Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,2,Mod(74,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.74");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.k (of order \(6\), degree \(2\), 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: | \(1.39738203537\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 74.4 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.74 |
Dual form | 175.2.k.a.149.4 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.09077 | − | 1.20711i | 1.47840 | − | 0.853553i | 0.478696 | − | 0.877981i | \(-0.341110\pi\) |
0.999702 | + | 0.0244272i | \(0.00777619\pi\) | |||||||
\(3\) | −0.358719 | − | 0.207107i | −0.207107 | − | 0.119573i | 0.392859 | − | 0.919599i | \(-0.371486\pi\) |
−0.599966 | + | 0.800025i | \(0.704819\pi\) | |||||||
\(4\) | 1.91421 | − | 3.31552i | 0.957107 | − | 1.65776i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.358719 | + | 2.62132i | −0.135583 | + | 0.990766i | ||||
\(8\) | − | 4.41421i | − | 1.56066i | ||||||
\(9\) | −1.41421 | − | 2.44949i | −0.471405 | − | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.414214 | − | 0.717439i | 0.124890 | − | 0.216316i | −0.796800 | − | 0.604243i | \(-0.793476\pi\) |
0.921690 | + | 0.387927i | \(0.126809\pi\) | |||||||
\(12\) | −1.37333 | + | 0.792893i | −0.396447 | + | 0.228889i | ||||
\(13\) | 4.82843i | 1.33916i | 0.742738 | + | 0.669582i | \(0.233527\pi\) | ||||
−0.742738 | + | 0.669582i | \(0.766473\pi\) | |||||||
\(14\) | 2.41421 | + | 5.91359i | 0.645226 | + | 1.58047i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | −4.18154 | − | 2.41421i | −1.01417 | − | 0.585533i | −0.101762 | − | 0.994809i | \(-0.532448\pi\) |
−0.912411 | + | 0.409276i | \(0.865781\pi\) | |||||||
\(18\) | −5.91359 | − | 3.41421i | −1.39385 | − | 0.804738i | ||||
\(19\) | 1.41421 | + | 2.44949i | 0.324443 | + | 0.561951i | 0.981399 | − | 0.191977i | \(-0.0614899\pi\) |
−0.656957 | + | 0.753928i | \(0.728157\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.671573 | − | 0.866025i | 0.146549 | − | 0.188982i | ||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | −0.358719 | + | 0.207107i | −0.0747982 | + | 0.0431847i | −0.536933 | − | 0.843625i | \(-0.680417\pi\) |
0.462134 | + | 0.886810i | \(0.347084\pi\) | |||||||
\(24\) | −0.914214 | + | 1.58346i | −0.186613 | + | 0.323223i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.82843 | + | 10.0951i | 1.14305 | + | 1.97982i | ||||
\(27\) | 2.41421i | 0.464616i | ||||||||
\(28\) | 8.00436 | + | 6.20711i | 1.51268 | + | 1.17303i | ||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | − | 5.19615i | 0.538816 | − | 0.933257i | −0.460152 | − | 0.887840i | \(-0.652205\pi\) |
0.998968 | − | 0.0454165i | \(-0.0144615\pi\) | |||||||
\(32\) | 1.37333 | + | 0.792893i | 0.242773 | + | 0.140165i | ||||
\(33\) | −0.297173 | + | 0.171573i | −0.0517312 | + | 0.0298670i | ||||
\(34\) | −11.6569 | −1.99913 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10.8284 | −1.80474 | ||||||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | 5.91359 | + | 3.41421i | 0.959311 | + | 0.553859i | ||||
\(39\) | 1.00000 | − | 1.73205i | 0.160128 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.82843 | −1.22259 | −0.611297 | − | 0.791401i | \(-0.709352\pi\) | ||||
−0.611297 | + | 0.791401i | \(0.709352\pi\) | |||||||
\(42\) | 0.358719 | − | 2.62132i | 0.0553516 | − | 0.404479i | ||||
\(43\) | − | 3.58579i | − | 0.546827i | −0.961897 | − | 0.273414i | \(-0.911847\pi\) | ||
0.961897 | − | 0.273414i | \(-0.0881528\pi\) | |||||||
\(44\) | −1.58579 | − | 2.74666i | −0.239066 | − | 0.414075i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.500000 | + | 0.866025i | −0.0737210 | + | 0.127688i | ||||
\(47\) | 1.73205 | − | 1.00000i | 0.252646 | − | 0.145865i | −0.368329 | − | 0.929695i | \(-0.620070\pi\) |
0.620975 | + | 0.783830i | \(0.286737\pi\) | |||||||
\(48\) | 1.24264i | 0.179360i | ||||||||
\(49\) | −6.74264 | − | 1.88064i | −0.963234 | − | 0.268662i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | + | 1.73205i | 0.140028 | + | 0.242536i | ||||
\(52\) | 16.0087 | + | 9.24264i | 2.22001 | + | 1.28172i | ||||
\(53\) | −1.01461 | − | 0.585786i | −0.139368 | − | 0.0804640i | 0.428695 | − | 0.903449i | \(-0.358974\pi\) |
−0.568063 | + | 0.822985i | \(0.692307\pi\) | |||||||
\(54\) | 2.91421 | + | 5.04757i | 0.396574 | + | 0.686887i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.5711 | + | 1.58346i | 1.54625 | + | 0.211599i | ||||
\(57\) | − | 1.17157i | − | 0.155179i | ||||||
\(58\) | 2.09077 | − | 1.20711i | 0.274532 | − | 0.158501i | ||||
\(59\) | 2.24264 | − | 3.88437i | 0.291967 | − | 0.505702i | −0.682308 | − | 0.731065i | \(-0.739024\pi\) |
0.974275 | + | 0.225363i | \(0.0723569\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.74264 | − | 4.75039i | −0.351159 | − | 0.608226i | 0.635294 | − | 0.772271i | \(-0.280879\pi\) |
−0.986453 | + | 0.164045i | \(0.947546\pi\) | |||||||
\(62\) | − | 14.4853i | − | 1.83963i | ||||||
\(63\) | 6.92820 | − | 2.82843i | 0.872872 | − | 0.356348i | ||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.414214 | + | 0.717439i | −0.0509862 | + | 0.0883106i | ||||
\(67\) | −8.30153 | − | 4.79289i | −1.01419 | − | 0.585545i | −0.101777 | − | 0.994807i | \(-0.532453\pi\) |
−0.912417 | + | 0.409262i | \(0.865786\pi\) | |||||||
\(68\) | −16.0087 | + | 9.24264i | −1.94134 | + | 1.12083i | ||||
\(69\) | 0.171573 | 0.0206549 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.48528 | 0.532305 | 0.266152 | − | 0.963931i | \(-0.414248\pi\) | ||||
0.266152 | + | 0.963931i | \(0.414248\pi\) | |||||||
\(72\) | −10.8126 | + | 6.24264i | −1.27427 | + | 0.735702i | ||||
\(73\) | −0.717439 | − | 0.414214i | −0.0839699 | − | 0.0484800i | 0.457427 | − | 0.889247i | \(-0.348771\pi\) |
−0.541397 | + | 0.840767i | \(0.682104\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.8284 | 1.24211 | ||||||||
\(77\) | 1.73205 | + | 1.34315i | 0.197386 | + | 0.153066i | ||||
\(78\) | − | 4.82843i | − | 0.546712i | ||||||
\(79\) | 7.41421 | + | 12.8418i | 0.834164 | + | 1.44481i | 0.894709 | + | 0.446649i | \(0.147383\pi\) |
−0.0605449 | + | 0.998165i | \(0.519284\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.74264 | + | 6.48244i | −0.415849 | + | 0.720272i | ||||
\(82\) | −16.3674 | + | 9.44975i | −1.80748 | + | 1.04355i | ||||
\(83\) | − | 13.7279i | − | 1.50684i | −0.657542 | − | 0.753418i | \(-0.728404\pi\) | ||
0.657542 | − | 0.753418i | \(-0.271596\pi\) | |||||||
\(84\) | −1.58579 | − | 3.88437i | −0.173023 | − | 0.423819i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.32843 | − | 7.49706i | −0.466746 | − | 0.808428i | ||||
\(87\) | −0.358719 | − | 0.207107i | −0.0384588 | − | 0.0222042i | ||||
\(88\) | −3.16693 | − | 1.82843i | −0.337596 | − | 0.194911i | ||||
\(89\) | −4.32843 | − | 7.49706i | −0.458812 | − | 0.794686i | 0.540086 | − | 0.841610i | \(-0.318392\pi\) |
−0.998898 | + | 0.0469234i | \(0.985058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.6569 | − | 1.73205i | −1.32680 | − | 0.181568i | ||||
\(92\) | 1.58579i | 0.165330i | ||||||||
\(93\) | −2.15232 | + | 1.24264i | −0.223185 | + | 0.128856i | ||||
\(94\) | 2.41421 | − | 4.18154i | 0.249007 | − | 0.431293i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.328427 | − | 0.568852i | −0.0335200 | − | 0.0580583i | ||||
\(97\) | 11.6569i | 1.18357i | 0.806094 | + | 0.591787i | \(0.201577\pi\) | ||||
−0.806094 | + | 0.591787i | \(0.798423\pi\) | |||||||
\(98\) | −16.3674 | + | 4.20711i | −1.65336 | + | 0.424982i | ||||
\(99\) | −2.34315 | −0.235495 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.15685 | − | 8.93193i | 0.513126 | − | 0.888761i | −0.486758 | − | 0.873537i | \(-0.661821\pi\) |
0.999884 | − | 0.0152237i | \(-0.00484604\pi\) | |||||||
\(102\) | 4.18154 | + | 2.41421i | 0.414034 | + | 0.239043i | ||||
\(103\) | 2.09077 | − | 1.20711i | 0.206010 | − | 0.118940i | −0.393446 | − | 0.919348i | \(-0.628717\pi\) |
0.599456 | + | 0.800408i | \(0.295384\pi\) | |||||||
\(104\) | 21.3137 | 2.08998 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.82843 | −0.274721 | ||||||||
\(107\) | 9.73641 | − | 5.62132i | 0.941255 | − | 0.543434i | 0.0509012 | − | 0.998704i | \(-0.483791\pi\) |
0.890353 | + | 0.455270i | \(0.150457\pi\) | |||||||
\(108\) | 8.00436 | + | 4.62132i | 0.770220 | + | 0.444687i | ||||
\(109\) | −6.74264 | + | 11.6786i | −0.645828 | + | 1.11861i | 0.338282 | + | 0.941045i | \(0.390154\pi\) |
−0.984110 | + | 0.177562i | \(0.943179\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.34847 | − | 3.00000i | 0.694365 | − | 0.283473i | ||||
\(113\) | 4.48528i | 0.421940i | 0.977493 | + | 0.210970i | \(0.0676622\pi\) | ||||
−0.977493 | + | 0.210970i | \(0.932338\pi\) | |||||||
\(114\) | −1.41421 | − | 2.44949i | −0.132453 | − | 0.229416i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.91421 | − | 3.31552i | 0.177730 | − | 0.307838i | ||||
\(117\) | 11.8272 | − | 6.82843i | 1.09342 | − | 0.631288i | ||||
\(118\) | − | 10.8284i | − | 0.996838i | ||||||
\(119\) | 7.82843 | − | 10.0951i | 0.717631 | − | 0.925419i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.15685 | + | 8.93193i | 0.468805 | + | 0.811994i | ||||
\(122\) | −11.4685 | − | 6.62132i | −1.03831 | − | 0.599466i | ||||
\(123\) | 2.80821 | + | 1.62132i | 0.253208 | + | 0.146190i | ||||
\(124\) | −11.4853 | − | 19.8931i | −1.03141 | − | 1.78645i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 11.0711 | − | 14.2767i | 0.986289 | − | 1.27187i | ||||
\(127\) | − | 9.31371i | − | 0.826458i | −0.910627 | − | 0.413229i | \(-0.864401\pi\) | ||
0.910627 | − | 0.413229i | \(-0.135599\pi\) | |||||||
\(128\) | 17.8023 | − | 10.2782i | 1.57352 | − | 0.908471i | ||||
\(129\) | −0.742641 | + | 1.28629i | −0.0653859 | + | 0.113252i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.65685 | + | 16.7262i | 0.843723 | + | 1.46137i | 0.886725 | + | 0.462297i | \(0.152974\pi\) |
−0.0430021 | + | 0.999075i | \(0.513692\pi\) | |||||||
\(132\) | 1.31371i | 0.114344i | ||||||||
\(133\) | −6.92820 | + | 2.82843i | −0.600751 | + | 0.245256i | ||||
\(134\) | −23.1421 | −1.99918 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.6569 | + | 18.4582i | −0.913818 | + | 1.58278i | ||||
\(137\) | 8.36308 | + | 4.82843i | 0.714506 | + | 0.412520i | 0.812727 | − | 0.582644i | \(-0.197982\pi\) |
−0.0982211 | + | 0.995165i | \(0.531315\pi\) | |||||||
\(138\) | 0.358719 | − | 0.207107i | 0.0305362 | − | 0.0176301i | ||||
\(139\) | 16.1421 | 1.36916 | 0.684579 | − | 0.728939i | \(-0.259986\pi\) | ||||
0.684579 | + | 0.728939i | \(0.259986\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.828427 | −0.0697661 | ||||||||
\(142\) | 9.37769 | − | 5.41421i | 0.786959 | − | 0.454351i | ||||
\(143\) | 3.46410 | + | 2.00000i | 0.289683 | + | 0.167248i | ||||
\(144\) | −4.24264 | + | 7.34847i | −0.353553 | + | 0.612372i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 2.02922 | + | 2.07107i | 0.167368 | + | 0.170819i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.08579 | − | 1.88064i | −0.0889511 | − | 0.154068i | 0.818117 | − | 0.575052i | \(-0.195018\pi\) |
−0.907068 | + | 0.420984i | \(0.861685\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.82843 | + | 10.0951i | −0.474311 | + | 0.821530i | −0.999567 | − | 0.0294137i | \(-0.990636\pi\) |
0.525257 | + | 0.850944i | \(0.323969\pi\) | |||||||
\(152\) | 10.8126 | − | 6.24264i | 0.877015 | − | 0.506345i | ||||
\(153\) | 13.6569i | 1.10409i | ||||||||
\(154\) | 5.24264 | + | 0.717439i | 0.422464 | + | 0.0578129i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.82843 | − | 6.63103i | −0.306519 | − | 0.530907i | ||||
\(157\) | −14.9941 | − | 8.65685i | −1.19666 | − | 0.690892i | −0.236851 | − | 0.971546i | \(-0.576115\pi\) |
−0.959809 | + | 0.280654i | \(0.909449\pi\) | |||||||
\(158\) | 31.0028 | + | 17.8995i | 2.46645 | + | 1.42401i | ||||
\(159\) | 0.242641 | + | 0.420266i | 0.0192427 | + | 0.0333293i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.414214 | − | 1.01461i | −0.0326446 | − | 0.0799626i | ||||
\(162\) | 18.0711i | 1.41980i | ||||||||
\(163\) | −10.6895 | + | 6.17157i | −0.837265 | + | 0.483395i | −0.856333 | − | 0.516423i | \(-0.827263\pi\) |
0.0190689 | + | 0.999818i | \(0.493930\pi\) | |||||||
\(164\) | −14.9853 | + | 25.9553i | −1.17015 | + | 2.02677i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.5711 | − | 28.7019i | −1.28616 | − | 2.22770i | ||||
\(167\) | 22.4142i | 1.73446i | 0.497904 | + | 0.867232i | \(0.334103\pi\) | ||||
−0.497904 | + | 0.867232i | \(0.665897\pi\) | |||||||
\(168\) | −3.82282 | − | 2.96447i | −0.294937 | − | 0.228714i | ||||
\(169\) | −10.3137 | −0.793362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | − | 6.92820i | 0.305888 | − | 0.529813i | ||||
\(172\) | −11.8887 | − | 6.86396i | −0.906507 | − | 0.523372i | ||||
\(173\) | −2.86976 | + | 1.65685i | −0.218183 | + | 0.125968i | −0.605109 | − | 0.796143i | \(-0.706870\pi\) |
0.386925 | + | 0.922111i | \(0.373537\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.48528 | −0.187335 | ||||||||
\(177\) | −1.60896 | + | 0.928932i | −0.120937 | + | 0.0698228i | ||||
\(178\) | −18.0995 | − | 10.4497i | −1.35661 | − | 0.783242i | ||||
\(179\) | −5.00000 | + | 8.66025i | −0.373718 | + | 0.647298i | −0.990134 | − | 0.140122i | \(-0.955250\pi\) |
0.616417 | + | 0.787420i | \(0.288584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.65685 | 0.197482 | 0.0987412 | − | 0.995113i | \(-0.468518\pi\) | ||||
0.0987412 | + | 0.995113i | \(0.468518\pi\) | |||||||
\(182\) | −28.5533 | + | 11.6569i | −2.11651 | + | 0.864064i | ||||
\(183\) | 2.27208i | 0.167957i | ||||||||
\(184\) | 0.914214 | + | 1.58346i | 0.0673967 | + | 0.116735i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.00000 | + | 5.19615i | −0.219971 | + | 0.381000i | ||||
\(187\) | −3.46410 | + | 2.00000i | −0.253320 | + | 0.146254i | ||||
\(188\) | − | 7.65685i | − | 0.558433i | ||||||
\(189\) | −6.32843 | − | 0.866025i | −0.460325 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.41421 | + | 11.1097i | 0.464116 | + | 0.803873i | 0.999161 | − | 0.0409507i | \(-0.0130387\pi\) |
−0.535045 | + | 0.844824i | \(0.679705\pi\) | |||||||
\(192\) | −3.52565 | − | 2.03553i | −0.254442 | − | 0.146902i | ||||
\(193\) | −1.73205 | − | 1.00000i | −0.124676 | − | 0.0719816i | 0.436365 | − | 0.899770i | \(-0.356266\pi\) |
−0.561041 | + | 0.827788i | \(0.689599\pi\) | |||||||
\(194\) | 14.0711 | + | 24.3718i | 1.01024 | + | 1.74979i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.1421 | + | 18.7554i | −1.36730 | + | 1.33967i | ||||
\(197\) | − | 12.3431i | − | 0.879413i | −0.898142 | − | 0.439706i | \(-0.855083\pi\) | ||
0.898142 | − | 0.439706i | \(-0.144917\pi\) | |||||||
\(198\) | −4.89898 | + | 2.82843i | −0.348155 | + | 0.201008i | ||||
\(199\) | −4.82843 | + | 8.36308i | −0.342278 | + | 0.592843i | −0.984855 | − | 0.173378i | \(-0.944532\pi\) |
0.642577 | + | 0.766221i | \(0.277865\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.98528 | + | 3.43861i | 0.140031 | + | 0.242541i | ||||
\(202\) | − | 24.8995i | − | 1.75192i | ||||||
\(203\) | −0.358719 | + | 2.62132i | −0.0251772 | + | 0.183981i | ||||
\(204\) | 7.65685 | 0.536087 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.91421 | − | 5.04757i | 0.203043 | − | 0.351681i | ||||
\(207\) | 1.01461 | + | 0.585786i | 0.0705204 | + | 0.0407150i | ||||
\(208\) | 12.5446 | − | 7.24264i | 0.869813 | − | 0.502187i | ||||
\(209\) | 2.34315 | 0.162079 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.4853 | 1.41026 | 0.705132 | − | 0.709076i | \(-0.250888\pi\) | ||||
0.705132 | + | 0.709076i | \(0.250888\pi\) | |||||||
\(212\) | −3.88437 | + | 2.24264i | −0.266779 | + | 0.154025i | ||||
\(213\) | −1.60896 | − | 0.928932i | −0.110244 | − | 0.0636494i | ||||
\(214\) | 13.5711 | − | 23.5058i | 0.927699 | − | 1.60682i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 10.6569 | 0.725107 | ||||||||
\(217\) | 12.5446 | + | 9.72792i | 0.851584 | + | 0.660374i | ||||
\(218\) | 32.5563i | 2.20499i | ||||||||
\(219\) | 0.171573 | + | 0.297173i | 0.0115938 | + | 0.0200811i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.6569 | − | 20.1903i | 0.784125 | − | 1.35814i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.343146i | − | 0.0229787i | −0.999934 | − | 0.0114894i | \(-0.996343\pi\) | ||
0.999934 | − | 0.0114894i | \(-0.00365726\pi\) | |||||||
\(224\) | −2.57107 | + | 3.31552i | −0.171787 | + | 0.221527i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.41421 | + | 9.37769i | 0.360148 | + | 0.623795i | ||||
\(227\) | 6.03668 | + | 3.48528i | 0.400669 | + | 0.231326i | 0.686773 | − | 0.726872i | \(-0.259027\pi\) |
−0.286104 | + | 0.958199i | \(0.592360\pi\) | |||||||
\(228\) | −3.88437 | − | 2.24264i | −0.257249 | − | 0.148523i | ||||
\(229\) | −5.82843 | − | 10.0951i | −0.385153 | − | 0.667105i | 0.606637 | − | 0.794979i | \(-0.292518\pi\) |
−0.991790 | + | 0.127874i | \(0.959185\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.343146 | − | 0.840532i | −0.0225773 | − | 0.0553029i | ||||
\(232\) | − | 4.41421i | − | 0.289807i | ||||||
\(233\) | 14.5738 | − | 8.41421i | 0.954764 | − | 0.551233i | 0.0602067 | − | 0.998186i | \(-0.480824\pi\) |
0.894558 | + | 0.446952i | \(0.147491\pi\) | |||||||
\(234\) | 16.4853 | − | 28.5533i | 1.07768 | − | 1.86659i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.58579 | − | 14.8710i | −0.558887 | − | 0.968021i | ||||
\(237\) | − | 6.14214i | − | 0.398975i | ||||||
\(238\) | 4.18154 | − | 30.5563i | 0.271049 | − | 1.98067i | ||||
\(239\) | 21.3137 | 1.37867 | 0.689335 | − | 0.724443i | \(-0.257903\pi\) | ||||
0.689335 | + | 0.724443i | \(0.257903\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.8284 | + | 23.9515i | −0.890767 | + | 1.54285i | −0.0518100 | + | 0.998657i | \(0.516499\pi\) |
−0.838957 | + | 0.544197i | \(0.816834\pi\) | |||||||
\(242\) | 21.5636 | + | 12.4497i | 1.38616 | + | 0.800300i | ||||
\(243\) | 8.95743 | − | 5.17157i | 0.574619 | − | 0.331757i | ||||
\(244\) | −21.0000 | −1.34439 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.82843 | 0.499122 | ||||||||
\(247\) | −11.8272 | + | 6.82843i | −0.752546 | + | 0.434482i | ||||
\(248\) | −22.9369 | − | 13.2426i | −1.45650 | − | 0.840909i | ||||
\(249\) | −2.84315 | + | 4.92447i | −0.180177 | + | 0.312076i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.31371 | −0.587876 | −0.293938 | − | 0.955824i | \(-0.594966\pi\) | ||||
−0.293938 | + | 0.955824i | \(0.594966\pi\) | |||||||
\(252\) | 3.88437 | − | 28.3848i | 0.244692 | − | 1.78807i | ||||
\(253\) | 0.343146i | 0.0215734i | ||||||||
\(254\) | −11.2426 | − | 19.4728i | −0.705426 | − | 1.22183i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.9853 | − | 25.9553i | 0.936580 | − | 1.62220i | ||||
\(257\) | 5.49333 | − | 3.17157i | 0.342664 | − | 0.197837i | −0.318785 | − | 0.947827i | \(-0.603275\pi\) |
0.661450 | + | 0.749990i | \(0.269942\pi\) | |||||||
\(258\) | 3.58579i | 0.223241i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.41421 | − | 2.44949i | −0.0875376 | − | 0.151620i | ||||
\(262\) | 40.3805 | + | 23.3137i | 2.49472 | + | 1.44033i | ||||
\(263\) | −25.1508 | − | 14.5208i | −1.55086 | − | 0.895392i | −0.998072 | − | 0.0620729i | \(-0.980229\pi\) |
−0.552793 | − | 0.833319i | \(-0.686438\pi\) | |||||||
\(264\) | 0.757359 | + | 1.31178i | 0.0466122 | + | 0.0807348i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −11.0711 | + | 14.2767i | −0.678811 | + | 0.875359i | ||||
\(267\) | 3.58579i | 0.219447i | ||||||||
\(268\) | −31.7818 | + | 18.3492i | −1.94138 | + | 1.12086i | ||||
\(269\) | 10.2279 | − | 17.7153i | 0.623607 | − | 1.08012i | −0.365201 | − | 0.930929i | \(-0.619000\pi\) |
0.988808 | − | 0.149191i | \(-0.0476669\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.24264 | − | 14.2767i | −0.500705 | − | 0.867246i | −1.00000 | 0.000813982i | \(-0.999741\pi\) | |
0.499295 | − | 0.866432i | \(-0.333592\pi\) | |||||||
\(272\) | 14.4853i | 0.878299i | ||||||||
\(273\) | 4.18154 | + | 3.24264i | 0.253078 | + | 0.196254i | ||||
\(274\) | 23.3137 | 1.40843 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.328427 | − | 0.568852i | 0.0197690 | − | 0.0342409i | ||||
\(277\) | −13.9795 | − | 8.07107i | −0.839947 | − | 0.484943i | 0.0172994 | − | 0.999850i | \(-0.494493\pi\) |
−0.857246 | + | 0.514907i | \(0.827826\pi\) | |||||||
\(278\) | 33.7495 | − | 19.4853i | 2.02416 | − | 1.16865i | ||||
\(279\) | −16.9706 | −1.01600 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.2843 | −1.80661 | −0.903304 | − | 0.429001i | \(-0.858866\pi\) | ||||
−0.903304 | + | 0.429001i | \(0.858866\pi\) | |||||||
\(282\) | −1.73205 | + | 1.00000i | −0.103142 | + | 0.0595491i | ||||
\(283\) | 12.1244 | + | 7.00000i | 0.720718 | + | 0.416107i | 0.815017 | − | 0.579437i | \(-0.196728\pi\) |
−0.0942988 | + | 0.995544i | \(0.530061\pi\) | |||||||
\(284\) | 8.58579 | − | 14.8710i | 0.509473 | − | 0.882433i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.65685 | 0.571022 | ||||||||
\(287\) | 2.80821 | − | 20.5208i | 0.165763 | − | 1.21131i | ||||
\(288\) | − | 4.48528i | − | 0.264298i | ||||||
\(289\) | 3.15685 | + | 5.46783i | 0.185697 | + | 0.321637i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.41421 | − | 4.18154i | 0.141524 | − | 0.245126i | ||||
\(292\) | −2.74666 | + | 1.58579i | −0.160736 | + | 0.0928011i | ||||
\(293\) | 16.0000i | 0.934730i | 0.884064 | + | 0.467365i | \(0.154797\pi\) | ||||
−0.884064 | + | 0.467365i | \(0.845203\pi\) | |||||||
\(294\) | 6.74264 | + | 1.88064i | 0.393239 | + | 0.109681i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.73205 | + | 1.00000i | 0.100504 | + | 0.0580259i | ||||
\(298\) | −4.54026 | − | 2.62132i | −0.263010 | − | 0.151849i | ||||
\(299\) | −1.00000 | − | 1.73205i | −0.0578315 | − | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.39949 | + | 1.28629i | 0.541778 | + | 0.0741406i | ||||
\(302\) | 28.1421i | 1.61940i | ||||||||
\(303\) | −3.69973 | + | 2.13604i | −0.212544 | + | 0.122712i | ||||
\(304\) | 4.24264 | − | 7.34847i | 0.243332 | − | 0.421464i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 16.4853 | + | 28.5533i | 0.942401 | + | 1.63229i | ||||
\(307\) | − | 4.75736i | − | 0.271517i | −0.990742 | − | 0.135758i | \(-0.956653\pi\) | ||
0.990742 | − | 0.135758i | \(-0.0433471\pi\) | |||||||
\(308\) | 7.76874 | − | 3.17157i | 0.442665 | − | 0.180717i | ||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.58579 | − | 11.4069i | 0.373446 | − | 0.646827i | −0.616647 | − | 0.787239i | \(-0.711510\pi\) |
0.990093 | + | 0.140413i | \(0.0448429\pi\) | |||||||
\(312\) | −7.64564 | − | 4.41421i | −0.432849 | − | 0.249906i | ||||
\(313\) | 5.49333 | − | 3.17157i | 0.310501 | − | 0.179268i | −0.336650 | − | 0.941630i | \(-0.609294\pi\) |
0.647151 | + | 0.762362i | \(0.275960\pi\) | |||||||
\(314\) | −41.7990 | −2.35885 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 56.7696 | 3.19354 | ||||||||
\(317\) | −11.9503 | + | 6.89949i | −0.671194 | + | 0.387514i | −0.796529 | − | 0.604600i | \(-0.793333\pi\) |
0.125335 | + | 0.992115i | \(0.460000\pi\) | |||||||
\(318\) | 1.01461 | + | 0.585786i | 0.0568966 | + | 0.0328493i | ||||
\(319\) | 0.414214 | − | 0.717439i | 0.0231915 | − | 0.0401689i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.65685 | −0.259920 | ||||||||
\(322\) | −2.09077 | − | 1.62132i | −0.116514 | − | 0.0903527i | ||||
\(323\) | − | 13.6569i | − | 0.759888i | ||||||
\(324\) | 14.3284 | + | 24.8176i | 0.796024 | + | 1.37875i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.8995 | + | 25.8067i | −0.825207 | + | 1.42930i | ||||
\(327\) | 4.83743 | − | 2.79289i | 0.267511 | − | 0.154447i | ||||
\(328\) | 34.5563i | 1.90806i | ||||||||
\(329\) | 2.00000 | + | 4.89898i | 0.110264 | + | 0.270089i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.4853 | − | 19.8931i | −0.631288 | − | 1.09342i | −0.987289 | − | 0.158937i | \(-0.949193\pi\) |
0.356001 | − | 0.934486i | \(-0.384140\pi\) | |||||||
\(332\) | −45.5151 | − | 26.2782i | −2.49797 | − | 1.44220i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 27.0563 | + | 46.8630i | 1.48046 | + | 2.56423i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.25736 | − | 0.445759i | −0.177704 | − | 0.0243182i | ||||
\(337\) | 9.17157i | 0.499607i | 0.968296 | + | 0.249804i | \(0.0803661\pi\) | ||||
−0.968296 | + | 0.249804i | \(0.919634\pi\) | |||||||
\(338\) | −21.5636 | + | 12.4497i | −1.17290 | + | 0.677177i | ||||
\(339\) | 0.928932 | − | 1.60896i | 0.0504527 | − | 0.0873866i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.48528 | − | 4.30463i | −0.134586 | − | 0.233109i | ||||
\(342\) | − | 19.3137i | − | 1.04437i | ||||||
\(343\) | 7.34847 | − | 17.0000i | 0.396780 | − | 0.917914i | ||||
\(344\) | −15.8284 | −0.853412 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.00000 | + | 6.92820i | −0.215041 | + | 0.372463i | ||||
\(347\) | −6.86666 | − | 3.96447i | −0.368621 | − | 0.212824i | 0.304235 | − | 0.952597i | \(-0.401599\pi\) |
−0.672856 | + | 0.739773i | \(0.734933\pi\) | |||||||
\(348\) | −1.37333 | + | 0.792893i | −0.0736183 | + | 0.0425035i | ||||
\(349\) | 15.3431 | 0.821300 | 0.410650 | − | 0.911793i | \(-0.365302\pi\) | ||||
0.410650 | + | 0.911793i | \(0.365302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.6569 | −0.622197 | ||||||||
\(352\) | 1.13770 | − | 0.656854i | 0.0606399 | − | 0.0350104i | ||||
\(353\) | −23.2341 | − | 13.4142i | −1.23663 | − | 0.713967i | −0.268223 | − | 0.963357i | \(-0.586436\pi\) |
−0.968403 | + | 0.249390i | \(0.919770\pi\) | |||||||
\(354\) | −2.24264 | + | 3.88437i | −0.119195 | + | 0.206452i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −33.1421 | −1.75653 | ||||||||
\(357\) | −4.89898 | + | 2.00000i | −0.259281 | + | 0.105851i | ||||
\(358\) | 24.1421i | 1.27595i | ||||||||
\(359\) | −5.00000 | − | 8.66025i | −0.263890 | − | 0.457071i | 0.703382 | − | 0.710812i | \(-0.251672\pi\) |
−0.967272 | + | 0.253741i | \(0.918339\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | − | 9.52628i | 0.289474 | − | 0.501383i | ||||
\(362\) | 5.55487 | − | 3.20711i | 0.291958 | − | 0.168562i | ||||
\(363\) | − | 4.27208i | − | 0.224226i | ||||||
\(364\) | −29.9706 | + | 38.6485i | −1.57088 | + | 2.02573i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.74264 | + | 4.75039i | 0.143360 | + | 0.248307i | ||||
\(367\) | 2.38794 | + | 1.37868i | 0.124650 | + | 0.0719665i | 0.561028 | − | 0.827797i | \(-0.310406\pi\) |
−0.436379 | + | 0.899763i | \(0.643739\pi\) | |||||||
\(368\) | 1.07616 | + | 0.621320i | 0.0560986 | + | 0.0323886i | ||||
\(369\) | 11.0711 | + | 19.1757i | 0.576337 | + | 0.998245i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.89949 | − | 2.44949i | 0.0986169 | − | 0.127171i | ||||
\(372\) | 9.51472i | 0.493315i | ||||||||
\(373\) | 18.1610 | − | 10.4853i | 0.940343 | − | 0.542907i | 0.0502752 | − | 0.998735i | \(-0.483990\pi\) |
0.890068 | + | 0.455828i | \(0.150657\pi\) | |||||||
\(374\) | −4.82843 | + | 8.36308i | −0.249672 | + | 0.432445i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.41421 | − | 7.64564i | −0.227646 | − | 0.394294i | ||||
\(377\) | 4.82843i | 0.248677i | ||||||||
\(378\) | −14.2767 | + | 5.82843i | −0.734313 | + | 0.299782i | ||||
\(379\) | −26.8284 | −1.37808 | −0.689042 | − | 0.724722i | \(-0.741968\pi\) | ||||
−0.689042 | + | 0.724722i | \(0.741968\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.92893 | + | 3.34101i | −0.0988222 | + | 0.171165i | ||||
\(382\) | 26.8213 | + | 15.4853i | 1.37230 | + | 0.792296i | ||||
\(383\) | 2.51104 | − | 1.44975i | 0.128308 | − | 0.0740786i | −0.434472 | − | 0.900685i | \(-0.643065\pi\) |
0.562780 | + | 0.826607i | \(0.309732\pi\) | |||||||
\(384\) | −8.51472 | −0.434515 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.82843 | −0.245760 | ||||||||
\(387\) | −8.78335 | + | 5.07107i | −0.446483 | + | 0.257777i | ||||
\(388\) | 38.6485 | + | 22.3137i | 1.96208 | + | 1.13281i | ||||
\(389\) | 11.8284 | − | 20.4874i | 0.599725 | − | 1.03875i | −0.393136 | − | 0.919480i | \(-0.628610\pi\) |
0.992861 | − | 0.119274i | \(-0.0380567\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | −8.30153 | + | 29.7635i | −0.419291 | + | 1.50328i | ||||
\(393\) | − | 8.00000i | − | 0.403547i | ||||||
\(394\) | −14.8995 | − | 25.8067i | −0.750626 | − | 1.30012i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.48528 | + | 7.76874i | −0.225394 | + | 0.390394i | ||||
\(397\) | −14.3998 | + | 8.31371i | −0.722704 | + | 0.417253i | −0.815747 | − | 0.578409i | \(-0.803674\pi\) |
0.0930434 | + | 0.995662i | \(0.470340\pi\) | |||||||
\(398\) | 23.3137i | 1.16861i | ||||||||
\(399\) | 3.07107 | + | 0.420266i | 0.153746 | + | 0.0210396i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.1569 | − | 26.2524i | −0.756897 | − | 1.31098i | −0.944426 | − | 0.328725i | \(-0.893381\pi\) |
0.187528 | − | 0.982259i | \(-0.439952\pi\) | |||||||
\(402\) | 8.30153 | + | 4.79289i | 0.414043 | + | 0.239048i | ||||
\(403\) | 25.0892 | + | 14.4853i | 1.24978 | + | 0.721563i | ||||
\(404\) | −19.7426 | − | 34.1953i | −0.982233 | − | 1.70128i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.41421 | + | 5.91359i | 0.119815 | + | 0.293487i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 7.64564 | − | 4.41421i | 0.378516 | − | 0.218536i | ||||
\(409\) | −7.39949 | + | 12.8163i | −0.365881 | + | 0.633725i | −0.988917 | − | 0.148468i | \(-0.952566\pi\) |
0.623036 | + | 0.782193i | \(0.285899\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.00000 | − | 3.46410i | −0.0986527 | − | 0.170872i | ||||
\(412\) | − | 9.24264i | − | 0.455352i | ||||||
\(413\) | 9.37769 | + | 7.27208i | 0.461446 | + | 0.357836i | ||||
\(414\) | 2.82843 | 0.139010 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.82843 | + | 6.63103i | −0.187704 | + | 0.325113i | ||||
\(417\) | −5.79050 | − | 3.34315i | −0.283562 | − | 0.163715i | ||||
\(418\) | 4.89898 | − | 2.82843i | 0.239617 | − | 0.138343i | ||||
\(419\) | 0.686292 | 0.0335275 | 0.0167638 | − | 0.999859i | \(-0.494664\pi\) | ||||
0.0167638 | + | 0.999859i | \(0.494664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.4853 | 0.657232 | 0.328616 | − | 0.944464i | \(-0.393418\pi\) | ||||
0.328616 | + | 0.944464i | \(0.393418\pi\) | |||||||
\(422\) | 42.8300 | − | 24.7279i | 2.08493 | − | 1.20374i | ||||
\(423\) | −4.89898 | − | 2.82843i | −0.238197 | − | 0.137523i | ||||
\(424\) | −2.58579 | + | 4.47871i | −0.125577 | + | 0.217506i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.48528 | −0.217313 | ||||||||
\(427\) | 13.4361 | − | 5.48528i | 0.650220 | − | 0.265451i | ||||
\(428\) | − | 43.0416i | − | 2.08050i | ||||||
\(429\) | −0.828427 | − | 1.43488i | −0.0399968 | − | 0.0692766i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.89949 | + | 15.4144i | −0.428674 | + | 0.742484i | −0.996756 | − | 0.0804875i | \(-0.974352\pi\) |
0.568082 | + | 0.822972i | \(0.307686\pi\) | |||||||
\(432\) | 6.27231 | − | 3.62132i | 0.301777 | − | 0.174231i | ||||
\(433\) | − | 7.79899i | − | 0.374796i | −0.982284 | − | 0.187398i | \(-0.939995\pi\) | ||
0.982284 | − | 0.187398i | \(-0.0600053\pi\) | |||||||
\(434\) | 37.9706 | + | 5.19615i | 1.82265 | + | 0.249423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 25.8137 | + | 44.7107i | 1.23625 | + | 2.14125i | ||||
\(437\) | −1.01461 | − | 0.585786i | −0.0485355 | − | 0.0280220i | ||||
\(438\) | 0.717439 | + | 0.414214i | 0.0342806 | + | 0.0197919i | ||||
\(439\) | −16.9706 | − | 29.3939i | −0.809961 | − | 1.40289i | −0.912890 | − | 0.408205i | \(-0.866155\pi\) |
0.102930 | − | 0.994689i | \(-0.467178\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.92893 | + | 19.1757i | 0.234711 | + | 0.913126i | ||||
\(442\) | − | 56.2843i | − | 2.67717i | ||||||
\(443\) | −26.1654 | + | 15.1066i | −1.24316 | + | 0.717736i | −0.969735 | − | 0.244158i | \(-0.921488\pi\) |
−0.273420 | + | 0.961895i | \(0.588155\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.414214 | − | 0.717439i | −0.0196136 | − | 0.0339717i | ||||
\(447\) | 0.899495i | 0.0425447i | ||||||||
\(448\) | −3.52565 | + | 25.7635i | −0.166571 | + | 1.21721i | ||||
\(449\) | −3.82843 | −0.180675 | −0.0903373 | − | 0.995911i | \(-0.528795\pi\) | ||||
−0.0903373 | + | 0.995911i | \(0.528795\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.24264 | + | 5.61642i | −0.152690 | + | 0.264467i | ||||
\(452\) | 14.8710 | + | 8.58579i | 0.699474 | + | 0.403841i | ||||
\(453\) | 4.18154 | − | 2.41421i | 0.196466 | − | 0.113430i | ||||
\(454\) | 16.8284 | 0.789797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.17157 | −0.242181 | ||||||||
\(457\) | 21.0308 | − | 12.1421i | 0.983779 | − | 0.567985i | 0.0803702 | − | 0.996765i | \(-0.474390\pi\) |
0.903409 | + | 0.428780i | \(0.141056\pi\) | |||||||
\(458\) | −24.3718 | − | 14.0711i | −1.13882 | − | 0.657498i | ||||
\(459\) | 5.82843 | − | 10.0951i | 0.272048 | − | 0.471200i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.3137 | 1.92417 | 0.962086 | − | 0.272748i | \(-0.0879324\pi\) | ||||
0.962086 | + | 0.272748i | \(0.0879324\pi\) | |||||||
\(462\) | −1.73205 | − | 1.34315i | −0.0805823 | − | 0.0624888i | ||||
\(463\) | 37.0416i | 1.72147i | 0.509053 | + | 0.860735i | \(0.329996\pi\) | ||||
−0.509053 | + | 0.860735i | \(0.670004\pi\) | |||||||
\(464\) | −1.50000 | − | 2.59808i | −0.0696358 | − | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.3137 | − | 35.1844i | 0.941014 | − | 1.62988i | ||||
\(467\) | −2.68512 | + | 1.55025i | −0.124252 | + | 0.0717371i | −0.560838 | − | 0.827926i | \(-0.689521\pi\) |
0.436586 | + | 0.899663i | \(0.356188\pi\) | |||||||
\(468\) | − | 52.2843i | − | 2.41684i | ||||||
\(469\) | 15.5416 | − | 20.0417i | 0.717646 | − | 0.925439i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.58579 | + | 6.21076i | 0.165224 | + | 0.286177i | ||||
\(472\) | −17.1464 | − | 9.89949i | −0.789228 | − | 0.455661i | ||||
\(473\) | −2.57258 | − | 1.48528i | −0.118287 | − | 0.0682933i | ||||
\(474\) | −7.41421 | − | 12.8418i | −0.340546 | − | 0.589843i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −18.4853 | − | 45.2795i | −0.847271 | − | 2.07538i | ||||
\(477\) | 3.31371i | 0.151724i | ||||||||
\(478\) | 44.5621 | − | 25.7279i | 2.03822 | − | 1.17677i | ||||
\(479\) | −17.8284 | + | 30.8797i | −0.814602 | + | 1.41093i | 0.0950120 | + | 0.995476i | \(0.469711\pi\) |
−0.909614 | + | 0.415455i | \(0.863622\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 66.7696i | 3.04127i | ||||||||
\(483\) | −0.0615465 | + | 0.449747i | −0.00280046 | + | 0.0204642i | ||||
\(484\) | 39.4853 | 1.79479 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.4853 | − | 21.6251i | 0.566344 | − | 0.980936i | ||||
\(487\) | −3.76127 | − | 2.17157i | −0.170440 | − | 0.0984034i | 0.412353 | − | 0.911024i | \(-0.364707\pi\) |
−0.582793 | + | 0.812621i | \(0.698040\pi\) | |||||||
\(488\) | −20.9692 | + | 12.1066i | −0.949233 | + | 0.548040i | ||||
\(489\) | 5.11270 | 0.231204 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.31371 | 0.420322 | 0.210161 | − | 0.977667i | \(-0.432601\pi\) | ||||
0.210161 | + | 0.977667i | \(0.432601\pi\) | |||||||
\(492\) | 10.7510 | − | 6.20711i | 0.484694 | − | 0.279838i | ||||
\(493\) | −4.18154 | − | 2.41421i | −0.188327 | − | 0.108731i | ||||
\(494\) | −16.4853 | + | 28.5533i | −0.741708 | + | 1.28468i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18.0000 | −0.808224 | ||||||||
\(497\) | −1.60896 | + | 11.7574i | −0.0721716 | + | 0.527390i | ||||
\(498\) | 13.7279i | 0.615163i | ||||||||
\(499\) | −0.414214 | − | 0.717439i | −0.0185427 | − | 0.0321170i | 0.856605 | − | 0.515973i | \(-0.172569\pi\) |
−0.875148 | + | 0.483856i | \(0.839236\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.64214 | − | 8.04041i | 0.207395 | − | 0.359219i | ||||
\(502\) | −19.4728 | + | 11.2426i | −0.869115 | + | 0.501784i | ||||
\(503\) | 15.8701i | 0.707611i | 0.935319 | + | 0.353805i | \(0.115113\pi\) | ||||
−0.935319 | + | 0.353805i | \(0.884887\pi\) | |||||||
\(504\) | −12.4853 | − | 30.5826i | −0.556139 | − | 1.36226i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.414214 | + | 0.717439i | 0.0184140 | + | 0.0318941i | ||||
\(507\) | 3.69973 | + | 2.13604i | 0.164311 | + | 0.0948648i | ||||
\(508\) | −30.8797 | − | 17.8284i | −1.37007 | − | 0.791009i | ||||
\(509\) | 6.67157 | + | 11.5555i | 0.295712 | + | 0.512189i | 0.975150 | − | 0.221544i | \(-0.0711097\pi\) |
−0.679438 | + | 0.733733i | \(0.737776\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.34315 | − | 1.73205i | 0.0594173 | − | 0.0766214i | ||||
\(512\) | − | 31.2426i | − | 1.38074i | ||||||
\(513\) | −5.91359 | + | 3.41421i | −0.261091 | + | 0.150741i | ||||
\(514\) | 7.65685 | − | 13.2621i | 0.337729 | − | 0.584964i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.84315 | + | 4.92447i | 0.125163 | + | 0.216788i | ||||
\(517\) | − | 1.65685i | − | 0.0728684i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.37258 | 0.0602497 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.48528 | + | 12.9649i | −0.327936 | + | 0.568002i | −0.982102 | − | 0.188349i | \(-0.939686\pi\) |
0.654166 | + | 0.756351i | \(0.273020\pi\) | |||||||
\(522\) | −5.91359 | − | 3.41421i | −0.258831 | − | 0.149436i | ||||
\(523\) | −30.8797 | + | 17.8284i | −1.35028 | + | 0.779583i | −0.988288 | − | 0.152600i | \(-0.951235\pi\) |
−0.361989 | + | 0.932182i | \(0.617902\pi\) | |||||||
\(524\) | 73.9411 | 3.23013 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −70.1127 | −3.05706 | ||||||||
\(527\) | −25.0892 | + | 14.4853i | −1.09290 | + | 0.630989i | ||||
\(528\) | 0.891519 | + | 0.514719i | 0.0387984 | + | 0.0224003i | ||||
\(529\) | −11.4142 | + | 19.7700i | −0.496270 | + | 0.859565i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.6863 | −0.550538 | ||||||||
\(532\) | −3.88437 | + | 28.3848i | −0.168409 | + | 1.23064i | ||||
\(533\) | − | 37.7990i | − | 1.63726i | ||||||
\(534\) | 4.32843 | + | 7.49706i | 0.187309 | + | 0.324429i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −21.1569 | + | 36.6447i | −0.913837 | + | 1.58281i | ||||
\(537\) | 3.58719 | − | 2.07107i | 0.154799 | − | 0.0893732i | ||||
\(538\) | − | 49.3848i | − | 2.12913i | ||||||
\(539\) | −4.14214 | + | 4.05845i | −0.178414 | + | 0.174810i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.67157 | − | 6.35935i | −0.157853 | − | 0.273410i | 0.776241 | − | 0.630436i | \(-0.217124\pi\) |
−0.934094 | + | 0.357026i | \(0.883791\pi\) | |||||||
\(542\) | −34.4669 | − | 19.8995i | −1.48048 | − | 0.854756i | ||||
\(543\) | −0.953065 | − | 0.550253i | −0.0408999 | − | 0.0236136i | ||||
\(544\) | −3.82843 | − | 6.63103i | −0.164142 | − | 0.284303i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.6569 | + | 1.73205i | 0.541663 | + | 0.0741249i | ||||
\(547\) | 24.8995i | 1.06463i | 0.846548 | + | 0.532313i | \(0.178677\pi\) | ||||
−0.846548 | + | 0.532313i | \(0.821323\pi\) | |||||||
\(548\) | 32.0174 | − | 18.4853i | 1.36772 | − | 0.789652i | ||||
\(549\) | −7.75736 | + | 13.4361i | −0.331076 | + | 0.573441i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.41421 | + | 2.44949i | 0.0602475 | + | 0.104352i | ||||
\(552\) | − | 0.757359i | − | 0.0322354i | ||||||
\(553\) | −36.3221 | + | 14.8284i | −1.54457 | + | 0.630569i | ||||
\(554\) | −38.9706 | −1.65570 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 30.8995 | − | 53.5195i | 1.31043 | − | 2.26973i | ||||
\(557\) | −19.2987 | − | 11.1421i | −0.817714 | − | 0.472107i | 0.0319135 | − | 0.999491i | \(-0.489840\pi\) |
−0.849628 | + | 0.527383i | \(0.823173\pi\) | |||||||
\(558\) | −35.4815 | + | 20.4853i | −1.50205 | + | 0.867211i | ||||
\(559\) | 17.3137 | 0.732292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.65685 | 0.0699524 | ||||||||
\(562\) | −63.3175 | + | 36.5563i | −2.67089 | + | 1.54204i | ||||
\(563\) | 36.1374 | + | 20.8640i | 1.52301 | + | 0.879311i | 0.999630 | + | 0.0272129i | \(0.00866320\pi\) |
0.523382 | + | 0.852098i | \(0.324670\pi\) | |||||||
\(564\) | −1.58579 | + | 2.74666i | −0.0667737 | + | 0.115655i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 33.7990 | 1.42068 | ||||||||
\(567\) | −15.6500 | − | 12.1360i | −0.657238 | − | 0.509666i | ||||
\(568\) | − | 19.7990i | − | 0.830747i | ||||||
\(569\) | 3.82843 | + | 6.63103i | 0.160496 | + | 0.277987i | 0.935047 | − | 0.354525i | \(-0.115357\pi\) |
−0.774551 | + | 0.632512i | \(0.782024\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.58579 | + | 7.94282i | −0.191909 | + | 0.332396i | −0.945883 | − | 0.324508i | \(-0.894801\pi\) |
0.753974 | + | 0.656905i | \(0.228135\pi\) | |||||||
\(572\) | 13.2621 | − | 7.65685i | 0.554515 | − | 0.320149i | ||||
\(573\) | − | 5.31371i | − | 0.221983i | ||||||
\(574\) | −18.8995 | − | 46.2941i | −0.788850 | − | 1.93228i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13.8995 | − | 24.0746i | −0.579146 | − | 1.00311i | ||||
\(577\) | 38.0541 | + | 21.9706i | 1.58421 | + | 0.914646i | 0.994234 | + | 0.107228i | \(0.0341976\pi\) |
0.589980 | + | 0.807418i | \(0.299136\pi\) | |||||||
\(578\) | 13.2005 | + | 7.62132i | 0.549069 | + | 0.317005i | ||||
\(579\) | 0.414214 | + | 0.717439i | 0.0172141 | + | 0.0298157i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.9853 | + | 4.92447i | 1.49292 | + | 0.204302i | ||||
\(582\) | − | 11.6569i | − | 0.483192i | ||||||
\(583\) | −0.840532 | + | 0.485281i | −0.0348113 | + | 0.0200983i | ||||
\(584\) | −1.82843 | + | 3.16693i | −0.0756609 | + | 0.131048i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.3137 | + | 33.4523i | 0.797842 | + | 1.38190i | ||||
\(587\) | − | 34.2843i | − | 1.41506i | −0.706682 | − | 0.707532i | \(-0.749809\pi\) | ||
0.706682 | − | 0.707532i | \(-0.250191\pi\) | |||||||
\(588\) | 10.7510 | − | 2.76346i | 0.443365 | − | 0.113963i | ||||
\(589\) | 16.9706 | 0.699260 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.55635 | + | 4.42773i | −0.105154 | + | 0.182132i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.63818 | + | 2.10051i | −0.149402 | + | 0.0862574i | −0.572838 | − | 0.819669i | \(-0.694157\pi\) |
0.423435 | + | 0.905926i | \(0.360824\pi\) | |||||||
\(594\) | 4.82843 | 0.198113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.31371 | −0.340543 | ||||||||
\(597\) | 3.46410 | − | 2.00000i | 0.141776 | − | 0.0818546i | ||||
\(598\) | −4.18154 | − | 2.41421i | −0.170996 | − | 0.0987245i | ||||
\(599\) | 3.17157 | − | 5.49333i | 0.129587 | − | 0.224451i | −0.793930 | − | 0.608010i | \(-0.791968\pi\) |
0.923517 | + | 0.383558i | \(0.125302\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.6569 | 0.801820 | 0.400910 | − | 0.916117i | \(-0.368694\pi\) | ||||
0.400910 | + | 0.916117i | \(0.368694\pi\) | |||||||
\(602\) | 21.2049 | − | 8.65685i | 0.864246 | − | 0.352827i | ||||
\(603\) | 27.1127i | 1.10411i | ||||||||
\(604\) | 22.3137 | + | 38.6485i | 0.907932 | + | 1.57258i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.15685 | + | 8.93193i | −0.209483 | + | 0.362835i | ||||
\(607\) | 33.0936 | − | 19.1066i | 1.34323 | − | 0.775513i | 0.355948 | − | 0.934506i | \(-0.384158\pi\) |
0.987280 | + | 0.158993i | \(0.0508246\pi\) | |||||||
\(608\) | 4.48528i | 0.181902i | ||||||||
\(609\) | 0.671573 | − | 0.866025i | 0.0272135 | − | 0.0350931i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.82843 | + | 8.36308i | 0.195337 | + | 0.338334i | ||||
\(612\) | 45.2795 | + | 26.1421i | 1.83032 | + | 1.05673i | ||||
\(613\) | 30.7057 | + | 17.7279i | 1.24019 | + | 0.716024i | 0.969133 | − | 0.246539i | \(-0.0792934\pi\) |
0.271057 | + | 0.962563i | \(0.412627\pi\) | |||||||
\(614\) | −5.74264 | − | 9.94655i | −0.231754 | − | 0.401410i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.92893 | − | 7.64564i | 0.238883 | − | 0.308052i | ||||
\(617\) | 11.3137i | 0.455473i | 0.973723 | + | 0.227736i | \(0.0731324\pi\) | ||||
−0.973723 | + | 0.227736i | \(0.926868\pi\) | |||||||
\(618\) | −2.09077 | + | 1.20711i | −0.0841031 | + | 0.0485570i | ||||
\(619\) | 12.7574 | − | 22.0964i | 0.512762 | − | 0.888129i | −0.487129 | − | 0.873330i | \(-0.661956\pi\) |
0.999890 | − | 0.0147990i | \(-0.00471084\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.500000 | − | 0.866025i | −0.0200643 | − | 0.0347524i | ||||
\(622\) | − | 31.7990i | − | 1.27502i | ||||||
\(623\) | 21.2049 | − | 8.65685i | 0.849555 | − | 0.346830i | ||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.65685 | − | 13.2621i | 0.306029 | − | 0.530059i | ||||
\(627\) | −0.840532 | − | 0.485281i | −0.0335676 | − | 0.0193803i | ||||
\(628\) | −57.4039 | + | 33.1421i | −2.29066 | + | 1.32252i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.1421 | −0.801846 | −0.400923 | − | 0.916112i | \(-0.631310\pi\) | ||||
−0.400923 | + | 0.916112i | \(0.631310\pi\) | |||||||
\(632\) | 56.6864 | − | 32.7279i | 2.25486 | − | 1.30185i | ||||
\(633\) | −7.34847 | − | 4.24264i | −0.292075 | − | 0.168630i | ||||
\(634\) | −16.6569 | + | 28.8505i | −0.661528 | + | 1.14580i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.85786 | 0.0736691 | ||||||||
\(637\) | 9.08052 | − | 32.5563i | 0.359783 | − | 1.28993i | ||||
\(638\) | − | 2.00000i | − | 0.0791808i | ||||||
\(639\) | −6.34315 | − | 10.9867i | −0.250931 | − | 0.434625i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.7426 | + | 27.2671i | −0.621797 | + | 1.07698i | 0.367354 | + | 0.930081i | \(0.380264\pi\) |
−0.989151 | + | 0.146903i | \(0.953070\pi\) | |||||||
\(642\) | −9.73641 | + | 5.62132i | −0.384266 | + | 0.221856i | ||||
\(643\) | − | 26.2843i | − | 1.03655i | −0.855214 | − | 0.518275i | \(-0.826574\pi\) | ||
0.855214 | − | 0.518275i | \(-0.173426\pi\) | |||||||
\(644\) | −4.15685 | − | 0.568852i | −0.163803 | − | 0.0224159i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.4853 | − | 28.5533i | −0.648605 | − | 1.12342i | ||||
\(647\) | 26.8828 | + | 15.5208i | 1.05687 | + | 0.610186i | 0.924566 | − | 0.381022i | \(-0.124428\pi\) |
0.132308 | + | 0.991209i | \(0.457761\pi\) | |||||||
\(648\) | 28.6149 | + | 16.5208i | 1.12410 | + | 0.648999i | ||||
\(649\) | −1.85786 | − | 3.21792i | −0.0729276 | − | 0.126314i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.48528 | − | 6.08767i | −0.0974059 | − | 0.238595i | ||||
\(652\) | 47.2548i | 1.85064i | ||||||||
\(653\) | 16.6031 | − | 9.58579i | 0.649728 | − | 0.375121i | −0.138624 | − | 0.990345i | \(-0.544268\pi\) |
0.788352 | + | 0.615224i | \(0.210935\pi\) | |||||||
\(654\) | 6.74264 | − | 11.6786i | 0.263658 | − | 0.456669i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.7426 | + | 20.3389i | 0.458473 | + | 0.794099i | ||||
\(657\) | 2.34315i | 0.0914148i | ||||||||
\(658\) | 10.0951 | + | 7.82843i | 0.393549 | + | 0.305184i | ||||
\(659\) | −21.1716 | −0.824727 | −0.412364 | − | 0.911019i | \(-0.635297\pi\) | ||||
−0.412364 | + | 0.911019i | \(0.635297\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.9142 | + | 27.5642i | −0.618991 | + | 1.07212i | 0.370679 | + | 0.928761i | \(0.379125\pi\) |
−0.989670 | + | 0.143363i | \(0.954208\pi\) | |||||||
\(662\) | −48.0262 | − | 27.7279i | −1.86659 | − | 1.07768i | ||||
\(663\) | −8.36308 | + | 4.82843i | −0.324795 | + | 0.187521i | ||||
\(664\) | −60.5980 | −2.35166 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.358719 | + | 0.207107i | −0.0138897 | + | 0.00801921i | ||||
\(668\) | 74.3147 | + | 42.9056i | 2.87532 | + | 1.66007i | ||||
\(669\) | −0.0710678 | + | 0.123093i | −0.00274764 | + | 0.00475905i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.54416 | −0.175425 | ||||||||
\(672\) | 1.60896 | − | 0.656854i | 0.0620669 | − | 0.0253387i | ||||
\(673\) | − | 29.6569i | − | 1.14319i | −0.820537 | − | 0.571594i | \(-0.806325\pi\) | ||
0.820537 | − | 0.571594i | \(-0.193675\pi\) | |||||||
\(674\) | 11.0711 | + | 19.1757i | 0.426442 | + | 0.738619i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.7426 | + | 34.1953i | −0.759332 | + | 1.31520i | ||||
\(677\) | −24.3718 | + | 14.0711i | −0.936685 | + | 0.540795i | −0.888919 | − | 0.458064i | \(-0.848543\pi\) |
−0.0477651 | + | 0.998859i | \(0.515210\pi\) | |||||||
\(678\) | − | 4.48528i | − | 0.172256i | ||||||
\(679\) | −30.5563 | − | 4.18154i | −1.17265 | − | 0.160473i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.44365 | − | 2.50048i | −0.0553208 | − | 0.0958185i | ||||
\(682\) | −10.3923 | − | 6.00000i | −0.397942 | − | 0.229752i | ||||
\(683\) | −30.1008 | − | 17.3787i | −1.15177 | − | 0.664977i | −0.202455 | − | 0.979292i | \(-0.564892\pi\) |
−0.949319 | + | 0.314315i | \(0.898225\pi\) | |||||||
\(684\) | −15.3137 | − | 26.5241i | −0.585534 | − | 1.01418i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.15685 | − | 44.4135i | −0.196890 | − | 1.69571i | ||||
\(687\) | 4.82843i | 0.184216i | ||||||||
\(688\) | −9.31615 | + | 5.37868i | −0.355175 | + | 0.205060i | ||||
\(689\) | 2.82843 | − | 4.89898i | 0.107754 | − | 0.186636i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.414214 | − | 0.717439i | −0.0157574 | − | 0.0272927i | 0.858039 | − | 0.513584i | \(-0.171683\pi\) |
−0.873797 | + | 0.486292i | \(0.838349\pi\) | |||||||
\(692\) | 12.6863i | 0.482260i | ||||||||
\(693\) | 0.840532 | − | 6.14214i | 0.0319292 | − | 0.233320i | ||||
\(694\) | −19.1421 | −0.726626 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.914214 | + | 1.58346i | −0.0346532 | + | 0.0600211i | ||||
\(697\) | 32.7349 | + | 18.8995i | 1.23992 | + | 0.715869i | ||||
\(698\) | 32.0790 | − | 18.5208i | 1.21421 | − | 0.701023i | ||||
\(699\) | −6.97056 | −0.263651 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.20101 | −0.120900 | −0.0604502 | − | 0.998171i | \(-0.519254\pi\) | ||||
−0.0604502 | + | 0.998171i | \(0.519254\pi\) | |||||||
\(702\) | −24.3718 | + | 14.0711i | −0.919854 | + | 0.531078i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.07107 | − | 7.05130i | 0.153434 | − | 0.265756i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −64.7696 | −2.43763 | ||||||||
\(707\) | 21.5636 | + | 16.7218i | 0.810982 | + | 0.628889i | ||||
\(708\) | 7.11270i | 0.267312i | ||||||||
\(709\) | 7.84315 | + | 13.5847i | 0.294556 | + | 0.510185i | 0.974881 | − | 0.222725i | \(-0.0714951\pi\) |
−0.680326 | + | 0.732910i | \(0.738162\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.9706 | − | 36.3221i | 0.786458 | − | 1.36218i | ||||
\(712\) | −33.0936 | + | 19.1066i | −1.24024 | + | 0.716050i | ||||
\(713\) | 2.48528i | 0.0930745i | ||||||||
\(714\) | −7.82843 | + | 10.0951i | −0.292972 | + | 0.377801i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.1421 | + | 33.1552i | 0.715375 | + | 1.23907i | ||||
\(717\) | −7.64564 | − | 4.41421i | −0.285532 | − | 0.164852i | ||||
\(718\) | −20.9077 | − | 12.0711i | −0.780269 | − | 0.450488i | ||||
\(719\) | 10.5563 | + | 18.2841i | 0.393685 | + | 0.681883i | 0.992932 | − | 0.118681i | \(-0.0378666\pi\) |
−0.599247 | + | 0.800564i | \(0.704533\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.41421 | + | 5.91359i | 0.0899100 | + | 0.220234i | ||||
\(722\) | − | 26.5563i | − | 0.988325i | ||||||
\(723\) | 9.92105 | − | 5.72792i | 0.368968 | − | 0.213024i | ||||
\(724\) | 5.08579 | − | 8.80884i | 0.189012 | − | 0.327378i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.15685 | − | 8.93193i | −0.191389 | − | 0.331495i | ||||
\(727\) | − | 37.5858i | − | 1.39398i | −0.717081 | − | 0.696990i | \(-0.754522\pi\) | ||
0.717081 | − | 0.696990i | \(-0.245478\pi\) | |||||||
\(728\) | −7.64564 | + | 55.8701i | −0.283366 | + | 2.07068i | ||||
\(729\) | 18.1716 | 0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.65685 | + | 14.9941i | −0.320185 | + | 0.554577i | ||||
\(732\) | 7.53311 | + | 4.34924i | 0.278432 | + | 0.160753i | ||||
\(733\) | 19.0526 | − | 11.0000i | 0.703722 | − | 0.406294i | −0.105010 | − | 0.994471i | \(-0.533487\pi\) |
0.808732 | + | 0.588177i | \(0.200154\pi\) | |||||||
\(734\) | 6.65685 | 0.245709 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.656854 | −0.0242120 | ||||||||
\(737\) | −6.87722 | + | 3.97056i | −0.253326 | + | 0.146258i | ||||
\(738\) | 46.2941 | + | 26.7279i | 1.70411 | + | 0.983868i | ||||
\(739\) | −10.5563 | + | 18.2841i | −0.388322 | + | 0.672593i | −0.992224 | − | 0.124466i | \(-0.960278\pi\) |
0.603902 | + | 0.797058i | \(0.293612\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.65685 | 0.207810 | ||||||||
\(742\) | 1.01461 | − | 7.41421i | 0.0372476 | − | 0.272184i | ||||
\(743\) | 16.0711i | 0.589590i | 0.955560 | + | 0.294795i | \(0.0952514\pi\) | ||||
−0.955560 | + | 0.294795i | \(0.904749\pi\) | |||||||
\(744\) | 5.48528 | + | 9.50079i | 0.201100 | + | 0.348316i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 25.3137 | − | 43.8446i | 0.926801 | − | 1.60527i | ||||
\(747\) | −33.6264 | + | 19.4142i | −1.23033 | + | 0.710329i | ||||
\(748\) | 15.3137i | 0.559925i | ||||||||
\(749\) | 11.2426 | + | 27.5387i | 0.410797 | + | 1.00624i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.1716 | + | 26.2779i | 0.553619 | + | 0.958895i | 0.998010 | + | 0.0630625i | \(0.0200868\pi\) |
−0.444391 | + | 0.895833i | \(0.646580\pi\) | |||||||
\(752\) | −5.19615 | − | 3.00000i | −0.189484 | − | 0.109399i | ||||
\(753\) | 3.34101 | + | 1.92893i | 0.121753 | + | 0.0702942i | ||||
\(754\) | 5.82843 | + | 10.0951i | 0.212259 | + | 0.367643i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −14.9853 | + | 19.3242i | −0.545009 | + | 0.702816i | ||||
\(757\) | − | 31.4558i | − | 1.14328i | −0.820504 | − | 0.571641i | \(-0.806307\pi\) | ||
0.820504 | − | 0.571641i | \(-0.193693\pi\) | |||||||
\(758\) | −56.0921 | + | 32.3848i | −2.03736 | + | 1.17627i | ||||
\(759\) | 0.0710678 | − | 0.123093i | 0.00257960 | − | 0.00446800i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.65685 | − | 8.06591i | −0.168811 | − | 0.292389i | 0.769191 | − | 0.639019i | \(-0.220659\pi\) |
−0.938002 | + | 0.346630i | \(0.887326\pi\) | |||||||
\(762\) | 9.31371i | 0.337400i | ||||||||
\(763\) | −28.1946 | − | 21.8640i | −1.02071 | − | 0.791529i | ||||
\(764\) | 49.1127 | 1.77684 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.50000 | − | 6.06218i | 0.126460 | − | 0.219035i | ||||
\(767\) | 18.7554 | + | 10.8284i | 0.677218 | + | 0.390992i | ||||
\(768\) | −10.7510 | + | 6.20711i | −0.387944 | + | 0.223980i | ||||
\(769\) | 0.627417 | 0.0226252 | 0.0113126 | − | 0.999936i | \(-0.496399\pi\) | ||||
0.0113126 | + | 0.999936i | \(0.496399\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.62742 | −0.0946241 | ||||||||
\(772\) | −6.63103 | + | 3.82843i | −0.238656 | + | 0.137788i | ||||
\(773\) | −32.1405 | − | 18.5563i | −1.15601 | − | 0.667425i | −0.205669 | − | 0.978622i | \(-0.565937\pi\) |
−0.950346 | + | 0.311196i | \(0.899270\pi\) | |||||||
\(774\) | −12.2426 | + | 21.2049i | −0.440053 | + | 0.762194i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 51.4558 | 1.84716 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 57.1127i | − | 2.04759i | ||||||
\(779\) | −11.0711 | − | 19.1757i | −0.396662 | − | 0.687039i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.85786 | − | 3.21792i | 0.0664796 | − | 0.115146i | ||||
\(782\) | 4.18154 | − | 2.41421i | 0.149532 | − | 0.0863321i | ||||
\(783\) | 2.41421i | 0.0862770i | ||||||||
\(784\) | 5.22792 | + | 20.3389i | 0.186712 | + | 0.726388i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −9.65685 | − | 16.7262i | −0.344449 | − | 0.596602i | ||||
\(787\) | −2.21386 | − | 1.27817i | −0.0789157 | − | 0.0455620i | 0.460023 | − | 0.887907i | \(-0.347841\pi\) |
−0.538939 | + | 0.842345i | \(0.681175\pi\) | |||||||
\(788\) | −40.9239 | − | 23.6274i | −1.45785 | − | 0.841692i | ||||
\(789\) | 6.01472 | + | 10.4178i | 0.214130 | + | 0.370883i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.7574 | − | 1.60896i | −0.418044 | − | 0.0572080i | ||||
\(792\) | 10.3431i | 0.367528i | ||||||||
\(793\) | 22.9369 | − | 13.2426i | 0.814514 | − | 0.470260i | ||||
\(794\) | −20.0711 | + | 34.7641i | −0.712296 | + | 1.23373i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.4853 | + | 32.0174i | 0.655193 | + | 1.13483i | ||||
\(797\) | − | 8.00000i | − | 0.283375i | −0.989911 | − | 0.141687i | \(-0.954747\pi\) | ||
0.989911 | − | 0.141687i | \(-0.0452527\pi\) | |||||||
\(798\) | 6.92820 | − | 2.82843i | 0.245256 | − | 0.100125i | ||||
\(799\) | −9.65685 | −0.341635 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.2426 | + | 21.2049i | −0.432572 | + | 0.749237i | ||||
\(802\) | −63.3790 | − | 36.5919i | −2.23799 | − | 1.29210i | ||||
\(803\) | −0.594346 | + | 0.343146i | −0.0209740 | + | 0.0121094i | ||||
\(804\) | 15.2010 | 0.536098 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 69.9411 | 2.46357 | ||||||||
\(807\) | −7.33791 | + | 4.23654i | −0.258307 | + | 0.149133i | ||||
\(808\) | −39.4275 | − | 22.7635i | −1.38705 | − | 0.800816i | ||||
\(809\) | 17.8137 | − | 30.8542i | 0.626297 | − | 1.08478i | −0.361992 | − | 0.932181i | \(-0.617903\pi\) |
0.988289 | − | 0.152596i | \(-0.0487634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.6274 | −0.724327 | −0.362163 | − | 0.932115i | \(-0.617962\pi\) | ||||
−0.362163 | + | 0.932115i | \(0.617962\pi\) | |||||||
\(812\) | 8.00436 | + | 6.20711i | 0.280898 | + | 0.217827i | ||||
\(813\) | 6.82843i | 0.239483i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.00000 | − | 5.19615i | 0.105021 | − | 0.181902i | ||||
\(817\) | 8.78335 | − | 5.07107i | 0.307290 | − | 0.177414i | ||||
\(818\) | 35.7279i | 1.24920i | ||||||||
\(819\) | 13.6569 | + | 33.4523i | 0.477209 | + | 1.16892i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.9706 | − | 41.5182i | −0.836578 | − | 1.44900i | −0.892739 | − | 0.450575i | \(-0.851219\pi\) |
0.0561604 | − | 0.998422i | \(-0.482114\pi\) | |||||||
\(822\) | −8.36308 | − | 4.82843i | −0.291696 | − | 0.168411i | ||||
\(823\) | 1.79360 | + | 1.03553i | 0.0625209 | + | 0.0360964i | 0.530935 | − | 0.847413i | \(-0.321841\pi\) |
−0.468414 | + | 0.883509i | \(0.655174\pi\) | |||||||
\(824\) | −5.32843 | − | 9.22911i | −0.185625 | − | 0.321511i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28.3848 | + | 3.88437i | 0.987633 | + | 0.135154i | ||||
\(827\) | − | 26.2132i | − | 0.911522i | −0.890102 | − | 0.455761i | \(-0.849367\pi\) | ||
0.890102 | − | 0.455761i | \(-0.150633\pi\) | |||||||
\(828\) | 3.88437 | − | 2.24264i | 0.134991 | − | 0.0779372i | ||||
\(829\) | 14.6569 | − | 25.3864i | 0.509054 | − | 0.881707i | −0.490891 | − | 0.871221i | \(-0.663329\pi\) |
0.999945 | − | 0.0104859i | \(-0.00333784\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.34315 | + | 5.79050i | 0.115972 | + | 0.200870i | ||||
\(832\) | 47.4558i | 1.64524i | ||||||||
\(833\) | 23.6544 | + | 24.1421i | 0.819575 | + | 0.836475i | ||||
\(834\) | −16.1421 | −0.558956 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.48528 | − | 7.76874i | 0.155127 | − | 0.268687i | ||||
\(837\) | 12.5446 | + | 7.24264i | 0.433606 | + | 0.250342i | ||||
\(838\) | 1.43488 | − | 0.828427i | 0.0495670 | − | 0.0286175i | ||||
\(839\) | −15.1716 | −0.523781 | −0.261890 | − | 0.965098i | \(-0.584346\pi\) | ||||
−0.261890 | + | 0.965098i | \(0.584346\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 28.1946 | − | 16.2782i | 0.971651 | − | 0.560983i | ||||
\(843\) | 10.8636 | + | 6.27208i | 0.374161 | + | 0.216022i | ||||
\(844\) | 39.2132 | − | 67.9193i | 1.34977 | − | 2.33788i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13.6569 | −0.469532 | ||||||||
\(847\) | −25.2633 | + | 10.3137i | −0.868058 | + | 0.354383i | ||||
\(848\) | 3.51472i | 0.120696i | ||||||||
\(849\) | −2.89949 | − | 5.02207i | −0.0995104 | − | 0.172357i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −6.15978 | + | 3.55635i | −0.211030 | + | 0.121839i | ||||
\(853\) | − | 2.54416i | − | 0.0871102i | −0.999051 | − | 0.0435551i | \(-0.986132\pi\) | ||
0.999051 | − | 0.0435551i | \(-0.0138684\pi\) | |||||||
\(854\) | 21.4706 | − | 27.6873i | 0.734708 | − | 0.947441i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24.8137 | − | 42.9786i | −0.848115 | − | 1.46898i | ||||
\(857\) | −29.6910 | − | 17.1421i | −1.01423 | − | 0.585564i | −0.101800 | − | 0.994805i | \(-0.532460\pi\) |
−0.912426 | + | 0.409241i | \(0.865794\pi\) | |||||||
\(858\) | −3.46410 | − | 2.00000i | −0.118262 | − | 0.0682789i | ||||
\(859\) | 0.686292 | + | 1.18869i | 0.0234160 | + | 0.0405576i | 0.877496 | − | 0.479584i | \(-0.159212\pi\) |
−0.854080 | + | 0.520142i | \(0.825879\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.25736 | + | 6.77962i | −0.179170 | + | 0.231049i | ||||
\(862\) | 42.9706i | 1.46358i | ||||||||
\(863\) | −12.6062 | + | 7.27817i | −0.429119 | + | 0.247752i | −0.698971 | − | 0.715150i | \(-0.746358\pi\) |
0.269852 | + | 0.962902i | \(0.413025\pi\) | |||||||
\(864\) | −1.91421 | + | 3.31552i | −0.0651229 | + | 0.112796i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.41421 | − | 16.3059i | −0.319908 | − | 0.554097i | ||||
\(867\) | − | 2.61522i | − | 0.0888177i | ||||||
\(868\) | 56.2662 | − | 22.9706i | 1.90980 | − | 0.779672i | ||||
\(869\) | 12.2843 | 0.416715 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.1421 | − | 40.0834i | 0.784141 | − | 1.35817i | ||||
\(872\) | 51.5518 | + | 29.7635i | 1.74576 | + | 1.00792i | ||||
\(873\) | 28.5533 | − | 16.4853i | 0.966384 | − | 0.557942i | ||||
\(874\) | −2.82843 | −0.0956730 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.31371 | 0.0443861 | ||||||||
\(877\) | 21.7992 | − | 12.5858i | 0.736107 | − | 0.424992i | −0.0845449 | − | 0.996420i | \(-0.526944\pi\) |
0.820652 | + | 0.571428i | \(0.193610\pi\) | |||||||
\(878\) | −70.9631 | − | 40.9706i | −2.39489 | − | 1.38269i | ||||
\(879\) | 3.31371 | − | 5.73951i | 0.111769 | − | 0.193589i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.82843 | 0.0616013 | 0.0308006 | − | 0.999526i | \(-0.490194\pi\) | ||||
0.0308006 | + | 0.999526i | \(0.490194\pi\) | |||||||
\(882\) | 33.4523 | + | 34.1421i | 1.12640 | + | 1.14963i | ||||
\(883\) | − | 18.2843i | − | 0.615315i | −0.951497 | − | 0.307657i | \(-0.900455\pi\) | ||
0.951497 | − | 0.307657i | \(-0.0995450\pi\) | |||||||
\(884\) | −44.6274 | − | 77.2970i | −1.50098 | − | 2.59978i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.4706 | + | 63.1689i | −1.22525 | + | 2.12220i | ||||
\(887\) | 25.9192 | − | 14.9645i | 0.870282 | − | 0.502458i | 0.00284012 | − | 0.999996i | \(-0.499096\pi\) |
0.867442 | + | 0.497538i | \(0.165763\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.4142 | + | 3.34101i | 0.818826 | + | 0.112054i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.10051 | + | 5.37023i | 0.103871 | + | 0.179910i | ||||
\(892\) | −1.13770 | − | 0.656854i | −0.0380932 | − | 0.0219931i | ||||
\(893\) | 4.89898 | + | 2.82843i | 0.163938 | + | 0.0946497i | ||||
\(894\) | 1.08579 | + | 1.88064i | 0.0363141 | + | 0.0628979i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 20.5563 | + | 50.3526i | 0.686739 | + | 1.68216i | ||||
\(897\) | 0.828427i | 0.0276604i | ||||||||
\(898\) | −8.00436 | + | 4.62132i | −0.267109 | + | 0.154215i | ||||
\(899\) | 3.00000 | − | 5.19615i | 0.100056 | − | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.82843 | + | 4.89898i | 0.0942286 | + | 0.163209i | ||||
\(902\) | 15.6569i | 0.521316i | ||||||||
\(903\) | −3.10538 | − | 2.40812i | −0.103341 | − | 0.0801371i | ||||
\(904\) | 19.7990 | 0.658505 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.82843 | − | 10.0951i | 0.193637 | − | 0.335388i | ||||
\(907\) | 12.3090 | + | 7.10660i | 0.408713 | + | 0.235971i | 0.690237 | − | 0.723584i | \(-0.257506\pi\) |
−0.281523 | + | 0.959554i | \(0.590840\pi\) | |||||||
\(908\) | 23.1110 | − | 13.3431i | 0.766966 | − | 0.442808i | ||||
\(909\) | −29.1716 | −0.967560 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.2010 | −0.337975 | −0.168987 | − | 0.985618i | \(-0.554050\pi\) | ||||
−0.168987 | + | 0.985618i | \(0.554050\pi\) | |||||||
\(912\) | −3.04384 | + | 1.75736i | −0.100791 | + | 0.0581920i | ||||
\(913\) | −9.84895 | − | 5.68629i | −0.325953 | − | 0.188189i | ||||
\(914\) | 29.3137 | − | 50.7728i | 0.969611 | − | 1.67942i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −44.6274 | −1.47453 | ||||||||
\(917\) | −47.3087 | + | 19.3137i | −1.56227 | + | 0.637795i | ||||
\(918\) | − | 28.1421i | − | 0.928829i | ||||||
\(919\) | −21.5563 | − | 37.3367i | −0.711078 | − | 1.23162i | −0.964453 | − | 0.264256i | \(-0.914874\pi\) |
0.253374 | − | 0.967368i | \(-0.418460\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.985281 | + | 1.70656i | −0.0324661 | + | 0.0562330i | ||||
\(922\) | 86.3775 | − | 49.8701i | 2.84469 | − | 1.64238i | ||||
\(923\) | 21.6569i | 0.712844i | ||||||||
\(924\) | −3.44365 | − | 0.471253i | −0.113288 | − | 0.0155031i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 44.7132 | + | 77.4455i | 1.46937 | + | 2.54502i | ||||
\(927\) | −5.91359 | − | 3.41421i | −0.194228 | − | 0.112137i | ||||
\(928\) | 1.37333 | + | 0.792893i | 0.0450818 | + | 0.0260280i | ||||
\(929\) | 2.74264 | + | 4.75039i | 0.0899831 | + | 0.155855i | 0.907504 | − | 0.420044i | \(-0.137985\pi\) |
−0.817521 | + | 0.575899i | \(0.804652\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.92893 | − | 19.1757i | −0.161539 | − | 0.628457i | ||||
\(932\) | − | 64.4264i | − | 2.11036i | ||||||
\(933\) | −4.72490 | + | 2.72792i | −0.154686 | + | 0.0893082i | ||||
\(934\) | −3.74264 | + | 6.48244i | −0.122463 | + | 0.212112i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −30.1421 | − | 52.2077i | −0.985227 | − | 1.70646i | ||||
\(937\) | 34.6274i | 1.13123i | 0.824670 | + | 0.565614i | \(0.191361\pi\) | ||||
−0.824670 | + | 0.565614i | \(0.808639\pi\) | |||||||
\(938\) | 8.30153 | − | 60.6630i | 0.271055 | − | 1.98072i | ||||
\(939\) | −2.62742 | −0.0857425 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.1421 | − | 40.0834i | 0.754412 | − | 1.30668i | −0.191254 | − | 0.981541i | \(-0.561255\pi\) |
0.945666 | − | 0.325139i | \(-0.105411\pi\) | |||||||
\(942\) | 14.9941 | + | 8.65685i | 0.488535 | + | 0.282056i | ||||
\(943\) | 2.80821 | − | 1.62132i | 0.0914479 | − | 0.0527975i | ||||
\(944\) | −13.4558 | −0.437950 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.17157 | −0.233168 | ||||||||
\(947\) | 28.7380 | − | 16.5919i | 0.933859 | − | 0.539164i | 0.0458290 | − | 0.998949i | \(-0.485407\pi\) |
0.888030 | + | 0.459786i | \(0.152074\pi\) | |||||||
\(948\) | −20.3643 | − | 11.7574i | −0.661403 | − | 0.381861i | ||||
\(949\) | 2.00000 | − | 3.46410i | 0.0649227 | − | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.71573 | 0.185345 | ||||||||
\(952\) | −44.5621 | − | 34.5563i | −1.44426 | − | 1.11998i | ||||
\(953\) | 13.6569i | 0.442389i | 0.975230 | + | 0.221194i | \(0.0709955\pi\) | ||||
−0.975230 | + | 0.221194i | \(0.929004\pi\) | |||||||
\(954\) | 4.00000 | + | 6.92820i | 0.129505 | + | 0.224309i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 40.7990 | − | 70.6659i | 1.31953 | − | 2.28550i | ||||
\(957\) | −0.297173 | + | 0.171573i | −0.00960624 | + | 0.00554616i | ||||
\(958\) | 86.0833i | 2.78122i | ||||||||
\(959\) | −15.6569 | + | 20.1903i | −0.505586 | + | 0.651978i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | − | 4.33013i | −0.0806452 | − | 0.139682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −27.5387 | − | 15.8995i | −0.887423 | − | 0.512354i | ||||
\(964\) | 52.9411 | + | 91.6967i | 1.70512 | + | 2.95335i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.414214 | + | 1.01461i | 0.0133271 | + | 0.0326446i | ||||
\(967\) | 37.5269i | 1.20678i | 0.797445 | + | 0.603392i | \(0.206185\pi\) | ||||
−0.797445 | + | 0.603392i | \(0.793815\pi\) | |||||||
\(968\) | 39.4275 | − | 22.7635i | 1.26725 | − | 0.731645i | ||||
\(969\) | −2.82843 | + | 4.89898i | −0.0908622 | + | 0.157378i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | + | 20.7846i | 0.385098 | + | 0.667010i | 0.991783 | − | 0.127933i | \(-0.0408342\pi\) |
−0.606685 | + | 0.794943i | \(0.707501\pi\) | |||||||
\(972\) | − | 39.5980i | − | 1.27011i | ||||||
\(973\) | −5.79050 | + | 42.3137i | −0.185635 | + | 1.35652i | ||||
\(974\) | −10.4853 | −0.335970 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.22792 | + | 14.2512i | −0.263369 | + | 0.456169i | ||||
\(977\) | 1.13770 | + | 0.656854i | 0.0363984 | + | 0.0210146i | 0.518089 | − | 0.855327i | \(-0.326644\pi\) |
−0.481690 | + | 0.876341i | \(0.659977\pi\) | |||||||
\(978\) | 10.6895 | − | 6.17157i | 0.341812 | − | 0.197345i | ||||
\(979\) | −7.17157 | −0.229204 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.1421 | 1.21778 | ||||||||
\(982\) | 19.4728 | − | 11.2426i | 0.621403 | − | 0.358767i | ||||
\(983\) | 24.4334 | + | 14.1066i | 0.779303 | + | 0.449931i | 0.836183 | − | 0.548450i | \(-0.184782\pi\) |
−0.0568803 | + | 0.998381i | \(0.518115\pi\) | |||||||
\(984\) | 7.15685 | − | 12.3960i | 0.228152 | − | 0.395171i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11.6569 | −0.371230 | ||||||||
\(987\) | 0.297173 | − | 2.17157i | 0.00945912 | − | 0.0691219i | ||||
\(988\) | 52.2843i | 1.66338i | ||||||||
\(989\) | 0.742641 | + | 1.28629i | 0.0236146 | + | 0.0409017i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.17157 | − | 3.76127i | 0.0689823 | − | 0.119481i | −0.829471 | − | 0.558549i | \(-0.811358\pi\) |
0.898454 | + | 0.439069i | \(0.144691\pi\) | |||||||
\(992\) | 8.23999 | − | 4.75736i | 0.261620 | − | 0.151046i | ||||
\(993\) | 9.51472i | 0.301940i | ||||||||
\(994\) | 10.8284 | + | 26.5241i | 0.343457 | + | 0.841294i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.8848 | + | 18.8530i | 0.344897 | + | 0.597380i | ||||
\(997\) | −28.9736 | − | 16.7279i | −0.917603 | − | 0.529779i | −0.0347337 | − | 0.999397i | \(-0.511058\pi\) |
−0.882870 | + | 0.469618i | \(0.844392\pi\) | |||||||
\(998\) | −1.73205 | − | 1.00000i | −0.0548271 | − | 0.0316544i | ||||
\(999\) | 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 | 175.2.k.a.74.4 | 8 | ||
5.2 | odd | 4 | 175.2.e.c.151.2 | 4 | |||
5.3 | odd | 4 | 35.2.e.a.11.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 175.2.k.a.74.1 | 8 | ||
7.2 | even | 3 | inner | 175.2.k.a.149.1 | 8 | ||
7.3 | odd | 6 | 1225.2.b.h.99.4 | 4 | |||
7.4 | even | 3 | 1225.2.b.g.99.4 | 4 | |||
15.8 | even | 4 | 315.2.j.e.46.2 | 4 | |||
20.3 | even | 4 | 560.2.q.k.81.1 | 4 | |||
35.2 | odd | 12 | 175.2.e.c.51.2 | 4 | |||
35.3 | even | 12 | 245.2.a.g.1.2 | 2 | |||
35.4 | even | 6 | 1225.2.b.g.99.1 | 4 | |||
35.9 | even | 6 | inner | 175.2.k.a.149.4 | 8 | ||
35.13 | even | 4 | 245.2.e.e.116.1 | 4 | |||
35.17 | even | 12 | 1225.2.a.m.1.1 | 2 | |||
35.18 | odd | 12 | 245.2.a.h.1.2 | 2 | |||
35.23 | odd | 12 | 35.2.e.a.16.1 | yes | 4 | ||
35.24 | odd | 6 | 1225.2.b.h.99.1 | 4 | |||
35.32 | odd | 12 | 1225.2.a.k.1.1 | 2 | |||
35.33 | even | 12 | 245.2.e.e.226.1 | 4 | |||
105.23 | even | 12 | 315.2.j.e.226.2 | 4 | |||
105.38 | odd | 12 | 2205.2.a.q.1.1 | 2 | |||
105.53 | even | 12 | 2205.2.a.n.1.1 | 2 | |||
140.3 | odd | 12 | 3920.2.a.bv.1.1 | 2 | |||
140.23 | even | 12 | 560.2.q.k.401.1 | 4 | |||
140.123 | even | 12 | 3920.2.a.bq.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.e.a.11.1 | ✓ | 4 | 5.3 | odd | 4 | ||
35.2.e.a.16.1 | yes | 4 | 35.23 | odd | 12 | ||
175.2.e.c.51.2 | 4 | 35.2 | odd | 12 | |||
175.2.e.c.151.2 | 4 | 5.2 | odd | 4 | |||
175.2.k.a.74.1 | 8 | 5.4 | even | 2 | inner | ||
175.2.k.a.74.4 | 8 | 1.1 | even | 1 | trivial | ||
175.2.k.a.149.1 | 8 | 7.2 | even | 3 | inner | ||
175.2.k.a.149.4 | 8 | 35.9 | even | 6 | inner | ||
245.2.a.g.1.2 | 2 | 35.3 | even | 12 | |||
245.2.a.h.1.2 | 2 | 35.18 | odd | 12 | |||
245.2.e.e.116.1 | 4 | 35.13 | even | 4 | |||
245.2.e.e.226.1 | 4 | 35.33 | even | 12 | |||
315.2.j.e.46.2 | 4 | 15.8 | even | 4 | |||
315.2.j.e.226.2 | 4 | 105.23 | even | 12 | |||
560.2.q.k.81.1 | 4 | 20.3 | even | 4 | |||
560.2.q.k.401.1 | 4 | 140.23 | even | 12 | |||
1225.2.a.k.1.1 | 2 | 35.32 | odd | 12 | |||
1225.2.a.m.1.1 | 2 | 35.17 | even | 12 | |||
1225.2.b.g.99.1 | 4 | 35.4 | even | 6 | |||
1225.2.b.g.99.4 | 4 | 7.4 | even | 3 | |||
1225.2.b.h.99.1 | 4 | 35.24 | odd | 6 | |||
1225.2.b.h.99.4 | 4 | 7.3 | odd | 6 | |||
2205.2.a.n.1.1 | 2 | 105.53 | even | 12 | |||
2205.2.a.q.1.1 | 2 | 105.38 | odd | 12 | |||
3920.2.a.bq.1.2 | 2 | 140.123 | even | 12 | |||
3920.2.a.bv.1.1 | 2 | 140.3 | odd | 12 |