Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(93,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.93");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.e (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: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.310217769.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.1 | ||
Root | \(-1.03075 + 1.78531i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.277 |
Dual form | 322.2.e.a.93.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.28821 | + | 2.23124i | −0.743747 | + | 1.28821i | 0.207031 | + | 0.978334i | \(0.433620\pi\) |
−0.950778 | + | 0.309873i | \(0.899713\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.663319 | − | 1.14890i | −0.296645 | − | 0.513804i | 0.678721 | − | 0.734396i | \(-0.262535\pi\) |
−0.975366 | + | 0.220592i | \(0.929201\pi\) | |||||||
\(6\) | 2.57641 | 1.05182 | ||||||||
\(7\) | −1.46157 | − | 2.20541i | −0.552422 | − | 0.833565i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.81896 | − | 3.15053i | −0.606319 | − | 1.05018i | ||||
\(10\) | −0.663319 | + | 1.14890i | −0.209760 | + | 0.363315i | ||||
\(11\) | −1.04567 | + | 1.81115i | −0.315280 | + | 0.546081i | −0.979497 | − | 0.201459i | \(-0.935432\pi\) |
0.664217 | + | 0.747540i | \(0.268765\pi\) | |||||||
\(12\) | −1.28821 | − | 2.23124i | −0.371873 | − | 0.644104i | ||||
\(13\) | 3.11142 | 0.862952 | 0.431476 | − | 0.902124i | \(-0.357993\pi\) | ||||
0.431476 | + | 0.902124i | \(0.357993\pi\) | |||||||
\(14\) | −1.17915 | + | 2.36846i | −0.315142 | + | 0.632997i | ||||
\(15\) | 3.41797 | 0.882516 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.47460 | − | 6.01818i | 0.842713 | − | 1.45962i | −0.0448794 | − | 0.998992i | \(-0.514290\pi\) |
0.887593 | − | 0.460629i | \(-0.152376\pi\) | |||||||
\(18\) | −1.81896 | + | 3.15053i | −0.428732 | + | 0.742586i | ||||
\(19\) | −3.88326 | − | 6.72601i | −0.890882 | − | 1.54305i | −0.838820 | − | 0.544409i | \(-0.816754\pi\) |
−0.0520619 | − | 0.998644i | \(-0.516579\pi\) | |||||||
\(20\) | 1.32664 | 0.296645 | ||||||||
\(21\) | 6.80360 | − | 0.420095i | 1.48467 | − | 0.0916722i | ||||
\(22\) | 2.09133 | 0.445873 | ||||||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | ||||
\(24\) | −1.28821 | + | 2.23124i | −0.262954 | + | 0.455450i | ||||
\(25\) | 1.62002 | − | 2.80595i | 0.324003 | − | 0.561190i | ||||
\(26\) | −1.55571 | − | 2.69457i | −0.305100 | − | 0.528448i | ||||
\(27\) | 1.64353 | 0.316298 | ||||||||
\(28\) | 2.64072 | − | 0.163054i | 0.499050 | − | 0.0308143i | ||||
\(29\) | 1.15845 | 0.215118 | 0.107559 | − | 0.994199i | \(-0.465697\pi\) | ||||
0.107559 | + | 0.994199i | \(0.465697\pi\) | |||||||
\(30\) | −1.70898 | − | 2.96005i | −0.312016 | − | 0.540428i | ||||
\(31\) | 4.35694 | − | 7.54644i | 0.782530 | − | 1.35538i | −0.147934 | − | 0.988997i | \(-0.547262\pi\) |
0.930464 | − | 0.366384i | \(-0.119404\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −2.69407 | − | 4.66626i | −0.468977 | − | 0.812292i | ||||
\(34\) | −6.94919 | −1.19178 | ||||||||
\(35\) | −1.56431 | + | 3.14209i | −0.264416 | + | 0.531110i | ||||
\(36\) | 3.63791 | 0.606319 | ||||||||
\(37\) | 1.65472 | + | 2.86606i | 0.272034 | + | 0.471177i | 0.969383 | − | 0.245555i | \(-0.0789702\pi\) |
−0.697348 | + | 0.716732i | \(0.745637\pi\) | |||||||
\(38\) | −3.88326 | + | 6.72601i | −0.629949 | + | 1.09110i | ||||
\(39\) | −4.00815 | + | 6.94232i | −0.641818 | + | 1.11166i | ||||
\(40\) | −0.663319 | − | 1.14890i | −0.104880 | − | 0.181657i | ||||
\(41\) | −4.26425 | −0.665964 | −0.332982 | − | 0.942933i | \(-0.608055\pi\) | ||||
−0.332982 | + | 0.942933i | \(0.608055\pi\) | |||||||
\(42\) | −3.76561 | − | 5.68204i | −0.581046 | − | 0.876758i | ||||
\(43\) | −8.36716 | −1.27598 | −0.637990 | − | 0.770045i | \(-0.720234\pi\) | ||||
−0.637990 | + | 0.770045i | \(0.720234\pi\) | |||||||
\(44\) | −1.04567 | − | 1.81115i | −0.157640 | − | 0.273040i | ||||
\(45\) | −2.41310 | + | 4.17961i | −0.359723 | + | 0.623059i | ||||
\(46\) | 0.500000 | − | 0.866025i | 0.0737210 | − | 0.127688i | ||||
\(47\) | 1.74065 | + | 3.01490i | 0.253900 | + | 0.439768i | 0.964596 | − | 0.263731i | \(-0.0849532\pi\) |
−0.710696 | + | 0.703499i | \(0.751620\pi\) | |||||||
\(48\) | 2.57641 | 0.371873 | ||||||||
\(49\) | −2.72763 | + | 6.44671i | −0.389661 | + | 0.920958i | ||||
\(50\) | −3.24003 | −0.458210 | ||||||||
\(51\) | 8.95200 | + | 15.5053i | 1.25353 | + | 2.17118i | ||||
\(52\) | −1.55571 | + | 2.69457i | −0.215738 | + | 0.373669i | ||||
\(53\) | −2.12002 | + | 3.67198i | −0.291207 | + | 0.504385i | −0.974095 | − | 0.226138i | \(-0.927390\pi\) |
0.682889 | + | 0.730522i | \(0.260723\pi\) | |||||||
\(54\) | −0.821765 | − | 1.42334i | −0.111828 | − | 0.193692i | ||||
\(55\) | 2.77444 | 0.374105 | ||||||||
\(56\) | −1.46157 | − | 2.20541i | −0.195311 | − | 0.294710i | ||||
\(57\) | 20.0098 | 2.65036 | ||||||||
\(58\) | −0.579223 | − | 1.00324i | −0.0760557 | − | 0.131732i | ||||
\(59\) | −4.59225 | + | 7.95401i | −0.597860 | + | 1.03552i | 0.395277 | + | 0.918562i | \(0.370649\pi\) |
−0.993136 | + | 0.116961i | \(0.962685\pi\) | |||||||
\(60\) | −1.70898 | + | 2.96005i | −0.220629 | + | 0.382140i | ||||
\(61\) | −6.01934 | − | 10.4258i | −0.770698 | − | 1.33489i | −0.937181 | − | 0.348844i | \(-0.886574\pi\) |
0.166483 | − | 0.986044i | \(-0.446759\pi\) | |||||||
\(62\) | −8.71388 | −1.10666 | ||||||||
\(63\) | −4.28965 | + | 8.61625i | −0.540446 | + | 1.08555i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.06386 | − | 3.57471i | −0.255991 | − | 0.443389i | ||||
\(66\) | −2.69407 | + | 4.66626i | −0.331617 | + | 0.574377i | ||||
\(67\) | 3.63160 | − | 6.29011i | 0.443670 | − | 0.768459i | −0.554288 | − | 0.832325i | \(-0.687010\pi\) |
0.997959 | + | 0.0638656i | \(0.0203429\pi\) | |||||||
\(68\) | 3.47460 | + | 6.01818i | 0.421357 | + | 0.729811i | ||||
\(69\) | −2.57641 | −0.310164 | ||||||||
\(70\) | 3.50328 | − | 0.216314i | 0.418722 | − | 0.0258544i | ||||
\(71\) | −7.41708 | −0.880245 | −0.440123 | − | 0.897938i | \(-0.645065\pi\) | ||||
−0.440123 | + | 0.897938i | \(0.645065\pi\) | |||||||
\(72\) | −1.81896 | − | 3.15053i | −0.214366 | − | 0.371293i | ||||
\(73\) | 2.18402 | − | 3.78284i | 0.255621 | − | 0.442748i | −0.709443 | − | 0.704763i | \(-0.751054\pi\) |
0.965064 | + | 0.262015i | \(0.0843868\pi\) | |||||||
\(74\) | 1.65472 | − | 2.86606i | 0.192357 | − | 0.333173i | ||||
\(75\) | 4.17383 | + | 7.22929i | 0.481953 | + | 0.834767i | ||||
\(76\) | 7.76653 | 0.890882 | ||||||||
\(77\) | 5.52262 | − | 0.341000i | 0.629361 | − | 0.0388606i | ||||
\(78\) | 8.01631 | 0.907668 | ||||||||
\(79\) | 0.398625 | + | 0.690439i | 0.0448488 | + | 0.0776805i | 0.887578 | − | 0.460657i | \(-0.152386\pi\) |
−0.842730 | + | 0.538337i | \(0.819053\pi\) | |||||||
\(80\) | −0.663319 | + | 1.14890i | −0.0741613 | + | 0.128451i | ||||
\(81\) | 3.33966 | − | 5.78446i | 0.371074 | − | 0.642718i | ||||
\(82\) | 2.13212 | + | 3.69295i | 0.235454 | + | 0.407818i | ||||
\(83\) | 10.3746 | 1.13876 | 0.569381 | − | 0.822074i | \(-0.307183\pi\) | ||||
0.569381 | + | 0.822074i | \(0.307183\pi\) | |||||||
\(84\) | −3.03798 | + | 6.10213i | −0.331471 | + | 0.665797i | ||||
\(85\) | −9.21906 | −0.999947 | ||||||||
\(86\) | 4.18358 | + | 7.24617i | 0.451127 | + | 0.781375i | ||||
\(87\) | −1.49232 | + | 2.58477i | −0.159993 | + | 0.277117i | ||||
\(88\) | −1.04567 | + | 1.81115i | −0.111468 | + | 0.193069i | ||||
\(89\) | −8.32132 | − | 14.4129i | −0.882058 | − | 1.52777i | −0.849049 | − | 0.528315i | \(-0.822824\pi\) |
−0.0330095 | − | 0.999455i | \(-0.510509\pi\) | |||||||
\(90\) | 4.82619 | 0.508725 | ||||||||
\(91\) | −4.54756 | − | 6.86194i | −0.476713 | − | 0.719327i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 11.2253 | + | 19.4428i | 1.16401 | + | 2.01612i | ||||
\(94\) | 1.74065 | − | 3.01490i | 0.179534 | − | 0.310963i | ||||
\(95\) | −5.15168 | + | 8.92298i | −0.528552 | + | 0.915478i | ||||
\(96\) | −1.28821 | − | 2.23124i | −0.131477 | − | 0.227725i | ||||
\(97\) | 6.65800 | 0.676018 | 0.338009 | − | 0.941143i | \(-0.390247\pi\) | ||||
0.338009 | + | 0.941143i | \(0.390247\pi\) | |||||||
\(98\) | 6.94683 | − | 0.861161i | 0.701735 | − | 0.0869904i | ||||
\(99\) | 7.60808 | 0.764641 | ||||||||
\(100\) | 1.62002 | + | 2.80595i | 0.162002 | + | 0.280595i | ||||
\(101\) | −4.57940 | + | 7.93175i | −0.455667 | + | 0.789238i | −0.998726 | − | 0.0504560i | \(-0.983933\pi\) |
0.543059 | + | 0.839694i | \(0.317266\pi\) | |||||||
\(102\) | 8.95200 | − | 15.5053i | 0.886380 | − | 1.53526i | ||||
\(103\) | −2.26606 | − | 3.92492i | −0.223281 | − | 0.386734i | 0.732521 | − | 0.680744i | \(-0.238343\pi\) |
−0.955802 | + | 0.294010i | \(0.905010\pi\) | |||||||
\(104\) | 3.11142 | 0.305100 | ||||||||
\(105\) | −4.99560 | − | 7.53801i | −0.487521 | − | 0.735634i | ||||
\(106\) | 4.24003 | 0.411828 | ||||||||
\(107\) | 6.16722 | + | 10.6819i | 0.596207 | + | 1.03266i | 0.993375 | + | 0.114916i | \(0.0366597\pi\) |
−0.397168 | + | 0.917746i | \(0.630007\pi\) | |||||||
\(108\) | −0.821765 | + | 1.42334i | −0.0790744 | + | 0.136961i | ||||
\(109\) | 0.549920 | − | 0.952489i | 0.0526728 | − | 0.0912319i | −0.838487 | − | 0.544922i | \(-0.816559\pi\) |
0.891160 | + | 0.453690i | \(0.149893\pi\) | |||||||
\(110\) | −1.38722 | − | 2.40273i | −0.132266 | − | 0.229092i | ||||
\(111\) | −8.52649 | −0.809299 | ||||||||
\(112\) | −1.17915 | + | 2.36846i | −0.111419 | + | 0.223798i | ||||
\(113\) | 4.44278 | 0.417942 | 0.208971 | − | 0.977922i | \(-0.432989\pi\) | ||||
0.208971 | + | 0.977922i | \(0.432989\pi\) | |||||||
\(114\) | −10.0049 | − | 17.3290i | −0.937045 | − | 1.62301i | ||||
\(115\) | 0.663319 | − | 1.14890i | 0.0618548 | − | 0.107136i | ||||
\(116\) | −0.579223 | + | 1.00324i | −0.0537795 | + | 0.0931489i | ||||
\(117\) | −5.65954 | − | 9.80260i | −0.523224 | − | 0.906251i | ||||
\(118\) | 9.18450 | 0.845501 | ||||||||
\(119\) | −18.3509 | + | 1.13309i | −1.68222 | + | 0.103871i | ||||
\(120\) | 3.41797 | 0.312016 | ||||||||
\(121\) | 3.31317 | + | 5.73857i | 0.301197 | + | 0.521689i | ||||
\(122\) | −6.01934 | + | 10.4258i | −0.544966 | + | 0.943908i | ||||
\(123\) | 5.49324 | − | 9.51457i | 0.495308 | − | 0.857899i | ||||
\(124\) | 4.35694 | + | 7.54644i | 0.391265 | + | 0.677691i | ||||
\(125\) | −10.9315 | −0.977746 | ||||||||
\(126\) | 9.60672 | − | 0.593177i | 0.855835 | − | 0.0528444i | ||||
\(127\) | 2.41201 | 0.214031 | 0.107015 | − | 0.994257i | \(-0.465871\pi\) | ||||
0.107015 | + | 0.994257i | \(0.465871\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 10.7786 | − | 18.6691i | 0.949006 | − | 1.64373i | ||||
\(130\) | −2.06386 | + | 3.57471i | −0.181013 | + | 0.313523i | ||||
\(131\) | −0.761712 | − | 1.31932i | −0.0665511 | − | 0.115270i | 0.830830 | − | 0.556526i | \(-0.187866\pi\) |
−0.897381 | + | 0.441257i | \(0.854533\pi\) | |||||||
\(132\) | 5.38814 | 0.468977 | ||||||||
\(133\) | −9.15792 | + | 18.3947i | −0.794092 | + | 1.59502i | ||||
\(134\) | −7.26319 | −0.627444 | ||||||||
\(135\) | −1.09018 | − | 1.88825i | −0.0938281 | − | 0.162515i | ||||
\(136\) | 3.47460 | − | 6.01818i | 0.297944 | − | 0.516054i | ||||
\(137\) | −4.81334 | + | 8.33695i | −0.411231 | + | 0.712274i | −0.995025 | − | 0.0996287i | \(-0.968235\pi\) |
0.583793 | + | 0.811902i | \(0.301568\pi\) | |||||||
\(138\) | 1.28821 | + | 2.23124i | 0.109660 | + | 0.189936i | ||||
\(139\) | 8.57676 | 0.727471 | 0.363736 | − | 0.931502i | \(-0.381501\pi\) | ||||
0.363736 | + | 0.931502i | \(0.381501\pi\) | |||||||
\(140\) | −1.93897 | − | 2.92577i | −0.163873 | − | 0.247273i | ||||
\(141\) | −8.96928 | −0.755349 | ||||||||
\(142\) | 3.70854 | + | 6.42338i | 0.311214 | + | 0.539038i | ||||
\(143\) | −3.25350 | + | 5.63523i | −0.272072 | + | 0.471242i | ||||
\(144\) | −1.81896 | + | 3.15053i | −0.151580 | + | 0.262544i | ||||
\(145\) | −0.768419 | − | 1.33094i | −0.0638137 | − | 0.110529i | ||||
\(146\) | −4.36805 | −0.361502 | ||||||||
\(147\) | −10.8704 | − | 14.3907i | −0.896576 | − | 1.18692i | ||||
\(148\) | −3.30944 | −0.272034 | ||||||||
\(149\) | −8.01069 | − | 13.8749i | −0.656261 | − | 1.13668i | −0.981576 | − | 0.191072i | \(-0.938804\pi\) |
0.325315 | − | 0.945606i | \(-0.394530\pi\) | |||||||
\(150\) | 4.17383 | − | 7.22929i | 0.340792 | − | 0.590269i | ||||
\(151\) | 6.96789 | − | 12.0687i | 0.567039 | − | 0.982140i | −0.429818 | − | 0.902915i | \(-0.641422\pi\) |
0.996857 | − | 0.0792244i | \(-0.0252443\pi\) | |||||||
\(152\) | −3.88326 | − | 6.72601i | −0.314974 | − | 0.545552i | ||||
\(153\) | −25.2806 | −2.04381 | ||||||||
\(154\) | −3.05663 | − | 4.61223i | −0.246310 | − | 0.371664i | ||||
\(155\) | −11.5602 | −0.928535 | ||||||||
\(156\) | −4.00815 | − | 6.94232i | −0.320909 | − | 0.555831i | ||||
\(157\) | 7.71135 | − | 13.3564i | 0.615433 | − | 1.06596i | −0.374876 | − | 0.927075i | \(-0.622315\pi\) |
0.990308 | − | 0.138885i | \(-0.0443520\pi\) | |||||||
\(158\) | 0.398625 | − | 0.690439i | 0.0317129 | − | 0.0549284i | ||||
\(159\) | −5.46204 | − | 9.46053i | −0.433168 | − | 0.750269i | ||||
\(160\) | 1.32664 | 0.104880 | ||||||||
\(161\) | 1.17915 | − | 2.36846i | 0.0929302 | − | 0.186661i | ||||
\(162\) | −6.67932 | −0.524777 | ||||||||
\(163\) | 4.30693 | + | 7.45983i | 0.337345 | + | 0.584299i | 0.983932 | − | 0.178541i | \(-0.0571378\pi\) |
−0.646587 | + | 0.762840i | \(0.723804\pi\) | |||||||
\(164\) | 2.13212 | − | 3.69295i | 0.166491 | − | 0.288371i | ||||
\(165\) | −3.57405 | + | 6.19044i | −0.278240 | + | 0.481925i | ||||
\(166\) | −5.18730 | − | 8.98468i | −0.402613 | − | 0.697346i | ||||
\(167\) | 11.9693 | 0.926211 | 0.463105 | − | 0.886303i | \(-0.346735\pi\) | ||||
0.463105 | + | 0.886303i | \(0.346735\pi\) | |||||||
\(168\) | 6.80360 | − | 0.420095i | 0.524909 | − | 0.0324110i | ||||
\(169\) | −3.31907 | −0.255313 | ||||||||
\(170\) | 4.60953 | + | 7.98394i | 0.353535 | + | 0.612340i | ||||
\(171\) | −14.1270 | + | 24.4686i | −1.08032 | + | 1.87116i | ||||
\(172\) | 4.18358 | − | 7.24617i | 0.318995 | − | 0.552515i | ||||
\(173\) | 9.90984 | + | 17.1644i | 0.753431 | + | 1.30498i | 0.946150 | + | 0.323727i | \(0.104936\pi\) |
−0.192719 | + | 0.981254i | \(0.561731\pi\) | |||||||
\(174\) | 2.98464 | 0.226265 | ||||||||
\(175\) | −8.55603 | + | 0.528301i | −0.646775 | + | 0.0399358i | ||||
\(176\) | 2.09133 | 0.157640 | ||||||||
\(177\) | −11.8315 | − | 20.4928i | −0.889313 | − | 1.54033i | ||||
\(178\) | −8.32132 | + | 14.4129i | −0.623709 | + | 1.08030i | ||||
\(179\) | 8.20481 | − | 14.2112i | 0.613257 | − | 1.06219i | −0.377431 | − | 0.926038i | \(-0.623193\pi\) |
0.990688 | − | 0.136154i | \(-0.0434742\pi\) | |||||||
\(180\) | −2.41310 | − | 4.17961i | −0.179862 | − | 0.311529i | ||||
\(181\) | −11.2306 | −0.834766 | −0.417383 | − | 0.908731i | \(-0.637053\pi\) | ||||
−0.417383 | + | 0.908731i | \(0.637053\pi\) | |||||||
\(182\) | −3.66884 | + | 7.36927i | −0.271952 | + | 0.546247i | ||||
\(183\) | 31.0167 | 2.29282 | ||||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | 2.19521 | − | 3.80222i | 0.161395 | − | 0.279545i | ||||
\(186\) | 11.2253 | − | 19.4428i | 0.823078 | − | 1.42561i | ||||
\(187\) | 7.26653 | + | 12.5860i | 0.531381 | + | 0.920379i | ||||
\(188\) | −3.48130 | −0.253900 | ||||||||
\(189\) | −2.40213 | − | 3.62465i | −0.174730 | − | 0.263655i | ||||
\(190\) | 10.3034 | 0.747485 | ||||||||
\(191\) | −3.18402 | − | 5.51489i | −0.230388 | − | 0.399044i | 0.727534 | − | 0.686071i | \(-0.240666\pi\) |
−0.957922 | + | 0.287028i | \(0.907333\pi\) | |||||||
\(192\) | −1.28821 | + | 2.23124i | −0.0929684 | + | 0.161026i | ||||
\(193\) | 7.02750 | − | 12.1720i | 0.505850 | − | 0.876158i | −0.494127 | − | 0.869390i | \(-0.664512\pi\) |
0.999977 | − | 0.00676850i | \(-0.00215450\pi\) | |||||||
\(194\) | −3.32900 | − | 5.76600i | −0.239008 | − | 0.413975i | ||||
\(195\) | 10.6347 | 0.761569 | ||||||||
\(196\) | −4.21920 | − | 5.58555i | −0.301371 | − | 0.398968i | ||||
\(197\) | −6.95570 | −0.495573 | −0.247786 | − | 0.968815i | \(-0.579703\pi\) | ||||
−0.247786 | + | 0.968815i | \(0.579703\pi\) | |||||||
\(198\) | −3.80404 | − | 6.58879i | −0.270341 | − | 0.468245i | ||||
\(199\) | −10.5449 | + | 18.2642i | −0.747506 | + | 1.29472i | 0.201509 | + | 0.979487i | \(0.435415\pi\) |
−0.949015 | + | 0.315231i | \(0.897918\pi\) | |||||||
\(200\) | 1.62002 | − | 2.80595i | 0.114552 | − | 0.198411i | ||||
\(201\) | 9.35650 | + | 16.2059i | 0.659956 | + | 1.14308i | ||||
\(202\) | 9.15879 | 0.644410 | ||||||||
\(203\) | −1.69315 | − | 2.55484i | −0.118836 | − | 0.179315i | ||||
\(204\) | −17.9040 | −1.25353 | ||||||||
\(205\) | 2.82856 | + | 4.89920i | 0.197555 | + | 0.342175i | ||||
\(206\) | −2.26606 | + | 3.92492i | −0.157884 | + | 0.273462i | ||||
\(207\) | 1.81896 | − | 3.15053i | 0.126426 | − | 0.218977i | ||||
\(208\) | −1.55571 | − | 2.69457i | −0.107869 | − | 0.186835i | ||||
\(209\) | 16.2424 | 1.12351 | ||||||||
\(210\) | −4.03030 | + | 8.09532i | −0.278117 | + | 0.558630i | ||||
\(211\) | 26.5036 | 1.82458 | 0.912290 | − | 0.409544i | \(-0.134312\pi\) | ||||
0.912290 | + | 0.409544i | \(0.134312\pi\) | |||||||
\(212\) | −2.12002 | − | 3.67198i | −0.145603 | − | 0.252192i | ||||
\(213\) | 9.55474 | − | 16.5493i | 0.654680 | − | 1.13394i | ||||
\(214\) | 6.16722 | − | 10.6819i | 0.421582 | − | 0.730202i | ||||
\(215\) | 5.55009 | + | 9.61304i | 0.378513 | + | 0.655604i | ||||
\(216\) | 1.64353 | 0.111828 | ||||||||
\(217\) | −23.0109 | + | 1.42083i | −1.56208 | + | 0.0964525i | ||||
\(218\) | −1.09984 | −0.0744906 | ||||||||
\(219\) | 5.62695 | + | 9.74617i | 0.380234 | + | 0.658585i | ||||
\(220\) | −1.38722 | + | 2.40273i | −0.0935263 | + | 0.161992i | ||||
\(221\) | 10.8109 | − | 18.7251i | 0.727221 | − | 1.25958i | ||||
\(222\) | 4.26325 | + | 7.38416i | 0.286130 | + | 0.495592i | ||||
\(223\) | −9.80109 | −0.656329 | −0.328165 | − | 0.944621i | \(-0.606430\pi\) | ||||
−0.328165 | + | 0.944621i | \(0.606430\pi\) | |||||||
\(224\) | 2.64072 | − | 0.163054i | 0.176441 | − | 0.0108945i | ||||
\(225\) | −11.7870 | −0.785797 | ||||||||
\(226\) | −2.22139 | − | 3.84756i | −0.147765 | − | 0.255936i | ||||
\(227\) | 14.2481 | − | 24.6784i | 0.945679 | − | 1.63796i | 0.191292 | − | 0.981533i | \(-0.438732\pi\) |
0.754387 | − | 0.656430i | \(-0.227934\pi\) | |||||||
\(228\) | −10.0049 | + | 17.3290i | −0.662591 | + | 1.14764i | ||||
\(229\) | 12.5957 | + | 21.8164i | 0.832347 | + | 1.44167i | 0.896172 | + | 0.443707i | \(0.146337\pi\) |
−0.0638246 | + | 0.997961i | \(0.520330\pi\) | |||||||
\(230\) | −1.32664 | −0.0874759 | ||||||||
\(231\) | −6.35343 | + | 12.7616i | −0.418025 | + | 0.839650i | ||||
\(232\) | 1.15845 | 0.0760557 | ||||||||
\(233\) | 6.58123 | + | 11.3990i | 0.431151 | + | 0.746775i | 0.996973 | − | 0.0777524i | \(-0.0247744\pi\) |
−0.565822 | + | 0.824527i | \(0.691441\pi\) | |||||||
\(234\) | −5.65954 | + | 9.80260i | −0.369975 | + | 0.640816i | ||||
\(235\) | 2.30921 | − | 3.99967i | 0.150636 | − | 0.260910i | ||||
\(236\) | −4.59225 | − | 7.95401i | −0.298930 | − | 0.517762i | ||||
\(237\) | −2.05405 | −0.133425 | ||||||||
\(238\) | 10.1567 | + | 15.3258i | 0.658363 | + | 0.993423i | ||||
\(239\) | −8.78283 | −0.568114 | −0.284057 | − | 0.958807i | \(-0.591681\pi\) | ||||
−0.284057 | + | 0.958807i | \(0.591681\pi\) | |||||||
\(240\) | −1.70898 | − | 2.96005i | −0.110314 | − | 0.191070i | ||||
\(241\) | −0.763776 | + | 1.32290i | −0.0491992 | + | 0.0852154i | −0.889576 | − | 0.456787i | \(-0.849000\pi\) |
0.840377 | + | 0.542002i | \(0.182334\pi\) | |||||||
\(242\) | 3.31317 | − | 5.73857i | 0.212978 | − | 0.368890i | ||||
\(243\) | 11.0697 | + | 19.1732i | 0.710118 | + | 1.22996i | ||||
\(244\) | 12.0387 | 0.770698 | ||||||||
\(245\) | 9.21592 | − | 1.14245i | 0.588784 | − | 0.0729884i | ||||
\(246\) | −10.9865 | −0.700472 | ||||||||
\(247\) | −12.0825 | − | 20.9274i | −0.768789 | − | 1.33158i | ||||
\(248\) | 4.35694 | − | 7.54644i | 0.276666 | − | 0.479200i | ||||
\(249\) | −13.3646 | + | 23.1483i | −0.846950 | + | 1.46696i | ||||
\(250\) | 5.46577 | + | 9.46699i | 0.345686 | + | 0.598745i | ||||
\(251\) | 1.04230 | 0.0657895 | 0.0328947 | − | 0.999459i | \(-0.489527\pi\) | ||||
0.0328947 | + | 0.999459i | \(0.489527\pi\) | |||||||
\(252\) | −5.31707 | − | 8.02307i | −0.334944 | − | 0.505406i | ||||
\(253\) | −2.09133 | −0.131481 | ||||||||
\(254\) | −1.20600 | − | 2.08886i | −0.0756714 | − | 0.131067i | ||||
\(255\) | 11.8761 | − | 20.5699i | 0.743707 | − | 1.28814i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.38705 | + | 5.86654i | 0.211278 | + | 0.365944i | 0.952115 | − | 0.305741i | \(-0.0989041\pi\) |
−0.740837 | + | 0.671685i | \(0.765571\pi\) | |||||||
\(258\) | −21.5573 | −1.34210 | ||||||||
\(259\) | 3.90234 | − | 7.83828i | 0.242479 | − | 0.487047i | ||||
\(260\) | 4.12772 | 0.255991 | ||||||||
\(261\) | −2.10716 | − | 3.64972i | −0.130430 | − | 0.225912i | ||||
\(262\) | −0.761712 | + | 1.31932i | −0.0470588 | + | 0.0815082i | ||||
\(263\) | −0.228543 | + | 0.395849i | −0.0140926 | + | 0.0244091i | −0.872986 | − | 0.487746i | \(-0.837819\pi\) |
0.858893 | + | 0.512155i | \(0.171153\pi\) | |||||||
\(264\) | −2.69407 | − | 4.66626i | −0.165808 | − | 0.287189i | ||||
\(265\) | 5.62499 | 0.345540 | ||||||||
\(266\) | 20.5092 | − | 1.26636i | 1.25750 | − | 0.0776458i | ||||
\(267\) | 42.8783 | 2.62411 | ||||||||
\(268\) | 3.63160 | + | 6.29011i | 0.221835 | + | 0.384229i | ||||
\(269\) | −9.27674 | + | 16.0678i | −0.565613 | + | 0.979671i | 0.431379 | + | 0.902171i | \(0.358027\pi\) |
−0.996992 | + | 0.0775000i | \(0.975306\pi\) | |||||||
\(270\) | −1.09018 | + | 1.88825i | −0.0663465 | + | 0.114916i | ||||
\(271\) | −9.14545 | − | 15.8404i | −0.555546 | − | 0.962235i | −0.997861 | − | 0.0653746i | \(-0.979176\pi\) |
0.442314 | − | 0.896860i | \(-0.354158\pi\) | |||||||
\(272\) | −6.94919 | −0.421357 | ||||||||
\(273\) | 21.1688 | − | 1.30709i | 1.28120 | − | 0.0791088i | ||||
\(274\) | 9.62668 | 0.581569 | ||||||||
\(275\) | 3.38799 | + | 5.86817i | 0.204304 | + | 0.353864i | ||||
\(276\) | 1.28821 | − | 2.23124i | 0.0775410 | − | 0.134305i | ||||
\(277\) | −10.0783 | + | 17.4562i | −0.605548 | + | 1.04884i | 0.386416 | + | 0.922325i | \(0.373713\pi\) |
−0.991965 | + | 0.126516i | \(0.959620\pi\) | |||||||
\(278\) | −4.28838 | − | 7.42769i | −0.257200 | − | 0.445483i | ||||
\(279\) | −31.7004 | −1.89785 | ||||||||
\(280\) | −1.56431 | + | 3.14209i | −0.0934852 | + | 0.187776i | ||||
\(281\) | −7.27365 | −0.433909 | −0.216955 | − | 0.976182i | \(-0.569612\pi\) | ||||
−0.216955 | + | 0.976182i | \(0.569612\pi\) | |||||||
\(282\) | 4.48464 | + | 7.76762i | 0.267056 | + | 0.462555i | ||||
\(283\) | 1.38120 | − | 2.39231i | 0.0821038 | − | 0.142208i | −0.822050 | − | 0.569416i | \(-0.807169\pi\) |
0.904153 | + | 0.427208i | \(0.140503\pi\) | |||||||
\(284\) | 3.70854 | − | 6.42338i | 0.220061 | − | 0.381157i | ||||
\(285\) | −13.2729 | − | 22.9893i | −0.786217 | − | 1.36177i | ||||
\(286\) | 6.50701 | 0.384767 | ||||||||
\(287\) | 6.23250 | + | 9.40440i | 0.367893 | + | 0.555124i | ||||
\(288\) | 3.63791 | 0.214366 | ||||||||
\(289\) | −15.6456 | − | 27.0990i | −0.920331 | − | 1.59406i | ||||
\(290\) | −0.768419 | + | 1.33094i | −0.0451231 | + | 0.0781556i | ||||
\(291\) | −8.57689 | + | 14.8556i | −0.502786 | + | 0.870851i | ||||
\(292\) | 2.18402 | + | 3.78284i | 0.127810 | + | 0.221374i | ||||
\(293\) | 25.3756 | 1.48246 | 0.741228 | − | 0.671253i | \(-0.234244\pi\) | ||||
0.741228 | + | 0.671253i | \(0.234244\pi\) | |||||||
\(294\) | −7.02750 | + | 16.6094i | −0.409852 | + | 0.968680i | ||||
\(295\) | 12.1845 | 0.709409 | ||||||||
\(296\) | 1.65472 | + | 2.86606i | 0.0961787 | + | 0.166586i | ||||
\(297\) | −1.71858 | + | 2.97667i | −0.0997223 | + | 0.172724i | ||||
\(298\) | −8.01069 | + | 13.8749i | −0.464047 | + | 0.803753i | ||||
\(299\) | 1.55571 | + | 2.69457i | 0.0899690 | + | 0.155831i | ||||
\(300\) | −8.34767 | −0.481953 | ||||||||
\(301\) | 12.2292 | + | 18.4530i | 0.704879 | + | 1.06361i | ||||
\(302\) | −13.9358 | −0.801914 | ||||||||
\(303\) | −11.7984 | − | 20.4355i | −0.677802 | − | 1.17399i | ||||
\(304\) | −3.88326 | + | 6.72601i | −0.222720 | + | 0.385763i | ||||
\(305\) | −7.98549 | + | 13.8313i | −0.457248 | + | 0.791976i | ||||
\(306\) | 12.6403 | + | 21.8936i | 0.722597 | + | 1.25157i | ||||
\(307\) | −29.2469 | −1.66921 | −0.834606 | − | 0.550848i | \(-0.814304\pi\) | ||||
−0.834606 | + | 0.550848i | \(0.814304\pi\) | |||||||
\(308\) | −2.46600 | + | 4.95323i | −0.140513 | + | 0.282237i | ||||
\(309\) | 11.6766 | 0.664259 | ||||||||
\(310\) | 5.78008 | + | 10.0114i | 0.328287 | + | 0.568609i | ||||
\(311\) | −13.6414 | + | 23.6276i | −0.773534 | + | 1.33980i | 0.162081 | + | 0.986778i | \(0.448180\pi\) |
−0.935615 | + | 0.353023i | \(0.885154\pi\) | |||||||
\(312\) | −4.00815 | + | 6.94232i | −0.226917 | + | 0.393032i | ||||
\(313\) | −1.28838 | − | 2.23154i | −0.0728236 | − | 0.126134i | 0.827314 | − | 0.561739i | \(-0.189868\pi\) |
−0.900138 | + | 0.435605i | \(0.856534\pi\) | |||||||
\(314\) | −15.4227 | −0.870353 | ||||||||
\(315\) | 12.7446 | − | 0.786930i | 0.718079 | − | 0.0443385i | ||||
\(316\) | −0.797250 | −0.0448488 | ||||||||
\(317\) | 6.25323 | + | 10.8309i | 0.351216 | + | 0.608325i | 0.986463 | − | 0.163985i | \(-0.0524348\pi\) |
−0.635246 | + | 0.772310i | \(0.719101\pi\) | |||||||
\(318\) | −5.46204 | + | 9.46053i | −0.306296 | + | 0.530520i | ||||
\(319\) | −1.21135 | + | 2.09812i | −0.0678224 | + | 0.117472i | ||||
\(320\) | −0.663319 | − | 1.14890i | −0.0370806 | − | 0.0642256i | ||||
\(321\) | −31.7786 | −1.77371 | ||||||||
\(322\) | −2.64072 | + | 0.163054i | −0.147162 | + | 0.00908665i | ||||
\(323\) | −53.9711 | −3.00303 | ||||||||
\(324\) | 3.33966 | + | 5.78446i | 0.185537 | + | 0.321359i | ||||
\(325\) | 5.04055 | − | 8.73049i | 0.279599 | − | 0.484280i | ||||
\(326\) | 4.30693 | − | 7.45983i | 0.238539 | − | 0.413162i | ||||
\(327\) | 1.41682 | + | 2.45401i | 0.0783504 | + | 0.135707i | ||||
\(328\) | −4.26425 | −0.235454 | ||||||||
\(329\) | 4.10498 | − | 8.24532i | 0.226315 | − | 0.454579i | ||||
\(330\) | 7.14810 | 0.393490 | ||||||||
\(331\) | −1.36699 | − | 2.36769i | −0.0751363 | − | 0.130140i | 0.826009 | − | 0.563657i | \(-0.190606\pi\) |
−0.901146 | + | 0.433517i | \(0.857273\pi\) | |||||||
\(332\) | −5.18730 | + | 8.98468i | −0.284690 | + | 0.493098i | ||||
\(333\) | 6.01973 | − | 10.4265i | 0.329879 | − | 0.571368i | ||||
\(334\) | −5.98464 | − | 10.3657i | −0.327465 | − | 0.567186i | ||||
\(335\) | −9.63562 | −0.526450 | ||||||||
\(336\) | −3.76561 | − | 5.68204i | −0.205431 | − | 0.309981i | ||||
\(337\) | 12.4355 | 0.677405 | 0.338703 | − | 0.940893i | \(-0.390012\pi\) | ||||
0.338703 | + | 0.940893i | \(0.390012\pi\) | |||||||
\(338\) | 1.65954 | + | 2.87440i | 0.0902669 | + | 0.156347i | ||||
\(339\) | −5.72323 | + | 9.91292i | −0.310843 | + | 0.538396i | ||||
\(340\) | 4.60953 | − | 7.98394i | 0.249987 | − | 0.432990i | ||||
\(341\) | 9.11181 | + | 15.7821i | 0.493432 | + | 0.854649i | ||||
\(342\) | 28.2540 | 1.52780 | ||||||||
\(343\) | 18.2042 | − | 3.40680i | 0.982936 | − | 0.183950i | ||||
\(344\) | −8.36716 | −0.451127 | ||||||||
\(345\) | 1.70898 | + | 2.96005i | 0.0920086 | + | 0.159364i | ||||
\(346\) | 9.90984 | − | 17.1644i | 0.532756 | − | 0.922761i | ||||
\(347\) | −1.10374 | + | 1.91173i | −0.0592518 | + | 0.102627i | −0.894130 | − | 0.447808i | \(-0.852205\pi\) |
0.834878 | + | 0.550435i | \(0.185538\pi\) | |||||||
\(348\) | −1.49232 | − | 2.58477i | −0.0799967 | − | 0.138558i | ||||
\(349\) | 10.7710 | 0.576558 | 0.288279 | − | 0.957546i | \(-0.406917\pi\) | ||||
0.288279 | + | 0.957546i | \(0.406917\pi\) | |||||||
\(350\) | 4.73554 | + | 7.14559i | 0.253125 | + | 0.381948i | ||||
\(351\) | 5.11371 | 0.272950 | ||||||||
\(352\) | −1.04567 | − | 1.81115i | −0.0557342 | − | 0.0965344i | ||||
\(353\) | 6.94849 | − | 12.0351i | 0.369831 | − | 0.640566i | −0.619708 | − | 0.784832i | \(-0.712749\pi\) |
0.989539 | + | 0.144267i | \(0.0460823\pi\) | |||||||
\(354\) | −11.8315 | + | 20.4928i | −0.628839 | + | 1.08918i | ||||
\(355\) | 4.91989 | + | 8.52149i | 0.261120 | + | 0.452274i | ||||
\(356\) | 16.6426 | 0.882058 | ||||||||
\(357\) | 21.1115 | − | 42.4049i | 1.11734 | − | 2.24430i | ||||
\(358\) | −16.4096 | −0.867276 | ||||||||
\(359\) | 9.73350 | + | 16.8589i | 0.513714 | + | 0.889780i | 0.999873 | + | 0.0159091i | \(0.00506425\pi\) |
−0.486159 | + | 0.873870i | \(0.661602\pi\) | |||||||
\(360\) | −2.41310 | + | 4.17961i | −0.127181 | + | 0.220285i | ||||
\(361\) | −20.6595 | + | 35.7833i | −1.08734 | + | 1.88333i | ||||
\(362\) | 5.61532 | + | 9.72601i | 0.295135 | + | 0.511188i | ||||
\(363\) | −17.0722 | −0.896057 | ||||||||
\(364\) | 8.21639 | − | 0.507330i | 0.430656 | − | 0.0265913i | ||||
\(365\) | −5.79482 | −0.303315 | ||||||||
\(366\) | −15.5083 | − | 26.8612i | −0.810633 | − | 1.40406i | ||||
\(367\) | −8.59369 | + | 14.8847i | −0.448587 | + | 0.776976i | −0.998294 | − | 0.0583816i | \(-0.981406\pi\) |
0.549707 | + | 0.835357i | \(0.314739\pi\) | |||||||
\(368\) | 0.500000 | − | 0.866025i | 0.0260643 | − | 0.0451447i | ||||
\(369\) | 7.75648 | + | 13.4346i | 0.403786 | + | 0.699379i | ||||
\(370\) | −4.39043 | −0.228248 | ||||||||
\(371\) | 11.1967 | − | 0.691355i | 0.581306 | − | 0.0358934i | ||||
\(372\) | −22.4506 | −1.16401 | ||||||||
\(373\) | 4.71828 | + | 8.17231i | 0.244303 | + | 0.423146i | 0.961936 | − | 0.273276i | \(-0.0881074\pi\) |
−0.717632 | + | 0.696422i | \(0.754774\pi\) | |||||||
\(374\) | 7.26653 | − | 12.5860i | 0.375743 | − | 0.650806i | ||||
\(375\) | 14.0821 | − | 24.3909i | 0.727196 | − | 1.25954i | ||||
\(376\) | 1.74065 | + | 3.01490i | 0.0897672 | + | 0.155481i | ||||
\(377\) | 3.60441 | 0.185637 | ||||||||
\(378\) | −1.93797 | + | 3.89264i | −0.0996785 | + | 0.200216i | ||||
\(379\) | 6.99131 | 0.359120 | 0.179560 | − | 0.983747i | \(-0.442533\pi\) | ||||
0.179560 | + | 0.983747i | \(0.442533\pi\) | |||||||
\(380\) | −5.15168 | − | 8.92298i | −0.264276 | − | 0.457739i | ||||
\(381\) | −3.10716 | + | 5.38177i | −0.159185 | + | 0.275716i | ||||
\(382\) | −3.18402 | + | 5.51489i | −0.162909 | + | 0.282166i | ||||
\(383\) | −13.7705 | − | 23.8512i | −0.703640 | − | 1.21874i | −0.967180 | − | 0.254092i | \(-0.918223\pi\) |
0.263540 | − | 0.964649i | \(-0.415110\pi\) | |||||||
\(384\) | 2.57641 | 0.131477 | ||||||||
\(385\) | −4.05504 | − | 6.11876i | −0.206664 | − | 0.311841i | ||||
\(386\) | −14.0550 | −0.715380 | ||||||||
\(387\) | 15.2195 | + | 26.3609i | 0.773651 | + | 1.34000i | ||||
\(388\) | −3.32900 | + | 5.76600i | −0.169004 | + | 0.292724i | ||||
\(389\) | −3.35222 | + | 5.80621i | −0.169964 | + | 0.294386i | −0.938407 | − | 0.345532i | \(-0.887698\pi\) |
0.768443 | + | 0.639918i | \(0.221032\pi\) | |||||||
\(390\) | −5.31737 | − | 9.20995i | −0.269255 | − | 0.466364i | ||||
\(391\) | 6.94919 | 0.351436 | ||||||||
\(392\) | −2.72763 | + | 6.44671i | −0.137766 | + | 0.325608i | ||||
\(393\) | 3.92497 | 0.197989 | ||||||||
\(394\) | 3.47785 | + | 6.02381i | 0.175211 | + | 0.303475i | ||||
\(395\) | 0.528831 | − | 0.915962i | 0.0266084 | − | 0.0460871i | ||||
\(396\) | −3.80404 | + | 6.58879i | −0.191160 | + | 0.331099i | ||||
\(397\) | −11.3026 | − | 19.5767i | −0.567262 | − | 0.982527i | −0.996835 | − | 0.0794950i | \(-0.974669\pi\) |
0.429573 | − | 0.903032i | \(-0.358664\pi\) | |||||||
\(398\) | 21.0897 | 1.05713 | ||||||||
\(399\) | −29.2457 | − | 44.1297i | −1.46412 | − | 2.20925i | ||||
\(400\) | −3.24003 | −0.162002 | ||||||||
\(401\) | 4.85413 | + | 8.40761i | 0.242404 | + | 0.419856i | 0.961398 | − | 0.275160i | \(-0.0887308\pi\) |
−0.718995 | + | 0.695016i | \(0.755397\pi\) | |||||||
\(402\) | 9.35650 | − | 16.2059i | 0.466660 | − | 0.808278i | ||||
\(403\) | 13.5563 | − | 23.4801i | 0.675286 | − | 1.16963i | ||||
\(404\) | −4.57940 | − | 7.93175i | −0.227833 | − | 0.394619i | ||||
\(405\) | −8.86104 | −0.440309 | ||||||||
\(406\) | −1.36598 | + | 2.74373i | −0.0677927 | + | 0.136169i | ||||
\(407\) | −6.92114 | −0.343068 | ||||||||
\(408\) | 8.95200 | + | 15.5053i | 0.443190 | + | 0.767628i | ||||
\(409\) | 18.1680 | − | 31.4679i | 0.898350 | − | 1.55599i | 0.0687468 | − | 0.997634i | \(-0.478100\pi\) |
0.829603 | − | 0.558354i | \(-0.188567\pi\) | |||||||
\(410\) | 2.82856 | − | 4.89920i | 0.139692 | − | 0.241954i | ||||
\(411\) | −12.4012 | − | 21.4794i | −0.611704 | − | 1.05950i | ||||
\(412\) | 4.53211 | 0.223281 | ||||||||
\(413\) | 24.2537 | − | 1.49757i | 1.19345 | − | 0.0736906i | ||||
\(414\) | −3.63791 | −0.178794 | ||||||||
\(415\) | −6.88167 | − | 11.9194i | −0.337808 | − | 0.585101i | ||||
\(416\) | −1.55571 | + | 2.69457i | −0.0762749 | + | 0.132112i | ||||
\(417\) | −11.0486 | + | 19.1368i | −0.541055 | + | 0.937134i | ||||
\(418\) | −8.12119 | − | 14.0663i | −0.397220 | − | 0.688006i | ||||
\(419\) | 9.98642 | 0.487868 | 0.243934 | − | 0.969792i | \(-0.421562\pi\) | ||||
0.243934 | + | 0.969792i | \(0.421562\pi\) | |||||||
\(420\) | 9.02590 | − | 0.557314i | 0.440419 | − | 0.0271941i | ||||
\(421\) | 14.1053 | 0.687448 | 0.343724 | − | 0.939071i | \(-0.388312\pi\) | ||||
0.343724 | + | 0.939071i | \(0.388312\pi\) | |||||||
\(422\) | −13.2518 | − | 22.9528i | −0.645087 | − | 1.11732i | ||||
\(423\) | 6.33234 | − | 10.9679i | 0.307889 | − | 0.533279i | ||||
\(424\) | −2.12002 | + | 3.67198i | −0.102957 | + | 0.178327i | ||||
\(425\) | −11.2578 | − | 19.4991i | −0.546084 | − | 0.945845i | ||||
\(426\) | −19.1095 | −0.925857 | ||||||||
\(427\) | −14.1954 | + | 28.5131i | −0.686966 | + | 1.37985i | ||||
\(428\) | −12.3344 | −0.596207 | ||||||||
\(429\) | −8.38237 | − | 14.5187i | −0.404705 | − | 0.700969i | ||||
\(430\) | 5.55009 | − | 9.61304i | 0.267649 | − | 0.463582i | ||||
\(431\) | 1.77185 | − | 3.06893i | 0.0853468 | − | 0.147825i | −0.820192 | − | 0.572088i | \(-0.806134\pi\) |
0.905539 | + | 0.424263i | \(0.139467\pi\) | |||||||
\(432\) | −0.821765 | − | 1.42334i | −0.0395372 | − | 0.0684804i | ||||
\(433\) | −16.2680 | −0.781792 | −0.390896 | − | 0.920435i | \(-0.627835\pi\) | ||||
−0.390896 | + | 0.920435i | \(0.627835\pi\) | |||||||
\(434\) | 12.7360 | + | 19.2176i | 0.611345 | + | 0.922477i | ||||
\(435\) | 3.95953 | 0.189845 | ||||||||
\(436\) | 0.549920 | + | 0.952489i | 0.0263364 | + | 0.0456160i | ||||
\(437\) | 3.88326 | − | 6.72601i | 0.185762 | − | 0.321749i | ||||
\(438\) | 5.62695 | − | 9.74617i | 0.268866 | − | 0.465690i | ||||
\(439\) | −0.585013 | − | 1.01327i | −0.0279211 | − | 0.0483608i | 0.851727 | − | 0.523985i | \(-0.175555\pi\) |
−0.879648 | + | 0.475625i | \(0.842222\pi\) | |||||||
\(440\) | 2.77444 | 0.132266 | ||||||||
\(441\) | 25.2720 | − | 3.13283i | 1.20343 | − | 0.149182i | ||||
\(442\) | −21.6218 | −1.02845 | ||||||||
\(443\) | −19.5037 | − | 33.7813i | −0.926647 | − | 1.60500i | −0.788891 | − | 0.614533i | \(-0.789345\pi\) |
−0.137755 | − | 0.990466i | \(-0.543989\pi\) | |||||||
\(444\) | 4.26325 | − | 7.38416i | 0.202325 | − | 0.350437i | ||||
\(445\) | −11.0394 | + | 19.1208i | −0.523317 | + | 0.906411i | ||||
\(446\) | 4.90054 | + | 8.48799i | 0.232047 | + | 0.401918i | ||||
\(447\) | 41.2777 | 1.95237 | ||||||||
\(448\) | −1.46157 | − | 2.20541i | −0.0690527 | − | 0.104196i | ||||
\(449\) | 32.1714 | 1.51826 | 0.759130 | − | 0.650939i | \(-0.225624\pi\) | ||||
0.759130 | + | 0.650939i | \(0.225624\pi\) | |||||||
\(450\) | 5.89348 | + | 10.2078i | 0.277821 | + | 0.481201i | ||||
\(451\) | 4.45898 | − | 7.72318i | 0.209965 | − | 0.363670i | ||||
\(452\) | −2.22139 | + | 3.84756i | −0.104485 | + | 0.180974i | ||||
\(453\) | 17.9522 | + | 31.0941i | 0.843467 | + | 1.46093i | ||||
\(454\) | −28.4962 | −1.33739 | ||||||||
\(455\) | −4.86721 | + | 9.77635i | −0.228179 | + | 0.458322i | ||||
\(456\) | 20.0098 | 0.937045 | ||||||||
\(457\) | 17.1774 | + | 29.7521i | 0.803524 | + | 1.39174i | 0.917283 | + | 0.398236i | \(0.130377\pi\) |
−0.113759 | + | 0.993508i | \(0.536289\pi\) | |||||||
\(458\) | 12.5957 | − | 21.8164i | 0.588558 | − | 1.01941i | ||||
\(459\) | 5.71060 | − | 9.89105i | 0.266548 | − | 0.461675i | ||||
\(460\) | 0.663319 | + | 1.14890i | 0.0309274 | + | 0.0535678i | ||||
\(461\) | 10.5155 | 0.489756 | 0.244878 | − | 0.969554i | \(-0.421252\pi\) | ||||
0.244878 | + | 0.969554i | \(0.421252\pi\) | |||||||
\(462\) | 14.2286 | − | 0.878558i | 0.661973 | − | 0.0408742i | ||||
\(463\) | −19.9943 | −0.929213 | −0.464606 | − | 0.885517i | \(-0.653804\pi\) | ||||
−0.464606 | + | 0.885517i | \(0.653804\pi\) | |||||||
\(464\) | −0.579223 | − | 1.00324i | −0.0268898 | − | 0.0465744i | ||||
\(465\) | 14.8919 | − | 25.7935i | 0.690595 | − | 1.19615i | ||||
\(466\) | 6.58123 | − | 11.3990i | 0.304870 | − | 0.528050i | ||||
\(467\) | 13.7321 | + | 23.7848i | 0.635448 | + | 1.10063i | 0.986420 | + | 0.164242i | \(0.0525177\pi\) |
−0.350973 | + | 0.936386i | \(0.614149\pi\) | |||||||
\(468\) | 11.3191 | 0.523224 | ||||||||
\(469\) | −19.1801 | + | 1.18429i | −0.885653 | + | 0.0546856i | ||||
\(470\) | −4.61843 | −0.213032 | ||||||||
\(471\) | 19.8676 | + | 34.4117i | 0.915452 | + | 1.58561i | ||||
\(472\) | −4.59225 | + | 7.95401i | −0.211375 | + | 0.366113i | ||||
\(473\) | 8.74925 | − | 15.1541i | 0.402291 | − | 0.696788i | ||||
\(474\) | 1.02702 | + | 1.77886i | 0.0471728 | + | 0.0817056i | ||||
\(475\) | −25.1638 | −1.15459 | ||||||||
\(476\) | 8.19415 | − | 16.4589i | 0.375578 | − | 0.754391i | ||||
\(477\) | 15.4249 | 0.706257 | ||||||||
\(478\) | 4.39142 | + | 7.60616i | 0.200859 | + | 0.347898i | ||||
\(479\) | 4.22275 | − | 7.31402i | 0.192943 | − | 0.334186i | −0.753282 | − | 0.657698i | \(-0.771530\pi\) |
0.946224 | + | 0.323512i | \(0.104864\pi\) | |||||||
\(480\) | −1.70898 | + | 2.96005i | −0.0780041 | + | 0.135107i | ||||
\(481\) | 5.14853 | + | 8.91751i | 0.234753 | + | 0.406604i | ||||
\(482\) | 1.52755 | 0.0695781 | ||||||||
\(483\) | 3.76561 | + | 5.68204i | 0.171341 | + | 0.258542i | ||||
\(484\) | −6.62633 | −0.301197 | ||||||||
\(485\) | −4.41638 | − | 7.64939i | −0.200537 | − | 0.347341i | ||||
\(486\) | 11.0697 | − | 19.1732i | 0.502130 | − | 0.869714i | ||||
\(487\) | −16.6395 | + | 28.8205i | −0.754009 | + | 1.30598i | 0.191856 | + | 0.981423i | \(0.438549\pi\) |
−0.945865 | + | 0.324559i | \(0.894784\pi\) | |||||||
\(488\) | −6.01934 | − | 10.4258i | −0.272483 | − | 0.471954i | ||||
\(489\) | −22.1929 | −1.00360 | ||||||||
\(490\) | −5.59735 | − | 7.41000i | −0.252862 | − | 0.334750i | ||||
\(491\) | 15.8532 | 0.715444 | 0.357722 | − | 0.933828i | \(-0.383553\pi\) | ||||
0.357722 | + | 0.933828i | \(0.383553\pi\) | |||||||
\(492\) | 5.49324 | + | 9.51457i | 0.247654 | + | 0.428950i | ||||
\(493\) | 4.02513 | − | 6.97173i | 0.181283 | − | 0.313991i | ||||
\(494\) | −12.0825 | + | 20.9274i | −0.543616 | + | 0.941570i | ||||
\(495\) | −5.04658 | − | 8.74094i | −0.226827 | − | 0.392876i | ||||
\(496\) | −8.71388 | −0.391265 | ||||||||
\(497\) | 10.8406 | + | 16.3577i | 0.486266 | + | 0.733742i | ||||
\(498\) | 26.7293 | 1.19777 | ||||||||
\(499\) | 9.66615 | + | 16.7423i | 0.432717 | + | 0.749487i | 0.997106 | − | 0.0760215i | \(-0.0242218\pi\) |
−0.564390 | + | 0.825509i | \(0.690888\pi\) | |||||||
\(500\) | 5.46577 | − | 9.46699i | 0.244437 | − | 0.423377i | ||||
\(501\) | −15.4189 | + | 26.7063i | −0.688866 | + | 1.19315i | ||||
\(502\) | −0.521150 | − | 0.902659i | −0.0232601 | − | 0.0402876i | ||||
\(503\) | 40.9220 | 1.82462 | 0.912310 | − | 0.409500i | \(-0.134297\pi\) | ||||
0.912310 | + | 0.409500i | \(0.134297\pi\) | |||||||
\(504\) | −4.28965 | + | 8.61625i | −0.191076 | + | 0.383798i | ||||
\(505\) | 12.1504 | 0.540686 | ||||||||
\(506\) | 1.04567 | + | 1.81115i | 0.0464855 | + | 0.0805152i | ||||
\(507\) | 4.27565 | − | 7.40565i | 0.189888 | − | 0.328897i | ||||
\(508\) | −1.20600 | + | 2.08886i | −0.0535077 | + | 0.0926781i | ||||
\(509\) | −0.260911 | − | 0.451912i | −0.0115647 | − | 0.0200306i | 0.860185 | − | 0.509982i | \(-0.170348\pi\) |
−0.871750 | + | 0.489951i | \(0.837015\pi\) | |||||||
\(510\) | −23.7521 | −1.05176 | ||||||||
\(511\) | −11.5348 | + | 0.712228i | −0.510270 | + | 0.0315071i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.38226 | − | 11.0544i | −0.281784 | − | 0.488064i | ||||
\(514\) | 3.38705 | − | 5.86654i | 0.149396 | − | 0.258762i | ||||
\(515\) | −3.00623 | + | 5.20695i | −0.132471 | + | 0.229446i | ||||
\(516\) | 10.7786 | + | 18.6691i | 0.474503 | + | 0.821863i | ||||
\(517\) | −7.28055 | −0.320198 | ||||||||
\(518\) | −8.73932 | + | 0.539618i | −0.383983 | + | 0.0237095i | ||||
\(519\) | −51.0637 | −2.24145 | ||||||||
\(520\) | −2.06386 | − | 3.57471i | −0.0905063 | − | 0.156762i | ||||
\(521\) | −6.14887 | + | 10.6502i | −0.269387 | + | 0.466592i | −0.968704 | − | 0.248220i | \(-0.920154\pi\) |
0.699317 | + | 0.714812i | \(0.253488\pi\) | |||||||
\(522\) | −2.10716 | + | 3.64972i | −0.0922281 | + | 0.159744i | ||||
\(523\) | −15.6891 | − | 27.1742i | −0.686034 | − | 1.18825i | −0.973111 | − | 0.230339i | \(-0.926017\pi\) |
0.287076 | − | 0.957908i | \(-0.407317\pi\) | |||||||
\(524\) | 1.52342 | 0.0665511 | ||||||||
\(525\) | 9.84317 | − | 19.7711i | 0.429591 | − | 0.862882i | ||||
\(526\) | 0.457086 | 0.0199299 | ||||||||
\(527\) | −30.2772 | − | 52.4417i | −1.31890 | − | 2.28440i | ||||
\(528\) | −2.69407 | + | 4.66626i | −0.117244 | + | 0.203073i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −2.81249 | − | 4.87138i | −0.122167 | − | 0.211599i | ||||
\(531\) | 33.4124 | 1.44997 | ||||||||
\(532\) | −11.3513 | − | 17.1283i | −0.492142 | − | 0.742608i | ||||
\(533\) | −13.2679 | −0.574695 | ||||||||
\(534\) | −21.4392 | − | 37.1337i | −0.927764 | − | 1.60693i | ||||
\(535\) | 8.18166 | − | 14.1711i | 0.353724 | − | 0.612668i | ||||
\(536\) | 3.63160 | − | 6.29011i | 0.156861 | − | 0.271691i | ||||
\(537\) | 21.1390 | + | 36.6138i | 0.912215 | + | 1.58000i | ||||
\(538\) | 18.5535 | 0.799898 | ||||||||
\(539\) | −8.82375 | − | 11.6812i | −0.380066 | − | 0.503146i | ||||
\(540\) | 2.18037 | 0.0938281 | ||||||||
\(541\) | −0.375985 | − | 0.651226i | −0.0161649 | − | 0.0279984i | 0.857830 | − | 0.513934i | \(-0.171812\pi\) |
−0.873995 | + | 0.485935i | \(0.838479\pi\) | |||||||
\(542\) | −9.14545 | + | 15.8404i | −0.392831 | + | 0.680403i | ||||
\(543\) | 14.4674 | − | 25.0582i | 0.620855 | − | 1.07535i | ||||
\(544\) | 3.47460 | + | 6.01818i | 0.148972 | + | 0.258027i | ||||
\(545\) | −1.45909 | −0.0625005 | ||||||||
\(546\) | −11.7164 | − | 17.6792i | −0.501415 | − | 0.756600i | ||||
\(547\) | −27.3113 | −1.16775 | −0.583874 | − | 0.811844i | \(-0.698464\pi\) | ||||
−0.583874 | + | 0.811844i | \(0.698464\pi\) | |||||||
\(548\) | −4.81334 | − | 8.33695i | −0.205616 | − | 0.356137i | ||||
\(549\) | −21.8979 | + | 37.9282i | −0.934578 | + | 1.61874i | ||||
\(550\) | 3.38799 | − | 5.86817i | 0.144464 | − | 0.250220i | ||||
\(551\) | −4.49855 | − | 7.79172i | −0.191645 | − | 0.331939i | ||||
\(552\) | −2.57641 | −0.109660 | ||||||||
\(553\) | 0.940079 | − | 1.88825i | 0.0399762 | − | 0.0802968i | ||||
\(554\) | 20.1567 | 0.856375 | ||||||||
\(555\) | 5.65578 | + | 9.79610i | 0.240075 | + | 0.415821i | ||||
\(556\) | −4.28838 | + | 7.42769i | −0.181868 | + | 0.315004i | ||||
\(557\) | −14.6243 | + | 25.3300i | −0.619650 | + | 1.07327i | 0.369899 | + | 0.929072i | \(0.379392\pi\) |
−0.989549 | + | 0.144194i | \(0.953941\pi\) | |||||||
\(558\) | 15.8502 | + | 27.4533i | 0.670992 | + | 1.16219i | ||||
\(559\) | −26.0337 | −1.10111 | ||||||||
\(560\) | 3.50328 | − | 0.216314i | 0.148041 | − | 0.00914092i | ||||
\(561\) | −37.4432 | −1.58085 | ||||||||
\(562\) | 3.63682 | + | 6.29916i | 0.153410 | + | 0.265714i | ||||
\(563\) | −0.257258 | + | 0.445584i | −0.0108421 | + | 0.0187791i | −0.871396 | − | 0.490581i | \(-0.836785\pi\) |
0.860553 | + | 0.509360i | \(0.170118\pi\) | |||||||
\(564\) | 4.48464 | − | 7.76762i | 0.188837 | − | 0.327076i | ||||
\(565\) | −2.94698 | − | 5.10432i | −0.123980 | − | 0.214740i | ||||
\(566\) | −2.76240 | −0.116112 | ||||||||
\(567\) | −17.6382 | + | 1.08909i | −0.740736 | + | 0.0457375i | ||||
\(568\) | −7.41708 | −0.311214 | ||||||||
\(569\) | −16.9002 | − | 29.2720i | −0.708493 | − | 1.22715i | −0.965416 | − | 0.260714i | \(-0.916042\pi\) |
0.256923 | − | 0.966432i | \(-0.417291\pi\) | |||||||
\(570\) | −13.2729 | + | 22.9893i | −0.555940 | + | 0.962915i | ||||
\(571\) | 6.69143 | − | 11.5899i | 0.280028 | − | 0.485022i | −0.691364 | − | 0.722507i | \(-0.742990\pi\) |
0.971391 | + | 0.237485i | \(0.0763230\pi\) | |||||||
\(572\) | −3.25350 | − | 5.63523i | −0.136036 | − | 0.235621i | ||||
\(573\) | 16.4067 | 0.685401 | ||||||||
\(574\) | 5.02820 | − | 10.0997i | 0.209873 | − | 0.421553i | ||||
\(575\) | 3.24003 | 0.135119 | ||||||||
\(576\) | −1.81896 | − | 3.15053i | −0.0757899 | − | 0.131272i | ||||
\(577\) | 18.3241 | − | 31.7382i | 0.762842 | − | 1.32128i | −0.178538 | − | 0.983933i | \(-0.557137\pi\) |
0.941380 | − | 0.337348i | \(-0.109530\pi\) | |||||||
\(578\) | −15.6456 | + | 27.0990i | −0.650772 | + | 1.12717i | ||||
\(579\) | 18.1057 | + | 31.3601i | 0.752449 | + | 1.30328i | ||||
\(580\) | 1.53684 | 0.0638137 | ||||||||
\(581\) | −15.1632 | − | 22.8802i | −0.629076 | − | 0.949231i | ||||
\(582\) | 17.1538 | 0.711047 | ||||||||
\(583\) | −4.43366 | − | 7.67932i | −0.183623 | − | 0.318045i | ||||
\(584\) | 2.18402 | − | 3.78284i | 0.0903756 | − | 0.156535i | ||||
\(585\) | −7.50815 | + | 13.0045i | −0.310424 | + | 0.537670i | ||||
\(586\) | −12.6878 | − | 21.9759i | −0.524127 | − | 0.907815i | ||||
\(587\) | −10.8300 | −0.447003 | −0.223502 | − | 0.974704i | \(-0.571749\pi\) | ||||
−0.223502 | + | 0.974704i | \(0.571749\pi\) | |||||||
\(588\) | 17.8979 | − | 2.21871i | 0.738097 | − | 0.0914980i | ||||
\(589\) | −67.6766 | −2.78857 | ||||||||
\(590\) | −6.09225 | − | 10.5521i | −0.250814 | − | 0.434422i | ||||
\(591\) | 8.96038 | − | 15.5198i | 0.368581 | − | 0.638401i | ||||
\(592\) | 1.65472 | − | 2.86606i | 0.0680086 | − | 0.117794i | ||||
\(593\) | 3.90397 | + | 6.76187i | 0.160317 | + | 0.277677i | 0.934982 | − | 0.354694i | \(-0.115415\pi\) |
−0.774665 | + | 0.632371i | \(0.782082\pi\) | |||||||
\(594\) | 3.43717 | 0.141029 | ||||||||
\(595\) | 13.4743 | + | 20.3318i | 0.552392 | + | 0.833521i | ||||
\(596\) | 16.0214 | 0.656261 | ||||||||
\(597\) | −27.1679 | − | 47.0563i | −1.11191 | − | 1.92588i | ||||
\(598\) | 1.55571 | − | 2.69457i | 0.0636177 | − | 0.110189i | ||||
\(599\) | 17.3699 | − | 30.0856i | 0.709715 | − | 1.22926i | −0.255248 | − | 0.966876i | \(-0.582157\pi\) |
0.964963 | − | 0.262387i | \(-0.0845097\pi\) | |||||||
\(600\) | 4.17383 | + | 7.22929i | 0.170396 | + | 0.295135i | ||||
\(601\) | −33.4939 | −1.36625 | −0.683123 | − | 0.730303i | \(-0.739379\pi\) | ||||
−0.683123 | + | 0.730303i | \(0.739379\pi\) | |||||||
\(602\) | 9.86615 | − | 19.8173i | 0.402114 | − | 0.807692i | ||||
\(603\) | −26.4229 | −1.07602 | ||||||||
\(604\) | 6.96789 | + | 12.0687i | 0.283519 | + | 0.491070i | ||||
\(605\) | 4.39537 | − | 7.61301i | 0.178697 | − | 0.309513i | ||||
\(606\) | −11.7984 | + | 20.4355i | −0.479278 | + | 0.830134i | ||||
\(607\) | 16.5199 | + | 28.6134i | 0.670523 | + | 1.16138i | 0.977756 | + | 0.209746i | \(0.0672637\pi\) |
−0.307233 | + | 0.951634i | \(0.599403\pi\) | |||||||
\(608\) | 7.76653 | 0.314974 | ||||||||
\(609\) | 7.88160 | − | 0.486658i | 0.319379 | − | 0.0197204i | ||||
\(610\) | 15.9710 | 0.646646 | ||||||||
\(611\) | 5.41589 | + | 9.38060i | 0.219104 | + | 0.379499i | ||||
\(612\) | 12.6403 | − | 21.8936i | 0.510953 | − | 0.884996i | ||||
\(613\) | −0.172305 | + | 0.298441i | −0.00695934 | + | 0.0120539i | −0.869484 | − | 0.493961i | \(-0.835549\pi\) |
0.862525 | + | 0.506015i | \(0.168882\pi\) | |||||||
\(614\) | 14.6235 | + | 25.3286i | 0.590155 | + | 1.02218i | ||||
\(615\) | −14.5751 | −0.587723 | ||||||||
\(616\) | 5.52262 | − | 0.341000i | 0.222513 | − | 0.0137393i | ||||
\(617\) | 18.8997 | 0.760872 | 0.380436 | − | 0.924807i | \(-0.375774\pi\) | ||||
0.380436 | + | 0.924807i | \(0.375774\pi\) | |||||||
\(618\) | −5.83830 | − | 10.1122i | −0.234851 | − | 0.406774i | ||||
\(619\) | −11.2136 | + | 19.4225i | −0.450712 | + | 0.780656i | −0.998430 | − | 0.0560067i | \(-0.982163\pi\) |
0.547718 | + | 0.836663i | \(0.315497\pi\) | |||||||
\(620\) | 5.78008 | − | 10.0114i | 0.232134 | − | 0.402067i | ||||
\(621\) | 0.821765 | + | 1.42334i | 0.0329763 | + | 0.0571166i | ||||
\(622\) | 27.2828 | 1.09394 | ||||||||
\(623\) | −19.6242 | + | 39.4174i | −0.786227 | + | 1.57923i | ||||
\(624\) | 8.01631 | 0.320909 | ||||||||
\(625\) | −0.848991 | − | 1.47050i | −0.0339596 | − | 0.0588198i | ||||
\(626\) | −1.28838 | + | 2.23154i | −0.0514940 | + | 0.0891903i | ||||
\(627\) | −20.9236 | + | 36.2407i | −0.835606 | + | 1.44731i | ||||
\(628\) | 7.71135 | + | 13.3564i | 0.307716 | + | 0.532980i | ||||
\(629\) | 22.9979 | 0.916988 | ||||||||
\(630\) | −7.05382 | − | 10.6437i | −0.281031 | − | 0.424056i | ||||
\(631\) | 45.9749 | 1.83023 | 0.915117 | − | 0.403189i | \(-0.132098\pi\) | ||||
0.915117 | + | 0.403189i | \(0.132098\pi\) | |||||||
\(632\) | 0.398625 | + | 0.690439i | 0.0158565 | + | 0.0274642i | ||||
\(633\) | −34.1421 | + | 59.1358i | −1.35703 | + | 2.35044i | ||||
\(634\) | 6.25323 | − | 10.8309i | 0.248348 | − | 0.430151i | ||||
\(635\) | −1.59993 | − | 2.77116i | −0.0634912 | − | 0.109970i | ||||
\(636\) | 10.9241 | 0.433168 | ||||||||
\(637\) | −8.48679 | + | 20.0584i | −0.336259 | + | 0.794743i | ||||
\(638\) | 2.42270 | 0.0959154 | ||||||||
\(639\) | 13.4913 | + | 23.3677i | 0.533709 | + | 0.924412i | ||||
\(640\) | −0.663319 | + | 1.14890i | −0.0262200 | + | 0.0454143i | ||||
\(641\) | 5.92284 | − | 10.2587i | 0.233938 | − | 0.405193i | −0.725025 | − | 0.688722i | \(-0.758172\pi\) |
0.958964 | + | 0.283529i | \(0.0915053\pi\) | |||||||
\(642\) | 15.8893 | + | 27.5211i | 0.627101 | + | 1.08617i | ||||
\(643\) | 40.7199 | 1.60584 | 0.802918 | − | 0.596089i | \(-0.203280\pi\) | ||||
0.802918 | + | 0.596089i | \(0.203280\pi\) | |||||||
\(644\) | 1.46157 | + | 2.20541i | 0.0575939 | + | 0.0869051i | ||||
\(645\) | −28.5987 | −1.12607 | ||||||||
\(646\) | 26.9855 | + | 46.7403i | 1.06173 | + | 1.83897i | ||||
\(647\) | −0.360840 | + | 0.624994i | −0.0141861 | + | 0.0245710i | −0.873031 | − | 0.487664i | \(-0.837849\pi\) |
0.858845 | + | 0.512235i | \(0.171182\pi\) | |||||||
\(648\) | 3.33966 | − | 5.78446i | 0.131194 | − | 0.227235i | ||||
\(649\) | −9.60391 | − | 16.6345i | −0.376986 | − | 0.652960i | ||||
\(650\) | −10.0811 | −0.395413 | ||||||||
\(651\) | 26.4726 | − | 53.1733i | 1.03754 | − | 2.08403i | ||||
\(652\) | −8.61387 | −0.337345 | ||||||||
\(653\) | 0.373131 | + | 0.646282i | 0.0146018 | + | 0.0252910i | 0.873234 | − | 0.487301i | \(-0.162019\pi\) |
−0.858632 | + | 0.512592i | \(0.828685\pi\) | |||||||
\(654\) | 1.41682 | − | 2.45401i | 0.0554021 | − | 0.0959593i | ||||
\(655\) | −1.01052 | + | 1.75027i | −0.0394841 | + | 0.0683885i | ||||
\(656\) | 2.13212 | + | 3.69295i | 0.0832455 | + | 0.144185i | ||||
\(657\) | −15.8906 | −0.619951 | ||||||||
\(658\) | −9.19315 | + | 0.567641i | −0.358386 | + | 0.0221289i | ||||
\(659\) | 6.85325 | 0.266965 | 0.133482 | − | 0.991051i | \(-0.457384\pi\) | ||||
0.133482 | + | 0.991051i | \(0.457384\pi\) | |||||||
\(660\) | −3.57405 | − | 6.19044i | −0.139120 | − | 0.240963i | ||||
\(661\) | −16.8918 | + | 29.2575i | −0.657016 | + | 1.13798i | 0.324369 | + | 0.945931i | \(0.394848\pi\) |
−0.981384 | + | 0.192054i | \(0.938485\pi\) | |||||||
\(662\) | −1.36699 | + | 2.36769i | −0.0531294 | + | 0.0920228i | ||||
\(663\) | 27.8534 | + | 48.2435i | 1.08174 | + | 1.87362i | ||||
\(664\) | 10.3746 | 0.402613 | ||||||||
\(665\) | 27.2083 | − | 1.68001i | 1.05509 | − | 0.0651478i | ||||
\(666\) | −12.0395 | −0.466520 | ||||||||
\(667\) | 0.579223 | + | 1.00324i | 0.0224276 | + | 0.0388458i | ||||
\(668\) | −5.98464 | + | 10.3657i | −0.231553 | + | 0.401061i | ||||
\(669\) | 12.6258 | − | 21.8686i | 0.488143 | − | 0.845488i | ||||
\(670\) | 4.81781 | + | 8.34469i | 0.186128 | + | 0.322384i | ||||
\(671\) | 25.1769 | 0.971943 | ||||||||
\(672\) | −3.03798 | + | 6.10213i | −0.117193 | + | 0.235395i | ||||
\(673\) | 32.6054 | 1.25684 | 0.628422 | − | 0.777873i | \(-0.283701\pi\) | ||||
0.628422 | + | 0.777873i | \(0.283701\pi\) | |||||||
\(674\) | −6.21775 | − | 10.7695i | −0.239499 | − | 0.414824i | ||||
\(675\) | 2.66255 | − | 4.61167i | 0.102481 | − | 0.177503i | ||||
\(676\) | 1.65954 | − | 2.87440i | 0.0638283 | − | 0.110554i | ||||
\(677\) | −12.5764 | − | 21.7829i | −0.483349 | − | 0.837184i | 0.516469 | − | 0.856306i | \(-0.327246\pi\) |
−0.999817 | + | 0.0191219i | \(0.993913\pi\) | |||||||
\(678\) | 11.4465 | 0.439598 | ||||||||
\(679\) | −9.73114 | − | 14.6836i | −0.373447 | − | 0.563505i | ||||
\(680\) | −9.21906 | −0.353535 | ||||||||
\(681\) | 36.7090 | + | 63.5818i | 1.40669 | + | 2.43646i | ||||
\(682\) | 9.11181 | − | 15.7821i | 0.348909 | − | 0.604328i | ||||
\(683\) | 16.8507 | − | 29.1863i | 0.644776 | − | 1.11678i | −0.339578 | − | 0.940578i | \(-0.610284\pi\) |
0.984353 | − | 0.176206i | \(-0.0563825\pi\) | |||||||
\(684\) | −14.1270 | − | 24.4686i | −0.540159 | − | 0.935582i | ||||
\(685\) | 12.7711 | 0.487959 | ||||||||
\(686\) | −12.0525 | − | 14.0619i | −0.460166 | − | 0.536887i | ||||
\(687\) | −64.9035 | −2.47622 | ||||||||
\(688\) | 4.18358 | + | 7.24617i | 0.159497 | + | 0.276258i | ||||
\(689\) | −6.59626 | + | 11.4251i | −0.251297 | + | 0.435260i | ||||
\(690\) | 1.70898 | − | 2.96005i | 0.0650599 | − | 0.112687i | ||||
\(691\) | −12.5502 | − | 21.7376i | −0.477431 | − | 0.826935i | 0.522234 | − | 0.852802i | \(-0.325099\pi\) |
−0.999665 | + | 0.0258668i | \(0.991765\pi\) | |||||||
\(692\) | −19.8197 | −0.753431 | ||||||||
\(693\) | −11.1197 | − | 16.7789i | −0.422404 | − | 0.637378i | ||||
\(694\) | 2.20748 | 0.0837947 | ||||||||
\(695\) | −5.68913 | − | 9.85385i | −0.215801 | − | 0.373778i | ||||
\(696\) | −1.49232 | + | 2.58477i | −0.0565662 | + | 0.0979756i | ||||
\(697\) | −14.8165 | + | 25.6630i | −0.561216 | + | 0.972055i | ||||
\(698\) | −5.38550 | − | 9.32796i | −0.203844 | − | 0.353069i | ||||
\(699\) | −33.9120 | −1.28267 | ||||||||
\(700\) | 3.82049 | − | 7.67389i | 0.144401 | − | 0.290046i | ||||
\(701\) | −32.8099 | −1.23921 | −0.619607 | − | 0.784912i | \(-0.712708\pi\) | ||||
−0.619607 | + | 0.784912i | \(0.712708\pi\) | |||||||
\(702\) | −2.55686 | − | 4.42860i | −0.0965023 | − | 0.167147i | ||||
\(703\) | 12.8514 | − | 22.2593i | 0.484701 | − | 0.839527i | ||||
\(704\) | −1.04567 | + | 1.81115i | −0.0394100 | + | 0.0682601i | ||||
\(705\) | 5.94949 | + | 10.3048i | 0.224071 | + | 0.388102i | ||||
\(706\) | −13.8970 | −0.523020 | ||||||||
\(707\) | 24.1858 | − | 1.49338i | 0.909602 | − | 0.0561643i | ||||
\(708\) | 23.6631 | 0.889313 | ||||||||
\(709\) | 9.54605 | + | 16.5343i | 0.358510 | + | 0.620957i | 0.987712 | − | 0.156285i | \(-0.0499517\pi\) |
−0.629202 | + | 0.777241i | \(0.716618\pi\) | |||||||
\(710\) | 4.91989 | − | 8.52149i | 0.184640 | − | 0.319806i | ||||
\(711\) | 1.45016 | − | 2.51176i | 0.0543854 | − | 0.0941983i | ||||
\(712\) | −8.32132 | − | 14.4129i | −0.311855 | − | 0.540148i | ||||
\(713\) | 8.71388 | 0.326338 | ||||||||
\(714\) | −47.2795 | + | 2.91932i | −1.76939 | + | 0.109253i | ||||
\(715\) | 8.63244 | 0.322835 | ||||||||
\(716\) | 8.20481 | + | 14.2112i | 0.306628 | + | 0.531096i | ||||
\(717\) | 11.3141 | − | 19.5966i | 0.422533 | − | 0.731849i | ||||
\(718\) | 9.73350 | − | 16.8589i | 0.363251 | − | 0.629169i | ||||
\(719\) | −10.5225 | − | 18.2254i | −0.392421 | − | 0.679693i | 0.600347 | − | 0.799740i | \(-0.295029\pi\) |
−0.992768 | + | 0.120046i | \(0.961696\pi\) | |||||||
\(720\) | 4.82619 | 0.179862 | ||||||||
\(721\) | −5.34405 | + | 10.7341i | −0.199023 | + | 0.399760i | ||||
\(722\) | 41.3190 | 1.53773 | ||||||||
\(723\) | −1.96780 | − | 3.40834i | −0.0731834 | − | 0.126757i | ||||
\(724\) | 5.61532 | − | 9.72601i | 0.208692 | − | 0.361464i | ||||
\(725\) | 1.87670 | − | 3.25054i | 0.0696990 | − | 0.120722i | ||||
\(726\) | 8.53609 | + | 14.7849i | 0.316804 | + | 0.548721i | ||||
\(727\) | 11.6826 | 0.433282 | 0.216641 | − | 0.976251i | \(-0.430490\pi\) | ||||
0.216641 | + | 0.976251i | \(0.430490\pi\) | |||||||
\(728\) | −4.54756 | − | 6.86194i | −0.168544 | − | 0.254320i | ||||
\(729\) | −37.0021 | −1.37045 | ||||||||
\(730\) | 2.89741 | + | 5.01846i | 0.107238 | + | 0.185741i | ||||
\(731\) | −29.0725 | + | 50.3550i | −1.07528 | + | 1.86245i | ||||
\(732\) | −15.5083 | + | 26.8612i | −0.573204 | + | 0.992819i | ||||
\(733\) | 12.1238 | + | 20.9990i | 0.447802 | + | 0.775615i | 0.998243 | − | 0.0592589i | \(-0.0188737\pi\) |
−0.550441 | + | 0.834874i | \(0.685540\pi\) | |||||||
\(734\) | 17.1874 | 0.634398 | ||||||||
\(735\) | −9.32294 | + | 22.0346i | −0.343882 | + | 0.812760i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 7.59487 | + | 13.1547i | 0.279761 | + | 0.484560i | ||||
\(738\) | 7.75648 | − | 13.4346i | 0.285520 | − | 0.494535i | ||||
\(739\) | 13.5595 | − | 23.4857i | 0.498793 | − | 0.863935i | −0.501206 | − | 0.865328i | \(-0.667110\pi\) |
0.999999 | + | 0.00139329i | \(0.000443498\pi\) | |||||||
\(740\) | 2.19521 | + | 3.80222i | 0.0806977 | + | 0.139773i | ||||
\(741\) | 62.2589 | 2.28714 | ||||||||
\(742\) | −6.19711 | − | 9.35099i | −0.227503 | − | 0.343286i | ||||
\(743\) | −10.3281 | −0.378902 | −0.189451 | − | 0.981890i | \(-0.560671\pi\) | ||||
−0.189451 | + | 0.981890i | \(0.560671\pi\) | |||||||
\(744\) | 11.2253 | + | 19.4428i | 0.411539 | + | 0.712807i | ||||
\(745\) | −10.6273 | + | 18.4070i | −0.389353 | + | 0.674380i | ||||
\(746\) | 4.71828 | − | 8.17231i | 0.172749 | − | 0.299209i | ||||
\(747\) | −18.8710 | − | 32.6855i | −0.690453 | − | 1.19590i | ||||
\(748\) | −14.5331 | −0.531381 | ||||||||
\(749\) | 14.5442 | − | 29.2136i | 0.531433 | − | 1.06744i | ||||
\(750\) | −28.1642 | −1.02841 | ||||||||
\(751\) | 5.15333 | + | 8.92583i | 0.188048 | + | 0.325708i | 0.944599 | − | 0.328226i | \(-0.106451\pi\) |
−0.756552 | + | 0.653934i | \(0.773117\pi\) | |||||||
\(752\) | 1.74065 | − | 3.01490i | 0.0634750 | − | 0.109942i | ||||
\(753\) | −1.34270 | + | 2.32562i | −0.0489307 | + | 0.0847505i | ||||
\(754\) | −1.80221 | − | 3.12151i | −0.0656325 | − | 0.113679i | ||||
\(755\) | −18.4877 | −0.672837 | ||||||||
\(756\) | 4.34011 | − | 0.267984i | 0.157848 | − | 0.00974650i | ||||
\(757\) | −39.6243 | −1.44017 | −0.720084 | − | 0.693887i | \(-0.755897\pi\) | ||||
−0.720084 | + | 0.693887i | \(0.755897\pi\) | |||||||
\(758\) | −3.49566 | − | 6.05465i | −0.126968 | − | 0.219915i | ||||
\(759\) | 2.69407 | − | 4.66626i | 0.0977885 | − | 0.169375i | ||||
\(760\) | −5.15168 | + | 8.92298i | −0.186871 | + | 0.323670i | ||||
\(761\) | 26.7319 | + | 46.3010i | 0.969031 | + | 1.67841i | 0.698372 | + | 0.715735i | \(0.253908\pi\) |
0.270658 | + | 0.962676i | \(0.412759\pi\) | |||||||
\(762\) | 6.21433 | 0.225121 | ||||||||
\(763\) | −2.90437 | + | 0.179333i | −0.105145 | + | 0.00649231i | ||||
\(764\) | 6.36805 | 0.230388 | ||||||||
\(765\) | 16.7691 | + | 29.0449i | 0.606287 | + | 1.05012i | ||||
\(766\) | −13.7705 | + | 23.8512i | −0.497549 | + | 0.861780i | ||||
\(767\) | −14.2884 | + | 24.7482i | −0.515924 | + | 0.893607i | ||||
\(768\) | −1.28821 | − | 2.23124i | −0.0464842 | − | 0.0805130i | ||||
\(769\) | 8.56383 | 0.308820 | 0.154410 | − | 0.988007i | \(-0.450652\pi\) | ||||
0.154410 | + | 0.988007i | \(0.450652\pi\) | |||||||
\(770\) | −3.27148 | + | 6.57114i | −0.117896 | + | 0.236808i | ||||
\(771\) | −17.4529 | −0.628550 | ||||||||
\(772\) | 7.02750 | + | 12.1720i | 0.252925 | + | 0.438079i | ||||
\(773\) | 15.8946 | − | 27.5302i | 0.571688 | − | 0.990193i | −0.424705 | − | 0.905332i | \(-0.639622\pi\) |
0.996393 | − | 0.0848607i | \(-0.0270445\pi\) | |||||||
\(774\) | 15.2195 | − | 26.3609i | 0.547054 | − | 0.947525i | ||||
\(775\) | −14.1166 | − | 24.4507i | −0.507085 | − | 0.878296i | ||||
\(776\) | 6.65800 | 0.239008 | ||||||||
\(777\) | 12.4621 | + | 18.8044i | 0.447074 | + | 0.674603i | ||||
\(778\) | 6.70443 | 0.240365 | ||||||||
\(779\) | 16.5592 | + | 28.6814i | 0.593295 | + | 1.02762i | ||||
\(780\) | −5.31737 | + | 9.20995i | −0.190392 | + | 0.329769i | ||||
\(781\) | 7.75578 | − | 13.4334i | 0.277524 | − | 0.480685i | ||||
\(782\) | −3.47460 | − | 6.01818i | −0.124251 | − | 0.215210i | ||||
\(783\) | 1.90394 | 0.0680413 | ||||||||
\(784\) | 6.94683 | − | 0.861161i | 0.248101 | − | 0.0307558i | ||||
\(785\) | −20.4603 | −0.730260 | ||||||||
\(786\) | −1.96249 | − | 3.39913i | −0.0699996 | − | 0.121243i | ||||
\(787\) | −5.21977 | + | 9.04091i | −0.186065 | + | 0.322274i | −0.943935 | − | 0.330132i | \(-0.892907\pi\) |
0.757870 | + | 0.652406i | \(0.226240\pi\) | |||||||
\(788\) | 3.47785 | − | 6.02381i | 0.123893 | − | 0.214589i | ||||
\(789\) | −0.588822 | − | 1.01987i | −0.0209626 | − | 0.0363083i | ||||
\(790\) | −1.05766 | −0.0376299 | ||||||||
\(791\) | −6.49344 | − | 9.79814i | −0.230880 | − | 0.348382i | ||||
\(792\) | 7.60808 | 0.270341 | ||||||||
\(793\) | −18.7287 | − | 32.4391i | −0.665076 | − | 1.15194i | ||||
\(794\) | −11.3026 | + | 19.5767i | −0.401115 | + | 0.694752i | ||||
\(795\) | −7.24615 | + | 12.5507i | −0.256994 | + | 0.445127i | ||||
\(796\) | −10.5449 | − | 18.2642i | −0.373753 | − | 0.647359i | ||||
\(797\) | 2.70514 | 0.0958211 | 0.0479105 | − | 0.998852i | \(-0.484744\pi\) | ||||
0.0479105 | + | 0.998852i | \(0.484744\pi\) | |||||||
\(798\) | −23.5946 | + | 47.3924i | −0.835240 | + | 1.67767i | ||||
\(799\) | 24.1922 | 0.855860 | ||||||||
\(800\) | 1.62002 | + | 2.80595i | 0.0572762 | + | 0.0992054i | ||||
\(801\) | −30.2722 | + | 52.4331i | −1.06962 | + | 1.85263i | ||||
\(802\) | 4.85413 | − | 8.40761i | 0.171405 | − | 0.296883i | ||||
\(803\) | 4.56752 | + | 7.91117i | 0.161184 | + | 0.279179i | ||||
\(804\) | −18.7130 | −0.659956 | ||||||||
\(805\) | −3.50328 | + | 0.216314i | −0.123474 | + | 0.00762406i | ||||
\(806\) | −27.1125 | −0.954999 | ||||||||
\(807\) | −23.9007 | − | 41.3973i | −0.841346 | − | 1.45725i | ||||
\(808\) | −4.57940 | + | 7.93175i | −0.161103 | + | 0.279038i | ||||
\(809\) | −11.1968 | + | 19.3935i | −0.393659 | + | 0.681837i | −0.992929 | − | 0.118710i | \(-0.962124\pi\) |
0.599270 | + | 0.800547i | \(0.295458\pi\) | |||||||
\(810\) | 4.43052 | + | 7.67389i | 0.155673 | + | 0.269633i | ||||
\(811\) | −23.7712 | −0.834719 | −0.417359 | − | 0.908742i | \(-0.637044\pi\) | ||||
−0.417359 | + | 0.908742i | \(0.637044\pi\) | |||||||
\(812\) | 3.05914 | − | 0.188889i | 0.107355 | − | 0.00662872i | ||||
\(813\) | 47.1249 | 1.65274 | ||||||||
\(814\) | 3.46057 | + | 5.99388i | 0.121293 | + | 0.210085i | ||||
\(815\) | 5.71374 | − | 9.89649i | 0.200144 | − | 0.346659i | ||||
\(816\) | 8.95200 | − | 15.5053i | 0.313383 | − | 0.542795i | ||||
\(817\) | 32.4919 | + | 56.2776i | 1.13675 | + | 1.96890i | ||||
\(818\) | −36.3360 | −1.27046 | ||||||||
\(819\) | −13.3469 | + | 26.8088i | −0.466379 | + | 0.936774i | ||||
\(820\) | −5.65711 | −0.197555 | ||||||||
\(821\) | 10.9377 | + | 18.9447i | 0.381729 | + | 0.661175i | 0.991310 | − | 0.131550i | \(-0.0419953\pi\) |
−0.609580 | + | 0.792724i | \(0.708662\pi\) | |||||||
\(822\) | −12.4012 | + | 21.4794i | −0.432540 | + | 0.749182i | ||||
\(823\) | 13.8484 | − | 23.9861i | 0.482724 | − | 0.836103i | −0.517079 | − | 0.855938i | \(-0.672981\pi\) |
0.999803 | + | 0.0198345i | \(0.00631394\pi\) | |||||||
\(824\) | −2.26606 | − | 3.92492i | −0.0789418 | − | 0.136731i | ||||
\(825\) | −17.4577 | −0.607801 | ||||||||
\(826\) | −13.4238 | − | 20.2555i | −0.467073 | − | 0.704780i | ||||
\(827\) | 44.6016 | 1.55095 | 0.775475 | − | 0.631378i | \(-0.217510\pi\) | ||||
0.775475 | + | 0.631378i | \(0.217510\pi\) | |||||||
\(828\) | 1.81896 | + | 3.15053i | 0.0632131 | + | 0.109488i | ||||
\(829\) | 18.1647 | − | 31.4621i | 0.630884 | − | 1.09272i | −0.356487 | − | 0.934300i | \(-0.616026\pi\) |
0.987371 | − | 0.158424i | \(-0.0506411\pi\) | |||||||
\(830\) | −6.88167 | + | 11.9194i | −0.238866 | + | 0.413729i | ||||
\(831\) | −25.9660 | − | 44.9744i | −0.900749 | − | 1.56014i | ||||
\(832\) | 3.11142 | 0.107869 | ||||||||
\(833\) | 29.3200 | + | 38.8150i | 1.01588 | + | 1.34486i | ||||
\(834\) | 22.0973 | 0.765167 | ||||||||
\(835\) | −7.93945 | − | 13.7515i | −0.274756 | − | 0.475891i | ||||
\(836\) | −8.12119 | + | 14.0663i | −0.280877 | + | 0.486494i | ||||
\(837\) | 7.16077 | − | 12.4028i | 0.247512 | − | 0.428704i | ||||
\(838\) | −4.99321 | − | 8.64849i | −0.172488 | − | 0.298757i | ||||
\(839\) | 51.3975 | 1.77444 | 0.887219 | − | 0.461348i | \(-0.152634\pi\) | ||||
0.887219 | + | 0.461348i | \(0.152634\pi\) | |||||||
\(840\) | −4.99560 | − | 7.53801i | −0.172365 | − | 0.260086i | ||||
\(841\) | −27.6580 | −0.953724 | ||||||||
\(842\) | −7.05263 | − | 12.2155i | −0.243050 | − | 0.420974i | ||||
\(843\) | 9.36997 | − | 16.2293i | 0.322719 | − | 0.558965i | ||||
\(844\) | −13.2518 | + | 22.9528i | −0.456145 | + | 0.790067i | ||||
\(845\) | 2.20160 | + | 3.81329i | 0.0757375 | + | 0.131181i | ||||
\(846\) | −12.6647 | −0.435421 | ||||||||
\(847\) | 7.81346 | − | 15.6942i | 0.268474 | − | 0.539259i | ||||
\(848\) | 4.24003 | 0.145603 | ||||||||
\(849\) | 3.55855 | + | 6.16358i | 0.122129 | + | 0.211534i | ||||
\(850\) | −11.2578 | + | 19.4991i | −0.386139 | + | 0.668813i | ||||
\(851\) | −1.65472 | + | 2.86606i | −0.0567231 | + | 0.0982473i | ||||
\(852\) | 9.55474 | + | 16.5493i | 0.327340 | + | 0.566969i | ||||
\(853\) | −36.8505 | −1.26174 | −0.630868 | − | 0.775890i | \(-0.717301\pi\) | ||||
−0.630868 | + | 0.775890i | \(0.717301\pi\) | |||||||
\(854\) | 31.7908 | − | 1.96296i | 1.08786 | − | 0.0671710i | ||||
\(855\) | 37.4828 | 1.28188 | ||||||||
\(856\) | 6.16722 | + | 10.6819i | 0.210791 | + | 0.365101i | ||||
\(857\) | 7.89362 | − | 13.6722i | 0.269641 | − | 0.467032i | −0.699128 | − | 0.714996i | \(-0.746428\pi\) |
0.968769 | + | 0.247965i | \(0.0797617\pi\) | |||||||
\(858\) | −8.38237 | + | 14.5187i | −0.286170 | + | 0.495660i | ||||
\(859\) | −15.1034 | − | 26.1599i | −0.515322 | − | 0.892563i | −0.999842 | − | 0.0177833i | \(-0.994339\pi\) |
0.484520 | − | 0.874780i | \(-0.338994\pi\) | |||||||
\(860\) | −11.1002 | −0.378513 | ||||||||
\(861\) | −29.0122 | + | 1.79139i | −0.988734 | + | 0.0610504i | ||||
\(862\) | −3.54369 | −0.120699 | ||||||||
\(863\) | −25.9658 | − | 44.9741i | −0.883886 | − | 1.53094i | −0.846985 | − | 0.531617i | \(-0.821584\pi\) |
−0.0369017 | − | 0.999319i | \(-0.511749\pi\) | |||||||
\(864\) | −0.821765 | + | 1.42334i | −0.0279570 | + | 0.0484230i | ||||
\(865\) | 13.1468 | − | 22.7709i | 0.447004 | − | 0.774233i | ||||
\(866\) | 8.13402 | + | 14.0885i | 0.276405 | + | 0.478748i | ||||
\(867\) | 80.6192 | 2.73797 | ||||||||
\(868\) | 10.2750 | − | 20.6385i | 0.348756 | − | 0.700516i | ||||
\(869\) | −1.66731 | −0.0565598 | ||||||||
\(870\) | −1.97977 | − | 3.42906i | −0.0671204 | − | 0.116256i | ||||
\(871\) | 11.2994 | − | 19.5712i | 0.382866 | − | 0.663143i | ||||
\(872\) | 0.549920 | − | 0.952489i | 0.0186226 | − | 0.0322554i | ||||
\(873\) | −12.1106 | − | 20.9762i | −0.409882 | − | 0.709937i | ||||
\(874\) | −7.76653 | −0.262707 | ||||||||
\(875\) | 15.9772 | + | 24.1085i | 0.540128 | + | 0.815015i | ||||
\(876\) | −11.2539 | −0.380234 | ||||||||
\(877\) | 5.65061 | + | 9.78714i | 0.190807 | + | 0.330488i | 0.945518 | − | 0.325570i | \(-0.105556\pi\) |
−0.754711 | + | 0.656058i | \(0.772223\pi\) | |||||||
\(878\) | −0.585013 | + | 1.01327i | −0.0197432 | + | 0.0341963i | ||||
\(879\) | −32.6890 | + | 56.6190i | −1.10257 | + | 1.90971i | ||||
\(880\) | −1.38722 | − | 2.40273i | −0.0467631 | − | 0.0809961i | ||||
\(881\) | 17.4345 | 0.587384 | 0.293692 | − | 0.955900i | \(-0.405116\pi\) | ||||
0.293692 | + | 0.955900i | \(0.405116\pi\) | |||||||
\(882\) | −15.3491 | − | 20.3197i | −0.516831 | − | 0.684201i | ||||
\(883\) | 48.0567 | 1.61724 | 0.808618 | − | 0.588333i | \(-0.200216\pi\) | ||||
0.808618 | + | 0.588333i | \(0.200216\pi\) | |||||||
\(884\) | 10.8109 | + | 18.7251i | 0.363611 | + | 0.629792i | ||||
\(885\) | −15.6962 | + | 27.1865i | −0.527621 | + | 0.913866i | ||||
\(886\) | −19.5037 | + | 33.7813i | −0.655238 | + | 1.13491i | ||||
\(887\) | 1.09716 | + | 1.90034i | 0.0368391 | + | 0.0638073i | 0.883857 | − | 0.467757i | \(-0.154938\pi\) |
−0.847018 | + | 0.531564i | \(0.821604\pi\) | |||||||
\(888\) | −8.52649 | −0.286130 | ||||||||
\(889\) | −3.52532 | − | 5.31945i | −0.118235 | − | 0.178409i | ||||
\(890\) | 22.0787 | 0.740081 | ||||||||
\(891\) | 6.98434 | + | 12.0972i | 0.233984 | + | 0.405272i | ||||
\(892\) | 4.90054 | − | 8.48799i | 0.164082 | − | 0.284199i | ||||
\(893\) | 13.5188 | − | 23.4153i | 0.452390 | − | 0.783562i | ||||
\(894\) | −20.6389 | − | 35.7476i | −0.690267 | − | 1.19558i | ||||
\(895\) | −21.7696 | −0.727678 | ||||||||
\(896\) | −1.17915 | + | 2.36846i | −0.0393927 | + | 0.0791247i | ||||
\(897\) | −8.01631 | −0.267657 | ||||||||
\(898\) | −16.0857 | − | 27.8612i | −0.536786 | − | 0.929741i | ||||
\(899\) | 5.04728 | − | 8.74215i | 0.168336 | − | 0.291567i | ||||
\(900\) | 5.89348 | − | 10.2078i | 0.196449 | − | 0.340260i | ||||
\(901\) | 14.7324 | + | 25.5173i | 0.490807 | + | 0.850103i | ||||
\(902\) | −8.91796 | −0.296935 | ||||||||
\(903\) | −56.9268 | + | 3.51500i | −1.89440 | + | 0.116972i | ||||
\(904\) | 4.44278 | 0.147765 | ||||||||
\(905\) | 7.44949 | + | 12.9029i | 0.247629 | + | 0.428907i | ||||
\(906\) | 17.9522 | − | 31.0941i | 0.596421 | − | 1.03303i | ||||
\(907\) | 15.1785 | − | 26.2899i | 0.503993 | − | 0.872942i | −0.495996 | − | 0.868325i | \(-0.665197\pi\) |
0.999989 | − | 0.00461698i | \(-0.00146963\pi\) | |||||||
\(908\) | 14.2481 | + | 24.6784i | 0.472839 | + | 0.818982i | ||||
\(909\) | 33.3189 | 1.10512 | ||||||||
\(910\) | 10.9002 | − | 0.673042i | 0.361337 | − | 0.0223111i | ||||
\(911\) | −1.09959 | −0.0364309 | −0.0182155 | − | 0.999834i | \(-0.505798\pi\) | ||||
−0.0182155 | + | 0.999834i | \(0.505798\pi\) | |||||||
\(912\) | −10.0049 | − | 17.3290i | −0.331295 | − | 0.573820i | ||||
\(913\) | −10.8484 | + | 18.7899i | −0.359029 | + | 0.621856i | ||||
\(914\) | 17.1774 | − | 29.7521i | 0.568177 | − | 0.984112i | ||||
\(915\) | −20.5739 | − | 35.6351i | −0.680153 | − | 1.17806i | ||||
\(916\) | −25.1914 | −0.832347 | ||||||||
\(917\) | −1.79635 | + | 3.60817i | −0.0593207 | + | 0.119152i | ||||
\(918\) | −11.4212 | −0.376956 | ||||||||
\(919\) | 4.83671 | + | 8.37743i | 0.159548 | + | 0.276346i | 0.934706 | − | 0.355422i | \(-0.115663\pi\) |
−0.775158 | + | 0.631768i | \(0.782330\pi\) | |||||||
\(920\) | 0.663319 | − | 1.14890i | 0.0218690 | − | 0.0378782i | ||||
\(921\) | 37.6761 | − | 65.2570i | 1.24147 | − | 2.15029i | ||||
\(922\) | −5.25776 | − | 9.10670i | −0.173155 | − | 0.299913i | ||||
\(923\) | −23.0776 | −0.759610 | ||||||||
\(924\) | −7.87514 | − | 11.8830i | −0.259073 | − | 0.390923i | ||||
\(925\) | 10.7227 | 0.352560 | ||||||||
\(926\) | 9.99714 | + | 17.3155i | 0.328526 | + | 0.569024i | ||||
\(927\) | −8.24372 | + | 14.2785i | −0.270759 | + | 0.468969i | ||||
\(928\) | −0.579223 | + | 1.00324i | −0.0190139 | + | 0.0329331i | ||||
\(929\) | −5.67186 | − | 9.82395i | −0.186088 | − | 0.322313i | 0.757855 | − | 0.652423i | \(-0.226248\pi\) |
−0.943943 | + | 0.330110i | \(0.892914\pi\) | |||||||
\(930\) | −29.7838 | −0.976649 | ||||||||
\(931\) | 53.9527 | − | 6.68823i | 1.76823 | − | 0.219198i | ||||
\(932\) | −13.1625 | −0.431151 | ||||||||
\(933\) | −35.1460 | − | 60.8746i | −1.15063 | − | 1.99294i | ||||
\(934\) | 13.7321 | − | 23.7848i | 0.449329 | − | 0.778261i | ||||
\(935\) | 9.64005 | − | 16.6971i | 0.315263 | − | 0.546052i | ||||
\(936\) | −5.65954 | − | 9.80260i | −0.184988 | − | 0.320408i | ||||
\(937\) | −1.06500 | −0.0347921 | −0.0173960 | − | 0.999849i | \(-0.505538\pi\) | ||||
−0.0173960 | + | 0.999849i | \(0.505538\pi\) | |||||||
\(938\) | 10.6157 | + | 16.0183i | 0.346614 | + | 0.523015i | ||||
\(939\) | 6.63880 | 0.216649 | ||||||||
\(940\) | 2.30921 | + | 3.99967i | 0.0753182 | + | 0.130455i | ||||
\(941\) | −23.3540 | + | 40.4502i | −0.761317 | + | 1.31864i | 0.180854 | + | 0.983510i | \(0.442114\pi\) |
−0.942172 | + | 0.335130i | \(0.891220\pi\) | |||||||
\(942\) | 19.8676 | − | 34.4117i | 0.647322 | − | 1.12120i | ||||
\(943\) | −2.13212 | − | 3.69295i | −0.0694315 | − | 0.120259i | ||||
\(944\) | 9.18450 | 0.298930 | ||||||||
\(945\) | −2.57099 | + | 5.16412i | −0.0836342 | + | 0.167989i | ||||
\(946\) | −17.4985 | −0.568925 | ||||||||
\(947\) | −23.4346 | − | 40.5900i | −0.761523 | − | 1.31900i | −0.942065 | − | 0.335429i | \(-0.891119\pi\) |
0.180543 | − | 0.983567i | \(-0.442215\pi\) | |||||||
\(948\) | 1.02702 | − | 1.77886i | 0.0333562 | − | 0.0577746i | ||||
\(949\) | 6.79541 | − | 11.7700i | 0.220588 | − | 0.382070i | ||||
\(950\) | 12.5819 | + | 21.7925i | 0.408211 | + | 0.707042i | ||||
\(951\) | −32.2218 | −1.04486 | ||||||||
\(952\) | −18.3509 | + | 1.13309i | −0.594755 | + | 0.0367238i | ||||
\(953\) | −42.2926 | −1.36999 | −0.684996 | − | 0.728547i | \(-0.740196\pi\) | ||||
−0.684996 | + | 0.728547i | \(0.740196\pi\) | |||||||
\(954\) | −7.71244 | − | 13.3583i | −0.249699 | − | 0.432492i | ||||
\(955\) | −4.22405 | + | 7.31626i | −0.136687 | + | 0.236749i | ||||
\(956\) | 4.39142 | − | 7.60616i | 0.142029 | − | 0.246001i | ||||
\(957\) | −3.12093 | − | 5.40562i | −0.100885 | − | 0.174739i | ||||
\(958\) | −8.44551 | −0.272862 | ||||||||
\(959\) | 25.4214 | − | 1.56967i | 0.820899 | − | 0.0506873i | ||||
\(960\) | 3.41797 | 0.110314 | ||||||||
\(961\) | −22.4659 | − | 38.9121i | −0.724706 | − | 1.25523i | ||||
\(962\) | 5.14853 | − | 8.91751i | 0.165995 | − | 0.287512i | ||||
\(963\) | 22.4358 | − | 38.8600i | 0.722984 | − | 1.25224i | ||||
\(964\) | −0.763776 | − | 1.32290i | −0.0245996 | − | 0.0426077i | ||||
\(965\) | −18.6459 | −0.600232 | ||||||||
\(966\) | 3.03798 | − | 6.10213i | 0.0977456 | − | 0.196333i | ||||
\(967\) | 42.5007 | 1.36673 | 0.683366 | − | 0.730076i | \(-0.260515\pi\) | ||||
0.683366 | + | 0.730076i | \(0.260515\pi\) | |||||||
\(968\) | 3.31317 | + | 5.73857i | 0.106489 | + | 0.184445i | ||||
\(969\) | 69.5259 | − | 120.422i | 2.23350 | − | 3.86853i | ||||
\(970\) | −4.41638 | + | 7.64939i | −0.141801 | + | 0.245607i | ||||
\(971\) | −0.516162 | − | 0.894019i | −0.0165644 | − | 0.0286904i | 0.857624 | − | 0.514277i | \(-0.171940\pi\) |
−0.874189 | + | 0.485586i | \(0.838606\pi\) | |||||||
\(972\) | −22.1393 | −0.710118 | ||||||||
\(973\) | −12.5355 | − | 18.9152i | −0.401871 | − | 0.606395i | ||||
\(974\) | 33.2791 | 1.06633 | ||||||||
\(975\) | 12.9865 | + | 22.4934i | 0.415902 | + | 0.720364i | ||||
\(976\) | −6.01934 | + | 10.4258i | −0.192674 | + | 0.333722i | ||||
\(977\) | −0.426210 | + | 0.738218i | −0.0136357 | + | 0.0236177i | −0.872763 | − | 0.488145i | \(-0.837674\pi\) |
0.859127 | + | 0.511762i | \(0.171007\pi\) | |||||||
\(978\) | 11.0964 | + | 19.2196i | 0.354825 | + | 0.614575i | ||||
\(979\) | 34.8053 | 1.11238 | ||||||||
\(980\) | −3.61857 | + | 8.55245i | −0.115591 | + | 0.273198i | ||||
\(981\) | −4.00112 | −0.127746 | ||||||||
\(982\) | −7.92659 | − | 13.7293i | −0.252948 | − | 0.438118i | ||||
\(983\) | 3.46068 | − | 5.99407i | 0.110379 | − | 0.191181i | −0.805544 | − | 0.592535i | \(-0.798127\pi\) |
0.915923 | + | 0.401354i | \(0.131460\pi\) | |||||||
\(984\) | 5.49324 | − | 9.51457i | 0.175118 | − | 0.303313i | ||||
\(985\) | 4.61384 | + | 7.99141i | 0.147009 | + | 0.254628i | ||||
\(986\) | −8.05027 | −0.256373 | ||||||||
\(987\) | 13.1092 | + | 19.7809i | 0.417271 | + | 0.629633i | ||||
\(988\) | 24.1649 | 0.768789 | ||||||||
\(989\) | −4.18358 | − | 7.24617i | −0.133030 | − | 0.230415i | ||||
\(990\) | −5.04658 | + | 8.74094i | −0.160391 | + | 0.277805i | ||||
\(991\) | 0.672979 | − | 1.16563i | 0.0213779 | − | 0.0370276i | −0.855139 | − | 0.518400i | \(-0.826528\pi\) |
0.876516 | + | 0.481372i | \(0.159861\pi\) | |||||||
\(992\) | 4.35694 | + | 7.54644i | 0.138333 | + | 0.239600i | ||||
\(993\) | 7.04384 | 0.223530 | ||||||||
\(994\) | 8.74586 | − | 17.5670i | 0.277402 | − | 0.557193i | ||||
\(995\) | 27.9784 | 0.886976 | ||||||||
\(996\) | −13.3646 | − | 23.1483i | −0.423475 | − | 0.733480i | ||||
\(997\) | −2.42089 | + | 4.19311i | −0.0766705 | + | 0.132797i | −0.901811 | − | 0.432130i | \(-0.857762\pi\) |
0.825141 | + | 0.564927i | \(0.191096\pi\) | |||||||
\(998\) | 9.66615 | − | 16.7423i | 0.305977 | − | 0.529967i | ||||
\(999\) | 2.71958 | + | 4.71046i | 0.0860438 | + | 0.149032i |
(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 | 322.2.e.a.277.1 | yes | 8 | |
7.2 | even | 3 | inner | 322.2.e.a.93.1 | ✓ | 8 | |
7.3 | odd | 6 | 2254.2.a.x.1.1 | 4 | |||
7.4 | even | 3 | 2254.2.a.z.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.e.a.93.1 | ✓ | 8 | 7.2 | even | 3 | inner | |
322.2.e.a.277.1 | yes | 8 | 1.1 | even | 1 | trivial | |
2254.2.a.x.1.1 | 4 | 7.3 | odd | 6 | |||
2254.2.a.z.1.4 | 4 | 7.4 | even | 3 |