Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,2,Mod(22,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("115.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.918279623245\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 6 x^{18} + 3 x^{16} + 80 x^{14} - 600 x^{12} + 3500 x^{10} - 15000 x^{8} + 50000 x^{6} + \cdots + 9765625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 22.3 | ||
Root | \(0.0985483 - 2.23390i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 115.22 |
Dual form | 115.2.e.a.68.3 |
$q$-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 \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.819998 | − | 0.819998i | −0.579826 | − | 0.579826i | 0.355029 | − | 0.934855i | \(-0.384471\pi\) |
−0.934855 | + | 0.355029i | \(0.884471\pi\) | |||||||
\(3\) | 1.37823 | − | 1.37823i | 0.795721 | − | 0.795721i | −0.186696 | − | 0.982418i | \(-0.559778\pi\) |
0.982418 | + | 0.186696i | \(0.0597781\pi\) | |||||||
\(4\) | − | 0.655207i | − | 0.327603i | ||||||
\(5\) | −2.23390 | + | 0.0985483i | −0.999028 | + | 0.0440721i | ||||
\(6\) | −2.26029 | −0.922760 | ||||||||
\(7\) | 1.78496 | − | 1.78496i | 0.674651 | − | 0.674651i | −0.284134 | − | 0.958785i | \(-0.591706\pi\) |
0.958785 | + | 0.284134i | \(0.0917059\pi\) | |||||||
\(8\) | −2.17726 | + | 2.17726i | −0.769779 | + | 0.769779i | ||||
\(9\) | − | 0.799034i | − | 0.266345i | ||||||
\(10\) | 1.91260 | + | 1.75098i | 0.604817 | + | 0.553709i | ||||
\(11\) | 1.86370i | 0.561927i | 0.959718 | + | 0.280964i | \(0.0906541\pi\) | ||||
−0.959718 | + | 0.280964i | \(0.909346\pi\) | |||||||
\(12\) | −0.903025 | − | 0.903025i | −0.260681 | − | 0.260681i | ||||
\(13\) | 1.52206 | − | 1.52206i | 0.422143 | − | 0.422143i | −0.463798 | − | 0.885941i | \(-0.653514\pi\) |
0.885941 | + | 0.463798i | \(0.153514\pi\) | |||||||
\(14\) | −2.92733 | −0.782361 | ||||||||
\(15\) | −2.94300 | + | 3.21464i | −0.759879 | + | 0.830017i | ||||
\(16\) | 2.26029 | 0.565073 | ||||||||
\(17\) | 5.17689 | − | 5.17689i | 1.25558 | − | 1.25558i | 0.302400 | − | 0.953181i | \(-0.402212\pi\) |
0.953181 | − | 0.302400i | \(-0.0977879\pi\) | |||||||
\(18\) | −0.655207 | + | 0.655207i | −0.154434 | + | 0.154434i | ||||
\(19\) | −3.69906 | −0.848622 | −0.424311 | − | 0.905517i | \(-0.639484\pi\) | ||||
−0.424311 | + | 0.905517i | \(0.639484\pi\) | |||||||
\(20\) | 0.0645695 | + | 1.46366i | 0.0144382 | + | 0.327285i | ||||
\(21\) | − | 4.92017i | − | 1.07367i | ||||||
\(22\) | 1.52823 | − | 1.52823i | 0.325820 | − | 0.325820i | ||||
\(23\) | 2.59017 | + | 4.03621i | 0.540087 | + | 0.841609i | ||||
\(24\) | 6.00154i | 1.22506i | ||||||||
\(25\) | 4.98058 | − | 0.440293i | 0.996115 | − | 0.0880586i | ||||
\(26\) | −2.49617 | −0.489539 | ||||||||
\(27\) | 3.03344 | + | 3.03344i | 0.583785 | + | 0.583785i | ||||
\(28\) | −1.16952 | − | 1.16952i | −0.221018 | − | 0.221018i | ||||
\(29\) | 4.99452i | 0.927460i | 0.885977 | + | 0.463730i | \(0.153489\pi\) | ||||
−0.885977 | + | 0.463730i | \(0.846511\pi\) | |||||||
\(30\) | 5.04925 | − | 0.222748i | 0.921863 | − | 0.0406680i | ||||
\(31\) | 0.833946 | 0.149781 | 0.0748905 | − | 0.997192i | \(-0.476139\pi\) | ||||
0.0748905 | + | 0.997192i | \(0.476139\pi\) | |||||||
\(32\) | 2.50109 | + | 2.50109i | 0.442135 | + | 0.442135i | ||||
\(33\) | 2.56861 | + | 2.56861i | 0.447138 | + | 0.447138i | ||||
\(34\) | −8.49009 | −1.45604 | ||||||||
\(35\) | −3.81151 | + | 4.16332i | −0.644262 | + | 0.703729i | ||||
\(36\) | −0.523533 | −0.0872554 | ||||||||
\(37\) | −3.00607 | + | 3.00607i | −0.494195 | + | 0.494195i | −0.909625 | − | 0.415430i | \(-0.863631\pi\) |
0.415430 | + | 0.909625i | \(0.363631\pi\) | |||||||
\(38\) | 3.03322 | + | 3.03322i | 0.492053 | + | 0.492053i | ||||
\(39\) | − | 4.19549i | − | 0.671816i | ||||||
\(40\) | 4.64921 | − | 5.07835i | 0.735105 | − | 0.802957i | ||||
\(41\) | 0.310413 | 0.0484784 | 0.0242392 | − | 0.999706i | \(-0.492284\pi\) | ||||
0.0242392 | + | 0.999706i | \(0.492284\pi\) | |||||||
\(42\) | −4.03453 | + | 4.03453i | −0.622541 | + | 0.622541i | ||||
\(43\) | 2.17082 | + | 2.17082i | 0.331048 | + | 0.331048i | 0.852984 | − | 0.521937i | \(-0.174790\pi\) |
−0.521937 | + | 0.852984i | \(0.674790\pi\) | |||||||
\(44\) | 1.22111 | 0.184089 | ||||||||
\(45\) | 0.0787435 | + | 1.78496i | 0.0117384 | + | 0.266086i | ||||
\(46\) | 1.18576 | − | 5.43362i | 0.174830 | − | 0.801144i | ||||
\(47\) | −8.19401 | − | 8.19401i | −1.19522 | − | 1.19522i | −0.975581 | − | 0.219639i | \(-0.929512\pi\) |
−0.219639 | − | 0.975581i | \(-0.570488\pi\) | |||||||
\(48\) | 3.11520 | − | 3.11520i | 0.449640 | − | 0.449640i | ||||
\(49\) | 0.627842i | 0.0896917i | ||||||||
\(50\) | −4.44510 | − | 3.72302i | −0.628632 | − | 0.526515i | ||||
\(51\) | − | 14.2699i | − | 1.99819i | ||||||
\(52\) | −0.997262 | − | 0.997262i | −0.138295 | − | 0.138295i | ||||
\(53\) | −6.21727 | − | 6.21727i | −0.854008 | − | 0.854008i | 0.136616 | − | 0.990624i | \(-0.456377\pi\) |
−0.990624 | + | 0.136616i | \(0.956377\pi\) | |||||||
\(54\) | − | 4.97482i | − | 0.676988i | ||||||
\(55\) | −0.183665 | − | 4.16332i | −0.0247653 | − | 0.561381i | ||||
\(56\) | 7.77265i | 1.03866i | ||||||||
\(57\) | −5.09815 | + | 5.09815i | −0.675267 | + | 0.675267i | ||||
\(58\) | 4.09550 | − | 4.09550i | 0.537765 | − | 0.537765i | ||||
\(59\) | − | 2.19330i | − | 0.285544i | −0.989756 | − | 0.142772i | \(-0.954398\pi\) | ||
0.989756 | − | 0.142772i | \(-0.0456015\pi\) | |||||||
\(60\) | 2.10626 | + | 1.92827i | 0.271916 | + | 0.248939i | ||||
\(61\) | 12.5637i | 1.60861i | 0.594213 | + | 0.804307i | \(0.297463\pi\) | ||||
−0.594213 | + | 0.804307i | \(0.702537\pi\) | |||||||
\(62\) | −0.683834 | − | 0.683834i | −0.0868470 | − | 0.0868470i | ||||
\(63\) | −1.42624 | − | 1.42624i | −0.179690 | − | 0.179690i | ||||
\(64\) | − | 8.62237i | − | 1.07780i | ||||||
\(65\) | −3.25012 | + | 3.55011i | −0.403128 | + | 0.440337i | ||||
\(66\) | − | 4.21251i | − | 0.518524i | ||||||
\(67\) | 1.14237 | − | 1.14237i | 0.139562 | − | 0.139562i | −0.633874 | − | 0.773436i | \(-0.718536\pi\) |
0.773436 | + | 0.633874i | \(0.218536\pi\) | |||||||
\(68\) | −3.39193 | − | 3.39193i | −0.411333 | − | 0.411333i | ||||
\(69\) | 9.13268 | + | 1.99298i | 1.09945 | + | 0.239927i | ||||
\(70\) | 6.53934 | − | 0.288483i | 0.781601 | − | 0.0344803i | ||||
\(71\) | −13.5516 | −1.60827 | −0.804137 | − | 0.594444i | \(-0.797372\pi\) | ||||
−0.804137 | + | 0.594444i | \(0.797372\pi\) | |||||||
\(72\) | 1.73971 | + | 1.73971i | 0.205027 | + | 0.205027i | ||||
\(73\) | −6.62331 | + | 6.62331i | −0.775200 | + | 0.775200i | −0.979010 | − | 0.203811i | \(-0.934667\pi\) |
0.203811 | + | 0.979010i | \(0.434667\pi\) | |||||||
\(74\) | 4.92994 | 0.573094 | ||||||||
\(75\) | 6.25755 | − | 7.47120i | 0.722560 | − | 0.862700i | ||||
\(76\) | 2.42365i | 0.278011i | ||||||||
\(77\) | 3.32663 | + | 3.32663i | 0.379105 | + | 0.379105i | ||||
\(78\) | −3.44029 | + | 3.44029i | −0.389537 | + | 0.389537i | ||||
\(79\) | −1.36002 | −0.153015 | −0.0765073 | − | 0.997069i | \(-0.524377\pi\) | ||||
−0.0765073 | + | 0.997069i | \(0.524377\pi\) | |||||||
\(80\) | −5.04925 | + | 0.222748i | −0.564524 | + | 0.0249040i | ||||
\(81\) | 10.7586 | 1.19541 | ||||||||
\(82\) | −0.254538 | − | 0.254538i | −0.0281090 | − | 0.0281090i | ||||
\(83\) | −0.256727 | − | 0.256727i | −0.0281794 | − | 0.0281794i | 0.692877 | − | 0.721056i | \(-0.256343\pi\) |
−0.721056 | + | 0.692877i | \(0.756343\pi\) | |||||||
\(84\) | −3.22373 | −0.351737 | ||||||||
\(85\) | −11.0545 | + | 12.0748i | −1.19903 | + | 1.30970i | ||||
\(86\) | − | 3.56014i | − | 0.383900i | ||||||
\(87\) | 6.88360 | + | 6.88360i | 0.738000 | + | 0.738000i | ||||
\(88\) | −4.05777 | − | 4.05777i | −0.432560 | − | 0.432560i | ||||
\(89\) | 10.8389 | 1.14892 | 0.574460 | − | 0.818533i | \(-0.305212\pi\) | ||||
0.574460 | + | 0.818533i | \(0.305212\pi\) | |||||||
\(90\) | 1.39909 | − | 1.52823i | 0.147477 | − | 0.161090i | ||||
\(91\) | − | 5.43362i | − | 0.569598i | ||||||
\(92\) | 2.64455 | − | 1.69710i | 0.275714 | − | 0.176934i | ||||
\(93\) | 1.14937 | − | 1.14937i | 0.119184 | − | 0.119184i | ||||
\(94\) | 13.4382i | 1.38604i | ||||||||
\(95\) | 8.26331 | − | 0.364536i | 0.847797 | − | 0.0374006i | ||||
\(96\) | 6.89416 | 0.703633 | ||||||||
\(97\) | 9.99507 | − | 9.99507i | 1.01485 | − | 1.01485i | 0.0149577 | − | 0.999888i | \(-0.495239\pi\) |
0.999888 | − | 0.0149577i | \(-0.00476137\pi\) | |||||||
\(98\) | 0.514829 | − | 0.514829i | 0.0520056 | − | 0.0520056i | ||||
\(99\) | 1.48916 | 0.149666 | ||||||||
\(100\) | −0.288483 | − | 3.26331i | −0.0288483 | − | 0.326331i | ||||
\(101\) | −7.07389 | −0.703878 | −0.351939 | − | 0.936023i | \(-0.614478\pi\) | ||||
−0.351939 | + | 0.936023i | \(0.614478\pi\) | |||||||
\(102\) | −11.7013 | + | 11.7013i | −1.15860 | + | 1.15860i | ||||
\(103\) | 2.90408 | + | 2.90408i | 0.286148 | + | 0.286148i | 0.835555 | − | 0.549407i | \(-0.185146\pi\) |
−0.549407 | + | 0.835555i | \(0.685146\pi\) | |||||||
\(104\) | 6.62784i | 0.649913i | ||||||||
\(105\) | 0.484874 | + | 10.9911i | 0.0473189 | + | 1.07263i | ||||
\(106\) | 10.1963i | 0.990352i | ||||||||
\(107\) | −11.4446 | + | 11.4446i | −1.10639 | + | 1.10639i | −0.112766 | + | 0.993622i | \(0.535971\pi\) |
−0.993622 | + | 0.112766i | \(0.964029\pi\) | |||||||
\(108\) | 1.98753 | − | 1.98753i | 0.191250 | − | 0.191250i | ||||
\(109\) | 0.846570 | 0.0810867 | 0.0405433 | − | 0.999178i | \(-0.487091\pi\) | ||||
0.0405433 | + | 0.999178i | \(0.487091\pi\) | |||||||
\(110\) | −3.26331 | + | 3.56452i | −0.311144 | + | 0.339863i | ||||
\(111\) | 8.28611i | 0.786483i | ||||||||
\(112\) | 4.03453 | − | 4.03453i | 0.381227 | − | 0.381227i | ||||
\(113\) | −5.48402 | − | 5.48402i | −0.515893 | − | 0.515893i | 0.400433 | − | 0.916326i | \(-0.368860\pi\) |
−0.916326 | + | 0.400433i | \(0.868860\pi\) | |||||||
\(114\) | 8.36095 | 0.783074 | ||||||||
\(115\) | −6.18393 | − | 8.76122i | −0.576654 | − | 0.816988i | ||||
\(116\) | 3.27244 | 0.303839 | ||||||||
\(117\) | −1.21618 | − | 1.21618i | −0.112436 | − | 0.112436i | ||||
\(118\) | −1.79850 | + | 1.79850i | −0.165566 | + | 0.165566i | ||||
\(119\) | − | 18.4811i | − | 1.69416i | ||||||
\(120\) | −0.591442 | − | 13.4068i | −0.0539910 | − | 1.22387i | ||||
\(121\) | 7.52661 | 0.684238 | ||||||||
\(122\) | 10.3022 | − | 10.3022i | 0.932717 | − | 0.932717i | ||||
\(123\) | 0.427821 | − | 0.427821i | 0.0385753 | − | 0.0385753i | ||||
\(124\) | − | 0.546407i | − | 0.0490688i | ||||||
\(125\) | −11.0827 | + | 1.47440i | −0.991266 | + | 0.131874i | ||||
\(126\) | 2.33903i | 0.208378i | ||||||||
\(127\) | −9.98331 | − | 9.98331i | −0.885876 | − | 0.885876i | 0.108248 | − | 0.994124i | \(-0.465476\pi\) |
−0.994124 | + | 0.108248i | \(0.965476\pi\) | |||||||
\(128\) | −2.06814 | + | 2.06814i | −0.182799 | + | 0.182799i | ||||
\(129\) | 5.98379 | 0.526843 | ||||||||
\(130\) | 5.57618 | − | 0.245993i | 0.489063 | − | 0.0215750i | ||||
\(131\) | 12.2649 | 1.07159 | 0.535794 | − | 0.844349i | \(-0.320012\pi\) | ||||
0.535794 | + | 0.844349i | \(0.320012\pi\) | |||||||
\(132\) | 1.68297 | − | 1.68297i | 0.146484 | − | 0.146484i | ||||
\(133\) | −6.60267 | + | 6.60267i | −0.572524 | + | 0.572524i | ||||
\(134\) | −1.87348 | −0.161844 | ||||||||
\(135\) | −7.07532 | − | 6.47744i | −0.608947 | − | 0.557489i | ||||
\(136\) | 22.5429i | 1.93304i | ||||||||
\(137\) | −8.61922 | + | 8.61922i | −0.736390 | + | 0.736390i | −0.971877 | − | 0.235487i | \(-0.924331\pi\) |
0.235487 | + | 0.971877i | \(0.424331\pi\) | |||||||
\(138\) | −5.85453 | − | 9.12302i | −0.498371 | − | 0.776603i | ||||
\(139\) | 12.3554i | 1.04797i | 0.851727 | + | 0.523987i | \(0.175556\pi\) | ||||
−0.851727 | + | 0.523987i | \(0.824444\pi\) | |||||||
\(140\) | 2.72783 | + | 2.49732i | 0.230544 | + | 0.211062i | ||||
\(141\) | −22.5865 | −1.90212 | ||||||||
\(142\) | 11.1123 | + | 11.1123i | 0.932519 | + | 0.932519i | ||||
\(143\) | 2.83666 | + | 2.83666i | 0.237214 | + | 0.237214i | ||||
\(144\) | − | 1.80605i | − | 0.150504i | ||||||
\(145\) | −0.492202 | − | 11.1572i | −0.0408751 | − | 0.926559i | ||||
\(146\) | 10.8622 | 0.898962 | ||||||||
\(147\) | 0.865311 | + | 0.865311i | 0.0713696 | + | 0.0713696i | ||||
\(148\) | 1.96960 | + | 1.96960i | 0.161900 | + | 0.161900i | ||||
\(149\) | 22.1174 | 1.81193 | 0.905964 | − | 0.423355i | \(-0.139148\pi\) | ||||
0.905964 | + | 0.423355i | \(0.139148\pi\) | |||||||
\(150\) | −11.2576 | + | 0.995191i | −0.919175 | + | 0.0812570i | ||||
\(151\) | −11.5971 | −0.943757 | −0.471879 | − | 0.881664i | \(-0.656424\pi\) | ||||
−0.471879 | + | 0.881664i | \(0.656424\pi\) | |||||||
\(152\) | 8.05382 | − | 8.05382i | 0.653251 | − | 0.653251i | ||||
\(153\) | −4.13652 | − | 4.13652i | −0.334418 | − | 0.334418i | ||||
\(154\) | − | 5.45566i | − | 0.439630i | ||||||
\(155\) | −1.86295 | + | 0.0821839i | −0.149636 | + | 0.00660117i | ||||
\(156\) | −2.74891 | −0.220089 | ||||||||
\(157\) | −9.45172 | + | 9.45172i | −0.754329 | + | 0.754329i | −0.975284 | − | 0.220955i | \(-0.929083\pi\) |
0.220955 | + | 0.975284i | \(0.429083\pi\) | |||||||
\(158\) | 1.11522 | + | 1.11522i | 0.0887219 | + | 0.0887219i | ||||
\(159\) | −17.1377 | −1.35910 | ||||||||
\(160\) | −5.83366 | − | 5.34070i | −0.461191 | − | 0.422220i | ||||
\(161\) | 11.8278 | + | 2.58113i | 0.932163 | + | 0.203422i | ||||
\(162\) | −8.82207 | − | 8.82207i | −0.693127 | − | 0.693127i | ||||
\(163\) | 10.2045 | − | 10.2045i | 0.799279 | − | 0.799279i | −0.183703 | − | 0.982982i | \(-0.558808\pi\) |
0.982982 | + | 0.183703i | \(0.0588084\pi\) | |||||||
\(164\) | − | 0.203385i | − | 0.0158817i | ||||||
\(165\) | −5.99114 | − | 5.48487i | −0.466410 | − | 0.426997i | ||||
\(166\) | 0.421031i | 0.0326783i | ||||||||
\(167\) | −2.98633 | − | 2.98633i | −0.231089 | − | 0.231089i | 0.582058 | − | 0.813147i | \(-0.302248\pi\) |
−0.813147 | + | 0.582058i | \(0.802248\pi\) | |||||||
\(168\) | 10.7125 | + | 10.7125i | 0.826488 | + | 0.826488i | ||||
\(169\) | 8.36668i | 0.643591i | ||||||||
\(170\) | 18.9660 | − | 0.836684i | 1.45462 | − | 0.0641707i | ||||
\(171\) | 2.95567i | 0.226026i | ||||||||
\(172\) | 1.42234 | − | 1.42234i | 0.108452 | − | 0.108452i | ||||
\(173\) | 7.72208 | − | 7.72208i | 0.587099 | − | 0.587099i | −0.349746 | − | 0.936845i | \(-0.613732\pi\) |
0.936845 | + | 0.349746i | \(0.113732\pi\) | |||||||
\(174\) | − | 11.2891i | − | 0.855823i | ||||||
\(175\) | 8.10422 | − | 9.67603i | 0.612621 | − | 0.731439i | ||||
\(176\) | 4.21251i | 0.317530i | ||||||||
\(177\) | −3.02287 | − | 3.02287i | −0.227213 | − | 0.227213i | ||||
\(178\) | −8.88787 | − | 8.88787i | −0.666174 | − | 0.666174i | ||||
\(179\) | − | 12.7829i | − | 0.955442i | −0.878512 | − | 0.477721i | \(-0.841463\pi\) | ||
0.878512 | − | 0.477721i | \(-0.158537\pi\) | |||||||
\(180\) | 1.16952 | − | 0.0515932i | 0.0871706 | − | 0.00384553i | ||||
\(181\) | − | 2.65927i | − | 0.197662i | −0.995104 | − | 0.0988311i | \(-0.968490\pi\) | ||
0.995104 | − | 0.0988311i | \(-0.0315104\pi\) | |||||||
\(182\) | −4.45556 | + | 4.45556i | −0.330268 | + | 0.330268i | ||||
\(183\) | 17.3156 | + | 17.3156i | 1.28001 | + | 1.28001i | ||||
\(184\) | −14.4274 | − | 3.14842i | −1.06360 | − | 0.232105i | ||||
\(185\) | 6.41900 | − | 7.01149i | 0.471934 | − | 0.515495i | ||||
\(186\) | −1.88496 | −0.138212 | ||||||||
\(187\) | 9.64819 | + | 9.64819i | 0.705546 | + | 0.705546i | ||||
\(188\) | −5.36877 | + | 5.36877i | −0.391558 | + | 0.391558i | ||||
\(189\) | 10.8291 | 0.787703 | ||||||||
\(190\) | −7.07481 | − | 6.47698i | −0.513261 | − | 0.469889i | ||||
\(191\) | − | 25.3411i | − | 1.83362i | −0.399325 | − | 0.916809i | \(-0.630755\pi\) | ||
0.399325 | − | 0.916809i | \(-0.369245\pi\) | |||||||
\(192\) | −11.8836 | − | 11.8836i | −0.857625 | − | 0.857625i | ||||
\(193\) | 4.70486 | − | 4.70486i | 0.338663 | − | 0.338663i | −0.517201 | − | 0.855864i | \(-0.673026\pi\) |
0.855864 | + | 0.517201i | \(0.173026\pi\) | |||||||
\(194\) | −16.3919 | −1.17687 | ||||||||
\(195\) | 0.413458 | + | 9.37228i | 0.0296084 | + | 0.671163i | ||||
\(196\) | 0.411366 | 0.0293833 | ||||||||
\(197\) | 11.0198 | + | 11.0198i | 0.785126 | + | 0.785126i | 0.980691 | − | 0.195565i | \(-0.0626540\pi\) |
−0.195565 | + | 0.980691i | \(0.562654\pi\) | |||||||
\(198\) | −1.22111 | − | 1.22111i | −0.0867805 | − | 0.0867805i | ||||
\(199\) | −14.2416 | −1.00956 | −0.504778 | − | 0.863249i | \(-0.668426\pi\) | ||||
−0.504778 | + | 0.863249i | \(0.668426\pi\) | |||||||
\(200\) | −9.88540 | + | 11.8027i | −0.699003 | + | 0.834574i | ||||
\(201\) | − | 3.14889i | − | 0.222105i | ||||||
\(202\) | 5.80057 | + | 5.80057i | 0.408127 | + | 0.408127i | ||||
\(203\) | 8.91502 | + | 8.91502i | 0.625712 | + | 0.625712i | ||||
\(204\) | −9.34973 | −0.654612 | ||||||||
\(205\) | −0.693430 | + | 0.0305907i | −0.0484313 | + | 0.00213655i | ||||
\(206\) | − | 4.76268i | − | 0.331832i | ||||||
\(207\) | 3.22507 | − | 2.06963i | 0.224158 | − | 0.143849i | ||||
\(208\) | 3.44029 | − | 3.44029i | 0.238541 | − | 0.238541i | ||||
\(209\) | − | 6.89394i | − | 0.476864i | ||||||
\(210\) | 8.61512 | − | 9.41031i | 0.594499 | − | 0.649373i | ||||
\(211\) | −0.547276 | −0.0376760 | −0.0188380 | − | 0.999823i | \(-0.505997\pi\) | ||||
−0.0188380 | + | 0.999823i | \(0.505997\pi\) | |||||||
\(212\) | −4.07360 | + | 4.07360i | −0.279776 | + | 0.279776i | ||||
\(213\) | −18.6772 | + | 18.6772i | −1.27974 | + | 1.27974i | ||||
\(214\) | 18.7690 | 1.28302 | ||||||||
\(215\) | −5.06333 | − | 4.63546i | −0.345316 | − | 0.316136i | ||||
\(216\) | −13.2092 | −0.898771 | ||||||||
\(217\) | 1.48856 | − | 1.48856i | 0.101050 | − | 0.101050i | ||||
\(218\) | −0.694186 | − | 0.694186i | −0.0470162 | − | 0.0470162i | ||||
\(219\) | 18.2569i | 1.23369i | ||||||||
\(220\) | −2.72783 | + | 0.120338i | −0.183910 | + | 0.00811321i | ||||
\(221\) | − | 15.7591i | − | 1.06007i | ||||||
\(222\) | 6.79459 | − | 6.79459i | 0.456023 | − | 0.456023i | ||||
\(223\) | 8.44122 | − | 8.44122i | 0.565266 | − | 0.565266i | −0.365533 | − | 0.930798i | \(-0.619113\pi\) |
0.930798 | + | 0.365533i | \(0.119113\pi\) | |||||||
\(224\) | 8.92870 | 0.596574 | ||||||||
\(225\) | −0.351809 | − | 3.97965i | −0.0234540 | − | 0.265310i | ||||
\(226\) | 8.99376i | 0.598256i | ||||||||
\(227\) | −2.86501 | + | 2.86501i | −0.190157 | + | 0.190157i | −0.795764 | − | 0.605607i | \(-0.792930\pi\) |
0.605607 | + | 0.795764i | \(0.292930\pi\) | |||||||
\(228\) | 3.34034 | + | 3.34034i | 0.221220 | + | 0.221220i | ||||
\(229\) | −16.8510 | −1.11355 | −0.556774 | − | 0.830664i | \(-0.687961\pi\) | ||||
−0.556774 | + | 0.830664i | \(0.687961\pi\) | |||||||
\(230\) | −2.11338 | + | 12.2550i | −0.139352 | + | 0.808070i | ||||
\(231\) | 9.16973 | 0.603324 | ||||||||
\(232\) | −10.8744 | − | 10.8744i | −0.713939 | − | 0.713939i | ||||
\(233\) | 7.69686 | − | 7.69686i | 0.504238 | − | 0.504238i | −0.408514 | − | 0.912752i | \(-0.633953\pi\) |
0.912752 | + | 0.408514i | \(0.133953\pi\) | |||||||
\(234\) | 1.99452i | 0.130386i | ||||||||
\(235\) | 19.1121 | + | 17.4971i | 1.24673 | + | 1.14138i | ||||
\(236\) | −1.43707 | −0.0935450 | ||||||||
\(237\) | −1.87442 | + | 1.87442i | −0.121757 | + | 0.121757i | ||||
\(238\) | −15.1545 | + | 15.1545i | −0.982317 | + | 0.982317i | ||||
\(239\) | 18.8007i | 1.21612i | 0.793892 | + | 0.608058i | \(0.208051\pi\) | ||||
−0.793892 | + | 0.608058i | \(0.791949\pi\) | |||||||
\(240\) | −6.65203 | + | 7.26603i | −0.429387 | + | 0.469020i | ||||
\(241\) | − | 2.15033i | − | 0.138515i | −0.997599 | − | 0.0692574i | \(-0.977937\pi\) | ||
0.997599 | − | 0.0692574i | \(-0.0220630\pi\) | |||||||
\(242\) | −6.17181 | − | 6.17181i | −0.396739 | − | 0.396739i | ||||
\(243\) | 5.72758 | − | 5.72758i | 0.367424 | − | 0.367424i | ||||
\(244\) | 8.23181 | 0.526987 | ||||||||
\(245\) | −0.0618728 | − | 1.40253i | −0.00395291 | − | 0.0896046i | ||||
\(246\) | −0.701624 | −0.0447339 | ||||||||
\(247\) | −5.63018 | + | 5.63018i | −0.358240 | + | 0.358240i | ||||
\(248\) | −1.81572 | + | 1.81572i | −0.115298 | + | 0.115298i | ||||
\(249\) | −0.707657 | −0.0448459 | ||||||||
\(250\) | 10.2968 | + | 7.87879i | 0.651226 | + | 0.498298i | ||||
\(251\) | − | 3.83797i | − | 0.242251i | −0.992637 | − | 0.121125i | \(-0.961350\pi\) | ||
0.992637 | − | 0.121125i | \(-0.0386503\pi\) | |||||||
\(252\) | −0.934484 | + | 0.934484i | −0.0588670 | + | 0.0588670i | ||||
\(253\) | −7.52230 | + | 4.82730i | −0.472923 | + | 0.303490i | ||||
\(254\) | 16.3726i | 1.02731i | ||||||||
\(255\) | 1.40627 | + | 31.8775i | 0.0880643 | + | 1.99624i | ||||
\(256\) | −13.8530 | −0.865812 | ||||||||
\(257\) | 16.6728 | + | 16.6728i | 1.04002 | + | 1.04002i | 0.999165 | + | 0.0408546i | \(0.0130081\pi\) |
0.0408546 | + | 0.999165i | \(0.486992\pi\) | |||||||
\(258\) | −4.90670 | − | 4.90670i | −0.305478 | − | 0.305478i | ||||
\(259\) | 10.7314i | 0.666818i | ||||||||
\(260\) | 2.32606 | + | 2.12950i | 0.144256 | + | 0.132066i | ||||
\(261\) | 3.99080 | 0.247024 | ||||||||
\(262\) | −10.0572 | − | 10.0572i | −0.621335 | − | 0.621335i | ||||
\(263\) | −9.73835 | − | 9.73835i | −0.600492 | − | 0.600492i | 0.339951 | − | 0.940443i | \(-0.389590\pi\) |
−0.940443 | + | 0.339951i | \(0.889590\pi\) | |||||||
\(264\) | −11.1851 | −0.688394 | ||||||||
\(265\) | 14.5014 | + | 13.2760i | 0.890816 | + | 0.815540i | ||||
\(266\) | 10.8283 | 0.663928 | ||||||||
\(267\) | 14.9385 | − | 14.9385i | 0.914220 | − | 0.914220i | ||||
\(268\) | −0.748486 | − | 0.748486i | −0.0457211 | − | 0.0457211i | ||||
\(269\) | − | 10.3305i | − | 0.629860i | −0.949115 | − | 0.314930i | \(-0.898019\pi\) | ||
0.949115 | − | 0.314930i | \(-0.101981\pi\) | |||||||
\(270\) | 0.490260 | + | 11.1132i | 0.0298363 | + | 0.676330i | ||||
\(271\) | 6.83506 | 0.415200 | 0.207600 | − | 0.978214i | \(-0.433435\pi\) | ||||
0.207600 | + | 0.978214i | \(0.433435\pi\) | |||||||
\(272\) | 11.7013 | − | 11.7013i | 0.709495 | − | 0.709495i | ||||
\(273\) | −7.48878 | − | 7.48878i | −0.453241 | − | 0.453241i | ||||
\(274\) | 14.1355 | 0.853956 | ||||||||
\(275\) | 0.820576 | + | 9.28231i | 0.0494826 | + | 0.559745i | ||||
\(276\) | 1.30582 | − | 5.98379i | 0.0786009 | − | 0.360182i | ||||
\(277\) | −4.78771 | − | 4.78771i | −0.287665 | − | 0.287665i | 0.548491 | − | 0.836156i | \(-0.315203\pi\) |
−0.836156 | + | 0.548491i | \(0.815203\pi\) | |||||||
\(278\) | 10.1314 | − | 10.1314i | 0.607642 | − | 0.607642i | ||||
\(279\) | − | 0.666351i | − | 0.0398934i | ||||||
\(280\) | −0.765982 | − | 17.3633i | −0.0457762 | − | 1.03766i | ||||
\(281\) | 18.7407i | 1.11798i | 0.829176 | + | 0.558988i | \(0.188810\pi\) | ||||
−0.829176 | + | 0.558988i | \(0.811190\pi\) | |||||||
\(282\) | 18.5209 | + | 18.5209i | 1.10290 | + | 1.10290i | ||||
\(283\) | −9.03344 | − | 9.03344i | −0.536982 | − | 0.536982i | 0.385659 | − | 0.922641i | \(-0.373974\pi\) |
−0.922641 | + | 0.385659i | \(0.873974\pi\) | |||||||
\(284\) | 8.87907i | 0.526876i | ||||||||
\(285\) | 10.8863 | − | 11.8911i | 0.644850 | − | 0.704371i | ||||
\(286\) | − | 4.65212i | − | 0.275085i | ||||||
\(287\) | 0.554075 | − | 0.554075i | 0.0327060 | − | 0.0327060i | ||||
\(288\) | 1.99846 | − | 1.99846i | 0.117760 | − | 0.117760i | ||||
\(289\) | − | 36.6005i | − | 2.15297i | ||||||
\(290\) | −8.74531 | + | 9.55252i | −0.513542 | + | 0.560943i | ||||
\(291\) | − | 27.5510i | − | 1.61507i | ||||||
\(292\) | 4.33964 | + | 4.33964i | 0.253958 | + | 0.253958i | ||||
\(293\) | 7.41003 | + | 7.41003i | 0.432899 | + | 0.432899i | 0.889613 | − | 0.456715i | \(-0.150974\pi\) |
−0.456715 | + | 0.889613i | \(0.650974\pi\) | |||||||
\(294\) | − | 1.41911i | − | 0.0827640i | ||||||
\(295\) | 0.216146 | + | 4.89961i | 0.0125845 | + | 0.285266i | ||||
\(296\) | − | 13.0900i | − | 0.760842i | ||||||
\(297\) | −5.65342 | + | 5.65342i | −0.328045 | + | 0.328045i | ||||
\(298\) | −18.1362 | − | 18.1362i | −1.05060 | − | 1.05060i | ||||
\(299\) | 10.0857 | + | 2.20097i | 0.583273 | + | 0.127285i | ||||
\(300\) | −4.89518 | − | 4.09999i | −0.282623 | − | 0.236713i | ||||
\(301\) | 7.74967 | 0.446683 | ||||||||
\(302\) | 9.50958 | + | 9.50958i | 0.547215 | + | 0.547215i | ||||
\(303\) | −9.74944 | + | 9.74944i | −0.560091 | + | 0.560091i | ||||
\(304\) | −8.36095 | −0.479533 | ||||||||
\(305\) | −1.23813 | − | 28.0660i | −0.0708951 | − | 1.60705i | ||||
\(306\) | 6.78387i | 0.387808i | ||||||||
\(307\) | −7.54028 | − | 7.54028i | −0.430347 | − | 0.430347i | 0.458400 | − | 0.888746i | \(-0.348423\pi\) |
−0.888746 | + | 0.458400i | \(0.848423\pi\) | |||||||
\(308\) | 2.17963 | − | 2.17963i | 0.124196 | − | 0.124196i | ||||
\(309\) | 8.00498 | 0.455387 | ||||||||
\(310\) | 1.59500 | + | 1.46022i | 0.0905901 | + | 0.0829351i | ||||
\(311\) | 0.679491 | 0.0385304 | 0.0192652 | − | 0.999814i | \(-0.493867\pi\) | ||||
0.0192652 | + | 0.999814i | \(0.493867\pi\) | |||||||
\(312\) | 9.13469 | + | 9.13469i | 0.517150 | + | 0.517150i | ||||
\(313\) | −4.45436 | − | 4.45436i | −0.251775 | − | 0.251775i | 0.569923 | − | 0.821698i | \(-0.306973\pi\) |
−0.821698 | + | 0.569923i | \(0.806973\pi\) | |||||||
\(314\) | 15.5008 | 0.874760 | ||||||||
\(315\) | 3.32663 | + | 3.04552i | 0.187435 | + | 0.171596i | ||||
\(316\) | 0.891096i | 0.0501281i | ||||||||
\(317\) | −13.4899 | − | 13.4899i | −0.757670 | − | 0.757670i | 0.218228 | − | 0.975898i | \(-0.429972\pi\) |
−0.975898 | + | 0.218228i | \(0.929972\pi\) | |||||||
\(318\) | 14.0528 | + | 14.0528i | 0.788044 | + | 0.788044i | ||||
\(319\) | −9.30831 | −0.521165 | ||||||||
\(320\) | 0.849720 | + | 19.2615i | 0.0475008 | + | 1.07675i | ||||
\(321\) | 31.5465i | 1.76075i | ||||||||
\(322\) | −7.58227 | − | 11.8153i | −0.422543 | − | 0.658442i | ||||
\(323\) | −19.1496 | + | 19.1496i | −1.06551 | + | 1.06551i | ||||
\(324\) | − | 7.04914i | − | 0.391619i | ||||||
\(325\) | 6.91057 | − | 8.25088i | 0.383330 | − | 0.457676i | ||||
\(326\) | −16.7354 | −0.926886 | ||||||||
\(327\) | 1.16677 | − | 1.16677i | 0.0645224 | − | 0.0645224i | ||||
\(328\) | −0.675851 | + | 0.675851i | −0.0373176 | + | 0.0373176i | ||||
\(329\) | −29.2520 | −1.61271 | ||||||||
\(330\) | 0.415136 | + | 9.41031i | 0.0228525 | + | 0.518020i | ||||
\(331\) | −15.2719 | −0.839420 | −0.419710 | − | 0.907658i | \(-0.637868\pi\) | ||||
−0.419710 | + | 0.907658i | \(0.637868\pi\) | |||||||
\(332\) | −0.168209 | + | 0.168209i | −0.00923167 | + | 0.00923167i | ||||
\(333\) | 2.40195 | + | 2.40195i | 0.131626 | + | 0.131626i | ||||
\(334\) | 4.89757i | 0.267983i | ||||||||
\(335\) | −2.43935 | + | 2.66451i | −0.133276 | + | 0.145578i | ||||
\(336\) | − | 11.1210i | − | 0.606701i | ||||||
\(337\) | 5.81558 | − | 5.81558i | 0.316795 | − | 0.316795i | −0.530740 | − | 0.847535i | \(-0.678086\pi\) |
0.847535 | + | 0.530740i | \(0.178086\pi\) | |||||||
\(338\) | 6.86066 | − | 6.86066i | 0.373171 | − | 0.373171i | ||||
\(339\) | −15.1165 | −0.821014 | ||||||||
\(340\) | 7.91150 | + | 7.24296i | 0.429061 | + | 0.392805i | ||||
\(341\) | 1.55423i | 0.0841661i | ||||||||
\(342\) | 2.42365 | − | 2.42365i | 0.131056 | − | 0.131056i | ||||
\(343\) | 13.6154 | + | 13.6154i | 0.735162 | + | 0.735162i | ||||
\(344\) | −9.45292 | −0.509667 | ||||||||
\(345\) | −20.5979 | − | 3.55211i | −1.10895 | − | 0.191239i | ||||
\(346\) | −12.6642 | −0.680830 | ||||||||
\(347\) | −8.76600 | − | 8.76600i | −0.470584 | − | 0.470584i | 0.431520 | − | 0.902103i | \(-0.357977\pi\) |
−0.902103 | + | 0.431520i | \(0.857977\pi\) | |||||||
\(348\) | 4.51018 | − | 4.51018i | 0.241771 | − | 0.241771i | ||||
\(349\) | − | 11.0595i | − | 0.592004i | −0.955187 | − | 0.296002i | \(-0.904346\pi\) | ||
0.955187 | − | 0.296002i | \(-0.0956535\pi\) | |||||||
\(350\) | −14.5798 | + | 1.28888i | −0.779321 | + | 0.0688936i | ||||
\(351\) | 9.23413 | 0.492881 | ||||||||
\(352\) | −4.66130 | + | 4.66130i | −0.248448 | + | 0.248448i | ||||
\(353\) | 22.3279 | − | 22.3279i | 1.18839 | − | 1.18839i | 0.210881 | − | 0.977512i | \(-0.432367\pi\) |
0.977512 | − | 0.210881i | \(-0.0676333\pi\) | |||||||
\(354\) | 4.95750i | 0.263488i | ||||||||
\(355\) | 30.2728 | − | 1.33548i | 1.60671 | − | 0.0708801i | ||||
\(356\) | − | 7.10171i | − | 0.376390i | ||||||
\(357\) | −25.4712 | − | 25.4712i | −1.34808 | − | 1.34808i | ||||
\(358\) | −10.4820 | + | 10.4820i | −0.553990 | + | 0.553990i | ||||
\(359\) | −19.7035 | −1.03991 | −0.519956 | − | 0.854193i | \(-0.674052\pi\) | ||||
−0.519956 | + | 0.854193i | \(0.674052\pi\) | |||||||
\(360\) | −4.05777 | − | 3.71488i | −0.213863 | − | 0.195791i | ||||
\(361\) | −5.31698 | −0.279841 | ||||||||
\(362\) | −2.18060 | + | 2.18060i | −0.114610 | + | 0.114610i | ||||
\(363\) | 10.3734 | − | 10.3734i | 0.544462 | − | 0.544462i | ||||
\(364\) | −3.56014 | −0.186602 | ||||||||
\(365\) | 14.1431 | − | 15.4485i | 0.740282 | − | 0.808611i | ||||
\(366\) | − | 28.3976i | − | 1.48437i | ||||||
\(367\) | 25.8561 | − | 25.8561i | 1.34968 | − | 1.34968i | 0.463671 | − | 0.886007i | \(-0.346532\pi\) |
0.886007 | − | 0.463671i | \(-0.153468\pi\) | |||||||
\(368\) | 5.85453 | + | 9.12302i | 0.305189 | + | 0.475570i | ||||
\(369\) | − | 0.248031i | − | 0.0129120i | ||||||
\(370\) | −11.0130 | + | 0.485837i | −0.572537 | + | 0.0252575i | ||||
\(371\) | −22.1952 | −1.15231 | ||||||||
\(372\) | −0.753074 | − | 0.753074i | −0.0390451 | − | 0.0390451i | ||||
\(373\) | 17.3315 | + | 17.3315i | 0.897389 | + | 0.897389i | 0.995205 | − | 0.0978153i | \(-0.0311854\pi\) |
−0.0978153 | + | 0.995205i | \(0.531185\pi\) | |||||||
\(374\) | − | 15.8230i | − | 0.818188i | ||||||
\(375\) | −13.2424 | + | 17.3066i | −0.683837 | + | 0.893707i | ||||
\(376\) | 35.6811 | 1.84011 | ||||||||
\(377\) | 7.60195 | + | 7.60195i | 0.391520 | + | 0.391520i | ||||
\(378\) | −8.87986 | − | 8.87986i | −0.456731 | − | 0.456731i | ||||
\(379\) | −26.0488 | −1.33804 | −0.669018 | − | 0.743246i | \(-0.733285\pi\) | ||||
−0.669018 | + | 0.743246i | \(0.733285\pi\) | |||||||
\(380\) | −0.238846 | − | 5.41417i | −0.0122526 | − | 0.277741i | ||||
\(381\) | −27.5186 | −1.40982 | ||||||||
\(382\) | −20.7797 | + | 20.7797i | −1.06318 | + | 1.06318i | ||||
\(383\) | 1.04098 | + | 1.04098i | 0.0531917 | + | 0.0531917i | 0.733202 | − | 0.680011i | \(-0.238025\pi\) |
−0.680011 | + | 0.733202i | \(0.738025\pi\) | |||||||
\(384\) | 5.70073i | 0.290914i | ||||||||
\(385\) | −7.75918 | − | 7.10352i | −0.395445 | − | 0.362029i | ||||
\(386\) | −7.71596 | −0.392732 | ||||||||
\(387\) | 1.73456 | − | 1.73456i | 0.0881728 | − | 0.0881728i | ||||
\(388\) | −6.54884 | − | 6.54884i | −0.332467 | − | 0.332467i | ||||
\(389\) | 11.1720 | 0.566443 | 0.283222 | − | 0.959054i | \(-0.408597\pi\) | ||||
0.283222 | + | 0.959054i | \(0.408597\pi\) | |||||||
\(390\) | 7.34622 | − | 8.02429i | 0.371990 | − | 0.406326i | ||||
\(391\) | 34.3041 | + | 7.48603i | 1.73483 | + | 0.378585i | ||||
\(392\) | −1.36698 | − | 1.36698i | −0.0690428 | − | 0.0690428i | ||||
\(393\) | 16.9038 | − | 16.9038i | 0.852686 | − | 0.852686i | ||||
\(394\) | − | 18.0724i | − | 0.910473i | ||||||
\(395\) | 3.03815 | − | 0.134028i | 0.152866 | − | 0.00674368i | ||||
\(396\) | − | 0.975709i | − | 0.0490312i | ||||||
\(397\) | 4.79153 | + | 4.79153i | 0.240480 | + | 0.240480i | 0.817049 | − | 0.576569i | \(-0.195609\pi\) |
−0.576569 | + | 0.817049i | \(0.695609\pi\) | |||||||
\(398\) | 11.6780 | + | 11.6780i | 0.585367 | + | 0.585367i | ||||
\(399\) | 18.2000i | 0.911139i | ||||||||
\(400\) | 11.2576 | − | 0.995191i | 0.562878 | − | 0.0497595i | ||||
\(401\) | − | 12.0884i | − | 0.603663i | −0.953361 | − | 0.301832i | \(-0.902402\pi\) | ||
0.953361 | − | 0.301832i | \(-0.0975981\pi\) | |||||||
\(402\) | −2.58208 | + | 2.58208i | −0.128783 | + | 0.128783i | ||||
\(403\) | 1.26931 | − | 1.26931i | 0.0632290 | − | 0.0632290i | ||||
\(404\) | 4.63486i | 0.230593i | ||||||||
\(405\) | −24.0337 | + | 1.06025i | −1.19424 | + | 0.0526841i | ||||
\(406\) | − | 14.6206i | − | 0.725608i | ||||||
\(407\) | −5.60242 | − | 5.60242i | −0.277702 | − | 0.277702i | ||||
\(408\) | 31.0693 | + | 31.0693i | 1.53816 | + | 1.53816i | ||||
\(409\) | 27.9704i | 1.38305i | 0.722353 | + | 0.691524i | \(0.243061\pi\) | ||||
−0.722353 | + | 0.691524i | \(0.756939\pi\) | |||||||
\(410\) | 0.593696 | + | 0.543527i | 0.0293205 | + | 0.0268429i | ||||
\(411\) | 23.7585i | 1.17192i | ||||||||
\(412\) | 1.90277 | − | 1.90277i | 0.0937429 | − | 0.0937429i | ||||
\(413\) | −3.91495 | − | 3.91495i | −0.192642 | − | 0.192642i | ||||
\(414\) | −4.34165 | − | 0.947459i | −0.213380 | − | 0.0465651i | ||||
\(415\) | 0.598801 | + | 0.548201i | 0.0293940 | + | 0.0269101i | ||||
\(416\) | 7.61362 | 0.373288 | ||||||||
\(417\) | 17.0286 | + | 17.0286i | 0.833895 | + | 0.833895i | ||||
\(418\) | −5.65302 | + | 5.65302i | −0.276498 | + | 0.276498i | ||||
\(419\) | −12.4527 | −0.608354 | −0.304177 | − | 0.952616i | \(-0.598381\pi\) | ||||
−0.304177 | + | 0.952616i | \(0.598381\pi\) | |||||||
\(420\) | 7.20147 | − | 0.317693i | 0.351396 | − | 0.0155018i | ||||
\(421\) | 27.8660i | 1.35811i | 0.734090 | + | 0.679053i | \(0.237609\pi\) | ||||
−0.734090 | + | 0.679053i | \(0.762391\pi\) | |||||||
\(422\) | 0.448765 | + | 0.448765i | 0.0218455 | + | 0.0218455i | ||||
\(423\) | −6.54730 | + | 6.54730i | −0.318341 | + | 0.318341i | ||||
\(424\) | 27.0733 | 1.31479 | ||||||||
\(425\) | 23.5046 | − | 28.0633i | 1.14014 | − | 1.36127i | ||||
\(426\) | 30.6305 | 1.48405 | ||||||||
\(427\) | 22.4257 | + | 22.4257i | 1.08525 | + | 1.08525i | ||||
\(428\) | 7.49855 | + | 7.49855i | 0.362456 | + | 0.362456i | ||||
\(429\) | 7.81915 | 0.377512 | ||||||||
\(430\) | 0.350846 | + | 7.95299i | 0.0169193 | + | 0.383527i | ||||
\(431\) | 8.73549i | 0.420774i | 0.977618 | + | 0.210387i | \(0.0674723\pi\) | ||||
−0.977618 | + | 0.210387i | \(0.932528\pi\) | |||||||
\(432\) | 6.85645 | + | 6.85645i | 0.329881 | + | 0.329881i | ||||
\(433\) | −24.7415 | − | 24.7415i | −1.18900 | − | 1.18900i | −0.977344 | − | 0.211656i | \(-0.932114\pi\) |
−0.211656 | − | 0.977344i | \(-0.567886\pi\) | |||||||
\(434\) | −2.44123 | −0.117183 | ||||||||
\(435\) | −16.0556 | − | 14.6989i | −0.769808 | − | 0.704757i | ||||
\(436\) | − | 0.554678i | − | 0.0265643i | ||||||
\(437\) | −9.58118 | − | 14.9302i | −0.458330 | − | 0.714208i | ||||
\(438\) | 14.9706 | − | 14.9706i | 0.715323 | − | 0.715323i | ||||
\(439\) | 26.8462i | 1.28130i | 0.767833 | + | 0.640650i | \(0.221335\pi\) | ||||
−0.767833 | + | 0.640650i | \(0.778665\pi\) | |||||||
\(440\) | 9.46453 | + | 8.66475i | 0.451204 | + | 0.413076i | ||||
\(441\) | 0.501668 | 0.0238889 | ||||||||
\(442\) | −12.9224 | + | 12.9224i | −0.614656 | + | 0.614656i | ||||
\(443\) | −22.9288 | + | 22.9288i | −1.08938 | + | 1.08938i | −0.0937869 | + | 0.995592i | \(0.529897\pi\) |
−0.995592 | + | 0.0937869i | \(0.970103\pi\) | |||||||
\(444\) | 5.42911 | 0.257654 | ||||||||
\(445\) | −24.2130 | + | 1.06815i | −1.14780 | + | 0.0506354i | ||||
\(446\) | −13.8436 | −0.655512 | ||||||||
\(447\) | 30.4828 | − | 30.4828i | 1.44179 | − | 1.44179i | ||||
\(448\) | −15.3906 | − | 15.3906i | −0.727136 | − | 0.727136i | ||||
\(449\) | 7.68005i | 0.362444i | 0.983442 | + | 0.181222i | \(0.0580052\pi\) | ||||
−0.983442 | + | 0.181222i | \(0.941995\pi\) | |||||||
\(450\) | −2.97482 | + | 3.55179i | −0.140235 | + | 0.167433i | ||||
\(451\) | 0.578518i | 0.0272413i | ||||||||
\(452\) | −3.59316 | + | 3.59316i | −0.169008 | + | 0.169008i | ||||
\(453\) | −15.9834 | + | 15.9834i | −0.750968 | + | 0.750968i | ||||
\(454\) | 4.69861 | 0.220516 | ||||||||
\(455\) | 0.535474 | + | 12.1381i | 0.0251034 | + | 0.569045i | ||||
\(456\) | − | 22.2000i | − | 1.03961i | ||||||
\(457\) | 0.788754 | − | 0.788754i | 0.0368964 | − | 0.0368964i | −0.688418 | − | 0.725314i | \(-0.741694\pi\) |
0.725314 | + | 0.688418i | \(0.241694\pi\) | |||||||
\(458\) | 13.8178 | + | 13.8178i | 0.645664 | + | 0.645664i | ||||
\(459\) | 31.4076 | 1.46598 | ||||||||
\(460\) | −5.74041 | + | 4.05175i | −0.267648 | + | 0.188914i | ||||
\(461\) | 28.3501 | 1.32040 | 0.660198 | − | 0.751092i | \(-0.270473\pi\) | ||||
0.660198 | + | 0.751092i | \(0.270473\pi\) | |||||||
\(462\) | −7.51916 | − | 7.51916i | −0.349823 | − | 0.349823i | ||||
\(463\) | −19.3363 | + | 19.3363i | −0.898632 | + | 0.898632i | −0.995315 | − | 0.0966834i | \(-0.969177\pi\) |
0.0966834 | + | 0.995315i | \(0.469177\pi\) | |||||||
\(464\) | 11.2891i | 0.524082i | ||||||||
\(465\) | −2.45430 | + | 2.68084i | −0.113815 | + | 0.124321i | ||||
\(466\) | −12.6228 | −0.584741 | ||||||||
\(467\) | −14.6609 | + | 14.6609i | −0.678424 | + | 0.678424i | −0.959643 | − | 0.281219i | \(-0.909261\pi\) |
0.281219 | + | 0.959643i | \(0.409261\pi\) | |||||||
\(468\) | −0.796847 | + | 0.796847i | −0.0368342 | + | 0.0368342i | ||||
\(469\) | − | 4.07816i | − | 0.188312i | ||||||
\(470\) | −1.32431 | − | 30.0194i | −0.0610857 | − | 1.38469i | ||||
\(471\) | 26.0533i | 1.20047i | ||||||||
\(472\) | 4.77540 | + | 4.77540i | 0.219806 | + | 0.219806i | ||||
\(473\) | −4.04577 | + | 4.04577i | −0.186025 | + | 0.186025i | ||||
\(474\) | 3.07405 | 0.141196 | ||||||||
\(475\) | −18.4234 | + | 1.62867i | −0.845325 | + | 0.0747285i | ||||
\(476\) | −12.1089 | −0.555012 | ||||||||
\(477\) | −4.96781 | + | 4.96781i | −0.227461 | + | 0.227461i | ||||
\(478\) | 15.4165 | − | 15.4165i | 0.705136 | − | 0.705136i | ||||
\(479\) | 18.4596 | 0.843439 | 0.421719 | − | 0.906726i | \(-0.361427\pi\) | ||||
0.421719 | + | 0.906726i | \(0.361427\pi\) | |||||||
\(480\) | −15.4008 | + | 0.679408i | −0.702949 | + | 0.0310106i | ||||
\(481\) | 9.15082i | 0.417241i | ||||||||
\(482\) | −1.76327 | + | 1.76327i | −0.0803145 | + | 0.0803145i | ||||
\(483\) | 19.8589 | − | 12.7441i | 0.903609 | − | 0.579875i | ||||
\(484\) | − | 4.93149i | − | 0.224158i | ||||||
\(485\) | −21.3429 | + | 23.3129i | −0.969133 | + | 1.05859i | ||||
\(486\) | −9.39321 | −0.426084 | ||||||||
\(487\) | 4.06167 | + | 4.06167i | 0.184052 | + | 0.184052i | 0.793119 | − | 0.609067i | \(-0.208456\pi\) |
−0.609067 | + | 0.793119i | \(0.708456\pi\) | |||||||
\(488\) | −27.3545 | − | 27.3545i | −1.23828 | − | 1.23828i | ||||
\(489\) | − | 28.1283i | − | 1.27201i | ||||||
\(490\) | −1.09934 | + | 1.20081i | −0.0496631 | + | 0.0542471i | ||||
\(491\) | −14.8576 | −0.670514 | −0.335257 | − | 0.942127i | \(-0.608823\pi\) | ||||
−0.335257 | + | 0.942127i | \(0.608823\pi\) | |||||||
\(492\) | −0.280311 | − | 0.280311i | −0.0126374 | − | 0.0126374i | ||||
\(493\) | 25.8561 | + | 25.8561i | 1.16450 | + | 1.16450i | ||||
\(494\) | 9.23347 | 0.415433 | ||||||||
\(495\) | −3.32663 | + | 0.146754i | −0.149521 | + | 0.00659612i | ||||
\(496\) | 1.88496 | 0.0846372 | ||||||||
\(497\) | −24.1890 | + | 24.1890i | −1.08502 | + | 1.08502i | ||||
\(498\) | 0.580277 | + | 0.580277i | 0.0260028 | + | 0.0260028i | ||||
\(499\) | 3.58013i | 0.160269i | 0.996784 | + | 0.0801343i | \(0.0255349\pi\) | ||||
−0.996784 | + | 0.0801343i | \(0.974465\pi\) | |||||||
\(500\) | 0.966034 | + | 7.26146i | 0.0432024 | + | 0.324742i | ||||
\(501\) | −8.23170 | −0.367765 | ||||||||
\(502\) | −3.14713 | + | 3.14713i | −0.140463 | + | 0.140463i | ||||
\(503\) | 6.36498 | + | 6.36498i | 0.283801 | + | 0.283801i | 0.834623 | − | 0.550822i | \(-0.185686\pi\) |
−0.550822 | + | 0.834623i | \(0.685686\pi\) | |||||||
\(504\) | 6.21062 | 0.276643 | ||||||||
\(505\) | 15.8023 | − | 0.697120i | 0.703194 | − | 0.0310214i | ||||
\(506\) | 10.1267 | + | 2.20989i | 0.450185 | + | 0.0982418i | ||||
\(507\) | 11.5312 | + | 11.5312i | 0.512119 | + | 0.512119i | ||||
\(508\) | −6.54113 | + | 6.54113i | −0.290216 | + | 0.290216i | ||||
\(509\) | − | 15.6300i | − | 0.692789i | −0.938089 | − | 0.346394i | \(-0.887406\pi\) | ||
0.938089 | − | 0.346394i | \(-0.112594\pi\) | |||||||
\(510\) | 24.9863 | − | 27.2926i | 1.10641 | − | 1.20854i | ||||
\(511\) | 23.6447i | 1.04598i | ||||||||
\(512\) | 15.4957 | + | 15.4957i | 0.684820 | + | 0.684820i | ||||
\(513\) | −11.2209 | − | 11.2209i | −0.495413 | − | 0.495413i | ||||
\(514\) | − | 27.3433i | − | 1.20606i | ||||||
\(515\) | −6.77360 | − | 6.20122i | −0.298481 | − | 0.273258i | ||||
\(516\) | − | 3.92062i | − | 0.172596i | ||||||
\(517\) | 15.2712 | − | 15.2712i | 0.671627 | − | 0.671627i | ||||
\(518\) | 8.79974 | − | 8.79974i | 0.386639 | − | 0.386639i | ||||
\(519\) | − | 21.2856i | − | 0.934334i | ||||||
\(520\) | −0.653163 | − | 14.8059i | −0.0286431 | − | 0.649282i | ||||
\(521\) | 10.2971i | 0.451124i | 0.974229 | + | 0.225562i | \(0.0724218\pi\) | ||||
−0.974229 | + | 0.225562i | \(0.927578\pi\) | |||||||
\(522\) | −3.27244 | − | 3.27244i | −0.143231 | − | 0.143231i | ||||
\(523\) | −28.9495 | − | 28.9495i | −1.26587 | − | 1.26587i | −0.948200 | − | 0.317674i | \(-0.897098\pi\) |
−0.317674 | − | 0.948200i | \(-0.602902\pi\) | |||||||
\(524\) | − | 8.03604i | − | 0.351056i | ||||||
\(525\) | −2.16632 | − | 24.5053i | −0.0945458 | − | 1.06950i | ||||
\(526\) | 15.9708i | 0.696362i | ||||||||
\(527\) | 4.31725 | − | 4.31725i | 0.188062 | − | 0.188062i | ||||
\(528\) | 5.80581 | + | 5.80581i | 0.252665 | + | 0.252665i | ||||
\(529\) | −9.58206 | + | 20.9090i | −0.416611 | + | 0.909085i | ||||
\(530\) | −1.00483 | − | 22.7775i | −0.0436470 | − | 0.989390i | ||||
\(531\) | −1.75252 | −0.0760531 | ||||||||
\(532\) | 4.32611 | + | 4.32611i | 0.187561 | + | 0.187561i | ||||
\(533\) | 0.472467 | − | 0.472467i | 0.0204648 | − | 0.0204648i | ||||
\(534\) | −24.4991 | −1.06018 | ||||||||
\(535\) | 24.4381 | − | 26.6938i | 1.05655 | − | 1.15407i | ||||
\(536\) | 4.97447i | 0.214864i | ||||||||
\(537\) | −17.6178 | − | 17.6178i | −0.760266 | − | 0.760266i | ||||
\(538\) | −8.47097 | + | 8.47097i | −0.365209 | + | 0.365209i | ||||
\(539\) | −1.17011 | −0.0504003 | ||||||||
\(540\) | −4.24406 | + | 4.63580i | −0.182635 | + | 0.199493i | ||||
\(541\) | −22.3203 | −0.959625 | −0.479812 | − | 0.877371i | \(-0.659295\pi\) | ||||
−0.479812 | + | 0.877371i | \(0.659295\pi\) | |||||||
\(542\) | −5.60474 | − | 5.60474i | −0.240744 | − | 0.240744i | ||||
\(543\) | −3.66509 | − | 3.66509i | −0.157284 | − | 0.157284i | ||||
\(544\) | 25.8958 | 1.11027 | ||||||||
\(545\) | −1.89115 | + | 0.0834280i | −0.0810079 | + | 0.00357366i | ||||
\(546\) | 12.2816i | 0.525602i | ||||||||
\(547\) | −19.4194 | − | 19.4194i | −0.830314 | − | 0.830314i | 0.157245 | − | 0.987560i | \(-0.449739\pi\) |
−0.987560 | + | 0.157245i | \(0.949739\pi\) | |||||||
\(548\) | 5.64737 | + | 5.64737i | 0.241244 | + | 0.241244i | ||||
\(549\) | 10.0388 | 0.428446 | ||||||||
\(550\) | 6.93861 | − | 8.28435i | 0.295863 | − | 0.353246i | ||||
\(551\) | − | 18.4750i | − | 0.787063i | ||||||
\(552\) | −24.2235 | + | 15.5450i | −1.03102 | + | 0.661639i | ||||
\(553\) | −2.42759 | + | 2.42759i | −0.103231 | + | 0.103231i | ||||
\(554\) | 7.85182i | 0.333592i | ||||||||
\(555\) | −0.816582 | − | 18.5103i | −0.0346620 | − | 0.785718i | ||||
\(556\) | 8.09535 | 0.343319 | ||||||||
\(557\) | −24.7614 | + | 24.7614i | −1.04917 | + | 1.04917i | −0.0504476 | + | 0.998727i | \(0.516065\pi\) |
−0.998727 | + | 0.0504476i | \(0.983935\pi\) | |||||||
\(558\) | −0.546407 | + | 0.546407i | −0.0231312 | + | 0.0231312i | ||||
\(559\) | 6.60824 | 0.279499 | ||||||||
\(560\) | −8.61512 | + | 9.41031i | −0.364055 | + | 0.397658i | ||||
\(561\) | 26.5948 | 1.12284 | ||||||||
\(562\) | 15.3673 | − | 15.3673i | 0.648232 | − | 0.648232i | ||||
\(563\) | −6.83152 | − | 6.83152i | −0.287914 | − | 0.287914i | 0.548341 | − | 0.836255i | \(-0.315260\pi\) |
−0.836255 | + | 0.548341i | \(0.815260\pi\) | |||||||
\(564\) | 14.7988i | 0.623142i | ||||||||
\(565\) | 12.7912 | + | 11.7103i | 0.538128 | + | 0.492655i | ||||
\(566\) | 14.8148i | 0.622713i | ||||||||
\(567\) | 19.2037 | − | 19.2037i | 0.806481 | − | 0.806481i | ||||
\(568\) | 29.5053 | − | 29.5053i | 1.23802 | − | 1.23802i | ||||
\(569\) | 23.5370 | 0.986722 | 0.493361 | − | 0.869825i | \(-0.335768\pi\) | ||||
0.493361 | + | 0.869825i | \(0.335768\pi\) | |||||||
\(570\) | −18.6775 | + | 0.823957i | −0.782314 | + | 0.0345118i | ||||
\(571\) | − | 23.7543i | − | 0.994085i | −0.867726 | − | 0.497043i | \(-0.834419\pi\) | ||
0.867726 | − | 0.497043i | \(-0.165581\pi\) | |||||||
\(572\) | 1.85860 | − | 1.85860i | 0.0777120 | − | 0.0777120i | ||||
\(573\) | −34.9259 | − | 34.9259i | −1.45905 | − | 1.45905i | ||||
\(574\) | −0.908680 | −0.0379276 | ||||||||
\(575\) | 14.6776 | + | 18.9622i | 0.612100 | + | 0.790780i | ||||
\(576\) | −6.88957 | −0.287065 | ||||||||
\(577\) | −16.4059 | − | 16.4059i | −0.682986 | − | 0.682986i | 0.277686 | − | 0.960672i | \(-0.410433\pi\) |
−0.960672 | + | 0.277686i | \(0.910433\pi\) | |||||||
\(578\) | −30.0123 | + | 30.0123i | −1.24835 | + | 1.24835i | ||||
\(579\) | − | 12.9688i | − | 0.538963i | ||||||
\(580\) | −7.31030 | + | 0.322494i | −0.303544 | + | 0.0133908i | ||||
\(581\) | −0.916493 | −0.0380225 | ||||||||
\(582\) | −22.5918 | + | 22.5918i | −0.936459 | + | 0.936459i | ||||
\(583\) | 11.5871 | − | 11.5871i | 0.479891 | − | 0.479891i | ||||
\(584\) | − | 28.8414i | − | 1.19347i | ||||||
\(585\) | 2.83666 | + | 2.59696i | 0.117282 | + | 0.107371i | ||||
\(586\) | − | 12.1524i | − | 0.502012i | ||||||
\(587\) | −0.365946 | − | 0.365946i | −0.0151042 | − | 0.0151042i | 0.699514 | − | 0.714619i | \(-0.253400\pi\) |
−0.714619 | + | 0.699514i | \(0.753400\pi\) | |||||||
\(588\) | 0.566957 | − | 0.566957i | 0.0233809 | − | 0.0233809i | ||||
\(589\) | −3.08481 | −0.127107 | ||||||||
\(590\) | 3.84043 | − | 4.19491i | 0.158108 | − | 0.172702i | ||||
\(591\) | 30.3755 | 1.24948 | ||||||||
\(592\) | −6.79459 | + | 6.79459i | −0.279256 | + | 0.279256i | ||||
\(593\) | −6.14484 | + | 6.14484i | −0.252338 | + | 0.252338i | −0.821929 | − | 0.569590i | \(-0.807102\pi\) |
0.569590 | + | 0.821929i | \(0.307102\pi\) | |||||||
\(594\) | 9.27159 | 0.380418 | ||||||||
\(595\) | 1.82128 | + | 41.2848i | 0.0746652 | + | 1.69251i | ||||
\(596\) | − | 14.4915i | − | 0.593593i | ||||||
\(597\) | −19.6281 | + | 19.6281i | −0.803326 | + | 0.803326i | ||||
\(598\) | −6.46550 | − | 10.0751i | −0.264394 | − | 0.412000i | ||||
\(599\) | − | 22.3478i | − | 0.913105i | −0.889697 | − | 0.456552i | \(-0.849084\pi\) | ||
0.889697 | − | 0.456552i | \(-0.150916\pi\) | |||||||
\(600\) | 2.64244 | + | 29.8911i | 0.107877 | + | 1.22030i | ||||
\(601\) | 5.68719 | 0.231985 | 0.115993 | − | 0.993250i | \(-0.462995\pi\) | ||||
0.115993 | + | 0.993250i | \(0.462995\pi\) | |||||||
\(602\) | −6.35471 | − | 6.35471i | −0.258999 | − | 0.258999i | ||||
\(603\) | −0.912790 | − | 0.912790i | −0.0371717 | − | 0.0371717i | ||||
\(604\) | 7.59848i | 0.309178i | ||||||||
\(605\) | −16.8137 | + | 0.741735i | −0.683573 | + | 0.0301558i | ||||
\(606\) | 15.9890 | 0.649511 | ||||||||
\(607\) | 29.8093 | + | 29.8093i | 1.20992 | + | 1.20992i | 0.971051 | + | 0.238872i | \(0.0767777\pi\) |
0.238872 | + | 0.971051i | \(0.423222\pi\) | |||||||
\(608\) | −9.25169 | − | 9.25169i | −0.375206 | − | 0.375206i | ||||
\(609\) | 24.5739 | 0.995784 | ||||||||
\(610\) | −21.9988 | + | 24.0293i | −0.890704 | + | 0.972917i | ||||
\(611\) | −24.9435 | −1.00911 | ||||||||
\(612\) | −2.71027 | + | 2.71027i | −0.109556 | + | 0.109556i | ||||
\(613\) | −11.5614 | − | 11.5614i | −0.466962 | − | 0.466962i | 0.433967 | − | 0.900929i | \(-0.357113\pi\) |
−0.900929 | + | 0.433967i | \(0.857113\pi\) | |||||||
\(614\) | 12.3660i | 0.499053i | ||||||||
\(615\) | −0.913545 | + | 0.997867i | −0.0368377 | + | 0.0402379i | ||||
\(616\) | −14.4859 | −0.583654 | ||||||||
\(617\) | 20.2525 | − | 20.2525i | 0.815335 | − | 0.815335i | −0.170093 | − | 0.985428i | \(-0.554407\pi\) |
0.985428 | + | 0.170093i | \(0.0544069\pi\) | |||||||
\(618\) | −6.56407 | − | 6.56407i | −0.264046 | − | 0.264046i | ||||
\(619\) | 23.4050 | 0.940725 | 0.470363 | − | 0.882473i | \(-0.344123\pi\) | ||||
0.470363 | + | 0.882473i | \(0.344123\pi\) | |||||||
\(620\) | 0.0538475 | + | 1.22062i | 0.00216257 | + | 0.0490211i | ||||
\(621\) | −4.38649 | + | 20.1007i | −0.176024 | + | 0.806614i | ||||
\(622\) | −0.557181 | − | 0.557181i | −0.0223409 | − | 0.0223409i | ||||
\(623\) | 19.3470 | − | 19.3470i | 0.775120 | − | 0.775120i | ||||
\(624\) | − | 9.48303i | − | 0.379625i | ||||||
\(625\) | 24.6123 | − | 4.38583i | 0.984491 | − | 0.175433i | ||||
\(626\) | 7.30513i | 0.291972i | ||||||||
\(627\) | −9.50144 | − | 9.50144i | −0.379451 | − | 0.379451i | ||||
\(628\) | 6.19283 | + | 6.19283i | 0.247121 | + | 0.247121i | ||||
\(629\) | 31.1242i | 1.24100i | ||||||||
\(630\) | −0.230508 | − | 5.22516i | −0.00918365 | − | 0.208175i | ||||
\(631\) | 0.768430i | 0.0305907i | 0.999883 | + | 0.0152954i | \(0.00486885\pi\) | ||||
−0.999883 | + | 0.0152954i | \(0.995131\pi\) | |||||||
\(632\) | 2.96113 | − | 2.96113i | 0.117787 | − | 0.117787i | ||||
\(633\) | −0.754272 | + | 0.754272i | −0.0299796 | + | 0.0299796i | ||||
\(634\) | 22.1234i | 0.878634i | ||||||||
\(635\) | 23.2855 | + | 21.3178i | 0.924058 | + | 0.845973i | ||||
\(636\) | 11.2287i | 0.445247i | ||||||||
\(637\) | 0.955612 | + | 0.955612i | 0.0378627 | + | 0.0378627i | ||||
\(638\) | 7.63279 | + | 7.63279i | 0.302185 | + | 0.302185i | ||||
\(639\) | 10.8282i | 0.428355i | ||||||||
\(640\) | 4.41619 | − | 4.82381i | 0.174565 | − | 0.190678i | ||||
\(641\) | 24.6345i | 0.973002i | 0.873680 | + | 0.486501i | \(0.161727\pi\) | ||||
−0.873680 | + | 0.486501i | \(0.838273\pi\) | |||||||
\(642\) | 25.8680 | − | 25.8680i | 1.02093 | − | 1.02093i | ||||
\(643\) | −11.9143 | − | 11.9143i | −0.469853 | − | 0.469853i | 0.432014 | − | 0.901867i | \(-0.357803\pi\) |
−0.901867 | + | 0.432014i | \(0.857803\pi\) | |||||||
\(644\) | 1.69118 | − | 7.74967i | 0.0666417 | − | 0.305380i | ||||
\(645\) | −13.3672 | + | 0.589692i | −0.526331 | + | 0.0232191i | ||||
\(646\) | 31.4053 | 1.23563 | ||||||||
\(647\) | 15.5990 | + | 15.5990i | 0.613260 | + | 0.613260i | 0.943794 | − | 0.330534i | \(-0.107229\pi\) |
−0.330534 | + | 0.943794i | \(0.607229\pi\) | |||||||
\(648\) | −23.4244 | + | 23.4244i | −0.920198 | + | 0.920198i | ||||
\(649\) | 4.08766 | 0.160455 | ||||||||
\(650\) | −12.4324 | + | 1.09905i | −0.487637 | + | 0.0431081i | ||||
\(651\) | − | 4.10315i | − | 0.160815i | ||||||
\(652\) | −6.68606 | − | 6.68606i | −0.261846 | − | 0.261846i | ||||
\(653\) | 2.42246 | − | 2.42246i | 0.0947982 | − | 0.0947982i | −0.658117 | − | 0.752915i | \(-0.728647\pi\) |
0.752915 | + | 0.658117i | \(0.228647\pi\) | |||||||
\(654\) | −1.91349 | −0.0748236 | ||||||||
\(655\) | −27.3985 | + | 1.20868i | −1.07055 | + | 0.0472272i | ||||
\(656\) | 0.701624 | 0.0273938 | ||||||||
\(657\) | 5.29225 | + | 5.29225i | 0.206470 | + | 0.206470i | ||||
\(658\) | 23.9866 | + | 23.9866i | 0.935093 | + | 0.935093i | ||||
\(659\) | −12.1720 | −0.474153 | −0.237077 | − | 0.971491i | \(-0.576189\pi\) | ||||
−0.237077 | + | 0.971491i | \(0.576189\pi\) | |||||||
\(660\) | −3.59373 | + | 3.92543i | −0.139886 | + | 0.152797i | ||||
\(661\) | − | 42.6358i | − | 1.65834i | −0.558995 | − | 0.829171i | \(-0.688813\pi\) | ||
0.558995 | − | 0.829171i | \(-0.311187\pi\) | |||||||
\(662\) | 12.5229 | + | 12.5229i | 0.486718 | + | 0.486718i | ||||
\(663\) | −21.7196 | − | 21.7196i | −0.843520 | − | 0.843520i | ||||
\(664\) | 1.11792 | 0.0433839 | ||||||||
\(665\) | 14.0990 | − | 15.4003i | 0.546735 | − | 0.597200i | ||||
\(666\) | − | 3.93919i | − | 0.152641i | ||||||
\(667\) | −20.1590 | + | 12.9367i | −0.780558 | + | 0.500909i | ||||
\(668\) | −1.95666 | + | 1.95666i | −0.0757056 | + | 0.0757056i | ||||
\(669\) | − | 23.2679i | − | 0.899588i | ||||||
\(670\) | 4.18515 | − | 0.184628i | 0.161686 | − | 0.00713280i | ||||
\(671\) | −23.4150 | −0.903925 | ||||||||
\(672\) | 12.3058 | − | 12.3058i | 0.474707 | − | 0.474707i | ||||
\(673\) | −1.88228 | + | 1.88228i | −0.0725567 | + | 0.0725567i | −0.742454 | − | 0.669897i | \(-0.766338\pi\) |
0.669897 | + | 0.742454i | \(0.266338\pi\) | |||||||
\(674\) | −9.53753 | −0.367372 | ||||||||
\(675\) | 16.4439 | + | 13.7727i | 0.632925 | + | 0.530110i | ||||
\(676\) | 5.48190 | 0.210842 | ||||||||
\(677\) | −25.4073 | + | 25.4073i | −0.976483 | + | 0.976483i | −0.999730 | − | 0.0232465i | \(-0.992600\pi\) |
0.0232465 | + | 0.999730i | \(0.492600\pi\) | |||||||
\(678\) | 12.3955 | + | 12.3955i | 0.476045 | + | 0.476045i | ||||
\(679\) | − | 35.6816i | − | 1.36933i | ||||||
\(680\) | −2.22157 | − | 50.3585i | −0.0851932 | − | 1.93116i | ||||
\(681\) | 7.89729i | 0.302625i | ||||||||
\(682\) | 1.27446 | − | 1.27446i | 0.0488017 | − | 0.0488017i | ||||
\(683\) | −9.66884 | + | 9.66884i | −0.369968 | + | 0.369968i | −0.867465 | − | 0.497498i | \(-0.834252\pi\) |
0.497498 | + | 0.867465i | \(0.334252\pi\) | |||||||
\(684\) | 1.93658 | 0.0740469 | ||||||||
\(685\) | 18.4050 | − | 20.1039i | 0.703220 | − | 0.768129i | ||||
\(686\) | − | 22.3292i | − | 0.852532i | ||||||
\(687\) | −23.2246 | + | 23.2246i | −0.886073 | + | 0.886073i | ||||
\(688\) | 4.90670 | + | 4.90670i | 0.187066 | + | 0.187066i | ||||
\(689\) | −18.9261 | −0.721027 | ||||||||
\(690\) | 13.9775 | + | 19.8029i | 0.532113 | + | 0.753884i | ||||
\(691\) | 15.0902 | 0.574059 | 0.287030 | − | 0.957922i | \(-0.407332\pi\) | ||||
0.287030 | + | 0.957922i | \(0.407332\pi\) | |||||||
\(692\) | −5.05956 | − | 5.05956i | −0.192335 | − | 0.192335i | ||||
\(693\) | 2.65809 | − | 2.65809i | 0.100973 | − | 0.100973i | ||||
\(694\) | 14.3762i | 0.545713i | ||||||||
\(695\) | −1.21761 | − | 27.6007i | −0.0461864 | − | 1.04695i | ||||
\(696\) | −29.9748 | −1.13619 | ||||||||
\(697\) | 1.60698 | − | 1.60698i | 0.0608686 | − | 0.0608686i | ||||
\(698\) | −9.06881 | + | 9.06881i | −0.343259 | + | 0.343259i | ||||
\(699\) | − | 21.2161i | − | 0.802466i | ||||||
\(700\) | −6.33980 | − | 5.30994i | −0.239622 | − | 0.200697i | ||||
\(701\) | − | 26.7926i | − | 1.01194i | −0.862550 | − | 0.505971i | \(-0.831134\pi\) | ||
0.862550 | − | 0.505971i | \(-0.168866\pi\) | |||||||
\(702\) | −7.57197 | − | 7.57197i | −0.285785 | − | 0.285785i | ||||
\(703\) | 11.1196 | − | 11.1196i | 0.419384 | − | 0.419384i | ||||
\(704\) | 16.0695 | 0.605643 | ||||||||
\(705\) | 50.4558 | − | 2.22586i | 1.90028 | − | 0.0838307i | ||||
\(706\) | −36.6176 | −1.37812 | ||||||||
\(707\) | −12.6266 | + | 12.6266i | −0.474872 | + | 0.474872i | ||||
\(708\) | −1.98061 | + | 1.98061i | −0.0744358 | + | 0.0744358i | ||||
\(709\) | 16.2692 | 0.611003 | 0.305502 | − | 0.952192i | \(-0.401176\pi\) | ||||
0.305502 | + | 0.952192i | \(0.401176\pi\) | |||||||
\(710\) | −25.9187 | − | 23.7285i | −0.972711 | − | 0.890515i | ||||
\(711\) | 1.08671i | 0.0407546i | ||||||||
\(712\) | −23.5991 | + | 23.5991i | −0.884415 | + | 0.884415i | ||||
\(713\) | 2.16006 | + | 3.36598i | 0.0808949 | + | 0.126057i | ||||
\(714\) | 41.7726i | 1.56330i | ||||||||
\(715\) | −6.61636 | − | 6.05726i | −0.247438 | − | 0.226529i | ||||
\(716\) | −8.37547 | −0.313006 | ||||||||
\(717\) | 25.9117 | + | 25.9117i | 0.967690 | + | 0.967690i | ||||
\(718\) | 16.1568 | + | 16.1568i | 0.602968 | + | 0.602968i | ||||
\(719\) | 33.1573i | 1.23656i | 0.785958 | + | 0.618280i | \(0.212170\pi\) | ||||
−0.785958 | + | 0.618280i | \(0.787830\pi\) | |||||||
\(720\) | 0.177983 | + | 4.03453i | 0.00663304 | + | 0.150358i | ||||
\(721\) | 10.3673 | 0.386100 | ||||||||
\(722\) | 4.35991 | + | 4.35991i | 0.162259 | + | 0.162259i | ||||
\(723\) | −2.96365 | − | 2.96365i | −0.110219 | − | 0.110219i | ||||
\(724\) | −1.74237 | −0.0647548 | ||||||||
\(725\) | 2.19906 | + | 24.8756i | 0.0816709 | + | 0.923857i | ||||
\(726\) | −17.0123 | −0.631387 | ||||||||
\(727\) | 21.5242 | − | 21.5242i | 0.798290 | − | 0.798290i | −0.184536 | − | 0.982826i | \(-0.559078\pi\) |
0.982826 | + | 0.184536i | \(0.0590781\pi\) | |||||||
\(728\) | 11.8304 | + | 11.8304i | 0.438465 | + | 0.438465i | ||||
\(729\) | 16.4881i | 0.610671i | ||||||||
\(730\) | −24.2650 | + | 1.07045i | −0.898089 | + | 0.0396192i | ||||
\(731\) | 22.4763 | 0.831314 | ||||||||
\(732\) | 11.3453 | − | 11.3453i | 0.419335 | − | 0.419335i | ||||
\(733\) | 31.6457 | + | 31.6457i | 1.16886 | + | 1.16886i | 0.982477 | + | 0.186384i | \(0.0596768\pi\) |
0.186384 | + | 0.982477i | \(0.440323\pi\) | |||||||
\(734\) | −42.4039 | −1.56516 | ||||||||
\(735\) | −2.01829 | − | 1.84774i | −0.0744457 | − | 0.0681549i | ||||
\(736\) | −3.61670 | + | 16.5732i | −0.133313 | + | 0.610896i | ||||
\(737\) | 2.12903 | + | 2.12903i | 0.0784239 | + | 0.0784239i | ||||
\(738\) | −0.203385 | + | 0.203385i | −0.00748669 | + | 0.00748669i | ||||
\(739\) | − | 25.3398i | − | 0.932141i | −0.884748 | − | 0.466071i | \(-0.845669\pi\) | ||
0.884748 | − | 0.466071i | \(-0.154331\pi\) | |||||||
\(740\) | −4.59397 | − | 4.20577i | −0.168878 | − | 0.154607i | ||||
\(741\) | 15.5194i | 0.570118i | ||||||||
\(742\) | 18.2000 | + | 18.2000i | 0.668142 | + | 0.668142i | ||||
\(743\) | 13.6789 | + | 13.6789i | 0.501830 | + | 0.501830i | 0.912006 | − | 0.410176i | \(-0.134533\pi\) |
−0.410176 | + | 0.912006i | \(0.634533\pi\) | |||||||
\(744\) | 5.00496i | 0.183491i | ||||||||
\(745\) | −49.4079 | + | 2.17963i | −1.81017 | + | 0.0798555i | ||||
\(746\) | − | 28.4235i | − | 1.04066i | ||||||
\(747\) | −0.205133 | + | 0.205133i | −0.00750544 | + | 0.00750544i | ||||
\(748\) | 6.32156 | − | 6.32156i | 0.231139 | − | 0.231139i | ||||
\(749\) | 40.8561i | 1.49285i | ||||||||
\(750\) | 25.0501 | − | 3.33257i | 0.914701 | − | 0.121688i | ||||
\(751\) | − | 15.6373i | − | 0.570613i | −0.958436 | − | 0.285307i | \(-0.907905\pi\) | ||
0.958436 | − | 0.285307i | \(-0.0920954\pi\) | |||||||
\(752\) | −18.5209 | − | 18.5209i | −0.675386 | − | 0.675386i | ||||
\(753\) | −5.28960 | − | 5.28960i | −0.192764 | − | 0.192764i | ||||
\(754\) | − | 12.4672i | − | 0.454028i | ||||||
\(755\) | 25.9067 | − | 1.14287i | 0.942840 | − | 0.0415934i | ||||
\(756\) | − | 7.09531i | − | 0.258054i | ||||||
\(757\) | 4.50831 | − | 4.50831i | 0.163857 | − | 0.163857i | −0.620416 | − | 0.784273i | \(-0.713036\pi\) |
0.784273 | + | 0.620416i | \(0.213036\pi\) | |||||||
\(758\) | 21.3599 | + | 21.3599i | 0.775828 | + | 0.775828i | ||||
\(759\) | −3.71433 | + | 17.0206i | −0.134822 | + | 0.617808i | ||||
\(760\) | −17.1977 | + | 18.7851i | −0.623826 | + | 0.681407i | ||||
\(761\) | 21.8465 | 0.791934 | 0.395967 | − | 0.918265i | \(-0.370409\pi\) | ||||
0.395967 | + | 0.918265i | \(0.370409\pi\) | |||||||
\(762\) | 22.5652 | + | 22.5652i | 0.817451 | + | 0.817451i | ||||
\(763\) | 1.51109 | − | 1.51109i | 0.0547052 | − | 0.0547052i | ||||
\(764\) | −16.6037 | −0.600700 | ||||||||
\(765\) | 9.64819 | + | 8.83290i | 0.348831 | + | 0.319354i | ||||
\(766\) | − | 1.70721i | − | 0.0616838i | ||||||
\(767\) | −3.33833 | − | 3.33833i | −0.120540 | − | 0.120540i | ||||
\(768\) | −19.0926 | + | 19.0926i | −0.688945 | + | 0.688945i | ||||
\(769\) | 3.09789 | 0.111713 | 0.0558564 | − | 0.998439i | \(-0.482211\pi\) | ||||
0.0558564 | + | 0.998439i | \(0.482211\pi\) | |||||||
\(770\) | 0.537647 | + | 12.1874i | 0.0193754 | + | 0.439203i | ||||
\(771\) | 45.9579 | 1.65513 | ||||||||
\(772\) | −3.08266 | − | 3.08266i | −0.110947 | − | 0.110947i | ||||
\(773\) | −4.26685 | − | 4.26685i | −0.153468 | − | 0.153468i | 0.626197 | − | 0.779665i | \(-0.284611\pi\) |
−0.779665 | + | 0.626197i | \(0.784611\pi\) | |||||||
\(774\) | −2.84468 | −0.102250 | ||||||||
\(775\) | 4.15353 | − | 0.367181i | 0.149199 | − | 0.0131895i | ||||
\(776\) | 43.5238i | 1.56241i | ||||||||
\(777\) | 14.7904 | + | 14.7904i | 0.530601 | + | 0.530601i | ||||
\(778\) | −9.16103 | − | 9.16103i | −0.328439 | − | 0.328439i | ||||
\(779\) | −1.14824 | −0.0411398 | ||||||||
\(780\) | 6.14078 | − | 0.270901i | 0.219875 | − | 0.00969980i | ||||
\(781\) | − | 25.2561i | − | 0.903733i | ||||||
\(782\) | −21.9907 | − | 34.2678i | −0.786388 | − | 1.22541i | ||||
\(783\) | −15.1506 | + | 15.1506i | −0.541437 | + | 0.541437i | ||||
\(784\) | 1.41911i | 0.0506824i | ||||||||
\(785\) | 20.1827 | − | 22.0456i | 0.720352 | − | 0.786841i | ||||
\(786\) | −27.7222 | −0.988819 | ||||||||
\(787\) | 19.8446 | − | 19.8446i | 0.707383 | − | 0.707383i | −0.258601 | − | 0.965984i | \(-0.583262\pi\) |
0.965984 | + | 0.258601i | \(0.0832616\pi\) | |||||||
\(788\) | 7.22022 | − | 7.22022i | 0.257210 | − | 0.257210i | ||||
\(789\) | −26.8434 | −0.955649 | ||||||||
\(790\) | −2.60118 | − | 2.38137i | −0.0925458 | − | 0.0847255i | ||||
\(791\) | −19.5775 | −0.696095 | ||||||||
\(792\) | −3.24230 | + | 3.24230i | −0.115210 | + | 0.115210i | ||||
\(793\) | 19.1226 | + | 19.1226i | 0.679065 | + | 0.679065i | ||||
\(794\) | − | 7.85809i | − | 0.278873i | ||||||
\(795\) | 38.2837 | − | 1.68889i | 1.35778 | − | 0.0598987i | ||||
\(796\) | 9.33116i | 0.330734i | ||||||||
\(797\) | 8.00378 | − | 8.00378i | 0.283509 | − | 0.283509i | −0.550998 | − | 0.834507i | \(-0.685753\pi\) |
0.834507 | + | 0.550998i | \(0.185753\pi\) | |||||||
\(798\) | 14.9239 | − | 14.9239i | 0.528302 | − | 0.528302i | ||||
\(799\) | −84.8391 | −3.00139 | ||||||||
\(800\) | 13.5581 | + | 11.3557i | 0.479351 | + | 0.401484i | ||||
\(801\) | − | 8.66065i | − | 0.306009i | ||||||
\(802\) | −9.91242 | + | 9.91242i | −0.350020 | + | 0.350020i | ||||
\(803\) | −12.3439 | − | 12.3439i | −0.435606 | − | 0.435606i | ||||
\(804\) | −2.06317 | −0.0727625 | ||||||||
\(805\) | −26.6765 | − | 4.60037i | −0.940222 | − | 0.162142i | ||||
\(806\) | −2.08167 | −0.0733237 | ||||||||
\(807\) | −14.2378 | − | 14.2378i | −0.501193 | − | 0.501193i | ||||
\(808\) | 15.4017 | − | 15.4017i | 0.541831 | − | 0.541831i | ||||
\(809\) | − | 2.43398i | − | 0.0855741i | −0.999084 | − | 0.0427871i | \(-0.986376\pi\) | ||
0.999084 | − | 0.0427871i | \(-0.0136237\pi\) | |||||||
\(810\) | 20.5770 | + | 18.8382i | 0.723001 | + | 0.661906i | ||||
\(811\) | −30.3188 | −1.06464 | −0.532319 | − | 0.846544i | \(-0.678679\pi\) | ||||
−0.532319 | + | 0.846544i | \(0.678679\pi\) | |||||||
\(812\) | 5.84118 | − | 5.84118i | 0.204985 | − | 0.204985i | ||||
\(813\) | 9.42028 | − | 9.42028i | 0.330384 | − | 0.330384i | ||||
\(814\) | 9.18794i | 0.322037i | ||||||||
\(815\) | −21.7902 | + | 23.8014i | −0.763276 | + | 0.833728i | ||||
\(816\) | − | 32.2541i | − | 1.12912i | ||||||
\(817\) | −8.03000 | − | 8.03000i | −0.280934 | − | 0.280934i | ||||
\(818\) | 22.9357 | − | 22.9357i | 0.801928 | − | 0.801928i | ||||
\(819\) | −4.34165 | −0.151710 | ||||||||
\(820\) | 0.0200432 | + | 0.454340i | 0.000699940 | + | 0.0158662i | ||||
\(821\) | 51.4053 | 1.79406 | 0.897028 | − | 0.441973i | \(-0.145721\pi\) | ||||
0.897028 | + | 0.441973i | \(0.145721\pi\) | |||||||
\(822\) | 19.4820 | − | 19.4820i | 0.679511 | − | 0.679511i | ||||
\(823\) | −2.89805 | + | 2.89805i | −0.101020 | + | 0.101020i | −0.755810 | − | 0.654791i | \(-0.772757\pi\) |
0.654791 | + | 0.755810i | \(0.272757\pi\) | |||||||
\(824\) | −12.6459 | −0.440541 | ||||||||
\(825\) | 13.9241 | + | 11.6622i | 0.484775 | + | 0.406026i | ||||
\(826\) | 6.42051i | 0.223398i | ||||||||
\(827\) | 24.4729 | − | 24.4729i | 0.851004 | − | 0.851004i | −0.139252 | − | 0.990257i | \(-0.544470\pi\) |
0.990257 | + | 0.139252i | \(0.0444699\pi\) | |||||||
\(828\) | −1.35604 | − | 2.11309i | −0.0471256 | − | 0.0734349i | ||||
\(829\) | − | 36.4441i | − | 1.26576i | −0.774251 | − | 0.632878i | \(-0.781873\pi\) | ||
0.774251 | − | 0.632878i | \(-0.218127\pi\) | |||||||
\(830\) | −0.0414919 | − | 0.940539i | −0.00144020 | − | 0.0326466i | ||||
\(831\) | −13.1971 | −0.457803 | ||||||||
\(832\) | −13.1237 | − | 13.1237i | −0.454984 | − | 0.454984i | ||||
\(833\) | 3.25027 | + | 3.25027i | 0.112615 | + | 0.112615i | ||||
\(834\) | − | 27.9268i | − | 0.967028i | ||||||
\(835\) | 6.96545 | + | 6.37685i | 0.241049 | + | 0.220680i | ||||
\(836\) | −4.51696 | −0.156222 | ||||||||
\(837\) | 2.52972 | + | 2.52972i | 0.0874400 | + | 0.0874400i | ||||
\(838\) | 10.2112 | + | 10.2112i | 0.352739 | + | 0.352739i | ||||
\(839\) | 26.5753 | 0.917481 | 0.458741 | − | 0.888570i | \(-0.348301\pi\) | ||||
0.458741 | + | 0.888570i | \(0.348301\pi\) | |||||||
\(840\) | −24.9863 | − | 22.8749i | −0.862110 | − | 0.789259i | ||||
\(841\) | 4.05473 | 0.139818 | ||||||||
\(842\) | 22.8501 | − | 22.8501i | 0.787465 | − | 0.787465i | ||||
\(843\) | 25.8290 | + | 25.8290i | 0.889597 | + | 0.889597i | ||||
\(844\) | 0.358579i | 0.0123428i | ||||||||
\(845\) | −0.824522 | − | 18.6903i | −0.0283644 | − | 0.642966i | ||||
\(846\) | 10.7375 | 0.369164 | ||||||||
\(847\) | 13.4347 | − | 13.4347i | 0.461622 | − | 0.461622i | ||||
\(848\) | −14.0528 | − | 14.0528i | −0.482577 | − | 0.482577i | ||||
\(849\) | −24.9003 | −0.854576 | ||||||||
\(850\) | −42.2855 | + | 3.73813i | −1.45038 | + | 0.128217i | ||||
\(851\) | −19.9194 | − | 4.34692i | −0.682827 | − | 0.149010i | ||||
\(852\) | 12.2374 | + | 12.2374i | 0.419246 | + | 0.419246i | ||||
\(853\) | −6.91723 | + | 6.91723i | −0.236841 | + | 0.236841i | −0.815541 | − | 0.578699i | \(-0.803560\pi\) |
0.578699 | + | 0.815541i | \(0.303560\pi\) | |||||||
\(854\) | − | 36.7780i | − | 1.25852i | ||||||
\(855\) | −0.291277 | − | 6.60267i | −0.00996145 | − | 0.225806i | ||||
\(856\) | − | 49.8357i | − | 1.70335i | ||||||
\(857\) | 11.5433 | + | 11.5433i | 0.394312 | + | 0.394312i | 0.876221 | − | 0.481909i | \(-0.160057\pi\) |
−0.481909 | + | 0.876221i | \(0.660057\pi\) | |||||||
\(858\) | −6.41168 | − | 6.41168i | −0.218891 | − | 0.218891i | ||||
\(859\) | 4.02478i | 0.137324i | 0.997640 | + | 0.0686618i | \(0.0218729\pi\) | ||||
−0.997640 | + | 0.0686618i | \(0.978127\pi\) | |||||||
\(860\) | −3.03719 | + | 3.31752i | −0.103567 | + | 0.113127i | ||||
\(861\) | − | 1.52728i | − | 0.0520497i | ||||||
\(862\) | 7.16308 | − | 7.16308i | 0.243976 | − | 0.243976i | ||||
\(863\) | −1.24478 | + | 1.24478i | −0.0423729 | + | 0.0423729i | −0.727976 | − | 0.685603i | \(-0.759539\pi\) |
0.685603 | + | 0.727976i | \(0.259539\pi\) | |||||||
\(864\) | 15.1738i | 0.516224i | ||||||||
\(865\) | −16.4893 | + | 18.0113i | −0.560654 | + | 0.612403i | ||||
\(866\) | 40.5760i | 1.37883i | ||||||||
\(867\) | −50.4438 | − | 50.4438i | −1.71316 | − | 1.71316i | ||||
\(868\) | −0.975314 | − | 0.975314i | −0.0331043 | − | 0.0331043i | ||||
\(869\) | − | 2.53468i | − | 0.0859831i | ||||||
\(870\) | 1.11252 | + | 25.2186i | 0.0377180 | + | 0.854991i | ||||
\(871\) | − | 3.47750i | − | 0.117830i | ||||||
\(872\) | −1.84321 | + | 1.84321i | −0.0624188 | + | 0.0624188i | ||||
\(873\) | −7.98641 | − | 7.98641i | −0.270299 | − | 0.270299i | ||||
\(874\) | −4.38618 | + | 20.0993i | −0.148365 | + | 0.679868i | ||||
\(875\) | −17.1504 | + | 22.4139i | −0.579790 | + | 0.757728i | ||||
\(876\) | 11.9620 | 0.404160 | ||||||||
\(877\) | −6.27788 | − | 6.27788i | −0.211989 | − | 0.211989i | 0.593123 | − | 0.805112i | \(-0.297895\pi\) |
−0.805112 | + | 0.593123i | \(0.797895\pi\) | |||||||
\(878\) | 22.0139 | − | 22.0139i | 0.742932 | − | 0.742932i | ||||
\(879\) | 20.4255 | 0.688934 | ||||||||
\(880\) | −0.415136 | − | 9.41031i | −0.0139942 | − | 0.317221i | ||||
\(881\) | 18.4565i | 0.621814i | 0.950440 | + | 0.310907i | \(0.100633\pi\) | ||||
−0.950440 | + | 0.310907i | \(0.899367\pi\) | |||||||
\(882\) | −0.411366 | − | 0.411366i | −0.0138514 | − | 0.0138514i | ||||
\(883\) | 3.42570 | − | 3.42570i | 0.115284 | − | 0.115284i | −0.647111 | − | 0.762395i | \(-0.724023\pi\) |
0.762395 | + | 0.647111i | \(0.224023\pi\) | |||||||
\(884\) | −10.3254 | −0.347282 | ||||||||
\(885\) | 7.05068 | + | 6.45489i | 0.237006 | + | 0.216979i | ||||
\(886\) | 37.6031 | 1.26330 | ||||||||
\(887\) | −32.7858 | − | 32.7858i | −1.10084 | − | 1.10084i | −0.994310 | − | 0.106528i | \(-0.966027\pi\) |
−0.106528 | − | 0.994310i | \(-0.533973\pi\) | |||||||
\(888\) | −18.0410 | − | 18.0410i | −0.605418 | − | 0.605418i | ||||
\(889\) | −35.6396 | −1.19531 | ||||||||
\(890\) | 20.7305 | + | 18.9787i | 0.694887 | + | 0.636167i | ||||
\(891\) | 20.0509i | 0.671731i | ||||||||
\(892\) | −5.53074 | − | 5.53074i | −0.185183 | − | 0.185183i | ||||
\(893\) | 30.3101 | + | 30.3101i | 1.01429 | + | 1.01429i | ||||
\(894\) | −49.9917 | −1.67197 | ||||||||
\(895\) | 1.25974 | + | 28.5558i | 0.0421084 | + | 0.954514i | ||||
\(896\) | 7.38307i | 0.246651i | ||||||||
\(897\) | 16.9339 | − | 10.8670i | 0.565406 | − | 0.362839i | ||||
\(898\) | 6.29762 | − | 6.29762i | 0.210154 | − | 0.210154i | ||||
\(899\) | 4.16516i | 0.138916i | ||||||||
\(900\) | −2.60749 | + | 0.230508i | −0.0869165 | + | 0.00768359i | ||||
\(901\) | −64.3723 | −2.14455 | ||||||||
\(902\) | 0.474383 | − | 0.474383i | 0.0157952 | − | 0.0157952i | ||||
\(903\) | 10.6808 | − | 10.6808i | 0.355435 | − | 0.355435i | ||||
\(904\) | 23.8803 | 0.794247 | ||||||||
\(905\) | 0.262067 | + | 5.94054i | 0.00871140 | + | 0.197470i | ||||
\(906\) | 26.2128 | 0.870861 | ||||||||
\(907\) | −0.435105 | + | 0.435105i | −0.0144474 | + | 0.0144474i | −0.714294 | − | 0.699846i | \(-0.753252\pi\) |
0.699846 | + | 0.714294i | \(0.253252\pi\) | |||||||
\(908\) | 1.87717 | + | 1.87717i | 0.0622962 | + | 0.0622962i | ||||
\(909\) | 5.65228i | 0.187474i | ||||||||
\(910\) | 9.51416 | − | 10.3923i | 0.315391 | − | 0.344503i | ||||
\(911\) | 16.4896i | 0.546324i | 0.961968 | + | 0.273162i | \(0.0880695\pi\) | ||||
−0.961968 | + | 0.273162i | \(0.911931\pi\) | |||||||
\(912\) | −11.5233 | + | 11.5233i | −0.381575 | + | 0.381575i | ||||
\(913\) | 0.478462 | − | 0.478462i | 0.0158348 | − | 0.0158348i | ||||
\(914\) | −1.29355 | −0.0427869 | ||||||||
\(915\) | −40.3878 | − | 36.9749i | −1.33518 | − | 1.22235i | ||||
\(916\) | 11.0409i | 0.364802i | ||||||||
\(917\) | 21.8923 | − | 21.8923i | 0.722948 | − | 0.722948i | ||||
\(918\) | −25.7541 | − | 25.7541i | −0.850013 | − | 0.850013i | ||||
\(919\) | 22.8467 | 0.753643 | 0.376822 | − | 0.926286i | \(-0.377017\pi\) | ||||
0.376822 | + | 0.926286i | \(0.377017\pi\) | |||||||
\(920\) | 32.5395 | + | 5.61146i | 1.07280 | + | 0.185004i | ||||
\(921\) | −20.7845 | −0.684872 | ||||||||
\(922\) | −23.2470 | − | 23.2470i | −0.765600 | − | 0.765600i | ||||
\(923\) | −20.6263 | + | 20.6263i | −0.678921 | + | 0.678921i | ||||
\(924\) | − | 6.00807i | − | 0.197651i | ||||||
\(925\) | −13.6484 | + | 16.2955i | −0.448757 | + | 0.535793i | ||||
\(926\) | 31.7114 | 1.04210 | ||||||||
\(927\) | 2.32046 | − | 2.32046i | 0.0762139 | − | 0.0762139i | ||||
\(928\) | −12.4918 | + | 12.4918i | −0.410063 | + | 0.410063i | ||||
\(929\) | − | 44.1020i | − | 1.44694i | −0.690355 | − | 0.723470i | \(-0.742546\pi\) | ||
0.690355 | − | 0.723470i | \(-0.257454\pi\) | |||||||
\(930\) | 4.21080 | − | 0.185760i | 0.138078 | − | 0.00609130i | ||||
\(931\) | − | 2.32242i | − | 0.0761144i | ||||||
\(932\) | −5.04303 | − | 5.04303i | −0.165190 | − | 0.165190i | ||||
\(933\) | 0.936494 | − | 0.936494i | 0.0306594 | − | 0.0306594i | ||||
\(934\) | 24.0438 | 0.786736 | ||||||||
\(935\) | −22.5039 | − | 20.6022i | −0.735955 | − | 0.673765i | ||||
\(936\) | 5.29587 | 0.173101 | ||||||||
\(937\) | −1.75039 | + | 1.75039i | −0.0571827 | + | 0.0571827i | −0.735120 | − | 0.677937i | \(-0.762874\pi\) |
0.677937 | + | 0.735120i | \(0.262874\pi\) | |||||||
\(938\) | −3.34408 | + | 3.34408i | −0.109188 | + | 0.109188i | ||||
\(939\) | −12.2783 | −0.400686 | ||||||||
\(940\) | 11.4642 | − | 12.5224i | 0.373921 | − | 0.408434i | ||||
\(941\) | − | 0.294994i | − | 0.00961654i | −0.999988 | − | 0.00480827i | \(-0.998469\pi\) | ||
0.999988 | − | 0.00480827i | \(-0.00153053\pi\) | |||||||
\(942\) | 21.3636 | − | 21.3636i | 0.696065 | − | 0.696065i | ||||
\(943\) | 0.804022 | + | 1.25289i | 0.0261826 | + | 0.0407998i | ||||
\(944\) | − | 4.95750i | − | 0.161353i | ||||||
\(945\) | −24.1911 | + | 1.06719i | −0.786937 | + | 0.0347157i | ||||
\(946\) | 6.63505 | 0.215724 | ||||||||
\(947\) | 21.6094 | + | 21.6094i | 0.702212 | + | 0.702212i | 0.964885 | − | 0.262673i | \(-0.0846041\pi\) |
−0.262673 | + | 0.964885i | \(0.584604\pi\) | |||||||
\(948\) | 1.22814 | + | 1.22814i | 0.0398880 | + | 0.0398880i | ||||
\(949\) | 20.1621i | 0.654490i | ||||||||
\(950\) | 16.4427 | + | 13.7717i | 0.533471 | + | 0.446812i | ||||
\(951\) | −37.1844 | −1.20579 | ||||||||
\(952\) | 40.2382 | + | 40.2382i | 1.30413 | + | 1.30413i | ||||
\(953\) | −22.4603 | − | 22.4603i | −0.727560 | − | 0.727560i | 0.242573 | − | 0.970133i | \(-0.422009\pi\) |
−0.970133 | + | 0.242573i | \(0.922009\pi\) | |||||||
\(954\) | 8.14719 | 0.263775 | ||||||||
\(955\) | 2.49732 | + | 56.6094i | 0.0808115 | + | 1.83184i | ||||
\(956\) | 12.3183 | 0.398404 | ||||||||
\(957\) | −12.8290 | + | 12.8290i | −0.414702 | + | 0.414702i | ||||
\(958\) | −15.1368 | − | 15.1368i | −0.489048 | − | 0.489048i | ||||
\(959\) | 30.7699i | 0.993613i | ||||||||
\(960\) | 27.7178 | + | 25.3756i | 0.894589 | + | 0.818994i | ||||
\(961\) | −30.3045 | −0.977566 | ||||||||
\(962\) | 7.50365 | − | 7.50365i | 0.241928 | − | 0.241928i | ||||
\(963\) | 9.14460 | + | 9.14460i | 0.294681 | + | 0.294681i | ||||
\(964\) | −1.40891 | −0.0453779 | ||||||||
\(965\) | −10.0465 | + | 10.9738i | −0.323409 | + | 0.353260i | ||||
\(966\) | −26.7343 | − | 5.83411i | −0.860163 | − | 0.187710i | ||||
\(967\) | −13.3362 | − | 13.3362i | −0.428863 | − | 0.428863i | 0.459378 | − | 0.888241i | \(-0.348072\pi\) |
−0.888241 | + | 0.459378i | \(0.848072\pi\) | |||||||
\(968\) | −16.3874 | + | 16.3874i | −0.526712 | + | 0.526712i | ||||
\(969\) | 52.7852i | 1.69570i | ||||||||
\(970\) | 36.6177 | − | 1.61539i | 1.17572 | − | 0.0518671i | ||||
\(971\) | − | 38.1082i | − | 1.22295i | −0.791263 | − | 0.611475i | \(-0.790576\pi\) | ||
0.791263 | − | 0.611475i | \(-0.209424\pi\) | |||||||
\(972\) | −3.75275 | − | 3.75275i | −0.120369 | − | 0.120369i | ||||
\(973\) | 22.0539 | + | 22.0539i | 0.707016 | + | 0.707016i | ||||
\(974\) | − | 6.66112i | − | 0.213436i | ||||||
\(975\) | −1.84725 | − | 20.8960i | −0.0591592 | − | 0.669206i | ||||
\(976\) | 28.3976i | 0.908984i | ||||||||
\(977\) | 19.6996 | − | 19.6996i | 0.630246 | − | 0.630246i | −0.317883 | − | 0.948130i | \(-0.602972\pi\) |
0.948130 | + | 0.317883i | \(0.102972\pi\) | |||||||
\(978\) | −23.0652 | + | 23.0652i | −0.737543 | + | 0.737543i | ||||
\(979\) | 20.2005i | 0.645610i | ||||||||
\(980\) | −0.918949 | + | 0.0405395i | −0.0293548 | + | 0.00129499i | ||||
\(981\) | − | 0.676438i | − | 0.0215970i | ||||||
\(982\) | 12.1832 | + | 12.1832i | 0.388781 | + | 0.388781i | ||||
\(983\) | −15.6702 | − | 15.6702i | −0.499801 | − | 0.499801i | 0.411575 | − | 0.911376i | \(-0.364979\pi\) |
−0.911376 | + | 0.411575i | \(0.864979\pi\) | |||||||
\(984\) | 1.86296i | 0.0593889i | ||||||||
\(985\) | −25.7030 | − | 23.5310i | −0.818965 | − | 0.749761i | ||||
\(986\) | − | 42.4039i | − | 1.35042i | ||||||
\(987\) | −40.3159 | + | 40.3159i | −1.28327 | + | 1.28327i | ||||
\(988\) | 3.68893 | + | 3.68893i | 0.117360 | + | 0.117360i | ||||
\(989\) | −3.13911 | + | 14.3847i | −0.0998180 | + | 0.457407i | ||||
\(990\) | 2.84817 | + | 2.60749i | 0.0905208 | + | 0.0828716i | ||||
\(991\) | 16.6072 | 0.527545 | 0.263773 | − | 0.964585i | \(-0.415033\pi\) | ||||
0.263773 | + | 0.964585i | \(0.415033\pi\) | |||||||
\(992\) | 2.08578 | + | 2.08578i | 0.0662235 | + | 0.0662235i | ||||
\(993\) | −21.0482 | + | 21.0482i | −0.667944 | + | 0.667944i | ||||
\(994\) | 39.6698 | 1.25825 | ||||||||
\(995\) | 31.8141 | − | 1.40348i | 1.00858 | − | 0.0444933i | ||||
\(996\) | 0.463661i | 0.0146917i | ||||||||
\(997\) | 16.3178 | + | 16.3178i | 0.516788 | + | 0.516788i | 0.916598 | − | 0.399810i | \(-0.130924\pi\) |
−0.399810 | + | 0.916598i | \(0.630924\pi\) | |||||||
\(998\) | 2.93570 | − | 2.93570i | 0.0929279 | − | 0.0929279i | ||||
\(999\) | −18.2374 | −0.577007 |
(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 | 115.2.e.a.22.3 | ✓ | 20 | |
5.2 | odd | 4 | 575.2.e.d.68.8 | 20 | |||
5.3 | odd | 4 | inner | 115.2.e.a.68.4 | yes | 20 | |
5.4 | even | 2 | 575.2.e.d.482.7 | 20 | |||
23.22 | odd | 2 | inner | 115.2.e.a.22.4 | yes | 20 | |
115.22 | even | 4 | 575.2.e.d.68.7 | 20 | |||
115.68 | even | 4 | inner | 115.2.e.a.68.3 | yes | 20 | |
115.114 | odd | 2 | 575.2.e.d.482.8 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.e.a.22.3 | ✓ | 20 | 1.1 | even | 1 | trivial | |
115.2.e.a.22.4 | yes | 20 | 23.22 | odd | 2 | inner | |
115.2.e.a.68.3 | yes | 20 | 115.68 | even | 4 | inner | |
115.2.e.a.68.4 | yes | 20 | 5.3 | odd | 4 | inner | |
575.2.e.d.68.7 | 20 | 115.22 | even | 4 | |||
575.2.e.d.68.8 | 20 | 5.2 | odd | 4 | |||
575.2.e.d.482.7 | 20 | 5.4 | even | 2 | |||
575.2.e.d.482.8 | 20 | 115.114 | odd | 2 |