Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,2,Mod(43,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.j (of order \(4\), 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: | \(0.638803216170\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.1 | ||
Root | \(0.235136 + 1.39453i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.43 |
Dual form | 80.2.j.b.67.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34716 | − | 0.430311i | −0.952584 | − | 0.304276i | ||||
\(3\) | − | 2.96561i | − | 1.71220i | −0.516813 | − | 0.856099i | \(-0.672882\pi\) | ||
0.516813 | − | 0.856099i | \(-0.327118\pi\) | |||||||
\(4\) | 1.62967 | + | 1.15939i | 0.814833 | + | 0.579696i | ||||
\(5\) | −2.22902 | − | 0.177336i | −0.996850 | − | 0.0793073i | ||||
\(6\) | −1.27613 | + | 3.99515i | −0.520980 | + | 1.63101i | ||||
\(7\) | −0.115101 | + | 0.115101i | −0.0435040 | + | 0.0435040i | −0.728524 | − | 0.685020i | \(-0.759793\pi\) |
0.685020 | + | 0.728524i | \(0.259793\pi\) | |||||||
\(8\) | −1.69652 | − | 2.26315i | −0.599809 | − | 0.800143i | ||||
\(9\) | −5.79486 | −1.93162 | ||||||||
\(10\) | 2.92654 | + | 1.19807i | 0.925452 | + | 0.378864i | ||||
\(11\) | 2.95966 | − | 2.95966i | 0.892372 | − | 0.892372i | −0.102374 | − | 0.994746i | \(-0.532644\pi\) |
0.994746 | + | 0.102374i | \(0.0326439\pi\) | |||||||
\(12\) | 3.43831 | − | 4.83296i | 0.992554 | − | 1.39515i | ||||
\(13\) | 1.55822 | 0.432172 | 0.216086 | − | 0.976374i | \(-0.430671\pi\) | ||||
0.216086 | + | 0.976374i | \(0.430671\pi\) | |||||||
\(14\) | 0.204588 | − | 0.105530i | 0.0546784 | − | 0.0282040i | ||||
\(15\) | −0.525911 | + | 6.61042i | −0.135790 | + | 1.70680i | ||||
\(16\) | 1.31162 | + | 3.77884i | 0.327905 | + | 0.944711i | ||||
\(17\) | 0.299668 | − | 0.299668i | 0.0726801 | − | 0.0726801i | −0.669832 | − | 0.742512i | \(-0.733634\pi\) |
0.742512 | + | 0.669832i | \(0.233634\pi\) | |||||||
\(18\) | 7.80658 | + | 2.49359i | 1.84003 | + | 0.587745i | ||||
\(19\) | 2.26261 | − | 2.26261i | 0.519079 | − | 0.519079i | −0.398214 | − | 0.917293i | \(-0.630370\pi\) |
0.917293 | + | 0.398214i | \(0.130370\pi\) | |||||||
\(20\) | −3.42696 | − | 2.87331i | −0.766292 | − | 0.642493i | ||||
\(21\) | 0.341344 | + | 0.341344i | 0.0744874 | + | 0.0744874i | ||||
\(22\) | −5.26071 | + | 2.71356i | −1.12159 | + | 0.578532i | ||||
\(23\) | 4.14573 | + | 4.14573i | 0.864444 | + | 0.864444i | 0.991851 | − | 0.127406i | \(-0.0406652\pi\) |
−0.127406 | + | 0.991851i | \(0.540665\pi\) | |||||||
\(24\) | −6.71162 | + | 5.03121i | −1.37000 | + | 1.02699i | ||||
\(25\) | 4.93710 | + | 0.790575i | 0.987421 | + | 0.158115i | ||||
\(26\) | −2.09917 | − | 0.670518i | −0.411680 | − | 0.131499i | ||||
\(27\) | 8.28846i | 1.59511i | ||||||||
\(28\) | −0.321023 | + | 0.0541288i | −0.0606676 | + | 0.0102294i | ||||
\(29\) | −0.289656 | − | 0.289656i | −0.0537878 | − | 0.0537878i | 0.679701 | − | 0.733489i | \(-0.262109\pi\) |
−0.733489 | + | 0.679701i | \(0.762109\pi\) | |||||||
\(30\) | 3.55302 | − | 8.67897i | 0.648690 | − | 1.58456i | ||||
\(31\) | − | 4.18508i | − | 0.751663i | −0.926688 | − | 0.375832i | \(-0.877357\pi\) | ||
0.926688 | − | 0.375832i | \(-0.122643\pi\) | |||||||
\(32\) | −0.140879 | − | 5.65510i | −0.0249041 | − | 0.999690i | ||||
\(33\) | −8.77721 | − | 8.77721i | −1.52792 | − | 1.52792i | ||||
\(34\) | −0.532650 | + | 0.274749i | −0.0913487 | + | 0.0471191i | ||||
\(35\) | 0.276974 | − | 0.236151i | 0.0468172 | − | 0.0399168i | ||||
\(36\) | −9.44368 | − | 6.71851i | −1.57395 | − | 1.11975i | ||||
\(37\) | 1.63643 | 0.269027 | 0.134514 | − | 0.990912i | \(-0.457053\pi\) | ||||
0.134514 | + | 0.990912i | \(0.457053\pi\) | |||||||
\(38\) | −4.02172 | + | 2.07447i | −0.652410 | + | 0.336523i | ||||
\(39\) | − | 4.62107i | − | 0.739964i | ||||||
\(40\) | 3.38024 | + | 5.34546i | 0.534463 | + | 0.845192i | ||||
\(41\) | 7.61648i | 1.18949i | 0.803913 | + | 0.594747i | \(0.202748\pi\) | ||||
−0.803913 | + | 0.594747i | \(0.797252\pi\) | |||||||
\(42\) | −0.312960 | − | 0.606729i | −0.0482908 | − | 0.0936203i | ||||
\(43\) | −6.72651 | −1.02578 | −0.512892 | − | 0.858453i | \(-0.671426\pi\) | ||||
−0.512892 | + | 0.858453i | \(0.671426\pi\) | |||||||
\(44\) | 8.25467 | − | 1.39185i | 1.24444 | − | 0.209829i | ||||
\(45\) | 12.9169 | + | 1.02764i | 1.92553 | + | 0.153191i | ||||
\(46\) | −3.80100 | − | 7.36890i | −0.560427 | − | 1.08649i | ||||
\(47\) | −4.38366 | − | 4.38366i | −0.639423 | − | 0.639423i | 0.310990 | − | 0.950413i | \(-0.399339\pi\) |
−0.950413 | + | 0.310990i | \(0.899339\pi\) | |||||||
\(48\) | 11.2066 | − | 3.88975i | 1.61753 | − | 0.561437i | ||||
\(49\) | 6.97350i | 0.996215i | ||||||||
\(50\) | −6.31086 | − | 3.18952i | −0.892491 | − | 0.451066i | ||||
\(51\) | −0.888698 | − | 0.888698i | −0.124443 | − | 0.124443i | ||||
\(52\) | 2.53938 | + | 1.80659i | 0.352148 | + | 0.250529i | ||||
\(53\) | 11.4324i | 1.57036i | 0.619265 | + | 0.785182i | \(0.287431\pi\) | ||||
−0.619265 | + | 0.785182i | \(0.712569\pi\) | |||||||
\(54\) | 3.56661 | − | 11.1659i | 0.485355 | − | 1.51948i | ||||
\(55\) | −7.12202 | + | 6.07231i | −0.960333 | + | 0.818790i | ||||
\(56\) | 0.455760 | + | 0.0652196i | 0.0609035 | + | 0.00871533i | ||||
\(57\) | −6.71003 | − | 6.71003i | −0.888766 | − | 0.888766i | ||||
\(58\) | 0.265570 | + | 0.514854i | 0.0348711 | + | 0.0676037i | ||||
\(59\) | −1.63497 | − | 1.63497i | −0.212855 | − | 0.212855i | 0.592624 | − | 0.805479i | \(-0.298092\pi\) |
−0.805479 | + | 0.592624i | \(0.798092\pi\) | |||||||
\(60\) | −8.52113 | + | 10.1630i | −1.10007 | + | 1.31204i | ||||
\(61\) | −1.23034 | + | 1.23034i | −0.157528 | + | 0.157528i | −0.781471 | − | 0.623942i | \(-0.785530\pi\) |
0.623942 | + | 0.781471i | \(0.285530\pi\) | |||||||
\(62\) | −1.80089 | + | 5.63796i | −0.228713 | + | 0.716022i | ||||
\(63\) | 0.666993 | − | 0.666993i | 0.0840332 | − | 0.0840332i | ||||
\(64\) | −2.24366 | + | 7.67893i | −0.280458 | + | 0.959866i | ||||
\(65\) | −3.47331 | − | 0.276329i | −0.430811 | − | 0.0342744i | ||||
\(66\) | 8.04736 | + | 15.6012i | 0.990561 | + | 1.92038i | ||||
\(67\) | 2.49337 | 0.304614 | 0.152307 | − | 0.988333i | \(-0.451330\pi\) | ||||
0.152307 | + | 0.988333i | \(0.451330\pi\) | |||||||
\(68\) | 0.835791 | − | 0.140926i | 0.101354 | − | 0.0170897i | ||||
\(69\) | 12.2946 | − | 12.2946i | 1.48010 | − | 1.48010i | ||||
\(70\) | −0.474746 | + | 0.198948i | −0.0567430 | + | 0.0237788i | ||||
\(71\) | 8.00096 | 0.949540 | 0.474770 | − | 0.880110i | \(-0.342531\pi\) | ||||
0.474770 | + | 0.880110i | \(0.342531\pi\) | |||||||
\(72\) | 9.83107 | + | 13.1146i | 1.15860 | + | 1.54557i | ||||
\(73\) | 1.12102 | − | 1.12102i | 0.131205 | − | 0.131205i | −0.638454 | − | 0.769660i | \(-0.720426\pi\) |
0.769660 | + | 0.638454i | \(0.220426\pi\) | |||||||
\(74\) | −2.20453 | − | 0.704173i | −0.256271 | − | 0.0818584i | ||||
\(75\) | 2.34454 | − | 14.6415i | 0.270724 | − | 1.69066i | ||||
\(76\) | 6.31056 | − | 1.06405i | 0.723871 | − | 0.122054i | ||||
\(77\) | 0.681319i | 0.0776435i | ||||||||
\(78\) | −1.98850 | + | 6.22531i | −0.225153 | + | 0.704878i | ||||
\(79\) | −3.62218 | −0.407527 | −0.203763 | − | 0.979020i | \(-0.565317\pi\) | ||||
−0.203763 | + | 0.979020i | \(0.565317\pi\) | |||||||
\(80\) | −2.25350 | − | 8.65573i | −0.251949 | − | 0.967740i | ||||
\(81\) | 7.19579 | 0.799532 | ||||||||
\(82\) | 3.27745 | − | 10.2606i | 0.361934 | − | 1.13309i | ||||
\(83\) | 1.62629i | 0.178509i | 0.996009 | + | 0.0892545i | \(0.0284484\pi\) | ||||
−0.996009 | + | 0.0892545i | \(0.971552\pi\) | |||||||
\(84\) | 0.160525 | + | 0.952029i | 0.0175147 | + | 0.103875i | ||||
\(85\) | −0.721109 | + | 0.614825i | −0.0782152 | + | 0.0666871i | ||||
\(86\) | 9.06167 | + | 2.89449i | 0.977145 | + | 0.312121i | ||||
\(87\) | −0.859007 | + | 0.859007i | −0.0920953 | + | 0.0920953i | ||||
\(88\) | −11.7193 | − | 1.67703i | −1.24928 | − | 0.178772i | ||||
\(89\) | 15.7149 | 1.66577 | 0.832887 | − | 0.553443i | \(-0.186686\pi\) | ||||
0.832887 | + | 0.553443i | \(0.186686\pi\) | |||||||
\(90\) | −16.9589 | − | 6.94266i | −1.78762 | − | 0.731821i | ||||
\(91\) | −0.179352 | + | 0.179352i | −0.0188012 | + | 0.0188012i | ||||
\(92\) | 1.94962 | + | 11.5627i | 0.203262 | + | 1.20549i | ||||
\(93\) | −12.4113 | −1.28700 | ||||||||
\(94\) | 4.01915 | + | 7.79182i | 0.414543 | + | 0.803665i | ||||
\(95\) | −5.44467 | + | 4.64218i | −0.558611 | + | 0.476277i | ||||
\(96\) | −16.7708 | + | 0.417792i | −1.71167 | + | 0.0426407i | ||||
\(97\) | 9.69217 | − | 9.69217i | 0.984091 | − | 0.984091i | −0.0157848 | − | 0.999875i | \(-0.505025\pi\) |
0.999875 | + | 0.0157848i | \(0.00502467\pi\) | |||||||
\(98\) | 3.00077 | − | 9.39441i | 0.303124 | − | 0.948978i | ||||
\(99\) | −17.1508 | + | 17.1508i | −1.72372 | + | 1.72372i | ||||
\(100\) | 7.12924 | + | 7.01241i | 0.712924 | + | 0.701241i | ||||
\(101\) | −12.8067 | − | 12.8067i | −1.27432 | − | 1.27432i | −0.943800 | − | 0.330516i | \(-0.892777\pi\) |
−0.330516 | − | 0.943800i | \(-0.607223\pi\) | |||||||
\(102\) | 0.814800 | + | 1.57963i | 0.0806772 | + | 0.156407i | ||||
\(103\) | −4.33738 | − | 4.33738i | −0.427375 | − | 0.427375i | 0.460358 | − | 0.887733i | \(-0.347721\pi\) |
−0.887733 | + | 0.460358i | \(0.847721\pi\) | |||||||
\(104\) | −2.64354 | − | 3.52648i | −0.259221 | − | 0.345800i | ||||
\(105\) | −0.700332 | − | 0.821398i | −0.0683454 | − | 0.0801602i | ||||
\(106\) | 4.91950 | − | 15.4013i | 0.477824 | − | 1.49590i | ||||
\(107\) | 11.9807i | 1.15822i | 0.815251 | + | 0.579108i | \(0.196599\pi\) | ||||
−0.815251 | + | 0.579108i | \(0.803401\pi\) | |||||||
\(108\) | −9.60958 | + | 13.5074i | −0.924682 | + | 1.29975i | ||||
\(109\) | −4.01503 | − | 4.01503i | −0.384570 | − | 0.384570i | 0.488175 | − | 0.872746i | \(-0.337663\pi\) |
−0.872746 | + | 0.488175i | \(0.837663\pi\) | |||||||
\(110\) | 12.2075 | − | 5.11567i | 1.16394 | − | 0.487760i | ||||
\(111\) | − | 4.85301i | − | 0.460628i | ||||||
\(112\) | −0.585916 | − | 0.283980i | −0.0553639 | − | 0.0268336i | ||||
\(113\) | 6.47754 | + | 6.47754i | 0.609356 | + | 0.609356i | 0.942778 | − | 0.333422i | \(-0.108203\pi\) |
−0.333422 | + | 0.942778i | \(0.608203\pi\) | |||||||
\(114\) | 6.15207 | + | 11.9269i | 0.576194 | + | 1.11705i | ||||
\(115\) | −8.50575 | − | 9.97612i | −0.793165 | − | 0.930278i | ||||
\(116\) | −0.136217 | − | 0.807867i | −0.0126475 | − | 0.0750086i | ||||
\(117\) | −9.02966 | −0.834792 | ||||||||
\(118\) | 1.49902 | + | 2.90611i | 0.137996 | + | 0.267529i | ||||
\(119\) | 0.0689840i | 0.00632375i | ||||||||
\(120\) | 15.8526 | − | 10.0245i | 1.44714 | − | 0.915105i | ||||
\(121\) | − | 6.51921i | − | 0.592655i | ||||||
\(122\) | 2.18688 | − | 1.12803i | 0.197991 | − | 0.102127i | ||||
\(123\) | 22.5875 | 2.03665 | ||||||||
\(124\) | 4.85215 | − | 6.82028i | 0.435736 | − | 0.612480i | ||||
\(125\) | −10.8647 | − | 2.63774i | −0.971771 | − | 0.235927i | ||||
\(126\) | −1.18556 | + | 0.611530i | −0.105618 | + | 0.0544794i | ||||
\(127\) | 12.2756 | + | 12.2756i | 1.08928 | + | 1.08928i | 0.995603 | + | 0.0936781i | \(0.0298625\pi\) |
0.0936781 | + | 0.995603i | \(0.470138\pi\) | |||||||
\(128\) | 6.32690 | − | 9.37925i | 0.559224 | − | 0.829017i | ||||
\(129\) | 19.9482i | 1.75634i | ||||||||
\(130\) | 4.56019 | + | 1.86686i | 0.399955 | + | 0.163735i | ||||
\(131\) | 7.99562 | + | 7.99562i | 0.698581 | + | 0.698581i | 0.964104 | − | 0.265524i | \(-0.0855448\pi\) |
−0.265524 | + | 0.964104i | \(0.585545\pi\) | |||||||
\(132\) | −4.12768 | − | 24.4802i | −0.359269 | − | 2.13072i | ||||
\(133\) | 0.520857i | 0.0451641i | ||||||||
\(134\) | −3.35896 | − | 1.07292i | −0.290170 | − | 0.0926865i | ||||
\(135\) | 1.46985 | − | 18.4752i | 0.126504 | − | 1.59009i | ||||
\(136\) | −1.18658 | − | 0.169801i | −0.101749 | − | 0.0145603i | ||||
\(137\) | 3.08551 | + | 3.08551i | 0.263613 | + | 0.263613i | 0.826520 | − | 0.562907i | \(-0.190317\pi\) |
−0.562907 | + | 0.826520i | \(0.690317\pi\) | |||||||
\(138\) | −21.8533 | + | 11.2723i | −1.86028 | + | 0.959561i | ||||
\(139\) | −12.2206 | − | 12.2206i | −1.03654 | − | 1.03654i | −0.999307 | − | 0.0372284i | \(-0.988147\pi\) |
−0.0372284 | − | 0.999307i | \(-0.511853\pi\) | |||||||
\(140\) | 0.725167 | − | 0.0637253i | 0.0612878 | − | 0.00538577i | ||||
\(141\) | −13.0002 | + | 13.0002i | −1.09482 | + | 1.09482i | ||||
\(142\) | −10.7786 | − | 3.44290i | −0.904516 | − | 0.288922i | ||||
\(143\) | 4.61180 | − | 4.61180i | 0.385658 | − | 0.385658i | ||||
\(144\) | −7.60064 | − | 21.8979i | −0.633386 | − | 1.82482i | ||||
\(145\) | 0.594284 | + | 0.697017i | 0.0493526 | + | 0.0578841i | ||||
\(146\) | −1.99258 | + | 1.02780i | −0.164907 | + | 0.0850616i | ||||
\(147\) | 20.6807 | 1.70572 | ||||||||
\(148\) | 2.66683 | + | 1.89726i | 0.219212 | + | 0.155954i | ||||
\(149\) | −2.59172 | + | 2.59172i | −0.212322 | + | 0.212322i | −0.805253 | − | 0.592931i | \(-0.797971\pi\) |
0.592931 | + | 0.805253i | \(0.297971\pi\) | |||||||
\(150\) | −9.45887 | + | 18.7156i | −0.772314 | + | 1.52812i | ||||
\(151\) | −16.9594 | −1.38014 | −0.690068 | − | 0.723745i | \(-0.742419\pi\) | ||||
−0.690068 | + | 0.723745i | \(0.742419\pi\) | |||||||
\(152\) | −8.95919 | − | 1.28207i | −0.726686 | − | 0.103989i | ||||
\(153\) | −1.73653 | + | 1.73653i | −0.140390 | + | 0.140390i | ||||
\(154\) | 0.293179 | − | 0.917844i | 0.0236250 | − | 0.0739620i | ||||
\(155\) | −0.742168 | + | 9.32865i | −0.0596124 | + | 0.749296i | ||||
\(156\) | 5.35764 | − | 7.53080i | 0.428954 | − | 0.602947i | ||||
\(157\) | − | 8.55235i | − | 0.682552i | −0.939963 | − | 0.341276i | \(-0.889141\pi\) | ||
0.939963 | − | 0.341276i | \(-0.110859\pi\) | |||||||
\(158\) | 4.87964 | + | 1.55866i | 0.388203 | + | 0.124000i | ||||
\(159\) | 33.9041 | 2.68877 | ||||||||
\(160\) | −0.688833 | + | 12.6303i | −0.0544571 | + | 0.998516i | ||||
\(161\) | −0.954354 | −0.0752136 | ||||||||
\(162\) | −9.69386 | − | 3.09643i | −0.761622 | − | 0.243278i | ||||
\(163\) | − | 3.57797i | − | 0.280248i | −0.990134 | − | 0.140124i | \(-0.955250\pi\) | ||
0.990134 | − | 0.140124i | \(-0.0447501\pi\) | |||||||
\(164\) | −8.83049 | + | 12.4123i | −0.689545 | + | 0.969238i | ||||
\(165\) | 18.0081 | + | 21.1211i | 1.40193 | + | 1.64428i | ||||
\(166\) | 0.699812 | − | 2.19087i | 0.0543159 | − | 0.170045i | ||||
\(167\) | 0.482874 | − | 0.482874i | 0.0373659 | − | 0.0373659i | −0.688177 | − | 0.725543i | \(-0.741589\pi\) |
0.725543 | + | 0.688177i | \(0.241589\pi\) | |||||||
\(168\) | 0.193416 | − | 1.35161i | 0.0149224 | − | 0.104279i | ||||
\(169\) | −10.5720 | −0.813227 | ||||||||
\(170\) | 1.23601 | − | 0.517965i | 0.0947978 | − | 0.0397261i | ||||
\(171\) | −13.1115 | + | 13.1115i | −1.00266 | + | 1.00266i | ||||
\(172\) | −10.9620 | − | 7.79867i | −0.835842 | − | 0.594643i | ||||
\(173\) | 11.8189 | 0.898576 | 0.449288 | − | 0.893387i | \(-0.351678\pi\) | ||||
0.449288 | + | 0.893387i | \(0.351678\pi\) | |||||||
\(174\) | 1.52686 | − | 0.787578i | 0.115751 | − | 0.0597061i | ||||
\(175\) | −0.659260 | + | 0.477269i | −0.0498354 | + | 0.0360781i | ||||
\(176\) | 15.0661 | + | 7.30216i | 1.13565 | + | 0.550421i | ||||
\(177\) | −4.84870 | + | 4.84870i | −0.364451 | + | 0.364451i | ||||
\(178\) | −21.1704 | − | 6.76228i | −1.58679 | − | 0.506855i | ||||
\(179\) | 4.71524 | − | 4.71524i | 0.352433 | − | 0.352433i | −0.508581 | − | 0.861014i | \(-0.669830\pi\) |
0.861014 | + | 0.508581i | \(0.169830\pi\) | |||||||
\(180\) | 19.8588 | + | 16.6504i | 1.48018 | + | 1.24105i | ||||
\(181\) | 13.1843 | + | 13.1843i | 0.979983 | + | 0.979983i | 0.999804 | − | 0.0198205i | \(-0.00630948\pi\) |
−0.0198205 | + | 0.999804i | \(0.506309\pi\) | |||||||
\(182\) | 0.318793 | − | 0.164439i | 0.0236305 | − | 0.0121890i | ||||
\(183\) | 3.64870 | + | 3.64870i | 0.269720 | + | 0.269720i | ||||
\(184\) | 2.34910 | − | 16.4157i | 0.173178 | − | 1.21018i | ||||
\(185\) | −3.64764 | − | 0.290199i | −0.268180 | − | 0.0213358i | ||||
\(186\) | 16.7200 | + | 5.34073i | 1.22597 | + | 0.391601i | ||||
\(187\) | − | 1.77383i | − | 0.129715i | ||||||
\(188\) | −2.06152 | − | 12.2263i | −0.150352 | − | 0.891694i | ||||
\(189\) | −0.954008 | − | 0.954008i | −0.0693939 | − | 0.0693939i | ||||
\(190\) | 9.33240 | − | 3.91085i | 0.677043 | − | 0.283723i | ||||
\(191\) | − | 13.9872i | − | 1.01208i | −0.862510 | − | 0.506040i | \(-0.831109\pi\) | ||
0.862510 | − | 0.506040i | \(-0.168891\pi\) | |||||||
\(192\) | 22.7727 | + | 6.65384i | 1.64348 | + | 0.480199i | ||||
\(193\) | 3.88875 | + | 3.88875i | 0.279919 | + | 0.279919i | 0.833076 | − | 0.553158i | \(-0.186577\pi\) |
−0.553158 | + | 0.833076i | \(0.686577\pi\) | |||||||
\(194\) | −17.2275 | + | 8.88623i | −1.23686 | + | 0.637994i | ||||
\(195\) | −0.819485 | + | 10.3005i | −0.0586845 | + | 0.737633i | ||||
\(196\) | −8.08503 | + | 11.3645i | −0.577502 | + | 0.811748i | ||||
\(197\) | −22.3277 | −1.59078 | −0.795391 | − | 0.606097i | \(-0.792734\pi\) | ||||
−0.795391 | + | 0.606097i | \(0.792734\pi\) | |||||||
\(198\) | 30.4850 | − | 15.7247i | 2.16648 | − | 1.11750i | ||||
\(199\) | 9.83847i | 0.697431i | 0.937229 | + | 0.348715i | \(0.113382\pi\) | ||||
−0.937229 | + | 0.348715i | \(0.886618\pi\) | |||||||
\(200\) | −6.58669 | − | 12.5146i | −0.465749 | − | 0.884917i | ||||
\(201\) | − | 7.39437i | − | 0.521559i | ||||||
\(202\) | 11.7418 | + | 22.7635i | 0.826150 | + | 1.60164i | ||||
\(203\) | 0.0666793 | 0.00467997 | ||||||||
\(204\) | −0.417931 | − | 2.47863i | −0.0292610 | − | 0.173539i | ||||
\(205\) | 1.35068 | − | 16.9773i | 0.0943355 | − | 1.18575i | ||||
\(206\) | 3.97671 | + | 7.70955i | 0.277071 | + | 0.537150i | ||||
\(207\) | −24.0239 | − | 24.0239i | −1.66978 | − | 1.66978i | ||||
\(208\) | 2.04379 | + | 5.88827i | 0.141711 | + | 0.408278i | ||||
\(209\) | − | 13.3931i | − | 0.926423i | ||||||
\(210\) | 0.590001 | + | 1.40791i | 0.0407140 | + | 0.0971552i | ||||
\(211\) | 11.0531 | + | 11.0531i | 0.760925 | + | 0.760925i | 0.976490 | − | 0.215565i | \(-0.0691592\pi\) |
−0.215565 | + | 0.976490i | \(0.569159\pi\) | |||||||
\(212\) | −13.2547 | + | 18.6310i | −0.910334 | + | 1.27958i | ||||
\(213\) | − | 23.7278i | − | 1.62580i | ||||||
\(214\) | 5.15541 | − | 16.1398i | 0.352417 | − | 1.10330i | ||||
\(215\) | 14.9936 | + | 1.19286i | 1.02255 | + | 0.0813521i | ||||
\(216\) | 18.7580 | − | 14.0615i | 1.27632 | − | 0.956764i | ||||
\(217\) | 0.481706 | + | 0.481706i | 0.0327004 | + | 0.0327004i | ||||
\(218\) | 3.68117 | + | 7.13659i | 0.249320 | + | 0.483351i | ||||
\(219\) | −3.32451 | − | 3.32451i | −0.224650 | − | 0.224650i | ||||
\(220\) | −18.6467 | + | 1.63861i | −1.25716 | + | 0.110475i | ||||
\(221\) | 0.466948 | − | 0.466948i | 0.0314103 | − | 0.0314103i | ||||
\(222\) | −2.08830 | + | 6.53777i | −0.140158 | + | 0.438787i | ||||
\(223\) | −5.93975 | + | 5.93975i | −0.397755 | + | 0.397755i | −0.877440 | − | 0.479686i | \(-0.840751\pi\) |
0.479686 | + | 0.877440i | \(0.340751\pi\) | |||||||
\(224\) | 0.667122 | + | 0.634691i | 0.0445740 | + | 0.0424071i | ||||
\(225\) | −28.6098 | − | 4.58127i | −1.90732 | − | 0.305418i | ||||
\(226\) | −5.93891 | − | 11.5136i | −0.395051 | − | 0.765875i | ||||
\(227\) | −23.2105 | −1.54054 | −0.770269 | − | 0.637720i | \(-0.779878\pi\) | ||||
−0.770269 | + | 0.637720i | \(0.779878\pi\) | |||||||
\(228\) | −3.15555 | − | 18.7147i | −0.208981 | − | 1.23941i | ||||
\(229\) | −5.59944 | + | 5.59944i | −0.370021 | + | 0.370021i | −0.867485 | − | 0.497464i | \(-0.834265\pi\) |
0.497464 | + | 0.867485i | \(0.334265\pi\) | |||||||
\(230\) | 7.16574 | + | 17.0995i | 0.472495 | + | 1.12751i | ||||
\(231\) | 2.02053 | 0.132941 | ||||||||
\(232\) | −0.164128 | + | 1.14694i | −0.0107755 | + | 0.0753003i | ||||
\(233\) | −3.01998 | + | 3.01998i | −0.197845 | + | 0.197845i | −0.799076 | − | 0.601230i | \(-0.794677\pi\) |
0.601230 | + | 0.799076i | \(0.294677\pi\) | |||||||
\(234\) | 12.1644 | + | 3.88556i | 0.795209 | + | 0.254007i | ||||
\(235\) | 8.99391 | + | 10.5487i | 0.586698 | + | 0.688120i | ||||
\(236\) | −0.768884 | − | 4.56004i | −0.0500501 | − | 0.296833i | ||||
\(237\) | 10.7420i | 0.697766i | ||||||||
\(238\) | 0.0296846 | − | 0.0929323i | 0.00192416 | − | 0.00602391i | ||||
\(239\) | 0.00138865 | 8.98241e−5 | 4.49120e−5 | − | 1.00000i | \(-0.499986\pi\) | ||||
4.49120e−5 | 1.00000i | \(0.499986\pi\) | ||||||||
\(240\) | −25.6696 | + | 6.68301i | −1.65696 | + | 0.431387i | ||||
\(241\) | −12.8578 | −0.828245 | −0.414123 | − | 0.910221i | \(-0.635912\pi\) | ||||
−0.414123 | + | 0.910221i | \(0.635912\pi\) | |||||||
\(242\) | −2.80529 | + | 8.78240i | −0.180331 | + | 0.564554i | ||||
\(243\) | 3.52546i | 0.226158i | ||||||||
\(244\) | −3.43148 | + | 0.578593i | −0.219678 | + | 0.0370407i | ||||
\(245\) | 1.23666 | − | 15.5441i | 0.0790071 | − | 0.993077i | ||||
\(246\) | −30.4289 | − | 9.71965i | −1.94008 | − | 0.619702i | ||||
\(247\) | 3.52565 | − | 3.52565i | 0.224332 | − | 0.224332i | ||||
\(248\) | −9.47146 | + | 7.10006i | −0.601438 | + | 0.450854i | ||||
\(249\) | 4.82296 | 0.305643 | ||||||||
\(250\) | 13.5015 | + | 8.22866i | 0.853907 | + | 0.520426i | ||||
\(251\) | −9.14111 | + | 9.14111i | −0.576982 | + | 0.576982i | −0.934071 | − | 0.357089i | \(-0.883769\pi\) |
0.357089 | + | 0.934071i | \(0.383769\pi\) | |||||||
\(252\) | 1.86028 | − | 0.313668i | 0.117187 | − | 0.0197593i | ||||
\(253\) | 24.5399 | 1.54281 | ||||||||
\(254\) | −11.2548 | − | 21.8194i | −0.706190 | − | 1.36907i | ||||
\(255\) | 1.82333 | + | 2.13853i | 0.114181 | + | 0.133920i | ||||
\(256\) | −12.5593 | + | 9.91280i | −0.784957 | + | 0.619550i | ||||
\(257\) | 21.2733 | − | 21.2733i | 1.32699 | − | 1.32699i | 0.419013 | − | 0.907980i | \(-0.362376\pi\) |
0.907980 | − | 0.419013i | \(-0.137624\pi\) | |||||||
\(258\) | 8.58394 | − | 26.8734i | 0.534413 | − | 1.67306i | ||||
\(259\) | −0.188354 | + | 0.188354i | −0.0117038 | + | 0.0117038i | ||||
\(260\) | −5.33996 | − | 4.47725i | −0.331170 | − | 0.277667i | ||||
\(261\) | 1.67851 | + | 1.67851i | 0.103897 | + | 0.103897i | ||||
\(262\) | −7.33076 | − | 14.2120i | −0.452896 | − | 0.878018i | ||||
\(263\) | −16.7214 | − | 16.7214i | −1.03108 | − | 1.03108i | −0.999501 | − | 0.0315818i | \(-0.989946\pi\) |
−0.0315818 | − | 0.999501i | \(-0.510054\pi\) | |||||||
\(264\) | −4.97343 | + | 34.7548i | −0.306094 | + | 2.13901i | ||||
\(265\) | 2.02739 | − | 25.4832i | 0.124541 | − | 1.56542i | ||||
\(266\) | 0.224131 | − | 0.701677i | 0.0137423 | − | 0.0430226i | ||||
\(267\) | − | 46.6043i | − | 2.85213i | ||||||
\(268\) | 4.06336 | + | 2.89079i | 0.248209 | + | 0.176583i | ||||
\(269\) | −15.9096 | − | 15.9096i | −0.970026 | − | 0.970026i | 0.0295378 | − | 0.999564i | \(-0.490596\pi\) |
−0.999564 | + | 0.0295378i | \(0.990596\pi\) | |||||||
\(270\) | −9.93018 | + | 24.2565i | −0.604332 | + | 1.47620i | ||||
\(271\) | 12.3601i | 0.750824i | 0.926858 | + | 0.375412i | \(0.122499\pi\) | ||||
−0.926858 | + | 0.375412i | \(0.877501\pi\) | |||||||
\(272\) | 1.52545 | + | 0.739348i | 0.0924938 | + | 0.0448295i | ||||
\(273\) | 0.531889 | + | 0.531889i | 0.0321914 | + | 0.0321914i | ||||
\(274\) | −2.82894 | − | 5.48440i | −0.170902 | − | 0.331324i | ||||
\(275\) | 16.9520 | − | 12.2723i | 1.02224 | − | 0.740049i | ||||
\(276\) | 34.2904 | − | 5.78183i | 2.06404 | − | 0.348025i | ||||
\(277\) | 21.0270 | 1.26339 | 0.631695 | − | 0.775217i | \(-0.282359\pi\) | ||||
0.631695 | + | 0.775217i | \(0.282359\pi\) | |||||||
\(278\) | 11.2044 | + | 21.7217i | 0.671994 | + | 1.30278i | ||||
\(279\) | 24.2520i | 1.45193i | ||||||||
\(280\) | −1.00434 | − | 0.226199i | −0.0600205 | − | 0.0135180i | ||||
\(281\) | 10.6807i | 0.637158i | 0.947896 | + | 0.318579i | \(0.103206\pi\) | ||||
−0.947896 | + | 0.318579i | \(0.896794\pi\) | |||||||
\(282\) | 23.1075 | − | 11.9192i | 1.37603 | − | 0.709780i | ||||
\(283\) | 12.5946 | 0.748673 | 0.374336 | − | 0.927293i | \(-0.377871\pi\) | ||||
0.374336 | + | 0.927293i | \(0.377871\pi\) | |||||||
\(284\) | 13.0389 | + | 9.27626i | 0.773716 | + | 0.550445i | ||||
\(285\) | 13.7669 | + | 16.1468i | 0.815481 | + | 0.956452i | ||||
\(286\) | −8.19733 | + | 4.22832i | −0.484718 | + | 0.250026i | ||||
\(287\) | −0.876663 | − | 0.876663i | −0.0517478 | − | 0.0517478i | ||||
\(288\) | 0.816372 | + | 32.7705i | 0.0481052 | + | 1.93102i | ||||
\(289\) | 16.8204i | 0.989435i | ||||||||
\(290\) | −0.500660 | − | 1.19472i | −0.0293998 | − | 0.0701563i | ||||
\(291\) | −28.7432 | − | 28.7432i | −1.68496 | − | 1.68496i | ||||
\(292\) | 3.12659 | − | 0.527185i | 0.182970 | − | 0.0308512i | ||||
\(293\) | 3.43132i | 0.200460i | 0.994964 | + | 0.100230i | \(0.0319579\pi\) | ||||
−0.994964 | + | 0.100230i | \(0.968042\pi\) | |||||||
\(294\) | −27.8602 | − | 8.89913i | −1.62484 | − | 0.519008i | ||||
\(295\) | 3.35446 | + | 3.93434i | 0.195304 | + | 0.229066i | ||||
\(296\) | −2.77623 | − | 3.70348i | −0.161365 | − | 0.215260i | ||||
\(297\) | 24.5310 | + | 24.5310i | 1.42344 | + | 1.42344i | ||||
\(298\) | 4.60670 | − | 2.37621i | 0.266859 | − | 0.137650i | ||||
\(299\) | 6.45996 | + | 6.45996i | 0.373589 | + | 0.373589i | ||||
\(300\) | 20.7961 | − | 21.1426i | 1.20066 | − | 1.22067i | ||||
\(301\) | 0.774227 | − | 0.774227i | 0.0446257 | − | 0.0446257i | ||||
\(302\) | 22.8470 | + | 7.29781i | 1.31470 | + | 0.419942i | ||||
\(303\) | −37.9798 | + | 37.9798i | −2.18188 | + | 2.18188i | ||||
\(304\) | 11.5177 | + | 5.58238i | 0.660588 | + | 0.320171i | ||||
\(305\) | 2.96063 | − | 2.52427i | 0.169525 | − | 0.144539i | ||||
\(306\) | 3.08663 | − | 1.59213i | 0.176451 | − | 0.0910162i | ||||
\(307\) | −11.8104 | −0.674053 | −0.337027 | − | 0.941495i | \(-0.609421\pi\) | ||||
−0.337027 | + | 0.941495i | \(0.609421\pi\) | |||||||
\(308\) | −0.789916 | + | 1.11032i | −0.0450097 | + | 0.0632665i | ||||
\(309\) | −12.8630 | + | 12.8630i | −0.731750 | + | 0.731750i | ||||
\(310\) | 5.01404 | − | 12.2478i | 0.284778 | − | 0.695628i | ||||
\(311\) | 22.6262 | 1.28301 | 0.641506 | − | 0.767118i | \(-0.278310\pi\) | ||||
0.641506 | + | 0.767118i | \(0.278310\pi\) | |||||||
\(312\) | −10.4582 | + | 7.83973i | −0.592077 | + | 0.443837i | ||||
\(313\) | −7.08945 | + | 7.08945i | −0.400719 | + | 0.400719i | −0.878486 | − | 0.477767i | \(-0.841446\pi\) |
0.477767 | + | 0.878486i | \(0.341446\pi\) | |||||||
\(314\) | −3.68017 | + | 11.5214i | −0.207684 | + | 0.650188i | ||||
\(315\) | −1.60503 | + | 1.36846i | −0.0904329 | + | 0.0771040i | ||||
\(316\) | −5.90294 | − | 4.19952i | −0.332066 | − | 0.236242i | ||||
\(317\) | 25.1265i | 1.41124i | 0.708589 | + | 0.705621i | \(0.249332\pi\) | ||||
−0.708589 | + | 0.705621i | \(0.750668\pi\) | |||||||
\(318\) | −45.6742 | − | 14.5893i | −2.56128 | − | 0.818128i | ||||
\(319\) | −1.71457 | −0.0959974 | ||||||||
\(320\) | 6.36294 | − | 16.7186i | 0.355699 | − | 0.934601i | ||||
\(321\) | 35.5300 | 1.98309 | ||||||||
\(322\) | 1.28566 | + | 0.410669i | 0.0716473 | + | 0.0228857i | ||||
\(323\) | − | 1.35606i | − | 0.0754535i | ||||||
\(324\) | 11.7267 | + | 8.34274i | 0.651485 | + | 0.463486i | ||||
\(325\) | 7.69309 | + | 1.23189i | 0.426736 | + | 0.0683329i | ||||
\(326\) | −1.53964 | + | 4.82008i | −0.0852726 | + | 0.266960i | ||||
\(327\) | −11.9070 | + | 11.9070i | −0.658460 | + | 0.658460i | ||||
\(328\) | 17.2372 | − | 12.9215i | 0.951765 | − | 0.713469i | ||||
\(329\) | 1.00913 | 0.0556349 | ||||||||
\(330\) | −15.1711 | − | 36.2026i | −0.835141 | − | 1.99289i | ||||
\(331\) | 5.80829 | − | 5.80829i | 0.319253 | − | 0.319253i | −0.529227 | − | 0.848480i | \(-0.677518\pi\) |
0.848480 | + | 0.529227i | \(0.177518\pi\) | |||||||
\(332\) | −1.88551 | + | 2.65032i | −0.103481 | + | 0.145455i | ||||
\(333\) | −9.48287 | −0.519658 | ||||||||
\(334\) | −0.858293 | + | 0.442721i | −0.0469637 | + | 0.0242246i | ||||
\(335\) | −5.55778 | − | 0.442166i | −0.303654 | − | 0.0241581i | ||||
\(336\) | −0.842174 | + | 1.73760i | −0.0459443 | + | 0.0947939i | ||||
\(337\) | −7.41679 | + | 7.41679i | −0.404019 | + | 0.404019i | −0.879647 | − | 0.475628i | \(-0.842221\pi\) |
0.475628 | + | 0.879647i | \(0.342221\pi\) | |||||||
\(338\) | 14.2421 | + | 4.54923i | 0.774667 | + | 0.247445i | ||||
\(339\) | 19.2099 | − | 19.2099i | 1.04334 | − | 1.04334i | ||||
\(340\) | −1.88799 | + | 0.165910i | −0.102391 | + | 0.00899776i | ||||
\(341\) | −12.3864 | − | 12.3864i | −0.670763 | − | 0.670763i | ||||
\(342\) | 23.3053 | − | 12.0213i | 1.26021 | − | 0.650035i | ||||
\(343\) | −1.60836 | − | 1.60836i | −0.0868434 | − | 0.0868434i | ||||
\(344\) | 11.4116 | + | 15.2231i | 0.615274 | + | 0.820774i | ||||
\(345\) | −29.5853 | + | 25.2247i | −1.59282 | + | 1.35805i | ||||
\(346\) | −15.9220 | − | 5.08581i | −0.855970 | − | 0.273415i | ||||
\(347\) | 18.2493i | 0.979673i | 0.871814 | + | 0.489837i | \(0.162944\pi\) | ||||
−0.871814 | + | 0.489837i | \(0.837056\pi\) | |||||||
\(348\) | −2.39582 | + | 0.403968i | −0.128430 | + | 0.0216549i | ||||
\(349\) | 19.4413 | + | 19.4413i | 1.04067 | + | 1.04067i | 0.999137 | + | 0.0415330i | \(0.0132242\pi\) |
0.0415330 | + | 0.999137i | \(0.486776\pi\) | |||||||
\(350\) | 1.09350 | − | 0.359269i | 0.0584501 | − | 0.0192038i | ||||
\(351\) | 12.9152i | 0.689364i | ||||||||
\(352\) | −17.1541 | − | 16.3202i | −0.914319 | − | 0.869871i | ||||
\(353\) | −1.13598 | − | 1.13598i | −0.0604622 | − | 0.0604622i | 0.676229 | − | 0.736691i | \(-0.263613\pi\) |
−0.736691 | + | 0.676229i | \(0.763613\pi\) | |||||||
\(354\) | 8.61841 | − | 4.44551i | 0.458063 | − | 0.236276i | ||||
\(355\) | −17.8343 | − | 1.41886i | −0.946549 | − | 0.0753054i | ||||
\(356\) | 25.6100 | + | 18.2197i | 1.35733 | + | 0.965643i | ||||
\(357\) | 0.204580 | 0.0108275 | ||||||||
\(358\) | −8.38118 | + | 4.32315i | −0.442959 | + | 0.228485i | ||||
\(359\) | − | 28.4140i | − | 1.49963i | −0.661645 | − | 0.749817i | \(-0.730141\pi\) | ||
0.661645 | − | 0.749817i | \(-0.269859\pi\) | |||||||
\(360\) | −19.5880 | − | 30.9762i | −1.03238 | − | 1.63259i | ||||
\(361\) | 8.76116i | 0.461114i | ||||||||
\(362\) | −12.0880 | − | 23.4347i | −0.635331 | − | 1.23170i | ||||
\(363\) | −19.3334 | −1.01474 | ||||||||
\(364\) | −0.500224 | + | 0.0843445i | −0.0262189 | + | 0.00442085i | ||||
\(365\) | −2.69758 | + | 2.29998i | −0.141198 | + | 0.120387i | ||||
\(366\) | −3.34530 | − | 6.48545i | −0.174861 | − | 0.339000i | ||||
\(367\) | 2.29692 | + | 2.29692i | 0.119898 | + | 0.119898i | 0.764510 | − | 0.644612i | \(-0.222981\pi\) |
−0.644612 | + | 0.764510i | \(0.722981\pi\) | |||||||
\(368\) | −10.2285 | + | 21.1037i | −0.533195 | + | 1.10011i | ||||
\(369\) | − | 44.1364i | − | 2.29765i | ||||||
\(370\) | 4.78907 | + | 1.96056i | 0.248972 | + | 0.101925i | ||||
\(371\) | −1.31588 | − | 1.31588i | −0.0683172 | − | 0.0683172i | ||||
\(372\) | −20.2263 | − | 14.3896i | −1.04869 | − | 0.746066i | ||||
\(373\) | − | 18.0787i | − | 0.936081i | −0.883707 | − | 0.468040i | \(-0.844960\pi\) | ||
0.883707 | − | 0.468040i | \(-0.155040\pi\) | |||||||
\(374\) | −0.763298 | + | 2.38963i | −0.0394692 | + | 0.123565i | ||||
\(375\) | −7.82251 | + | 32.2206i | −0.403953 | + | 1.66386i | ||||
\(376\) | −2.48392 | + | 17.3578i | −0.128098 | + | 0.895162i | ||||
\(377\) | −0.451348 | − | 0.451348i | −0.0232456 | − | 0.0232456i | ||||
\(378\) | 0.874679 | + | 1.69572i | 0.0449886 | + | 0.0872184i | ||||
\(379\) | 2.79031 | + | 2.79031i | 0.143328 | + | 0.143328i | 0.775130 | − | 0.631802i | \(-0.217684\pi\) |
−0.631802 | + | 0.775130i | \(0.717684\pi\) | |||||||
\(380\) | −14.2551 | + | 1.25269i | −0.731271 | + | 0.0642617i | ||||
\(381\) | 36.4046 | − | 36.4046i | 1.86506 | − | 1.86506i | ||||
\(382\) | −6.01885 | + | 18.8430i | −0.307951 | + | 0.964090i | ||||
\(383\) | 8.12206 | − | 8.12206i | 0.415018 | − | 0.415018i | −0.468464 | − | 0.883482i | \(-0.655193\pi\) |
0.883482 | + | 0.468464i | \(0.155193\pi\) | |||||||
\(384\) | −27.8152 | − | 18.7631i | −1.41944 | − | 0.957501i | ||||
\(385\) | 0.120823 | − | 1.51868i | 0.00615770 | − | 0.0773990i | ||||
\(386\) | −3.56539 | − | 6.91213i | −0.181474 | − | 0.351818i | ||||
\(387\) | 38.9792 | 1.98142 | ||||||||
\(388\) | 27.0320 | − | 4.55796i | 1.37234 | − | 0.231396i | ||||
\(389\) | 14.4341 | − | 14.4341i | 0.731839 | − | 0.731839i | −0.239145 | − | 0.970984i | \(-0.576867\pi\) |
0.970984 | + | 0.239145i | \(0.0768670\pi\) | |||||||
\(390\) | 5.53639 | − | 13.5237i | 0.280346 | − | 0.684801i | ||||
\(391\) | 2.48468 | 0.125656 | ||||||||
\(392\) | 15.7821 | − | 11.8307i | 0.797114 | − | 0.597539i | ||||
\(393\) | 23.7119 | − | 23.7119i | 1.19611 | − | 1.19611i | ||||
\(394\) | 30.0789 | + | 9.60785i | 1.51535 | + | 0.484036i | ||||
\(395\) | 8.07392 | + | 0.642344i | 0.406243 | + | 0.0323198i | ||||
\(396\) | −47.8346 | + | 8.06556i | −2.40378 | + | 0.405310i | ||||
\(397\) | 35.1624i | 1.76475i | 0.470549 | + | 0.882374i | \(0.344056\pi\) | ||||
−0.470549 | + | 0.882374i | \(0.655944\pi\) | |||||||
\(398\) | 4.23360 | − | 13.2540i | 0.212211 | − | 0.664362i | ||||
\(399\) | 1.54466 | 0.0773298 | ||||||||
\(400\) | 3.48814 | + | 19.6935i | 0.174407 | + | 0.984674i | ||||
\(401\) | −23.5164 | −1.17435 | −0.587176 | − | 0.809459i | \(-0.699760\pi\) | ||||
−0.587176 | + | 0.809459i | \(0.699760\pi\) | |||||||
\(402\) | −3.18188 | + | 9.96138i | −0.158698 | + | 0.496828i | ||||
\(403\) | − | 6.52128i | − | 0.324848i | ||||||
\(404\) | −6.02265 | − | 35.7187i | −0.299638 | − | 1.77707i | ||||
\(405\) | −16.0396 | − | 1.27608i | −0.797014 | − | 0.0634087i | ||||
\(406\) | −0.0898275 | − | 0.0286928i | −0.00445806 | − | 0.00142400i | ||||
\(407\) | 4.84328 | − | 4.84328i | 0.240072 | − | 0.240072i | ||||
\(408\) | −0.503563 | + | 3.51895i | −0.0249301 | + | 0.174214i | ||||
\(409\) | −23.2595 | −1.15011 | −0.575054 | − | 0.818115i | \(-0.695019\pi\) | ||||
−0.575054 | + | 0.818115i | \(0.695019\pi\) | |||||||
\(410\) | −9.12510 | + | 22.2899i | −0.450657 | + | 1.10082i | ||||
\(411\) | 9.15043 | − | 9.15043i | 0.451357 | − | 0.451357i | ||||
\(412\) | −2.03975 | − | 12.0972i | −0.100491 | − | 0.595986i | ||||
\(413\) | 0.376374 | 0.0185201 | ||||||||
\(414\) | 22.0262 | + | 42.7017i | 1.08253 | + | 2.09868i | ||||
\(415\) | 0.288401 | − | 3.62505i | 0.0141571 | − | 0.177947i | ||||
\(416\) | −0.219520 | − | 8.81188i | −0.0107628 | − | 0.432038i | ||||
\(417\) | −36.2415 | + | 36.2415i | −1.77475 | + | 1.77475i | ||||
\(418\) | −5.76322 | + | 18.0427i | −0.281888 | + | 0.882496i | ||||
\(419\) | −6.63975 | + | 6.63975i | −0.324373 | + | 0.324373i | −0.850442 | − | 0.526069i | \(-0.823665\pi\) |
0.526069 | + | 0.850442i | \(0.323665\pi\) | |||||||
\(420\) | −0.188985 | − | 2.15056i | −0.00922151 | − | 0.104937i | ||||
\(421\) | 7.28216 | + | 7.28216i | 0.354911 | + | 0.354911i | 0.861933 | − | 0.507022i | \(-0.169254\pi\) |
−0.507022 | + | 0.861933i | \(0.669254\pi\) | |||||||
\(422\) | −10.1340 | − | 19.6465i | −0.493314 | − | 0.956376i | ||||
\(423\) | 25.4027 | + | 25.4027i | 1.23512 | + | 1.23512i | ||||
\(424\) | 25.8733 | − | 19.3953i | 1.25652 | − | 0.941919i | ||||
\(425\) | 1.71640 | − | 1.24258i | 0.0832576 | − | 0.0602740i | ||||
\(426\) | −10.2103 | + | 31.9650i | −0.494691 | + | 1.54871i | ||||
\(427\) | − | 0.283225i | − | 0.0137062i | ||||||
\(428\) | −13.8903 | + | 19.5245i | −0.671413 | + | 0.943751i | ||||
\(429\) | −13.6768 | − | 13.6768i | −0.660323 | − | 0.660323i | ||||
\(430\) | −19.6854 | − | 8.05886i | −0.949314 | − | 0.388633i | ||||
\(431\) | − | 11.7250i | − | 0.564771i | −0.959301 | − | 0.282386i | \(-0.908874\pi\) | ||
0.959301 | − | 0.282386i | \(-0.0911258\pi\) | |||||||
\(432\) | −31.3208 | + | 10.8713i | −1.50692 | + | 0.523045i | ||||
\(433\) | −20.8827 | − | 20.8827i | −1.00356 | − | 1.00356i | −0.999994 | − | 0.00356603i | \(-0.998865\pi\) |
−0.00356603 | − | 0.999994i | \(-0.501135\pi\) | |||||||
\(434\) | −0.441651 | − | 0.856218i | −0.0211999 | − | 0.0410998i | ||||
\(435\) | 2.06708 | − | 1.76242i | 0.0991090 | − | 0.0845014i | ||||
\(436\) | −1.88816 | − | 11.1982i | −0.0904265 | − | 0.536294i | ||||
\(437\) | 18.7604 | 0.897430 | ||||||||
\(438\) | 3.04807 | + | 5.90921i | 0.145642 | + | 0.282353i | ||||
\(439\) | 7.53661i | 0.359703i | 0.983694 | + | 0.179851i | \(0.0575617\pi\) | ||||
−0.983694 | + | 0.179851i | \(0.942438\pi\) | |||||||
\(440\) | 25.8251 | + | 5.81640i | 1.23117 | + | 0.277286i | ||||
\(441\) | − | 40.4105i | − | 1.92431i | ||||||
\(442\) | −0.829985 | + | 0.428120i | −0.0394784 | + | 0.0203636i | ||||
\(443\) | −25.7280 | −1.22237 | −0.611187 | − | 0.791486i | \(-0.709308\pi\) | ||||
−0.611187 | + | 0.791486i | \(0.709308\pi\) | |||||||
\(444\) | 5.62655 | − | 7.90879i | 0.267024 | − | 0.375334i | ||||
\(445\) | −35.0289 | − | 2.78682i | −1.66053 | − | 0.132108i | ||||
\(446\) | 10.5577 | − | 5.44584i | 0.499922 | − | 0.257868i | ||||
\(447\) | 7.68604 | + | 7.68604i | 0.363537 | + | 0.363537i | ||||
\(448\) | −0.625604 | − | 1.14210i | −0.0295570 | − | 0.0539591i | ||||
\(449\) | − | 2.33824i | − | 0.110348i | −0.998477 | − | 0.0551741i | \(-0.982429\pi\) | ||
0.998477 | − | 0.0551741i | \(-0.0175714\pi\) | |||||||
\(450\) | 36.5705 | + | 18.4828i | 1.72395 | + | 0.871287i | ||||
\(451\) | 22.5422 | + | 22.5422i | 1.06147 | + | 1.06147i | ||||
\(452\) | 3.04621 | + | 18.0662i | 0.143282 | + | 0.849765i | ||||
\(453\) | 50.2950i | 2.36306i | ||||||||
\(454\) | 31.2682 | + | 9.98774i | 1.46749 | + | 0.468748i | ||||
\(455\) | 0.431586 | − | 0.367975i | 0.0202331 | − | 0.0172509i | ||||
\(456\) | −3.80211 | + | 26.5695i | −0.178050 | + | 1.24423i | ||||
\(457\) | −10.4561 | − | 10.4561i | −0.489115 | − | 0.489115i | 0.418912 | − | 0.908027i | \(-0.362412\pi\) |
−0.908027 | + | 0.418912i | \(0.862412\pi\) | |||||||
\(458\) | 9.95282 | − | 5.13383i | 0.465065 | − | 0.239888i | ||||
\(459\) | 2.48378 | + | 2.48378i | 0.115933 | + | 0.115933i | ||||
\(460\) | −2.29528 | − | 26.1192i | −0.107018 | − | 1.21782i | ||||
\(461\) | 15.6903 | − | 15.6903i | 0.730769 | − | 0.730769i | −0.240003 | − | 0.970772i | \(-0.577148\pi\) |
0.970772 | + | 0.240003i | \(0.0771484\pi\) | |||||||
\(462\) | −2.72197 | − | 0.869455i | −0.126637 | − | 0.0404507i | ||||
\(463\) | 19.6332 | − | 19.6332i | 0.912434 | − | 0.912434i | −0.0840297 | − | 0.996463i | \(-0.526779\pi\) |
0.996463 | + | 0.0840297i | \(0.0267791\pi\) | |||||||
\(464\) | 0.714647 | − | 1.47448i | 0.0331766 | − | 0.0684511i | ||||
\(465\) | 27.6652 | + | 2.20098i | 1.28294 | + | 0.102068i | ||||
\(466\) | 5.36791 | − | 2.76886i | 0.248664 | − | 0.128265i | ||||
\(467\) | −24.4862 | −1.13309 | −0.566543 | − | 0.824032i | \(-0.691719\pi\) | ||||
−0.566543 | + | 0.824032i | \(0.691719\pi\) | |||||||
\(468\) | −14.7153 | − | 10.4689i | −0.680216 | − | 0.483926i | ||||
\(469\) | −0.286989 | + | 0.286989i | −0.0132519 | + | 0.0132519i | ||||
\(470\) | −7.57700 | − | 18.0809i | −0.349501 | − | 0.834010i | ||||
\(471\) | −25.3630 | −1.16866 | ||||||||
\(472\) | −0.926426 | + | 6.47395i | −0.0426422 | + | 0.297987i | ||||
\(473\) | −19.9082 | + | 19.9082i | −0.915380 | + | 0.915380i | ||||
\(474\) | 4.62239 | − | 14.4711i | 0.212313 | − | 0.664681i | ||||
\(475\) | 12.9595 | − | 9.38199i | 0.594624 | − | 0.430475i | ||||
\(476\) | −0.0799795 | + | 0.112421i | −0.00366586 | + | 0.00515280i | ||||
\(477\) | − | 66.2493i | − | 3.03335i | ||||||
\(478\) | −0.00187073 | 0.000597550i | −8.55650e−5 | 2.73313e-5i | ||||||
\(479\) | −37.0609 | −1.69335 | −0.846677 | − | 0.532108i | \(-0.821400\pi\) | ||||
−0.846677 | + | 0.532108i | \(0.821400\pi\) | |||||||
\(480\) | 37.4567 | + | 2.04281i | 1.70966 | + | 0.0932412i | ||||
\(481\) | 2.54991 | 0.116266 | ||||||||
\(482\) | 17.3215 | + | 5.53286i | 0.788973 | + | 0.252015i | ||||
\(483\) | 2.83024i | 0.128781i | ||||||||
\(484\) | 7.55832 | − | 10.6241i | 0.343560 | − | 0.482915i | ||||
\(485\) | −23.3229 | + | 19.8853i | −1.05904 | + | 0.902945i | ||||
\(486\) | 1.51704 | − | 4.74935i | 0.0688145 | − | 0.215435i | ||||
\(487\) | 20.1912 | − | 20.1912i | 0.914950 | − | 0.914950i | −0.0817061 | − | 0.996656i | \(-0.526037\pi\) |
0.996656 | + | 0.0817061i | \(0.0260369\pi\) | |||||||
\(488\) | 4.87172 | + | 0.697145i | 0.220532 | + | 0.0315583i | ||||
\(489\) | −10.6109 | −0.479840 | ||||||||
\(490\) | −8.35477 | + | 20.4082i | −0.377430 | + | 0.921949i | ||||
\(491\) | −7.45822 | + | 7.45822i | −0.336585 | + | 0.336585i | −0.855080 | − | 0.518496i | \(-0.826492\pi\) |
0.518496 | + | 0.855080i | \(0.326492\pi\) | |||||||
\(492\) | 36.8101 | + | 26.1878i | 1.65953 | + | 1.18064i | ||||
\(493\) | −0.173601 | −0.00781860 | ||||||||
\(494\) | −6.26673 | + | 3.23248i | −0.281953 | + | 0.145436i | ||||
\(495\) | 41.2711 | − | 35.1881i | 1.85500 | − | 1.58159i | ||||
\(496\) | 15.8148 | − | 5.48923i | 0.710104 | − | 0.246474i | ||||
\(497\) | −0.920917 | + | 0.920917i | −0.0413088 | + | 0.0413088i | ||||
\(498\) | −6.49728 | − | 2.07537i | −0.291150 | − | 0.0929996i | ||||
\(499\) | −8.17420 | + | 8.17420i | −0.365927 | + | 0.365927i | −0.865990 | − | 0.500062i | \(-0.833311\pi\) |
0.500062 | + | 0.865990i | \(0.333311\pi\) | |||||||
\(500\) | −14.6477 | − | 16.8951i | −0.655065 | − | 0.755573i | ||||
\(501\) | −1.43202 | − | 1.43202i | −0.0639778 | − | 0.0639778i | ||||
\(502\) | 16.2480 | − | 8.38100i | 0.725185 | − | 0.374062i | ||||
\(503\) | −29.2327 | − | 29.2327i | −1.30342 | − | 1.30342i | −0.926072 | − | 0.377348i | \(-0.876836\pi\) |
−0.377348 | − | 0.926072i | \(-0.623164\pi\) | |||||||
\(504\) | −2.64107 | − | 0.377938i | −0.117642 | − | 0.0168347i | ||||
\(505\) | 26.2754 | + | 30.8176i | 1.16924 | + | 1.37136i | ||||
\(506\) | −33.0591 | − | 10.5598i | −1.46966 | − | 0.469440i | ||||
\(507\) | 31.3523i | 1.39241i | ||||||||
\(508\) | 5.77287 | + | 34.2373i | 0.256130 | + | 1.51903i | ||||
\(509\) | 20.0340 | + | 20.0340i | 0.887992 | + | 0.887992i | 0.994330 | − | 0.106338i | \(-0.0339125\pi\) |
−0.106338 | + | 0.994330i | \(0.533912\pi\) | |||||||
\(510\) | −1.53608 | − | 3.66553i | −0.0680189 | − | 0.162313i | ||||
\(511\) | 0.258061i | 0.0114159i | ||||||||
\(512\) | 21.1850 | − | 7.94969i | 0.936252 | − | 0.351330i | ||||
\(513\) | 18.7536 | + | 18.7536i | 0.827991 | + | 0.827991i | ||||
\(514\) | −37.8126 | + | 19.5044i | −1.66784 | + | 0.860301i | ||||
\(515\) | 8.89895 | + | 10.4373i | 0.392135 | + | 0.459922i | ||||
\(516\) | −23.1278 | + | 32.5089i | −1.01815 | + | 1.43113i | ||||
\(517\) | −25.9483 | −1.14121 | ||||||||
\(518\) | 0.334794 | − | 0.172692i | 0.0147100 | − | 0.00758765i | ||||
\(519\) | − | 35.0504i | − | 1.53854i | ||||||
\(520\) | 5.26715 | + | 8.32940i | 0.230980 | + | 0.365269i | ||||
\(521\) | − | 5.89264i | − | 0.258161i | −0.991634 | − | 0.129081i | \(-0.958797\pi\) | ||
0.991634 | − | 0.129081i | \(-0.0412026\pi\) | |||||||
\(522\) | −1.53894 | − | 2.98351i | −0.0673576 | − | 0.130585i | ||||
\(523\) | −24.6537 | −1.07803 | −0.539015 | − | 0.842296i | \(-0.681203\pi\) | ||||
−0.539015 | + | 0.842296i | \(0.681203\pi\) | |||||||
\(524\) | 3.76012 | + | 22.3003i | 0.164262 | + | 0.974191i | ||||
\(525\) | 1.41539 | + | 1.95511i | 0.0617729 | + | 0.0853280i | ||||
\(526\) | 15.3309 | + | 29.7217i | 0.668460 | + | 1.29593i | ||||
\(527\) | −1.25413 | − | 1.25413i | −0.0546309 | − | 0.0546309i | ||||
\(528\) | 21.6554 | − | 44.6801i | 0.942429 | − | 1.94445i | ||||
\(529\) | 11.3742i | 0.494528i | ||||||||
\(530\) | −13.6969 | + | 33.4574i | −0.594955 | + | 1.45330i | ||||
\(531\) | 9.47444 | + | 9.47444i | 0.411156 | + | 0.411156i | ||||
\(532\) | −0.603878 | + | 0.848823i | −0.0261814 | + | 0.0368012i | ||||
\(533\) | 11.8681i | 0.514066i | ||||||||
\(534\) | −20.0543 | + | 62.7833i | −0.867835 | + | 2.71690i | ||||
\(535\) | 2.12461 | − | 26.7052i | 0.0918549 | − | 1.15457i | ||||
\(536\) | −4.23004 | − | 5.64286i | −0.182710 | − | 0.243735i | ||||
\(537\) | −13.9836 | − | 13.9836i | −0.603435 | − | 0.603435i | ||||
\(538\) | 14.5867 | + | 28.2788i | 0.628876 | + | 1.21919i | ||||
\(539\) | 20.6392 | + | 20.6392i | 0.888994 | + | 0.888994i | ||||
\(540\) | 23.8153 | − | 28.4042i | 1.02485 | − | 1.22232i | ||||
\(541\) | −27.1762 | + | 27.1762i | −1.16840 | + | 1.16840i | −0.185812 | + | 0.982585i | \(0.559492\pi\) |
−0.982585 | + | 0.185812i | \(0.940508\pi\) | |||||||
\(542\) | 5.31869 | − | 16.6510i | 0.228457 | − | 0.715223i | ||||
\(543\) | 39.0996 | − | 39.0996i | 1.67792 | − | 1.67792i | ||||
\(544\) | −1.73687 | − | 1.65243i | −0.0744676 | − | 0.0708475i | ||||
\(545\) | 8.23759 | + | 9.66162i | 0.352860 | + | 0.413858i | ||||
\(546\) | −0.487661 | − | 0.945416i | −0.0208700 | − | 0.0404601i | ||||
\(547\) | 3.69225 | 0.157869 | 0.0789347 | − | 0.996880i | \(-0.474848\pi\) | ||||
0.0789347 | + | 0.996880i | \(0.474848\pi\) | |||||||
\(548\) | 1.45103 | + | 8.60567i | 0.0619850 | + | 0.367616i | ||||
\(549\) | 7.12962 | − | 7.12962i | 0.304285 | − | 0.304285i | ||||
\(550\) | −28.1179 | + | 9.23813i | −1.19895 | + | 0.393915i | ||||
\(551\) | −1.31076 | −0.0558402 | ||||||||
\(552\) | −48.6826 | − | 6.96651i | −2.07207 | − | 0.296514i | ||||
\(553\) | 0.416915 | − | 0.416915i | 0.0177290 | − | 0.0177290i | ||||
\(554\) | −28.3267 | − | 9.04815i | −1.20349 | − | 0.384419i | ||||
\(555\) | −0.860616 | + | 10.8175i | −0.0365311 | + | 0.459177i | ||||
\(556\) | −5.74700 | − | 34.0839i | −0.243727 | − | 1.44548i | ||||
\(557\) | − | 12.2117i | − | 0.517426i | −0.965954 | − | 0.258713i | \(-0.916702\pi\) | ||
0.965954 | − | 0.258713i | \(-0.0832984\pi\) | |||||||
\(558\) | 10.4359 | − | 32.6712i | 0.441786 | − | 1.38308i | ||||
\(559\) | −10.4814 | −0.443315 | ||||||||
\(560\) | 1.25566 | + | 0.736902i | 0.0530614 | + | 0.0311398i | ||||
\(561\) | −5.26049 | −0.222098 | ||||||||
\(562\) | 4.59603 | − | 14.3886i | 0.193872 | − | 0.606947i | ||||
\(563\) | − | 12.2211i | − | 0.515057i | −0.966271 | − | 0.257528i | \(-0.917092\pi\) | ||
0.966271 | − | 0.257528i | \(-0.0829081\pi\) | |||||||
\(564\) | −36.2584 | + | 6.11366i | −1.52676 | + | 0.257432i | ||||
\(565\) | −13.2899 | − | 15.5873i | −0.559110 | − | 0.655763i | ||||
\(566\) | −16.9669 | − | 5.41960i | −0.713174 | − | 0.227803i | ||||
\(567\) | −0.828241 | + | 0.828241i | −0.0347829 | + | 0.0347829i | ||||
\(568\) | −13.5738 | − | 18.1074i | −0.569543 | − | 0.759768i | ||||
\(569\) | 30.9592 | 1.29788 | 0.648938 | − | 0.760841i | \(-0.275213\pi\) | ||||
0.648938 | + | 0.760841i | \(0.275213\pi\) | |||||||
\(570\) | −11.5981 | − | 27.6763i | −0.485789 | − | 1.15923i | ||||
\(571\) | 30.1508 | − | 30.1508i | 1.26177 | − | 1.26177i | 0.311539 | − | 0.950233i | \(-0.399156\pi\) |
0.950233 | − | 0.311539i | \(-0.100844\pi\) | |||||||
\(572\) | 12.8626 | − | 2.16881i | 0.537812 | − | 0.0906823i | ||||
\(573\) | −41.4806 | −1.73288 | ||||||||
\(574\) | 0.803765 | + | 1.55824i | 0.0335485 | + | 0.0650397i | ||||
\(575\) | 17.1904 | + | 23.7454i | 0.716889 | + | 0.990252i | ||||
\(576\) | 13.0017 | − | 44.4983i | 0.541738 | − | 1.85410i | ||||
\(577\) | 1.98215 | − | 1.98215i | 0.0825181 | − | 0.0825181i | −0.664643 | − | 0.747161i | \(-0.731416\pi\) |
0.747161 | + | 0.664643i | \(0.231416\pi\) | |||||||
\(578\) | 7.23800 | − | 22.6597i | 0.301061 | − | 0.942520i | ||||
\(579\) | 11.5325 | − | 11.5325i | 0.479276 | − | 0.479276i | ||||
\(580\) | 0.160367 | + | 1.82491i | 0.00665890 | + | 0.0757754i | ||||
\(581\) | −0.187188 | − | 0.187188i | −0.00776586 | − | 0.00776586i | ||||
\(582\) | 26.3531 | + | 51.0901i | 1.09237 | + | 2.11775i | ||||
\(583\) | 33.8361 | + | 33.8361i | 1.40135 | + | 1.40135i | ||||
\(584\) | −4.43886 | − | 0.635204i | −0.183681 | − | 0.0262849i | ||||
\(585\) | 20.1273 | + | 1.60129i | 0.832163 | + | 0.0662051i | ||||
\(586\) | 1.47653 | − | 4.62253i | 0.0609951 | − | 0.190955i | ||||
\(587\) | − | 26.9680i | − | 1.11309i | −0.830818 | − | 0.556544i | \(-0.812127\pi\) | ||
0.830818 | − | 0.556544i | \(-0.187873\pi\) | |||||||
\(588\) | 33.7026 | + | 23.9771i | 1.38987 | + | 0.988797i | ||||
\(589\) | −9.46923 | − | 9.46923i | −0.390173 | − | 0.390173i | ||||
\(590\) | −2.82599 | − | 6.74363i | −0.116344 | − | 0.277631i | ||||
\(591\) | 66.2153i | 2.72373i | ||||||||
\(592\) | 2.14637 | + | 6.18381i | 0.0882152 | + | 0.254153i | ||||
\(593\) | 16.6701 | + | 16.6701i | 0.684560 | + | 0.684560i | 0.961024 | − | 0.276464i | \(-0.0891626\pi\) |
−0.276464 | + | 0.961024i | \(0.589163\pi\) | |||||||
\(594\) | −22.4912 | − | 43.6032i | −0.922825 | − | 1.78906i | ||||
\(595\) | 0.0122334 | − | 0.153767i | 0.000501520 | − | 0.00630383i | ||||
\(596\) | −7.22846 | + | 1.21882i | −0.296089 | + | 0.0499247i | ||||
\(597\) | 29.1771 | 1.19414 | ||||||||
\(598\) | −5.92279 | − | 11.4824i | −0.242201 | − | 0.469549i | ||||
\(599\) | 28.8376i | 1.17827i | 0.808033 | + | 0.589137i | \(0.200532\pi\) | ||||
−0.808033 | + | 0.589137i | \(0.799468\pi\) | |||||||
\(600\) | −37.1135 | + | 19.5336i | −1.51515 | + | 0.797455i | ||||
\(601\) | − | 1.91377i | − | 0.0780642i | −0.999238 | − | 0.0390321i | \(-0.987573\pi\) | ||
0.999238 | − | 0.0390321i | \(-0.0124275\pi\) | |||||||
\(602\) | −1.37616 | + | 0.709847i | −0.0560882 | + | 0.0289312i | ||||
\(603\) | −14.4487 | −0.588397 | ||||||||
\(604\) | −27.6381 | − | 19.6626i | −1.12458 | − | 0.800059i | ||||
\(605\) | −1.15609 | + | 14.5315i | −0.0470019 | + | 0.590789i | ||||
\(606\) | 67.5078 | − | 34.8216i | 2.74232 | − | 1.41453i | ||||
\(607\) | 7.89049 | + | 7.89049i | 0.320265 | + | 0.320265i | 0.848869 | − | 0.528604i | \(-0.177284\pi\) |
−0.528604 | + | 0.848869i | \(0.677284\pi\) | |||||||
\(608\) | −13.1141 | − | 12.4766i | −0.531845 | − | 0.505991i | ||||
\(609\) | − | 0.197745i | − | 0.00801303i | ||||||
\(610\) | −5.07466 | + | 2.12659i | −0.205467 | + | 0.0861031i | ||||
\(611\) | −6.83071 | − | 6.83071i | −0.276341 | − | 0.276341i | ||||
\(612\) | −4.84329 | + | 0.816643i | −0.195778 | + | 0.0330109i | ||||
\(613\) | − | 40.1035i | − | 1.61976i | −0.586592 | − | 0.809882i | \(-0.699531\pi\) | ||
0.586592 | − | 0.809882i | \(-0.300469\pi\) | |||||||
\(614\) | 15.9104 | + | 5.08213i | 0.642092 | + | 0.205098i | ||||
\(615\) | −50.3481 | − | 4.00559i | −2.03023 | − | 0.161521i | ||||
\(616\) | 1.54193 | − | 1.15587i | 0.0621259 | − | 0.0465713i | ||||
\(617\) | −14.5821 | − | 14.5821i | −0.587052 | − | 0.587052i | 0.349780 | − | 0.936832i | \(-0.386256\pi\) |
−0.936832 | + | 0.349780i | \(0.886256\pi\) | |||||||
\(618\) | 22.8635 | − | 11.7934i | 0.919707 | − | 0.474399i | ||||
\(619\) | 4.01752 | + | 4.01752i | 0.161478 | + | 0.161478i | 0.783221 | − | 0.621743i | \(-0.213575\pi\) |
−0.621743 | + | 0.783221i | \(0.713575\pi\) | |||||||
\(620\) | −12.0251 | + | 14.3421i | −0.482938 | + | 0.575993i | ||||
\(621\) | −34.3617 | + | 34.3617i | −1.37889 | + | 1.37889i | ||||
\(622\) | −30.4810 | − | 9.73628i | −1.22218 | − | 0.390389i | ||||
\(623\) | −1.80880 | + | 1.80880i | −0.0724679 | + | 0.0724679i | ||||
\(624\) | 17.4623 | − | 6.06108i | 0.699052 | − | 0.242638i | ||||
\(625\) | 23.7500 | + | 7.80630i | 0.949999 | + | 0.312252i | ||||
\(626\) | 12.6013 | − | 6.49993i | 0.503648 | − | 0.259790i | ||||
\(627\) | −39.7189 | −1.58622 | ||||||||
\(628\) | 9.91553 | − | 13.9375i | 0.395673 | − | 0.556166i | ||||
\(629\) | 0.490385 | − | 0.490385i | 0.0195529 | − | 0.0195529i | ||||
\(630\) | 2.75108 | − | 1.15287i | 0.109606 | − | 0.0459315i | ||||
\(631\) | −26.9309 | −1.07210 | −0.536052 | − | 0.844185i | \(-0.680085\pi\) | ||||
−0.536052 | + | 0.844185i | \(0.680085\pi\) | |||||||
\(632\) | 6.14508 | + | 8.19752i | 0.244438 | + | 0.326080i | ||||
\(633\) | 32.7791 | − | 32.7791i | 1.30285 | − | 1.30285i | ||||
\(634\) | 10.8122 | − | 33.8493i | 0.429407 | − | 1.34433i | ||||
\(635\) | −25.1856 | − | 29.5395i | −0.999462 | − | 1.17224i | ||||
\(636\) | 55.2524 | + | 39.3082i | 2.19090 | + | 1.55867i | ||||
\(637\) | 10.8662i | 0.430536i | ||||||||
\(638\) | 2.30979 | + | 0.737797i | 0.0914456 | + | 0.0292097i | ||||
\(639\) | −46.3644 | −1.83415 | ||||||||
\(640\) | −15.7661 | + | 19.7846i | −0.623209 | + | 0.782055i | ||||
\(641\) | 18.6880 | 0.738131 | 0.369065 | − | 0.929403i | \(-0.379678\pi\) | ||||
0.369065 | + | 0.929403i | \(0.379678\pi\) | |||||||
\(642\) | −47.8645 | − | 15.2890i | −1.88906 | − | 0.603407i | ||||
\(643\) | 29.6249i | 1.16829i | 0.811648 | + | 0.584146i | \(0.198571\pi\) | ||||
−0.811648 | + | 0.584146i | \(0.801429\pi\) | |||||||
\(644\) | −1.55528 | − | 1.10647i | −0.0612865 | − | 0.0436011i | ||||
\(645\) | 3.53755 | − | 44.4651i | 0.139291 | − | 1.75081i | ||||
\(646\) | −0.583529 | + | 1.82683i | −0.0229586 | + | 0.0718758i | ||||
\(647\) | −5.04426 | + | 5.04426i | −0.198310 | + | 0.198310i | −0.799275 | − | 0.600965i | \(-0.794783\pi\) |
0.600965 | + | 0.799275i | \(0.294783\pi\) | |||||||
\(648\) | −12.2078 | − | 16.2851i | −0.479567 | − | 0.639740i | ||||
\(649\) | −9.67794 | −0.379893 | ||||||||
\(650\) | −9.83371 | − | 4.96997i | −0.385710 | − | 0.194938i | ||||
\(651\) | 1.42855 | − | 1.42855i | 0.0559895 | − | 0.0559895i | ||||
\(652\) | 4.14827 | − | 5.83089i | 0.162459 | − | 0.228355i | ||||
\(653\) | 3.04934 | 0.119330 | 0.0596649 | − | 0.998218i | \(-0.480997\pi\) | ||||
0.0596649 | + | 0.998218i | \(0.480997\pi\) | |||||||
\(654\) | 21.1644 | − | 10.9169i | 0.827592 | − | 0.426885i | ||||
\(655\) | −16.4045 | − | 19.2404i | −0.640978 | − | 0.751783i | ||||
\(656\) | −28.7815 | + | 9.98991i | −1.12373 | + | 0.390040i | ||||
\(657\) | −6.49615 | + | 6.49615i | −0.253439 | + | 0.253439i | ||||
\(658\) | −1.35945 | − | 0.434238i | −0.0529970 | − | 0.0169284i | ||||
\(659\) | −22.0441 | + | 22.0441i | −0.858718 | + | 0.858718i | −0.991187 | − | 0.132469i | \(-0.957709\pi\) |
0.132469 | + | 0.991187i | \(0.457709\pi\) | |||||||
\(660\) | 4.85949 | + | 55.2989i | 0.189155 | + | 2.15251i | ||||
\(661\) | 8.09788 | + | 8.09788i | 0.314971 | + | 0.314971i | 0.846832 | − | 0.531861i | \(-0.178507\pi\) |
−0.531861 | + | 0.846832i | \(0.678507\pi\) | |||||||
\(662\) | −10.3241 | + | 5.32531i | −0.401256 | + | 0.206974i | ||||
\(663\) | −1.38479 | − | 1.38479i | −0.0537807 | − | 0.0537807i | ||||
\(664\) | 3.68054 | − | 2.75904i | 0.142833 | − | 0.107071i | ||||
\(665\) | 0.0923670 | − | 1.16100i | 0.00358184 | − | 0.0450218i | ||||
\(666\) | 12.7749 | + | 4.08058i | 0.495018 | + | 0.158119i | ||||
\(667\) | − | 2.40167i | − | 0.0929931i | ||||||
\(668\) | 1.34676 | − | 0.227083i | 0.0521078 | − | 0.00878609i | ||||
\(669\) | 17.6150 | + | 17.6150i | 0.681035 | + | 0.681035i | ||||
\(670\) | 7.29694 | + | 2.98724i | 0.281905 | + | 0.115407i | ||||
\(671\) | 7.28276i | 0.281148i | ||||||||
\(672\) | 1.88225 | − | 1.97842i | 0.0726093 | − | 0.0763194i | ||||
\(673\) | −27.1768 | − | 27.1768i | −1.04759 | − | 1.04759i | −0.998810 | − | 0.0487786i | \(-0.984467\pi\) |
−0.0487786 | − | 0.998810i | \(-0.515533\pi\) | |||||||
\(674\) | 13.1831 | − | 6.80006i | 0.507795 | − | 0.261929i | ||||
\(675\) | −6.55265 | + | 40.9210i | −0.252212 | + | 1.57505i | ||||
\(676\) | −17.2287 | − | 12.2570i | −0.662644 | − | 0.471425i | ||||
\(677\) | 28.6501 | 1.10111 | 0.550557 | − | 0.834798i | \(-0.314415\pi\) | ||||
0.550557 | + | 0.834798i | \(0.314415\pi\) | |||||||
\(678\) | −34.1450 | + | 17.6125i | −1.31133 | + | 0.676405i | ||||
\(679\) | 2.23115i | 0.0856238i | ||||||||
\(680\) | 2.61481 | + | 0.588915i | 0.100273 | + | 0.0225838i | ||||
\(681\) | 68.8334i | 2.63770i | ||||||||
\(682\) | 11.3565 | + | 22.0165i | 0.434861 | + | 0.843055i | ||||
\(683\) | 30.8472 | 1.18034 | 0.590168 | − | 0.807281i | \(-0.299062\pi\) | ||||
0.590168 | + | 0.807281i | \(0.299062\pi\) | |||||||
\(684\) | −36.5688 | + | 6.16599i | −1.39824 | + | 0.235763i | ||||
\(685\) | −6.33051 | − | 7.42485i | −0.241876 | − | 0.283689i | ||||
\(686\) | 1.47462 | + | 2.85881i | 0.0563013 | + | 0.109150i | ||||
\(687\) | 16.6058 | + | 16.6058i | 0.633549 | + | 0.633549i | ||||
\(688\) | −8.82261 | − | 25.4184i | −0.336359 | − | 0.969069i | ||||
\(689\) | 17.8142i | 0.678668i | ||||||||
\(690\) | 50.7106 | − | 21.2508i | 1.93052 | − | 0.809005i | ||||
\(691\) | 0.253186 | + | 0.253186i | 0.00963164 | + | 0.00963164i | 0.711906 | − | 0.702275i | \(-0.247832\pi\) |
−0.702275 | + | 0.711906i | \(0.747832\pi\) | |||||||
\(692\) | 19.2609 | + | 13.7028i | 0.732189 | + | 0.520901i | ||||
\(693\) | − | 3.94815i | − | 0.149978i | ||||||
\(694\) | 7.85286 | − | 24.5847i | 0.298091 | − | 0.933221i | ||||
\(695\) | 25.0728 | + | 29.4071i | 0.951066 | + | 1.11548i | ||||
\(696\) | 3.40138 | + | 0.486740i | 0.128929 | + | 0.0184498i | ||||
\(697\) | 2.28241 | + | 2.28241i | 0.0864525 | + | 0.0864525i | ||||
\(698\) | −17.8247 | − | 34.5563i | −0.674675 | − | 1.30798i | ||||
\(699\) | 8.95608 | + | 8.95608i | 0.338750 | + | 0.338750i | ||||
\(700\) | −1.62772 | + | 0.0134468i | −0.0615219 | + | 0.000508242i | ||||
\(701\) | 10.5238 | − | 10.5238i | 0.397479 | − | 0.397479i | −0.479864 | − | 0.877343i | \(-0.659314\pi\) |
0.877343 | + | 0.479864i | \(0.159314\pi\) | |||||||
\(702\) | 5.55756 | − | 17.3989i | 0.209757 | − | 0.656677i | ||||
\(703\) | 3.70261 | − | 3.70261i | 0.139646 | − | 0.139646i | ||||
\(704\) | 16.0866 | + | 29.3675i | 0.606285 | + | 1.10683i | ||||
\(705\) | 31.2833 | − | 26.6725i | 1.17820 | − | 1.00454i | ||||
\(706\) | 1.04152 | + | 2.01917i | 0.0391982 | + | 0.0759925i | ||||
\(707\) | 2.94813 | 0.110876 | ||||||||
\(708\) | −13.5233 | + | 2.28021i | −0.508237 | + | 0.0856956i | ||||
\(709\) | −1.58968 | + | 1.58968i | −0.0597015 | + | 0.0597015i | −0.736327 | − | 0.676626i | \(-0.763442\pi\) |
0.676626 | + | 0.736327i | \(0.263442\pi\) | |||||||
\(710\) | 23.4151 | + | 9.58574i | 0.878754 | + | 0.359747i | ||||
\(711\) | 20.9900 | 0.787186 | ||||||||
\(712\) | −26.6606 | − | 35.5651i | −0.999147 | − | 1.33286i | ||||
\(713\) | 17.3502 | − | 17.3502i | 0.649771 | − | 0.649771i | ||||
\(714\) | −0.275601 | − | 0.0880329i | −0.0103141 | − | 0.00329455i | ||||
\(715\) | −11.0977 | + | 9.46198i | −0.415029 | + | 0.353858i | ||||
\(716\) | 13.1511 | − | 2.21745i | 0.491478 | − | 0.0828699i | ||||
\(717\) | − | 0.00411819i | − | 0.000153797i | ||||||
\(718\) | −12.2269 | + | 38.2781i | −0.456302 | + | 1.42853i | ||||
\(719\) | 22.8919 | 0.853722 | 0.426861 | − | 0.904317i | \(-0.359619\pi\) | ||||
0.426861 | + | 0.904317i | \(0.359619\pi\) | |||||||
\(720\) | 13.0587 | + | 50.1587i | 0.486670 | + | 1.86931i | ||||
\(721\) | 0.998472 | 0.0371850 | ||||||||
\(722\) | 3.77002 | − | 11.8027i | 0.140306 | − | 0.439249i | ||||
\(723\) | 38.1313i | 1.41812i | ||||||||
\(724\) | 6.20023 | + | 36.7718i | 0.230430 | + | 1.36661i | ||||
\(725\) | −1.20107 | − | 1.65906i | −0.0446065 | − | 0.0616158i | ||||
\(726\) | 26.0452 | + | 8.31939i | 0.966628 | + | 0.308762i | ||||
\(727\) | 20.1893 | − | 20.1893i | 0.748780 | − | 0.748780i | −0.225470 | − | 0.974250i | \(-0.572392\pi\) |
0.974250 | + | 0.225470i | \(0.0723919\pi\) | |||||||
\(728\) | 0.710175 | + | 0.101626i | 0.0263208 | + | 0.00376653i | ||||
\(729\) | 32.0425 | 1.18676 | ||||||||
\(730\) | 4.62377 | − | 1.93764i | 0.171133 | − | 0.0717154i | ||||
\(731\) | −2.01572 | + | 2.01572i | −0.0745540 | + | 0.0745540i | ||||
\(732\) | 1.71588 | + | 10.1764i | 0.0634209 | + | 0.376132i | ||||
\(733\) | −14.3253 | −0.529118 | −0.264559 | − | 0.964370i | \(-0.585226\pi\) | ||||
−0.264559 | + | 0.964370i | \(0.585226\pi\) | |||||||
\(734\) | −2.10592 | − | 4.08270i | −0.0777311 | − | 0.150695i | ||||
\(735\) | −46.0978 | − | 3.66744i | −1.70034 | − | 0.135276i | ||||
\(736\) | 22.8605 | − | 24.0286i | 0.842648 | − | 0.885705i | ||||
\(737\) | 7.37954 | − | 7.37954i | 0.271829 | − | 0.271829i | ||||
\(738\) | −18.9924 | + | 59.4587i | −0.699119 | + | 2.18870i | ||||
\(739\) | 32.3401 | − | 32.3401i | 1.18965 | − | 1.18965i | 0.212487 | − | 0.977164i | \(-0.431844\pi\) |
0.977164 | − | 0.212487i | \(-0.0681564\pi\) | |||||||
\(740\) | −5.60798 | − | 4.70197i | −0.206153 | − | 0.172848i | ||||
\(741\) | −10.4557 | − | 10.4557i | −0.384100 | − | 0.384100i | ||||
\(742\) | 1.20646 | + | 2.33894i | 0.0442906 | + | 0.0858651i | ||||
\(743\) | −6.06842 | − | 6.06842i | −0.222629 | − | 0.222629i | 0.586976 | − | 0.809605i | \(-0.300318\pi\) |
−0.809605 | + | 0.586976i | \(0.800318\pi\) | |||||||
\(744\) | 21.0560 | + | 28.0887i | 0.771952 | + | 1.02978i | ||||
\(745\) | 6.23662 | − | 5.31741i | 0.228492 | − | 0.194815i | ||||
\(746\) | −7.77947 | + | 24.3549i | −0.284827 | + | 0.891696i | ||||
\(747\) | − | 9.42414i | − | 0.344811i | ||||||
\(748\) | 2.05657 | − | 2.89075i | 0.0751955 | − | 0.105696i | ||||
\(749\) | −1.37898 | − | 1.37898i | −0.0503870 | − | 0.0503870i | ||||
\(750\) | 24.4030 | − | 40.0401i | 0.891072 | − | 1.46206i | ||||
\(751\) | − | 49.6431i | − | 1.81150i | −0.423810 | − | 0.905751i | \(-0.639308\pi\) | ||
0.423810 | − | 0.905751i | \(-0.360692\pi\) | |||||||
\(752\) | 10.8155 | − | 22.3149i | 0.394400 | − | 0.813740i | ||||
\(753\) | 27.1090 | + | 27.1090i | 0.987907 | + | 0.987907i | ||||
\(754\) | 0.413816 | + | 0.802256i | 0.0150703 | + | 0.0292164i | ||||
\(755\) | 37.8029 | + | 3.00752i | 1.37579 | + | 0.109455i | ||||
\(756\) | −0.448644 | − | 2.66078i | −0.0163170 | − | 0.0967718i | ||||
\(757\) | −9.18443 | −0.333814 | −0.166907 | − | 0.985973i | \(-0.553378\pi\) | ||||
−0.166907 | + | 0.985973i | \(0.553378\pi\) | |||||||
\(758\) | −2.55828 | − | 4.95968i | −0.0929211 | − | 0.180144i | ||||
\(759\) | − | 72.7759i | − | 2.64160i | ||||||
\(760\) | 19.7429 | + | 4.44655i | 0.716150 | + | 0.161293i | ||||
\(761\) | 4.75310i | 0.172300i | 0.996282 | + | 0.0861499i | \(0.0274564\pi\) | ||||
−0.996282 | + | 0.0861499i | \(0.972544\pi\) | |||||||
\(762\) | −64.7080 | + | 33.3774i | −2.34412 | + | 1.20914i | ||||
\(763\) | 0.924267 | 0.0334607 | ||||||||
\(764\) | 16.2167 | − | 22.7945i | 0.586698 | − | 0.824675i | ||||
\(765\) | 4.17872 | − | 3.56282i | 0.151082 | − | 0.128814i | ||||
\(766\) | −14.4367 | + | 7.44668i | −0.521619 | + | 0.269060i | ||||
\(767\) | −2.54765 | − | 2.54765i | −0.0919902 | − | 0.0919902i | ||||
\(768\) | 29.3975 | + | 37.2461i | 1.06079 | + | 1.34400i | ||||
\(769\) | − | 19.4153i | − | 0.700135i | −0.936724 | − | 0.350067i | \(-0.886159\pi\) | ||
0.936724 | − | 0.350067i | \(-0.113841\pi\) | |||||||
\(770\) | −0.816270 | + | 1.99391i | −0.0294163 | + | 0.0718554i | ||||
\(771\) | −63.0884 | − | 63.0884i | −2.27207 | − | 2.27207i | ||||
\(772\) | 1.82877 | + | 10.8460i | 0.0658190 | + | 0.390355i | ||||
\(773\) | 26.0890i | 0.938356i | 0.883104 | + | 0.469178i | \(0.155450\pi\) | ||||
−0.883104 | + | 0.469178i | \(0.844550\pi\) | |||||||
\(774\) | −52.5111 | − | 16.7732i | −1.88747 | − | 0.602899i | ||||
\(775\) | 3.30862 | − | 20.6622i | 0.118849 | − | 0.742208i | ||||
\(776\) | −38.3777 | − | 5.49187i | −1.37768 | − | 0.197147i | ||||
\(777\) | 0.558586 | + | 0.558586i | 0.0200392 | + | 0.0200392i | ||||
\(778\) | −25.6562 | + | 13.2339i | −0.919819 | + | 0.474458i | ||||
\(779\) | 17.2331 | + | 17.2331i | 0.617442 | + | 0.617442i | ||||
\(780\) | −13.2778 | + | 15.8362i | −0.475421 | + | 0.567028i | ||||
\(781\) | 23.6802 | − | 23.6802i | 0.847343 | − | 0.847343i | ||||
\(782\) | −3.34726 | − | 1.06919i | −0.119698 | − | 0.0382340i | ||||
\(783\) | 2.40080 | − | 2.40080i | 0.0857977 | − | 0.0857977i | ||||
\(784\) | −26.3518 | + | 9.14657i | −0.941135 | + | 0.326663i | ||||
\(785\) | −1.51664 | + | 19.0634i | −0.0541313 | + | 0.680402i | ||||
\(786\) | −42.1472 | + | 21.7402i | −1.50334 | + | 0.775447i | ||||
\(787\) | −14.2339 | −0.507384 | −0.253692 | − | 0.967285i | \(-0.581645\pi\) | ||||
−0.253692 | + | 0.967285i | \(0.581645\pi\) | |||||||
\(788\) | −36.3867 | − | 25.8866i | −1.29622 | − | 0.922170i | ||||
\(789\) | −49.5891 | + | 49.5891i | −1.76542 | + | 1.76542i | ||||
\(790\) | −10.6004 | − | 4.33963i | −0.377147 | − | 0.154397i | ||||
\(791\) | −1.49114 | −0.0530189 | ||||||||
\(792\) | 67.9115 | + | 9.71817i | 2.41313 | + | 0.345320i | ||||
\(793\) | −1.91713 | + | 1.91713i | −0.0680794 | + | 0.0680794i | ||||
\(794\) | 15.1307 | − | 47.3692i | 0.536970 | − | 1.68107i | ||||
\(795\) | −75.5732 | − | 6.01244i | −2.68030 | − | 0.213239i | ||||
\(796\) | −11.4067 | + | 16.0334i | −0.404298 | + | 0.568289i | ||||
\(797\) | − | 19.8283i | − | 0.702353i | −0.936309 | − | 0.351176i | \(-0.885782\pi\) | ||
0.936309 | − | 0.351176i | \(-0.114218\pi\) | |||||||
\(798\) | −2.08090 | − | 0.664684i | −0.0736631 | − | 0.0235296i | ||||
\(799\) | −2.62729 | −0.0929467 | ||||||||
\(800\) | 3.77525 | − | 28.0312i | 0.133475 | − | 0.991052i | ||||
\(801\) | −91.0655 | −3.21764 | ||||||||
\(802\) | 31.6803 | + | 10.1194i | 1.11867 | + | 0.357327i | ||||
\(803\) | − | 6.63568i | − | 0.234168i | ||||||
\(804\) | 8.57298 | − | 12.0503i | 0.302346 | − | 0.424983i | ||||
\(805\) | 2.12728 | + | 0.169242i | 0.0749767 | + | 0.00596499i | ||||
\(806\) | −2.80618 | + | 8.78518i | −0.0988433 | + | 0.309445i | ||||
\(807\) | −47.1817 | + | 47.1817i | −1.66088 | + | 1.66088i | ||||
\(808\) | −7.25667 | + | 50.7103i | −0.255289 | + | 1.78398i | ||||
\(809\) | −21.3864 | −0.751907 | −0.375954 | − | 0.926639i | \(-0.622685\pi\) | ||||
−0.375954 | + | 0.926639i | \(0.622685\pi\) | |||||||
\(810\) | 21.0587 | + | 8.62108i | 0.739929 | + | 0.302914i | ||||
\(811\) | −9.90624 | + | 9.90624i | −0.347855 | + | 0.347855i | −0.859310 | − | 0.511455i | \(-0.829107\pi\) |
0.511455 | + | 0.859310i | \(0.329107\pi\) | |||||||
\(812\) | 0.108665 | + | 0.0773075i | 0.00381339 | + | 0.00271296i | ||||
\(813\) | 36.6553 | 1.28556 | ||||||||
\(814\) | −8.60877 | + | 4.44054i | −0.301737 | + | 0.155641i | ||||
\(815\) | −0.634504 | + | 7.97538i | −0.0222257 | + | 0.279365i | ||||
\(816\) | 2.19262 | − | 4.52388i | 0.0767570 | − | 0.158368i | ||||
\(817\) | −15.2195 | + | 15.2195i | −0.532463 | + | 0.532463i | ||||
\(818\) | 31.3342 | + | 10.0088i | 1.09557 | + | 0.349950i | ||||
\(819\) | 1.03932 | − | 1.03932i | 0.0363168 | − | 0.0363168i | ||||
\(820\) | 21.8845 | − | 26.1014i | 0.764241 | − | 0.911500i | ||||
\(821\) | 22.6209 | + | 22.6209i | 0.789474 | + | 0.789474i | 0.981408 | − | 0.191934i | \(-0.0614759\pi\) |
−0.191934 | + | 0.981408i | \(0.561476\pi\) | |||||||
\(822\) | −16.2646 | + | 8.38954i | −0.567293 | + | 0.292619i | ||||
\(823\) | 4.89892 | + | 4.89892i | 0.170766 | + | 0.170766i | 0.787316 | − | 0.616550i | \(-0.211470\pi\) |
−0.616550 | + | 0.787316i | \(0.711470\pi\) | |||||||
\(824\) | −2.45769 | + | 17.1746i | −0.0856177 | + | 0.598304i | ||||
\(825\) | −36.3950 | − | 50.2731i | −1.26711 | − | 1.75028i | ||||
\(826\) | −0.507034 | − | 0.161958i | −0.0176420 | − | 0.00563523i | ||||
\(827\) | − | 1.05434i | − | 0.0366630i | −0.999832 | − | 0.0183315i | \(-0.994165\pi\) | ||
0.999832 | − | 0.0183315i | \(-0.00583542\pi\) | |||||||
\(828\) | −11.2978 | − | 67.0041i | −0.392625 | − | 2.32855i | ||||
\(829\) | −11.7754 | − | 11.7754i | −0.408978 | − | 0.408978i | 0.472404 | − | 0.881382i | \(-0.343386\pi\) |
−0.881382 | + | 0.472404i | \(0.843386\pi\) | |||||||
\(830\) | −1.94842 | + | 4.75941i | −0.0676307 | + | 0.165202i | ||||
\(831\) | − | 62.3580i | − | 2.16317i | ||||||
\(832\) | −3.49612 | + | 11.9655i | −0.121206 | + | 0.414828i | ||||
\(833\) | 2.08973 | + | 2.08973i | 0.0724050 | + | 0.0724050i | ||||
\(834\) | 64.4181 | − | 33.2279i | 2.23061 | − | 1.15059i | ||||
\(835\) | −1.16197 | + | 0.990707i | −0.0402116 | + | 0.0342848i | ||||
\(836\) | 15.5279 | − | 21.8263i | 0.537044 | − | 0.754880i | ||||
\(837\) | 34.6879 | 1.19899 | ||||||||
\(838\) | 11.8019 | − | 6.08763i | 0.407691 | − | 0.210294i | ||||
\(839\) | 41.1678i | 1.42127i | 0.703560 | + | 0.710636i | \(0.251593\pi\) | ||||
−0.703560 | + | 0.710636i | \(0.748407\pi\) | |||||||
\(840\) | −0.670819 | + | 2.97847i | −0.0231454 | + | 0.102767i | ||||
\(841\) | − | 28.8322i | − | 0.994214i | ||||||
\(842\) | −6.67662 | − | 12.9438i | −0.230092 | − | 0.446073i | ||||
\(843\) | 31.6749 | 1.09094 | ||||||||
\(844\) | 5.19796 | + | 30.8277i | 0.178921 | + | 1.06113i | ||||
\(845\) | 23.5651 | + | 1.87479i | 0.810666 | + | 0.0644948i | ||||
\(846\) | −23.2904 | − | 45.1525i | −0.800740 | − | 1.55237i | ||||
\(847\) | 0.750366 | + | 0.750366i | 0.0257829 | + | 0.0257829i | ||||
\(848\) | −43.2013 | + | 14.9950i | −1.48354 | + | 0.514930i | ||||
\(849\) | − | 37.3508i | − | 1.28188i | ||||||
\(850\) | −2.84696 | + | 0.935366i | −0.0976498 | + | 0.0320828i | ||||
\(851\) | 6.78419 | + | 6.78419i | 0.232559 | + | 0.232559i | ||||
\(852\) | 27.5098 | − | 38.6683i | 0.942470 | − | 1.32475i | ||||
\(853\) | 11.7179i | 0.401212i | 0.979672 | + | 0.200606i | \(0.0642911\pi\) | ||||
−0.979672 | + | 0.200606i | \(0.935709\pi\) | |||||||
\(854\) | −0.121875 | + | 0.381549i | −0.00417047 | + | 0.0130563i | ||||
\(855\) | 31.5511 | − | 26.9008i | 1.07902 | − | 0.919986i | ||||
\(856\) | 27.1140 | − | 20.3254i | 0.926738 | − | 0.694708i | ||||
\(857\) | 12.2154 | + | 12.2154i | 0.417270 | + | 0.417270i | 0.884262 | − | 0.466992i | \(-0.154662\pi\) |
−0.466992 | + | 0.884262i | \(0.654662\pi\) | |||||||
\(858\) | 12.5395 | + | 24.3101i | 0.428093 | + | 0.829933i | ||||
\(859\) | −17.2170 | − | 17.2170i | −0.587436 | − | 0.587436i | 0.349500 | − | 0.936936i | \(-0.386351\pi\) |
−0.936936 | + | 0.349500i | \(0.886351\pi\) | |||||||
\(860\) | 23.0515 | + | 19.3274i | 0.786050 | + | 0.659058i | ||||
\(861\) | −2.59984 | + | 2.59984i | −0.0886024 | + | 0.0886024i | ||||
\(862\) | −5.04537 | + | 15.7954i | −0.171846 | + | 0.537992i | ||||
\(863\) | 11.1929 | − | 11.1929i | 0.381011 | − | 0.381011i | −0.490455 | − | 0.871466i | \(-0.663169\pi\) |
0.871466 | + | 0.490455i | \(0.163169\pi\) | |||||||
\(864\) | 46.8721 | − | 1.16767i | 1.59462 | − | 0.0397249i | ||||
\(865\) | −26.3447 | − | 2.09593i | −0.895746 | − | 0.0712637i | ||||
\(866\) | 19.1463 | + | 37.1184i | 0.650616 | + | 1.26133i | ||||
\(867\) | 49.8828 | 1.69411 | ||||||||
\(868\) | 0.226533 | + | 1.34351i | 0.00768905 | + | 0.0456016i | ||||
\(869\) | −10.7204 | + | 10.7204i | −0.363665 | + | 0.363665i | ||||
\(870\) | −3.54307 | + | 1.48476i | −0.120121 | + | 0.0503382i | ||||
\(871\) | 3.88522 | 0.131646 | ||||||||
\(872\) | −2.27504 | + | 15.8982i | −0.0770425 | + | 0.538380i | ||||
\(873\) | −56.1647 | + | 56.1647i | −1.90089 | + | 1.90089i | ||||
\(874\) | −25.2732 | − | 8.07279i | −0.854878 | − | 0.273066i | ||||
\(875\) | 1.55415 | − | 0.946933i | 0.0525397 | − | 0.0320122i | ||||
\(876\) | −1.56343 | − | 9.27225i | −0.0528233 | − | 0.313280i | ||||
\(877\) | − | 43.1739i | − | 1.45788i | −0.684578 | − | 0.728940i | \(-0.740013\pi\) | ||
0.684578 | − | 0.728940i | \(-0.259987\pi\) | |||||||
\(878\) | 3.24308 | − | 10.1530i | 0.109449 | − | 0.342647i | ||||
\(879\) | 10.1760 | 0.343227 | ||||||||
\(880\) | −32.2877 | − | 18.9484i | −1.08842 | − | 0.638752i | ||||
\(881\) | −33.4204 | −1.12596 | −0.562981 | − | 0.826470i | \(-0.690346\pi\) | ||||
−0.562981 | + | 0.826470i | \(0.690346\pi\) | |||||||
\(882\) | −17.3891 | + | 54.4392i | −0.585520 | + | 1.83306i | ||||
\(883\) | 2.00362i | 0.0674270i | 0.999432 | + | 0.0337135i | \(0.0107334\pi\) | ||||
−0.999432 | + | 0.0337135i | \(0.989267\pi\) | |||||||
\(884\) | 1.30234 | − | 0.219593i | 0.0438026 | − | 0.00738571i | ||||
\(885\) | 11.6677 | − | 9.94802i | 0.392206 | − | 0.334399i | ||||
\(886\) | 34.6597 | + | 11.0710i | 1.16441 | + | 0.371939i | ||||
\(887\) | −16.1765 | + | 16.1765i | −0.543154 | + | 0.543154i | −0.924452 | − | 0.381298i | \(-0.875477\pi\) |
0.381298 | + | 0.924452i | \(0.375477\pi\) | |||||||
\(888\) | −10.9831 | + | 8.23322i | −0.368568 | + | 0.276289i | ||||
\(889\) | −2.82586 | −0.0947762 | ||||||||
\(890\) | 45.9902 | + | 18.8276i | 1.54160 | + | 0.631102i | ||||
\(891\) | 21.2971 | − | 21.2971i | 0.713480 | − | 0.713480i | ||||
\(892\) | −16.5663 | + | 2.79330i | −0.554681 | + | 0.0935266i | ||||
\(893\) | −19.8371 | −0.663822 | ||||||||
\(894\) | −7.04692 | − | 13.6617i | −0.235684 | − | 0.456915i | ||||
\(895\) | −11.3466 | + | 9.67419i | −0.379274 | + | 0.323373i | ||||
\(896\) | 0.351329 | + | 1.80779i | 0.0117371 | + | 0.0603940i | ||||
\(897\) | 19.1577 | − | 19.1577i | 0.639658 | − | 0.639658i | ||||
\(898\) | −1.00617 | + | 3.14997i | −0.0335763 | + | 0.105116i | ||||
\(899\) | −1.21223 | + | 1.21223i | −0.0404303 | + | 0.0404303i | ||||
\(900\) | −41.3129 | − | 40.6359i | −1.37710 | − | 1.35453i | ||||
\(901\) | 3.42593 | + | 3.42593i | 0.114134 | + | 0.114134i | ||||
\(902\) | −20.6677 | − | 40.0680i | −0.688161 | − | 1.33412i | ||||
\(903\) | −2.29606 | − | 2.29606i | −0.0764080 | − | 0.0764080i | ||||
\(904\) | 3.67037 | − | 25.6489i | 0.122075 | − | 0.853070i | ||||
\(905\) | −27.0501 | − | 31.7262i | −0.899176 | − | 1.05462i | ||||
\(906\) | 21.6425 | − | 67.7552i | 0.719023 | − | 2.25102i | ||||
\(907\) | 29.7116i | 0.986559i | 0.869871 | + | 0.493279i | \(0.164202\pi\) | ||||
−0.869871 | + | 0.493279i | \(0.835798\pi\) | |||||||
\(908\) | −37.8254 | − | 26.9101i | −1.25528 | − | 0.893044i | ||||
\(909\) | 74.2131 | + | 74.2131i | 2.46149 | + | 2.46149i | ||||
\(910\) | −0.739758 | + | 0.310004i | −0.0245227 | + | 0.0102765i | ||||
\(911\) | 44.6931i | 1.48075i | 0.672195 | + | 0.740374i | \(0.265352\pi\) | ||||
−0.672195 | + | 0.740374i | \(0.734648\pi\) | |||||||
\(912\) | 16.5552 | − | 34.1572i | 0.548196 | − | 1.13106i | ||||
\(913\) | 4.81328 | + | 4.81328i | 0.159296 | + | 0.159296i | ||||
\(914\) | 9.58663 | + | 18.5854i | 0.317097 | + | 0.614749i | ||||
\(915\) | −7.48599 | − | 8.78009i | −0.247479 | − | 0.290261i | ||||
\(916\) | −15.6172 | + | 2.63326i | −0.516005 | + | 0.0870055i | ||||
\(917\) | −1.84061 | −0.0607821 | ||||||||
\(918\) | −2.27725 | − | 4.41485i | −0.0751604 | − | 0.145712i | ||||
\(919\) | 40.1278i | 1.32369i | 0.749639 | + | 0.661847i | \(0.230227\pi\) | ||||
−0.749639 | + | 0.661847i | \(0.769773\pi\) | |||||||
\(920\) | −8.14729 | + | 36.1744i | −0.268608 | + | 1.19263i | ||||
\(921\) | 35.0250i | 1.15411i | ||||||||
\(922\) | −27.8890 | + | 14.3856i | −0.918474 | + | 0.473764i | ||||
\(923\) | 12.4673 | 0.410365 | ||||||||
\(924\) | 3.29279 | + | 2.34259i | 0.108325 | + | 0.0770654i | ||||
\(925\) | 8.07922 | + | 1.29372i | 0.265643 | + | 0.0425372i | ||||
\(926\) | −34.8974 | + | 18.0007i | −1.14680 | + | 0.591538i | ||||
\(927\) | 25.1345 | + | 25.1345i | 0.825525 | + | 0.825525i | ||||
\(928\) | −1.59723 | + | 1.67884i | −0.0524316 | + | 0.0551106i | ||||
\(929\) | − | 27.7519i | − | 0.910512i | −0.890361 | − | 0.455256i | \(-0.849548\pi\) | ||
0.890361 | − | 0.455256i | \(-0.150452\pi\) | |||||||
\(930\) | −36.3222 | − | 14.8697i | −1.19105 | − | 0.487596i | ||||
\(931\) | 15.7783 | + | 15.7783i | 0.517114 | + | 0.517114i | ||||
\(932\) | −8.42289 | + | 1.42021i | −0.275901 | + | 0.0465206i | ||||
\(933\) | − | 67.1004i | − | 2.19677i | ||||||
\(934\) | 32.9867 | + | 10.5367i | 1.07936 | + | 0.344770i | ||||
\(935\) | −0.314565 | + | 3.95391i | −0.0102874 | + | 0.129307i | ||||
\(936\) | 15.3190 | + | 20.4354i | 0.500716 | + | 0.667953i | ||||
\(937\) | 17.2805 | + | 17.2805i | 0.564531 | + | 0.564531i | 0.930591 | − | 0.366060i | \(-0.119294\pi\) |
−0.366060 | + | 0.930591i | \(0.619294\pi\) | |||||||
\(938\) | 0.510114 | − | 0.263125i | 0.0166558 | − | 0.00859133i | ||||
\(939\) | 21.0245 | + | 21.0245i | 0.686110 | + | 0.686110i | ||||
\(940\) | 2.42701 | + | 27.6183i | 0.0791602 | + | 0.900809i | ||||
\(941\) | −4.81532 | + | 4.81532i | −0.156975 | + | 0.156975i | −0.781225 | − | 0.624250i | \(-0.785405\pi\) |
0.624250 | + | 0.781225i | \(0.285405\pi\) | |||||||
\(942\) | 34.1679 | + | 10.9140i | 1.11325 | + | 0.355596i | ||||
\(943\) | −31.5759 | + | 31.5759i | −1.02825 | + | 1.02825i | ||||
\(944\) | 4.03385 | − | 8.32277i | 0.131291 | − | 0.270883i | ||||
\(945\) | 1.95733 | + | 2.29569i | 0.0636719 | + | 0.0746788i | ||||
\(946\) | 35.3862 | − | 18.2528i | 1.15050 | − | 0.593449i | ||||
\(947\) | 3.37347 | 0.109623 | 0.0548115 | − | 0.998497i | \(-0.482544\pi\) | ||||
0.0548115 | + | 0.998497i | \(0.482544\pi\) | |||||||
\(948\) | −12.4542 | + | 17.5058i | −0.404492 | + | 0.568563i | ||||
\(949\) | 1.74680 | − | 1.74680i | 0.0567034 | − | 0.0567034i | ||||
\(950\) | −21.4957 | + | 7.06240i | −0.697412 | + | 0.229134i | ||||
\(951\) | 74.5153 | 2.41632 | ||||||||
\(952\) | 0.156121 | − | 0.117032i | 0.00505991 | − | 0.00379304i | ||||
\(953\) | −14.3663 | + | 14.3663i | −0.465369 | + | 0.465369i | −0.900410 | − | 0.435041i | \(-0.856734\pi\) |
0.435041 | + | 0.900410i | \(0.356734\pi\) | |||||||
\(954\) | −28.5078 | + | 89.2482i | −0.922973 | + | 2.88952i | ||||
\(955\) | −2.48044 | + | 31.1778i | −0.0802652 | + | 1.00889i | ||||
\(956\) | 0.00226303 | + | 0.00160999i | 7.31916e−5 | + | 5.20707e-5i | ||||
\(957\) | 5.08475i | 0.164366i | ||||||||
\(958\) | 49.9268 | + | 15.9477i | 1.61306 | + | 0.515246i | ||||
\(959\) | −0.710289 | −0.0229364 | ||||||||
\(960\) | −49.5810 | − | 18.8700i | −1.60022 | − | 0.609027i | ||||
\(961\) | 13.4851 | 0.435003 | ||||||||
\(962\) | −3.43514 | − | 1.09726i | −0.110753 | − | 0.0353769i | ||||
\(963\) | − | 69.4263i | − | 2.23723i | ||||||
\(964\) | −20.9539 | − | 14.9073i | −0.674881 | − | 0.480131i | ||||
\(965\) | −7.97851 | − | 9.35775i | −0.256837 | − | 0.301236i | ||||
\(966\) | 1.21788 | − | 3.81278i | 0.0391848 | − | 0.122674i | ||||
\(967\) | −11.8576 | + | 11.8576i | −0.381315 | + | 0.381315i | −0.871576 | − | 0.490260i | \(-0.836902\pi\) |
0.490260 | + | 0.871576i | \(0.336902\pi\) | |||||||
\(968\) | −14.7539 | + | 11.0599i | −0.474209 | + | 0.355480i | ||||
\(969\) | −4.02156 | −0.129191 | ||||||||
\(970\) | 39.9764 | − | 16.7526i | 1.28357 | − | 0.537892i | ||||
\(971\) | −14.6082 | + | 14.6082i | −0.468799 | + | 0.468799i | −0.901525 | − | 0.432726i | \(-0.857552\pi\) |
0.432726 | + | 0.901525i | \(0.357552\pi\) | |||||||
\(972\) | −4.08739 | + | 5.74532i | −0.131103 | + | 0.184281i | ||||
\(973\) | 2.81319 | 0.0901869 | ||||||||
\(974\) | −35.8892 | + | 18.5122i | −1.14996 | + | 0.593170i | ||||
\(975\) | 3.65330 | − | 22.8147i | 0.116999 | − | 0.730656i | ||||
\(976\) | −6.26298 | − | 3.03552i | −0.200473 | − | 0.0971645i | ||||
\(977\) | 12.9249 | − | 12.9249i | 0.413504 | − | 0.413504i | −0.469454 | − | 0.882957i | \(-0.655549\pi\) |
0.882957 | + | 0.469454i | \(0.155549\pi\) | |||||||
\(978\) | 14.2945 | + | 4.56597i | 0.457088 | + | 0.146004i | ||||
\(979\) | 46.5108 | − | 46.5108i | 1.48649 | − | 1.48649i | ||||
\(980\) | 20.0371 | − | 23.8979i | 0.640061 | − | 0.763391i | ||||
\(981\) | 23.2665 | + | 23.2665i | 0.742843 | + | 0.742843i | ||||
\(982\) | 13.2567 | − | 6.83804i | 0.423040 | − | 0.218211i | ||||
\(983\) | −0.133323 | − | 0.133323i | −0.00425235 | − | 0.00425235i | 0.704977 | − | 0.709230i | \(-0.250957\pi\) |
−0.709230 | + | 0.704977i | \(0.750957\pi\) | |||||||
\(984\) | −38.3201 | − | 51.1189i | −1.22160 | − | 1.62961i | ||||
\(985\) | 49.7690 | + | 3.95951i | 1.58577 | + | 0.126161i | ||||
\(986\) | 0.233868 | + | 0.0747024i | 0.00744787 | + | 0.00237901i | ||||
\(987\) | − | 2.99268i | − | 0.0952580i | ||||||
\(988\) | 9.83324 | − | 1.65802i | 0.312837 | − | 0.0527485i | ||||
\(989\) | −27.8863 | − | 27.8863i | −0.886733 | − | 0.886733i | ||||
\(990\) | −70.7405 | + | 29.6446i | −2.24828 | + | 0.942166i | ||||
\(991\) | 47.9032i | 1.52170i | 0.648930 | + | 0.760848i | \(0.275217\pi\) | ||||
−0.648930 | + | 0.760848i | \(0.724783\pi\) | |||||||
\(992\) | −23.6671 | + | 0.589589i | −0.751430 | + | 0.0187195i | ||||
\(993\) | −17.2251 | − | 17.2251i | −0.546624 | − | 0.546624i | ||||
\(994\) | 1.63690 | − | 0.844340i | 0.0519194 | − | 0.0267808i | ||||
\(995\) | 1.74472 | − | 21.9302i | 0.0553114 | − | 0.695234i | ||||
\(996\) | 7.85981 | + | 5.59170i | 0.249048 | + | 0.177180i | ||||
\(997\) | −54.9379 | −1.73990 | −0.869951 | − | 0.493138i | \(-0.835850\pi\) | ||||
−0.869951 | + | 0.493138i | \(0.835850\pi\) | |||||||
\(998\) | 14.5294 | − | 7.49449i | 0.459919 | − | 0.237234i | ||||
\(999\) | 13.5635i | 0.429129i |
(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 | 80.2.j.b.43.1 | ✓ | 18 | |
3.2 | odd | 2 | 720.2.bd.g.523.9 | 18 | |||
4.3 | odd | 2 | 320.2.j.b.143.9 | 18 | |||
5.2 | odd | 4 | 80.2.s.b.27.5 | yes | 18 | ||
5.3 | odd | 4 | 400.2.s.d.107.5 | 18 | |||
5.4 | even | 2 | 400.2.j.d.43.9 | 18 | |||
8.3 | odd | 2 | 640.2.j.c.543.1 | 18 | |||
8.5 | even | 2 | 640.2.j.d.543.9 | 18 | |||
15.2 | even | 4 | 720.2.z.g.667.5 | 18 | |||
16.3 | odd | 4 | 80.2.s.b.3.5 | yes | 18 | ||
16.5 | even | 4 | 640.2.s.c.223.1 | 18 | |||
16.11 | odd | 4 | 640.2.s.d.223.9 | 18 | |||
16.13 | even | 4 | 320.2.s.b.303.9 | 18 | |||
20.3 | even | 4 | 1600.2.s.d.207.1 | 18 | |||
20.7 | even | 4 | 320.2.s.b.207.9 | 18 | |||
20.19 | odd | 2 | 1600.2.j.d.143.1 | 18 | |||
40.27 | even | 4 | 640.2.s.c.287.1 | 18 | |||
40.37 | odd | 4 | 640.2.s.d.287.9 | 18 | |||
48.35 | even | 4 | 720.2.z.g.163.5 | 18 | |||
80.3 | even | 4 | 400.2.j.d.307.9 | 18 | |||
80.13 | odd | 4 | 1600.2.j.d.1007.9 | 18 | |||
80.19 | odd | 4 | 400.2.s.d.243.5 | 18 | |||
80.27 | even | 4 | 640.2.j.d.607.1 | 18 | |||
80.29 | even | 4 | 1600.2.s.d.943.1 | 18 | |||
80.37 | odd | 4 | 640.2.j.c.607.9 | 18 | |||
80.67 | even | 4 | inner | 80.2.j.b.67.1 | yes | 18 | |
80.77 | odd | 4 | 320.2.j.b.47.1 | 18 | |||
240.227 | odd | 4 | 720.2.bd.g.307.9 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.j.b.43.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
80.2.j.b.67.1 | yes | 18 | 80.67 | even | 4 | inner | |
80.2.s.b.3.5 | yes | 18 | 16.3 | odd | 4 | ||
80.2.s.b.27.5 | yes | 18 | 5.2 | odd | 4 | ||
320.2.j.b.47.1 | 18 | 80.77 | odd | 4 | |||
320.2.j.b.143.9 | 18 | 4.3 | odd | 2 | |||
320.2.s.b.207.9 | 18 | 20.7 | even | 4 | |||
320.2.s.b.303.9 | 18 | 16.13 | even | 4 | |||
400.2.j.d.43.9 | 18 | 5.4 | even | 2 | |||
400.2.j.d.307.9 | 18 | 80.3 | even | 4 | |||
400.2.s.d.107.5 | 18 | 5.3 | odd | 4 | |||
400.2.s.d.243.5 | 18 | 80.19 | odd | 4 | |||
640.2.j.c.543.1 | 18 | 8.3 | odd | 2 | |||
640.2.j.c.607.9 | 18 | 80.37 | odd | 4 | |||
640.2.j.d.543.9 | 18 | 8.5 | even | 2 | |||
640.2.j.d.607.1 | 18 | 80.27 | even | 4 | |||
640.2.s.c.223.1 | 18 | 16.5 | even | 4 | |||
640.2.s.c.287.1 | 18 | 40.27 | even | 4 | |||
640.2.s.d.223.9 | 18 | 16.11 | odd | 4 | |||
640.2.s.d.287.9 | 18 | 40.37 | odd | 4 | |||
720.2.z.g.163.5 | 18 | 48.35 | even | 4 | |||
720.2.z.g.667.5 | 18 | 15.2 | even | 4 | |||
720.2.bd.g.307.9 | 18 | 240.227 | odd | 4 | |||
720.2.bd.g.523.9 | 18 | 3.2 | odd | 2 | |||
1600.2.j.d.143.1 | 18 | 20.19 | odd | 2 | |||
1600.2.j.d.1007.9 | 18 | 80.13 | odd | 4 | |||
1600.2.s.d.207.1 | 18 | 20.3 | even | 4 | |||
1600.2.s.d.943.1 | 18 | 80.29 | even | 4 |