Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(481,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.3010058496.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 6x^{6} + 2x^{5} - 17x^{4} + 6x^{3} + 54x^{2} - 108x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 481.1 | ||
Root | \(1.14729 + 1.29759i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.481 |
Dual form | 1440.2.q.i.961.1 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.69739 | − | 0.344784i | −0.979987 | − | 0.199061i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.69739 | + | 2.93996i | 0.641552 | + | 1.11120i | 0.985086 | + | 0.172061i | \(0.0550425\pi\) |
−0.343534 | + | 0.939140i | \(0.611624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.76225 | + | 1.17046i | 0.920749 | + | 0.390154i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.84467 | + | 3.19507i | 0.556190 | + | 0.963349i | 0.997810 | + | 0.0661468i | \(0.0210706\pi\) |
−0.441620 | + | 0.897202i | \(0.645596\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.867473 | − | 1.50251i | 0.240594 | − | 0.416721i | −0.720290 | − | 0.693673i | \(-0.755991\pi\) |
0.960884 | + | 0.276953i | \(0.0893245\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.14729 | + | 1.29759i | −0.296228 | + | 0.335036i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.93536 | −1.43954 | −0.719768 | − | 0.694215i | \(-0.755752\pi\) | ||||
−0.719768 | + | 0.694215i | \(0.755752\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.10020 | 1.17007 | 0.585034 | − | 0.811009i | \(-0.301081\pi\) | ||||
0.585034 | + | 0.811009i | \(0.301081\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.86747 | − | 5.57549i | −0.407516 | − | 1.21667i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.43233 | + | 4.21293i | −0.507177 | + | 0.878456i | 0.492789 | + | 0.870149i | \(0.335978\pi\) |
−0.999965 | + | 0.00830696i | \(0.997356\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.28505 | − | 2.93911i | −0.824658 | − | 0.565632i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.600205 | − | 1.03958i | −0.111455 | − | 0.193046i | 0.804902 | − | 0.593408i | \(-0.202218\pi\) |
−0.916357 | + | 0.400362i | \(0.868884\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.28505 | + | 3.95782i | −0.410407 | + | 0.710846i | −0.994934 | − | 0.100528i | \(-0.967947\pi\) |
0.584527 | + | 0.811374i | \(0.301280\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.02952 | − | 6.05928i | −0.353294 | − | 1.05479i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.39477 | 0.573822 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.14581 | −0.517167 | −0.258584 | − | 0.965989i | \(-0.583256\pi\) | ||||
−0.258584 | + | 0.965989i | \(0.583256\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.99048 | + | 2.25125i | −0.318732 | + | 0.360488i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.32187 | + | 7.48570i | −0.674963 | + | 1.16907i | 0.301517 | + | 0.953461i | \(0.402507\pi\) |
−0.976480 | + | 0.215609i | \(0.930826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.55010 | − | 6.14896i | −0.541386 | − | 0.937707i | −0.998825 | − | 0.0484664i | \(-0.984567\pi\) |
0.457439 | − | 0.889241i | \(-0.348767\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.39477 | − | 1.80695i | 0.356992 | − | 0.269364i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.95292 | + | 3.38256i | 0.284863 | + | 0.493396i | 0.972576 | − | 0.232586i | \(-0.0747187\pi\) |
−0.687713 | + | 0.725982i | \(0.741385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.26225 | + | 3.91833i | −0.323178 | + | 0.559761i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.0746 | + | 2.04641i | 1.41073 | + | 0.286555i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.25944 | 1.13452 | 0.567261 | − | 0.823538i | \(-0.308003\pi\) | ||||
0.567261 | + | 0.823538i | \(0.308003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.68935 | 0.497471 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.65702 | − | 1.75847i | −1.14665 | − | 0.232915i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.39477 | + | 2.41582i | −0.181584 | + | 0.314513i | −0.942420 | − | 0.334431i | \(-0.891456\pi\) |
0.760836 | + | 0.648944i | \(0.224789\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0729031 | + | 0.126272i | 0.00933429 | + | 0.0161675i | 0.870655 | − | 0.491894i | \(-0.163695\pi\) |
−0.861321 | + | 0.508062i | \(0.830362\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.24749 | + | 10.1076i | 0.157169 | + | 1.27344i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.867473 | − | 1.50251i | −0.107597 | − | 0.186363i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.54206 | + | 6.13503i | −0.432732 | + | 0.749513i | −0.997107 | − | 0.0760049i | \(-0.975784\pi\) |
0.564376 | + | 0.825518i | \(0.309117\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.58116 | − | 6.31234i | 0.671893 | − | 0.759916i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.110246 | −0.0130837 | −0.00654187 | − | 0.999979i | \(-0.502082\pi\) | ||||
−0.00654187 | + | 0.999979i | \(0.502082\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.3787 | 1.79994 | 0.899970 | − | 0.435952i | \(-0.143588\pi\) | ||||
0.899970 | + | 0.435952i | \(0.143588\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.550102 | + | 1.64237i | 0.0635203 | + | 0.189645i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.26225 | + | 10.8465i | −0.713649 | + | 1.23608i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.39477 | + | 4.14787i | 0.269433 | + | 0.466672i | 0.968716 | − | 0.248174i | \(-0.0798303\pi\) |
−0.699282 | + | 0.714846i | \(0.746497\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.26003 | + | 6.46622i | 0.695559 | + | 0.718469i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.38673 | + | 14.5262i | 0.920564 | + | 1.59446i | 0.798545 | + | 0.601935i | \(0.205603\pi\) |
0.122018 | + | 0.992528i | \(0.461063\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.96768 | + | 5.14017i | −0.321890 | + | 0.557530i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.660348 | + | 1.97152i | 0.0707967 | + | 0.211369i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.37869 | −0.252141 | −0.126070 | − | 0.992021i | \(-0.540237\pi\) | ||||
−0.126070 | + | 0.992021i | \(0.540237\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.88975 | 0.617414 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.24321 | − | 5.93011i | 0.543695 | − | 0.614924i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.55010 | − | 4.41691i | 0.261635 | − | 0.453165i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.76003 | + | 6.51257i | 0.381773 | + | 0.661251i | 0.991316 | − | 0.131502i | \(-0.0419801\pi\) |
−0.609542 | + | 0.792753i | \(0.708647\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.35574 | + | 10.9847i | 0.136257 | + | 1.10400i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.92931 | + | 3.34167i | 0.191974 | + | 0.332508i | 0.945904 | − | 0.324446i | \(-0.105178\pi\) |
−0.753930 | + | 0.656954i | \(0.771844\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.18484 | − | 3.78426i | 0.215279 | − | 0.372874i | −0.738080 | − | 0.674713i | \(-0.764267\pi\) |
0.953359 | + | 0.301839i | \(0.0976005\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.76225 | − | 1.17046i | −0.562338 | − | 0.114225i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −20.0550 | −1.93879 | −0.969397 | − | 0.245499i | \(-0.921048\pi\) | ||||
−0.969397 | + | 0.245499i | \(0.921048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.7839 | 1.70339 | 0.851696 | − | 0.524036i | \(-0.175574\pi\) | ||||
0.851696 | + | 0.524036i | \(0.175574\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.33965 | + | 1.08462i | 0.506817 | + | 0.102948i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.81907 | + | 15.2751i | −0.829628 | + | 1.43696i | 0.0687022 | + | 0.997637i | \(0.478114\pi\) |
−0.898330 | + | 0.439321i | \(0.855219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.43233 | + | 4.21293i | 0.226816 | + | 0.392857i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.15481 | − | 3.13496i | 0.384112 | − | 0.289827i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.0746 | − | 17.4497i | −0.923537 | − | 1.59961i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.30563 | + | 2.26142i | −0.118694 | + | 0.205584i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.91684 | − | 11.2160i | 0.894171 | − | 1.01131i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.7544 | −0.954301 | −0.477150 | − | 0.878822i | \(-0.658330\pi\) | ||||
−0.477150 | + | 0.878822i | \(0.658330\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.90584 | + | 11.6612i | 0.343890 | + | 1.02671i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.459419 | − | 0.795737i | 0.0401396 | − | 0.0695238i | −0.845258 | − | 0.534359i | \(-0.820553\pi\) |
0.885397 | + | 0.464835i | \(0.153886\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.65702 | + | 14.9944i | 0.750659 | + | 1.30018i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.68787 | + | 2.24141i | −0.403467 | + | 0.192910i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.59518 | − | 9.69114i | −0.478029 | − | 0.827970i | 0.521654 | − | 0.853157i | \(-0.325315\pi\) |
−0.999683 | + | 0.0251870i | \(0.991982\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.73495 | + | 9.93322i | −0.486432 | + | 0.842525i | −0.999878 | − | 0.0155969i | \(-0.995035\pi\) |
0.513447 | + | 0.858122i | \(0.328368\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.14861 | − | 6.41484i | −0.180946 | − | 0.540227i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.40082 | 0.535263 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.20041 | −0.0996886 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.19089 | − | 5.87094i | 0.428137 | − | 0.484227i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.467678 | − | 0.810042i | 0.0383137 | − | 0.0663612i | −0.846233 | − | 0.532814i | \(-0.821135\pi\) |
0.884546 | + | 0.466452i | \(0.154468\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.73443 | + | 13.3964i | 0.629419 | + | 1.09019i | 0.987669 | + | 0.156559i | \(0.0500403\pi\) |
−0.358250 | + | 0.933626i | \(0.616626\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.3949 | − | 6.94711i | −1.32545 | − | 0.561641i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.28505 | + | 3.95782i | 0.183540 | + | 0.317900i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.9839 | − | 19.0247i | 0.876612 | − | 1.51834i | 0.0215762 | − | 0.999767i | \(-0.493132\pi\) |
0.855036 | − | 0.518569i | \(-0.173535\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.0195 | − | 2.84772i | −1.11182 | − | 0.225839i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.5145 | −1.30152 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.1492 | −1.89151 | −0.945756 | − | 0.324879i | \(-0.894676\pi\) | ||||
−0.945756 | + | 0.324879i | \(0.894676\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.26225 | − | 1.27203i | −0.487515 | − | 0.0990271i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.52302 | − | 16.4944i | 0.736913 | − | 1.27637i | −0.216966 | − | 0.976179i | \(-0.569616\pi\) |
0.953879 | − | 0.300192i | \(-0.0970507\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.99498 | + | 8.65156i | 0.384229 | + | 0.665504i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.0880 | + | 5.96960i | 1.07734 | + | 0.456507i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.2138 | − | 17.6909i | −0.776544 | − | 1.34501i | −0.933923 | − | 0.357475i | \(-0.883638\pi\) |
0.157379 | − | 0.987538i | \(-0.449696\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.69739 | − | 2.93996i | 0.128310 | − | 0.222240i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.20041 | − | 3.61969i | 0.240557 | − | 0.272072i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.21945 | −0.165890 | −0.0829448 | − | 0.996554i | \(-0.526433\pi\) | ||||
−0.0829448 | + | 0.996554i | \(0.526433\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7795 | 1.54453 | 0.772264 | − | 0.635301i | \(-0.219124\pi\) | ||||
0.772264 | + | 0.635301i | \(0.219124\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.0802084 | − | 0.239468i | −0.00592917 | − | 0.0177020i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.57290 | + | 2.72435i | −0.115642 | + | 0.200298i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.9488 | − | 18.9639i | −0.800655 | − | 1.38677i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.36747 | − | 17.5867i | 0.0994691 | − | 1.27924i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.02000 | + | 12.1590i | 0.507949 | + | 0.879794i | 0.999958 | + | 0.00920328i | \(0.00292954\pi\) |
−0.492009 | + | 0.870590i | \(0.663737\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.9576 | + | 18.9792i | −0.788748 | + | 1.36615i | 0.137986 | + | 0.990434i | \(0.455937\pi\) |
−0.926734 | + | 0.375717i | \(0.877396\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.954398 | + | 2.84943i | 0.0683459 | + | 0.204052i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.4599 | −1.17272 | −0.586358 | − | 0.810052i | \(-0.699439\pi\) | ||||
−0.586358 | + | 0.810052i | \(0.699439\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.69939 | 0.333131 | 0.166565 | − | 0.986030i | \(-0.446732\pi\) | ||||
0.166565 | + | 0.986030i | \(0.446732\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.12751 | − | 9.19228i | 0.573270 | − | 0.648373i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.03756 | − | 3.52916i | 0.143009 | − | 0.247698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.32187 | + | 7.48570i | 0.301853 | + | 0.522824i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.6498 | + | 8.79019i | −0.809716 | + | 0.610961i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.40821 | + | 16.2955i | 0.650779 | + | 1.12718i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.45594 | − | 2.52176i | 0.100231 | − | 0.173605i | −0.811549 | − | 0.584285i | \(-0.801375\pi\) |
0.911780 | + | 0.410679i | \(0.134708\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.187129 | + | 0.0380109i | 0.0128219 | + | 0.00260446i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.10020 | −0.484230 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.5145 | −1.05319 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26.1036 | − | 5.30232i | −1.76392 | − | 0.358298i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.14876 | + | 8.91792i | −0.346343 | + | 0.599884i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.29309 | + | 5.70380i | 0.220522 | + | 0.381955i | 0.954967 | − | 0.296714i | \(-0.0958907\pi\) |
−0.734445 | + | 0.678668i | \(0.762557\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.367473 | − | 2.97741i | −0.0244982 | − | 0.198494i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.61475 | + | 4.52887i | 0.173547 | + | 0.300592i | 0.939657 | − | 0.342117i | \(-0.111144\pi\) |
−0.766111 | + | 0.642709i | \(0.777811\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.82409 | − | 8.35556i | 0.318785 | − | 0.552151i | −0.661450 | − | 0.749989i | \(-0.730059\pi\) |
0.980235 | + | 0.197838i | \(0.0633920\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.3692 | − | 16.2516i | 0.945422 | − | 1.06928i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.4333 | 0.945556 | 0.472778 | − | 0.881181i | \(-0.343251\pi\) | ||||
0.472778 | + | 0.881181i | \(0.343251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.90584 | 0.254789 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.63474 | − | 7.86623i | −0.171145 | − | 0.510966i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.1136 | − | 24.4455i | 0.912935 | − | 1.58125i | 0.103039 | − | 0.994677i | \(-0.467143\pi\) |
0.809896 | − | 0.586573i | \(-0.199523\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.97270 | − | 12.0771i | −0.449151 | − | 0.777952i | 0.549180 | − | 0.835704i | \(-0.314940\pi\) |
−0.998331 | + | 0.0577518i | \(0.981607\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.39625 | − | 13.1340i | −0.538620 | − | 0.842549i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.26225 | + | 3.91833i | 0.144530 | + | 0.250333i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.42429 | − | 7.66310i | 0.281511 | − | 0.487591i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.22712 | − | 27.5483i | −0.584745 | − | 1.74580i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.5279 | 0.980112 | 0.490056 | − | 0.871691i | \(-0.336976\pi\) | ||||
0.490056 | + | 0.871691i | \(0.336976\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.9474 | −1.12835 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.80955 | − | 7.70165i | 0.426430 | − | 0.482296i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.119247 | + | 0.206541i | −0.00743841 | + | 0.0128837i | −0.869721 | − | 0.493544i | \(-0.835701\pi\) |
0.862282 | + | 0.506428i | \(0.169034\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.33965 | − | 9.24855i | −0.331790 | − | 0.574677i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.441119 | − | 3.57411i | −0.0273046 | − | 0.221232i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.92879 | − | 8.53692i | −0.303922 | − | 0.526409i | 0.673098 | − | 0.739553i | \(-0.264963\pi\) |
−0.977021 | + | 0.213144i | \(0.931630\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.12972 | − | 7.15289i | 0.253687 | − | 0.439398i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.03756 | + | 0.820134i | 0.247095 | + | 0.0501914i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.9534 | −1.64338 | −0.821688 | − | 0.569938i | \(-0.806967\pi\) | ||||
−0.821688 | + | 0.569938i | \(0.806967\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.4677 | 1.72929 | 0.864644 | − | 0.502385i | \(-0.167544\pi\) | ||||
0.864644 | + | 0.502385i | \(0.167544\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.99720 | − | 2.03069i | −0.605058 | − | 0.122903i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.84467 | − | 3.19507i | 0.111238 | − | 0.192670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.2817 | + | 28.2008i | 0.978274 | + | 1.69442i | 0.668678 | + | 0.743552i | \(0.266861\pi\) |
0.309596 | + | 0.950868i | \(0.399806\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.9444 | + | 8.25792i | −0.655222 | + | 0.494389i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.79781 | − | 11.7742i | −0.405523 | − | 0.702387i | 0.588859 | − | 0.808236i | \(-0.299577\pi\) |
−0.994382 | + | 0.105849i | \(0.966244\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.26749 | − | 14.3197i | 0.491451 | − | 0.851218i | −0.508501 | − | 0.861062i | \(-0.669800\pi\) |
0.999952 | + | 0.00984353i | \(0.00313334\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.85139 | + | 6.61797i | −0.346606 | + | 0.392015i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29.3436 | −1.73210 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.2285 | 1.07226 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.13681 | − | 12.3507i | −0.242504 | − | 0.724014i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.6570 | − | 21.9226i | 0.739431 | − | 1.28073i | −0.213321 | − | 0.976982i | \(-0.568428\pi\) |
0.952752 | − | 0.303750i | \(-0.0982388\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.39477 | + | 2.41582i | 0.0812069 | + | 0.140655i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.48613 | − | 19.1127i | 0.0862341 | − | 1.10903i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.21997 | + | 7.30920i | 0.244047 | + | 0.422702i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0518 | − | 20.8743i | 0.694654 | − | 1.20318i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.12264 | − | 6.33730i | −0.121942 | − | 0.364068i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.145806 | 0.00834884 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.62323 | −0.378008 | −0.189004 | − | 0.981976i | \(-0.560526\pi\) | ||||
−0.189004 | + | 0.981976i | \(0.560526\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.01328 | + | 5.67006i | −0.285196 | + | 0.322558i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.01556 | − | 6.95516i | 0.227702 | − | 0.394391i | −0.729425 | − | 0.684061i | \(-0.760212\pi\) |
0.957127 | + | 0.289670i | \(0.0935455\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5407 | + | 18.2571i | 0.595798 | + | 1.03195i | 0.993434 | + | 0.114408i | \(0.0364973\pi\) |
−0.397636 | + | 0.917543i | \(0.630169\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.37721 | + | 3.97346i | 0.528346 | + | 0.223879i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.8058 | + | 18.7162i | 0.606913 | + | 1.05120i | 0.991746 | + | 0.128219i | \(0.0409259\pi\) |
−0.384832 | + | 0.922986i | \(0.625741\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.21436 | − | 3.83539i | 0.123980 | − | 0.214740i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 34.0412 | + | 6.91465i | 1.89999 | + | 0.385938i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −30.2715 | −1.68435 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.73495 | −0.0962375 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −30.1862 | − | 6.13161i | −1.66930 | − | 0.339079i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.62972 | + | 11.4830i | −0.365508 | + | 0.633079i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.8146 | − | 20.4635i | −0.649391 | − | 1.12478i | −0.983269 | − | 0.182162i | \(-0.941691\pi\) |
0.333877 | − | 0.942616i | \(-0.391643\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.68950 | − | 3.68205i | −0.476182 | − | 0.201775i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.54206 | + | 6.13503i | 0.193523 | + | 0.335192i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.87367 | − | 13.6376i | 0.428906 | − | 0.742887i | −0.567870 | − | 0.823118i | \(-0.692232\pi\) |
0.996776 | + | 0.0802309i | \(0.0255658\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.2360 | − | 22.8870i | 1.09907 | − | 1.24305i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.8607 | −0.913057 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.40378 | 0.453761 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.67607 | − | 7.98960i | −0.144075 | − | 0.430146i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.29405 | + | 14.3657i | −0.445248 | + | 0.771192i | −0.998069 | − | 0.0621076i | \(-0.980218\pi\) |
0.552822 | + | 0.833300i | \(0.313551\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.2088 | − | 21.1463i | −0.653523 | − | 1.13194i | −0.982262 | − | 0.187514i | \(-0.939957\pi\) |
0.328739 | − | 0.944421i | \(-0.393376\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.13320 | + | 3.88872i | −0.434118 | + | 0.207565i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.40082 | + | 11.0865i | 0.340681 | + | 0.590077i | 0.984559 | − | 0.175051i | \(-0.0560090\pi\) |
−0.643878 | + | 0.765128i | \(0.722676\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.0551228 | + | 0.0954754i | −0.00292561 | + | 0.00506731i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.0841 | + | 33.0925i | 0.586634 | + | 1.75144i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.4568 | −1.13244 | −0.566222 | − | 0.824252i | \(-0.691596\pi\) | ||||
−0.566222 | + | 0.824252i | \(0.691596\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.01209 | 0.369057 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.99587 | − | 3.38835i | 0.157242 | − | 0.177842i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.68935 | − | 13.3183i | 0.402479 | − | 0.697114i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.9098 | − | 18.8962i | −0.569484 | − | 0.986376i | −0.996617 | − | 0.0821868i | \(-0.973810\pi\) |
0.427133 | − | 0.904189i | \(-0.359524\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.6998 | + | 15.6188i | −1.07759 | + | 0.813081i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.0195 | + | 24.2824i | 0.727855 | + | 1.26068i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.1197 | + | 19.2599i | −0.575755 | + | 0.997237i | 0.420204 | + | 0.907430i | \(0.361959\pi\) |
−0.995959 | + | 0.0898076i | \(0.971375\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.69739 | + | 0.344784i | 0.0876527 | + | 0.0178046i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.08265 | −0.107262 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.880753 | 0.0452413 | 0.0226206 | − | 0.999744i | \(-0.492799\pi\) | ||||
0.0226206 | + | 0.999744i | \(0.492799\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.2544 | + | 3.70795i | 0.935202 | + | 0.189964i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.87419 | − | 6.71029i | 0.197962 | − | 0.342880i | −0.749906 | − | 0.661545i | \(-0.769901\pi\) |
0.947867 | + | 0.318665i | \(0.103234\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.26225 | + | 10.8465i | 0.319154 | + | 0.552790i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.60914 | − | 21.1402i | −0.132630 | − | 1.07462i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.02730 | + | 12.1716i | 0.356298 | + | 0.617127i | 0.987339 | − | 0.158623i | \(-0.0507054\pi\) |
−0.631041 | + | 0.775750i | \(0.717372\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.4368 | − | 25.0052i | 0.730099 | − | 1.26457i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.05417 | + | 1.19227i | −0.0531758 | + | 0.0601422i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.78955 | 0.240988 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.16232 | 0.208901 | 0.104451 | − | 0.994530i | \(-0.466692\pi\) | ||||
0.104451 | + | 0.994530i | \(0.466692\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.52450 | − | 28.4361i | −0.476821 | − | 1.42359i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.49941 | + | 11.2573i | −0.324565 | + | 0.562163i | −0.981424 | − | 0.191850i | \(-0.938551\pi\) |
0.656859 | + | 0.754013i | \(0.271885\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.96444 | + | 6.86661i | 0.197483 | + | 0.342050i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.72993 | − | 2.18824i | 0.433794 | − | 0.108734i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.80298 | − | 10.0511i | −0.287643 | − | 0.498213i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.05460 | + | 13.9510i | −0.398274 | + | 0.689832i | −0.993513 | − | 0.113717i | \(-0.963724\pi\) |
0.595239 | + | 0.803549i | \(0.297058\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.15585 | + | 18.3788i | 0.303646 | + | 0.906557i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.46989 | −0.465983 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.7735 | 0.823377 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.1592 | − | 14.8832i | 0.644411 | − | 0.728834i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.73443 | + | 9.93232i | −0.280145 | + | 0.485226i | −0.971420 | − | 0.237366i | \(-0.923716\pi\) |
0.691275 | + | 0.722592i | \(0.257049\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.32409 | − | 5.75749i | −0.162006 | − | 0.280603i | 0.773582 | − | 0.633696i | \(-0.218463\pi\) |
−0.935588 | + | 0.353093i | \(0.885130\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.43529 | + | 11.6293i | 0.0697863 | + | 0.565435i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.96768 | + | 5.14017i | 0.143954 | + | 0.249335i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.247490 | + | 0.428665i | −0.0119769 | + | 0.0207445i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.8647 | − | 2.20690i | −0.524551 | − | 0.106550i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.4599 | 0.503833 | 0.251917 | − | 0.967749i | \(-0.418939\pi\) | ||||
0.251917 | + | 0.967749i | \(0.418939\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.3831 | 1.17178 | 0.585889 | − | 0.810391i | \(-0.300745\pi\) | ||||
0.585889 | + | 0.810391i | \(0.300745\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.03756 | + | 0.413882i | 0.0976935 | + | 0.0198441i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.4054 | + | 21.4868i | −0.593431 | + | 1.02785i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.2594 | − | 22.9660i | −0.632839 | − | 1.09611i | −0.986969 | − | 0.160913i | \(-0.948556\pi\) |
0.354130 | − | 0.935196i | \(-0.384777\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.8352 | + | 8.17552i | −0.515960 | + | 0.389310i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.77199 | − | 11.7294i | −0.321747 | − | 0.557282i | 0.659102 | − | 0.752054i | \(-0.270937\pi\) |
−0.980849 | + | 0.194772i | \(0.937603\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.18935 | + | 2.06001i | −0.0563804 | + | 0.0976537i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.07312 | + | 1.21371i | −0.0507568 | + | 0.0574064i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.5511 | −0.875478 | −0.437739 | − | 0.899102i | \(-0.644221\pi\) | ||||
−0.437739 | + | 0.899102i | \(0.644221\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.8898 | −1.50163 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.50945 | − | 25.4056i | −0.399809 | − | 1.19366i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.94488 | − | 5.10068i | 0.138058 | − | 0.239123i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.9606 | − | 27.6446i | −0.746605 | − | 1.29316i | −0.949441 | − | 0.313945i | \(-0.898349\pi\) |
0.202836 | − | 0.979213i | \(-0.434984\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.4333 | + | 17.4446i | 1.18712 | + | 0.814247i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.03454 | + | 5.25597i | 0.141333 | + | 0.244795i | 0.927999 | − | 0.372584i | \(-0.121528\pi\) |
−0.786666 | + | 0.617379i | \(0.788195\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.4989 | + | 21.6487i | −0.580873 | + | 1.00610i | 0.414503 | + | 0.910048i | \(0.363955\pi\) |
−0.995376 | + | 0.0960534i | \(0.969378\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.51402 | − | 7.50580i | −0.116585 | − | 0.348073i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.46089 | 0.206425 | 0.103213 | − | 0.994659i | \(-0.467088\pi\) | ||||
0.103213 | + | 0.994659i | \(0.467088\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.0490 | −1.11048 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.2034 | + | 28.5052i | −1.16131 | + | 1.31345i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.0976 | − | 22.6856i | 0.602226 | − | 1.04309i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.55010 | − | 4.41691i | −0.117007 | − | 0.202662i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.8146 | + | 9.66737i | 1.04461 | + | 0.442639i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.5496 | + | 25.2006i | 0.664787 | + | 1.15145i | 0.979343 | + | 0.202206i | \(0.0648112\pi\) |
−0.314556 | + | 0.949239i | \(0.601855\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.72890 | + | 4.72660i | −0.124427 | + | 0.215514i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28.0314 | + | 5.69392i | 1.27547 | + | 0.259082i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.52007 | 0.341469 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.1873 | −0.642887 | −0.321444 | − | 0.946929i | \(-0.604168\pi\) | ||||
−0.321444 | + | 0.946929i | \(0.604168\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.9905 | + | 8.32625i | 1.85366 | + | 0.376526i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.0902 | − | 33.0651i | 0.861527 | − | 1.49221i | −0.00892773 | − | 0.999960i | \(-0.502842\pi\) |
0.870455 | − | 0.492248i | \(-0.163825\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.56243 | + | 6.17031i | 0.160444 | + | 0.277897i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.1909 | + | 4.31824i | 0.458046 | + | 0.194091i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.187129 | − | 0.324118i | −0.00839390 | − | 0.0145387i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.70839 | + | 4.69106i | −0.121244 | + | 0.210001i | −0.920259 | − | 0.391311i | \(-0.872022\pi\) |
0.799014 | + | 0.601312i | \(0.205355\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.8512 | + | 24.7139i | −0.976241 | + | 1.10414i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.1544 | −0.497349 | −0.248674 | − | 0.968587i | \(-0.579995\pi\) | ||||
−0.248674 | + | 0.968587i | \(0.579995\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.85863 | 0.171707 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.49550 | − | 16.4072i | −0.244064 | − | 0.728671i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.90821 | − | 17.1615i | 0.439174 | − | 0.760671i | −0.558452 | − | 0.829537i | \(-0.688605\pi\) |
0.997626 | + | 0.0688656i | \(0.0219380\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.1036 | + | 45.2128i | 1.15476 | + | 2.00009i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −21.8546 | − | 14.9900i | −0.964905 | − | 0.661827i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.18484 | − | 3.78426i | −0.0962758 | − | 0.166755i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.20499 | + | 12.4794i | −0.316875 | + | 0.548844i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.2373 | + | 33.5499i | 0.493263 | + | 1.47268i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.7807 | −0.603743 | −0.301871 | − | 0.953349i | \(-0.597611\pi\) | ||||
−0.301871 | + | 0.953349i | \(0.597611\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.66117 | −0.0726381 | −0.0363190 | − | 0.999340i | \(-0.511563\pi\) | ||||
−0.0363190 | + | 0.999340i | \(0.511563\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.89477 | + | 4.40502i | −0.169982 | + | 0.192251i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.5626 | − | 23.4911i | 0.590795 | − | 1.02329i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.332502 | − | 0.575910i | −0.0144566 | − | 0.0250395i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.68034 | + | 5.04057i | −0.289902 | + | 0.218742i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.49822 | + | 12.9873i | 0.324784 | + | 0.562542i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.0275 | + | 17.3682i | −0.433527 | + | 0.750892i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.76727 | + | 0.765231i | 0.162570 | + | 0.0330221i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.6924 | −0.718994 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.9678 | −1.67536 | −0.837679 | − | 0.546163i | \(-0.816088\pi\) | ||||
−0.837679 | + | 0.546163i | \(0.816088\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −35.2709 | − | 7.16444i | −1.51362 | − | 0.307455i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.89197 | − | 15.4013i | 0.380890 | − | 0.659721i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.3706 | + | 19.6945i | 0.486174 | + | 0.842078i | 0.999874 | − | 0.0158922i | \(-0.00505885\pi\) |
−0.513700 | + | 0.857970i | \(0.671726\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.0535799 | + | 0.434125i | 0.00228674 | + | 0.0185280i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.06117 | − | 5.30210i | −0.130410 | − | 0.225877i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.12972 | + | 14.0811i | −0.345711 | + | 0.598789i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.60914 | − | 4.08196i | 0.153199 | − | 0.173270i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.7193 | 1.38636 | 0.693181 | − | 0.720764i | \(-0.256209\pi\) | ||||
0.693181 | + | 0.720764i | \(0.256209\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.3185 | −0.521016 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0459 | + | 35.9640i | 0.508579 | + | 1.51840i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.75251 | − | 16.8918i | 0.411019 | − | 0.711906i | −0.583982 | − | 0.811766i | \(-0.698506\pi\) |
0.995001 | + | 0.0998602i | \(0.0318395\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.81907 | + | 15.2751i | 0.371021 | + | 0.642627i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.38473 | + | 29.3799i | −0.352126 | + | 1.23384i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.46989 | − | 11.2062i | −0.271232 | − | 0.469788i | 0.697946 | − | 0.716151i | \(-0.254098\pi\) |
−0.969178 | + | 0.246363i | \(0.920764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.123678 | + | 0.214217i | −0.00517578 | + | 0.00896472i | −0.868602 | − | 0.495511i | \(-0.834981\pi\) |
0.863426 | + | 0.504476i | \(0.168314\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.72343 | − | 23.0589i | −0.322651 | − | 0.963299i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.86467 | 0.202871 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.0431 | 0.792774 | 0.396387 | − | 0.918084i | \(-0.370264\pi\) | ||||
0.396387 | + | 0.918084i | \(0.370264\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.1431 | − | 28.4370i | 1.04491 | − | 1.18180i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.4711 | + | 49.3133i | −1.18118 | + | 2.04586i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.2360 | + | 26.3895i | 0.631009 | + | 1.09294i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.637547 | − | 5.16565i | −0.0263593 | − | 0.213573i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.408861 | − | 0.708167i | −0.0168755 | − | 0.0292292i | 0.857464 | − | 0.514543i | \(-0.172039\pi\) |
−0.874340 | + | 0.485314i | \(0.838705\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.6542 | + | 20.1857i | −0.480204 | + | 0.831737i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.9387 | + | 5.67509i | 1.14925 | + | 0.233442i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 45.3441 | 1.86206 | 0.931030 | − | 0.364942i | \(-0.118911\pi\) | ||||
0.931030 | + | 0.364942i | \(0.118911\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.1492 | −0.826037 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.97668 | − | 1.62027i | −0.326464 | − | 0.0663133i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.43594 | − | 2.48713i | 0.0586711 | − | 0.101621i | −0.835198 | − | 0.549949i | \(-0.814647\pi\) |
0.893869 | + | 0.448328i | \(0.147980\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.3821 | − | 40.4990i | −0.953775 | − | 1.65199i | −0.737147 | − | 0.675733i | \(-0.763827\pi\) |
−0.216628 | − | 0.976254i | \(-0.569506\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.9649 | + | 12.8006i | −0.690863 | + | 0.521282i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.30563 | + | 2.26142i | 0.0530816 | + | 0.0919400i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.89123 | + | 13.6680i | −0.320295 | + | 0.554768i | −0.980549 | − | 0.196275i | \(-0.937115\pi\) |
0.660254 | + | 0.751043i | \(0.270449\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.67532 | + | 5.28783i | −0.189454 | + | 0.214274i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.77642 | 0.274145 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.6216 | 0.429003 | 0.214502 | − | 0.976724i | \(-0.431187\pi\) | ||||
0.214502 | + | 0.976724i | \(0.431187\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.75494 | − | 14.1962i | −0.191738 | − | 0.572448i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.2789 | − | 26.4639i | 0.615106 | − | 1.06540i | −0.375260 | − | 0.926920i | \(-0.622446\pi\) |
0.990366 | − | 0.138475i | \(-0.0442202\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.57358 | − | 16.5819i | −0.384795 | − | 0.666484i | 0.606946 | − | 0.794743i | \(-0.292394\pi\) |
−0.991741 | + | 0.128259i | \(0.959061\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.8049 | − | 10.9037i | 0.915130 | − | 0.437551i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.03756 | − | 6.99326i | −0.161761 | − | 0.280179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.3510 | − | 30.9036i | −0.413377 | − | 1.23417i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.6715 | 0.744481 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.5750 | 1.29679 | 0.648395 | − | 0.761304i | \(-0.275441\pi\) | ||||
0.648395 | + | 0.761304i | \(0.275441\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.34076 | + | 3.77843i | −0.132783 | + | 0.150179i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.37721 | + | 9.31360i | −0.213388 | + | 0.369599i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.92488 | + | 6.79809i | 0.155509 | + | 0.269350i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.304526 | − | 0.129038i | −0.0120468 | − | 0.00510468i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.51624 | + | 7.82235i | 0.178381 | + | 0.308964i | 0.941326 | − | 0.337499i | \(-0.109581\pi\) |
−0.762945 | + | 0.646463i | \(0.776247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.02656 | − | 12.1704i | 0.277101 | − | 0.479952i | −0.693562 | − | 0.720397i | \(-0.743960\pi\) |
0.970663 | + | 0.240444i | \(0.0772931\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.0518 | + | 2.44803i | 0.474539 | + | 0.0963913i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.4970 | 0.687879 | 0.343940 | − | 0.938992i | \(-0.388238\pi\) | ||||
0.343940 | + | 0.938992i | \(0.388238\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.2916 | −0.403981 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.3340 | + | 5.34913i | 1.03211 | + | 0.209649i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.8102 | − | 29.1162i | 0.657835 | − | 1.13940i | −0.323340 | − | 0.946283i | \(-0.604806\pi\) |
0.981175 | − | 0.193120i | \(-0.0618608\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.459419 | − | 0.795737i | −0.0179510 | − | 0.0310920i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 42.4798 | + | 18.0002i | 1.65729 | + | 0.702254i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.9944 | + | 22.5069i | 0.506190 | + | 0.876746i | 0.999974 | + | 0.00716194i | \(0.00227973\pi\) |
−0.493785 | + | 0.869584i | \(0.664387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.0902 | − | 33.0651i | 0.742521 | − | 1.28608i | −0.208823 | − | 0.977954i | \(-0.566963\pi\) |
0.951344 | − | 0.308131i | \(-0.0997035\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.8142 | − | 13.3620i | 0.458826 | − | 0.518935i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.3140 | 0.671410 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.83959 | 0.226110 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.62307 | − | 10.8170i | −0.140076 | − | 0.418208i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.268965 | + | 0.465861i | −0.0103833 | + | 0.0179844i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.4436 | − | 25.0171i | −0.556760 | − | 0.964337i | −0.997764 | − | 0.0668322i | \(-0.978711\pi\) |
0.441004 | − | 0.897505i | \(-0.354623\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.402817 | + | 5.18052i | −0.0155044 | + | 0.199398i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.372494 | − | 0.645178i | −0.0143161 | − | 0.0247962i | 0.858779 | − | 0.512347i | \(-0.171224\pi\) |
−0.873095 | + | 0.487551i | \(0.837890\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.7645 | + | 22.1087i | −0.489855 | + | 0.848454i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.87676 | − | 8.58877i | −0.110238 | − | 0.329123i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.3877 | −0.550530 | −0.275265 | − | 0.961368i | \(-0.588766\pi\) | ||||
−0.275265 | + | 0.961368i | \(0.588766\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.1904 | −0.427562 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.0692 | + | 12.5194i | −0.422317 | + | 0.477644i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.16485 | − | 12.4099i | 0.272959 | − | 0.472779i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.49498 | − | 2.58938i | −0.0568717 | − | 0.0985047i | 0.836188 | − | 0.548443i | \(-0.184779\pi\) |
−0.893060 | + | 0.449938i | \(0.851446\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −29.9934 | + | 22.6311i | −1.13935 | + | 0.859684i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.73495 | + | 9.93322i | 0.217539 | + | 0.376788i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.6518 | − | 44.4303i | 0.971633 | − | 1.68292i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.4989 | − | 4.97636i | −0.926633 | − | 0.188223i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.3731 | −0.845020 | −0.422510 | − | 0.906358i | \(-0.638851\pi\) | ||||
−0.422510 | + | 0.906358i | \(0.638851\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.0443 | −0.605121 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.62972 | − | 1.34667i | −0.249690 | − | 0.0507185i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.54958 | + | 11.3442i | −0.246322 | + | 0.426643i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.7494 | − | 35.9390i | −0.779260 | − | 1.34972i | −0.932369 | − | 0.361509i | \(-0.882262\pi\) |
0.153109 | − | 0.988209i | \(-0.451072\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.76003 | + | 14.2604i | 0.0660064 | + | 0.534809i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.1160 | − | 19.2535i | −0.416298 | − | 0.721049i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.20041 | − | 5.54327i | 0.119689 | − | 0.207307i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −32.3847 | + | 36.6274i | −1.20943 | + | 1.36788i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.5511 | −0.766425 | −0.383213 | − | 0.923660i | \(-0.625182\pi\) | ||||
−0.383213 | + | 0.923660i | \(0.625182\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.8341 | 0.552451 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.67139 | + | 22.9035i | 0.285302 | + | 0.851792i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.600205 | + | 1.03958i | −0.0222910 | + | 0.0386092i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.0475 | + | 32.9913i | 0.706433 | + | 1.22358i | 0.966172 | + | 0.257899i | \(0.0830303\pi\) |
−0.259739 | + | 0.965679i | \(0.583636\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.72329 | + | 25.1884i | 0.360122 | + | 0.932905i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.0711 | + | 36.4963i | 0.779344 | + | 1.34986i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.3287 | + | 23.0859i | −0.492305 | + | 0.852698i | −0.999961 | − | 0.00886253i | \(-0.997179\pi\) |
0.507656 | + | 0.861560i | \(0.330512\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.48894 | − | 7.43091i | −0.0918058 | − | 0.274093i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.1358 | −0.962723 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.4888 | −0.864048 | −0.432024 | − | 0.901862i | \(-0.642200\pi\) | ||||
−0.432024 | + | 0.901862i | \(0.642200\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.1518 | + | 11.4818i | −0.372938 | + | 0.421795i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.3838 | − | 26.6455i | 0.564376 | − | 0.977528i | −0.432731 | − | 0.901523i | \(-0.642450\pi\) |
0.997107 | − | 0.0760050i | \(-0.0242165\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.467678 | − | 0.810042i | −0.0171344 | − | 0.0296776i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.16380 | + | 49.9415i | 0.225522 | + | 1.82726i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.0412 | − | 58.9610i | −1.24384 | − | 2.15439i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.981478 | − | 1.69997i | 0.0358146 | − | 0.0620328i | −0.847562 | − | 0.530696i | \(-0.821931\pi\) |
0.883377 | + | 0.468663i | \(0.155264\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.3568 | − | 5.35376i | −0.960497 | − | 0.195102i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.4689 | 0.562969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.4631 | −0.961818 | −0.480909 | − | 0.876771i | \(-0.659693\pi\) | ||||
−0.480909 | + | 0.876771i | \(0.659693\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 30.4638 | + | 6.18799i | 1.10576 | + | 0.224610i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.08618 | − | 8.80953i | 0.184374 | − | 0.319345i | −0.758991 | − | 0.651101i | \(-0.774308\pi\) |
0.943365 | + | 0.331756i | \(0.107641\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.1862 | + | 52.2841i | 1.09282 | + | 1.89281i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.2138 | + | 10.7249i | −0.513903 | + | 0.387758i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.41986 | + | 4.19132i | 0.0873761 | + | 0.151340i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.06406 | + | 10.5033i | −0.218675 | + | 0.378757i | −0.954403 | − | 0.298520i | \(-0.903507\pi\) |
0.735728 | + | 0.677277i | \(0.236840\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.273620 | − | 0.309467i | 0.00985419 | − | 0.0111452i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.3385 | 1.41491 | 0.707454 | − | 0.706759i | \(-0.249844\pi\) | ||||
0.707454 | + | 0.706759i | \(0.249844\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.57010 | 0.164163 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.87471 | + | 17.5394i | 0.210754 | + | 0.629222i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.0424 | + | 38.1786i | −0.789752 | + | 1.36789i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.203367 | − | 0.352242i | −0.00727704 | − | 0.0126042i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.483545 | + | 6.21874i | −0.0172805 | + | 0.222240i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.9839 | − | 19.0247i | −0.392033 | − | 0.679021i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.13924 | − | 3.70528i | 0.0762558 | − | 0.132079i | −0.825376 | − | 0.564584i | \(-0.809037\pi\) |
0.901632 | + | 0.432505i | \(0.142370\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.42268 | + | 16.1898i | 0.193053 | + | 0.576373i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −59.8775 | −2.12900 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.252966 | 0.00898309 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.47594 | + | 10.7174i | −0.336077 | + | 0.380106i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.46709 | + | 12.9334i | −0.264498 | + | 0.458124i | −0.967432 | − | 0.253131i | \(-0.918540\pi\) |
0.702934 | + | 0.711255i | \(0.251873\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.5913 | − | 20.0767i | −0.410070 | − | 0.710262i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.57053 | − | 2.78417i | −0.232158 | − | 0.0983738i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.3686 | + | 49.1359i | 1.00111 | + | 1.73397i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.25723 | + | 14.3019i | −0.291029 | + | 0.504077i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 45.7503 | + | 9.29308i | 1.61049 | + | 0.327132i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.8988 | 0.383180 | 0.191590 | − | 0.981475i | \(-0.438636\pi\) | ||||
0.191590 | + | 0.981475i | \(0.438636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.70452 | 0.235427 | 0.117714 | − | 0.993048i | \(-0.462443\pi\) | ||||
0.117714 | + | 0.993048i | \(0.462443\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −48.3207 | − | 9.81519i | −1.69468 | − | 0.344234i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0746 | + | 20.9138i | −0.422955 | + | 0.732579i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.1062 | − | 31.3609i | −0.633457 | − | 1.09718i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.2690 | + | 6.89374i | 0.568484 | + | 0.240887i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.1129 | − | 22.7122i | −0.457643 | − | 0.792661i | 0.541193 | − | 0.840899i | \(-0.317973\pi\) |
−0.998836 | + | 0.0482373i | \(0.984640\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.0826 | − | 43.4444i | 0.874326 | − | 1.51438i | 0.0168468 | − | 0.999858i | \(-0.494637\pi\) |
0.857479 | − | 0.514519i | \(-0.172029\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.23273 | + | 4.78725i | −0.147365 | + | 0.166671i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.2344 | −1.15567 | −0.577836 | − | 0.816153i | \(-0.696103\pi\) | ||||
−0.577836 | + | 0.816153i | \(0.696103\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.90114 | −0.343881 | −0.171940 | − | 0.985107i | \(-0.555004\pi\) | ||||
−0.171940 | + | 0.985107i | \(0.555004\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.9132 | − | 53.4813i | −0.621403 | − | 1.85525i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.4272 | − | 23.2567i | 0.465227 | − | 0.805796i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.52302 | − | 16.4944i | −0.329558 | − | 0.570811i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.4240 | − | 10.2435i | 0.740522 | − | 0.354066i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.9909 | + | 36.3573i | 0.724687 | + | 1.25519i | 0.959103 | + | 0.283058i | \(0.0913489\pi\) |
−0.234416 | + | 0.972136i | \(0.575318\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.7795 | − | 23.8668i | 0.475155 | − | 0.822993i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.47898 | + | 22.3291i | 0.257590 | + | 0.769054i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.98996 | 0.343665 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.86467 | −0.304594 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.9703 | + | 21.4556i | −0.651060 | + | 0.736354i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.65165 | − | 13.2531i | 0.262295 | − | 0.454309i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.4450 | + | 28.4835i | 0.563065 | + | 0.975257i | 0.997227 | + | 0.0744220i | \(0.0237112\pi\) |
−0.434162 | + | 0.900835i | \(0.642955\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.2138 | − | 9.21579i | 0.417705 | − | 0.315173i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.77066 | − | 8.26303i | −0.162963 | − | 0.282260i | 0.772967 | − | 0.634446i | \(-0.218772\pi\) |
−0.935930 | + | 0.352186i | \(0.885438\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.01261 | + | 1.75389i | −0.0345497 | + | 0.0598418i | −0.882783 | − | 0.469781i | \(-0.844333\pi\) |
0.848234 | + | 0.529622i | \(0.177666\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 49.8074 | + | 10.1172i | 1.69743 | + | 0.344793i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.6322 | 0.736370 | 0.368185 | − | 0.929753i | \(-0.379979\pi\) | ||||
0.368185 | + | 0.929753i | \(0.379979\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.4277 | −0.694562 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.9407 | − | 6.28487i | −1.05080 | − | 0.213445i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.83515 | + | 15.3029i | −0.299712 | + | 0.519116i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.14529 | + | 10.6439i | 0.208225 | + | 0.360656i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.76342 | + | 22.3903i | 0.0935277 | + | 0.757797i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.69739 | − | 2.93996i | −0.0573822 | − | 0.0993888i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.2417 | − | 19.4713i | 0.379606 | − | 0.657497i | −0.611399 | − | 0.791323i | \(-0.709393\pi\) |
0.991005 | + | 0.133825i | \(0.0427261\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.0424 | + | 32.8472i | −0.979577 | + | 1.10791i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.1045 | 1.58699 | 0.793495 | − | 0.608577i | \(-0.208259\pi\) | ||||
0.793495 | + | 0.608577i | \(0.208259\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3746 | 0.349132 | 0.174566 | − | 0.984646i | \(-0.444148\pi\) | ||||
0.174566 | + | 0.984646i | \(0.444148\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.53454 | − | 4.58148i | −0.0515829 | − | 0.154005i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.23945 | − | 9.07499i | 0.175923 | − | 0.304708i | −0.764557 | − | 0.644556i | \(-0.777042\pi\) |
0.940480 | + | 0.339848i | \(0.110376\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.2544 | − | 31.6176i | −0.612234 | − | 1.06042i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.11229 | + | 31.9293i | −0.305273 | + | 1.06967i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.96029 | + | 17.2517i | 0.333308 | + | 0.577307i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.10973 | + | 1.92210i | −0.0370940 | + | 0.0642488i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.64283 | − | 13.8615i | −0.155020 | − | 0.462823i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.48599 | 0.182968 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.0227 | −1.63318 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.6537 | + | 31.2766i | −0.920257 | + | 1.04082i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.3898 | − | 17.9956i | 0.345367 | − | 0.598193i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.73951 | + | 4.74497i | 0.0909640 | + | 0.157554i | 0.907917 | − | 0.419150i | \(-0.137672\pi\) |
−0.816953 | + | 0.576704i | \(0.804339\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.41794 | + | 11.4887i | 0.0470302 | + | 0.381056i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.95483 | − | 15.5102i | −0.296687 | − | 0.513877i | 0.678689 | − | 0.734426i | \(-0.262548\pi\) |
−0.975376 | + | 0.220549i | \(0.929215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.9416 | + | 53.5923i | −1.02402 | + | 1.77365i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.247490 | − | 0.0502716i | −0.00818176 | − | 0.00166193i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.11925 | 0.103007 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.3306 | 1.00051 | 0.500257 | − | 0.865877i | \(-0.333239\pi\) | ||||
0.500257 | + | 0.865877i | \(0.333239\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.2422 | + | 2.28358i | 0.370443 | + | 0.0752465i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.0956351 | + | 0.165645i | −0.00314787 | + | 0.00545227i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.57290 | + | 2.72435i | 0.0517167 | + | 0.0895760i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.4644 | − | 7.89579i | 0.343697 | − | 0.259332i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.8973 | + | 32.7310i | 0.619999 | + | 1.07387i | 0.989485 | + | 0.144634i | \(0.0462005\pi\) |
−0.369486 | + | 0.929236i | \(0.620466\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.5379 | + | 19.9843i | −0.378140 | + | 0.654958i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.21400 | + | 10.4211i | −0.301653 | + | 0.341172i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.8976 | −0.716127 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.15733 | −0.168483 | −0.0842413 | − | 0.996445i | \(-0.526847\pi\) | ||||
−0.0842413 | + | 0.996445i | \(0.526847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.5970 | − | 34.6236i | −0.378453 | − | 1.12990i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.8596 | − | 22.2736i | 0.419213 | − | 0.726097i | −0.576648 | − | 0.816993i | \(-0.695640\pi\) |
0.995860 | + | 0.0908953i | \(0.0289729\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.0245 | − | 36.4155i | −0.684651 | − | 1.18585i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.5468 | − | 9.97761i | −0.473207 | − | 0.324572i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.0695 | + | 31.2973i | 0.587180 | + | 1.01703i | 0.994600 | + | 0.103785i | \(0.0330954\pi\) |
−0.407419 | + | 0.913241i | \(0.633571\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.3406 | − | 23.1066i | 0.433054 | − | 0.750072i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.8886 | − | 35.4943i | −0.385514 | − | 1.15098i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.3261 | 0.690821 | 0.345411 | − | 0.938452i | \(-0.387740\pi\) | ||||
0.345411 | + | 0.938452i | \(0.387740\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.0400 | 0.454323 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.08101 | + | 5.74666i | −0.164246 | + | 0.185763i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.9944 | − | 32.8992i | 0.613361 | − | 1.06237i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.05710 | + | 8.75915i | 0.163132 | + | 0.282553i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −55.3970 | − | 23.4737i | −1.78514 | − | 0.756429i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.9576 | + | 18.9792i | 0.352739 | + | 0.610962i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.4179 | − | 28.4366i | 0.527963 | − | 0.914458i | −0.471506 | − | 0.881863i | \(-0.656289\pi\) |
0.999469 | − | 0.0325955i | \(-0.0103773\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 51.3825 | + | 10.4371i | 1.65064 | + | 0.335289i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.3434 | −0.845401 | −0.422701 | − | 0.906269i | \(-0.638918\pi\) | ||||
−0.422701 | + | 0.906269i | \(0.638918\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −38.9377 | −1.24829 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.94488 | + | 0.598181i | 0.0943116 | + | 0.0191571i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.18109 | − | 2.04570i | 0.0377863 | − | 0.0654478i | −0.846514 | − | 0.532367i | \(-0.821303\pi\) |
0.884300 | + | 0.466919i | \(0.154636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.38791 | − | 7.60007i | −0.140238 | − | 0.242899i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 49.1237 | + | 20.8154i | 1.56840 | + | 0.664586i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.60766 | + | 16.6410i | 0.306437 | + | 0.530764i | 0.977580 | − | 0.210564i | \(-0.0675299\pi\) |
−0.671143 | + | 0.741327i | \(0.734197\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.22993 | + | 14.2547i | −0.262227 | + | 0.454191i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.2124 | − | 17.2053i | 0.484215 | − | 0.547651i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.5401 | 1.09831 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.5578 | −0.843638 | −0.421819 | − | 0.906680i | \(-0.638608\pi\) | ||||
−0.421819 | + | 0.906680i | \(0.638608\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.9985 | + | 38.8081i | 0.412495 | + | 1.23154i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.34969 | − | 4.06979i | 0.0744903 | − | 0.129021i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.640786 | + | 1.10987i | 0.0202939 | + | 0.0351500i | 0.875994 | − | 0.482322i | \(-0.160206\pi\) |
−0.855700 | + | 0.517472i | \(0.826873\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.4799 | + | 9.24586i | 0.426486 | + | 0.292526i |
(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 | 1440.2.q.i.481.1 | ✓ | 8 | |
3.2 | odd | 2 | 4320.2.q.k.1441.4 | 8 | |||
4.3 | odd | 2 | 1440.2.q.n.481.4 | yes | 8 | ||
9.2 | odd | 6 | 4320.2.q.k.2881.4 | 8 | |||
9.7 | even | 3 | inner | 1440.2.q.i.961.1 | yes | 8 | |
12.11 | even | 2 | 4320.2.q.i.1441.1 | 8 | |||
36.7 | odd | 6 | 1440.2.q.n.961.4 | yes | 8 | ||
36.11 | even | 6 | 4320.2.q.i.2881.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.q.i.481.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1440.2.q.i.961.1 | yes | 8 | 9.7 | even | 3 | inner | |
1440.2.q.n.481.4 | yes | 8 | 4.3 | odd | 2 | ||
1440.2.q.n.961.4 | yes | 8 | 36.7 | odd | 6 | ||
4320.2.q.i.1441.1 | 8 | 12.11 | even | 2 | |||
4320.2.q.i.2881.1 | 8 | 36.11 | even | 6 | |||
4320.2.q.k.1441.4 | 8 | 3.2 | odd | 2 | |||
4320.2.q.k.2881.4 | 8 | 9.2 | odd | 6 |