Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.q (of order \(3\), 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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 30 x^{10} - 53 x^{9} + 798 x^{8} - 1096 x^{7} + 4060 x^{6} - 915 x^{5} + 10392 x^{4} - 7038 x^{3} + 4869 x^{2} - 675 x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 3781.3 | ||
Root | \(0.307496 + 0.532598i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.3781 |
Dual form | 4020.2.q.j.841.3 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.550200 | − | 0.952975i | −0.207956 | − | 0.360191i | 0.743114 | − | 0.669164i | \(-0.233348\pi\) |
−0.951071 | + | 0.308974i | \(0.900014\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.589441 | − | 1.02094i | −0.177723 | − | 0.307826i | 0.763377 | − | 0.645953i | \(-0.223540\pi\) |
−0.941100 | + | 0.338127i | \(0.890207\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.83022 | + | 3.17003i | −0.443894 | + | 0.768846i | −0.997974 | − | 0.0636166i | \(-0.979737\pi\) |
0.554081 | + | 0.832463i | \(0.313070\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.26255 | + | 5.65090i | −0.748480 | + | 1.29641i | 0.200071 | + | 0.979781i | \(0.435883\pi\) |
−0.948551 | + | 0.316624i | \(0.897451\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.550200 | − | 0.952975i | −0.120064 | − | 0.207956i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.11217 | − | 7.12248i | 0.857446 | − | 1.48514i | −0.0169115 | − | 0.999857i | \(-0.505383\pi\) |
0.874357 | − | 0.485283i | \(-0.161283\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.58485 | + | 7.94120i | 0.851386 | + | 1.47464i | 0.879958 | + | 0.475052i | \(0.157571\pi\) |
−0.0285719 | + | 0.999592i | \(0.509096\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.12291 | + | 1.94493i | 0.201680 | + | 0.349320i | 0.949070 | − | 0.315066i | \(-0.102027\pi\) |
−0.747390 | + | 0.664386i | \(0.768693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.589441 | − | 1.02094i | −0.102609 | − | 0.177723i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.550200 | + | 0.952975i | 0.0930008 | + | 0.161082i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.58203 | + | 9.66835i | −0.917680 | + | 1.58947i | −0.114750 | + | 0.993394i | \(0.536607\pi\) |
−0.802930 | + | 0.596073i | \(0.796727\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | − | 0.866025i | 0.0800641 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.73507 | − | 8.20139i | −0.739494 | − | 1.28084i | −0.952723 | − | 0.303839i | \(-0.901731\pi\) |
0.213229 | − | 0.977002i | \(-0.431602\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.52510 | 0.537572 | 0.268786 | − | 0.963200i | \(-0.413377\pi\) | ||||
0.268786 | + | 0.963200i | \(0.413377\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.16548 | + | 8.94687i | 0.753462 | + | 1.30503i | 0.946135 | + | 0.323772i | \(0.104951\pi\) |
−0.192673 | + | 0.981263i | \(0.561716\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.89456 | − | 5.01352i | 0.413508 | − | 0.716218i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.83022 | + | 3.17003i | −0.256282 | + | 0.443894i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.24582 | 0.171126 | 0.0855629 | − | 0.996333i | \(-0.472731\pi\) | ||||
0.0855629 | + | 0.996333i | \(0.472731\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.589441 | + | 1.02094i | 0.0794802 | + | 0.137664i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.26255 | + | 5.65090i | −0.432135 | + | 0.748480i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.73327 | 1.13697 | 0.568487 | − | 0.822692i | \(-0.307529\pi\) | ||||
0.568487 | + | 0.822692i | \(0.307529\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.40027 | − | 12.8176i | 0.947507 | − | 1.64113i | 0.196854 | − | 0.980433i | \(-0.436927\pi\) |
0.750652 | − | 0.660697i | \(-0.229739\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.550200 | − | 0.952975i | −0.0693187 | − | 0.120064i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.500000 | + | 0.866025i | −0.0620174 | + | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.12438 | − | 0.997229i | 0.992551 | − | 0.121831i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.11217 | − | 7.12248i | 0.495047 | − | 0.857446i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.07575 | + | 5.32736i | 0.365024 | + | 0.632241i | 0.988780 | − | 0.149379i | \(-0.0477273\pi\) |
−0.623756 | + | 0.781619i | \(0.714394\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.45329 | + | 7.71333i | −0.521218 | + | 0.902777i | 0.478477 | + | 0.878100i | \(0.341189\pi\) |
−0.999695 | + | 0.0246766i | \(0.992144\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.648621 | + | 1.12345i | −0.0739173 | + | 0.128028i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.22597 | − | 2.12344i | −0.137932 | − | 0.238906i | 0.788781 | − | 0.614674i | \(-0.210712\pi\) |
−0.926714 | + | 0.375768i | \(0.877379\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.48704 | + | 9.50384i | −0.602281 | + | 1.04318i | 0.390194 | + | 0.920733i | \(0.372408\pi\) |
−0.992475 | + | 0.122449i | \(0.960925\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.83022 | − | 3.17003i | 0.198515 | − | 0.343839i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.58485 | + | 7.94120i | 0.491548 | + | 0.851386i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.19709 | 0.762890 | 0.381445 | − | 0.924392i | \(-0.375427\pi\) | ||||
0.381445 | + | 0.924392i | \(0.375427\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.10040 | −0.115353 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.12291 | + | 1.94493i | 0.116440 | + | 0.201680i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.26255 | − | 5.65090i | 0.334730 | − | 0.579770i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.18799 | − | 5.52175i | 0.323691 | − | 0.560649i | −0.657556 | − | 0.753406i | \(-0.728410\pi\) |
0.981247 | + | 0.192757i | \(0.0617429\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.589441 | − | 1.02094i | −0.0592411 | − | 0.102609i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.77764 | + | 13.4713i | 0.773904 | + | 1.34044i | 0.935408 | + | 0.353570i | \(0.115032\pi\) |
−0.161504 | + | 0.986872i | \(0.551634\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.21517 | − | 3.83680i | −0.218268 | − | 0.378051i | 0.736011 | − | 0.676970i | \(-0.236707\pi\) |
−0.954278 | + | 0.298919i | \(0.903374\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.550200 | + | 0.952975i | 0.0536940 | + | 0.0930008i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.6613 | 1.41736 | 0.708682 | − | 0.705528i | \(-0.249290\pi\) | ||||
0.708682 | + | 0.705528i | \(0.249290\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.127209 | −0.0121844 | −0.00609222 | − | 0.999981i | \(-0.501939\pi\) | ||||
−0.00609222 | + | 0.999981i | \(0.501939\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.58203 | + | 9.66835i | −0.529823 | + | 0.917680i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.12291 | + | 3.67698i | 0.199706 | + | 0.345902i | 0.948433 | − | 0.316977i | \(-0.102668\pi\) |
−0.748727 | + | 0.662879i | \(0.769335\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.11217 | + | 7.12248i | −0.383461 | + | 0.664175i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.500000 | − | 0.866025i | 0.0462250 | − | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.02795 | 0.369242 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.80512 | − | 8.32271i | 0.436829 | − | 0.756610i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.73507 | − | 8.20139i | −0.426947 | − | 0.739494i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.22138 | − | 9.04370i | −0.463323 | − | 0.802499i | 0.535801 | − | 0.844344i | \(-0.320010\pi\) |
−0.999124 | + | 0.0418455i | \(0.986676\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.52510 | 0.310368 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.81740 | 0.420899 | 0.210449 | − | 0.977605i | \(-0.432507\pi\) | ||||
0.210449 | + | 0.977605i | \(0.432507\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.18022 | 0.622604 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.833998 | −0.0712533 | −0.0356266 | − | 0.999365i | \(-0.511343\pi\) | ||||
−0.0356266 | + | 0.999365i | \(0.511343\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8727 | −0.922206 | −0.461103 | − | 0.887347i | \(-0.652546\pi\) | ||||
−0.461103 | + | 0.887347i | \(0.652546\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.16548 | + | 8.94687i | 0.435012 | + | 0.753462i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.17888 | −0.0985831 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.58485 | − | 7.94120i | −0.380751 | − | 0.659481i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.89456 | − | 5.01352i | 0.238739 | − | 0.413508i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.32992 | −0.272798 | −0.136399 | − | 0.990654i | \(-0.543553\pi\) | ||||
−0.136399 | + | 0.990654i | \(0.543553\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.834754 | + | 1.44584i | −0.0679313 | + | 0.117661i | −0.897991 | − | 0.440015i | \(-0.854973\pi\) |
0.830059 | + | 0.557675i | \(0.188307\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.83022 | + | 3.17003i | −0.147965 | + | 0.256282i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.12291 | − | 1.94493i | −0.0901941 | − | 0.156221i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.29941 | − | 16.1071i | 0.742174 | − | 1.28548i | −0.209330 | − | 0.977845i | \(-0.567128\pi\) |
0.951504 | − | 0.307638i | \(-0.0995385\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.24582 | 0.0987996 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.05006 | −0.713245 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.29454 | + | 7.43836i | 0.336374 | + | 0.582617i | 0.983748 | − | 0.179555i | \(-0.0574659\pi\) |
−0.647374 | + | 0.762173i | \(0.724133\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.589441 | + | 1.02094i | 0.0458879 | + | 0.0794802i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.73292 | − | 9.92970i | −0.443626 | − | 0.768384i | 0.554329 | − | 0.832298i | \(-0.312975\pi\) |
−0.997955 | + | 0.0639141i | \(0.979642\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.26255 | + | 5.65090i | −0.249493 | + | 0.432135i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.77239 | + | 9.99807i | −0.438867 | + | 0.760139i | −0.997602 | − | 0.0692065i | \(-0.977953\pi\) |
0.558736 | + | 0.829346i | \(0.311287\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.550200 | − | 0.952975i | −0.0415912 | − | 0.0720381i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.73327 | 0.656433 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.1723 | 1.73198 | 0.865990 | − | 0.500061i | \(-0.166689\pi\) | ||||
0.865990 | + | 0.500061i | \(0.166689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6327 | + | 20.1484i | 0.864650 | + | 1.49762i | 0.867394 | + | 0.497621i | \(0.165793\pi\) |
−0.00274431 | + | 0.999996i | \(0.500874\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.40027 | − | 12.8176i | 0.547043 | − | 0.947507i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.58203 | − | 9.66835i | 0.410399 | − | 0.710832i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.31523 | 0.315561 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.550200 | − | 0.952975i | −0.0400212 | − | 0.0693187i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.97540 | + | 3.42150i | −0.142935 | + | 0.247571i | −0.928601 | − | 0.371080i | \(-0.878987\pi\) |
0.785665 | + | 0.618652i | \(0.212321\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.6912 | −1.20146 | −0.600729 | − | 0.799452i | \(-0.705123\pi\) | ||||
−0.600729 | + | 0.799452i | \(0.705123\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.500000 | + | 0.866025i | −0.0358057 | + | 0.0620174i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.67221 | + | 15.0207i | 0.617869 | + | 1.07018i | 0.989874 | + | 0.141950i | \(0.0453372\pi\) |
−0.372005 | + | 0.928231i | \(0.621330\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8250 | + | 22.2136i | −0.909141 | + | 1.57468i | −0.0938817 | + | 0.995583i | \(0.529928\pi\) |
−0.815260 | + | 0.579096i | \(0.803406\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.12438 | − | 0.997229i | 0.573050 | − | 0.0703391i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.04518 | − | 8.73850i | 0.354102 | − | 0.613322i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.73507 | + | 8.20139i | 0.330712 | + | 0.572810i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.11217 | − | 7.12248i | 0.285815 | − | 0.495047i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.69232 | 0.532089 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.91507 | + | 10.2452i | −0.407210 | + | 0.705309i | −0.994576 | − | 0.104013i | \(-0.966832\pi\) |
0.587366 | + | 0.809322i | \(0.300165\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.07575 | + | 5.32736i | 0.210747 | + | 0.365024i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.52510 | −0.240410 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.23565 | − | 2.14021i | 0.0838813 | − | 0.145287i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.45329 | + | 7.71333i | −0.300926 | + | 0.521218i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.83022 | + | 3.17003i | 0.123114 | + | 0.213240i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.1821 | 0.949705 | 0.474853 | − | 0.880065i | \(-0.342501\pi\) | ||||
0.474853 | + | 0.880065i | \(0.342501\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0669 | + | 19.1684i | 0.734533 | + | 1.27225i | 0.954928 | + | 0.296838i | \(0.0959322\pi\) |
−0.220395 | + | 0.975411i | \(0.570734\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.26322 | − | 14.3123i | 0.546049 | − | 0.945784i | −0.452491 | − | 0.891769i | \(-0.649465\pi\) |
0.998540 | − | 0.0540155i | \(-0.0172020\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.648621 | + | 1.12345i | −0.0426762 | + | 0.0739173i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.96682 | + | 5.13868i | 0.194363 | + | 0.336646i | 0.946691 | − | 0.322142i | \(-0.104403\pi\) |
−0.752329 | + | 0.658788i | \(0.771069\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.16548 | − | 8.94687i | −0.336959 | − | 0.583629i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.22597 | − | 2.12344i | −0.0796353 | − | 0.137932i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.6186 | + | 21.8561i | 0.816230 | + | 1.41375i | 0.908442 | + | 0.418012i | \(0.137273\pi\) |
−0.0922117 | + | 0.995739i | \(0.529394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.6342 | −1.07150 | −0.535752 | − | 0.844376i | \(-0.679972\pi\) | ||||
−0.535752 | + | 0.844376i | \(0.679972\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.89456 | + | 5.01352i | −0.184927 | + | 0.320302i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.26255 | + | 5.65090i | 0.207591 | + | 0.359558i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.48704 | + | 9.50384i | −0.347727 | + | 0.602281i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1153 | − | 19.2523i | 0.701593 | − | 1.21520i | −0.266313 | − | 0.963886i | \(-0.585806\pi\) |
0.967907 | − | 0.251309i | \(-0.0808610\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.69552 | −0.609552 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.83022 | − | 3.17003i | 0.114613 | − | 0.198515i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.81593 | − | 8.34143i | −0.300409 | − | 0.520324i | 0.675819 | − | 0.737067i | \(-0.263790\pi\) |
−0.976229 | + | 0.216743i | \(0.930457\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.2849 | 0.763349 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.58485 | + | 7.94120i | 0.283795 | + | 0.491548i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.9838 | −0.738955 | −0.369477 | − | 0.929240i | \(-0.620463\pi\) | ||||
−0.369477 | + | 0.929240i | \(0.620463\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.24582 | −0.0765298 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.19709 | 0.440455 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.5058 | −1.67706 | −0.838531 | − | 0.544854i | \(-0.816585\pi\) | ||||
−0.838531 | + | 0.544854i | \(0.816585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.99762 | −0.425075 | −0.212538 | − | 0.977153i | \(-0.568173\pi\) | ||||
−0.212538 | + | 0.977153i | \(0.568173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.10040 | −0.0665993 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.589441 | − | 1.02094i | −0.0355446 | − | 0.0615651i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.51028 | −0.210912 | −0.105456 | − | 0.994424i | \(-0.533630\pi\) | ||||
−0.105456 | + | 0.994424i | \(0.533630\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.12291 | + | 1.94493i | 0.0672267 | + | 0.116440i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.60328 | − | 2.77696i | 0.0956437 | − | 0.165660i | −0.814233 | − | 0.580538i | \(-0.802842\pi\) |
0.909877 | + | 0.414878i | \(0.136176\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.280187 | 0.0166554 | 0.00832771 | − | 0.999965i | \(-0.497349\pi\) | ||||
0.00832771 | + | 0.999965i | \(0.497349\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.26255 | − | 5.65090i | 0.193257 | − | 0.334730i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.21048 | + | 9.02481i | −0.307565 | + | 0.532718i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.80059 | + | 3.11871i | 0.105917 | + | 0.183454i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.18799 | − | 5.52175i | 0.186883 | − | 0.323691i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.10378 | 0.415007 | 0.207504 | − | 0.978234i | \(-0.433466\pi\) | ||||
0.207504 | + | 0.978234i | \(0.433466\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.73327 | −0.508471 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.589441 | − | 1.02094i | −0.0342028 | − | 0.0592411i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.11217 | − | 7.12248i | −0.237813 | − | 0.411904i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.93951 | − | 3.35933i | −0.111791 | − | 0.193629i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.77764 | + | 13.4713i | 0.446814 | + | 0.773904i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.40027 | + | 12.8176i | −0.423738 | + | 0.733936i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.76165 | + | 9.97946i | −0.328835 | + | 0.569558i | −0.982281 | − | 0.187415i | \(-0.939989\pi\) |
0.653446 | + | 0.756973i | \(0.273323\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.21517 | − | 3.83680i | −0.126017 | − | 0.218268i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.66677 | 0.548152 | 0.274076 | − | 0.961708i | \(-0.411628\pi\) | ||||
0.274076 | + | 0.961708i | \(0.411628\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.8904 | −1.12427 | −0.562136 | − | 0.827045i | \(-0.690020\pi\) | ||||
−0.562136 | + | 0.827045i | \(0.690020\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.550200 | + | 0.952975i | 0.0310003 | + | 0.0536940i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.59315 | + | 4.49147i | −0.145646 | + | 0.252266i | −0.929614 | − | 0.368535i | \(-0.879859\pi\) |
0.783968 | + | 0.620801i | \(0.213193\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.40500 | − | 9.36174i | 0.302622 | − | 0.524157i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.6613 | 0.818316 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.9424 | − | 20.6848i | −0.664491 | − | 1.15093i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.500000 | − | 0.866025i | 0.0277350 | − | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.127209 | −0.00703469 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.68409 | − | 9.84514i | 0.313374 | − | 0.542780i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.39598 | − | 5.88201i | −0.186660 | − | 0.323305i | 0.757475 | − | 0.652865i | \(-0.226433\pi\) |
−0.944135 | + | 0.329560i | \(0.893100\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.58203 | + | 9.66835i | −0.305893 | + | 0.529823i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.12438 | + | 0.997229i | −0.443882 | + | 0.0544845i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.38886 | − | 11.0658i | 0.348023 | − | 0.602794i | −0.637875 | − | 0.770140i | \(-0.720186\pi\) |
0.985898 | + | 0.167346i | \(0.0535197\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.12291 | + | 3.67698i | 0.115301 | + | 0.199706i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.32378 | − | 2.29285i | 0.0716865 | − | 0.124165i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.0732 | −0.759879 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.11217 | + | 7.12248i | −0.221392 | + | 0.383461i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.55027 | − | 11.3454i | −0.351637 | − | 0.609053i | 0.634900 | − | 0.772595i | \(-0.281041\pi\) |
−0.986536 | + | 0.163542i | \(0.947708\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.1701 | −0.597921 | −0.298961 | − | 0.954265i | \(-0.596640\pi\) | ||||
−0.298961 | + | 0.954265i | \(0.596640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.500000 | − | 0.866025i | 0.0266880 | − | 0.0462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0197 | − | 20.8187i | 0.639744 | − | 1.10807i | −0.345745 | − | 0.938329i | \(-0.612374\pi\) |
0.985489 | − | 0.169741i | \(-0.0542930\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.07575 | − | 5.32736i | −0.163244 | − | 0.282747i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.02795 | 0.213182 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.57364 | 0.135831 | 0.0679157 | − | 0.997691i | \(-0.478365\pi\) | ||||
0.0679157 | + | 0.997691i | \(0.478365\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.7885 | − | 20.4182i | −0.620445 | − | 1.07464i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.80512 | − | 8.32271i | 0.252203 | − | 0.436829i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.45329 | − | 7.71333i | 0.233096 | − | 0.403734i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.74432 | − | 8.21741i | −0.247652 | − | 0.428945i | 0.715222 | − | 0.698897i | \(-0.246326\pi\) |
−0.962874 | + | 0.269952i | \(0.912992\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.73507 | − | 8.20139i | −0.246498 | − | 0.426947i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.685448 | − | 1.18723i | −0.0355867 | − | 0.0616379i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.2664 | − | 28.1742i | −0.842241 | − | 1.45880i | −0.887996 | − | 0.459852i | \(-0.847903\pi\) |
0.0457545 | − | 0.998953i | \(-0.485431\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.16971 | 0.472264 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.4141 | − | 33.6262i | 0.997235 | − | 1.72726i | 0.434265 | − | 0.900785i | \(-0.357008\pi\) |
0.562970 | − | 0.826477i | \(-0.309659\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.22138 | − | 9.04370i | −0.267500 | − | 0.463323i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.3203 | + | 33.4638i | −0.987223 | + | 1.70992i | −0.355615 | + | 0.934633i | \(0.615728\pi\) |
−0.631608 | + | 0.775288i | \(0.717605\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.648621 | − | 1.12345i | 0.0330568 | − | 0.0572561i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.52510 | 0.179191 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.5748 | − | 26.9763i | 0.789673 | − | 1.36775i | −0.136495 | − | 0.990641i | \(-0.543584\pi\) |
0.926168 | − | 0.377112i | \(-0.123083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.0523 | + | 26.0714i | 0.761229 | + | 1.31849i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.81740 | 0.243006 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.22597 | + | 2.12344i | 0.0616853 | + | 0.106842i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.53785 | 0.378314 | 0.189157 | − | 0.981947i | \(-0.439425\pi\) | ||||
0.189157 | + | 0.981947i | \(0.439425\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.18022 | 0.359461 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.2999 | 1.06366 | 0.531832 | − | 0.846850i | \(-0.321504\pi\) | ||||
0.531832 | + | 0.846850i | \(0.321504\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.24582 | 0.111872 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.1611 | 0.652372 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.93011 | − | 8.53921i | −0.243778 | − | 0.422237i | 0.718009 | − | 0.696034i | \(-0.245054\pi\) |
−0.961787 | + | 0.273797i | \(0.911720\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.833998 | −0.0411381 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.80505 | − | 8.32259i | −0.236441 | − | 0.409528i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.48704 | − | 9.50384i | 0.269348 | − | 0.466525i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.8727 | −0.532436 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.661016 | − | 1.14491i | 0.0322927 | − | 0.0559327i | −0.849427 | − | 0.527706i | \(-0.823052\pi\) |
0.881720 | + | 0.471773i | \(0.156386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.94550 | + | 15.4941i | −0.435977 | + | 0.755134i | −0.997375 | − | 0.0724119i | \(-0.976930\pi\) |
0.561398 | + | 0.827546i | \(0.310264\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.16548 | + | 8.94687i | 0.251154 | + | 0.435012i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.83022 | + | 3.17003i | −0.0887787 | + | 0.153769i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.2865 | −0.788160 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.17888 | −0.0569170 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.59453 | + | 2.76181i | 0.0768059 | + | 0.133032i | 0.901870 | − | 0.432007i | \(-0.142194\pi\) |
−0.825064 | + | 0.565039i | \(0.808861\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.21629 | − | 7.30283i | −0.202622 | − | 0.350952i | 0.746750 | − | 0.665104i | \(-0.231613\pi\) |
−0.949372 | + | 0.314153i | \(0.898280\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.58485 | − | 7.94120i | −0.219827 | − | 0.380751i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.8323 | + | 46.4749i | 1.28356 | + | 2.22320i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.7918 | + | 27.3521i | −0.753700 | + | 1.30545i | 0.192318 | + | 0.981333i | \(0.438399\pi\) |
−0.946018 | + | 0.324114i | \(0.894934\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.89456 | − | 5.01352i | 0.137836 | − | 0.238739i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.7479 | − | 27.2761i | −0.748203 | − | 1.29593i | −0.948683 | − | 0.316228i | \(-0.897583\pi\) |
0.200480 | − | 0.979698i | \(-0.435750\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.19709 | −0.341175 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.32992 | −0.157500 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.1863 | + | 29.7675i | 0.811070 | + | 1.40482i | 0.912116 | + | 0.409933i | \(0.134448\pi\) |
−0.101045 | + | 0.994882i | \(0.532219\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.58209 | + | 9.66847i | −0.262851 | + | 0.455271i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.834754 | + | 1.44584i | −0.0392202 | + | 0.0679313i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.10040 | 0.0515876 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.3788 | + | 28.3689i | 0.766167 | + | 1.32704i | 0.939627 | + | 0.342199i | \(0.111172\pi\) |
−0.173461 | + | 0.984841i | \(0.555495\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.83022 | + | 3.17003i | −0.0854274 | + | 0.147965i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.30790 | −0.0609148 | −0.0304574 | − | 0.999536i | \(-0.509696\pi\) | ||||
−0.0304574 | + | 0.999536i | \(0.509696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.87930 | + | 8.45120i | −0.226760 | + | 0.392761i | −0.956846 | − | 0.290595i | \(-0.906147\pi\) |
0.730086 | + | 0.683356i | \(0.239480\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.12291 | − | 1.94493i | −0.0520736 | − | 0.0901941i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.2035 | + | 26.3332i | −0.703532 | + | 1.21855i | 0.263687 | + | 0.964608i | \(0.415062\pi\) |
−0.967219 | + | 0.253945i | \(0.918272\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.42037 | − | 7.19365i | −0.250289 | − | 0.332172i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.29941 | − | 16.1071i | 0.428494 | − | 0.742174i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.07784 | − | 3.59892i | −0.0955391 | − | 0.165479i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.26255 | + | 5.65090i | −0.149696 | + | 0.259281i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.24582 | 0.0570420 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.11692 | − | 1.93456i | 0.0510332 | − | 0.0883922i | −0.839380 | − | 0.543545i | \(-0.817082\pi\) |
0.890414 | + | 0.455152i | \(0.150415\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.58203 | + | 9.66835i | 0.254519 | + | 0.440839i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.05006 | −0.411792 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.18799 | + | 5.52175i | −0.144759 | + | 0.250730i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.2557 | + | 26.4237i | −0.691304 | + | 1.19737i | 0.280107 | + | 0.959969i | \(0.409630\pi\) |
−0.971411 | + | 0.237405i | \(0.923703\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.29454 | + | 7.43836i | 0.194206 | + | 0.336374i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.5642 | 0.476756 | 0.238378 | − | 0.971172i | \(-0.423384\pi\) | ||||
0.238378 | + | 0.971172i | \(0.423384\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.5652 | −1.51170 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.589441 | + | 1.02094i | 0.0264934 | + | 0.0458879i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.38456 | − | 5.86223i | 0.151818 | − | 0.262957i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.1578 | + | 21.0579i | −0.544257 | + | 0.942680i | 0.454397 | + | 0.890800i | \(0.349855\pi\) |
−0.998653 | + | 0.0518808i | \(0.983478\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.73292 | − | 9.92970i | −0.256128 | − | 0.443626i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.535297 | + | 0.927162i | 0.0238677 | + | 0.0413401i | 0.877713 | − | 0.479188i | \(-0.159069\pi\) |
−0.853845 | + | 0.520528i | \(0.825735\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.77764 | − | 13.4713i | −0.346101 | − | 0.599464i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | + | 10.3923i | 0.266469 | + | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.89902 | −0.350118 | −0.175059 | − | 0.984558i | \(-0.556012\pi\) | ||||
−0.175059 | + | 0.984558i | \(0.556012\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.80081 | 0.433562 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.26255 | + | 5.65090i | −0.144045 | + | 0.249493i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.21517 | + | 3.83680i | 0.0976123 | + | 0.169069i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.08949 | − | 10.5473i | 0.267815 | − | 0.463870i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.77239 | + | 9.99807i | −0.253380 | + | 0.438867i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.4657 | 1.37854 | 0.689268 | − | 0.724506i | \(-0.257932\pi\) | ||||
0.689268 | + | 0.724506i | \(0.257932\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.6369 | − | 18.4237i | 0.465119 | − | 0.805610i | −0.534088 | − | 0.845429i | \(-0.679345\pi\) |
0.999207 | + | 0.0398188i | \(0.0126781\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.550200 | − | 0.952975i | −0.0240127 | − | 0.0415912i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.22067 | −0.358098 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3198 | − | 38.6590i | −0.970427 | − | 1.68083i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.73327 | 0.378992 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.47015 | −0.410198 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.6613 | −0.633865 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.1723 | 0.999960 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.82469 | −0.293960 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.429557 | 0.0184681 | 0.00923405 | − | 0.999957i | \(-0.497061\pi\) | ||||
0.00923405 | + | 0.999957i | \(0.497061\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.6327 | + | 20.1484i | 0.499206 | + | 0.864650i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.127209 | 0.00544905 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.68237 | − | 16.7704i | −0.413988 | − | 0.717049i | 0.581333 | − | 0.813666i | \(-0.302531\pi\) |
−0.995322 | + | 0.0966166i | \(0.969198\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.40027 | − | 12.8176i | 0.315836 | − | 0.547043i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −59.8332 | −2.54898 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.34906 | + | 2.33664i | −0.0573678 | + | 0.0993640i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.58203 | − | 9.66835i | 0.236944 | − | 0.410399i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.71292 | + | 2.96686i | 0.0725787 | + | 0.125710i | 0.900031 | − | 0.435826i | \(-0.143544\pi\) |
−0.827452 | + | 0.561536i | \(0.810210\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.76255 | − | 3.05282i | 0.0745479 | − | 0.129121i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.31523 | 0.182189 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.9250 | −1.64049 | −0.820247 | − | 0.572009i | \(-0.806164\pi\) | ||||
−0.820247 | + | 0.572009i | \(0.806164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.12291 | − | 3.67698i | −0.0893114 | − | 0.154692i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.550200 | − | 0.952975i | −0.0231062 | − | 0.0400212i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.3476 | + | 28.3149i | 0.685328 | + | 1.18702i | 0.973334 | + | 0.229394i | \(0.0736744\pi\) |
−0.288006 | + | 0.957629i | \(0.592992\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.36307 | − | 7.55706i | −0.182589 | − | 0.316253i | 0.760173 | − | 0.649721i | \(-0.225114\pi\) |
−0.942761 | + | 0.333468i | \(0.891781\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.97540 | + | 3.42150i | −0.0825237 | + | 0.142935i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.11217 | − | 7.12248i | 0.171489 | − | 0.297028i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.51029 | + | 4.34795i | 0.104505 | + | 0.181008i | 0.913536 | − | 0.406758i | \(-0.133341\pi\) |
−0.809031 | + | 0.587766i | \(0.800008\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.6912 | −0.693663 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0759 | 0.500992 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.734335 | − | 1.27191i | −0.0304130 | − | 0.0526769i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.500000 | + | 0.866025i | −0.0206725 | + | 0.0358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.17510 | + | 2.03533i | −0.0485016 | + | 0.0840072i | −0.889257 | − | 0.457408i | \(-0.848778\pi\) |
0.840755 | + | 0.541415i | \(0.182111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.6542 | −0.603814 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.67221 | + | 15.0207i | 0.356727 | + | 0.617869i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.1748 | − | 33.2117i | 0.787414 | − | 1.36384i | −0.140132 | − | 0.990133i | \(-0.544753\pi\) |
0.927546 | − | 0.373709i | \(-0.121914\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.02795 | −0.165130 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.8250 | + | 22.2136i | −0.524893 | + | 0.909141i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.1881 | + | 26.3066i | 0.620570 | + | 1.07486i | 0.989380 | + | 0.145354i | \(0.0464321\pi\) |
−0.368810 | + | 0.929505i | \(0.620235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.8525 | − | 32.6535i | 0.769009 | − | 1.33196i | −0.169092 | − | 0.985600i | \(-0.554083\pi\) |
0.938101 | − | 0.346362i | \(-0.112583\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.12438 | − | 0.997229i | 0.330850 | − | 0.0406103i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.80512 | + | 8.32271i | −0.195356 | + | 0.338366i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.71292 | + | 2.96687i | 0.0695254 | + | 0.120422i | 0.898692 | − | 0.438579i | \(-0.144518\pi\) |
−0.829167 | + | 0.559001i | \(0.811185\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.04518 | − | 8.73850i | 0.204441 | − | 0.354102i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3310 | 0.417946 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.3393 | − | 38.6929i | 0.902277 | − | 1.56279i | 0.0777468 | − | 0.996973i | \(-0.475227\pi\) |
0.824531 | − | 0.565817i | \(-0.191439\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.73507 | + | 8.20139i | 0.190937 | + | 0.330712i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.269780 | −0.0108609 | −0.00543047 | − | 0.999985i | \(-0.501729\pi\) | ||||
−0.00543047 | + | 0.999985i | \(0.501729\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.26633 | − | 3.92540i | 0.0910915 | − | 0.157775i | −0.816879 | − | 0.576809i | \(-0.804298\pi\) |
0.907971 | + | 0.419034i | \(0.137631\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.11217 | − | 7.12248i | 0.165016 | − | 0.285815i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.95984 | − | 6.85864i | −0.158648 | − | 0.274786i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.69232 | 0.307202 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.4327 | − | 35.3904i | −0.814704 | − | 1.41111i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.96580 | − | 5.13691i | 0.118067 | − | 0.204497i | −0.800935 | − | 0.598751i | \(-0.795664\pi\) |
0.919001 | + | 0.394254i | \(0.128997\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.91507 | + | 10.2452i | −0.235103 | + | 0.407210i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.22138 | + | 9.04370i | 0.207204 | + | 0.358888i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.89456 | − | 5.01352i | −0.114687 | − | 0.198643i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.07575 | + | 5.32736i | 0.121675 | + | 0.210747i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.10945 | − | 1.92162i | −0.0438206 | − | 0.0758995i | 0.843283 | − | 0.537469i | \(-0.180620\pi\) |
−0.887104 | + | 0.461570i | \(0.847286\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.6290 | 1.40507 | 0.702535 | − | 0.711649i | \(-0.252051\pi\) | ||||
0.702535 | + | 0.711649i | \(0.252051\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.52510 | −0.138801 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.2079 | − | 36.7331i | 0.833767 | − | 1.44413i | −0.0612630 | − | 0.998122i | \(-0.519513\pi\) |
0.895030 | − | 0.446005i | \(-0.147154\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.14775 | − | 8.91616i | −0.202067 | − | 0.349990i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.23565 | − | 2.14021i | 0.0484289 | − | 0.0838813i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.50356 | − | 9.53244i | 0.215371 | − | 0.373033i | −0.738016 | − | 0.674783i | \(-0.764237\pi\) |
0.953387 | + | 0.301749i | \(0.0975706\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.81740 | −0.188232 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.45329 | + | 7.71333i | −0.173739 | + | 0.300926i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.49622 | − | 2.59154i | −0.0582846 | − | 0.100952i | 0.835411 | − | 0.549626i | \(-0.185230\pi\) |
−0.893695 | + | 0.448674i | \(0.851896\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.9573 | −1.35968 | −0.679842 | − | 0.733359i | \(-0.737951\pi\) | ||||
−0.679842 | + | 0.733359i | \(0.737951\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.83022 | + | 3.17003i | 0.0710799 | + | 0.123114i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.18022 | −0.278437 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 75.4147 | 2.92007 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.1821 | 0.548313 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.4481 | −0.673576 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.1603 | −0.700029 | −0.350014 | − | 0.936744i | \(-0.613823\pi\) | ||||
−0.350014 | + | 0.936744i | \(0.613823\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.2194 | − | 40.2172i | −0.892393 | − | 1.54567i | −0.836998 | − | 0.547206i | \(-0.815691\pi\) |
−0.0553957 | − | 0.998464i | \(-0.517642\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.01612 | −0.269254 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.0669 | + | 19.1684i | 0.424083 | + | 0.734533i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.4869 | + | 23.3600i | −0.516062 | + | 0.893845i | 0.483764 | + | 0.875198i | \(0.339269\pi\) |
−0.999826 | + | 0.0186468i | \(0.994064\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.833998 | 0.0318654 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.26322 | − | 14.3123i | 0.315261 | − | 0.546049i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.622908 | − | 1.07891i | 0.0237309 | − | 0.0411031i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.2380 | − | 22.9288i | −0.503596 | − | 0.872254i | −0.999991 | − | 0.00415771i | \(-0.998677\pi\) |
0.496395 | − | 0.868097i | \(-0.334657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.648621 | + | 1.12345i | −0.0246391 | + | 0.0426762i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.8727 | 0.412423 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.6649 | 1.31303 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.96682 | + | 5.13868i | 0.112215 | + | 0.194363i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.9887 | + | 32.8894i | 0.717193 | + | 1.24221i | 0.962108 | + | 0.272669i | \(0.0879065\pi\) |
−0.244915 | + | 0.969544i | \(0.578760\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.4233 | − | 63.0870i | −1.37373 | − | 2.37937i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.16548 | − | 8.94687i | −0.194543 | − | 0.336959i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.55852 | − | 14.8238i | 0.321876 | − | 0.557506i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.8930 | + | 29.2596i | −0.634431 | + | 1.09887i | 0.352204 | + | 0.935923i | \(0.385432\pi\) |
−0.986635 | + | 0.162944i | \(0.947901\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.22597 | − | 2.12344i | −0.0459775 | − | 0.0796353i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.4703 | 0.691719 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.17888 | 0.0440877 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.6186 | + | 21.8561i | 0.471250 | + | 0.816230i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.8064 | + | 42.9659i | −0.925121 | + | 1.60236i | −0.133755 | + | 0.991014i | \(0.542703\pi\) |
−0.791366 | + | 0.611342i | \(0.790630\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.43758 | + | 4.22201i | −0.0907802 | + | 0.157236i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.6342 | −0.618633 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.58485 | + | 7.94120i | 0.170277 | + | 0.294929i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.7465 | + | 27.2737i | −0.584005 | + | 1.01153i | 0.410994 | + | 0.911638i | \(0.365182\pi\) |
−0.994999 | + | 0.0998877i | \(0.968152\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.45171 | + | 11.1747i | −0.238625 | + | 0.413311i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.4492 | − | 33.6871i | −0.718374 | − | 1.24426i | −0.961644 | − | 0.274301i | \(-0.911553\pi\) |
0.243270 | − | 0.969959i | \(-0.421780\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.89456 | + | 5.01352i | −0.106767 | + | 0.184927i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.80696 | − | 7.70671i | −0.213902 | − | 0.283880i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.6016 | + | 23.5587i | −0.500344 | + | 0.866622i | 0.499656 | + | 0.866224i | \(0.333460\pi\) |
−1.00000 | 0.000397539i | \(0.999873\pi\) | ||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.26255 | + | 5.65090i | 0.119853 | + | 0.207591i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.431423 | + | 0.747246i | −0.0158274 | + | 0.0274138i | −0.873831 | − | 0.486230i | \(-0.838372\pi\) |
0.858003 | + | 0.513644i | \(0.171705\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.32992 | 0.121999 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.48704 | + | 9.50384i | −0.200760 | + | 0.347727i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.06667 | − | 13.9719i | −0.294750 | − | 0.510522i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.9831 | 1.89689 | 0.948444 | − | 0.316944i | \(-0.102657\pi\) | ||||
0.948444 | + | 0.316944i | \(0.102657\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.1153 | − | 19.2523i | 0.405065 | − | 0.701593i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.834754 | − | 1.44584i | 0.0303798 | − | 0.0526194i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.4768 | − | 21.6104i | −0.453475 | − | 0.785442i | 0.545124 | − | 0.838355i | \(-0.316483\pi\) |
−0.998599 | + | 0.0529134i | \(0.983149\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.69552 | −0.351925 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.7143 | −1.11339 | −0.556697 | − | 0.830716i | \(-0.687932\pi\) | ||||
−0.556697 | + | 0.830716i | \(0.687932\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.0699906 | + | 0.121227i | 0.00253383 | + | 0.00438872i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.83022 | − | 3.17003i | 0.0661718 | − | 0.114613i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.36664 | − | 7.56323i | 0.157670 | − | 0.273093i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.1945 | − | 38.4420i | −0.800353 | − | 1.38625i | −0.919384 | − | 0.393362i | \(-0.871312\pi\) |
0.119031 | − | 0.992891i | \(-0.462021\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.81593 | − | 8.34143i | −0.173441 | − | 0.300409i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.2720 | − | 42.0404i | −0.873004 | − | 1.51209i | −0.858874 | − | 0.512188i | \(-0.828835\pi\) |
−0.0141307 | − | 0.999900i | \(-0.504498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.12291 | + | 1.94493i | 0.0403360 | + | 0.0698641i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.2849 | 0.440719 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 61.7936 | 2.21399 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.62595 | − | 6.28033i | 0.129747 | − | 0.224728i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.58485 | + | 7.94120i | 0.163849 | + | 0.283795i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.29941 | + | 16.1071i | −0.331910 | + | 0.574885i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.9491 | + | 29.3567i | −0.604171 | + | 1.04645i | 0.388011 | + | 0.921655i | \(0.373162\pi\) |
−0.992182 | + | 0.124800i | \(0.960171\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.9838 | −0.426636 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.33605 | − | 4.04615i | 0.0830603 | − | 0.143865i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.40027 | − | 12.8176i | −0.262791 | − | 0.455168i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.24582 | −0.0441845 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.4290 | − | 37.1161i | −0.759053 | − | 1.31472i | −0.943334 | − | 0.331845i | \(-0.892329\pi\) |
0.184281 | − | 0.982874i | \(-0.441005\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.8158 | −1.33783 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.19709 | 0.254297 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.4998 | 0.370530 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.05006 | 0.318973 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.5058 | −0.968252 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.4308 | 1.49179 | 0.745893 | − | 0.666065i | \(-0.232023\pi\) | ||||
0.745893 | + | 0.666065i | \(0.232023\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.8418 | + | 20.5106i | 0.415822 | + | 0.720224i | 0.995514 | − | 0.0946111i | \(-0.0301608\pi\) |
−0.579693 | + | 0.814835i | \(0.696827\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.99762 | −0.245417 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.29454 | − | 7.43836i | −0.150431 | − | 0.260554i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.5008 | + | 19.9200i | −0.402362 | + | 0.696912i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.10040 | −0.0384511 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.69814 | − | 8.13742i | 0.163966 | − | 0.283998i | −0.772321 | − | 0.635232i | \(-0.780904\pi\) |
0.936288 | + | 0.351234i | \(0.114238\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.2804 | + | 35.1267i | −0.706930 | + | 1.22444i | 0.259061 | + | 0.965861i | \(0.416587\pi\) |
−0.965990 | + | 0.258578i | \(0.916746\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.589441 | − | 1.02094i | −0.0205217 | − | 0.0355446i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.1528 | − | 26.2454i | 0.526915 | − | 0.912643i | −0.472593 | − | 0.881281i | \(-0.656682\pi\) |
0.999508 | − | 0.0313624i | \(-0.00998459\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.3326 | −0.775642 | −0.387821 | − | 0.921735i | \(-0.626772\pi\) | ||||
−0.387821 | + | 0.921735i | \(0.626772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.51028 | −0.121770 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5954 | + | 18.3517i | 0.367108 | + | 0.635849i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.73292 | + | 9.92970i | 0.198396 | + | 0.343632i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.12291 | + | 1.94493i | 0.0388134 | + | 0.0672267i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.34310 | + | 7.52248i | 0.149941 | + | 0.259705i | 0.931205 | − | 0.364495i | \(-0.118758\pi\) |
−0.781265 | + | 0.624200i | \(0.785425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.5418 | + | 47.7037i | −0.949716 | + | 1.64496i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.60328 | − | 2.77696i | 0.0552199 | − | 0.0956437i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.00000 | − | 10.3923i | −0.206406 | − | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.5751 | −0.363365 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.280187 | 0.00961601 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.9084 | + | 79.5158i | 1.57372 | + | 2.72576i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.24107 | − | 14.2739i | 0.282169 | − | 0.488731i | −0.689750 | − | 0.724048i | \(-0.742280\pi\) |
0.971919 | + | 0.235317i | \(0.0756129\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.26255 | − | 5.65090i | 0.111577 | − | 0.193257i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.0863 | −0.822772 | −0.411386 | − | 0.911461i | \(-0.634955\pi\) | ||||
−0.411386 | + | 0.911461i | \(0.634955\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.9354 | + | 34.5292i | 0.680188 | + | 1.17812i | 0.974923 | + | 0.222541i | \(0.0714353\pi\) |
−0.294735 | + | 0.955579i | \(0.595231\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.21048 | + | 9.02481i | −0.177573 | + | 0.307565i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45.2344 | −1.53980 | −0.769898 | − | 0.638167i | \(-0.779693\pi\) | ||||
−0.769898 | + | 0.638167i | \(0.779693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.77239 | − | 9.99807i | 0.196267 | − | 0.339945i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.80059 | + | 3.11871i | 0.0611512 | + | 0.105917i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.44528 | + | 2.50329i | −0.0490276 | + | 0.0849183i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.19856 | − | 7.53453i | 0.108379 | − | 0.255298i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.18799 | − | 5.52175i | 0.107897 | − | 0.186883i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.550200 | + | 0.952975i | 0.0186002 | + | 0.0322164i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.06823 | − | 7.04638i | 0.137374 | − | 0.237939i | −0.789128 | − | 0.614229i | \(-0.789467\pi\) |
0.926502 | + | 0.376290i | \(0.122800\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.10378 | 0.239604 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.8350 | − | 23.9630i | 0.466114 | − | 0.807333i | −0.533137 | − | 0.846029i | \(-0.678987\pi\) |
0.999251 | + | 0.0386961i | \(0.0123204\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.4030 | + | 38.8032i | 0.753922 | + | 1.30583i | 0.945908 | + | 0.324434i | \(0.105174\pi\) |
−0.191986 | + | 0.981398i | \(0.561493\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.73327 | −0.293566 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.70319 | − | 8.14617i | 0.157918 | − | 0.273522i | −0.776200 | − | 0.630487i | \(-0.782855\pi\) |
0.934118 | + | 0.356965i | \(0.116189\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.74561 | + | 9.95169i | −0.192702 | + | 0.333769i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.589441 | − | 1.02094i | −0.0197470 | − | 0.0342028i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −67.4105 | −2.25581 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.1723 | −0.774565 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.11217 | − | 7.12248i | −0.137301 | − | 0.237813i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.2967 | + | 17.8345i | −0.343415 | + | 0.594813i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.28012 | + | 3.94928i | −0.0759617 | + | 0.131569i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.93951 | − | 3.35933i | −0.0645429 | − | 0.111791i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.6327 | − | 20.1484i | −0.386683 | − | 0.669755i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.19999 | + | 10.7387i | 0.205867 | + | 0.356573i | 0.950409 | − | 0.311004i | \(-0.100665\pi\) |
−0.744541 | + | 0.667576i | \(0.767332\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.77764 | + | 13.4713i | 0.257968 | + | 0.446814i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.3176 | −1.07073 | −0.535365 | − | 0.844621i | \(-0.679826\pi\) | ||||
−0.535365 | + | 0.844621i | \(0.679826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.9372 | 0.428157 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.40027 | + | 12.8176i | −0.244645 | + | 0.423738i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.65054 | − | 4.59086i | −0.0875284 | − | 0.151604i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.8807 | − | 43.0946i | 0.820737 | − | 1.42156i | −0.0843968 | − | 0.996432i | \(-0.526896\pi\) |
0.905134 | − | 0.425126i | \(-0.139770\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.76165 | + | 9.97946i | −0.189853 | + | 0.328835i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.15150 | 0.202479 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.58203 | + | 9.66835i | −0.183536 | + | 0.317894i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.21517 | − | 3.83680i | −0.0727559 | − | 0.126017i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.38322 | 0.275044 | 0.137522 | − | 0.990499i | \(-0.456086\pi\) | ||||
0.137522 | + | 0.990499i | \(0.456086\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.8873 | + | 32.7137i | 0.619006 | + | 1.07215i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.66677 | 0.316476 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.31523 | −0.141123 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.9476 | −1.69706 | −0.848528 | − | 0.529151i | \(-0.822511\pi\) | ||||
−0.848528 | + | 0.529151i | \(0.822511\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.8904 | −0.649099 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.2896 | 0.531026 | 0.265513 | − | 0.964107i | \(-0.414459\pi\) | ||||
0.265513 | + | 0.964107i | \(0.414459\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −77.8856 | −2.53630 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.550200 | + | 0.952975i | 0.0178980 | + | 0.0310003i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.49425 | −0.0810522 | −0.0405261 | − | 0.999178i | \(-0.512903\pi\) | ||||
−0.0405261 | + | 0.999178i | \(0.512903\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.45329 | + | 7.71333i | 0.144560 | + | 0.250385i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.59315 | + | 4.49147i | −0.0840887 | + | 0.145646i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.9196 | 0.386113 | 0.193056 | − | 0.981188i | \(-0.438160\pi\) | ||||
0.193056 | + | 0.981188i | \(0.438160\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.97540 | − | 3.42150i | 0.0639226 | − | 0.110717i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.40500 | − | 9.36174i | 0.174719 | − | 0.302622i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.458866 | + | 0.794779i | 0.0148176 | + | 0.0256648i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.9782 | − | 22.4788i | 0.418650 | − | 0.725123i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.6613 | 0.472455 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.6912 | 0.537309 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.64293 | − | 11.5059i | −0.213622 | − | 0.370005i | 0.739223 | − | 0.673460i | \(-0.235193\pi\) |
−0.952845 | + | 0.303456i | \(0.901859\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.9424 | − | 20.6848i | −0.383644 | − | 0.664491i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.04198 | + | 15.6612i | 0.290171 | + | 0.502591i | 0.973850 | − | 0.227192i | \(-0.0729545\pi\) |
−0.683679 | + | 0.729783i | \(0.739621\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.98214 | + | 10.3614i | 0.191778 | + | 0.332170i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.500000 | − | 0.866025i | 0.0160128 | − | 0.0277350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.76151 | − | 13.4433i | 0.248313 | − | 0.430090i | −0.714745 | − | 0.699385i | \(-0.753457\pi\) |
0.963058 | + | 0.269295i | \(0.0867906\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.24226 | − | 7.34781i | −0.135583 | − | 0.234837i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.127209 | −0.00406148 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.34963 | −0.138732 | −0.0693658 | − | 0.997591i | \(-0.522098\pi\) | ||||
−0.0693658 | + | 0.997591i | \(0.522098\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.67221 | − | 15.0207i | −0.276319 | − | 0.478599i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.68409 | − | 9.84514i | 0.180927 | − | 0.313374i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.4958 | − | 25.1074i | 0.460939 | − | 0.798370i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.7433 | −0.881296 | −0.440648 | − | 0.897680i | \(-0.645251\pi\) | ||||
−0.440648 | + | 0.897680i | \(0.645251\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.39598 | − | 5.88201i | −0.107768 | − | 0.186660i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.8250 | − | 22.2136i | 0.406580 | − | 0.704218i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.2526 | −0.578065 | −0.289033 | − | 0.957319i | \(-0.593334\pi\) | ||||
−0.289033 | + | 0.957319i | \(0.593334\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.58203 | + | 9.66835i | −0.176608 | + | 0.305893i |
(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 | 4020.2.q.j.3781.3 | yes | 12 | |
67.37 | even | 3 | inner | 4020.2.q.j.841.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.j.841.3 | ✓ | 12 | 67.37 | even | 3 | inner | |
4020.2.q.j.3781.3 | yes | 12 | 1.1 | even | 1 | trivial |