Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
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 | 3781.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.3781 |
Dual form | 4020.2.q.h.841.1 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | 0.944911 | − | 0.327327i | \(-0.106148\pi\) |
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.50000 | + | 4.33013i | −0.693375 | + | 1.20096i | 0.277350 | + | 0.960769i | \(0.410544\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | + | 0.866025i | 0.109109 | + | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.50000 | + | 2.59808i | −0.312772 | + | 0.541736i | −0.978961 | − | 0.204046i | \(-0.934591\pi\) |
0.666190 | + | 0.745782i | \(0.267924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.50000 | + | 2.59808i | 0.278543 | + | 0.482451i | 0.971023 | − | 0.238987i | \(-0.0768152\pi\) |
−0.692480 | + | 0.721437i | \(0.743482\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | − | 4.33013i | −0.449013 | − | 0.777714i | 0.549309 | − | 0.835619i | \(-0.314891\pi\) |
−0.998322 | + | 0.0579057i | \(0.981558\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.500000 | − | 0.866025i | −0.0845154 | − | 0.146385i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.50000 | − | 6.06218i | 0.575396 | − | 0.996616i | −0.420602 | − | 0.907245i | \(-0.638181\pi\) |
0.995998 | − | 0.0893706i | \(-0.0284856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.50000 | + | 4.33013i | −0.400320 | + | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.50000 | − | 7.79423i | −0.702782 | − | 1.21725i | −0.967486 | − | 0.252924i | \(-0.918608\pi\) |
0.264704 | − | 0.964330i | \(-0.414726\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.50000 | + | 2.59808i | 0.218797 | + | 0.378968i | 0.954441 | − | 0.298401i | \(-0.0964533\pi\) |
−0.735643 | + | 0.677369i | \(0.763120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | − | 5.19615i | 0.428571 | − | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50000 | + | 2.59808i | −0.210042 | + | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.50000 | + | 2.59808i | 0.202260 | + | 0.350325i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.500000 | − | 0.866025i | 0.0662266 | − | 0.114708i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.500000 | + | 0.866025i | 0.0629941 | + | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.50000 | − | 4.33013i | 0.310087 | − | 0.537086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | − | 1.73205i | −0.977356 | − | 0.211604i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.50000 | + | 2.59808i | −0.180579 | + | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.50000 | − | 2.59808i | −0.178017 | − | 0.308335i | 0.763184 | − | 0.646181i | \(-0.223635\pi\) |
−0.941201 | + | 0.337846i | \(0.890302\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.50000 | − | 6.06218i | 0.409644 | − | 0.709524i | −0.585206 | − | 0.810885i | \(-0.698986\pi\) |
0.994850 | + | 0.101361i | \(0.0323196\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.50000 | − | 2.59808i | 0.170941 | − | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.50000 | − | 14.7224i | −0.956325 | − | 1.65640i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
−0.225018 | − | 0.974355i | \(-0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.50000 | + | 12.9904i | −0.823232 | + | 1.42588i | 0.0800311 | + | 0.996792i | \(0.474498\pi\) |
−0.903263 | + | 0.429087i | \(0.858835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.50000 | − | 2.59808i | 0.162698 | − | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.50000 | + | 2.59808i | 0.160817 | + | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.00000 | −0.524142 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.50000 | − | 4.33013i | −0.259238 | − | 0.449013i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.500000 | + | 0.866025i | −0.0512989 | + | 0.0888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.50000 | + | 14.7224i | −0.863044 | + | 1.49484i | 0.00593185 | + | 0.999982i | \(0.498112\pi\) |
−0.868976 | + | 0.494854i | \(0.835222\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.50000 | − | 2.59808i | −0.150756 | − | 0.261116i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.50000 | + | 2.59808i | 0.149256 | + | 0.258518i | 0.930953 | − | 0.365140i | \(-0.118979\pi\) |
−0.781697 | + | 0.623658i | \(0.785646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.50000 | + | 11.2583i | 0.640464 | + | 1.10932i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) |
−0.344865 | + | 0.938652i | \(0.612075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.500000 | − | 0.866025i | −0.0487950 | − | 0.0845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.50000 | − | 6.06218i | 0.332205 | − | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.50000 | + | 7.79423i | 0.423324 | + | 0.733219i | 0.996262 | − | 0.0863794i | \(-0.0275297\pi\) |
−0.572938 | + | 0.819599i | \(0.694196\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50000 | − | 2.59808i | 0.139876 | − | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.50000 | + | 4.33013i | −0.231125 | + | 0.400320i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | −0.275010 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.50000 | − | 7.79423i | −0.405751 | − | 0.702782i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.50000 | + | 11.2583i | 0.576782 | + | 0.999015i | 0.995846 | + | 0.0910585i | \(0.0290250\pi\) |
−0.419064 | + | 0.907957i | \(0.637642\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.00000 | −0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.0000 | −1.53784 | −0.768922 | − | 0.639343i | \(-0.779207\pi\) | ||||
−0.768922 | + | 0.639343i | \(0.779207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0000 | 1.69638 | 0.848189 | − | 0.529694i | \(-0.177693\pi\) | ||||
0.848189 | + | 0.529694i | \(0.177693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.50000 | + | 2.59808i | 0.126323 | + | 0.218797i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.0000 | 1.25436 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.50000 | − | 2.59808i | −0.124568 | − | 0.215758i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.00000 | − | 5.19615i | 0.247436 | − | 0.428571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.500000 | − | 0.866025i | 0.0406894 | − | 0.0704761i | −0.844963 | − | 0.534824i | \(-0.820378\pi\) |
0.885653 | + | 0.464348i | \(0.153711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.50000 | + | 2.59808i | −0.121268 | + | 0.210042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.50000 | + | 4.33013i | 0.200805 | + | 0.347804i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.50000 | − | 6.06218i | 0.279330 | − | 0.483814i | −0.691888 | − | 0.722005i | \(-0.743221\pi\) |
0.971219 | + | 0.238190i | \(0.0765542\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.00000 | −0.236433 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50000 | − | 9.52628i | −0.430793 | − | 0.746156i | 0.566149 | − | 0.824303i | \(-0.308433\pi\) |
−0.996942 | + | 0.0781474i | \(0.975100\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.50000 | + | 2.59808i | 0.116775 | + | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.5000 | − | 18.1865i | −0.812514 | − | 1.40732i | −0.911099 | − | 0.412188i | \(-0.864765\pi\) |
0.0985846 | − | 0.995129i | \(-0.468568\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | − | 10.3923i | −0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | − | 0.866025i | 0.0382360 | − | 0.0662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5000 | − | 18.1865i | 0.798300 | − | 1.38270i | −0.122422 | − | 0.992478i | \(-0.539066\pi\) |
0.920722 | − | 0.390218i | \(-0.127601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | + | 0.866025i | 0.0377964 | + | 0.0654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0000 | −0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.50000 | + | 11.2583i | 0.483141 | + | 0.836825i | 0.999813 | − | 0.0193587i | \(-0.00616244\pi\) |
−0.516671 | + | 0.856184i | \(0.672829\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.500000 | − | 0.866025i | 0.0369611 | − | 0.0640184i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.50000 | + | 6.06218i | −0.257325 | + | 0.445700i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | 0.658145 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.500000 | + | 0.866025i | 0.0363696 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.50000 | − | 2.59808i | 0.108536 | − | 0.187990i | −0.806641 | − | 0.591041i | \(-0.798717\pi\) |
0.915177 | + | 0.403051i | \(0.132050\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.0000 | −1.58359 | −0.791797 | − | 0.610784i | \(-0.790854\pi\) | ||||
−0.791797 | + | 0.610784i | \(0.790854\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.50000 | − | 4.33013i | 0.179029 | − | 0.310087i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.50000 | − | 2.59808i | −0.106871 | − | 0.185105i | 0.807630 | − | 0.589689i | \(-0.200750\pi\) |
−0.914501 | + | 0.404584i | \(0.867416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.50000 | + | 9.52628i | −0.389885 | + | 0.675300i | −0.992434 | − | 0.122782i | \(-0.960818\pi\) |
0.602549 | + | 0.798082i | \(0.294152\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | − | 1.73205i | −0.564276 | − | 0.122169i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.50000 | + | 2.59808i | −0.105279 | + | 0.182349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.50000 | + | 7.79423i | 0.314294 | + | 0.544373i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.50000 | + | 2.59808i | −0.104257 | + | 0.180579i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5000 | + | 19.9186i | −0.791693 | + | 1.37125i | 0.133226 | + | 0.991086i | \(0.457467\pi\) |
−0.924918 | + | 0.380166i | \(0.875867\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.50000 | − | 2.59808i | −0.102778 | − | 0.178017i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | 0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.50000 | − | 4.33013i | 0.169711 | − | 0.293948i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.50000 | − | 6.06218i | 0.236508 | − | 0.409644i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.50000 | − | 12.9904i | −0.504505 | − | 0.873828i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.50000 | + | 2.59808i | 0.0995585 | + | 0.172440i | 0.911502 | − | 0.411296i | \(-0.134924\pi\) |
−0.811943 | + | 0.583736i | \(0.801590\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.5000 | + | 19.9186i | −0.759941 | + | 1.31626i | 0.182939 | + | 0.983124i | \(0.441439\pi\) |
−0.942880 | + | 0.333133i | \(0.891894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.50000 | − | 2.59808i | 0.0986928 | − | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.5000 | + | 18.1865i | 0.687878 | + | 1.19144i | 0.972523 | + | 0.232806i | \(0.0747909\pi\) |
−0.284645 | + | 0.958633i | \(0.591876\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.50000 | − | 2.59808i | −0.0978492 | − | 0.169480i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.50000 | − | 14.7224i | −0.552134 | − | 0.956325i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.5000 | − | 23.3827i | −0.873242 | − | 1.51250i | −0.858623 | − | 0.512607i | \(-0.828680\pi\) |
−0.0146191 | − | 0.999893i | \(-0.504654\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | + | 5.19615i | −0.191663 | + | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.50000 | + | 4.33013i | 0.159071 | + | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.50000 | + | 12.9904i | −0.475293 | + | 0.823232i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.50000 | − | 12.9904i | 0.473396 | − | 0.819946i | −0.526140 | − | 0.850398i | \(-0.676361\pi\) |
0.999536 | + | 0.0304521i | \(0.00969471\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000 | 0.565825 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.50000 | − | 2.59808i | 0.0939336 | − | 0.162698i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.5000 | − | 23.3827i | −0.842107 | − | 1.45857i | −0.888110 | − | 0.459631i | \(-0.847982\pi\) |
0.0460033 | − | 0.998941i | \(-0.485352\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.00000 | 0.434959 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.50000 | + | 2.59808i | 0.0928477 | + | 0.160817i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.0000 | −1.47990 | −0.739952 | − | 0.672660i | \(-0.765152\pi\) | ||||
−0.739952 | + | 0.672660i | \(0.765152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0000 | 1.21491 | 0.607457 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.00000 | −0.302614 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.50000 | − | 4.33013i | −0.149671 | − | 0.259238i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.50000 | + | 7.79423i | −0.268447 | + | 0.464965i | −0.968461 | − | 0.249165i | \(-0.919844\pi\) |
0.700014 | + | 0.714130i | \(0.253177\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.0000 | −1.66443 | −0.832214 | − | 0.554455i | \(-0.812927\pi\) | ||||
−0.832214 | + | 0.554455i | \(0.812927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.500000 | + | 0.866025i | −0.0296174 | + | 0.0512989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.50000 | − | 7.79423i | 0.265627 | − | 0.460079i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.50000 | + | 14.7224i | −0.498279 | + | 0.863044i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | 0.698667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.50000 | − | 2.59808i | −0.0870388 | − | 0.150756i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.50000 | − | 12.9904i | −0.433736 | − | 0.751253i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | − | 3.46410i | −0.115278 | − | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.50000 | + | 2.59808i | 0.0861727 | + | 0.149256i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.500000 | + | 0.866025i | −0.0286299 | + | 0.0495885i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.50000 | + | 4.33013i | −0.142683 | + | 0.247133i | −0.928506 | − | 0.371318i | \(-0.878906\pi\) |
0.785823 | + | 0.618451i | \(0.212239\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.50000 | + | 11.2583i | 0.369772 | + | 0.640464i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.0000 | 1.46961 | 0.734803 | − | 0.678280i | \(-0.237274\pi\) | ||||
0.734803 | + | 0.678280i | \(0.237274\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.500000 | − | 0.866025i | −0.0281718 | − | 0.0487950i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.50000 | + | 12.9904i | −0.421242 | + | 0.729612i | −0.996061 | − | 0.0886679i | \(-0.971739\pi\) |
0.574819 | + | 0.818280i | \(0.305072\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50000 | − | 7.79423i | 0.251952 | − | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.0000 | −0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.50000 | + | 2.59808i | 0.0834622 | + | 0.144561i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.50000 | + | 4.33013i | −0.138675 | + | 0.240192i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00000 | 0.110600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.50000 | + | 2.59808i | −0.0826977 | + | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50000 | − | 14.7224i | −0.467202 | − | 0.809218i | 0.532096 | − | 0.846684i | \(-0.321405\pi\) |
−0.999298 | + | 0.0374662i | \(0.988071\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.50000 | − | 6.06218i | 0.191799 | − | 0.332205i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.00000 | + | 1.73205i | 0.437087 | + | 0.0946320i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.5000 | − | 26.8468i | 0.844339 | − | 1.46244i | −0.0418554 | − | 0.999124i | \(-0.513327\pi\) |
0.886194 | − | 0.463314i | \(-0.153340\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.50000 | + | 7.79423i | 0.244406 | + | 0.423324i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.50000 | + | 12.9904i | −0.406148 | + | 0.703469i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.50000 | − | 2.59808i | 0.0807573 | − | 0.139876i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.5000 | + | 23.3827i | 0.724718 | + | 1.25525i | 0.959090 | + | 0.283101i | \(0.0913633\pi\) |
−0.234372 | + | 0.972147i | \(0.575303\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.50000 | + | 4.33013i | −0.133440 | + | 0.231125i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.5000 | − | 18.1865i | 0.558859 | − | 0.967972i | −0.438733 | − | 0.898617i | \(-0.644573\pi\) |
0.997592 | − | 0.0693543i | \(-0.0220939\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.50000 | + | 2.59808i | 0.0796117 | + | 0.137892i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.00000 | −0.158777 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | − | 1.73205i | 0.0524864 | − | 0.0909091i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.50000 | + | 6.06218i | −0.183198 | + | 0.317309i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.5000 | − | 19.9186i | −0.600295 | − | 1.03974i | −0.992776 | − | 0.119982i | \(-0.961716\pi\) |
0.392481 | − | 0.919760i | \(-0.371617\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.50000 | − | 7.79423i | −0.234261 | − | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.00000 | − | 5.19615i | −0.155752 | − | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.5000 | + | 26.8468i | 0.802560 | + | 1.39007i | 0.917926 | + | 0.396751i | \(0.129862\pi\) |
−0.115367 | + | 0.993323i | \(0.536804\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.0000 | −0.772539 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.5000 | + | 19.9186i | −0.590715 | + | 1.02315i | 0.403421 | + | 0.915014i | \(0.367821\pi\) |
−0.994136 | + | 0.108134i | \(0.965512\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.50000 | + | 11.2583i | 0.333005 | + | 0.576782i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.5000 | − | 28.5788i | 0.843111 | − | 1.46031i | −0.0441413 | − | 0.999025i | \(-0.514055\pi\) |
0.887252 | − | 0.461285i | \(-0.152611\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.50000 | + | 2.59808i | −0.0764471 | + | 0.132410i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00000 | −0.203331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.50000 | − | 2.59808i | 0.0760530 | − | 0.131728i | −0.825491 | − | 0.564416i | \(-0.809102\pi\) |
0.901544 | + | 0.432688i | \(0.142435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.50000 | − | 7.79423i | −0.227575 | − | 0.394171i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0000 | −0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.50000 | + | 14.7224i | 0.427681 | + | 0.740766i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.0000 | −1.70641 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.00000 | 0.0500626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.0000 | 0.898877 | 0.449439 | − | 0.893311i | \(-0.351624\pi\) | ||||
0.449439 | + | 0.893311i | \(0.351624\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.0000 | 1.24534 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.0000 | −1.04093 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.50000 | + | 11.2583i | 0.321404 | + | 0.556689i | 0.980778 | − | 0.195127i | \(-0.0625118\pi\) |
−0.659374 | + | 0.751815i | \(0.729178\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0000 | −0.887875 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.00000 | − | 10.3923i | −0.295241 | − | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.50000 | − | 12.9904i | 0.368161 | − | 0.637673i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.0000 | 0.979404 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5000 | + | 18.1865i | −0.512959 | + | 0.888470i | 0.486928 | + | 0.873442i | \(0.338117\pi\) |
−0.999887 | + | 0.0150285i | \(0.995216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.50000 | − | 11.2583i | 0.316791 | − | 0.548697i | −0.663026 | − | 0.748596i | \(-0.730728\pi\) |
0.979817 | + | 0.199899i | \(0.0640614\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.50000 | + | 2.59808i | 0.0729325 | + | 0.126323i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.50000 | + | 2.59808i | −0.0727607 | + | 0.126025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.00000 | 0.0483934 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.0000 | 0.724207 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.5000 | + | 18.1865i | 0.505767 | + | 0.876014i | 0.999978 | + | 0.00667224i | \(0.00212386\pi\) |
−0.494211 | + | 0.869342i | \(0.664543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.50000 | + | 16.4545i | 0.456541 | + | 0.790752i | 0.998775 | − | 0.0494752i | \(-0.0157549\pi\) |
−0.542234 | + | 0.840227i | \(0.682422\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.50000 | − | 2.59808i | −0.0719195 | − | 0.124568i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.50000 | + | 2.59808i | 0.0717547 | + | 0.124283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5000 | − | 21.6506i | 0.596592 | − | 1.03333i | −0.396728 | − | 0.917936i | \(-0.629854\pi\) |
0.993320 | − | 0.115392i | \(-0.0368124\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | − | 5.19615i | 0.142857 | − | 0.247436i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.50000 | + | 12.9904i | 0.356336 | + | 0.617192i | 0.987346 | − | 0.158583i | \(-0.0506926\pi\) |
−0.631010 | + | 0.775775i | \(0.717359\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | 0.284427 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.50000 | + | 2.59808i | 0.0707894 | + | 0.122611i | 0.899247 | − | 0.437440i | \(-0.144115\pi\) |
−0.828458 | + | 0.560051i | \(0.810782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.5000 | + | 23.3827i | −0.635690 | + | 1.10105i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.500000 | − | 0.866025i | 0.0234920 | − | 0.0406894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.00000 | 0.234404 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.50000 | + | 16.4545i | 0.444391 | + | 0.769708i | 0.998010 | − | 0.0630623i | \(-0.0200867\pi\) |
−0.553618 | + | 0.832771i | \(0.686753\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.50000 | + | 2.59808i | −0.0700140 | + | 0.121268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.5000 | − | 26.8468i | 0.720346 | − | 1.24768i | −0.240515 | − | 0.970645i | \(-0.577316\pi\) |
0.960861 | − | 0.277031i | \(-0.0893503\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.50000 | + | 4.33013i | 0.115935 | + | 0.200805i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.50000 | − | 7.79423i | 0.208235 | − | 0.360674i | −0.742923 | − | 0.669376i | \(-0.766561\pi\) |
0.951159 | + | 0.308702i | \(0.0998947\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.50000 | − | 7.79423i | −0.115439 | − | 0.359904i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.50000 | − | 6.06218i | 0.161271 | − | 0.279330i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.00000 | + | 10.3923i | 0.275880 | + | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.500000 | − | 0.866025i | 0.0229416 | − | 0.0397360i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.50000 | + | 7.79423i | −0.205610 | + | 0.356127i | −0.950327 | − | 0.311253i | \(-0.899251\pi\) |
0.744717 | + | 0.667381i | \(0.232585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.5000 | + | 30.3109i | 0.797931 | + | 1.38206i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.00000 | −0.136505 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.50000 | − | 14.7224i | 0.385965 | − | 0.668511i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.5000 | + | 25.1147i | −0.657058 | + | 1.13806i | 0.324316 | + | 0.945949i | \(0.394866\pi\) |
−0.981374 | + | 0.192109i | \(0.938467\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.50000 | − | 9.52628i | −0.248719 | − | 0.430793i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | −0.405340 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.50000 | + | 2.59808i | 0.0674200 | + | 0.116775i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.50000 | − | 2.59808i | 0.0672842 | − | 0.116540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.50000 | − | 11.2583i | 0.290980 | − | 0.503992i | −0.683062 | − | 0.730361i | \(-0.739352\pi\) |
0.974042 | + | 0.226369i | \(0.0726854\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.5000 | − | 18.1865i | −0.469105 | − | 0.812514i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.5000 | + | 33.7750i | 0.869462 | + | 1.50595i | 0.862547 | + | 0.505976i | \(0.168868\pi\) |
0.00691465 | + | 0.999976i | \(0.497799\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.50000 | − | 2.59808i | −0.0667491 | − | 0.115613i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.00000 | − | 10.3923i | −0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.00000 | 0.309662 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.500000 | − | 0.866025i | 0.0220755 | − | 0.0382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.50000 | − | 11.2583i | −0.286424 | − | 0.496101i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.50000 | − | 7.79423i | 0.197910 | − | 0.342790i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.5000 | − | 18.1865i | 0.460899 | − | 0.798300i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.5000 | − | 26.8468i | 0.677768 | − | 1.17393i | −0.297884 | − | 0.954602i | \(-0.596281\pi\) |
0.975652 | − | 0.219326i | \(-0.0703858\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.500000 | + | 0.866025i | 0.0218218 | + | 0.0377964i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.0000 | 0.653410 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.0000 | −0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 45.0000 | 1.94917 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0000 | 0.518805 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0000 | 0.517838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.0000 | −0.775315 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.0000 | −0.945854 | −0.472927 | − | 0.881102i | \(-0.656803\pi\) | ||||
−0.472927 | + | 0.881102i | \(0.656803\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.50000 | + | 11.2583i | 0.278942 | + | 0.483141i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.500000 | + | 0.866025i | 0.0213785 | + | 0.0370286i | 0.876517 | − | 0.481371i | \(-0.159861\pi\) |
−0.855138 | + | 0.518400i | \(0.826528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.500000 | − | 0.866025i | 0.0213395 | − | 0.0369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | 0.127804 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.50000 | − | 14.7224i | 0.361457 | − | 0.626061i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.50000 | + | 6.06218i | −0.148567 | + | 0.257325i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.5000 | + | 18.1865i | 0.444899 | + | 0.770588i | 0.998045 | − | 0.0624962i | \(-0.0199061\pi\) |
−0.553146 | + | 0.833084i | \(0.686573\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0000 | − | 17.3205i | 0.422955 | − | 0.732579i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.00000 | 0.379980 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.0000 | 1.51722 | 0.758610 | − | 0.651546i | \(-0.225879\pi\) | ||||
0.758610 | + | 0.651546i | \(0.225879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.50000 | − | 7.79423i | −0.189316 | − | 0.327906i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.500000 | + | 0.866025i | 0.0209980 | + | 0.0363696i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.50000 | + | 12.9904i | 0.314416 | + | 0.544585i | 0.979313 | − | 0.202350i | \(-0.0648579\pi\) |
−0.664897 | + | 0.746935i | \(0.731525\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.50000 | − | 14.7224i | −0.355714 | − | 0.616115i | 0.631526 | − | 0.775355i | \(-0.282429\pi\) |
−0.987240 | + | 0.159240i | \(0.949096\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.50000 | − | 2.59808i | 0.0626634 | − | 0.108536i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.50000 | + | 2.59808i | −0.0625543 | + | 0.108347i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.5000 | − | 25.1147i | −0.603643 | − | 1.04554i | −0.992264 | − | 0.124143i | \(-0.960382\pi\) |
0.388621 | − | 0.921397i | \(-0.372951\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.0000 | −0.914289 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0000 | −0.622305 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | + | 15.5885i | 0.372742 | + | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.50000 | − | 4.33013i | 0.103362 | − | 0.179029i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.5000 | + | 33.7750i | −0.804851 | + | 1.39404i | 0.111540 | + | 0.993760i | \(0.464422\pi\) |
−0.916392 | + | 0.400283i | \(0.868912\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | −0.206021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.50000 | − | 2.59808i | −0.0617018 | − | 0.106871i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.5000 | − | 28.5788i | 0.677574 | − | 1.17359i | −0.298136 | − | 0.954524i | \(-0.596365\pi\) |
0.975709 | − | 0.219069i | \(-0.0703019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.00000 | 0.122988 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.50000 | + | 9.52628i | −0.225100 | + | 0.389885i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.5000 | − | 33.7750i | −0.796748 | − | 1.38001i | −0.921723 | − | 0.387849i | \(-0.873218\pi\) |
0.124975 | − | 0.992160i | \(-0.460115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.50000 | − | 11.2583i | 0.265141 | − | 0.459237i | −0.702460 | − | 0.711723i | \(-0.747915\pi\) |
0.967600 | + | 0.252486i | \(0.0812483\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.00000 | − | 1.73205i | −0.325785 | − | 0.0705346i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | + | 1.73205i | −0.0406558 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.50000 | − | 9.52628i | −0.223238 | − | 0.386660i | 0.732551 | − | 0.680712i | \(-0.238329\pi\) |
−0.955789 | + | 0.294052i | \(0.904996\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.50000 | + | 2.59808i | −0.0607831 | + | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0000 | −0.606835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.50000 | + | 4.33013i | −0.100974 | + | 0.174892i | −0.912086 | − | 0.409998i | \(-0.865529\pi\) |
0.811112 | + | 0.584891i | \(0.198863\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.50000 | + | 7.79423i | 0.181458 | + | 0.314294i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.0000 | −1.69086 | −0.845428 | − | 0.534089i | \(-0.820655\pi\) | ||||
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.5000 | − | 32.0429i | 0.743578 | − | 1.28791i | −0.207279 | − | 0.978282i | \(-0.566461\pi\) |
0.950856 | − | 0.309633i | \(-0.100206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.50000 | + | 2.59808i | −0.0601929 | + | 0.104257i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.00000 | − | 5.19615i | −0.120192 | − | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.00000 | −0.119808 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.5000 | + | 18.1865i | 0.418662 | + | 0.725145i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.5000 | − | 21.6506i | 0.497617 | − | 0.861898i | −0.502379 | − | 0.864647i | \(-0.667542\pi\) |
0.999996 | + | 0.00274930i | \(0.000875132\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.5000 | + | 19.9186i | −0.457084 | + | 0.791693i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.50000 | − | 11.2583i | −0.257945 | − | 0.446773i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0000 | + | 25.9808i | 0.594322 | + | 1.02940i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.50000 | − | 2.59808i | −0.0593391 | − | 0.102778i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | − | 18.1865i | −0.414725 | − | 0.718325i | 0.580674 | − | 0.814136i | \(-0.302789\pi\) |
−0.995400 | + | 0.0958109i | \(0.969456\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.00000 | −0.157745 | −0.0788723 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788723 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.00000 | 0.157500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.5000 | − | 28.5788i | 0.648682 | − | 1.12355i | −0.334756 | − | 0.942305i | \(-0.608654\pi\) |
0.983438 | − | 0.181245i | \(-0.0580128\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.0000 | + | 31.1769i | 0.706562 | + | 1.22380i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.50000 | − | 4.33013i | 0.0979827 | − | 0.169711i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.50000 | − | 7.79423i | 0.176099 | − | 0.305012i | −0.764442 | − | 0.644692i | \(-0.776986\pi\) |
0.940541 | + | 0.339680i | \(0.110319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0000 | 0.468879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.50000 | − | 6.06218i | 0.136548 | − | 0.236508i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.50000 | − | 12.9904i | −0.292159 | − | 0.506033i | 0.682161 | − | 0.731202i | \(-0.261040\pi\) |
−0.974320 | + | 0.225168i | \(0.927707\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.0000 | 1.01128 | 0.505641 | − | 0.862744i | \(-0.331256\pi\) | ||||
0.505641 | + | 0.862744i | \(0.331256\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.50000 | − | 12.9904i | −0.291276 | − | 0.504505i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.00000 | −0.0387783 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00000 | −0.348481 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.00000 | 0.309298 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.00000 | −0.115814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.5000 | + | 28.5788i | 0.634147 | + | 1.09837i | 0.986695 | + | 0.162581i | \(0.0519817\pi\) |
−0.352549 | + | 0.935793i | \(0.614685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.0000 | −0.652400 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.50000 | + | 2.59808i | 0.0574801 | + | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.5000 | + | 33.7750i | −0.746147 | + | 1.29236i | 0.203510 | + | 0.979073i | \(0.434765\pi\) |
−0.949657 | + | 0.313291i | \(0.898568\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | 0.687745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.5000 | + | 19.9186i | −0.438752 | + | 0.759941i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.0000 | − | 25.9808i | 0.571454 | − | 0.989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.50000 | − | 14.7224i | −0.323355 | − | 0.560068i | 0.657823 | − | 0.753173i | \(-0.271478\pi\) |
−0.981178 | + | 0.193105i | \(0.938144\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.50000 | − | 2.59808i | 0.0569803 | − | 0.0986928i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.0000 | −0.758643 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.0000 | 1.02270 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.5000 | + | 18.1865i | 0.397146 | + | 0.687878i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.50000 | + | 2.59808i | 0.0566542 | + | 0.0981280i | 0.892962 | − | 0.450133i | \(-0.148623\pi\) |
−0.836307 | + | 0.548261i | \(0.815290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.50000 | − | 6.06218i | −0.132005 | − | 0.228639i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.50000 | − | 2.59808i | −0.0564933 | − | 0.0978492i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.50000 | + | 2.59808i | −0.0564133 | + | 0.0977107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5000 | + | 19.9186i | −0.431892 | + | 0.748058i | −0.997036 | − | 0.0769337i | \(-0.975487\pi\) |
0.565145 | + | 0.824992i | \(0.308820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.50000 | − | 14.7224i | −0.318775 | − | 0.552134i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.0000 | 0.561754 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.0000 | −0.560968 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.5000 | − | 23.3827i | −0.504167 | − | 0.873242i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.50000 | + | 7.79423i | −0.167822 | + | 0.290676i | −0.937654 | − | 0.347571i | \(-0.887007\pi\) |
0.769832 | + | 0.638247i | \(0.220340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.50000 | + | 11.2583i | −0.242073 | + | 0.419282i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.0000 | −0.371904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.50000 | + | 2.59808i | 0.0557086 | + | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.50000 | − | 6.06218i | 0.129808 | − | 0.224834i | −0.793794 | − | 0.608186i | \(-0.791897\pi\) |
0.923602 | + | 0.383353i | \(0.125231\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | − | 10.3923i | 0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.5000 | + | 26.8468i | 0.572506 | + | 0.991609i | 0.996308 | + | 0.0858539i | \(0.0273618\pi\) |
−0.423802 | + | 0.905755i | \(0.639305\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.00000 | + | 5.19615i | −0.110657 | + | 0.191663i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.50000 | + | 23.3827i | 0.276266 | + | 0.861312i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.5000 | − | 21.6506i | 0.459820 | − | 0.796431i | −0.539131 | − | 0.842222i | \(-0.681247\pi\) |
0.998951 | + | 0.0457903i | \(0.0145806\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.50000 | + | 4.33013i | 0.0918398 | + | 0.159071i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.50000 | − | 7.79423i | 0.165089 | − | 0.285943i | −0.771598 | − | 0.636111i | \(-0.780542\pi\) |
0.936687 | + | 0.350168i | \(0.113876\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | 0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.50000 | + | 12.9904i | −0.274411 | + | 0.475293i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | − | 10.3923i | −0.219235 | − | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.0000 | −1.45962 | −0.729810 | − | 0.683650i | \(-0.760392\pi\) | ||||
−0.729810 | + | 0.683650i | \(0.760392\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.50000 | − | 12.9904i | 0.273315 | − | 0.473396i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.500000 | + | 0.866025i | −0.0181969 | + | 0.0315179i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.5000 | + | 37.2391i | 0.781431 | + | 1.35348i | 0.931108 | + | 0.364743i | \(0.118843\pi\) |
−0.149677 | + | 0.988735i | \(0.547824\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.00000 | 0.326679 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.00000 | + | 1.73205i | 0.0362024 | + | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.50000 | − | 2.59808i | 0.0542326 | − | 0.0939336i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.0000 | − | 51.9615i | 1.08324 | − | 1.87622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.5000 | + | 42.4352i | 0.883493 | + | 1.53025i | 0.847432 | + | 0.530904i | \(0.178148\pi\) |
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.5000 | − | 23.3827i | −0.486191 | − | 0.842107i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.5000 | + | 18.1865i | 0.377659 | + | 0.654124i | 0.990721 | − | 0.135910i | \(-0.0433959\pi\) |
−0.613062 | + | 0.790034i | \(0.710063\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.50000 | − | 4.33013i | −0.0898027 | − | 0.155543i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.00000 | 0.251124 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.00000 | −0.322458 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.50000 | + | 7.79423i | −0.161023 | + | 0.278899i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.50000 | + | 2.59808i | 0.0536056 | + | 0.0928477i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.50000 | + | 6.06218i | −0.124920 | + | 0.216368i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.50000 | + | 14.7224i | −0.302992 | + | 0.524798i | −0.976812 | − | 0.214097i | \(-0.931319\pi\) |
0.673820 | + | 0.738896i | \(0.264652\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.0000 | −0.854423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.50000 | + | 7.79423i | −0.160002 | + | 0.277131i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.50000 | + | 4.33013i | 0.0887776 | + | 0.153767i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.00000 | 0.212798 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.5000 | − | 33.7750i | −0.690725 | − | 1.19637i | −0.971601 | − | 0.236627i | \(-0.923958\pi\) |
0.280875 | − | 0.959744i | \(-0.409375\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.00000 | −0.318397 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.0000 | −0.741074 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.00000 | 0.105736 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.00000 | 0.211210 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0000 | 0.632846 | 0.316423 | − | 0.948618i | \(-0.397518\pi\) | ||||
0.316423 | + | 0.948618i | \(0.397518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.50000 | + | 6.06218i | 0.122902 | + | 0.212872i | 0.920911 | − | 0.389774i | \(-0.127447\pi\) |
−0.798009 | + | 0.602645i | \(0.794113\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.0000 | 0.701431 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.50000 | + | 9.52628i | 0.192657 | + | 0.333691i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.00000 | + | 3.46410i | −0.0699711 | + | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.00000 | −0.174714 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.50000 | − | 12.9904i | 0.261752 | − | 0.453367i | −0.704956 | − | 0.709251i | \(-0.749033\pi\) |
0.966708 | + | 0.255884i | \(0.0823665\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.50000 | + | 4.33013i | −0.0871445 | + | 0.150939i | −0.906303 | − | 0.422628i | \(-0.861108\pi\) |
0.819159 | + | 0.573567i | \(0.194441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.50000 | − | 2.59808i | −0.0522233 | − | 0.0904534i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.50000 | − | 7.79423i | 0.156480 | − | 0.271032i | −0.777117 | − | 0.629356i | \(-0.783319\pi\) |
0.933597 | + | 0.358325i | \(0.116652\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.0000 | −0.346896 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.00000 | + | 15.5885i | 0.311832 | + | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5000 | + | 18.1865i | 0.363367 | + | 0.629371i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.50000 | − | 4.33013i | −0.0864126 | − | 0.149671i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.5000 | + | 38.9711i | 0.776786 | + | 1.34543i | 0.933785 | + | 0.357834i | \(0.116485\pi\) |
−0.156999 | + | 0.987599i | \(0.550182\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.50000 | + | 7.79423i | −0.154988 | + | 0.268447i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.00000 | + | 10.3923i | 0.206406 | + | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | 0.0687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.0000 | −0.960958 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.5000 | + | 18.1865i | 0.359935 | + | 0.623426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.50000 | + | 14.7224i | −0.291034 | + | 0.504086i | −0.974055 | − | 0.226313i | \(-0.927333\pi\) |
0.683020 | + | 0.730400i | \(0.260666\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.500000 | + | 0.866025i | −0.0170996 | + | 0.0296174i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.50000 | + | 6.06218i | 0.119418 | + | 0.206839i | 0.919537 | − | 0.393003i | \(-0.128564\pi\) |
−0.800119 | + | 0.599841i | \(0.795230\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.50000 | − | 7.79423i | 0.153360 | − | 0.265627i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.5000 | + | 18.1865i | −0.357011 | + | 0.618361i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.00000 | + | 6.92820i | 0.135847 | + | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.5000 | + | 44.1673i | −0.865028 | + | 1.49827i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.5000 | − | 30.3109i | 0.931802 | − | 1.02705i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.50000 | + | 14.7224i | −0.287681 | + | 0.498279i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.500000 | − | 0.866025i | −0.0169031 | − | 0.0292770i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.50000 | − | 16.4545i | 0.320792 | − | 0.555628i | −0.659860 | − | 0.751389i | \(-0.729384\pi\) |
0.980652 | + | 0.195761i | \(0.0627176\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.00000 | 0.202375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.50000 | + | 7.79423i | −0.151609 | + | 0.262594i | −0.931819 | − | 0.362923i | \(-0.881779\pi\) |
0.780210 | + | 0.625517i | \(0.215112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.5000 | + | 32.0429i | 0.622575 | + | 1.07833i | 0.989005 | + | 0.147885i | \(0.0472466\pi\) |
−0.366430 | + | 0.930446i | \(0.619420\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.0000 | 0.403376 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.50000 | + | 12.9904i | −0.251825 | + | 0.436174i | −0.964028 | − | 0.265799i | \(-0.914364\pi\) |
0.712203 | + | 0.701974i | \(0.247698\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.50000 | + | 11.2583i | −0.218003 | + | 0.377592i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | − | 2.59808i | −0.0502519 | − | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.00000 | 0.100391 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.50000 | − | 12.9904i | −0.250418 | − | 0.433736i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.50000 | − | 12.9904i | 0.250139 | − | 0.433253i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000 | − | 15.5885i | 0.299833 | − | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.00000 | − | 3.46410i | −0.0665558 | − | 0.115278i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.50000 | − | 11.2583i | −0.216067 | − | 0.374240i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.5000 | − | 30.3109i | −0.581078 | − | 1.00646i | −0.995352 | − | 0.0963043i | \(-0.969298\pi\) |
0.414274 | − | 0.910152i | \(-0.364036\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.50000 | + | 2.59808i | 0.0497519 | + | 0.0861727i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.0000 | 1.48928 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.500000 | + | 0.866025i | −0.0165295 | + | 0.0286299i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.00000 | − | 10.3923i | −0.198137 | − | 0.343184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5000 | − | 21.6506i | 0.412337 | − | 0.714189i | −0.582808 | − | 0.812610i | \(-0.698046\pi\) |
0.995145 | + | 0.0984214i | \(0.0313793\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.50000 | + | 4.33013i | −0.0823778 | + | 0.142683i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.0000 | 0.493731 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.50000 | − | 6.06218i | 0.115079 | − | 0.199323i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.50000 | + | 11.2583i | 0.213488 | + | 0.369772i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.0000 | −1.77168 | −0.885841 | − | 0.463988i | \(-0.846418\pi\) | ||||
−0.885841 | + | 0.463988i | \(0.846418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.00000 | − | 5.19615i | −0.0983210 | − | 0.170297i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.00000 | −0.294331 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.0000 | 1.24141 | 0.620703 | − | 0.784046i | \(-0.286847\pi\) | ||||
0.620703 | + | 0.784046i | \(0.286847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.0000 | 0.848478 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.0000 | 1.76035 | 0.880175 | − | 0.474650i | \(-0.157425\pi\) | ||||
0.880175 | + | 0.474650i | \(0.157425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.0000 | 0.879241 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.500000 | − | 0.866025i | −0.0162650 | − | 0.0281718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.5000 | + | 30.3109i | 0.568074 | + | 0.983933i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.50000 | + | 12.9904i | −0.243204 | + | 0.421242i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.0000 | 1.74923 | 0.874616 | − | 0.484817i | \(-0.161114\pi\) | ||||
0.874616 | + | 0.484817i | \(0.161114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.50000 | + | 2.59808i | −0.0485389 | + | 0.0840718i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.50000 | − | 7.79423i | 0.145464 | − | 0.251952i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.00000 | − | 15.5885i | −0.290625 | − | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0000 | −0.386695 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.0000 | 0.708205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.5000 | − | 30.3109i | −0.562762 | − | 0.974732i | −0.997254 | − | 0.0740568i | \(-0.976405\pi\) |
0.434492 | − | 0.900676i | \(-0.356928\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.50000 | + | 2.59808i | 0.0481869 | + | 0.0834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.50000 | − | 12.9904i | −0.240686 | − | 0.416881i | 0.720224 | − | 0.693742i | \(-0.244039\pi\) |
−0.960910 | + | 0.276861i | \(0.910706\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.0000 | + | 17.3205i | 0.320585 | + | 0.555270i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.50000 | + | 4.33013i | −0.0800641 | + | 0.138675i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.5000 | + | 33.7750i | −0.623860 | + | 1.08056i | 0.364900 | + | 0.931047i | \(0.381103\pi\) |
−0.988760 | + | 0.149511i | \(0.952230\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.00000 | + | 15.5885i | 0.287641 | + | 0.498209i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.0000 | 0.765481 | 0.382741 | − | 0.923856i | \(-0.374980\pi\) | ||||
0.382741 | + | 0.923856i | \(0.374980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.50000 | + | 2.59808i | 0.0477940 | + | 0.0827816i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.50000 | + | 2.59808i | −0.0477455 | + | 0.0826977i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.00000 | − | 10.3923i | 0.190789 | − | 0.330456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.0000 | −1.27064 | −0.635321 | − | 0.772248i | \(-0.719132\pi\) | ||||
−0.635321 | + | 0.772248i | \(0.719132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.50000 | − | 14.7224i | −0.269739 | − | 0.467202i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.50000 | − | 9.52628i | 0.174362 | − | 0.302003i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.0000 | 0.823428 | 0.411714 | − | 0.911313i | \(-0.364930\pi\) | ||||
0.411714 | + | 0.911313i | \(0.364930\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.50000 | − | 6.06218i | 0.110735 | − | 0.191799i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4020.2.q.h.3781.1 | yes | 2 | |
67.37 | even | 3 | inner | 4020.2.q.h.841.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.h.841.1 | ✓ | 2 | 67.37 | even | 3 | inner | |
4020.2.q.h.3781.1 | yes | 2 | 1.1 | even | 1 | trivial |