Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(100,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.8 | ||
Root | \(1.21707 + 2.10803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.100 |
Dual form | 273.2.j.b.172.8 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.21707 | + | 2.10803i | 0.860600 | + | 1.49060i | 0.871351 | + | 0.490661i | \(0.163245\pi\) |
−0.0107503 | + | 0.999942i | \(0.503422\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.96253 | + | 3.39920i | −0.981265 | + | 1.69960i | ||||
\(5\) | −0.613891 | + | 1.06329i | −0.274540 | + | 0.475518i | −0.970019 | − | 0.243029i | \(-0.921859\pi\) |
0.695479 | + | 0.718547i | \(0.255192\pi\) | |||||||
\(6\) | −1.21707 | − | 2.10803i | −0.496868 | − | 0.860600i | ||||
\(7\) | −2.37183 | + | 1.17236i | −0.896467 | + | 0.443111i | ||||
\(8\) | −4.68588 | −1.65671 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.98860 | −0.945078 | ||||||||
\(11\) | 3.49255 | 1.05304 | 0.526522 | − | 0.850162i | \(-0.323496\pi\) | ||||
0.526522 | + | 0.850162i | \(0.323496\pi\) | |||||||
\(12\) | 1.96253 | − | 3.39920i | 0.566534 | − | 0.981265i | ||||
\(13\) | −2.87580 | − | 2.17480i | −0.797604 | − | 0.603181i | ||||
\(14\) | −5.35806 | − | 3.57304i | −1.43200 | − | 0.954935i | ||||
\(15\) | 0.613891 | − | 1.06329i | 0.158506 | − | 0.274540i | ||||
\(16\) | −1.77799 | − | 3.07957i | −0.444498 | − | 0.769894i | ||||
\(17\) | −2.26353 | + | 3.92054i | −0.548986 | + | 0.950871i | 0.449359 | + | 0.893351i | \(0.351653\pi\) |
−0.998344 | + | 0.0575196i | \(0.981681\pi\) | |||||||
\(18\) | 1.21707 | + | 2.10803i | 0.286867 | + | 0.496868i | ||||
\(19\) | 1.35541 | 0.310953 | 0.155476 | − | 0.987840i | \(-0.450309\pi\) | ||||
0.155476 | + | 0.987840i | \(0.450309\pi\) | |||||||
\(20\) | −2.40956 | − | 4.17348i | −0.538794 | − | 0.933219i | ||||
\(21\) | 2.37183 | − | 1.17236i | 0.517575 | − | 0.255830i | ||||
\(22\) | 4.25069 | + | 7.36241i | 0.906250 | + | 1.56967i | ||||
\(23\) | 0.336664 | + | 0.583119i | 0.0701992 | + | 0.121589i | 0.898989 | − | 0.437972i | \(-0.144303\pi\) |
−0.828789 | + | 0.559561i | \(0.810970\pi\) | |||||||
\(24\) | 4.68588 | 0.956501 | ||||||||
\(25\) | 1.74628 | + | 3.02464i | 0.349255 | + | 0.604928i | ||||
\(26\) | 1.08449 | − | 8.70917i | 0.212686 | − | 1.70801i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.669691 | − | 10.3631i | 0.126560 | − | 1.95845i | ||||
\(29\) | 2.64824 | − | 4.58688i | 0.491766 | − | 0.851763i | −0.508189 | − | 0.861245i | \(-0.669685\pi\) |
0.999955 | + | 0.00948238i | \(0.00301838\pi\) | |||||||
\(30\) | 2.98860 | 0.545641 | ||||||||
\(31\) | 4.99846 | + | 8.65759i | 0.897750 | + | 1.55495i | 0.830364 | + | 0.557222i | \(0.188133\pi\) |
0.0673864 | + | 0.997727i | \(0.478534\pi\) | |||||||
\(32\) | −0.357986 | + | 0.620050i | −0.0632836 | + | 0.109610i | ||||
\(33\) | −3.49255 | −0.607975 | ||||||||
\(34\) | −11.0195 | −1.88983 | ||||||||
\(35\) | 0.209483 | − | 3.24164i | 0.0354091 | − | 0.547938i | ||||
\(36\) | −1.96253 | + | 3.39920i | −0.327088 | + | 0.566534i | ||||
\(37\) | 1.54118 | + | 2.66940i | 0.253368 | + | 0.438847i | 0.964451 | − | 0.264262i | \(-0.0851282\pi\) |
−0.711083 | + | 0.703108i | \(0.751795\pi\) | |||||||
\(38\) | 1.64963 | + | 2.85725i | 0.267606 | + | 0.463507i | ||||
\(39\) | 2.87580 | + | 2.17480i | 0.460497 | + | 0.348247i | ||||
\(40\) | 2.87662 | − | 4.98245i | 0.454834 | − | 0.787795i | ||||
\(41\) | 3.61102 | − | 6.25447i | 0.563947 | − | 0.976784i | −0.433200 | − | 0.901298i | \(-0.642616\pi\) |
0.997147 | − | 0.0754865i | \(-0.0240510\pi\) | |||||||
\(42\) | 5.35806 | + | 3.57304i | 0.826767 | + | 0.551332i | ||||
\(43\) | 4.48886 | + | 7.77494i | 0.684545 | + | 1.18567i | 0.973579 | + | 0.228348i | \(0.0733325\pi\) |
−0.289034 | + | 0.957319i | \(0.593334\pi\) | |||||||
\(44\) | −6.85424 | + | 11.8719i | −1.03332 | + | 1.78975i | ||||
\(45\) | −0.613891 | + | 1.06329i | −0.0915135 | + | 0.158506i | ||||
\(46\) | −0.819488 | + | 1.41940i | −0.120827 | + | 0.209278i | ||||
\(47\) | 2.58008 | − | 4.46883i | 0.376344 | − | 0.651846i | −0.614184 | − | 0.789163i | \(-0.710515\pi\) |
0.990527 | + | 0.137317i | \(0.0438479\pi\) | |||||||
\(48\) | 1.77799 | + | 3.07957i | 0.256631 | + | 0.444498i | ||||
\(49\) | 4.25114 | − | 5.56128i | 0.607305 | − | 0.794469i | ||||
\(50\) | −4.25069 | + | 7.36241i | −0.601138 | + | 1.04120i | ||||
\(51\) | 2.26353 | − | 3.92054i | 0.316957 | − | 0.548986i | ||||
\(52\) | 13.0364 | − | 5.50732i | 1.80783 | − | 0.763728i | ||||
\(53\) | −4.95271 | − | 8.57835i | −0.680308 | − | 1.17833i | −0.974887 | − | 0.222700i | \(-0.928513\pi\) |
0.294579 | − | 0.955627i | \(-0.404820\pi\) | |||||||
\(54\) | −1.21707 | − | 2.10803i | −0.165623 | − | 0.286867i | ||||
\(55\) | −2.14405 | + | 3.71360i | −0.289103 | + | 0.500741i | ||||
\(56\) | 11.1141 | − | 5.49354i | 1.48518 | − | 0.734106i | ||||
\(57\) | −1.35541 | −0.179529 | ||||||||
\(58\) | 12.8924 | 1.69285 | ||||||||
\(59\) | −0.401721 | + | 0.695802i | −0.0522997 | + | 0.0905857i | −0.890990 | − | 0.454023i | \(-0.849988\pi\) |
0.838690 | + | 0.544609i | \(0.183322\pi\) | |||||||
\(60\) | 2.40956 | + | 4.17348i | 0.311073 | + | 0.538794i | ||||
\(61\) | 4.64974 | 0.595339 | 0.297669 | − | 0.954669i | \(-0.403791\pi\) | ||||
0.297669 | + | 0.954669i | \(0.403791\pi\) | |||||||
\(62\) | −12.1670 | + | 21.0738i | −1.54521 | + | 2.67638i | ||||
\(63\) | −2.37183 | + | 1.17236i | −0.298822 | + | 0.147704i | ||||
\(64\) | −8.85475 | −1.10684 | ||||||||
\(65\) | 4.07787 | − | 1.72272i | 0.505798 | − | 0.213677i | ||||
\(66\) | −4.25069 | − | 7.36241i | −0.523223 | − | 0.906250i | ||||
\(67\) | −2.12136 | −0.259165 | −0.129583 | − | 0.991569i | \(-0.541364\pi\) | ||||
−0.129583 | + | 0.991569i | \(0.541364\pi\) | |||||||
\(68\) | −8.88448 | − | 15.3884i | −1.07740 | − | 1.86611i | ||||
\(69\) | −0.336664 | − | 0.583119i | −0.0405295 | − | 0.0701992i | ||||
\(70\) | 7.08845 | − | 3.50372i | 0.847231 | − | 0.418775i | ||||
\(71\) | −2.52793 | − | 4.37850i | −0.300010 | − | 0.519632i | 0.676128 | − | 0.736784i | \(-0.263657\pi\) |
−0.976138 | + | 0.217152i | \(0.930323\pi\) | |||||||
\(72\) | −4.68588 | −0.552236 | ||||||||
\(73\) | −6.04227 | − | 10.4655i | −0.707194 | − | 1.22490i | −0.965894 | − | 0.258939i | \(-0.916627\pi\) |
0.258699 | − | 0.965958i | \(-0.416706\pi\) | |||||||
\(74\) | −3.75145 | + | 6.49771i | −0.436098 | + | 0.755343i | ||||
\(75\) | −1.74628 | − | 3.02464i | −0.201643 | − | 0.349255i | ||||
\(76\) | −2.66004 | + | 4.60732i | −0.305127 | + | 0.528496i | ||||
\(77\) | −8.28373 | + | 4.09453i | −0.944019 | + | 0.466615i | ||||
\(78\) | −1.08449 | + | 8.70917i | −0.122794 | + | 0.986120i | ||||
\(79\) | −5.90140 | + | 10.2215i | −0.663960 | + | 1.15001i | 0.315607 | + | 0.948890i | \(0.397792\pi\) |
−0.979566 | + | 0.201122i | \(0.935541\pi\) | |||||||
\(80\) | 4.36598 | 0.488131 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 17.5795 | 1.94133 | ||||||||
\(83\) | 12.6805 | 1.39187 | 0.695935 | − | 0.718105i | \(-0.254990\pi\) | ||||
0.695935 | + | 0.718105i | \(0.254990\pi\) | |||||||
\(84\) | −0.669691 | + | 10.3631i | −0.0730693 | + | 1.13071i | ||||
\(85\) | −2.77912 | − | 4.81357i | −0.301438 | − | 0.522105i | ||||
\(86\) | −10.9265 | + | 18.9253i | −1.17824 | + | 2.04077i | ||||
\(87\) | −2.64824 | + | 4.58688i | −0.283921 | + | 0.491766i | ||||
\(88\) | −16.3657 | −1.74459 | ||||||||
\(89\) | 1.55233 | + | 2.68871i | 0.164546 | + | 0.285003i | 0.936494 | − | 0.350683i | \(-0.114051\pi\) |
−0.771948 | + | 0.635686i | \(0.780717\pi\) | |||||||
\(90\) | −2.98860 | −0.315026 | ||||||||
\(91\) | 9.37056 | + | 1.78677i | 0.982302 | + | 0.187305i | ||||
\(92\) | −2.64285 | −0.275536 | ||||||||
\(93\) | −4.99846 | − | 8.65759i | −0.518316 | − | 0.897750i | ||||
\(94\) | 12.5606 | 1.29553 | ||||||||
\(95\) | −0.832075 | + | 1.44120i | −0.0853691 | + | 0.147864i | ||||
\(96\) | 0.357986 | − | 0.620050i | 0.0365368 | − | 0.0632836i | ||||
\(97\) | −3.59585 | − | 6.22820i | −0.365104 | − | 0.632378i | 0.623689 | − | 0.781672i | \(-0.285633\pi\) |
−0.988793 | + | 0.149294i | \(0.952300\pi\) | |||||||
\(98\) | 16.8973 | + | 2.19305i | 1.70688 | + | 0.221531i | ||||
\(99\) | 3.49255 | 0.351015 | ||||||||
\(100\) | −13.7085 | −1.37085 | ||||||||
\(101\) | −1.54577 | −0.153810 | −0.0769050 | − | 0.997038i | \(-0.524504\pi\) | ||||
−0.0769050 | + | 0.997038i | \(0.524504\pi\) | |||||||
\(102\) | 11.0195 | 1.09109 | ||||||||
\(103\) | −2.75895 | + | 4.77865i | −0.271848 | + | 0.470854i | −0.969335 | − | 0.245743i | \(-0.920968\pi\) |
0.697487 | + | 0.716597i | \(0.254301\pi\) | |||||||
\(104\) | 13.4757 | + | 10.1909i | 1.32140 | + | 0.999296i | ||||
\(105\) | −0.209483 | + | 3.24164i | −0.0204435 | + | 0.316352i | ||||
\(106\) | 12.0556 | − | 20.8810i | 1.17095 | − | 2.02814i | ||||
\(107\) | −0.724187 | − | 1.25433i | −0.0700098 | − | 0.121261i | 0.828896 | − | 0.559403i | \(-0.188970\pi\) |
−0.898905 | + | 0.438143i | \(0.855636\pi\) | |||||||
\(108\) | 1.96253 | − | 3.39920i | 0.188845 | − | 0.327088i | ||||
\(109\) | −8.20485 | − | 14.2112i | −0.785882 | − | 1.36119i | −0.928471 | − | 0.371406i | \(-0.878876\pi\) |
0.142588 | − | 0.989782i | \(-0.454458\pi\) | |||||||
\(110\) | −10.4378 | −0.995209 | ||||||||
\(111\) | −1.54118 | − | 2.66940i | −0.146282 | − | 0.253368i | ||||
\(112\) | 7.82747 | + | 5.21977i | 0.739626 | + | 0.493222i | ||||
\(113\) | 5.38049 | + | 9.31929i | 0.506154 | + | 0.876685i | 0.999975 | + | 0.00712097i | \(0.00226669\pi\) |
−0.493820 | + | 0.869564i | \(0.664400\pi\) | |||||||
\(114\) | −1.64963 | − | 2.85725i | −0.154502 | − | 0.267606i | ||||
\(115\) | −0.826699 | −0.0770901 | ||||||||
\(116\) | 10.3945 | + | 18.0038i | 0.965105 | + | 1.67161i | ||||
\(117\) | −2.87580 | − | 2.17480i | −0.265868 | − | 0.201060i | ||||
\(118\) | −1.95570 | −0.180036 | ||||||||
\(119\) | 0.772402 | − | 11.9525i | 0.0708060 | − | 1.09569i | ||||
\(120\) | −2.87662 | + | 4.98245i | −0.262598 | + | 0.454834i | ||||
\(121\) | 1.19791 | 0.108901 | ||||||||
\(122\) | 5.65908 | + | 9.80181i | 0.512349 | + | 0.887414i | ||||
\(123\) | −3.61102 | + | 6.25447i | −0.325595 | + | 0.563947i | ||||
\(124\) | −39.2385 | −3.52372 | ||||||||
\(125\) | −10.4270 | −0.932619 | ||||||||
\(126\) | −5.35806 | − | 3.57304i | −0.477334 | − | 0.318312i | ||||
\(127\) | 8.24568 | − | 14.2819i | 0.731686 | − | 1.26732i | −0.224476 | − | 0.974480i | \(-0.572067\pi\) |
0.956162 | − | 0.292838i | \(-0.0945996\pi\) | |||||||
\(128\) | −10.0609 | − | 17.4260i | −0.889267 | − | 1.54026i | ||||
\(129\) | −4.48886 | − | 7.77494i | −0.395222 | − | 0.684545i | ||||
\(130\) | 8.59462 | + | 6.49961i | 0.753798 | + | 0.570053i | ||||
\(131\) | 3.52172 | − | 6.09979i | 0.307694 | − | 0.532942i | −0.670164 | − | 0.742213i | \(-0.733776\pi\) |
0.977857 | + | 0.209272i | \(0.0671094\pi\) | |||||||
\(132\) | 6.85424 | − | 11.8719i | 0.596585 | − | 1.03332i | ||||
\(133\) | −3.21480 | + | 1.58903i | −0.278759 | + | 0.137787i | ||||
\(134\) | −2.58185 | − | 4.47189i | −0.223038 | − | 0.386312i | ||||
\(135\) | 0.613891 | − | 1.06329i | 0.0528353 | − | 0.0915135i | ||||
\(136\) | 10.6066 | − | 18.3712i | 0.909509 | − | 1.57532i | ||||
\(137\) | 9.66065 | − | 16.7327i | 0.825365 | − | 1.42957i | −0.0762752 | − | 0.997087i | \(-0.524303\pi\) |
0.901640 | − | 0.432487i | \(-0.142364\pi\) | |||||||
\(138\) | 0.819488 | − | 1.41940i | 0.0697595 | − | 0.120827i | ||||
\(139\) | 7.76176 | + | 13.4438i | 0.658343 | + | 1.14028i | 0.981044 | + | 0.193783i | \(0.0620759\pi\) |
−0.322701 | + | 0.946501i | \(0.604591\pi\) | |||||||
\(140\) | 10.6079 | + | 7.07390i | 0.896530 | + | 0.597854i | ||||
\(141\) | −2.58008 | + | 4.46883i | −0.217282 | + | 0.376344i | ||||
\(142\) | 6.15334 | − | 10.6579i | 0.516377 | − | 0.894392i | ||||
\(143\) | −10.0439 | − | 7.59560i | −0.839912 | − | 0.635176i | ||||
\(144\) | −1.77799 | − | 3.07957i | −0.148166 | − | 0.256631i | ||||
\(145\) | 3.25146 | + | 5.63169i | 0.270019 | + | 0.467687i | ||||
\(146\) | 14.7078 | − | 25.4746i | 1.21722 | − | 2.10829i | ||||
\(147\) | −4.25114 | + | 5.56128i | −0.350628 | + | 0.458687i | ||||
\(148\) | −12.0984 | −0.994486 | ||||||||
\(149\) | 17.5332 | 1.43637 | 0.718187 | − | 0.695850i | \(-0.244972\pi\) | ||||
0.718187 | + | 0.695850i | \(0.244972\pi\) | |||||||
\(150\) | 4.25069 | − | 7.36241i | 0.347067 | − | 0.601138i | ||||
\(151\) | −7.01950 | − | 12.1581i | −0.571239 | − | 0.989415i | −0.996439 | − | 0.0843154i | \(-0.973130\pi\) |
0.425200 | − | 0.905099i | \(-0.360204\pi\) | |||||||
\(152\) | −6.35130 | −0.515158 | ||||||||
\(153\) | −2.26353 | + | 3.92054i | −0.182995 | + | 0.316957i | ||||
\(154\) | −18.7133 | − | 12.4790i | −1.50796 | − | 1.00559i | ||||
\(155\) | −12.2740 | −0.985875 | ||||||||
\(156\) | −13.0364 | + | 5.50732i | −1.04375 | + | 0.440939i | ||||
\(157\) | 5.62295 | + | 9.73923i | 0.448760 | + | 0.777275i | 0.998306 | − | 0.0581884i | \(-0.0185324\pi\) |
−0.549545 | + | 0.835464i | \(0.685199\pi\) | |||||||
\(158\) | −28.7297 | −2.28562 | ||||||||
\(159\) | 4.95271 | + | 8.57835i | 0.392776 | + | 0.680308i | ||||
\(160\) | −0.439529 | − | 0.761287i | −0.0347478 | − | 0.0601850i | ||||
\(161\) | −1.48213 | − | 0.988365i | −0.116809 | − | 0.0778941i | ||||
\(162\) | 1.21707 | + | 2.10803i | 0.0956222 | + | 0.165623i | ||||
\(163\) | 11.6079 | 0.909205 | 0.454602 | − | 0.890695i | \(-0.349781\pi\) | ||||
0.454602 | + | 0.890695i | \(0.349781\pi\) | |||||||
\(164\) | 14.1735 | + | 24.5492i | 1.10676 | + | 1.91697i | ||||
\(165\) | 2.14405 | − | 3.71360i | 0.166914 | − | 0.289103i | ||||
\(166\) | 15.4331 | + | 26.7310i | 1.19784 | + | 2.07472i | ||||
\(167\) | 3.44594 | − | 5.96855i | 0.266655 | − | 0.461860i | −0.701341 | − | 0.712826i | \(-0.747415\pi\) |
0.967996 | + | 0.250966i | \(0.0807482\pi\) | |||||||
\(168\) | −11.1141 | + | 5.49354i | −0.857471 | + | 0.423836i | ||||
\(169\) | 3.54048 | + | 12.5086i | 0.272345 | + | 0.962200i | ||||
\(170\) | 6.76477 | − | 11.7169i | 0.518834 | − | 0.898648i | ||||
\(171\) | 1.35541 | 0.103651 | ||||||||
\(172\) | −35.2381 | −2.68688 | ||||||||
\(173\) | −15.8386 | −1.20419 | −0.602093 | − | 0.798426i | \(-0.705666\pi\) | ||||
−0.602093 | + | 0.798426i | \(0.705666\pi\) | |||||||
\(174\) | −12.8924 | −0.977370 | ||||||||
\(175\) | −7.68783 | − | 5.12665i | −0.581146 | − | 0.387539i | ||||
\(176\) | −6.20973 | − | 10.7556i | −0.468076 | − | 0.810732i | ||||
\(177\) | 0.401721 | − | 0.695802i | 0.0301952 | − | 0.0522997i | ||||
\(178\) | −3.77859 | + | 6.54471i | −0.283217 | + | 0.490547i | ||||
\(179\) | 21.1031 | 1.57732 | 0.788658 | − | 0.614832i | \(-0.210776\pi\) | ||||
0.788658 | + | 0.614832i | \(0.210776\pi\) | |||||||
\(180\) | −2.40956 | − | 4.17348i | −0.179598 | − | 0.311073i | ||||
\(181\) | 15.0685 | 1.12003 | 0.560015 | − | 0.828483i | \(-0.310796\pi\) | ||||
0.560015 | + | 0.828483i | \(0.310796\pi\) | |||||||
\(182\) | 7.63808 | + | 21.9281i | 0.566172 | + | 1.62542i | ||||
\(183\) | −4.64974 | −0.343719 | ||||||||
\(184\) | −1.57757 | − | 2.73242i | −0.116300 | − | 0.201437i | ||||
\(185\) | −3.78446 | −0.278239 | ||||||||
\(186\) | 12.1670 | − | 21.0738i | 0.892126 | − | 1.54521i | ||||
\(187\) | −7.90548 | + | 13.6927i | −0.578106 | + | 1.00131i | ||||
\(188\) | 10.1270 | + | 17.5404i | 0.738586 | + | 1.27927i | ||||
\(189\) | 2.37183 | − | 1.17236i | 0.172525 | − | 0.0852768i | ||||
\(190\) | −4.05078 | −0.293875 | ||||||||
\(191\) | −9.49806 | −0.687255 | −0.343628 | − | 0.939106i | \(-0.611656\pi\) | ||||
−0.343628 | + | 0.939106i | \(0.611656\pi\) | |||||||
\(192\) | 8.85475 | 0.639037 | ||||||||
\(193\) | −18.5435 | −1.33479 | −0.667395 | − | 0.744704i | \(-0.732591\pi\) | ||||
−0.667395 | + | 0.744704i | \(0.732591\pi\) | |||||||
\(194\) | 8.75283 | − | 15.1603i | 0.628416 | − | 1.08845i | ||||
\(195\) | −4.07787 | + | 1.72272i | −0.292023 | + | 0.123367i | ||||
\(196\) | 10.5609 | + | 25.3647i | 0.754352 | + | 1.81176i | ||||
\(197\) | −12.8786 | + | 22.3065i | −0.917565 | + | 1.58927i | −0.114463 | + | 0.993427i | \(0.536515\pi\) |
−0.803102 | + | 0.595842i | \(0.796819\pi\) | |||||||
\(198\) | 4.25069 | + | 7.36241i | 0.302083 | + | 0.523223i | ||||
\(199\) | −8.84779 | + | 15.3248i | −0.627203 | + | 1.08635i | 0.360907 | + | 0.932602i | \(0.382467\pi\) |
−0.988110 | + | 0.153746i | \(0.950866\pi\) | |||||||
\(200\) | −8.18284 | − | 14.1731i | −0.578614 | − | 1.00219i | ||||
\(201\) | 2.12136 | 0.149629 | ||||||||
\(202\) | −1.88132 | − | 3.25854i | −0.132369 | − | 0.229270i | ||||
\(203\) | −0.903681 | + | 13.9840i | −0.0634259 | + | 0.981484i | ||||
\(204\) | 8.88448 | + | 15.3884i | 0.622038 | + | 1.07740i | ||||
\(205\) | 4.43355 | + | 7.67913i | 0.309652 | + | 0.536334i | ||||
\(206\) | −13.4314 | −0.935809 | ||||||||
\(207\) | 0.336664 | + | 0.583119i | 0.0233997 | + | 0.0405295i | ||||
\(208\) | −1.58430 | + | 12.7230i | −0.109852 | + | 0.882183i | ||||
\(209\) | 4.73385 | 0.327447 | ||||||||
\(210\) | −7.08845 | + | 3.50372i | −0.489149 | + | 0.241780i | ||||
\(211\) | −6.23896 | + | 10.8062i | −0.429508 | + | 0.743929i | −0.996830 | − | 0.0795669i | \(-0.974646\pi\) |
0.567322 | + | 0.823496i | \(0.307980\pi\) | |||||||
\(212\) | 38.8794 | 2.67025 | ||||||||
\(213\) | 2.52793 | + | 4.37850i | 0.173211 | + | 0.300010i | ||||
\(214\) | 1.76278 | − | 3.05322i | 0.120501 | − | 0.208714i | ||||
\(215\) | −11.0227 | −0.751741 | ||||||||
\(216\) | 4.68588 | 0.318834 | ||||||||
\(217\) | −22.0053 | − | 14.6743i | −1.49382 | − | 0.996157i | ||||
\(218\) | 19.9718 | − | 34.5922i | 1.35266 | − | 2.34288i | ||||
\(219\) | 6.04227 | + | 10.4655i | 0.408299 | + | 0.707194i | ||||
\(220\) | −8.41551 | − | 14.5761i | −0.567374 | − | 0.982720i | ||||
\(221\) | 15.0359 | − | 6.35199i | 1.01142 | − | 0.427281i | ||||
\(222\) | 3.75145 | − | 6.49771i | 0.251781 | − | 0.436098i | ||||
\(223\) | −4.65232 | + | 8.05805i | −0.311542 | + | 0.539607i | −0.978696 | − | 0.205313i | \(-0.934179\pi\) |
0.667154 | + | 0.744920i | \(0.267512\pi\) | |||||||
\(224\) | 0.122159 | − | 1.89034i | 0.00816207 | − | 0.126304i | ||||
\(225\) | 1.74628 | + | 3.02464i | 0.116418 | + | 0.201643i | ||||
\(226\) | −13.0969 | + | 22.6845i | −0.871193 | + | 1.50895i | ||||
\(227\) | −4.76651 | + | 8.25583i | −0.316364 | + | 0.547959i | −0.979727 | − | 0.200340i | \(-0.935795\pi\) |
0.663362 | + | 0.748298i | \(0.269129\pi\) | |||||||
\(228\) | 2.66004 | − | 4.60732i | 0.176165 | − | 0.305127i | ||||
\(229\) | 3.22423 | − | 5.58453i | 0.213063 | − | 0.369036i | −0.739608 | − | 0.673037i | \(-0.764989\pi\) |
0.952672 | + | 0.304001i | \(0.0983226\pi\) | |||||||
\(230\) | −1.00615 | − | 1.74271i | −0.0663438 | − | 0.114911i | ||||
\(231\) | 8.28373 | − | 4.09453i | 0.545029 | − | 0.269400i | ||||
\(232\) | −12.4093 | + | 21.4936i | −0.814712 | + | 1.41112i | ||||
\(233\) | 12.2379 | − | 21.1967i | 0.801733 | − | 1.38864i | −0.116742 | − | 0.993162i | \(-0.537245\pi\) |
0.918475 | − | 0.395479i | \(-0.129421\pi\) | |||||||
\(234\) | 1.08449 | − | 8.70917i | 0.0708952 | − | 0.569336i | ||||
\(235\) | 3.16778 | + | 5.48675i | 0.206643 | + | 0.357916i | ||||
\(236\) | −1.57678 | − | 2.73107i | −0.102640 | − | 0.177777i | ||||
\(237\) | 5.90140 | − | 10.2215i | 0.383337 | − | 0.663960i | ||||
\(238\) | 26.1364 | − | 12.9188i | 1.69417 | − | 0.837404i | ||||
\(239\) | 3.62130 | 0.234242 | 0.117121 | − | 0.993118i | \(-0.462633\pi\) | ||||
0.117121 | + | 0.993118i | \(0.462633\pi\) | |||||||
\(240\) | −4.36598 | −0.281823 | ||||||||
\(241\) | −12.5649 | + | 21.7631i | −0.809377 | + | 1.40188i | 0.103919 | + | 0.994586i | \(0.466862\pi\) |
−0.913296 | + | 0.407297i | \(0.866471\pi\) | |||||||
\(242\) | 1.45795 | + | 2.52524i | 0.0937203 | + | 0.162328i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.12527 | + | 15.8054i | −0.584185 | + | 1.01184i | ||||
\(245\) | 3.30352 | + | 7.93421i | 0.211054 | + | 0.506898i | ||||
\(246\) | −17.5795 | −1.12083 | ||||||||
\(247\) | −3.89790 | − | 2.94775i | −0.248017 | − | 0.187561i | ||||
\(248\) | −23.4222 | − | 40.5684i | −1.48731 | − | 2.57610i | ||||
\(249\) | −12.6805 | −0.803596 | ||||||||
\(250\) | −12.6904 | − | 21.9804i | −0.802613 | − | 1.39017i | ||||
\(251\) | 0.280269 | + | 0.485440i | 0.0176904 | + | 0.0306407i | 0.874735 | − | 0.484601i | \(-0.161035\pi\) |
−0.857045 | + | 0.515242i | \(0.827702\pi\) | |||||||
\(252\) | 0.669691 | − | 10.3631i | 0.0421866 | − | 0.652815i | ||||
\(253\) | 1.17581 | + | 2.03657i | 0.0739229 | + | 0.128038i | ||||
\(254\) | 40.1424 | 2.51876 | ||||||||
\(255\) | 2.77912 | + | 4.81357i | 0.174035 | + | 0.301438i | ||||
\(256\) | 15.6349 | − | 27.0805i | 0.977184 | − | 1.69253i | ||||
\(257\) | 11.8793 | + | 20.5756i | 0.741013 | + | 1.28347i | 0.952034 | + | 0.305991i | \(0.0989879\pi\) |
−0.211021 | + | 0.977482i | \(0.567679\pi\) | |||||||
\(258\) | 10.9265 | − | 18.9253i | 0.680257 | − | 1.17824i | ||||
\(259\) | −6.78491 | − | 4.52454i | −0.421594 | − | 0.281141i | ||||
\(260\) | −2.14707 | + | 17.2424i | −0.133156 | + | 1.06933i | ||||
\(261\) | 2.64824 | − | 4.58688i | 0.163922 | − | 0.283921i | ||||
\(262\) | 17.1447 | 1.05921 | ||||||||
\(263\) | −7.07522 | −0.436277 | −0.218138 | − | 0.975918i | \(-0.569998\pi\) | ||||
−0.218138 | + | 0.975918i | \(0.569998\pi\) | |||||||
\(264\) | 16.3657 | 1.00724 | ||||||||
\(265\) | 12.1617 | 0.747088 | ||||||||
\(266\) | −7.26238 | − | 4.84294i | −0.445285 | − | 0.296940i | ||||
\(267\) | −1.55233 | − | 2.68871i | −0.0950009 | − | 0.164546i | ||||
\(268\) | 4.16323 | − | 7.21093i | 0.254310 | − | 0.440478i | ||||
\(269\) | 5.19422 | − | 8.99665i | 0.316697 | − | 0.548536i | −0.663100 | − | 0.748531i | \(-0.730759\pi\) |
0.979797 | + | 0.199996i | \(0.0640928\pi\) | |||||||
\(270\) | 2.98860 | 0.181880 | ||||||||
\(271\) | 0.0613862 | + | 0.106324i | 0.00372894 | + | 0.00645872i | 0.867884 | − | 0.496767i | \(-0.165480\pi\) |
−0.864155 | + | 0.503226i | \(0.832146\pi\) | |||||||
\(272\) | 16.0981 | 0.976093 | ||||||||
\(273\) | −9.37056 | − | 1.78677i | −0.567132 | − | 0.108140i | ||||
\(274\) | 47.0308 | 2.84124 | ||||||||
\(275\) | 6.09896 | + | 10.5637i | 0.367781 | + | 0.637015i | ||||
\(276\) | 2.64285 | 0.159081 | ||||||||
\(277\) | 2.68599 | − | 4.65228i | 0.161386 | − | 0.279528i | −0.773980 | − | 0.633210i | \(-0.781737\pi\) |
0.935366 | + | 0.353682i | \(0.115070\pi\) | |||||||
\(278\) | −18.8932 | + | 32.7240i | −1.13314 | + | 1.96266i | ||||
\(279\) | 4.99846 | + | 8.65759i | 0.299250 | + | 0.518316i | ||||
\(280\) | −0.981613 | + | 15.1900i | −0.0586626 | + | 0.907774i | ||||
\(281\) | −14.8847 | −0.887945 | −0.443972 | − | 0.896040i | \(-0.646431\pi\) | ||||
−0.443972 | + | 0.896040i | \(0.646431\pi\) | |||||||
\(282\) | −12.5606 | −0.747972 | ||||||||
\(283\) | 4.48537 | 0.266628 | 0.133314 | − | 0.991074i | \(-0.457438\pi\) | ||||
0.133314 | + | 0.991074i | \(0.457438\pi\) | |||||||
\(284\) | 19.8446 | 1.17756 | ||||||||
\(285\) | 0.832075 | − | 1.44120i | 0.0492879 | − | 0.0853691i | ||||
\(286\) | 3.78763 | − | 30.4172i | 0.223967 | − | 1.79861i | ||||
\(287\) | −1.23222 | + | 19.0680i | −0.0727356 | + | 1.12555i | ||||
\(288\) | −0.357986 | + | 0.620050i | −0.0210945 | + | 0.0365368i | ||||
\(289\) | −1.74710 | − | 3.02606i | −0.102770 | − | 0.178004i | ||||
\(290\) | −7.91453 | + | 13.7084i | −0.464757 | + | 0.804983i | ||||
\(291\) | 3.59585 | + | 6.22820i | 0.210793 | + | 0.365104i | ||||
\(292\) | 47.4326 | 2.77578 | ||||||||
\(293\) | −11.0016 | − | 19.0553i | −0.642719 | − | 1.11322i | −0.984823 | − | 0.173560i | \(-0.944473\pi\) |
0.342105 | − | 0.939662i | \(-0.388860\pi\) | |||||||
\(294\) | −16.8973 | − | 2.19305i | −0.985470 | − | 0.127901i | ||||
\(295\) | −0.493226 | − | 0.854293i | −0.0287168 | − | 0.0497389i | ||||
\(296\) | −7.22178 | − | 12.5085i | −0.419757 | − | 0.727041i | ||||
\(297\) | −3.49255 | −0.202658 | ||||||||
\(298\) | 21.3392 | + | 36.9605i | 1.23614 | + | 2.14106i | ||||
\(299\) | 0.299989 | − | 2.40911i | 0.0173488 | − | 0.139322i | ||||
\(300\) | 13.7085 | 0.791459 | ||||||||
\(301\) | −19.7619 | − | 13.1782i | −1.13905 | − | 0.759582i | ||||
\(302\) | 17.0865 | − | 29.5947i | 0.983217 | − | 1.70298i | ||||
\(303\) | 1.54577 | 0.0888023 | ||||||||
\(304\) | −2.40991 | − | 4.17409i | −0.138218 | − | 0.239401i | ||||
\(305\) | −2.85444 | + | 4.94403i | −0.163445 | + | 0.283094i | ||||
\(306\) | −11.0195 | −0.629943 | ||||||||
\(307\) | 32.9959 | 1.88318 | 0.941589 | − | 0.336764i | \(-0.109333\pi\) | ||||
0.941589 | + | 0.336764i | \(0.109333\pi\) | |||||||
\(308\) | 2.33893 | − | 36.1937i | 0.133273 | − | 2.06233i | ||||
\(309\) | 2.75895 | − | 4.77865i | 0.156951 | − | 0.271848i | ||||
\(310\) | −14.9384 | − | 25.8741i | −0.848444 | − | 1.46955i | ||||
\(311\) | 4.11532 | + | 7.12794i | 0.233358 | + | 0.404188i | 0.958794 | − | 0.284101i | \(-0.0916952\pi\) |
−0.725436 | + | 0.688290i | \(0.758362\pi\) | |||||||
\(312\) | −13.4757 | − | 10.1909i | −0.762909 | − | 0.576944i | ||||
\(313\) | 7.14348 | − | 12.3729i | 0.403773 | − | 0.699356i | −0.590405 | − | 0.807107i | \(-0.701032\pi\) |
0.994178 | + | 0.107752i | \(0.0343651\pi\) | |||||||
\(314\) | −13.6871 | + | 23.7067i | −0.772406 | + | 1.33785i | ||||
\(315\) | 0.209483 | − | 3.24164i | 0.0118030 | − | 0.182646i | ||||
\(316\) | −23.1634 | − | 40.1201i | −1.30304 | − | 2.25693i | ||||
\(317\) | 4.68195 | − | 8.10938i | 0.262965 | − | 0.455468i | −0.704064 | − | 0.710137i | \(-0.748633\pi\) |
0.967028 | + | 0.254669i | \(0.0819664\pi\) | |||||||
\(318\) | −12.0556 | + | 20.8810i | −0.676046 | + | 1.17095i | ||||
\(319\) | 9.24911 | − | 16.0199i | 0.517851 | − | 0.896944i | ||||
\(320\) | 5.43585 | − | 9.41518i | 0.303874 | − | 0.526324i | ||||
\(321\) | 0.724187 | + | 1.25433i | 0.0404202 | + | 0.0700098i | ||||
\(322\) | 0.279641 | − | 4.32730i | 0.0155838 | − | 0.241151i | ||||
\(323\) | −3.06801 | + | 5.31395i | −0.170709 | + | 0.295676i | ||||
\(324\) | −1.96253 | + | 3.39920i | −0.109029 | + | 0.188845i | ||||
\(325\) | 1.55604 | − | 12.4961i | 0.0863137 | − | 0.693157i | ||||
\(326\) | 14.1277 | + | 24.4699i | 0.782462 | + | 1.35526i | ||||
\(327\) | 8.20485 | + | 14.2112i | 0.453729 | + | 0.785882i | ||||
\(328\) | −16.9208 | + | 29.3077i | −0.934295 | + | 1.61825i | ||||
\(329\) | −0.880423 | + | 13.6241i | −0.0485393 | + | 0.751121i | ||||
\(330\) | 10.4378 | 0.574584 | ||||||||
\(331\) | −24.4779 | −1.34543 | −0.672714 | − | 0.739903i | \(-0.734871\pi\) | ||||
−0.672714 | + | 0.739903i | \(0.734871\pi\) | |||||||
\(332\) | −24.8859 | + | 43.1037i | −1.36579 | + | 2.36562i | ||||
\(333\) | 1.54118 | + | 2.66940i | 0.0844561 | + | 0.146282i | ||||
\(334\) | 16.7759 | 0.917934 | ||||||||
\(335\) | 1.30228 | − | 2.25562i | 0.0711513 | − | 0.123238i | ||||
\(336\) | −7.82747 | − | 5.21977i | −0.427023 | − | 0.284762i | ||||
\(337\) | −13.1685 | −0.717334 | −0.358667 | − | 0.933466i | \(-0.616769\pi\) | ||||
−0.358667 | + | 0.933466i | \(0.616769\pi\) | |||||||
\(338\) | −22.0595 | + | 22.6873i | −1.19988 | + | 1.23403i | ||||
\(339\) | −5.38049 | − | 9.31929i | −0.292228 | − | 0.506154i | ||||
\(340\) | 21.8164 | 1.18316 | ||||||||
\(341\) | 17.4574 | + | 30.2371i | 0.945370 | + | 1.63743i | ||||
\(342\) | 1.64963 | + | 2.85725i | 0.0892020 | + | 0.154502i | ||||
\(343\) | −3.56314 | + | 18.1743i | −0.192391 | + | 0.981318i | ||||
\(344\) | −21.0343 | − | 36.4324i | −1.13409 | − | 1.96430i | ||||
\(345\) | 0.826699 | 0.0445080 | ||||||||
\(346\) | −19.2767 | − | 33.3882i | −1.03632 | − | 1.79496i | ||||
\(347\) | −7.33666 | + | 12.7075i | −0.393853 | + | 0.682173i | −0.992954 | − | 0.118501i | \(-0.962191\pi\) |
0.599101 | + | 0.800673i | \(0.295525\pi\) | |||||||
\(348\) | −10.3945 | − | 18.0038i | −0.557204 | − | 0.965105i | ||||
\(349\) | 12.1698 | − | 21.0787i | 0.651433 | − | 1.12831i | −0.331342 | − | 0.943511i | \(-0.607502\pi\) |
0.982775 | − | 0.184804i | \(-0.0591652\pi\) | |||||||
\(350\) | 1.45050 | − | 22.4457i | 0.0775324 | − | 1.19977i | ||||
\(351\) | 2.87580 | + | 2.17480i | 0.153499 | + | 0.116082i | ||||
\(352\) | −1.25029 | + | 2.16556i | −0.0666404 | + | 0.115425i | ||||
\(353\) | −0.669625 | −0.0356405 | −0.0178203 | − | 0.999841i | \(-0.505673\pi\) | ||||
−0.0178203 | + | 0.999841i | \(0.505673\pi\) | |||||||
\(354\) | 1.95570 | 0.103944 | ||||||||
\(355\) | 6.20749 | 0.329459 | ||||||||
\(356\) | −12.1860 | −0.645855 | ||||||||
\(357\) | −0.772402 | + | 11.9525i | −0.0408798 | + | 0.632595i | ||||
\(358\) | 25.6840 | + | 44.4859i | 1.35744 | + | 2.35115i | ||||
\(359\) | 17.8146 | − | 30.8557i | 0.940216 | − | 1.62850i | 0.175158 | − | 0.984540i | \(-0.443956\pi\) |
0.765058 | − | 0.643962i | \(-0.222710\pi\) | |||||||
\(360\) | 2.87662 | − | 4.98245i | 0.151611 | − | 0.262598i | ||||
\(361\) | −17.1629 | −0.903308 | ||||||||
\(362\) | 18.3394 | + | 31.7648i | 0.963897 | + | 1.66952i | ||||
\(363\) | −1.19791 | −0.0628741 | ||||||||
\(364\) | −24.4636 | + | 28.3458i | −1.28224 | + | 1.48573i | ||||
\(365\) | 14.8372 | 0.776614 | ||||||||
\(366\) | −5.65908 | − | 9.80181i | −0.295805 | − | 0.512349i | ||||
\(367\) | 10.2224 | 0.533602 | 0.266801 | − | 0.963752i | \(-0.414033\pi\) | ||||
0.266801 | + | 0.963752i | \(0.414033\pi\) | |||||||
\(368\) | 1.19717 | − | 2.07356i | 0.0624069 | − | 0.108092i | ||||
\(369\) | 3.61102 | − | 6.25447i | 0.187982 | − | 0.325595i | ||||
\(370\) | −4.60597 | − | 7.97777i | −0.239453 | − | 0.414745i | ||||
\(371\) | 21.8039 | + | 14.5400i | 1.13200 | + | 0.754879i | ||||
\(372\) | 39.2385 | 2.03442 | ||||||||
\(373\) | 4.95108 | 0.256357 | 0.128179 | − | 0.991751i | \(-0.459087\pi\) | ||||
0.128179 | + | 0.991751i | \(0.459087\pi\) | |||||||
\(374\) | −38.4862 | −1.99007 | ||||||||
\(375\) | 10.4270 | 0.538448 | ||||||||
\(376\) | −12.0900 | + | 20.9404i | −0.623492 | + | 1.07992i | ||||
\(377\) | −17.5914 | + | 7.43158i | −0.906002 | + | 0.382746i | ||||
\(378\) | 5.35806 | + | 3.57304i | 0.275589 | + | 0.183777i | ||||
\(379\) | 6.33641 | − | 10.9750i | 0.325479 | − | 0.563747i | −0.656130 | − | 0.754648i | \(-0.727808\pi\) |
0.981609 | + | 0.190901i | \(0.0611410\pi\) | |||||||
\(380\) | −3.26595 | − | 5.65679i | −0.167540 | − | 0.290187i | ||||
\(381\) | −8.24568 | + | 14.2819i | −0.422439 | + | 0.731686i | ||||
\(382\) | −11.5598 | − | 20.0222i | −0.591452 | − | 1.02442i | ||||
\(383\) | −23.7902 | −1.21562 | −0.607810 | − | 0.794082i | \(-0.707952\pi\) | ||||
−0.607810 | + | 0.794082i | \(0.707952\pi\) | |||||||
\(384\) | 10.0609 | + | 17.4260i | 0.513418 | + | 0.889267i | ||||
\(385\) | 0.731631 | − | 11.3216i | 0.0372874 | − | 0.577003i | ||||
\(386\) | −22.5688 | − | 39.0903i | −1.14872 | − | 1.98964i | ||||
\(387\) | 4.48886 | + | 7.77494i | 0.228182 | + | 0.395222i | ||||
\(388\) | 28.2279 | 1.43305 | ||||||||
\(389\) | 12.7721 | + | 22.1218i | 0.647569 | + | 1.12162i | 0.983702 | + | 0.179808i | \(0.0575475\pi\) |
−0.336133 | + | 0.941815i | \(0.609119\pi\) | |||||||
\(390\) | −8.59462 | − | 6.49961i | −0.435206 | − | 0.329121i | ||||
\(391\) | −3.04819 | −0.154153 | ||||||||
\(392\) | −19.9203 | + | 26.0595i | −1.00613 | + | 1.31620i | ||||
\(393\) | −3.52172 | + | 6.09979i | −0.177647 | + | 0.307694i | ||||
\(394\) | −62.6969 | −3.15863 | ||||||||
\(395\) | −7.24564 | − | 12.5498i | −0.364568 | − | 0.631450i | ||||
\(396\) | −6.85424 | + | 11.8719i | −0.344438 | + | 0.596585i | ||||
\(397\) | −2.12736 | −0.106769 | −0.0533846 | − | 0.998574i | \(-0.517001\pi\) | ||||
−0.0533846 | + | 0.998574i | \(0.517001\pi\) | |||||||
\(398\) | −43.0736 | −2.15908 | ||||||||
\(399\) | 3.21480 | − | 1.58903i | 0.160942 | − | 0.0795511i | ||||
\(400\) | 6.20973 | − | 10.7556i | 0.310487 | − | 0.537779i | ||||
\(401\) | −0.293644 | − | 0.508607i | −0.0146639 | − | 0.0253986i | 0.858600 | − | 0.512646i | \(-0.171334\pi\) |
−0.873264 | + | 0.487247i | \(0.838001\pi\) | |||||||
\(402\) | 2.58185 | + | 4.47189i | 0.128771 | + | 0.223038i | ||||
\(403\) | 4.45394 | − | 35.7682i | 0.221867 | − | 1.78174i | ||||
\(404\) | 3.03362 | − | 5.25439i | 0.150928 | − | 0.261416i | ||||
\(405\) | −0.613891 | + | 1.06329i | −0.0305045 | + | 0.0528353i | ||||
\(406\) | −30.5785 | + | 15.1145i | −1.51759 | + | 0.750122i | ||||
\(407\) | 5.38265 | + | 9.32302i | 0.266808 | + | 0.462125i | ||||
\(408\) | −10.6066 | + | 18.3712i | −0.525105 | + | 0.909509i | ||||
\(409\) | 2.17228 | − | 3.76249i | 0.107412 | − | 0.186043i | −0.807309 | − | 0.590129i | \(-0.799077\pi\) |
0.914721 | + | 0.404086i | \(0.132410\pi\) | |||||||
\(410\) | −10.7919 | + | 18.6921i | −0.532974 | + | 0.923138i | ||||
\(411\) | −9.66065 | + | 16.7327i | −0.476525 | + | 0.825365i | ||||
\(412\) | −10.8291 | − | 18.7565i | −0.533510 | − | 0.924066i | ||||
\(413\) | 0.137083 | − | 2.12129i | 0.00674540 | − | 0.104382i | ||||
\(414\) | −0.819488 | + | 1.41940i | −0.0402756 | + | 0.0697595i | ||||
\(415\) | −7.78446 | + | 13.4831i | −0.382124 | + | 0.661859i | ||||
\(416\) | 2.37798 | − | 1.00459i | 0.116590 | − | 0.0492543i | ||||
\(417\) | −7.76176 | − | 13.4438i | −0.380095 | − | 0.658343i | ||||
\(418\) | 5.76143 | + | 9.97909i | 0.281801 | + | 0.488093i | ||||
\(419\) | −4.72818 | + | 8.18946i | −0.230987 | + | 0.400081i | −0.958099 | − | 0.286438i | \(-0.907529\pi\) |
0.727112 | + | 0.686519i | \(0.240862\pi\) | |||||||
\(420\) | −10.6079 | − | 7.07390i | −0.517612 | − | 0.345171i | ||||
\(421\) | −11.9569 | −0.582741 | −0.291371 | − | 0.956610i | \(-0.594111\pi\) | ||||
−0.291371 | + | 0.956610i | \(0.594111\pi\) | |||||||
\(422\) | −30.3731 | −1.47854 | ||||||||
\(423\) | 2.58008 | − | 4.46883i | 0.125448 | − | 0.217282i | ||||
\(424\) | 23.2078 | + | 40.1971i | 1.12707 | + | 1.95214i | ||||
\(425\) | −15.8110 | −0.766944 | ||||||||
\(426\) | −6.15334 | + | 10.6579i | −0.298131 | + | 0.516377i | ||||
\(427\) | −11.0284 | + | 5.45118i | −0.533701 | + | 0.263801i | ||||
\(428\) | 5.68496 | 0.274793 | ||||||||
\(429\) | 10.0439 | + | 7.59560i | 0.484923 | + | 0.366719i | ||||
\(430\) | −13.4154 | − | 23.2362i | −0.646949 | − | 1.12055i | ||||
\(431\) | −26.4705 | −1.27504 | −0.637519 | − | 0.770435i | \(-0.720039\pi\) | ||||
−0.637519 | + | 0.770435i | \(0.720039\pi\) | |||||||
\(432\) | 1.77799 | + | 3.07957i | 0.0855437 | + | 0.148166i | ||||
\(433\) | 4.13088 | + | 7.15489i | 0.198517 | + | 0.343842i | 0.948048 | − | 0.318128i | \(-0.103054\pi\) |
−0.749531 | + | 0.661970i | \(0.769721\pi\) | |||||||
\(434\) | 4.15184 | − | 64.2476i | 0.199295 | − | 3.08398i | ||||
\(435\) | −3.25146 | − | 5.63169i | −0.155896 | − | 0.270019i | ||||
\(436\) | 64.4091 | 3.08464 | ||||||||
\(437\) | 0.456318 | + | 0.790366i | 0.0218286 | + | 0.0378083i | ||||
\(438\) | −14.7078 | + | 25.4746i | −0.702764 | + | 1.21722i | ||||
\(439\) | −17.5522 | − | 30.4012i | −0.837719 | − | 1.45097i | −0.891797 | − | 0.452435i | \(-0.850555\pi\) |
0.0540784 | − | 0.998537i | \(-0.482778\pi\) | |||||||
\(440\) | 10.0467 | − | 17.4015i | 0.478960 | − | 0.829582i | ||||
\(441\) | 4.25114 | − | 5.56128i | 0.202435 | − | 0.264823i | ||||
\(442\) | 31.6899 | + | 23.9652i | 1.50734 | + | 1.13991i | ||||
\(443\) | 0.192275 | − | 0.333030i | 0.00913525 | − | 0.0158227i | −0.861422 | − | 0.507890i | \(-0.830425\pi\) |
0.870557 | + | 0.492068i | \(0.163759\pi\) | |||||||
\(444\) | 12.0984 | 0.574167 | ||||||||
\(445\) | −3.81184 | −0.180699 | ||||||||
\(446\) | −22.6488 | −1.07245 | ||||||||
\(447\) | −17.5332 | −0.829291 | ||||||||
\(448\) | 21.0020 | − | 10.3810i | 0.992249 | − | 0.490455i | ||||
\(449\) | −18.9728 | − | 32.8619i | −0.895382 | − | 1.55085i | −0.833331 | − | 0.552774i | \(-0.813569\pi\) |
−0.0620505 | − | 0.998073i | \(-0.519764\pi\) | |||||||
\(450\) | −4.25069 | + | 7.36241i | −0.200379 | + | 0.347067i | ||||
\(451\) | 12.6117 | − | 21.8441i | 0.593860 | − | 1.02860i | ||||
\(452\) | −42.2375 | −1.98669 | ||||||||
\(453\) | 7.01950 | + | 12.1581i | 0.329805 | + | 0.571239i | ||||
\(454\) | −23.2047 | −1.08905 | ||||||||
\(455\) | −7.65236 | + | 8.86675i | −0.358748 | + | 0.415679i | ||||
\(456\) | 6.35130 | 0.297427 | ||||||||
\(457\) | 7.19474 | + | 12.4617i | 0.336556 | + | 0.582932i | 0.983782 | − | 0.179366i | \(-0.0574046\pi\) |
−0.647227 | + | 0.762298i | \(0.724071\pi\) | |||||||
\(458\) | 15.6965 | 0.733449 | ||||||||
\(459\) | 2.26353 | − | 3.92054i | 0.105652 | − | 0.182995i | ||||
\(460\) | 1.62242 | − | 2.81012i | 0.0756459 | − | 0.131022i | ||||
\(461\) | 1.79501 | + | 3.10905i | 0.0836019 | + | 0.144803i | 0.904795 | − | 0.425848i | \(-0.140024\pi\) |
−0.821193 | + | 0.570651i | \(0.806691\pi\) | |||||||
\(462\) | 18.7133 | + | 12.4790i | 0.870622 | + | 0.580577i | ||||
\(463\) | 4.69484 | 0.218188 | 0.109094 | − | 0.994031i | \(-0.465205\pi\) | ||||
0.109094 | + | 0.994031i | \(0.465205\pi\) | |||||||
\(464\) | −18.8342 | −0.874356 | ||||||||
\(465\) | 12.2740 | 0.569195 | ||||||||
\(466\) | 59.5777 | 2.75988 | ||||||||
\(467\) | 20.0343 | − | 34.7003i | 0.927075 | − | 1.60574i | 0.138885 | − | 0.990309i | \(-0.455648\pi\) |
0.788190 | − | 0.615432i | \(-0.211018\pi\) | |||||||
\(468\) | 13.0364 | − | 5.50732i | 0.602610 | − | 0.254576i | ||||
\(469\) | 5.03150 | − | 2.48700i | 0.232333 | − | 0.114839i | ||||
\(470\) | −7.71083 | + | 13.3556i | −0.355674 | + | 0.616046i | ||||
\(471\) | −5.62295 | − | 9.73923i | −0.259092 | − | 0.448760i | ||||
\(472\) | 1.88242 | − | 3.26044i | 0.0866453 | − | 0.150074i | ||||
\(473\) | 15.6776 | + | 27.1544i | 0.720856 | + | 1.24856i | ||||
\(474\) | 28.7297 | 1.31960 | ||||||||
\(475\) | 2.36692 | + | 4.09963i | 0.108602 | + | 0.188104i | ||||
\(476\) | 39.1132 | + | 26.0827i | 1.79275 | + | 1.19550i | ||||
\(477\) | −4.95271 | − | 8.57835i | −0.226769 | − | 0.392776i | ||||
\(478\) | 4.40738 | + | 7.63381i | 0.201589 | + | 0.349162i | ||||
\(479\) | 20.4700 | 0.935300 | 0.467650 | − | 0.883914i | \(-0.345101\pi\) | ||||
0.467650 | + | 0.883914i | \(0.345101\pi\) | |||||||
\(480\) | 0.439529 | + | 0.761287i | 0.0200617 | + | 0.0347478i | ||||
\(481\) | 1.37329 | − | 11.0284i | 0.0626165 | − | 0.502853i | ||||
\(482\) | −61.1696 | −2.78620 | ||||||||
\(483\) | 1.48213 | + | 0.988365i | 0.0674394 | + | 0.0449722i | ||||
\(484\) | −2.35094 | + | 4.07195i | −0.106861 | + | 0.185088i | ||||
\(485\) | 8.82985 | 0.400943 | ||||||||
\(486\) | −1.21707 | − | 2.10803i | −0.0552075 | − | 0.0956222i | ||||
\(487\) | −16.7968 | + | 29.0930i | −0.761138 | + | 1.31833i | 0.181127 | + | 0.983460i | \(0.442026\pi\) |
−0.942264 | + | 0.334870i | \(0.891308\pi\) | |||||||
\(488\) | −21.7881 | −0.986303 | ||||||||
\(489\) | −11.6079 | −0.524930 | ||||||||
\(490\) | −12.7049 | + | 16.6204i | −0.573951 | + | 0.750835i | ||||
\(491\) | 20.2312 | − | 35.0415i | 0.913021 | − | 1.58140i | 0.103248 | − | 0.994656i | \(-0.467077\pi\) |
0.809773 | − | 0.586743i | \(-0.199590\pi\) | |||||||
\(492\) | −14.1735 | − | 24.5492i | −0.638990 | − | 1.10676i | ||||
\(493\) | 11.9887 | + | 20.7651i | 0.539944 | + | 0.935211i | ||||
\(494\) | 1.46993 | − | 11.8045i | 0.0661352 | − | 0.531110i | ||||
\(495\) | −2.14405 | + | 3.71360i | −0.0963677 | + | 0.166914i | ||||
\(496\) | 17.7745 | − | 30.7863i | 0.798097 | − | 1.38234i | ||||
\(497\) | 11.1290 | + | 7.42140i | 0.499204 | + | 0.332896i | ||||
\(498\) | −15.4331 | − | 26.7310i | −0.691575 | − | 1.19784i | ||||
\(499\) | −2.38204 | + | 4.12581i | −0.106635 | + | 0.184697i | −0.914405 | − | 0.404801i | \(-0.867341\pi\) |
0.807770 | + | 0.589498i | \(0.200674\pi\) | |||||||
\(500\) | 20.4633 | − | 35.4435i | 0.915147 | − | 1.58508i | ||||
\(501\) | −3.44594 | + | 5.96855i | −0.153953 | + | 0.266655i | ||||
\(502\) | −0.682215 | + | 1.18163i | −0.0304487 | + | 0.0527388i | ||||
\(503\) | −0.350346 | − | 0.606817i | −0.0156212 | − | 0.0270567i | 0.858109 | − | 0.513467i | \(-0.171639\pi\) |
−0.873730 | + | 0.486411i | \(0.838306\pi\) | |||||||
\(504\) | 11.1141 | − | 5.49354i | 0.495061 | − | 0.244702i | ||||
\(505\) | 0.948935 | − | 1.64360i | 0.0422271 | − | 0.0731394i | ||||
\(506\) | −2.86210 | + | 4.95731i | −0.127236 | + | 0.220379i | ||||
\(507\) | −3.54048 | − | 12.5086i | −0.157238 | − | 0.555526i | ||||
\(508\) | 32.3648 | + | 56.0575i | 1.43596 | + | 2.48715i | ||||
\(509\) | −13.4457 | − | 23.2886i | −0.595970 | − | 1.03225i | −0.993409 | − | 0.114622i | \(-0.963434\pi\) |
0.397439 | − | 0.917628i | \(-0.369899\pi\) | |||||||
\(510\) | −6.76477 | + | 11.7169i | −0.299549 | + | 0.518834i | ||||
\(511\) | 26.6006 | + | 17.7387i | 1.17674 | + | 0.784713i | ||||
\(512\) | 35.8718 | 1.58533 | ||||||||
\(513\) | −1.35541 | −0.0598429 | ||||||||
\(514\) | −28.9161 | + | 50.0841i | −1.27543 | + | 2.20911i | ||||
\(515\) | −3.38739 | − | 5.86714i | −0.149266 | − | 0.258537i | ||||
\(516\) | 35.2381 | 1.55127 | ||||||||
\(517\) | 9.01107 | − | 15.6076i | 0.396306 | − | 0.686423i | ||||
\(518\) | 1.28014 | − | 19.8095i | 0.0562461 | − | 0.870380i | ||||
\(519\) | 15.8386 | 0.695237 | ||||||||
\(520\) | −19.1084 | + | 8.07247i | −0.837960 | + | 0.354001i | ||||
\(521\) | −15.4700 | − | 26.7948i | −0.677753 | − | 1.17390i | −0.975656 | − | 0.219306i | \(-0.929621\pi\) |
0.297903 | − | 0.954596i | \(-0.403713\pi\) | |||||||
\(522\) | 12.8924 | 0.564285 | ||||||||
\(523\) | 0.851131 | + | 1.47420i | 0.0372173 | + | 0.0644623i | 0.884034 | − | 0.467422i | \(-0.154817\pi\) |
−0.846817 | + | 0.531885i | \(0.821484\pi\) | |||||||
\(524\) | 13.8230 | + | 23.9421i | 0.603859 | + | 1.04591i | ||||
\(525\) | 7.68783 | + | 5.12665i | 0.335525 | + | 0.223746i | ||||
\(526\) | −8.61105 | − | 14.9148i | −0.375460 | − | 0.650315i | ||||
\(527\) | −45.2566 | −1.97141 | ||||||||
\(528\) | 6.20973 | + | 10.7556i | 0.270244 | + | 0.468076i | ||||
\(529\) | 11.2733 | − | 19.5260i | 0.490144 | − | 0.848955i | ||||
\(530\) | 14.8017 | + | 25.6373i | 0.642944 | + | 1.11361i | ||||
\(531\) | −0.401721 | + | 0.695802i | −0.0174332 | + | 0.0301952i | ||||
\(532\) | 0.907707 | − | 14.0463i | 0.0393541 | − | 0.608984i | ||||
\(533\) | −23.9868 | + | 10.1334i | −1.03898 | + | 0.438925i | ||||
\(534\) | 3.77859 | − | 6.54471i | 0.163516 | − | 0.283217i | ||||
\(535\) | 1.77829 | 0.0768821 | ||||||||
\(536\) | 9.94043 | 0.429361 | ||||||||
\(537\) | −21.1031 | −0.910664 | ||||||||
\(538\) | 25.2870 | 1.09020 | ||||||||
\(539\) | 14.8473 | − | 19.4231i | 0.639519 | − | 0.836610i | ||||
\(540\) | 2.40956 | + | 4.17348i | 0.103691 | + | 0.179598i | ||||
\(541\) | 1.00845 | − | 1.74668i | 0.0433566 | − | 0.0750958i | −0.843533 | − | 0.537078i | \(-0.819528\pi\) |
0.886889 | + | 0.461982i | \(0.152862\pi\) | |||||||
\(542\) | −0.149423 | + | 0.258808i | −0.00641826 | + | 0.0111168i | ||||
\(543\) | −15.0685 | −0.646649 | ||||||||
\(544\) | −1.62062 | − | 2.80700i | −0.0694836 | − | 0.120349i | ||||
\(545\) | 20.1475 | 0.863026 | ||||||||
\(546\) | −7.63808 | − | 21.9281i | −0.326880 | − | 0.938435i | ||||
\(547\) | −2.08074 | −0.0889658 | −0.0444829 | − | 0.999010i | \(-0.514164\pi\) | ||||
−0.0444829 | + | 0.999010i | \(0.514164\pi\) | |||||||
\(548\) | 37.9186 | + | 65.6770i | 1.61980 | + | 2.80558i | ||||
\(549\) | 4.64974 | 0.198446 | ||||||||
\(550\) | −14.8457 | + | 25.7136i | −0.633025 | + | 1.09643i | ||||
\(551\) | 3.58945 | − | 6.21712i | 0.152916 | − | 0.264858i | ||||
\(552\) | 1.57757 | + | 2.73242i | 0.0671456 | + | 0.116300i | ||||
\(553\) | 2.01379 | − | 31.1623i | 0.0856349 | − | 1.32516i | ||||
\(554\) | 13.0762 | 0.555554 | ||||||||
\(555\) | 3.78446 | 0.160642 | ||||||||
\(556\) | −60.9307 | −2.58404 | ||||||||
\(557\) | 19.6341 | 0.831922 | 0.415961 | − | 0.909383i | \(-0.363445\pi\) | ||||
0.415961 | + | 0.909383i | \(0.363445\pi\) | |||||||
\(558\) | −12.1670 | + | 21.0738i | −0.515069 | + | 0.892126i | ||||
\(559\) | 3.99986 | − | 32.1216i | 0.169176 | − | 1.35860i | ||||
\(560\) | −10.3553 | + | 5.11850i | −0.437593 | + | 0.216296i | ||||
\(561\) | 7.90548 | − | 13.6927i | 0.333770 | − | 0.578106i | ||||
\(562\) | −18.1157 | − | 31.3773i | −0.764166 | − | 1.32357i | ||||
\(563\) | 11.6699 | − | 20.2128i | 0.491826 | − | 0.851868i | −0.508130 | − | 0.861281i | \(-0.669663\pi\) |
0.999956 | + | 0.00941281i | \(0.00299623\pi\) | |||||||
\(564\) | −10.1270 | − | 17.5404i | −0.426423 | − | 0.738586i | ||||
\(565\) | −13.2121 | −0.555839 | ||||||||
\(566\) | 5.45902 | + | 9.45531i | 0.229460 | + | 0.397436i | ||||
\(567\) | −2.37183 | + | 1.17236i | −0.0996074 | + | 0.0492346i | ||||
\(568\) | 11.8456 | + | 20.5171i | 0.497029 | + | 0.860880i | ||||
\(569\) | 10.8206 | + | 18.7419i | 0.453625 | + | 0.785702i | 0.998608 | − | 0.0527455i | \(-0.0167972\pi\) |
−0.544983 | + | 0.838447i | \(0.683464\pi\) | |||||||
\(570\) | 4.05078 | 0.169669 | ||||||||
\(571\) | −3.91282 | − | 6.77720i | −0.163746 | − | 0.283617i | 0.772463 | − | 0.635060i | \(-0.219025\pi\) |
−0.936209 | + | 0.351443i | \(0.885691\pi\) | |||||||
\(572\) | 45.5304 | − | 19.2346i | 1.90372 | − | 0.804239i | ||||
\(573\) | 9.49806 | 0.396787 | ||||||||
\(574\) | −41.6955 | + | 20.6095i | −1.74034 | + | 0.860225i | ||||
\(575\) | −1.17581 | + | 2.03657i | −0.0490349 | + | 0.0849309i | ||||
\(576\) | −8.85475 | −0.368948 | ||||||||
\(577\) | 5.92244 | + | 10.2580i | 0.246555 | + | 0.427045i | 0.962568 | − | 0.271042i | \(-0.0873682\pi\) |
−0.716013 | + | 0.698087i | \(0.754035\pi\) | |||||||
\(578\) | 4.25269 | − | 7.36587i | 0.176889 | − | 0.306380i | ||||
\(579\) | 18.5435 | 0.770642 | ||||||||
\(580\) | −25.5244 | −1.05984 | ||||||||
\(581\) | −30.0760 | + | 14.8662i | −1.24776 | + | 0.616752i | ||||
\(582\) | −8.75283 | + | 15.1603i | −0.362816 | + | 0.628416i | ||||
\(583\) | −17.2976 | − | 29.9603i | −0.716394 | − | 1.24083i | ||||
\(584\) | 28.3134 | + | 49.0402i | 1.17161 | + | 2.02930i | ||||
\(585\) | 4.07787 | − | 1.72272i | 0.168599 | − | 0.0712258i | ||||
\(586\) | 26.7794 | − | 46.3833i | 1.10625 | − | 1.91608i | ||||
\(587\) | −2.24869 | + | 3.89484i | −0.0928134 | + | 0.160757i | −0.908694 | − | 0.417463i | \(-0.862919\pi\) |
0.815881 | + | 0.578220i | \(0.196253\pi\) | |||||||
\(588\) | −10.5609 | − | 25.3647i | −0.435526 | − | 1.04602i | ||||
\(589\) | 6.77497 | + | 11.7346i | 0.279158 | + | 0.483516i | ||||
\(590\) | 1.20058 | − | 2.07947i | 0.0494273 | − | 0.0856106i | ||||
\(591\) | 12.8786 | − | 22.3065i | 0.529756 | − | 0.917565i | ||||
\(592\) | 5.48041 | − | 9.49235i | 0.225244 | − | 0.390133i | ||||
\(593\) | 17.8835 | − | 30.9751i | 0.734388 | − | 1.27200i | −0.220604 | − | 0.975363i | \(-0.570803\pi\) |
0.954992 | − | 0.296633i | \(-0.0958638\pi\) | |||||||
\(594\) | −4.25069 | − | 7.36241i | −0.174408 | − | 0.302083i | ||||
\(595\) | 12.2348 | + | 8.15883i | 0.501579 | + | 0.334480i | ||||
\(596\) | −34.4094 | + | 59.5988i | −1.40946 | + | 2.44126i | ||||
\(597\) | 8.84779 | − | 15.3248i | 0.362116 | − | 0.627203i | ||||
\(598\) | 5.44359 | − | 2.29968i | 0.222605 | − | 0.0940408i | ||||
\(599\) | −9.70429 | − | 16.8083i | −0.396507 | − | 0.686769i | 0.596786 | − | 0.802401i | \(-0.296444\pi\) |
−0.993292 | + | 0.115631i | \(0.963111\pi\) | |||||||
\(600\) | 8.18284 | + | 14.1731i | 0.334063 | + | 0.578614i | ||||
\(601\) | −20.4135 | + | 35.3571i | −0.832682 | + | 1.44225i | 0.0632213 | + | 0.998000i | \(0.479863\pi\) |
−0.895904 | + | 0.444248i | \(0.853471\pi\) | |||||||
\(602\) | 3.72856 | − | 57.6975i | 0.151965 | − | 2.35157i | ||||
\(603\) | −2.12136 | −0.0863884 | ||||||||
\(604\) | 55.1039 | 2.24215 | ||||||||
\(605\) | −0.735387 | + | 1.27373i | −0.0298977 | + | 0.0517844i | ||||
\(606\) | 1.88132 | + | 3.25854i | 0.0764232 | + | 0.132369i | ||||
\(607\) | 0.942690 | 0.0382626 | 0.0191313 | − | 0.999817i | \(-0.493910\pi\) | ||||
0.0191313 | + | 0.999817i | \(0.493910\pi\) | |||||||
\(608\) | −0.485219 | + | 0.840424i | −0.0196782 | + | 0.0340837i | ||||
\(609\) | 0.903681 | − | 13.9840i | 0.0366190 | − | 0.566660i | ||||
\(610\) | −13.8962 | −0.562642 | ||||||||
\(611\) | −17.1386 | + | 7.24032i | −0.693355 | + | 0.292912i | ||||
\(612\) | −8.88448 | − | 15.3884i | −0.359134 | − | 0.622038i | ||||
\(613\) | 0.921093 | 0.0372026 | 0.0186013 | − | 0.999827i | \(-0.494079\pi\) | ||||
0.0186013 | + | 0.999827i | \(0.494079\pi\) | |||||||
\(614\) | 40.1585 | + | 69.5565i | 1.62066 | + | 2.80707i | ||||
\(615\) | −4.43355 | − | 7.67913i | −0.178778 | − | 0.309652i | ||||
\(616\) | 38.8166 | − | 19.1865i | 1.56396 | − | 0.773045i | ||||
\(617\) | 12.3732 | + | 21.4311i | 0.498127 | + | 0.862782i | 0.999998 | − | 0.00216105i | \(-0.000687883\pi\) |
−0.501870 | + | 0.864943i | \(0.667355\pi\) | |||||||
\(618\) | 13.4314 | 0.540290 | ||||||||
\(619\) | −12.0229 | − | 20.8243i | −0.483242 | − | 0.836999i | 0.516573 | − | 0.856243i | \(-0.327207\pi\) |
−0.999815 | + | 0.0192441i | \(0.993874\pi\) | |||||||
\(620\) | 24.0882 | − | 41.7220i | 0.967405 | − | 1.67559i | ||||
\(621\) | −0.336664 | − | 0.583119i | −0.0135098 | − | 0.0233997i | ||||
\(622\) | −10.0173 | + | 17.3504i | −0.401656 | + | 0.695689i | ||||
\(623\) | −6.83400 | − | 4.55727i | −0.273798 | − | 0.182583i | ||||
\(624\) | 1.58430 | − | 12.7230i | 0.0634229 | − | 0.509329i | ||||
\(625\) | −2.33033 | + | 4.03626i | −0.0932133 | + | 0.161450i | ||||
\(626\) | 34.7765 | 1.38995 | ||||||||
\(627\) | −4.73385 | −0.189052 | ||||||||
\(628\) | −44.1408 | −1.76141 | ||||||||
\(629\) | −13.9540 | −0.556382 | ||||||||
\(630\) | 7.08845 | − | 3.50372i | 0.282410 | − | 0.139592i | ||||
\(631\) | −14.7428 | − | 25.5353i | −0.586902 | − | 1.01654i | −0.994635 | − | 0.103443i | \(-0.967014\pi\) |
0.407734 | − | 0.913101i | \(-0.366319\pi\) | |||||||
\(632\) | 27.6533 | − | 47.8969i | 1.09999 | − | 1.90523i | ||||
\(633\) | 6.23896 | − | 10.8062i | 0.247976 | − | 0.429508i | ||||
\(634\) | 22.7931 | 0.905229 | ||||||||
\(635\) | 10.1239 | + | 17.5351i | 0.401755 | + | 0.695860i | ||||
\(636\) | −38.8794 | −1.54167 | ||||||||
\(637\) | −24.3201 | + | 6.74777i | −0.963598 | + | 0.267356i | ||||
\(638\) | 45.0273 | 1.78265 | ||||||||
\(639\) | −2.52793 | − | 4.37850i | −0.100003 | − | 0.173211i | ||||
\(640\) | 24.7052 | 0.976559 | ||||||||
\(641\) | −1.09270 | + | 1.89260i | −0.0431589 | + | 0.0747534i | −0.886798 | − | 0.462157i | \(-0.847075\pi\) |
0.843639 | + | 0.536911i | \(0.180409\pi\) | |||||||
\(642\) | −1.76278 | + | 3.05322i | −0.0695712 | + | 0.120501i | ||||
\(643\) | 5.19137 | + | 8.99172i | 0.204728 | + | 0.354599i | 0.950046 | − | 0.312110i | \(-0.101036\pi\) |
−0.745318 | + | 0.666709i | \(0.767702\pi\) | |||||||
\(644\) | 6.26839 | − | 3.09838i | 0.247009 | − | 0.122093i | ||||
\(645\) | 11.0227 | 0.434018 | ||||||||
\(646\) | −14.9360 | −0.587648 | ||||||||
\(647\) | −12.1316 | −0.476943 | −0.238471 | − | 0.971150i | \(-0.576646\pi\) | ||||
−0.238471 | + | 0.971150i | \(0.576646\pi\) | |||||||
\(648\) | −4.68588 | −0.184079 | ||||||||
\(649\) | −1.40303 | + | 2.43012i | −0.0550738 | + | 0.0953907i | ||||
\(650\) | 28.2359 | − | 11.9284i | 1.10750 | − | 0.467872i | ||||
\(651\) | 22.0053 | + | 14.6743i | 0.862456 | + | 0.575131i | ||||
\(652\) | −22.7810 | + | 39.4578i | −0.892171 | + | 1.54529i | ||||
\(653\) | 12.0127 | + | 20.8065i | 0.470091 | + | 0.814222i | 0.999415 | − | 0.0341978i | \(-0.0108876\pi\) |
−0.529324 | + | 0.848420i | \(0.677554\pi\) | |||||||
\(654\) | −19.9718 | + | 34.5922i | −0.780959 | + | 1.35266i | ||||
\(655\) | 4.32390 | + | 7.48922i | 0.168949 | + | 0.292628i | ||||
\(656\) | −25.6815 | −1.00269 | ||||||||
\(657\) | −6.04227 | − | 10.4655i | −0.235731 | − | 0.408299i | ||||
\(658\) | −29.7916 | + | 14.7255i | −1.16140 | + | 0.574062i | ||||
\(659\) | 10.4678 | + | 18.1307i | 0.407766 | + | 0.706272i | 0.994639 | − | 0.103407i | \(-0.0329744\pi\) |
−0.586873 | + | 0.809679i | \(0.699641\pi\) | |||||||
\(660\) | 8.41551 | + | 14.5761i | 0.327573 | + | 0.567374i | ||||
\(661\) | −21.4780 | −0.835398 | −0.417699 | − | 0.908586i | \(-0.637163\pi\) | ||||
−0.417699 | + | 0.908586i | \(0.637163\pi\) | |||||||
\(662\) | −29.7914 | − | 51.6002i | −1.15787 | − | 2.00550i | ||||
\(663\) | −15.0359 | + | 6.35199i | −0.583944 | + | 0.246691i | ||||
\(664\) | −59.4194 | −2.30592 | ||||||||
\(665\) | 0.283936 | − | 4.39376i | 0.0110106 | − | 0.170383i | ||||
\(666\) | −3.75145 | + | 6.49771i | −0.145366 | + | 0.251781i | ||||
\(667\) | 3.56626 | 0.138086 | ||||||||
\(668\) | 13.5255 | + | 23.4269i | 0.523319 | + | 0.906415i | ||||
\(669\) | 4.65232 | − | 8.05805i | 0.179869 | − | 0.311542i | ||||
\(670\) | 6.33989 | 0.244931 | ||||||||
\(671\) | 16.2395 | 0.626918 | ||||||||
\(672\) | −0.122159 | + | 1.89034i | −0.00471237 | + | 0.0729215i | ||||
\(673\) | −0.483978 | + | 0.838274i | −0.0186560 | + | 0.0323131i | −0.875203 | − | 0.483756i | \(-0.839272\pi\) |
0.856547 | + | 0.516070i | \(0.172605\pi\) | |||||||
\(674\) | −16.0270 | − | 27.7596i | −0.617338 | − | 1.06926i | ||||
\(675\) | −1.74628 | − | 3.02464i | −0.0672142 | − | 0.116418i | ||||
\(676\) | −49.4676 | − | 12.5137i | −1.90260 | − | 0.481296i | ||||
\(677\) | −23.4146 | + | 40.5552i | −0.899895 | + | 1.55866i | −0.0722691 | + | 0.997385i | \(0.523024\pi\) |
−0.827626 | + | 0.561279i | \(0.810309\pi\) | |||||||
\(678\) | 13.0969 | − | 22.6845i | 0.502983 | − | 0.871193i | ||||
\(679\) | 15.8304 | + | 10.5566i | 0.607517 | + | 0.405124i | ||||
\(680\) | 13.0226 | + | 22.5558i | 0.499394 | + | 0.864976i | ||||
\(681\) | 4.76651 | − | 8.25583i | 0.182653 | − | 0.316364i | ||||
\(682\) | −42.4938 | + | 73.6014i | −1.62717 | + | 2.81834i | ||||
\(683\) | −8.94014 | + | 15.4848i | −0.342085 | + | 0.592509i | −0.984820 | − | 0.173580i | \(-0.944466\pi\) |
0.642735 | + | 0.766089i | \(0.277800\pi\) | |||||||
\(684\) | −2.66004 | + | 4.60732i | −0.101709 | + | 0.176165i | ||||
\(685\) | 11.8612 | + | 20.5442i | 0.453192 | + | 0.784952i | ||||
\(686\) | −42.6485 | + | 14.6082i | −1.62833 | + | 0.557744i | ||||
\(687\) | −3.22423 | + | 5.58453i | −0.123012 | + | 0.213063i | ||||
\(688\) | 15.9623 | − | 27.6476i | 0.608558 | − | 1.05405i | ||||
\(689\) | −4.41318 | + | 35.4408i | −0.168129 | + | 1.35019i | ||||
\(690\) | 1.00615 | + | 1.74271i | 0.0383036 | + | 0.0663438i | ||||
\(691\) | 16.6082 | + | 28.7663i | 0.631806 | + | 1.09432i | 0.987182 | + | 0.159597i | \(0.0510193\pi\) |
−0.355377 | + | 0.934723i | \(0.615647\pi\) | |||||||
\(692\) | 31.0837 | − | 53.8386i | 1.18163 | − | 2.04664i | ||||
\(693\) | −8.28373 | + | 4.09453i | −0.314673 | + | 0.155538i | ||||
\(694\) | −35.7170 | −1.35580 | ||||||||
\(695\) | −19.0595 | −0.722968 | ||||||||
\(696\) | 12.4093 | − | 21.4936i | 0.470374 | − | 0.814712i | ||||
\(697\) | 16.3473 | + | 28.3143i | 0.619197 | + | 1.07248i | ||||
\(698\) | 59.2460 | 2.24249 | ||||||||
\(699\) | −12.2379 | + | 21.1967i | −0.462881 | + | 0.801733i | ||||
\(700\) | 32.5142 | − | 16.0713i | 1.22892 | − | 0.607438i | ||||
\(701\) | 29.1267 | 1.10010 | 0.550050 | − | 0.835132i | \(-0.314609\pi\) | ||||
0.550050 | + | 0.835132i | \(0.314609\pi\) | |||||||
\(702\) | −1.08449 | + | 8.70917i | −0.0409314 | + | 0.328707i | ||||
\(703\) | 2.08893 | + | 3.61814i | 0.0787856 | + | 0.136461i | ||||
\(704\) | −30.9257 | −1.16556 | ||||||||
\(705\) | −3.16778 | − | 5.48675i | −0.119305 | − | 0.206643i | ||||
\(706\) | −0.814982 | − | 1.41159i | −0.0306723 | − | 0.0531259i | ||||
\(707\) | 3.66630 | − | 1.81220i | 0.137886 | − | 0.0681549i | ||||
\(708\) | 1.57678 | + | 2.73107i | 0.0592591 | + | 0.102640i | ||||
\(709\) | 11.4015 | 0.428191 | 0.214096 | − | 0.976813i | \(-0.431320\pi\) | ||||
0.214096 | + | 0.976813i | \(0.431320\pi\) | |||||||
\(710\) | 7.55497 | + | 13.0856i | 0.283533 | + | 0.491093i | ||||
\(711\) | −5.90140 | + | 10.2215i | −0.221320 | + | 0.383337i | ||||
\(712\) | −7.27402 | − | 12.5990i | −0.272605 | − | 0.472166i | ||||
\(713\) | −3.36560 | + | 5.82939i | −0.126043 | + | 0.218312i | ||||
\(714\) | −26.1364 | + | 12.9188i | −0.978129 | + | 0.483475i | ||||
\(715\) | 14.2422 | − | 6.01670i | 0.532628 | − | 0.225012i | ||||
\(716\) | −41.4154 | + | 71.7336i | −1.54777 | + | 2.68081i | ||||
\(717\) | −3.62130 | −0.135240 | ||||||||
\(718\) | 86.7264 | 3.23660 | ||||||||
\(719\) | −36.2517 | −1.35196 | −0.675980 | − | 0.736920i | \(-0.736280\pi\) | ||||
−0.675980 | + | 0.736920i | \(0.736280\pi\) | |||||||
\(720\) | 4.36598 | 0.162710 | ||||||||
\(721\) | 0.941461 | − | 14.5686i | 0.0350618 | − | 0.542564i | ||||
\(722\) | −20.8884 | − | 36.1798i | −0.777387 | − | 1.34647i | ||||
\(723\) | 12.5649 | − | 21.7631i | 0.467294 | − | 0.809377i | ||||
\(724\) | −29.5723 | + | 51.2207i | −1.09905 | + | 1.90360i | ||||
\(725\) | 18.4982 | 0.687006 | ||||||||
\(726\) | −1.45795 | − | 2.52524i | −0.0541094 | − | 0.0937203i | ||||
\(727\) | 4.46075 | 0.165440 | 0.0827200 | − | 0.996573i | \(-0.473639\pi\) | ||||
0.0827200 | + | 0.996573i | \(0.473639\pi\) | |||||||
\(728\) | −43.9093 | − | 8.37261i | −1.62739 | − | 0.310309i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 18.0579 | + | 31.2773i | 0.668354 | + | 1.15762i | ||||
\(731\) | −40.6426 | −1.50322 | ||||||||
\(732\) | 9.12527 | − | 15.8054i | 0.337280 | − | 0.584185i | ||||
\(733\) | 5.24983 | − | 9.09297i | 0.193907 | − | 0.335856i | −0.752635 | − | 0.658438i | \(-0.771217\pi\) |
0.946542 | + | 0.322582i | \(0.104551\pi\) | |||||||
\(734\) | 12.4413 | + | 21.5490i | 0.459218 | + | 0.795390i | ||||
\(735\) | −3.30352 | − | 7.93421i | −0.121852 | − | 0.292658i | ||||
\(736\) | −0.482084 | −0.0177698 | ||||||||
\(737\) | −7.40895 | −0.272912 | ||||||||
\(738\) | 17.5795 | 0.647110 | ||||||||
\(739\) | −4.64923 | −0.171025 | −0.0855123 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855123 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(740\) | 7.42713 | − | 12.8642i | 0.273027 | − | 0.472896i | ||||
\(741\) | 3.89790 | + | 2.94775i | 0.143193 | + | 0.108288i | ||||
\(742\) | −4.11384 | + | 63.6596i | −0.151024 | + | 2.33702i | ||||
\(743\) | 9.95236 | − | 17.2380i | 0.365117 | − | 0.632400i | −0.623678 | − | 0.781681i | \(-0.714362\pi\) |
0.988795 | + | 0.149281i | \(0.0476958\pi\) | |||||||
\(744\) | 23.4222 | + | 40.5684i | 0.858699 | + | 1.48731i | ||||
\(745\) | −10.7635 | + | 18.6429i | −0.394343 | + | 0.683022i | ||||
\(746\) | 6.02582 | + | 10.4370i | 0.220621 | + | 0.382127i | ||||
\(747\) | 12.6805 | 0.463956 | ||||||||
\(748\) | −31.0295 | − | 53.7447i | −1.13455 | − | 1.96510i | ||||
\(749\) | 3.18817 | + | 2.12604i | 0.116493 | + | 0.0776839i | ||||
\(750\) | 12.6904 | + | 21.9804i | 0.463389 | + | 0.802613i | ||||
\(751\) | 20.9950 | + | 36.3645i | 0.766120 | + | 1.32696i | 0.939652 | + | 0.342131i | \(0.111149\pi\) |
−0.173532 | + | 0.984828i | \(0.555518\pi\) | |||||||
\(752\) | −18.3495 | −0.669136 | ||||||||
\(753\) | −0.280269 | − | 0.485440i | −0.0102136 | − | 0.0176904i | ||||
\(754\) | −37.0760 | − | 28.0384i | −1.35023 | − | 1.02110i | ||||
\(755\) | 17.2368 | 0.627313 | ||||||||
\(756\) | −0.669691 | + | 10.3631i | −0.0243564 | + | 0.376903i | ||||
\(757\) | 21.8795 | − | 37.8965i | 0.795225 | − | 1.37737i | −0.127471 | − | 0.991842i | \(-0.540686\pi\) |
0.922696 | − | 0.385528i | \(-0.125981\pi\) | |||||||
\(758\) | 30.8475 | 1.12043 | ||||||||
\(759\) | −1.17581 | − | 2.03657i | −0.0426794 | − | 0.0739229i | ||||
\(760\) | 3.89900 | − | 6.75327i | 0.141432 | − | 0.244967i | ||||
\(761\) | 12.0389 | 0.436411 | 0.218206 | − | 0.975903i | \(-0.429980\pi\) | ||||
0.218206 | + | 0.975903i | \(0.429980\pi\) | |||||||
\(762\) | −40.1424 | −1.45420 | ||||||||
\(763\) | 36.1212 | + | 24.0875i | 1.30767 | + | 0.872027i | ||||
\(764\) | 18.6402 | − | 32.2858i | 0.674380 | − | 1.16806i | ||||
\(765\) | −2.77912 | − | 4.81357i | −0.100479 | − | 0.174035i | ||||
\(766\) | −28.9544 | − | 50.1504i | −1.04616 | − | 1.81201i | ||||
\(767\) | 2.66850 | − | 1.12732i | 0.0963540 | − | 0.0407053i | ||||
\(768\) | −15.6349 | + | 27.0805i | −0.564178 | + | 0.977184i | ||||
\(769\) | 13.1918 | − | 22.8489i | 0.475708 | − | 0.823951i | −0.523905 | − | 0.851777i | \(-0.675525\pi\) |
0.999613 | + | 0.0278261i | \(0.00885848\pi\) | |||||||
\(770\) | 24.7568 | − | 12.2369i | 0.892172 | − | 0.440988i | ||||
\(771\) | −11.8793 | − | 20.5756i | −0.427824 | − | 0.741013i | ||||
\(772\) | 36.3922 | − | 63.0331i | 1.30978 | − | 2.26861i | ||||
\(773\) | 4.94438 | − | 8.56392i | 0.177837 | − | 0.308023i | −0.763302 | − | 0.646041i | \(-0.776423\pi\) |
0.941139 | + | 0.338018i | \(0.109757\pi\) | |||||||
\(774\) | −10.9265 | + | 18.9253i | −0.392747 | + | 0.680257i | ||||
\(775\) | −17.4574 | + | 30.2371i | −0.627088 | + | 1.08615i | ||||
\(776\) | 16.8497 | + | 29.1846i | 0.604870 | + | 1.04767i | ||||
\(777\) | 6.78491 | + | 4.52454i | 0.243407 | + | 0.162317i | ||||
\(778\) | −31.0890 | + | 53.8478i | −1.11460 | + | 1.93054i | ||||
\(779\) | 4.89442 | − | 8.47738i | 0.175361 | − | 0.303734i | ||||
\(780\) | 2.14707 | − | 17.2424i | 0.0768775 | − | 0.617378i | ||||
\(781\) | −8.82892 | − | 15.2921i | −0.315924 | − | 0.547196i | ||||
\(782\) | −3.70987 | − | 6.42567i | −0.132665 | − | 0.229782i | ||||
\(783\) | −2.64824 | + | 4.58688i | −0.0946403 | + | 0.163922i | ||||
\(784\) | −24.6849 | − | 3.20378i | −0.881602 | − | 0.114421i | ||||
\(785\) | −13.8075 | −0.492811 | ||||||||
\(786\) | −17.1447 | −0.611533 | ||||||||
\(787\) | 19.2333 | − | 33.3130i | 0.685593 | − | 1.18748i | −0.287657 | − | 0.957733i | \(-0.592876\pi\) |
0.973250 | − | 0.229748i | \(-0.0737902\pi\) | |||||||
\(788\) | −50.5495 | − | 87.5542i | −1.80075 | − | 3.11899i | ||||
\(789\) | 7.07522 | 0.251884 | ||||||||
\(790\) | 17.6369 | − | 30.5481i | 0.627494 | − | 1.08685i | ||||
\(791\) | −23.6872 | − | 15.7959i | −0.842219 | − | 0.561636i | ||||
\(792\) | −16.3657 | −0.581529 | ||||||||
\(793\) | −13.3717 | − | 10.1123i | −0.474845 | − | 0.359097i | ||||
\(794\) | −2.58915 | − | 4.48454i | −0.0918856 | − | 0.159151i | ||||
\(795\) | −12.1617 | −0.431331 | ||||||||
\(796\) | −34.7281 | − | 60.1509i | −1.23091 | − | 2.13199i | ||||
\(797\) | 4.91617 | + | 8.51506i | 0.174140 | + | 0.301619i | 0.939863 | − | 0.341551i | \(-0.110952\pi\) |
−0.765723 | + | 0.643170i | \(0.777619\pi\) | |||||||
\(798\) | 7.26238 | + | 4.84294i | 0.257086 | + | 0.171438i | ||||
\(799\) | 11.6802 | + | 20.2306i | 0.413214 | + | 0.715709i | ||||
\(800\) | −2.50057 | −0.0884085 | ||||||||
\(801\) | 1.55233 | + | 2.68871i | 0.0548488 | + | 0.0950009i | ||||
\(802\) | 0.714773 | − | 1.23802i | 0.0252395 | − | 0.0437161i | ||||
\(803\) | −21.1029 | − | 36.5514i | −0.744707 | − | 1.28987i | ||||
\(804\) | −4.16323 | + | 7.21093i | −0.146826 | + | 0.254310i | ||||
\(805\) | 1.96079 | − | 0.969190i | 0.0691087 | − | 0.0341595i | ||||
\(806\) | 80.8212 | − | 34.1434i | 2.84681 | − | 1.20265i | ||||
\(807\) | −5.19422 | + | 8.99665i | −0.182845 | + | 0.316697i | ||||
\(808\) | 7.24330 | 0.254818 | ||||||||
\(809\) | −21.2555 | −0.747305 | −0.373653 | − | 0.927569i | \(-0.621895\pi\) | ||||
−0.373653 | + | 0.927569i | \(0.621895\pi\) | |||||||
\(810\) | −2.98860 | −0.105009 | ||||||||
\(811\) | 35.9695 | 1.26306 | 0.631531 | − | 0.775351i | \(-0.282427\pi\) | ||||
0.631531 | + | 0.775351i | \(0.282427\pi\) | |||||||
\(812\) | −45.7609 | − | 30.5158i | −1.60589 | − | 1.07090i | ||||
\(813\) | −0.0613862 | − | 0.106324i | −0.00215291 | − | 0.00372894i | ||||
\(814\) | −13.1021 | + | 22.6936i | −0.459230 | + | 0.795409i | ||||
\(815\) | −7.12602 | + | 12.3426i | −0.249613 | + | 0.432343i | ||||
\(816\) | −16.0981 | −0.563547 | ||||||||
\(817\) | 6.08426 | + | 10.5382i | 0.212861 | + | 0.368687i | ||||
\(818\) | 10.5753 | 0.369756 | ||||||||
\(819\) | 9.37056 | + | 1.78677i | 0.327434 | + | 0.0624349i | ||||
\(820\) | −34.8039 | −1.21540 | ||||||||
\(821\) | −18.4057 | − | 31.8795i | −0.642362 | − | 1.11260i | −0.984904 | − | 0.173101i | \(-0.944621\pi\) |
0.342542 | − | 0.939503i | \(-0.388712\pi\) | |||||||
\(822\) | −47.0308 | −1.64039 | ||||||||
\(823\) | 18.8162 | − | 32.5906i | 0.655892 | − | 1.13604i | −0.325777 | − | 0.945447i | \(-0.605626\pi\) |
0.981669 | − | 0.190592i | \(-0.0610407\pi\) | |||||||
\(824\) | 12.9281 | − | 22.3922i | 0.450373 | − | 0.780068i | ||||
\(825\) | −6.09896 | − | 10.5637i | −0.212338 | − | 0.367781i | ||||
\(826\) | 4.63858 | − | 2.29278i | 0.161397 | − | 0.0797761i | ||||
\(827\) | −28.9693 | −1.00736 | −0.503681 | − | 0.863890i | \(-0.668021\pi\) | ||||
−0.503681 | + | 0.863890i | \(0.668021\pi\) | |||||||
\(828\) | −2.64285 | −0.0918454 | ||||||||
\(829\) | 8.86111 | 0.307759 | 0.153880 | − | 0.988090i | \(-0.450823\pi\) | ||||
0.153880 | + | 0.988090i | \(0.450823\pi\) | |||||||
\(830\) | −37.8970 | −1.31543 | ||||||||
\(831\) | −2.68599 | + | 4.65228i | −0.0931761 | + | 0.161386i | ||||
\(832\) | 25.4645 | + | 19.2573i | 0.882824 | + | 0.667628i | ||||
\(833\) | 12.1807 | + | 29.2549i | 0.422035 | + | 1.01362i | ||||
\(834\) | 18.8932 | − | 32.7240i | 0.654219 | − | 1.13314i | ||||
\(835\) | 4.23087 | + | 7.32808i | 0.146415 | + | 0.253599i | ||||
\(836\) | −9.29032 | + | 16.0913i | −0.321312 | + | 0.556529i | ||||
\(837\) | −4.99846 | − | 8.65759i | −0.172772 | − | 0.299250i | ||||
\(838\) | −23.0182 | −0.795150 | ||||||||
\(839\) | 15.9655 | + | 27.6530i | 0.551190 | + | 0.954689i | 0.998189 | + | 0.0601547i | \(0.0191594\pi\) |
−0.446999 | + | 0.894534i | \(0.647507\pi\) | |||||||
\(840\) | 0.981613 | − | 15.1900i | 0.0338689 | − | 0.524103i | ||||
\(841\) | 0.473666 | + | 0.820413i | 0.0163333 | + | 0.0282901i | ||||
\(842\) | −14.5524 | − | 25.2054i | −0.501507 | − | 0.868636i | ||||
\(843\) | 14.8847 | 0.512655 | ||||||||
\(844\) | −24.4883 | − | 42.4150i | −0.842922 | − | 1.45998i | ||||
\(845\) | −15.4737 | − | 3.91436i | −0.532313 | − | 0.134658i | ||||
\(846\) | 12.5606 | 0.431842 | ||||||||
\(847\) | −2.84124 | + | 1.40439i | −0.0976262 | + | 0.0482553i | ||||
\(848\) | −17.6118 | + | 30.5045i | −0.604791 | + | 1.04753i | ||||
\(849\) | −4.48537 | −0.153938 | ||||||||
\(850\) | −19.2431 | − | 33.3300i | −0.660032 | − | 1.14321i | ||||
\(851\) | −1.03772 | + | 1.79738i | −0.0355725 | + | 0.0616134i | ||||
\(852\) | −19.8446 | −0.679863 | ||||||||
\(853\) | 5.62395 | 0.192560 | 0.0962801 | − | 0.995354i | \(-0.469306\pi\) | ||||
0.0962801 | + | 0.995354i | \(0.469306\pi\) | |||||||
\(854\) | −24.9136 | − | 16.6137i | −0.852526 | − | 0.568510i | ||||
\(855\) | −0.832075 | + | 1.44120i | −0.0284564 | + | 0.0492879i | ||||
\(856\) | 3.39345 | + | 5.87763i | 0.115986 | + | 0.200893i | ||||
\(857\) | 23.8452 | + | 41.3011i | 0.814537 | + | 1.41082i | 0.909660 | + | 0.415354i | \(0.136342\pi\) |
−0.0951229 | + | 0.995466i | \(0.530324\pi\) | |||||||
\(858\) | −3.78763 | + | 30.4172i | −0.129308 | + | 1.03843i | ||||
\(859\) | −24.8420 | + | 43.0276i | −0.847598 | + | 1.46808i | 0.0357469 | + | 0.999361i | \(0.488619\pi\) |
−0.883345 | + | 0.468723i | \(0.844714\pi\) | |||||||
\(860\) | 21.6324 | − | 37.4684i | 0.737658 | − | 1.27766i | ||||
\(861\) | 1.23222 | − | 19.0680i | 0.0419939 | − | 0.649834i | ||||
\(862\) | −32.2165 | − | 55.8006i | −1.09730 | − | 1.90058i | ||||
\(863\) | 11.4553 | − | 19.8412i | 0.389944 | − | 0.675402i | −0.602498 | − | 0.798121i | \(-0.705828\pi\) |
0.992442 | + | 0.122718i | \(0.0391611\pi\) | |||||||
\(864\) | 0.357986 | − | 0.620050i | 0.0121789 | − | 0.0210945i | ||||
\(865\) | 9.72317 | − | 16.8410i | 0.330598 | − | 0.572612i | ||||
\(866\) | −10.0552 | + | 17.4160i | −0.341688 | + | 0.591821i | ||||
\(867\) | 1.74710 | + | 3.02606i | 0.0593346 | + | 0.102770i | ||||
\(868\) | 93.0671 | − | 46.0018i | 3.15890 | − | 1.56140i | ||||
\(869\) | −20.6109 | + | 35.6992i | −0.699179 | + | 1.21101i | ||||
\(870\) | 7.91453 | − | 13.7084i | 0.268328 | − | 0.464757i | ||||
\(871\) | 6.10061 | + | 4.61353i | 0.206711 | + | 0.156324i | ||||
\(872\) | 38.4470 | + | 66.5921i | 1.30198 | + | 2.25509i | ||||
\(873\) | −3.59585 | − | 6.22820i | −0.121701 | − | 0.210793i | ||||
\(874\) | −1.11074 | + | 1.92387i | −0.0375715 | + | 0.0650757i | ||||
\(875\) | 24.7311 | − | 12.2242i | 0.836062 | − | 0.413254i | ||||
\(876\) | −47.4326 | −1.60260 | ||||||||
\(877\) | −32.3047 | −1.09085 | −0.545427 | − | 0.838158i | \(-0.683632\pi\) | ||||
−0.545427 | + | 0.838158i | \(0.683632\pi\) | |||||||
\(878\) | 42.7245 | − | 74.0010i | 1.44188 | − | 2.49741i | ||||
\(879\) | 11.0016 | + | 19.0553i | 0.371074 | + | 0.642719i | ||||
\(880\) | 15.2484 | 0.514023 | ||||||||
\(881\) | 18.8690 | − | 32.6821i | 0.635714 | − | 1.10109i | −0.350650 | − | 0.936507i | \(-0.614039\pi\) |
0.986363 | − | 0.164582i | \(-0.0526274\pi\) | |||||||
\(882\) | 16.8973 | + | 2.19305i | 0.568962 | + | 0.0738438i | ||||
\(883\) | −34.3867 | −1.15720 | −0.578602 | − | 0.815610i | \(-0.696401\pi\) | ||||
−0.578602 | + | 0.815610i | \(0.696401\pi\) | |||||||
\(884\) | −7.91663 | + | 63.5759i | −0.266265 | + | 2.13829i | ||||
\(885\) | 0.493226 | + | 0.854293i | 0.0165796 | + | 0.0287168i | ||||
\(886\) | 0.936050 | 0.0314472 | ||||||||
\(887\) | −11.8396 | − | 20.5069i | −0.397536 | − | 0.688553i | 0.595885 | − | 0.803070i | \(-0.296801\pi\) |
−0.993421 | + | 0.114517i | \(0.963468\pi\) | |||||||
\(888\) | 7.22178 | + | 12.5085i | 0.242347 | + | 0.419757i | ||||
\(889\) | −2.81374 | + | 43.5412i | −0.0943699 | + | 1.46033i | ||||
\(890\) | −4.63929 | − | 8.03548i | −0.155509 | − | 0.269350i | ||||
\(891\) | 3.49255 | 0.117005 | ||||||||
\(892\) | −18.2606 | − | 31.6284i | −0.611412 | − | 1.05900i | ||||
\(893\) | 3.49707 | − | 6.05711i | 0.117025 | − | 0.202693i | ||||
\(894\) | −21.3392 | − | 36.9605i | −0.713688 | − | 1.23614i | ||||
\(895\) | −12.9550 | + | 22.4387i | −0.433037 | + | 0.750043i | ||||
\(896\) | 44.2923 | + | 29.5365i | 1.47970 | + | 0.986744i | ||||
\(897\) | −0.299989 | + | 2.40911i | −0.0100163 | + | 0.0804379i | ||||
\(898\) | 46.1825 | − | 79.9905i | 1.54113 | − | 2.66932i | ||||
\(899\) | 52.9485 | 1.76593 | ||||||||
\(900\) | −13.7085 | −0.456949 | ||||||||
\(901\) | 44.8424 | 1.49392 | ||||||||
\(902\) | 61.3973 | 2.04431 | ||||||||
\(903\) | 19.7619 | + | 13.1782i | 0.657633 | + | 0.438545i | ||||
\(904\) | −25.2123 | − | 43.6691i | −0.838550 | − | 1.45241i | ||||
\(905\) | −9.25039 | + | 16.0221i | −0.307493 | + | 0.532594i | ||||
\(906\) | −17.0865 | + | 29.5947i | −0.567660 | + | 0.983217i | ||||
\(907\) | −9.26733 | −0.307717 | −0.153858 | − | 0.988093i | \(-0.549170\pi\) | ||||
−0.153858 | + | 0.988093i | \(0.549170\pi\) | |||||||
\(908\) | −18.7088 | − | 32.4046i | −0.620874 | − | 1.07539i | ||||
\(909\) | −1.54577 | −0.0512700 | ||||||||
\(910\) | −28.0049 | − | 5.33995i | −0.928352 | − | 0.177018i | ||||
\(911\) | −10.2739 | −0.340390 | −0.170195 | − | 0.985410i | \(-0.554440\pi\) | ||||
−0.170195 | + | 0.985410i | \(0.554440\pi\) | |||||||
\(912\) | 2.40991 | + | 4.17409i | 0.0798002 | + | 0.138218i | ||||
\(913\) | 44.2874 | 1.46570 | ||||||||
\(914\) | −17.5130 | + | 30.3335i | −0.579280 | + | 1.00334i | ||||
\(915\) | 2.85444 | − | 4.94403i | 0.0943648 | − | 0.163445i | ||||
\(916\) | 12.6553 | + | 21.9196i | 0.418143 | + | 0.724245i | ||||
\(917\) | −1.20175 | + | 18.5964i | −0.0396851 | + | 0.614107i | ||||
\(918\) | 11.0195 | 0.363698 | ||||||||
\(919\) | −4.63206 | −0.152797 | −0.0763987 | − | 0.997077i | \(-0.524342\pi\) | ||||
−0.0763987 | + | 0.997077i | \(0.524342\pi\) | |||||||
\(920\) | 3.87381 | 0.127716 | ||||||||
\(921\) | −32.9959 | −1.08725 | ||||||||
\(922\) | −4.36931 | + | 7.56787i | −0.143896 | + | 0.249235i | ||||
\(923\) | −2.25254 | + | 18.0894i | −0.0741434 | + | 0.595421i | ||||
\(924\) | −2.33893 | + | 36.1937i | −0.0769451 | + | 1.19069i | ||||
\(925\) | −5.38265 | + | 9.32302i | −0.176980 | + | 0.306539i | ||||
\(926\) | 5.71396 | + | 9.89687i | 0.187772 | + | 0.325231i | ||||
\(927\) | −2.75895 | + | 4.77865i | −0.0906159 | + | 0.156951i | ||||
\(928\) | 1.89607 | + | 3.28408i | 0.0622414 | + | 0.107805i | ||||
\(929\) | 3.09036 | 0.101392 | 0.0506958 | − | 0.998714i | \(-0.483856\pi\) | ||||
0.0506958 | + | 0.998714i | \(0.483856\pi\) | |||||||
\(930\) | 14.9384 | + | 25.8741i | 0.489849 | + | 0.848444i | ||||
\(931\) | 5.76204 | − | 7.53783i | 0.188843 | − | 0.247042i | ||||
\(932\) | 48.0346 | + | 83.1983i | 1.57342 | + | 2.72525i | ||||
\(933\) | −4.11532 | − | 7.12794i | −0.134729 | − | 0.233358i | ||||
\(934\) | 97.5326 | 3.19136 | ||||||||
\(935\) | −9.70621 | − | 16.8116i | −0.317427 | − | 0.549800i | ||||
\(936\) | 13.4757 | + | 10.1909i | 0.440466 | + | 0.333099i | ||||
\(937\) | −41.8382 | −1.36680 | −0.683398 | − | 0.730046i | \(-0.739498\pi\) | ||||
−0.683398 | + | 0.730046i | \(0.739498\pi\) | |||||||
\(938\) | 11.3664 | + | 7.57970i | 0.371125 | + | 0.247486i | ||||
\(939\) | −7.14348 | + | 12.3729i | −0.233119 | + | 0.403773i | ||||
\(940\) | −24.8675 | −0.811087 | ||||||||
\(941\) | −18.9382 | − | 32.8019i | −0.617368 | − | 1.06931i | −0.989964 | − | 0.141319i | \(-0.954866\pi\) |
0.372596 | − | 0.927994i | \(-0.378468\pi\) | |||||||
\(942\) | 13.6871 | − | 23.7067i | 0.445949 | − | 0.772406i | ||||
\(943\) | 4.86280 | 0.158354 | ||||||||
\(944\) | 2.85703 | 0.0929885 | ||||||||
\(945\) | −0.209483 | + | 3.24164i | −0.00681449 | + | 0.105451i | ||||
\(946\) | −38.1615 | + | 66.0977i | −1.24074 | + | 2.14902i | ||||
\(947\) | 0.390777 | + | 0.676846i | 0.0126986 | + | 0.0219946i | 0.872305 | − | 0.488962i | \(-0.162624\pi\) |
−0.859606 | + | 0.510957i | \(0.829291\pi\) | |||||||
\(948\) | 23.1634 | + | 40.1201i | 0.752311 | + | 1.30304i | ||||
\(949\) | −5.38405 | + | 43.2375i | −0.174773 | + | 1.40355i | ||||
\(950\) | −5.76143 | + | 9.97909i | −0.186926 | + | 0.323765i | ||||
\(951\) | −4.68195 | + | 8.10938i | −0.151823 | + | 0.262965i | ||||
\(952\) | −3.61938 | + | 56.0081i | −0.117305 | + | 1.81523i | ||||
\(953\) | 14.6233 | + | 25.3283i | 0.473695 | + | 0.820463i | 0.999547 | − | 0.0301129i | \(-0.00958667\pi\) |
−0.525852 | + | 0.850576i | \(0.676253\pi\) | |||||||
\(954\) | 12.0556 | − | 20.8810i | 0.390315 | − | 0.676046i | ||||
\(955\) | 5.83077 | − | 10.0992i | 0.188679 | − | 0.326802i | ||||
\(956\) | −7.10691 | + | 12.3095i | −0.229854 | + | 0.398119i | ||||
\(957\) | −9.24911 | + | 16.0199i | −0.298981 | + | 0.517851i | ||||
\(958\) | 24.9135 | + | 43.1515i | 0.804919 | + | 1.39416i | ||||
\(959\) | −3.29658 | + | 51.0129i | −0.106452 | + | 1.64729i | ||||
\(960\) | −5.43585 | + | 9.41518i | −0.175441 | + | 0.303874i | ||||
\(961\) | −34.4692 | + | 59.7025i | −1.11191 | + | 1.92589i | ||||
\(962\) | 24.9197 | − | 10.5275i | 0.803442 | − | 0.339419i | ||||
\(963\) | −0.724187 | − | 1.25433i | −0.0233366 | − | 0.0404202i | ||||
\(964\) | −49.3181 | − | 85.4214i | −1.58843 | − | 2.75124i | ||||
\(965\) | 11.3837 | − | 19.7171i | 0.366454 | − | 0.634717i | ||||
\(966\) | −0.279641 | + | 4.32730i | −0.00899730 | + | 0.139229i | ||||
\(967\) | −30.4010 | −0.977631 | −0.488816 | − | 0.872387i | \(-0.662571\pi\) | ||||
−0.488816 | + | 0.872387i | \(0.662571\pi\) | |||||||
\(968\) | −5.61327 | −0.180417 | ||||||||
\(969\) | 3.06801 | − | 5.31395i | 0.0985587 | − | 0.170709i | ||||
\(970\) | 10.7466 | + | 18.6136i | 0.345051 | + | 0.597647i | ||||
\(971\) | 8.91863 | 0.286212 | 0.143106 | − | 0.989707i | \(-0.454291\pi\) | ||||
0.143106 | + | 0.989707i | \(0.454291\pi\) | |||||||
\(972\) | 1.96253 | − | 3.39920i | 0.0629482 | − | 0.109029i | ||||
\(973\) | −34.1705 | − | 22.7867i | −1.09546 | − | 0.730508i | ||||
\(974\) | −81.7719 | −2.62014 | ||||||||
\(975\) | −1.55604 | + | 12.4961i | −0.0498332 | + | 0.400194i | ||||
\(976\) | −8.26721 | − | 14.3192i | −0.264627 | − | 0.458348i | ||||
\(977\) | 23.6062 | 0.755229 | 0.377615 | − | 0.925963i | \(-0.376744\pi\) | ||||
0.377615 | + | 0.925963i | \(0.376744\pi\) | |||||||
\(978\) | −14.1277 | − | 24.4699i | −0.451754 | − | 0.782462i | ||||
\(979\) | 5.42158 | + | 9.39046i | 0.173275 | + | 0.300120i | ||||
\(980\) | −33.4533 | − | 4.34180i | −1.06863 | − | 0.138694i | ||||
\(981\) | −8.20485 | − | 14.2112i | −0.261961 | − | 0.453729i | ||||
\(982\) | 98.4913 | 3.14298 | ||||||||
\(983\) | −10.1644 | − | 17.6053i | −0.324195 | − | 0.561523i | 0.657154 | − | 0.753756i | \(-0.271760\pi\) |
−0.981349 | + | 0.192234i | \(0.938427\pi\) | |||||||
\(984\) | 16.9208 | − | 29.3077i | 0.539416 | − | 0.934295i | ||||
\(985\) | −15.8122 | − | 27.3875i | −0.503817 | − | 0.872637i | ||||
\(986\) | −29.1823 | + | 50.5452i | −0.929353 | + | 1.60969i | ||||
\(987\) | 0.880423 | − | 13.6241i | 0.0280242 | − | 0.433660i | ||||
\(988\) | 17.6698 | − | 7.46469i | 0.562150 | − | 0.237484i | ||||
\(989\) | −3.02247 | + | 5.23508i | −0.0961091 | + | 0.166466i | ||||
\(990\) | −10.4378 | −0.331736 | ||||||||
\(991\) | −45.2804 | −1.43838 | −0.719190 | − | 0.694813i | \(-0.755487\pi\) | ||||
−0.719190 | + | 0.694813i | \(0.755487\pi\) | |||||||
\(992\) | −7.15752 | −0.227252 | ||||||||
\(993\) | 24.4779 | 0.776783 | ||||||||
\(994\) | −2.09976 | + | 32.4927i | −0.0666003 | + | 1.03060i | ||||
\(995\) | −10.8632 | − | 18.8155i | −0.344385 | − | 0.596493i | ||||
\(996\) | 24.8859 | − | 43.1037i | 0.788541 | − | 1.36579i | ||||
\(997\) | 9.65104 | − | 16.7161i | 0.305652 | − | 0.529404i | −0.671755 | − | 0.740774i | \(-0.734459\pi\) |
0.977406 | + | 0.211370i | \(0.0677924\pi\) | |||||||
\(998\) | −11.5965 | −0.367079 | ||||||||
\(999\) | −1.54118 | − | 2.66940i | −0.0487607 | − | 0.0844561i |
(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 | 273.2.j.b.100.8 | ✓ | 16 | |
3.2 | odd | 2 | 819.2.n.e.100.1 | 16 | |||
7.4 | even | 3 | 273.2.l.b.256.1 | yes | 16 | ||
13.3 | even | 3 | 273.2.l.b.16.1 | yes | 16 | ||
21.11 | odd | 6 | 819.2.s.e.802.8 | 16 | |||
39.29 | odd | 6 | 819.2.s.e.289.8 | 16 | |||
91.81 | even | 3 | inner | 273.2.j.b.172.8 | yes | 16 | |
273.263 | odd | 6 | 819.2.n.e.172.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.j.b.100.8 | ✓ | 16 | 1.1 | even | 1 | trivial | |
273.2.j.b.172.8 | yes | 16 | 91.81 | even | 3 | inner | |
273.2.l.b.16.1 | yes | 16 | 13.3 | even | 3 | ||
273.2.l.b.256.1 | yes | 16 | 7.4 | even | 3 | ||
819.2.n.e.100.1 | 16 | 3.2 | odd | 2 | |||
819.2.n.e.172.1 | 16 | 273.263 | odd | 6 | |||
819.2.s.e.289.8 | 16 | 39.29 | odd | 6 | |||
819.2.s.e.802.8 | 16 | 21.11 | odd | 6 |