Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 697.8 | ||
Character | \(\chi\) | \(=\) | 1110.697 |
Dual form | 1110.2.l.a.43.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.05054 | + | 0.891783i | 0.917030 | + | 0.398817i | ||||
\(6\) | −0.707107 | + | 0.707107i | −0.288675 | + | 0.288675i | ||||
\(7\) | −1.56460 | − | 1.56460i | −0.591365 | − | 0.591365i | 0.346635 | − | 0.938000i | \(-0.387324\pi\) |
−0.938000 | + | 0.346635i | \(0.887324\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0.891783 | − | 2.05054i | 0.282007 | − | 0.648438i | ||||
\(11\) | − | 3.92190i | − | 1.18250i | −0.806489 | − | 0.591249i | \(-0.798635\pi\) | ||
0.806489 | − | 0.591249i | \(-0.201365\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | 0.319413i | 0.0885893i | 0.999019 | + | 0.0442946i | \(0.0141040\pi\) | ||||
−0.999019 | + | 0.0442946i | \(0.985896\pi\) | |||||||
\(14\) | −1.56460 | + | 1.56460i | −0.418158 | + | 0.418158i | ||||
\(15\) | −0.819367 | − | 2.08054i | −0.211560 | − | 0.537193i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.25497 | 0.304376 | 0.152188 | − | 0.988352i | \(-0.451368\pi\) | ||||
0.152188 | + | 0.988352i | \(0.451368\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.17875 | − | 2.17875i | −0.499839 | − | 0.499839i | 0.411549 | − | 0.911388i | \(-0.364988\pi\) |
−0.911388 | + | 0.411549i | \(0.864988\pi\) | |||||||
\(20\) | −2.05054 | − | 0.891783i | −0.458515 | − | 0.199409i | ||||
\(21\) | 2.21268i | 0.482847i | ||||||||
\(22\) | −3.92190 | −0.836152 | ||||||||
\(23\) | 1.15203i | 0.240215i | 0.992761 | + | 0.120107i | \(0.0383239\pi\) | ||||
−0.992761 | + | 0.120107i | \(0.961676\pi\) | |||||||
\(24\) | 0.707107 | − | 0.707107i | 0.144338 | − | 0.144338i | ||||
\(25\) | 3.40945 | + | 3.65728i | 0.681889 | + | 0.731455i | ||||
\(26\) | 0.319413 | 0.0626421 | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 1.56460 | + | 1.56460i | 0.295682 | + | 0.295682i | ||||
\(29\) | 1.22361 | − | 1.22361i | 0.227218 | − | 0.227218i | −0.584312 | − | 0.811529i | \(-0.698635\pi\) |
0.811529 | + | 0.584312i | \(0.198635\pi\) | |||||||
\(30\) | −2.08054 | + | 0.819367i | −0.379853 | + | 0.149595i | ||||
\(31\) | −6.78274 | − | 6.78274i | −1.21822 | − | 1.21822i | −0.968256 | − | 0.249959i | \(-0.919583\pi\) |
−0.249959 | − | 0.968256i | \(-0.580417\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −2.77320 | + | 2.77320i | −0.482753 | + | 0.482753i | ||||
\(34\) | − | 1.25497i | − | 0.215226i | ||||||
\(35\) | −1.81300 | − | 4.60357i | −0.306453 | − | 0.778146i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 0.0100817 | − | 6.08275i | 0.00165742 | − | 0.999999i | ||||
\(38\) | −2.17875 | + | 2.17875i | −0.353440 | + | 0.353440i | ||||
\(39\) | 0.225859 | − | 0.225859i | 0.0361664 | − | 0.0361664i | ||||
\(40\) | −0.891783 | + | 2.05054i | −0.141003 | + | 0.324219i | ||||
\(41\) | − | 3.92813i | − | 0.613470i | −0.951795 | − | 0.306735i | \(-0.900763\pi\) | ||
0.951795 | − | 0.306735i | \(-0.0992366\pi\) | |||||||
\(42\) | 2.21268 | 0.341425 | ||||||||
\(43\) | 1.87330i | 0.285675i | 0.989746 | + | 0.142838i | \(0.0456227\pi\) | ||||
−0.989746 | + | 0.142838i | \(0.954377\pi\) | |||||||
\(44\) | 3.92190i | 0.591249i | ||||||||
\(45\) | −0.891783 | + | 2.05054i | −0.132939 | + | 0.305677i | ||||
\(46\) | 1.15203 | 0.169857 | ||||||||
\(47\) | −4.88442 | − | 4.88442i | −0.712466 | − | 0.712466i | 0.254585 | − | 0.967051i | \(-0.418061\pi\) |
−0.967051 | + | 0.254585i | \(0.918061\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 2.10403i | − | 0.300576i | ||||||
\(50\) | 3.65728 | − | 3.40945i | 0.517217 | − | 0.482169i | ||||
\(51\) | −0.887401 | − | 0.887401i | −0.124261 | − | 0.124261i | ||||
\(52\) | − | 0.319413i | − | 0.0442946i | ||||||
\(53\) | −3.03226 | + | 3.03226i | −0.416513 | + | 0.416513i | −0.884000 | − | 0.467487i | \(-0.845160\pi\) |
0.467487 | + | 0.884000i | \(0.345160\pi\) | |||||||
\(54\) | −0.707107 | − | 0.707107i | −0.0962250 | − | 0.0962250i | ||||
\(55\) | 3.49748 | − | 8.04202i | 0.471601 | − | 1.08439i | ||||
\(56\) | 1.56460 | − | 1.56460i | 0.209079 | − | 0.209079i | ||||
\(57\) | 3.08122i | 0.408117i | ||||||||
\(58\) | −1.22361 | − | 1.22361i | −0.160667 | − | 0.160667i | ||||
\(59\) | −4.70399 | − | 4.70399i | −0.612407 | − | 0.612407i | 0.331165 | − | 0.943573i | \(-0.392558\pi\) |
−0.943573 | + | 0.331165i | \(0.892558\pi\) | |||||||
\(60\) | 0.819367 | + | 2.08054i | 0.105780 | + | 0.268596i | ||||
\(61\) | −5.56135 | − | 5.56135i | −0.712058 | − | 0.712058i | 0.254908 | − | 0.966965i | \(-0.417955\pi\) |
−0.966965 | + | 0.254908i | \(0.917955\pi\) | |||||||
\(62\) | −6.78274 | + | 6.78274i | −0.861408 | + | 0.861408i | ||||
\(63\) | 1.56460 | − | 1.56460i | 0.197122 | − | 0.197122i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.284847 | + | 0.654970i | −0.0353309 | + | 0.0812390i | ||||
\(66\) | 2.77320 | + | 2.77320i | 0.341358 | + | 0.341358i | ||||
\(67\) | −6.88391 | + | 6.88391i | −0.841003 | + | 0.841003i | −0.988989 | − | 0.147986i | \(-0.952721\pi\) |
0.147986 | + | 0.988989i | \(0.452721\pi\) | |||||||
\(68\) | −1.25497 | −0.152188 | ||||||||
\(69\) | 0.814607 | − | 0.814607i | 0.0980672 | − | 0.0980672i | ||||
\(70\) | −4.60357 | + | 1.81300i | −0.550232 | + | 0.216695i | ||||
\(71\) | −3.29012 | −0.390466 | −0.195233 | − | 0.980757i | \(-0.562546\pi\) | ||||
−0.195233 | + | 0.980757i | \(0.562546\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 8.53399 | + | 8.53399i | 0.998828 | + | 0.998828i | 0.999999 | − | 0.00117124i | \(-0.000372817\pi\) |
−0.00117124 | + | 0.999999i | \(0.500373\pi\) | |||||||
\(74\) | −6.08275 | − | 0.0100817i | −0.707106 | − | 0.00117198i | ||||
\(75\) | 0.175243 | − | 4.99693i | 0.0202353 | − | 0.576996i | ||||
\(76\) | 2.17875 | + | 2.17875i | 0.249920 | + | 0.249920i | ||||
\(77\) | −6.13622 | + | 6.13622i | −0.699287 | + | 0.699287i | ||||
\(78\) | −0.225859 | − | 0.225859i | −0.0255735 | − | 0.0255735i | ||||
\(79\) | 3.59077 | + | 3.59077i | 0.403993 | + | 0.403993i | 0.879638 | − | 0.475645i | \(-0.157785\pi\) |
−0.475645 | + | 0.879638i | \(0.657785\pi\) | |||||||
\(80\) | 2.05054 | + | 0.891783i | 0.229258 | + | 0.0997044i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −3.92813 | −0.433789 | ||||||||
\(83\) | −1.13008 | + | 1.13008i | −0.124042 | + | 0.124042i | −0.766403 | − | 0.642360i | \(-0.777955\pi\) |
0.642360 | + | 0.766403i | \(0.277955\pi\) | |||||||
\(84\) | − | 2.21268i | − | 0.241424i | ||||||
\(85\) | 2.57338 | + | 1.11916i | 0.279122 | + | 0.121390i | ||||
\(86\) | 1.87330 | 0.202003 | ||||||||
\(87\) | −1.73044 | −0.185523 | ||||||||
\(88\) | 3.92190 | 0.418076 | ||||||||
\(89\) | −1.33809 | + | 1.33809i | −0.141837 | + | 0.141837i | −0.774460 | − | 0.632623i | \(-0.781978\pi\) |
0.632623 | + | 0.774460i | \(0.281978\pi\) | |||||||
\(90\) | 2.05054 | + | 0.891783i | 0.216146 | + | 0.0940022i | ||||
\(91\) | 0.499755 | − | 0.499755i | 0.0523886 | − | 0.0523886i | ||||
\(92\) | − | 1.15203i | − | 0.120107i | ||||||
\(93\) | 9.59224i | 0.994669i | ||||||||
\(94\) | −4.88442 | + | 4.88442i | −0.503790 | + | 0.503790i | ||||
\(95\) | −2.52465 | − | 6.41059i | −0.259023 | − | 0.657712i | ||||
\(96\) | −0.707107 | + | 0.707107i | −0.0721688 | + | 0.0721688i | ||||
\(97\) | 4.01884 | 0.408051 | 0.204025 | − | 0.978966i | \(-0.434597\pi\) | ||||
0.204025 | + | 0.978966i | \(0.434597\pi\) | |||||||
\(98\) | −2.10403 | −0.212539 | ||||||||
\(99\) | 3.92190 | 0.394166 | ||||||||
\(100\) | −3.40945 | − | 3.65728i | −0.340945 | − | 0.365728i | ||||
\(101\) | − | 11.0673i | − | 1.10124i | −0.834757 | − | 0.550618i | \(-0.814392\pi\) | ||
0.834757 | − | 0.550618i | \(-0.185608\pi\) | |||||||
\(102\) | −0.887401 | + | 0.887401i | −0.0878658 | + | 0.0878658i | ||||
\(103\) | 13.8134 | 1.36107 | 0.680536 | − | 0.732715i | \(-0.261747\pi\) | ||||
0.680536 | + | 0.732715i | \(0.261747\pi\) | |||||||
\(104\) | −0.319413 | −0.0313210 | ||||||||
\(105\) | −1.97323 | + | 4.53720i | −0.192568 | + | 0.442785i | ||||
\(106\) | 3.03226 | + | 3.03226i | 0.294520 | + | 0.294520i | ||||
\(107\) | 1.55870 | + | 1.55870i | 0.150685 | + | 0.150685i | 0.778424 | − | 0.627739i | \(-0.216019\pi\) |
−0.627739 | + | 0.778424i | \(0.716019\pi\) | |||||||
\(108\) | −0.707107 | + | 0.707107i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | 4.24101 | + | 4.24101i | 0.406215 | + | 0.406215i | 0.880416 | − | 0.474201i | \(-0.157263\pi\) |
−0.474201 | + | 0.880416i | \(0.657263\pi\) | |||||||
\(110\) | −8.04202 | − | 3.49748i | −0.766777 | − | 0.333472i | ||||
\(111\) | −4.30829 | + | 4.29403i | −0.408924 | + | 0.407571i | ||||
\(112\) | −1.56460 | − | 1.56460i | −0.147841 | − | 0.147841i | ||||
\(113\) | −16.5384 | −1.55580 | −0.777899 | − | 0.628390i | \(-0.783714\pi\) | ||||
−0.777899 | + | 0.628390i | \(0.783714\pi\) | |||||||
\(114\) | 3.08122 | 0.288582 | ||||||||
\(115\) | −1.02736 | + | 2.36228i | −0.0958018 | + | 0.220284i | ||||
\(116\) | −1.22361 | + | 1.22361i | −0.113609 | + | 0.113609i | ||||
\(117\) | −0.319413 | −0.0295298 | ||||||||
\(118\) | −4.70399 | + | 4.70399i | −0.433037 | + | 0.433037i | ||||
\(119\) | −1.96354 | − | 1.96354i | −0.179997 | − | 0.179997i | ||||
\(120\) | 2.08054 | − | 0.819367i | 0.189926 | − | 0.0747976i | ||||
\(121\) | −4.38131 | −0.398301 | ||||||||
\(122\) | −5.56135 | + | 5.56135i | −0.503501 | + | 0.503501i | ||||
\(123\) | −2.77761 | + | 2.77761i | −0.250448 | + | 0.250448i | ||||
\(124\) | 6.78274 | + | 6.78274i | 0.609108 | + | 0.609108i | ||||
\(125\) | 3.72972 | + | 10.5399i | 0.333596 | + | 0.942716i | ||||
\(126\) | −1.56460 | − | 1.56460i | −0.139386 | − | 0.139386i | ||||
\(127\) | 7.06209 | + | 7.06209i | 0.626659 | + | 0.626659i | 0.947226 | − | 0.320567i | \(-0.103873\pi\) |
−0.320567 | + | 0.947226i | \(0.603873\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 1.32462 | − | 1.32462i | 0.116626 | − | 0.116626i | ||||
\(130\) | 0.654970 | + | 0.284847i | 0.0574447 | + | 0.0249828i | ||||
\(131\) | −9.32171 | − | 9.32171i | −0.814442 | − | 0.814442i | 0.170855 | − | 0.985296i | \(-0.445347\pi\) |
−0.985296 | + | 0.170855i | \(0.945347\pi\) | |||||||
\(132\) | 2.77320 | − | 2.77320i | 0.241376 | − | 0.241376i | ||||
\(133\) | 6.81776i | 0.591174i | ||||||||
\(134\) | 6.88391 | + | 6.88391i | 0.594679 | + | 0.594679i | ||||
\(135\) | 2.08054 | − | 0.819367i | 0.179064 | − | 0.0705198i | ||||
\(136\) | 1.25497i | 0.107613i | ||||||||
\(137\) | −14.5752 | − | 14.5752i | −1.24525 | − | 1.24525i | −0.957796 | − | 0.287450i | \(-0.907193\pi\) |
−0.287450 | − | 0.957796i | \(-0.592807\pi\) | |||||||
\(138\) | −0.814607 | − | 0.814607i | −0.0693440 | − | 0.0693440i | ||||
\(139\) | 1.20629 | 0.102316 | 0.0511582 | − | 0.998691i | \(-0.483709\pi\) | ||||
0.0511582 | + | 0.998691i | \(0.483709\pi\) | |||||||
\(140\) | 1.81300 | + | 4.60357i | 0.153226 | + | 0.389073i | ||||
\(141\) | 6.90761i | 0.581726i | ||||||||
\(142\) | 3.29012i | 0.276101i | ||||||||
\(143\) | 1.25271 | 0.104757 | ||||||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 3.60025 | − | 1.41786i | 0.298984 | − | 0.117747i | ||||
\(146\) | 8.53399 | − | 8.53399i | 0.706278 | − | 0.706278i | ||||
\(147\) | −1.48777 | + | 1.48777i | −0.122710 | + | 0.122710i | ||||
\(148\) | −0.0100817 | + | 6.08275i | −0.000828712 | + | 0.499999i | ||||
\(149\) | − | 0.425764i | − | 0.0348800i | −0.999848 | − | 0.0174400i | \(-0.994448\pi\) | ||
0.999848 | − | 0.0174400i | \(-0.00555160\pi\) | |||||||
\(150\) | −4.99693 | − | 0.175243i | −0.407997 | − | 0.0143085i | ||||
\(151\) | − | 18.6559i | − | 1.51820i | −0.650976 | − | 0.759098i | \(-0.725640\pi\) | ||
0.650976 | − | 0.759098i | \(-0.274360\pi\) | |||||||
\(152\) | 2.17875 | − | 2.17875i | 0.176720 | − | 0.176720i | ||||
\(153\) | 1.25497i | 0.101459i | ||||||||
\(154\) | 6.13622 | + | 6.13622i | 0.494471 | + | 0.494471i | ||||
\(155\) | −7.85956 | − | 19.9570i | −0.631295 | − | 1.60299i | ||||
\(156\) | −0.225859 | + | 0.225859i | −0.0180832 | + | 0.0180832i | ||||
\(157\) | 6.23375 | + | 6.23375i | 0.497507 | + | 0.497507i | 0.910661 | − | 0.413154i | \(-0.135573\pi\) |
−0.413154 | + | 0.910661i | \(0.635573\pi\) | |||||||
\(158\) | 3.59077 | − | 3.59077i | 0.285666 | − | 0.285666i | ||||
\(159\) | 4.28827 | 0.340082 | ||||||||
\(160\) | 0.891783 | − | 2.05054i | 0.0705016 | − | 0.162110i | ||||
\(161\) | 1.80247 | − | 1.80247i | 0.142054 | − | 0.142054i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 15.4091 | 1.20693 | 0.603466 | − | 0.797389i | \(-0.293786\pi\) | ||||
0.603466 | + | 0.797389i | \(0.293786\pi\) | |||||||
\(164\) | 3.92813i | 0.306735i | ||||||||
\(165\) | −8.15967 | + | 3.21347i | −0.635229 | + | 0.250169i | ||||
\(166\) | 1.13008 | + | 1.13008i | 0.0877111 | + | 0.0877111i | ||||
\(167\) | 16.8371 | 1.30289 | 0.651447 | − | 0.758694i | \(-0.274162\pi\) | ||||
0.651447 | + | 0.758694i | \(0.274162\pi\) | |||||||
\(168\) | −2.21268 | −0.170712 | ||||||||
\(169\) | 12.8980 | 0.992152 | ||||||||
\(170\) | 1.11916 | − | 2.57338i | 0.0858360 | − | 0.197369i | ||||
\(171\) | 2.17875 | − | 2.17875i | 0.166613 | − | 0.166613i | ||||
\(172\) | − | 1.87330i | − | 0.142838i | ||||||
\(173\) | 5.18404 | + | 5.18404i | 0.394136 | + | 0.394136i | 0.876159 | − | 0.482023i | \(-0.160098\pi\) |
−0.482023 | + | 0.876159i | \(0.660098\pi\) | |||||||
\(174\) | 1.73044i | 0.131184i | ||||||||
\(175\) | 0.387756 | − | 11.0566i | 0.0293116 | − | 0.835802i | ||||
\(176\) | − | 3.92190i | − | 0.295624i | ||||||
\(177\) | 6.65245i | 0.500029i | ||||||||
\(178\) | 1.33809 | + | 1.33809i | 0.100294 | + | 0.100294i | ||||
\(179\) | −1.70251 | + | 1.70251i | −0.127252 | + | 0.127252i | −0.767864 | − | 0.640613i | \(-0.778680\pi\) |
0.640613 | + | 0.767864i | \(0.278680\pi\) | |||||||
\(180\) | 0.891783 | − | 2.05054i | 0.0664696 | − | 0.152838i | ||||
\(181\) | 8.75170 | 0.650509 | 0.325254 | − | 0.945627i | \(-0.394550\pi\) | ||||
0.325254 | + | 0.945627i | \(0.394550\pi\) | |||||||
\(182\) | −0.499755 | − | 0.499755i | −0.0370443 | − | 0.0370443i | ||||
\(183\) | 7.86494i | 0.581393i | ||||||||
\(184\) | −1.15203 | −0.0849287 | ||||||||
\(185\) | 5.44517 | − | 12.4640i | 0.400337 | − | 0.916368i | ||||
\(186\) | 9.59224 | 0.703337 | ||||||||
\(187\) | − | 4.92188i | − | 0.359924i | ||||||
\(188\) | 4.88442 | + | 4.88442i | 0.356233 | + | 0.356233i | ||||
\(189\) | −2.21268 | −0.160949 | ||||||||
\(190\) | −6.41059 | + | 2.52465i | −0.465073 | + | 0.183157i | ||||
\(191\) | 4.56780 | − | 4.56780i | 0.330514 | − | 0.330514i | −0.522268 | − | 0.852782i | \(-0.674914\pi\) |
0.852782 | + | 0.522268i | \(0.174914\pi\) | |||||||
\(192\) | 0.707107 | + | 0.707107i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 5.51547i | 0.397012i | 0.980100 | + | 0.198506i | \(0.0636090\pi\) | ||||
−0.980100 | + | 0.198506i | \(0.936391\pi\) | |||||||
\(194\) | − | 4.01884i | − | 0.288536i | ||||||
\(195\) | 0.664551 | − | 0.261716i | 0.0475895 | − | 0.0187419i | ||||
\(196\) | 2.10403i | 0.150288i | ||||||||
\(197\) | −3.48510 | − | 3.48510i | −0.248303 | − | 0.248303i | 0.571971 | − | 0.820274i | \(-0.306179\pi\) |
−0.820274 | + | 0.571971i | \(0.806179\pi\) | |||||||
\(198\) | − | 3.92190i | − | 0.278717i | ||||||
\(199\) | −11.0862 | + | 11.0862i | −0.785883 | + | 0.785883i | −0.980817 | − | 0.194933i | \(-0.937551\pi\) |
0.194933 | + | 0.980817i | \(0.437551\pi\) | |||||||
\(200\) | −3.65728 | + | 3.40945i | −0.258609 | + | 0.241084i | ||||
\(201\) | 9.73532 | 0.686676 | ||||||||
\(202\) | −11.0673 | −0.778692 | ||||||||
\(203\) | −3.82892 | −0.268737 | ||||||||
\(204\) | 0.887401 | + | 0.887401i | 0.0621305 | + | 0.0621305i | ||||
\(205\) | 3.50304 | − | 8.05479i | 0.244663 | − | 0.562571i | ||||
\(206\) | − | 13.8134i | − | 0.962423i | ||||||
\(207\) | −1.15203 | −0.0800715 | ||||||||
\(208\) | 0.319413i | 0.0221473i | ||||||||
\(209\) | −8.54484 | + | 8.54484i | −0.591059 | + | 0.591059i | ||||
\(210\) | 4.53720 | + | 1.97323i | 0.313097 | + | 0.136166i | ||||
\(211\) | 27.2170 | 1.87370 | 0.936848 | − | 0.349737i | \(-0.113729\pi\) | ||||
0.936848 | + | 0.349737i | \(0.113729\pi\) | |||||||
\(212\) | 3.03226 | − | 3.03226i | 0.208257 | − | 0.208257i | ||||
\(213\) | 2.32647 | + | 2.32647i | 0.159407 | + | 0.159407i | ||||
\(214\) | 1.55870 | − | 1.55870i | 0.106551 | − | 0.106551i | ||||
\(215\) | −1.67057 | + | 3.84128i | −0.113932 | + | 0.261973i | ||||
\(216\) | 0.707107 | + | 0.707107i | 0.0481125 | + | 0.0481125i | ||||
\(217\) | 21.2246i | 1.44082i | ||||||||
\(218\) | 4.24101 | − | 4.24101i | 0.287237 | − | 0.287237i | ||||
\(219\) | − | 12.0689i | − | 0.815540i | ||||||
\(220\) | −3.49748 | + | 8.04202i | −0.235800 | + | 0.542193i | ||||
\(221\) | 0.400855i | 0.0269644i | ||||||||
\(222\) | 4.29403 | + | 4.30829i | 0.288196 | + | 0.289153i | ||||
\(223\) | 11.1865 | − | 11.1865i | 0.749103 | − | 0.749103i | −0.225208 | − | 0.974311i | \(-0.572306\pi\) |
0.974311 | + | 0.225208i | \(0.0723061\pi\) | |||||||
\(224\) | −1.56460 | + | 1.56460i | −0.104539 | + | 0.104539i | ||||
\(225\) | −3.65728 | + | 3.40945i | −0.243818 | + | 0.227296i | ||||
\(226\) | 16.5384i | 1.10011i | ||||||||
\(227\) | 1.74912 | 0.116093 | 0.0580467 | − | 0.998314i | \(-0.481513\pi\) | ||||
0.0580467 | + | 0.998314i | \(0.481513\pi\) | |||||||
\(228\) | − | 3.08122i | − | 0.204058i | ||||||
\(229\) | − | 8.51464i | − | 0.562663i | −0.959611 | − | 0.281332i | \(-0.909224\pi\) | ||
0.959611 | − | 0.281332i | \(-0.0907761\pi\) | |||||||
\(230\) | 2.36228 | + | 1.02736i | 0.155764 | + | 0.0677421i | ||||
\(231\) | 8.67793 | 0.570966 | ||||||||
\(232\) | 1.22361 | + | 1.22361i | 0.0803336 | + | 0.0803336i | ||||
\(233\) | −6.42533 | − | 6.42533i | −0.420938 | − | 0.420938i | 0.464589 | − | 0.885526i | \(-0.346202\pi\) |
−0.885526 | + | 0.464589i | \(0.846202\pi\) | |||||||
\(234\) | 0.319413i | 0.0208807i | ||||||||
\(235\) | −5.65987 | − | 14.3716i | −0.369209 | − | 0.937497i | ||||
\(236\) | 4.70399 | + | 4.70399i | 0.306204 | + | 0.306204i | ||||
\(237\) | − | 5.07811i | − | 0.329859i | ||||||
\(238\) | −1.96354 | + | 1.96354i | −0.127277 | + | 0.127277i | ||||
\(239\) | 10.4976 | + | 10.4976i | 0.679036 | + | 0.679036i | 0.959782 | − | 0.280746i | \(-0.0905818\pi\) |
−0.280746 | + | 0.959782i | \(0.590582\pi\) | |||||||
\(240\) | −0.819367 | − | 2.08054i | −0.0528899 | − | 0.134298i | ||||
\(241\) | 6.66851 | − | 6.66851i | 0.429556 | − | 0.429556i | −0.458921 | − | 0.888477i | \(-0.651764\pi\) |
0.888477 | + | 0.458921i | \(0.151764\pi\) | |||||||
\(242\) | 4.38131i | 0.281641i | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 5.56135 | + | 5.56135i | 0.356029 | + | 0.356029i | ||||
\(245\) | 1.87634 | − | 4.31440i | 0.119875 | − | 0.275637i | ||||
\(246\) | 2.77761 | + | 2.77761i | 0.177094 | + | 0.177094i | ||||
\(247\) | 0.695921 | − | 0.695921i | 0.0442804 | − | 0.0442804i | ||||
\(248\) | 6.78274 | − | 6.78274i | 0.430704 | − | 0.430704i | ||||
\(249\) | 1.59817 | 0.101280 | ||||||||
\(250\) | 10.5399 | − | 3.72972i | 0.666601 | − | 0.235888i | ||||
\(251\) | 19.9946 | + | 19.9946i | 1.26205 | + | 1.26205i | 0.950099 | + | 0.311948i | \(0.100981\pi\) |
0.311948 | + | 0.950099i | \(0.399019\pi\) | |||||||
\(252\) | −1.56460 | + | 1.56460i | −0.0985608 | + | 0.0985608i | ||||
\(253\) | 4.51814 | 0.284053 | ||||||||
\(254\) | 7.06209 | − | 7.06209i | 0.443115 | − | 0.443115i | ||||
\(255\) | −1.02828 | − | 2.61102i | −0.0643936 | − | 0.163508i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 31.3639 | 1.95642 | 0.978212 | − | 0.207609i | \(-0.0665682\pi\) | ||||
0.978212 | + | 0.207609i | \(0.0665682\pi\) | |||||||
\(258\) | −1.32462 | − | 1.32462i | −0.0824673 | − | 0.0824673i | ||||
\(259\) | −9.53287 | + | 9.50133i | −0.592344 | + | 0.590384i | ||||
\(260\) | 0.284847 | − | 0.654970i | 0.0176655 | − | 0.0406195i | ||||
\(261\) | 1.22361 | + | 1.22361i | 0.0757393 | + | 0.0757393i | ||||
\(262\) | −9.32171 | + | 9.32171i | −0.575897 | + | 0.575897i | ||||
\(263\) | −7.40341 | − | 7.40341i | −0.456514 | − | 0.456514i | 0.440995 | − | 0.897509i | \(-0.354626\pi\) |
−0.897509 | + | 0.440995i | \(0.854626\pi\) | |||||||
\(264\) | −2.77320 | − | 2.77320i | −0.170679 | − | 0.170679i | ||||
\(265\) | −8.92191 | + | 3.51366i | −0.548068 | + | 0.215843i | ||||
\(266\) | 6.81776 | 0.418023 | ||||||||
\(267\) | 1.89234 | 0.115809 | ||||||||
\(268\) | 6.88391 | − | 6.88391i | 0.420502 | − | 0.420502i | ||||
\(269\) | 3.41947i | 0.208489i | 0.994552 | + | 0.104244i | \(0.0332424\pi\) | ||||
−0.994552 | + | 0.104244i | \(0.966758\pi\) | |||||||
\(270\) | −0.819367 | − | 2.08054i | −0.0498651 | − | 0.126618i | ||||
\(271\) | 17.8704 | 1.08555 | 0.542775 | − | 0.839878i | \(-0.317374\pi\) | ||||
0.542775 | + | 0.839878i | \(0.317374\pi\) | |||||||
\(272\) | 1.25497 | 0.0760940 | ||||||||
\(273\) | −0.706760 | −0.0427751 | ||||||||
\(274\) | −14.5752 | + | 14.5752i | −0.880522 | + | 0.880522i | ||||
\(275\) | 14.3435 | − | 13.3715i | 0.864944 | − | 0.806333i | ||||
\(276\) | −0.814607 | + | 0.814607i | −0.0490336 | + | 0.0490336i | ||||
\(277\) | − | 14.8527i | − | 0.892410i | −0.894931 | − | 0.446205i | \(-0.852775\pi\) | ||
0.894931 | − | 0.446205i | \(-0.147225\pi\) | |||||||
\(278\) | − | 1.20629i | − | 0.0723486i | ||||||
\(279\) | 6.78274 | − | 6.78274i | 0.406072 | − | 0.406072i | ||||
\(280\) | 4.60357 | − | 1.81300i | 0.275116 | − | 0.108347i | ||||
\(281\) | 4.56193 | − | 4.56193i | 0.272142 | − | 0.272142i | −0.557820 | − | 0.829962i | \(-0.688362\pi\) |
0.829962 | + | 0.557820i | \(0.188362\pi\) | |||||||
\(282\) | 6.90761 | 0.411342 | ||||||||
\(283\) | −32.3891 | −1.92533 | −0.962666 | − | 0.270692i | \(-0.912748\pi\) | ||||
−0.962666 | + | 0.270692i | \(0.912748\pi\) | |||||||
\(284\) | 3.29012 | 0.195233 | ||||||||
\(285\) | −2.74778 | + | 6.31816i | −0.162764 | + | 0.374256i | ||||
\(286\) | − | 1.25271i | − | 0.0740741i | ||||||
\(287\) | −6.14596 | + | 6.14596i | −0.362785 | + | 0.362785i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −15.4250 | −0.907355 | ||||||||
\(290\) | −1.41786 | − | 3.60025i | −0.0832599 | − | 0.211414i | ||||
\(291\) | −2.84175 | − | 2.84175i | −0.166586 | − | 0.166586i | ||||
\(292\) | −8.53399 | − | 8.53399i | −0.499414 | − | 0.499414i | ||||
\(293\) | 2.93182 | − | 2.93182i | 0.171279 | − | 0.171279i | −0.616262 | − | 0.787541i | \(-0.711354\pi\) |
0.787541 | + | 0.616262i | \(0.211354\pi\) | |||||||
\(294\) | 1.48777 | + | 1.48777i | 0.0867688 | + | 0.0867688i | ||||
\(295\) | −5.45079 | − | 13.8407i | −0.317357 | − | 0.805835i | ||||
\(296\) | 6.08275 | + | 0.0100817i | 0.353553 | + | 0.000585988i | ||||
\(297\) | −2.77320 | − | 2.77320i | −0.160918 | − | 0.160918i | ||||
\(298\) | −0.425764 | −0.0246639 | ||||||||
\(299\) | −0.367973 | −0.0212804 | ||||||||
\(300\) | −0.175243 | + | 4.99693i | −0.0101176 | + | 0.288498i | ||||
\(301\) | 2.93097 | − | 2.93097i | 0.168938 | − | 0.168938i | ||||
\(302\) | −18.6559 | −1.07353 | ||||||||
\(303\) | −7.82575 | + | 7.82575i | −0.449578 | + | 0.449578i | ||||
\(304\) | −2.17875 | − | 2.17875i | −0.124960 | − | 0.124960i | ||||
\(305\) | −6.44427 | − | 16.3633i | −0.368998 | − | 0.936960i | ||||
\(306\) | 1.25497 | 0.0717421 | ||||||||
\(307\) | −0.225281 | + | 0.225281i | −0.0128575 | + | 0.0128575i | −0.713506 | − | 0.700649i | \(-0.752894\pi\) |
0.700649 | + | 0.713506i | \(0.252894\pi\) | |||||||
\(308\) | 6.13622 | − | 6.13622i | 0.349644 | − | 0.349644i | ||||
\(309\) | −9.76753 | − | 9.76753i | −0.555655 | − | 0.555655i | ||||
\(310\) | −19.9570 | + | 7.85956i | −1.13348 | + | 0.446393i | ||||
\(311\) | 8.19803 | + | 8.19803i | 0.464868 | + | 0.464868i | 0.900247 | − | 0.435379i | \(-0.143386\pi\) |
−0.435379 | + | 0.900247i | \(0.643386\pi\) | |||||||
\(312\) | 0.225859 | + | 0.225859i | 0.0127868 | + | 0.0127868i | ||||
\(313\) | 12.1187i | 0.684987i | 0.939520 | + | 0.342494i | \(0.111271\pi\) | ||||
−0.939520 | + | 0.342494i | \(0.888729\pi\) | |||||||
\(314\) | 6.23375 | − | 6.23375i | 0.351791 | − | 0.351791i | ||||
\(315\) | 4.60357 | − | 1.81300i | 0.259382 | − | 0.102151i | ||||
\(316\) | −3.59077 | − | 3.59077i | −0.201996 | − | 0.201996i | ||||
\(317\) | 5.46058 | − | 5.46058i | 0.306697 | − | 0.306697i | −0.536930 | − | 0.843627i | \(-0.680416\pi\) |
0.843627 | + | 0.536930i | \(0.180416\pi\) | |||||||
\(318\) | − | 4.28827i | − | 0.240474i | ||||||
\(319\) | −4.79886 | − | 4.79886i | −0.268685 | − | 0.268685i | ||||
\(320\) | −2.05054 | − | 0.891783i | −0.114629 | − | 0.0498522i | ||||
\(321\) | − | 2.20433i | − | 0.123034i | ||||||
\(322\) | −1.80247 | − | 1.80247i | −0.100448 | − | 0.100448i | ||||
\(323\) | −2.73427 | − | 2.73427i | −0.152139 | − | 0.152139i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −1.16818 | + | 1.08902i | −0.0647991 | + | 0.0604081i | ||||
\(326\) | − | 15.4091i | − | 0.853430i | ||||||
\(327\) | − | 5.99769i | − | 0.331673i | ||||||
\(328\) | 3.92813 | 0.216895 | ||||||||
\(329\) | 15.2844i | 0.842654i | ||||||||
\(330\) | 3.21347 | + | 8.15967i | 0.176896 | + | 0.449175i | ||||
\(331\) | 14.2462 | − | 14.2462i | 0.783041 | − | 0.783041i | −0.197302 | − | 0.980343i | \(-0.563218\pi\) |
0.980343 | + | 0.197302i | \(0.0632180\pi\) | |||||||
\(332\) | 1.13008 | − | 1.13008i | 0.0620211 | − | 0.0620211i | ||||
\(333\) | 6.08275 | + | 0.0100817i | 0.333333 | + | 0.000552474i | ||||
\(334\) | − | 16.8371i | − | 0.921285i | ||||||
\(335\) | −20.2547 | + | 7.97679i | −1.10663 | + | 0.435819i | ||||
\(336\) | 2.21268i | 0.120712i | ||||||||
\(337\) | −23.4318 | + | 23.4318i | −1.27641 | + | 1.27641i | −0.333746 | + | 0.942663i | \(0.608313\pi\) |
−0.942663 | + | 0.333746i | \(0.891687\pi\) | |||||||
\(338\) | − | 12.8980i | − | 0.701557i | ||||||
\(339\) | 11.6944 | + | 11.6944i | 0.635152 | + | 0.635152i | ||||
\(340\) | −2.57338 | − | 1.11916i | −0.139561 | − | 0.0606952i | ||||
\(341\) | −26.6012 | + | 26.6012i | −1.44054 | + | 1.44054i | ||||
\(342\) | −2.17875 | − | 2.17875i | −0.117813 | − | 0.117813i | ||||
\(343\) | −14.2442 | + | 14.2442i | −0.769115 | + | 0.769115i | ||||
\(344\) | −1.87330 | −0.101001 | ||||||||
\(345\) | 2.39684 | − | 0.943934i | 0.129041 | − | 0.0508197i | ||||
\(346\) | 5.18404 | − | 5.18404i | 0.278696 | − | 0.278696i | ||||
\(347\) | 4.74393i | 0.254667i | 0.991860 | + | 0.127334i | \(0.0406419\pi\) | ||||
−0.991860 | + | 0.127334i | \(0.959358\pi\) | |||||||
\(348\) | 1.73044 | 0.0927613 | ||||||||
\(349\) | − | 14.8248i | − | 0.793556i | −0.917915 | − | 0.396778i | \(-0.870128\pi\) | ||
0.917915 | − | 0.396778i | \(-0.129872\pi\) | |||||||
\(350\) | −11.0566 | − | 0.387756i | −0.591001 | − | 0.0207264i | ||||
\(351\) | 0.225859 | + | 0.225859i | 0.0120555 | + | 0.0120555i | ||||
\(352\) | −3.92190 | −0.209038 | ||||||||
\(353\) | −23.4920 | −1.25035 | −0.625177 | − | 0.780483i | \(-0.714973\pi\) | ||||
−0.625177 | + | 0.780483i | \(0.714973\pi\) | |||||||
\(354\) | 6.65245 | 0.353574 | ||||||||
\(355\) | −6.74653 | − | 2.93407i | −0.358069 | − | 0.155725i | ||||
\(356\) | 1.33809 | − | 1.33809i | 0.0709185 | − | 0.0709185i | ||||
\(357\) | 2.77686i | 0.146967i | ||||||||
\(358\) | 1.70251 | + | 1.70251i | 0.0899805 | + | 0.0899805i | ||||
\(359\) | 3.71905i | 0.196284i | 0.995172 | + | 0.0981419i | \(0.0312899\pi\) | ||||
−0.995172 | + | 0.0981419i | \(0.968710\pi\) | |||||||
\(360\) | −2.05054 | − | 0.891783i | −0.108073 | − | 0.0470011i | ||||
\(361\) | − | 9.50611i | − | 0.500322i | ||||||
\(362\) | − | 8.75170i | − | 0.459979i | ||||||
\(363\) | 3.09806 | + | 3.09806i | 0.162606 | + | 0.162606i | ||||
\(364\) | −0.499755 | + | 0.499755i | −0.0261943 | + | 0.0261943i | ||||
\(365\) | 9.88884 | + | 25.1098i | 0.517606 | + | 1.31431i | ||||
\(366\) | 7.86494 | 0.411107 | ||||||||
\(367\) | 20.2784 | + | 20.2784i | 1.05852 | + | 1.05852i | 0.998178 | + | 0.0603458i | \(0.0192203\pi\) |
0.0603458 | + | 0.998178i | \(0.480780\pi\) | |||||||
\(368\) | 1.15203i | 0.0600536i | ||||||||
\(369\) | 3.92813 | 0.204490 | ||||||||
\(370\) | −12.4640 | − | 5.44517i | −0.647970 | − | 0.283081i | ||||
\(371\) | 9.48858 | 0.492623 | ||||||||
\(372\) | − | 9.59224i | − | 0.497334i | ||||||
\(373\) | 17.0249 | + | 17.0249i | 0.881515 | + | 0.881515i | 0.993689 | − | 0.112174i | \(-0.0357814\pi\) |
−0.112174 | + | 0.993689i | \(0.535781\pi\) | |||||||
\(374\) | −4.92188 | −0.254505 | ||||||||
\(375\) | 4.81552 | − | 10.0901i | 0.248672 | − | 0.521052i | ||||
\(376\) | 4.88442 | − | 4.88442i | 0.251895 | − | 0.251895i | ||||
\(377\) | 0.390836 | + | 0.390836i | 0.0201291 | + | 0.0201291i | ||||
\(378\) | 2.21268i | 0.113808i | ||||||||
\(379\) | 3.59500i | 0.184663i | 0.995728 | + | 0.0923313i | \(0.0294319\pi\) | ||||
−0.995728 | + | 0.0923313i | \(0.970568\pi\) | |||||||
\(380\) | 2.52465 | + | 6.41059i | 0.129512 | + | 0.328856i | ||||
\(381\) | − | 9.98731i | − | 0.511665i | ||||||
\(382\) | −4.56780 | − | 4.56780i | −0.233709 | − | 0.233709i | ||||
\(383\) | 18.9973i | 0.970715i | 0.874316 | + | 0.485358i | \(0.161311\pi\) | ||||
−0.874316 | + | 0.485358i | \(0.838689\pi\) | |||||||
\(384\) | 0.707107 | − | 0.707107i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | −18.0548 | + | 7.11040i | −0.920156 | + | 0.362380i | ||||
\(386\) | 5.51547 | 0.280730 | ||||||||
\(387\) | −1.87330 | −0.0952251 | ||||||||
\(388\) | −4.01884 | −0.204025 | ||||||||
\(389\) | 9.52518 | + | 9.52518i | 0.482946 | + | 0.482946i | 0.906071 | − | 0.423125i | \(-0.139067\pi\) |
−0.423125 | + | 0.906071i | \(0.639067\pi\) | |||||||
\(390\) | −0.261716 | − | 0.664551i | −0.0132525 | − | 0.0336509i | ||||
\(391\) | 1.44577i | 0.0731155i | ||||||||
\(392\) | 2.10403 | 0.106270 | ||||||||
\(393\) | 13.1829i | 0.664989i | ||||||||
\(394\) | −3.48510 | + | 3.48510i | −0.175577 | + | 0.175577i | ||||
\(395\) | 4.16084 | + | 10.5652i | 0.209354 | + | 0.531593i | ||||
\(396\) | −3.92190 | −0.197083 | ||||||||
\(397\) | 6.55806 | − | 6.55806i | 0.329139 | − | 0.329139i | −0.523120 | − | 0.852259i | \(-0.675232\pi\) |
0.852259 | + | 0.523120i | \(0.175232\pi\) | |||||||
\(398\) | 11.0862 | + | 11.0862i | 0.555703 | + | 0.555703i | ||||
\(399\) | 4.82088 | − | 4.82088i | 0.241346 | − | 0.241346i | ||||
\(400\) | 3.40945 | + | 3.65728i | 0.170472 | + | 0.182864i | ||||
\(401\) | −3.25081 | − | 3.25081i | −0.162337 | − | 0.162337i | 0.621264 | − | 0.783601i | \(-0.286619\pi\) |
−0.783601 | + | 0.621264i | \(0.786619\pi\) | |||||||
\(402\) | − | 9.73532i | − | 0.485554i | ||||||
\(403\) | 2.16650 | − | 2.16650i | 0.107921 | − | 0.107921i | ||||
\(404\) | 11.0673i | 0.550618i | ||||||||
\(405\) | −2.05054 | − | 0.891783i | −0.101892 | − | 0.0443130i | ||||
\(406\) | 3.82892i | 0.190026i | ||||||||
\(407\) | −23.8560 | − | 0.0395395i | −1.18250 | − | 0.00195990i | ||||
\(408\) | 0.887401 | − | 0.887401i | 0.0439329 | − | 0.0439329i | ||||
\(409\) | 13.3605 | − | 13.3605i | 0.660637 | − | 0.660637i | −0.294893 | − | 0.955530i | \(-0.595284\pi\) |
0.955530 | + | 0.294893i | \(0.0952842\pi\) | |||||||
\(410\) | −8.05479 | − | 3.50304i | −0.397798 | − | 0.173003i | ||||
\(411\) | 20.6125i | 1.01674i | ||||||||
\(412\) | −13.8134 | −0.680536 | ||||||||
\(413\) | 14.7198i | 0.724312i | ||||||||
\(414\) | 1.15203i | 0.0566191i | ||||||||
\(415\) | −3.32506 | + | 1.30949i | −0.163221 | + | 0.0642803i | ||||
\(416\) | 0.319413 | 0.0156605 | ||||||||
\(417\) | −0.852977 | − | 0.852977i | −0.0417705 | − | 0.0417705i | ||||
\(418\) | 8.54484 | + | 8.54484i | 0.417942 | + | 0.417942i | ||||
\(419\) | − | 18.6060i | − | 0.908963i | −0.890756 | − | 0.454481i | \(-0.849825\pi\) | ||
0.890756 | − | 0.454481i | \(-0.150175\pi\) | |||||||
\(420\) | 1.97323 | − | 4.53720i | 0.0962839 | − | 0.221393i | ||||
\(421\) | 4.15626 | + | 4.15626i | 0.202564 | + | 0.202564i | 0.801098 | − | 0.598534i | \(-0.204250\pi\) |
−0.598534 | + | 0.801098i | \(0.704250\pi\) | |||||||
\(422\) | − | 27.2170i | − | 1.32490i | ||||||
\(423\) | 4.88442 | − | 4.88442i | 0.237489 | − | 0.237489i | ||||
\(424\) | −3.03226 | − | 3.03226i | −0.147260 | − | 0.147260i | ||||
\(425\) | 4.27877 | + | 4.58979i | 0.207551 | + | 0.222637i | ||||
\(426\) | 2.32647 | − | 2.32647i | 0.112718 | − | 0.112718i | ||||
\(427\) | 17.4026i | 0.842172i | ||||||||
\(428\) | −1.55870 | − | 1.55870i | −0.0753426 | − | 0.0753426i | ||||
\(429\) | −0.885798 | − | 0.885798i | −0.0427667 | − | 0.0427667i | ||||
\(430\) | 3.84128 | + | 1.67057i | 0.185243 | + | 0.0805623i | ||||
\(431\) | −7.99513 | − | 7.99513i | −0.385112 | − | 0.385112i | 0.487828 | − | 0.872940i | \(-0.337789\pi\) |
−0.872940 | + | 0.487828i | \(0.837789\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | 21.8861 | − | 21.8861i | 1.05178 | − | 1.05178i | 0.0531948 | − | 0.998584i | \(-0.483060\pi\) |
0.998584 | − | 0.0531948i | \(-0.0169404\pi\) | |||||||
\(434\) | 21.2246 | 1.01881 | ||||||||
\(435\) | −3.54834 | − | 1.54318i | −0.170130 | − | 0.0739897i | ||||
\(436\) | −4.24101 | − | 4.24101i | −0.203107 | − | 0.203107i | ||||
\(437\) | 2.50998 | − | 2.50998i | 0.120069 | − | 0.120069i | ||||
\(438\) | −12.0689 | −0.576674 | ||||||||
\(439\) | −19.4929 | + | 19.4929i | −0.930345 | + | 0.930345i | −0.997727 | − | 0.0673822i | \(-0.978535\pi\) |
0.0673822 | + | 0.997727i | \(0.478535\pi\) | |||||||
\(440\) | 8.04202 | + | 3.49748i | 0.383388 | + | 0.166736i | ||||
\(441\) | 2.10403 | 0.100192 | ||||||||
\(442\) | 0.400855 | 0.0190667 | ||||||||
\(443\) | 1.25482 | + | 1.25482i | 0.0596181 | + | 0.0596181i | 0.736287 | − | 0.676669i | \(-0.236577\pi\) |
−0.676669 | + | 0.736287i | \(0.736577\pi\) | |||||||
\(444\) | 4.30829 | − | 4.29403i | 0.204462 | − | 0.203786i | ||||
\(445\) | −3.93709 | + | 1.55052i | −0.186636 | + | 0.0735018i | ||||
\(446\) | −11.1865 | − | 11.1865i | −0.529696 | − | 0.529696i | ||||
\(447\) | −0.301061 | + | 0.301061i | −0.0142397 | + | 0.0142397i | ||||
\(448\) | 1.56460 | + | 1.56460i | 0.0739206 | + | 0.0739206i | ||||
\(449\) | 5.51963 | + | 5.51963i | 0.260487 | + | 0.260487i | 0.825252 | − | 0.564765i | \(-0.191033\pi\) |
−0.564765 | + | 0.825252i | \(0.691033\pi\) | |||||||
\(450\) | 3.40945 | + | 3.65728i | 0.160723 | + | 0.172406i | ||||
\(451\) | −15.4057 | −0.725427 | ||||||||
\(452\) | 16.5384 | 0.777899 | ||||||||
\(453\) | −13.1917 | + | 13.1917i | −0.619801 | + | 0.619801i | ||||
\(454\) | − | 1.74912i | − | 0.0820905i | ||||||
\(455\) | 1.47044 | − | 0.579096i | 0.0689354 | − | 0.0271484i | ||||
\(456\) | −3.08122 | −0.144291 | ||||||||
\(457\) | −6.65948 | −0.311517 | −0.155759 | − | 0.987795i | \(-0.549782\pi\) | ||||
−0.155759 | + | 0.987795i | \(0.549782\pi\) | |||||||
\(458\) | −8.51464 | −0.397863 | ||||||||
\(459\) | 0.887401 | − | 0.887401i | 0.0414203 | − | 0.0414203i | ||||
\(460\) | 1.02736 | − | 2.36228i | 0.0479009 | − | 0.110142i | ||||
\(461\) | −24.8127 | + | 24.8127i | −1.15564 | + | 1.15564i | −0.170240 | + | 0.985403i | \(0.554454\pi\) |
−0.985403 | + | 0.170240i | \(0.945546\pi\) | |||||||
\(462\) | − | 8.67793i | − | 0.403734i | ||||||
\(463\) | − | 0.607120i | − | 0.0282153i | −0.999900 | − | 0.0141076i | \(-0.995509\pi\) | ||
0.999900 | − | 0.0141076i | \(-0.00449075\pi\) | |||||||
\(464\) | 1.22361 | − | 1.22361i | 0.0568045 | − | 0.0568045i | ||||
\(465\) | −8.55419 | + | 19.6693i | −0.396691 | + | 0.912141i | ||||
\(466\) | −6.42533 | + | 6.42533i | −0.297648 | + | 0.297648i | ||||
\(467\) | −14.2821 | −0.660896 | −0.330448 | − | 0.943824i | \(-0.607200\pi\) | ||||
−0.330448 | + | 0.943824i | \(0.607200\pi\) | |||||||
\(468\) | 0.319413 | 0.0147649 | ||||||||
\(469\) | 21.5412 | 0.994679 | ||||||||
\(470\) | −14.3716 | + | 5.65987i | −0.662910 | + | 0.261070i | ||||
\(471\) | − | 8.81585i | − | 0.406213i | ||||||
\(472\) | 4.70399 | − | 4.70399i | 0.216519 | − | 0.216519i | ||||
\(473\) | 7.34689 | 0.337810 | ||||||||
\(474\) | −5.07811 | −0.233245 | ||||||||
\(475\) | 0.539960 | − | 15.3966i | 0.0247751 | − | 0.706445i | ||||
\(476\) | 1.96354 | + | 1.96354i | 0.0899986 | + | 0.0899986i | ||||
\(477\) | −3.03226 | − | 3.03226i | −0.138838 | − | 0.138838i | ||||
\(478\) | 10.4976 | − | 10.4976i | 0.480151 | − | 0.480151i | ||||
\(479\) | 12.8987 | + | 12.8987i | 0.589358 | + | 0.589358i | 0.937458 | − | 0.348100i | \(-0.113173\pi\) |
−0.348100 | + | 0.937458i | \(0.613173\pi\) | |||||||
\(480\) | −2.08054 | + | 0.819367i | −0.0949631 | + | 0.0373988i | ||||
\(481\) | 1.94291 | + | 0.00322023i | 0.0885891 | + | 0.000146830i | ||||
\(482\) | −6.66851 | − | 6.66851i | −0.303742 | − | 0.303742i | ||||
\(483\) | −2.54907 | −0.115987 | ||||||||
\(484\) | 4.38131 | 0.199151 | ||||||||
\(485\) | 8.24079 | + | 3.58393i | 0.374195 | + | 0.162738i | ||||
\(486\) | 0.707107 | − | 0.707107i | 0.0320750 | − | 0.0320750i | ||||
\(487\) | 0.169467 | 0.00767930 | 0.00383965 | − | 0.999993i | \(-0.498778\pi\) | ||||
0.00383965 | + | 0.999993i | \(0.498778\pi\) | |||||||
\(488\) | 5.56135 | − | 5.56135i | 0.251750 | − | 0.251750i | ||||
\(489\) | −10.8959 | − | 10.8959i | −0.492728 | − | 0.492728i | ||||
\(490\) | −4.31440 | − | 1.87634i | −0.194905 | − | 0.0847644i | ||||
\(491\) | 11.6118 | 0.524033 | 0.262016 | − | 0.965063i | \(-0.415613\pi\) | ||||
0.262016 | + | 0.965063i | \(0.415613\pi\) | |||||||
\(492\) | 2.77761 | − | 2.77761i | 0.125224 | − | 0.125224i | ||||
\(493\) | 1.53559 | − | 1.53559i | 0.0691596 | − | 0.0691596i | ||||
\(494\) | −0.695921 | − | 0.695921i | −0.0313110 | − | 0.0313110i | ||||
\(495\) | 8.04202 | + | 3.49748i | 0.361462 | + | 0.157200i | ||||
\(496\) | −6.78274 | − | 6.78274i | −0.304554 | − | 0.304554i | ||||
\(497\) | 5.14774 | + | 5.14774i | 0.230908 | + | 0.230908i | ||||
\(498\) | − | 1.59817i | − | 0.0716158i | ||||||
\(499\) | −15.8556 | + | 15.8556i | −0.709793 | + | 0.709793i | −0.966492 | − | 0.256698i | \(-0.917365\pi\) |
0.256698 | + | 0.966492i | \(0.417365\pi\) | |||||||
\(500\) | −3.72972 | − | 10.5399i | −0.166798 | − | 0.471358i | ||||
\(501\) | −11.9056 | − | 11.9056i | −0.531904 | − | 0.531904i | ||||
\(502\) | 19.9946 | − | 19.9946i | 0.892402 | − | 0.892402i | ||||
\(503\) | − | 22.2525i | − | 0.992190i | −0.868268 | − | 0.496095i | \(-0.834767\pi\) | ||
0.868268 | − | 0.496095i | \(-0.165233\pi\) | |||||||
\(504\) | 1.56460 | + | 1.56460i | 0.0696930 | + | 0.0696930i | ||||
\(505\) | 9.86962 | − | 22.6939i | 0.439192 | − | 1.00987i | ||||
\(506\) | − | 4.51814i | − | 0.200856i | ||||||
\(507\) | −9.12025 | − | 9.12025i | −0.405044 | − | 0.405044i | ||||
\(508\) | −7.06209 | − | 7.06209i | −0.313330 | − | 0.313330i | ||||
\(509\) | 23.6164 | 1.04678 | 0.523390 | − | 0.852093i | \(-0.324667\pi\) | ||||
0.523390 | + | 0.852093i | \(0.324667\pi\) | |||||||
\(510\) | −2.61102 | + | 1.02828i | −0.115618 | + | 0.0455332i | ||||
\(511\) | − | 26.7046i | − | 1.18134i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −3.08122 | −0.136039 | ||||||||
\(514\) | − | 31.3639i | − | 1.38340i | ||||||
\(515\) | 28.3249 | + | 12.3185i | 1.24814 | + | 0.542819i | ||||
\(516\) | −1.32462 | + | 1.32462i | −0.0583132 | + | 0.0583132i | ||||
\(517\) | −19.1562 | + | 19.1562i | −0.842489 | + | 0.842489i | ||||
\(518\) | 9.50133 | + | 9.53287i | 0.417464 | + | 0.418850i | ||||
\(519\) | − | 7.33134i | − | 0.321810i | ||||||
\(520\) | −0.654970 | − | 0.284847i | −0.0287223 | − | 0.0124914i | ||||
\(521\) | 17.0507i | 0.747006i | 0.927629 | + | 0.373503i | \(0.121843\pi\) | ||||
−0.927629 | + | 0.373503i | \(0.878157\pi\) | |||||||
\(522\) | 1.22361 | − | 1.22361i | 0.0535558 | − | 0.0535558i | ||||
\(523\) | 23.5794i | 1.03105i | 0.856873 | + | 0.515527i | \(0.172404\pi\) | ||||
−0.856873 | + | 0.515527i | \(0.827596\pi\) | |||||||
\(524\) | 9.32171 | + | 9.32171i | 0.407221 | + | 0.407221i | ||||
\(525\) | −8.09240 | + | 7.54403i | −0.353181 | + | 0.329248i | ||||
\(526\) | −7.40341 | + | 7.40341i | −0.322804 | + | 0.322804i | ||||
\(527\) | −8.51216 | − | 8.51216i | −0.370795 | − | 0.370795i | ||||
\(528\) | −2.77320 | + | 2.77320i | −0.120688 | + | 0.120688i | ||||
\(529\) | 21.6728 | 0.942297 | ||||||||
\(530\) | 3.51366 | + | 8.92191i | 0.152624 | + | 0.387543i | ||||
\(531\) | 4.70399 | − | 4.70399i | 0.204136 | − | 0.204136i | ||||
\(532\) | − | 6.81776i | − | 0.295587i | ||||||
\(533\) | 1.25470 | 0.0543469 | ||||||||
\(534\) | − | 1.89234i | − | 0.0818896i | ||||||
\(535\) | 1.80616 | + | 4.58620i | 0.0780870 | + | 0.198279i | ||||
\(536\) | −6.88391 | − | 6.88391i | −0.297340 | − | 0.297340i | ||||
\(537\) | 2.40771 | 0.103901 | ||||||||
\(538\) | 3.41947 | 0.147424 | ||||||||
\(539\) | −8.25180 | −0.355430 | ||||||||
\(540\) | −2.08054 | + | 0.819367i | −0.0895321 | + | 0.0352599i | ||||
\(541\) | −10.2113 | + | 10.2113i | −0.439020 | + | 0.439020i | −0.891682 | − | 0.452662i | \(-0.850474\pi\) |
0.452662 | + | 0.891682i | \(0.350474\pi\) | |||||||
\(542\) | − | 17.8704i | − | 0.767600i | ||||||
\(543\) | −6.18839 | − | 6.18839i | −0.265569 | − | 0.265569i | ||||
\(544\) | − | 1.25497i | − | 0.0538066i | ||||||
\(545\) | 4.91431 | + | 12.4784i | 0.210506 | + | 0.534517i | ||||
\(546\) | 0.706760i | 0.0302465i | ||||||||
\(547\) | 26.3899i | 1.12835i | 0.825655 | + | 0.564176i | \(0.190806\pi\) | ||||
−0.825655 | + | 0.564176i | \(0.809194\pi\) | |||||||
\(548\) | 14.5752 | + | 14.5752i | 0.622623 | + | 0.622623i | ||||
\(549\) | 5.56135 | − | 5.56135i | 0.237353 | − | 0.237353i | ||||
\(550\) | −13.3715 | − | 14.3435i | −0.570163 | − | 0.611608i | ||||
\(551\) | −5.33186 | −0.227145 | ||||||||
\(552\) | 0.814607 | + | 0.814607i | 0.0346720 | + | 0.0346720i | ||||
\(553\) | − | 11.2363i | − | 0.477814i | ||||||
\(554\) | −14.8527 | −0.631029 | ||||||||
\(555\) | −12.6637 | + | 4.96303i | −0.537543 | + | 0.210669i | ||||
\(556\) | −1.20629 | −0.0511582 | ||||||||
\(557\) | − | 33.0054i | − | 1.39849i | −0.714885 | − | 0.699243i | \(-0.753521\pi\) | ||
0.714885 | − | 0.699243i | \(-0.246479\pi\) | |||||||
\(558\) | −6.78274 | − | 6.78274i | −0.287136 | − | 0.287136i | ||||
\(559\) | −0.598356 | −0.0253078 | ||||||||
\(560\) | −1.81300 | − | 4.60357i | −0.0766132 | − | 0.194536i | ||||
\(561\) | −3.48030 | + | 3.48030i | −0.146938 | + | 0.146938i | ||||
\(562\) | −4.56193 | − | 4.56193i | −0.192434 | − | 0.192434i | ||||
\(563\) | − | 2.41113i | − | 0.101617i | −0.998708 | − | 0.0508086i | \(-0.983820\pi\) | ||
0.998708 | − | 0.0508086i | \(-0.0161798\pi\) | |||||||
\(564\) | − | 6.90761i | − | 0.290863i | ||||||
\(565\) | −33.9126 | − | 14.7486i | −1.42671 | − | 0.620479i | ||||
\(566\) | 32.3891i | 1.36142i | ||||||||
\(567\) | 1.56460 | + | 1.56460i | 0.0657072 | + | 0.0657072i | ||||
\(568\) | − | 3.29012i | − | 0.138050i | ||||||
\(569\) | −16.6810 | + | 16.6810i | −0.699306 | + | 0.699306i | −0.964261 | − | 0.264955i | \(-0.914643\pi\) |
0.264955 | + | 0.964261i | \(0.414643\pi\) | |||||||
\(570\) | 6.31816 | + | 2.74778i | 0.264639 | + | 0.115092i | ||||
\(571\) | −34.7939 | −1.45608 | −0.728041 | − | 0.685534i | \(-0.759569\pi\) | ||||
−0.728041 | + | 0.685534i | \(0.759569\pi\) | |||||||
\(572\) | −1.25271 | −0.0523783 | ||||||||
\(573\) | −6.45984 | −0.269864 | ||||||||
\(574\) | 6.14596 | + | 6.14596i | 0.256528 | + | 0.256528i | ||||
\(575\) | −4.21329 | + | 3.92778i | −0.175706 | + | 0.163800i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 42.4452 | 1.76702 | 0.883509 | − | 0.468414i | \(-0.155174\pi\) | ||||
0.883509 | + | 0.468414i | \(0.155174\pi\) | |||||||
\(578\) | 15.4250i | 0.641597i | ||||||||
\(579\) | 3.90003 | − | 3.90003i | 0.162080 | − | 0.162080i | ||||
\(580\) | −3.60025 | + | 1.41786i | −0.149492 | + | 0.0588736i | ||||
\(581\) | 3.53625 | 0.146708 | ||||||||
\(582\) | −2.84175 | + | 2.84175i | −0.117794 | + | 0.117794i | ||||
\(583\) | 11.8922 | + | 11.8922i | 0.492526 | + | 0.492526i | ||||
\(584\) | −8.53399 | + | 8.53399i | −0.353139 | + | 0.353139i | ||||
\(585\) | −0.654970 | − | 0.284847i | −0.0270797 | − | 0.0117770i | ||||
\(586\) | −2.93182 | − | 2.93182i | −0.121112 | − | 0.121112i | ||||
\(587\) | − | 25.7512i | − | 1.06287i | −0.847100 | − | 0.531433i | \(-0.821654\pi\) | ||
0.847100 | − | 0.531433i | \(-0.178346\pi\) | |||||||
\(588\) | 1.48777 | − | 1.48777i | 0.0613548 | − | 0.0613548i | ||||
\(589\) | 29.5558i | 1.21782i | ||||||||
\(590\) | −13.8407 | + | 5.45079i | −0.569811 | + | 0.224406i | ||||
\(591\) | 4.92868i | 0.202739i | ||||||||
\(592\) | 0.0100817 | − | 6.08275i | 0.000414356 | − | 0.250000i | ||||
\(593\) | −17.7350 | + | 17.7350i | −0.728289 | + | 0.728289i | −0.970279 | − | 0.241990i | \(-0.922200\pi\) |
0.241990 | + | 0.970279i | \(0.422200\pi\) | |||||||
\(594\) | −2.77320 | + | 2.77320i | −0.113786 | + | 0.113786i | ||||
\(595\) | −2.27527 | − | 5.77736i | −0.0932768 | − | 0.236849i | ||||
\(596\) | 0.425764i | 0.0174400i | ||||||||
\(597\) | 15.6783 | 0.641671 | ||||||||
\(598\) | 0.367973i | 0.0150475i | ||||||||
\(599\) | − | 33.5799i | − | 1.37204i | −0.727583 | − | 0.686020i | \(-0.759356\pi\) | ||
0.727583 | − | 0.686020i | \(-0.240644\pi\) | |||||||
\(600\) | 4.99693 | + | 0.175243i | 0.203999 | + | 0.00715425i | ||||
\(601\) | −28.5324 | −1.16386 | −0.581930 | − | 0.813239i | \(-0.697702\pi\) | ||||
−0.581930 | + | 0.813239i | \(0.697702\pi\) | |||||||
\(602\) | −2.93097 | − | 2.93097i | −0.119457 | − | 0.119457i | ||||
\(603\) | −6.88391 | − | 6.88391i | −0.280334 | − | 0.280334i | ||||
\(604\) | 18.6559i | 0.759098i | ||||||||
\(605\) | −8.98406 | − | 3.90718i | −0.365254 | − | 0.158849i | ||||
\(606\) | 7.82575 | + | 7.82575i | 0.317900 | + | 0.317900i | ||||
\(607\) | 26.3325i | 1.06880i | 0.845231 | + | 0.534401i | \(0.179463\pi\) | ||||
−0.845231 | + | 0.534401i | \(0.820537\pi\) | |||||||
\(608\) | −2.17875 | + | 2.17875i | −0.0883599 | + | 0.0883599i | ||||
\(609\) | 2.70745 | + | 2.70745i | 0.109712 | + | 0.109712i | ||||
\(610\) | −16.3633 | + | 6.44427i | −0.662531 | + | 0.260921i | ||||
\(611\) | 1.56015 | − | 1.56015i | 0.0631168 | − | 0.0631168i | ||||
\(612\) | − | 1.25497i | − | 0.0507293i | ||||||
\(613\) | −18.6885 | − | 18.6885i | −0.754820 | − | 0.754820i | 0.220555 | − | 0.975375i | \(-0.429213\pi\) |
−0.975375 | + | 0.220555i | \(0.929213\pi\) | |||||||
\(614\) | 0.225281 | + | 0.225281i | 0.00909162 | + | 0.00909162i | ||||
\(615\) | −8.17262 | + | 3.21858i | −0.329552 | + | 0.129786i | ||||
\(616\) | −6.13622 | − | 6.13622i | −0.247235 | − | 0.247235i | ||||
\(617\) | −3.48887 | + | 3.48887i | −0.140457 | + | 0.140457i | −0.773839 | − | 0.633382i | \(-0.781666\pi\) |
0.633382 | + | 0.773839i | \(0.281666\pi\) | |||||||
\(618\) | −9.76753 | + | 9.76753i | −0.392907 | + | 0.392907i | ||||
\(619\) | 3.83734 | 0.154236 | 0.0771178 | − | 0.997022i | \(-0.475428\pi\) | ||||
0.0771178 | + | 0.997022i | \(0.475428\pi\) | |||||||
\(620\) | 7.85956 | + | 19.9570i | 0.315647 | + | 0.801493i | ||||
\(621\) | 0.814607 | + | 0.814607i | 0.0326891 | + | 0.0326891i | ||||
\(622\) | 8.19803 | − | 8.19803i | 0.328711 | − | 0.328711i | ||||
\(623\) | 4.18715 | 0.167755 | ||||||||
\(624\) | 0.225859 | − | 0.225859i | 0.00904160 | − | 0.00904160i | ||||
\(625\) | −1.75135 | + | 24.9386i | −0.0700540 | + | 0.997543i | ||||
\(626\) | 12.1187 | 0.484359 | ||||||||
\(627\) | 12.0842 | 0.482597 | ||||||||
\(628\) | −6.23375 | − | 6.23375i | −0.248754 | − | 0.248754i | ||||
\(629\) | 0.0126523 | − | 7.63370i | 0.000504480 | − | 0.304376i | ||||
\(630\) | −1.81300 | − | 4.60357i | −0.0722316 | − | 0.183411i | ||||
\(631\) | 15.4358 | + | 15.4358i | 0.614490 | + | 0.614490i | 0.944113 | − | 0.329623i | \(-0.106922\pi\) |
−0.329623 | + | 0.944113i | \(0.606922\pi\) | |||||||
\(632\) | −3.59077 | + | 3.59077i | −0.142833 | + | 0.142833i | ||||
\(633\) | −19.2453 | − | 19.2453i | −0.764933 | − | 0.764933i | ||||
\(634\) | −5.46058 | − | 5.46058i | −0.216868 | − | 0.216868i | ||||
\(635\) | 8.18326 | + | 20.7790i | 0.324743 | + | 0.824588i | ||||
\(636\) | −4.28827 | −0.170041 | ||||||||
\(637\) | 0.672055 | 0.0266278 | ||||||||
\(638\) | −4.79886 | + | 4.79886i | −0.189989 | + | 0.189989i | ||||
\(639\) | − | 3.29012i | − | 0.130155i | ||||||
\(640\) | −0.891783 | + | 2.05054i | −0.0352508 | + | 0.0810548i | ||||
\(641\) | −41.6890 | −1.64662 | −0.823309 | − | 0.567594i | \(-0.807874\pi\) | ||||
−0.823309 | + | 0.567594i | \(0.807874\pi\) | |||||||
\(642\) | −2.20433 | −0.0869982 | ||||||||
\(643\) | −3.74780 | −0.147799 | −0.0738993 | − | 0.997266i | \(-0.523544\pi\) | ||||
−0.0738993 | + | 0.997266i | \(0.523544\pi\) | |||||||
\(644\) | −1.80247 | + | 1.80247i | −0.0710272 | + | 0.0710272i | ||||
\(645\) | 3.89747 | − | 1.53492i | 0.153463 | − | 0.0604373i | ||||
\(646\) | −2.73427 | + | 2.73427i | −0.107579 | + | 0.107579i | ||||
\(647\) | − | 3.49319i | − | 0.137331i | −0.997640 | − | 0.0686657i | \(-0.978126\pi\) | ||
0.997640 | − | 0.0686657i | \(-0.0218742\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −18.4486 | + | 18.4486i | −0.724170 | + | 0.724170i | ||||
\(650\) | 1.08902 | + | 1.16818i | 0.0427150 | + | 0.0458199i | ||||
\(651\) | 15.0080 | − | 15.0080i | 0.588212 | − | 0.588212i | ||||
\(652\) | −15.4091 | −0.603466 | ||||||||
\(653\) | −32.5364 | −1.27325 | −0.636624 | − | 0.771175i | \(-0.719670\pi\) | ||||
−0.636624 | + | 0.771175i | \(0.719670\pi\) | |||||||
\(654\) | −5.99769 | −0.234528 | ||||||||
\(655\) | −10.8016 | − | 27.4275i | −0.422054 | − | 1.07168i | ||||
\(656\) | − | 3.92813i | − | 0.153368i | ||||||
\(657\) | −8.53399 | + | 8.53399i | −0.332943 | + | 0.332943i | ||||
\(658\) | 15.2844 | 0.595847 | ||||||||
\(659\) | 2.62449 | 0.102236 | 0.0511178 | − | 0.998693i | \(-0.483722\pi\) | ||||
0.0511178 | + | 0.998693i | \(0.483722\pi\) | |||||||
\(660\) | 8.15967 | − | 3.21347i | 0.317615 | − | 0.125084i | ||||
\(661\) | 0.358911 | + | 0.358911i | 0.0139600 | + | 0.0139600i | 0.714052 | − | 0.700092i | \(-0.246858\pi\) |
−0.700092 | + | 0.714052i | \(0.746858\pi\) | |||||||
\(662\) | −14.2462 | − | 14.2462i | −0.553693 | − | 0.553693i | ||||
\(663\) | 0.283447 | − | 0.283447i | 0.0110082 | − | 0.0110082i | ||||
\(664\) | −1.13008 | − | 1.13008i | −0.0438556 | − | 0.0438556i | ||||
\(665\) | −6.07996 | + | 13.9801i | −0.235771 | + | 0.542125i | ||||
\(666\) | 0.0100817 | − | 6.08275i | 0.000390658 | − | 0.235702i | ||||
\(667\) | 1.40963 | + | 1.40963i | 0.0545810 | + | 0.0545810i | ||||
\(668\) | −16.8371 | −0.651447 | ||||||||
\(669\) | −15.8201 | −0.611640 | ||||||||
\(670\) | 7.97679 | + | 20.2547i | 0.308170 | + | 0.782507i | ||||
\(671\) | −21.8111 | + | 21.8111i | −0.842007 | + | 0.842007i | ||||
\(672\) | 2.21268 | 0.0853561 | ||||||||
\(673\) | −14.4928 | + | 14.4928i | −0.558658 | + | 0.558658i | −0.928925 | − | 0.370267i | \(-0.879266\pi\) |
0.370267 | + | 0.928925i | \(0.379266\pi\) | |||||||
\(674\) | 23.4318 | + | 23.4318i | 0.902557 | + | 0.902557i | ||||
\(675\) | 4.99693 | + | 0.175243i | 0.192332 | + | 0.00674509i | ||||
\(676\) | −12.8980 | −0.496076 | ||||||||
\(677\) | 9.12580 | − | 9.12580i | 0.350733 | − | 0.350733i | −0.509649 | − | 0.860382i | \(-0.670225\pi\) |
0.860382 | + | 0.509649i | \(0.170225\pi\) | |||||||
\(678\) | 11.6944 | − | 11.6944i | 0.449120 | − | 0.449120i | ||||
\(679\) | −6.28788 | − | 6.28788i | −0.241307 | − | 0.241307i | ||||
\(680\) | −1.11916 | + | 2.57338i | −0.0429180 | + | 0.0986845i | ||||
\(681\) | −1.23682 | − | 1.23682i | −0.0473949 | − | 0.0473949i | ||||
\(682\) | 26.6012 | + | 26.6012i | 1.01861 | + | 1.01861i | ||||
\(683\) | − | 24.7098i | − | 0.945493i | −0.881199 | − | 0.472746i | \(-0.843263\pi\) | ||
0.881199 | − | 0.472746i | \(-0.156737\pi\) | |||||||
\(684\) | −2.17875 | + | 2.17875i | −0.0833065 | + | 0.0833065i | ||||
\(685\) | −16.8892 | − | 42.8850i | −0.645302 | − | 1.63855i | ||||
\(686\) | 14.2442 | + | 14.2442i | 0.543846 | + | 0.543846i | ||||
\(687\) | −6.02076 | + | 6.02076i | −0.229706 | + | 0.229706i | ||||
\(688\) | 1.87330i | 0.0714188i | ||||||||
\(689\) | −0.968545 | − | 0.968545i | −0.0368986 | − | 0.0368986i | ||||
\(690\) | −0.943934 | − | 2.39684i | −0.0359349 | − | 0.0912461i | ||||
\(691\) | − | 47.7183i | − | 1.81529i | −0.419739 | − | 0.907645i | \(-0.637879\pi\) | ||
0.419739 | − | 0.907645i | \(-0.362121\pi\) | |||||||
\(692\) | −5.18404 | − | 5.18404i | −0.197068 | − | 0.197068i | ||||
\(693\) | −6.13622 | − | 6.13622i | −0.233096 | − | 0.233096i | ||||
\(694\) | 4.74393 | 0.180077 | ||||||||
\(695\) | 2.47355 | + | 1.07575i | 0.0938272 | + | 0.0408055i | ||||
\(696\) | − | 1.73044i | − | 0.0655921i | ||||||
\(697\) | − | 4.92970i | − | 0.186726i | ||||||
\(698\) | −14.8248 | −0.561128 | ||||||||
\(699\) | 9.08679i | 0.343694i | ||||||||
\(700\) | −0.387756 | + | 11.0566i | −0.0146558 | + | 0.417901i | ||||
\(701\) | −2.69605 | + | 2.69605i | −0.101828 | + | 0.101828i | −0.756186 | − | 0.654357i | \(-0.772939\pi\) |
0.654357 | + | 0.756186i | \(0.272939\pi\) | |||||||
\(702\) | 0.225859 | − | 0.225859i | 0.00852451 | − | 0.00852451i | ||||
\(703\) | −13.2748 | + | 13.2308i | −0.500667 | + | 0.499010i | ||||
\(704\) | 3.92190i | 0.147812i | ||||||||
\(705\) | −6.16009 | + | 14.1644i | −0.232002 | + | 0.533460i | ||||
\(706\) | 23.4920i | 0.884134i | ||||||||
\(707\) | −17.3159 | + | 17.3159i | −0.651232 | + | 0.651232i | ||||
\(708\) | − | 6.65245i | − | 0.250014i | ||||||
\(709\) | 20.0239 | + | 20.0239i | 0.752014 | + | 0.752014i | 0.974855 | − | 0.222841i | \(-0.0715331\pi\) |
−0.222841 | + | 0.974855i | \(0.571533\pi\) | |||||||
\(710\) | −2.93407 | + | 6.74653i | −0.110114 | + | 0.253193i | ||||
\(711\) | −3.59077 | + | 3.59077i | −0.134664 | + | 0.134664i | ||||
\(712\) | −1.33809 | − | 1.33809i | −0.0501470 | − | 0.0501470i | ||||
\(713\) | 7.81391 | − | 7.81391i | 0.292633 | − | 0.292633i | ||||
\(714\) | 2.77686 | 0.103921 | ||||||||
\(715\) | 2.56873 | + | 1.11714i | 0.0960650 | + | 0.0417788i | ||||
\(716\) | 1.70251 | − | 1.70251i | 0.0636258 | − | 0.0636258i | ||||
\(717\) | − | 14.8459i | − | 0.554431i | ||||||
\(718\) | 3.71905 | 0.138794 | ||||||||
\(719\) | − | 32.6337i | − | 1.21703i | −0.793541 | − | 0.608517i | \(-0.791765\pi\) | ||
0.793541 | − | 0.608517i | \(-0.208235\pi\) | |||||||
\(720\) | −0.891783 | + | 2.05054i | −0.0332348 | + | 0.0764192i | ||||
\(721\) | −21.6124 | − | 21.6124i | −0.804889 | − | 0.804889i | ||||
\(722\) | −9.50611 | −0.353781 | ||||||||
\(723\) | −9.43070 | −0.350731 | ||||||||
\(724\) | −8.75170 | −0.325254 | ||||||||
\(725\) | 8.64688 | + | 0.303247i | 0.321137 | + | 0.0112623i | ||||
\(726\) | 3.09806 | − | 3.09806i | 0.114980 | − | 0.114980i | ||||
\(727\) | − | 21.1503i | − | 0.784422i | −0.919875 | − | 0.392211i | \(-0.871710\pi\) | ||
0.919875 | − | 0.392211i | \(-0.128290\pi\) | |||||||
\(728\) | 0.499755 | + | 0.499755i | 0.0185222 | + | 0.0185222i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 25.1098 | − | 9.88884i | 0.929354 | − | 0.366002i | ||||
\(731\) | 2.35094i | 0.0869527i | ||||||||
\(732\) | − | 7.86494i | − | 0.290696i | ||||||
\(733\) | −26.3403 | − | 26.3403i | −0.972902 | − | 0.972902i | 0.0267403 | − | 0.999642i | \(-0.491487\pi\) |
−0.999642 | + | 0.0267403i | \(0.991487\pi\) | |||||||
\(734\) | 20.2784 | − | 20.2784i | 0.748489 | − | 0.748489i | ||||
\(735\) | −4.37752 | + | 1.72397i | −0.161467 | + | 0.0635897i | ||||
\(736\) | 1.15203 | 0.0424643 | ||||||||
\(737\) | 26.9980 | + | 26.9980i | 0.994485 | + | 0.994485i | ||||
\(738\) | − | 3.92813i | − | 0.144596i | ||||||
\(739\) | −27.2865 | −1.00375 | −0.501876 | − | 0.864940i | \(-0.667357\pi\) | ||||
−0.501876 | + | 0.864940i | \(0.667357\pi\) | |||||||
\(740\) | −5.44517 | + | 12.4640i | −0.200168 | + | 0.458184i | ||||
\(741\) | −0.984181 | −0.0361548 | ||||||||
\(742\) | − | 9.48858i | − | 0.348337i | ||||||
\(743\) | 18.6520 | + | 18.6520i | 0.684276 | + | 0.684276i | 0.960961 | − | 0.276684i | \(-0.0892357\pi\) |
−0.276684 | + | 0.960961i | \(0.589236\pi\) | |||||||
\(744\) | −9.59224 | −0.351668 | ||||||||
\(745\) | 0.379689 | − | 0.873048i | 0.0139107 | − | 0.0319860i | ||||
\(746\) | 17.0249 | − | 17.0249i | 0.623325 | − | 0.623325i | ||||
\(747\) | −1.13008 | − | 1.13008i | −0.0413474 | − | 0.0413474i | ||||
\(748\) | 4.92188i | 0.179962i | ||||||||
\(749\) | − | 4.87750i | − | 0.178220i | ||||||
\(750\) | −10.0901 | − | 4.81552i | −0.368440 | − | 0.175838i | ||||
\(751\) | 29.3632i | 1.07148i | 0.844384 | + | 0.535738i | \(0.179967\pi\) | ||||
−0.844384 | + | 0.535738i | \(0.820033\pi\) | |||||||
\(752\) | −4.88442 | − | 4.88442i | −0.178116 | − | 0.178116i | ||||
\(753\) | − | 28.2766i | − | 1.03046i | ||||||
\(754\) | 0.390836 | − | 0.390836i | 0.0142334 | − | 0.0142334i | ||||
\(755\) | 16.6370 | − | 38.2547i | 0.605483 | − | 1.39223i | ||||
\(756\) | 2.21268 | 0.0804745 | ||||||||
\(757\) | 36.6279 | 1.33126 | 0.665631 | − | 0.746281i | \(-0.268162\pi\) | ||||
0.665631 | + | 0.746281i | \(0.268162\pi\) | |||||||
\(758\) | 3.59500 | 0.130576 | ||||||||
\(759\) | −3.19481 | − | 3.19481i | −0.115964 | − | 0.115964i | ||||
\(760\) | 6.41059 | − | 2.52465i | 0.232536 | − | 0.0915785i | ||||
\(761\) | 13.4727i | 0.488386i | 0.969727 | + | 0.244193i | \(0.0785230\pi\) | ||||
−0.969727 | + | 0.244193i | \(0.921477\pi\) | |||||||
\(762\) | −9.98731 | −0.361802 | ||||||||
\(763\) | − | 13.2710i | − | 0.480442i | ||||||
\(764\) | −4.56780 | + | 4.56780i | −0.165257 | + | 0.165257i | ||||
\(765\) | −1.11916 | + | 2.57338i | −0.0404635 | + | 0.0930407i | ||||
\(766\) | 18.9973 | 0.686399 | ||||||||
\(767\) | 1.50252 | − | 1.50252i | 0.0542527 | − | 0.0542527i | ||||
\(768\) | −0.707107 | − | 0.707107i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | 11.9916 | − | 11.9916i | 0.432427 | − | 0.432427i | −0.457026 | − | 0.889453i | \(-0.651085\pi\) |
0.889453 | + | 0.457026i | \(0.151085\pi\) | |||||||
\(770\) | 7.11040 | + | 18.0548i | 0.256241 | + | 0.650648i | ||||
\(771\) | −22.1776 | − | 22.1776i | −0.798707 | − | 0.798707i | ||||
\(772\) | − | 5.51547i | − | 0.198506i | ||||||
\(773\) | 14.0271 | − | 14.0271i | 0.504520 | − | 0.504520i | −0.408319 | − | 0.912839i | \(-0.633885\pi\) |
0.912839 | + | 0.408319i | \(0.133885\pi\) | |||||||
\(774\) | 1.87330i | 0.0673343i | ||||||||
\(775\) | 1.68097 | − | 47.9317i | 0.0603822 | − | 1.72176i | ||||
\(776\) | 4.01884i | 0.144268i | ||||||||
\(777\) | 13.4592 | + | 0.0223076i | 0.482846 | + | 0.000800282i | ||||
\(778\) | 9.52518 | − | 9.52518i | 0.341494 | − | 0.341494i | ||||
\(779\) | −8.55840 | + | 8.55840i | −0.306637 | + | 0.306637i | ||||
\(780\) | −0.664551 | + | 0.261716i | −0.0237948 | + | 0.00937095i | ||||
\(781\) | 12.9035i | 0.461725i | ||||||||
\(782\) | 1.44577 | 0.0517005 | ||||||||
\(783\) | − | 1.73044i | − | 0.0618409i | ||||||
\(784\) | − | 2.10403i | − | 0.0751440i | ||||||
\(785\) | 7.22341 | + | 18.3417i | 0.257815 | + | 0.654644i | ||||
\(786\) | 13.1829 | 0.470218 | ||||||||
\(787\) | −7.13187 | − | 7.13187i | −0.254224 | − | 0.254224i | 0.568476 | − | 0.822700i | \(-0.307533\pi\) |
−0.822700 | + | 0.568476i | \(0.807533\pi\) | |||||||
\(788\) | 3.48510 | + | 3.48510i | 0.124152 | + | 0.124152i | ||||
\(789\) | 10.4700i | 0.372742i | ||||||||
\(790\) | 10.5652 | − | 4.16084i | 0.375893 | − | 0.148036i | ||||
\(791\) | 25.8760 | + | 25.8760i | 0.920043 | + | 0.920043i | ||||
\(792\) | 3.92190i | 0.139359i | ||||||||
\(793\) | 1.77637 | − | 1.77637i | 0.0630807 | − | 0.0630807i | ||||
\(794\) | −6.55806 | − | 6.55806i | −0.232737 | − | 0.232737i | ||||
\(795\) | 8.79328 | + | 3.82420i | 0.311865 | + | 0.135631i | ||||
\(796\) | 11.0862 | − | 11.0862i | 0.392942 | − | 0.392942i | ||||
\(797\) | 5.26825i | 0.186611i | 0.995638 | + | 0.0933054i | \(0.0297433\pi\) | ||||
−0.995638 | + | 0.0933054i | \(0.970257\pi\) | |||||||
\(798\) | −4.82088 | − | 4.82088i | −0.170657 | − | 0.170657i | ||||
\(799\) | −6.12982 | − | 6.12982i | −0.216857 | − | 0.216857i | ||||
\(800\) | 3.65728 | − | 3.40945i | 0.129304 | − | 0.120542i | ||||
\(801\) | −1.33809 | − | 1.33809i | −0.0472790 | − | 0.0472790i | ||||
\(802\) | −3.25081 | + | 3.25081i | −0.114790 | + | 0.114790i | ||||
\(803\) | 33.4695 | − | 33.4695i | 1.18111 | − | 1.18111i | ||||
\(804\) | −9.73532 | −0.343338 | ||||||||
\(805\) | 5.30345 | − | 2.08863i | 0.186922 | − | 0.0736144i | ||||
\(806\) | −2.16650 | − | 2.16650i | −0.0763115 | − | 0.0763115i | ||||
\(807\) | 2.41793 | − | 2.41793i | 0.0851151 | − | 0.0851151i | ||||
\(808\) | 11.0673 | 0.389346 | ||||||||
\(809\) | 7.49771 | − | 7.49771i | 0.263605 | − | 0.263605i | −0.562912 | − | 0.826517i | \(-0.690319\pi\) |
0.826517 | + | 0.562912i | \(0.190319\pi\) | |||||||
\(810\) | −0.891783 | + | 2.05054i | −0.0313341 | + | 0.0720487i | ||||
\(811\) | 17.4655 | 0.613296 | 0.306648 | − | 0.951823i | \(-0.400793\pi\) | ||||
0.306648 | + | 0.951823i | \(0.400793\pi\) | |||||||
\(812\) | 3.82892 | 0.134369 | ||||||||
\(813\) | −12.6363 | − | 12.6363i | −0.443174 | − | 0.443174i | ||||
\(814\) | −0.0395395 | + | 23.8560i | −0.00138586 | + | 0.836151i | ||||
\(815\) | 31.5970 | + | 13.7416i | 1.10679 | + | 0.481346i | ||||
\(816\) | −0.887401 | − | 0.887401i | −0.0310652 | − | 0.0310652i | ||||
\(817\) | 4.08144 | − | 4.08144i | 0.142792 | − | 0.142792i | ||||
\(818\) | −13.3605 | − | 13.3605i | −0.467141 | − | 0.467141i | ||||
\(819\) | 0.499755 | + | 0.499755i | 0.0174629 | + | 0.0174629i | ||||
\(820\) | −3.50304 | + | 8.05479i | −0.122331 | + | 0.281286i | ||||
\(821\) | −30.4173 | −1.06157 | −0.530786 | − | 0.847506i | \(-0.678103\pi\) | ||||
−0.530786 | + | 0.847506i | \(0.678103\pi\) | |||||||
\(822\) | 20.6125 | 0.718943 | ||||||||
\(823\) | 34.7921 | − | 34.7921i | 1.21278 | − | 1.21278i | 0.242667 | − | 0.970110i | \(-0.421978\pi\) |
0.970110 | − | 0.242667i | \(-0.0780221\pi\) | |||||||
\(824\) | 13.8134i | 0.481211i | ||||||||
\(825\) | −19.5975 | − | 0.687284i | −0.682296 | − | 0.0239282i | ||||
\(826\) | 14.7198 | 0.512166 | ||||||||
\(827\) | −37.5059 | −1.30421 | −0.652104 | − | 0.758129i | \(-0.726114\pi\) | ||||
−0.652104 | + | 0.758129i | \(0.726114\pi\) | |||||||
\(828\) | 1.15203 | 0.0400358 | ||||||||
\(829\) | 38.6319 | − | 38.6319i | 1.34174 | − | 1.34174i | 0.447414 | − | 0.894327i | \(-0.352345\pi\) |
0.894327 | − | 0.447414i | \(-0.147655\pi\) | |||||||
\(830\) | 1.30949 | + | 3.32506i | 0.0454530 | + | 0.115414i | ||||
\(831\) | −10.5024 | + | 10.5024i | −0.364325 | + | 0.364325i | ||||
\(832\) | − | 0.319413i | − | 0.0110737i | ||||||
\(833\) | − | 2.64050i | − | 0.0914881i | ||||||
\(834\) | −0.852977 | + | 0.852977i | −0.0295362 | + | 0.0295362i | ||||
\(835\) | 34.5252 | + | 15.0150i | 1.19479 | + | 0.519617i | ||||
\(836\) | 8.54484 | − | 8.54484i | 0.295529 | − | 0.295529i | ||||
\(837\) | −9.59224 | −0.331556 | ||||||||
\(838\) | −18.6060 | −0.642734 | ||||||||
\(839\) | 14.2744 | 0.492807 | 0.246404 | − | 0.969167i | \(-0.420751\pi\) | ||||
0.246404 | + | 0.969167i | \(0.420751\pi\) | |||||||
\(840\) | −4.53720 | − | 1.97323i | −0.156548 | − | 0.0680830i | ||||
\(841\) | 26.0056i | 0.896744i | ||||||||
\(842\) | 4.15626 | − | 4.15626i | 0.143234 | − | 0.143234i | ||||
\(843\) | −6.45155 | −0.222203 | ||||||||
\(844\) | −27.2170 | −0.936848 | ||||||||
\(845\) | 26.4478 | + | 11.5022i | 0.909833 | + | 0.395687i | ||||
\(846\) | −4.88442 | − | 4.88442i | −0.167930 | − | 0.167930i | ||||
\(847\) | 6.85502 | + | 6.85502i | 0.235541 | + | 0.235541i | ||||
\(848\) | −3.03226 | + | 3.03226i | −0.104128 | + | 0.104128i | ||||
\(849\) | 22.9026 | + | 22.9026i | 0.786014 | + | 0.786014i | ||||
\(850\) | 4.58979 | − | 4.27877i | 0.157428 | − | 0.146760i | ||||
\(851\) | 7.00751 | + | 0.0116144i | 0.240214 | + | 0.000398137i | ||||
\(852\) | −2.32647 | − | 2.32647i | −0.0797035 | − | 0.0797035i | ||||
\(853\) | 37.6236 | 1.28821 | 0.644104 | − | 0.764938i | \(-0.277231\pi\) | ||||
0.644104 | + | 0.764938i | \(0.277231\pi\) | |||||||
\(854\) | 17.4026 | 0.595505 | ||||||||
\(855\) | 6.41059 | − | 2.52465i | 0.219237 | − | 0.0863410i | ||||
\(856\) | −1.55870 | + | 1.55870i | −0.0532753 | + | 0.0532753i | ||||
\(857\) | 25.5393 | 0.872405 | 0.436202 | − | 0.899849i | \(-0.356323\pi\) | ||||
0.436202 | + | 0.899849i | \(0.356323\pi\) | |||||||
\(858\) | −0.885798 | + | 0.885798i | −0.0302406 | + | 0.0302406i | ||||
\(859\) | −35.0362 | − | 35.0362i | −1.19542 | − | 1.19542i | −0.975523 | − | 0.219897i | \(-0.929428\pi\) |
−0.219897 | − | 0.975523i | \(-0.570572\pi\) | |||||||
\(860\) | 1.67057 | − | 3.84128i | 0.0569661 | − | 0.130986i | ||||
\(861\) | 8.69170 | 0.296212 | ||||||||
\(862\) | −7.99513 | + | 7.99513i | −0.272315 | + | 0.272315i | ||||
\(863\) | −34.9362 | + | 34.9362i | −1.18924 | + | 1.18924i | −0.211964 | + | 0.977277i | \(0.567986\pi\) |
−0.977277 | + | 0.211964i | \(0.932014\pi\) | |||||||
\(864\) | −0.707107 | − | 0.707107i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | 6.00706 | + | 15.2531i | 0.204246 | + | 0.518622i | ||||
\(866\) | −21.8861 | − | 21.8861i | −0.743720 | − | 0.743720i | ||||
\(867\) | 10.9072 | + | 10.9072i | 0.370426 | + | 0.370426i | ||||
\(868\) | − | 21.2246i | − | 0.720409i | ||||||
\(869\) | 14.0826 | − | 14.0826i | 0.477721 | − | 0.477721i | ||||
\(870\) | −1.54318 | + | 3.54834i | −0.0523186 | + | 0.120300i | ||||
\(871\) | −2.19881 | − | 2.19881i | −0.0745039 | − | 0.0745039i | ||||
\(872\) | −4.24101 | + | 4.24101i | −0.143619 | + | 0.143619i | ||||
\(873\) | 4.01884i | 0.136017i | ||||||||
\(874\) | −2.50998 | − | 2.50998i | −0.0849014 | − | 0.0849014i | ||||
\(875\) | 10.6552 | − | 22.3263i | 0.360212 | − | 0.754766i | ||||
\(876\) | 12.0689i | 0.407770i | ||||||||
\(877\) | −36.4441 | − | 36.4441i | −1.23063 | − | 1.23063i | −0.963722 | − | 0.266909i | \(-0.913998\pi\) |
−0.266909 | − | 0.963722i | \(-0.586002\pi\) | |||||||
\(878\) | 19.4929 | + | 19.4929i | 0.657853 | + | 0.657853i | ||||
\(879\) | −4.14622 | −0.139848 | ||||||||
\(880\) | 3.49748 | − | 8.04202i | 0.117900 | − | 0.271097i | ||||
\(881\) | 41.8468i | 1.40986i | 0.709279 | + | 0.704928i | \(0.249021\pi\) | ||||
−0.709279 | + | 0.704928i | \(0.750979\pi\) | |||||||
\(882\) | − | 2.10403i | − | 0.0708464i | ||||||
\(883\) | 6.73598 | 0.226684 | 0.113342 | − | 0.993556i | \(-0.463844\pi\) | ||||
0.113342 | + | 0.993556i | \(0.463844\pi\) | |||||||
\(884\) | − | 0.400855i | − | 0.0134822i | ||||||
\(885\) | −5.93254 | + | 13.6411i | −0.199420 | + | 0.458541i | ||||
\(886\) | 1.25482 | − | 1.25482i | 0.0421564 | − | 0.0421564i | ||||
\(887\) | −5.08587 | + | 5.08587i | −0.170767 | + | 0.170767i | −0.787316 | − | 0.616549i | \(-0.788530\pi\) |
0.616549 | + | 0.787316i | \(0.288530\pi\) | |||||||
\(888\) | −4.29403 | − | 4.30829i | −0.144098 | − | 0.144577i | ||||
\(889\) | − | 22.0987i | − | 0.741168i | ||||||
\(890\) | 1.55052 | + | 3.93709i | 0.0519736 | + | 0.131972i | ||||
\(891\) | 3.92190i | 0.131389i | ||||||||
\(892\) | −11.1865 | + | 11.1865i | −0.374551 | + | 0.374551i | ||||
\(893\) | 21.2838i | 0.712237i | ||||||||
\(894\) | 0.301061 | + | 0.301061i | 0.0100690 | + | 0.0100690i | ||||
\(895\) | −5.00934 | + | 1.97280i | −0.167444 | + | 0.0659435i | ||||
\(896\) | 1.56460 | − | 1.56460i | 0.0522697 | − | 0.0522697i | ||||
\(897\) | 0.260196 | + | 0.260196i | 0.00868770 | + | 0.00868770i | ||||
\(898\) | 5.51963 | − | 5.51963i | 0.184192 | − | 0.184192i | ||||
\(899\) | −16.5988 | −0.553601 | ||||||||
\(900\) | 3.65728 | − | 3.40945i | 0.121909 | − | 0.113648i | ||||
\(901\) | −3.80541 | + | 3.80541i | −0.126777 | + | 0.126777i | ||||
\(902\) | 15.4057i | 0.512955i | ||||||||
\(903\) | −4.14502 | −0.137937 | ||||||||
\(904\) | − | 16.5384i | − | 0.550057i | ||||||
\(905\) | 17.9457 | + | 7.80462i | 0.596536 | + | 0.259434i | ||||
\(906\) | 13.1917 | + | 13.1917i | 0.438265 | + | 0.438265i | ||||
\(907\) | −5.02600 | −0.166886 | −0.0834428 | − | 0.996513i | \(-0.526592\pi\) | ||||
−0.0834428 | + | 0.996513i | \(0.526592\pi\) | |||||||
\(908\) | −1.74912 | −0.0580467 | ||||||||
\(909\) | 11.0673 | 0.367079 | ||||||||
\(910\) | −0.579096 | − | 1.47044i | −0.0191968 | − | 0.0487447i | ||||
\(911\) | −6.78195 | + | 6.78195i | −0.224696 | + | 0.224696i | −0.810473 | − | 0.585777i | \(-0.800790\pi\) |
0.585777 | + | 0.810473i | \(0.300790\pi\) | |||||||
\(912\) | 3.08122i | 0.102029i | ||||||||
\(913\) | 4.43206 | + | 4.43206i | 0.146680 | + | 0.146680i | ||||
\(914\) | 6.65948i | 0.220276i | ||||||||
\(915\) | −7.01382 | + | 16.1274i | −0.231870 | + | 0.533155i | ||||
\(916\) | 8.51464i | 0.281332i | ||||||||
\(917\) | 29.1696i | 0.963264i | ||||||||
\(918\) | −0.887401 | − | 0.887401i | −0.0292886 | − | 0.0292886i | ||||
\(919\) | 5.23943 | − | 5.23943i | 0.172833 | − | 0.172833i | −0.615390 | − | 0.788223i | \(-0.711001\pi\) |
0.788223 | + | 0.615390i | \(0.211001\pi\) | |||||||
\(920\) | −2.36228 | − | 1.02736i | −0.0778822 | − | 0.0338710i | ||||
\(921\) | 0.318596 | 0.0104981 | ||||||||
\(922\) | 24.8127 | + | 24.8127i | 0.817163 | + | 0.817163i | ||||
\(923\) | − | 1.05091i | − | 0.0345911i | ||||||
\(924\) | −8.67793 | −0.285483 | ||||||||
\(925\) | 22.2807 | − | 20.7020i | 0.732585 | − | 0.680676i | ||||
\(926\) | −0.607120 | −0.0199512 | ||||||||
\(927\) | 13.8134i | 0.453690i | ||||||||
\(928\) | −1.22361 | − | 1.22361i | −0.0401668 | − | 0.0401668i | ||||
\(929\) | −41.3020 | −1.35507 | −0.677537 | − | 0.735488i | \(-0.736953\pi\) | ||||
−0.677537 | + | 0.735488i | \(0.736953\pi\) | |||||||
\(930\) | 19.6693 | + | 8.55419i | 0.644981 | + | 0.280503i | ||||
\(931\) | −4.58415 | + | 4.58415i | −0.150240 | + | 0.150240i | ||||
\(932\) | 6.42533 | + | 6.42533i | 0.210469 | + | 0.210469i | ||||
\(933\) | − | 11.5938i | − | 0.379563i | ||||||
\(934\) | 14.2821i | 0.467324i | ||||||||
\(935\) | 4.38925 | − | 10.0925i | 0.143544 | − | 0.330061i | ||||
\(936\) | − | 0.319413i | − | 0.0104403i | ||||||
\(937\) | 30.8614 | + | 30.8614i | 1.00820 | + | 1.00820i | 0.999966 | + | 0.00823050i | \(0.00261988\pi\) |
0.00823050 | + | 0.999966i | \(0.497380\pi\) | |||||||
\(938\) | − | 21.5412i | − | 0.703344i | ||||||
\(939\) | 8.56918 | − | 8.56918i | 0.279645 | − | 0.279645i | ||||
\(940\) | 5.65987 | + | 14.3716i | 0.184605 | + | 0.468748i | ||||
\(941\) | −5.06512 | −0.165118 | −0.0825590 | − | 0.996586i | \(-0.526309\pi\) | ||||
−0.0825590 | + | 0.996586i | \(0.526309\pi\) | |||||||
\(942\) | −8.81585 | −0.287236 | ||||||||
\(943\) | 4.52532 | 0.147365 | ||||||||
\(944\) | −4.70399 | − | 4.70399i | −0.153102 | − | 0.153102i | ||||
\(945\) | −4.53720 | − | 1.97323i | −0.147595 | − | 0.0641893i | ||||
\(946\) | − | 7.34689i | − | 0.238868i | ||||||
\(947\) | 59.8123 | 1.94364 | 0.971819 | − | 0.235726i | \(-0.0757469\pi\) | ||||
0.971819 | + | 0.235726i | \(0.0757469\pi\) | |||||||
\(948\) | 5.07811i | 0.164929i | ||||||||
\(949\) | −2.72587 | + | 2.72587i | −0.0884855 | + | 0.0884855i | ||||
\(950\) | −15.3966 | − | 0.539960i | −0.499532 | − | 0.0175186i | ||||
\(951\) | −7.72243 | −0.250417 | ||||||||
\(952\) | 1.96354 | − | 1.96354i | 0.0636386 | − | 0.0636386i | ||||
\(953\) | −17.6361 | − | 17.6361i | −0.571291 | − | 0.571291i | 0.361198 | − | 0.932489i | \(-0.382368\pi\) |
−0.932489 | + | 0.361198i | \(0.882368\pi\) | |||||||
\(954\) | −3.03226 | + | 3.03226i | −0.0981732 | + | 0.0981732i | ||||
\(955\) | 13.4399 | − | 5.29298i | 0.434906 | − | 0.171277i | ||||
\(956\) | −10.4976 | − | 10.4976i | −0.339518 | − | 0.339518i | ||||
\(957\) | 6.78661i | 0.219380i | ||||||||
\(958\) | 12.8987 | − | 12.8987i | 0.416739 | − | 0.416739i | ||||
\(959\) | 45.6089i | 1.47279i | ||||||||
\(960\) | 0.819367 | + | 2.08054i | 0.0264449 | + | 0.0671491i | ||||
\(961\) | 61.0110i | 1.96810i | ||||||||
\(962\) | 0.00322023 | − | 1.94291i | 0.000103824 | − | 0.0626420i | ||||
\(963\) | −1.55870 | + | 1.55870i | −0.0502284 | + | 0.0502284i | ||||
\(964\) | −6.66851 | + | 6.66851i | −0.214778 | + | 0.214778i | ||||
\(965\) | −4.91860 | + | 11.3097i | −0.158335 | + | 0.364072i | ||||
\(966\) | 2.54907i | 0.0820151i | ||||||||
\(967\) | 39.1113 | 1.25773 | 0.628867 | − | 0.777513i | \(-0.283519\pi\) | ||||
0.628867 | + | 0.777513i | \(0.283519\pi\) | |||||||
\(968\) | − | 4.38131i | − | 0.140821i | ||||||
\(969\) | 3.86685i | 0.124221i | ||||||||
\(970\) | 3.58393 | − | 8.24079i | 0.115073 | − | 0.264596i | ||||
\(971\) | 49.6084 | 1.59201 | 0.796004 | − | 0.605291i | \(-0.206943\pi\) | ||||
0.796004 | + | 0.605291i | \(0.206943\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | −1.88737 | − | 1.88737i | −0.0605063 | − | 0.0605063i | ||||
\(974\) | − | 0.169467i | − | 0.00543009i | ||||||
\(975\) | 1.59608 | + | 0.0559748i | 0.0511156 | + | 0.00179263i | ||||
\(976\) | −5.56135 | − | 5.56135i | −0.178014 | − | 0.178014i | ||||
\(977\) | − | 17.0944i | − | 0.546899i | −0.961886 | − | 0.273450i | \(-0.911835\pi\) | ||
0.961886 | − | 0.273450i | \(-0.0881646\pi\) | |||||||
\(978\) | −10.8959 | + | 10.8959i | −0.348411 | + | 0.348411i | ||||
\(979\) | 5.24785 | + | 5.24785i | 0.167722 | + | 0.167722i | ||||
\(980\) | −1.87634 | + | 4.31440i | −0.0599374 | + | 0.137819i | ||||
\(981\) | −4.24101 | + | 4.24101i | −0.135405 | + | 0.135405i | ||||
\(982\) | − | 11.6118i | − | 0.370547i | ||||||
\(983\) | −14.4506 | − | 14.4506i | −0.460901 | − | 0.460901i | 0.438050 | − | 0.898951i | \(-0.355669\pi\) |
−0.898951 | + | 0.438050i | \(0.855669\pi\) | |||||||
\(984\) | −2.77761 | − | 2.77761i | −0.0885468 | − | 0.0885468i | ||||
\(985\) | −4.03839 | − | 10.2543i | −0.128674 | − | 0.326729i | ||||
\(986\) | −1.53559 | − | 1.53559i | −0.0489033 | − | 0.0489033i | ||||
\(987\) | 10.8077 | − | 10.8077i | 0.344012 | − | 0.344012i | ||||
\(988\) | −0.695921 | + | 0.695921i | −0.0221402 | + | 0.0221402i | ||||
\(989\) | −2.15809 | −0.0686233 | ||||||||
\(990\) | 3.49748 | − | 8.04202i | 0.111157 | − | 0.255592i | ||||
\(991\) | −10.9464 | − | 10.9464i | −0.347723 | − | 0.347723i | 0.511538 | − | 0.859261i | \(-0.329076\pi\) |
−0.859261 | + | 0.511538i | \(0.829076\pi\) | |||||||
\(992\) | −6.78274 | + | 6.78274i | −0.215352 | + | 0.215352i | ||||
\(993\) | −20.1471 | −0.639350 | ||||||||
\(994\) | 5.14774 | − | 5.14774i | 0.163276 | − | 0.163276i | ||||
\(995\) | −32.6193 | + | 12.8463i | −1.03410 | + | 0.407255i | ||||
\(996\) | −1.59817 | −0.0506400 | ||||||||
\(997\) | 32.8775 | 1.04124 | 0.520621 | − | 0.853788i | \(-0.325701\pi\) | ||||
0.520621 | + | 0.853788i | \(0.325701\pi\) | |||||||
\(998\) | 15.8556 | + | 15.8556i | 0.501899 | + | 0.501899i | ||||
\(999\) | −4.29403 | − | 4.30829i | −0.135857 | − | 0.136308i |
(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 | 1110.2.l.a.697.8 | yes | 36 | |
5.3 | odd | 4 | 1110.2.o.a.253.11 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.o.a.487.11 | yes | 36 | ||
185.43 | even | 4 | inner | 1110.2.l.a.43.8 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.8 | ✓ | 36 | 185.43 | even | 4 | inner | |
1110.2.l.a.697.8 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.253.11 | yes | 36 | 5.3 | odd | 4 | ||
1110.2.o.a.487.11 | yes | 36 | 37.6 | odd | 4 |