Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1040,2,Mod(641,1040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1040.641");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1040 = 2^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1040.da (of order \(6\), degree \(2\), not 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: | \(8.30444181021\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.58891012706304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 520) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 881.2 | ||
Root | \(0.759479 + 1.19298i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1040.881 |
Dual form | 1040.2.da.e.641.2 |
$q$-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 \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(417\) | \(561\) | \(911\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −0.653409 | − | 1.13174i | −0.377246 | − | 0.653409i | 0.613415 | − | 0.789761i | \(-0.289795\pi\) |
−0.990660 | + | 0.136352i | \(0.956462\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.51573 | − | 1.45245i | −0.950855 | − | 0.548976i | −0.0575085 | − | 0.998345i | \(-0.518316\pi\) |
−0.893346 | + | 0.449369i | \(0.851649\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.646115 | − | 1.11910i | 0.215372 | − | 0.373034i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.174603 | + | 0.100807i | −0.0526449 | + | 0.0303946i | −0.526091 | − | 0.850428i | \(-0.676343\pi\) |
0.473447 | + | 0.880823i | \(0.343010\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.15455 | − | 2.89101i | 0.597564 | − | 0.801821i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.13174 | + | 0.653409i | −0.292213 | + | 0.168709i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.53093 | + | 2.65165i | −0.371305 | + | 0.643119i | −0.989767 | − | 0.142696i | \(-0.954423\pi\) |
0.618462 | + | 0.785815i | \(0.287756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0122700 | + | 0.00708410i | 0.00281494 | + | 0.00162520i | 0.501407 | − | 0.865212i | \(-0.332816\pi\) |
−0.498592 | + | 0.866837i | \(0.666149\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.79619i | 0.828396i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.36476 | − | 4.09588i | −0.493086 | − | 0.854050i | 0.506882 | − | 0.862015i | \(-0.330798\pi\) |
−0.999968 | + | 0.00796522i | \(0.997465\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.60916 | −1.07948 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.05550 | + | 1.82818i | 0.196001 | + | 0.339484i | 0.947228 | − | 0.320560i | \(-0.103871\pi\) |
−0.751227 | + | 0.660044i | \(0.770538\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.79645i | 0.322651i | 0.986901 | + | 0.161326i | \(0.0515769\pi\) | ||||
−0.986901 | + | 0.161326i | \(0.948423\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.228175 | + | 0.131737i | 0.0397201 | + | 0.0229324i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.45245 | + | 2.51573i | −0.245510 | + | 0.425235i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.503609 | + | 0.290759i | −0.0827928 | + | 0.0478004i | −0.540825 | − | 0.841135i | \(-0.681888\pi\) |
0.458032 | + | 0.888936i | \(0.348554\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.67966 | − | 0.549370i | −0.749345 | − | 0.0879695i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.87817 | + | 3.97111i | −1.07419 | + | 0.620184i | −0.929323 | − | 0.369267i | \(-0.879609\pi\) |
−0.144867 | + | 0.989451i | \(0.546275\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.63035 | + | 8.02001i | −0.706122 | + | 1.22304i | 0.260163 | + | 0.965565i | \(0.416224\pi\) |
−0.966285 | + | 0.257475i | \(0.917110\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.11910 | − | 0.646115i | −0.166826 | − | 0.0963171i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.37618i | − | 1.36766i | −0.729643 | − | 0.683828i | \(-0.760314\pi\) | ||
0.729643 | − | 0.683828i | \(-0.239686\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.719250 | + | 1.24578i | 0.102750 | + | 0.177968i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00129 | 0.560293 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.70777 | −0.646662 | −0.323331 | − | 0.946286i | \(-0.604803\pi\) | ||||
−0.323331 | + | 0.946286i | \(0.604803\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.100807 | + | 0.174603i | 0.0135929 | + | 0.0235435i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.0185152i | − | 0.00245240i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.03504 | − | 2.90698i | −0.655506 | − | 0.378457i | 0.135057 | − | 0.990838i | \(-0.456878\pi\) |
−0.790563 | + | 0.612381i | \(0.790212\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.95119 | + | 3.37956i | −0.249824 | + | 0.432708i | −0.963477 | − | 0.267792i | \(-0.913706\pi\) |
0.713653 | + | 0.700499i | \(0.247039\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.25089 | + | 1.87690i | −0.409574 | + | 0.236468i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.89101 | − | 2.15455i | −0.358585 | − | 0.267239i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.80553 | − | 1.04242i | 0.220581 | − | 0.127352i | −0.385638 | − | 0.922650i | \(-0.626019\pi\) |
0.606219 | + | 0.795298i | \(0.292685\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.09031 | + | 5.35257i | −0.372029 | + | 0.644373i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65201 | + | 3.26319i | 0.670770 | + | 0.387269i | 0.796368 | − | 0.604812i | \(-0.206752\pi\) |
−0.125598 | + | 0.992081i | \(0.540085\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.2027i | − | 1.42822i | −0.700033 | − | 0.714111i | \(-0.746831\pi\) | ||
0.700033 | − | 0.714111i | \(-0.253169\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.653409 | + | 1.13174i | 0.0754491 | + | 0.130682i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.585672 | 0.0667436 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8293 | 1.21839 | 0.609195 | − | 0.793020i | \(-0.291493\pi\) | ||||
0.609195 | + | 0.793020i | \(0.291493\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.72673 | + | 2.99078i | 0.191859 | + | 0.332309i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.2892i | 1.67821i | 0.543971 | + | 0.839104i | \(0.316920\pi\) | ||||
−0.543971 | + | 0.839104i | \(0.683080\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.65165 | + | 1.53093i | 0.287612 | + | 0.166053i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.37935 | − | 2.38910i | 0.147881 | − | 0.256138i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.67609 | + | 1.54504i | −0.283665 | + | 0.163774i | −0.635081 | − | 0.772445i | \(-0.719033\pi\) |
0.351417 | + | 0.936219i | \(0.385700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.61931 | + | 4.14360i | −1.00838 | + | 0.434368i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.03310 | − | 1.17381i | 0.210823 | − | 0.121719i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.00708410 | − | 0.0122700i | 0.000726813 | − | 0.00125888i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.9695 | − | 9.22000i | −1.62146 | − | 0.936149i | −0.986531 | − | 0.163577i | \(-0.947697\pi\) |
−0.634927 | − | 0.772572i | \(-0.718970\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.260532i | 0.0261845i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.79773 | + | 4.84581i | 0.278384 | + | 0.482176i | 0.970983 | − | 0.239147i | \(-0.0768678\pi\) |
−0.692599 | + | 0.721323i | \(0.743534\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.97220 | −0.194326 | −0.0971632 | − | 0.995268i | \(-0.530977\pi\) | ||||
−0.0971632 | + | 0.995268i | \(0.530977\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.79619 | 0.370470 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.667577 | − | 1.15628i | −0.0645371 | − | 0.111781i | 0.831951 | − | 0.554848i | \(-0.187224\pi\) |
−0.896489 | + | 0.443067i | \(0.853890\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.66841i | − | 0.447153i | −0.974686 | − | 0.223576i | \(-0.928227\pi\) | ||
0.974686 | − | 0.223576i | \(-0.0717732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.658125 | + | 0.379969i | 0.0624664 | + | 0.0360650i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.46901 | − | 9.47260i | 0.514481 | − | 0.891107i | −0.485378 | − | 0.874304i | \(-0.661318\pi\) |
0.999859 | − | 0.0168025i | \(-0.00534866\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.09588 | + | 2.36476i | −0.381943 | + | 0.220515i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.84325 | − | 4.27908i | −0.170409 | − | 0.395601i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.70280 | − | 4.44721i | 0.706114 | − | 0.407675i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.47968 | + | 9.49108i | −0.498152 | + | 0.862825i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.98851 | + | 5.18952i | 0.810467 | + | 0.467923i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.05980 | − | 10.4959i | −0.537720 | − | 0.931358i | −0.999026 | − | 0.0441173i | \(-0.985952\pi\) |
0.461306 | − | 0.887241i | \(-0.347381\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.1020 | 1.06553 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.1852 | 1.23937 | 0.619685 | − | 0.784850i | \(-0.287260\pi\) | ||||
0.619685 | + | 0.784850i | \(0.287260\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0205787 | − | 0.0356433i | −0.00178440 | − | 0.00309067i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.60916i | 0.482759i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.5623 | − | 8.98490i | −1.32958 | − | 0.767632i | −0.344343 | − | 0.938844i | \(-0.611898\pi\) |
−0.985234 | + | 0.171212i | \(0.945232\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0521243 | − | 0.0902819i | 0.00442113 | − | 0.00765761i | −0.863806 | − | 0.503824i | \(-0.831926\pi\) |
0.868228 | + | 0.496166i | \(0.165259\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.6114 | + | 6.12648i | −0.893639 | + | 0.515942i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0847563 | + | 0.721974i | −0.00708768 | + | 0.0603745i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.82818 | − | 1.05550i | 0.151822 | − | 0.0876545i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.939928 | − | 1.62800i | 0.0775239 | − | 0.134275i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.4101 | − | 8.89704i | −1.26245 | − | 0.728874i | −0.288900 | − | 0.957359i | \(-0.593289\pi\) |
−0.973547 | + | 0.228485i | \(0.926623\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.1805i | − | 0.991238i | −0.868540 | − | 0.495619i | \(-0.834941\pi\) | ||
0.868540 | − | 0.495619i | \(-0.165059\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.97831 | + | 3.42654i | 0.159937 | + | 0.277019i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.79645 | 0.144294 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.95336 | 0.794364 | 0.397182 | − | 0.917740i | \(-0.369988\pi\) | ||||
0.397182 | + | 0.917740i | \(0.369988\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.07610 | + | 5.32796i | 0.243950 | + | 0.422534i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.7388i | 1.08277i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.80493 | + | 4.50618i | 0.611329 | + | 0.352951i | 0.773485 | − | 0.633814i | \(-0.218512\pi\) |
−0.162156 | + | 0.986765i | \(0.551845\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.131737 | − | 0.228175i | 0.0102557 | − | 0.0177634i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.9204 | − | 8.03692i | 1.07719 | − | 0.621915i | 0.147052 | − | 0.989129i | \(-0.453021\pi\) |
0.930137 | + | 0.367213i | \(0.119688\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.71586 | − | 12.4576i | −0.285835 | − | 0.958279i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0158557 | − | 0.00915428i | 0.00121251 | − | 0.000700045i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.38307 | + | 12.7879i | −0.561324 | + | 0.972242i | 0.436057 | + | 0.899919i | \(0.356375\pi\) |
−0.997381 | + | 0.0723233i | \(0.976959\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.51573 | + | 1.45245i | 0.190171 | + | 0.109795i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.59778i | 0.571084i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.75375 | + | 3.03758i | 0.131081 | + | 0.227039i | 0.924094 | − | 0.382166i | \(-0.124822\pi\) |
−0.793012 | + | 0.609205i | \(0.791488\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8577 | 1.17869 | 0.589346 | − | 0.807881i | \(-0.299385\pi\) | ||||
0.589346 | + | 0.807881i | \(0.299385\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.09969 | 0.376980 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.290759 | + | 0.503609i | 0.0213770 | + | 0.0370261i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.617316i | − | 0.0451426i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.1111 | + | 8.14705i | 1.02643 | + | 0.592611i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.16545 | − | 3.75067i | 0.156686 | − | 0.271389i | −0.776985 | − | 0.629519i | \(-0.783252\pi\) |
0.933672 | + | 0.358130i | \(0.116585\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.4890 | − | 10.6746i | 1.33087 | − | 0.768377i | 0.345435 | − | 0.938443i | \(-0.387731\pi\) |
0.985433 | + | 0.170066i | \(0.0543981\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.549370 | + | 4.67966i | −0.0393412 | + | 0.335117i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0261 | − | 10.4074i | 1.28431 | − | 0.741494i | 0.306673 | − | 0.951815i | \(-0.400784\pi\) |
0.977632 | + | 0.210321i | \(0.0674510\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.4432 | − | 21.5522i | 0.882072 | − | 1.52779i | 0.0330394 | − | 0.999454i | \(-0.489481\pi\) |
0.849033 | − | 0.528340i | \(-0.177185\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.35950 | − | 1.36226i | −0.166426 | − | 0.0960863i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 6.13226i | − | 0.430401i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.97111 | + | 6.87817i | 0.277355 | + | 0.480392i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.11162 | −0.424787 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.00285652 | −0.000197589 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.84952 | − | 8.39962i | −0.333855 | − | 0.578254i | 0.649409 | − | 0.760439i | \(-0.275016\pi\) |
−0.983264 | + | 0.182185i | \(0.941683\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.52878i | − | 0.584383i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.02001 | + | 4.63035i | 0.546960 | + | 0.315787i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.60926 | − | 4.51936i | 0.177128 | − | 0.306794i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.8103 | + | 7.97337i | −0.933212 | + | 0.538790i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.36748 | + | 10.1390i | 0.293788 | + | 0.682025i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.14775 | + | 0.662655i | −0.0768591 | + | 0.0443746i | −0.537937 | − | 0.842985i | \(-0.680796\pi\) |
0.461078 | + | 0.887360i | \(0.347463\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.646115 | + | 1.11910i | −0.0430743 | + | 0.0746069i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.25811 | + | 0.726372i | 0.0835039 | + | 0.0482110i | 0.541171 | − | 0.840913i | \(-0.317981\pi\) |
−0.457667 | + | 0.889124i | \(0.651315\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 27.4918i | − | 1.81671i | −0.418199 | − | 0.908355i | \(-0.637339\pi\) | ||
0.418199 | − | 0.908355i | \(-0.362661\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.382683 | − | 0.662827i | −0.0251787 | − | 0.0436108i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.9607 | 1.56972 | 0.784859 | − | 0.619674i | \(-0.212735\pi\) | ||||
0.784859 | + | 0.619674i | \(0.212735\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.37618 | −0.611635 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.07595 | − | 12.2559i | −0.459632 | − | 0.796106i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4.99651i | − | 0.323197i | −0.986857 | − | 0.161599i | \(-0.948335\pi\) | ||
0.986857 | − | 0.161599i | \(-0.0516650\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4047 | + | 6.58448i | 0.734638 | + | 0.424144i | 0.820117 | − | 0.572196i | \(-0.193908\pi\) |
−0.0854782 | + | 0.996340i | \(0.527242\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.15722 | + | 10.6646i | −0.394986 | + | 0.684136i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.24578 | − | 0.719250i | 0.0795898 | − | 0.0459512i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0469165 | − | 0.0202097i | 0.00298523 | − | 0.00128591i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.3034 | − | 9.99009i | 1.09656 | − | 0.633097i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.66087 | + | 13.2690i | −0.483550 | + | 0.837533i | −0.999822 | − | 0.0188920i | \(-0.993986\pi\) |
0.516272 | + | 0.856425i | \(0.327319\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.825789 | + | 0.476770i | 0.0519169 | + | 0.0299743i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 4.00129i | − | 0.250570i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.30055 | + | 12.6449i | 0.455395 | + | 0.788768i | 0.998711 | − | 0.0507606i | \(-0.0161645\pi\) |
−0.543315 | + | 0.839529i | \(0.682831\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.68926 | 0.104965 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.72790 | 0.168853 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.25088 | − | 10.8269i | −0.385446 | − | 0.667612i | 0.606385 | − | 0.795171i | \(-0.292619\pi\) |
−0.991831 | + | 0.127559i | \(0.959286\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.70777i | 0.289196i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.49716 | + | 2.01908i | 0.214023 | + | 0.123566i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.1182 | + | 17.5252i | −0.616916 | + | 1.06853i | 0.373129 | + | 0.927779i | \(0.378285\pi\) |
−0.990045 | + | 0.140750i | \(0.955049\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.03983 | − | 1.75505i | 0.184657 | − | 0.106611i | −0.404822 | − | 0.914395i | \(-0.632667\pi\) |
0.589479 | + | 0.807784i | \(0.299333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.9748 | + | 8.17906i | 0.664225 | + | 0.495019i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.174603 | − | 0.100807i | 0.0105290 | − | 0.00607891i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.70447 | − | 2.95224i | 0.102412 | − | 0.177383i | −0.810266 | − | 0.586062i | \(-0.800677\pi\) |
0.912678 | + | 0.408680i | \(0.134011\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.01041 | + | 1.16071i | 0.120360 | + | 0.0694899i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.4204i | 1.51646i | 0.651989 | + | 0.758228i | \(0.273935\pi\) | ||||
−0.651989 | + | 0.758228i | \(0.726065\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.5336 | − | 18.2447i | −0.626155 | − | 1.08453i | −0.988316 | − | 0.152417i | \(-0.951294\pi\) |
0.362162 | − | 0.932115i | \(-0.382039\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0185152 | −0.00109675 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.0715 | 1.36186 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.81251 | + | 6.60346i | 0.224265 | + | 0.388439i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.0977i | 1.41263i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.5039 | − | 11.8379i | −1.19785 | − | 0.691579i | −0.237774 | − | 0.971320i | \(-0.576418\pi\) |
−0.960075 | + | 0.279742i | \(0.909751\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.90698 | + | 5.03504i | −0.169251 | + | 0.293151i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.979378 | − | 0.565444i | 0.0568293 | − | 0.0328104i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.9362 | − | 1.98823i | −0.979446 | − | 0.114982i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.2974 | − | 13.4508i | 1.34284 | − | 0.775289i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.65612 | − | 6.33258i | 0.210038 | − | 0.363797i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.37956 | + | 1.95119i | 0.193513 | + | 0.111725i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 25.7386i | − | 1.46898i | −0.678621 | − | 0.734488i | \(-0.737422\pi\) | ||
0.678621 | − | 0.734488i | \(-0.262578\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.28865 | + | 2.23201i | 0.0733088 | + | 0.126975i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.94438 | −0.393779 | −0.196890 | − | 0.980426i | \(-0.563084\pi\) | ||||
−0.196890 | + | 0.980426i | \(0.563084\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.9872 | −1.01669 | −0.508347 | − | 0.861152i | \(-0.669743\pi\) | ||||
−0.508347 | + | 0.861152i | \(0.669743\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.87690 | + | 3.25089i | 0.105752 | + | 0.183167i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.52532i | − | 0.0856707i | −0.999082 | − | 0.0428353i | \(-0.986361\pi\) | ||
0.999082 | − | 0.0428353i | \(-0.0136391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.368588 | − | 0.212804i | −0.0206370 | − | 0.0119148i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.872401 | + | 1.51104i | −0.0486927 | + | 0.0843381i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0375691 | + | 0.0216905i | −0.00209040 | + | 0.00120689i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.15455 | + | 2.89101i | −0.119513 | + | 0.160364i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.28341 | + | 3.05038i | −0.292173 | + | 0.168686i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.6185 | + | 23.5879i | −0.750811 | + | 1.30044i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1459 | + | 9.89916i | 0.942421 | + | 0.544107i | 0.890719 | − | 0.454555i | \(-0.150202\pi\) |
0.0517029 | + | 0.998663i | \(0.483535\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.751454i | 0.0411794i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.04242 | − | 1.80553i | −0.0569538 | − | 0.0986468i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.4107 | 1.05737 | 0.528684 | − | 0.848819i | \(-0.322686\pi\) | ||||
0.528684 | + | 0.848819i | \(0.322686\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.2940 | −0.776342 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.181095 | − | 0.313665i | −0.00980683 | − | 0.0169859i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.1557i | 0.872323i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.35257 | + | 3.09031i | 0.288172 | + | 0.166376i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.95435 | + | 17.2414i | −0.534377 | + | 0.925569i | 0.464816 | + | 0.885407i | \(0.346121\pi\) |
−0.999193 | + | 0.0401615i | \(0.987213\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.8255 | − | 7.40482i | 0.686535 | − | 0.396371i | −0.115778 | − | 0.993275i | \(-0.536936\pi\) |
0.802313 | + | 0.596904i | \(0.203603\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.0852 | + | 16.2161i | −0.645060 | + | 0.865553i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.6040 | + | 9.58631i | −0.883740 | + | 0.510228i | −0.871890 | − | 0.489702i | \(-0.837105\pi\) |
−0.0118503 | + | 0.999930i | \(0.503772\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.26319 | − | 5.65201i | 0.173192 | − | 0.299978i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.0661 | − | 5.81169i | −0.532757 | − | 0.307587i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 17.0500i | − | 0.899865i | −0.893062 | − | 0.449933i | \(-0.851448\pi\) | ||
0.893062 | − | 0.449933i | \(-0.148552\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.49990 | − | 16.4543i | −0.499995 | − | 0.866016i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.3219 | 0.751703 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.2027 | −0.638720 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7091 | − | 22.0128i | −0.663408 | − | 1.14906i | −0.979714 | − | 0.200400i | \(-0.935776\pi\) |
0.316306 | − | 0.948657i | \(-0.397557\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.2632i | 0.534280i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.8435 | + | 6.83782i | 0.614882 | + | 0.355002i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.09970 | − | 5.36884i | 0.160497 | − | 0.277988i | −0.774550 | − | 0.632512i | \(-0.782024\pi\) |
0.935047 | + | 0.354524i | \(0.115357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.13174 | − | 0.653409i | 0.0584426 | − | 0.0337419i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.55941 | + | 0.887438i | 0.389329 | + | 0.0457054i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.51857 | + | 3.76350i | −0.334837 | + | 0.193318i | −0.657986 | − | 0.753030i | \(-0.728592\pi\) |
0.323150 | + | 0.946348i | \(0.395258\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.91904 | + | 13.7162i | −0.405705 | + | 0.702702i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.8268 | − | 14.9111i | −1.31969 | − | 0.761923i | −0.336011 | − | 0.941858i | \(-0.609078\pi\) |
−0.983679 | + | 0.179935i | \(0.942411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 0.585672i | − | 0.0298486i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.98348 | + | 10.3637i | 0.304157 | + | 0.526816i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.0850 | −0.866245 | −0.433122 | − | 0.901335i | \(-0.642588\pi\) | ||||
−0.433122 | + | 0.901335i | \(0.642588\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.4811 | 0.732341 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.26876 | − | 16.0540i | −0.467547 | − | 0.809815i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 10.8293i | − | 0.544881i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.38344 | + | 3.10813i | 0.270187 | + | 0.155993i | 0.628973 | − | 0.777427i | \(-0.283476\pi\) |
−0.358786 | + | 0.933420i | \(0.616809\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0268926 | + | 0.0465793i | −0.00134631 | + | 0.00233188i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.18917 | + | 0.686569i | −0.0593844 | + | 0.0342856i | −0.529398 | − | 0.848373i | \(-0.677582\pi\) |
0.470014 | + | 0.882659i | \(0.344249\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.19354 | + | 3.87052i | 0.258709 | + | 0.192805i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.99078 | − | 1.72673i | 0.148613 | − | 0.0858018i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0586212 | − | 0.101535i | 0.00290575 | − | 0.00503290i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.1731 | − | 13.3790i | −1.14584 | − | 0.661549i | −0.197968 | − | 0.980209i | \(-0.563434\pi\) |
−0.947869 | + | 0.318659i | \(0.896767\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.4832i | 1.15834i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.44451 | + | 14.6263i | 0.415527 | + | 0.719714i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.2892 | 0.750517 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.136234 | −0.00667140 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.6575 | − | 23.6555i | −0.667212 | − | 1.15565i | −0.978680 | − | 0.205389i | \(-0.934154\pi\) |
0.311468 | − | 0.950257i | \(-0.399179\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 18.4971i | − | 0.901493i | −0.892652 | − | 0.450746i | \(-0.851158\pi\) | ||
0.892652 | − | 0.450746i | \(-0.148842\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.4929 | − | 6.05809i | −0.510183 | − | 0.294554i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.53093 | − | 2.65165i | 0.0742610 | − | 0.128624i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.81730 | − | 5.66802i | 0.475093 | − | 0.274295i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.872465 | − | 0.375822i | 0.0421230 | − | 0.0181449i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.27873 | + | 4.20237i | −0.350604 | + | 0.202421i | −0.664951 | − | 0.746887i | \(-0.731548\pi\) |
0.314347 | + | 0.949308i | \(0.398214\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.75170 | + | 15.1584i | −0.420580 | + | 0.728465i | −0.995996 | − | 0.0893951i | \(-0.971507\pi\) |
0.575417 | + | 0.817861i | \(0.304840\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.38910 | − | 1.37935i | −0.114548 | − | 0.0661345i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 0.0670087i | − | 0.00320546i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.8296 | + | 32.6138i | 0.898687 | + | 1.55657i | 0.829174 | + | 0.558991i | \(0.188811\pi\) |
0.0695136 | + | 0.997581i | \(0.477855\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.85887 | 0.0885177 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.5697 | 1.49992 | 0.749960 | − | 0.661483i | \(-0.230073\pi\) | ||||
0.749960 | + | 0.661483i | \(0.230073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.54504 | + | 2.67609i | 0.0732419 | + | 0.126859i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.2536i | 1.09986i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.4173 | − | 7.74649i | −0.633202 | − | 0.365580i | 0.148789 | − | 0.988869i | \(-0.452463\pi\) |
−0.781991 | + | 0.623289i | \(0.785796\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.800635 | − | 1.38674i | 0.0377004 | − | 0.0652990i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.7852 | + | 7.95886i | −0.647683 | + | 0.373940i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.14360 | + | 9.61931i | 0.194255 | + | 0.450960i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.9160 | − | 9.18912i | 0.744520 | − | 0.429849i | −0.0791904 | − | 0.996860i | \(-0.525233\pi\) |
0.823710 | + | 0.567011i | \(0.191900\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.58723 | − | 14.8735i | 0.400817 | − | 0.694236i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.7199 | − | 11.9626i | −0.965020 | − | 0.557154i | −0.0673055 | − | 0.997732i | \(-0.521440\pi\) |
−0.897714 | + | 0.440578i | \(0.854774\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.8775i | − | 1.38852i | −0.719723 | − | 0.694262i | \(-0.755731\pi\) | ||
0.719723 | − | 0.694262i | \(-0.244269\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.17381 | − | 2.03310i | −0.0544343 | − | 0.0942829i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.2809 | 0.707116 | 0.353558 | − | 0.935413i | \(-0.384972\pi\) | ||||
0.353558 | + | 0.935413i | \(0.384972\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.05630 | −0.279654 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.50361 | − | 11.2646i | −0.299670 | − | 0.519044i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.86709i | − | 0.0858491i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0122700 | − | 0.00708410i | −0.000562987 | − | 0.000325041i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.04176 | + | 5.26848i | −0.139273 | + | 0.241227i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.8839 | + | 12.0573i | −0.954209 | + | 0.550913i | −0.894386 | − | 0.447296i | \(-0.852387\pi\) |
−0.0598232 | + | 0.998209i | \(0.519054\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.244463 | + | 2.08239i | −0.0111465 | + | 0.0949489i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.5487 | − | 8.97706i | 0.707491 | − | 0.408470i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.22000 | + | 15.9695i | −0.418659 | + | 0.725138i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.28811 | − | 5.36249i | −0.420884 | − | 0.242998i | 0.274571 | − | 0.961567i | \(-0.411464\pi\) |
−0.695456 | + | 0.718569i | \(0.744797\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 11.7775i | − | 0.532597i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.7535 | + | 29.0178i | 0.756073 | + | 1.30956i | 0.944839 | + | 0.327535i | \(0.106218\pi\) |
−0.188766 | + | 0.982022i | \(0.560449\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.46358 | −0.291105 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.260532 | 0.0117101 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.47927 | − | 16.4186i | −0.425203 | − | 0.736474i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.744396i | − | 0.0333237i | −0.999861 | − | 0.0166619i | \(-0.994696\pi\) | ||
0.999861 | − | 0.0166619i | \(-0.00530388\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.1914 | − | 10.5028i | −0.812730 | − | 0.469230i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.38218 | + | 9.32221i | −0.239980 | + | 0.415657i | −0.960708 | − | 0.277561i | \(-0.910474\pi\) |
0.720729 | + | 0.693217i | \(0.243807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.84581 | − | 2.79773i | 0.215636 | − | 0.124497i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.6708 | + | 12.3453i | −0.518317 | + | 0.548274i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.4548 | − | 14.1190i | 1.08394 | − | 0.625814i | 0.151985 | − | 0.988383i | \(-0.451434\pi\) |
0.931957 | + | 0.362569i | \(0.118100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.7239 | + | 30.6987i | −0.784060 | + | 1.35803i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.0688245 | − | 0.0397358i | −0.00303868 | − | 0.00175438i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.97220i | 0.0869054i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.945188 | + | 1.63711i | 0.0415693 | + | 0.0720002i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.2966 | 0.847029 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.86998 | −0.169547 | −0.0847734 | − | 0.996400i | \(-0.527017\pi\) | ||||
−0.0847734 | + | 0.996400i | \(0.527017\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.6421 | − | 34.0211i | −0.858889 | − | 1.48764i | −0.872990 | − | 0.487738i | \(-0.837822\pi\) |
0.0141014 | − | 0.999901i | \(-0.495511\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 3.79619i | − | 0.165679i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.76354 | − | 2.75023i | −0.207503 | − | 0.119802i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.315843 | − | 0.547055i | 0.0137323 | − | 0.0237850i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.50642 | + | 3.75648i | −0.282355 | + | 0.163018i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.33881 | + | 28.4408i | −0.144620 | + | 1.23191i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.15628 | + | 0.667577i | −0.0499902 | + | 0.0288619i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.29183 | − | 3.96956i | 0.0988996 | − | 0.171299i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.251167 | − | 0.145011i | −0.0108185 | − | 0.00624608i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.24167i | 0.397330i | 0.980067 | + | 0.198665i | \(0.0636606\pi\) | ||||
−0.980067 | + | 0.198665i | \(0.936339\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.3615 | − | 17.9467i | −0.444656 | − | 0.770167i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.66841 | −0.199973 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.91834 | −0.381321 | −0.190660 | − | 0.981656i | \(-0.561063\pi\) | ||||
−0.190660 | + | 0.981656i | \(0.561063\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.52138 | + | 4.36716i | 0.107610 | + | 0.186386i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0299091i | 0.00127417i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.2435 | − | 15.7291i | −1.15851 | − | 0.668867i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.379969 | − | 0.658125i | 0.0161288 | − | 0.0279358i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.17367 | + | 1.25497i | −0.0921012 | + | 0.0531746i | −0.545343 | − | 0.838213i | \(-0.683601\pi\) |
0.453242 | + | 0.891387i | \(0.350267\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.2096 | + | 30.6659i | 0.558706 | + | 1.29703i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.698639 | + | 0.403359i | −0.0294965 | + | 0.0170298i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.96884 | + | 12.0704i | −0.293702 | + | 0.508706i | −0.974682 | − | 0.223595i | \(-0.928221\pi\) |
0.680980 | + | 0.732302i | \(0.261554\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.47260 | − | 5.46901i | −0.398515 | − | 0.230083i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 10.0320i | − | 0.421303i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.3977 | − | 21.4735i | −0.519739 | − | 0.900215i | −0.999737 | − | 0.0229448i | \(-0.992696\pi\) |
0.479998 | − | 0.877270i | \(-0.340638\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.78548 | 0.116569 | 0.0582843 | − | 0.998300i | \(-0.481437\pi\) | ||||
0.0582843 | + | 0.998300i | \(0.481437\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.65969 | −0.236437 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.36476 | + | 4.09588i | 0.0986172 | + | 0.170810i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.0538i | 1.20952i | 0.796406 | + | 0.604762i | \(0.206732\pi\) | ||||
−0.796406 | + | 0.604762i | \(0.793268\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.1617 | − | 13.9498i | −1.00413 | − | 0.579733i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.2069 | − | 38.4634i | 0.921296 | − | 1.59573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.821993 | − | 0.474578i | 0.0340435 | − | 0.0196550i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.27908 | + | 1.84325i | −0.176918 | + | 0.0762092i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.23339 | + | 1.86680i | −0.133456 | + | 0.0770510i | −0.565242 | − | 0.824925i | \(-0.691217\pi\) |
0.431785 | + | 0.901976i | \(0.357884\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0127262 | + | 0.0220424i | −0.000524374 | + | 0.000908242i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.5568 | − | 13.6005i | −0.968997 | − | 0.559451i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.5374i | 0.514848i | 0.966299 | + | 0.257424i | \(0.0828737\pi\) | ||||
−0.966299 | + | 0.257424i | \(0.917126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.44721 | − | 7.70280i | −0.182318 | − | 0.315784i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.5219 | −1.33103 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.65827 | −0.394626 | −0.197313 | − | 0.980341i | \(-0.563222\pi\) | ||||
−0.197313 | + | 0.980341i | \(0.563222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0400 | − | 38.1744i | −0.899031 | − | 1.55717i | −0.828736 | − | 0.559640i | \(-0.810939\pi\) |
−0.0702951 | − | 0.997526i | \(-0.522394\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.69410i | − | 0.109712i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.49108 | + | 5.47968i | 0.385867 | + | 0.222781i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.27578 | + | 5.67382i | −0.132960 | + | 0.230293i | −0.924816 | − | 0.380414i | \(-0.875781\pi\) |
0.791856 | + | 0.610707i | \(0.209115\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.94011 | + | 4.00687i | −0.281227 | + | 0.162367i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.1066 | − | 20.2014i | −1.09662 | − | 0.817262i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.1583 | + | 8.75167i | −0.612240 | + | 0.353477i | −0.773842 | − | 0.633379i | \(-0.781667\pi\) |
0.161602 | + | 0.986856i | \(0.448334\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.18952 | − | 8.98851i | 0.209262 | − | 0.362452i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.28725 | − | 4.20729i | −0.293374 | − | 0.169379i | 0.346089 | − | 0.938202i | \(-0.387510\pi\) |
−0.639462 | + | 0.768823i | \(0.720843\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 32.8802i | − | 1.32157i | −0.750576 | − | 0.660784i | \(-0.770224\pi\) | ||
0.750576 | − | 0.660784i | \(-0.229776\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.2643 | + | 22.9744i | 0.532278 | + | 0.921933i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.97640 | 0.359632 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.00186647 | + | 0.00323282i | 7.45397e−5 | + | 0.000129107i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.78052i | − | 0.0709942i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.46259 | − | 1.42178i | −0.0980342 | − | 0.0566001i | 0.450181 | − | 0.892937i | \(-0.351359\pi\) |
−0.548216 | + | 0.836337i | \(0.684693\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.33744 | + | 10.9768i | −0.251891 | + | 0.436287i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.4959 | + | 6.05980i | −0.416516 | + | 0.240476i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.15121 | + | 0.604727i | 0.204098 | + | 0.0239602i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.30369 | − | 4.21679i | 0.288930 | − | 0.166814i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.3090 | − | 28.2480i | 0.644166 | − | 1.11573i | −0.340327 | − | 0.940307i | \(-0.610538\pi\) |
0.984493 | − | 0.175422i | \(-0.0561289\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.5719 | + | 10.7225i | 0.732406 | + | 0.422855i | 0.819302 | − | 0.573363i | \(-0.194361\pi\) |
−0.0868960 | + | 0.996217i | \(0.527695\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 12.1020i | − | 0.476518i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7500 | + | 35.9401i | 0.815768 | + | 1.41295i | 0.908775 | + | 0.417287i | \(0.137019\pi\) |
−0.0930064 | + | 0.995666i | \(0.529648\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.17218 | 0.0460121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.81964 | −0.267283 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.2686 | + | 31.6421i | 0.714905 | + | 1.23825i | 0.962996 | + | 0.269515i | \(0.0868634\pi\) |
−0.248091 | + | 0.968737i | \(0.579803\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 14.1852i | − | 0.554263i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.6561 | − | 7.88436i | −0.532776 | − | 0.307598i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.4024 | + | 33.6059i | −0.755810 | + | 1.30910i | 0.189161 | + | 0.981946i | \(0.439423\pi\) |
−0.944971 | + | 0.327155i | \(0.893910\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.7925 | + | 17.2007i | −1.15880 | + | 0.669031i | −0.951015 | − | 0.309144i | \(-0.899957\pi\) |
−0.207781 | + | 0.978175i | \(0.566624\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.62096 | − | 11.5678i | 0.334810 | − | 0.449255i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0356433 | + | 0.0205787i | −0.00138219 | + | 0.000798006i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.99200 | − | 8.64640i | 0.193291 | − | 0.334790i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.49990 | + | 0.865968i | 0.0579895 | + | 0.0334803i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 0.786776i | − | 0.0303731i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0929 | + | 29.6058i | 0.658884 | + | 1.14122i | 0.980905 | + | 0.194488i | \(0.0623044\pi\) |
−0.322021 | + | 0.946732i | \(0.604362\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.60916 | 0.215897 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.1215 | −0.389001 | −0.194500 | − | 0.980902i | \(-0.562309\pi\) | ||||
−0.194500 | + | 0.980902i | \(0.562309\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.7833 | + | 46.3900i | 1.02785 | + | 1.78028i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1.89847i | − | 0.0727495i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.4636 | + | 18.1655i | 1.20392 | + | 0.695083i | 0.961424 | − | 0.275069i | \(-0.0887007\pi\) |
0.242495 | + | 0.970153i | \(0.422034\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.98490 | + | 15.5623i | −0.343295 | + | 0.594605i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −31.1135 | + | 17.9634i | −1.18705 | + | 0.685346i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.1431 | + | 13.6102i | −0.386422 | + | 0.518508i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.4030 | − | 7.16085i | 0.471830 | − | 0.272411i | −0.245175 | − | 0.969479i | \(-0.578845\pi\) |
0.717006 | + | 0.697067i | \(0.245512\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.378411 | − | 0.655428i | 0.0143747 | − | 0.0248976i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.0902819 | − | 0.0521243i | −0.00342459 | − | 0.00197719i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 24.3180i | − | 0.921109i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.6561 | − | 27.1172i | −0.592169 | − | 1.02567i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.9203 | 1.73438 | 0.867192 | − | 0.497973i | \(-0.165922\pi\) | ||||
0.867192 | + | 0.497973i | \(0.165922\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.00823906 | −0.000310742 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.12648 | + | 10.6114i | 0.230736 | + | 0.399647i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 16.2543i | − | 0.611305i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.9608 | + | 16.1432i | 1.05009 | + | 0.606270i | 0.922675 | − | 0.385579i | \(-0.125998\pi\) |
0.127416 | + | 0.991849i | \(0.459332\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.99696 | − | 12.1191i | 0.262407 | − | 0.454502i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.35802 | − | 4.24816i | 0.275560 | − | 0.159095i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.721974 | + | 0.0847563i | 0.0270003 | + | 0.00316971i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.65473 | + | 3.26476i | −0.211180 | + | 0.121925i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.49588 | − | 16.4473i | 0.354136 | − | 0.613382i | −0.632833 | − | 0.774288i | \(-0.718108\pi\) |
0.986970 | + | 0.160906i | \(0.0514415\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.96151 | + | 2.86453i | 0.184776 | + | 0.106681i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 17.2094i | − | 0.640025i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.05550 | − | 1.82818i | −0.0392003 | − | 0.0678969i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.8696 | −1.29324 | −0.646622 | − | 0.762811i | \(-0.723819\pi\) | ||||
−0.646622 | + | 0.762811i | \(0.723819\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.4531 | 0.979744 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.1775 | − | 24.5561i | −0.524373 | − | 0.908241i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 7.05777i | − | 0.260685i | −0.991469 | − | 0.130342i | \(-0.958392\pi\) | ||
0.991469 | − | 0.130342i | \(-0.0416076\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.62800 | − | 0.939928i | −0.0600498 | − | 0.0346698i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.210168 | + | 0.364022i | −0.00774164 | + | 0.0134089i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.3087 | − | 6.52909i | 0.415998 | − | 0.240177i | −0.277366 | − | 0.960764i | \(-0.589461\pi\) |
0.693364 | + | 0.720588i | \(0.256128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0535277 | − | 0.0398919i | −0.00196639 | − | 0.00146547i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.2360 | + | 14.5700i | −0.925819 | + | 0.534522i | −0.885487 | − | 0.464664i | \(-0.846175\pi\) |
−0.0403324 | + | 0.999186i | \(0.512842\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.89704 | + | 15.4101i | −0.325962 | + | 0.564583i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.1102 | + | 9.87858i | 0.626029 | + | 0.361438i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.87850i | 0.141717i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.12718 | + | 14.0767i | 0.296565 | + | 0.513666i | 0.975348 | − | 0.220673i | \(-0.0708255\pi\) |
−0.678783 | + | 0.734339i | \(0.737492\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.0227 | 0.729668 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.1805 | −0.443295 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.9791 | + | 27.6766i | 0.580770 | + | 1.00592i | 0.995388 | + | 0.0959276i | \(0.0305817\pi\) |
−0.414618 | + | 0.909995i | \(0.636085\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.24610i | − | 0.0452306i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0342 | − | 8.68000i | −0.544990 | − | 0.314650i | 0.202109 | − | 0.979363i | \(-0.435220\pi\) |
−0.747099 | + | 0.664713i | \(0.768554\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.78066 | + | 11.7444i | −0.245476 | + | 0.425177i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.42654 | − | 1.97831i | 0.123887 | − | 0.0715260i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.2523 | + | 8.29311i | −0.695161 | + | 0.299447i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.25269 | − | 4.18734i | 0.261539 | − | 0.150999i | −0.363498 | − | 0.931595i | \(-0.618417\pi\) |
0.625036 | + | 0.780596i | \(0.285084\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.54048 | − | 16.5246i | 0.343592 | − | 0.595119i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.2609 | + | 18.0485i | 1.12438 | + | 0.649160i | 0.942515 | − | 0.334164i | \(-0.108454\pi\) |
0.181863 | + | 0.983324i | \(0.441787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.79645i | − | 0.0645302i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.10377 | − | 1.91179i | −0.0395977 | − | 0.0685852i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.112527 | −0.00403170 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.31581 | −0.0470835 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.92047 | − | 10.2545i | −0.211580 | − | 0.366468i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 9.95336i | − | 0.355250i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.4824 | − | 23.9499i | −1.47869 | − | 0.853721i | −0.478979 | − | 0.877827i | \(-0.658993\pi\) |
−0.999709 | + | 0.0241057i | \(0.992326\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.16876 | + | 14.1487i | −0.290816 | + | 0.503707i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.5170 | + | 15.8870i | −0.978393 | + | 0.564876i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.56640 | + | 12.9223i | 0.197669 | + | 0.458885i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.32796 | − | 3.07610i | 0.188963 | − | 0.109098i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.1525 | − | 19.3168i | 0.395043 | − | 0.684235i | −0.598063 | − | 0.801449i | \(-0.704063\pi\) |
0.993107 | + | 0.117214i | \(0.0373963\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.8623 | + | 14.3543i | 0.879566 | + | 0.507818i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.99309i | 0.141089i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.23012 | + | 2.13064i | 0.0434101 | + | 0.0751886i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.7388 | 0.484230 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.4452 | 0.930915 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.07676 | + | 3.59705i | 0.0730148 | + | 0.126465i | 0.900221 | − | 0.435433i | \(-0.143405\pi\) |
−0.827206 | + | 0.561898i | \(0.810071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35.8894i | − | 1.26025i | −0.776494 | − | 0.630124i | \(-0.783004\pi\) | ||
0.776494 | − | 0.630124i | \(-0.216996\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.97250 | − | 2.29352i | −0.139322 | − | 0.0804374i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.50618 | − | 7.80493i | 0.157845 | − | 0.273395i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.113629 | + | 0.0656038i | −0.00397538 | + | 0.00229519i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.57805 | + | 13.4422i | −0.0551417 | + | 0.469710i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.6474 | − | 17.1169i | 1.03470 | − | 0.597385i | 0.116373 | − | 0.993206i | \(-0.462873\pi\) |
0.918328 | + | 0.395821i | \(0.129540\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.6762 | + | 47.9366i | −0.964731 | + | 1.67096i | −0.254395 | + | 0.967100i | \(0.581876\pi\) |
−0.710336 | + | 0.703863i | \(0.751457\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.228175 | − | 0.131737i | −0.00794402 | − | 0.00458648i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.3781i | 1.57795i | 0.614425 | + | 0.788975i | \(0.289388\pi\) | ||||
−0.614425 | + | 0.788975i | \(0.710612\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.81278 | + | 11.8001i | 0.236618 | + | 0.409834i | 0.959742 | − | 0.280885i | \(-0.0906278\pi\) |
−0.723124 | + | 0.690718i | \(0.757295\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.45487 | −0.154538 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.40448 | −0.152606 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.03692 | − | 13.9204i | −0.278129 | − | 0.481734i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 10.0765i | − | 0.348296i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.5499 | − | 20.5247i | −1.22732 | − | 0.708592i | −0.260850 | − | 0.965379i | \(-0.584003\pi\) |
−0.966468 | + | 0.256787i | \(0.917336\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.2718 | − | 21.2554i | 0.423167 | − | 0.732947i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.7692 | − | 16.6099i | 0.990865 | − | 0.572076i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.4576 | + | 3.71586i | −0.428555 | + | 0.127829i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.5707 | − | 15.9180i | 0.947341 | − | 0.546948i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.7654 | + | 23.8424i | −0.472428 | + | 0.818270i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.38183 | + | 1.37515i | 0.0816480 | + | 0.0471395i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 55.0548i | − | 1.88504i | −0.334148 | − | 0.942521i | \(-0.608448\pi\) | ||
0.334148 | − | 0.942521i | \(-0.391552\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.00915428 | − | 0.0158557i | −0.000313070 | − | 0.000542253i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.9165 | 0.953609 | 0.476805 | − | 0.879009i | \(-0.341795\pi\) | ||||
0.476805 | + | 0.879009i | \(0.341795\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.1918 | −0.757174 | −0.378587 | − | 0.925566i | \(-0.623590\pi\) | ||||
−0.378587 | + | 0.925566i | \(0.623590\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.0751 | − | 26.1108i | −0.513758 | − | 0.889854i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.5089i | 0.391768i | 0.980627 | + | 0.195884i | \(0.0627576\pi\) | ||||
−0.980627 | + | 0.195884i | \(0.937242\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.7879 | + | 7.38307i | 0.434800 | + | 0.251032i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.98225 | − | 8.62952i | 0.169206 | − | 0.293074i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.89083 | + | 1.09167i | −0.0641420 | + | 0.0370324i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.876445 | − | 7.46576i | 0.0296972 | − | 0.252968i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.6363 | + | 11.9144i | −0.698432 | + | 0.403240i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.45245 | − | 2.51573i | 0.0491019 | − | 0.0850470i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.8575 | + | 17.2383i | 1.00822 | + | 0.582094i | 0.910669 | − | 0.413136i | \(-0.135567\pi\) |
0.0975480 | + | 0.995231i | \(0.468900\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.9400i | 1.04358i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.6960 | + | 23.7222i | 0.461430 | + | 0.799220i | 0.999032 | − | 0.0439786i | \(-0.0140033\pi\) |
−0.537603 | + | 0.843198i | \(0.680670\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.8229 | 0.936316 | 0.468158 | − | 0.883645i | \(-0.344918\pi\) | ||||
0.468158 | + | 0.883645i | \(0.344918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.59778 | 0.255397 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.94929 | + | 15.5006i | 0.300488 | + | 0.520460i | 0.976247 | − | 0.216663i | \(-0.0695172\pi\) |
−0.675759 | + | 0.737123i | \(0.736184\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.2063i | 1.18078i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.602985 | − | 0.348134i | −0.0202008 | − | 0.0116629i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.0664218 | − | 0.115046i | 0.00222272 | − | 0.00384987i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.03758 | − | 1.75375i | 0.101535 | − | 0.0586213i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.81611 | + | 20.4665i | 0.294361 | + | 0.683355i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.28422 | + | 1.89615i | −0.109535 | + | 0.0632401i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.20726 | − | 12.4833i | 0.240109 | − | 0.415881i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.4454 | − | 17.5777i | −1.01316 | − | 0.584949i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 15.8577i | − | 0.527127i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.74344 | + | 3.01972i | 0.0578898 | + | 0.100268i | 0.893518 | − | 0.449027i | \(-0.148229\pi\) |
−0.835628 | + | 0.549296i | \(0.814896\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.23061 | 0.239824 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9862 | −0.562778 | −0.281389 | − | 0.959594i | \(-0.590795\pi\) | ||||
−0.281389 | + | 0.959594i | \(0.590795\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.54126 | − | 2.66955i | −0.0510084 | − | 0.0883491i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 5.09969i | − | 0.168591i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35.6862 | − | 20.6034i | −1.17846 | − | 0.680385i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.7765 | − | 18.6654i | 0.355482 | − | 0.615714i | −0.631718 | − | 0.775198i | \(-0.717650\pi\) |
0.987200 | + | 0.159485i | \(0.0509833\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.1293 | + | 16.8178i | −0.959842 | + | 0.554165i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.6114 | − | 9.30932i | 0.711349 | − | 0.306420i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.503609 | − | 0.290759i | 0.0165586 | − | 0.00956009i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.27427 | + | 2.20709i | −0.0418524 | + | 0.0724905i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.6458 | + | 10.1878i | 0.578941 | + | 0.334252i | 0.760712 | − | 0.649089i | \(-0.224850\pi\) |
−0.181771 | + | 0.983341i | \(0.558183\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0203809i | 0.000667959i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.53752 | + | 7.85921i | 0.148552 | + | 0.257299i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.617316 | −0.0201884 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.1601 | 0.658602 | 0.329301 | − | 0.944225i | \(-0.393187\pi\) | ||||
0.329301 | + | 0.944225i | \(0.393187\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.7530 | + | 20.3567i | 0.383544 | + | 0.664317i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.2121i | 0.463300i | 0.972799 | + | 0.231650i | \(0.0744124\pi\) | ||||
−0.972799 | + | 0.231650i | \(0.925588\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.5304 | + | 18.7814i | 1.05934 | + | 0.611608i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.14705 | − | 14.1111i | 0.265024 | − | 0.459034i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.63562 | − | 0.944323i | 0.0531504 | − | 0.0306864i | −0.473189 | − | 0.880961i | \(-0.656897\pi\) |
0.526340 | + | 0.850274i | \(0.323564\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.2782 | − | 26.2913i | −1.14518 | − | 0.853453i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.72626 | + | 0.996659i | −0.0559780 | + | 0.0323189i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.0550 | − | 27.8081i | 0.520072 | − | 0.900792i | −0.479655 | − | 0.877457i | \(-0.659238\pi\) |
0.999728 | − | 0.0233346i | \(-0.00742831\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.75067 | − | 2.16545i | −0.121369 | − | 0.0700723i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.556192i | 0.0179791i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26.1003 | + | 45.2071i | 0.842823 | + | 1.45981i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.7728 | 0.895896 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.72532 | −0.0555978 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.6746 | − | 18.4890i | −0.343629 | − | 0.595182i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.0621i | 1.73852i | 0.494357 | + | 0.869259i | \(0.335404\pi\) | ||||
−0.494357 | + | 0.869259i | \(0.664596\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0490959 | + | 0.0283455i | 0.00157719 | + | 0.000910590i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.3278 | − | 42.1369i | 0.780715 | − | 1.35224i | −0.150811 | − | 0.988563i | \(-0.548188\pi\) |
0.931526 | − | 0.363676i | \(-0.118478\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.262261 | + | 0.151416i | −0.00840770 | + | 0.00485419i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.67966 | + | 0.549370i | 0.149869 | + | 0.0175939i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.4838 | + | 8.36225i | −0.463379 | + | 0.267532i | −0.713464 | − | 0.700692i | \(-0.752875\pi\) |
0.250085 | + | 0.968224i | \(0.419541\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.311503 | − | 0.539539i | 0.00995567 | − | 0.0172437i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.22444 | − | 3.01633i | −0.166803 | − | 0.0963040i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 35.7213i | − | 1.13933i | −0.821876 | − | 0.569666i | \(-0.807072\pi\) | ||
0.821876 | − | 0.569666i | \(-0.192928\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.4074 | − | 18.0261i | −0.331606 | − | 0.574359i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 35.5937 | 1.13296 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43.7987 | 1.39272 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.608309 | + | 1.05362i | 0.0193236 | + | 0.0334694i | 0.875525 | − | 0.483172i | \(-0.160515\pi\) |
−0.856202 | + | 0.516641i | \(0.827182\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 25.8728i | − | 0.821048i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.5522 | − | 12.4432i | −0.683250 | − | 0.394475i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.1849 | + | 33.2291i | −0.607590 | + | 1.05238i | 0.384046 | + | 0.923314i | \(0.374530\pi\) |
−0.991636 | + | 0.129063i | \(0.958803\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.82482 | − | 1.63091i | 0.0893734 | − | 0.0515998i |
(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 | 1040.2.da.e.881.2 | 12 | ||
4.3 | odd | 2 | 520.2.bu.a.361.5 | yes | 12 | ||
13.4 | even | 6 | inner | 1040.2.da.e.641.2 | 12 | ||
52.11 | even | 12 | 6760.2.a.bj.1.2 | 6 | |||
52.15 | even | 12 | 6760.2.a.bg.1.2 | 6 | |||
52.43 | odd | 6 | 520.2.bu.a.121.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
520.2.bu.a.121.5 | ✓ | 12 | 52.43 | odd | 6 | ||
520.2.bu.a.361.5 | yes | 12 | 4.3 | odd | 2 | ||
1040.2.da.e.641.2 | 12 | 13.4 | even | 6 | inner | ||
1040.2.da.e.881.2 | 12 | 1.1 | even | 1 | trivial | ||
6760.2.a.bg.1.2 | 6 | 52.15 | even | 12 | |||
6760.2.a.bj.1.2 | 6 | 52.11 | even | 12 |