Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(2899,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3450.2899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.d (of order \(2\), degree \(1\), 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: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.181494784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 12x^{3} + 49x^{2} - 14x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2899.5 | ||
Root | \(0.138157 - 0.138157i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.2899 |
Dual form | 3450.2.d.ba.2899.2 |
$q$-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 \(\left(\mathbb{Z}/3450\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(1151\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | − 0.723686i | − 0.273528i | −0.990604 | − | 0.136764i | \(-0.956330\pi\) | ||||
0.990604 | − | 0.136764i | \(-0.0436701\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.51445 | 1.66267 | 0.831335 | − | 0.555771i | \(-0.187577\pi\) | ||||
0.831335 | + | 0.555771i | \(0.187577\pi\) | |||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | 4.96183i | 1.37616i | 0.725634 | + | 0.688081i | \(0.241547\pi\) | ||||
−0.725634 | + | 0.688081i | \(0.758453\pi\) | |||||||
\(14\) | 0.723686 | 0.193413 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 4.23814i | − 1.02790i | −0.857820 | − | 0.513950i | \(-0.828182\pi\) | ||||
0.857820 | − | 0.513950i | \(-0.171818\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | −4.96183 | −1.13832 | −0.569160 | − | 0.822227i | \(-0.692732\pi\) | ||||
−0.569160 | + | 0.822227i | \(0.692732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.723686 | 0.157921 | ||||||||
\(22\) | 5.51445i | 1.17569i | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.96183 | −0.973094 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0.723686i | 0.136764i | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 5.51445i | 0.959943i | ||||||||
\(34\) | 4.23814 | 0.726835 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.23814i | 0.696746i | 0.937356 | + | 0.348373i | \(0.113266\pi\) | ||||
−0.937356 | + | 0.348373i | \(0.886734\pi\) | |||||||
\(38\) | − 4.96183i | − 0.804914i | ||||||||
\(39\) | −4.96183 | −0.794528 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.03817 | 0.162136 | 0.0810678 | − | 0.996709i | \(-0.474167\pi\) | ||||
0.0810678 | + | 0.996709i | \(0.474167\pi\) | |||||||
\(42\) | 0.723686i | 0.111667i | ||||||||
\(43\) | − 0.961825i | − 0.146677i | −0.997307 | − | 0.0733385i | \(-0.976635\pi\) | ||||
0.997307 | − | 0.0733385i | \(-0.0233653\pi\) | |||||||
\(44\) | −5.51445 | −0.831335 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 7.96183i | 1.16135i | 0.814135 | + | 0.580676i | \(0.197212\pi\) | ||||
−0.814135 | + | 0.580676i | \(0.802788\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 6.47628 | 0.925183 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.23814 | 0.593458 | ||||||||
\(52\) | − 4.96183i | − 0.688081i | ||||||||
\(53\) | − 6.47628i | − 0.889585i | −0.895634 | − | 0.444793i | \(-0.853277\pi\) | ||||
0.895634 | − | 0.444793i | \(-0.146723\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.723686 | −0.0967066 | ||||||||
\(57\) | − 4.96183i | − 0.657210i | ||||||||
\(58\) | 1.00000i | 0.131306i | ||||||||
\(59\) | 9.02891 | 1.17546 | 0.587732 | − | 0.809056i | \(-0.300021\pi\) | ||||
0.587732 | + | 0.809056i | \(0.300021\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.44737 | 0.953538 | 0.476769 | − | 0.879029i | \(-0.341808\pi\) | ||||
0.476769 | + | 0.879029i | \(0.341808\pi\) | |||||||
\(62\) | 6.00000i | 0.762001i | ||||||||
\(63\) | 0.723686i | 0.0911759i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.51445 | −0.678782 | ||||||||
\(67\) | 11.9237i | 1.45671i | 0.685202 | + | 0.728353i | \(0.259714\pi\) | ||||
−0.685202 | + | 0.728353i | \(0.740286\pi\) | |||||||
\(68\) | 4.23814i | 0.513950i | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.514453 | −0.0610544 | −0.0305272 | − | 0.999534i | \(-0.509719\pi\) | ||||
−0.0305272 | + | 0.999534i | \(0.509719\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − 0.447372i | − 0.0523609i | −0.999657 | − | 0.0261805i | \(-0.991666\pi\) | ||||
0.999657 | − | 0.0261805i | \(-0.00833445\pi\) | |||||||
\(74\) | −4.23814 | −0.492674 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.96183 | 0.569160 | ||||||||
\(77\) | − 3.99073i | − 0.454786i | ||||||||
\(78\) | − 4.96183i | − 0.561816i | ||||||||
\(79\) | 5.51445 | 0.620424 | 0.310212 | − | 0.950667i | \(-0.399600\pi\) | ||||
0.310212 | + | 0.950667i | \(0.399600\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.03817i | 0.114647i | ||||||||
\(83\) | 6.17106i | 0.677362i | 0.940901 | + | 0.338681i | \(0.109981\pi\) | ||||
−0.940901 | + | 0.338681i | \(0.890019\pi\) | |||||||
\(84\) | −0.723686 | −0.0789606 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.961825 | 0.103716 | ||||||||
\(87\) | 1.00000i | 0.107211i | ||||||||
\(88\) | − 5.51445i | − 0.587843i | ||||||||
\(89\) | 2.23814 | 0.237242 | 0.118621 | − | 0.992940i | \(-0.462153\pi\) | ||||
0.118621 | + | 0.992940i | \(0.462153\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.59080 | 0.376418 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 6.00000i | 0.622171i | ||||||||
\(94\) | −7.96183 | −0.821200 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | − 2.55263i | − 0.259180i | −0.991568 | − | 0.129590i | \(-0.958634\pi\) | ||||
0.991568 | − | 0.129590i | \(-0.0413661\pi\) | |||||||
\(98\) | 6.47628i | 0.654203i | ||||||||
\(99\) | −5.51445 | −0.554223 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.06708 | −0.106179 | −0.0530893 | − | 0.998590i | \(-0.516907\pi\) | ||||
−0.0530893 | + | 0.998590i | \(0.516907\pi\) | |||||||
\(102\) | 4.23814i | 0.419638i | ||||||||
\(103\) | − 5.75259i | − 0.566820i | −0.958999 | − | 0.283410i | \(-0.908534\pi\) | ||||
0.958999 | − | 0.283410i | \(-0.0914657\pi\) | |||||||
\(104\) | 4.96183 | 0.486547 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.47628 | 0.629032 | ||||||||
\(107\) | 15.9237i | 1.53940i | 0.638407 | + | 0.769699i | \(0.279594\pi\) | ||||
−0.638407 | + | 0.769699i | \(0.720406\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −17.2670 | −1.65388 | −0.826942 | − | 0.562288i | \(-0.809921\pi\) | ||||
−0.826942 | + | 0.562288i | \(0.809921\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.23814 | −0.402266 | ||||||||
\(112\) | − 0.723686i | − 0.0683819i | ||||||||
\(113\) | 6.23814i | 0.586835i | 0.955984 | + | 0.293417i | \(0.0947926\pi\) | ||||
−0.955984 | + | 0.293417i | \(0.905207\pi\) | |||||||
\(114\) | 4.96183 | 0.464718 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | − 4.96183i | − 0.458721i | ||||||||
\(118\) | 9.02891i | 0.831178i | ||||||||
\(119\) | −3.06708 | −0.281159 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.4092 | 1.76447 | ||||||||
\(122\) | 7.44737i | 0.674253i | ||||||||
\(123\) | 1.03817i | 0.0936091i | ||||||||
\(124\) | −6.00000 | −0.538816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.723686 | −0.0644711 | ||||||||
\(127\) | − 12.9526i | − 1.14935i | −0.818380 | − | 0.574677i | \(-0.805128\pi\) | ||||
0.818380 | − | 0.574677i | \(-0.194872\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 0.961825 | 0.0846840 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.5815 | 1.01188 | 0.505942 | − | 0.862568i | \(-0.331145\pi\) | ||||
0.505942 | + | 0.862568i | \(0.331145\pi\) | |||||||
\(132\) | − 5.51445i | − 0.479972i | ||||||||
\(133\) | 3.59080i | 0.311362i | ||||||||
\(134\) | −11.9237 | −1.03005 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.23814 | −0.363417 | ||||||||
\(137\) | 22.2381i | 1.89993i | 0.312353 | + | 0.949966i | \(0.398883\pi\) | ||||
−0.312353 | + | 0.949966i | \(0.601117\pi\) | |||||||
\(138\) | 1.00000i | 0.0851257i | ||||||||
\(139\) | −18.9907 | −1.61077 | −0.805386 | − | 0.592750i | \(-0.798042\pi\) | ||||
−0.805386 | + | 0.592750i | \(0.798042\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.96183 | −0.670507 | ||||||||
\(142\) | − 0.514453i | − 0.0431720i | ||||||||
\(143\) | 27.3618i | 2.28810i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.447372 | 0.0370248 | ||||||||
\(147\) | 6.47628i | 0.534154i | ||||||||
\(148\) | − 4.23814i | − 0.348373i | ||||||||
\(149\) | 5.92365 | 0.485284 | 0.242642 | − | 0.970116i | \(-0.421986\pi\) | ||||
0.242642 | + | 0.970116i | \(0.421986\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.47628 | 0.527032 | 0.263516 | − | 0.964655i | \(-0.415118\pi\) | ||||
0.263516 | + | 0.964655i | \(0.415118\pi\) | |||||||
\(152\) | 4.96183i | 0.402457i | ||||||||
\(153\) | 4.23814i | 0.342633i | ||||||||
\(154\) | 3.99073 | 0.321582 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.96183 | 0.397264 | ||||||||
\(157\) | 9.37102i | 0.747889i | 0.927451 | + | 0.373944i | \(0.121995\pi\) | ||||
−0.927451 | + | 0.373944i | \(0.878005\pi\) | |||||||
\(158\) | 5.51445i | 0.438706i | ||||||||
\(159\) | 6.47628 | 0.513602 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.723686 | −0.0570344 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 13.9237i | 1.09058i | 0.838246 | + | 0.545292i | \(0.183581\pi\) | ||||
−0.838246 | + | 0.545292i | \(0.816419\pi\) | |||||||
\(164\) | −1.03817 | −0.0810678 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.17106 | −0.478967 | ||||||||
\(167\) | 9.61971i | 0.744396i | 0.928153 | + | 0.372198i | \(0.121396\pi\) | ||||
−0.928153 | + | 0.372198i | \(0.878604\pi\) | |||||||
\(168\) | − 0.723686i | − 0.0558336i | ||||||||
\(169\) | −11.6197 | −0.893824 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.96183 | 0.379440 | ||||||||
\(172\) | 0.961825i | 0.0733385i | ||||||||
\(173\) | − 1.51445i | − 0.115142i | −0.998341 | − | 0.0575709i | \(-0.981664\pi\) | ||||
0.998341 | − | 0.0575709i | \(-0.0183355\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.51445 | 0.415668 | ||||||||
\(177\) | 9.02891i | 0.678654i | ||||||||
\(178\) | 2.23814i | 0.167756i | ||||||||
\(179\) | −10.4763 | −0.783034 | −0.391517 | − | 0.920171i | \(-0.628050\pi\) | ||||
−0.391517 | + | 0.920171i | \(0.628050\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.7433 | −1.61617 | −0.808084 | − | 0.589067i | \(-0.799495\pi\) | ||||
−0.808084 | + | 0.589067i | \(0.799495\pi\) | |||||||
\(182\) | 3.59080i | 0.266168i | ||||||||
\(183\) | 7.44737i | 0.550526i | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.00000 | −0.439941 | ||||||||
\(187\) | − 23.3710i | − 1.70906i | ||||||||
\(188\) | − 7.96183i | − 0.580676i | ||||||||
\(189\) | −0.723686 | −0.0526404 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.40920 | 0.608468 | 0.304234 | − | 0.952597i | \(-0.401600\pi\) | ||||
0.304234 | + | 0.952597i | \(0.401600\pi\) | |||||||
\(192\) | − 1.00000i | − 0.0721688i | ||||||||
\(193\) | 12.9907i | 0.935093i | 0.883968 | + | 0.467547i | \(0.154862\pi\) | ||||
−0.883968 | + | 0.467547i | \(0.845138\pi\) | |||||||
\(194\) | 2.55263 | 0.183268 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.47628 | −0.462591 | ||||||||
\(197\) | 20.5815i | 1.46637i | 0.680027 | + | 0.733187i | \(0.261968\pi\) | ||||
−0.680027 | + | 0.733187i | \(0.738032\pi\) | |||||||
\(198\) | − 5.51445i | − 0.391895i | ||||||||
\(199\) | 4.64734 | 0.329441 | 0.164720 | − | 0.986340i | \(-0.447328\pi\) | ||||
0.164720 | + | 0.986340i | \(0.447328\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.9237 | −0.841029 | ||||||||
\(202\) | − 1.06708i | − 0.0750796i | ||||||||
\(203\) | − 0.723686i | − 0.0507928i | ||||||||
\(204\) | −4.23814 | −0.296729 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.75259 | 0.400802 | ||||||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | 4.96183i | 0.344041i | ||||||||
\(209\) | −27.3618 | −1.89265 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.3328 | −1.60630 | −0.803150 | − | 0.595777i | \(-0.796844\pi\) | ||||
−0.803150 | + | 0.595777i | \(0.796844\pi\) | |||||||
\(212\) | 6.47628i | 0.444793i | ||||||||
\(213\) | − 0.514453i | − 0.0352498i | ||||||||
\(214\) | −15.9237 | −1.08852 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | − 4.34212i | − 0.294762i | ||||||||
\(218\) | − 17.2670i | − 1.16947i | ||||||||
\(219\) | 0.447372 | 0.0302306 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.0289 | 1.41456 | ||||||||
\(222\) | − 4.23814i | − 0.284445i | ||||||||
\(223\) | − 25.2947i | − 1.69386i | −0.531707 | − | 0.846928i | \(-0.678449\pi\) | ||||
0.531707 | − | 0.846928i | \(-0.321551\pi\) | |||||||
\(224\) | 0.723686 | 0.0483533 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.23814 | −0.414955 | ||||||||
\(227\) | 7.13288i | 0.473426i | 0.971580 | + | 0.236713i | \(0.0760701\pi\) | ||||
−0.971580 | + | 0.236713i | \(0.923930\pi\) | |||||||
\(228\) | 4.96183i | 0.328605i | ||||||||
\(229\) | 7.58154 | 0.501002 | 0.250501 | − | 0.968116i | \(-0.419405\pi\) | ||||
0.250501 | + | 0.968116i | \(0.419405\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.99073 | 0.262571 | ||||||||
\(232\) | − 1.00000i | − 0.0656532i | ||||||||
\(233\) | − 24.8855i | − 1.63030i | −0.579249 | − | 0.815151i | \(-0.696654\pi\) | ||||
0.579249 | − | 0.815151i | \(-0.303346\pi\) | |||||||
\(234\) | 4.96183 | 0.324365 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.02891 | −0.587732 | ||||||||
\(237\) | 5.51445i | 0.358202i | ||||||||
\(238\) | − 3.06708i | − 0.198809i | ||||||||
\(239\) | 18.0960 | 1.17053 | 0.585266 | − | 0.810841i | \(-0.300990\pi\) | ||||
0.585266 | + | 0.810841i | \(0.300990\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.8762 | 1.73125 | 0.865624 | − | 0.500694i | \(-0.166922\pi\) | ||||
0.865624 | + | 0.500694i | \(0.166922\pi\) | |||||||
\(242\) | 19.4092i | 1.24767i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −7.44737 | −0.476769 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.03817 | −0.0661916 | ||||||||
\(247\) | − 24.6197i | − 1.56651i | ||||||||
\(248\) | − 6.00000i | − 0.381000i | ||||||||
\(249\) | −6.17106 | −0.391075 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.79077 | −0.554868 | −0.277434 | − | 0.960745i | \(-0.589484\pi\) | ||||
−0.277434 | + | 0.960745i | \(0.589484\pi\) | |||||||
\(252\) | − 0.723686i | − 0.0455879i | ||||||||
\(253\) | − 5.51445i | − 0.346691i | ||||||||
\(254\) | 12.9526 | 0.812716 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 10.9526i | − 0.683202i | −0.939845 | − | 0.341601i | \(-0.889031\pi\) | ||||
0.939845 | − | 0.341601i | \(-0.110969\pi\) | |||||||
\(258\) | 0.961825i | 0.0598806i | ||||||||
\(259\) | 3.06708 | 0.190579 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 11.5815i | 0.715510i | ||||||||
\(263\) | − 20.8762i | − 1.28728i | −0.765327 | − | 0.643641i | \(-0.777423\pi\) | ||||
0.765327 | − | 0.643641i | \(-0.222577\pi\) | |||||||
\(264\) | 5.51445 | 0.339391 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.59080 | −0.220166 | ||||||||
\(267\) | 2.23814i | 0.136972i | ||||||||
\(268\) | − 11.9237i | − 0.728353i | ||||||||
\(269\) | −21.3618 | −1.30245 | −0.651225 | − | 0.758885i | \(-0.725744\pi\) | ||||
−0.651225 | + | 0.758885i | \(0.725744\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0289 | 0.669958 | 0.334979 | − | 0.942226i | \(-0.391271\pi\) | ||||
0.334979 | + | 0.942226i | \(0.391271\pi\) | |||||||
\(272\) | − 4.23814i | − 0.256975i | ||||||||
\(273\) | 3.59080i | 0.217325i | ||||||||
\(274\) | −22.2381 | −1.34346 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | − 15.4381i | − 0.927586i | −0.885944 | − | 0.463793i | \(-0.846488\pi\) | ||||
0.885944 | − | 0.463793i | \(-0.153512\pi\) | |||||||
\(278\) | − 18.9907i | − 1.13899i | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.16179 | −0.128962 | −0.0644808 | − | 0.997919i | \(-0.520539\pi\) | ||||
−0.0644808 | + | 0.997919i | \(0.520539\pi\) | |||||||
\(282\) | − 7.96183i | − 0.474120i | ||||||||
\(283\) | 16.9526i | 1.00772i | 0.863784 | + | 0.503862i | \(0.168088\pi\) | ||||
−0.863784 | + | 0.503862i | \(0.831912\pi\) | |||||||
\(284\) | 0.514453 | 0.0305272 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −27.3618 | −1.61793 | ||||||||
\(287\) | − 0.751312i | − 0.0443486i | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −0.961825 | −0.0565780 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.55263 | 0.149638 | ||||||||
\(292\) | 0.447372i | 0.0261805i | ||||||||
\(293\) | 13.0289i | 0.761157i | 0.924749 | + | 0.380578i | \(0.124275\pi\) | ||||
−0.924749 | + | 0.380578i | \(0.875725\pi\) | |||||||
\(294\) | −6.47628 | −0.377704 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.23814 | 0.246337 | ||||||||
\(297\) | − 5.51445i | − 0.319981i | ||||||||
\(298\) | 5.92365i | 0.343148i | ||||||||
\(299\) | 4.96183 | 0.286950 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.696059 | −0.0401202 | ||||||||
\(302\) | 6.47628i | 0.372668i | ||||||||
\(303\) | − 1.06708i | − 0.0613022i | ||||||||
\(304\) | −4.96183 | −0.284580 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.23814 | −0.242278 | ||||||||
\(307\) | − 27.0671i | − 1.54480i | −0.635136 | − | 0.772400i | \(-0.719056\pi\) | ||||
0.635136 | − | 0.772400i | \(-0.280944\pi\) | |||||||
\(308\) | 3.99073i | 0.227393i | ||||||||
\(309\) | 5.75259 | 0.327254 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.4670 | −1.78433 | −0.892165 | − | 0.451709i | \(-0.850814\pi\) | ||||
−0.892165 | + | 0.451709i | \(0.850814\pi\) | |||||||
\(312\) | 4.96183i | 0.280908i | ||||||||
\(313\) | 27.2947i | 1.54279i | 0.636359 | + | 0.771393i | \(0.280440\pi\) | ||||
−0.636359 | + | 0.771393i | \(0.719560\pi\) | |||||||
\(314\) | −9.37102 | −0.528837 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.51445 | −0.310212 | ||||||||
\(317\) | 11.0000i | 0.617822i | 0.951091 | + | 0.308911i | \(0.0999645\pi\) | ||||
−0.951091 | + | 0.308911i | \(0.900036\pi\) | |||||||
\(318\) | 6.47628i | 0.363172i | ||||||||
\(319\) | 5.51445 | 0.308750 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.9237 | −0.888772 | ||||||||
\(322\) | − 0.723686i | − 0.0403294i | ||||||||
\(323\) | 21.0289i | 1.17008i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.9237 | −0.771160 | ||||||||
\(327\) | − 17.2670i | − 0.954870i | ||||||||
\(328\) | − 1.03817i | − 0.0573236i | ||||||||
\(329\) | 5.76186 | 0.317662 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.51445 | −0.467997 | −0.233998 | − | 0.972237i | \(-0.575181\pi\) | ||||
−0.233998 | + | 0.972237i | \(0.575181\pi\) | |||||||
\(332\) | − 6.17106i | − 0.338681i | ||||||||
\(333\) | − 4.23814i | − 0.232249i | ||||||||
\(334\) | −9.61971 | −0.526367 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.723686 | 0.0394803 | ||||||||
\(337\) | 1.52372i | 0.0830024i | 0.999138 | + | 0.0415012i | \(0.0132140\pi\) | ||||
−0.999138 | + | 0.0415012i | \(0.986786\pi\) | |||||||
\(338\) | − 11.6197i | − 0.632029i | ||||||||
\(339\) | −6.23814 | −0.338809 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.0867 | 1.79175 | ||||||||
\(342\) | 4.96183i | 0.268305i | ||||||||
\(343\) | − 9.75259i | − 0.526591i | ||||||||
\(344\) | −0.961825 | −0.0518581 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.51445 | 0.0814175 | ||||||||
\(347\) | − 25.5815i | − 1.37329i | −0.726993 | − | 0.686644i | \(-0.759083\pi\) | ||||
0.726993 | − | 0.686644i | \(-0.240917\pi\) | |||||||
\(348\) | − 1.00000i | − 0.0536056i | ||||||||
\(349\) | 26.8855 | 1.43915 | 0.719573 | − | 0.694417i | \(-0.244337\pi\) | ||||
0.719573 | + | 0.694417i | \(0.244337\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.96183 | 0.264843 | ||||||||
\(352\) | 5.51445i | 0.293921i | ||||||||
\(353\) | 10.6197i | 0.565230i | 0.959233 | + | 0.282615i | \(0.0912019\pi\) | ||||
−0.959233 | + | 0.282615i | \(0.908798\pi\) | |||||||
\(354\) | −9.02891 | −0.479881 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.23814 | −0.118621 | ||||||||
\(357\) | − 3.06708i | − 0.162327i | ||||||||
\(358\) | − 10.4763i | − 0.553689i | ||||||||
\(359\) | 5.43810 | 0.287012 | 0.143506 | − | 0.989649i | \(-0.454162\pi\) | ||||
0.143506 | + | 0.989649i | \(0.454162\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.61971 | 0.295774 | ||||||||
\(362\) | − 21.7433i | − 1.14280i | ||||||||
\(363\) | 19.4092i | 1.01872i | ||||||||
\(364\) | −3.59080 | −0.188209 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.44737 | −0.389280 | ||||||||
\(367\) | − 8.56190i | − 0.446927i | −0.974712 | − | 0.223464i | \(-0.928264\pi\) | ||||
0.974712 | − | 0.223464i | \(-0.0717364\pi\) | |||||||
\(368\) | − 1.00000i | − 0.0521286i | ||||||||
\(369\) | −1.03817 | −0.0540452 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.68679 | −0.243326 | ||||||||
\(372\) | − 6.00000i | − 0.311086i | ||||||||
\(373\) | − 26.2960i | − 1.36155i | −0.732491 | − | 0.680776i | \(-0.761643\pi\) | ||||
0.732491 | − | 0.680776i | \(-0.238357\pi\) | |||||||
\(374\) | 23.3710 | 1.20849 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.96183 | 0.410600 | ||||||||
\(377\) | 4.96183i | 0.255547i | ||||||||
\(378\) | − 0.723686i | − 0.0372224i | ||||||||
\(379\) | 6.34212 | 0.325773 | 0.162886 | − | 0.986645i | \(-0.447920\pi\) | ||||
0.162886 | + | 0.986645i | \(0.447920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.9526 | 0.663580 | ||||||||
\(382\) | 8.40920i | 0.430252i | ||||||||
\(383\) | 35.4959i | 1.81376i | 0.421393 | + | 0.906878i | \(0.361541\pi\) | ||||
−0.421393 | + | 0.906878i | \(0.638459\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.9907 | −0.661211 | ||||||||
\(387\) | 0.961825i | 0.0488923i | ||||||||
\(388\) | 2.55263i | 0.129590i | ||||||||
\(389\) | 9.84730 | 0.499278 | 0.249639 | − | 0.968339i | \(-0.419688\pi\) | ||||
0.249639 | + | 0.968339i | \(0.419688\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.23814 | −0.214332 | ||||||||
\(392\) | − 6.47628i | − 0.327101i | ||||||||
\(393\) | 11.5815i | 0.584211i | ||||||||
\(394\) | −20.5815 | −1.03688 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.51445 | 0.277112 | ||||||||
\(397\) | 18.8762i | 0.947370i | 0.880694 | + | 0.473685i | \(0.157076\pi\) | ||||
−0.880694 | + | 0.473685i | \(0.842924\pi\) | |||||||
\(398\) | 4.64734i | 0.232950i | ||||||||
\(399\) | −3.59080 | −0.179765 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.5052 | 1.67317 | 0.836585 | − | 0.547838i | \(-0.184549\pi\) | ||||
0.836585 | + | 0.547838i | \(0.184549\pi\) | |||||||
\(402\) | − 11.9237i | − 0.594698i | ||||||||
\(403\) | 29.7710i | 1.48300i | ||||||||
\(404\) | 1.06708 | 0.0530893 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.723686 | 0.0359159 | ||||||||
\(407\) | 23.3710i | 1.15846i | ||||||||
\(408\) | − 4.23814i | − 0.209819i | ||||||||
\(409\) | 25.5341 | 1.26258 | 0.631290 | − | 0.775547i | \(-0.282526\pi\) | ||||
0.631290 | + | 0.775547i | \(0.282526\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.2381 | −1.09693 | ||||||||
\(412\) | 5.75259i | 0.283410i | ||||||||
\(413\) | − 6.53409i | − 0.321522i | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.96183 | −0.243273 | ||||||||
\(417\) | − 18.9907i | − 0.929980i | ||||||||
\(418\) | − 27.3618i | − 1.33831i | ||||||||
\(419\) | 37.2000 | 1.81734 | 0.908669 | − | 0.417518i | \(-0.137100\pi\) | ||||
0.908669 | + | 0.417518i | \(0.137100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.5815 | −0.564449 | −0.282225 | − | 0.959348i | \(-0.591072\pi\) | ||||
−0.282225 | + | 0.959348i | \(0.591072\pi\) | |||||||
\(422\) | − 23.3328i | − 1.13583i | ||||||||
\(423\) | − 7.96183i | − 0.387117i | ||||||||
\(424\) | −6.47628 | −0.314516 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.514453 | 0.0249254 | ||||||||
\(427\) | − 5.38956i | − 0.260819i | ||||||||
\(428\) | − 15.9237i | − 0.769699i | ||||||||
\(429\) | −27.3618 | −1.32104 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.37102 | 0.355050 | 0.177525 | − | 0.984116i | \(-0.443191\pi\) | ||||
0.177525 | + | 0.984116i | \(0.443191\pi\) | |||||||
\(432\) | − 1.00000i | − 0.0481125i | ||||||||
\(433\) | 19.3710i | 0.930912i | 0.885071 | + | 0.465456i | \(0.154110\pi\) | ||||
−0.885071 | + | 0.465456i | \(0.845890\pi\) | |||||||
\(434\) | 4.34212 | 0.208428 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.2670 | 0.826942 | ||||||||
\(437\) | 4.96183i | 0.237356i | ||||||||
\(438\) | 0.447372i | 0.0213763i | ||||||||
\(439\) | −17.5052 | −0.835477 | −0.417738 | − | 0.908567i | \(-0.637177\pi\) | ||||
−0.417738 | + | 0.908567i | \(0.637177\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.47628 | −0.308394 | ||||||||
\(442\) | 21.0289i | 1.00024i | ||||||||
\(443\) | − 17.3710i | − 0.825322i | −0.910885 | − | 0.412661i | \(-0.864599\pi\) | ||||
0.910885 | − | 0.412661i | \(-0.135401\pi\) | |||||||
\(444\) | 4.23814 | 0.201133 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 25.2947 | 1.19774 | ||||||||
\(447\) | 5.92365i | 0.280179i | ||||||||
\(448\) | 0.723686i | 0.0341909i | ||||||||
\(449\) | 16.8947 | 0.797312 | 0.398656 | − | 0.917100i | \(-0.369477\pi\) | ||||
0.398656 | + | 0.917100i | \(0.369477\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.72497 | 0.269578 | ||||||||
\(452\) | − 6.23814i | − 0.293417i | ||||||||
\(453\) | 6.47628i | 0.304282i | ||||||||
\(454\) | −7.13288 | −0.334763 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.96183 | −0.232359 | ||||||||
\(457\) | − 21.9237i | − 1.02555i | −0.858524 | − | 0.512773i | \(-0.828618\pi\) | ||||
0.858524 | − | 0.512773i | \(-0.171382\pi\) | |||||||
\(458\) | 7.58154i | 0.354262i | ||||||||
\(459\) | −4.23814 | −0.197819 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.65788 | −0.123790 | −0.0618950 | − | 0.998083i | \(-0.519714\pi\) | ||||
−0.0618950 | + | 0.998083i | \(0.519714\pi\) | |||||||
\(462\) | 3.99073i | 0.185666i | ||||||||
\(463\) | − 12.0000i | − 0.557687i | −0.960337 | − | 0.278844i | \(-0.910049\pi\) | ||||
0.960337 | − | 0.278844i | \(-0.0899511\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.8855 | 1.15280 | ||||||||
\(467\) | 15.8289i | 0.732476i | 0.930521 | + | 0.366238i | \(0.119354\pi\) | ||||
−0.930521 | + | 0.366238i | \(0.880646\pi\) | |||||||
\(468\) | 4.96183i | 0.229360i | ||||||||
\(469\) | 8.62898 | 0.398449 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.37102 | −0.431794 | ||||||||
\(472\) | − 9.02891i | − 0.415589i | ||||||||
\(473\) | − 5.30394i | − 0.243875i | ||||||||
\(474\) | −5.51445 | −0.253287 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.06708 | 0.140579 | ||||||||
\(477\) | 6.47628i | 0.296528i | ||||||||
\(478\) | 18.0960i | 0.827691i | ||||||||
\(479\) | −27.5723 | −1.25981 | −0.629905 | − | 0.776673i | \(-0.716906\pi\) | ||||
−0.629905 | + | 0.776673i | \(0.716906\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.0289 | −0.958836 | ||||||||
\(482\) | 26.8762i | 1.22418i | ||||||||
\(483\) | − 0.723686i | − 0.0329288i | ||||||||
\(484\) | −19.4092 | −0.882236 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | − 16.6868i | − 0.756151i | −0.925775 | − | 0.378075i | \(-0.876586\pi\) | ||||
0.925775 | − | 0.378075i | \(-0.123414\pi\) | |||||||
\(488\) | − 7.44737i | − 0.337127i | ||||||||
\(489\) | −13.9237 | −0.629649 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4288 | −0.606035 | −0.303017 | − | 0.952985i | \(-0.597994\pi\) | ||||
−0.303017 | + | 0.952985i | \(0.597994\pi\) | |||||||
\(492\) | − 1.03817i | − 0.0468045i | ||||||||
\(493\) | − 4.23814i | − 0.190876i | ||||||||
\(494\) | 24.6197 | 1.10769 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 0.372303i | 0.0167001i | ||||||||
\(498\) | − 6.17106i | − 0.276532i | ||||||||
\(499\) | 8.99073 | 0.402480 | 0.201240 | − | 0.979542i | \(-0.435503\pi\) | ||||
0.201240 | + | 0.979542i | \(0.435503\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.61971 | −0.429777 | ||||||||
\(502\) | − 8.79077i | − 0.392351i | ||||||||
\(503\) | 18.9618i | 0.845466i | 0.906254 | + | 0.422733i | \(0.138929\pi\) | ||||
−0.906254 | + | 0.422733i | \(0.861071\pi\) | |||||||
\(504\) | 0.723686 | 0.0322355 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.51445 | 0.245147 | ||||||||
\(507\) | − 11.6197i | − 0.516049i | ||||||||
\(508\) | 12.9526i | 0.574677i | ||||||||
\(509\) | −26.2276 | −1.16252 | −0.581259 | − | 0.813719i | \(-0.697440\pi\) | ||||
−0.581259 | + | 0.813719i | \(0.697440\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.323757 | −0.0143222 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 4.96183i | 0.219070i | ||||||||
\(514\) | 10.9526 | 0.483097 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.961825 | −0.0423420 | ||||||||
\(517\) | 43.9051i | 1.93094i | ||||||||
\(518\) | 3.06708i | 0.134760i | ||||||||
\(519\) | 1.51445 | 0.0664771 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.2381 | 1.41238 | 0.706189 | − | 0.708023i | \(-0.250413\pi\) | ||||
0.706189 | + | 0.708023i | \(0.250413\pi\) | |||||||
\(522\) | − 1.00000i | − 0.0437688i | ||||||||
\(523\) | 5.59080i | 0.244469i | 0.992501 | + | 0.122234i | \(0.0390060\pi\) | ||||
−0.992501 | + | 0.122234i | \(0.960994\pi\) | |||||||
\(524\) | −11.5815 | −0.505942 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.8762 | 0.910246 | ||||||||
\(527\) | − 25.4288i | − 1.10770i | ||||||||
\(528\) | 5.51445i | 0.239986i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.02891 | −0.391821 | ||||||||
\(532\) | − 3.59080i | − 0.155681i | ||||||||
\(533\) | 5.15124i | 0.223125i | ||||||||
\(534\) | −2.23814 | −0.0968538 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.9237 | 0.515023 | ||||||||
\(537\) | − 10.4763i | − 0.452085i | ||||||||
\(538\) | − 21.3618i | − 0.920971i | ||||||||
\(539\) | 35.7131 | 1.53827 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.6486 | 1.01673 | 0.508367 | − | 0.861141i | \(-0.330249\pi\) | ||||
0.508367 | + | 0.861141i | \(0.330249\pi\) | |||||||
\(542\) | 11.0289i | 0.473732i | ||||||||
\(543\) | − 21.7433i | − 0.933095i | ||||||||
\(544\) | 4.23814 | 0.181709 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.59080 | −0.153672 | ||||||||
\(547\) | − 39.3328i | − 1.68175i | −0.541229 | − | 0.840876i | \(-0.682041\pi\) | ||||
0.541229 | − | 0.840876i | \(-0.317959\pi\) | |||||||
\(548\) | − 22.2381i | − 0.949966i | ||||||||
\(549\) | −7.44737 | −0.317846 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.96183 | −0.211381 | ||||||||
\(552\) | − 1.00000i | − 0.0425628i | ||||||||
\(553\) | − 3.99073i | − 0.169703i | ||||||||
\(554\) | 15.4381 | 0.655902 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.9907 | 0.805386 | ||||||||
\(557\) | 34.2658i | 1.45189i | 0.687754 | + | 0.725944i | \(0.258597\pi\) | ||||
−0.687754 | + | 0.725944i | \(0.741403\pi\) | |||||||
\(558\) | − 6.00000i | − 0.254000i | ||||||||
\(559\) | 4.77241 | 0.201851 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.3710 | 0.986725 | ||||||||
\(562\) | − 2.16179i | − 0.0911896i | ||||||||
\(563\) | 20.5434i | 0.865799i | 0.901442 | + | 0.432900i | \(0.142510\pi\) | ||||
−0.901442 | + | 0.432900i | \(0.857490\pi\) | |||||||
\(564\) | 7.96183 | 0.335253 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.9526 | −0.712569 | ||||||||
\(567\) | − 0.723686i | − 0.0303920i | ||||||||
\(568\) | 0.514453i | 0.0215860i | ||||||||
\(569\) | 27.4474 | 1.15065 | 0.575327 | − | 0.817924i | \(-0.304875\pi\) | ||||
0.575327 | + | 0.817924i | \(0.304875\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.58154 | −0.233580 | −0.116790 | − | 0.993157i | \(-0.537260\pi\) | ||||
−0.116790 | + | 0.993157i | \(0.537260\pi\) | |||||||
\(572\) | − 27.3618i | − 1.14405i | ||||||||
\(573\) | 8.40920i | 0.351299i | ||||||||
\(574\) | 0.751312 | 0.0313592 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − 4.56190i | − 0.189914i | −0.995481 | − | 0.0949571i | \(-0.969729\pi\) | ||||
0.995481 | − | 0.0949571i | \(-0.0302714\pi\) | |||||||
\(578\) | − 0.961825i | − 0.0400067i | ||||||||
\(579\) | −12.9907 | −0.539876 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.46591 | 0.185277 | ||||||||
\(582\) | 2.55263i | 0.105810i | ||||||||
\(583\) | − 35.7131i | − 1.47909i | ||||||||
\(584\) | −0.447372 | −0.0185124 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.0289 | −0.538219 | ||||||||
\(587\) | 23.4474i | 0.967777i | 0.875130 | + | 0.483888i | \(0.160776\pi\) | ||||
−0.875130 | + | 0.483888i | \(0.839224\pi\) | |||||||
\(588\) | − 6.47628i | − 0.267077i | ||||||||
\(589\) | −29.7710 | −1.22669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.5815 | −0.846611 | ||||||||
\(592\) | 4.23814i | 0.174186i | ||||||||
\(593\) | 14.4092i | 0.591715i | 0.955232 | + | 0.295857i | \(0.0956053\pi\) | ||||
−0.955232 | + | 0.295857i | \(0.904395\pi\) | |||||||
\(594\) | 5.51445 | 0.226261 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.92365 | −0.242642 | ||||||||
\(597\) | 4.64734i | 0.190203i | ||||||||
\(598\) | 4.96183i | 0.202904i | ||||||||
\(599\) | −27.9815 | −1.14329 | −0.571646 | − | 0.820500i | \(-0.693695\pi\) | ||||
−0.571646 | + | 0.820500i | \(0.693695\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.38029 | −0.260257 | −0.130129 | − | 0.991497i | \(-0.541539\pi\) | ||||
−0.130129 | + | 0.991497i | \(0.541539\pi\) | |||||||
\(602\) | − 0.696059i | − 0.0283693i | ||||||||
\(603\) | − 11.9237i | − 0.485569i | ||||||||
\(604\) | −6.47628 | −0.263516 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.06708 | 0.0433472 | ||||||||
\(607\) | − 41.6946i | − 1.69233i | −0.532920 | − | 0.846166i | \(-0.678905\pi\) | ||||
0.532920 | − | 0.846166i | \(-0.321095\pi\) | |||||||
\(608\) | − 4.96183i | − 0.201229i | ||||||||
\(609\) | 0.723686 | 0.0293252 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.5052 | −1.59821 | ||||||||
\(612\) | − 4.23814i | − 0.171317i | ||||||||
\(613\) | − 10.8486i | − 0.438170i | −0.975706 | − | 0.219085i | \(-0.929693\pi\) | ||||
0.975706 | − | 0.219085i | \(-0.0703072\pi\) | |||||||
\(614\) | 27.0671 | 1.09234 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.99073 | −0.160791 | ||||||||
\(617\) | − 17.5052i | − 0.704732i | −0.935862 | − | 0.352366i | \(-0.885377\pi\) | ||||
0.935862 | − | 0.352366i | \(-0.114623\pi\) | |||||||
\(618\) | 5.75259i | 0.231403i | ||||||||
\(619\) | −22.3421 | −0.898005 | −0.449003 | − | 0.893530i | \(-0.648221\pi\) | ||||
−0.449003 | + | 0.893530i | \(0.648221\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | − 31.4670i | − 1.26171i | ||||||||
\(623\) | − 1.61971i | − 0.0648923i | ||||||||
\(624\) | −4.96183 | −0.198632 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −27.2947 | −1.09091 | ||||||||
\(627\) | − 27.3618i | − 1.09272i | ||||||||
\(628\) | − 9.37102i | − 0.373944i | ||||||||
\(629\) | 17.9618 | 0.716185 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.4105 | −0.533863 | −0.266931 | − | 0.963716i | \(-0.586010\pi\) | ||||
−0.266931 | + | 0.963716i | \(0.586010\pi\) | |||||||
\(632\) | − 5.51445i | − 0.219353i | ||||||||
\(633\) | − 23.3328i | − 0.927397i | ||||||||
\(634\) | −11.0000 | −0.436866 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.47628 | −0.256801 | ||||||||
\(637\) | 32.1342i | 1.27320i | ||||||||
\(638\) | 5.51445i | 0.218319i | ||||||||
\(639\) | 0.514453 | 0.0203515 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.9538 | 1.42009 | 0.710046 | − | 0.704156i | \(-0.248674\pi\) | ||||
0.710046 | + | 0.704156i | \(0.248674\pi\) | |||||||
\(642\) | − 15.9237i | − 0.628456i | ||||||||
\(643\) | 2.48555i | 0.0980204i | 0.998798 | + | 0.0490102i | \(0.0156067\pi\) | ||||
−0.998798 | + | 0.0490102i | \(0.984393\pi\) | |||||||
\(644\) | 0.723686 | 0.0285172 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.0289 | −0.827371 | ||||||||
\(647\) | − 44.4381i | − 1.74704i | −0.486786 | − | 0.873521i | \(-0.661831\pi\) | ||||
0.486786 | − | 0.873521i | \(-0.338169\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 49.7895 | 1.95441 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.34212 | 0.170181 | ||||||||
\(652\) | − 13.9237i | − 0.545292i | ||||||||
\(653\) | − 21.5526i | − 0.843420i | −0.906731 | − | 0.421710i | \(-0.861430\pi\) | ||||
0.906731 | − | 0.421710i | \(-0.138570\pi\) | |||||||
\(654\) | 17.2670 | 0.675195 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.03817 | 0.0405339 | ||||||||
\(657\) | 0.447372i | 0.0174536i | ||||||||
\(658\) | 5.76186i | 0.224621i | ||||||||
\(659\) | 7.33413 | 0.285697 | 0.142849 | − | 0.989745i | \(-0.454374\pi\) | ||||
0.142849 | + | 0.989745i | \(0.454374\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.1618 | −1.79549 | −0.897743 | − | 0.440520i | \(-0.854794\pi\) | ||||
−0.897743 | + | 0.440520i | \(0.854794\pi\) | |||||||
\(662\) | − 8.51445i | − 0.330924i | ||||||||
\(663\) | 21.0289i | 0.816695i | ||||||||
\(664\) | 6.17106 | 0.239483 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.23814 | 0.164225 | ||||||||
\(667\) | − 1.00000i | − 0.0387202i | ||||||||
\(668\) | − 9.61971i | − 0.372198i | ||||||||
\(669\) | 25.2947 | 0.977949 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.0682 | 1.58542 | ||||||||
\(672\) | 0.723686i | 0.0279168i | ||||||||
\(673\) | − 37.8184i | − 1.45779i | −0.684624 | − | 0.728896i | \(-0.740034\pi\) | ||||
0.684624 | − | 0.728896i | \(-0.259966\pi\) | |||||||
\(674\) | −1.52372 | −0.0586916 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.6197 | 0.446912 | ||||||||
\(677\) | − 2.21051i | − 0.0849569i | −0.999097 | − | 0.0424785i | \(-0.986475\pi\) | ||||
0.999097 | − | 0.0424785i | \(-0.0135254\pi\) | |||||||
\(678\) | − 6.23814i | − 0.239574i | ||||||||
\(679\) | −1.84730 | −0.0708929 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.13288 | −0.273333 | ||||||||
\(682\) | 33.0867i | 1.26696i | ||||||||
\(683\) | − 29.6393i | − 1.13412i | −0.823677 | − | 0.567059i | \(-0.808081\pi\) | ||||
0.823677 | − | 0.567059i | \(-0.191919\pi\) | |||||||
\(684\) | −4.96183 | −0.189720 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.75259 | 0.372356 | ||||||||
\(687\) | 7.58154i | 0.289254i | ||||||||
\(688\) | − 0.961825i | − 0.0366692i | ||||||||
\(689\) | 32.1342 | 1.22421 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.1512 | −1.52743 | −0.763713 | − | 0.645556i | \(-0.776626\pi\) | ||||
−0.763713 | + | 0.645556i | \(0.776626\pi\) | |||||||
\(692\) | 1.51445i | 0.0575709i | ||||||||
\(693\) | 3.99073i | 0.151595i | ||||||||
\(694\) | 25.5815 | 0.971062 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.00000 | 0.0379049 | ||||||||
\(697\) | − 4.39993i | − 0.166659i | ||||||||
\(698\) | 26.8855i | 1.01763i | ||||||||
\(699\) | 24.8855 | 0.941255 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.8762 | −1.54387 | −0.771937 | − | 0.635700i | \(-0.780712\pi\) | ||||
−0.771937 | + | 0.635700i | \(0.780712\pi\) | |||||||
\(702\) | 4.96183i | 0.187272i | ||||||||
\(703\) | − 21.0289i | − 0.793120i | ||||||||
\(704\) | −5.51445 | −0.207834 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.6197 | −0.399678 | ||||||||
\(707\) | 0.772232i | 0.0290428i | ||||||||
\(708\) | − 9.02891i | − 0.339327i | ||||||||
\(709\) | 25.0565 | 0.941018 | 0.470509 | − | 0.882395i | \(-0.344070\pi\) | ||||
0.470509 | + | 0.882395i | \(0.344070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.51445 | −0.206808 | ||||||||
\(712\) | − 2.23814i | − 0.0838778i | ||||||||
\(713\) | − 6.00000i | − 0.224702i | ||||||||
\(714\) | 3.06708 | 0.114783 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.4763 | 0.391517 | ||||||||
\(717\) | 18.0960i | 0.675807i | ||||||||
\(718\) | 5.43810i | 0.202948i | ||||||||
\(719\) | 34.5145 | 1.28717 | 0.643586 | − | 0.765374i | \(-0.277446\pi\) | ||||
0.643586 | + | 0.765374i | \(0.277446\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.16307 | −0.155041 | ||||||||
\(722\) | 5.61971i | 0.209144i | ||||||||
\(723\) | 26.8762i | 0.999537i | ||||||||
\(724\) | 21.7433 | 0.808084 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −19.4092 | −0.720343 | ||||||||
\(727\) | − 37.0289i | − 1.37333i | −0.726976 | − | 0.686663i | \(-0.759075\pi\) | ||||
0.726976 | − | 0.686663i | \(-0.240925\pi\) | |||||||
\(728\) | − 3.59080i | − 0.133084i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.07635 | −0.150769 | ||||||||
\(732\) | − 7.44737i | − 0.275263i | ||||||||
\(733\) | 8.02763i | 0.296507i | 0.988949 | + | 0.148254i | \(0.0473652\pi\) | ||||
−0.988949 | + | 0.148254i | \(0.952635\pi\) | |||||||
\(734\) | 8.56190 | 0.316025 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 65.7524i | 2.42202i | ||||||||
\(738\) | − 1.03817i | − 0.0382157i | ||||||||
\(739\) | 34.3432 | 1.26334 | 0.631668 | − | 0.775239i | \(-0.282371\pi\) | ||||
0.631668 | + | 0.775239i | \(0.282371\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.6197 | 0.904428 | ||||||||
\(742\) | − 4.68679i | − 0.172058i | ||||||||
\(743\) | − 30.8855i | − 1.13308i | −0.824035 | − | 0.566539i | \(-0.808282\pi\) | ||||
0.824035 | − | 0.566539i | \(-0.191718\pi\) | |||||||
\(744\) | 6.00000 | 0.219971 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.2960 | 0.962763 | ||||||||
\(747\) | − 6.17106i | − 0.225787i | ||||||||
\(748\) | 23.3710i | 0.854529i | ||||||||
\(749\) | 11.5237 | 0.421068 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0658 | 0.695721 | 0.347860 | − | 0.937546i | \(-0.386908\pi\) | ||||
0.347860 | + | 0.937546i | \(0.386908\pi\) | |||||||
\(752\) | 7.96183i | 0.290338i | ||||||||
\(753\) | − 8.79077i | − 0.320353i | ||||||||
\(754\) | −4.96183 | −0.180699 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.723686 | 0.0263202 | ||||||||
\(757\) | 26.1040i | 0.948765i | 0.880319 | + | 0.474383i | \(0.157329\pi\) | ||||
−0.880319 | + | 0.474383i | \(0.842671\pi\) | |||||||
\(758\) | 6.34212i | 0.230356i | ||||||||
\(759\) | 5.51445 | 0.200162 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.9433 | 0.614194 | 0.307097 | − | 0.951678i | \(-0.400642\pi\) | ||||
0.307097 | + | 0.951678i | \(0.400642\pi\) | |||||||
\(762\) | 12.9526i | 0.469222i | ||||||||
\(763\) | 12.4959i | 0.452383i | ||||||||
\(764\) | −8.40920 | −0.304234 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −35.4959 | −1.28252 | ||||||||
\(767\) | 44.7999i | 1.61763i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 41.5815 | 1.49947 | 0.749734 | − | 0.661739i | \(-0.230181\pi\) | ||||
0.749734 | + | 0.661739i | \(0.230181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.9526 | 0.394447 | ||||||||
\(772\) | − 12.9907i | − 0.467547i | ||||||||
\(773\) | 39.2183i | 1.41059i | 0.708916 | + | 0.705293i | \(0.249184\pi\) | ||||
−0.708916 | + | 0.705293i | \(0.750816\pi\) | |||||||
\(774\) | −0.961825 | −0.0345721 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.55263 | −0.0916340 | ||||||||
\(777\) | 3.06708i | 0.110031i | ||||||||
\(778\) | 9.84730i | 0.353043i | ||||||||
\(779\) | −5.15124 | −0.184562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.83693 | −0.101513 | ||||||||
\(782\) | − 4.23814i | − 0.151556i | ||||||||
\(783\) | − 1.00000i | − 0.0357371i | ||||||||
\(784\) | 6.47628 | 0.231296 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11.5815 | −0.413100 | ||||||||
\(787\) | 17.3039i | 0.616819i | 0.951254 | + | 0.308409i | \(0.0997967\pi\) | ||||
−0.951254 | + | 0.308409i | \(0.900203\pi\) | |||||||
\(788\) | − 20.5815i | − 0.733187i | ||||||||
\(789\) | 20.8762 | 0.743213 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.51445 | 0.160515 | ||||||||
\(792\) | 5.51445i | 0.195948i | ||||||||
\(793\) | 36.9526i | 1.31222i | ||||||||
\(794\) | −18.8762 | −0.669892 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.64734 | −0.164720 | ||||||||
\(797\) | − 12.3236i | − 0.436524i | −0.975890 | − | 0.218262i | \(-0.929961\pi\) | ||||
0.975890 | − | 0.218262i | \(-0.0700387\pi\) | |||||||
\(798\) | − 3.59080i | − 0.127113i | ||||||||
\(799\) | 33.7433 | 1.19375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.23814 | −0.0790808 | ||||||||
\(802\) | 33.5052i | 1.18311i | ||||||||
\(803\) | − 2.46701i | − 0.0870589i | ||||||||
\(804\) | 11.9237 | 0.420515 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −29.7710 | −1.04864 | ||||||||
\(807\) | − 21.3618i | − 0.751969i | ||||||||
\(808\) | 1.06708i | 0.0375398i | ||||||||
\(809\) | 21.3618 | 0.751039 | 0.375520 | − | 0.926814i | \(-0.377464\pi\) | ||||
0.375520 | + | 0.926814i | \(0.377464\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.0104 | 1.65076 | 0.825379 | − | 0.564579i | \(-0.190962\pi\) | ||||
0.825379 | + | 0.564579i | \(0.190962\pi\) | |||||||
\(812\) | 0.723686i | 0.0253964i | ||||||||
\(813\) | 11.0289i | 0.386801i | ||||||||
\(814\) | −23.3710 | −0.819154 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.23814 | 0.148365 | ||||||||
\(817\) | 4.77241i | 0.166965i | ||||||||
\(818\) | 25.5341i | 0.892779i | ||||||||
\(819\) | −3.59080 | −0.125473 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.4855 | 1.06395 | 0.531976 | − | 0.846759i | \(-0.321449\pi\) | ||||
0.531976 | + | 0.846759i | \(0.321449\pi\) | |||||||
\(822\) | − 22.2381i | − 0.775644i | ||||||||
\(823\) | − 6.34212i | − 0.221072i | −0.993872 | − | 0.110536i | \(-0.964743\pi\) | ||||
0.993872 | − | 0.110536i | \(-0.0352568\pi\) | |||||||
\(824\) | −5.75259 | −0.200401 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.53409 | 0.227350 | ||||||||
\(827\) | − 56.1340i | − 1.95197i | −0.217838 | − | 0.975985i | \(-0.569900\pi\) | ||||
0.217838 | − | 0.975985i | \(-0.430100\pi\) | |||||||
\(828\) | − 1.00000i | − 0.0347524i | ||||||||
\(829\) | 9.93292 | 0.344985 | 0.172492 | − | 0.985011i | \(-0.444818\pi\) | ||||
0.172492 | + | 0.985011i | \(0.444818\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.4381 | 0.535542 | ||||||||
\(832\) | − 4.96183i | − 0.172020i | ||||||||
\(833\) | − 27.4474i | − 0.950995i | ||||||||
\(834\) | 18.9907 | 0.657595 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 27.3618 | 0.946326 | ||||||||
\(837\) | − 6.00000i | − 0.207390i | ||||||||
\(838\) | 37.2000i | 1.28505i | ||||||||
\(839\) | −31.7802 | −1.09718 | −0.548588 | − | 0.836093i | \(-0.684834\pi\) | ||||
−0.548588 | + | 0.836093i | \(0.684834\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | − 11.5815i | − 0.399126i | ||||||||
\(843\) | − 2.16179i | − 0.0744560i | ||||||||
\(844\) | 23.3328 | 0.803150 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.96183 | 0.273733 | ||||||||
\(847\) | − 14.0462i | − 0.482632i | ||||||||
\(848\) | − 6.47628i | − 0.222396i | ||||||||
\(849\) | −16.9526 | −0.581810 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.23814 | 0.145282 | ||||||||
\(852\) | 0.514453i | 0.0176249i | ||||||||
\(853\) | − 5.30394i | − 0.181603i | −0.995869 | − | 0.0908017i | \(-0.971057\pi\) | ||||
0.995869 | − | 0.0908017i | \(-0.0289430\pi\) | |||||||
\(854\) | 5.38956 | 0.184427 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.9237 | 0.544259 | ||||||||
\(857\) | 19.6579i | 0.671501i | 0.941951 | + | 0.335750i | \(0.108990\pi\) | ||||
−0.941951 | + | 0.335750i | \(0.891010\pi\) | |||||||
\(858\) | − 27.3618i | − 0.934115i | ||||||||
\(859\) | −57.7524 | −1.97049 | −0.985244 | − | 0.171159i | \(-0.945249\pi\) | ||||
−0.985244 | + | 0.171159i | \(0.945249\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.751312 | 0.0256047 | ||||||||
\(862\) | 7.37102i | 0.251058i | ||||||||
\(863\) | − 27.3328i | − 0.930421i | −0.885200 | − | 0.465210i | \(-0.845979\pi\) | ||||
0.885200 | − | 0.465210i | \(-0.154021\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.3710 | −0.658254 | ||||||||
\(867\) | − 0.961825i | − 0.0326653i | ||||||||
\(868\) | 4.34212i | 0.147381i | ||||||||
\(869\) | 30.4092 | 1.03156 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −59.1631 | −2.00466 | ||||||||
\(872\) | 17.2670i | 0.584736i | ||||||||
\(873\) | 2.55263i | 0.0863934i | ||||||||
\(874\) | −4.96183 | −0.167836 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.447372 | −0.0151153 | ||||||||
\(877\) | − 14.0000i | − 0.472746i | −0.971662 | − | 0.236373i | \(-0.924041\pi\) | ||||
0.971662 | − | 0.236373i | \(-0.0759588\pi\) | |||||||
\(878\) | − 17.5052i | − 0.590771i | ||||||||
\(879\) | −13.0289 | −0.439454 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.4474 | 0.655199 | 0.327599 | − | 0.944817i | \(-0.393760\pi\) | ||||
0.327599 | + | 0.944817i | \(0.393760\pi\) | |||||||
\(882\) | − 6.47628i | − 0.218068i | ||||||||
\(883\) | − 34.2854i | − 1.15380i | −0.816816 | − | 0.576898i | \(-0.804263\pi\) | ||||
0.816816 | − | 0.576898i | \(-0.195737\pi\) | |||||||
\(884\) | −21.0289 | −0.707279 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.3710 | 0.583591 | ||||||||
\(887\) | 35.9433i | 1.20686i | 0.797417 | + | 0.603429i | \(0.206199\pi\) | ||||
−0.797417 | + | 0.603429i | \(0.793801\pi\) | |||||||
\(888\) | 4.23814i | 0.142223i | ||||||||
\(889\) | −9.37358 | −0.314380 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.51445 | 0.184741 | ||||||||
\(892\) | 25.2947i | 0.846928i | ||||||||
\(893\) | − 39.5052i | − 1.32199i | ||||||||
\(894\) | −5.92365 | −0.198117 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.723686 | −0.0241766 | ||||||||
\(897\) | 4.96183i | 0.165671i | ||||||||
\(898\) | 16.8947i | 0.563785i | ||||||||
\(899\) | 6.00000 | 0.200111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.4474 | −0.914405 | ||||||||
\(902\) | 5.72497i | 0.190621i | ||||||||
\(903\) | − 0.696059i | − 0.0231634i | ||||||||
\(904\) | 6.23814 | 0.207477 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.47628 | −0.215160 | ||||||||
\(907\) | − 34.0671i | − 1.13118i | −0.824687 | − | 0.565589i | \(-0.808649\pi\) | ||||
0.824687 | − | 0.565589i | \(-0.191351\pi\) | |||||||
\(908\) | − 7.13288i | − 0.236713i | ||||||||
\(909\) | 1.06708 | 0.0353929 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0671 | 0.532326 | 0.266163 | − | 0.963928i | \(-0.414244\pi\) | ||||
0.266163 | + | 0.963928i | \(0.414244\pi\) | |||||||
\(912\) | − 4.96183i | − 0.164302i | ||||||||
\(913\) | 34.0300i | 1.12623i | ||||||||
\(914\) | 21.9237 | 0.725170 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.58154 | −0.250501 | ||||||||
\(917\) | − 8.38139i | − 0.276778i | ||||||||
\(918\) | − 4.23814i | − 0.139879i | ||||||||
\(919\) | 19.7619 | 0.651884 | 0.325942 | − | 0.945390i | \(-0.394319\pi\) | ||||
0.325942 | + | 0.945390i | \(0.394319\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.0671 | 0.891891 | ||||||||
\(922\) | − 2.65788i | − 0.0875328i | ||||||||
\(923\) | − 2.55263i | − 0.0840208i | ||||||||
\(924\) | −3.99073 | −0.131285 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12.0000 | 0.394344 | ||||||||
\(927\) | 5.75259i | 0.188940i | ||||||||
\(928\) | 1.00000i | 0.0328266i | ||||||||
\(929\) | 6.33285 | 0.207774 | 0.103887 | − | 0.994589i | \(-0.466872\pi\) | ||||
0.103887 | + | 0.994589i | \(0.466872\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.1342 | −1.05315 | ||||||||
\(932\) | 24.8855i | 0.815151i | ||||||||
\(933\) | − 31.4670i | − 1.03018i | ||||||||
\(934\) | −15.8289 | −0.517939 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.96183 | −0.162182 | ||||||||
\(937\) | − 25.8473i | − 0.844395i | −0.906504 | − | 0.422197i | \(-0.861259\pi\) | ||||
0.906504 | − | 0.422197i | \(-0.138741\pi\) | |||||||
\(938\) | 8.62898i | 0.281746i | ||||||||
\(939\) | −27.2947 | −0.890728 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.04744 | −0.294938 | −0.147469 | − | 0.989067i | \(-0.547113\pi\) | ||||
−0.147469 | + | 0.989067i | \(0.547113\pi\) | |||||||
\(942\) | − 9.37102i | − 0.305324i | ||||||||
\(943\) | − 1.03817i | − 0.0338076i | ||||||||
\(944\) | 9.02891 | 0.293866 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.30394 | 0.172446 | ||||||||
\(947\) | − 0.971093i | − 0.0315563i | −0.999876 | − | 0.0157781i | \(-0.994977\pi\) | ||||
0.999876 | − | 0.0157781i | \(-0.00502255\pi\) | |||||||
\(948\) | − 5.51445i | − 0.179101i | ||||||||
\(949\) | 2.21978 | 0.0720571 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.0000 | −0.356699 | ||||||||
\(952\) | 3.06708i | 0.0994047i | ||||||||
\(953\) | 5.19070i | 0.168143i | 0.996460 | + | 0.0840716i | \(0.0267924\pi\) | ||||
−0.996460 | + | 0.0840716i | \(0.973208\pi\) | |||||||
\(954\) | −6.47628 | −0.209677 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.0960 | −0.585266 | ||||||||
\(957\) | 5.51445i | 0.178257i | ||||||||
\(958\) | − 27.5723i | − 0.890820i | ||||||||
\(959\) | 16.0934 | 0.519684 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | − 21.0289i | − 0.677999i | ||||||||
\(963\) | − 15.9237i | − 0.513132i | ||||||||
\(964\) | −26.8762 | −0.865624 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.723686 | 0.0232842 | ||||||||
\(967\) | − 17.0289i | − 0.547613i | −0.961785 | − | 0.273806i | \(-0.911717\pi\) | ||||
0.961785 | − | 0.273806i | \(-0.0882827\pi\) | |||||||
\(968\) | − 19.4092i | − 0.623835i | ||||||||
\(969\) | −21.0289 | −0.675546 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.4683 | −0.817316 | −0.408658 | − | 0.912688i | \(-0.634003\pi\) | ||||
−0.408658 | + | 0.912688i | \(0.634003\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | 13.7433i | 0.440591i | ||||||||
\(974\) | 16.6868 | 0.534679 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.44737 | 0.238385 | ||||||||
\(977\) | 23.9513i | 0.766269i | 0.923693 | + | 0.383135i | \(0.125155\pi\) | ||||
−0.923693 | + | 0.383135i | \(0.874845\pi\) | |||||||
\(978\) | − 13.9237i | − 0.445229i | ||||||||
\(979\) | 12.3421 | 0.394456 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.2670 | 0.551294 | ||||||||
\(982\) | − 13.4288i | − 0.428531i | ||||||||
\(983\) | 13.5723i | 0.432888i | 0.976295 | + | 0.216444i | \(0.0694459\pi\) | ||||
−0.976295 | + | 0.216444i | \(0.930554\pi\) | |||||||
\(984\) | 1.03817 | 0.0330958 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.23814 | 0.134970 | ||||||||
\(987\) | 5.76186i | 0.183402i | ||||||||
\(988\) | 24.6197i | 0.783257i | ||||||||
\(989\) | −0.961825 | −0.0305843 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.9237 | 0.823492 | 0.411746 | − | 0.911299i | \(-0.364919\pi\) | ||||
0.411746 | + | 0.911299i | \(0.364919\pi\) | |||||||
\(992\) | 6.00000i | 0.190500i | ||||||||
\(993\) | − 8.51445i | − 0.270198i | ||||||||
\(994\) | −0.372303 | −0.0118087 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.17106 | 0.195537 | ||||||||
\(997\) | 2.06708i | 0.0654651i | 0.999464 | + | 0.0327326i | \(0.0104210\pi\) | ||||
−0.999464 | + | 0.0327326i | \(0.989579\pi\) | |||||||
\(998\) | 8.99073i | 0.284597i | ||||||||
\(999\) | 4.23814 | 0.134089 |
(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 | 3450.2.d.ba.2899.5 | 6 | ||
5.2 | odd | 4 | 3450.2.a.bp.1.2 | ✓ | 3 | ||
5.3 | odd | 4 | 3450.2.a.bs.1.2 | yes | 3 | ||
5.4 | even | 2 | inner | 3450.2.d.ba.2899.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3450.2.a.bp.1.2 | ✓ | 3 | 5.2 | odd | 4 | ||
3450.2.a.bs.1.2 | yes | 3 | 5.3 | odd | 4 | ||
3450.2.d.ba.2899.2 | 6 | 5.4 | even | 2 | inner | ||
3450.2.d.ba.2899.5 | 6 | 1.1 | even | 1 | trivial |