Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [330,2,Mod(31,330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(330, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("330.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 330.m (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.63506326670\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(-0.309017 - 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 330.31 |
Dual form | 330.2.m.b.181.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/330\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(211\) | \(221\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | − | 0.951057i | 0.218508 | − | 0.672499i | ||||
\(3\) | 0.809017 | − | 0.587785i | 0.467086 | − | 0.339358i | ||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | −0.309017 | − | 0.951057i | −0.138197 | − | 0.425325i | ||||
\(6\) | −0.309017 | − | 0.951057i | −0.126156 | − | 0.388267i | ||||
\(7\) | −1.00000 | − | 0.726543i | −0.377964 | − | 0.274607i | 0.382541 | − | 0.923938i | \(-0.375049\pi\) |
−0.760506 | + | 0.649331i | \(0.775049\pi\) | |||||||
\(8\) | −0.809017 | + | 0.587785i | −0.286031 | + | 0.207813i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −2.54508 | − | 2.12663i | −0.767372 | − | 0.641202i | ||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.73607 | − | 5.34307i | 0.481499 | − | 1.48190i | −0.355490 | − | 0.934680i | \(-0.615686\pi\) |
0.836989 | − | 0.547220i | \(-0.184314\pi\) | |||||||
\(14\) | −1.00000 | + | 0.726543i | −0.267261 | + | 0.194177i | ||||
\(15\) | −0.809017 | − | 0.587785i | −0.208887 | − | 0.151765i | ||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | 1.57295 | + | 4.84104i | 0.381496 | + | 1.17412i | 0.938990 | + | 0.343944i | \(0.111763\pi\) |
−0.557494 | + | 0.830181i | \(0.688237\pi\) | |||||||
\(18\) | −0.809017 | − | 0.587785i | −0.190687 | − | 0.138542i | ||||
\(19\) | 2.61803 | − | 1.90211i | 0.600618 | − | 0.436375i | −0.245480 | − | 0.969402i | \(-0.578946\pi\) |
0.846098 | + | 0.533027i | \(0.178946\pi\) | |||||||
\(20\) | −0.309017 | + | 0.951057i | −0.0690983 | + | 0.212663i | ||||
\(21\) | −1.23607 | −0.269732 | ||||||||
\(22\) | −2.80902 | + | 1.76336i | −0.598884 | + | 0.375949i | ||||
\(23\) | 0.145898 | 0.0304218 | 0.0152109 | − | 0.999884i | \(-0.495158\pi\) | ||||
0.0152109 | + | 0.999884i | \(0.495158\pi\) | |||||||
\(24\) | −0.309017 | + | 0.951057i | −0.0630778 | + | 0.194134i | ||||
\(25\) | −0.809017 | + | 0.587785i | −0.161803 | + | 0.117557i | ||||
\(26\) | −4.54508 | − | 3.30220i | −0.891364 | − | 0.647614i | ||||
\(27\) | −0.309017 | − | 0.951057i | −0.0594703 | − | 0.183031i | ||||
\(28\) | 0.381966 | + | 1.17557i | 0.0721848 | + | 0.222162i | ||||
\(29\) | 0.309017 | + | 0.224514i | 0.0573830 | + | 0.0416912i | 0.616107 | − | 0.787662i | \(-0.288709\pi\) |
−0.558724 | + | 0.829354i | \(0.688709\pi\) | |||||||
\(30\) | −0.809017 | + | 0.587785i | −0.147706 | + | 0.107314i | ||||
\(31\) | −1.11803 | + | 3.44095i | −0.200805 | + | 0.618014i | 0.799055 | + | 0.601258i | \(0.205334\pi\) |
−0.999860 | + | 0.0167555i | \(0.994666\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.30902 | − | 0.224514i | −0.576026 | − | 0.0390829i | ||||
\(34\) | 5.09017 | 0.872957 | ||||||||
\(35\) | −0.381966 | + | 1.17557i | −0.0645640 | + | 0.198708i | ||||
\(36\) | −0.809017 | + | 0.587785i | −0.134836 | + | 0.0979642i | ||||
\(37\) | 6.97214 | + | 5.06555i | 1.14621 | + | 0.832772i | 0.987973 | − | 0.154629i | \(-0.0494182\pi\) |
0.158239 | + | 0.987401i | \(0.449418\pi\) | |||||||
\(38\) | −1.00000 | − | 3.07768i | −0.162221 | − | 0.499266i | ||||
\(39\) | −1.73607 | − | 5.34307i | −0.277993 | − | 0.855576i | ||||
\(40\) | 0.809017 | + | 0.587785i | 0.127917 | + | 0.0929370i | ||||
\(41\) | 2.61803 | − | 1.90211i | 0.408868 | − | 0.297060i | −0.364275 | − | 0.931291i | \(-0.618683\pi\) |
0.773143 | + | 0.634231i | \(0.218683\pi\) | |||||||
\(42\) | −0.381966 | + | 1.17557i | −0.0589386 | + | 0.181394i | ||||
\(43\) | 11.0902 | 1.69124 | 0.845618 | − | 0.533789i | \(-0.179232\pi\) | ||||
0.845618 | + | 0.533789i | \(0.179232\pi\) | |||||||
\(44\) | 0.809017 | + | 3.21644i | 0.121964 | + | 0.484897i | ||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0.0450850 | − | 0.138757i | 0.00664742 | − | 0.0204586i | ||||
\(47\) | −9.16312 | + | 6.65740i | −1.33658 | + | 0.971081i | −0.337016 | + | 0.941499i | \(0.609418\pi\) |
−0.999562 | + | 0.0295820i | \(0.990582\pi\) | |||||||
\(48\) | 0.809017 | + | 0.587785i | 0.116772 | + | 0.0848395i | ||||
\(49\) | −1.69098 | − | 5.20431i | −0.241569 | − | 0.743473i | ||||
\(50\) | 0.309017 | + | 0.951057i | 0.0437016 | + | 0.134500i | ||||
\(51\) | 4.11803 | + | 2.99193i | 0.576640 | + | 0.418954i | ||||
\(52\) | −4.54508 | + | 3.30220i | −0.630290 | + | 0.457932i | ||||
\(53\) | −0.145898 | + | 0.449028i | −0.0200406 | + | 0.0616787i | −0.960577 | − | 0.278015i | \(-0.910323\pi\) |
0.940536 | + | 0.339694i | \(0.110323\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.23607 | + | 3.07768i | −0.166671 | + | 0.414995i | ||||
\(56\) | 1.23607 | 0.165177 | ||||||||
\(57\) | 1.00000 | − | 3.07768i | 0.132453 | − | 0.407649i | ||||
\(58\) | 0.309017 | − | 0.224514i | 0.0405759 | − | 0.0294801i | ||||
\(59\) | −2.35410 | − | 1.71036i | −0.306478 | − | 0.222669i | 0.423906 | − | 0.905706i | \(-0.360659\pi\) |
−0.730384 | + | 0.683037i | \(0.760659\pi\) | |||||||
\(60\) | 0.309017 | + | 0.951057i | 0.0398939 | + | 0.122781i | ||||
\(61\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(62\) | 2.92705 | + | 2.12663i | 0.371736 | + | 0.270082i | ||||
\(63\) | −1.00000 | + | 0.726543i | −0.125988 | + | 0.0915358i | ||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | −5.61803 | −0.696831 | ||||||||
\(66\) | −1.23607 | + | 3.07768i | −0.152149 | + | 0.378837i | ||||
\(67\) | 6.09017 | 0.744033 | 0.372016 | − | 0.928226i | \(-0.378667\pi\) | ||||
0.372016 | + | 0.928226i | \(0.378667\pi\) | |||||||
\(68\) | 1.57295 | − | 4.84104i | 0.190748 | − | 0.587062i | ||||
\(69\) | 0.118034 | − | 0.0857567i | 0.0142096 | − | 0.0103239i | ||||
\(70\) | 1.00000 | + | 0.726543i | 0.119523 | + | 0.0868384i | ||||
\(71\) | 0.472136 | + | 1.45309i | 0.0560322 | + | 0.172449i | 0.975156 | − | 0.221520i | \(-0.0711017\pi\) |
−0.919124 | + | 0.393969i | \(0.871102\pi\) | |||||||
\(72\) | 0.309017 | + | 0.951057i | 0.0364180 | + | 0.112083i | ||||
\(73\) | 10.8541 | + | 7.88597i | 1.27038 | + | 0.922983i | 0.999218 | − | 0.0395520i | \(-0.0125931\pi\) |
0.271159 | + | 0.962535i | \(0.412593\pi\) | |||||||
\(74\) | 6.97214 | − | 5.06555i | 0.810494 | − | 0.588859i | ||||
\(75\) | −0.309017 | + | 0.951057i | −0.0356822 | + | 0.109819i | ||||
\(76\) | −3.23607 | −0.371202 | ||||||||
\(77\) | 1.00000 | + | 3.97574i | 0.113961 | + | 0.453078i | ||||
\(78\) | −5.61803 | −0.636117 | ||||||||
\(79\) | 2.19098 | − | 6.74315i | 0.246505 | − | 0.758664i | −0.748880 | − | 0.662705i | \(-0.769408\pi\) |
0.995385 | − | 0.0959588i | \(-0.0305917\pi\) | |||||||
\(80\) | 0.809017 | − | 0.587785i | 0.0904508 | − | 0.0657164i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −1.00000 | − | 3.07768i | −0.110432 | − | 0.339873i | ||||
\(83\) | 1.23607 | + | 3.80423i | 0.135676 | + | 0.417568i | 0.995695 | − | 0.0926948i | \(-0.0295481\pi\) |
−0.860018 | + | 0.510263i | \(0.829548\pi\) | |||||||
\(84\) | 1.00000 | + | 0.726543i | 0.109109 | + | 0.0792723i | ||||
\(85\) | 4.11803 | − | 2.99193i | 0.446663 | − | 0.324520i | ||||
\(86\) | 3.42705 | − | 10.5474i | 0.369548 | − | 1.13735i | ||||
\(87\) | 0.381966 | 0.0409511 | ||||||||
\(88\) | 3.30902 | + | 0.224514i | 0.352742 | + | 0.0239333i | ||||
\(89\) | 12.7639 | 1.35297 | 0.676487 | − | 0.736455i | \(-0.263501\pi\) | ||||
0.676487 | + | 0.736455i | \(0.263501\pi\) | |||||||
\(90\) | −0.309017 | + | 0.951057i | −0.0325733 | + | 0.100250i | ||||
\(91\) | −5.61803 | + | 4.08174i | −0.588930 | + | 0.427883i | ||||
\(92\) | −0.118034 | − | 0.0857567i | −0.0123059 | − | 0.00894076i | ||||
\(93\) | 1.11803 | + | 3.44095i | 0.115935 | + | 0.356810i | ||||
\(94\) | 3.50000 | + | 10.7719i | 0.360997 | + | 1.11104i | ||||
\(95\) | −2.61803 | − | 1.90211i | −0.268605 | − | 0.195153i | ||||
\(96\) | 0.809017 | − | 0.587785i | 0.0825700 | − | 0.0599906i | ||||
\(97\) | −3.90983 | + | 12.0332i | −0.396983 | + | 1.22179i | 0.530423 | + | 0.847733i | \(0.322033\pi\) |
−0.927406 | + | 0.374055i | \(0.877967\pi\) | |||||||
\(98\) | −5.47214 | −0.552769 | ||||||||
\(99\) | −2.80902 | + | 1.76336i | −0.282317 | + | 0.177224i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 4.13525 | − | 12.7270i | 0.411473 | − | 1.26638i | −0.503894 | − | 0.863765i | \(-0.668100\pi\) |
0.915368 | − | 0.402619i | \(-0.131900\pi\) | |||||||
\(102\) | 4.11803 | − | 2.99193i | 0.407746 | − | 0.296245i | ||||
\(103\) | −9.09017 | − | 6.60440i | −0.895681 | − | 0.650750i | 0.0416720 | − | 0.999131i | \(-0.486732\pi\) |
−0.937353 | + | 0.348381i | \(0.886732\pi\) | |||||||
\(104\) | 1.73607 | + | 5.34307i | 0.170235 | + | 0.523931i | ||||
\(105\) | 0.381966 | + | 1.17557i | 0.0372761 | + | 0.114724i | ||||
\(106\) | 0.381966 | + | 0.277515i | 0.0370998 | + | 0.0269546i | ||||
\(107\) | −15.9443 | + | 11.5842i | −1.54139 | + | 1.11989i | −0.591935 | + | 0.805986i | \(0.701636\pi\) |
−0.949456 | + | 0.313900i | \(0.898364\pi\) | |||||||
\(108\) | −0.309017 | + | 0.951057i | −0.0297352 | + | 0.0915155i | ||||
\(109\) | 6.47214 | 0.619918 | 0.309959 | − | 0.950750i | \(-0.399685\pi\) | ||||
0.309959 | + | 0.950750i | \(0.399685\pi\) | |||||||
\(110\) | 2.54508 | + | 2.12663i | 0.242664 | + | 0.202766i | ||||
\(111\) | 8.61803 | 0.817988 | ||||||||
\(112\) | 0.381966 | − | 1.17557i | 0.0360924 | − | 0.111081i | ||||
\(113\) | −0.454915 | + | 0.330515i | −0.0427948 | + | 0.0310922i | −0.608977 | − | 0.793188i | \(-0.708420\pi\) |
0.566182 | + | 0.824280i | \(0.308420\pi\) | |||||||
\(114\) | −2.61803 | − | 1.90211i | −0.245201 | − | 0.178149i | ||||
\(115\) | −0.0450850 | − | 0.138757i | −0.00420420 | − | 0.0129392i | ||||
\(116\) | −0.118034 | − | 0.363271i | −0.0109592 | − | 0.0337289i | ||||
\(117\) | −4.54508 | − | 3.30220i | −0.420193 | − | 0.305288i | ||||
\(118\) | −2.35410 | + | 1.71036i | −0.216713 | + | 0.157451i | ||||
\(119\) | 1.94427 | − | 5.98385i | 0.178231 | − | 0.548539i | ||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 1.95492 | + | 10.8249i | 0.177720 | + | 0.984081i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.00000 | − | 3.07768i | 0.0901670 | − | 0.277505i | ||||
\(124\) | 2.92705 | − | 2.12663i | 0.262857 | − | 0.190977i | ||||
\(125\) | 0.809017 | + | 0.587785i | 0.0723607 | + | 0.0525731i | ||||
\(126\) | 0.381966 | + | 1.17557i | 0.0340282 | + | 0.104728i | ||||
\(127\) | −5.14590 | − | 15.8374i | −0.456625 | − | 1.40535i | −0.869217 | − | 0.494430i | \(-0.835377\pi\) |
0.412593 | − | 0.910916i | \(-0.364623\pi\) | |||||||
\(128\) | −0.809017 | − | 0.587785i | −0.0715077 | − | 0.0519534i | ||||
\(129\) | 8.97214 | − | 6.51864i | 0.789953 | − | 0.573934i | ||||
\(130\) | −1.73607 | + | 5.34307i | −0.152263 | + | 0.468618i | ||||
\(131\) | −5.61803 | −0.490850 | −0.245425 | − | 0.969416i | \(-0.578927\pi\) | ||||
−0.245425 | + | 0.969416i | \(0.578927\pi\) | |||||||
\(132\) | 2.54508 | + | 2.12663i | 0.221521 | + | 0.185099i | ||||
\(133\) | −4.00000 | −0.346844 | ||||||||
\(134\) | 1.88197 | − | 5.79210i | 0.162577 | − | 0.500361i | ||||
\(135\) | −0.809017 | + | 0.587785i | −0.0696291 | + | 0.0505885i | ||||
\(136\) | −4.11803 | − | 2.99193i | −0.353119 | − | 0.256556i | ||||
\(137\) | 3.64590 | + | 11.2209i | 0.311490 | + | 0.958668i | 0.977175 | + | 0.212435i | \(0.0681394\pi\) |
−0.665685 | + | 0.746233i | \(0.731861\pi\) | |||||||
\(138\) | −0.0450850 | − | 0.138757i | −0.00383789 | − | 0.0118118i | ||||
\(139\) | −10.7082 | − | 7.77997i | −0.908258 | − | 0.659888i | 0.0323157 | − | 0.999478i | \(-0.489712\pi\) |
−0.940574 | + | 0.339590i | \(0.889712\pi\) | |||||||
\(140\) | 1.00000 | − | 0.726543i | 0.0845154 | − | 0.0614041i | ||||
\(141\) | −3.50000 | + | 10.7719i | −0.294753 | + | 0.907157i | ||||
\(142\) | 1.52786 | 0.128216 | ||||||||
\(143\) | −15.7812 | + | 9.90659i | −1.31969 | + | 0.828431i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.118034 | − | 0.363271i | 0.00980219 | − | 0.0301680i | ||||
\(146\) | 10.8541 | − | 7.88597i | 0.898292 | − | 0.652647i | ||||
\(147\) | −4.42705 | − | 3.21644i | −0.365137 | − | 0.265288i | ||||
\(148\) | −2.66312 | − | 8.19624i | −0.218907 | − | 0.673727i | ||||
\(149\) | −1.66312 | − | 5.11855i | −0.136248 | − | 0.419328i | 0.859534 | − | 0.511079i | \(-0.170754\pi\) |
−0.995782 | + | 0.0917502i | \(0.970754\pi\) | |||||||
\(150\) | 0.809017 | + | 0.587785i | 0.0660560 | + | 0.0479925i | ||||
\(151\) | −2.47214 | + | 1.79611i | −0.201180 | + | 0.146166i | −0.683814 | − | 0.729656i | \(-0.739680\pi\) |
0.482634 | + | 0.875822i | \(0.339680\pi\) | |||||||
\(152\) | −1.00000 | + | 3.07768i | −0.0811107 | + | 0.249633i | ||||
\(153\) | 5.09017 | 0.411516 | ||||||||
\(154\) | 4.09017 | + | 0.277515i | 0.329595 | + | 0.0223628i | ||||
\(155\) | 3.61803 | 0.290607 | ||||||||
\(156\) | −1.73607 | + | 5.34307i | −0.138997 | + | 0.427788i | ||||
\(157\) | −19.6353 | + | 14.2658i | −1.56706 | + | 1.13854i | −0.637163 | + | 0.770729i | \(0.719892\pi\) |
−0.929901 | + | 0.367809i | \(0.880108\pi\) | |||||||
\(158\) | −5.73607 | − | 4.16750i | −0.456337 | − | 0.331548i | ||||
\(159\) | 0.145898 | + | 0.449028i | 0.0115705 | + | 0.0356102i | ||||
\(160\) | −0.309017 | − | 0.951057i | −0.0244299 | − | 0.0751876i | ||||
\(161\) | −0.145898 | − | 0.106001i | −0.0114984 | − | 0.00835406i | ||||
\(162\) | −0.809017 | + | 0.587785i | −0.0635624 | + | 0.0461808i | ||||
\(163\) | −1.80902 | + | 5.56758i | −0.141693 | + | 0.436087i | −0.996571 | − | 0.0827427i | \(-0.973632\pi\) |
0.854878 | + | 0.518829i | \(0.173632\pi\) | |||||||
\(164\) | −3.23607 | −0.252694 | ||||||||
\(165\) | 0.809017 | + | 3.21644i | 0.0629819 | + | 0.250400i | ||||
\(166\) | 4.00000 | 0.310460 | ||||||||
\(167\) | 6.26393 | − | 19.2784i | 0.484718 | − | 1.49181i | −0.347672 | − | 0.937616i | \(-0.613028\pi\) |
0.832389 | − | 0.554191i | \(-0.186972\pi\) | |||||||
\(168\) | 1.00000 | − | 0.726543i | 0.0771517 | − | 0.0560540i | ||||
\(169\) | −15.0172 | − | 10.9106i | −1.15517 | − | 0.839281i | ||||
\(170\) | −1.57295 | − | 4.84104i | −0.120640 | − | 0.371291i | ||||
\(171\) | −1.00000 | − | 3.07768i | −0.0764719 | − | 0.235356i | ||||
\(172\) | −8.97214 | − | 6.51864i | −0.684119 | − | 0.497042i | ||||
\(173\) | 14.9443 | − | 10.8576i | 1.13619 | − | 0.825492i | 0.149608 | − | 0.988745i | \(-0.452199\pi\) |
0.986584 | + | 0.163254i | \(0.0521989\pi\) | |||||||
\(174\) | 0.118034 | − | 0.363271i | 0.00894813 | − | 0.0275395i | ||||
\(175\) | 1.23607 | 0.0934380 | ||||||||
\(176\) | 1.23607 | − | 3.07768i | 0.0931721 | − | 0.231989i | ||||
\(177\) | −2.90983 | −0.218716 | ||||||||
\(178\) | 3.94427 | − | 12.1392i | 0.295636 | − | 0.909873i | ||||
\(179\) | −20.1074 | + | 14.6089i | −1.50290 | + | 1.09192i | −0.533687 | + | 0.845682i | \(0.679194\pi\) |
−0.969210 | + | 0.246237i | \(0.920806\pi\) | |||||||
\(180\) | 0.809017 | + | 0.587785i | 0.0603006 | + | 0.0438109i | ||||
\(181\) | −4.29180 | − | 13.2088i | −0.319007 | − | 0.981802i | −0.974074 | − | 0.226231i | \(-0.927360\pi\) |
0.655067 | − | 0.755571i | \(-0.272640\pi\) | |||||||
\(182\) | 2.14590 | + | 6.60440i | 0.159065 | + | 0.489550i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.118034 | + | 0.0857567i | −0.00870158 | + | 0.00632207i | ||||
\(185\) | 2.66312 | − | 8.19624i | 0.195796 | − | 0.602599i | ||||
\(186\) | 3.61803 | 0.265287 | ||||||||
\(187\) | 6.29180 | − | 15.6659i | 0.460102 | − | 1.14561i | ||||
\(188\) | 11.3262 | 0.826051 | ||||||||
\(189\) | −0.381966 | + | 1.17557i | −0.0277839 | + | 0.0855102i | ||||
\(190\) | −2.61803 | + | 1.90211i | −0.189932 | + | 0.137994i | ||||
\(191\) | −3.85410 | − | 2.80017i | −0.278873 | − | 0.202613i | 0.439553 | − | 0.898217i | \(-0.355137\pi\) |
−0.718426 | + | 0.695604i | \(0.755137\pi\) | |||||||
\(192\) | −0.309017 | − | 0.951057i | −0.0223014 | − | 0.0686366i | ||||
\(193\) | −0.944272 | − | 2.90617i | −0.0679702 | − | 0.209191i | 0.911302 | − | 0.411738i | \(-0.135078\pi\) |
−0.979273 | + | 0.202547i | \(0.935078\pi\) | |||||||
\(194\) | 10.2361 | + | 7.43694i | 0.734907 | + | 0.533941i | ||||
\(195\) | −4.54508 | + | 3.30220i | −0.325480 | + | 0.236475i | ||||
\(196\) | −1.69098 | + | 5.20431i | −0.120785 | + | 0.371736i | ||||
\(197\) | −6.94427 | −0.494759 | −0.247379 | − | 0.968919i | \(-0.579569\pi\) | ||||
−0.247379 | + | 0.968919i | \(0.579569\pi\) | |||||||
\(198\) | 0.809017 | + | 3.21644i | 0.0574943 | + | 0.228582i | ||||
\(199\) | −20.9787 | −1.48714 | −0.743571 | − | 0.668657i | \(-0.766869\pi\) | ||||
−0.743571 | + | 0.668657i | \(0.766869\pi\) | |||||||
\(200\) | 0.309017 | − | 0.951057i | 0.0218508 | − | 0.0672499i | ||||
\(201\) | 4.92705 | − | 3.57971i | 0.347527 | − | 0.252493i | ||||
\(202\) | −10.8262 | − | 7.86572i | −0.761731 | − | 0.553430i | ||||
\(203\) | −0.145898 | − | 0.449028i | −0.0102400 | − | 0.0315156i | ||||
\(204\) | −1.57295 | − | 4.84104i | −0.110128 | − | 0.338941i | ||||
\(205\) | −2.61803 | − | 1.90211i | −0.182851 | − | 0.132849i | ||||
\(206\) | −9.09017 | + | 6.60440i | −0.633342 | + | 0.460150i | ||||
\(207\) | 0.0450850 | − | 0.138757i | 0.00313362 | − | 0.00964430i | ||||
\(208\) | 5.61803 | 0.389541 | ||||||||
\(209\) | −10.7082 | − | 0.726543i | −0.740702 | − | 0.0502560i | ||||
\(210\) | 1.23607 | 0.0852968 | ||||||||
\(211\) | −6.41641 | + | 19.7477i | −0.441724 | + | 1.35949i | 0.444313 | + | 0.895871i | \(0.353448\pi\) |
−0.886037 | + | 0.463614i | \(0.846552\pi\) | |||||||
\(212\) | 0.381966 | − | 0.277515i | 0.0262335 | − | 0.0190598i | ||||
\(213\) | 1.23607 | + | 0.898056i | 0.0846940 | + | 0.0615338i | ||||
\(214\) | 6.09017 | + | 18.7436i | 0.416315 | + | 1.28129i | ||||
\(215\) | −3.42705 | − | 10.5474i | −0.233723 | − | 0.719325i | ||||
\(216\) | 0.809017 | + | 0.587785i | 0.0550466 | + | 0.0399937i | ||||
\(217\) | 3.61803 | − | 2.62866i | 0.245608 | − | 0.178445i | ||||
\(218\) | 2.00000 | − | 6.15537i | 0.135457 | − | 0.416894i | ||||
\(219\) | 13.4164 | 0.906597 | ||||||||
\(220\) | 2.80902 | − | 1.76336i | 0.189384 | − | 0.118885i | ||||
\(221\) | 28.5967 | 1.92363 | ||||||||
\(222\) | 2.66312 | − | 8.19624i | 0.178737 | − | 0.550095i | ||||
\(223\) | −2.23607 | + | 1.62460i | −0.149738 | + | 0.108791i | −0.660132 | − | 0.751150i | \(-0.729500\pi\) |
0.510394 | + | 0.859941i | \(0.329500\pi\) | |||||||
\(224\) | −1.00000 | − | 0.726543i | −0.0668153 | − | 0.0485442i | ||||
\(225\) | 0.309017 | + | 0.951057i | 0.0206011 | + | 0.0634038i | ||||
\(226\) | 0.173762 | + | 0.534785i | 0.0115585 | + | 0.0355733i | ||||
\(227\) | 19.7082 | + | 14.3188i | 1.30808 | + | 0.950375i | 1.00000 | 0.000985137i | \(-0.000313579\pi\) | |
0.308080 | + | 0.951360i | \(0.400314\pi\) | |||||||
\(228\) | −2.61803 | + | 1.90211i | −0.173384 | + | 0.125971i | ||||
\(229\) | 1.61803 | − | 4.97980i | 0.106923 | − | 0.329074i | −0.883254 | − | 0.468894i | \(-0.844652\pi\) |
0.990177 | + | 0.139820i | \(0.0446525\pi\) | |||||||
\(230\) | −0.145898 | −0.00962023 | ||||||||
\(231\) | 3.14590 | + | 2.62866i | 0.206985 | + | 0.172953i | ||||
\(232\) | −0.381966 | −0.0250773 | ||||||||
\(233\) | −7.59017 | + | 23.3601i | −0.497249 | + | 1.53037i | 0.316174 | + | 0.948701i | \(0.397602\pi\) |
−0.813423 | + | 0.581673i | \(0.802398\pi\) | |||||||
\(234\) | −4.54508 | + | 3.30220i | −0.297121 | + | 0.215871i | ||||
\(235\) | 9.16312 | + | 6.65740i | 0.597736 | + | 0.434281i | ||||
\(236\) | 0.899187 | + | 2.76741i | 0.0585321 | + | 0.180143i | ||||
\(237\) | −2.19098 | − | 6.74315i | −0.142320 | − | 0.438015i | ||||
\(238\) | −5.09017 | − | 3.69822i | −0.329947 | − | 0.239720i | ||||
\(239\) | −1.00000 | + | 0.726543i | −0.0646846 | + | 0.0469961i | −0.619658 | − | 0.784872i | \(-0.712729\pi\) |
0.554973 | + | 0.831868i | \(0.312729\pi\) | |||||||
\(240\) | 0.309017 | − | 0.951057i | 0.0199470 | − | 0.0613904i | ||||
\(241\) | 11.8885 | 0.765808 | 0.382904 | − | 0.923788i | \(-0.374924\pi\) | ||||
0.382904 | + | 0.923788i | \(0.374924\pi\) | |||||||
\(242\) | 10.8992 | + | 1.48584i | 0.700626 | + | 0.0955135i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.42705 | + | 3.21644i | −0.282834 | + | 0.205491i | ||||
\(246\) | −2.61803 | − | 1.90211i | −0.166920 | − | 0.121274i | ||||
\(247\) | −5.61803 | − | 17.2905i | −0.357467 | − | 1.10017i | ||||
\(248\) | −1.11803 | − | 3.44095i | −0.0709952 | − | 0.218501i | ||||
\(249\) | 3.23607 | + | 2.35114i | 0.205077 | + | 0.148998i | ||||
\(250\) | 0.809017 | − | 0.587785i | 0.0511667 | − | 0.0371748i | ||||
\(251\) | 3.28115 | − | 10.0984i | 0.207105 | − | 0.637402i | −0.792516 | − | 0.609851i | \(-0.791229\pi\) |
0.999620 | − | 0.0275509i | \(-0.00877084\pi\) | |||||||
\(252\) | 1.23607 | 0.0778650 | ||||||||
\(253\) | −0.371323 | − | 0.310271i | −0.0233449 | − | 0.0195066i | ||||
\(254\) | −16.6525 | −1.04487 | ||||||||
\(255\) | 1.57295 | − | 4.84104i | 0.0985019 | − | 0.303158i | ||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 11.6180 | + | 8.44100i | 0.724713 | + | 0.526535i | 0.887887 | − | 0.460063i | \(-0.152173\pi\) |
−0.163173 | + | 0.986597i | \(0.552173\pi\) | |||||||
\(258\) | −3.42705 | − | 10.5474i | −0.213359 | − | 0.656651i | ||||
\(259\) | −3.29180 | − | 10.1311i | −0.204542 | − | 0.629516i | ||||
\(260\) | 4.54508 | + | 3.30220i | 0.281874 | + | 0.204794i | ||||
\(261\) | 0.309017 | − | 0.224514i | 0.0191277 | − | 0.0138971i | ||||
\(262\) | −1.73607 | + | 5.34307i | −0.107255 | + | 0.330096i | ||||
\(263\) | 0.145898 | 0.00899646 | 0.00449823 | − | 0.999990i | \(-0.498568\pi\) | ||||
0.00449823 | + | 0.999990i | \(0.498568\pi\) | |||||||
\(264\) | 2.80902 | − | 1.76336i | 0.172883 | − | 0.108527i | ||||
\(265\) | 0.472136 | 0.0290031 | ||||||||
\(266\) | −1.23607 | + | 3.80423i | −0.0757882 | + | 0.233252i | ||||
\(267\) | 10.3262 | − | 7.50245i | 0.631955 | − | 0.459143i | ||||
\(268\) | −4.92705 | − | 3.57971i | −0.300968 | − | 0.218666i | ||||
\(269\) | 8.59017 | + | 26.4378i | 0.523752 | + | 1.61194i | 0.766771 | + | 0.641921i | \(0.221862\pi\) |
−0.243019 | + | 0.970022i | \(0.578138\pi\) | |||||||
\(270\) | 0.309017 | + | 0.951057i | 0.0188062 | + | 0.0578795i | ||||
\(271\) | 6.97214 | + | 5.06555i | 0.423527 | + | 0.307710i | 0.779055 | − | 0.626955i | \(-0.215699\pi\) |
−0.355528 | + | 0.934666i | \(0.615699\pi\) | |||||||
\(272\) | −4.11803 | + | 2.99193i | −0.249692 | + | 0.181412i | ||||
\(273\) | −2.14590 | + | 6.60440i | −0.129876 | + | 0.399716i | ||||
\(274\) | 11.7984 | 0.712766 | ||||||||
\(275\) | 3.30902 | + | 0.224514i | 0.199541 | + | 0.0135387i | ||||
\(276\) | −0.145898 | −0.00878203 | ||||||||
\(277\) | 4.48278 | − | 13.7966i | 0.269344 | − | 0.828956i | −0.721317 | − | 0.692606i | \(-0.756463\pi\) |
0.990661 | − | 0.136350i | \(-0.0435373\pi\) | |||||||
\(278\) | −10.7082 | + | 7.77997i | −0.642235 | + | 0.466611i | ||||
\(279\) | 2.92705 | + | 2.12663i | 0.175238 | + | 0.127318i | ||||
\(280\) | −0.381966 | − | 1.17557i | −0.0228268 | − | 0.0702538i | ||||
\(281\) | −5.09017 | − | 15.6659i | −0.303654 | − | 0.934551i | −0.980176 | − | 0.198129i | \(-0.936514\pi\) |
0.676522 | − | 0.736422i | \(-0.263486\pi\) | |||||||
\(282\) | 9.16312 | + | 6.65740i | 0.545656 | + | 0.396442i | ||||
\(283\) | 5.39919 | − | 3.92274i | 0.320948 | − | 0.233183i | −0.415632 | − | 0.909533i | \(-0.636439\pi\) |
0.736580 | + | 0.676350i | \(0.236439\pi\) | |||||||
\(284\) | 0.472136 | − | 1.45309i | 0.0280161 | − | 0.0862247i | ||||
\(285\) | −3.23607 | −0.191688 | ||||||||
\(286\) | 4.54508 | + | 18.0701i | 0.268757 | + | 1.06851i | ||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | 0.309017 | − | 0.951057i | 0.0182090 | − | 0.0560415i | ||||
\(289\) | −7.20820 | + | 5.23707i | −0.424012 | + | 0.308063i | ||||
\(290\) | −0.309017 | − | 0.224514i | −0.0181461 | − | 0.0131839i | ||||
\(291\) | 3.90983 | + | 12.0332i | 0.229198 | + | 0.705400i | ||||
\(292\) | −4.14590 | − | 12.7598i | −0.242620 | − | 0.746709i | ||||
\(293\) | 16.1803 | + | 11.7557i | 0.945266 | + | 0.686776i | 0.949682 | − | 0.313215i | \(-0.101406\pi\) |
−0.00441682 | + | 0.999990i | \(0.501406\pi\) | |||||||
\(294\) | −4.42705 | + | 3.21644i | −0.258191 | + | 0.187587i | ||||
\(295\) | −0.899187 | + | 2.76741i | −0.0523527 | + | 0.161125i | ||||
\(296\) | −8.61803 | −0.500913 | ||||||||
\(297\) | −1.23607 | + | 3.07768i | −0.0717239 | + | 0.178585i | ||||
\(298\) | −5.38197 | −0.311769 | ||||||||
\(299\) | 0.253289 | − | 0.779543i | 0.0146481 | − | 0.0450821i | ||||
\(300\) | 0.809017 | − | 0.587785i | 0.0467086 | − | 0.0339358i | ||||
\(301\) | −11.0902 | − | 8.05748i | −0.639227 | − | 0.464425i | ||||
\(302\) | 0.944272 | + | 2.90617i | 0.0543367 | + | 0.167231i | ||||
\(303\) | −4.13525 | − | 12.7270i | −0.237564 | − | 0.731147i | ||||
\(304\) | 2.61803 | + | 1.90211i | 0.150155 | + | 0.109094i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.57295 | − | 4.84104i | 0.0899195 | − | 0.276744i | ||||
\(307\) | 22.4508 | 1.28134 | 0.640669 | − | 0.767817i | \(-0.278657\pi\) | ||||
0.640669 | + | 0.767817i | \(0.278657\pi\) | |||||||
\(308\) | 1.52786 | − | 3.80423i | 0.0870581 | − | 0.216766i | ||||
\(309\) | −11.2361 | −0.639198 | ||||||||
\(310\) | 1.11803 | − | 3.44095i | 0.0635001 | − | 0.195433i | ||||
\(311\) | −3.85410 | + | 2.80017i | −0.218546 | + | 0.158783i | −0.691672 | − | 0.722212i | \(-0.743126\pi\) |
0.473126 | + | 0.880995i | \(0.343126\pi\) | |||||||
\(312\) | 4.54508 | + | 3.30220i | 0.257315 | + | 0.186950i | ||||
\(313\) | −0.145898 | − | 0.449028i | −0.00824664 | − | 0.0253806i | 0.946849 | − | 0.321680i | \(-0.104247\pi\) |
−0.955095 | + | 0.296299i | \(0.904247\pi\) | |||||||
\(314\) | 7.50000 | + | 23.0826i | 0.423249 | + | 1.30263i | ||||
\(315\) | 1.00000 | + | 0.726543i | 0.0563436 | + | 0.0409360i | ||||
\(316\) | −5.73607 | + | 4.16750i | −0.322679 | + | 0.234440i | ||||
\(317\) | −0.180340 | + | 0.555029i | −0.0101289 | + | 0.0311735i | −0.955993 | − | 0.293389i | \(-0.905217\pi\) |
0.945864 | + | 0.324562i | \(0.105217\pi\) | |||||||
\(318\) | 0.472136 | 0.0264761 | ||||||||
\(319\) | −0.309017 | − | 1.22857i | −0.0173016 | − | 0.0687868i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −6.09017 | + | 18.7436i | −0.339920 | + | 1.04617i | ||||
\(322\) | −0.145898 | + | 0.106001i | −0.00813058 | + | 0.00590721i | ||||
\(323\) | 13.3262 | + | 9.68208i | 0.741492 | + | 0.538725i | ||||
\(324\) | 0.309017 | + | 0.951057i | 0.0171676 | + | 0.0528365i | ||||
\(325\) | 1.73607 | + | 5.34307i | 0.0962997 | + | 0.296380i | ||||
\(326\) | 4.73607 | + | 3.44095i | 0.262307 | + | 0.190577i | ||||
\(327\) | 5.23607 | − | 3.80423i | 0.289555 | − | 0.210374i | ||||
\(328\) | −1.00000 | + | 3.07768i | −0.0552158 | + | 0.169937i | ||||
\(329\) | 14.0000 | 0.771845 | ||||||||
\(330\) | 3.30902 | + | 0.224514i | 0.182155 | + | 0.0123591i | ||||
\(331\) | 4.76393 | 0.261849 | 0.130925 | − | 0.991392i | \(-0.458205\pi\) | ||||
0.130925 | + | 0.991392i | \(0.458205\pi\) | |||||||
\(332\) | 1.23607 | − | 3.80423i | 0.0678380 | − | 0.208784i | ||||
\(333\) | 6.97214 | − | 5.06555i | 0.382071 | − | 0.277591i | ||||
\(334\) | −16.3992 | − | 11.9147i | −0.897324 | − | 0.651944i | ||||
\(335\) | −1.88197 | − | 5.79210i | −0.102823 | − | 0.316456i | ||||
\(336\) | −0.381966 | − | 1.17557i | −0.0208380 | − | 0.0641326i | ||||
\(337\) | 8.70820 | + | 6.32688i | 0.474366 | + | 0.344647i | 0.799140 | − | 0.601144i | \(-0.205288\pi\) |
−0.324774 | + | 0.945792i | \(0.605288\pi\) | |||||||
\(338\) | −15.0172 | + | 10.9106i | −0.816829 | + | 0.593461i | ||||
\(339\) | −0.173762 | + | 0.534785i | −0.00943746 | + | 0.0290455i | ||||
\(340\) | −5.09017 | −0.276053 | ||||||||
\(341\) | 10.1631 | − | 6.37988i | 0.550364 | − | 0.345490i | ||||
\(342\) | −3.23607 | −0.174987 | ||||||||
\(343\) | −4.76393 | + | 14.6619i | −0.257228 | + | 0.791667i | ||||
\(344\) | −8.97214 | + | 6.51864i | −0.483745 | + | 0.351461i | ||||
\(345\) | −0.118034 | − | 0.0857567i | −0.00635474 | − | 0.00461699i | ||||
\(346\) | −5.70820 | − | 17.5680i | −0.306875 | − | 0.944464i | ||||
\(347\) | 0.0344419 | + | 0.106001i | 0.00184894 | + | 0.00569044i | 0.951977 | − | 0.306170i | \(-0.0990477\pi\) |
−0.950128 | + | 0.311861i | \(0.899048\pi\) | |||||||
\(348\) | −0.309017 | − | 0.224514i | −0.0165650 | − | 0.0120352i | ||||
\(349\) | −12.4721 | + | 9.06154i | −0.667618 | + | 0.485053i | −0.869227 | − | 0.494413i | \(-0.835383\pi\) |
0.201609 | + | 0.979466i | \(0.435383\pi\) | |||||||
\(350\) | 0.381966 | − | 1.17557i | 0.0204169 | − | 0.0628369i | ||||
\(351\) | −5.61803 | −0.299868 | ||||||||
\(352\) | −2.54508 | − | 2.12663i | −0.135653 | − | 0.113350i | ||||
\(353\) | 21.3820 | 1.13805 | 0.569024 | − | 0.822321i | \(-0.307321\pi\) | ||||
0.569024 | + | 0.822321i | \(0.307321\pi\) | |||||||
\(354\) | −0.899187 | + | 2.76741i | −0.0477912 | + | 0.147086i | ||||
\(355\) | 1.23607 | − | 0.898056i | 0.0656037 | − | 0.0476639i | ||||
\(356\) | −10.3262 | − | 7.50245i | −0.547290 | − | 0.397629i | ||||
\(357\) | −1.94427 | − | 5.98385i | −0.102902 | − | 0.316699i | ||||
\(358\) | 7.68034 | + | 23.6377i | 0.405919 | + | 1.24929i | ||||
\(359\) | −8.23607 | − | 5.98385i | −0.434683 | − | 0.315816i | 0.348836 | − | 0.937184i | \(-0.386577\pi\) |
−0.783519 | + | 0.621368i | \(0.786577\pi\) | |||||||
\(360\) | 0.809017 | − | 0.587785i | 0.0426389 | − | 0.0309790i | ||||
\(361\) | −2.63525 | + | 8.11048i | −0.138698 | + | 0.426867i | ||||
\(362\) | −13.8885 | −0.729966 | ||||||||
\(363\) | 7.94427 | + | 7.60845i | 0.416966 | + | 0.399340i | ||||
\(364\) | 6.94427 | 0.363979 | ||||||||
\(365\) | 4.14590 | − | 12.7598i | 0.217006 | − | 0.667876i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.2705 | + | 18.3601i | 1.31911 | + | 0.958389i | 0.999943 | + | 0.0106909i | \(0.00340310\pi\) |
0.319167 | + | 0.947698i | \(0.396597\pi\) | |||||||
\(368\) | 0.0450850 | + | 0.138757i | 0.00235022 | + | 0.00723322i | ||||
\(369\) | −1.00000 | − | 3.07768i | −0.0520579 | − | 0.160218i | ||||
\(370\) | −6.97214 | − | 5.06555i | −0.362464 | − | 0.263346i | ||||
\(371\) | 0.472136 | − | 0.343027i | 0.0245121 | − | 0.0178091i | ||||
\(372\) | 1.11803 | − | 3.44095i | 0.0579674 | − | 0.178405i | ||||
\(373\) | −20.4721 | −1.06001 | −0.530004 | − | 0.847995i | \(-0.677809\pi\) | ||||
−0.530004 | + | 0.847995i | \(0.677809\pi\) | |||||||
\(374\) | −12.9549 | − | 10.8249i | −0.669883 | − | 0.559742i | ||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 3.50000 | − | 10.7719i | 0.180499 | − | 0.555518i | ||||
\(377\) | 1.73607 | − | 1.26133i | 0.0894120 | − | 0.0649617i | ||||
\(378\) | 1.00000 | + | 0.726543i | 0.0514344 | + | 0.0373693i | ||||
\(379\) | 10.0000 | + | 30.7768i | 0.513665 | + | 1.58090i | 0.785697 | + | 0.618612i | \(0.212304\pi\) |
−0.272032 | + | 0.962288i | \(0.587696\pi\) | |||||||
\(380\) | 1.00000 | + | 3.07768i | 0.0512989 | + | 0.157882i | ||||
\(381\) | −13.4721 | − | 9.78808i | −0.690198 | − | 0.501459i | ||||
\(382\) | −3.85410 | + | 2.80017i | −0.197193 | + | 0.143269i | ||||
\(383\) | 4.73607 | − | 14.5761i | 0.242002 | − | 0.744805i | −0.754113 | − | 0.656744i | \(-0.771933\pi\) |
0.996115 | − | 0.0880606i | \(-0.0280669\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 3.47214 | − | 2.17963i | 0.176956 | − | 0.111084i | ||||
\(386\) | −3.05573 | −0.155532 | ||||||||
\(387\) | 3.42705 | − | 10.5474i | 0.174207 | − | 0.536153i | ||||
\(388\) | 10.2361 | − | 7.43694i | 0.519658 | − | 0.377553i | ||||
\(389\) | −0.118034 | − | 0.0857567i | −0.00598456 | − | 0.00434804i | 0.584789 | − | 0.811185i | \(-0.301177\pi\) |
−0.590774 | + | 0.806837i | \(0.701177\pi\) | |||||||
\(390\) | 1.73607 | + | 5.34307i | 0.0879092 | + | 0.270557i | ||||
\(391\) | 0.229490 | + | 0.706298i | 0.0116058 | + | 0.0357190i | ||||
\(392\) | 4.42705 | + | 3.21644i | 0.223600 | + | 0.162455i | ||||
\(393\) | −4.54508 | + | 3.30220i | −0.229269 | + | 0.166574i | ||||
\(394\) | −2.14590 | + | 6.60440i | −0.108109 | + | 0.332725i | ||||
\(395\) | −7.09017 | −0.356745 | ||||||||
\(396\) | 3.30902 | + | 0.224514i | 0.166284 | + | 0.0112823i | ||||
\(397\) | 26.7984 | 1.34497 | 0.672486 | − | 0.740110i | \(-0.265227\pi\) | ||||
0.672486 | + | 0.740110i | \(0.265227\pi\) | |||||||
\(398\) | −6.48278 | + | 19.9519i | −0.324952 | + | 1.00010i | ||||
\(399\) | −3.23607 | + | 2.35114i | −0.162006 | + | 0.117704i | ||||
\(400\) | −0.809017 | − | 0.587785i | −0.0404508 | − | 0.0293893i | ||||
\(401\) | −11.1459 | − | 34.3035i | −0.556600 | − | 1.71304i | −0.691681 | − | 0.722203i | \(-0.743130\pi\) |
0.135082 | − | 0.990834i | \(-0.456870\pi\) | |||||||
\(402\) | −1.88197 | − | 5.79210i | −0.0938639 | − | 0.288883i | ||||
\(403\) | 16.4443 | + | 11.9475i | 0.819148 | + | 0.595146i | ||||
\(404\) | −10.8262 | + | 7.86572i | −0.538625 | + | 0.391334i | ||||
\(405\) | −0.309017 | + | 0.951057i | −0.0153552 | + | 0.0472584i | ||||
\(406\) | −0.472136 | −0.0234317 | ||||||||
\(407\) | −6.97214 | − | 27.7194i | −0.345596 | − | 1.37400i | ||||
\(408\) | −5.09017 | −0.252001 | ||||||||
\(409\) | −10.5000 | + | 32.3157i | −0.519192 | + | 1.59791i | 0.256332 | + | 0.966589i | \(0.417486\pi\) |
−0.775524 | + | 0.631319i | \(0.782514\pi\) | |||||||
\(410\) | −2.61803 | + | 1.90211i | −0.129295 | + | 0.0939387i | ||||
\(411\) | 9.54508 | + | 6.93491i | 0.470824 | + | 0.342074i | ||||
\(412\) | 3.47214 | + | 10.6861i | 0.171060 | + | 0.526468i | ||||
\(413\) | 1.11146 | + | 3.42071i | 0.0546912 | + | 0.168322i | ||||
\(414\) | −0.118034 | − | 0.0857567i | −0.00580105 | − | 0.00421471i | ||||
\(415\) | 3.23607 | − | 2.35114i | 0.158852 | − | 0.115413i | ||||
\(416\) | 1.73607 | − | 5.34307i | 0.0851177 | − | 0.261965i | ||||
\(417\) | −13.2361 | −0.648173 | ||||||||
\(418\) | −4.00000 | + | 9.95959i | −0.195646 | + | 0.487140i | ||||
\(419\) | 16.1459 | 0.788779 | 0.394389 | − | 0.918943i | \(-0.370956\pi\) | ||||
0.394389 | + | 0.918943i | \(0.370956\pi\) | |||||||
\(420\) | 0.381966 | − | 1.17557i | 0.0186380 | − | 0.0573620i | ||||
\(421\) | −5.23607 | + | 3.80423i | −0.255190 | + | 0.185407i | −0.708024 | − | 0.706188i | \(-0.750413\pi\) |
0.452834 | + | 0.891595i | \(0.350413\pi\) | |||||||
\(422\) | 16.7984 | + | 12.2047i | 0.817732 | + | 0.594117i | ||||
\(423\) | 3.50000 | + | 10.7719i | 0.170176 | + | 0.523747i | ||||
\(424\) | −0.145898 | − | 0.449028i | −0.00708543 | − | 0.0218067i | ||||
\(425\) | −4.11803 | − | 2.99193i | −0.199754 | − | 0.145130i | ||||
\(426\) | 1.23607 | − | 0.898056i | 0.0598877 | − | 0.0435110i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 19.7082 | 0.952632 | ||||||||
\(429\) | −6.94427 | + | 17.2905i | −0.335273 | + | 0.834795i | ||||
\(430\) | −11.0902 | −0.534815 | ||||||||
\(431\) | −6.90983 | + | 21.2663i | −0.332835 | + | 1.02436i | 0.634944 | + | 0.772558i | \(0.281023\pi\) |
−0.967779 | + | 0.251802i | \(0.918977\pi\) | |||||||
\(432\) | 0.809017 | − | 0.587785i | 0.0389238 | − | 0.0282798i | ||||
\(433\) | −24.9443 | − | 18.1231i | −1.19875 | − | 0.870939i | −0.204584 | − | 0.978849i | \(-0.565584\pi\) |
−0.994161 | + | 0.107910i | \(0.965584\pi\) | |||||||
\(434\) | −1.38197 | − | 4.25325i | −0.0663365 | − | 0.204163i | ||||
\(435\) | −0.118034 | − | 0.363271i | −0.00565930 | − | 0.0174175i | ||||
\(436\) | −5.23607 | − | 3.80423i | −0.250762 | − | 0.182189i | ||||
\(437\) | 0.381966 | − | 0.277515i | 0.0182719 | − | 0.0132753i | ||||
\(438\) | 4.14590 | − | 12.7598i | 0.198099 | − | 0.609685i | ||||
\(439\) | 17.3262 | 0.826936 | 0.413468 | − | 0.910519i | \(-0.364317\pi\) | ||||
0.413468 | + | 0.910519i | \(0.364317\pi\) | |||||||
\(440\) | −0.809017 | − | 3.21644i | −0.0385684 | − | 0.153338i | ||||
\(441\) | −5.47214 | −0.260578 | ||||||||
\(442\) | 8.83688 | − | 27.1971i | 0.420328 | − | 1.29364i | ||||
\(443\) | −10.2361 | + | 7.43694i | −0.486330 | + | 0.353340i | −0.803771 | − | 0.594938i | \(-0.797176\pi\) |
0.317441 | + | 0.948278i | \(0.397176\pi\) | |||||||
\(444\) | −6.97214 | − | 5.06555i | −0.330883 | − | 0.240401i | ||||
\(445\) | −3.94427 | − | 12.1392i | −0.186976 | − | 0.575454i | ||||
\(446\) | 0.854102 | + | 2.62866i | 0.0404429 | + | 0.124470i | ||||
\(447\) | −4.35410 | − | 3.16344i | −0.205942 | − | 0.149626i | ||||
\(448\) | −1.00000 | + | 0.726543i | −0.0472456 | + | 0.0343259i | ||||
\(449\) | 9.00000 | − | 27.6992i | 0.424736 | − | 1.30720i | −0.478510 | − | 0.878082i | \(-0.658823\pi\) |
0.903247 | − | 0.429122i | \(-0.141177\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −10.7082 | − | 0.726543i | −0.504230 | − | 0.0342116i | ||||
\(452\) | 0.562306 | 0.0264486 | ||||||||
\(453\) | −0.944272 | + | 2.90617i | −0.0443658 | + | 0.136544i | ||||
\(454\) | 19.7082 | − | 14.3188i | 0.924952 | − | 0.672017i | ||||
\(455\) | 5.61803 | + | 4.08174i | 0.263377 | + | 0.191355i | ||||
\(456\) | 1.00000 | + | 3.07768i | 0.0468293 | + | 0.144126i | ||||
\(457\) | −8.23607 | − | 25.3480i | −0.385267 | − | 1.18573i | −0.936286 | − | 0.351237i | \(-0.885761\pi\) |
0.551019 | − | 0.834492i | \(-0.314239\pi\) | |||||||
\(458\) | −4.23607 | − | 3.07768i | −0.197938 | − | 0.143811i | ||||
\(459\) | 4.11803 | − | 2.99193i | 0.192213 | − | 0.139651i | ||||
\(460\) | −0.0450850 | + | 0.138757i | −0.00210210 | + | 0.00646959i | ||||
\(461\) | −28.2148 | −1.31409 | −0.657047 | − | 0.753850i | \(-0.728195\pi\) | ||||
−0.657047 | + | 0.753850i | \(0.728195\pi\) | |||||||
\(462\) | 3.47214 | − | 2.17963i | 0.161538 | − | 0.101405i | ||||
\(463\) | −23.8885 | −1.11019 | −0.555097 | − | 0.831785i | \(-0.687319\pi\) | ||||
−0.555097 | + | 0.831785i | \(0.687319\pi\) | |||||||
\(464\) | −0.118034 | + | 0.363271i | −0.00547959 | + | 0.0168644i | ||||
\(465\) | 2.92705 | − | 2.12663i | 0.135739 | − | 0.0986200i | ||||
\(466\) | 19.8713 | + | 14.4374i | 0.920521 | + | 0.668798i | ||||
\(467\) | −11.9098 | − | 36.6547i | −0.551121 | − | 1.69618i | −0.705973 | − | 0.708239i | \(-0.749490\pi\) |
0.154852 | − | 0.987938i | \(-0.450510\pi\) | |||||||
\(468\) | 1.73607 | + | 5.34307i | 0.0802498 | + | 0.246983i | ||||
\(469\) | −6.09017 | − | 4.42477i | −0.281218 | − | 0.204317i | ||||
\(470\) | 9.16312 | − | 6.65740i | 0.422663 | − | 0.307083i | ||||
\(471\) | −7.50000 | + | 23.0826i | −0.345582 | + | 1.06359i | ||||
\(472\) | 2.90983 | 0.133936 | ||||||||
\(473\) | −28.2254 | − | 23.5847i | −1.29781 | − | 1.08442i | ||||
\(474\) | −7.09017 | −0.325662 | ||||||||
\(475\) | −1.00000 | + | 3.07768i | −0.0458831 | + | 0.141214i | ||||
\(476\) | −5.09017 | + | 3.69822i | −0.233308 | + | 0.169508i | ||||
\(477\) | 0.381966 | + | 0.277515i | 0.0174890 | + | 0.0127065i | ||||
\(478\) | 0.381966 | + | 1.17557i | 0.0174707 | + | 0.0537693i | ||||
\(479\) | 5.32624 | + | 16.3925i | 0.243362 | + | 0.748991i | 0.995902 | + | 0.0904442i | \(0.0288287\pi\) |
−0.752540 | + | 0.658547i | \(0.771171\pi\) | |||||||
\(480\) | −0.809017 | − | 0.587785i | −0.0369264 | − | 0.0268286i | ||||
\(481\) | 39.1697 | − | 28.4585i | 1.78598 | − | 1.29759i | ||||
\(482\) | 3.67376 | − | 11.3067i | 0.167335 | − | 0.515005i | ||||
\(483\) | −0.180340 | −0.00820575 | ||||||||
\(484\) | 4.78115 | − | 9.90659i | 0.217325 | − | 0.450300i | ||||
\(485\) | 12.6525 | 0.574519 | ||||||||
\(486\) | −0.309017 | + | 0.951057i | −0.0140173 | + | 0.0431408i | ||||
\(487\) | 12.4721 | − | 9.06154i | 0.565166 | − | 0.410617i | −0.268180 | − | 0.963369i | \(-0.586422\pi\) |
0.833346 | + | 0.552751i | \(0.186422\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.80902 | + | 5.56758i | 0.0818066 | + | 0.251775i | ||||
\(490\) | 1.69098 | + | 5.20431i | 0.0763908 | + | 0.235107i | ||||
\(491\) | 0.836881 | + | 0.608030i | 0.0377679 | + | 0.0274400i | 0.606509 | − | 0.795077i | \(-0.292569\pi\) |
−0.568741 | + | 0.822517i | \(0.692569\pi\) | |||||||
\(492\) | −2.61803 | + | 1.90211i | −0.118030 | + | 0.0857539i | ||||
\(493\) | −0.600813 | + | 1.84911i | −0.0270593 | + | 0.0832798i | ||||
\(494\) | −18.1803 | −0.817972 | ||||||||
\(495\) | 2.54508 | + | 2.12663i | 0.114393 | + | 0.0955848i | ||||
\(496\) | −3.61803 | −0.162455 | ||||||||
\(497\) | 0.583592 | − | 1.79611i | 0.0261777 | − | 0.0805666i | ||||
\(498\) | 3.23607 | − | 2.35114i | 0.145012 | − | 0.105357i | ||||
\(499\) | 19.0344 | + | 13.8293i | 0.852099 | + | 0.619086i | 0.925724 | − | 0.378200i | \(-0.123457\pi\) |
−0.0736252 | + | 0.997286i | \(0.523457\pi\) | |||||||
\(500\) | −0.309017 | − | 0.951057i | −0.0138197 | − | 0.0425325i | ||||
\(501\) | −6.26393 | − | 19.2784i | −0.279852 | − | 0.861295i | ||||
\(502\) | −8.59017 | − | 6.24112i | −0.383398 | − | 0.278555i | ||||
\(503\) | 7.01722 | − | 5.09831i | 0.312882 | − | 0.227322i | −0.420250 | − | 0.907408i | \(-0.638058\pi\) |
0.733132 | + | 0.680086i | \(0.238058\pi\) | |||||||
\(504\) | 0.381966 | − | 1.17557i | 0.0170141 | − | 0.0523641i | ||||
\(505\) | −13.3820 | −0.595490 | ||||||||
\(506\) | −0.409830 | + | 0.257270i | −0.0182192 | + | 0.0114371i | ||||
\(507\) | −18.5623 | −0.824381 | ||||||||
\(508\) | −5.14590 | + | 15.8374i | −0.228312 | + | 0.702673i | ||||
\(509\) | 12.7812 | − | 9.28605i | 0.566515 | − | 0.411597i | −0.267323 | − | 0.963607i | \(-0.586139\pi\) |
0.833837 | + | 0.552010i | \(0.186139\pi\) | |||||||
\(510\) | −4.11803 | − | 2.99193i | −0.182350 | − | 0.132485i | ||||
\(511\) | −5.12461 | − | 15.7719i | −0.226699 | − | 0.697709i | ||||
\(512\) | 0.309017 | + | 0.951057i | 0.0136568 | + | 0.0420312i | ||||
\(513\) | −2.61803 | − | 1.90211i | −0.115589 | − | 0.0839803i | ||||
\(514\) | 11.6180 | − | 8.44100i | 0.512450 | − | 0.372316i | ||||
\(515\) | −3.47214 | + | 10.6861i | −0.153001 | + | 0.470887i | ||||
\(516\) | −11.0902 | −0.488218 | ||||||||
\(517\) | 37.4787 | + | 2.54290i | 1.64831 | + | 0.111837i | ||||
\(518\) | −10.6525 | −0.468043 | ||||||||
\(519\) | 5.70820 | − | 17.5680i | 0.250562 | − | 0.771152i | ||||
\(520\) | 4.54508 | − | 3.30220i | 0.199315 | − | 0.144811i | ||||
\(521\) | −34.2705 | − | 24.8990i | −1.50142 | − | 1.09084i | −0.969812 | − | 0.243852i | \(-0.921589\pi\) |
−0.531606 | − | 0.846992i | \(-0.678411\pi\) | |||||||
\(522\) | −0.118034 | − | 0.363271i | −0.00516621 | − | 0.0159000i | ||||
\(523\) | −4.58359 | − | 14.1068i | −0.200426 | − | 0.616849i | −0.999870 | − | 0.0161084i | \(-0.994872\pi\) |
0.799444 | − | 0.600741i | \(-0.205128\pi\) | |||||||
\(524\) | 4.54508 | + | 3.30220i | 0.198553 | + | 0.144257i | ||||
\(525\) | 1.00000 | − | 0.726543i | 0.0436436 | − | 0.0317089i | ||||
\(526\) | 0.0450850 | − | 0.138757i | 0.00196580 | − | 0.00605010i | ||||
\(527\) | −18.4164 | −0.802231 | ||||||||
\(528\) | −0.809017 | − | 3.21644i | −0.0352079 | − | 0.139978i | ||||
\(529\) | −22.9787 | −0.999075 | ||||||||
\(530\) | 0.145898 | − | 0.449028i | 0.00633741 | − | 0.0195045i | ||||
\(531\) | −2.35410 | + | 1.71036i | −0.102159 | + | 0.0742231i | ||||
\(532\) | 3.23607 | + | 2.35114i | 0.140301 | + | 0.101935i | ||||
\(533\) | −5.61803 | − | 17.2905i | −0.243344 | − | 0.748936i | ||||
\(534\) | −3.94427 | − | 12.1392i | −0.170685 | − | 0.525315i | ||||
\(535\) | 15.9443 | + | 11.5842i | 0.689331 | + | 0.500828i | ||||
\(536\) | −4.92705 | + | 3.57971i | −0.212816 | + | 0.154620i | ||||
\(537\) | −7.68034 | + | 23.6377i | −0.331431 | + | 1.02004i | ||||
\(538\) | 27.7984 | 1.19847 | ||||||||
\(539\) | −6.76393 | + | 16.8415i | −0.291343 | + | 0.725415i | ||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −9.90983 | + | 30.4993i | −0.426057 | + | 1.31127i | 0.475922 | + | 0.879488i | \(0.342115\pi\) |
−0.901979 | + | 0.431781i | \(0.857885\pi\) | |||||||
\(542\) | 6.97214 | − | 5.06555i | 0.299479 | − | 0.217584i | ||||
\(543\) | −11.2361 | − | 8.16348i | −0.482186 | − | 0.350329i | ||||
\(544\) | 1.57295 | + | 4.84104i | 0.0674396 | + | 0.207558i | ||||
\(545\) | −2.00000 | − | 6.15537i | −0.0856706 | − | 0.263667i | ||||
\(546\) | 5.61803 | + | 4.08174i | 0.240430 | + | 0.174682i | ||||
\(547\) | −15.1074 | + | 10.9762i | −0.645945 | + | 0.469307i | −0.861888 | − | 0.507099i | \(-0.830718\pi\) |
0.215942 | + | 0.976406i | \(0.430718\pi\) | |||||||
\(548\) | 3.64590 | − | 11.2209i | 0.155745 | − | 0.479334i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.23607 | − | 3.07768i | 0.0527061 | − | 0.131233i | ||||
\(551\) | 1.23607 | 0.0526583 | ||||||||
\(552\) | −0.0450850 | + | 0.138757i | −0.00191894 | + | 0.00590590i | ||||
\(553\) | −7.09017 | + | 5.15131i | −0.301505 | + | 0.219056i | ||||
\(554\) | −11.7361 | − | 8.52675i | −0.498618 | − | 0.362267i | ||||
\(555\) | −2.66312 | − | 8.19624i | −0.113043 | − | 0.347911i | ||||
\(556\) | 4.09017 | + | 12.5882i | 0.173462 | + | 0.533861i | ||||
\(557\) | −4.14590 | − | 3.01217i | −0.175667 | − | 0.127630i | 0.496477 | − | 0.868050i | \(-0.334627\pi\) |
−0.672145 | + | 0.740420i | \(0.734627\pi\) | |||||||
\(558\) | 2.92705 | − | 2.12663i | 0.123912 | − | 0.0900273i | ||||
\(559\) | 19.2533 | − | 59.2555i | 0.814327 | − | 2.50624i | ||||
\(560\) | −1.23607 | −0.0522334 | ||||||||
\(561\) | −4.11803 | − | 16.3722i | −0.173864 | − | 0.691236i | ||||
\(562\) | −16.4721 | −0.694835 | ||||||||
\(563\) | 10.7984 | − | 33.2340i | 0.455097 | − | 1.40065i | −0.415924 | − | 0.909399i | \(-0.636542\pi\) |
0.871021 | − | 0.491246i | \(-0.163458\pi\) | |||||||
\(564\) | 9.16312 | − | 6.65740i | 0.385837 | − | 0.280327i | ||||
\(565\) | 0.454915 | + | 0.330515i | 0.0191384 | + | 0.0139049i | ||||
\(566\) | −2.06231 | − | 6.34712i | −0.0866852 | − | 0.266790i | ||||
\(567\) | 0.381966 | + | 1.17557i | 0.0160411 | + | 0.0493693i | ||||
\(568\) | −1.23607 | − | 0.898056i | −0.0518643 | − | 0.0376816i | ||||
\(569\) | −1.14590 | + | 0.832544i | −0.0480385 | + | 0.0349020i | −0.611545 | − | 0.791209i | \(-0.709452\pi\) |
0.563507 | + | 0.826111i | \(0.309452\pi\) | |||||||
\(570\) | −1.00000 | + | 3.07768i | −0.0418854 | + | 0.128910i | ||||
\(571\) | 16.3607 | 0.684673 | 0.342337 | − | 0.939577i | \(-0.388782\pi\) | ||||
0.342337 | + | 0.939577i | \(0.388782\pi\) | |||||||
\(572\) | 18.5902 | + | 1.26133i | 0.777294 | + | 0.0527387i | ||||
\(573\) | −4.76393 | −0.199016 | ||||||||
\(574\) | −1.23607 | + | 3.80423i | −0.0515925 | + | 0.158785i | ||||
\(575\) | −0.118034 | + | 0.0857567i | −0.00492236 | + | 0.00357630i | ||||
\(576\) | −0.809017 | − | 0.587785i | −0.0337090 | − | 0.0244911i | ||||
\(577\) | 10.7984 | + | 33.2340i | 0.449542 | + | 1.38355i | 0.877425 | + | 0.479714i | \(0.159260\pi\) |
−0.427883 | + | 0.903834i | \(0.640740\pi\) | |||||||
\(578\) | 2.75329 | + | 8.47375i | 0.114522 | + | 0.352462i | ||||
\(579\) | −2.47214 | − | 1.79611i | −0.102738 | − | 0.0746439i | ||||
\(580\) | −0.309017 | + | 0.224514i | −0.0128312 | + | 0.00932244i | ||||
\(581\) | 1.52786 | − | 4.70228i | 0.0633865 | − | 0.195084i | ||||
\(582\) | 12.6525 | 0.524462 | ||||||||
\(583\) | 1.32624 | − | 0.832544i | 0.0549272 | − | 0.0344804i | ||||
\(584\) | −13.4164 | −0.555175 | ||||||||
\(585\) | −1.73607 | + | 5.34307i | −0.0717776 | + | 0.220909i | ||||
\(586\) | 16.1803 | − | 11.7557i | 0.668404 | − | 0.485624i | ||||
\(587\) | 32.1246 | + | 23.3399i | 1.32592 | + | 0.963341i | 0.999838 | + | 0.0180007i | \(0.00573013\pi\) |
0.326087 | + | 0.945340i | \(0.394270\pi\) | |||||||
\(588\) | 1.69098 | + | 5.20431i | 0.0697350 | + | 0.214622i | ||||
\(589\) | 3.61803 | + | 11.1352i | 0.149078 | + | 0.458816i | ||||
\(590\) | 2.35410 | + | 1.71036i | 0.0969168 | + | 0.0704142i | ||||
\(591\) | −5.61803 | + | 4.08174i | −0.231095 | + | 0.167900i | ||||
\(592\) | −2.66312 | + | 8.19624i | −0.109454 | + | 0.336863i | ||||
\(593\) | −33.3262 | −1.36854 | −0.684272 | − | 0.729227i | \(-0.739880\pi\) | ||||
−0.684272 | + | 0.729227i | \(0.739880\pi\) | |||||||
\(594\) | 2.54508 | + | 2.12663i | 0.104426 | + | 0.0872566i | ||||
\(595\) | −6.29180 | −0.257938 | ||||||||
\(596\) | −1.66312 | + | 5.11855i | −0.0681240 | + | 0.209664i | ||||
\(597\) | −16.9721 | + | 12.3310i | −0.694623 | + | 0.504673i | ||||
\(598\) | −0.663119 | − | 0.481784i | −0.0271170 | − | 0.0197016i | ||||
\(599\) | −1.29180 | − | 3.97574i | −0.0527814 | − | 0.162444i | 0.921191 | − | 0.389110i | \(-0.127217\pi\) |
−0.973973 | + | 0.226666i | \(0.927217\pi\) | |||||||
\(600\) | −0.309017 | − | 0.951057i | −0.0126156 | − | 0.0388267i | ||||
\(601\) | 0.854102 | + | 0.620541i | 0.0348395 | + | 0.0253124i | 0.605069 | − | 0.796173i | \(-0.293146\pi\) |
−0.570229 | + | 0.821486i | \(0.693146\pi\) | |||||||
\(602\) | −11.0902 | + | 8.05748i | −0.452002 | + | 0.328398i | ||||
\(603\) | 1.88197 | − | 5.79210i | 0.0766396 | − | 0.235872i | ||||
\(604\) | 3.05573 | 0.124336 | ||||||||
\(605\) | 9.69098 | − | 5.20431i | 0.393994 | − | 0.211585i | ||||
\(606\) | −13.3820 | −0.543605 | ||||||||
\(607\) | 1.38197 | − | 4.25325i | 0.0560923 | − | 0.172634i | −0.919085 | − | 0.394059i | \(-0.871071\pi\) |
0.975178 | + | 0.221425i | \(0.0710706\pi\) | |||||||
\(608\) | 2.61803 | − | 1.90211i | 0.106175 | − | 0.0771409i | ||||
\(609\) | −0.381966 | − | 0.277515i | −0.0154780 | − | 0.0112455i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.6631 | + | 60.5169i | 0.795485 | + | 2.44825i | ||||
\(612\) | −4.11803 | − | 2.99193i | −0.166462 | − | 0.120941i | ||||
\(613\) | −4.85410 | + | 3.52671i | −0.196055 | + | 0.142443i | −0.681482 | − | 0.731835i | \(-0.738664\pi\) |
0.485427 | + | 0.874277i | \(0.338664\pi\) | |||||||
\(614\) | 6.93769 | − | 21.3520i | 0.279983 | − | 0.861698i | ||||
\(615\) | −3.23607 | −0.130491 | ||||||||
\(616\) | −3.14590 | − | 2.62866i | −0.126752 | − | 0.105912i | ||||
\(617\) | −18.3607 | −0.739173 | −0.369587 | − | 0.929196i | \(-0.620501\pi\) | ||||
−0.369587 | + | 0.929196i | \(0.620501\pi\) | |||||||
\(618\) | −3.47214 | + | 10.6861i | −0.139670 | + | 0.429859i | ||||
\(619\) | −14.9443 | + | 10.8576i | −0.600661 | + | 0.436406i | −0.846113 | − | 0.533003i | \(-0.821063\pi\) |
0.245452 | + | 0.969409i | \(0.421063\pi\) | |||||||
\(620\) | −2.92705 | − | 2.12663i | −0.117553 | − | 0.0854074i | ||||
\(621\) | −0.0450850 | − | 0.138757i | −0.00180920 | − | 0.00556814i | ||||
\(622\) | 1.47214 | + | 4.53077i | 0.0590273 | + | 0.181667i | ||||
\(623\) | −12.7639 | − | 9.27354i | −0.511376 | − | 0.371537i | ||||
\(624\) | 4.54508 | − | 3.30220i | 0.181949 | − | 0.132194i | ||||
\(625\) | 0.309017 | − | 0.951057i | 0.0123607 | − | 0.0380423i | ||||
\(626\) | −0.472136 | −0.0188703 | ||||||||
\(627\) | −9.09017 | + | 5.70634i | −0.363026 | + | 0.227889i | ||||
\(628\) | 24.2705 | 0.968499 | ||||||||
\(629\) | −13.5557 | + | 41.7202i | −0.540502 | + | 1.66349i | ||||
\(630\) | 1.00000 | − | 0.726543i | 0.0398410 | − | 0.0289461i | ||||
\(631\) | 17.2533 | + | 12.5352i | 0.686843 | + | 0.499020i | 0.875621 | − | 0.482999i | \(-0.160453\pi\) |
−0.188778 | + | 0.982020i | \(0.560453\pi\) | |||||||
\(632\) | 2.19098 | + | 6.74315i | 0.0871526 | + | 0.268228i | ||||
\(633\) | 6.41641 | + | 19.7477i | 0.255029 | + | 0.784900i | ||||
\(634\) | 0.472136 | + | 0.343027i | 0.0187509 | + | 0.0136233i | ||||
\(635\) | −13.4721 | + | 9.78808i | −0.534625 | + | 0.388428i | ||||
\(636\) | 0.145898 | − | 0.449028i | 0.00578523 | − | 0.0178051i | ||||
\(637\) | −30.7426 | −1.21807 | ||||||||
\(638\) | −1.26393 | − | 0.0857567i | −0.0500395 | − | 0.00339514i | ||||
\(639\) | 1.52786 | 0.0604414 | ||||||||
\(640\) | −0.309017 | + | 0.951057i | −0.0122150 | + | 0.0375938i | ||||
\(641\) | 8.23607 | − | 5.98385i | 0.325305 | − | 0.236348i | −0.413131 | − | 0.910672i | \(-0.635565\pi\) |
0.738436 | + | 0.674324i | \(0.235565\pi\) | |||||||
\(642\) | 15.9443 | + | 11.5842i | 0.629270 | + | 0.457192i | ||||
\(643\) | 6.11803 | + | 18.8294i | 0.241272 | + | 0.742558i | 0.996227 | + | 0.0867821i | \(0.0276584\pi\) |
−0.754956 | + | 0.655776i | \(0.772342\pi\) | |||||||
\(644\) | 0.0557281 | + | 0.171513i | 0.00219599 | + | 0.00675858i | ||||
\(645\) | −8.97214 | − | 6.51864i | −0.353278 | − | 0.256671i | ||||
\(646\) | 13.3262 | − | 9.68208i | 0.524314 | − | 0.380936i | ||||
\(647\) | −4.51722 | + | 13.9026i | −0.177590 | + | 0.546567i | −0.999742 | − | 0.0227013i | \(-0.992773\pi\) |
0.822152 | + | 0.569268i | \(0.192773\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 2.35410 | + | 9.35930i | 0.0924066 | + | 0.367385i | ||||
\(650\) | 5.61803 | 0.220357 | ||||||||
\(651\) | 1.38197 | − | 4.25325i | 0.0541635 | − | 0.166698i | ||||
\(652\) | 4.73607 | − | 3.44095i | 0.185479 | − | 0.134758i | ||||
\(653\) | 34.4164 | + | 25.0050i | 1.34682 | + | 0.978521i | 0.999163 | + | 0.0408980i | \(0.0130219\pi\) |
0.347655 | + | 0.937623i | \(0.386978\pi\) | |||||||
\(654\) | −2.00000 | − | 6.15537i | −0.0782062 | − | 0.240694i | ||||
\(655\) | 1.73607 | + | 5.34307i | 0.0678338 | + | 0.208771i | ||||
\(656\) | 2.61803 | + | 1.90211i | 0.102217 | + | 0.0742650i | ||||
\(657\) | 10.8541 | − | 7.88597i | 0.423459 | − | 0.307661i | ||||
\(658\) | 4.32624 | − | 13.3148i | 0.168654 | − | 0.519065i | ||||
\(659\) | 11.4164 | 0.444720 | 0.222360 | − | 0.974965i | \(-0.428624\pi\) | ||||
0.222360 | + | 0.974965i | \(0.428624\pi\) | |||||||
\(660\) | 1.23607 | − | 3.07768i | 0.0481139 | − | 0.119799i | ||||
\(661\) | −36.3607 | −1.41427 | −0.707133 | − | 0.707080i | \(-0.750012\pi\) | ||||
−0.707133 | + | 0.707080i | \(0.750012\pi\) | |||||||
\(662\) | 1.47214 | − | 4.53077i | 0.0572162 | − | 0.176093i | ||||
\(663\) | 23.1353 | − | 16.8087i | 0.898499 | − | 0.652798i | ||||
\(664\) | −3.23607 | − | 2.35114i | −0.125584 | − | 0.0912420i | ||||
\(665\) | 1.23607 | + | 3.80423i | 0.0479327 | + | 0.147522i | ||||
\(666\) | −2.66312 | − | 8.19624i | −0.103194 | − | 0.317598i | ||||
\(667\) | 0.0450850 | + | 0.0327561i | 0.00174570 | + | 0.00126832i | ||||
\(668\) | −16.3992 | + | 11.9147i | −0.634504 | + | 0.460994i | ||||
\(669\) | −0.854102 | + | 2.62866i | −0.0330215 | + | 0.101630i | ||||
\(670\) | −6.09017 | −0.235284 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.23607 | −0.0476824 | ||||||||
\(673\) | −0.708204 | + | 2.17963i | −0.0272993 | + | 0.0840185i | −0.963778 | − | 0.266706i | \(-0.914065\pi\) |
0.936479 | + | 0.350725i | \(0.114065\pi\) | |||||||
\(674\) | 8.70820 | − | 6.32688i | 0.335427 | − | 0.243702i | ||||
\(675\) | 0.809017 | + | 0.587785i | 0.0311391 | + | 0.0226239i | ||||
\(676\) | 5.73607 | + | 17.6538i | 0.220618 | + | 0.678992i | ||||
\(677\) | 7.03444 | + | 21.6498i | 0.270356 | + | 0.832069i | 0.990411 | + | 0.138152i | \(0.0441163\pi\) |
−0.720055 | + | 0.693917i | \(0.755884\pi\) | |||||||
\(678\) | 0.454915 | + | 0.330515i | 0.0174709 | + | 0.0126934i | ||||
\(679\) | 12.6525 | − | 9.19256i | 0.485557 | − | 0.352778i | ||||
\(680\) | −1.57295 | + | 4.84104i | −0.0603198 | + | 0.185645i | ||||
\(681\) | 24.3607 | 0.933503 | ||||||||
\(682\) | −2.92705 | − | 11.6372i | −0.112083 | − | 0.445611i | ||||
\(683\) | −19.1246 | −0.731783 | −0.365891 | − | 0.930658i | \(-0.619236\pi\) | ||||
−0.365891 | + | 0.930658i | \(0.619236\pi\) | |||||||
\(684\) | −1.00000 | + | 3.07768i | −0.0382360 | + | 0.117678i | ||||
\(685\) | 9.54508 | − | 6.93491i | 0.364699 | − | 0.264969i | ||||
\(686\) | 12.4721 | + | 9.06154i | 0.476188 | + | 0.345971i | ||||
\(687\) | −1.61803 | − | 4.97980i | −0.0617318 | − | 0.189991i | ||||
\(688\) | 3.42705 | + | 10.5474i | 0.130655 | + | 0.402115i | ||||
\(689\) | 2.14590 | + | 1.55909i | 0.0817522 | + | 0.0593965i | ||||
\(690\) | −0.118034 | + | 0.0857567i | −0.00449348 | + | 0.00326470i | ||||
\(691\) | 3.29180 | − | 10.1311i | 0.125226 | − | 0.385405i | −0.868716 | − | 0.495310i | \(-0.835054\pi\) |
0.993942 | + | 0.109904i | \(0.0350545\pi\) | |||||||
\(692\) | −18.4721 | −0.702205 | ||||||||
\(693\) | 4.09017 | + | 0.277515i | 0.155373 | + | 0.0105419i | ||||
\(694\) | 0.111456 | 0.00423082 | ||||||||
\(695\) | −4.09017 | + | 12.5882i | −0.155149 | + | 0.477499i | ||||
\(696\) | −0.309017 | + | 0.224514i | −0.0117133 | + | 0.00851018i | ||||
\(697\) | 13.3262 | + | 9.68208i | 0.504767 | + | 0.366735i | ||||
\(698\) | 4.76393 | + | 14.6619i | 0.180317 | + | 0.554960i | ||||
\(699\) | 7.59017 | + | 23.3601i | 0.287087 | + | 0.883562i | ||||
\(700\) | −1.00000 | − | 0.726543i | −0.0377964 | − | 0.0274607i | ||||
\(701\) | 10.0902 | − | 7.33094i | 0.381100 | − | 0.276886i | −0.380698 | − | 0.924699i | \(-0.624316\pi\) |
0.761799 | + | 0.647814i | \(0.224316\pi\) | |||||||
\(702\) | −1.73607 | + | 5.34307i | −0.0655237 | + | 0.201661i | ||||
\(703\) | 27.8885 | 1.05184 | ||||||||
\(704\) | −2.80902 | + | 1.76336i | −0.105869 | + | 0.0664590i | ||||
\(705\) | 11.3262 | 0.426571 | ||||||||
\(706\) | 6.60739 | − | 20.3355i | 0.248672 | − | 0.765335i | ||||
\(707\) | −13.3820 | + | 9.72257i | −0.503281 | + | 0.365655i | ||||
\(708\) | 2.35410 | + | 1.71036i | 0.0884726 | + | 0.0642791i | ||||
\(709\) | −11.5623 | − | 35.5851i | −0.434232 | − | 1.33643i | −0.893872 | − | 0.448322i | \(-0.852022\pi\) |
0.459641 | − | 0.888105i | \(-0.347978\pi\) | |||||||
\(710\) | −0.472136 | − | 1.45309i | −0.0177189 | − | 0.0545333i | ||||
\(711\) | −5.73607 | − | 4.16750i | −0.215119 | − | 0.156293i | ||||
\(712\) | −10.3262 | + | 7.50245i | −0.386992 | + | 0.281166i | ||||
\(713\) | −0.163119 | + | 0.502029i | −0.00610885 | + | 0.0188011i | ||||
\(714\) | −6.29180 | −0.235465 | ||||||||
\(715\) | 14.2984 | + | 11.9475i | 0.534729 | + | 0.446810i | ||||
\(716\) | 24.8541 | 0.928841 | ||||||||
\(717\) | −0.381966 | + | 1.17557i | −0.0142648 | + | 0.0439025i | ||||
\(718\) | −8.23607 | + | 5.98385i | −0.307367 | + | 0.223315i | ||||
\(719\) | −7.56231 | − | 5.49434i | −0.282026 | − | 0.204904i | 0.437774 | − | 0.899085i | \(-0.355767\pi\) |
−0.719801 | + | 0.694181i | \(0.755767\pi\) | |||||||
\(720\) | −0.309017 | − | 0.951057i | −0.0115164 | − | 0.0354438i | ||||
\(721\) | 4.29180 | + | 13.2088i | 0.159835 | + | 0.491921i | ||||
\(722\) | 6.89919 | + | 5.01255i | 0.256761 | + | 0.186548i | ||||
\(723\) | 9.61803 | − | 6.98791i | 0.357699 | − | 0.259883i | ||||
\(724\) | −4.29180 | + | 13.2088i | −0.159503 | + | 0.490901i | ||||
\(725\) | −0.381966 | −0.0141859 | ||||||||
\(726\) | 9.69098 | − | 5.20431i | 0.359666 | − | 0.193150i | ||||
\(727\) | −27.8197 | −1.03177 | −0.515887 | − | 0.856657i | \(-0.672538\pi\) | ||||
−0.515887 | + | 0.856657i | \(0.672538\pi\) | |||||||
\(728\) | 2.14590 | − | 6.60440i | 0.0795323 | − | 0.244775i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | −10.8541 | − | 7.88597i | −0.401728 | − | 0.291873i | ||||
\(731\) | 17.4443 | + | 53.6879i | 0.645200 | + | 1.98572i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.8607 | − | 20.9685i | −1.06599 | − | 0.774490i | −0.0908057 | − | 0.995869i | \(-0.528944\pi\) |
−0.975188 | + | 0.221379i | \(0.928944\pi\) | |||||||
\(734\) | 25.2705 | − | 18.3601i | 0.932752 | − | 0.677684i | ||||
\(735\) | −1.69098 | + | 5.20431i | −0.0623728 | + | 0.191964i | ||||
\(736\) | 0.145898 | 0.00537787 | ||||||||
\(737\) | −15.5000 | − | 12.9515i | −0.570950 | − | 0.477075i | ||||
\(738\) | −3.23607 | −0.119121 | ||||||||
\(739\) | −15.1459 | + | 46.6143i | −0.557151 | + | 1.71473i | 0.133044 | + | 0.991110i | \(0.457525\pi\) |
−0.690195 | + | 0.723624i | \(0.742475\pi\) | |||||||
\(740\) | −6.97214 | + | 5.06555i | −0.256301 | + | 0.186213i | ||||
\(741\) | −14.7082 | − | 10.6861i | −0.540319 | − | 0.392565i | ||||
\(742\) | −0.180340 | − | 0.555029i | −0.00662049 | − | 0.0203758i | ||||
\(743\) | −4.26393 | − | 13.1230i | −0.156428 | − | 0.481437i | 0.841874 | − | 0.539674i | \(-0.181452\pi\) |
−0.998303 | + | 0.0582362i | \(0.981452\pi\) | |||||||
\(744\) | −2.92705 | − | 2.12663i | −0.107311 | − | 0.0779659i | ||||
\(745\) | −4.35410 | + | 3.16344i | −0.159522 | + | 0.115899i | ||||
\(746\) | −6.32624 | + | 19.4702i | −0.231620 | + | 0.712853i | ||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | −14.2984 | + | 8.97578i | −0.522800 | + | 0.328187i | ||||
\(749\) | 24.3607 | 0.890120 | ||||||||
\(750\) | 0.309017 | − | 0.951057i | 0.0112837 | − | 0.0347277i | ||||
\(751\) | −0.0278640 | + | 0.0202444i | −0.00101677 | + | 0.000738729i | −0.588294 | − | 0.808647i | \(-0.700200\pi\) |
0.587277 | + | 0.809386i | \(0.300200\pi\) | |||||||
\(752\) | −9.16312 | − | 6.65740i | −0.334145 | − | 0.242770i | ||||
\(753\) | −3.28115 | − | 10.0984i | −0.119572 | − | 0.368004i | ||||
\(754\) | −0.663119 | − | 2.04087i | −0.0241494 | − | 0.0743241i | ||||
\(755\) | 2.47214 | + | 1.79611i | 0.0899702 | + | 0.0653672i | ||||
\(756\) | 1.00000 | − | 0.726543i | 0.0363696 | − | 0.0264241i | ||||
\(757\) | −14.5689 | + | 44.8384i | −0.529515 | + | 1.62968i | 0.225696 | + | 0.974198i | \(0.427534\pi\) |
−0.755211 | + | 0.655482i | \(0.772466\pi\) | |||||||
\(758\) | 32.3607 | 1.17539 | ||||||||
\(759\) | −0.482779 | − | 0.0327561i | −0.0175238 | − | 0.00118897i | ||||
\(760\) | 3.23607 | 0.117385 | ||||||||
\(761\) | −3.09017 | + | 9.51057i | −0.112019 | + | 0.344758i | −0.991314 | − | 0.131520i | \(-0.958014\pi\) |
0.879295 | + | 0.476278i | \(0.158014\pi\) | |||||||
\(762\) | −13.4721 | + | 9.78808i | −0.488044 | + | 0.354585i | ||||
\(763\) | −6.47214 | − | 4.70228i | −0.234307 | − | 0.170234i | ||||
\(764\) | 1.47214 | + | 4.53077i | 0.0532600 | + | 0.163917i | ||||
\(765\) | −1.57295 | − | 4.84104i | −0.0568701 | − | 0.175028i | ||||
\(766\) | −12.3992 | − | 9.00854i | −0.448001 | − | 0.325492i | ||||
\(767\) | −13.2254 | + | 9.60883i | −0.477542 | + | 0.346955i | ||||
\(768\) | −0.309017 | + | 0.951057i | −0.0111507 | + | 0.0343183i | ||||
\(769\) | 31.4508 | 1.13415 | 0.567073 | − | 0.823667i | \(-0.308076\pi\) | ||||
0.567073 | + | 0.823667i | \(0.308076\pi\) | |||||||
\(770\) | −1.00000 | − | 3.97574i | −0.0360375 | − | 0.143276i | ||||
\(771\) | 14.3607 | 0.517187 | ||||||||
\(772\) | −0.944272 | + | 2.90617i | −0.0339851 | + | 0.104595i | ||||
\(773\) | 23.9443 | − | 17.3965i | 0.861216 | − | 0.625710i | −0.0669998 | − | 0.997753i | \(-0.521343\pi\) |
0.928215 | + | 0.372043i | \(0.121343\pi\) | |||||||
\(774\) | −8.97214 | − | 6.51864i | −0.322497 | − | 0.234308i | ||||
\(775\) | −1.11803 | − | 3.44095i | −0.0401610 | − | 0.123603i | ||||
\(776\) | −3.90983 | − | 12.0332i | −0.140355 | − | 0.431967i | ||||
\(777\) | −8.61803 | − | 6.26137i | −0.309170 | − | 0.224625i | ||||
\(778\) | −0.118034 | + | 0.0857567i | −0.00423172 | + | 0.00307453i | ||||
\(779\) | 3.23607 | − | 9.95959i | 0.115944 | − | 0.356839i | ||||
\(780\) | 5.61803 | 0.201158 | ||||||||
\(781\) | 1.88854 | − | 4.70228i | 0.0675774 | − | 0.168261i | ||||
\(782\) | 0.742646 | 0.0265570 | ||||||||
\(783\) | 0.118034 | − | 0.363271i | 0.00421819 | − | 0.0129823i | ||||
\(784\) | 4.42705 | − | 3.21644i | 0.158109 | − | 0.114873i | ||||
\(785\) | 19.6353 | + | 14.2658i | 0.700812 | + | 0.509170i | ||||
\(786\) | 1.73607 | + | 5.34307i | 0.0619235 | + | 0.190581i | ||||
\(787\) | −2.48278 | − | 7.64121i | −0.0885015 | − | 0.272380i | 0.897004 | − | 0.442022i | \(-0.145739\pi\) |
−0.985506 | + | 0.169642i | \(0.945739\pi\) | |||||||
\(788\) | 5.61803 | + | 4.08174i | 0.200134 | + | 0.145406i | ||||
\(789\) | 0.118034 | − | 0.0857567i | 0.00420212 | − | 0.00305302i | ||||
\(790\) | −2.19098 | + | 6.74315i | −0.0779517 | + | 0.239911i | ||||
\(791\) | 0.695048 | 0.0247131 | ||||||||
\(792\) | 1.23607 | − | 3.07768i | 0.0439218 | − | 0.109361i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 8.28115 | − | 25.4868i | 0.293887 | − | 0.904492i | ||||
\(795\) | 0.381966 | − | 0.277515i | 0.0135469 | − | 0.00984243i | ||||
\(796\) | 16.9721 | + | 12.3310i | 0.601561 | + | 0.437060i | ||||
\(797\) | −2.56231 | − | 7.88597i | −0.0907615 | − | 0.279335i | 0.895364 | − | 0.445334i | \(-0.146915\pi\) |
−0.986126 | + | 0.165999i | \(0.946915\pi\) | |||||||
\(798\) | 1.23607 | + | 3.80423i | 0.0437563 | + | 0.134668i | ||||
\(799\) | −46.6418 | − | 33.8873i | −1.65007 | − | 1.19885i | ||||
\(800\) | −0.809017 | + | 0.587785i | −0.0286031 | + | 0.0207813i | ||||
\(801\) | 3.94427 | − | 12.1392i | 0.139364 | − | 0.428918i | ||||
\(802\) | −36.0689 | −1.27364 | ||||||||
\(803\) | −10.8541 | − | 43.1531i | −0.383033 | − | 1.52284i | ||||
\(804\) | −6.09017 | −0.214784 | ||||||||
\(805\) | −0.0557281 | + | 0.171513i | −0.00196416 | + | 0.00604505i | ||||
\(806\) | 16.4443 | − | 11.9475i | 0.579225 | − | 0.420831i | ||||
\(807\) | 22.4894 | + | 16.3395i | 0.791663 | + | 0.575177i | ||||
\(808\) | 4.13525 | + | 12.7270i | 0.145478 | + | 0.447735i | ||||
\(809\) | 8.85410 | + | 27.2501i | 0.311294 | + | 0.958063i | 0.977253 | + | 0.212076i | \(0.0680223\pi\) |
−0.665960 | + | 0.745988i | \(0.731978\pi\) | |||||||
\(810\) | 0.809017 | + | 0.587785i | 0.0284260 | + | 0.0206527i | ||||
\(811\) | 25.4164 | − | 18.4661i | 0.892491 | − | 0.648433i | −0.0440355 | − | 0.999030i | \(-0.514021\pi\) |
0.936526 | + | 0.350597i | \(0.114021\pi\) | |||||||
\(812\) | −0.145898 | + | 0.449028i | −0.00512002 | + | 0.0157578i | ||||
\(813\) | 8.61803 | 0.302248 | ||||||||
\(814\) | −28.5172 | − | 1.93487i | −0.999528 | − | 0.0678171i | ||||
\(815\) | 5.85410 | 0.205060 | ||||||||
\(816\) | −1.57295 | + | 4.84104i | −0.0550642 | + | 0.169470i | ||||
\(817\) | 29.0344 | − | 21.0948i | 1.01579 | − | 0.738012i | ||||
\(818\) | 27.4894 | + | 19.9722i | 0.961143 | + | 0.698311i | ||||
\(819\) | 2.14590 | + | 6.60440i | 0.0749837 | + | 0.230776i | ||||
\(820\) | 1.00000 | + | 3.07768i | 0.0349215 | + | 0.107477i | ||||
\(821\) | −15.6180 | − | 11.3472i | −0.545073 | − | 0.396019i | 0.280893 | − | 0.959739i | \(-0.409370\pi\) |
−0.825966 | + | 0.563720i | \(0.809370\pi\) | |||||||
\(822\) | 9.54508 | − | 6.93491i | 0.332923 | − | 0.241883i | ||||
\(823\) | −5.32624 | + | 16.3925i | −0.185661 | + | 0.571406i | −0.999959 | − | 0.00904109i | \(-0.997122\pi\) |
0.814298 | + | 0.580447i | \(0.197122\pi\) | |||||||
\(824\) | 11.2361 | 0.391427 | ||||||||
\(825\) | 2.80902 | − | 1.76336i | 0.0977974 | − | 0.0613922i | ||||
\(826\) | 3.59675 | 0.125147 | ||||||||
\(827\) | 13.5066 | − | 41.5690i | 0.469670 | − | 1.44549i | −0.383344 | − | 0.923606i | \(-0.625228\pi\) |
0.853013 | − | 0.521889i | \(-0.174772\pi\) | |||||||
\(828\) | −0.118034 | + | 0.0857567i | −0.00410196 | + | 0.00298025i | ||||
\(829\) | 11.0000 | + | 7.99197i | 0.382046 | + | 0.277573i | 0.762188 | − | 0.647355i | \(-0.224125\pi\) |
−0.380142 | + | 0.924928i | \(0.624125\pi\) | |||||||
\(830\) | −1.23607 | − | 3.80423i | −0.0429045 | − | 0.132047i | ||||
\(831\) | −4.48278 | − | 13.7966i | −0.155506 | − | 0.478598i | ||||
\(832\) | −4.54508 | − | 3.30220i | −0.157572 | − | 0.114483i | ||||
\(833\) | 22.5344 | − | 16.3722i | 0.780772 | − | 0.567264i | ||||
\(834\) | −4.09017 | + | 12.5882i | −0.141631 | + | 0.435895i | ||||
\(835\) | −20.2705 | −0.701490 | ||||||||
\(836\) | 8.23607 | + | 6.88191i | 0.284850 | + | 0.238016i | ||||
\(837\) | 3.61803 | 0.125058 | ||||||||
\(838\) | 4.98936 | − | 15.3557i | 0.172354 | − | 0.530453i | ||||
\(839\) | 44.2148 | − | 32.1239i | 1.52646 | − | 1.10904i | 0.568300 | − | 0.822822i | \(-0.307601\pi\) |
0.958164 | − | 0.286219i | \(-0.0923985\pi\) | |||||||
\(840\) | −1.00000 | − | 0.726543i | −0.0345033 | − | 0.0250681i | ||||
\(841\) | −8.91641 | − | 27.4419i | −0.307462 | − | 0.946272i | ||||
\(842\) | 2.00000 | + | 6.15537i | 0.0689246 | + | 0.212128i | ||||
\(843\) | −13.3262 | − | 9.68208i | −0.458980 | − | 0.333469i | ||||
\(844\) | 16.7984 | − | 12.2047i | 0.578224 | − | 0.420104i | ||||
\(845\) | −5.73607 | + | 17.6538i | −0.197327 | + | 0.607309i | ||||
\(846\) | 11.3262 | 0.389404 | ||||||||
\(847\) | 5.90983 | − | 12.2452i | 0.203064 | − | 0.420751i | ||||
\(848\) | −0.472136 | −0.0162132 | ||||||||
\(849\) | 2.06231 | − | 6.34712i | 0.0707782 | − | 0.217833i | ||||
\(850\) | −4.11803 | + | 2.99193i | −0.141247 | + | 0.102622i | ||||
\(851\) | 1.01722 | + | 0.739054i | 0.0348699 | + | 0.0253345i | ||||
\(852\) | −0.472136 | − | 1.45309i | −0.0161751 | − | 0.0497819i | ||||
\(853\) | −11.2705 | − | 34.6871i | −0.385895 | − | 1.18766i | −0.935829 | − | 0.352454i | \(-0.885347\pi\) |
0.549934 | − | 0.835208i | \(-0.314653\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.61803 | + | 1.90211i | −0.0895349 | + | 0.0650509i | ||||
\(856\) | 6.09017 | − | 18.7436i | 0.208158 | − | 0.640644i | ||||
\(857\) | −45.1591 | −1.54260 | −0.771302 | − | 0.636469i | \(-0.780394\pi\) | ||||
−0.771302 | + | 0.636469i | \(0.780394\pi\) | |||||||
\(858\) | 14.2984 | + | 11.9475i | 0.488138 | + | 0.407880i | ||||
\(859\) | 21.1246 | 0.720762 | 0.360381 | − | 0.932805i | \(-0.382647\pi\) | ||||
0.360381 | + | 0.932805i | \(0.382647\pi\) | |||||||
\(860\) | −3.42705 | + | 10.5474i | −0.116861 | + | 0.359663i | ||||
\(861\) | −3.23607 | + | 2.35114i | −0.110285 | + | 0.0801267i | ||||
\(862\) | 18.0902 | + | 13.1433i | 0.616154 | + | 0.447662i | ||||
\(863\) | 14.6287 | + | 45.0224i | 0.497966 | + | 1.53258i | 0.812283 | + | 0.583264i | \(0.198225\pi\) |
−0.314317 | + | 0.949318i | \(0.601775\pi\) | |||||||
\(864\) | −0.309017 | − | 0.951057i | −0.0105130 | − | 0.0323556i | ||||
\(865\) | −14.9443 | − | 10.8576i | −0.508120 | − | 0.369171i | ||||
\(866\) | −24.9443 | + | 18.1231i | −0.847641 | + | 0.615847i | ||||
\(867\) | −2.75329 | + | 8.47375i | −0.0935066 | + | 0.287784i | ||||
\(868\) | −4.47214 | −0.151794 | ||||||||
\(869\) | −19.9164 | + | 12.5025i | −0.675618 | + | 0.424118i | ||||
\(870\) | −0.381966 | −0.0129499 | ||||||||
\(871\) | 10.5729 | − | 32.5402i | 0.358251 | − | 1.10258i | ||||
\(872\) | −5.23607 | + | 3.80423i | −0.177316 | + | 0.128827i | ||||
\(873\) | 10.2361 | + | 7.43694i | 0.346438 | + | 0.251702i | ||||
\(874\) | −0.145898 | − | 0.449028i | −0.00493507 | − | 0.0151886i | ||||
\(875\) | −0.381966 | − | 1.17557i | −0.0129128 | − | 0.0397415i | ||||
\(876\) | −10.8541 | − | 7.88597i | −0.366726 | − | 0.266442i | ||||
\(877\) | −38.8607 | + | 28.2339i | −1.31223 | + | 0.953392i | −0.312238 | + | 0.950004i | \(0.601079\pi\) |
−0.999994 | + | 0.00338827i | \(0.998921\pi\) | |||||||
\(878\) | 5.35410 | − | 16.4782i | 0.180692 | − | 0.556113i | ||||
\(879\) | 20.0000 | 0.674583 | ||||||||
\(880\) | −3.30902 | − | 0.224514i | −0.111547 | − | 0.00756837i | ||||
\(881\) | 8.00000 | 0.269527 | 0.134763 | − | 0.990878i | \(-0.456973\pi\) | ||||
0.134763 | + | 0.990878i | \(0.456973\pi\) | |||||||
\(882\) | −1.69098 | + | 5.20431i | −0.0569384 | + | 0.175238i | ||||
\(883\) | 16.4443 | − | 11.9475i | 0.553394 | − | 0.402064i | −0.275641 | − | 0.961261i | \(-0.588890\pi\) |
0.829035 | + | 0.559196i | \(0.188890\pi\) | |||||||
\(884\) | −23.1353 | − | 16.8087i | −0.778123 | − | 0.565339i | ||||
\(885\) | 0.899187 | + | 2.76741i | 0.0302258 | + | 0.0930256i | ||||
\(886\) | 3.90983 | + | 12.0332i | 0.131353 | + | 0.404264i | ||||
\(887\) | −10.8820 | − | 7.90621i | −0.365381 | − | 0.265465i | 0.389912 | − | 0.920852i | \(-0.372505\pi\) |
−0.755293 | + | 0.655387i | \(0.772505\pi\) | |||||||
\(888\) | −6.97214 | + | 5.06555i | −0.233970 | + | 0.169989i | ||||
\(889\) | −6.36068 | + | 19.5762i | −0.213330 | + | 0.656563i | ||||
\(890\) | −12.7639 | −0.427848 | ||||||||
\(891\) | 0.809017 | + | 3.21644i | 0.0271031 | + | 0.107755i | ||||
\(892\) | 2.76393 | 0.0925433 | ||||||||
\(893\) | −11.3262 | + | 34.8586i | −0.379018 | + | 1.16650i | ||||
\(894\) | −4.35410 | + | 3.16344i | −0.145623 | + | 0.105801i | ||||
\(895\) | 20.1074 | + | 14.6089i | 0.672116 | + | 0.488321i | ||||
\(896\) | 0.381966 | + | 1.17557i | 0.0127606 | + | 0.0392731i | ||||
\(897\) | −0.253289 | − | 0.779543i | −0.00845707 | − | 0.0260282i | ||||
\(898\) | −23.5623 | − | 17.1190i | −0.786284 | − | 0.571269i | ||||
\(899\) | −1.11803 | + | 0.812299i | −0.0372885 | + | 0.0270917i | ||||
\(900\) | 0.309017 | − | 0.951057i | 0.0103006 | − | 0.0317019i | ||||
\(901\) | −2.40325 | −0.0800639 | ||||||||
\(902\) | −4.00000 | + | 9.95959i | −0.133185 | + | 0.331618i | ||||
\(903\) | −13.7082 | −0.456180 | ||||||||
\(904\) | 0.173762 | − | 0.534785i | 0.00577924 | − | 0.0177867i | ||||
\(905\) | −11.2361 | + | 8.16348i | −0.373500 | + | 0.271363i | ||||
\(906\) | 2.47214 | + | 1.79611i | 0.0821312 | + | 0.0596718i | ||||
\(907\) | 4.48278 | + | 13.7966i | 0.148848 | + | 0.458108i | 0.997486 | − | 0.0708670i | \(-0.0225766\pi\) |
−0.848638 | + | 0.528975i | \(0.822577\pi\) | |||||||
\(908\) | −7.52786 | − | 23.1684i | −0.249821 | − | 0.768870i | ||||
\(909\) | −10.8262 | − | 7.86572i | −0.359084 | − | 0.260890i | ||||
\(910\) | 5.61803 | − | 4.08174i | 0.186236 | − | 0.135308i | ||||
\(911\) | 3.85410 | − | 11.8617i | 0.127692 | − | 0.392996i | −0.866690 | − | 0.498847i | \(-0.833757\pi\) |
0.994382 | + | 0.105852i | \(0.0337568\pi\) | |||||||
\(912\) | 3.23607 | 0.107157 | ||||||||
\(913\) | 4.94427 | − | 12.3107i | 0.163632 | − | 0.407426i | ||||
\(914\) | −26.6525 | −0.881586 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.23607 | + | 3.07768i | −0.139964 | + | 0.101690i | ||||
\(917\) | 5.61803 | + | 4.08174i | 0.185524 | + | 0.134791i | ||||
\(918\) | −1.57295 | − | 4.84104i | −0.0519151 | − | 0.159778i | ||||
\(919\) | −14.0106 | − | 43.1203i | −0.462168 | − | 1.42241i | −0.862509 | − | 0.506042i | \(-0.831108\pi\) |
0.400340 | − | 0.916366i | \(-0.368892\pi\) | |||||||
\(920\) | 0.118034 | + | 0.0857567i | 0.00389147 | + | 0.00282732i | ||||
\(921\) | 18.1631 | − | 13.1963i | 0.598495 | − | 0.434832i | ||||
\(922\) | −8.71885 | + | 26.8339i | −0.287140 | + | 0.883726i | ||||
\(923\) | 8.58359 | 0.282532 | ||||||||
\(924\) | −1.00000 | − | 3.97574i | −0.0328976 | − | 0.130792i | ||||
\(925\) | −8.61803 | −0.283359 | ||||||||
\(926\) | −7.38197 | + | 22.7194i | −0.242586 | + | 0.746604i | ||||
\(927\) | −9.09017 | + | 6.60440i | −0.298560 | + | 0.216917i | ||||
\(928\) | 0.309017 | + | 0.224514i | 0.0101440 | + | 0.00737003i | ||||
\(929\) | −6.65248 | − | 20.4742i | −0.218261 | − | 0.671737i | −0.998906 | − | 0.0467630i | \(-0.985109\pi\) |
0.780645 | − | 0.624974i | \(-0.214891\pi\) | |||||||
\(930\) | −1.11803 | − | 3.44095i | −0.0366618 | − | 0.112833i | ||||
\(931\) | −14.3262 | − | 10.4086i | −0.469523 | − | 0.341129i | ||||
\(932\) | 19.8713 | − | 14.4374i | 0.650907 | − | 0.472911i | ||||
\(933\) | −1.47214 | + | 4.53077i | −0.0481956 | + | 0.148331i | ||||
\(934\) | −38.5410 | −1.26110 | ||||||||
\(935\) | −16.8435 | − | 1.14281i | −0.550840 | − | 0.0373740i | ||||
\(936\) | 5.61803 | 0.183631 | ||||||||
\(937\) | −3.50658 | + | 10.7921i | −0.114555 | + | 0.352564i | −0.991854 | − | 0.127380i | \(-0.959343\pi\) |
0.877299 | + | 0.479944i | \(0.159343\pi\) | |||||||
\(938\) | −6.09017 | + | 4.42477i | −0.198851 | + | 0.144474i | ||||
\(939\) | −0.381966 | − | 0.277515i | −0.0124650 | − | 0.00905635i | ||||
\(940\) | −3.50000 | − | 10.7719i | −0.114157 | − | 0.351340i | ||||
\(941\) | 14.8262 | + | 45.6305i | 0.483322 | + | 1.48751i | 0.834397 | + | 0.551164i | \(0.185816\pi\) |
−0.351076 | + | 0.936347i | \(0.614184\pi\) | |||||||
\(942\) | 19.6353 | + | 14.2658i | 0.639751 | + | 0.464806i | ||||
\(943\) | 0.381966 | − | 0.277515i | 0.0124385 | − | 0.00903712i | ||||
\(944\) | 0.899187 | − | 2.76741i | 0.0292660 | − | 0.0900716i | ||||
\(945\) | 1.23607 | 0.0402093 | ||||||||
\(946\) | −31.1525 | + | 19.5559i | −1.01285 | + | 0.635818i | ||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | −2.19098 | + | 6.74315i | −0.0711598 | + | 0.219007i | ||||
\(949\) | 60.9787 | − | 44.3036i | 1.97945 | − | 1.43816i | ||||
\(950\) | 2.61803 | + | 1.90211i | 0.0849402 | + | 0.0617127i | ||||
\(951\) | 0.180340 | + | 0.555029i | 0.00584792 | + | 0.0179981i | ||||
\(952\) | 1.94427 | + | 5.98385i | 0.0630142 | + | 0.193938i | ||||
\(953\) | 6.29837 | + | 4.57604i | 0.204024 | + | 0.148232i | 0.685106 | − | 0.728443i | \(-0.259756\pi\) |
−0.481082 | + | 0.876676i | \(0.659756\pi\) | |||||||
\(954\) | 0.381966 | − | 0.277515i | 0.0123666 | − | 0.00898487i | ||||
\(955\) | −1.47214 | + | 4.53077i | −0.0476372 | + | 0.146612i | ||||
\(956\) | 1.23607 | 0.0399773 | ||||||||
\(957\) | −0.972136 | − | 0.812299i | −0.0314247 | − | 0.0262579i | ||||
\(958\) | 17.2361 | 0.556872 | ||||||||
\(959\) | 4.50658 | − | 13.8698i | 0.145525 | − | 0.447880i | ||||
\(960\) | −0.809017 | + | 0.587785i | −0.0261109 | + | 0.0189707i | ||||
\(961\) | 14.4894 | + | 10.5271i | 0.467399 | + | 0.339585i | ||||
\(962\) | −14.9615 | − | 46.0467i | −0.482378 | − | 1.48461i | ||||
\(963\) | 6.09017 | + | 18.7436i | 0.196253 | + | 0.604005i | ||||
\(964\) | −9.61803 | − | 6.98791i | −0.309776 | − | 0.225065i | ||||
\(965\) | −2.47214 | + | 1.79611i | −0.0795809 | + | 0.0578189i | ||||
\(966\) | −0.0557281 | + | 0.171513i | −0.00179302 | + | 0.00551835i | ||||
\(967\) | −9.30495 | −0.299227 | −0.149614 | − | 0.988745i | \(-0.547803\pi\) | ||||
−0.149614 | + | 0.988745i | \(0.547803\pi\) | |||||||
\(968\) | −7.94427 | − | 7.60845i | −0.255339 | − | 0.244545i | ||||
\(969\) | 16.4721 | 0.529161 | ||||||||
\(970\) | 3.90983 | − | 12.0332i | 0.125537 | − | 0.386363i | ||||
\(971\) | 29.4164 | − | 21.3723i | 0.944017 | − | 0.685869i | −0.00536690 | − | 0.999986i | \(-0.501708\pi\) |
0.949384 | + | 0.314117i | \(0.101708\pi\) | |||||||
\(972\) | 0.809017 | + | 0.587785i | 0.0259492 | + | 0.0188532i | ||||
\(973\) | 5.05573 | + | 15.5599i | 0.162079 | + | 0.498828i | ||||
\(974\) | −4.76393 | − | 14.6619i | −0.152646 | − | 0.469797i | ||||
\(975\) | 4.54508 | + | 3.30220i | 0.145559 | + | 0.105755i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.67376 | + | 23.6174i | −0.245505 | + | 0.755588i | 0.750048 | + | 0.661384i | \(0.230031\pi\) |
−0.995553 | + | 0.0942040i | \(0.969969\pi\) | |||||||
\(978\) | 5.85410 | 0.187194 | ||||||||
\(979\) | −32.4853 | − | 27.1441i | −1.03823 | − | 0.867530i | ||||
\(980\) | 5.47214 | 0.174801 | ||||||||
\(981\) | 2.00000 | − | 6.15537i | 0.0638551 | − | 0.196526i | ||||
\(982\) | 0.836881 | − | 0.608030i | 0.0267059 | − | 0.0194030i | ||||
\(983\) | −38.1803 | − | 27.7396i | −1.21776 | − | 0.884757i | −0.221851 | − | 0.975081i | \(-0.571210\pi\) |
−0.995912 | + | 0.0903234i | \(0.971210\pi\) | |||||||
\(984\) | 1.00000 | + | 3.07768i | 0.0318788 | + | 0.0981130i | ||||
\(985\) | 2.14590 | + | 6.60440i | 0.0683740 | + | 0.210434i | ||||
\(986\) | 1.57295 | + | 1.14281i | 0.0500929 | + | 0.0363946i | ||||
\(987\) | 11.3262 | − | 8.22899i | 0.360518 | − | 0.261932i | ||||
\(988\) | −5.61803 | + | 17.2905i | −0.178733 | + | 0.550085i | ||||
\(989\) | 1.61803 | 0.0514505 | ||||||||
\(990\) | 2.80902 | − | 1.76336i | 0.0892764 | − | 0.0560431i | ||||
\(991\) | −59.5197 | −1.89071 | −0.945353 | − | 0.326048i | \(-0.894283\pi\) | ||||
−0.945353 | + | 0.326048i | \(0.894283\pi\) | |||||||
\(992\) | −1.11803 | + | 3.44095i | −0.0354976 | + | 0.109250i | ||||
\(993\) | 3.85410 | − | 2.80017i | 0.122306 | − | 0.0888607i | ||||
\(994\) | −1.52786 | − | 1.11006i | −0.0484609 | − | 0.0352089i | ||||
\(995\) | 6.48278 | + | 19.9519i | 0.205518 | + | 0.632519i | ||||
\(996\) | −1.23607 | − | 3.80423i | −0.0391663 | − | 0.120542i | ||||
\(997\) | −3.26393 | − | 2.37139i | −0.103370 | − | 0.0751025i | 0.534900 | − | 0.844916i | \(-0.320349\pi\) |
−0.638269 | + | 0.769813i | \(0.720349\pi\) | |||||||
\(998\) | 19.0344 | − | 13.8293i | 0.602525 | − | 0.437760i | ||||
\(999\) | 2.66312 | − | 8.19624i | 0.0842574 | − | 0.259317i |
(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 | 330.2.m.b.31.1 | ✓ | 4 | |
3.2 | odd | 2 | 990.2.n.e.361.1 | 4 | |||
11.4 | even | 5 | 3630.2.a.bj.1.2 | 2 | |||
11.5 | even | 5 | inner | 330.2.m.b.181.1 | yes | 4 | |
11.7 | odd | 10 | 3630.2.a.bb.1.1 | 2 | |||
33.5 | odd | 10 | 990.2.n.e.181.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.m.b.31.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
330.2.m.b.181.1 | yes | 4 | 11.5 | even | 5 | inner | |
990.2.n.e.181.1 | 4 | 33.5 | odd | 10 | |||
990.2.n.e.361.1 | 4 | 3.2 | odd | 2 | |||
3630.2.a.bb.1.1 | 2 | 11.7 | odd | 10 | |||
3630.2.a.bj.1.2 | 2 | 11.4 | even | 5 |