Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(71,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.n (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: | \(6.14848095564\) |
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 | 631.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.631 |
Dual form | 770.2.n.b.421.1 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | ||||
\(3\) | 0.118034 | − | 0.363271i | 0.0681470 | − | 0.209735i | −0.911184 | − | 0.412000i | \(-0.864830\pi\) |
0.979331 | + | 0.202265i | \(0.0648303\pi\) | |||||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 0.809017 | − | 0.587785i | 0.361803 | − | 0.262866i | ||||
\(6\) | 0.309017 | − | 0.224514i | 0.126156 | − | 0.0916575i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | −0.309017 | + | 0.951057i | −0.109254 | + | 0.336249i | ||||
\(9\) | 2.30902 | + | 1.67760i | 0.769672 | + | 0.559200i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0.309017 | − | 3.30220i | 0.0931721 | − | 0.995650i | ||||
\(12\) | 0.381966 | 0.110264 | ||||||||
\(13\) | 1.61803 | + | 1.17557i | 0.448762 | + | 0.326045i | 0.789107 | − | 0.614256i | \(-0.210544\pi\) |
−0.340345 | + | 0.940301i | \(0.610544\pi\) | |||||||
\(14\) | 0.309017 | − | 0.951057i | 0.0825883 | − | 0.254181i | ||||
\(15\) | −0.118034 | − | 0.363271i | −0.0304762 | − | 0.0937962i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | 0.500000 | − | 0.363271i | 0.121268 | − | 0.0881062i | −0.525498 | − | 0.850795i | \(-0.676121\pi\) |
0.646766 | + | 0.762688i | \(0.276121\pi\) | |||||||
\(18\) | 0.881966 | + | 2.71441i | 0.207881 | + | 0.639793i | ||||
\(19\) | −0.0450850 | + | 0.138757i | −0.0103432 | + | 0.0318331i | −0.956095 | − | 0.293057i | \(-0.905327\pi\) |
0.945752 | + | 0.324890i | \(0.105327\pi\) | |||||||
\(20\) | 0.809017 | + | 0.587785i | 0.180902 | + | 0.131433i | ||||
\(21\) | −0.381966 | −0.0833518 | ||||||||
\(22\) | 2.19098 | − | 2.48990i | 0.467119 | − | 0.530848i | ||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | 0.309017 | + | 0.224514i | 0.0630778 | + | 0.0458287i | ||||
\(25\) | 0.309017 | − | 0.951057i | 0.0618034 | − | 0.190211i | ||||
\(26\) | 0.618034 | + | 1.90211i | 0.121206 | + | 0.373035i | ||||
\(27\) | 1.80902 | − | 1.31433i | 0.348145 | − | 0.252942i | ||||
\(28\) | 0.809017 | − | 0.587785i | 0.152890 | − | 0.111081i | ||||
\(29\) | 0.381966 | + | 1.17557i | 0.0709293 | + | 0.218298i | 0.980237 | − | 0.197826i | \(-0.0633882\pi\) |
−0.909308 | + | 0.416124i | \(0.863388\pi\) | |||||||
\(30\) | 0.118034 | − | 0.363271i | 0.0215500 | − | 0.0663240i | ||||
\(31\) | −2.61803 | − | 1.90211i | −0.470213 | − | 0.341630i | 0.327311 | − | 0.944917i | \(-0.393857\pi\) |
−0.797524 | + | 0.603287i | \(0.793857\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.16312 | − | 0.502029i | −0.202473 | − | 0.0873920i | ||||
\(34\) | 0.618034 | 0.105992 | ||||||||
\(35\) | −0.809017 | − | 0.587785i | −0.136749 | − | 0.0993538i | ||||
\(36\) | −0.881966 | + | 2.71441i | −0.146994 | + | 0.452402i | ||||
\(37\) | 0.763932 | + | 2.35114i | 0.125590 | + | 0.386525i | 0.994008 | − | 0.109307i | \(-0.0348631\pi\) |
−0.868418 | + | 0.495832i | \(0.834863\pi\) | |||||||
\(38\) | −0.118034 | + | 0.0857567i | −0.0191476 | + | 0.0139116i | ||||
\(39\) | 0.618034 | − | 0.449028i | 0.0989646 | − | 0.0719020i | ||||
\(40\) | 0.309017 | + | 0.951057i | 0.0488599 | + | 0.150375i | ||||
\(41\) | −1.64590 | + | 5.06555i | −0.257046 | + | 0.791107i | 0.736374 | + | 0.676575i | \(0.236537\pi\) |
−0.993420 | + | 0.114531i | \(0.963463\pi\) | |||||||
\(42\) | −0.309017 | − | 0.224514i | −0.0476824 | − | 0.0346433i | ||||
\(43\) | 4.85410 | 0.740244 | 0.370122 | − | 0.928983i | \(-0.379316\pi\) | ||||
0.370122 | + | 0.928983i | \(0.379316\pi\) | |||||||
\(44\) | 3.23607 | − | 0.726543i | 0.487856 | − | 0.109530i | ||||
\(45\) | 2.85410 | 0.425464 | ||||||||
\(46\) | 4.85410 | + | 3.52671i | 0.715698 | + | 0.519985i | ||||
\(47\) | 1.47214 | − | 4.53077i | 0.214733 | − | 0.660881i | −0.784439 | − | 0.620206i | \(-0.787049\pi\) |
0.999172 | − | 0.0406750i | \(-0.0129508\pi\) | |||||||
\(48\) | 0.118034 | + | 0.363271i | 0.0170367 | + | 0.0524337i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 0.809017 | − | 0.587785i | 0.114412 | − | 0.0831254i | ||||
\(51\) | −0.0729490 | − | 0.224514i | −0.0102149 | − | 0.0314382i | ||||
\(52\) | −0.618034 | + | 1.90211i | −0.0857059 | + | 0.263776i | ||||
\(53\) | 2.61803 | + | 1.90211i | 0.359615 | + | 0.261275i | 0.752891 | − | 0.658145i | \(-0.228659\pi\) |
−0.393277 | + | 0.919420i | \(0.628659\pi\) | |||||||
\(54\) | 2.23607 | 0.304290 | ||||||||
\(55\) | −1.69098 | − | 2.85317i | −0.228012 | − | 0.384721i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0.0450850 | + | 0.0327561i | 0.00597165 | + | 0.00433866i | ||||
\(58\) | −0.381966 | + | 1.17557i | −0.0501546 | + | 0.154360i | ||||
\(59\) | −1.66312 | − | 5.11855i | −0.216520 | − | 0.666379i | −0.999042 | − | 0.0437567i | \(-0.986067\pi\) |
0.782523 | − | 0.622622i | \(-0.213933\pi\) | |||||||
\(60\) | 0.309017 | − | 0.224514i | 0.0398939 | − | 0.0289846i | ||||
\(61\) | −10.0902 | + | 7.33094i | −1.29191 | + | 0.938630i | −0.999842 | − | 0.0177660i | \(-0.994345\pi\) |
−0.292072 | + | 0.956396i | \(0.594345\pi\) | |||||||
\(62\) | −1.00000 | − | 3.07768i | −0.127000 | − | 0.390866i | ||||
\(63\) | 0.881966 | − | 2.71441i | 0.111117 | − | 0.341984i | ||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | −0.645898 | − | 1.08981i | −0.0795046 | − | 0.134147i | ||||
\(67\) | −5.09017 | −0.621863 | −0.310932 | − | 0.950432i | \(-0.600641\pi\) | ||||
−0.310932 | + | 0.950432i | \(0.600641\pi\) | |||||||
\(68\) | 0.500000 | + | 0.363271i | 0.0606339 | + | 0.0440531i | ||||
\(69\) | 0.708204 | − | 2.17963i | 0.0852577 | − | 0.262396i | ||||
\(70\) | −0.309017 | − | 0.951057i | −0.0369346 | − | 0.113673i | ||||
\(71\) | −3.00000 | + | 2.17963i | −0.356034 | + | 0.258674i | −0.751396 | − | 0.659851i | \(-0.770619\pi\) |
0.395362 | + | 0.918526i | \(0.370619\pi\) | |||||||
\(72\) | −2.30902 | + | 1.67760i | −0.272120 | + | 0.197707i | ||||
\(73\) | −2.20820 | − | 6.79615i | −0.258451 | − | 0.795430i | −0.993130 | − | 0.117015i | \(-0.962667\pi\) |
0.734679 | − | 0.678414i | \(-0.237333\pi\) | |||||||
\(74\) | −0.763932 | + | 2.35114i | −0.0888053 | + | 0.273315i | ||||
\(75\) | −0.309017 | − | 0.224514i | −0.0356822 | − | 0.0259246i | ||||
\(76\) | −0.145898 | −0.0167357 | ||||||||
\(77\) | −3.23607 | + | 0.726543i | −0.368784 | + | 0.0827972i | ||||
\(78\) | 0.763932 | 0.0864983 | ||||||||
\(79\) | 0.381966 | + | 0.277515i | 0.0429745 | + | 0.0312228i | 0.609065 | − | 0.793120i | \(-0.291545\pi\) |
−0.566091 | + | 0.824343i | \(0.691545\pi\) | |||||||
\(80\) | −0.309017 | + | 0.951057i | −0.0345492 | + | 0.106331i | ||||
\(81\) | 2.38197 | + | 7.33094i | 0.264663 | + | 0.814549i | ||||
\(82\) | −4.30902 | + | 3.13068i | −0.475851 | + | 0.345726i | ||||
\(83\) | −4.30902 | + | 3.13068i | −0.472976 | + | 0.343637i | −0.798600 | − | 0.601862i | \(-0.794426\pi\) |
0.325624 | + | 0.945499i | \(0.394426\pi\) | |||||||
\(84\) | −0.118034 | − | 0.363271i | −0.0128786 | − | 0.0396361i | ||||
\(85\) | 0.190983 | − | 0.587785i | 0.0207150 | − | 0.0637543i | ||||
\(86\) | 3.92705 | + | 2.85317i | 0.423465 | + | 0.307665i | ||||
\(87\) | 0.472136 | 0.0506183 | ||||||||
\(88\) | 3.04508 | + | 1.31433i | 0.324607 | + | 0.140108i | ||||
\(89\) | 1.90983 | 0.202442 | 0.101221 | − | 0.994864i | \(-0.467725\pi\) | ||||
0.101221 | + | 0.994864i | \(0.467725\pi\) | |||||||
\(90\) | 2.30902 | + | 1.67760i | 0.243392 | + | 0.176834i | ||||
\(91\) | 0.618034 | − | 1.90211i | 0.0647876 | − | 0.199396i | ||||
\(92\) | 1.85410 | + | 5.70634i | 0.193303 | + | 0.594927i | ||||
\(93\) | −1.00000 | + | 0.726543i | −0.103695 | + | 0.0753390i | ||||
\(94\) | 3.85410 | − | 2.80017i | 0.397520 | − | 0.288815i | ||||
\(95\) | 0.0450850 | + | 0.138757i | 0.00462562 | + | 0.0142362i | ||||
\(96\) | −0.118034 | + | 0.363271i | −0.0120468 | + | 0.0370762i | ||||
\(97\) | −8.54508 | − | 6.20837i | −0.867622 | − | 0.630364i | 0.0623259 | − | 0.998056i | \(-0.480148\pi\) |
−0.929948 | + | 0.367692i | \(0.880148\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 6.25329 | − | 7.10642i | 0.628479 | − | 0.714222i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −7.23607 | − | 5.25731i | −0.720016 | − | 0.523122i | 0.166374 | − | 0.986063i | \(-0.446794\pi\) |
−0.886389 | + | 0.462941i | \(0.846794\pi\) | |||||||
\(102\) | 0.0729490 | − | 0.224514i | 0.00722303 | − | 0.0222302i | ||||
\(103\) | 0.291796 | + | 0.898056i | 0.0287515 | + | 0.0884881i | 0.964403 | − | 0.264438i | \(-0.0851866\pi\) |
−0.935651 | + | 0.352926i | \(0.885187\pi\) | |||||||
\(104\) | −1.61803 | + | 1.17557i | −0.158661 | + | 0.115274i | ||||
\(105\) | −0.309017 | + | 0.224514i | −0.0301570 | + | 0.0219103i | ||||
\(106\) | 1.00000 | + | 3.07768i | 0.0971286 | + | 0.298931i | ||||
\(107\) | −5.44427 | + | 16.7557i | −0.526318 | + | 1.61984i | 0.235378 | + | 0.971904i | \(0.424367\pi\) |
−0.761695 | + | 0.647935i | \(0.775633\pi\) | |||||||
\(108\) | 1.80902 | + | 1.31433i | 0.174073 | + | 0.126471i | ||||
\(109\) | −8.47214 | −0.811483 | −0.405742 | − | 0.913988i | \(-0.632987\pi\) | ||||
−0.405742 | + | 0.913988i | \(0.632987\pi\) | |||||||
\(110\) | 0.309017 | − | 3.30220i | 0.0294636 | − | 0.314852i | ||||
\(111\) | 0.944272 | 0.0896263 | ||||||||
\(112\) | 0.809017 | + | 0.587785i | 0.0764449 | + | 0.0555405i | ||||
\(113\) | 1.95492 | − | 6.01661i | 0.183903 | − | 0.565995i | −0.816025 | − | 0.578017i | \(-0.803827\pi\) |
0.999928 | + | 0.0120219i | \(0.00382677\pi\) | |||||||
\(114\) | 0.0172209 | + | 0.0530006i | 0.00161289 | + | 0.00496396i | ||||
\(115\) | 4.85410 | − | 3.52671i | 0.452647 | − | 0.328868i | ||||
\(116\) | −1.00000 | + | 0.726543i | −0.0928477 | + | 0.0674578i | ||||
\(117\) | 1.76393 | + | 5.42882i | 0.163076 | + | 0.501895i | ||||
\(118\) | 1.66312 | − | 5.11855i | 0.153103 | − | 0.471201i | ||||
\(119\) | −0.500000 | − | 0.363271i | −0.0458349 | − | 0.0333010i | ||||
\(120\) | 0.381966 | 0.0348686 | ||||||||
\(121\) | −10.8090 | − | 2.04087i | −0.982638 | − | 0.185534i | ||||
\(122\) | −12.4721 | −1.12917 | ||||||||
\(123\) | 1.64590 | + | 1.19581i | 0.148406 | + | 0.107823i | ||||
\(124\) | 1.00000 | − | 3.07768i | 0.0898027 | − | 0.276384i | ||||
\(125\) | −0.309017 | − | 0.951057i | −0.0276393 | − | 0.0850651i | ||||
\(126\) | 2.30902 | − | 1.67760i | 0.205704 | − | 0.149452i | ||||
\(127\) | 12.4721 | − | 9.06154i | 1.10672 | − | 0.804081i | 0.124579 | − | 0.992210i | \(-0.460242\pi\) |
0.982144 | + | 0.188128i | \(0.0602421\pi\) | |||||||
\(128\) | −0.309017 | − | 0.951057i | −0.0273135 | − | 0.0840623i | ||||
\(129\) | 0.572949 | − | 1.76336i | 0.0504453 | − | 0.155255i | ||||
\(130\) | 1.61803 | + | 1.17557i | 0.141911 | + | 0.103104i | ||||
\(131\) | −16.7984 | −1.46768 | −0.733840 | − | 0.679322i | \(-0.762274\pi\) | ||||
−0.733840 | + | 0.679322i | \(0.762274\pi\) | |||||||
\(132\) | 0.118034 | − | 1.26133i | 0.0102735 | − | 0.109784i | ||||
\(133\) | 0.145898 | 0.0126510 | ||||||||
\(134\) | −4.11803 | − | 2.99193i | −0.355744 | − | 0.258463i | ||||
\(135\) | 0.690983 | − | 2.12663i | 0.0594703 | − | 0.183031i | ||||
\(136\) | 0.190983 | + | 0.587785i | 0.0163767 | + | 0.0504022i | ||||
\(137\) | −8.16312 | + | 5.93085i | −0.697422 | + | 0.506707i | −0.879092 | − | 0.476653i | \(-0.841850\pi\) |
0.181669 | + | 0.983360i | \(0.441850\pi\) | |||||||
\(138\) | 1.85410 | − | 1.34708i | 0.157832 | − | 0.114671i | ||||
\(139\) | −2.94427 | − | 9.06154i | −0.249730 | − | 0.768590i | −0.994822 | − | 0.101628i | \(-0.967595\pi\) |
0.745093 | − | 0.666961i | \(-0.232405\pi\) | |||||||
\(140\) | 0.309017 | − | 0.951057i | 0.0261167 | − | 0.0803789i | ||||
\(141\) | −1.47214 | − | 1.06957i | −0.123976 | − | 0.0900740i | ||||
\(142\) | −3.70820 | −0.311186 | ||||||||
\(143\) | 4.38197 | − | 4.97980i | 0.366438 | − | 0.416432i | ||||
\(144\) | −2.85410 | −0.237842 | ||||||||
\(145\) | 1.00000 | + | 0.726543i | 0.0830455 | + | 0.0603361i | ||||
\(146\) | 2.20820 | − | 6.79615i | 0.182752 | − | 0.562454i | ||||
\(147\) | 0.118034 | + | 0.363271i | 0.00973528 | + | 0.0299621i | ||||
\(148\) | −2.00000 | + | 1.45309i | −0.164399 | + | 0.119443i | ||||
\(149\) | 1.47214 | − | 1.06957i | 0.120602 | − | 0.0876225i | −0.525849 | − | 0.850578i | \(-0.676252\pi\) |
0.646451 | + | 0.762955i | \(0.276252\pi\) | |||||||
\(150\) | −0.118034 | − | 0.363271i | −0.00963743 | − | 0.0296610i | ||||
\(151\) | −4.85410 | + | 14.9394i | −0.395021 | + | 1.21575i | 0.533924 | + | 0.845533i | \(0.320717\pi\) |
−0.928945 | + | 0.370218i | \(0.879283\pi\) | |||||||
\(152\) | −0.118034 | − | 0.0857567i | −0.00957382 | − | 0.00695579i | ||||
\(153\) | 1.76393 | 0.142605 | ||||||||
\(154\) | −3.04508 | − | 1.31433i | −0.245380 | − | 0.105912i | ||||
\(155\) | −3.23607 | −0.259927 | ||||||||
\(156\) | 0.618034 | + | 0.449028i | 0.0494823 | + | 0.0359510i | ||||
\(157\) | 4.23607 | − | 13.0373i | 0.338075 | − | 1.04049i | −0.627112 | − | 0.778929i | \(-0.715763\pi\) |
0.965187 | − | 0.261559i | \(-0.0842367\pi\) | |||||||
\(158\) | 0.145898 | + | 0.449028i | 0.0116070 | + | 0.0357227i | ||||
\(159\) | 1.00000 | − | 0.726543i | 0.0793052 | − | 0.0576186i | ||||
\(160\) | −0.809017 | + | 0.587785i | −0.0639584 | + | 0.0464685i | ||||
\(161\) | −1.85410 | − | 5.70634i | −0.146124 | − | 0.449723i | ||||
\(162\) | −2.38197 | + | 7.33094i | −0.187145 | + | 0.575973i | ||||
\(163\) | 3.11803 | + | 2.26538i | 0.244223 | + | 0.177439i | 0.703163 | − | 0.711029i | \(-0.251771\pi\) |
−0.458939 | + | 0.888468i | \(0.651771\pi\) | |||||||
\(164\) | −5.32624 | −0.415909 | ||||||||
\(165\) | −1.23607 | + | 0.277515i | −0.0962278 | + | 0.0216045i | ||||
\(166\) | −5.32624 | −0.413396 | ||||||||
\(167\) | −2.00000 | − | 1.45309i | −0.154765 | − | 0.112443i | 0.507708 | − | 0.861529i | \(-0.330493\pi\) |
−0.662473 | + | 0.749086i | \(0.730493\pi\) | |||||||
\(168\) | 0.118034 | − | 0.363271i | 0.00910652 | − | 0.0280270i | ||||
\(169\) | −2.78115 | − | 8.55951i | −0.213935 | − | 0.658424i | ||||
\(170\) | 0.500000 | − | 0.363271i | 0.0383482 | − | 0.0278616i | ||||
\(171\) | −0.336881 | + | 0.244758i | −0.0257619 | + | 0.0187171i | ||||
\(172\) | 1.50000 | + | 4.61653i | 0.114374 | + | 0.352007i | ||||
\(173\) | −3.70820 | + | 11.4127i | −0.281930 | + | 0.867690i | 0.705373 | + | 0.708837i | \(0.250780\pi\) |
−0.987302 | + | 0.158853i | \(0.949220\pi\) | |||||||
\(174\) | 0.381966 | + | 0.277515i | 0.0289568 | + | 0.0210383i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 1.69098 | + | 2.85317i | 0.127463 | + | 0.215066i | ||||
\(177\) | −2.05573 | −0.154518 | ||||||||
\(178\) | 1.54508 | + | 1.12257i | 0.115809 | + | 0.0841402i | ||||
\(179\) | −2.66312 | + | 8.19624i | −0.199051 | + | 0.612616i | 0.800855 | + | 0.598859i | \(0.204379\pi\) |
−0.999905 | + | 0.0137566i | \(0.995621\pi\) | |||||||
\(180\) | 0.881966 | + | 2.71441i | 0.0657379 | + | 0.202320i | ||||
\(181\) | −10.0902 | + | 7.33094i | −0.749996 | + | 0.544904i | −0.895826 | − | 0.444405i | \(-0.853415\pi\) |
0.145829 | + | 0.989310i | \(0.453415\pi\) | |||||||
\(182\) | 1.61803 | − | 1.17557i | 0.119937 | − | 0.0871391i | ||||
\(183\) | 1.47214 | + | 4.53077i | 0.108823 | + | 0.334924i | ||||
\(184\) | −1.85410 | + | 5.70634i | −0.136686 | + | 0.420677i | ||||
\(185\) | 2.00000 | + | 1.45309i | 0.147043 | + | 0.106833i | ||||
\(186\) | −1.23607 | −0.0906329 | ||||||||
\(187\) | −1.04508 | − | 1.76336i | −0.0764242 | − | 0.128949i | ||||
\(188\) | 4.76393 | 0.347445 | ||||||||
\(189\) | −1.80902 | − | 1.31433i | −0.131587 | − | 0.0956033i | ||||
\(190\) | −0.0450850 | + | 0.138757i | −0.00327081 | + | 0.0100665i | ||||
\(191\) | −3.23607 | − | 9.95959i | −0.234154 | − | 0.720651i | −0.997233 | − | 0.0743455i | \(-0.976313\pi\) |
0.763079 | − | 0.646305i | \(-0.223687\pi\) | |||||||
\(192\) | −0.309017 | + | 0.224514i | −0.0223014 | + | 0.0162029i | ||||
\(193\) | −1.61803 | + | 1.17557i | −0.116469 | + | 0.0846194i | −0.644495 | − | 0.764609i | \(-0.722932\pi\) |
0.528026 | + | 0.849228i | \(0.322932\pi\) | |||||||
\(194\) | −3.26393 | − | 10.0453i | −0.234337 | − | 0.721214i | ||||
\(195\) | 0.236068 | − | 0.726543i | 0.0169052 | − | 0.0520288i | ||||
\(196\) | −0.809017 | − | 0.587785i | −0.0577869 | − | 0.0419847i | ||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 9.23607 | − | 2.07363i | 0.656379 | − | 0.147366i | ||||
\(199\) | 7.41641 | 0.525735 | 0.262868 | − | 0.964832i | \(-0.415332\pi\) | ||||
0.262868 | + | 0.964832i | \(0.415332\pi\) | |||||||
\(200\) | 0.809017 | + | 0.587785i | 0.0572061 | + | 0.0415627i | ||||
\(201\) | −0.600813 | + | 1.84911i | −0.0423781 | + | 0.130426i | ||||
\(202\) | −2.76393 | − | 8.50651i | −0.194470 | − | 0.598516i | ||||
\(203\) | 1.00000 | − | 0.726543i | 0.0701862 | − | 0.0509933i | ||||
\(204\) | 0.190983 | − | 0.138757i | 0.0133715 | − | 0.00971495i | ||||
\(205\) | 1.64590 | + | 5.06555i | 0.114955 | + | 0.353794i | ||||
\(206\) | −0.291796 | + | 0.898056i | −0.0203304 | + | 0.0625705i | ||||
\(207\) | 13.8541 | + | 10.0656i | 0.962927 | + | 0.699607i | ||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | 0.444272 | + | 0.191758i | 0.0307309 | + | 0.0132642i | ||||
\(210\) | −0.381966 | −0.0263582 | ||||||||
\(211\) | −18.0172 | − | 13.0903i | −1.24036 | − | 0.901172i | −0.242735 | − | 0.970093i | \(-0.578044\pi\) |
−0.997622 | + | 0.0689209i | \(0.978044\pi\) | |||||||
\(212\) | −1.00000 | + | 3.07768i | −0.0686803 | + | 0.211376i | ||||
\(213\) | 0.437694 | + | 1.34708i | 0.0299903 | + | 0.0923007i | ||||
\(214\) | −14.2533 | + | 10.3556i | −0.974335 | + | 0.707896i | ||||
\(215\) | 3.92705 | − | 2.85317i | 0.267823 | − | 0.194585i | ||||
\(216\) | 0.690983 | + | 2.12663i | 0.0470154 | + | 0.144699i | ||||
\(217\) | −1.00000 | + | 3.07768i | −0.0678844 | + | 0.208927i | ||||
\(218\) | −6.85410 | − | 4.97980i | −0.464218 | − | 0.337274i | ||||
\(219\) | −2.72949 | −0.184442 | ||||||||
\(220\) | 2.19098 | − | 2.48990i | 0.147716 | − | 0.167869i | ||||
\(221\) | 1.23607 | 0.0831469 | ||||||||
\(222\) | 0.763932 | + | 0.555029i | 0.0512718 | + | 0.0372511i | ||||
\(223\) | 6.09017 | − | 18.7436i | 0.407828 | − | 1.25517i | −0.510683 | − | 0.859769i | \(-0.670607\pi\) |
0.918511 | − | 0.395396i | \(-0.129393\pi\) | |||||||
\(224\) | 0.309017 | + | 0.951057i | 0.0206471 | + | 0.0635451i | ||||
\(225\) | 2.30902 | − | 1.67760i | 0.153934 | − | 0.111840i | ||||
\(226\) | 5.11803 | − | 3.71847i | 0.340447 | − | 0.247349i | ||||
\(227\) | −2.86475 | − | 8.81678i | −0.190140 | − | 0.585190i | 0.809859 | − | 0.586624i | \(-0.199543\pi\) |
−0.999999 | + | 0.00143420i | \(0.999543\pi\) | |||||||
\(228\) | −0.0172209 | + | 0.0530006i | −0.00114048 | + | 0.00351005i | ||||
\(229\) | 23.5623 | + | 17.1190i | 1.55704 | + | 1.13126i | 0.938384 | + | 0.345596i | \(0.112323\pi\) |
0.618657 | + | 0.785661i | \(0.287677\pi\) | |||||||
\(230\) | 6.00000 | 0.395628 | ||||||||
\(231\) | −0.118034 | + | 1.26133i | −0.00776607 | + | 0.0829892i | ||||
\(232\) | −1.23607 | −0.0811518 | ||||||||
\(233\) | 17.8713 | + | 12.9843i | 1.17079 | + | 0.850628i | 0.991103 | − | 0.133096i | \(-0.0424918\pi\) |
0.179686 | + | 0.983724i | \(0.442492\pi\) | |||||||
\(234\) | −1.76393 | + | 5.42882i | −0.115312 | + | 0.354893i | ||||
\(235\) | −1.47214 | − | 4.53077i | −0.0960316 | − | 0.295555i | ||||
\(236\) | 4.35410 | − | 3.16344i | 0.283428 | − | 0.205922i | ||||
\(237\) | 0.145898 | − | 0.106001i | 0.00947710 | − | 0.00688551i | ||||
\(238\) | −0.190983 | − | 0.587785i | −0.0123796 | − | 0.0381005i | ||||
\(239\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(240\) | 0.309017 | + | 0.224514i | 0.0199470 | + | 0.0144923i | ||||
\(241\) | −27.2705 | −1.75665 | −0.878324 | − | 0.478066i | \(-0.841338\pi\) | ||||
−0.878324 | + | 0.478066i | \(0.841338\pi\) | |||||||
\(242\) | −7.54508 | − | 8.00448i | −0.485016 | − | 0.514547i | ||||
\(243\) | 9.65248 | 0.619207 | ||||||||
\(244\) | −10.0902 | − | 7.33094i | −0.645957 | − | 0.469315i | ||||
\(245\) | −0.309017 | + | 0.951057i | −0.0197424 | + | 0.0607608i | ||||
\(246\) | 0.628677 | + | 1.93487i | 0.0400830 | + | 0.123363i | ||||
\(247\) | −0.236068 | + | 0.171513i | −0.0150206 | + | 0.0109131i | ||||
\(248\) | 2.61803 | − | 1.90211i | 0.166245 | − | 0.120784i | ||||
\(249\) | 0.628677 | + | 1.93487i | 0.0398408 | + | 0.122617i | ||||
\(250\) | 0.309017 | − | 0.951057i | 0.0195440 | − | 0.0601501i | ||||
\(251\) | 21.7082 | + | 15.7719i | 1.37021 | + | 0.995516i | 0.997721 | + | 0.0674790i | \(0.0214956\pi\) |
0.372489 | + | 0.928037i | \(0.378504\pi\) | |||||||
\(252\) | 2.85410 | 0.179792 | ||||||||
\(253\) | 1.85410 | − | 19.8132i | 0.116566 | − | 1.24564i | ||||
\(254\) | 15.4164 | 0.967311 | ||||||||
\(255\) | −0.190983 | − | 0.138757i | −0.0119598 | − | 0.00868932i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | 2.91641 | + | 8.97578i | 0.181921 | + | 0.559894i | 0.999882 | − | 0.0153796i | \(-0.00489567\pi\) |
−0.817961 | + | 0.575273i | \(0.804896\pi\) | |||||||
\(258\) | 1.50000 | − | 1.08981i | 0.0933859 | − | 0.0678488i | ||||
\(259\) | 2.00000 | − | 1.45309i | 0.124274 | − | 0.0902903i | ||||
\(260\) | 0.618034 | + | 1.90211i | 0.0383288 | + | 0.117964i | ||||
\(261\) | −1.09017 | + | 3.35520i | −0.0674798 | + | 0.207682i | ||||
\(262\) | −13.5902 | − | 9.87384i | −0.839604 | − | 0.610008i | ||||
\(263\) | 2.18034 | 0.134446 | 0.0672228 | − | 0.997738i | \(-0.478586\pi\) | ||||
0.0672228 | + | 0.997738i | \(0.478586\pi\) | |||||||
\(264\) | 0.836881 | − | 0.951057i | 0.0515065 | − | 0.0585335i | ||||
\(265\) | 3.23607 | 0.198790 | ||||||||
\(266\) | 0.118034 | + | 0.0857567i | 0.00723713 | + | 0.00525808i | ||||
\(267\) | 0.225425 | − | 0.693786i | 0.0137958 | − | 0.0424590i | ||||
\(268\) | −1.57295 | − | 4.84104i | −0.0960832 | − | 0.295714i | ||||
\(269\) | −8.23607 | + | 5.98385i | −0.502162 | + | 0.364842i | −0.809842 | − | 0.586648i | \(-0.800447\pi\) |
0.307680 | + | 0.951490i | \(0.400447\pi\) | |||||||
\(270\) | 1.80902 | − | 1.31433i | 0.110093 | − | 0.0799874i | ||||
\(271\) | −5.38197 | − | 16.5640i | −0.326931 | − | 1.00619i | −0.970561 | − | 0.240854i | \(-0.922573\pi\) |
0.643630 | − | 0.765337i | \(-0.277427\pi\) | |||||||
\(272\) | −0.190983 | + | 0.587785i | −0.0115800 | + | 0.0356397i | ||||
\(273\) | −0.618034 | − | 0.449028i | −0.0374051 | − | 0.0271764i | ||||
\(274\) | −10.0902 | −0.609569 | ||||||||
\(275\) | −3.04508 | − | 1.31433i | −0.183626 | − | 0.0792569i | ||||
\(276\) | 2.29180 | 0.137950 | ||||||||
\(277\) | 15.9443 | + | 11.5842i | 0.957998 | + | 0.696027i | 0.952685 | − | 0.303959i | \(-0.0983087\pi\) |
0.00531342 | + | 0.999986i | \(0.498309\pi\) | |||||||
\(278\) | 2.94427 | − | 9.06154i | 0.176586 | − | 0.543475i | ||||
\(279\) | −2.85410 | − | 8.78402i | −0.170871 | − | 0.525886i | ||||
\(280\) | 0.809017 | − | 0.587785i | 0.0483480 | − | 0.0351269i | ||||
\(281\) | 4.07295 | − | 2.95917i | 0.242972 | − | 0.176529i | −0.459634 | − | 0.888108i | \(-0.652020\pi\) |
0.702606 | + | 0.711579i | \(0.252020\pi\) | |||||||
\(282\) | −0.562306 | − | 1.73060i | −0.0334848 | − | 0.103056i | ||||
\(283\) | 3.70820 | − | 11.4127i | 0.220430 | − | 0.678413i | −0.778294 | − | 0.627901i | \(-0.783914\pi\) |
0.998723 | − | 0.0505127i | \(-0.0160855\pi\) | |||||||
\(284\) | −3.00000 | − | 2.17963i | −0.178017 | − | 0.129337i | ||||
\(285\) | 0.0557281 | 0.00330105 | ||||||||
\(286\) | 6.47214 | − | 1.45309i | 0.382705 | − | 0.0859227i | ||||
\(287\) | 5.32624 | 0.314398 | ||||||||
\(288\) | −2.30902 | − | 1.67760i | −0.136060 | − | 0.0988535i | ||||
\(289\) | −5.13525 | + | 15.8047i | −0.302074 | + | 0.929688i | ||||
\(290\) | 0.381966 | + | 1.17557i | 0.0224298 | + | 0.0690319i | ||||
\(291\) | −3.26393 | + | 2.37139i | −0.191335 | + | 0.139013i | ||||
\(292\) | 5.78115 | − | 4.20025i | 0.338316 | − | 0.245801i | ||||
\(293\) | −2.32624 | − | 7.15942i | −0.135900 | − | 0.418258i | 0.859829 | − | 0.510583i | \(-0.170570\pi\) |
−0.995729 | + | 0.0923246i | \(0.970570\pi\) | |||||||
\(294\) | −0.118034 | + | 0.363271i | −0.00688388 | + | 0.0211864i | ||||
\(295\) | −4.35410 | − | 3.16344i | −0.253506 | − | 0.184183i | ||||
\(296\) | −2.47214 | −0.143690 | ||||||||
\(297\) | −3.78115 | − | 6.37988i | −0.219405 | − | 0.370198i | ||||
\(298\) | 1.81966 | 0.105410 | ||||||||
\(299\) | 9.70820 | + | 7.05342i | 0.561440 | + | 0.407910i | ||||
\(300\) | 0.118034 | − | 0.363271i | 0.00681470 | − | 0.0209735i | ||||
\(301\) | −1.50000 | − | 4.61653i | −0.0864586 | − | 0.266092i | ||||
\(302\) | −12.7082 | + | 9.23305i | −0.731275 | + | 0.531302i | ||||
\(303\) | −2.76393 | + | 2.00811i | −0.158784 | + | 0.115363i | ||||
\(304\) | −0.0450850 | − | 0.138757i | −0.00258580 | − | 0.00795828i | ||||
\(305\) | −3.85410 | + | 11.8617i | −0.220685 | + | 0.679199i | ||||
\(306\) | 1.42705 | + | 1.03681i | 0.0815791 | + | 0.0592707i | ||||
\(307\) | 7.43769 | 0.424492 | 0.212246 | − | 0.977216i | \(-0.431922\pi\) | ||||
0.212246 | + | 0.977216i | \(0.431922\pi\) | |||||||
\(308\) | −1.69098 | − | 2.85317i | −0.0963527 | − | 0.162574i | ||||
\(309\) | 0.360680 | 0.0205184 | ||||||||
\(310\) | −2.61803 | − | 1.90211i | −0.148694 | − | 0.108033i | ||||
\(311\) | 3.43769 | − | 10.5801i | 0.194934 | − | 0.599944i | −0.805044 | − | 0.593216i | \(-0.797858\pi\) |
0.999977 | − | 0.00672876i | \(-0.00214185\pi\) | |||||||
\(312\) | 0.236068 | + | 0.726543i | 0.0133647 | + | 0.0411324i | ||||
\(313\) | −4.73607 | + | 3.44095i | −0.267698 | + | 0.194494i | −0.713534 | − | 0.700621i | \(-0.752907\pi\) |
0.445836 | + | 0.895115i | \(0.352907\pi\) | |||||||
\(314\) | 11.0902 | − | 8.05748i | 0.625854 | − | 0.454710i | ||||
\(315\) | −0.881966 | − | 2.71441i | −0.0496932 | − | 0.152940i | ||||
\(316\) | −0.145898 | + | 0.449028i | −0.00820741 | + | 0.0252598i | ||||
\(317\) | 20.4164 | + | 14.8334i | 1.14670 | + | 0.833126i | 0.988039 | − | 0.154207i | \(-0.0492823\pi\) |
0.158661 | + | 0.987333i | \(0.449282\pi\) | |||||||
\(318\) | 1.23607 | 0.0693153 | ||||||||
\(319\) | 4.00000 | − | 0.898056i | 0.223957 | − | 0.0502815i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 5.44427 | + | 3.95550i | 0.303870 | + | 0.220774i | ||||
\(322\) | 1.85410 | − | 5.70634i | 0.103325 | − | 0.318002i | ||||
\(323\) | 0.0278640 | + | 0.0857567i | 0.00155040 | + | 0.00477163i | ||||
\(324\) | −6.23607 | + | 4.53077i | −0.346448 | + | 0.251709i | ||||
\(325\) | 1.61803 | − | 1.17557i | 0.0897524 | − | 0.0652089i | ||||
\(326\) | 1.19098 | + | 3.66547i | 0.0659624 | + | 0.203012i | ||||
\(327\) | −1.00000 | + | 3.07768i | −0.0553001 | + | 0.170196i | ||||
\(328\) | −4.30902 | − | 3.13068i | −0.237926 | − | 0.172863i | ||||
\(329\) | −4.76393 | −0.262644 | ||||||||
\(330\) | −1.16312 | − | 0.502029i | −0.0640276 | − | 0.0276358i | ||||
\(331\) | −23.0344 | −1.26609 | −0.633044 | − | 0.774116i | \(-0.718195\pi\) | ||||
−0.633044 | + | 0.774116i | \(0.718195\pi\) | |||||||
\(332\) | −4.30902 | − | 3.13068i | −0.236488 | − | 0.171819i | ||||
\(333\) | −2.18034 | + | 6.71040i | −0.119482 | + | 0.367727i | ||||
\(334\) | −0.763932 | − | 2.35114i | −0.0418005 | − | 0.128649i | ||||
\(335\) | −4.11803 | + | 2.99193i | −0.224992 | + | 0.163466i | ||||
\(336\) | 0.309017 | − | 0.224514i | 0.0168583 | − | 0.0122482i | ||||
\(337\) | 4.13525 | + | 12.7270i | 0.225262 | + | 0.693284i | 0.998265 | + | 0.0588821i | \(0.0187536\pi\) |
−0.773003 | + | 0.634402i | \(0.781246\pi\) | |||||||
\(338\) | 2.78115 | − | 8.55951i | 0.151275 | − | 0.465576i | ||||
\(339\) | −1.95492 | − | 1.42033i | −0.106176 | − | 0.0771417i | ||||
\(340\) | 0.618034 | 0.0335176 | ||||||||
\(341\) | −7.09017 | + | 8.05748i | −0.383954 | + | 0.436337i | ||||
\(342\) | −0.416408 | −0.0225168 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | −1.50000 | + | 4.61653i | −0.0808746 | + | 0.248906i | ||||
\(345\) | −0.708204 | − | 2.17963i | −0.0381284 | − | 0.117347i | ||||
\(346\) | −9.70820 | + | 7.05342i | −0.521916 | + | 0.379194i | ||||
\(347\) | −8.35410 | + | 6.06961i | −0.448472 | + | 0.325834i | −0.788992 | − | 0.614403i | \(-0.789397\pi\) |
0.340520 | + | 0.940237i | \(0.389397\pi\) | |||||||
\(348\) | 0.145898 | + | 0.449028i | 0.00782096 | + | 0.0240704i | ||||
\(349\) | −4.47214 | + | 13.7638i | −0.239388 | + | 0.736760i | 0.757121 | + | 0.653275i | \(0.226605\pi\) |
−0.996509 | + | 0.0834857i | \(0.973395\pi\) | |||||||
\(350\) | −0.809017 | − | 0.587785i | −0.0432438 | − | 0.0314184i | ||||
\(351\) | 4.47214 | 0.238705 | ||||||||
\(352\) | −0.309017 | + | 3.30220i | −0.0164707 | + | 0.176008i | ||||
\(353\) | 27.4508 | 1.46106 | 0.730531 | − | 0.682880i | \(-0.239273\pi\) | ||||
0.730531 | + | 0.682880i | \(0.239273\pi\) | |||||||
\(354\) | −1.66312 | − | 1.20833i | −0.0883938 | − | 0.0642218i | ||||
\(355\) | −1.14590 | + | 3.52671i | −0.0608180 | + | 0.187178i | ||||
\(356\) | 0.590170 | + | 1.81636i | 0.0312789 | + | 0.0962667i | ||||
\(357\) | −0.190983 | + | 0.138757i | −0.0101079 | + | 0.00734381i | ||||
\(358\) | −6.97214 | + | 5.06555i | −0.368489 | + | 0.267723i | ||||
\(359\) | 3.90983 | + | 12.0332i | 0.206353 | + | 0.635089i | 0.999655 | + | 0.0262609i | \(0.00836008\pi\) |
−0.793302 | + | 0.608828i | \(0.791640\pi\) | |||||||
\(360\) | −0.881966 | + | 2.71441i | −0.0464837 | + | 0.143062i | ||||
\(361\) | 15.3541 | + | 11.1554i | 0.808111 | + | 0.587127i | ||||
\(362\) | −12.4721 | −0.655521 | ||||||||
\(363\) | −2.01722 | + | 3.68571i | −0.105877 | + | 0.193450i | ||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | −5.78115 | − | 4.20025i | −0.302599 | − | 0.219851i | ||||
\(366\) | −1.47214 | + | 4.53077i | −0.0769498 | + | 0.236827i | ||||
\(367\) | 1.79837 | + | 5.53483i | 0.0938744 | + | 0.288916i | 0.986959 | − | 0.160974i | \(-0.0514634\pi\) |
−0.893084 | + | 0.449889i | \(0.851463\pi\) | |||||||
\(368\) | −4.85410 | + | 3.52671i | −0.253038 | + | 0.183843i | ||||
\(369\) | −12.2984 | + | 8.93529i | −0.640228 | + | 0.465153i | ||||
\(370\) | 0.763932 | + | 2.35114i | 0.0397149 | + | 0.122230i | ||||
\(371\) | 1.00000 | − | 3.07768i | 0.0519174 | − | 0.159785i | ||||
\(372\) | −1.00000 | − | 0.726543i | −0.0518476 | − | 0.0376695i | ||||
\(373\) | 15.5279 | 0.804002 | 0.402001 | − | 0.915639i | \(-0.368315\pi\) | ||||
0.402001 | + | 0.915639i | \(0.368315\pi\) | |||||||
\(374\) | 0.190983 | − | 2.04087i | 0.00987550 | − | 0.105531i | ||||
\(375\) | −0.381966 | −0.0197246 | ||||||||
\(376\) | 3.85410 | + | 2.80017i | 0.198760 | + | 0.144408i | ||||
\(377\) | −0.763932 | + | 2.35114i | −0.0393445 | + | 0.121090i | ||||
\(378\) | −0.690983 | − | 2.12663i | −0.0355403 | − | 0.109382i | ||||
\(379\) | 17.1074 | − | 12.4292i | 0.878748 | − | 0.638448i | −0.0541722 | − | 0.998532i | \(-0.517252\pi\) |
0.932920 | + | 0.360084i | \(0.117252\pi\) | |||||||
\(380\) | −0.118034 | + | 0.0857567i | −0.00605502 | + | 0.00439923i | ||||
\(381\) | −1.81966 | − | 5.60034i | −0.0932240 | − | 0.286914i | ||||
\(382\) | 3.23607 | − | 9.95959i | 0.165572 | − | 0.509577i | ||||
\(383\) | 19.4164 | + | 14.1068i | 0.992132 | + | 0.720826i | 0.960387 | − | 0.278670i | \(-0.0898935\pi\) |
0.0317451 | + | 0.999496i | \(0.489894\pi\) | |||||||
\(384\) | −0.381966 | −0.0194921 | ||||||||
\(385\) | −2.19098 | + | 2.48990i | −0.111663 | + | 0.126897i | ||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | 11.2082 | + | 8.14324i | 0.569745 | + | 0.413944i | ||||
\(388\) | 3.26393 | − | 10.0453i | 0.165701 | − | 0.509975i | ||||
\(389\) | 6.43769 | + | 19.8132i | 0.326404 | + | 1.00457i | 0.970803 | + | 0.239879i | \(0.0771077\pi\) |
−0.644399 | + | 0.764690i | \(0.722892\pi\) | |||||||
\(390\) | 0.618034 | − | 0.449028i | 0.0312954 | − | 0.0227374i | ||||
\(391\) | 3.00000 | − | 2.17963i | 0.151717 | − | 0.110229i | ||||
\(392\) | −0.309017 | − | 0.951057i | −0.0156077 | − | 0.0480356i | ||||
\(393\) | −1.98278 | + | 6.10237i | −0.100018 | + | 0.307824i | ||||
\(394\) | −4.85410 | − | 3.52671i | −0.244546 | − | 0.177673i | ||||
\(395\) | 0.472136 | 0.0237557 | ||||||||
\(396\) | 8.69098 | + | 3.75123i | 0.436738 | + | 0.188506i | ||||
\(397\) | 0.944272 | 0.0473916 | 0.0236958 | − | 0.999719i | \(-0.492457\pi\) | ||||
0.0236958 | + | 0.999719i | \(0.492457\pi\) | |||||||
\(398\) | 6.00000 | + | 4.35926i | 0.300753 | + | 0.218510i | ||||
\(399\) | 0.0172209 | − | 0.0530006i | 0.000862125 | − | 0.00265335i | ||||
\(400\) | 0.309017 | + | 0.951057i | 0.0154508 | + | 0.0475528i | ||||
\(401\) | −9.30902 | + | 6.76340i | −0.464870 | + | 0.337748i | −0.795439 | − | 0.606034i | \(-0.792760\pi\) |
0.330569 | + | 0.943782i | \(0.392760\pi\) | |||||||
\(402\) | −1.57295 | + | 1.14281i | −0.0784516 | + | 0.0569984i | ||||
\(403\) | −2.00000 | − | 6.15537i | −0.0996271 | − | 0.306621i | ||||
\(404\) | 2.76393 | − | 8.50651i | 0.137511 | − | 0.423215i | ||||
\(405\) | 6.23607 | + | 4.53077i | 0.309873 | + | 0.225136i | ||||
\(406\) | 1.23607 | 0.0613450 | ||||||||
\(407\) | 8.00000 | − | 1.79611i | 0.396545 | − | 0.0890300i | ||||
\(408\) | 0.236068 | 0.0116871 | ||||||||
\(409\) | −6.38197 | − | 4.63677i | −0.315568 | − | 0.229274i | 0.418714 | − | 0.908118i | \(-0.362481\pi\) |
−0.734282 | + | 0.678845i | \(0.762481\pi\) | |||||||
\(410\) | −1.64590 | + | 5.06555i | −0.0812851 | + | 0.250170i | ||||
\(411\) | 1.19098 | + | 3.66547i | 0.0587469 | + | 0.180804i | ||||
\(412\) | −0.763932 | + | 0.555029i | −0.0376362 | + | 0.0273443i | ||||
\(413\) | −4.35410 | + | 3.16344i | −0.214251 | + | 0.155663i | ||||
\(414\) | 5.29180 | + | 16.2865i | 0.260078 | + | 0.800437i | ||||
\(415\) | −1.64590 | + | 5.06555i | −0.0807940 | + | 0.248658i | ||||
\(416\) | −1.61803 | − | 1.17557i | −0.0793306 | − | 0.0576371i | ||||
\(417\) | −3.63932 | −0.178218 | ||||||||
\(418\) | 0.246711 | + | 0.416272i | 0.0120670 | + | 0.0203605i | ||||
\(419\) | −3.32624 | −0.162497 | −0.0812487 | − | 0.996694i | \(-0.525891\pi\) | ||||
−0.0812487 | + | 0.996694i | \(0.525891\pi\) | |||||||
\(420\) | −0.309017 | − | 0.224514i | −0.0150785 | − | 0.0109552i | ||||
\(421\) | 11.8541 | − | 36.4832i | 0.577734 | − | 1.77808i | −0.0489429 | − | 0.998802i | \(-0.515585\pi\) |
0.626676 | − | 0.779280i | \(-0.284415\pi\) | |||||||
\(422\) | −6.88197 | − | 21.1805i | −0.335009 | − | 1.03105i | ||||
\(423\) | 11.0000 | − | 7.99197i | 0.534838 | − | 0.388583i | ||||
\(424\) | −2.61803 | + | 1.90211i | −0.127143 | + | 0.0923748i | ||||
\(425\) | −0.190983 | − | 0.587785i | −0.00926404 | − | 0.0285118i | ||||
\(426\) | −0.437694 | + | 1.34708i | −0.0212063 | + | 0.0652664i | ||||
\(427\) | 10.0902 | + | 7.33094i | 0.488298 | + | 0.354769i | ||||
\(428\) | −17.6180 | −0.851600 | ||||||||
\(429\) | −1.29180 | − | 2.17963i | −0.0623685 | − | 0.105233i | ||||
\(430\) | 4.85410 | 0.234086 | ||||||||
\(431\) | 21.6525 | + | 15.7314i | 1.04296 | + | 0.757757i | 0.970862 | − | 0.239640i | \(-0.0770295\pi\) |
0.0721013 | + | 0.997397i | \(0.477030\pi\) | |||||||
\(432\) | −0.690983 | + | 2.12663i | −0.0332449 | + | 0.102317i | ||||
\(433\) | −12.1910 | − | 37.5200i | −0.585861 | − | 1.80310i | −0.595784 | − | 0.803145i | \(-0.703159\pi\) |
0.00992266 | − | 0.999951i | \(-0.496841\pi\) | |||||||
\(434\) | −2.61803 | + | 1.90211i | −0.125670 | + | 0.0913043i | ||||
\(435\) | 0.381966 | − | 0.277515i | 0.0183139 | − | 0.0133058i | ||||
\(436\) | −2.61803 | − | 8.05748i | −0.125381 | − | 0.385883i | ||||
\(437\) | −0.270510 | + | 0.832544i | −0.0129402 | + | 0.0398260i | ||||
\(438\) | −2.20820 | − | 1.60435i | −0.105512 | − | 0.0766590i | ||||
\(439\) | −2.65248 | −0.126596 | −0.0632979 | − | 0.997995i | \(-0.520162\pi\) | ||||
−0.0632979 | + | 0.997995i | \(0.520162\pi\) | |||||||
\(440\) | 3.23607 | − | 0.726543i | 0.154273 | − | 0.0346366i | ||||
\(441\) | −2.85410 | −0.135910 | ||||||||
\(442\) | 1.00000 | + | 0.726543i | 0.0475651 | + | 0.0345581i | ||||
\(443\) | −0.319660 | + | 0.983813i | −0.0151875 | + | 0.0467424i | −0.958363 | − | 0.285553i | \(-0.907823\pi\) |
0.943176 | + | 0.332295i | \(0.107823\pi\) | |||||||
\(444\) | 0.291796 | + | 0.898056i | 0.0138480 | + | 0.0426198i | ||||
\(445\) | 1.54508 | − | 1.12257i | 0.0732441 | − | 0.0532149i | ||||
\(446\) | 15.9443 | − | 11.5842i | 0.754983 | − | 0.548527i | ||||
\(447\) | −0.214782 | − | 0.661030i | −0.0101588 | − | 0.0312657i | ||||
\(448\) | −0.309017 | + | 0.951057i | −0.0145997 | + | 0.0449332i | ||||
\(449\) | 25.4443 | + | 18.4863i | 1.20079 | + | 0.872425i | 0.994362 | − | 0.106037i | \(-0.0338163\pi\) |
0.206427 | + | 0.978462i | \(0.433816\pi\) | |||||||
\(450\) | 2.85410 | 0.134544 | ||||||||
\(451\) | 16.2188 | + | 7.00042i | 0.763716 | + | 0.329637i | ||||
\(452\) | 6.32624 | 0.297561 | ||||||||
\(453\) | 4.85410 | + | 3.52671i | 0.228066 | + | 0.165699i | ||||
\(454\) | 2.86475 | − | 8.81678i | 0.134449 | − | 0.413792i | ||||
\(455\) | −0.618034 | − | 1.90211i | −0.0289739 | − | 0.0891724i | ||||
\(456\) | −0.0450850 | + | 0.0327561i | −0.00211130 | + | 0.00153395i | ||||
\(457\) | 1.83688 | − | 1.33457i | 0.0859257 | − | 0.0624287i | −0.543993 | − | 0.839090i | \(-0.683088\pi\) |
0.629919 | + | 0.776661i | \(0.283088\pi\) | |||||||
\(458\) | 9.00000 | + | 27.6992i | 0.420542 | + | 1.29430i | ||||
\(459\) | 0.427051 | − | 1.31433i | 0.0199330 | − | 0.0613476i | ||||
\(460\) | 4.85410 | + | 3.52671i | 0.226324 | + | 0.164434i | ||||
\(461\) | 10.9443 | 0.509726 | 0.254863 | − | 0.966977i | \(-0.417970\pi\) | ||||
0.254863 | + | 0.966977i | \(0.417970\pi\) | |||||||
\(462\) | −0.836881 | + | 0.951057i | −0.0389352 | + | 0.0442472i | ||||
\(463\) | 19.4164 | 0.902357 | 0.451178 | − | 0.892434i | \(-0.351004\pi\) | ||||
0.451178 | + | 0.892434i | \(0.351004\pi\) | |||||||
\(464\) | −1.00000 | − | 0.726543i | −0.0464238 | − | 0.0337289i | ||||
\(465\) | −0.381966 | + | 1.17557i | −0.0177132 | + | 0.0545158i | ||||
\(466\) | 6.82624 | + | 21.0090i | 0.316219 | + | 0.973223i | ||||
\(467\) | −14.4721 | + | 10.5146i | −0.669691 | + | 0.486559i | −0.869922 | − | 0.493190i | \(-0.835831\pi\) |
0.200231 | + | 0.979749i | \(0.435831\pi\) | |||||||
\(468\) | −4.61803 | + | 3.35520i | −0.213469 | + | 0.155094i | ||||
\(469\) | 1.57295 | + | 4.84104i | 0.0726320 | + | 0.223538i | ||||
\(470\) | 1.47214 | − | 4.53077i | 0.0679046 | − | 0.208989i | ||||
\(471\) | −4.23607 | − | 3.07768i | −0.195188 | − | 0.141812i | ||||
\(472\) | 5.38197 | 0.247725 | ||||||||
\(473\) | 1.50000 | − | 16.0292i | 0.0689701 | − | 0.737024i | ||||
\(474\) | 0.180340 | 0.00828329 | ||||||||
\(475\) | 0.118034 | + | 0.0857567i | 0.00541577 | + | 0.00393479i | ||||
\(476\) | 0.190983 | − | 0.587785i | 0.00875369 | − | 0.0269411i | ||||
\(477\) | 2.85410 | + | 8.78402i | 0.130680 | + | 0.402193i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.70820 | + | 1.24108i | −0.0780498 | + | 0.0567065i | −0.626126 | − | 0.779722i | \(-0.715360\pi\) |
0.548076 | + | 0.836428i | \(0.315360\pi\) | |||||||
\(480\) | 0.118034 | + | 0.363271i | 0.00538749 | + | 0.0165810i | ||||
\(481\) | −1.52786 | + | 4.70228i | −0.0696646 | + | 0.214406i | ||||
\(482\) | −22.0623 | − | 16.0292i | −1.00491 | − | 0.730110i | ||||
\(483\) | −2.29180 | −0.104280 | ||||||||
\(484\) | −1.39919 | − | 10.9106i | −0.0635994 | − | 0.495939i | ||||
\(485\) | −10.5623 | −0.479610 | ||||||||
\(486\) | 7.80902 | + | 5.67358i | 0.354224 | + | 0.257359i | ||||
\(487\) | 8.29180 | − | 25.5195i | 0.375737 | − | 1.15640i | −0.567243 | − | 0.823551i | \(-0.691990\pi\) |
0.942980 | − | 0.332849i | \(-0.108010\pi\) | |||||||
\(488\) | −3.85410 | − | 11.8617i | −0.174467 | − | 0.536954i | ||||
\(489\) | 1.19098 | − | 0.865300i | 0.0538581 | − | 0.0391302i | ||||
\(490\) | −0.809017 | + | 0.587785i | −0.0365477 | + | 0.0265534i | ||||
\(491\) | −1.70163 | − | 5.23707i | −0.0767933 | − | 0.236346i | 0.905290 | − | 0.424795i | \(-0.139654\pi\) |
−0.982083 | + | 0.188449i | \(0.939654\pi\) | |||||||
\(492\) | −0.628677 | + | 1.93487i | −0.0283430 | + | 0.0872306i | ||||
\(493\) | 0.618034 | + | 0.449028i | 0.0278349 | + | 0.0202232i | ||||
\(494\) | −0.291796 | −0.0131285 | ||||||||
\(495\) | 0.881966 | − | 9.42481i | 0.0396414 | − | 0.423614i | ||||
\(496\) | 3.23607 | 0.145304 | ||||||||
\(497\) | 3.00000 | + | 2.17963i | 0.134568 | + | 0.0977697i | ||||
\(498\) | −0.628677 | + | 1.93487i | −0.0281717 | + | 0.0867036i | ||||
\(499\) | −12.2984 | − | 37.8505i | −0.550551 | − | 1.69442i | −0.707413 | − | 0.706801i | \(-0.750138\pi\) |
0.156862 | − | 0.987621i | \(-0.449862\pi\) | |||||||
\(500\) | 0.809017 | − | 0.587785i | 0.0361803 | − | 0.0262866i | ||||
\(501\) | −0.763932 | + | 0.555029i | −0.0341300 | + | 0.0247969i | ||||
\(502\) | 8.29180 | + | 25.5195i | 0.370081 | + | 1.13899i | ||||
\(503\) | −7.14590 | + | 21.9928i | −0.318620 | + | 0.980611i | 0.655619 | + | 0.755092i | \(0.272408\pi\) |
−0.974239 | + | 0.225519i | \(0.927592\pi\) | |||||||
\(504\) | 2.30902 | + | 1.67760i | 0.102852 | + | 0.0747262i | ||||
\(505\) | −8.94427 | −0.398015 | ||||||||
\(506\) | 13.1459 | − | 14.9394i | 0.584406 | − | 0.664137i | ||||
\(507\) | −3.43769 | −0.152673 | ||||||||
\(508\) | 12.4721 | + | 9.06154i | 0.553362 | + | 0.402041i | ||||
\(509\) | −10.6525 | + | 32.7849i | −0.472163 | + | 1.45317i | 0.377584 | + | 0.925975i | \(0.376755\pi\) |
−0.849746 | + | 0.527192i | \(0.823245\pi\) | |||||||
\(510\) | −0.0729490 | − | 0.224514i | −0.00323024 | − | 0.00994165i | ||||
\(511\) | −5.78115 | + | 4.20025i | −0.255743 | + | 0.185808i | ||||
\(512\) | 0.809017 | − | 0.587785i | 0.0357538 | − | 0.0259767i | ||||
\(513\) | 0.100813 | + | 0.310271i | 0.00445101 | + | 0.0136988i | ||||
\(514\) | −2.91641 | + | 8.97578i | −0.128637 | + | 0.395905i | ||||
\(515\) | 0.763932 | + | 0.555029i | 0.0336629 | + | 0.0244575i | ||||
\(516\) | 1.85410 | 0.0816223 | ||||||||
\(517\) | −14.5066 | − | 6.26137i | −0.637999 | − | 0.275375i | ||||
\(518\) | 2.47214 | 0.108619 | ||||||||
\(519\) | 3.70820 | + | 2.69417i | 0.162772 | + | 0.118261i | ||||
\(520\) | −0.618034 | + | 1.90211i | −0.0271026 | + | 0.0834132i | ||||
\(521\) | 3.46149 | + | 10.6534i | 0.151651 | + | 0.466733i | 0.997806 | − | 0.0662032i | \(-0.0210886\pi\) |
−0.846155 | + | 0.532936i | \(0.821089\pi\) | |||||||
\(522\) | −2.85410 | + | 2.07363i | −0.124921 | + | 0.0907602i | ||||
\(523\) | −33.1525 | + | 24.0867i | −1.44966 | + | 1.05324i | −0.463745 | + | 0.885969i | \(0.653495\pi\) |
−0.985911 | + | 0.167269i | \(0.946505\pi\) | |||||||
\(524\) | −5.19098 | − | 15.9762i | −0.226769 | − | 0.697924i | ||||
\(525\) | −0.118034 | + | 0.363271i | −0.00515143 | + | 0.0158545i | ||||
\(526\) | 1.76393 | + | 1.28157i | 0.0769111 | + | 0.0558792i | ||||
\(527\) | −2.00000 | −0.0871214 | ||||||||
\(528\) | 1.23607 | − | 0.277515i | 0.0537930 | − | 0.0120773i | ||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 2.61803 | + | 1.90211i | 0.113720 | + | 0.0826225i | ||||
\(531\) | 4.74671 | − | 14.6089i | 0.205990 | − | 0.633971i | ||||
\(532\) | 0.0450850 | + | 0.138757i | 0.00195468 | + | 0.00601589i | ||||
\(533\) | −8.61803 | + | 6.26137i | −0.373288 | + | 0.271210i | ||||
\(534\) | 0.590170 | − | 0.428784i | 0.0255392 | − | 0.0185553i | ||||
\(535\) | 5.44427 | + | 16.7557i | 0.235376 | + | 0.724414i | ||||
\(536\) | 1.57295 | − | 4.84104i | 0.0679410 | − | 0.209101i | ||||
\(537\) | 2.66312 | + | 1.93487i | 0.114922 | + | 0.0834958i | ||||
\(538\) | −10.1803 | −0.438906 | ||||||||
\(539\) | 1.69098 | + | 2.85317i | 0.0728358 | + | 0.122895i | ||||
\(540\) | 2.23607 | 0.0962250 | ||||||||
\(541\) | −31.4164 | − | 22.8254i | −1.35070 | − | 0.981339i | −0.998976 | − | 0.0452336i | \(-0.985597\pi\) |
−0.351720 | − | 0.936105i | \(-0.614403\pi\) | |||||||
\(542\) | 5.38197 | − | 16.5640i | 0.231175 | − | 0.711484i | ||||
\(543\) | 1.47214 | + | 4.53077i | 0.0631754 | + | 0.194434i | ||||
\(544\) | −0.500000 | + | 0.363271i | −0.0214373 | + | 0.0155751i | ||||
\(545\) | −6.85410 | + | 4.97980i | −0.293597 | + | 0.213311i | ||||
\(546\) | −0.236068 | − | 0.726543i | −0.0101028 | − | 0.0310931i | ||||
\(547\) | 8.98936 | − | 27.6664i | 0.384357 | − | 1.18293i | −0.552588 | − | 0.833454i | \(-0.686360\pi\) |
0.936946 | − | 0.349475i | \(-0.113640\pi\) | |||||||
\(548\) | −8.16312 | − | 5.93085i | −0.348711 | − | 0.253353i | ||||
\(549\) | −35.5967 | −1.51923 | ||||||||
\(550\) | −1.69098 | − | 2.85317i | −0.0721038 | − | 0.121660i | ||||
\(551\) | −0.180340 | −0.00768274 | ||||||||
\(552\) | 1.85410 | + | 1.34708i | 0.0789158 | + | 0.0573357i | ||||
\(553\) | 0.145898 | − | 0.449028i | 0.00620422 | − | 0.0190946i | ||||
\(554\) | 6.09017 | + | 18.7436i | 0.258747 | + | 0.796340i | ||||
\(555\) | 0.763932 | − | 0.555029i | 0.0324271 | − | 0.0235597i | ||||
\(556\) | 7.70820 | − | 5.60034i | 0.326901 | − | 0.237507i | ||||
\(557\) | −4.88854 | − | 15.0454i | −0.207134 | − | 0.637494i | −0.999619 | − | 0.0276019i | \(-0.991213\pi\) |
0.792485 | − | 0.609892i | \(-0.208787\pi\) | |||||||
\(558\) | 2.85410 | − | 8.78402i | 0.120824 | − | 0.371857i | ||||
\(559\) | 7.85410 | + | 5.70634i | 0.332193 | + | 0.241352i | ||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | −0.763932 | + | 0.171513i | −0.0322532 | + | 0.00724130i | ||||
\(562\) | 5.03444 | 0.212365 | ||||||||
\(563\) | 33.5795 | + | 24.3970i | 1.41521 | + | 1.02821i | 0.992539 | + | 0.121925i | \(0.0389067\pi\) |
0.422669 | + | 0.906284i | \(0.361093\pi\) | |||||||
\(564\) | 0.562306 | − | 1.73060i | 0.0236773 | − | 0.0728714i | ||||
\(565\) | −1.95492 | − | 6.01661i | −0.0822439 | − | 0.253121i | ||||
\(566\) | 9.70820 | − | 7.05342i | 0.408066 | − | 0.296477i | ||||
\(567\) | 6.23607 | − | 4.53077i | 0.261890 | − | 0.190274i | ||||
\(568\) | −1.14590 | − | 3.52671i | −0.0480808 | − | 0.147978i | ||||
\(569\) | −0.954915 | + | 2.93893i | −0.0400321 | + | 0.123206i | −0.969075 | − | 0.246765i | \(-0.920632\pi\) |
0.929043 | + | 0.369971i | \(0.120632\pi\) | |||||||
\(570\) | 0.0450850 | + | 0.0327561i | 0.00188840 | + | 0.00137200i | ||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 6.09017 | + | 2.62866i | 0.254643 | + | 0.109910i | ||||
\(573\) | −4.00000 | −0.167102 | ||||||||
\(574\) | 4.30902 | + | 3.13068i | 0.179855 | + | 0.130672i | ||||
\(575\) | 1.85410 | − | 5.70634i | 0.0773214 | − | 0.237971i | ||||
\(576\) | −0.881966 | − | 2.71441i | −0.0367486 | − | 0.113101i | ||||
\(577\) | 21.2082 | − | 15.4087i | 0.882909 | − | 0.641471i | −0.0511104 | − | 0.998693i | \(-0.516276\pi\) |
0.934020 | + | 0.357222i | \(0.116276\pi\) | |||||||
\(578\) | −13.4443 | + | 9.76784i | −0.559208 | + | 0.406288i | ||||
\(579\) | 0.236068 | + | 0.726543i | 0.00981065 | + | 0.0301941i | ||||
\(580\) | −0.381966 | + | 1.17557i | −0.0158603 | + | 0.0488129i | ||||
\(581\) | 4.30902 | + | 3.13068i | 0.178768 | + | 0.129883i | ||||
\(582\) | −4.03444 | −0.167233 | ||||||||
\(583\) | 7.09017 | − | 8.05748i | 0.293645 | − | 0.333707i | ||||
\(584\) | 7.14590 | 0.295699 | ||||||||
\(585\) | 4.61803 | + | 3.35520i | 0.190932 | + | 0.138720i | ||||
\(586\) | 2.32624 | − | 7.15942i | 0.0960960 | − | 0.295753i | ||||
\(587\) | −12.2812 | − | 37.7975i | −0.506897 | − | 1.56007i | −0.797557 | − | 0.603243i | \(-0.793875\pi\) |
0.290660 | − | 0.956826i | \(-0.406125\pi\) | |||||||
\(588\) | −0.309017 | + | 0.224514i | −0.0127436 | + | 0.00925880i | ||||
\(589\) | 0.381966 | − | 0.277515i | 0.0157386 | − | 0.0114348i | ||||
\(590\) | −1.66312 | − | 5.11855i | −0.0684695 | − | 0.210728i | ||||
\(591\) | −0.708204 | + | 2.17963i | −0.0291316 | + | 0.0896579i | ||||
\(592\) | −2.00000 | − | 1.45309i | −0.0821995 | − | 0.0597214i | ||||
\(593\) | −0.909830 | −0.0373622 | −0.0186811 | − | 0.999825i | \(-0.505947\pi\) | ||||
−0.0186811 | + | 0.999825i | \(0.505947\pi\) | |||||||
\(594\) | 0.690983 | − | 7.38394i | 0.0283514 | − | 0.302967i | ||||
\(595\) | −0.618034 | −0.0253369 | ||||||||
\(596\) | 1.47214 | + | 1.06957i | 0.0603010 | + | 0.0438113i | ||||
\(597\) | 0.875388 | − | 2.69417i | 0.0358273 | − | 0.110265i | ||||
\(598\) | 3.70820 | + | 11.4127i | 0.151640 | + | 0.466699i | ||||
\(599\) | 16.7984 | − | 12.2047i | 0.686363 | − | 0.498672i | −0.189100 | − | 0.981958i | \(-0.560557\pi\) |
0.875463 | + | 0.483286i | \(0.160557\pi\) | |||||||
\(600\) | 0.309017 | − | 0.224514i | 0.0126156 | − | 0.00916575i | ||||
\(601\) | 5.53444 | + | 17.0333i | 0.225755 | + | 0.694801i | 0.998214 | + | 0.0597372i | \(0.0190263\pi\) |
−0.772460 | + | 0.635064i | \(0.780974\pi\) | |||||||
\(602\) | 1.50000 | − | 4.61653i | 0.0611354 | − | 0.188156i | ||||
\(603\) | −11.7533 | − | 8.53926i | −0.478631 | − | 0.347746i | ||||
\(604\) | −15.7082 | −0.639158 | ||||||||
\(605\) | −9.94427 | + | 4.70228i | −0.404292 | + | 0.191175i | ||||
\(606\) | −3.41641 | −0.138782 | ||||||||
\(607\) | 15.8541 | + | 11.5187i | 0.643498 | + | 0.467529i | 0.861050 | − | 0.508520i | \(-0.169807\pi\) |
−0.217552 | + | 0.976049i | \(0.569807\pi\) | |||||||
\(608\) | 0.0450850 | − | 0.138757i | 0.00182844 | − | 0.00562735i | ||||
\(609\) | −0.145898 | − | 0.449028i | −0.00591209 | − | 0.0181955i | ||||
\(610\) | −10.0902 | + | 7.33094i | −0.408539 | + | 0.296821i | ||||
\(611\) | 7.70820 | − | 5.60034i | 0.311841 | − | 0.226565i | ||||
\(612\) | 0.545085 | + | 1.67760i | 0.0220338 | + | 0.0678129i | ||||
\(613\) | 3.27051 | − | 10.0656i | 0.132095 | − | 0.406546i | −0.863032 | − | 0.505149i | \(-0.831438\pi\) |
0.995127 | + | 0.0986035i | \(0.0314375\pi\) | |||||||
\(614\) | 6.01722 | + | 4.37177i | 0.242835 | + | 0.176430i | ||||
\(615\) | 2.03444 | 0.0820366 | ||||||||
\(616\) | 0.309017 | − | 3.30220i | 0.0124506 | − | 0.133049i | ||||
\(617\) | −6.03444 | −0.242937 | −0.121469 | − | 0.992595i | \(-0.538760\pi\) | ||||
−0.121469 | + | 0.992595i | \(0.538760\pi\) | |||||||
\(618\) | 0.291796 | + | 0.212002i | 0.0117378 | + | 0.00852798i | ||||
\(619\) | 10.6074 | − | 32.6462i | 0.426347 | − | 1.31216i | −0.475352 | − | 0.879796i | \(-0.657679\pi\) |
0.901699 | − | 0.432365i | \(-0.142321\pi\) | |||||||
\(620\) | −1.00000 | − | 3.07768i | −0.0401610 | − | 0.123603i | ||||
\(621\) | 10.8541 | − | 7.88597i | 0.435560 | − | 0.316453i | ||||
\(622\) | 9.00000 | − | 6.53888i | 0.360867 | − | 0.262185i | ||||
\(623\) | −0.590170 | − | 1.81636i | −0.0236447 | − | 0.0727708i | ||||
\(624\) | −0.236068 | + | 0.726543i | −0.00945028 | + | 0.0290850i | ||||
\(625\) | −0.809017 | − | 0.587785i | −0.0323607 | − | 0.0235114i | ||||
\(626\) | −5.85410 | −0.233977 | ||||||||
\(627\) | 0.122099 | − | 0.138757i | 0.00487618 | − | 0.00554143i | ||||
\(628\) | 13.7082 | 0.547017 | ||||||||
\(629\) | 1.23607 | + | 0.898056i | 0.0492853 | + | 0.0358078i | ||||
\(630\) | 0.881966 | − | 2.71441i | 0.0351384 | − | 0.108145i | ||||
\(631\) | −3.18034 | − | 9.78808i | −0.126607 | − | 0.389657i | 0.867583 | − | 0.497292i | \(-0.165672\pi\) |
−0.994190 | + | 0.107635i | \(0.965672\pi\) | |||||||
\(632\) | −0.381966 | + | 0.277515i | −0.0151938 | + | 0.0110389i | ||||
\(633\) | −6.88197 | + | 5.00004i | −0.273534 | + | 0.198734i | ||||
\(634\) | 7.79837 | + | 24.0009i | 0.309713 | + | 0.953199i | ||||
\(635\) | 4.76393 | − | 14.6619i | 0.189051 | − | 0.581839i | ||||
\(636\) | 1.00000 | + | 0.726543i | 0.0396526 | + | 0.0288093i | ||||
\(637\) | −2.00000 | −0.0792429 | ||||||||
\(638\) | 3.76393 | + | 1.62460i | 0.149015 | + | 0.0643185i | ||||
\(639\) | −10.5836 | −0.418680 | ||||||||
\(640\) | −0.809017 | − | 0.587785i | −0.0319792 | − | 0.0232343i | ||||
\(641\) | 7.62461 | − | 23.4661i | 0.301154 | − | 0.926857i | −0.679930 | − | 0.733277i | \(-0.737990\pi\) |
0.981084 | − | 0.193580i | \(-0.0620100\pi\) | |||||||
\(642\) | 2.07953 | + | 6.40013i | 0.0820724 | + | 0.252593i | ||||
\(643\) | −25.8713 | + | 18.7966i | −1.02027 | + | 0.741266i | −0.966337 | − | 0.257279i | \(-0.917174\pi\) |
−0.0539281 | + | 0.998545i | \(0.517174\pi\) | |||||||
\(644\) | 4.85410 | − | 3.52671i | 0.191278 | − | 0.138972i | ||||
\(645\) | −0.572949 | − | 1.76336i | −0.0225598 | − | 0.0694321i | ||||
\(646\) | −0.0278640 | + | 0.0857567i | −0.00109630 | + | 0.00337405i | ||||
\(647\) | 17.9443 | + | 13.0373i | 0.705462 | + | 0.512548i | 0.881707 | − | 0.471798i | \(-0.156395\pi\) |
−0.176244 | + | 0.984346i | \(0.556395\pi\) | |||||||
\(648\) | −7.70820 | −0.302807 | ||||||||
\(649\) | −17.4164 | + | 3.91023i | −0.683654 | + | 0.153490i | ||||
\(650\) | 2.00000 | 0.0784465 | ||||||||
\(651\) | 1.00000 | + | 0.726543i | 0.0391931 | + | 0.0284754i | ||||
\(652\) | −1.19098 | + | 3.66547i | −0.0466425 | + | 0.143551i | ||||
\(653\) | −8.29180 | − | 25.5195i | −0.324483 | − | 0.998656i | −0.971673 | − | 0.236328i | \(-0.924056\pi\) |
0.647190 | − | 0.762328i | \(-0.275944\pi\) | |||||||
\(654\) | −2.61803 | + | 1.90211i | −0.102373 | + | 0.0743785i | ||||
\(655\) | −13.5902 | + | 9.87384i | −0.531012 | + | 0.385803i | ||||
\(656\) | −1.64590 | − | 5.06555i | −0.0642615 | − | 0.197777i | ||||
\(657\) | 6.30244 | − | 19.3969i | 0.245882 | − | 0.756746i | ||||
\(658\) | −3.85410 | − | 2.80017i | −0.150249 | − | 0.109162i | ||||
\(659\) | 7.09017 | 0.276194 | 0.138097 | − | 0.990419i | \(-0.455901\pi\) | ||||
0.138097 | + | 0.990419i | \(0.455901\pi\) | |||||||
\(660\) | −0.645898 | − | 1.08981i | −0.0251415 | − | 0.0424209i | ||||
\(661\) | −10.1115 | −0.393290 | −0.196645 | − | 0.980475i | \(-0.563005\pi\) | ||||
−0.196645 | + | 0.980475i | \(0.563005\pi\) | |||||||
\(662\) | −18.6353 | − | 13.5393i | −0.724280 | − | 0.526220i | ||||
\(663\) | 0.145898 | − | 0.449028i | 0.00566621 | − | 0.0174388i | ||||
\(664\) | −1.64590 | − | 5.06555i | −0.0638732 | − | 0.196582i | ||||
\(665\) | 0.118034 | − | 0.0857567i | 0.00457716 | − | 0.00332550i | ||||
\(666\) | −5.70820 | + | 4.14725i | −0.221188 | + | 0.160703i | ||||
\(667\) | 2.29180 | + | 7.05342i | 0.0887387 | + | 0.273110i | ||||
\(668\) | 0.763932 | − | 2.35114i | 0.0295574 | − | 0.0909684i | ||||
\(669\) | −6.09017 | − | 4.42477i | −0.235460 | − | 0.171071i | ||||
\(670\) | −5.09017 | −0.196650 | ||||||||
\(671\) | 21.0902 | + | 35.5851i | 0.814177 | + | 1.37375i | ||||
\(672\) | 0.381966 | 0.0147347 | ||||||||
\(673\) | −26.0066 | − | 18.8949i | −1.00248 | − | 0.728344i | −0.0398614 | − | 0.999205i | \(-0.512692\pi\) |
−0.962618 | + | 0.270861i | \(0.912692\pi\) | |||||||
\(674\) | −4.13525 | + | 12.7270i | −0.159284 | + | 0.490226i | ||||
\(675\) | −0.690983 | − | 2.12663i | −0.0265959 | − | 0.0818539i | ||||
\(676\) | 7.28115 | − | 5.29007i | 0.280044 | − | 0.203464i | ||||
\(677\) | 28.7984 | − | 20.9232i | 1.10681 | − | 0.804146i | 0.124653 | − | 0.992200i | \(-0.460218\pi\) |
0.982159 | + | 0.188055i | \(0.0602183\pi\) | |||||||
\(678\) | −0.746711 | − | 2.29814i | −0.0286773 | − | 0.0882596i | ||||
\(679\) | −3.26393 | + | 10.0453i | −0.125258 | + | 0.385505i | ||||
\(680\) | 0.500000 | + | 0.363271i | 0.0191741 | + | 0.0139308i | ||||
\(681\) | −3.54102 | −0.135692 | ||||||||
\(682\) | −10.4721 | + | 2.35114i | −0.400999 | + | 0.0900298i | ||||
\(683\) | −48.9443 | −1.87280 | −0.936400 | − | 0.350934i | \(-0.885864\pi\) | ||||
−0.936400 | + | 0.350934i | \(0.885864\pi\) | |||||||
\(684\) | −0.336881 | − | 0.244758i | −0.0128810 | − | 0.00935857i | ||||
\(685\) | −3.11803 | + | 9.59632i | −0.119134 | + | 0.366657i | ||||
\(686\) | 0.309017 | + | 0.951057i | 0.0117983 | + | 0.0363115i | ||||
\(687\) | 9.00000 | − | 6.53888i | 0.343371 | − | 0.249474i | ||||
\(688\) | −3.92705 | + | 2.85317i | −0.149717 | + | 0.108776i | ||||
\(689\) | 2.00000 | + | 6.15537i | 0.0761939 | + | 0.234501i | ||||
\(690\) | 0.708204 | − | 2.17963i | 0.0269609 | − | 0.0829770i | ||||
\(691\) | −22.5344 | − | 16.3722i | −0.857251 | − | 0.622829i | 0.0698850 | − | 0.997555i | \(-0.477737\pi\) |
−0.927136 | + | 0.374726i | \(0.877737\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | −8.69098 | − | 3.75123i | −0.330143 | − | 0.142497i | ||||
\(694\) | −10.3262 | −0.391979 | ||||||||
\(695\) | −7.70820 | − | 5.60034i | −0.292389 | − | 0.212433i | ||||
\(696\) | −0.145898 | + | 0.449028i | −0.00553025 | + | 0.0170204i | ||||
\(697\) | 1.01722 | + | 3.13068i | 0.0385300 | + | 0.118583i | ||||
\(698\) | −11.7082 | + | 8.50651i | −0.443162 | + | 0.321976i | ||||
\(699\) | 6.82624 | − | 4.95955i | 0.258192 | − | 0.187587i | ||||
\(700\) | −0.309017 | − | 0.951057i | −0.0116797 | − | 0.0359466i | ||||
\(701\) | −3.14590 | + | 9.68208i | −0.118819 | + | 0.365687i | −0.992724 | − | 0.120409i | \(-0.961579\pi\) |
0.873905 | + | 0.486096i | \(0.161579\pi\) | |||||||
\(702\) | 3.61803 | + | 2.62866i | 0.136554 | + | 0.0992122i | ||||
\(703\) | −0.360680 | −0.0136033 | ||||||||
\(704\) | −2.19098 | + | 2.48990i | −0.0825758 | + | 0.0938416i | ||||
\(705\) | −1.81966 | −0.0685324 | ||||||||
\(706\) | 22.2082 | + | 16.1352i | 0.835817 | + | 0.607256i | ||||
\(707\) | −2.76393 | + | 8.50651i | −0.103948 | + | 0.319920i | ||||
\(708\) | −0.635255 | − | 1.95511i | −0.0238743 | − | 0.0734777i | ||||
\(709\) | 5.70820 | − | 4.14725i | 0.214376 | − | 0.155753i | −0.475415 | − | 0.879761i | \(-0.657702\pi\) |
0.689791 | + | 0.724008i | \(0.257702\pi\) | |||||||
\(710\) | −3.00000 | + | 2.17963i | −0.112588 | + | 0.0818000i | ||||
\(711\) | 0.416408 | + | 1.28157i | 0.0156165 | + | 0.0480627i | ||||
\(712\) | −0.590170 | + | 1.81636i | −0.0221176 | + | 0.0680708i | ||||
\(713\) | −15.7082 | − | 11.4127i | −0.588277 | − | 0.427408i | ||||
\(714\) | −0.236068 | −0.00883462 | ||||||||
\(715\) | 0.618034 | − | 6.60440i | 0.0231132 | − | 0.246990i | ||||
\(716\) | −8.61803 | −0.322071 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.90983 | + | 12.0332i | −0.145914 | + | 0.449076i | ||||
\(719\) | −3.81966 | − | 11.7557i | −0.142449 | − | 0.438414i | 0.854225 | − | 0.519904i | \(-0.174032\pi\) |
−0.996674 | + | 0.0814899i | \(0.974032\pi\) | |||||||
\(720\) | −2.30902 | + | 1.67760i | −0.0860520 | + | 0.0625204i | ||||
\(721\) | 0.763932 | − | 0.555029i | 0.0284503 | − | 0.0206704i | ||||
\(722\) | 5.86475 | + | 18.0498i | 0.218263 | + | 0.671745i | ||||
\(723\) | −3.21885 | + | 9.90659i | −0.119710 | + | 0.368430i | ||||
\(724\) | −10.0902 | − | 7.33094i | −0.374998 | − | 0.272452i | ||||
\(725\) | 1.23607 | 0.0459064 | ||||||||
\(726\) | −3.79837 | + | 1.79611i | −0.140971 | + | 0.0666600i | ||||
\(727\) | −14.8328 | −0.550119 | −0.275059 | − | 0.961427i | \(-0.588698\pi\) | ||||
−0.275059 | + | 0.961427i | \(0.588698\pi\) | |||||||
\(728\) | 1.61803 | + | 1.17557i | 0.0599683 | + | 0.0435695i | ||||
\(729\) | −6.00658 | + | 18.4863i | −0.222466 | + | 0.684679i | ||||
\(730\) | −2.20820 | − | 6.79615i | −0.0817293 | − | 0.251537i | ||||
\(731\) | 2.42705 | − | 1.76336i | 0.0897677 | − | 0.0652201i | ||||
\(732\) | −3.85410 | + | 2.80017i | −0.142452 | + | 0.103497i | ||||
\(733\) | 2.70820 | + | 8.33499i | 0.100030 | + | 0.307860i | 0.988532 | − | 0.151013i | \(-0.0482534\pi\) |
−0.888502 | + | 0.458873i | \(0.848253\pi\) | |||||||
\(734\) | −1.79837 | + | 5.53483i | −0.0663792 | + | 0.204294i | ||||
\(735\) | 0.309017 | + | 0.224514i | 0.0113983 | + | 0.00828132i | ||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | −1.57295 | + | 16.8087i | −0.0579403 | + | 0.619158i | ||||
\(738\) | −15.2016 | −0.559580 | ||||||||
\(739\) | −32.6246 | − | 23.7032i | −1.20012 | − | 0.871935i | −0.205820 | − | 0.978590i | \(-0.565986\pi\) |
−0.994296 | + | 0.106655i | \(0.965986\pi\) | |||||||
\(740\) | −0.763932 | + | 2.35114i | −0.0280827 | + | 0.0864297i | ||||
\(741\) | 0.0344419 | + | 0.106001i | 0.00126525 | + | 0.00389405i | ||||
\(742\) | 2.61803 | − | 1.90211i | 0.0961111 | − | 0.0698288i | ||||
\(743\) | −38.7426 | + | 28.1482i | −1.42133 | + | 1.03266i | −0.429780 | + | 0.902934i | \(0.641409\pi\) |
−0.991550 | + | 0.129723i | \(0.958591\pi\) | |||||||
\(744\) | −0.381966 | − | 1.17557i | −0.0140036 | − | 0.0430985i | ||||
\(745\) | 0.562306 | − | 1.73060i | 0.0206013 | − | 0.0634043i | ||||
\(746\) | 12.5623 | + | 9.12705i | 0.459939 | + | 0.334165i | ||||
\(747\) | −15.2016 | −0.556198 | ||||||||
\(748\) | 1.35410 | − | 1.53884i | 0.0495109 | − | 0.0562656i | ||||
\(749\) | 17.6180 | 0.643749 | ||||||||
\(750\) | −0.309017 | − | 0.224514i | −0.0112837 | − | 0.00819809i | ||||
\(751\) | −0.416408 | + | 1.28157i | −0.0151949 | + | 0.0467652i | −0.958367 | − | 0.285541i | \(-0.907827\pi\) |
0.943172 | + | 0.332306i | \(0.107827\pi\) | |||||||
\(752\) | 1.47214 | + | 4.53077i | 0.0536833 | + | 0.165220i | ||||
\(753\) | 8.29180 | − | 6.02434i | 0.302170 | − | 0.219539i | ||||
\(754\) | −2.00000 | + | 1.45309i | −0.0728357 | + | 0.0529182i | ||||
\(755\) | 4.85410 | + | 14.9394i | 0.176659 | + | 0.543700i | ||||
\(756\) | 0.690983 | − | 2.12663i | 0.0251308 | − | 0.0773447i | ||||
\(757\) | 12.8541 | + | 9.33905i | 0.467190 | + | 0.339434i | 0.796345 | − | 0.604842i | \(-0.206764\pi\) |
−0.329155 | + | 0.944276i | \(0.606764\pi\) | |||||||
\(758\) | 21.1459 | 0.768054 | ||||||||
\(759\) | −6.97871 | − | 3.01217i | −0.253311 | − | 0.109335i | ||||
\(760\) | −0.145898 | −0.00529228 | ||||||||
\(761\) | −5.82624 | − | 4.23301i | −0.211201 | − | 0.153446i | 0.477156 | − | 0.878819i | \(-0.341668\pi\) |
−0.688357 | + | 0.725372i | \(0.741668\pi\) | |||||||
\(762\) | 1.81966 | − | 5.60034i | 0.0659193 | − | 0.202879i | ||||
\(763\) | 2.61803 | + | 8.05748i | 0.0947792 | + | 0.291700i | ||||
\(764\) | 8.47214 | − | 6.15537i | 0.306511 | − | 0.222693i | ||||
\(765\) | 1.42705 | − | 1.03681i | 0.0515951 | − | 0.0374861i | ||||
\(766\) | 7.41641 | + | 22.8254i | 0.267966 | + | 0.824714i | ||||
\(767\) | 3.32624 | − | 10.2371i | 0.120103 | − | 0.369641i | ||||
\(768\) | −0.309017 | − | 0.224514i | −0.0111507 | − | 0.00810145i | ||||
\(769\) | −27.8885 | −1.00569 | −0.502843 | − | 0.864378i | \(-0.667713\pi\) | ||||
−0.502843 | + | 0.864378i | \(0.667713\pi\) | |||||||
\(770\) | −3.23607 | + | 0.726543i | −0.116620 | + | 0.0261828i | ||||
\(771\) | 3.60488 | 0.129827 | ||||||||
\(772\) | −1.61803 | − | 1.17557i | −0.0582343 | − | 0.0423097i | ||||
\(773\) | 2.05573 | − | 6.32688i | 0.0739394 | − | 0.227562i | −0.907256 | − | 0.420579i | \(-0.861827\pi\) |
0.981196 | + | 0.193017i | \(0.0618271\pi\) | |||||||
\(774\) | 4.28115 | + | 13.1760i | 0.153883 | + | 0.473603i | ||||
\(775\) | −2.61803 | + | 1.90211i | −0.0940426 | + | 0.0683259i | ||||
\(776\) | 8.54508 | − | 6.20837i | 0.306751 | − | 0.222867i | ||||
\(777\) | −0.291796 | − | 0.898056i | −0.0104681 | − | 0.0322176i | ||||
\(778\) | −6.43769 | + | 19.8132i | −0.230803 | + | 0.710337i | ||||
\(779\) | −0.628677 | − | 0.456761i | −0.0225247 | − | 0.0163651i | ||||
\(780\) | 0.763932 | 0.0273532 | ||||||||
\(781\) | 6.27051 | + | 10.5801i | 0.224376 | + | 0.378587i | ||||
\(782\) | 3.70820 | 0.132605 | ||||||||
\(783\) | 2.23607 | + | 1.62460i | 0.0799106 | + | 0.0580584i | ||||
\(784\) | 0.309017 | − | 0.951057i | 0.0110363 | − | 0.0339663i | ||||
\(785\) | −4.23607 | − | 13.0373i | −0.151192 | − | 0.465320i | ||||
\(786\) | −5.19098 | + | 3.77147i | −0.185156 | + | 0.134524i | ||||
\(787\) | −29.2082 | + | 21.2210i | −1.04116 | + | 0.756447i | −0.970512 | − | 0.241054i | \(-0.922507\pi\) |
−0.0706484 | + | 0.997501i | \(0.522507\pi\) | |||||||
\(788\) | −1.85410 | − | 5.70634i | −0.0660496 | − | 0.203280i | ||||
\(789\) | 0.257354 | − | 0.792055i | 0.00916205 | − | 0.0281979i | ||||
\(790\) | 0.381966 | + | 0.277515i | 0.0135897 | + | 0.00987352i | ||||
\(791\) | −6.32624 | −0.224935 | ||||||||
\(792\) | 4.82624 | + | 8.14324i | 0.171493 | + | 0.289357i | ||||
\(793\) | −24.9443 | −0.885797 | ||||||||
\(794\) | 0.763932 | + | 0.555029i | 0.0271109 | + | 0.0196972i | ||||
\(795\) | 0.381966 | − | 1.17557i | 0.0135469 | − | 0.0416932i | ||||
\(796\) | 2.29180 | + | 7.05342i | 0.0812306 | + | 0.250002i | ||||
\(797\) | −31.0344 | + | 22.5478i | −1.09930 | + | 0.798686i | −0.980945 | − | 0.194286i | \(-0.937761\pi\) |
−0.118351 | + | 0.992972i | \(0.537761\pi\) | |||||||
\(798\) | 0.0450850 | − | 0.0327561i | 0.00159599 | − | 0.00115956i | ||||
\(799\) | −0.909830 | − | 2.80017i | −0.0321875 | − | 0.0990629i | ||||
\(800\) | −0.309017 | + | 0.951057i | −0.0109254 | + | 0.0336249i | ||||
\(801\) | 4.40983 | + | 3.20393i | 0.155814 | + | 0.113205i | ||||
\(802\) | −11.5066 | −0.406311 | ||||||||
\(803\) | −23.1246 | + | 5.19180i | −0.816050 | + | 0.183215i | ||||
\(804\) | −1.94427 | −0.0685692 | ||||||||
\(805\) | −4.85410 | − | 3.52671i | −0.171085 | − | 0.124300i | ||||
\(806\) | 2.00000 | − | 6.15537i | 0.0704470 | − | 0.216814i | ||||
\(807\) | 1.20163 | + | 3.69822i | 0.0422992 | + | 0.130184i | ||||
\(808\) | 7.23607 | − | 5.25731i | 0.254564 | − | 0.184952i | ||||
\(809\) | 41.9164 | − | 30.4541i | 1.47370 | − | 1.07071i | 0.494183 | − | 0.869358i | \(-0.335467\pi\) |
0.979519 | − | 0.201350i | \(-0.0645327\pi\) | |||||||
\(810\) | 2.38197 | + | 7.33094i | 0.0836938 | + | 0.257583i | ||||
\(811\) | −10.7918 | + | 33.2137i | −0.378951 | + | 1.16629i | 0.561823 | + | 0.827258i | \(0.310100\pi\) |
−0.940774 | + | 0.339034i | \(0.889900\pi\) | |||||||
\(812\) | 1.00000 | + | 0.726543i | 0.0350931 | + | 0.0254966i | ||||
\(813\) | −6.65248 | −0.233313 | ||||||||
\(814\) | 7.52786 | + | 3.24920i | 0.263851 | + | 0.113884i | ||||
\(815\) | 3.85410 | 0.135003 | ||||||||
\(816\) | 0.190983 | + | 0.138757i | 0.00668574 | + | 0.00485748i | ||||
\(817\) | −0.218847 | + | 0.673542i | −0.00765649 | + | 0.0235643i | ||||
\(818\) | −2.43769 | − | 7.50245i | −0.0852320 | − | 0.262317i | ||||
\(819\) | 4.61803 | − | 3.35520i | 0.161367 | − | 0.117240i | ||||
\(820\) | −4.30902 | + | 3.13068i | −0.150477 | + | 0.109328i | ||||
\(821\) | −15.1246 | − | 46.5488i | −0.527853 | − | 1.62456i | −0.758605 | − | 0.651551i | \(-0.774119\pi\) |
0.230752 | − | 0.973012i | \(-0.425881\pi\) | |||||||
\(822\) | −1.19098 | + | 3.66547i | −0.0415403 | + | 0.127848i | ||||
\(823\) | −41.1246 | − | 29.8788i | −1.43351 | − | 1.04151i | −0.989349 | − | 0.145564i | \(-0.953500\pi\) |
−0.444165 | − | 0.895945i | \(-0.646500\pi\) | |||||||
\(824\) | −0.944272 | −0.0328953 | ||||||||
\(825\) | −0.836881 | + | 0.951057i | −0.0291365 | + | 0.0331115i | ||||
\(826\) | −5.38197 | −0.187263 | ||||||||
\(827\) | 1.40983 | + | 1.02430i | 0.0490246 | + | 0.0356185i | 0.612028 | − | 0.790836i | \(-0.290354\pi\) |
−0.563003 | + | 0.826455i | \(0.690354\pi\) | |||||||
\(828\) | −5.29180 | + | 16.2865i | −0.183903 | + | 0.565994i | ||||
\(829\) | 3.65248 | + | 11.2412i | 0.126856 | + | 0.390422i | 0.994235 | − | 0.107227i | \(-0.0341970\pi\) |
−0.867379 | + | 0.497648i | \(0.834197\pi\) | |||||||
\(830\) | −4.30902 | + | 3.13068i | −0.149568 | + | 0.108668i | ||||
\(831\) | 6.09017 | − | 4.42477i | 0.211266 | − | 0.153493i | ||||
\(832\) | −0.618034 | − | 1.90211i | −0.0214265 | − | 0.0659439i | ||||
\(833\) | −0.190983 | + | 0.587785i | −0.00661717 | + | 0.0203656i | ||||
\(834\) | −2.94427 | − | 2.13914i | −0.101952 | − | 0.0740723i | ||||
\(835\) | −2.47214 | −0.0855518 | ||||||||
\(836\) | −0.0450850 | + | 0.481784i | −0.00155930 | + | 0.0166629i | ||||
\(837\) | −7.23607 | −0.250115 | ||||||||
\(838\) | −2.69098 | − | 1.95511i | −0.0929585 | − | 0.0675383i | ||||
\(839\) | −1.38197 | + | 4.25325i | −0.0477108 | + | 0.146839i | −0.972074 | − | 0.234676i | \(-0.924597\pi\) |
0.924363 | + | 0.381514i | \(0.124597\pi\) | |||||||
\(840\) | −0.118034 | − | 0.363271i | −0.00407256 | − | 0.0125340i | ||||
\(841\) | 22.2254 | − | 16.1477i | 0.766394 | − | 0.556818i | ||||
\(842\) | 31.0344 | − | 22.5478i | 1.06952 | − | 0.777050i | ||||
\(843\) | −0.594235 | − | 1.82887i | −0.0204665 | − | 0.0629896i | ||||
\(844\) | 6.88197 | − | 21.1805i | 0.236887 | − | 0.729063i | ||||
\(845\) | −7.28115 | − | 5.29007i | −0.250479 | − | 0.181984i | ||||
\(846\) | 13.5967 | 0.467466 | ||||||||
\(847\) | 1.39919 | + | 10.9106i | 0.0480766 | + | 0.374894i | ||||
\(848\) | −3.23607 | −0.111127 | ||||||||
\(849\) | −3.70820 | − | 2.69417i | −0.127265 | − | 0.0924636i | ||||
\(850\) | 0.190983 | − | 0.587785i | 0.00655066 | − | 0.0201609i | ||||
\(851\) | 4.58359 | + | 14.1068i | 0.157124 | + | 0.483576i | ||||
\(852\) | −1.14590 | + | 0.832544i | −0.0392578 | + | 0.0285225i | ||||
\(853\) | −14.3262 | + | 10.4086i | −0.490521 | + | 0.356384i | −0.805385 | − | 0.592753i | \(-0.798041\pi\) |
0.314864 | + | 0.949137i | \(0.398041\pi\) | |||||||
\(854\) | 3.85410 | + | 11.8617i | 0.131885 | + | 0.405899i | ||||
\(855\) | −0.128677 | + | 0.396027i | −0.00440066 | + | 0.0135439i | ||||
\(856\) | −14.2533 | − | 10.3556i | −0.487167 | − | 0.353948i | ||||
\(857\) | −24.2705 | −0.829065 | −0.414532 | − | 0.910035i | \(-0.636055\pi\) | ||||
−0.414532 | + | 0.910035i | \(0.636055\pi\) | |||||||
\(858\) | 0.236068 | − | 2.52265i | 0.00805923 | − | 0.0861220i | ||||
\(859\) | −27.5623 | −0.940414 | −0.470207 | − | 0.882556i | \(-0.655821\pi\) | ||||
−0.470207 | + | 0.882556i | \(0.655821\pi\) | |||||||
\(860\) | 3.92705 | + | 2.85317i | 0.133911 | + | 0.0972923i | ||||
\(861\) | 0.628677 | − | 1.93487i | 0.0214253 | − | 0.0659402i | ||||
\(862\) | 8.27051 | + | 25.4540i | 0.281695 | + | 0.866967i | ||||
\(863\) | −9.09017 | + | 6.60440i | −0.309433 | + | 0.224816i | −0.731653 | − | 0.681677i | \(-0.761251\pi\) |
0.422220 | + | 0.906493i | \(0.361251\pi\) | |||||||
\(864\) | −1.80902 | + | 1.31433i | −0.0615440 | + | 0.0447143i | ||||
\(865\) | 3.70820 | + | 11.4127i | 0.126083 | + | 0.388043i | ||||
\(866\) | 12.1910 | − | 37.5200i | 0.414266 | − | 1.27498i | ||||
\(867\) | 5.13525 | + | 3.73098i | 0.174402 | + | 0.126711i | ||||
\(868\) | −3.23607 | −0.109839 | ||||||||
\(869\) | 1.03444 | − | 1.17557i | 0.0350910 | − | 0.0398785i | ||||
\(870\) | 0.472136 | 0.0160069 | ||||||||
\(871\) | −8.23607 | − | 5.98385i | −0.279069 | − | 0.202755i | ||||
\(872\) | 2.61803 | − | 8.05748i | 0.0886578 | − | 0.272861i | ||||
\(873\) | −9.31559 | − | 28.6705i | −0.315285 | − | 0.970348i | ||||
\(874\) | −0.708204 | + | 0.514540i | −0.0239554 | + | 0.0174046i | ||||
\(875\) | −0.809017 | + | 0.587785i | −0.0273498 | + | 0.0198708i | ||||
\(876\) | −0.843459 | − | 2.59590i | −0.0284978 | − | 0.0877073i | ||||
\(877\) | −5.56231 | + | 17.1190i | −0.187826 | + | 0.578068i | −0.999986 | − | 0.00536681i | \(-0.998292\pi\) |
0.812160 | + | 0.583435i | \(0.198292\pi\) | |||||||
\(878\) | −2.14590 | − | 1.55909i | −0.0724206 | − | 0.0526166i | ||||
\(879\) | −2.87539 | −0.0969844 | ||||||||
\(880\) | 3.04508 | + | 1.31433i | 0.102650 | + | 0.0443060i | ||||
\(881\) | 10.8541 | 0.365684 | 0.182842 | − | 0.983142i | \(-0.441470\pi\) | ||||
0.182842 | + | 0.983142i | \(0.441470\pi\) | |||||||
\(882\) | −2.30902 | − | 1.67760i | −0.0777486 | − | 0.0564877i | ||||
\(883\) | 6.97214 | − | 21.4580i | 0.234631 | − | 0.722120i | −0.762539 | − | 0.646942i | \(-0.776048\pi\) |
0.997170 | − | 0.0751780i | \(-0.0239525\pi\) | |||||||
\(884\) | 0.381966 | + | 1.17557i | 0.0128469 | + | 0.0395387i | ||||
\(885\) | −1.66312 | + | 1.20833i | −0.0559051 | + | 0.0406175i | ||||
\(886\) | −0.836881 | + | 0.608030i | −0.0281156 | + | 0.0204272i | ||||
\(887\) | −12.4721 | − | 38.3853i | −0.418773 | − | 1.28885i | −0.908832 | − | 0.417162i | \(-0.863025\pi\) |
0.490059 | − | 0.871689i | \(-0.336975\pi\) | |||||||
\(888\) | −0.291796 | + | 0.898056i | −0.00979203 | + | 0.0301368i | ||||
\(889\) | −12.4721 | − | 9.06154i | −0.418302 | − | 0.303914i | ||||
\(890\) | 1.90983 | 0.0640176 | ||||||||
\(891\) | 24.9443 | − | 5.60034i | 0.835665 | − | 0.187618i | ||||
\(892\) | 19.7082 | 0.659879 | ||||||||
\(893\) | 0.562306 | + | 0.408539i | 0.0188168 | + | 0.0136712i | ||||
\(894\) | 0.214782 | − | 0.661030i | 0.00718338 | − | 0.0221082i | ||||
\(895\) | 2.66312 | + | 8.19624i | 0.0890182 | + | 0.273970i | ||||
\(896\) | −0.809017 | + | 0.587785i | −0.0270274 | + | 0.0196365i | ||||
\(897\) | 3.70820 | − | 2.69417i | 0.123813 | − | 0.0899556i | ||||
\(898\) | 9.71885 | + | 29.9115i | 0.324322 | + | 0.998161i | ||||
\(899\) | 1.23607 | − | 3.80423i | 0.0412252 | − | 0.126878i | ||||
\(900\) | 2.30902 | + | 1.67760i | 0.0769672 | + | 0.0559200i | ||||
\(901\) | 2.00000 | 0.0666297 | ||||||||
\(902\) | 9.00658 | + | 15.1967i | 0.299886 | + | 0.505993i | ||||
\(903\) | −1.85410 | −0.0617007 | ||||||||
\(904\) | 5.11803 | + | 3.71847i | 0.170223 | + | 0.123674i | ||||
\(905\) | −3.85410 | + | 11.8617i | −0.128115 | + | 0.394296i | ||||
\(906\) | 1.85410 | + | 5.70634i | 0.0615984 | + | 0.189580i | ||||
\(907\) | 9.11803 | − | 6.62464i | 0.302759 | − | 0.219968i | −0.426024 | − | 0.904712i | \(-0.640086\pi\) |
0.728783 | + | 0.684744i | \(0.240086\pi\) | |||||||
\(908\) | 7.50000 | − | 5.44907i | 0.248896 | − | 0.180834i | ||||
\(909\) | −7.88854 | − | 24.2784i | −0.261646 | − | 0.805265i | ||||
\(910\) | 0.618034 | − | 1.90211i | 0.0204876 | − | 0.0630544i | ||||
\(911\) | 1.94427 | + | 1.41260i | 0.0644166 | + | 0.0468014i | 0.619528 | − | 0.784975i | \(-0.287324\pi\) |
−0.555111 | + | 0.831776i | \(0.687324\pi\) | |||||||
\(912\) | −0.0557281 | −0.00184534 | ||||||||
\(913\) | 9.00658 | + | 15.1967i | 0.298074 | + | 0.502936i | ||||
\(914\) | 2.27051 | 0.0751018 | ||||||||
\(915\) | 3.85410 | + | 2.80017i | 0.127413 | + | 0.0925707i | ||||
\(916\) | −9.00000 | + | 27.6992i | −0.297368 | + | 0.915206i | ||||
\(917\) | 5.19098 | + | 15.9762i | 0.171421 | + | 0.527581i | ||||
\(918\) | 1.11803 | − | 0.812299i | 0.0369006 | − | 0.0268099i | ||||
\(919\) | 36.2705 | − | 26.3521i | 1.19645 | − | 0.869275i | 0.202522 | − | 0.979278i | \(-0.435086\pi\) |
0.993931 | + | 0.110003i | \(0.0350861\pi\) | |||||||
\(920\) | 1.85410 | + | 5.70634i | 0.0611279 | + | 0.188132i | ||||
\(921\) | 0.877901 | − | 2.70190i | 0.0289278 | − | 0.0890306i | ||||
\(922\) | 8.85410 | + | 6.43288i | 0.291594 | + | 0.211856i | ||||
\(923\) | −7.41641 | −0.244114 | ||||||||
\(924\) | −1.23607 | + | 0.277515i | −0.0406637 | + | 0.00912956i | ||||
\(925\) | 2.47214 | 0.0812833 | ||||||||
\(926\) | 15.7082 | + | 11.4127i | 0.516204 | + | 0.375044i | ||||
\(927\) | −0.832816 | + | 2.56314i | −0.0273533 | + | 0.0841847i | ||||
\(928\) | −0.381966 | − | 1.17557i | −0.0125386 | − | 0.0385900i | ||||
\(929\) | 37.0066 | − | 26.8869i | 1.21415 | − | 0.882129i | 0.218546 | − | 0.975827i | \(-0.429869\pi\) |
0.995601 | + | 0.0936977i | \(0.0298687\pi\) | |||||||
\(930\) | −1.00000 | + | 0.726543i | −0.0327913 | + | 0.0238243i | ||||
\(931\) | −0.0450850 | − | 0.138757i | −0.00147760 | − | 0.00454759i | ||||
\(932\) | −6.82624 | + | 21.0090i | −0.223601 | + | 0.688173i | ||||
\(933\) | −3.43769 | − | 2.49763i | −0.112545 | − | 0.0817688i | ||||
\(934\) | −17.8885 | −0.585331 | ||||||||
\(935\) | −1.88197 | − | 0.812299i | −0.0615469 | − | 0.0265650i | ||||
\(936\) | −5.70820 | −0.186578 | ||||||||
\(937\) | −32.6803 | − | 23.7437i | −1.06762 | − | 0.775671i | −0.0921372 | − | 0.995746i | \(-0.529370\pi\) |
−0.975483 | + | 0.220075i | \(0.929370\pi\) | |||||||
\(938\) | −1.57295 | + | 4.84104i | −0.0513586 | + | 0.158066i | ||||
\(939\) | 0.690983 | + | 2.12663i | 0.0225494 | + | 0.0693998i | ||||
\(940\) | 3.85410 | − | 2.80017i | 0.125707 | − | 0.0913314i | ||||
\(941\) | 9.56231 | − | 6.94742i | 0.311722 | − | 0.226479i | −0.420913 | − | 0.907101i | \(-0.638290\pi\) |
0.732635 | + | 0.680622i | \(0.238290\pi\) | |||||||
\(942\) | −1.61803 | − | 4.97980i | −0.0527184 | − | 0.162251i | ||||
\(943\) | −9.87539 | + | 30.3933i | −0.321587 | + | 0.989743i | ||||
\(944\) | 4.35410 | + | 3.16344i | 0.141714 | + | 0.102961i | ||||
\(945\) | −2.23607 | −0.0727393 | ||||||||
\(946\) | 10.6353 | − | 12.0862i | 0.345782 | − | 0.392957i | ||||
\(947\) | −53.0902 | −1.72520 | −0.862599 | − | 0.505888i | \(-0.831165\pi\) | ||||
−0.862599 | + | 0.505888i | \(0.831165\pi\) | |||||||
\(948\) | 0.145898 | + | 0.106001i | 0.00473855 | + | 0.00344276i | ||||
\(949\) | 4.41641 | − | 13.5923i | 0.143363 | − | 0.441225i | ||||
\(950\) | 0.0450850 | + | 0.138757i | 0.00146275 | + | 0.00450188i | ||||
\(951\) | 7.79837 | − | 5.66585i | 0.252880 | − | 0.183728i | ||||
\(952\) | 0.500000 | − | 0.363271i | 0.0162051 | − | 0.0117737i | ||||
\(953\) | 8.17376 | + | 25.1563i | 0.264774 | + | 0.814891i | 0.991745 | + | 0.128223i | \(0.0409273\pi\) |
−0.726971 | + | 0.686668i | \(0.759073\pi\) | |||||||
\(954\) | −2.85410 | + | 8.78402i | −0.0924050 | + | 0.284393i | ||||
\(955\) | −8.47214 | − | 6.15537i | −0.274152 | − | 0.199183i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.145898 | − | 1.55909i | 0.00471621 | − | 0.0503981i | ||||
\(958\) | −2.11146 | −0.0682181 | ||||||||
\(959\) | 8.16312 | + | 5.93085i | 0.263601 | + | 0.191517i | ||||
\(960\) | −0.118034 | + | 0.363271i | −0.00380953 | + | 0.0117245i | ||||
\(961\) | −6.34346 | − | 19.5232i | −0.204628 | − | 0.629779i | ||||
\(962\) | −4.00000 | + | 2.90617i | −0.128965 | + | 0.0936987i | ||||
\(963\) | −40.6803 | + | 29.5560i | −1.31091 | + | 0.952429i | ||||
\(964\) | −8.42705 | − | 25.9358i | −0.271417 | − | 0.835336i | ||||
\(965\) | −0.618034 | + | 1.90211i | −0.0198952 | + | 0.0612312i | ||||
\(966\) | −1.85410 | − | 1.34708i | −0.0596548 | − | 0.0433417i | ||||
\(967\) | 49.0132 | 1.57616 | 0.788078 | − | 0.615575i | \(-0.211076\pi\) | ||||
0.788078 | + | 0.615575i | \(0.211076\pi\) | |||||||
\(968\) | 5.28115 | − | 9.64932i | 0.169743 | − | 0.310141i | ||||
\(969\) | 0.0344419 | 0.00110643 | ||||||||
\(970\) | −8.54508 | − | 6.20837i | −0.274366 | − | 0.199339i | ||||
\(971\) | 8.29180 | − | 25.5195i | 0.266096 | − | 0.818961i | −0.725342 | − | 0.688388i | \(-0.758319\pi\) |
0.991439 | − | 0.130572i | \(-0.0416815\pi\) | |||||||
\(972\) | 2.98278 | + | 9.18005i | 0.0956727 | + | 0.294450i | ||||
\(973\) | −7.70820 | + | 5.60034i | −0.247114 | + | 0.179539i | ||||
\(974\) | 21.7082 | − | 15.7719i | 0.695576 | − | 0.505365i | ||||
\(975\) | −0.236068 | − | 0.726543i | −0.00756023 | − | 0.0232680i | ||||
\(976\) | 3.85410 | − | 11.8617i | 0.123367 | − | 0.379684i | ||||
\(977\) | 15.6180 | + | 11.3472i | 0.499665 | + | 0.363028i | 0.808889 | − | 0.587961i | \(-0.200069\pi\) |
−0.309224 | + | 0.950989i | \(0.600069\pi\) | |||||||
\(978\) | 1.47214 | 0.0470737 | ||||||||
\(979\) | 0.590170 | − | 6.30664i | 0.0188619 | − | 0.201561i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −19.5623 | − | 14.2128i | −0.624576 | − | 0.453781i | ||||
\(982\) | 1.70163 | − | 5.23707i | 0.0543011 | − | 0.167122i | ||||
\(983\) | 5.14590 | + | 15.8374i | 0.164129 | + | 0.505136i | 0.998971 | − | 0.0453530i | \(-0.0144413\pi\) |
−0.834842 | + | 0.550489i | \(0.814441\pi\) | |||||||
\(984\) | −1.64590 | + | 1.19581i | −0.0524693 | + | 0.0381212i | ||||
\(985\) | −4.85410 | + | 3.52671i | −0.154665 | + | 0.112370i | ||||
\(986\) | 0.236068 | + | 0.726543i | 0.00751794 | + | 0.0231378i | ||||
\(987\) | −0.562306 | + | 1.73060i | −0.0178984 | + | 0.0550856i | ||||
\(988\) | −0.236068 | − | 0.171513i | −0.00751032 | − | 0.00545657i | ||||
\(989\) | 29.1246 | 0.926109 | ||||||||
\(990\) | 6.25329 | − | 7.10642i | 0.198743 | − | 0.225857i | ||||
\(991\) | −10.6525 | −0.338387 | −0.169194 | − | 0.985583i | \(-0.554116\pi\) | ||||
−0.169194 | + | 0.985583i | \(0.554116\pi\) | |||||||
\(992\) | 2.61803 | + | 1.90211i | 0.0831227 | + | 0.0603921i | ||||
\(993\) | −2.71885 | + | 8.36775i | −0.0862800 | + | 0.265543i | ||||
\(994\) | 1.14590 | + | 3.52671i | 0.0363457 | + | 0.111860i | ||||
\(995\) | 6.00000 | − | 4.35926i | 0.190213 | − | 0.138198i | ||||
\(996\) | −1.64590 | + | 1.19581i | −0.0521523 | + | 0.0378908i | ||||
\(997\) | −5.29180 | − | 16.2865i | −0.167593 | − | 0.515798i | 0.831625 | − | 0.555337i | \(-0.187411\pi\) |
−0.999218 | + | 0.0395396i | \(0.987411\pi\) | |||||||
\(998\) | 12.2984 | − | 37.8505i | 0.389298 | − | 1.19814i | ||||
\(999\) | 4.47214 | + | 3.24920i | 0.141492 | + | 0.102800i |
(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 | 770.2.n.b.631.1 | yes | 4 | |
11.3 | even | 5 | inner | 770.2.n.b.421.1 | ✓ | 4 | |
11.5 | even | 5 | 8470.2.a.bt.1.1 | 2 | |||
11.6 | odd | 10 | 8470.2.a.cf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.b.421.1 | ✓ | 4 | 11.3 | even | 5 | inner | |
770.2.n.b.631.1 | yes | 4 | 1.1 | even | 1 | trivial | |
8470.2.a.bt.1.1 | 2 | 11.5 | even | 5 | |||
8470.2.a.cf.1.1 | 2 | 11.6 | odd | 10 |