Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [243,2,Mod(28,243)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(243, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("243.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 243 = 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 243.e (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.94036476912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.1952986685049.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 136.1 | ||
Root | \(0.500000 - 1.00210i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 243.136 |
Dual form | 243.2.e.b.109.1 |
$q$-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 \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.807660 | − | 0.677707i | −0.571102 | − | 0.479211i | 0.310910 | − | 0.950439i | \(-0.399366\pi\) |
−0.882011 | + | 0.471228i | \(0.843811\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.154269 | − | 0.874902i | −0.0771344 | − | 0.437451i | ||||
\(5\) | −1.64050 | − | 0.597094i | −0.733655 | − | 0.267029i | −0.0519440 | − | 0.998650i | \(-0.516542\pi\) |
−0.681711 | + | 0.731621i | \(0.738764\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.427044 | − | 2.42189i | 0.161407 | − | 0.915387i | −0.791284 | − | 0.611448i | \(-0.790587\pi\) |
0.952692 | − | 0.303938i | \(-0.0983017\pi\) | |||||||
\(8\) | −1.52266 | + | 2.63732i | −0.538340 | + | 0.932432i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.920313 | + | 1.59403i | 0.291029 | + | 0.504076i | ||||
\(11\) | −1.17857 | + | 0.428966i | −0.355354 | + | 0.129338i | −0.513528 | − | 0.858073i | \(-0.671662\pi\) |
0.158174 | + | 0.987411i | \(0.449439\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.48476 | + | 2.92406i | −0.966498 | + | 0.810988i | −0.981998 | − | 0.188892i | \(-0.939511\pi\) |
0.0154998 | + | 0.999880i | \(0.495066\pi\) | |||||||
\(14\) | −1.98623 | + | 1.66665i | −0.530843 | + | 0.445431i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.34747 | − | 0.490439i | 0.336868 | − | 0.122610i | ||||
\(17\) | −3.32358 | − | 5.75662i | −0.806088 | − | 1.39618i | −0.915554 | − | 0.402194i | \(-0.868248\pi\) |
0.109467 | − | 0.993990i | \(-0.465086\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.124578 | + | 0.215776i | −0.0285802 | + | 0.0495023i | −0.879962 | − | 0.475045i | \(-0.842432\pi\) |
0.851382 | + | 0.524547i | \(0.175765\pi\) | |||||||
\(20\) | −0.269321 | + | 1.52739i | −0.0602219 | + | 0.341536i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.24260 | + | 0.452270i | 0.264923 | + | 0.0964242i | ||||
\(23\) | −0.146212 | − | 0.829209i | −0.0304873 | − | 0.172902i | 0.965762 | − | 0.259429i | \(-0.0835343\pi\) |
−0.996250 | + | 0.0865268i | \(0.972423\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.49549 | − | 1.25487i | −0.299099 | − | 0.250974i | ||||
\(26\) | 4.79615 | 0.940603 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.18479 | −0.412887 | ||||||||
\(29\) | 0.392508 | + | 0.329353i | 0.0728869 | + | 0.0611594i | 0.678503 | − | 0.734597i | \(-0.262629\pi\) |
−0.605616 | + | 0.795757i | \(0.707073\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.142392 | − | 0.807546i | −0.0255744 | − | 0.145040i | 0.969347 | − | 0.245696i | \(-0.0790167\pi\) |
−0.994921 | + | 0.100657i | \(0.967906\pi\) | |||||||
\(32\) | 4.30264 | + | 1.56603i | 0.760607 | + | 0.276838i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.21697 | + | 6.90180i | −0.208709 | + | 1.18365i | ||||
\(35\) | −2.14666 | + | 3.71812i | −0.362852 | + | 0.628478i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.30403 | − | 2.25865i | −0.214381 | − | 0.371319i | 0.738700 | − | 0.674035i | \(-0.235440\pi\) |
−0.953081 | + | 0.302715i | \(0.902107\pi\) | |||||||
\(38\) | 0.246849 | − | 0.0898458i | 0.0400442 | − | 0.0145749i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.07265 | − | 3.41736i | 0.643942 | − | 0.540332i | ||||
\(41\) | 6.24542 | − | 5.24053i | 0.975370 | − | 0.818433i | −0.00801406 | − | 0.999968i | \(-0.502551\pi\) |
0.983385 | + | 0.181535i | \(0.0581065\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.06619 | + | 1.47997i | −0.620087 | + | 0.225693i | −0.632911 | − | 0.774224i | \(-0.718140\pi\) |
0.0128237 | + | 0.999918i | \(0.495918\pi\) | |||||||
\(44\) | 0.557121 | + | 0.964962i | 0.0839891 | + | 0.145473i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.443871 | + | 0.768808i | −0.0654452 | + | 0.113354i | ||||
\(47\) | 0.920741 | − | 5.22178i | 0.134304 | − | 0.761675i | −0.841038 | − | 0.540976i | \(-0.818055\pi\) |
0.975342 | − | 0.220699i | \(-0.0708339\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.894687 | + | 0.325640i | 0.127812 | + | 0.0465199i | ||||
\(50\) | 0.357417 | + | 2.02701i | 0.0505464 | + | 0.286663i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.09586 | + | 2.59773i | 0.429318 | + | 0.360241i | ||||
\(53\) | 10.4841 | 1.44010 | 0.720052 | − | 0.693920i | \(-0.244118\pi\) | ||||
0.720052 | + | 0.693920i | \(0.244118\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.18959 | 0.295244 | ||||||||
\(56\) | 5.73704 | + | 4.81395i | 0.766644 | + | 0.643291i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.0938079 | − | 0.532011i | −0.0123176 | − | 0.0698565i | ||||
\(59\) | −2.82491 | − | 1.02818i | −0.367772 | − | 0.133858i | 0.151522 | − | 0.988454i | \(-0.451583\pi\) |
−0.519293 | + | 0.854596i | \(0.673805\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500658 | − | 2.83937i | 0.0641026 | − | 0.363544i | −0.935836 | − | 0.352437i | \(-0.885353\pi\) |
0.999938 | − | 0.0111075i | \(-0.00353569\pi\) | |||||||
\(62\) | −0.432275 | + | 0.748722i | −0.0548990 | + | 0.0950878i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.84771 | − | 6.66442i | −0.480963 | − | 0.833053i | ||||
\(65\) | 7.46270 | − | 2.71620i | 0.925634 | − | 0.336903i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.72653 | − | 6.48333i | 0.943945 | − | 0.792064i | −0.0343221 | − | 0.999411i | \(-0.510927\pi\) |
0.978268 | + | 0.207347i | \(0.0664828\pi\) | |||||||
\(68\) | −4.52375 | + | 3.79588i | −0.548586 | + | 0.460318i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.25357 | − | 1.54817i | 0.508399 | − | 0.185042i | ||||
\(71\) | 0.0447378 | + | 0.0774882i | 0.00530940 | + | 0.00919615i | 0.868668 | − | 0.495395i | \(-0.164977\pi\) |
−0.863358 | + | 0.504591i | \(0.831643\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.66057 | − | 4.60824i | 0.311396 | − | 0.539354i | −0.667269 | − | 0.744817i | \(-0.732537\pi\) |
0.978665 | + | 0.205463i | \(0.0658701\pi\) | |||||||
\(74\) | −0.477488 | + | 2.70797i | −0.0555069 | + | 0.314795i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.208001 | + | 0.0757062i | 0.0238594 | + | 0.00868410i | ||||
\(77\) | 0.535604 | + | 3.03756i | 0.0610377 | + | 0.346162i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.65933 | + | 3.07054i | 0.411707 | + | 0.345463i | 0.824998 | − | 0.565136i | \(-0.191176\pi\) |
−0.413291 | + | 0.910599i | \(0.635621\pi\) | |||||||
\(80\) | −2.50337 | −0.279885 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.59571 | −0.949238 | ||||||||
\(83\) | −6.15950 | − | 5.16844i | −0.676093 | − | 0.567310i | 0.238769 | − | 0.971077i | \(-0.423256\pi\) |
−0.914862 | + | 0.403767i | \(0.867701\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.01511 | + | 11.4282i | 0.218569 | + | 1.23957i | ||||
\(86\) | 4.28708 | + | 1.56037i | 0.462288 | + | 0.168259i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.663244 | − | 3.76144i | 0.0707020 | − | 0.400971i | ||||
\(89\) | 3.35189 | − | 5.80564i | 0.355299 | − | 0.615396i | −0.631870 | − | 0.775074i | \(-0.717712\pi\) |
0.987169 | + | 0.159678i | \(0.0510457\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.59359 | + | 9.68839i | 0.586368 | + | 1.01562i | ||||
\(92\) | −0.702921 | + | 0.255842i | −0.0732846 | + | 0.0266734i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.28248 | + | 3.59343i | −0.441704 | + | 0.370634i | ||||
\(95\) | 0.333209 | − | 0.279596i | 0.0341865 | − | 0.0286859i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.15946 | + | 1.87789i | −0.523863 | + | 0.190671i | −0.590396 | − | 0.807114i | \(-0.701028\pi\) |
0.0665329 | + | 0.997784i | \(0.478806\pi\) | |||||||
\(98\) | −0.501915 | − | 0.869342i | −0.0507010 | − | 0.0878168i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.867179 | + | 1.50200i | −0.0867179 | + | 0.150200i | ||||
\(101\) | −0.869190 | + | 4.92942i | −0.0864876 | + | 0.490496i | 0.910538 | + | 0.413425i | \(0.135668\pi\) |
−0.997026 | + | 0.0770703i | \(0.975443\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9184 | − | 3.97399i | −1.07583 | − | 0.391569i | −0.257473 | − | 0.966285i | \(-0.582890\pi\) |
−0.818352 | + | 0.574717i | \(0.805112\pi\) | |||||||
\(104\) | −2.40558 | − | 13.6427i | −0.235887 | − | 1.33778i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.46760 | − | 7.10516i | −0.822446 | − | 0.690114i | ||||
\(107\) | −19.4581 | −1.88109 | −0.940544 | − | 0.339673i | \(-0.889684\pi\) | ||||
−0.940544 | + | 0.339673i | \(0.889684\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.31515 | 0.604881 | 0.302441 | − | 0.953168i | \(-0.402199\pi\) | ||||
0.302441 | + | 0.953168i | \(0.402199\pi\) | |||||||
\(110\) | −1.76844 | − | 1.48390i | −0.168614 | − | 0.141484i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.612359 | − | 3.47286i | −0.0578625 | − | 0.328154i | ||||
\(113\) | −6.49866 | − | 2.36532i | −0.611342 | − | 0.222510i | 0.0177483 | − | 0.999842i | \(-0.494350\pi\) |
−0.629090 | + | 0.777332i | \(0.716572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.255255 | + | 1.44762i | −0.0238026 | + | 0.134991i | ||||
\(116\) | 0.227600 | − | 0.394215i | 0.0211322 | − | 0.0366020i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.58476 | + | 2.74488i | 0.145889 | + | 0.252687i | ||||
\(119\) | −15.3612 | + | 5.59101i | −1.40816 | + | 0.512527i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.22146 | + | 6.05953i | −0.656497 | + | 0.550866i | ||||
\(122\) | −2.32862 | + | 1.95395i | −0.210824 | + | 0.176902i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.684557 | + | 0.249158i | −0.0614750 | + | 0.0223751i | ||||
\(125\) | 6.06855 | + | 10.5110i | 0.542788 | + | 0.940136i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.01162 | + | 10.4124i | −0.533445 | + | 0.923954i | 0.465792 | + | 0.884894i | \(0.345770\pi\) |
−0.999237 | + | 0.0390598i | \(0.987564\pi\) | |||||||
\(128\) | 0.181303 | − | 1.02822i | 0.0160251 | − | 0.0908828i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.86811 | − | 2.86376i | −0.690079 | − | 0.251168i | ||||
\(131\) | 2.44580 | + | 13.8708i | 0.213690 | + | 1.21190i | 0.883164 | + | 0.469063i | \(0.155408\pi\) |
−0.669474 | + | 0.742835i | \(0.733480\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.469383 | + | 0.393859i | 0.0407007 | + | 0.0341519i | ||||
\(134\) | −10.6342 | −0.918655 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.2427 | 1.73580 | ||||||||
\(137\) | −1.72984 | − | 1.45150i | −0.147790 | − | 0.124010i | 0.565895 | − | 0.824477i | \(-0.308531\pi\) |
−0.713685 | + | 0.700467i | \(0.752975\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.38486 | − | 7.85393i | −0.117462 | − | 0.666162i | −0.985502 | − | 0.169666i | \(-0.945731\pi\) |
0.868039 | − | 0.496496i | \(-0.165380\pi\) | |||||||
\(140\) | 3.58416 | + | 1.30453i | 0.302917 | + | 0.110253i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.0163813 | − | 0.0929032i | 0.00137469 | − | 0.00779626i | ||||
\(143\) | 2.85273 | − | 4.94107i | 0.238557 | − | 0.413193i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.447256 | − | 0.774670i | −0.0371426 | − | 0.0643328i | ||||
\(146\) | −5.27187 | + | 1.91880i | −0.436303 | + | 0.158801i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.77492 | + | 1.48934i | −0.145898 | + | 0.122423i | ||||
\(149\) | 0.0819196 | − | 0.0687387i | 0.00671111 | − | 0.00563129i | −0.639426 | − | 0.768853i | \(-0.720828\pi\) |
0.646137 | + | 0.763221i | \(0.276383\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.0376 | − | 6.92913i | 1.54926 | − | 0.563884i | 0.581016 | − | 0.813892i | \(-0.302655\pi\) |
0.968244 | + | 0.250008i | \(0.0804333\pi\) | |||||||
\(152\) | −0.379379 | − | 0.657104i | −0.0307717 | − | 0.0532982i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.62599 | − | 2.81630i | 0.131026 | − | 0.226944i | ||||
\(155\) | −0.248586 | + | 1.40980i | −0.0199669 | + | 0.113238i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.4985 | + | 7.09686i | 1.55615 | + | 0.566391i | 0.969850 | − | 0.243704i | \(-0.0783626\pi\) |
0.586298 | + | 0.810096i | \(0.300585\pi\) | |||||||
\(158\) | −0.874566 | − | 4.95991i | −0.0695767 | − | 0.394589i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.12343 | − | 5.13816i | −0.484099 | − | 0.406208i | ||||
\(161\) | −2.07069 | −0.163193 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.1346 | −1.57706 | −0.788531 | − | 0.614995i | \(-0.789158\pi\) | ||||
−0.788531 | + | 0.614995i | \(0.789158\pi\) | |||||||
\(164\) | −5.54842 | − | 4.65568i | −0.433259 | − | 0.363548i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.47210 | + | 8.34868i | 0.114257 | + | 0.647983i | ||||
\(167\) | −18.6647 | − | 6.79341i | −1.44432 | − | 0.525690i | −0.503322 | − | 0.864099i | \(-0.667889\pi\) |
−0.940999 | + | 0.338409i | \(0.890111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.33599 | − | 7.57678i | 0.102769 | − | 0.582830i | ||||
\(170\) | 6.11748 | − | 10.5958i | 0.469189 | − | 0.812660i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.92212 | + | 3.32920i | 0.146560 | + | 0.253849i | ||||
\(173\) | 17.7838 | − | 6.47277i | 1.35208 | − | 0.492116i | 0.438481 | − | 0.898740i | \(-0.355517\pi\) |
0.913595 | + | 0.406625i | \(0.133294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.67779 | + | 3.08603i | −0.278015 | + | 0.233282i | ||||
\(176\) | −1.37771 | + | 1.15604i | −0.103849 | + | 0.0871397i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.64170 | + | 2.41738i | −0.497817 | + | 0.181190i | ||||
\(179\) | 5.45683 | + | 9.45151i | 0.407863 | + | 0.706439i | 0.994650 | − | 0.103302i | \(-0.0329409\pi\) |
−0.586787 | + | 0.809741i | \(0.699608\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.97393 | − | 15.5433i | 0.667027 | − | 1.15532i | −0.311704 | − | 0.950179i | \(-0.600900\pi\) |
0.978731 | − | 0.205146i | \(-0.0657668\pi\) | |||||||
\(182\) | 2.04817 | − | 11.6157i | 0.151820 | − | 0.861016i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.40952 | + | 0.876993i | 0.177632 | + | 0.0646528i | ||||
\(185\) | 0.790641 | + | 4.48395i | 0.0581291 | + | 0.329666i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.38649 | + | 5.35890i | 0.467026 | + | 0.391881i | ||||
\(188\) | −4.71059 | −0.343555 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.458604 | −0.0332706 | ||||||||
\(191\) | 20.6572 | + | 17.3334i | 1.49470 | + | 1.25420i | 0.888485 | + | 0.458905i | \(0.151758\pi\) |
0.606217 | + | 0.795299i | \(0.292686\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.97890 | − | 16.8942i | −0.214426 | − | 1.21607i | −0.881900 | − | 0.471437i | \(-0.843735\pi\) |
0.667474 | − | 0.744633i | \(-0.267376\pi\) | |||||||
\(194\) | 5.43974 | + | 1.97990i | 0.390551 | + | 0.142149i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.146880 | − | 0.833000i | 0.0104915 | − | 0.0595000i | ||||
\(197\) | 1.25612 | − | 2.17567i | 0.0894951 | − | 0.155010i | −0.817803 | − | 0.575499i | \(-0.804808\pi\) |
0.907298 | + | 0.420489i | \(0.138141\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.26942 | − | 16.0551i | −0.657092 | − | 1.13812i | −0.981365 | − | 0.192153i | \(-0.938453\pi\) |
0.324273 | − | 0.945964i | \(-0.394880\pi\) | |||||||
\(200\) | 5.58660 | − | 2.03336i | 0.395033 | − | 0.143780i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.04271 | − | 3.39224i | 0.284444 | − | 0.238677i | ||||
\(203\) | 0.965274 | − | 0.809961i | 0.0677490 | − | 0.0568481i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.3747 | + | 4.86800i | −0.934131 | + | 0.339996i | ||||
\(206\) | 6.12519 | + | 10.6091i | 0.426762 | + | 0.739173i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.26154 | + | 5.64915i | −0.226147 | + | 0.391698i | ||||
\(209\) | 0.0542642 | − | 0.307747i | 0.00375353 | − | 0.0212873i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.46857 | + | 1.26246i | 0.238787 | + | 0.0869112i | 0.458642 | − | 0.888621i | \(-0.348336\pi\) |
−0.219855 | + | 0.975533i | \(0.570558\pi\) | |||||||
\(212\) | −1.61737 | − | 9.17258i | −0.111082 | − | 0.629975i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.7155 | + | 13.1869i | 1.07429 | + | 0.901438i | ||||
\(215\) | 7.55427 | 0.515197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.01659 | −0.136895 | ||||||||
\(218\) | −5.10049 | − | 4.27982i | −0.345449 | − | 0.289866i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.337785 | − | 1.91568i | −0.0227735 | − | 0.129155i | ||||
\(221\) | 28.4146 | + | 10.3421i | 1.91137 | + | 0.695682i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.68847 | + | 20.9183i | −0.246998 | + | 1.40080i | 0.568808 | + | 0.822470i | \(0.307405\pi\) |
−0.815806 | + | 0.578326i | \(0.803706\pi\) | |||||||
\(224\) | 5.63017 | − | 9.75174i | 0.376181 | − | 0.651565i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.64571 | + | 6.31456i | 0.242509 | + | 0.420038i | ||||
\(227\) | −13.4752 | + | 4.90459i | −0.894383 | + | 0.325529i | −0.748000 | − | 0.663699i | \(-0.768986\pi\) |
−0.146383 | + | 0.989228i | \(0.546763\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.9353 | − | 10.8540i | 0.854787 | − | 0.717252i | −0.106051 | − | 0.994361i | \(-0.533821\pi\) |
0.960839 | + | 0.277109i | \(0.0893763\pi\) | |||||||
\(230\) | 1.18722 | − | 0.996198i | 0.0782832 | − | 0.0656874i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.46626 | + | 0.533676i | −0.0962650 | + | 0.0350376i | ||||
\(233\) | 2.79972 | + | 4.84926i | 0.183416 | + | 0.317686i | 0.943042 | − | 0.332675i | \(-0.107951\pi\) |
−0.759626 | + | 0.650361i | \(0.774618\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.62837 | + | 8.01658i | −0.301922 | + | 0.522944i | ||||
\(236\) | −0.463764 | + | 2.63013i | −0.0301884 | + | 0.171207i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.1957 | + | 5.89474i | 1.04981 | + | 0.382100i | ||||
\(239\) | 0.915868 | + | 5.19415i | 0.0592426 | + | 0.335981i | 0.999995 | − | 0.00311238i | \(-0.000990704\pi\) |
−0.940753 | + | 0.339094i | \(0.889880\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.81969 | − | 5.72240i | −0.439295 | − | 0.368612i | 0.396150 | − | 0.918186i | \(-0.370346\pi\) |
−0.835446 | + | 0.549573i | \(0.814790\pi\) | |||||||
\(242\) | 9.93907 | 0.638907 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.56141 | −0.163977 | ||||||||
\(245\) | −1.27330 | − | 1.06843i | −0.0813481 | − | 0.0682592i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.196816 | − | 1.11620i | −0.0125231 | − | 0.0710221i | ||||
\(248\) | 2.34657 | + | 0.854081i | 0.149007 | + | 0.0542342i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.22208 | − | 12.6020i | 0.140537 | − | 0.797024i | ||||
\(251\) | −3.89010 | + | 6.73786i | −0.245541 | + | 0.425290i | −0.962284 | − | 0.272048i | \(-0.912299\pi\) |
0.716742 | + | 0.697338i | \(0.245632\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.528024 | + | 0.914565i | 0.0331966 | + | 0.0574982i | ||||
\(254\) | 11.9119 | − | 4.33559i | 0.747421 | − | 0.272039i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.6333 | + | 10.6006i | −0.789583 | + | 0.662538i | ||||
\(257\) | 15.6553 | − | 13.1364i | 0.976551 | − | 0.819424i | −0.00701430 | − | 0.999975i | \(-0.502233\pi\) |
0.983566 | + | 0.180552i | \(0.0577883\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.02706 | + | 2.19367i | −0.374503 | + | 0.136308i | ||||
\(260\) | −3.52767 | − | 6.11011i | −0.218777 | − | 0.378933i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.42498 | − | 12.8604i | 0.458717 | − | 0.794520i | ||||
\(263\) | −1.95872 | + | 11.1084i | −0.120780 | + | 0.684976i | 0.862946 | + | 0.505297i | \(0.168617\pi\) |
−0.983725 | + | 0.179679i | \(0.942494\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.1992 | − | 6.26001i | −1.05654 | − | 0.384549i | ||||
\(266\) | −0.112181 | − | 0.636209i | −0.00687824 | − | 0.0390085i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.86424 | − | 5.75978i | −0.419300 | − | 0.351835i | ||||
\(269\) | 0.307761 | 0.0187645 | 0.00938226 | − | 0.999956i | \(-0.497013\pi\) | ||||
0.00938226 | + | 0.999956i | \(0.497013\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.22251 | −0.135008 | −0.0675040 | − | 0.997719i | \(-0.521504\pi\) | ||||
−0.0675040 | + | 0.997719i | \(0.521504\pi\) | |||||||
\(272\) | −7.30171 | − | 6.12686i | −0.442731 | − | 0.371495i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.413424 | + | 2.34464i | 0.0249759 | + | 0.141645i | ||||
\(275\) | 2.30085 | + | 0.837439i | 0.138746 | + | 0.0504995i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.05116 | + | 22.9753i | −0.243411 | + | 1.38045i | 0.580744 | + | 0.814087i | \(0.302762\pi\) |
−0.824154 | + | 0.566365i | \(0.808349\pi\) | |||||||
\(278\) | −4.20417 | + | 7.28184i | −0.252149 | + | 0.436735i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.53725 | − | 11.3228i | −0.390675 | − | 0.676670i | ||||
\(281\) | 6.78971 | − | 2.47125i | 0.405040 | − | 0.147422i | −0.131463 | − | 0.991321i | \(-0.541967\pi\) |
0.536503 | + | 0.843899i | \(0.319745\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.45446 | − | 4.57683i | 0.324234 | − | 0.272065i | −0.466112 | − | 0.884726i | \(-0.654345\pi\) |
0.790346 | + | 0.612661i | \(0.209901\pi\) | |||||||
\(284\) | 0.0608929 | − | 0.0510952i | 0.00361333 | − | 0.00303194i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.65263 | + | 2.05739i | −0.334247 | + | 0.121656i | ||||
\(287\) | −10.0249 | − | 17.3636i | −0.591751 | − | 1.02494i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5924 | + | 23.5428i | −0.799555 | + | 1.38487i | ||||
\(290\) | −0.163769 | + | 0.928778i | −0.00961682 | + | 0.0545397i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.44220 | − | 1.61683i | −0.259960 | − | 0.0946178i | ||||
\(293\) | −0.0959380 | − | 0.544092i | −0.00560476 | − | 0.0317862i | 0.981877 | − | 0.189519i | \(-0.0606927\pi\) |
−0.987482 | + | 0.157732i | \(0.949582\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.02035 | + | 3.37347i | 0.234074 | + | 0.196411i | ||||
\(296\) | 7.94236 | 0.461640 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.112748 | −0.00653131 | ||||||||
\(299\) | 2.93417 | + | 2.46206i | 0.169687 | + | 0.142385i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.84788 | + | 10.4798i | 0.106510 | + | 0.604048i | ||||
\(302\) | −20.0718 | − | 7.30555i | −1.15500 | − | 0.420387i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.0620405 | + | 0.351849i | −0.00355827 | + | 0.0201799i | ||||
\(305\) | −2.51670 | + | 4.35906i | −0.144106 | + | 0.249599i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.36438 | − | 5.82728i | −0.192015 | − | 0.332580i | 0.753903 | − | 0.656986i | \(-0.228169\pi\) |
−0.945918 | + | 0.324406i | \(0.894836\pi\) | |||||||
\(308\) | 2.57494 | − | 0.937202i | 0.146721 | − | 0.0534020i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.15621 | − | 0.970173i | 0.0656681 | − | 0.0551021i | ||||
\(311\) | −11.8151 | + | 9.91400i | −0.669970 | + | 0.562172i | −0.913057 | − | 0.407833i | \(-0.866285\pi\) |
0.243087 | + | 0.970005i | \(0.421840\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.1400 | − | 8.05829i | 1.25143 | − | 0.455482i | 0.370542 | − | 0.928816i | \(-0.379172\pi\) |
0.880883 | + | 0.473334i | \(0.156950\pi\) | |||||||
\(314\) | −10.9385 | − | 18.9461i | −0.617297 | − | 1.06919i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.12191 | − | 3.67525i | 0.119367 | − | 0.206749i | ||||
\(317\) | −1.25930 | + | 7.14187i | −0.0707296 | + | 0.401127i | 0.928804 | + | 0.370573i | \(0.120839\pi\) |
−0.999533 | + | 0.0305547i | \(0.990273\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.603882 | − | 0.219795i | −0.0338109 | − | 0.0123062i | ||||
\(320\) | 2.33289 | + | 13.2305i | 0.130412 | + | 0.739605i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.67241 | + | 1.40332i | 0.0931998 | + | 0.0782039i | ||||
\(323\) | 1.65618 | 0.0921525 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.88074 | 0.492615 | ||||||||
\(326\) | 16.2619 | + | 13.6453i | 0.900663 | + | 0.755746i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.31131 | + | 24.4507i | 0.238052 | + | 1.35006i | ||||
\(329\) | −12.2534 | − | 4.45986i | −0.675549 | − | 0.245880i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.04178 | − | 28.5934i | 0.277121 | − | 1.57163i | −0.455020 | − | 0.890481i | \(-0.650368\pi\) |
0.732142 | − | 0.681152i | \(-0.238521\pi\) | |||||||
\(332\) | −3.57166 | + | 6.18629i | −0.196020 | + | 0.339517i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.4708 | + | 18.1360i | 0.572938 | + | 0.992357i | ||||
\(335\) | −16.5465 | + | 6.02245i | −0.904035 | + | 0.329042i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.887919 | + | 0.745052i | −0.0483680 | + | 0.0405856i | −0.666651 | − | 0.745370i | \(-0.732273\pi\) |
0.618283 | + | 0.785955i | \(0.287828\pi\) | |||||||
\(338\) | −6.21387 | + | 5.21405i | −0.337990 | + | 0.283607i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.68773 | − | 3.52604i | 0.525391 | − | 0.191227i | ||||
\(341\) | 0.514230 | + | 0.890672i | 0.0278471 | + | 0.0482326i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.77810 | − | 16.9362i | 0.527968 | − | 0.914467i | ||||
\(344\) | 2.28825 | − | 12.9773i | 0.123374 | − | 0.699689i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.7499 | − | 6.82440i | −1.00800 | − | 0.366882i | ||||
\(347\) | −1.02274 | − | 5.80023i | −0.0549034 | − | 0.311373i | 0.944972 | − | 0.327151i | \(-0.106089\pi\) |
−0.999876 | + | 0.0157782i | \(0.994977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.4354 | − | 19.6646i | −1.25447 | − | 1.05262i | −0.996249 | − | 0.0865352i | \(-0.972420\pi\) |
−0.258217 | − | 0.966087i | \(-0.583135\pi\) | |||||||
\(350\) | 5.06182 | 0.270566 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.74276 | −0.306090 | ||||||||
\(353\) | −28.3140 | − | 23.7582i | −1.50700 | − | 1.26452i | −0.869348 | − | 0.494200i | \(-0.835461\pi\) |
−0.637653 | − | 0.770324i | \(-0.720094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.0271248 | − | 0.153832i | −0.00143963 | − | 0.00816457i | ||||
\(356\) | −5.59646 | − | 2.03694i | −0.296612 | − | 0.107958i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.99809 | − | 11.3317i | 0.105602 | − | 0.598901i | ||||
\(359\) | −13.1880 | + | 22.8423i | −0.696037 | + | 1.20557i | 0.273792 | + | 0.961789i | \(0.411722\pi\) |
−0.969830 | + | 0.243783i | \(0.921611\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.46896 | + | 16.4007i | 0.498366 | + | 0.863196i | ||||
\(362\) | −17.7817 | + | 6.47201i | −0.934585 | + | 0.340161i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.61347 | − | 6.38846i | 0.399055 | − | 0.334846i | ||||
\(365\) | −7.11623 | + | 5.97122i | −0.372480 | + | 0.312548i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.6309 | − | 3.86932i | 0.554927 | − | 0.201977i | −0.0493074 | − | 0.998784i | \(-0.515701\pi\) |
0.604234 | + | 0.796807i | \(0.293479\pi\) | |||||||
\(368\) | −0.603693 | − | 1.04563i | −0.0314697 | − | 0.0545071i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.40023 | − | 4.15733i | 0.124782 | − | 0.216129i | ||||
\(371\) | 4.47717 | − | 25.3913i | 0.232443 | − | 1.31825i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.49164 | − | 1.99879i | −0.284346 | − | 0.103494i | 0.195910 | − | 0.980622i | \(-0.437234\pi\) |
−0.480256 | + | 0.877128i | \(0.659456\pi\) | |||||||
\(374\) | −1.52634 | − | 8.65633i | −0.0789254 | − | 0.447608i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.3695 | + | 10.3793i | 0.637909 | + | 0.535269i | ||||
\(377\) | −2.33085 | −0.120045 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.3265 | 1.24957 | 0.624783 | − | 0.780798i | \(-0.285187\pi\) | ||||
0.624783 | + | 0.780798i | \(0.285187\pi\) | |||||||
\(380\) | −0.296023 | − | 0.248393i | −0.0151856 | − | 0.0127423i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.93699 | − | 27.9991i | −0.252598 | − | 1.43256i | ||||
\(383\) | −3.58591 | − | 1.30517i | −0.183232 | − | 0.0666909i | 0.248775 | − | 0.968561i | \(-0.419972\pi\) |
−0.432007 | + | 0.901870i | \(0.642194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.935050 | − | 5.30293i | 0.0476546 | − | 0.270262i | ||||
\(386\) | −9.04337 | + | 15.6636i | −0.460295 | + | 0.797255i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.43891 | + | 4.22432i | 0.123817 | + | 0.214457i | ||||
\(389\) | 10.1880 | − | 3.70813i | 0.516552 | − | 0.188010i | −0.0705716 | − | 0.997507i | \(-0.522482\pi\) |
0.587124 | + | 0.809497i | \(0.300260\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.28749 | + | 3.59763i | −0.216828 | + | 0.181940i | ||||
\(392\) | −2.22111 | + | 1.86374i | −0.112183 | + | 0.0941329i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.48899 | + | 0.905917i | −0.125393 | + | 0.0456394i | ||||
\(395\) | −4.16974 | − | 7.22221i | −0.209802 | − | 0.363389i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.25461 | − | 9.10124i | 0.263721 | − | 0.456778i | −0.703507 | − | 0.710689i | \(-0.748383\pi\) |
0.967228 | + | 0.253910i | \(0.0817168\pi\) | |||||||
\(398\) | −3.39412 | + | 19.2490i | −0.170132 | + | 0.964866i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.63057 | − | 0.957449i | −0.131529 | − | 0.0478725i | ||||
\(401\) | −2.49456 | − | 14.1473i | −0.124572 | − | 0.706484i | −0.981561 | − | 0.191149i | \(-0.938779\pi\) |
0.856989 | − | 0.515335i | \(-0.172332\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.85751 | + | 2.39774i | 0.142343 | + | 0.119440i | ||||
\(404\) | 4.44685 | 0.221239 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.32853 | −0.0659338 | ||||||||
\(407\) | 2.50578 | + | 2.10260i | 0.124207 | + | 0.104222i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.07049 | + | 17.4136i | 0.151826 | + | 0.861048i | 0.961630 | + | 0.274348i | \(0.0884621\pi\) |
−0.809804 | + | 0.586700i | \(0.800427\pi\) | |||||||
\(410\) | 14.1013 | + | 5.13245i | 0.696413 | + | 0.253474i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.79248 | + | 10.1656i | −0.0883089 | + | 0.500825i | ||||
\(413\) | −3.69650 | + | 6.40252i | −0.181893 | + | 0.315047i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.01864 | + | 12.1566i | 0.344532 | + | 0.596746i | ||||
\(416\) | −19.5728 | + | 7.12393i | −0.959637 | + | 0.349279i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.252390 | + | 0.211780i | −0.0123448 | + | 0.0103585i | ||||
\(419\) | −6.99687 | + | 5.87107i | −0.341819 | + | 0.286821i | −0.797495 | − | 0.603325i | \(-0.793842\pi\) |
0.455676 | + | 0.890146i | \(0.349398\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.7358 | + | 8.27515i | −1.10807 | + | 0.403306i | −0.830287 | − | 0.557337i | \(-0.811823\pi\) |
−0.277787 | + | 0.960643i | \(0.589601\pi\) | |||||||
\(422\) | −1.94585 | − | 3.37031i | −0.0947226 | − | 0.164064i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.9637 | + | 27.6499i | −0.775265 | + | 1.34280i | ||||
\(425\) | −2.25340 | + | 12.7796i | −0.109306 | + | 0.619904i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.66283 | − | 2.42507i | −0.322437 | − | 0.117357i | ||||
\(428\) | 3.00178 | + | 17.0240i | 0.145097 | + | 0.822884i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.10128 | − | 5.11958i | −0.294230 | − | 0.246888i | ||||
\(431\) | 29.5332 | 1.42256 | 0.711282 | − | 0.702907i | \(-0.248115\pi\) | ||||
0.711282 | + | 0.702907i | \(0.248115\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.669754 | 0.0321863 | 0.0160932 | − | 0.999870i | \(-0.494877\pi\) | ||||
0.0160932 | + | 0.999870i | \(0.494877\pi\) | |||||||
\(434\) | 1.62872 | + | 1.36666i | 0.0781810 | + | 0.0656017i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.974231 | − | 5.52514i | −0.0466572 | − | 0.264606i | ||||
\(437\) | 0.197138 | + | 0.0717523i | 0.00943038 | + | 0.00343238i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.10247 | + | 6.25242i | −0.0526180 | + | 0.298412i | −0.999748 | − | 0.0224379i | \(-0.992857\pi\) |
0.947130 | + | 0.320849i | \(0.103968\pi\) | |||||||
\(440\) | −3.33399 | + | 5.77464i | −0.158942 | + | 0.275295i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.9404 | − | 27.6096i | −0.758209 | − | 1.31326i | ||||
\(443\) | 14.4280 | − | 5.25135i | 0.685494 | − | 0.249499i | 0.0242891 | − | 0.999705i | \(-0.492268\pi\) |
0.661204 | + | 0.750206i | \(0.270046\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.96529 | + | 7.52277i | −0.424996 | + | 0.356614i | ||||
\(446\) | 17.1555 | − | 14.3952i | 0.812338 | − | 0.681633i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −17.7836 | + | 6.47270i | −0.840196 | + | 0.305806i | ||||
\(449\) | −16.0199 | − | 27.7473i | −0.756027 | − | 1.30948i | −0.944862 | − | 0.327468i | \(-0.893805\pi\) |
0.188836 | − | 0.982009i | \(-0.439529\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.11268 | + | 8.85543i | −0.240747 | + | 0.416986i | ||||
\(452\) | −1.06688 | + | 6.05058i | −0.0501819 | + | 0.284596i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.2073 | + | 5.17103i | 0.666781 | + | 0.242688i | ||||
\(455\) | −3.39143 | − | 19.2337i | −0.158992 | − | 0.901691i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.6836 | + | 12.3210i | 0.686868 | + | 0.576351i | 0.918004 | − | 0.396570i | \(-0.129800\pi\) |
−0.231136 | + | 0.972921i | \(0.574244\pi\) | |||||||
\(458\) | −17.8031 | −0.831886 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.30591 | 0.0608882 | ||||||||
\(461\) | 3.99898 | + | 3.35554i | 0.186251 | + | 0.156283i | 0.731146 | − | 0.682221i | \(-0.238986\pi\) |
−0.544895 | + | 0.838504i | \(0.683430\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.294749 | + | 1.67160i | 0.0136981 | + | 0.0776859i | 0.990890 | − | 0.134670i | \(-0.0429975\pi\) |
−0.977192 | + | 0.212356i | \(0.931886\pi\) | |||||||
\(464\) | 0.690421 | + | 0.251293i | 0.0320520 | + | 0.0116660i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.02516 | − | 5.81395i | 0.0474894 | − | 0.269326i | ||||
\(467\) | 9.84136 | − | 17.0457i | 0.455404 | − | 0.788783i | −0.543307 | − | 0.839534i | \(-0.682828\pi\) |
0.998711 | + | 0.0507511i | \(0.0161615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.4023 | − | 21.4814i | −0.572685 | − | 0.991920i | ||||
\(470\) | 9.17104 | − | 3.33799i | 0.423029 | − | 0.153970i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.01300 | − | 5.88461i | 0.322800 | − | 0.270861i | ||||
\(473\) | 4.15745 | − | 3.48851i | 0.191160 | − | 0.160402i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.457076 | − | 0.166362i | 0.0209721 | − | 0.00763321i | ||||
\(476\) | 7.26134 | + | 12.5770i | 0.332823 | + | 0.576467i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.78040 | − | 4.81579i | 0.127173 | − | 0.220269i | ||||
\(479\) | 5.07980 | − | 28.8090i | 0.232102 | − | 1.31632i | −0.616529 | − | 0.787332i | \(-0.711462\pi\) |
0.848631 | − | 0.528985i | \(-0.177427\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.1487 | + | 4.05778i | 0.508335 | + | 0.185019i | ||||
\(482\) | 1.62988 | + | 9.24351i | 0.0742390 | + | 0.421030i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.41554 | + | 5.38328i | 0.291616 | + | 0.244694i | ||||
\(485\) | 9.58538 | 0.435250 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.5056 | −0.929199 | −0.464600 | − | 0.885521i | \(-0.653802\pi\) | ||||
−0.464600 | + | 0.885521i | \(0.653802\pi\) | |||||||
\(488\) | 6.72599 | + | 5.64378i | 0.304471 | + | 0.255482i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.304314 | + | 1.72585i | 0.0137475 | + | 0.0779659i | ||||
\(491\) | 16.4700 | + | 5.99458i | 0.743280 | + | 0.270532i | 0.685775 | − | 0.727813i | \(-0.259463\pi\) |
0.0575048 | + | 0.998345i | \(0.481686\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.591428 | − | 3.35415i | 0.0266366 | − | 0.151063i | ||||
\(494\) | −0.597496 | + | 1.03489i | −0.0268826 | + | 0.0465620i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.587922 | − | 1.01831i | −0.0263985 | − | 0.0457235i | ||||
\(497\) | 0.206772 | − | 0.0752590i | 0.00927501 | − | 0.00337583i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.6360 | + | 12.2811i | −0.655199 | + | 0.549777i | −0.908643 | − | 0.417573i | \(-0.862881\pi\) |
0.253445 | + | 0.967350i | \(0.418436\pi\) | |||||||
\(500\) | 8.25995 | − | 6.93092i | 0.369396 | − | 0.309960i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.70817 | − | 2.80555i | 0.344033 | − | 0.125218i | ||||
\(503\) | −5.48381 | − | 9.49824i | −0.244511 | − | 0.423506i | 0.717483 | − | 0.696576i | \(-0.245294\pi\) |
−0.961994 | + | 0.273070i | \(0.911961\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.36924 | − | 7.56774i | 0.194429 | − | 0.336760i | ||||
\(506\) | 0.193343 | − | 1.09650i | 0.00859515 | − | 0.0487455i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.0373 | + | 3.65327i | 0.445332 | + | 0.162088i | ||||
\(509\) | 3.45549 | + | 19.5970i | 0.153162 | + | 0.868624i | 0.960447 | + | 0.278462i | \(0.0898247\pi\) |
−0.807285 | + | 0.590161i | \(0.799064\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0245 | − | 8.41151i | −0.443456 | − | 0.372103i | ||||
\(512\) | 15.2994 | 0.676143 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.5468 | −0.950387 | ||||||||
\(515\) | 15.5389 | + | 13.0387i | 0.684725 | + | 0.574553i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.15480 | + | 6.54922i | 0.0507883 | + | 0.288035i | ||||
\(518\) | 6.35448 | + | 2.31284i | 0.279200 | + | 0.101620i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.19964 | + | 23.8173i | −0.184166 | + | 1.04446i | ||||
\(521\) | 17.5583 | − | 30.4119i | 0.769244 | − | 1.33237i | −0.168729 | − | 0.985662i | \(-0.553966\pi\) |
0.937973 | − | 0.346708i | \(-0.112700\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.12269 | + | 12.3369i | 0.311453 | + | 0.539453i | 0.978677 | − | 0.205404i | \(-0.0658509\pi\) |
−0.667224 | + | 0.744857i | \(0.732518\pi\) | |||||||
\(524\) | 11.7583 | − | 4.27967i | 0.513664 | − | 0.186958i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.11025 | − | 7.64441i | 0.397226 | − | 0.333312i | ||||
\(527\) | −4.17548 | + | 3.50364i | −0.181887 | + | 0.152621i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.9467 | − | 7.62398i | 0.910727 | − | 0.331478i | ||||
\(530\) | 9.64867 | + | 16.7120i | 0.419111 | + | 0.725922i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.272177 | − | 0.471425i | 0.0118004 | − | 0.0204389i | ||||
\(533\) | −6.44016 | + | 36.5240i | −0.278954 | + | 1.58203i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.9211 | + | 11.6183i | 1.38007 | + | 0.502304i | ||||
\(536\) | 5.33374 | + | 30.2492i | 0.230383 | + | 1.30657i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.248566 | − | 0.208572i | −0.0107164 | − | 0.00899217i | ||||
\(539\) | −1.19414 | −0.0514354 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.2368 | −0.569094 | −0.284547 | − | 0.958662i | \(-0.591843\pi\) | ||||
−0.284547 | + | 0.958662i | \(0.591843\pi\) | |||||||
\(542\) | 1.79503 | + | 1.50621i | 0.0771033 | + | 0.0646974i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.28514 | − | 29.9735i | −0.226598 | − | 1.28510i | ||||
\(545\) | −10.3600 | − | 3.77074i | −0.443775 | − | 0.161521i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.83132 | + | 16.0572i | −0.121058 | + | 0.686557i | 0.862513 | + | 0.506035i | \(0.168890\pi\) |
−0.983571 | + | 0.180521i | \(0.942222\pi\) | |||||||
\(548\) | −1.00306 | + | 1.73736i | −0.0428488 | + | 0.0742163i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.29076 | − | 2.23567i | −0.0550383 | − | 0.0953291i | ||||
\(551\) | −0.119964 | + | 0.0436635i | −0.00511065 | + | 0.00186013i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.99920 | − | 7.55123i | 0.382685 | − | 0.321111i | ||||
\(554\) | 18.8425 | − | 15.8107i | 0.800540 | − | 0.671733i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.65778 | + | 2.42324i | −0.282353 | + | 0.102768i | ||||
\(557\) | 15.4486 | + | 26.7577i | 0.654577 | + | 1.13376i | 0.982000 | + | 0.188883i | \(0.0604867\pi\) |
−0.327422 | + | 0.944878i | \(0.606180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.84215 | − | 17.0471i | 0.416279 | − | 0.721016i | ||||
\(560\) | −1.06905 | + | 6.06287i | −0.0451755 | + | 0.256203i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.15856 | − | 2.60550i | −0.301965 | − | 0.109906i | ||||
\(563\) | −4.64959 | − | 26.3692i | −0.195957 | − | 1.11133i | −0.911049 | − | 0.412298i | \(-0.864726\pi\) |
0.715092 | − | 0.699030i | \(-0.246385\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.24875 | + | 7.76062i | 0.389098 | + | 0.326492i | ||||
\(566\) | −7.50710 | −0.315547 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.272481 | −0.0114331 | ||||||||
\(569\) | −14.6013 | − | 12.2519i | −0.612118 | − | 0.513628i | 0.283197 | − | 0.959062i | \(-0.408605\pi\) |
−0.895315 | + | 0.445434i | \(0.853050\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.26011 | − | 18.4890i | −0.136431 | − | 0.773740i | −0.973852 | − | 0.227182i | \(-0.927049\pi\) |
0.837421 | − | 0.546558i | \(-0.184062\pi\) | |||||||
\(572\) | −4.76304 | − | 1.73360i | −0.199153 | − | 0.0724856i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.67075 | + | 20.8178i | −0.153214 | + | 0.868920i | ||||
\(575\) | −0.821889 | + | 1.42355i | −0.0342751 | + | 0.0593663i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.42981 | + | 4.20856i | 0.101154 | + | 0.175204i | 0.912161 | − | 0.409833i | \(-0.134413\pi\) |
−0.811006 | + | 0.585038i | \(0.801080\pi\) | |||||||
\(578\) | 26.9332 | − | 9.80287i | 1.12027 | − | 0.407746i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.608763 | + | 0.510813i | −0.0252775 | + | 0.0212103i | ||||
\(581\) | −15.1477 | + | 12.7105i | −0.628434 | + | 0.527319i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.3563 | + | 4.49733i | −0.511746 | + | 0.186260i | ||||
\(584\) | 8.10226 | + | 14.0335i | 0.335274 | + | 0.580712i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.291249 | + | 0.504459i | −0.0120314 | + | 0.0208390i | ||||
\(587\) | 5.69520 | − | 32.2991i | 0.235066 | − | 1.33313i | −0.607409 | − | 0.794390i | \(-0.707791\pi\) |
0.842475 | − | 0.538736i | \(-0.181098\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.191988 | + | 0.0698778i | 0.00791071 | + | 0.00287926i | ||||
\(590\) | −0.960847 | − | 5.44923i | −0.0395574 | − | 0.224341i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.86487 | − | 2.40391i | −0.117746 | − | 0.0988003i | ||||
\(593\) | −17.3446 | −0.712258 | −0.356129 | − | 0.934437i | \(-0.615904\pi\) | ||||
−0.356129 | + | 0.934437i | \(0.615904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.5384 | 1.16996 | ||||||||
\(596\) | −0.0727773 | − | 0.0610674i | −0.00298107 | − | 0.00250142i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.701255 | − | 3.97702i | −0.0286765 | − | 0.162632i | ||||
\(599\) | 22.9359 | + | 8.34800i | 0.937137 | + | 0.341090i | 0.765035 | − | 0.643989i | \(-0.222722\pi\) |
0.172102 | + | 0.985079i | \(0.444944\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.36666 | − | 7.75070i | 0.0557471 | − | 0.316158i | −0.944164 | − | 0.329475i | \(-0.893128\pi\) |
0.999911 | + | 0.0133177i | \(0.00423928\pi\) | |||||||
\(602\) | 5.60981 | − | 9.71647i | 0.228639 | − | 0.396014i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.99922 | − | 15.5871i | −0.366173 | − | 0.634230i | ||||
\(605\) | 15.4649 | − | 5.62878i | 0.628739 | − | 0.228842i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.84236 | + | 6.58052i | −0.318311 | + | 0.267095i | −0.787917 | − | 0.615781i | \(-0.788841\pi\) |
0.469606 | + | 0.882876i | \(0.344396\pi\) | |||||||
\(608\) | −0.873926 | + | 0.733311i | −0.0354424 | + | 0.0297397i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.98680 | − | 1.81505i | 0.201910 | − | 0.0734891i | ||||
\(611\) | 12.0602 | + | 20.8889i | 0.487905 | + | 0.845076i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.11753 | + | 1.93563i | −0.0451368 | + | 0.0781792i | −0.887711 | − | 0.460401i | \(-0.847706\pi\) |
0.842574 | + | 0.538580i | \(0.181039\pi\) | |||||||
\(614\) | −1.23191 | + | 6.98652i | −0.0497159 | + | 0.281953i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.82655 | − | 3.21260i | −0.355632 | − | 0.129439i | ||||
\(617\) | −5.89982 | − | 33.4595i | −0.237518 | − | 1.34703i | −0.837246 | − | 0.546826i | \(-0.815836\pi\) |
0.599729 | − | 0.800203i | \(-0.295275\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.1050 | − | 18.5483i | −0.888473 | − | 0.745518i | 0.0794301 | − | 0.996840i | \(-0.474690\pi\) |
−0.967903 | + | 0.251323i | \(0.919134\pi\) | |||||||
\(620\) | 1.27179 | 0.0510763 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.2613 | 0.652020 | ||||||||
\(623\) | −12.6292 | − | 10.5971i | −0.505977 | − | 0.424565i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.98439 | − | 11.2541i | −0.0793758 | − | 0.450162i | ||||
\(626\) | −23.3427 | − | 8.49606i | −0.932963 | − | 0.339571i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.20105 | − | 18.1541i | 0.127736 | − | 0.724427i | ||||
\(629\) | −8.66811 | + | 15.0136i | −0.345620 | + | 0.598632i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.57039 | + | 2.71999i | 0.0625162 | + | 0.108281i | 0.895590 | − | 0.444881i | \(-0.146754\pi\) |
−0.833073 | + | 0.553163i | \(0.813421\pi\) | |||||||
\(632\) | −13.6699 | + | 4.97544i | −0.543759 | + | 0.197912i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.85718 | − | 4.91476i | 0.232618 | − | 0.195190i | ||||
\(635\) | 16.0793 | − | 13.4921i | 0.638087 | − | 0.535419i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.06996 | + | 1.48134i | −0.161258 | + | 0.0586930i | ||||
\(638\) | 0.338774 | + | 0.586774i | 0.0134122 | + | 0.0232306i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.911374 | + | 1.57855i | −0.0360252 | + | 0.0623975i | ||||
\(641\) | 5.52593 | − | 31.3391i | 0.218261 | − | 1.23782i | −0.656896 | − | 0.753981i | \(-0.728131\pi\) |
0.875157 | − | 0.483838i | \(-0.160758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0723 | + | 4.39396i | 0.476085 | + | 0.173281i | 0.568907 | − | 0.822402i | \(-0.307367\pi\) |
−0.0928219 | + | 0.995683i | \(0.529589\pi\) | |||||||
\(644\) | 0.319443 | + | 1.81165i | 0.0125878 | + | 0.0713890i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.33763 | − | 1.12241i | −0.0526285 | − | 0.0441605i | ||||
\(647\) | −28.2444 | −1.11040 | −0.555200 | − | 0.831717i | \(-0.687358\pi\) | ||||
−0.555200 | + | 0.831717i | \(0.687358\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.77042 | 0.148002 | ||||||||
\(650\) | −7.17262 | − | 6.01854i | −0.281333 | − | 0.236067i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.10614 | + | 17.6158i | 0.121646 | + | 0.689888i | ||||
\(653\) | 24.4231 | + | 8.88927i | 0.955749 | + | 0.347864i | 0.772366 | − | 0.635178i | \(-0.219073\pi\) |
0.183383 | + | 0.983042i | \(0.441295\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.26984 | − | 24.2155i | 0.166837 | − | 0.946178i | ||||
\(656\) | 5.84536 | − | 10.1245i | 0.228223 | − | 0.395294i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.87407 | + | 11.9062i | 0.267979 | + | 0.464153i | ||||
\(659\) | −44.7461 | + | 16.2863i | −1.74306 | + | 0.634422i | −0.999417 | − | 0.0341533i | \(-0.989127\pi\) |
−0.743644 | + | 0.668576i | \(0.766904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.671444 | + | 0.563408i | −0.0261161 | + | 0.0219140i | −0.655752 | − | 0.754976i | \(-0.727648\pi\) |
0.629636 | + | 0.776890i | \(0.283204\pi\) | |||||||
\(662\) | −23.4500 | + | 19.6769i | −0.911409 | + | 0.764763i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.0096 | − | 8.37481i | 0.892946 | − | 0.325006i | ||||
\(665\) | −0.534854 | − | 0.926394i | −0.0207407 | − | 0.0359240i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.215714 | − | 0.373627i | 0.00835246 | − | 0.0144669i | ||||
\(668\) | −3.06418 | + | 17.3778i | −0.118557 | + | 0.672369i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17.4454 | + | 6.34962i | 0.673976 | + | 0.245307i | ||||
\(671\) | 0.627931 | + | 3.56118i | 0.0242410 | + | 0.137478i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.6037 | + | 24.0013i | 1.10259 | + | 0.925183i | 0.997597 | − | 0.0692894i | \(-0.0220732\pi\) |
0.104994 | + | 0.994473i | \(0.466518\pi\) | |||||||
\(674\) | 1.22206 | 0.0470721 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.83505 | −0.262886 | ||||||||
\(677\) | 10.5095 | + | 8.81851i | 0.403913 | + | 0.338923i | 0.822004 | − | 0.569482i | \(-0.192856\pi\) |
−0.418091 | + | 0.908405i | \(0.637301\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.34472 | + | 13.2975i | 0.0899820 | + | 0.510313i | ||||
\(680\) | −33.2082 | − | 12.0868i | −1.27348 | − | 0.463508i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.188292 | − | 1.06786i | 0.00721007 | − | 0.0408903i | ||||
\(683\) | 24.9943 | − | 43.2914i | 0.956381 | − | 1.65650i | 0.225206 | − | 0.974311i | \(-0.427694\pi\) |
0.731175 | − | 0.682190i | \(-0.238972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.97112 | + | 3.41407i | 0.0753125 | + | 0.130445i | ||||
\(686\) | −19.3751 | + | 7.05197i | −0.739746 | + | 0.269245i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.75323 | + | 3.98843i | −0.181215 | + | 0.152058i | ||||
\(689\) | −36.5346 | + | 30.6562i | −1.39186 | + | 1.16791i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.3788 | + | 8.14523i | −0.851331 | + | 0.309859i | −0.730583 | − | 0.682824i | \(-0.760752\pi\) |
−0.120748 | + | 0.992683i | \(0.538529\pi\) | |||||||
\(692\) | −8.40653 | − | 14.5605i | −0.319568 | − | 0.553508i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.10483 | + | 5.37773i | −0.117858 | + | 0.204136i | ||||
\(695\) | −2.41767 | + | 13.7113i | −0.0917075 | + | 0.520099i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.9249 | − | 18.5351i | −1.92892 | − | 0.702069i | ||||
\(698\) | 5.60096 | + | 31.7646i | 0.211999 | + | 1.20231i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.26734 | + | 2.74163i | 0.123494 | + | 0.103624i | ||||
\(701\) | −34.4493 | −1.30113 | −0.650565 | − | 0.759450i | \(-0.725468\pi\) | ||||
−0.650565 | + | 0.759450i | \(0.725468\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.649815 | 0.0245082 | ||||||||
\(704\) | 7.39362 | + | 6.20398i | 0.278658 | + | 0.233821i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.76693 | + | 38.3772i | 0.254677 | + | 1.44434i | ||||
\(707\) | 11.5673 | + | 4.21016i | 0.435033 | + | 0.158339i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.69559 | − | 15.2874i | 0.101235 | − | 0.574132i | −0.891423 | − | 0.453173i | \(-0.850292\pi\) |
0.992658 | − | 0.120959i | \(-0.0385969\pi\) | |||||||
\(710\) | −0.0823456 | + | 0.142627i | −0.00309038 | + | 0.00535269i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.2075 | + | 17.6800i | 0.382543 | + | 0.662585i | ||||
\(713\) | −0.648805 | + | 0.236146i | −0.0242979 | + | 0.00884373i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.63019 | + | 6.40249i | −0.285353 | + | 0.239439i | ||||
\(716\) | 7.42733 | − | 6.23227i | 0.277572 | − | 0.232911i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.1318 | − | 9.51121i | 0.975232 | − | 0.354955i | ||||
\(719\) | 6.02686 | + | 10.4388i | 0.224764 | + | 0.389303i | 0.956249 | − | 0.292555i | \(-0.0945056\pi\) |
−0.731485 | + | 0.681858i | \(0.761172\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.2872 | + | 24.7461i | −0.532083 | + | 0.921594i | ||||
\(722\) | 3.46718 | − | 19.6634i | 0.129035 | − | 0.731795i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.9833 | − | 5.45347i | −0.556849 | − | 0.202676i | ||||
\(725\) | −0.173698 | − | 0.985092i | −0.00645099 | − | 0.0365854i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.2302 | − | 20.3315i | −0.898647 | − | 0.754055i | 0.0712781 | − | 0.997456i | \(-0.477292\pi\) |
−0.969926 | + | 0.243402i | \(0.921737\pi\) | |||||||
\(728\) | −34.0685 | −1.26266 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.79423 | 0.362501 | ||||||||
\(731\) | 22.0339 | + | 18.4887i | 0.814955 | + | 0.683828i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.30466 | − | 18.7417i | −0.122060 | − | 0.692239i | −0.983010 | − | 0.183550i | \(-0.941241\pi\) |
0.860950 | − | 0.508690i | \(-0.169870\pi\) | |||||||
\(734\) | −11.2084 | − | 4.07952i | −0.413709 | − | 0.150578i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.669471 | − | 3.79676i | 0.0246770 | − | 0.139950i | ||||
\(737\) | −6.32516 | + | 10.9555i | −0.232990 | + | 0.403551i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.30036 | − | 14.3767i | −0.305334 | − | 0.528854i | 0.672002 | − | 0.740550i | \(-0.265435\pi\) |
−0.977336 | + | 0.211696i | \(0.932101\pi\) | |||||||
\(740\) | 3.80105 | − | 1.38347i | 0.139729 | − | 0.0508573i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.8239 | + | 17.4733i | −0.764470 | + | 0.641466i | ||||
\(743\) | 25.5120 | − | 21.4071i | 0.935944 | − | 0.785350i | −0.0409308 | − | 0.999162i | \(-0.513032\pi\) |
0.976875 | + | 0.213812i | \(0.0685879\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.175433 | + | 0.0638523i | −0.00642736 | + | 0.00233937i | ||||
\(746\) | 3.08078 | + | 5.33606i | 0.112795 | + | 0.195367i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.70328 | − | 6.41426i | 0.135405 | − | 0.234529i | ||||
\(749\) | −8.30947 | + | 47.1253i | −0.303621 | + | 1.72192i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.1062 | − | 9.50187i | −0.952627 | − | 0.346728i | −0.181487 | − | 0.983393i | \(-0.558091\pi\) |
−0.771140 | + | 0.636665i | \(0.780313\pi\) | |||||||
\(752\) | −1.32030 | − | 7.48777i | −0.0481462 | − | 0.273051i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.88253 | + | 1.57963i | 0.0685577 | + | 0.0575267i | ||||
\(755\) | −35.3686 | −1.28720 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.12036 | −0.113411 | −0.0567057 | − | 0.998391i | \(-0.518060\pi\) | ||||
−0.0567057 | + | 0.998391i | \(0.518060\pi\) | |||||||
\(758\) | −19.6475 | − | 16.4862i | −0.713629 | − | 0.598806i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.230020 | + | 1.30451i | 0.00834369 | + | 0.0473194i | ||||
\(761\) | −41.3081 | − | 15.0349i | −1.49742 | − | 0.545016i | −0.542028 | − | 0.840360i | \(-0.682343\pi\) |
−0.955391 | + | 0.295345i | \(0.904566\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.69684 | − | 15.2946i | 0.0976323 | − | 0.553700i | ||||
\(764\) | 11.9783 | − | 20.7470i | 0.433360 | − | 0.750602i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.01168 | + | 3.48433i | 0.0726849 | + | 0.125894i | ||||
\(767\) | 12.8506 | − | 4.67723i | 0.464008 | − | 0.168885i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.84421 | − | 2.38658i | 0.102565 | − | 0.0860622i | −0.590063 | − | 0.807357i | \(-0.700897\pi\) |
0.692628 | + | 0.721295i | \(0.256453\pi\) | |||||||
\(770\) | −4.34904 | + | 3.64927i | −0.156728 | + | 0.131511i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.3212 | + | 5.21250i | −0.515432 | + | 0.187602i | ||||
\(773\) | −4.48452 | − | 7.76741i | −0.161297 | − | 0.279374i | 0.774037 | − | 0.633140i | \(-0.218234\pi\) |
−0.935334 | + | 0.353766i | \(0.884901\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.800417 | + | 1.38636i | −0.0287518 | + | 0.0497996i | ||||
\(776\) | 2.90349 | − | 16.4665i | 0.104229 | − | 0.591113i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.7415 | − | 3.90957i | −0.385100 | − | 0.140165i | ||||
\(779\) | 0.352736 | + | 2.00046i | 0.0126381 | + | 0.0716741i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0859667 | − | 0.0721346i | −0.00307613 | − | 0.00258118i | ||||
\(782\) | 5.90098 | 0.211018 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.36527 | 0.0487597 | ||||||||
\(785\) | −27.7498 | − | 23.2849i | −0.990433 | − | 0.831072i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.61472 | + | 43.1852i | 0.271435 | + | 1.53939i | 0.750061 | + | 0.661368i | \(0.230024\pi\) |
−0.478626 | + | 0.878019i | \(0.658865\pi\) | |||||||
\(788\) | −2.09728 | − | 0.763347i | −0.0747125 | − | 0.0271931i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.52681 | + | 8.65895i | −0.0543213 | + | 0.308072i | ||||
\(791\) | −8.50374 | + | 14.7289i | −0.302358 | + | 0.523699i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.55782 | + | 11.3585i | 0.232875 | + | 0.403351i | ||||
\(794\) | −10.4119 | + | 3.78962i | −0.369505 | + | 0.134489i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.6167 | + | 10.5866i | −0.447186 | + | 0.375234i | ||||
\(797\) | −9.20480 | + | 7.72375i | −0.326051 | + | 0.273589i | −0.791088 | − | 0.611702i | \(-0.790485\pi\) |
0.465038 | + | 0.885291i | \(0.346041\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.1200 | + | 12.0547i | −1.17170 | + | 0.426464i | ||||
\(800\) | −4.46940 | − | 7.74124i | −0.158017 | − | 0.273694i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.57299 | + | 13.1168i | −0.267412 | + | 0.463171i | ||||
\(803\) | −1.15890 | + | 6.57245i | −0.0408967 | + | 0.231937i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.39697 | + | 1.23640i | 0.119727 | + | 0.0435772i | ||||
\(806\) | −0.682935 | − | 3.87312i | −0.0240554 | − | 0.136425i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.6770 | − | 9.79814i | −0.410794 | − | 0.344697i | ||||
\(809\) | 8.02937 | 0.282298 | 0.141149 | − | 0.989988i | \(-0.454920\pi\) | ||||
0.141149 | + | 0.989988i | \(0.454920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.8345 | −0.450681 | −0.225341 | − | 0.974280i | \(-0.572349\pi\) | ||||
−0.225341 | + | 0.974280i | \(0.572349\pi\) | |||||||
\(812\) | −0.857549 | − | 0.719569i | −0.0300941 | − | 0.0252519i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.598872 | − | 3.39637i | −0.0209904 | − | 0.119043i | ||||
\(815\) | 33.0308 | + | 12.0222i | 1.15702 | + | 0.421121i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.187216 | − | 1.06176i | 0.00654986 | − | 0.0371461i | ||||
\(818\) | 9.32142 | − | 16.1452i | 0.325916 | − | 0.564503i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.32233 | + | 10.9506i | 0.220785 | + | 0.382411i | ||||
\(821\) | −27.8763 | + | 10.1462i | −0.972891 | + | 0.354103i | −0.779072 | − | 0.626934i | \(-0.784310\pi\) |
−0.193819 | + | 0.981037i | \(0.562087\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.9504 | − | 31.8442i | 1.32287 | − | 1.11002i | 0.337179 | − | 0.941440i | \(-0.390527\pi\) |
0.985688 | − | 0.168577i | \(-0.0539173\pi\) | |||||||
\(824\) | 27.1057 | − | 22.7444i | 0.944271 | − | 0.792338i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.32454 | − | 2.66592i | 0.254854 | − | 0.0927591i | ||||
\(827\) | 20.4215 | + | 35.3711i | 0.710126 | + | 1.22997i | 0.964809 | + | 0.262950i | \(0.0846955\pi\) |
−0.254683 | + | 0.967025i | \(0.581971\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.72638 | − | 8.18633i | 0.164154 | − | 0.284323i | −0.772201 | − | 0.635379i | \(-0.780844\pi\) |
0.936355 | + | 0.351056i | \(0.114177\pi\) | |||||||
\(830\) | 2.56997 | − | 14.5750i | 0.0892049 | − | 0.505906i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 32.8955 | + | 11.9730i | 1.14045 | + | 0.415088i | ||||
\(833\) | −1.09899 | − | 6.23266i | −0.0380776 | − | 0.215949i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.5633 | + | 22.2892i | 0.919259 | + | 0.771350i | ||||
\(836\) | −0.277620 | −0.00960170 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.62995 | 0.332661 | ||||||||
\(839\) | 9.41230 | + | 7.89786i | 0.324949 | + | 0.272664i | 0.790638 | − | 0.612284i | \(-0.209749\pi\) |
−0.465689 | + | 0.884948i | \(0.654194\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.99021 | − | 28.3009i | −0.172076 | − | 0.975892i | ||||
\(842\) | 23.9709 | + | 8.72469i | 0.826092 | + | 0.300673i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.569434 | − | 3.22942i | 0.0196007 | − | 0.111161i | ||||
\(845\) | −6.71575 | + | 11.6320i | −0.231029 | + | 0.400154i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.5916 | + | 20.0772i | 0.398292 | + | 0.689862i | ||||
\(848\) | 14.1270 | − | 5.14182i | 0.485125 | − | 0.176571i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.4808 | − | 8.79446i | 0.359489 | − | 0.301647i | ||||
\(851\) | −1.68223 | + | 1.41156i | −0.0576660 | + | 0.0483875i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.0044 | − | 10.5567i | 0.993092 | − | 0.361456i | 0.206175 | − | 0.978515i | \(-0.433898\pi\) |
0.786917 | + | 0.617059i | \(0.211676\pi\) | |||||||
\(854\) | 3.73781 | + | 6.47408i | 0.127905 | + | 0.221538i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.6280 | − | 51.3172i | 1.01266 | − | 1.75399i | ||||
\(857\) | −1.93549 | + | 10.9767i | −0.0661150 | + | 0.374957i | 0.933740 | + | 0.357951i | \(0.116525\pi\) |
−0.999855 | + | 0.0170059i | \(0.994587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.89848 | − | 1.41893i | −0.133014 | − | 0.0484133i | 0.274655 | − | 0.961543i | \(-0.411436\pi\) |
−0.407670 | + | 0.913129i | \(0.633659\pi\) | |||||||
\(860\) | −1.16539 | − | 6.60925i | −0.0397394 | − | 0.225374i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.8528 | − | 20.0149i | −0.812429 | − | 0.681709i | ||||
\(863\) | 47.2534 | 1.60852 | 0.804262 | − | 0.594275i | \(-0.202561\pi\) | ||||
0.804262 | + | 0.594275i | \(0.202561\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.0392 | −1.12337 | ||||||||
\(866\) | −0.540933 | − | 0.453897i | −0.0183817 | − | 0.0154240i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.311097 | + | 1.76432i | 0.0105593 | + | 0.0598849i | ||||
\(869\) | −5.62996 | − | 2.04914i | −0.190983 | − | 0.0695122i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.96745 | + | 45.1857i | −0.269967 | + | 1.53106i | ||||
\(872\) | −9.61579 | + | 16.6550i | −0.325632 | + | 0.564011i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.110593 | − | 0.191553i | −0.00374087 | − | 0.00647938i | ||||
\(875\) | 28.0481 | − | 10.2087i | 0.948198 | − | 0.345116i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.9268 | − | 22.5943i | 0.909253 | − | 0.762954i | −0.0627236 | − | 0.998031i | \(-0.519979\pi\) |
0.971977 | + | 0.235077i | \(0.0755342\pi\) | |||||||
\(878\) | 5.12773 | − | 4.30267i | 0.173052 | − | 0.145208i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.95041 | − | 1.07386i | 0.0994582 | − | 0.0361998i | ||||
\(881\) | −9.67981 | − | 16.7659i | −0.326121 | − | 0.564858i | 0.655618 | − | 0.755093i | \(-0.272408\pi\) |
−0.981739 | + | 0.190235i | \(0.939075\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.89302 | − | 11.9391i | 0.231969 | − | 0.401781i | −0.726419 | − | 0.687252i | \(-0.758817\pi\) |
0.958387 | + | 0.285471i | \(0.0921500\pi\) | |||||||
\(884\) | 4.66481 | − | 26.4554i | 0.156895 | − | 0.889793i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.2118 | − | 5.53663i | −0.511049 | − | 0.186007i | ||||
\(887\) | 5.17775 | + | 29.3645i | 0.173852 | + | 0.985962i | 0.939461 | + | 0.342656i | \(0.111327\pi\) |
−0.765609 | + | 0.643306i | \(0.777562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.6505 | + | 19.0060i | 0.759673 | + | 0.637442i | ||||
\(890\) | 12.3391 | 0.413609 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.8705 | 0.631832 | ||||||||
\(893\) | 1.01203 | + | 0.849193i | 0.0338662 | + | 0.0284172i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.30851 | − | 18.7635i | −0.110591 | − | 0.627194i | ||||
\(896\) | −2.41281 | − | 0.878191i | −0.0806063 | − | 0.0293383i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.86590 | + | 33.2672i | −0.195748 | + | 1.11014i | ||||
\(899\) | 0.210078 | − | 0.363866i | 0.00700649 | − | 0.0121356i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.8448 | − | 60.3530i | −1.16085 | − | 2.01065i | ||||
\(902\) | 10.1307 | − | 3.68727i | 0.337315 | − | 0.122773i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.1333 | − | 13.5374i | 0.536586 | − | 0.450249i | ||||
\(905\) | −24.0026 | + | 20.1406i | −0.797873 | + | 0.669495i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.85576 | − | 2.13132i | 0.194437 | − | 0.0707694i | −0.242966 | − | 0.970035i | \(-0.578120\pi\) |
0.437403 | + | 0.899265i | \(0.355898\pi\) | |||||||
\(908\) | 6.36984 | + | 11.0329i | 0.211391 | + | 0.366139i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.2957 | + | 17.8327i | −0.341300 | + | 0.591148i | ||||
\(911\) | 5.49414 | − | 31.1588i | 0.182029 | − | 1.03234i | −0.747685 | − | 0.664054i | \(-0.768835\pi\) |
0.929714 | − | 0.368283i | \(-0.120054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.47652 | + | 3.44917i | 0.313627 | + | 0.114151i | ||||
\(914\) | −3.50931 | − | 19.9023i | −0.116078 | − | 0.658310i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.4917 | − | 9.64268i | −0.379696 | − | 0.318603i | ||||
\(917\) | 34.6380 | 1.14385 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.0031 | 1.18763 | 0.593816 | − | 0.804601i | \(-0.297621\pi\) | ||||
0.593816 | + | 0.804601i | \(0.297621\pi\) | |||||||
\(920\) | −3.42917 | − | 2.87742i | −0.113057 | − | 0.0948657i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.955739 | − | 5.42027i | −0.0314756 | − | 0.178507i | ||||
\(923\) | −0.382481 | − | 0.139212i | −0.0125895 | − | 0.00458220i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.884135 | + | 5.01418i | −0.0290702 | + | 0.164865i | ||||
\(926\) | 0.894800 | − | 1.54984i | 0.0294049 | − | 0.0509309i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.17304 | + | 2.03177i | 0.0385070 | + | 0.0666961i | ||||
\(929\) | 23.9130 | − | 8.70363i | 0.784561 | − | 0.285557i | 0.0814880 | − | 0.996674i | \(-0.474033\pi\) |
0.703073 | + | 0.711117i | \(0.251811\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.181723 | + | 0.152484i | −0.00595575 | + | 0.00499746i | ||||
\(932\) | 3.81072 | − | 3.19758i | 0.124824 | − | 0.104740i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19.5005 | + | 7.09760i | −0.638075 | + | 0.232240i | ||||
\(935\) | −7.27728 | − | 12.6046i | −0.237993 | − | 0.412215i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.1524 | + | 24.5127i | −0.462338 | + | 0.800794i | −0.999077 | − | 0.0429549i | \(-0.986323\pi\) |
0.536739 | + | 0.843749i | \(0.319656\pi\) | |||||||
\(938\) | −4.54127 | + | 25.7548i | −0.148278 | + | 0.840924i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.72774 | + | 2.81267i | 0.252051 | + | 0.0917391i | ||||
\(941\) | −1.44031 | − | 8.16843i | −0.0469529 | − | 0.266283i | 0.952290 | − | 0.305195i | \(-0.0987218\pi\) |
−0.999243 | + | 0.0389123i | \(0.987611\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.25865 | − | 4.41253i | −0.171245 | − | 0.143692i | ||||
\(944\) | −4.31074 | −0.140303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.72199 | −0.186038 | ||||||||
\(947\) | 34.0511 | + | 28.5723i | 1.10651 | + | 0.928475i | 0.997846 | − | 0.0656031i | \(-0.0208971\pi\) |
0.108668 | + | 0.994078i | \(0.465342\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.20333 | + | 23.8383i | 0.136446 | + | 0.773823i | ||||
\(950\) | −0.481906 | − | 0.175399i | −0.0156351 | − | 0.00569071i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.64452 | − | 49.0255i | 0.280170 | − | 1.58893i | ||||
\(953\) | −4.83574 | + | 8.37576i | −0.156645 | + | 0.271317i | −0.933657 | − | 0.358169i | \(-0.883401\pi\) |
0.777012 | + | 0.629486i | \(0.216735\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.5385 | − | 40.7699i | −0.761688 | − | 1.31928i | ||||
\(956\) | 4.40308 | − | 1.60259i | 0.142406 | − | 0.0518315i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.6268 | + | 19.8252i | −0.763348 | + | 0.640525i | ||||
\(959\) | −4.25409 | + | 3.56961i | −0.137372 | + | 0.115269i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.4986 | − | 10.3726i | 0.919310 | − | 0.334602i | ||||
\(962\) | −6.25433 | − | 10.8328i | −0.201648 | − | 0.349264i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.95448 | + | 6.84936i | −0.127365 | + | 0.220603i | ||||
\(965\) | −5.20053 | + | 29.4937i | −0.167411 | + | 0.949434i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.1180 | + | 11.3260i | 1.00069 | + | 0.364220i | 0.789850 | − | 0.613301i | \(-0.210159\pi\) |
0.210838 | + | 0.977521i | \(0.432381\pi\) | |||||||
\(968\) | −4.98509 | − | 28.2719i | −0.160227 | − | 0.908692i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.74172 | − | 6.49608i | −0.248572 | − | 0.208576i | ||||
\(971\) | 27.4309 | 0.880298 | 0.440149 | − | 0.897925i | \(-0.354926\pi\) | ||||
0.440149 | + | 0.897925i | \(0.354926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.6127 | −0.628755 | ||||||||
\(974\) | 16.5616 | + | 13.8968i | 0.530667 | + | 0.445283i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.717917 | − | 4.07151i | −0.0229800 | − | 0.130326i | ||||
\(977\) | 34.1837 | + | 12.4419i | 1.09363 | + | 0.398050i | 0.824966 | − | 0.565182i | \(-0.191194\pi\) |
0.268669 | + | 0.963233i | \(0.413416\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.46003 | + | 8.28022i | −0.0466626 | + | 0.264637i | ||||
\(980\) | −0.738337 | + | 1.27884i | −0.0235853 | + | 0.0408510i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.23957 | − | 16.0034i | −0.294847 | − | 0.510689i | ||||
\(983\) | 39.5960 | − | 14.4118i | 1.26292 | − | 0.459664i | 0.378170 | − | 0.925736i | \(-0.376553\pi\) |
0.884747 | + | 0.466072i | \(0.154331\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.35975 | + | 2.81917i | −0.107051 | + | 0.0898262i | ||||
\(986\) | −2.75081 | + | 2.30820i | −0.0876035 | + | 0.0735081i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.946203 | + | 0.344390i | −0.0301027 | + | 0.0109565i | ||||
\(989\) | 1.82173 | + | 3.15533i | 0.0579276 | + | 0.100334i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7705 | + | 22.1191i | −0.405667 | + | 0.702635i | −0.994399 | − | 0.105693i | \(-0.966294\pi\) |
0.588732 | + | 0.808328i | \(0.299627\pi\) | |||||||
\(992\) | 0.651981 | − | 3.69757i | 0.0207004 | − | 0.117398i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.218005 | − | 0.0793475i | −0.00691471 | − | 0.00251675i | ||||
\(995\) | 5.62010 | + | 31.8732i | 0.178169 | + | 1.01045i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.0272 | + | 15.1266i | 0.570928 | + | 0.479066i | 0.881954 | − | 0.471336i | \(-0.156228\pi\) |
−0.311026 | + | 0.950402i | \(0.600673\pi\) | |||||||
\(998\) | 20.1439 | 0.637644 | ||||||||
\(999\) | 0 | 0 |
(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 | 243.2.e.b.136.1 | 12 | ||
3.2 | odd | 2 | 243.2.e.c.136.2 | 12 | |||
9.2 | odd | 6 | 27.2.e.a.25.2 | yes | 12 | ||
9.4 | even | 3 | 243.2.e.a.55.2 | 12 | |||
9.5 | odd | 6 | 243.2.e.d.55.1 | 12 | |||
9.7 | even | 3 | 81.2.e.a.73.1 | 12 | |||
27.2 | odd | 18 | 729.2.c.e.244.2 | 12 | |||
27.4 | even | 9 | 81.2.e.a.10.1 | 12 | |||
27.5 | odd | 18 | 243.2.e.c.109.2 | 12 | |||
27.7 | even | 9 | 729.2.a.d.1.2 | 6 | |||
27.11 | odd | 18 | 729.2.c.e.487.2 | 12 | |||
27.13 | even | 9 | 243.2.e.a.190.2 | 12 | |||
27.14 | odd | 18 | 243.2.e.d.190.1 | 12 | |||
27.16 | even | 9 | 729.2.c.b.487.5 | 12 | |||
27.20 | odd | 18 | 729.2.a.a.1.5 | 6 | |||
27.22 | even | 9 | inner | 243.2.e.b.109.1 | 12 | ||
27.23 | odd | 18 | 27.2.e.a.13.2 | ✓ | 12 | ||
27.25 | even | 9 | 729.2.c.b.244.5 | 12 | |||
36.11 | even | 6 | 432.2.u.c.241.2 | 12 | |||
45.2 | even | 12 | 675.2.u.b.349.3 | 24 | |||
45.29 | odd | 6 | 675.2.l.c.376.1 | 12 | |||
45.38 | even | 12 | 675.2.u.b.349.2 | 24 | |||
108.23 | even | 18 | 432.2.u.c.337.2 | 12 | |||
135.23 | even | 36 | 675.2.u.b.499.3 | 24 | |||
135.77 | even | 36 | 675.2.u.b.499.2 | 24 | |||
135.104 | odd | 18 | 675.2.l.c.526.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.13.2 | ✓ | 12 | 27.23 | odd | 18 | ||
27.2.e.a.25.2 | yes | 12 | 9.2 | odd | 6 | ||
81.2.e.a.10.1 | 12 | 27.4 | even | 9 | |||
81.2.e.a.73.1 | 12 | 9.7 | even | 3 | |||
243.2.e.a.55.2 | 12 | 9.4 | even | 3 | |||
243.2.e.a.190.2 | 12 | 27.13 | even | 9 | |||
243.2.e.b.109.1 | 12 | 27.22 | even | 9 | inner | ||
243.2.e.b.136.1 | 12 | 1.1 | even | 1 | trivial | ||
243.2.e.c.109.2 | 12 | 27.5 | odd | 18 | |||
243.2.e.c.136.2 | 12 | 3.2 | odd | 2 | |||
243.2.e.d.55.1 | 12 | 9.5 | odd | 6 | |||
243.2.e.d.190.1 | 12 | 27.14 | odd | 18 | |||
432.2.u.c.241.2 | 12 | 36.11 | even | 6 | |||
432.2.u.c.337.2 | 12 | 108.23 | even | 18 | |||
675.2.l.c.376.1 | 12 | 45.29 | odd | 6 | |||
675.2.l.c.526.1 | 12 | 135.104 | odd | 18 | |||
675.2.u.b.349.2 | 24 | 45.38 | even | 12 | |||
675.2.u.b.349.3 | 24 | 45.2 | even | 12 | |||
675.2.u.b.499.2 | 24 | 135.77 | even | 36 | |||
675.2.u.b.499.3 | 24 | 135.23 | even | 36 | |||
729.2.a.a.1.5 | 6 | 27.20 | odd | 18 | |||
729.2.a.d.1.2 | 6 | 27.7 | even | 9 | |||
729.2.c.b.244.5 | 12 | 27.25 | even | 9 | |||
729.2.c.b.487.5 | 12 | 27.16 | even | 9 | |||
729.2.c.e.244.2 | 12 | 27.2 | odd | 18 | |||
729.2.c.e.487.2 | 12 | 27.11 | odd | 18 |