\pi\) | |||||||
\(150\) | 3.30278 | 0.269671 | ||||||||
\(151\) | −2.93692 | + | 5.08689i | −0.239003 | + | 0.413965i | −0.960428 | − | 0.278527i | \(-0.910154\pi\) |
0.721425 | + | 0.692492i | \(0.243487\pi\) | |||||||
\(152\) | −3.13815 | + | 5.43544i | −0.254538 | + | 0.440872i | ||||
\(153\) | 0.243381 | − | 0.421549i | 0.0196762 | − | 0.0340802i | ||||
\(154\) | −4.68642 | − | 3.07609i | −0.377643 | − | 0.247878i | ||||
\(155\) | 5.84524 | 0.469501 | ||||||||
\(156\) | −3.13815 | + | 1.77539i | −0.251253 | + | 0.142145i | ||||
\(157\) | −3.12248 | + | 5.40829i | −0.249201 | + | 0.431628i | −0.963304 | − | 0.268412i | \(-0.913501\pi\) |
0.714104 | + | 0.700040i | \(0.246835\pi\) | |||||||
\(158\) | 7.16738 | + | 12.4143i | 0.570206 | + | 0.987626i | ||||
\(159\) | −8.58119 | −0.680533 | ||||||||
\(160\) | −0.651388 | − | 1.12824i | −0.0514967 | − | 0.0891950i | ||||
\(161\) | 11.3188 | − | 5.69765i | 0.892044 | − | 0.449037i | ||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | 1.30383 | − | 2.25831i | 0.102124 | − | 0.176884i | −0.810435 | − | 0.585828i | \(-0.800769\pi\) |
0.912560 | + | 0.408944i | \(0.134103\pi\) | |||||||
\(164\) | −6.31845 | + | 10.9439i | −0.493388 | + | 0.854573i | ||||
\(165\) | −2.76031 | −0.214890 | ||||||||
\(166\) | −3.48676 | −0.270625 | ||||||||
\(167\) | −3.45416 | + | 5.98279i | −0.267291 | + | 0.462962i | −0.968161 | − | 0.250327i | \(-0.919462\pi\) |
0.700870 | + | 0.713289i | \(0.252795\pi\) | |||||||
\(168\) | −2.21184 | − | 1.45181i | −0.170647 | − | 0.112010i | ||||
\(169\) | −12.9980 | − | 0.227438i | −0.999847 | − | 0.0174952i | ||||
\(170\) | 0.317071 | + | 0.549183i | 0.0243182 | + | 0.0421204i | ||||
\(171\) | 3.13815 | + | 5.43544i | 0.239980 | + | 0.415658i | ||||
\(172\) | −4.01356 | − | 6.95169i | −0.306031 | − | 0.530061i | ||||
\(173\) | 3.86355 | − | 6.69186i | 0.293740 | − | 0.508773i | −0.680951 | − | 0.732329i | \(-0.738433\pi\) |
0.974691 | + | 0.223556i | \(0.0717666\pi\) | |||||||
\(174\) | 3.48676 | 0.264331 | ||||||||
\(175\) | −0.500000 | + | 8.72401i | −0.0377964 | + | 0.659473i | ||||
\(176\) | −1.05939 | − | 1.83493i | −0.0798549 | − | 0.138313i | ||||
\(177\) | 4.57507 | + | 7.92425i | 0.343883 | + | 0.595623i | ||||
\(178\) | −9.39720 | −0.704350 | ||||||||
\(179\) | −9.57539 | − | 16.5851i | −0.715698 | − | 1.23963i | −0.962690 | − | 0.270608i | \(-0.912775\pi\) |
0.246992 | − | 0.969018i | \(-0.420558\pi\) | |||||||
\(180\) | −1.30278 | −0.0971032 | ||||||||
\(181\) | 13.0972 | 0.973506 | 0.486753 | − | 0.873540i | \(-0.338181\pi\) | ||||
0.486753 | + | 0.873540i | \(0.338181\pi\) | |||||||
\(182\) | −4.21447 | − | 8.55793i | −0.312397 | − | 0.634356i | ||||
\(183\) | −10.1846 | −0.752869 | ||||||||
\(184\) | 4.78954 | 0.353089 | ||||||||
\(185\) | −0.753989 | − | 1.30595i | −0.0554344 | − | 0.0960151i | ||||
\(186\) | 4.48676 | 0.328985 | ||||||||
\(187\) | 0.515673 | + | 0.893172i | 0.0377098 | + | 0.0653152i | ||||
\(188\) | −3.98570 | − | 6.90344i | −0.290687 | − | 0.503485i | ||||
\(189\) | −2.36323 | + | 1.18960i | −0.171900 | + | 0.0865309i | ||||
\(190\) | −8.17661 | −0.593194 | ||||||||
\(191\) | 5.74444 | − | 9.94966i | 0.415653 | − | 0.719932i | −0.579844 | − | 0.814728i | \(-0.696886\pi\) |
0.995497 | + | 0.0947956i | \(0.0302197\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 0.138150 | + | 0.239283i | 0.00994426 | + | 0.0172240i | 0.870955 | − | 0.491363i | \(-0.163501\pi\) |
−0.861010 | + | 0.508587i | \(0.830168\pi\) | |||||||
\(194\) | −0.698602 | − | 1.21001i | −0.0501567 | − | 0.0868740i | ||||
\(195\) | −4.04721 | − | 2.38411i | −0.289827 | − | 0.170730i | ||||
\(196\) | 4.16969 | − | 5.62260i | 0.297835 | − | 0.401615i | ||||
\(197\) | −6.63552 | + | 11.4931i | −0.472761 | + | 0.818846i | −0.999514 | − | 0.0311721i | \(-0.990076\pi\) |
0.526753 | + | 0.850019i | \(0.323409\pi\) | |||||||
\(198\) | −2.11879 | −0.150576 | ||||||||
\(199\) | 19.0219 | 1.34842 | 0.674212 | − | 0.738538i | \(-0.264483\pi\) | ||||
0.674212 | + | 0.738538i | \(0.264483\pi\) | |||||||
\(200\) | −1.65139 | + | 2.86029i | −0.116771 | + | 0.202253i | ||||
\(201\) | 1.67924 | − | 2.90853i | 0.118445 | − | 0.205152i | ||||
\(202\) | −3.01725 | − | 5.22602i | −0.212293 | − | 0.367702i | ||||
\(203\) | −0.527853 | + | 9.20999i | −0.0370480 | + | 0.646415i | ||||
\(204\) | 0.243381 | + | 0.421549i | 0.0170401 | + | 0.0295143i | ||||
\(205\) | −16.4630 | −1.14983 | ||||||||
\(206\) | −5.64770 | − | 9.78210i | −0.393494 | − | 0.681551i | ||||
\(207\) | 2.39477 | − | 4.14786i | 0.166448 | − | 0.288296i | ||||
\(208\) | 0.0315412 | − | 3.60541i | 0.00218699 | − | 0.249990i | ||||
\(209\) | −13.2982 | −0.919853 | ||||||||
\(210\) | 0.197224 | − | 3.44117i | 0.0136098 | − | 0.237464i | ||||
\(211\) | −1.98750 | + | 3.44245i | −0.136825 | + | 0.236988i | −0.926293 | − | 0.376804i | \(-0.877023\pi\) |
0.789468 | + | 0.613792i | \(0.210357\pi\) | |||||||
\(212\) | 4.29060 | − | 7.43153i | 0.294679 | − | 0.510400i | ||||
\(213\) | 1.46740 | − | 2.54161i | 0.100545 | − | 0.174148i | ||||
\(214\) | 14.0292 | 0.959019 | ||||||||
\(215\) | 5.22877 | − | 9.05649i | 0.356599 | − | 0.617647i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −0.679241 | + | 11.8514i | −0.0461099 | + | 0.804526i | ||||
\(218\) | 5.50000 | − | 9.52628i | 0.372507 | − | 0.645201i | ||||
\(219\) | 16.1867 | 1.09380 | ||||||||
\(220\) | 1.38015 | − | 2.39050i | 0.0930499 | − | 0.161167i | ||||
\(221\) | −0.0153530 | + | 1.75498i | −0.00103276 | + | 0.118053i | ||||
\(222\) | −0.578756 | − | 1.00243i | −0.0388435 | − | 0.0672790i | ||||
\(223\) | 9.58013 | − | 16.5933i | 0.641533 | − | 1.11117i | −0.343557 | − | 0.939132i | \(-0.611632\pi\) |
0.985091 | − | 0.172036i | \(-0.0550347\pi\) | |||||||
\(224\) | 2.36323 | − | 1.18960i | 0.157900 | − | 0.0794837i | ||||
\(225\) | 1.65139 | + | 2.86029i | 0.110093 | + | 0.190686i | ||||
\(226\) | −3.56552 | − | 6.17566i | −0.237175 | − | 0.410799i | ||||
\(227\) | −1.18251 | −0.0784861 | −0.0392430 | − | 0.999230i | \(-0.512495\pi\) | ||||
−0.0392430 | + | 0.999230i | \(0.512495\pi\) | |||||||
\(228\) | −6.27630 | −0.415658 | ||||||||
\(229\) | 7.51599 | + | 13.0181i | 0.496671 | + | 0.860259i | 0.999993 | − | 0.00383994i | \(-0.00122229\pi\) |
−0.503322 | + | 0.864099i | \(0.667889\pi\) | |||||||
\(230\) | 3.11985 | + | 5.40373i | 0.205717 | + | 0.356312i | ||||
\(231\) | 0.320759 | − | 5.59660i | 0.0211044 | − | 0.368230i | ||||
\(232\) | −1.74338 | + | 3.01962i | −0.114459 | + | 0.198248i | ||||
\(233\) | −2.59706 | − | 4.49824i | −0.170139 | − | 0.294689i | 0.768329 | − | 0.640055i | \(-0.221088\pi\) |
−0.938468 | + | 0.345365i | \(0.887755\pi\) | |||||||
\(234\) | −3.10661 | − | 1.83002i | −0.203085 | − | 0.119632i | ||||
\(235\) | 5.19248 | − | 8.99364i | 0.338720 | − | 0.586680i | ||||
\(236\) | −9.15014 | −0.595623 | ||||||||
\(237\) | −7.16738 | + | 12.4143i | −0.465571 | + | 0.806393i | ||||
\(238\) | −1.15033 | + | 0.579054i | −0.0745648 | + | 0.0375345i | ||||
\(239\) | 25.3978 | 1.64285 | 0.821425 | − | 0.570317i | \(-0.193179\pi\) | ||||
0.821425 | + | 0.570317i | \(0.193179\pi\) | |||||||
\(240\) | 0.651388 | − | 1.12824i | 0.0420469 | − | 0.0728274i | ||||
\(241\) | −11.8575 | −0.763808 | −0.381904 | − | 0.924202i | \(-0.624732\pi\) | ||||
−0.381904 | + | 0.924202i | \(0.624732\pi\) | |||||||
\(242\) | −3.25537 | + | 5.63846i | −0.209263 | + | 0.362454i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 5.09231 | − | 8.82015i | 0.326002 | − | 0.564652i | ||||
\(245\) | 9.05971 | + | 1.04190i | 0.578804 | + | 0.0665648i | ||||
\(246\) | −12.6369 | −0.805699 | ||||||||
\(247\) | −19.4980 | − | 11.4858i | −1.24063 | − | 0.730822i | ||||
\(248\) | −2.24338 | + | 3.88565i | −0.142455 | + | 0.246739i | ||||
\(249\) | −1.74338 | − | 3.01962i | −0.110482 | − | 0.191361i | ||||
\(250\) | −10.8167 | −0.684105 | ||||||||
\(251\) | 10.7397 | + | 18.6017i | 0.677883 | + | 1.17413i | 0.975617 | + | 0.219480i | \(0.0704359\pi\) |
−0.297734 | + | 0.954649i | \(0.596231\pi\) | |||||||
\(252\) | 0.151388 | − | 2.64142i | 0.00953654 | − | 0.166394i | ||||
\(253\) | 5.07401 | + | 8.78844i | 0.319000 | + | 0.552525i | ||||
\(254\) | −2.59305 | + | 4.49130i | −0.162702 | + | 0.281809i | ||||
\(255\) | −0.317071 | + | 0.549183i | −0.0198558 | + | 0.0343912i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.84589 | −0.427035 | −0.213517 | − | 0.976939i | \(-0.568492\pi\) | ||||
−0.213517 | + | 0.976939i | \(0.568492\pi\) | |||||||
\(258\) | 4.01356 | − | 6.95169i | 0.249873 | − | 0.432793i | ||||
\(259\) | 2.73546 | − | 1.37698i | 0.169973 | − | 0.0855613i | ||||
\(260\) | 4.08831 | − | 2.31294i | 0.253546 | − | 0.143442i | ||||
\(261\) | 1.74338 | + | 3.01962i | 0.107913 | + | 0.186910i | ||||
\(262\) | −4.03186 | − | 6.98339i | −0.249089 | − | 0.431435i | ||||
\(263\) | −7.69998 | − | 13.3368i | −0.474801 | − | 0.822380i | 0.524782 | − | 0.851236i | \(-0.324147\pi\) |
−0.999584 | + | 0.0288567i | \(0.990813\pi\) | |||||||
\(264\) | 1.05939 | − | 1.83493i | 0.0652012 | − | 0.112932i | ||||
\(265\) | 11.1794 | 0.686743 | ||||||||
\(266\) | 0.950155 | − | 16.5783i | 0.0582578 | − | 1.01648i | ||||
\(267\) | −4.69860 | − | 8.13822i | −0.287550 | − | 0.498051i | ||||
\(268\) | 1.67924 | + | 2.90853i | 0.102576 | + | 0.177667i | ||||
\(269\) | −11.7313 | −0.715272 | −0.357636 | − | 0.933861i | \(-0.616417\pi\) | ||||
−0.357636 | + | 0.933861i | \(0.616417\pi\) | |||||||
\(270\) | −0.651388 | − | 1.12824i | −0.0396422 | − | 0.0686623i | ||||
\(271\) | −26.0856 | −1.58459 | −0.792293 | − | 0.610141i | \(-0.791113\pi\) | ||||
−0.792293 | + | 0.610141i | \(0.791113\pi\) | |||||||
\(272\) | −0.486762 | −0.0295143 | ||||||||
\(273\) | 5.30415 | − | 7.92881i | 0.321022 | − | 0.479873i | ||||
\(274\) | 6.79165 | 0.410299 | ||||||||
\(275\) | −6.99788 | −0.421988 | ||||||||
\(276\) | 2.39477 | + | 4.14786i | 0.144148 | + | 0.249672i | ||||
\(277\) | 23.4307 | 1.40781 | 0.703906 | − | 0.710293i | \(-0.251438\pi\) | ||||
0.703906 | + | 0.710293i | \(0.251438\pi\) | |||||||
\(278\) | −6.45522 | − | 11.1808i | −0.387158 | − | 0.670578i | ||||
\(279\) | 2.24338 | + | 3.88565i | 0.134308 | + | 0.232628i | ||||
\(280\) | 2.88153 | + | 1.89139i | 0.172204 | + | 0.113032i | ||||
\(281\) | 6.15751 | 0.367326 | 0.183663 | − | 0.982989i | \(-0.441204\pi\) | ||||
0.183663 | + | 0.982989i | \(0.441204\pi\) | |||||||
\(282\) | 3.98570 | − | 6.90344i | 0.237345 | − | 0.411094i | ||||
\(283\) | −10.9661 | − | 18.9939i | −0.651870 | − | 1.12907i | −0.982669 | − | 0.185370i | \(-0.940651\pi\) |
0.330799 | − | 0.943701i | \(-0.392682\pi\) | |||||||
\(284\) | 1.46740 | + | 2.54161i | 0.0870742 | + | 0.150817i | ||||
\(285\) | −4.08831 | − | 7.08115i | −0.242170 | − | 0.419451i | ||||
\(286\) | 6.64908 | − | 3.76168i | 0.393168 | − | 0.222433i | ||||
\(287\) | 1.91307 | − | 33.3793i | 0.112925 | − | 1.97032i | ||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | −16.7631 | −0.986062 | ||||||||
\(290\) | −4.54247 | −0.266743 | ||||||||
\(291\) | 0.698602 | − | 1.21001i | 0.0409528 | − | 0.0709323i | ||||
\(292\) | −8.09337 | + | 14.0181i | −0.473629 | + | 0.820349i | ||||
\(293\) | −8.74075 | − | 15.1394i | −0.510640 | − | 0.884455i | −0.999924 | − | 0.0123300i | \(-0.996075\pi\) |
0.489284 | − | 0.872125i | \(-0.337258\pi\) | |||||||
\(294\) | 6.95416 | + | 0.799757i | 0.405575 | + | 0.0466428i | ||||
\(295\) | −5.96029 | − | 10.3235i | −0.347021 | − | 0.601059i | ||||
\(296\) | 1.15751 | 0.0672790 | ||||||||
\(297\) | −1.05939 | − | 1.83493i | −0.0614723 | − | 0.106473i | ||||
\(298\) | −11.6820 | + | 20.2338i | −0.676720 | + | 1.17211i | ||||
\(299\) | −0.151068 | + | 17.2683i | −0.00873646 | + | 0.998649i | ||||
\(300\) | −3.30278 | −0.190686 | ||||||||
\(301\) | 17.7547 | + | 11.6539i | 1.02336 | + | 0.671718i | ||||
\(302\) | 2.93692 | − | 5.08689i | 0.169001 | − | 0.292718i | ||||
\(303\) | 3.01725 | − | 5.22602i | 0.173336 | − | 0.300227i | ||||
\(304\) | 3.13815 | − | 5.43544i | 0.179985 | − | 0.311744i | ||||
\(305\) | 13.2683 | 0.759740 | ||||||||
\(306\) | −0.243381 | + | 0.421549i | −0.0139132 | + | 0.0240983i | ||||
\(307\) | −12.0673 | −0.688718 | −0.344359 | − | 0.938838i | \(-0.611904\pi\) | ||||
−0.344359 | + | 0.938838i | \(0.611904\pi\) | |||||||
\(308\) | 4.68642 | + | 3.07609i | 0.267034 | + | 0.175276i | ||||
\(309\) | 5.64770 | − | 9.78210i | 0.321286 | − | 0.556484i | ||||
\(310\) | −5.84524 | −0.331988 | ||||||||
\(311\) | 0.755881 | − | 1.30923i | 0.0428621 | − | 0.0742393i | −0.843798 | − | 0.536660i | \(-0.819686\pi\) |
0.886661 | + | 0.462421i | \(0.153019\pi\) | |||||||
\(312\) | 3.13815 | − | 1.77539i | 0.177663 | − | 0.100512i | ||||
\(313\) | −0.862908 | − | 1.49460i | −0.0487744 | − | 0.0844798i | 0.840607 | − | 0.541645i | \(-0.182198\pi\) |
−0.889382 | + | 0.457165i | \(0.848865\pi\) | |||||||
\(314\) | 3.12248 | − | 5.40829i | 0.176212 | − | 0.305207i | ||||
\(315\) | 3.07876 | − | 1.54979i | 0.173468 | − | 0.0873205i | ||||
\(316\) | −7.16738 | − | 12.4143i | −0.403197 | − | 0.698357i | ||||
\(317\) | −10.6520 | − | 18.4499i | −0.598278 | − | 1.03625i | −0.993075 | − | 0.117479i | \(-0.962519\pi\) |
0.394798 | − | 0.918768i | \(-0.370815\pi\) | |||||||
\(318\) | 8.58119 | 0.481209 | ||||||||
\(319\) | −7.38771 | −0.413633 | ||||||||
\(320\) | 0.651388 | + | 1.12824i | 0.0364137 | + | 0.0630704i | ||||
\(321\) | 7.01462 | + | 12.1497i | 0.391518 | + | 0.678128i | ||||
\(322\) | −11.3188 | + | 5.69765i | −0.630770 | + | 0.317517i | ||||
\(323\) | −1.52753 | + | 2.64576i | −0.0849942 | + | 0.147214i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −10.2604 | − | 6.04415i | −0.569146 | − | 0.335269i | ||||
\(326\) | −1.30383 | + | 2.25831i | −0.0722126 | + | 0.125076i | ||||
\(327\) | 11.0000 | 0.608301 | ||||||||
\(328\) | 6.31845 | − | 10.9439i | 0.348878 | − | 0.604274i | ||||
\(329\) | 17.6315 | + | 11.5730i | 0.972055 | + | 0.638040i | ||||
\(330\) | 2.76031 | 0.151950 | ||||||||
\(331\) | −8.21691 | + | 14.2321i | −0.451642 | + | 0.782267i | −0.998488 | − | 0.0549662i | \(-0.982495\pi\) |
0.546846 | + | 0.837233i | \(0.315828\pi\) | |||||||
\(332\) | 3.48676 | 0.191361 | ||||||||
\(333\) | 0.578756 | − | 1.00243i | 0.0317156 | − | 0.0549331i | ||||
\(334\) | 3.45416 | − | 5.98279i | 0.189003 | − | 0.327364i | ||||
\(335\) | −2.18767 | + | 3.78916i | −0.119525 | + | 0.207024i | ||||
\(336\) | 2.21184 | + | 1.45181i | 0.120666 | + | 0.0792029i | ||||
\(337\) | −12.9178 | −0.703678 | −0.351839 | − | 0.936060i | \(-0.614444\pi\) | ||||
−0.351839 | + | 0.936060i | \(0.614444\pi\) | |||||||
\(338\) | 12.9980 | + | 0.227438i | 0.706999 | + | 0.0123710i | ||||
\(339\) | 3.56552 | − | 6.17566i | 0.193652 | − | 0.335416i | ||||
\(340\) | −0.317071 | − | 0.549183i | −0.0171956 | − | 0.0297836i | ||||
\(341\) | −9.50650 | −0.514806 | ||||||||
\(342\) | −3.13815 | − | 5.43544i | −0.169692 | − | 0.293915i | ||||
\(343\) | −3.16527 | + | 18.2478i | −0.170908 | + | 0.985287i | ||||
\(344\) | 4.01356 | + | 6.95169i | 0.216397 | + | 0.374810i | ||||
\(345\) | −3.11985 | + | 5.40373i | −0.167967 | + | 0.290927i | ||||
\(346\) | −3.86355 | + | 6.69186i | −0.207706 | + | 0.359757i | ||||
\(347\) | −16.0387 | −0.861004 | −0.430502 | − | 0.902590i | \(-0.641663\pi\) | ||||
−0.430502 | + | 0.902590i | \(0.641663\pi\) | |||||||
\(348\) | −3.48676 | −0.186910 | ||||||||
\(349\) | −3.81951 | + | 6.61558i | −0.204453 | + | 0.354124i | −0.949958 | − | 0.312376i | \(-0.898875\pi\) |
0.745505 | + | 0.666500i | \(0.232208\pi\) | |||||||
\(350\) | 0.500000 | − | 8.72401i | 0.0267261 | − | 0.466318i | ||||
\(351\) | 0.0315412 | − | 3.60541i | 0.00168354 | − | 0.192443i | ||||
\(352\) | 1.05939 | + | 1.83493i | 0.0564659 | + | 0.0978018i | ||||
\(353\) | 16.1956 | + | 28.0515i | 0.862002 | + | 1.49303i | 0.869993 | + | 0.493064i | \(0.164123\pi\) |
−0.00799069 | + | 0.999968i | \(0.502544\pi\) | |||||||
\(354\) | −4.57507 | − | 7.92425i | −0.243162 | − | 0.421169i | ||||
\(355\) | −1.91169 | + | 3.31115i | −0.101462 | + | 0.175738i | ||||
\(356\) | 9.39720 | 0.498051 | ||||||||
\(357\) | −1.07664 | − | 0.706688i | −0.0569818 | − | 0.0374019i | ||||
\(358\) | 9.57539 | + | 16.5851i | 0.506075 | + | 0.876548i | ||||
\(359\) | 1.57507 | + | 2.72810i | 0.0831289 | + | 0.143983i | 0.904592 | − | 0.426278i | \(-0.140175\pi\) |
−0.821463 | + | 0.570261i | \(0.806842\pi\) | |||||||
\(360\) | 1.30278 | 0.0686623 | ||||||||
\(361\) | −10.1960 | − | 17.6599i | −0.536630 | − | 0.929471i | ||||
\(362\) | −13.0972 | −0.688373 | ||||||||
\(363\) | −6.51073 | −0.341725 | ||||||||
\(364\) | 4.21447 | + | 8.55793i | 0.220898 | + | 0.448558i | ||||
\(365\) | −21.0877 | −1.10378 | ||||||||
\(366\) | 10.1846 | 0.532359 | ||||||||
\(367\) | 2.23463 | + | 3.87049i | 0.116647 | + | 0.202038i | 0.918437 | − | 0.395568i | \(-0.129452\pi\) |
−0.801790 | + | 0.597606i | \(0.796119\pi\) | |||||||
\(368\) | −4.78954 | −0.249672 | ||||||||
\(369\) | −6.31845 | − | 10.9439i | −0.328925 | − | 0.569715i | ||||
\(370\) | 0.753989 | + | 1.30595i | 0.0391980 | + | 0.0678929i | ||||
\(371\) | −1.29909 | + | 22.6665i | −0.0674453 | + | 1.17679i | ||||
\(372\) | −4.48676 | −0.232628 | ||||||||
\(373\) | −2.47615 | + | 4.28883i | −0.128210 | + | 0.222067i | −0.922983 | − | 0.384840i | \(-0.874257\pi\) |
0.794773 | + | 0.606907i | \(0.207590\pi\) | |||||||
\(374\) | −0.515673 | − | 0.893172i | −0.0266648 | − | 0.0461848i | ||||
\(375\) | −5.40833 | − | 9.36750i | −0.279285 | − | 0.483735i | ||||
\(376\) | 3.98570 | + | 6.90344i | 0.205547 | + | 0.356018i | ||||
\(377\) | −10.8320 | − | 6.38085i | −0.557877 | − | 0.328631i | ||||
\(378\) | 2.36323 | − | 1.18960i | 0.121551 | − | 0.0611866i | ||||
\(379\) | 6.55920 | − | 11.3609i | 0.336923 | − | 0.583569i | −0.646929 | − | 0.762550i | \(-0.723947\pi\) |
0.983852 | + | 0.178982i | \(0.0572803\pi\) | |||||||
\(380\) | 8.17661 | 0.419451 | ||||||||
\(381\) | −5.18610 | −0.265692 | ||||||||
\(382\) | −5.74444 | + | 9.94966i | −0.293911 | + | 0.509069i | ||||
\(383\) | 6.09000 | − | 10.5482i | 0.311185 | − | 0.538988i | −0.667434 | − | 0.744669i | \(-0.732608\pi\) |
0.978619 | + | 0.205681i | \(0.0659409\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | −0.417877 | + | 7.29112i | −0.0212970 | + | 0.371590i | ||||
\(386\) | −0.138150 | − | 0.239283i | −0.00703165 | − | 0.0121792i | ||||
\(387\) | 8.02712 | 0.408041 | ||||||||
\(388\) | 0.698602 | + | 1.21001i | 0.0354662 | + | 0.0614292i | ||||
\(389\) | 3.34598 | − | 5.79541i | 0.169648 | − | 0.293839i | −0.768648 | − | 0.639672i | \(-0.779070\pi\) |
0.938296 | + | 0.345833i | \(0.112404\pi\) | |||||||
\(390\) | 4.04721 | + | 2.38411i | 0.204939 | + | 0.120724i | ||||
\(391\) | 2.33137 | 0.117902 | ||||||||
\(392\) | −4.16969 | + | 5.62260i | −0.210601 | + | 0.283984i | ||||
\(393\) | 4.03186 | − | 6.98339i | 0.203381 | − | 0.352265i | ||||
\(394\) | 6.63552 | − | 11.4931i | 0.334293 | − | 0.579012i | ||||
\(395\) | 9.33749 | − | 16.1730i | 0.469820 | − | 0.813752i | ||||
\(396\) | 2.11879 | 0.106473 | ||||||||
\(397\) | −12.2912 | + | 21.2890i | −0.616879 | + | 1.06847i | 0.373172 | + | 0.927762i | \(0.378270\pi\) |
−0.990052 | + | 0.140704i | \(0.955063\pi\) | |||||||
\(398\) | −19.0219 | −0.953479 | ||||||||
\(399\) | 14.8323 | − | 7.46630i | 0.742545 | − | 0.373783i | ||||
\(400\) | 1.65139 | − | 2.86029i | 0.0825694 | − | 0.143014i | ||||
\(401\) | 34.6545 | 1.73056 | 0.865282 | − | 0.501285i | \(-0.167139\pi\) | ||||
0.865282 | + | 0.501285i | \(0.167139\pi\) | |||||||
\(402\) | −1.67924 | + | 2.90853i | −0.0837529 | + | 0.145064i | ||||
\(403\) | −13.9386 | − | 8.21087i | −0.694332 | − | 0.409013i | ||||
\(404\) | 3.01725 | + | 5.22602i | 0.150114 | + | 0.260004i | ||||
\(405\) | 0.651388 | − | 1.12824i | 0.0323677 | − | 0.0560625i | ||||
\(406\) | 0.527853 | − | 9.20999i | 0.0261969 | − | 0.457084i | ||||
\(407\) | 1.22626 | + | 2.12395i | 0.0607835 | + | 0.105280i | ||||
\(408\) | −0.243381 | − | 0.421549i | −0.0120492 | − | 0.0208698i | ||||
\(409\) | −23.9090 | −1.18222 | −0.591111 | − | 0.806590i | \(-0.701311\pi\) | ||||
−0.591111 | + | 0.806590i | \(0.701311\pi\) | |||||||
\(410\) | 16.4630 | 0.813052 | ||||||||
\(411\) | 3.39583 | + | 5.88174i | 0.167504 | + | 0.290125i | ||||
\(412\) | 5.64770 | + | 9.78210i | 0.278242 | + | 0.481930i | ||||
\(413\) | 21.6239 | − | 10.8850i | 1.06404 | − | 0.535617i | ||||
\(414\) | −2.39477 | + | 4.14786i | −0.117696 | + | 0.203856i | ||||
\(415\) | 2.27123 | + | 3.93389i | 0.111491 | + | 0.193107i | ||||
\(416\) | −0.0315412 | + | 3.60541i | −0.00154643 | + | 0.176770i | ||||
\(417\) | 6.45522 | − | 11.1808i | 0.316114 | − | 0.547525i | ||||
\(418\) | 13.2982 | 0.650434 | ||||||||
\(419\) | −6.09738 | + | 10.5610i | −0.297876 | + | 0.515937i | −0.975650 | − | 0.219334i | \(-0.929612\pi\) |
0.677773 | + | 0.735271i | \(0.262945\pi\) | |||||||
\(420\) | −0.197224 | + | 3.44117i | −0.00962356 | + | 0.167912i | ||||
\(421\) | 14.0504 | 0.684777 | 0.342388 | − | 0.939558i | \(-0.388764\pi\) | ||||
0.342388 | + | 0.939558i | \(0.388764\pi\) | |||||||
\(422\) | 1.98750 | − | 3.44245i | 0.0967500 | − | 0.167576i | ||||
\(423\) | 7.97141 | 0.387583 | ||||||||
\(424\) | −4.29060 | + | 7.43153i | −0.208370 | + | 0.360907i | ||||
\(425\) | −0.803833 | + | 1.39228i | −0.0389916 | + | 0.0675355i | ||||
\(426\) | −1.46740 | + | 2.54161i | −0.0710958 | + | 0.123142i | ||||
\(427\) | −1.54183 | + | 26.9018i | −0.0746143 | + | 1.30187i | ||||
\(428\) | −14.0292 | −0.678128 | ||||||||
\(429\) | 6.58225 | + | 3.87743i | 0.317794 | + | 0.187204i | ||||
\(430\) | −5.22877 | + | 9.05649i | −0.252153 | + | 0.436743i | ||||
\(431\) | −8.65171 | − | 14.9852i | −0.416738 | − | 0.721812i | 0.578871 | − | 0.815419i | \(-0.303493\pi\) |
−0.995609 | + | 0.0936075i | \(0.970160\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 10.1803 | + | 17.6328i | 0.489234 | + | 0.847378i | 0.999923 | − | 0.0123873i | \(-0.00394309\pi\) |
−0.510689 | + | 0.859765i | \(0.670610\pi\) | |||||||
\(434\) | 0.679241 | − | 11.8514i | 0.0326046 | − | 0.568886i | ||||
\(435\) | −2.27123 | − | 3.93389i | −0.108897 | − | 0.188616i | ||||
\(436\) | −5.50000 | + | 9.52628i | −0.263402 | + | 0.456226i | ||||
\(437\) | −15.0303 | + | 26.0332i | −0.718996 | + | 1.24534i | ||||
\(438\) | −16.1867 | −0.773432 | ||||||||
\(439\) | 4.04398 | 0.193009 | 0.0965044 | − | 0.995333i | \(-0.469234\pi\) | ||||
0.0965044 | + | 0.995333i | \(0.469234\pi\) | |||||||
\(440\) | −1.38015 | + | 2.39050i | −0.0657962 | + | 0.113962i | ||||
\(441\) | 2.78447 | + | 6.42236i | 0.132594 | + | 0.305827i | ||||
\(442\) | 0.0153530 | − | 1.75498i | 0.000730270 | − | 0.0834758i | ||||
\(443\) | 10.1092 | + | 17.5097i | 0.480304 | + | 0.831912i | 0.999745 | − | 0.0225951i | \(-0.00719285\pi\) |
−0.519440 | + | 0.854507i | \(0.673860\pi\) | |||||||
\(444\) | 0.578756 | + | 1.00243i | 0.0274665 | + | 0.0475734i | ||||
\(445\) | 6.12122 | + | 10.6023i | 0.290174 | + | 0.502596i | ||||
\(446\) | −9.58013 | + | 16.5933i | −0.453632 | + | 0.785714i | ||||
\(447\) | −23.3640 | −1.10508 | ||||||||
\(448\) | −2.36323 | + | 1.18960i | −0.111652 | + | 0.0562034i | ||||
\(449\) | −19.8059 | − | 34.3047i | −0.934696 | − | 1.61894i | −0.775175 | − | 0.631746i | \(-0.782338\pi\) |
−0.159521 | − | 0.987195i | \(-0.550995\pi\) | |||||||
\(450\) | −1.65139 | − | 2.86029i | −0.0778472 | − | 0.134835i | ||||
\(451\) | 26.7749 | 1.26078 | ||||||||
\(452\) | 3.56552 | + | 6.17566i | 0.167708 | + | 0.290479i | ||||
\(453\) | 5.87384 | 0.275977 | ||||||||
\(454\) | 1.18251 | 0.0554980 | ||||||||
\(455\) | −6.91012 | + | 10.3295i | −0.323952 | + | 0.484252i | ||||
\(456\) | 6.27630 | 0.293915 | ||||||||
\(457\) | −6.64742 | −0.310953 | −0.155477 | − | 0.987840i | \(-0.549691\pi\) | ||||
−0.155477 | + | 0.987840i | \(0.549691\pi\) | |||||||
\(458\) | −7.51599 | − | 13.0181i | −0.351199 | − | 0.608295i | ||||
\(459\) | −0.486762 | −0.0227201 | ||||||||
\(460\) | −3.11985 | − | 5.40373i | −0.145464 | − | 0.251950i | ||||
\(461\) | −10.2371 | − | 17.7311i | −0.476788 | − | 0.825820i | 0.522859 | − | 0.852419i | \(-0.324866\pi\) |
−0.999646 | + | 0.0265991i | \(0.991532\pi\) | |||||||
\(462\) | −0.320759 | + | 5.59660i | −0.0149231 | + | 0.260378i | ||||
\(463\) | 17.2668 | 0.802457 | 0.401228 | − | 0.915978i | \(-0.368583\pi\) | ||||
0.401228 | + | 0.915978i | \(0.368583\pi\) | |||||||
\(464\) | 1.74338 | − | 3.01962i | 0.0809344 | − | 0.140183i | ||||
\(465\) | −2.92262 | − | 5.06213i | −0.135533 | − | 0.234751i | ||||
\(466\) | 2.59706 | + | 4.49824i | 0.120306 | + | 0.208377i | ||||
\(467\) | 4.37922 | + | 7.58503i | 0.202646 | + | 0.350994i | 0.949380 | − | 0.314129i | \(-0.101713\pi\) |
−0.746734 | + | 0.665123i | \(0.768379\pi\) | |||||||
\(468\) | 3.10661 | + | 1.83002i | 0.143603 | + | 0.0845928i | ||||
\(469\) | −7.42843 | − | 4.87589i | −0.343013 | − | 0.225148i | ||||
\(470\) | −5.19248 | + | 8.99364i | −0.239511 | + | 0.414846i | ||||
\(471\) | 6.24495 | 0.287752 | ||||||||
\(472\) | 9.15014 | 0.421169 | ||||||||
\(473\) | −8.50388 | + | 14.7292i | −0.391009 | + | 0.677247i | ||||
\(474\) | 7.16738 | − | 12.4143i | 0.329209 | − | 0.570206i | ||||
\(475\) | −10.3646 | − | 17.9520i | −0.475561 | − | 0.823695i | ||||
\(476\) | 1.15033 | − | 0.579054i | 0.0527253 | − | 0.0265409i | ||||
\(477\) | 4.29060 | + | 7.43153i | 0.196453 | + | 0.340266i | ||||
\(478\) | −25.3978 | −1.16167 | ||||||||
\(479\) | 13.5126 | + | 23.4046i | 0.617408 | + | 1.06938i | 0.989957 | + | 0.141369i | \(0.0451504\pi\) |
−0.372549 | + | 0.928012i | \(0.621516\pi\) | |||||||
\(480\) | −0.651388 | + | 1.12824i | −0.0297317 | + | 0.0514967i | ||||
\(481\) | −0.0365092 | + | 4.17331i | −0.00166468 | + | 0.190286i | ||||
\(482\) | 11.8575 | 0.540094 | ||||||||
\(483\) | −10.5937 | − | 6.95352i | −0.482030 | − | 0.316396i | ||||
\(484\) | 3.25537 | − | 5.63846i | 0.147971 | − | 0.256294i | ||||
\(485\) | −0.910122 | + | 1.57638i | −0.0413265 | + | 0.0715796i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 21.9435 | 0.994353 | 0.497177 | − | 0.867649i | \(-0.334370\pi\) | ||||
0.497177 | + | 0.867649i | \(0.334370\pi\) | |||||||
\(488\) | −5.09231 | + | 8.82015i | −0.230518 | + | 0.399269i | ||||
\(489\) | −2.60767 | −0.117923 | ||||||||
\(490\) | −9.05971 | − | 1.04190i | −0.409276 | − | 0.0470684i | ||||
\(491\) | −7.09020 | + | 12.2806i | −0.319976 | + | 0.554215i | −0.980483 | − | 0.196605i | \(-0.937008\pi\) |
0.660507 | + | 0.750820i | \(0.270342\pi\) | |||||||
\(492\) | 12.6369 | 0.569715 | ||||||||
\(493\) | −0.848612 | + | 1.46984i | −0.0382196 | + | 0.0661982i | ||||
\(494\) | 19.4980 | + | 11.4858i | 0.877257 | + | 0.516769i | ||||
\(495\) | 1.38015 | + | 2.39050i | 0.0620333 | + | 0.107445i | ||||
\(496\) | 2.24338 | − | 3.88565i | 0.100731 | − | 0.174471i | ||||
\(497\) | −6.49131 | − | 4.26079i | −0.291175 | − | 0.191122i | ||||
\(498\) | 1.74338 | + | 3.01962i | 0.0781228 | + | 0.135313i | ||||
\(499\) | 14.7488 | + | 25.5456i | 0.660245 | + | 1.14358i | 0.980551 | + | 0.196264i | \(0.0628811\pi\) |
−0.320306 | + | 0.947314i | \(0.603786\pi\) | |||||||
\(500\) | 10.8167 | 0.483735 | ||||||||
\(501\) | 6.90833 | 0.308641 | ||||||||
\(502\) | −10.7397 | − | 18.6017i | −0.479336 | − | 0.830234i | ||||
\(503\) | −7.49400 | − | 12.9800i | −0.334141 | − | 0.578749i | 0.649178 | − | 0.760636i | \(-0.275113\pi\) |
−0.983319 | + | 0.181887i | \(0.941780\pi\) | |||||||
\(504\) | −0.151388 | + | 2.64142i | −0.00674335 | + | 0.117658i | ||||
\(505\) | −3.93079 | + | 6.80834i | −0.174918 | + | 0.302967i | ||||
\(506\) | −5.07401 | − | 8.78844i | −0.225567 | − | 0.390694i | ||||
\(507\) | 6.30204 | + | 11.3703i | 0.279883 | + | 0.504974i | ||||
\(508\) | 2.59305 | − | 4.49130i | 0.115048 | − | 0.199269i | ||||
\(509\) | 41.9674 | 1.86017 | 0.930087 | − | 0.367340i | \(-0.119731\pi\) | ||||
0.930087 | + | 0.367340i | \(0.119731\pi\) | |||||||
\(510\) | 0.317071 | − | 0.549183i | 0.0140401 | − | 0.0243182i | ||||
\(511\) | 2.45048 | − | 42.7559i | 0.108403 | − | 1.89141i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.13815 | − | 5.43544i | 0.138553 | − | 0.239980i | ||||
\(514\) | 6.84589 | 0.301959 | ||||||||
\(515\) | −7.35769 | + | 12.7439i | −0.324218 | + | 0.561563i | ||||
\(516\) | −4.01356 | + | 6.95169i | −0.176687 | + | 0.306031i | ||||
\(517\) | −8.44487 | + | 14.6269i | −0.371405 | + | 0.643292i | ||||
\(518\) | −2.73546 | + | 1.37698i | −0.120189 | + | 0.0605010i | ||||
\(519\) | −7.72710 | −0.339182 | ||||||||
\(520\) | −4.08831 | + | 2.31294i | −0.179284 | + | 0.101429i | ||||
\(521\) | −8.68748 | + | 15.0472i | −0.380605 | + | 0.659228i | −0.991149 | − | 0.132755i | \(-0.957618\pi\) |
0.610544 | + | 0.791983i | \(0.290951\pi\) | |||||||
\(522\) | −1.74338 | − | 3.01962i | −0.0763057 | − | 0.132165i | ||||
\(523\) | 33.0034 | 1.44314 | 0.721569 | − | 0.692343i | \(-0.243421\pi\) | ||||
0.721569 | + | 0.692343i | \(0.243421\pi\) | |||||||
\(524\) | 4.03186 | + | 6.98339i | 0.176133 | + | 0.305071i | ||||
\(525\) | 7.80521 | − | 3.92899i | 0.340647 | − | 0.171475i | ||||
\(526\) | 7.69998 | + | 13.3368i | 0.335735 | + | 0.581510i | ||||
\(527\) | −1.09199 | + | 1.89139i | −0.0475680 | + | 0.0823902i | ||||
\(528\) | −1.05939 | + | 1.83493i | −0.0461042 | + | 0.0798549i | ||||
\(529\) | −0.0603265 | −0.00262289 | ||||||||
\(530\) | −11.1794 | −0.485601 | ||||||||
\(531\) | 4.57507 | − | 7.92425i | 0.198541 | − | 0.343883i | ||||
\(532\) | −0.950155 | + | 16.5783i | −0.0411945 | + | 0.718761i | ||||
\(533\) | 39.2579 | + | 23.1258i | 1.70045 | + | 1.00169i | ||||
\(534\) | 4.69860 | + | 8.13822i | 0.203328 | + | 0.352175i | ||||
\(535\) | −9.13847 | − | 15.8283i | −0.395091 | − | 0.684317i | ||||
\(536\) | −1.67924 | − | 2.90853i | −0.0725322 | − | 0.125629i | ||||
\(537\) | −9.57539 | + | 16.5851i | −0.413208 | + | 0.715698i | ||||
\(538\) | 11.7313 | 0.505773 | ||||||||
\(539\) | −14.7344 | − | 1.69452i | −0.634656 | − | 0.0729879i | ||||
\(540\) | 0.651388 | + | 1.12824i | 0.0280313 | + | 0.0485516i | ||||
\(541\) | −8.93967 | − | 15.4840i | −0.384347 | − | 0.665708i | 0.607332 | − | 0.794448i | \(-0.292240\pi\) |
−0.991678 | + | 0.128741i | \(0.958907\pi\) | |||||||
\(542\) | 26.0856 | 1.12047 | ||||||||
\(543\) | −6.54859 | − | 11.3425i | −0.281027 | − | 0.486753i | ||||
\(544\) | 0.486762 | 0.0208698 | ||||||||
\(545\) | −14.3305 | −0.613853 | ||||||||
\(546\) | −5.30415 | + | 7.92881i | −0.226997 | + | 0.339322i | ||||
\(547\) | 11.4550 | 0.489782 | 0.244891 | − | 0.969551i | \(-0.421248\pi\) | ||||
0.244891 | + | 0.969551i | \(0.421248\pi\) | |||||||
\(548\) | −6.79165 | −0.290125 | ||||||||
\(549\) | 5.09231 | + | 8.82015i | 0.217335 | + | 0.376435i | ||||
\(550\) | 6.99788 | 0.298391 | ||||||||
\(551\) | −10.9420 | − | 18.9521i | −0.466144 | − | 0.807385i | ||||
\(552\) | −2.39477 | − | 4.14786i | −0.101928 | − | 0.176545i | ||||
\(553\) | 31.7062 | + | 20.8114i | 1.34828 | + | 0.884991i | ||||
\(554\) | −23.4307 | −0.995474 | ||||||||
\(555\) | −0.753989 | + | 1.30595i | −0.0320050 | + | 0.0554344i | ||||
\(556\) | 6.45522 | + | 11.1808i | 0.273762 | + | 0.474170i | ||||
\(557\) | −20.3122 | − | 35.1817i | −0.860654 | − | 1.49070i | −0.871298 | − | 0.490754i | \(-0.836722\pi\) |
0.0106442 | − | 0.999943i | \(-0.496612\pi\) | |||||||
\(558\) | −2.24338 | − | 3.88565i | −0.0949699 | − | 0.164493i | ||||
\(559\) | −25.1903 | + | 14.2513i | −1.06544 | + | 0.602765i | ||||
\(560\) | −2.88153 | − | 1.89139i | −0.121767 | − | 0.0799257i | ||||
\(561\) | 0.515673 | − | 0.893172i | 0.0217717 | − | 0.0377098i | ||||
\(562\) | −6.15751 | −0.259739 | ||||||||
\(563\) | 33.1855 | 1.39860 | 0.699301 | − | 0.714827i | \(-0.253495\pi\) | ||||
0.699301 | + | 0.714827i | \(0.253495\pi\) | |||||||
\(564\) | −3.98570 | + | 6.90344i | −0.167828 | + | 0.290687i | ||||
\(565\) | −4.64507 | + | 8.04550i | −0.195420 | + | 0.338477i | ||||
\(566\) | 10.9661 | + | 18.9939i | 0.460942 | + | 0.798374i | ||||
\(567\) | 2.21184 | + | 1.45181i | 0.0928885 | + | 0.0609705i | ||||
\(568\) | −1.46740 | − | 2.54161i | −0.0615708 | − | 0.106644i | ||||
\(569\) | 0.0679534 | 0.00284876 | 0.00142438 | − | 0.999999i | \(-0.499547\pi\) | ||||
0.00142438 | + | 0.999999i | \(0.499547\pi\) | |||||||
\(570\) | 4.08831 | + | 7.08115i | 0.171240 | + | 0.296597i | ||||
\(571\) | −10.2822 | + | 17.8092i | −0.430295 | + | 0.745293i | −0.996899 | − | 0.0786977i | \(-0.974924\pi\) |
0.566603 | + | 0.823991i | \(0.308257\pi\) | |||||||
\(572\) | −6.64908 | + | 3.76168i | −0.278012 | + | 0.157284i | ||||
\(573\) | −11.4889 | −0.479955 | ||||||||
\(574\) | −1.91307 | + | 33.3793i | −0.0798501 | + | 1.39323i | ||||
\(575\) | −7.90938 | + | 13.6995i | −0.329844 | + | 0.571307i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 22.7814 | − | 39.4586i | 0.948403 | − | 1.64268i | 0.199613 | − | 0.979875i | \(-0.436031\pi\) |
0.748790 | − | 0.662808i | \(-0.230635\pi\) | |||||||
\(578\) | 16.7631 | 0.697251 | ||||||||
\(579\) | 0.138150 | − | 0.239283i | 0.00574132 | − | 0.00994426i | ||||
\(580\) | 4.54247 | 0.188616 | ||||||||
\(581\) | −8.24001 | + | 4.14786i | −0.341853 | + | 0.172082i | ||||
\(582\) | −0.698602 | + | 1.21001i | −0.0289580 | + | 0.0501567i | ||||
\(583\) | −18.1817 | −0.753010 | ||||||||
\(584\) | 8.09337 | − | 14.0181i | 0.334906 | − | 0.580074i | ||||
\(585\) | −0.0410911 | + | 4.69704i | −0.00169891 | + | 0.194199i | ||||
\(586\) | 8.74075 | + | 15.1394i | 0.361077 | + | 0.625404i | ||||
\(587\) | 2.71527 | − | 4.70298i | 0.112071 | − | 0.194113i | −0.804534 | − | 0.593906i | \(-0.797585\pi\) |
0.916605 | + | 0.399794i | \(0.130918\pi\) | |||||||
\(588\) | −6.95416 | − | 0.799757i | −0.286785 | − | 0.0329814i | ||||
\(589\) | −14.0801 | − | 24.3875i | −0.580162 | − | 1.00487i | ||||
\(590\) | 5.96029 | + | 10.3235i | 0.245381 | + | 0.425013i | ||||
\(591\) | 13.2710 | 0.545898 | ||||||||
\(592\) | −1.15751 | −0.0475734 | ||||||||
\(593\) | −2.77524 | − | 4.80686i | −0.113966 | − | 0.197394i | 0.803400 | − | 0.595439i | \(-0.203022\pi\) |
−0.917366 | + | 0.398045i | \(0.869689\pi\) | |||||||
\(594\) | 1.05939 | + | 1.83493i | 0.0434675 | + | 0.0752879i | ||||
\(595\) | 1.40262 | + | 0.920656i | 0.0575018 | + | 0.0377432i | ||||
\(596\) | 11.6820 | − | 20.2338i | 0.478513 | − | 0.828809i | ||||
\(597\) | −9.51093 | − | 16.4734i | −0.389256 | − | 0.674212i | ||||
\(598\) | 0.151068 | − | 17.2683i | 0.00617761 | − | 0.706152i | ||||
\(599\) | −7.94019 | + | 13.7528i | −0.324427 | + | 0.561925i | −0.981396 | − | 0.191993i | \(-0.938505\pi\) |
0.656969 | + | 0.753918i | \(0.271838\pi\) | |||||||
\(600\) | 3.30278 | 0.134835 | ||||||||
\(601\) | 19.1239 | − | 33.1235i | 0.780078 | − | 1.35114i | −0.151817 | − | 0.988409i | \(-0.548513\pi\) |
0.931896 | − | 0.362727i | \(-0.118154\pi\) | |||||||
\(602\) | −17.7547 | − | 11.6539i | −0.723627 | − | 0.474977i | ||||
\(603\) | −3.35848 | −0.136768 | ||||||||
\(604\) | −2.93692 | + | 5.08689i | −0.119501 | + | 0.206983i | ||||
\(605\) | 8.48202 | 0.344843 | ||||||||
\(606\) | −3.01725 | + | 5.22602i | −0.122567 | + | 0.212293i | ||||
\(607\) | 9.66094 | − | 16.7332i | 0.392125 | − | 0.679181i | −0.600604 | − | 0.799546i | \(-0.705073\pi\) |
0.992730 | + | 0.120365i | \(0.0384066\pi\) | |||||||
\(608\) | −3.13815 | + | 5.43544i | −0.127269 | + | 0.220436i | ||||
\(609\) | 8.24001 | − | 4.14786i | 0.333902 | − | 0.168080i | ||||
\(610\) | −13.2683 | −0.537217 | ||||||||
\(611\) | −25.0155 | + | 14.1524i | −1.01202 | + | 0.572544i | ||||
\(612\) | 0.243381 | − | 0.421549i | 0.00983810 | − | 0.0170401i | ||||
\(613\) | 15.2625 | + | 26.4355i | 0.616448 | + | 1.06772i | 0.990129 | + | 0.140162i | \(0.0447625\pi\) |
−0.373680 | + | 0.927558i | \(0.621904\pi\) | |||||||
\(614\) | 12.0673 | 0.486997 | ||||||||
\(615\) | 8.23152 | + | 14.2574i | 0.331927 | + | 0.574914i | ||||
\(616\) | −4.68642 | − | 3.07609i | −0.188821 | − | 0.123939i | ||||
\(617\) | −12.5446 | − | 21.7279i | −0.505026 | − | 0.874731i | −0.999983 | − | 0.00581322i | \(-0.998150\pi\) |
0.494957 | − | 0.868917i | \(-0.335184\pi\) | |||||||
\(618\) | −5.64770 | + | 9.78210i | −0.227184 | + | 0.393494i | ||||
\(619\) | 9.35717 | − | 16.2071i | 0.376096 | − | 0.651418i | −0.614394 | − | 0.788999i | \(-0.710599\pi\) |
0.990490 | + | 0.137581i | \(0.0439328\pi\) | |||||||
\(620\) | 5.84524 | 0.234751 | ||||||||
\(621\) | −4.78954 | −0.192198 | ||||||||
\(622\) | −0.755881 | + | 1.30923i | −0.0303081 | + | 0.0524951i | ||||
\(623\) | −22.2077 | + | 11.1789i | −0.889734 | + | 0.447875i | ||||
\(624\) | −3.13815 | + | 1.77539i | −0.125627 | + | 0.0710725i | ||||
\(625\) | −1.21110 | − | 2.09769i | −0.0484441 | − | 0.0839076i | ||||
\(626\) | 0.862908 | + | 1.49460i | 0.0344887 | + | 0.0597362i | ||||
\(627\) | 6.64908 | + | 11.5165i | 0.265539 | + | 0.459926i | ||||
\(628\) | −3.12248 | + | 5.40829i | −0.124600 | + | 0.215814i | ||||
\(629\) | 0.563433 | 0.0224655 | ||||||||
\(630\) | −3.07876 | + | 1.54979i | −0.122661 | + | 0.0617449i | ||||
\(631\) | −14.4362 | − | 25.0042i | −0.574695 | − | 0.995401i | −0.996075 | − | 0.0885169i | \(-0.971787\pi\) |
0.421379 | − | 0.906884i | \(-0.361546\pi\) | |||||||
\(632\) | 7.16738 | + | 12.4143i | 0.285103 | + | 0.493813i | ||||
\(633\) | 3.97500 | 0.157992 | ||||||||
\(634\) | 10.6520 | + | 18.4499i | 0.423046 | + | 0.732737i | ||||
\(635\) | 6.75633 | 0.268117 | ||||||||
\(636\) | −8.58119 | −0.340266 | ||||||||
\(637\) | −20.1403 | − | 15.2108i | −0.797988 | − | 0.602674i | ||||
\(638\) | 7.38771 | 0.292482 | ||||||||
\(639\) | −2.93480 | −0.116099 | ||||||||
\(640\) | −0.651388 | − | 1.12824i | −0.0257484 | − | 0.0445975i | ||||
\(641\) | 2.19822 | 0.0868243 | 0.0434121 | − | 0.999057i | \(-0.486177\pi\) | ||||
0.0434121 | + | 0.999057i | \(0.486177\pi\) | |||||||
\(642\) | −7.01462 | − | 12.1497i | −0.276845 | − | 0.479509i | ||||
\(643\) | 8.74713 | + | 15.1505i | 0.344953 | + | 0.597476i | 0.985345 | − | 0.170572i | \(-0.0545615\pi\) |
−0.640392 | + | 0.768048i | \(0.721228\pi\) | |||||||
\(644\) | 11.3188 | − | 5.69765i | 0.446022 | − | 0.224519i | ||||
\(645\) | −10.4575 | −0.411765 | ||||||||
\(646\) | 1.52753 | − | 2.64576i | 0.0601000 | − | 0.104096i | ||||
\(647\) | −16.0868 | − | 27.8631i | −0.632436 | − | 1.09541i | −0.987052 | − | 0.160400i | \(-0.948722\pi\) |
0.354616 | − | 0.935012i | \(-0.384612\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 9.69360 | + | 16.7898i | 0.380507 | + | 0.659058i | ||||
\(650\) | 10.2604 | + | 6.04415i | 0.402447 | + | 0.237071i | ||||
\(651\) | 10.6032 | − | 5.33746i | 0.415574 | − | 0.209192i | ||||
\(652\) | 1.30383 | − | 2.25831i | 0.0510621 | − | 0.0884421i | ||||
\(653\) | 47.5661 | 1.86141 | 0.930703 | − | 0.365775i | \(-0.119196\pi\) | ||||
0.930703 | + | 0.365775i | \(0.119196\pi\) | |||||||
\(654\) | −11.0000 | −0.430134 | ||||||||
\(655\) | −5.25261 | + | 9.09779i | −0.205236 | + | 0.355480i | ||||
\(656\) | −6.31845 | + | 10.9439i | −0.246694 | + | 0.427287i | ||||
\(657\) | −8.09337 | − | 14.0181i | −0.315752 | − | 0.546899i | ||||
\(658\) | −17.6315 | − | 11.5730i | −0.687347 | − | 0.451163i | ||||
\(659\) | −3.69892 | − | 6.40672i | −0.144090 | − | 0.249570i | 0.784943 | − | 0.619568i | \(-0.212692\pi\) |
−0.929033 | + | 0.369997i | \(0.879359\pi\) | |||||||
\(660\) | −2.76031 | −0.107445 | ||||||||
\(661\) | −6.11485 | − | 10.5912i | −0.237840 | − | 0.411951i | 0.722254 | − | 0.691628i | \(-0.243106\pi\) |
−0.960094 | + | 0.279677i | \(0.909773\pi\) | |||||||
\(662\) | 8.21691 | − | 14.2321i | 0.319359 | − | 0.553146i | ||||
\(663\) | 1.52753 | − | 0.864193i | 0.0593245 | − | 0.0335625i | ||||
\(664\) | −3.48676 | −0.135313 | ||||||||
\(665\) | −19.3232 | + | 9.72692i | −0.749321 | + | 0.377194i | ||||
\(666\) | −0.578756 | + | 1.00243i | −0.0224263 | + | 0.0388435i | ||||
\(667\) | −8.34999 | + | 14.4626i | −0.323313 | + | 0.559994i | ||||
\(668\) | −3.45416 | + | 5.98279i | −0.133646 | + | 0.231481i | ||||
\(669\) | −19.1603 | −0.740779 | ||||||||
\(670\) | 2.18767 | − | 3.78916i | 0.0845172 | − | 0.146388i | ||||
\(671\) | −21.5791 | −0.833051 | ||||||||
\(672\) | −2.21184 | − | 1.45181i | −0.0853236 | − | 0.0560049i | ||||
\(673\) | 24.4511 | − | 42.3506i | 0.942521 | − | 1.63249i | 0.181882 | − | 0.983320i | \(-0.441781\pi\) |
0.760640 | − | 0.649174i | \(-0.224885\pi\) | |||||||
\(674\) | 12.9178 | 0.497576 | ||||||||
\(675\) | 1.65139 | − | 2.86029i | 0.0635619 | − | 0.110093i | ||||
\(676\) | −12.9980 | − | 0.227438i | −0.499923 | − | 0.00874761i | ||||
\(677\) | −9.74027 | − | 16.8707i | −0.374349 | − | 0.648392i | 0.615880 | − | 0.787840i | \(-0.288801\pi\) |
−0.990229 | + | 0.139448i | \(0.955467\pi\) | |||||||
\(678\) | −3.56552 | + | 6.17566i | −0.136933 | + | 0.237175i | ||||
\(679\) | −3.09039 | − | 2.02848i | −0.118598 | − | 0.0778460i | ||||
\(680\) | 0.317071 | + | 0.549183i | 0.0121591 | + | 0.0210602i | ||||
\(681\) | 0.591256 | + | 1.02409i | 0.0226570 | + | 0.0392430i | ||||
\(682\) | 9.50650 | 0.364023 | ||||||||
\(683\) | −18.1603 | −0.694883 | −0.347442 | − | 0.937702i | \(-0.612950\pi\) | ||||
−0.347442 | + | 0.937702i | \(0.612950\pi\) | |||||||
\(684\) | 3.13815 | + | 5.43544i | 0.119990 | + | 0.207829i | ||||
\(685\) | −4.42400 | − | 7.66259i | −0.169032 | − | 0.292773i | ||||
\(686\) | 3.16527 | − | 18.2478i | 0.120850 | − | 0.696703i | ||||
\(687\) | 7.51599 | − | 13.0181i | 0.286753 | − | 0.496671i | ||||
\(688\) | −4.01356 | − | 6.95169i | −0.153015 | − | 0.265031i | ||||
\(689\) | −26.6584 | − | 15.7038i | −1.01560 | − | 0.598266i | ||||
\(690\) | 3.11985 | − | 5.40373i | 0.118771 | − | 0.205717i | ||||
\(691\) | 37.0049 | 1.40773 | 0.703866 | − | 0.710333i | \(-0.251456\pi\) | ||||
0.703866 | + | 0.710333i | \(0.251456\pi\) | |||||||
\(692\) | 3.86355 | − | 6.69186i | 0.146870 | − | 0.254386i | ||||
\(693\) | −5.00718 | + | 2.52052i | −0.190207 | + | 0.0957465i | ||||
\(694\) | 16.0387 | 0.608822 | ||||||||
\(695\) | −8.40970 | + | 14.5660i | −0.318998 | + | 0.552521i | ||||
\(696\) | 3.48676 | 0.132165 | ||||||||
\(697\) | 3.07558 | − | 5.32707i | 0.116496 | − | 0.201777i | ||||
\(698\) | 3.81951 | − | 6.61558i | 0.144570 | − | 0.250403i | ||||
\(699\) | −2.59706 | + | 4.49824i | −0.0982298 | + | 0.170139i | ||||
\(700\) | −0.500000 | + | 8.72401i | −0.0188982 | + | 0.329736i | ||||
\(701\) | 36.3972 | 1.37470 | 0.687352 | − | 0.726325i | \(-0.258773\pi\) | ||||
0.687352 | + | 0.726325i | \(0.258773\pi\) | |||||||
\(702\) | −0.0315412 | + | 3.60541i | −0.00119044 | + | 0.136078i | ||||
\(703\) | −3.63244 | + | 6.29158i | −0.137000 | + | 0.237291i | ||||
\(704\) | −1.05939 | − | 1.83493i | −0.0399274 | − | 0.0691563i | ||||
\(705\) | −10.3850 | −0.391120 | ||||||||
\(706\) | −16.1956 | − | 28.0515i | −0.609528 | − | 1.05573i | ||||
\(707\) | −13.3473 | − | 8.76096i | −0.501978 | − | 0.329490i | ||||
\(708\) | 4.57507 | + | 7.92425i | 0.171942 | + | 0.297812i | ||||
\(709\) | 0.165683 | − | 0.286972i | 0.00622236 | − | 0.0107774i | −0.862897 | − | 0.505379i | \(-0.831353\pi\) |
0.869120 | + | 0.494602i | \(0.164686\pi\) | |||||||
\(710\) | 1.91169 | − | 3.31115i | 0.0717446 | − | 0.124265i | ||||
\(711\) | 14.3348 | 0.537596 | ||||||||
\(712\) | −9.39720 | −0.352175 | ||||||||
\(713\) | −10.7448 | + | 18.6105i | −0.402394 | + | 0.696968i | ||||
\(714\) | 1.07664 | + | 0.706688i | 0.0402922 | + | 0.0264471i | ||||
\(715\) | −8.57519 | − | 5.05142i | −0.320694 | − | 0.188912i | ||||
\(716\) | −9.57539 | − | 16.5851i | −0.357849 | − | 0.619813i | ||||
\(717\) | −12.6989 | − | 21.9952i | −0.474250 | − | 0.821425i | ||||
\(718\) | −1.57507 | − | 2.72810i | −0.0587810 | − | 0.101812i | ||||
\(719\) | −23.7931 | + | 41.2108i | −0.887333 | + | 1.53691i | −0.0443159 | + | 0.999018i | \(0.514111\pi\) |
−0.843017 | + | 0.537887i | \(0.819223\pi\) | |||||||
\(720\) | −1.30278 | −0.0485516 | ||||||||
\(721\) | −24.9836 | − | 16.3988i | −0.930439 | − | 0.610724i | ||||
\(722\) | 10.1960 | + | 17.6599i | 0.379455 | + | 0.657235i | ||||
\(723\) | 5.92875 | + | 10.2689i | 0.220492 | + | 0.381904i | ||||
\(724\) | 13.0972 | 0.486753 | ||||||||
\(725\) | −5.75800 | − | 9.97314i | −0.213847 | − | 0.370393i | ||||
\(726\) | 6.51073 | 0.241636 | ||||||||
\(727\) | −32.9021 | −1.22027 | −0.610136 | − | 0.792297i | \(-0.708885\pi\) | ||||
−0.610136 | + | 0.792297i | \(0.708885\pi\) | |||||||
\(728\) | −4.21447 | − | 8.55793i | −0.156199 | − | 0.317178i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 21.0877 | 0.780491 | ||||||||
\(731\) | 1.95365 | + | 3.38382i | 0.0722583 | + | 0.125155i | ||||
\(732\) | −10.1846 | −0.376435 | ||||||||
\(733\) | −10.5040 | − | 18.1935i | −0.387974 | − | 0.671991i | 0.604203 | − | 0.796831i | \(-0.293492\pi\) |
−0.992177 | + | 0.124839i | \(0.960158\pi\) | |||||||
\(734\) | −2.23463 | − | 3.87049i | −0.0824816 | − | 0.142862i | ||||
\(735\) | −3.62754 | − | 8.36689i | −0.133804 | − | 0.308618i | ||||
\(736\) | 4.78954 | 0.176545 | ||||||||
\(737\) | 3.55796 | − | 6.16256i | 0.131059 | − | 0.227001i | ||||
\(738\) | 6.31845 | + | 10.9439i | 0.232585 | + | 0.402850i | ||||
\(739\) | −3.26085 | − | 5.64796i | −0.119952 | − | 0.207763i | 0.799796 | − | 0.600272i | \(-0.204941\pi\) |
−0.919749 | + | 0.392508i | \(0.871607\pi\) | |||||||
\(740\) | −0.753989 | − | 1.30595i | −0.0277172 | − | 0.0480076i | ||||
\(741\) | −0.197962 | + | 22.6287i | −0.00727231 | + | 0.831284i | ||||
\(742\) | 1.29909 | − | 22.6665i | 0.0476910 | − | 0.832113i | ||||
\(743\) | −8.64802 | + | 14.9788i | −0.317265 | + | 0.549519i | −0.979916 | − | 0.199409i | \(-0.936098\pi\) |
0.662651 | + | 0.748928i | \(0.269431\pi\) | |||||||
\(744\) | 4.48676 | 0.164493 | ||||||||
\(745\) | 30.4380 | 1.11516 | ||||||||
\(746\) | 2.47615 | − | 4.28883i | 0.0906585 | − | 0.157025i | ||||
\(747\) | −1.74338 | + | 3.01962i | −0.0637870 | + | 0.110482i | ||||
\(748\) | 0.515673 | + | 0.893172i | 0.0188549 | + | 0.0326576i | ||||
\(749\) | 33.1543 | − | 16.6892i | 1.21143 | − | 0.609810i | ||||
\(750\) | 5.40833 | + | 9.36750i | 0.197484 | + | 0.342053i | ||||
\(751\) | −9.62426 | −0.351194 | −0.175597 | − | 0.984462i | \(-0.556186\pi\) | ||||
−0.175597 | + | 0.984462i | \(0.556186\pi\) | |||||||
\(752\) | −3.98570 | − | 6.90344i | −0.145344 | − | 0.251743i | ||||
\(753\) | 10.7397 | − | 18.6017i | 0.391376 | − | 0.677883i | ||||
\(754\) | 10.8320 | + | 6.38085i | 0.394478 | + | 0.232377i | ||||
\(755\) | −7.65229 | −0.278495 | ||||||||
\(756\) | −2.36323 | + | 1.18960i | −0.0859498 | + | 0.0432654i | ||||
\(757\) | −19.5740 | + | 33.9032i | −0.711429 | + | 1.23223i | 0.252891 | + | 0.967495i | \(0.418619\pi\) |
−0.964321 | + | 0.264737i | \(0.914715\pi\) | |||||||
\(758\) | −6.55920 | + | 11.3609i | −0.238241 | + | 0.412645i | ||||
\(759\) | 5.07401 | − | 8.78844i | 0.184175 | − | 0.319000i | ||||
\(760\) | −8.17661 | −0.296597 | ||||||||
\(761\) | 5.18879 | − | 8.98725i | 0.188094 | − | 0.325788i | −0.756521 | − | 0.653969i | \(-0.773103\pi\) |
0.944615 | + | 0.328182i | \(0.106436\pi\) | |||||||
\(762\) | 5.18610 | 0.187873 | ||||||||
\(763\) | 1.66527 | − | 29.0556i | 0.0602867 | − | 1.05188i | ||||
\(764\) | 5.74444 | − | 9.94966i | 0.207827 | − | 0.359966i | ||||
\(765\) | 0.634142 | 0.0229275 | ||||||||
\(766\) | −6.09000 | + | 10.5482i | −0.220041 | + | 0.381122i | ||||
\(767\) | −0.288606 | + | 32.9900i | −0.0104210 | + | 1.19120i | ||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | 17.5102 | − | 30.3285i | 0.631434 | − | 1.09368i | −0.355825 | − | 0.934553i | \(-0.615800\pi\) |
0.987259 | − | 0.159123i | \(-0.0508665\pi\) | |||||||
\(770\) | 0.417877 | − | 7.29112i | 0.0150592 | − | 0.262754i | ||||
\(771\) | 3.42294 | + | 5.92871i | 0.123274 | + | 0.213517i | ||||
\(772\) | 0.138150 | + | 0.239283i | 0.00497213 | + | 0.00861198i | ||||
\(773\) | 20.1234 | 0.723789 | 0.361894 | − | 0.932219i | \(-0.382130\pi\) | ||||
0.361894 | + | 0.932219i | \(0.382130\pi\) | |||||||
\(774\) | −8.02712 | −0.288529 | ||||||||
\(775\) | −7.40938 | − | 12.8334i | −0.266153 | − | 0.460990i | ||||
\(776\) | −0.698602 | − | 1.21001i | −0.0250784 | − | 0.0434370i | ||||
\(777\) | −2.56023 | − | 1.68049i | −0.0918477 | − | 0.0602873i | ||||
\(778\) | −3.34598 | + | 5.79541i | −0.119959 | + | 0.207776i | ||||
\(779\) | 39.6565 | + | 68.6870i | 1.42084 | + | 2.46097i | ||||
\(780\) | −4.04721 | − | 2.38411i | −0.144914 | − | 0.0853648i | ||||
\(781\) | 3.10911 | − | 5.38514i | 0.111253 | − | 0.192696i | ||||
\(782\) | −2.33137 | −0.0833695 | ||||||||
\(783\) | 1.74338 | − | 3.01962i | 0.0623034 | − | 0.107913i | ||||
\(784\) | 4.16969 | − | 5.62260i | 0.148918 | − | 0.200807i | ||||
\(785\) | −8.13577 | −0.290378 | ||||||||
\(786\) | −4.03186 | + | 6.98339i | −0.143812 | + | 0.249089i | ||||
\(787\) | 1.90307 | 0.0678370 | 0.0339185 | − | 0.999425i | \(-0.489201\pi\) | ||||
0.0339185 | + | 0.999425i | \(0.489201\pi\) | |||||||
\(788\) | −6.63552 | + | 11.4931i | −0.236381 | + | 0.409423i | ||||
\(789\) | −7.69998 | + | 13.3368i | −0.274127 | + | 0.474801i | ||||
\(790\) | −9.33749 | + | 16.1730i | −0.332213 | + | 0.575410i | ||||
\(791\) | −15.7727 | − | 10.3529i | −0.560813 | − | 0.368108i | ||||
\(792\) | −2.11879 | −0.0752879 | ||||||||
\(793\) | −31.6397 | − | 18.6381i | −1.12356 | − | 0.661858i | ||||
\(794\) | 12.2912 | − | 21.2890i | 0.436200 | − | 0.755520i | ||||
\(795\) | −5.58968 | − | 9.68162i | −0.198246 | − | 0.343372i | ||||
\(796\) | 19.0219 | 0.674212 | ||||||||
\(797\) | 10.9112 | + | 18.8987i | 0.386494 | + | 0.669427i | 0.991975 | − | 0.126433i | \(-0.0403527\pi\) |
−0.605481 | + | 0.795859i | \(0.707019\pi\) | |||||||
\(798\) | −14.8323 | + | 7.46630i | −0.525059 | + | 0.264304i | ||||
\(799\) | 1.94009 | + | 3.36034i | 0.0686355 | + | 0.118880i | ||||
\(800\) | −1.65139 | + | 2.86029i | −0.0583854 | + | 0.101126i | ||||
\(801\) | −4.69860 | + | 8.13822i | −0.166017 | + | 0.287550i | ||||
\(802\) | −34.6545 | −1.22369 | ||||||||
\(803\) | 34.2963 | 1.21029 | ||||||||
\(804\) | 1.67924 | − | 2.90853i | 0.0592223 | − | 0.102576i | ||||
\(805\) | 13.8012 | + | 9.05887i | 0.486428 | + | 0.319283i | ||||
\(806\) | 13.9386 | + | 8.21087i | 0.490967 | + | 0.289216i | ||||
\(807\) | 5.86566 | + | 10.1596i | 0.206481 | + | 0.357636i | ||||
\(808\) | −3.01725 | − | 5.22602i | −0.106146 | − | 0.183851i | ||||
\(809\) | −22.9519 | − | 39.7538i | −0.806944 | − | 1.39767i | −0.914971 | − | 0.403520i | \(-0.867786\pi\) |
0.108026 | − | 0.994148i | \(-0.465547\pi\) | |||||||
\(810\) | −0.651388 | + | 1.12824i | −0.0228874 | + | 0.0396422i | ||||
\(811\) | 3.66652 | 0.128749 | 0.0643744 | − | 0.997926i | \(-0.479495\pi\) | ||||
0.0643744 | + | 0.997926i | \(0.479495\pi\) | |||||||
\(812\) | −0.527853 | + | 9.20999i | −0.0185240 | + | 0.323207i | ||||
\(813\) | 13.0428 | + | 22.5908i | 0.457431 | + | 0.792293i | ||||
\(814\) | −1.22626 | − | 2.12395i | −0.0429804 | − | 0.0744443i | ||||
\(815\) | 3.39720 | 0.118999 | ||||||||
\(816\) | 0.243381 | + | 0.421549i | 0.00852004 | + | 0.0147571i | ||||
\(817\) | −50.3806 | −1.76259 | ||||||||
\(818\) | 23.9090 | 0.835957 | ||||||||
\(819\) | −9.51862 | − | 0.629129i | −0.332608 | − | 0.0219835i | ||||
\(820\) | −16.4630 | −0.574914 | ||||||||
\(821\) | −20.3484 | −0.710162 | −0.355081 | − | 0.934835i | \(-0.615547\pi\) | ||||
−0.355081 | + | 0.934835i | \(0.615547\pi\) | |||||||
\(822\) | −3.39583 | − | 5.88174i | −0.118443 | − | 0.205149i | ||||
\(823\) | 27.7345 | 0.966763 | 0.483381 | − | 0.875410i | \(-0.339408\pi\) | ||||
0.483381 | + | 0.875410i | \(0.339408\pi\) | |||||||
\(824\) | −5.64770 | − | 9.78210i | −0.196747 | − | 0.340776i | ||||
\(825\) | 3.49894 | + | 6.06035i | 0.121818 | + | 0.210994i | ||||
\(826\) | −21.6239 | + | 10.8850i | −0.752390 | + | 0.378738i | ||||
\(827\) | 36.6640 | 1.27493 | 0.637466 | − | 0.770478i | \(-0.279983\pi\) | ||||
0.637466 | + | 0.770478i | \(0.279983\pi\) | |||||||
\(828\) | 2.39477 | − | 4.14786i | 0.0832240 | − | 0.144148i | ||||
\(829\) | −7.23120 | − | 12.5248i | −0.251150 | − | 0.435005i | 0.712693 | − | 0.701476i | \(-0.247475\pi\) |
−0.963843 | + | 0.266472i | \(0.914142\pi\) | |||||||
\(830\) | −2.27123 | − | 3.93389i | −0.0788357 | − | 0.136547i | ||||
\(831\) | −11.7153 | − | 20.2916i | −0.406400 | − | 0.703906i | ||||
\(832\) | 0.0315412 | − | 3.60541i | 0.00109349 | − | 0.124995i | ||||
\(833\) | −2.02965 | + | 2.73687i | −0.0703232 | + | 0.0948270i | ||||
\(834\) | −6.45522 | + | 11.1808i | −0.223526 | + | 0.387158i | ||||
\(835\) | −9.00000 | −0.311458 | ||||||||
\(836\) | −13.2982 | −0.459926 | ||||||||
\(837\) | 2.24338 | − | 3.88565i | 0.0775426 | − | 0.134308i | ||||
\(838\) | 6.09738 | − | 10.5610i | 0.210630 | − | 0.364823i | ||||
\(839\) | −2.51779 | − | 4.36094i | −0.0869237 | − | 0.150556i | 0.819286 | − | 0.573386i | \(-0.194370\pi\) |
−0.906209 | + | 0.422829i | \(0.861037\pi\) | |||||||
\(840\) | 0.197224 | − | 3.44117i | 0.00680489 | − | 0.118732i | ||||
\(841\) | 8.42124 | + | 14.5860i | 0.290388 | + | 0.502966i | ||||
\(842\) | −14.0504 | −0.484210 | ||||||||
\(843\) | −3.07876 | − | 5.33256i | −0.106038 | − | 0.183663i | ||||
\(844\) | −1.98750 | + | 3.44245i | −0.0684126 | + | 0.118494i | ||||
\(845\) | −8.21014 | − | 14.8130i | −0.282437 | − | 0.509582i | ||||
\(846\) | −7.97141 | −0.274063 | ||||||||
\(847\) | −0.985646 | + | 17.1976i | −0.0338672 | + | 0.590915i | ||||
\(848\) | 4.29060 | − | 7.43153i | 0.147340 | − | 0.255200i | ||||
\(849\) | −10.9661 | + | 18.9939i | −0.376357 | + | 0.651870i | ||||
\(850\) | 0.803833 | − | 1.39228i | 0.0275713 | − | 0.0477548i | ||||
\(851\) | 5.54394 | 0.190044 | ||||||||
\(852\) | 1.46740 | − | 2.54161i | 0.0502723 | − | 0.0870742i | ||||
\(853\) | 21.9833 | 0.752693 | 0.376346 | − | 0.926479i | \(-0.377180\pi\) | ||||
0.376346 | + | 0.926479i | \(0.377180\pi\) | |||||||
\(854\) | 1.54183 | − | 26.9018i | 0.0527603 | − | 0.920562i | ||||
\(855\) | −4.08831 | + | 7.08115i | −0.139817 | + | 0.242170i | ||||
\(856\) | 14.0292 | 0.479509 | ||||||||
\(857\) | 21.6450 | − | 37.4902i | 0.739378 | − | 1.28064i | −0.213397 | − | 0.976965i | \(-0.568453\pi\) |
0.952776 | − | 0.303675i | \(-0.0982137\pi\) | |||||||
\(858\) | −6.58225 | − | 3.87743i | −0.224714 | − | 0.132373i | ||||
\(859\) | 22.6834 | + | 39.2888i | 0.773947 | + | 1.34052i | 0.935385 | + | 0.353632i | \(0.115054\pi\) |
−0.161438 | + | 0.986883i | \(0.551613\pi\) | |||||||
\(860\) | 5.22877 | − | 9.05649i | 0.178299 | − | 0.308824i | ||||
\(861\) | −29.8639 | + | 15.0329i | −1.01776 | + | 0.512319i | ||||
\(862\) | 8.65171 | + | 14.9852i | 0.294678 | + | 0.510398i | ||||
\(863\) | −6.76755 | − | 11.7217i | −0.230370 | − | 0.399012i | 0.727547 | − | 0.686058i | \(-0.240660\pi\) |
−0.957917 | + | 0.287045i | \(0.907327\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 10.0667 | 0.342277 | ||||||||
\(866\) | −10.1803 | − | 17.6328i | −0.345941 | − | 0.599187i | ||||
\(867\) | 8.38153 | + | 14.5172i | 0.284652 | + | 0.493031i | ||||
\(868\) | −0.679241 | + | 11.8514i | −0.0230549 | + | 0.402263i | ||||
\(869\) | −15.1862 | + | 26.3032i | −0.515155 | + | 0.892275i | ||||
\(870\) | 2.27123 | + | 3.93389i | 0.0770021 | + | 0.133371i | ||||
\(871\) | 10.5394 | − | 5.96262i | 0.357115 | − | 0.202036i | ||||
\(872\) | 5.50000 | − | 9.52628i | 0.186254 | − | 0.322601i | ||||
\(873\) | −1.39720 | −0.0472882 | ||||||||
\(874\) | 15.0303 | − | 26.0332i | 0.508407 | − | 0.880587i | ||||
\(875\) | −25.5622 | + | 12.8675i | −0.864161 | + | 0.435002i | ||||
\(876\) | 16.1867 | 0.546899 | ||||||||
\(877\) | −9.71091 | + | 16.8198i | −0.327914 | + | 0.567964i | −0.982098 | − | 0.188372i | \(-0.939679\pi\) |
0.654184 | + | 0.756336i | \(0.273012\pi\) | |||||||
\(878\) | −4.04398 | −0.136478 | ||||||||
\(879\) | −8.74075 | + | 15.1394i | −0.294818 | + | 0.510640i | ||||
\(880\) | 1.38015 | − | 2.39050i | 0.0465250 | − | 0.0805836i | ||||
\(881\) | −2.77059 | + | 4.79881i | −0.0933437 | + | 0.161676i | −0.908916 | − | 0.416979i | \(-0.863089\pi\) |
0.815572 | + | 0.578655i | \(0.196422\pi\) | |||||||
\(882\) | −2.78447 | − | 6.42236i | −0.0937581 | − | 0.216252i | ||||
\(883\) | 51.6940 | 1.73964 | 0.869821 | − | 0.493367i | \(-0.164234\pi\) | ||||
0.869821 | + | 0.493367i | \(0.164234\pi\) | |||||||
\(884\) | −0.0153530 | + | 1.75498i | −0.000516379 | + | 0.0590263i | ||||
\(885\) | −5.96029 | + | 10.3235i | −0.200353 | + | 0.347021i | ||||
\(886\) | −10.1092 | − | 17.5097i | −0.339627 | − | 0.588250i | ||||
\(887\) | −3.54837 | −0.119143 | −0.0595713 | − | 0.998224i | \(-0.518973\pi\) | ||||
−0.0595713 | + | 0.998224i | \(0.518973\pi\) | |||||||
\(888\) | −0.578756 | − | 1.00243i | −0.0194218 | − | 0.0336395i | ||||
\(889\) | −0.785113 | + | 13.6987i | −0.0263318 | + | 0.459438i | ||||
\(890\) | −6.12122 | − | 10.6023i | −0.205184 | − | 0.355389i | ||||
\(891\) | −1.05939 | + | 1.83493i | −0.0354911 | + | 0.0614723i | ||||
\(892\) | 9.58013 | − | 16.5933i | 0.320767 | − | 0.555584i | ||||
\(893\) | −50.0310 | −1.67422 | ||||||||
\(894\) | 23.3640 | 0.781409 | ||||||||
\(895\) | 12.4746 | − | 21.6066i | 0.416979 | − | 0.722229i | ||||
\(896\) | 2.36323 | − | 1.18960i | 0.0789499 | − | 0.0397418i | ||||
\(897\) | 15.0303 | − | 8.50330i | 0.501847 | − | 0.283917i | ||||
\(898\) | 19.8059 | + | 34.3047i | 0.660930 | + | 1.14476i | ||||
\(899\) | −7.82214 | − | 13.5483i | −0.260883 | − | 0.451862i | ||||
\(900\) | 1.65139 | + | 2.86029i | 0.0550463 | + | 0.0953429i | ||||
\(901\) | −2.08850 | + | 3.61739i | −0.0695780 | + | 0.120513i | ||||
\(902\) | −26.7749 | −0.891507 | ||||||||
\(903\) | 1.21521 | − | 21.2030i | 0.0404396 | − | 0.705590i | ||||
\(904\) | −3.56552 | − | 6.17566i | −0.118587 | − | 0.205399i | ||||
\(905\) | 8.53135 | + | 14.7767i | 0.283592 | + | 0.491195i | ||||
\(906\) | −5.87384 | −0.195145 | ||||||||
\(907\) | 21.8453 | + | 37.8372i | 0.725362 | + | 1.25636i | 0.958825 | + | 0.283998i | \(0.0916608\pi\) |
−0.233463 | + | 0.972366i | \(0.575006\pi\) | |||||||
\(908\) | −1.18251 | −0.0392430 | ||||||||
\(909\) | −6.03449 | −0.200151 | ||||||||
\(910\) | 6.91012 | − | 10.3295i | 0.229068 | − | 0.342418i | ||||
\(911\) | −5.97013 | −0.197799 | −0.0988996 | − | 0.995097i | \(-0.531532\pi\) | ||||
−0.0988996 | + | 0.995097i | \(0.531532\pi\) | |||||||
\(912\) | −6.27630 | −0.207829 | ||||||||
\(913\) | −3.69386 | − | 6.39795i | −0.122249 | − | 0.211741i | ||||
\(914\) | 6.64742 | 0.219877 | ||||||||
\(915\) | −6.63414 | − | 11.4907i | −0.219318 | − | 0.379870i | ||||
\(916\) | 7.51599 | + | 13.0181i | 0.248335 | + | 0.430130i | ||||
\(917\) | −17.8357 | − | 11.7070i | −0.588986 | − | 0.386600i | ||||
\(918\) | 0.486762 | 0.0160655 | ||||||||
\(919\) | 28.8290 | − | 49.9332i | 0.950980 | − | 1.64715i | 0.207668 | − | 0.978199i | \(-0.433413\pi\) |
0.743311 | − | 0.668946i | \(-0.233254\pi\) | |||||||
\(920\) | 3.11985 | + | 5.40373i | 0.102858 | + | 0.178156i | ||||
\(921\) | 6.03366 | + | 10.4506i | 0.198816 | + | 0.344359i | ||||
\(922\) | 10.2371 | + | 17.7311i | 0.337140 | + | 0.583943i | ||||
\(923\) | 9.20985 | − | 5.21042i | 0.303146 | − | 0.171503i | ||||
\(924\) | 0.320759 | − | 5.59660i | 0.0105522 | − | 0.184115i | ||||
\(925\) | −1.91150 | + | 3.31081i | −0.0628497 | + | 0.108859i | ||||
\(926\) | −17.2668 | −0.567423 | ||||||||
\(927\) | −11.2954 | −0.370990 | ||||||||
\(928\) | −1.74338 | + | 3.01962i | −0.0572293 | + | 0.0991240i | ||||
\(929\) | −2.05959 | + | 3.56731i | −0.0675729 | + | 0.117040i | −0.897832 | − | 0.440337i | \(-0.854859\pi\) |
0.830259 | + | 0.557377i | \(0.188192\pi\) | |||||||
\(930\) | 2.92262 | + | 5.06213i | 0.0958366 | + | 0.165994i | ||||
\(931\) | −17.4762 | − | 40.3087i | −0.572759 | − | 1.32106i | ||||
\(932\) | −2.59706 | − | 4.49824i | −0.0850695 | − | 0.147345i | ||||
\(933\) | −1.51176 | −0.0494929 | ||||||||
\(934\) | −4.37922 | − | 7.58503i | −0.143292 | − | 0.248190i | ||||
\(935\) | −0.671807 | + | 1.16360i | −0.0219704 | + | 0.0380539i | ||||
\(936\) | −3.10661 | − | 1.83002i | −0.101543 | − | 0.0598161i | ||||
\(937\) | 22.6483 | 0.739888 | 0.369944 | − | 0.929054i | \(-0.379377\pi\) | ||||
0.369944 | + | 0.929054i | \(0.379377\pi\) | |||||||
\(938\) | 7.42843 | + | 4.87589i | 0.242547 | + | 0.159204i | ||||
\(939\) | −0.862908 | + | 1.49460i | −0.0281599 | + | 0.0487744i | ||||
\(940\) | 5.19248 | − | 8.99364i | 0.169360 | − | 0.293340i | ||||
\(941\) | 10.0011 | − | 17.3223i | 0.326025 | − | 0.564692i | −0.655694 | − | 0.755027i | \(-0.727624\pi\) |
0.981719 | + | 0.190334i | \(0.0609572\pi\) | |||||||
\(942\) | −6.24495 | −0.203472 | ||||||||
\(943\) | 30.2625 | − | 52.4161i | 0.985481 | − | 1.70690i | ||||
\(944\) | −9.15014 | −0.297812 | ||||||||
\(945\) | −2.88153 | − | 1.89139i | −0.0937362 | − | 0.0615269i | ||||
\(946\) | 8.50388 | − | 14.7292i | 0.276485 | − | 0.478886i | ||||
\(947\) | 7.53183 | 0.244752 | 0.122376 | − | 0.992484i | \(-0.460949\pi\) | ||||
0.122376 | + | 0.992484i | \(0.460949\pi\) | |||||||
\(948\) | −7.16738 | + | 12.4143i | −0.232786 | + | 0.403197i | ||||
\(949\) | 50.2859 | + | 29.6221i | 1.63235 | + | 0.961574i | ||||
\(950\) | 10.3646 | + | 17.9520i | 0.336272 | + | 0.582441i | ||||
\(951\) | −10.6520 | + | 18.4499i | −0.345416 | + | 0.598278i | ||||
\(952\) | −1.15033 | + | 0.579054i | −0.0372824 | + | 0.0187672i | ||||
\(953\) | −2.65075 | − | 4.59123i | −0.0858661 | − | 0.148724i | 0.819894 | − | 0.572516i | \(-0.194032\pi\) |
−0.905760 | + | 0.423791i | \(0.860699\pi\) | |||||||
\(954\) | −4.29060 | − | 7.43153i | −0.138913 | − | 0.240605i | ||||
\(955\) | 14.9674 | 0.484335 | ||||||||
\(956\) | 25.3978 | 0.821425 | ||||||||
\(957\) | 3.69386 | + | 6.39795i | 0.119405 | + | 0.206816i | ||||
\(958\) | −13.5126 | − | 23.4046i | −0.436573 | − | 0.756167i | ||||
\(959\) | 16.0502 | − | 8.07937i | 0.518289 | − | 0.260896i | ||||
\(960\) | 0.651388 | − | 1.12824i | 0.0210235 | − | 0.0364137i | ||||
\(961\) | 5.43448 | + | 9.41280i | 0.175306 | + | 0.303639i | ||||
\(962\) | 0.0365092 | − | 4.17331i | 0.00117711 | − | 0.134553i | ||||
\(963\) | 7.01462 | − | 12.1497i | 0.226043 | − | 0.391518i | ||||
\(964\) | −11.8575 | −0.381904 | ||||||||
\(965\) | −0.179979 | + | 0.311732i | −0.00579372 | + | 0.0100350i | ||||
\(966\) | 10.5937 | + | 6.95352i | 0.340846 | + | 0.223726i | ||||
\(967\) | −7.46926 | −0.240195 | −0.120098 | − | 0.992762i | \(-0.538321\pi\) | ||||
−0.120098 | + | 0.992762i | \(0.538321\pi\) | |||||||
\(968\) | −3.25537 | + | 5.63846i | −0.104631 | + | 0.181227i | ||||
\(969\) | 3.05507 | 0.0981429 | ||||||||
\(970\) | 0.910122 | − | 1.57638i | 0.0292223 | − | 0.0506144i | ||||
\(971\) | 1.64395 | − | 2.84741i | 0.0527570 | − | 0.0913778i | −0.838441 | − | 0.544993i | \(-0.816532\pi\) |
0.891198 | + | 0.453615i | \(0.149866\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | −28.5558 | − | 18.7436i | −0.915458 | − | 0.600891i | ||||
\(974\) | −21.9435 | −0.703114 | ||||||||
\(975\) | −0.104173 | + | 11.9079i | −0.00333622 | + | 0.381357i | ||||
\(976\) | 5.09231 | − | 8.82015i | 0.163001 | − | 0.282326i | ||||
\(977\) | 0.416499 | + | 0.721397i | 0.0133250 | + | 0.0230795i | 0.872611 | − | 0.488416i | \(-0.162425\pi\) |
−0.859286 | + | 0.511495i | \(0.829092\pi\) | |||||||
\(978\) | 2.60767 | 0.0833840 | ||||||||
\(979\) | −9.95535 | − | 17.2432i | −0.318174 | − | 0.551094i | ||||
\(980\) | 9.05971 | + | 1.04190i | 0.289402 | + | 0.0332824i | ||||
\(981\) | −5.50000 | − | 9.52628i | −0.175601 | − | 0.304151i | ||||
\(982\) | 7.09020 | − | 12.2806i | 0.226257 | − | 0.391889i | ||||
\(983\) | 20.9860 | − | 36.3487i | 0.669348 | − | 1.15934i | −0.308739 | − | 0.951147i | \(-0.599907\pi\) |
0.978087 | − | 0.208198i | \(-0.0667598\pi\) | |||||||
\(984\) | −12.6369 | −0.402850 | ||||||||
\(985\) | −17.2892 | −0.550879 | ||||||||
\(986\) | 0.848612 | − | 1.46984i | 0.0270253 | − | 0.0468092i | ||||
\(987\) | 1.20677 | − | 21.0558i | 0.0384120 | − | 0.670214i | ||||
\(988\) | −19.4980 | − | 11.4858i | −0.620314 | − | 0.365411i | ||||
\(989\) | 19.2231 | + | 33.2954i | 0.611259 | + | 1.05873i | ||||
\(990\) | −1.38015 | − | 2.39050i | −0.0438642 | − | 0.0759749i | ||||
\(991\) | 25.9607 | + | 44.9653i | 0.824670 | + | 1.42837i | 0.902171 | + | 0.431378i | \(0.141972\pi\) |
−0.0775015 | + | 0.996992i | \(0.524694\pi\) | |||||||
\(992\) | −2.24338 | + | 3.88565i | −0.0712274 | + | 0.123370i | ||||
\(993\) | 16.4338 | 0.521511 | ||||||||
\(994\) | 6.49131 | + | 4.26079i | 0.205892 | + | 0.135144i | ||||
\(995\) | 12.3906 | + | 21.4612i | 0.392809 | + | 0.680364i | ||||
\(996\) | −1.74338 | − | 3.01962i | −0.0552411 | − | 0.0956805i | ||||
\(997\) | −48.5174 | −1.53656 | −0.768281 | − | 0.640113i | \(-0.778888\pi\) | ||||
−0.768281 | + | 0.640113i | \(0.778888\pi\) | |||||||
\(998\) | −14.7488 | − | 25.5456i | −0.466864 | − | 0.808632i | ||||
\(999\) | −1.15751 | −0.0366220 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 546.2.j.b.529.3 | yes | 8 | |
3.2 | odd | 2 | 1638.2.m.i.1621.1 | 8 | |||
7.2 | even | 3 | 546.2.k.d.373.4 | yes | 8 | ||
13.3 | even | 3 | 546.2.k.d.445.4 | yes | 8 | ||
21.2 | odd | 6 | 1638.2.p.g.919.2 | 8 | |||
39.29 | odd | 6 | 1638.2.p.g.991.2 | 8 | |||
91.16 | even | 3 | inner | 546.2.j.b.289.3 | ✓ | 8 | |
273.107 | odd | 6 | 1638.2.m.i.289.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.b.289.3 | ✓ | 8 | 91.16 | even | 3 | inner | |
546.2.j.b.529.3 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.k.d.373.4 | yes | 8 | 7.2 | even | 3 | ||
546.2.k.d.445.4 | yes | 8 | 13.3 | even | 3 | ||
1638.2.m.i.289.1 | 8 | 273.107 | odd | 6 | |||
1638.2.m.i.1621.1 | 8 | 3.2 | odd | 2 | |||
1638.2.p.g.919.2 | 8 | 21.2 | odd | 6 | |||
1638.2.p.g.991.2 | 8 | 39.29 | odd | 6 |