Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(379,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, 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("630.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.g (of order \(2\), degree \(1\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.4 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.379 |
Dual form | 630.2.g.g.379.2 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.224745 | − | 2.22474i | 0.100509 | − | 0.994936i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.22474 | + | 0.224745i | 0.703526 | + | 0.0710706i | ||||
\(11\) | −4.89898 | −1.47710 | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.449490i | 0.124666i | 0.998055 | + | 0.0623330i | \(0.0198541\pi\) | ||||
−0.998055 | + | 0.0623330i | \(0.980146\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.44949 | −1.47961 | −0.739807 | − | 0.672819i | \(-0.765083\pi\) | ||||
−0.739807 | + | 0.672819i | \(0.765083\pi\) | |||||||
\(20\) | −0.224745 | + | 2.22474i | −0.0502545 | + | 0.497468i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 4.89898i | − | 1.04447i | ||||||
\(23\) | − | 6.89898i | − | 1.43854i | −0.694732 | − | 0.719268i | \(-0.744477\pi\) | ||
0.694732 | − | 0.719268i | \(-0.255523\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.89898 | − | 1.00000i | −0.979796 | − | 0.200000i | ||||
\(26\) | −0.449490 | −0.0881522 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | −2.89898 | −0.538327 | −0.269163 | − | 0.963095i | \(-0.586747\pi\) | ||||
−0.269163 | + | 0.963095i | \(0.586747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.898979 | −0.161461 | −0.0807307 | − | 0.996736i | \(-0.525725\pi\) | ||||
−0.0807307 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | −2.22474 | − | 0.224745i | −0.376051 | − | 0.0379888i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | − | 6.44949i | − | 1.04625i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.22474 | − | 0.224745i | −0.351763 | − | 0.0355353i | ||||
\(41\) | 10.8990 | 1.70213 | 0.851067 | − | 0.525057i | \(-0.175956\pi\) | ||||
0.851067 | + | 0.525057i | \(0.175956\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.89898i | − | 1.35708i | −0.734563 | − | 0.678541i | \(-0.762613\pi\) | ||
0.734563 | − | 0.678541i | \(-0.237387\pi\) | |||||||
\(44\) | 4.89898 | 0.738549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.89898 | 1.01720 | ||||||||
\(47\) | 0.898979i | 0.131130i | 0.997848 | + | 0.0655648i | \(0.0208849\pi\) | ||||
−0.997848 | + | 0.0655648i | \(0.979115\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 1.00000 | − | 4.89898i | 0.141421 | − | 0.692820i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 0.449490i | − | 0.0623330i | ||||||
\(53\) | − | 1.10102i | − | 0.151237i | −0.997137 | − | 0.0756184i | \(-0.975907\pi\) | ||
0.997137 | − | 0.0756184i | \(-0.0240931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.10102 | + | 10.8990i | −0.148462 | + | 1.46962i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 2.89898i | − | 0.380655i | ||||||
\(59\) | −6.44949 | −0.839652 | −0.419826 | − | 0.907605i | \(-0.637909\pi\) | ||||
−0.419826 | + | 0.907605i | \(0.637909\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.44949 | 1.08185 | 0.540923 | − | 0.841072i | \(-0.318075\pi\) | ||||
0.540923 | + | 0.841072i | \(0.318075\pi\) | |||||||
\(62\) | − | 0.898979i | − | 0.114171i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.00000 | + | 0.101021i | 0.124035 | + | 0.0125301i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 2.00000i | 0.242536i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.224745 | − | 2.22474i | 0.0268622 | − | 0.265908i | ||||
\(71\) | 10.8990 | 1.29347 | 0.646735 | − | 0.762714i | \(-0.276134\pi\) | ||||
0.646735 | + | 0.762714i | \(0.276134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.89898i | 0.807464i | 0.914877 | + | 0.403732i | \(0.132287\pi\) | ||||
−0.914877 | + | 0.403732i | \(0.867713\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.44949 | 0.739807 | ||||||||
\(77\) | 4.89898i | 0.558291i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.89898 | 0.326161 | 0.163080 | − | 0.986613i | \(-0.447857\pi\) | ||||
0.163080 | + | 0.986613i | \(0.447857\pi\) | |||||||
\(80\) | 0.224745 | − | 2.22474i | 0.0251272 | − | 0.248734i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.8990i | 1.20359i | ||||||||
\(83\) | 2.44949i | 0.268866i | 0.990923 | + | 0.134433i | \(0.0429214\pi\) | ||||
−0.990923 | + | 0.134433i | \(0.957079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.44949 | − | 0.449490i | −0.482615 | − | 0.0487540i | ||||
\(86\) | 8.89898 | 0.959602 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.89898i | 0.522233i | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.449490 | 0.0471193 | ||||||||
\(92\) | 6.89898i | 0.719268i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.898979 | −0.0927227 | ||||||||
\(95\) | −1.44949 | + | 14.3485i | −0.148715 | + | 1.47212i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.79796i | − | 0.385624i | −0.981236 | − | 0.192812i | \(-0.938239\pi\) | ||
0.981236 | − | 0.192812i | \(-0.0617608\pi\) | |||||||
\(98\) | − | 1.00000i | − | 0.101015i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.89898 | + | 1.00000i | 0.489898 | + | 0.100000i | ||||
\(101\) | −8.44949 | −0.840756 | −0.420378 | − | 0.907349i | \(-0.638102\pi\) | ||||
−0.420378 | + | 0.907349i | \(0.638102\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.10102i | − | 0.305553i | −0.988261 | − | 0.152776i | \(-0.951179\pi\) | ||
0.988261 | − | 0.152776i | \(-0.0488214\pi\) | |||||||
\(104\) | 0.449490 | 0.0440761 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.10102 | 0.106941 | ||||||||
\(107\) | 8.00000i | 0.773389i | 0.922208 | + | 0.386695i | \(0.126383\pi\) | ||||
−0.922208 | + | 0.386695i | \(0.873617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.89898 | 0.277672 | 0.138836 | − | 0.990315i | \(-0.455664\pi\) | ||||
0.138836 | + | 0.990315i | \(0.455664\pi\) | |||||||
\(110\) | −10.8990 | − | 1.10102i | −1.03918 | − | 0.104978i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | 0.202041i | 0.0190064i | 0.999955 | + | 0.00950321i | \(0.00302501\pi\) | ||||
−0.999955 | + | 0.00950321i | \(0.996975\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.3485 | − | 1.55051i | −1.43125 | − | 0.144586i | ||||
\(116\) | 2.89898 | 0.269163 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.44949i | − | 0.593724i | ||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 8.44949i | 0.764981i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.898979 | 0.0807307 | ||||||||
\(125\) | −3.32577 | + | 10.6742i | −0.297465 | + | 0.954733i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.10102i | − | 0.452642i | −0.974053 | − | 0.226321i | \(-0.927330\pi\) | ||
0.974053 | − | 0.226321i | \(-0.0726699\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.101021 | + | 1.00000i | −0.00886009 | + | 0.0877058i | ||||
\(131\) | 1.55051 | 0.135469 | 0.0677344 | − | 0.997703i | \(-0.478423\pi\) | ||||
0.0677344 | + | 0.997703i | \(0.478423\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.44949i | 0.559242i | ||||||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00000 | −0.171499 | ||||||||
\(137\) | − | 17.7980i | − | 1.52058i | −0.649582 | − | 0.760291i | \(-0.725056\pi\) | ||
0.649582 | − | 0.760291i | \(-0.274944\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.44949 | −0.547039 | −0.273519 | − | 0.961867i | \(-0.588188\pi\) | ||||
−0.273519 | + | 0.961867i | \(0.588188\pi\) | |||||||
\(140\) | 2.22474 | + | 0.224745i | 0.188025 | + | 0.0189944i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.8990i | 0.914622i | ||||||||
\(143\) | − | 2.20204i | − | 0.184144i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.651531 | + | 6.44949i | −0.0541067 | + | 0.535601i | ||||
\(146\) | −6.89898 | −0.570964 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 2.00000i | − | 0.164399i | ||||||
\(149\) | 15.7980 | 1.29422 | 0.647110 | − | 0.762397i | \(-0.275978\pi\) | ||||
0.647110 | + | 0.762397i | \(0.275978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5959 | −1.59469 | −0.797347 | − | 0.603522i | \(-0.793764\pi\) | ||||
−0.797347 | + | 0.603522i | \(0.793764\pi\) | |||||||
\(152\) | 6.44949i | 0.523123i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.89898 | −0.394771 | ||||||||
\(155\) | −0.202041 | + | 2.00000i | −0.0162283 | + | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.44949i | 0.674343i | 0.941443 | + | 0.337171i | \(0.109470\pi\) | ||||
−0.941443 | + | 0.337171i | \(0.890530\pi\) | |||||||
\(158\) | 2.89898i | 0.230630i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.22474 | + | 0.224745i | 0.175882 | + | 0.0177676i | ||||
\(161\) | −6.89898 | −0.543716 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.8990i | 1.32363i | 0.749667 | + | 0.661815i | \(0.230214\pi\) | ||||
−0.749667 | + | 0.661815i | \(0.769786\pi\) | |||||||
\(164\) | −10.8990 | −0.851067 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.44949 | −0.190117 | ||||||||
\(167\) | − | 4.89898i | − | 0.379094i | −0.981872 | − | 0.189547i | \(-0.939298\pi\) | ||
0.981872 | − | 0.189547i | \(-0.0607020\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7980 | 0.984458 | ||||||||
\(170\) | 0.449490 | − | 4.44949i | 0.0344743 | − | 0.341260i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.89898i | 0.678541i | ||||||||
\(173\) | 18.2474i | 1.38733i | 0.720299 | + | 0.693664i | \(0.244005\pi\) | ||||
−0.720299 | + | 0.693664i | \(0.755995\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | + | 4.89898i | −0.0755929 | + | 0.370328i | ||||
\(176\) | −4.89898 | −0.369274 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 10.0000i | − | 0.749532i | ||||||
\(179\) | −5.79796 | −0.433360 | −0.216680 | − | 0.976243i | \(-0.569523\pi\) | ||||
−0.216680 | + | 0.976243i | \(0.569523\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.2474 | 1.05900 | 0.529502 | − | 0.848309i | \(-0.322379\pi\) | ||||
0.529502 | + | 0.848309i | \(0.322379\pi\) | |||||||
\(182\) | 0.449490i | 0.0333184i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.89898 | −0.508600 | ||||||||
\(185\) | 4.44949 | + | 0.449490i | 0.327133 | + | 0.0330471i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.79796i | 0.716498i | ||||||||
\(188\) | − | 0.898979i | − | 0.0655648i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.3485 | − | 1.44949i | −1.04095 | − | 0.105157i | ||||
\(191\) | 16.6969 | 1.20815 | 0.604074 | − | 0.796928i | \(-0.293543\pi\) | ||||
0.604074 | + | 0.796928i | \(0.293543\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 17.5959i | − | 1.26658i | −0.773914 | − | 0.633291i | \(-0.781704\pi\) | ||
0.773914 | − | 0.633291i | \(-0.218296\pi\) | |||||||
\(194\) | 3.79796 | 0.272678 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − | 9.10102i | − | 0.648421i | −0.945985 | − | 0.324210i | \(-0.894901\pi\) | ||
0.945985 | − | 0.324210i | \(-0.105099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.10102 | −0.503378 | −0.251689 | − | 0.967808i | \(-0.580986\pi\) | ||||
−0.251689 | + | 0.967808i | \(0.580986\pi\) | |||||||
\(200\) | −1.00000 | + | 4.89898i | −0.0707107 | + | 0.346410i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 8.44949i | − | 0.594504i | ||||||
\(203\) | 2.89898i | 0.203468i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.44949 | − | 24.2474i | 0.171080 | − | 1.69352i | ||||
\(206\) | 3.10102 | 0.216058 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.449490i | 0.0311665i | ||||||||
\(209\) | 31.5959 | 2.18554 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 1.10102i | 0.0756184i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.00000 | −0.546869 | ||||||||
\(215\) | −19.7980 | − | 2.00000i | −1.35021 | − | 0.136399i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.898979i | 0.0610267i | ||||||||
\(218\) | 2.89898i | 0.196344i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.10102 | − | 10.8990i | 0.0742308 | − | 0.734809i | ||||
\(221\) | 0.898979 | 0.0604719 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000i | 0.267860i | 0.990991 | + | 0.133930i | \(0.0427597\pi\) | ||||
−0.990991 | + | 0.133930i | \(0.957240\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.202041 | −0.0134396 | ||||||||
\(227\) | 7.34847i | 0.487735i | 0.969809 | + | 0.243868i | \(0.0784162\pi\) | ||||
−0.969809 | + | 0.243868i | \(0.921584\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.1464 | −1.00090 | −0.500452 | − | 0.865764i | \(-0.666833\pi\) | ||||
−0.500452 | + | 0.865764i | \(0.666833\pi\) | |||||||
\(230\) | 1.55051 | − | 15.3485i | 0.102238 | − | 1.01205i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.89898i | 0.190327i | ||||||||
\(233\) | 10.2020i | 0.668358i | 0.942510 | + | 0.334179i | \(0.108459\pi\) | ||||
−0.942510 | + | 0.334179i | \(0.891541\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | + | 0.202041i | 0.130466 | + | 0.0131797i | ||||
\(236\) | 6.44949 | 0.419826 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 2.00000i | − | 0.129641i | ||||||
\(239\) | −25.7980 | −1.66873 | −0.834366 | − | 0.551211i | \(-0.814166\pi\) | ||||
−0.834366 | + | 0.551211i | \(0.814166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.6969 | 1.33321 | 0.666604 | − | 0.745412i | \(-0.267747\pi\) | ||||
0.666604 | + | 0.745412i | \(0.267747\pi\) | |||||||
\(242\) | 13.0000i | 0.835672i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.44949 | −0.540923 | ||||||||
\(245\) | −0.224745 | + | 2.22474i | −0.0143584 | + | 0.142134i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.89898i | − | 0.184458i | ||||||
\(248\) | 0.898979i | 0.0570853i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.6742 | − | 3.32577i | −0.675098 | − | 0.210340i | ||||
\(251\) | 1.55051 | 0.0978673 | 0.0489337 | − | 0.998802i | \(-0.484418\pi\) | ||||
0.0489337 | + | 0.998802i | \(0.484418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 33.7980i | 2.12486i | ||||||||
\(254\) | 5.10102 | 0.320066 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 20.6969i | − | 1.29104i | −0.763744 | − | 0.645520i | \(-0.776641\pi\) | ||
0.763744 | − | 0.645520i | \(-0.223359\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | −1.00000 | − | 0.101021i | −0.0620174 | − | 0.00626503i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.55051i | 0.0957908i | ||||||||
\(263\) | − | 9.79796i | − | 0.604168i | −0.953281 | − | 0.302084i | \(-0.902318\pi\) | ||
0.953281 | − | 0.302084i | \(-0.0976823\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.44949 | − | 0.247449i | −0.150471 | − | 0.0152007i | ||||
\(266\) | −6.44949 | −0.395444 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | −15.1464 | −0.923494 | −0.461747 | − | 0.887012i | \(-0.652777\pi\) | ||||
−0.461747 | + | 0.887012i | \(0.652777\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(272\) | − | 2.00000i | − | 0.121268i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.7980 | 1.07521 | ||||||||
\(275\) | 24.0000 | + | 4.89898i | 1.44725 | + | 0.295420i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.10102i | − | 0.306491i | −0.988188 | − | 0.153245i | \(-0.951028\pi\) | ||
0.988188 | − | 0.153245i | \(-0.0489725\pi\) | |||||||
\(278\) | − | 6.44949i | − | 0.386815i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.224745 | + | 2.22474i | −0.0134311 | + | 0.132954i | ||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 28.2474i | − | 1.67914i | −0.543254 | − | 0.839568i | \(-0.682808\pi\) | ||
0.543254 | − | 0.839568i | \(-0.317192\pi\) | |||||||
\(284\) | −10.8990 | −0.646735 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.20204 | 0.130209 | ||||||||
\(287\) | − | 10.8990i | − | 0.643346i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | −6.44949 | − | 0.651531i | −0.378727 | − | 0.0382592i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 6.89898i | − | 0.403732i | ||||||
\(293\) | − | 6.24745i | − | 0.364980i | −0.983208 | − | 0.182490i | \(-0.941584\pi\) | ||
0.983208 | − | 0.182490i | \(-0.0584157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.44949 | + | 14.3485i | −0.0843926 | + | 0.835400i | ||||
\(296\) | 2.00000 | 0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.7980i | 0.915151i | ||||||||
\(299\) | 3.10102 | 0.179337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.89898 | −0.512929 | ||||||||
\(302\) | − | 19.5959i | − | 1.12762i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.44949 | −0.369904 | ||||||||
\(305\) | 1.89898 | − | 18.7980i | 0.108735 | − | 1.07637i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.24745i | 0.242415i | 0.992627 | + | 0.121207i | \(0.0386766\pi\) | ||||
−0.992627 | + | 0.121207i | \(0.961323\pi\) | |||||||
\(308\) | − | 4.89898i | − | 0.279145i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.00000 | − | 0.202041i | −0.113592 | − | 0.0114752i | ||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 17.5959i | − | 0.994580i | −0.867584 | − | 0.497290i | \(-0.834328\pi\) | ||
0.867584 | − | 0.497290i | \(-0.165672\pi\) | |||||||
\(314\) | −8.44949 | −0.476832 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.89898 | −0.163080 | ||||||||
\(317\) | − | 26.4949i | − | 1.48810i | −0.668123 | − | 0.744051i | \(-0.732902\pi\) | ||
0.668123 | − | 0.744051i | \(-0.267098\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.2020 | 0.795162 | ||||||||
\(320\) | −0.224745 | + | 2.22474i | −0.0125636 | + | 0.124367i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 6.89898i | − | 0.384465i | ||||||
\(323\) | 12.8990i | 0.717718i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.449490 | − | 2.20204i | 0.0249332 | − | 0.122147i | ||||
\(326\) | −16.8990 | −0.935948 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 10.8990i | − | 0.601795i | ||||||
\(329\) | 0.898979 | 0.0495623 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6969 | 0.587957 | 0.293978 | − | 0.955812i | \(-0.405021\pi\) | ||||
0.293978 | + | 0.955812i | \(0.405021\pi\) | |||||||
\(332\) | − | 2.44949i | − | 0.134433i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.89898 | 0.268060 | ||||||||
\(335\) | −17.7980 | − | 1.79796i | −0.972406 | − | 0.0982330i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 29.5959i | − | 1.61219i | −0.591785 | − | 0.806096i | \(-0.701576\pi\) | ||
0.591785 | − | 0.806096i | \(-0.298424\pi\) | |||||||
\(338\) | 12.7980i | 0.696117i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.44949 | + | 0.449490i | 0.241307 | + | 0.0243770i | ||||
\(341\) | 4.40408 | 0.238494 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −8.89898 | −0.479801 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.2474 | −0.980989 | ||||||||
\(347\) | − | 19.1010i | − | 1.02540i | −0.858569 | − | 0.512698i | \(-0.828646\pi\) | ||
0.858569 | − | 0.512698i | \(-0.171354\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.55051 | 0.190054 | 0.0950272 | − | 0.995475i | \(-0.469706\pi\) | ||||
0.0950272 | + | 0.995475i | \(0.469706\pi\) | |||||||
\(350\) | −4.89898 | − | 1.00000i | −0.261861 | − | 0.0534522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.89898i | − | 0.261116i | ||||||
\(353\) | 13.1010i | 0.697297i | 0.937254 | + | 0.348648i | \(0.113359\pi\) | ||||
−0.937254 | + | 0.348648i | \(0.886641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.44949 | − | 24.2474i | 0.130005 | − | 1.28692i | ||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 5.79796i | − | 0.306432i | ||||||
\(359\) | 11.5959 | 0.612009 | 0.306005 | − | 0.952030i | \(-0.401008\pi\) | ||||
0.306005 | + | 0.952030i | \(0.401008\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.5959 | 1.18926 | ||||||||
\(362\) | 14.2474i | 0.748829i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.449490 | −0.0235597 | ||||||||
\(365\) | 15.3485 | + | 1.55051i | 0.803376 | + | 0.0811574i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.0000i | 1.67039i | 0.549957 | + | 0.835193i | \(0.314644\pi\) | ||||
−0.549957 | + | 0.835193i | \(0.685356\pi\) | |||||||
\(368\) | − | 6.89898i | − | 0.359634i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.449490 | + | 4.44949i | −0.0233679 | + | 0.231318i | ||||
\(371\) | −1.10102 | −0.0571621 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 24.6969i | − | 1.27876i | −0.768891 | − | 0.639380i | \(-0.779191\pi\) | ||
0.768891 | − | 0.639380i | \(-0.220809\pi\) | |||||||
\(374\) | −9.79796 | −0.506640 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.898979 | 0.0463613 | ||||||||
\(377\) | − | 1.30306i | − | 0.0671111i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.30306 | −0.0669338 | −0.0334669 | − | 0.999440i | \(-0.510655\pi\) | ||||
−0.0334669 | + | 0.999440i | \(0.510655\pi\) | |||||||
\(380\) | 1.44949 | − | 14.3485i | 0.0743573 | − | 0.736061i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.6969i | 0.854290i | ||||||||
\(383\) | − | 16.8990i | − | 0.863498i | −0.901994 | − | 0.431749i | \(-0.857897\pi\) | ||
0.901994 | − | 0.431749i | \(-0.142103\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.8990 | + | 1.10102i | 0.555463 | + | 0.0561132i | ||||
\(386\) | 17.5959 | 0.895609 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.79796i | 0.192812i | ||||||||
\(389\) | 22.8990 | 1.16102 | 0.580512 | − | 0.814252i | \(-0.302852\pi\) | ||||
0.580512 | + | 0.814252i | \(0.302852\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.7980 | −0.697793 | ||||||||
\(392\) | 1.00000i | 0.0505076i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.10102 | 0.458503 | ||||||||
\(395\) | 0.651531 | − | 6.44949i | 0.0327821 | − | 0.324509i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 17.3485i | − | 0.870695i | −0.900263 | − | 0.435347i | \(-0.856626\pi\) | ||
0.900263 | − | 0.435347i | \(-0.143374\pi\) | |||||||
\(398\) | − | 7.10102i | − | 0.355942i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.89898 | − | 1.00000i | −0.244949 | − | 0.0500000i | ||||
\(401\) | −29.3939 | −1.46786 | −0.733930 | − | 0.679225i | \(-0.762316\pi\) | ||||
−0.733930 | + | 0.679225i | \(0.762316\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.404082i | − | 0.0201288i | ||||||
\(404\) | 8.44949 | 0.420378 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.89898 | −0.143874 | ||||||||
\(407\) | − | 9.79796i | − | 0.485667i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.4949 | 0.716727 | 0.358363 | − | 0.933582i | \(-0.383335\pi\) | ||||
0.358363 | + | 0.933582i | \(0.383335\pi\) | |||||||
\(410\) | 24.2474 | + | 2.44949i | 1.19750 | + | 0.120972i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.10102i | 0.152776i | ||||||||
\(413\) | 6.44949i | 0.317359i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.44949 | + | 0.550510i | 0.267505 | + | 0.0270235i | ||||
\(416\) | −0.449490 | −0.0220380 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 31.5959i | 1.54541i | ||||||||
\(419\) | −6.44949 | −0.315078 | −0.157539 | − | 0.987513i | \(-0.550356\pi\) | ||||
−0.157539 | + | 0.987513i | \(0.550356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.7980 | −1.15984 | −0.579921 | − | 0.814673i | \(-0.696917\pi\) | ||||
−0.579921 | + | 0.814673i | \(0.696917\pi\) | |||||||
\(422\) | 12.0000i | 0.584151i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.10102 | −0.0534703 | ||||||||
\(425\) | −2.00000 | + | 9.79796i | −0.0970143 | + | 0.475271i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.44949i | − | 0.408899i | ||||||
\(428\) | − | 8.00000i | − | 0.386695i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.00000 | − | 19.7980i | 0.0964486 | − | 0.954742i | ||||
\(431\) | −17.7980 | −0.857298 | −0.428649 | − | 0.903471i | \(-0.641010\pi\) | ||||
−0.428649 | + | 0.903471i | \(0.641010\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.7980i | 0.951429i | 0.879600 | + | 0.475715i | \(0.157810\pi\) | ||||
−0.879600 | + | 0.475715i | \(0.842190\pi\) | |||||||
\(434\) | −0.898979 | −0.0431524 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.89898 | −0.138836 | ||||||||
\(437\) | 44.4949i | 2.12848i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.3939 | −1.78471 | −0.892356 | − | 0.451332i | \(-0.850949\pi\) | ||||
−0.892356 | + | 0.451332i | \(0.850949\pi\) | |||||||
\(440\) | 10.8990 | + | 1.10102i | 0.519588 | + | 0.0524891i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.898979i | 0.0427601i | ||||||||
\(443\) | − | 9.79796i | − | 0.465515i | −0.972535 | − | 0.232758i | \(-0.925225\pi\) | ||
0.972535 | − | 0.232758i | \(-0.0747749\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.24745 | + | 22.2474i | −0.106539 | + | 1.05463i | ||||
\(446\) | −4.00000 | −0.189405 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000i | 0.0472456i | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −53.3939 | −2.51422 | ||||||||
\(452\) | − | 0.202041i | − | 0.00950321i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.34847 | −0.344881 | ||||||||
\(455\) | 0.101021 | − | 1.00000i | 0.00473591 | − | 0.0468807i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 9.59592i | − | 0.448878i | −0.974488 | − | 0.224439i | \(-0.927945\pi\) | ||
0.974488 | − | 0.224439i | \(-0.0720550\pi\) | |||||||
\(458\) | − | 15.1464i | − | 0.707746i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 15.3485 | + | 1.55051i | 0.715626 | + | 0.0722929i | ||||
\(461\) | −2.65153 | −0.123494 | −0.0617470 | − | 0.998092i | \(-0.519667\pi\) | ||||
−0.0617470 | + | 0.998092i | \(0.519667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.5959i | 1.65428i | 0.561994 | + | 0.827141i | \(0.310034\pi\) | ||||
−0.561994 | + | 0.827141i | \(0.689966\pi\) | |||||||
\(464\) | −2.89898 | −0.134582 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.2020 | −0.472600 | ||||||||
\(467\) | − | 5.55051i | − | 0.256847i | −0.991719 | − | 0.128423i | \(-0.959008\pi\) | ||
0.991719 | − | 0.128423i | \(-0.0409917\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | −0.202041 | + | 2.00000i | −0.00931946 | + | 0.0922531i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.44949i | 0.296862i | ||||||||
\(473\) | 43.5959i | 2.00454i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.5959 | + | 6.44949i | 1.44972 | + | 0.295923i | ||||
\(476\) | 2.00000 | 0.0916698 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 25.7980i | − | 1.17997i | ||||||
\(479\) | 38.6969 | 1.76811 | 0.884054 | − | 0.467385i | \(-0.154804\pi\) | ||||
0.884054 | + | 0.467385i | \(0.154804\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.898979 | −0.0409899 | ||||||||
\(482\) | 20.6969i | 0.942720i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.0000 | −0.590909 | ||||||||
\(485\) | −8.44949 | − | 0.853572i | −0.383672 | − | 0.0387587i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 36.6969i | − | 1.66290i | −0.555602 | − | 0.831449i | \(-0.687512\pi\) | ||
0.555602 | − | 0.831449i | \(-0.312488\pi\) | |||||||
\(488\) | − | 8.44949i | − | 0.382490i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.22474 | − | 0.224745i | −0.100504 | − | 0.0101529i | ||||
\(491\) | 19.5959 | 0.884351 | 0.442176 | − | 0.896928i | \(-0.354207\pi\) | ||||
0.442176 | + | 0.896928i | \(0.354207\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.79796i | 0.261127i | ||||||||
\(494\) | 2.89898 | 0.130431 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.898979 | −0.0403654 | ||||||||
\(497\) | − | 10.8990i | − | 0.488886i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.7980 | −1.15488 | −0.577438 | − | 0.816435i | \(-0.695947\pi\) | ||||
−0.577438 | + | 0.816435i | \(0.695947\pi\) | |||||||
\(500\) | 3.32577 | − | 10.6742i | 0.148733 | − | 0.477366i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.55051i | 0.0692027i | ||||||||
\(503\) | − | 4.00000i | − | 0.178351i | −0.996016 | − | 0.0891756i | \(-0.971577\pi\) | ||
0.996016 | − | 0.0891756i | \(-0.0284232\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.89898 | + | 18.7980i | −0.0845035 | + | 0.836498i | ||||
\(506\) | −33.7980 | −1.50250 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.10102i | 0.226321i | ||||||||
\(509\) | −36.4495 | −1.61560 | −0.807798 | − | 0.589460i | \(-0.799341\pi\) | ||||
−0.807798 | + | 0.589460i | \(0.799341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.89898 | 0.305193 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.6969 | 0.912903 | ||||||||
\(515\) | −6.89898 | − | 0.696938i | −0.304005 | − | 0.0307108i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.40408i | − | 0.193691i | ||||||
\(518\) | 2.00000i | 0.0878750i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.101021 | − | 1.00000i | 0.00443004 | − | 0.0438529i | ||||
\(521\) | −3.30306 | −0.144710 | −0.0723549 | − | 0.997379i | \(-0.523051\pi\) | ||||
−0.0723549 | + | 0.997379i | \(0.523051\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.14643i | − | 0.0501298i | −0.999686 | − | 0.0250649i | \(-0.992021\pi\) | ||
0.999686 | − | 0.0250649i | \(-0.00797924\pi\) | |||||||
\(524\) | −1.55051 | −0.0677344 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.79796 | 0.427211 | ||||||||
\(527\) | 1.79796i | 0.0783203i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24.5959 | −1.06939 | ||||||||
\(530\) | 0.247449 | − | 2.44949i | 0.0107485 | − | 0.106399i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 6.44949i | − | 0.279621i | ||||||
\(533\) | 4.89898i | 0.212198i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.7980 | + | 1.79796i | 0.769473 | + | 0.0777325i | ||||
\(536\) | −8.00000 | −0.345547 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 15.1464i | − | 0.653009i | ||||||
\(539\) | 4.89898 | 0.211014 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.5959 | −1.27243 | −0.636214 | − | 0.771513i | \(-0.719500\pi\) | ||||
−0.636214 | + | 0.771513i | \(0.719500\pi\) | |||||||
\(542\) | 12.0000i | 0.515444i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | 0.651531 | − | 6.44949i | 0.0279085 | − | 0.276266i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6969i | 0.457368i | 0.973501 | + | 0.228684i | \(0.0734423\pi\) | ||||
−0.973501 | + | 0.228684i | \(0.926558\pi\) | |||||||
\(548\) | 17.7980i | 0.760291i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.89898 | + | 24.0000i | −0.208893 | + | 1.02336i | ||||
\(551\) | 18.6969 | 0.796516 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.89898i | − | 0.123277i | ||||||
\(554\) | 5.10102 | 0.216722 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.44949 | 0.273519 | ||||||||
\(557\) | 16.6969i | 0.707472i | 0.935345 | + | 0.353736i | \(0.115089\pi\) | ||||
−0.935345 | + | 0.353736i | \(0.884911\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | −2.22474 | − | 0.224745i | −0.0940126 | − | 0.00949720i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0000i | 0.759284i | ||||||||
\(563\) | 14.0454i | 0.591943i | 0.955197 | + | 0.295972i | \(0.0956434\pi\) | ||||
−0.955197 | + | 0.295972i | \(0.904357\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.449490 | + | 0.0454077i | 0.0189102 | + | 0.00191032i | ||||
\(566\) | 28.2474 | 1.18733 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 10.8990i | − | 0.457311i | ||||||
\(569\) | 14.2020 | 0.595381 | 0.297690 | − | 0.954663i | \(-0.403784\pi\) | ||||
0.297690 | + | 0.954663i | \(0.403784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.8990 | −0.874595 | −0.437298 | − | 0.899317i | \(-0.644064\pi\) | ||||
−0.437298 | + | 0.899317i | \(0.644064\pi\) | |||||||
\(572\) | 2.20204i | 0.0920720i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.8990 | 0.454915 | ||||||||
\(575\) | −6.89898 | + | 33.7980i | −0.287707 | + | 1.40947i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.4949i | 1.93561i | 0.251705 | + | 0.967804i | \(0.419009\pi\) | ||||
−0.251705 | + | 0.967804i | \(0.580991\pi\) | |||||||
\(578\) | 13.0000i | 0.540729i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.651531 | − | 6.44949i | 0.0270533 | − | 0.267800i | ||||
\(581\) | 2.44949 | 0.101622 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.39388i | 0.223392i | ||||||||
\(584\) | 6.89898 | 0.285482 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.24745 | 0.258080 | ||||||||
\(587\) | 33.1464i | 1.36810i | 0.729435 | + | 0.684050i | \(0.239783\pi\) | ||||
−0.729435 | + | 0.684050i | \(0.760217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.79796 | 0.238901 | ||||||||
\(590\) | −14.3485 | − | 1.44949i | −0.590717 | − | 0.0596745i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.00000i | 0.0821995i | ||||||||
\(593\) | − | 1.10102i | − | 0.0452135i | −0.999744 | − | 0.0226067i | \(-0.992803\pi\) | ||
0.999744 | − | 0.0226067i | \(-0.00719656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.449490 | + | 4.44949i | −0.0184273 | + | 0.182411i | ||||
\(596\) | −15.7980 | −0.647110 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.10102i | 0.126810i | ||||||||
\(599\) | −22.8990 | −0.935627 | −0.467813 | − | 0.883827i | \(-0.654958\pi\) | ||||
−0.467813 | + | 0.883827i | \(0.654958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.3939 | 0.791093 | 0.395546 | − | 0.918446i | \(-0.370555\pi\) | ||||
0.395546 | + | 0.918446i | \(0.370555\pi\) | |||||||
\(602\) | − | 8.89898i | − | 0.362695i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19.5959 | 0.797347 | ||||||||
\(605\) | 2.92168 | − | 28.9217i | 0.118783 | − | 1.17583i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 25.3939i | − | 1.03071i | −0.856978 | − | 0.515353i | \(-0.827661\pi\) | ||
0.856978 | − | 0.515353i | \(-0.172339\pi\) | |||||||
\(608\) | − | 6.44949i | − | 0.261561i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.7980 | + | 1.89898i | 0.761107 | + | 0.0768874i | ||||
\(611\) | −0.404082 | −0.0163474 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.20204i | 0.331277i | 0.986187 | + | 0.165639i | \(0.0529685\pi\) | ||||
−0.986187 | + | 0.165639i | \(0.947031\pi\) | |||||||
\(614\) | −4.24745 | −0.171413 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.89898 | 0.197386 | ||||||||
\(617\) | 9.59592i | 0.386317i | 0.981168 | + | 0.193159i | \(0.0618732\pi\) | ||||
−0.981168 | + | 0.193159i | \(0.938127\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.4495 | 1.86696 | 0.933481 | − | 0.358626i | \(-0.116755\pi\) | ||||
0.933481 | + | 0.358626i | \(0.116755\pi\) | |||||||
\(620\) | 0.202041 | − | 2.00000i | 0.00811416 | − | 0.0803219i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 12.0000i | − | 0.481156i | ||||||
\(623\) | 10.0000i | 0.400642i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.0000 | + | 9.79796i | 0.920000 | + | 0.391918i | ||||
\(626\) | 17.5959 | 0.703274 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 8.44949i | − | 0.337171i | ||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.49490 | 0.258558 | 0.129279 | − | 0.991608i | \(-0.458734\pi\) | ||||
0.129279 | + | 0.991608i | \(0.458734\pi\) | |||||||
\(632\) | − | 2.89898i | − | 0.115315i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26.4949 | 1.05225 | ||||||||
\(635\) | −11.3485 | − | 1.14643i | −0.450350 | − | 0.0454946i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.449490i | − | 0.0178094i | ||||||
\(638\) | 14.2020i | 0.562264i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.22474 | − | 0.224745i | −0.0879408 | − | 0.00888382i | ||||
\(641\) | −6.20204 | −0.244966 | −0.122483 | − | 0.992471i | \(-0.539086\pi\) | ||||
−0.122483 | + | 0.992471i | \(0.539086\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.14643i | 0.360700i | 0.983603 | + | 0.180350i | \(0.0577230\pi\) | ||||
−0.983603 | + | 0.180350i | \(0.942277\pi\) | |||||||
\(644\) | 6.89898 | 0.271858 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.8990 | −0.507504 | ||||||||
\(647\) | − | 22.2929i | − | 0.876423i | −0.898872 | − | 0.438211i | \(-0.855612\pi\) | ||
0.898872 | − | 0.438211i | \(-0.144388\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.5959 | 1.24025 | ||||||||
\(650\) | 2.20204 | + | 0.449490i | 0.0863712 | + | 0.0176304i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 16.8990i | − | 0.661815i | ||||||
\(653\) | − | 39.7980i | − | 1.55741i | −0.627387 | − | 0.778707i | \(-0.715876\pi\) | ||
0.627387 | − | 0.778707i | \(-0.284124\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.348469 | − | 3.44949i | 0.0136158 | − | 0.134783i | ||||
\(656\) | 10.8990 | 0.425534 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.898979i | 0.0350459i | ||||||||
\(659\) | 7.10102 | 0.276616 | 0.138308 | − | 0.990389i | \(-0.455834\pi\) | ||||
0.138308 | + | 0.990389i | \(0.455834\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.9444 | 0.503478 | 0.251739 | − | 0.967795i | \(-0.418997\pi\) | ||||
0.251739 | + | 0.967795i | \(0.418997\pi\) | |||||||
\(662\) | 10.6969i | 0.415748i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.44949 | 0.0950586 | ||||||||
\(665\) | 14.3485 | + | 1.44949i | 0.556410 | + | 0.0562088i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.0000i | 0.774403i | ||||||||
\(668\) | 4.89898i | 0.189547i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.79796 | − | 17.7980i | 0.0694612 | − | 0.687595i | ||||
\(671\) | −41.3939 | −1.59799 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.79796i | − | 0.0693062i | −0.999399 | − | 0.0346531i | \(-0.988967\pi\) | ||
0.999399 | − | 0.0346531i | \(-0.0110326\pi\) | |||||||
\(674\) | 29.5959 | 1.13999 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.7980 | −0.492229 | ||||||||
\(677\) | 31.5505i | 1.21258i | 0.795242 | + | 0.606292i | \(0.207344\pi\) | ||||
−0.795242 | + | 0.606292i | \(0.792656\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.79796 | −0.145752 | ||||||||
\(680\) | −0.449490 | + | 4.44949i | −0.0172371 | + | 0.170630i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.40408i | 0.168641i | ||||||||
\(683\) | − | 35.5959i | − | 1.36204i | −0.732265 | − | 0.681020i | \(-0.761537\pi\) | ||
0.732265 | − | 0.681020i | \(-0.238463\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.5959 | − | 4.00000i | −1.51288 | − | 0.152832i | ||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 8.89898i | − | 0.339270i | ||||||
\(689\) | 0.494897 | 0.0188541 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.1464 | −0.500114 | −0.250057 | − | 0.968231i | \(-0.580449\pi\) | ||||
−0.250057 | + | 0.968231i | \(0.580449\pi\) | |||||||
\(692\) | − | 18.2474i | − | 0.693664i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.1010 | 0.725065 | ||||||||
\(695\) | −1.44949 | + | 14.3485i | −0.0549823 | + | 0.544268i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 21.7980i | − | 0.825657i | ||||||
\(698\) | 3.55051i | 0.134389i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | − | 4.89898i | 0.0377964 | − | 0.185164i | ||||
\(701\) | −40.6969 | −1.53710 | −0.768551 | − | 0.639788i | \(-0.779022\pi\) | ||||
−0.768551 | + | 0.639788i | \(0.779022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 12.8990i | − | 0.486494i | ||||||
\(704\) | 4.89898 | 0.184637 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.1010 | −0.493063 | ||||||||
\(707\) | 8.44949i | 0.317776i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.2929 | −1.51323 | −0.756615 | − | 0.653861i | \(-0.773148\pi\) | ||||
−0.756615 | + | 0.653861i | \(0.773148\pi\) | |||||||
\(710\) | 24.2474 | + | 2.44949i | 0.909991 | + | 0.0919277i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.0000i | 0.374766i | ||||||||
\(713\) | 6.20204i | 0.232268i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.89898 | − | 0.494897i | −0.183211 | − | 0.0185081i | ||||
\(716\) | 5.79796 | 0.216680 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.5959i | 0.432756i | ||||||||
\(719\) | 44.4949 | 1.65938 | 0.829690 | − | 0.558225i | \(-0.188517\pi\) | ||||
0.829690 | + | 0.558225i | \(0.188517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.10102 | −0.115488 | ||||||||
\(722\) | 22.5959i | 0.840933i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.2474 | −0.529502 | ||||||||
\(725\) | 14.2020 | + | 2.89898i | 0.527451 | + | 0.107665i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6.69694i | − | 0.248376i | −0.992259 | − | 0.124188i | \(-0.960367\pi\) | ||
0.992259 | − | 0.124188i | \(-0.0396325\pi\) | |||||||
\(728\) | − | 0.449490i | − | 0.0166592i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.55051 | + | 15.3485i | −0.0573870 | + | 0.568072i | ||||
\(731\) | −17.7980 | −0.658281 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.6413i | 1.61193i | 0.591964 | + | 0.805965i | \(0.298353\pi\) | ||||
−0.591964 | + | 0.805965i | \(0.701647\pi\) | |||||||
\(734\) | −32.0000 | −1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.89898 | 0.254300 | ||||||||
\(737\) | 39.1918i | 1.44365i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.4949 | 1.63677 | 0.818386 | − | 0.574669i | \(-0.194869\pi\) | ||||
0.818386 | + | 0.574669i | \(0.194869\pi\) | |||||||
\(740\) | −4.44949 | − | 0.449490i | −0.163566 | − | 0.0165236i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 1.10102i | − | 0.0404197i | ||||||
\(743\) | − | 15.3031i | − | 0.561415i | −0.959793 | − | 0.280707i | \(-0.909431\pi\) | ||
0.959793 | − | 0.280707i | \(-0.0905691\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.55051 | − | 35.1464i | 0.130081 | − | 1.28767i | ||||
\(746\) | 24.6969 | 0.904219 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 9.79796i | − | 0.358249i | ||||||
\(749\) | 8.00000 | 0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.2020 | −0.810164 | −0.405082 | − | 0.914280i | \(-0.632757\pi\) | ||||
−0.405082 | + | 0.914280i | \(0.632757\pi\) | |||||||
\(752\) | 0.898979i | 0.0327824i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.30306 | 0.0474547 | ||||||||
\(755\) | −4.40408 | + | 43.5959i | −0.160281 | + | 1.58662i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 32.2020i | − | 1.17040i | −0.810888 | − | 0.585202i | \(-0.801015\pi\) | ||
0.810888 | − | 0.585202i | \(-0.198985\pi\) | |||||||
\(758\) | − | 1.30306i | − | 0.0473293i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 14.3485 | + | 1.44949i | 0.520474 | + | 0.0525785i | ||||
\(761\) | 30.8990 | 1.12009 | 0.560044 | − | 0.828463i | \(-0.310784\pi\) | ||||
0.560044 | + | 0.828463i | \(0.310784\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 2.89898i | − | 0.104950i | ||||||
\(764\) | −16.6969 | −0.604074 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.8990 | 0.610585 | ||||||||
\(767\) | − | 2.89898i | − | 0.104676i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.3031 | 0.407599 | 0.203799 | − | 0.979013i | \(-0.434671\pi\) | ||||
0.203799 | + | 0.979013i | \(0.434671\pi\) | |||||||
\(770\) | −1.10102 | + | 10.8990i | −0.0396780 | + | 0.392772i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.5959i | 0.633291i | ||||||||
\(773\) | − | 13.3485i | − | 0.480111i | −0.970759 | − | 0.240056i | \(-0.922834\pi\) | ||
0.970759 | − | 0.240056i | \(-0.0771657\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.40408 | + | 0.898979i | 0.158199 | + | 0.0322923i | ||||
\(776\) | −3.79796 | −0.136339 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.8990i | 0.820968i | ||||||||
\(779\) | −70.2929 | −2.51850 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.3939 | −1.91058 | ||||||||
\(782\) | − | 13.7980i | − | 0.493414i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 18.7980 | + | 1.89898i | 0.670928 | + | 0.0677775i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.5505i | 1.62370i | 0.583866 | + | 0.811850i | \(0.301539\pi\) | ||||
−0.583866 | + | 0.811850i | \(0.698461\pi\) | |||||||
\(788\) | 9.10102i | 0.324210i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.44949 | + | 0.651531i | 0.229463 | + | 0.0231804i | ||||
\(791\) | 0.202041 | 0.00718375 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.79796i | 0.134869i | ||||||||
\(794\) | 17.3485 | 0.615674 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.10102 | 0.251689 | ||||||||
\(797\) | − | 52.9444i | − | 1.87539i | −0.347464 | − | 0.937693i | \(-0.612957\pi\) | ||
0.347464 | − | 0.937693i | \(-0.387043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.79796 | 0.0636072 | ||||||||
\(800\) | 1.00000 | − | 4.89898i | 0.0353553 | − | 0.173205i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 29.3939i | − | 1.03793i | ||||||
\(803\) | − | 33.7980i | − | 1.19270i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.55051 | + | 15.3485i | −0.0546483 | + | 0.540962i | ||||
\(806\) | 0.404082 | 0.0142332 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.44949i | 0.297252i | ||||||||
\(809\) | 8.40408 | 0.295472 | 0.147736 | − | 0.989027i | \(-0.452801\pi\) | ||||
0.147736 | + | 0.989027i | \(0.452801\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.9444 | −1.36752 | −0.683761 | − | 0.729706i | \(-0.739657\pi\) | ||||
−0.683761 | + | 0.729706i | \(0.739657\pi\) | |||||||
\(812\) | − | 2.89898i | − | 0.101734i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.79796 | 0.343418 | ||||||||
\(815\) | 37.5959 | + | 3.79796i | 1.31693 | + | 0.133037i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 57.3939i | 2.00796i | ||||||||
\(818\) | 14.4949i | 0.506802i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.44949 | + | 24.2474i | −0.0855399 | + | 0.846758i | ||||
\(821\) | −27.7980 | −0.970155 | −0.485078 | − | 0.874471i | \(-0.661209\pi\) | ||||
−0.485078 | + | 0.874471i | \(0.661209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 39.1918i | − | 1.36614i | −0.730352 | − | 0.683071i | \(-0.760644\pi\) | ||
0.730352 | − | 0.683071i | \(-0.239356\pi\) | |||||||
\(824\) | −3.10102 | −0.108029 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.44949 | −0.224406 | ||||||||
\(827\) | − | 23.5959i | − | 0.820510i | −0.911971 | − | 0.410255i | \(-0.865440\pi\) | ||
0.911971 | − | 0.410255i | \(-0.134560\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.6413 | −1.37680 | −0.688400 | − | 0.725331i | \(-0.741687\pi\) | ||||
−0.688400 | + | 0.725331i | \(0.741687\pi\) | |||||||
\(830\) | −0.550510 | + | 5.44949i | −0.0191085 | + | 0.189155i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 0.449490i | − | 0.0155833i | ||||||
\(833\) | 2.00000i | 0.0692959i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.8990 | − | 1.10102i | −0.377175 | − | 0.0381024i | ||||
\(836\) | −31.5959 | −1.09277 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 6.44949i | − | 0.222794i | ||||||
\(839\) | 27.1010 | 0.935631 | 0.467816 | − | 0.883826i | \(-0.345041\pi\) | ||||
0.467816 | + | 0.883826i | \(0.345041\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5959 | −0.710204 | ||||||||
\(842\) | − | 23.7980i | − | 0.820132i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.0000 | −0.413057 | ||||||||
\(845\) | 2.87628 | − | 28.4722i | 0.0989469 | − | 0.979473i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 13.0000i | − | 0.446685i | ||||||
\(848\) | − | 1.10102i | − | 0.0378092i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.79796 | − | 2.00000i | −0.336067 | − | 0.0685994i | ||||
\(851\) | 13.7980 | 0.472988 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 29.8434i | − | 1.02182i | −0.859635 | − | 0.510909i | \(-0.829309\pi\) | ||
0.859635 | − | 0.510909i | \(-0.170691\pi\) | |||||||
\(854\) | 8.44949 | 0.289136 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.00000 | 0.273434 | ||||||||
\(857\) | − | 25.1918i | − | 0.860537i | −0.902701 | − | 0.430268i | \(-0.858419\pi\) | ||
0.902701 | − | 0.430268i | \(-0.141581\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.6413 | 1.01135 | 0.505674 | − | 0.862724i | \(-0.331244\pi\) | ||||
0.505674 | + | 0.862724i | \(0.331244\pi\) | |||||||
\(860\) | 19.7980 | + | 2.00000i | 0.675105 | + | 0.0681994i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 17.7980i | − | 0.606201i | ||||||
\(863\) | 13.3939i | 0.455933i | 0.973669 | + | 0.227966i | \(0.0732076\pi\) | ||||
−0.973669 | + | 0.227966i | \(0.926792\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.5959 | + | 4.10102i | 1.38030 | + | 0.139439i | ||||
\(866\) | −19.7980 | −0.672762 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 0.898979i | − | 0.0305134i | ||||||
\(869\) | −14.2020 | −0.481771 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.59592 | 0.121843 | ||||||||
\(872\) | − | 2.89898i | − | 0.0981718i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −44.4949 | −1.50506 | ||||||||
\(875\) | 10.6742 | + | 3.32577i | 0.360855 | + | 0.112431i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.3939i | 0.654885i | 0.944871 | + | 0.327442i | \(0.106187\pi\) | ||||
−0.944871 | + | 0.327442i | \(0.893813\pi\) | |||||||
\(878\) | − | 37.3939i | − | 1.26198i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.10102 | + | 10.8990i | −0.0371154 | + | 0.367405i | ||||
\(881\) | −27.7980 | −0.936537 | −0.468269 | − | 0.883586i | \(-0.655122\pi\) | ||||
−0.468269 | + | 0.883586i | \(0.655122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 41.7980i | − | 1.40661i | −0.710887 | − | 0.703307i | \(-0.751706\pi\) | ||
0.710887 | − | 0.703307i | \(-0.248294\pi\) | |||||||
\(884\) | −0.898979 | −0.0302360 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.79796 | 0.329169 | ||||||||
\(887\) | 26.6969i | 0.896395i | 0.893934 | + | 0.448198i | \(0.147934\pi\) | ||||
−0.893934 | + | 0.448198i | \(0.852066\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.10102 | −0.171083 | ||||||||
\(890\) | −22.2474 | − | 2.24745i | −0.745736 | − | 0.0753347i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 4.00000i | − | 0.133930i | ||||||
\(893\) | − | 5.79796i | − | 0.194021i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.30306 | + | 12.8990i | −0.0435565 | + | 0.431165i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 10.0000i | − | 0.333704i | ||||||
\(899\) | 2.60612 | 0.0869191 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.20204 | −0.0733606 | ||||||||
\(902\) | − | 53.3939i | − | 1.77782i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.202041 | 0.00671978 | ||||||||
\(905\) | 3.20204 | − | 31.6969i | 0.106439 | − | 1.05364i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 22.2020i | − | 0.737207i | −0.929587 | − | 0.368603i | \(-0.879836\pi\) | ||
0.929587 | − | 0.368603i | \(-0.120164\pi\) | |||||||
\(908\) | − | 7.34847i | − | 0.243868i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.00000 | + | 0.101021i | 0.0331497 | + | 0.00334880i | ||||
\(911\) | −3.59592 | −0.119138 | −0.0595690 | − | 0.998224i | \(-0.518973\pi\) | ||||
−0.0595690 | + | 0.998224i | \(0.518973\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.0000i | − | 0.397142i | ||||||
\(914\) | 9.59592 | 0.317405 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.1464 | 0.500452 | ||||||||
\(917\) | − | 1.55051i | − | 0.0512024i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.1010 | 0.564111 | 0.282055 | − | 0.959398i | \(-0.408984\pi\) | ||||
0.282055 | + | 0.959398i | \(0.408984\pi\) | |||||||
\(920\) | −1.55051 | + | 15.3485i | −0.0511188 | + | 0.506024i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 2.65153i | − | 0.0873235i | ||||||
\(923\) | 4.89898i | 0.161252i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | − | 9.79796i | 0.0657596 | − | 0.322155i | ||||
\(926\) | −35.5959 | −1.16975 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 2.89898i | − | 0.0951637i | ||||||
\(929\) | 40.2929 | 1.32197 | 0.660983 | − | 0.750401i | \(-0.270140\pi\) | ||||
0.660983 | + | 0.750401i | \(0.270140\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.44949 | 0.211373 | ||||||||
\(932\) | − | 10.2020i | − | 0.334179i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.55051 | 0.181618 | ||||||||
\(935\) | 21.7980 | + | 2.20204i | 0.712869 | + | 0.0720144i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 50.8990i | − | 1.66280i | −0.555677 | − | 0.831399i | \(-0.687541\pi\) | ||
0.555677 | − | 0.831399i | \(-0.312459\pi\) | |||||||
\(938\) | − | 8.00000i | − | 0.261209i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.00000 | − | 0.202041i | −0.0652328 | − | 0.00658985i | ||||
\(941\) | 24.4495 | 0.797031 | 0.398515 | − | 0.917162i | \(-0.369526\pi\) | ||||
0.398515 | + | 0.917162i | \(0.369526\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 75.1918i | − | 2.44858i | ||||||
\(944\) | −6.44949 | −0.209913 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.5959 | −1.41743 | ||||||||
\(947\) | 44.0908i | 1.43276i | 0.697711 | + | 0.716379i | \(0.254202\pi\) | ||||
−0.697711 | + | 0.716379i | \(0.745798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.10102 | −0.100663 | ||||||||
\(950\) | −6.44949 | + | 31.5959i | −0.209249 | + | 1.02511i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.00000i | 0.0648204i | ||||||||
\(953\) | 21.7980i | 0.706105i | 0.935603 | + | 0.353053i | \(0.114856\pi\) | ||||
−0.935603 | + | 0.353053i | \(0.885144\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.75255 | − | 37.1464i | 0.121430 | − | 1.20203i | ||||
\(956\) | 25.7980 | 0.834366 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 38.6969i | 1.25024i | ||||||||
\(959\) | −17.7980 | −0.574726 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1918 | −0.973930 | ||||||||
\(962\) | − | 0.898979i | − | 0.0289843i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.6969 | −0.666604 | ||||||||
\(965\) | −39.1464 | − | 3.95459i | −1.26017 | − | 0.127303i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.2929i | 1.03847i | 0.854632 | + | 0.519234i | \(0.173783\pi\) | ||||
−0.854632 | + | 0.519234i | \(0.826217\pi\) | |||||||
\(968\) | − | 13.0000i | − | 0.417836i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.853572 | − | 8.44949i | 0.0274065 | − | 0.271297i | ||||
\(971\) | 14.4495 | 0.463706 | 0.231853 | − | 0.972751i | \(-0.425521\pi\) | ||||
0.231853 | + | 0.972751i | \(0.425521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.44949i | 0.206761i | ||||||||
\(974\) | 36.6969 | 1.17585 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.44949 | 0.270462 | ||||||||
\(977\) | − | 29.3939i | − | 0.940393i | −0.882562 | − | 0.470197i | \(-0.844183\pi\) | ||
0.882562 | − | 0.470197i | \(-0.155817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.9898 | 1.56572 | ||||||||
\(980\) | 0.224745 | − | 2.22474i | 0.00717921 | − | 0.0710669i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.5959i | 0.625331i | ||||||||
\(983\) | − | 42.6969i | − | 1.36182i | −0.732367 | − | 0.680910i | \(-0.761584\pi\) | ||
0.732367 | − | 0.680910i | \(-0.238416\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.2474 | − | 2.04541i | −0.645137 | − | 0.0651721i | ||||
\(986\) | −5.79796 | −0.184645 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.89898i | 0.0922288i | ||||||||
\(989\) | −61.3939 | −1.95221 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.6969 | 1.92810 | 0.964051 | − | 0.265718i | \(-0.0856089\pi\) | ||||
0.964051 | + | 0.265718i | \(0.0856089\pi\) | |||||||
\(992\) | − | 0.898979i | − | 0.0285426i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.8990 | 0.345695 | ||||||||
\(995\) | −1.59592 | + | 15.7980i | −0.0505940 | + | 0.500829i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.6515i | 1.35079i | 0.737457 | + | 0.675394i | \(0.236026\pi\) | ||||
−0.737457 | + | 0.675394i | \(0.763974\pi\) | |||||||
\(998\) | − | 25.7980i | − | 0.816620i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 630.2.g.g.379.4 | 4 | ||
3.2 | odd | 2 | 70.2.c.a.29.1 | ✓ | 4 | ||
4.3 | odd | 2 | 5040.2.t.t.1009.3 | 4 | |||
5.2 | odd | 4 | 3150.2.a.bs.1.1 | 2 | |||
5.3 | odd | 4 | 3150.2.a.bt.1.1 | 2 | |||
5.4 | even | 2 | inner | 630.2.g.g.379.2 | 4 | ||
12.11 | even | 2 | 560.2.g.e.449.3 | 4 | |||
15.2 | even | 4 | 350.2.a.h.1.1 | 2 | |||
15.8 | even | 4 | 350.2.a.g.1.2 | 2 | |||
15.14 | odd | 2 | 70.2.c.a.29.4 | yes | 4 | ||
20.19 | odd | 2 | 5040.2.t.t.1009.4 | 4 | |||
21.2 | odd | 6 | 490.2.i.c.459.2 | 8 | |||
21.5 | even | 6 | 490.2.i.f.459.1 | 8 | |||
21.11 | odd | 6 | 490.2.i.c.79.3 | 8 | |||
21.17 | even | 6 | 490.2.i.f.79.4 | 8 | |||
21.20 | even | 2 | 490.2.c.e.99.2 | 4 | |||
24.5 | odd | 2 | 2240.2.g.j.449.4 | 4 | |||
24.11 | even | 2 | 2240.2.g.i.449.2 | 4 | |||
60.23 | odd | 4 | 2800.2.a.bm.1.1 | 2 | |||
60.47 | odd | 4 | 2800.2.a.bl.1.2 | 2 | |||
60.59 | even | 2 | 560.2.g.e.449.1 | 4 | |||
105.44 | odd | 6 | 490.2.i.c.459.3 | 8 | |||
105.59 | even | 6 | 490.2.i.f.79.1 | 8 | |||
105.62 | odd | 4 | 2450.2.a.bq.1.2 | 2 | |||
105.74 | odd | 6 | 490.2.i.c.79.2 | 8 | |||
105.83 | odd | 4 | 2450.2.a.bl.1.1 | 2 | |||
105.89 | even | 6 | 490.2.i.f.459.4 | 8 | |||
105.104 | even | 2 | 490.2.c.e.99.3 | 4 | |||
120.29 | odd | 2 | 2240.2.g.j.449.2 | 4 | |||
120.59 | even | 2 | 2240.2.g.i.449.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.c.a.29.1 | ✓ | 4 | 3.2 | odd | 2 | ||
70.2.c.a.29.4 | yes | 4 | 15.14 | odd | 2 | ||
350.2.a.g.1.2 | 2 | 15.8 | even | 4 | |||
350.2.a.h.1.1 | 2 | 15.2 | even | 4 | |||
490.2.c.e.99.2 | 4 | 21.20 | even | 2 | |||
490.2.c.e.99.3 | 4 | 105.104 | even | 2 | |||
490.2.i.c.79.2 | 8 | 105.74 | odd | 6 | |||
490.2.i.c.79.3 | 8 | 21.11 | odd | 6 | |||
490.2.i.c.459.2 | 8 | 21.2 | odd | 6 | |||
490.2.i.c.459.3 | 8 | 105.44 | odd | 6 | |||
490.2.i.f.79.1 | 8 | 105.59 | even | 6 | |||
490.2.i.f.79.4 | 8 | 21.17 | even | 6 | |||
490.2.i.f.459.1 | 8 | 21.5 | even | 6 | |||
490.2.i.f.459.4 | 8 | 105.89 | even | 6 | |||
560.2.g.e.449.1 | 4 | 60.59 | even | 2 | |||
560.2.g.e.449.3 | 4 | 12.11 | even | 2 | |||
630.2.g.g.379.2 | 4 | 5.4 | even | 2 | inner | ||
630.2.g.g.379.4 | 4 | 1.1 | even | 1 | trivial | ||
2240.2.g.i.449.2 | 4 | 24.11 | even | 2 | |||
2240.2.g.i.449.4 | 4 | 120.59 | even | 2 | |||
2240.2.g.j.449.2 | 4 | 120.29 | odd | 2 | |||
2240.2.g.j.449.4 | 4 | 24.5 | odd | 2 | |||
2450.2.a.bl.1.1 | 2 | 105.83 | odd | 4 | |||
2450.2.a.bq.1.2 | 2 | 105.62 | odd | 4 | |||
2800.2.a.bl.1.2 | 2 | 60.47 | odd | 4 | |||
2800.2.a.bm.1.1 | 2 | 60.23 | odd | 4 | |||
3150.2.a.bs.1.1 | 2 | 5.2 | odd | 4 | |||
3150.2.a.bt.1.1 | 2 | 5.3 | odd | 4 | |||
5040.2.t.t.1009.3 | 4 | 4.3 | odd | 2 | |||
5040.2.t.t.1009.4 | 4 | 20.19 | odd | 2 |