Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(165,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.i (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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 165.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.165 |
Dual form | 1148.2.i.a.821.1 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | −0.973494 | − | 0.228714i | \(-0.926548\pi\) |
0.684819 | + | 0.728714i | \(0.259881\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | + | 2.59808i | 0.670820 | + | 1.16190i | 0.977672 | + | 0.210138i | \(0.0673912\pi\) |
−0.306851 | + | 0.951757i | \(0.599275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | −0.774597 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.50000 | + | 6.06218i | 0.802955 | + | 1.39076i | 0.917663 | + | 0.397360i | \(0.130073\pi\) |
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | + | 1.73205i | −0.436436 | + | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000 | − | 8.66025i | 0.898027 | − | 1.55543i | 0.0680129 | − | 0.997684i | \(-0.478334\pi\) |
0.830014 | − | 0.557743i | \(-0.188333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.50000 | + | 7.79423i | 0.253546 | + | 1.31747i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | − | 1.73205i | −0.164399 | − | 0.284747i | 0.772043 | − | 0.635571i | \(-0.219235\pi\) |
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | − | 3.46410i | 0.320256 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | + | 5.19615i | −0.447214 | + | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | − | 10.3923i | −0.875190 | − | 1.51587i | −0.856560 | − | 0.516047i | \(-0.827403\pi\) |
−0.0186297 | − | 0.999826i | \(-0.505930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | − | 5.19615i | 0.412082 | − | 0.713746i | −0.583036 | − | 0.812447i | \(-0.698135\pi\) |
0.995117 | + | 0.0987002i | \(0.0314685\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.00000 | −1.21356 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.00000 | −0.927173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00000 | + | 5.19615i | −0.390567 | + | 0.676481i | −0.992524 | − | 0.122047i | \(-0.961054\pi\) |
0.601958 | + | 0.798528i | \(0.294388\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | + | 11.2583i | 0.832240 | + | 1.44148i | 0.896258 | + | 0.443533i | \(0.146275\pi\) |
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | + | 5.19615i | 0.125988 | + | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.00000 | − | 10.3923i | −0.744208 | − | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00000 | −1.06810 | −0.534052 | − | 0.845452i | \(-0.679331\pi\) | ||||
−0.534052 | + | 0.845452i | \(0.679331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | + | 12.1244i | −0.819288 | + | 1.41905i | 0.0869195 | + | 0.996215i | \(0.472298\pi\) |
−0.906208 | + | 0.422833i | \(0.861036\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.00000 | − | 3.46410i | −0.230940 | − | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.00000 | + | 5.19615i | −0.683763 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.00000 | + | 5.19615i | −0.321634 | + | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | + | 10.3923i | 0.635999 | + | 1.10158i | 0.986303 | + | 0.164946i | \(0.0527450\pi\) |
−0.350304 | + | 0.936636i | \(0.613922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | − | 3.46410i | −1.04828 | − | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.00000 | + | 8.66025i | 0.518476 | + | 0.898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.5000 | + | 18.1865i | −1.07728 | + | 1.86590i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | + | 3.46410i | 0.197066 | + | 0.341328i | 0.947576 | − | 0.319531i | \(-0.103525\pi\) |
−0.750510 | + | 0.660859i | \(0.770192\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.50000 | − | 2.59808i | −0.731925 | − | 0.253546i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | − | 5.19615i | −0.290021 | − | 0.502331i | 0.683793 | − | 0.729676i | \(-0.260329\pi\) |
−0.973814 | + | 0.227345i | \(0.926996\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.00000 | + | 6.92820i | −0.383131 | + | 0.663602i | −0.991508 | − | 0.130046i | \(-0.958487\pi\) |
0.608377 | + | 0.793648i | \(0.291821\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | −0.282216 | −0.141108 | − | 0.989994i | \(-0.545067\pi\) | ||||
−0.141108 | + | 0.989994i | \(0.545067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.00000 | − | 15.5885i | 0.839254 | − | 1.45363i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.00000 | − | 6.92820i | −0.369800 | − | 0.640513i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.500000 | − | 0.866025i | 0.0450835 | − | 0.0780869i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0000 | 1.24230 | 0.621150 | − | 0.783692i | \(-0.286666\pi\) | ||||
0.621150 | + | 0.783692i | \(0.286666\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.00000 | − | 3.46410i | 0.176090 | − | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.00000 | − | 15.5885i | −0.786334 | − | 1.36197i | −0.928199 | − | 0.372084i | \(-0.878643\pi\) |
0.141865 | − | 0.989886i | \(-0.454690\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.50000 | + | 18.1865i | 0.303488 | + | 1.57697i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.50000 | − | 12.9904i | −0.645497 | − | 1.11803i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | − | 10.3923i | 0.512615 | − | 0.887875i | −0.487278 | − | 0.873247i | \(-0.662010\pi\) |
0.999893 | − | 0.0146279i | \(-0.00465636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | 1.01058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.00000 | − | 10.3923i | 0.501745 | − | 0.869048i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.00000 | + | 15.5885i | 0.747409 | + | 1.29455i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.50000 | + | 2.59808i | −0.536111 | + | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.00000 | − | 15.5885i | −0.737309 | − | 1.27706i | −0.953703 | − | 0.300750i | \(-0.902763\pi\) |
0.216394 | − | 0.976306i | \(-0.430570\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | − | 3.46410i | 0.162758 | − | 0.281905i | −0.773099 | − | 0.634285i | \(-0.781294\pi\) |
0.935857 | + | 0.352381i | \(0.114628\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 30.0000 | 2.40966 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | + | 12.1244i | −0.558661 | + | 0.967629i | 0.438948 | + | 0.898513i | \(0.355351\pi\) |
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | + | 5.19615i | 0.237915 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.00000 | − | 15.5885i | −0.236433 | − | 1.22854i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.00000 | − | 12.1244i | −0.548282 | − | 0.949653i | −0.998392 | − | 0.0566798i | \(-0.981949\pi\) |
0.450110 | − | 0.892973i | \(-0.351385\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.50000 | − | 7.79423i | 0.350325 | − | 0.606780i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.00000 | + | 12.1244i | −0.535303 | + | 0.927173i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5000 | + | 18.1865i | 0.798300 | + | 1.38270i | 0.920722 | + | 0.390218i | \(0.127601\pi\) |
−0.122422 | + | 0.992478i | \(0.539066\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.00000 | + | 6.92820i | −0.604743 | + | 0.523723i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.00000 | − | 5.19615i | −0.225494 | − | 0.390567i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.50000 | + | 2.59808i | −0.112115 | + | 0.194189i | −0.916623 | − | 0.399753i | \(-0.869096\pi\) |
0.804508 | + | 0.593942i | \(0.202429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.00000 | −0.297318 | −0.148659 | − | 0.988889i | \(-0.547496\pi\) | ||||
−0.148659 | + | 0.988889i | \(0.547496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.0000 | −0.960988 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | − | 5.19615i | 0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.5000 | − | 4.33013i | −0.909241 | − | 0.314970i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | + | 12.1244i | −0.503871 | + | 0.872730i | 0.496119 | + | 0.868255i | \(0.334758\pi\) |
−0.999990 | + | 0.00447566i | \(0.998575\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0000 | 0.859338 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.00000 | 0.213741 | 0.106871 | − | 0.994273i | \(-0.465917\pi\) | ||||
0.106871 | + | 0.994273i | \(0.465917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | − | 13.8564i | 0.567105 | − | 0.982255i | −0.429745 | − | 0.902950i | \(-0.641397\pi\) |
0.996850 | − | 0.0793045i | \(-0.0252700\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | + | 3.46410i | 0.141069 | + | 0.244339i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.0000 | + | 5.19615i | 1.05279 | + | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.50000 | − | 2.59808i | −0.104765 | − | 0.181458i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | − | 10.3923i | 0.417029 | − | 0.722315i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.0000 | −1.45260 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0000 | 1.58339 | 0.791693 | − | 0.610920i | \(-0.209200\pi\) | ||||
0.791693 | + | 0.610920i | \(0.209200\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.50000 | − | 7.79423i | 0.308335 | − | 0.534052i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.00000 | − | 10.3923i | −0.409197 | − | 0.708749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.0000 | − | 17.3205i | 1.35769 | − | 1.17579i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.00000 | − | 12.1244i | −0.473016 | − | 0.819288i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.00000 | −0.533333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5000 | + | 18.1865i | −0.696909 | + | 1.20708i | 0.272623 | + | 0.962121i | \(0.412109\pi\) |
−0.969533 | + | 0.244962i | \(0.921225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | + | 3.46410i | 0.132164 | + | 0.228914i | 0.924510 | − | 0.381157i | \(-0.124474\pi\) |
−0.792347 | + | 0.610071i | \(0.791141\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.50000 | − | 7.79423i | −0.0986928 | − | 0.512823i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | − | 5.19615i | −0.196537 | − | 0.340411i | 0.750867 | − | 0.660454i | \(-0.229636\pi\) |
−0.947403 | + | 0.320043i | \(0.896303\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.0000 | − | 31.1769i | 1.17419 | − | 2.03376i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.0000 | −1.74648 | −0.873242 | − | 0.487286i | \(-0.837987\pi\) | ||||
−0.873242 | + | 0.487286i | \(0.837987\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0000 | − | 19.0526i | 0.708572 | − | 1.22728i | −0.256814 | − | 0.966461i | \(-0.582673\pi\) |
0.965387 | − | 0.260822i | \(-0.0839937\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.00000 | − | 13.8564i | −0.513200 | − | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | + | 20.7846i | −0.191663 | + | 1.32788i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.0000 | − | 24.2487i | −0.890799 | − | 1.54291i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | + | 10.3923i | −0.380235 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.00000 | + | 5.19615i | 0.187135 | + | 0.324127i | 0.944294 | − | 0.329104i | \(-0.106747\pi\) |
−0.757159 | + | 0.653231i | \(0.773413\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | − | 5.19615i | −0.0621370 | − | 0.322873i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | + | 10.3923i | 0.371391 | + | 0.643268i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.00000 | + | 10.3923i | −0.369976 | + | 0.640817i | −0.989561 | − | 0.144112i | \(-0.953967\pi\) |
0.619586 | + | 0.784929i | \(0.287301\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0000 | 1.10573 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.0000 | −0.734388 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.50000 | − | 12.9904i | 0.457283 | − | 0.792038i | −0.541533 | − | 0.840679i | \(-0.682156\pi\) |
0.998816 | + | 0.0486418i | \(0.0154893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | − | 6.92820i | −0.242983 | − | 0.420858i | 0.718580 | − | 0.695444i | \(-0.244792\pi\) |
−0.961563 | + | 0.274586i | \(0.911459\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.00000 | − | 6.92820i | 0.484182 | − | 0.419314i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.00000 | − | 10.3923i | −0.361814 | − | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.50000 | − | 11.2583i | 0.390547 | − | 0.676448i | −0.601975 | − | 0.798515i | \(-0.705619\pi\) |
0.992522 | + | 0.122068i | \(0.0389525\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.0000 | 1.19737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0000 | + | 22.5167i | −0.772770 | + | 1.33848i | 0.163270 | + | 0.986581i | \(0.447796\pi\) |
−0.936039 | + | 0.351895i | \(0.885537\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.5000 | − | 18.1865i | −0.621966 | − | 1.07728i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.50000 | − | 0.866025i | −0.147570 | − | 0.0511199i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.00000 | + | 1.73205i | −0.0586210 | + | 0.101535i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0000 | 0.701047 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.0000 | −1.04800 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.50000 | − | 12.9904i | 0.435194 | − | 0.753778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0000 | + | 20.7846i | 0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0000 | − | 3.46410i | −0.576390 | − | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.5000 | + | 33.7750i | −1.11657 | + | 1.93395i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.00000 | + | 10.3923i | −0.340229 | + | 0.589294i | −0.984475 | − | 0.175525i | \(-0.943838\pi\) |
0.644246 | + | 0.764818i | \(0.277171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0000 | − | 17.3205i | −0.565233 | − | 0.979013i | −0.997028 | − | 0.0770410i | \(-0.975453\pi\) |
0.431795 | − | 0.901972i | \(-0.357881\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.0000 | + | 10.3923i | −0.676123 | + | 0.585540i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.00000 | + | 15.5885i | 0.505490 | + | 0.875535i | 0.999980 | + | 0.00635137i | \(0.00202172\pi\) |
−0.494489 | + | 0.869184i | \(0.664645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | + | 15.5885i | −0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | 0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.00000 | − | 13.8564i | 0.443760 | − | 0.768615i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.00000 | − | 6.92820i | −0.221201 | − | 0.383131i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.00000 | − | 31.1769i | −0.330791 | − | 1.71884i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | + | 24.2487i | 0.769510 | + | 1.33283i | 0.937829 | + | 0.347097i | \(0.112833\pi\) |
−0.168320 | + | 0.985732i | \(0.553834\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.00000 | − | 3.46410i | 0.109599 | − | 0.189832i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0000 | 0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0000 | 1.25289 | 0.626445 | − | 0.779466i | \(-0.284509\pi\) | ||||
0.626445 | + | 0.779466i | \(0.284509\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.50000 | − | 2.59808i | 0.0814688 | − | 0.141108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0000 | + | 25.9808i | 0.812296 | + | 1.40694i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.00000 | + | 15.5885i | 0.484544 | + | 0.839254i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.50000 | − | 12.9904i | 0.402621 | − | 0.697360i | −0.591420 | − | 0.806363i | \(-0.701433\pi\) |
0.994041 | + | 0.109003i | \(0.0347659\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.0000 | 1.06752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.50000 | − | 12.9904i | 0.399185 | − | 0.691408i | −0.594441 | − | 0.804139i | \(-0.702627\pi\) |
0.993626 | + | 0.112731i | \(0.0359599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.5000 | − | 23.3827i | −0.716506 | − | 1.24102i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.0000 | − | 31.1769i | −0.950004 | − | 1.64545i | −0.745409 | − | 0.666608i | \(-0.767746\pi\) |
−0.204595 | − | 0.978847i | \(-0.565588\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −42.0000 | −2.19838 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.0000 | − | 24.2487i | 0.730794 | − | 1.26577i | −0.225750 | − | 0.974185i | \(-0.572483\pi\) |
0.956544 | − | 0.291587i | \(-0.0941834\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.00000 | − | 1.73205i | −0.0520579 | − | 0.0901670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | − | 10.3923i | 0.623009 | − | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5000 | − | 25.1147i | −0.750782 | − | 1.30039i | −0.947444 | − | 0.319921i | \(-0.896344\pi\) |
0.196663 | − | 0.980471i | \(-0.436990\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.50000 | + | 2.59808i | −0.0774597 | + | 0.134164i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.00000 | + | 12.1244i | −0.358621 | + | 0.621150i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.5000 | + | 23.3827i | 0.689818 | + | 1.19480i | 0.971897 | + | 0.235408i | \(0.0756427\pi\) |
−0.282079 | + | 0.959391i | \(0.591024\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.5000 | − | 7.79423i | −1.14671 | − | 0.397231i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00000 | − | 6.92820i | −0.203331 | − | 0.352180i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.50000 | + | 12.9904i | −0.380265 | + | 0.658638i | −0.991100 | − | 0.133120i | \(-0.957501\pi\) |
0.610835 | + | 0.791758i | \(0.290834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.0000 | 0.907980 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.50000 | + | 2.59808i | −0.0754732 | + | 0.130723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.00000 | − | 12.1244i | −0.351320 | − | 0.608504i | 0.635161 | − | 0.772380i | \(-0.280934\pi\) |
−0.986481 | + | 0.163876i | \(0.947600\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.5000 | − | 6.06218i | −0.876096 | − | 0.303488i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5000 | − | 23.3827i | −0.674158 | − | 1.16768i | −0.976714 | − | 0.214544i | \(-0.931173\pi\) |
0.302556 | − | 0.953131i | \(-0.402160\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.0000 | + | 34.6410i | −0.996271 | + | 1.72559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.00000 | −0.149071 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000 | 0.297409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.5000 | − | 26.8468i | 0.766426 | − | 1.32749i | −0.173064 | − | 0.984911i | \(-0.555367\pi\) |
0.939490 | − | 0.342578i | \(-0.111300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | + | 10.3923i | 0.295958 | + | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0000 | + | 10.3923i | −0.590481 | + | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.0000 | + | 31.1769i | 0.883585 | + | 1.53041i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.00000 | + | 12.1244i | −0.342791 | + | 0.593732i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.00000 | −0.293119 | −0.146560 | − | 0.989202i | \(-0.546820\pi\) | ||||
−0.146560 | + | 0.989202i | \(0.546820\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.0000 | − | 20.7846i | 0.583460 | − | 1.01058i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.50000 | + | 33.7750i | 0.314557 | + | 1.63449i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.00000 | + | 10.3923i | 0.289683 | + | 0.501745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.00000 | + | 15.5885i | −0.433515 | + | 0.750870i | −0.997173 | − | 0.0751385i | \(-0.976060\pi\) |
0.563658 | + | 0.826008i | \(0.309393\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.0000 | 1.10531 | 0.552655 | − | 0.833410i | \(-0.313615\pi\) | ||||
0.552655 | + | 0.833410i | \(0.313615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.0000 | −0.863034 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.0000 | − | 36.3731i | 1.00457 | − | 1.73996i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.500000 | + | 0.866025i | 0.0238637 | + | 0.0413331i | 0.877711 | − | 0.479191i | \(-0.159070\pi\) |
−0.853847 | + | 0.520524i | \(0.825737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | + | 13.8564i | −0.0952381 | + | 0.659829i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.00000 | − | 15.5885i | −0.427603 | − | 0.740630i | 0.569057 | − | 0.822298i | \(-0.307309\pi\) |
−0.996660 | + | 0.0816684i | \(0.973975\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.0000 | + | 31.1769i | −0.853282 | + | 1.47793i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.0000 | 0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.00000 | 0.424736 | 0.212368 | − | 0.977190i | \(-0.431882\pi\) | ||||
0.212368 | + | 0.977190i | \(0.431882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.50000 | − | 2.59808i | 0.0706322 | − | 0.122339i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.00000 | + | 3.46410i | 0.0939682 | + | 0.162758i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.00000 | − | 31.1769i | −0.281284 | − | 1.46160i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.00000 | + | 13.8564i | 0.374224 | + | 0.648175i | 0.990211 | − | 0.139581i | \(-0.0445757\pi\) |
−0.615986 | + | 0.787757i | \(0.711242\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.0000 | 1.25752 | 0.628758 | − | 0.777601i | \(-0.283564\pi\) | ||||
0.628758 | + | 0.777601i | \(0.283564\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.00000 | −0.0464739 | −0.0232370 | − | 0.999730i | \(-0.507397\pi\) | ||||
−0.0232370 | + | 0.999730i | \(0.507397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.0000 | + | 25.9808i | −0.695608 | + | 1.20483i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.0000 | − | 25.9808i | −0.694117 | − | 1.20225i | −0.970477 | − | 0.241192i | \(-0.922462\pi\) |
0.276360 | − | 0.961054i | \(-0.410872\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | − | 6.92820i | 0.369406 | − | 0.319915i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.00000 | − | 12.1244i | −0.322543 | − | 0.558661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.00000 | − | 10.3923i | 0.275880 | − | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.0000 | −1.28473 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.5000 | + | 18.1865i | −0.479757 | + | 0.830964i | −0.999730 | − | 0.0232187i | \(-0.992609\pi\) |
0.519973 | + | 0.854183i | \(0.325942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | + | 6.92820i | 0.182384 | + | 0.315899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.0000 | + | 5.19615i | 0.682524 | + | 0.236433i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.00000 | + | 5.19615i | 0.136223 | + | 0.235945i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.00000 | + | 6.92820i | −0.181257 | + | 0.313947i | −0.942309 | − | 0.334744i | \(-0.891350\pi\) |
0.761052 | + | 0.648691i | \(0.224683\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.0000 | 0.633102 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −42.0000 | −1.89543 | −0.947717 | − | 0.319113i | \(-0.896615\pi\) | ||||
−0.947717 | + | 0.319113i | \(0.896615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.00000 | − | 15.5885i | −0.404520 | − | 0.700649i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.5000 | − | 7.79423i | −1.00926 | − | 0.349619i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.00000 | + | 3.46410i | 0.0895323 | + | 0.155074i | 0.907314 | − | 0.420455i | \(-0.138129\pi\) |
−0.817781 | + | 0.575529i | \(0.804796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | + | 10.3923i | −0.268060 | + | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.00000 | 0.401290 | 0.200645 | − | 0.979664i | \(-0.435696\pi\) | ||||
0.200645 | + | 0.979664i | \(0.435696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.50000 | + | 2.59808i | −0.0666173 | + | 0.115385i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.00000 | + | 15.5885i | 0.398918 | + | 0.690946i | 0.993593 | − | 0.113020i | \(-0.0360525\pi\) |
−0.594675 | + | 0.803966i | \(0.702719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0000 | + | 24.2487i | −1.23865 | + | 1.07270i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.5000 | − | 30.3109i | −0.772644 | − | 1.33826i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.00000 | + | 10.3923i | −0.264392 | + | 0.457940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.0000 | 1.58328 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.0000 | −0.921798 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0000 | + | 25.9808i | −0.657162 | + | 1.13824i | 0.324185 | + | 0.945994i | \(0.394910\pi\) |
−0.981347 | + | 0.192244i | \(0.938423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0000 | − | 32.9090i | −0.830812 | − | 1.43901i | −0.897395 | − | 0.441228i | \(-0.854543\pi\) |
0.0665832 | − | 0.997781i | \(-0.478790\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.00000 | − | 10.3923i | −0.0872872 | − | 0.453557i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.0000 | −0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.00000 | 0.173259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.00000 | − | 15.5885i | 0.389104 | − | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.50000 | − | 2.59808i | −0.0647298 | − | 0.112115i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.5000 | + | 7.79423i | −0.839924 | + | 0.335721i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.00000 | − | 12.1244i | −0.300954 | − | 0.521267i | 0.675399 | − | 0.737453i | \(-0.263972\pi\) |
−0.976352 | + | 0.216186i | \(0.930638\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.00000 | − | 3.46410i | 0.0858282 | − | 0.148659i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.0000 | −1.02805 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.0000 | + | 22.5167i | −0.554826 | + | 0.960988i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.0000 | + | 36.3731i | 0.894630 | + | 1.54954i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.500000 | + | 2.59808i | 0.0212622 | + | 0.110481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.00000 | + | 5.19615i | 0.127343 | + | 0.220564i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.00000 | − | 10.3923i | 0.254228 | − | 0.440336i | −0.710457 | − | 0.703740i | \(-0.751512\pi\) |
0.964686 | + | 0.263404i | \(0.0848453\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.50000 | − | 12.9904i | 0.316087 | − | 0.547479i | −0.663581 | − | 0.748105i | \(-0.730964\pi\) |
0.979668 | + | 0.200625i | \(0.0642974\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.50000 | − | 7.79423i | −0.189316 | − | 0.327906i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.00000 | + | 1.73205i | −0.0839921 | + | 0.0727393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.0000 | − | 25.9808i | −0.628833 | − | 1.08917i | −0.987786 | − | 0.155815i | \(-0.950200\pi\) |
0.358954 | − | 0.933355i | \(-0.383134\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.50000 | + | 4.33013i | −0.104622 | + | 0.181210i | −0.913584 | − | 0.406651i | \(-0.866697\pi\) |
0.808962 | + | 0.587861i | \(0.200030\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0000 | 1.00087 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.0000 | + | 17.3205i | −0.416305 | + | 0.721062i | −0.995565 | − | 0.0940813i | \(-0.970009\pi\) |
0.579259 | + | 0.815144i | \(0.303342\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.00000 | − | 12.1244i | −0.290910 | − | 0.503871i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.0000 | + | 10.3923i | 1.24461 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | + | 15.5885i | 0.372742 | + | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.0000 | − | 20.7846i | 0.496139 | − | 0.859338i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.0000 | −1.36206 | −0.681028 | − | 0.732257i | \(-0.738467\pi\) | ||||
−0.681028 | + | 0.732257i | \(0.738467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 70.0000 | 2.88430 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.50000 | + | 2.59808i | −0.0617018 | + | 0.106871i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.00000 | + | 5.19615i | 0.123195 | + | 0.213380i | 0.921026 | − | 0.389501i | \(-0.127353\pi\) |
−0.797831 | + | 0.602881i | \(0.794019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.00000 | + | 13.8564i | 0.327418 | + | 0.567105i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.0000 | − | 25.9808i | 0.612883 | − | 1.06155i | −0.377869 | − | 0.925859i | \(-0.623343\pi\) |
0.990752 | − | 0.135686i | \(-0.0433238\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.0000 | −1.38689 | −0.693444 | − | 0.720510i | \(-0.743908\pi\) | ||||
−0.693444 | + | 0.720510i | \(0.743908\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.00000 | + | 5.19615i | −0.121967 | + | 0.211254i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0000 | + | 24.2487i | 0.568242 | + | 0.984225i | 0.996740 | + | 0.0806818i | \(0.0257098\pi\) |
−0.428497 | + | 0.903543i | \(0.640957\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.0000 | + | 10.3923i | −0.486265 | + | 0.421117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000 | + | 41.5692i | 0.970936 | + | 1.68171i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.50000 | − | 6.06218i | 0.141364 | − | 0.244849i | −0.786647 | − | 0.617403i | \(-0.788185\pi\) |
0.928010 | + | 0.372554i | \(0.121518\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.00000 | 0.120972 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.0000 | −1.08698 | −0.543490 | − | 0.839416i | \(-0.682897\pi\) | ||||
−0.543490 | + | 0.839416i | \(0.682897\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.0000 | + | 38.1051i | −0.884255 | + | 1.53157i | −0.0376891 | + | 0.999290i | \(0.512000\pi\) |
−0.846566 | + | 0.532284i | \(0.821334\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.0000 | + | 25.9808i | 0.601929 | + | 1.04257i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.00000 | + | 31.1769i | 0.240385 | + | 1.24908i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.5000 | − | 18.1865i | 0.419330 | − | 0.726300i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.5000 | + | 19.9186i | −0.457084 | + | 0.791693i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.0000 | + | 36.3731i | 0.833360 | + | 1.44342i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.0000 | − | 17.3205i | −0.871672 | − | 0.686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.00000 | − | 15.5885i | −0.356034 | − | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.00000 | + | 10.3923i | −0.236986 | + | 0.410471i | −0.959848 | − | 0.280521i | \(-0.909493\pi\) |
0.722862 | + | 0.690992i | \(0.242826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.00000 | 0.197181 | 0.0985904 | − | 0.995128i | \(-0.468567\pi\) | ||||
0.0985904 | + | 0.995128i | \(0.468567\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.0000 | 0.472500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.00000 | − | 10.3923i | 0.235884 | − | 0.408564i | −0.723645 | − | 0.690172i | \(-0.757535\pi\) |
0.959529 | + | 0.281609i | \(0.0908680\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | − | 15.5885i | −0.353281 | − | 0.611900i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.00000 | + | 25.9808i | 0.195965 | + | 1.01827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0000 | − | 31.1769i | −0.704394 | − | 1.22005i | −0.966910 | − | 0.255119i | \(-0.917885\pi\) |
0.262515 | − | 0.964928i | \(-0.415448\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.0000 | − | 46.7654i | 1.05498 | − | 1.82727i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.0000 | −1.09238 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −48.0000 | −1.86981 | −0.934907 | − | 0.354892i | \(-0.884518\pi\) | ||||
−0.934907 | + | 0.354892i | \(0.884518\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.5000 | − | 26.8468i | 0.602880 | − | 1.04422i | −0.389503 | − | 0.921025i | \(-0.627353\pi\) |
0.992383 | − | 0.123194i | \(-0.0393136\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −42.0000 | + | 36.3731i | −1.62869 | + | 1.41049i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.0000 | − | 31.1769i | −0.696963 | − | 1.20717i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.00000 | + | 6.92820i | −0.154649 | + | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −39.0000 | −1.50558 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.0000 | −0.848038 | −0.424019 | − | 0.905653i | \(-0.639381\pi\) | ||||
−0.424019 | + | 0.905653i | \(0.639381\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0000 | − | 17.3205i | 0.384900 | − | 0.666667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.50000 | + | 12.9904i | 0.288248 | + | 0.499261i | 0.973392 | − | 0.229147i | \(-0.0735938\pi\) |
−0.685143 | + | 0.728408i | \(0.740260\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.00000 | + | 1.73205i | 0.191882 | + | 0.0664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5000 | − | 18.1865i | −0.402361 | − | 0.696909i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.00000 | + | 10.3923i | −0.229584 | + | 0.397650i | −0.957685 | − | 0.287819i | \(-0.907070\pi\) |
0.728101 | + | 0.685470i | \(0.240403\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.0000 | 1.37549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.00000 | −0.152610 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0000 | + | 20.7846i | −0.457164 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.500000 | + | 0.866025i | 0.0190209 | + | 0.0329452i | 0.875379 | − | 0.483437i | \(-0.160612\pi\) |
−0.856358 | + | 0.516382i | \(0.827278\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.0000 | − | 5.19615i | −0.569803 | − | 0.197386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.0000 | + | 36.3731i | 0.796575 | + | 1.37971i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.0000 | 0.566542 | 0.283271 | − | 0.959040i | \(-0.408580\pi\) | ||||
0.283271 | + | 0.959040i | \(0.408580\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.00000 | − | 12.1244i | 0.264010 | − | 0.457279i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.0000 | + | 31.1769i | 0.677919 | + | 1.17419i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | + | 8.66025i | 0.187779 | + | 0.325243i | 0.944509 | − | 0.328484i | \(-0.106538\pi\) |
−0.756730 | + | 0.653727i | \(0.773204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.00000 | + | 1.73205i | −0.0375029 | + | 0.0649570i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −60.0000 | −2.24702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.0000 | 1.34632 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.5000 | − | 23.3827i | 0.504167 | − | 0.873242i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.50000 | − | 2.59808i | −0.0559406 | − | 0.0968919i | 0.836699 | − | 0.547663i | \(-0.184482\pi\) |
−0.892640 | + | 0.450771i | \(0.851149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.00000 | + | 10.3923i | 0.0744839 | + | 0.387030i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.0000 | + | 19.0526i | 0.409094 | + | 0.708572i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.0000 | + | 20.7846i | −0.445669 | + | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.0000 | −1.48352 | −0.741759 | − | 0.670667i | \(-0.766008\pi\) | ||||
−0.741759 | + | 0.670667i | \(0.766008\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0000 | + | 19.0526i | 0.406294 | + | 0.703722i | 0.994471 | − | 0.105010i | \(-0.0334875\pi\) |
−0.588177 | + | 0.808732i | \(0.700154\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.5000 | − | 12.9904i | −0.608612 | − | 0.479157i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.00000 | + | 10.3923i | 0.221013 | + | 0.382805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.00000 | − | 13.8564i | 0.294285 | − | 0.509716i | −0.680534 | − | 0.732717i | \(-0.738252\pi\) |
0.974818 | + | 0.223001i | \(0.0715853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.0000 | 1.02861 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.00000 | 0.220119 | 0.110059 | − | 0.993925i | \(-0.464896\pi\) | ||||
0.110059 | + | 0.993925i | \(0.464896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.0000 | − | 46.7654i | 0.989203 | − | 1.71335i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | + | 20.7846i | 0.439057 | + | 0.760469i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.00000 | − | 15.5885i | −0.109618 | − | 0.569590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.5000 | + | 37.2391i | 0.784546 | + | 1.35887i | 0.929270 | + | 0.369402i | \(0.120437\pi\) |
−0.144724 | + | 0.989472i | \(0.546229\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.00000 | + | 10.3923i | −0.218652 | + | 0.378717i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.0000 | −1.45382 | −0.726912 | − | 0.686730i | \(-0.759045\pi\) | ||||
−0.726912 | + | 0.686730i | \(0.759045\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.00000 | + | 15.5885i | −0.326679 | + | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.00000 | − | 15.5885i | −0.326250 | − | 0.565081i | 0.655515 | − | 0.755182i | \(-0.272452\pi\) |
−0.981764 | + | 0.190101i | \(0.939118\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0000 | + | 13.8564i | −0.579239 | + | 0.501636i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.0000 | − | 20.7846i | 0.433295 | − | 0.750489i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.0000 | 1.26213 | 0.631066 | − | 0.775729i | \(-0.282618\pi\) | ||||
0.631066 | + | 0.775729i | \(0.282618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.0000 | + | 31.1769i | −0.647415 | + | 1.12136i | 0.336323 | + | 0.941747i | \(0.390817\pi\) |
−0.983738 | + | 0.179609i | \(0.942517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.0000 | + | 34.6410i | 0.718421 | + | 1.24434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.00000 | + | 1.73205i | 0.179374 | + | 0.0621370i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.50000 | − | 6.06218i | −0.125401 | − | 0.217200i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.5000 | − | 23.3827i | 0.483068 | − | 0.836698i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −30.0000 | −1.07211 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42.0000 | −1.49904 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.0000 | − | 24.2487i | 0.499046 | − | 0.864373i | −0.500953 | − | 0.865474i | \(-0.667017\pi\) |
0.999999 | + | 0.00110111i | \(0.000350496\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.00000 | − | 10.3923i | −0.213606 | − | 0.369976i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.50000 | − | 2.59808i | −0.266669 | − | 0.0923770i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.0000 | − | 45.0333i | −0.923287 | − | 1.59918i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.00000 | + | 15.5885i | −0.319197 | + | 0.552866i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.0000 | −1.06265 | −0.531327 | − | 0.847167i | \(-0.678307\pi\) | ||||
−0.531327 | + | 0.847167i | \(0.678307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.0000 | + | 20.7846i | −0.423999 | + | 0.734388i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.0000 | − | 36.3731i | −0.741074 | − | 1.28358i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 36.0000 | − | 31.1769i | 1.26883 | − | 1.09884i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.50000 | + | 12.9904i | 0.264013 | + | 0.457283i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.00000 | − | 10.3923i | 0.210949 | − | 0.365374i | −0.741063 | − | 0.671436i | \(-0.765678\pi\) |
0.952012 | + | 0.306062i | \(0.0990113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.0000 | 1.33436 | 0.667180 | − | 0.744896i | \(-0.267501\pi\) | ||||
0.667180 | + | 0.744896i | \(0.267501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.00000 | 0.280572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.0000 | − | 36.3731i | 0.735598 | − | 1.27409i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.0000 | − | 24.2487i | −0.489798 | − | 0.848355i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.00000 | − | 20.7846i | −0.139771 | − | 0.726273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.50000 | + | 7.79423i | 0.157051 | + | 0.272020i | 0.933804 | − | 0.357785i | \(-0.116468\pi\) |
−0.776753 | + | 0.629805i | \(0.783135\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | 12.0000 | 0.417786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.0000 | + | 32.9090i | −0.659897 | + | 1.14298i | 0.320745 | + | 0.947166i | \(0.396067\pi\) |
−0.980642 | + | 0.195810i | \(0.937266\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.50000 | + | 11.2583i | 0.225483 | + | 0.390547i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | + | 31.1769i | 0.622916 | + | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.0000 | + | 43.3013i | −0.864126 | + | 1.49671i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.00000 | −0.103572 | −0.0517858 | − | 0.998658i | \(-0.516491\pi\) | ||||
−0.0517858 | + | 0.998658i | \(0.516491\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.00000 | + | 5.19615i | −0.103325 | + | 0.178965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.50000 | + | 7.79423i | 0.154805 | + | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | + | 5.19615i | 0.0343604 | + | 0.178542i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.0000 | − | 22.5167i | −0.446159 | − | 0.772770i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | + | 10.3923i | −0.205677 | + | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.0000 | −1.67773 | −0.838864 | − | 0.544341i | \(-0.816780\pi\) | ||||
−0.838864 | + | 0.544341i | \(0.816780\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −42.0000 | −1.43637 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.50000 | − | 2.59808i | 0.0512390 | − | 0.0887486i | −0.839268 | − | 0.543718i | \(-0.817016\pi\) |
0.890507 | + | 0.454969i | \(0.150350\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | − | 6.92820i | −0.136478 | − | 0.236387i | 0.789683 | − | 0.613515i | \(-0.210245\pi\) |
−0.926161 | + | 0.377128i | \(0.876912\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.00000 | − | 1.73205i | 0.0681598 | − | 0.0590281i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.0000 | − | 20.7846i | −0.408485 | − | 0.707516i | 0.586235 | − | 0.810141i | \(-0.300609\pi\) |
−0.994720 | + | 0.102624i | \(0.967276\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.5000 | + | 54.5596i | −1.07103 | + | 1.85508i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.0000 | −0.577350 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.00000 | −0.101768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | + | 13.8564i | −0.271070 | + | 0.469506i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.00000 | + | 3.46410i | 0.0676897 | + | 0.117242i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.50000 | + | 2.59808i | 0.253546 | + | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.50000 | − | 14.7224i | −0.287025 | − | 0.497141i | 0.686074 | − | 0.727532i | \(-0.259333\pi\) |
−0.973098 | + | 0.230391i | \(0.925999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.00000 | + | 10.3923i | −0.202375 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.0000 | 1.51609 | 0.758044 | − | 0.652203i | \(-0.226155\pi\) | ||||
0.758044 | + | 0.652203i | \(0.226155\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.0000 | 1.07689 | 0.538443 | − | 0.842662i | \(-0.319013\pi\) | ||||
0.538443 | + | 0.842662i | \(0.319013\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.00000 | − | 15.5885i | 0.302532 | − | 0.524000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.50000 | − | 2.59808i | −0.0503651 | − | 0.0872349i | 0.839744 | − | 0.542983i | \(-0.182705\pi\) |
−0.890109 | + | 0.455748i | \(0.849372\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.0000 | + | 12.1244i | 1.17386 | + | 0.406638i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | − | 2.59808i | −0.0502519 | − | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.0000 | − | 72.7461i | 1.40548 | − | 2.43436i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.00000 | −0.300837 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.0000 | −0.801337 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.0000 | − | 51.9615i | 1.00056 | − | 1.73301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000 | − | 6.92820i | 0.266223 | − | 0.230556i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.00000 | − | 10.3923i | −0.199447 | − | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.00000 | − | 8.66025i | 0.166022 | − | 0.287559i | −0.770996 | − | 0.636841i | \(-0.780241\pi\) |
0.937018 | + | 0.349281i | \(0.113574\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | + | 31.1769i | −0.595713 | + | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.5000 | − | 33.7750i | −0.644650 | − | 1.11657i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.00000 | − | 46.7654i | −0.297206 | − | 1.54433i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.5000 | − | 51.0955i | −0.973115 | − | 1.68548i | −0.686020 | − | 0.727583i | \(-0.740644\pi\) |
−0.287096 | − | 0.957902i | \(-0.592690\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0000 | + | 17.3205i | −0.329511 | + | 0.570730i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.0000 | 1.18495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00000 | + | 6.92820i | −0.131377 | + | 0.227552i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.00000 | + | 48.4974i | −0.229416 | + | 1.58944i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.00000 | − | 10.3923i | −0.196431 | − | 0.340229i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.0000 | 0.652675 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.5000 | − | 38.9711i | 0.733479 | − | 1.27042i | −0.221908 | − | 0.975068i | \(-0.571229\pi\) |
0.955387 | − | 0.295355i | \(-0.0954381\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.00000 | + | 5.19615i | 0.0976934 | + | 0.169210i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.50000 | − | 38.9711i | −0.243975 | − | 1.26773i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.00000 | + | 15.5885i | 0.292461 | + | 0.506557i | 0.974391 | − | 0.224860i | \(-0.0721926\pi\) |
−0.681930 | + | 0.731417i | \(0.738859\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.0000 | − | 48.4974i | 0.908918 | − | 1.57429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.00000 | −0.194359 | −0.0971795 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971795 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.00000 | − | 15.5885i | −0.290929 | − | 0.503903i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.0000 | − | 20.7846i | 0.775000 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.5000 | − | 59.7558i | −1.11290 | − | 1.92760i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | − | 10.3923i | 0.193347 | − | 0.334887i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42.0000 | −1.35203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.0000 | 0.739630 | 0.369815 | − | 0.929105i | \(-0.379421\pi\) | ||||
0.369815 | + | 0.929105i | \(0.379421\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.0000 | + | 12.1244i | 1.12205 | + | 0.388689i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.00000 | + | 13.8564i | 0.256205 | + | 0.443760i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.0000 | − | 36.3731i | 0.671850 | − | 1.16368i | −0.305530 | − | 0.952183i | \(-0.598833\pi\) |
0.977379 | − | 0.211495i | \(-0.0678332\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.0000 | −1.15056 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.0000 | −0.510841 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.00000 | + | 10.3923i | −0.191370 | + | 0.331463i | −0.945705 | − | 0.325027i | \(-0.894626\pi\) |
0.754334 | + | 0.656490i | \(0.227960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.50000 | + | 7.79423i | 0.143382 | + | 0.248345i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 30.0000 | + | 10.3923i | 0.954911 | + | 0.330791i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000 | + | 20.7846i | 0.381578 | + | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5000 | − | 37.2391i | 0.682970 | − | 1.18294i | −0.291100 | − | 0.956693i | \(-0.594021\pi\) |
0.974070 | − | 0.226246i | \(-0.0726454\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.0000 | −0.888553 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.0000 | 1.52170 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.0000 | − | 24.2487i | 0.443384 | − | 0.767964i | −0.554554 | − | 0.832148i | \(-0.687111\pi\) |
0.997938 | + | 0.0641836i | \(0.0204443\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.00000 | + | 8.66025i | 0.158193 | + | 0.273998i |
(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 | 1148.2.i.a.165.1 | ✓ | 2 | |
7.2 | even | 3 | inner | 1148.2.i.a.821.1 | yes | 2 | |
7.3 | odd | 6 | 8036.2.a.c.1.1 | 1 | |||
7.4 | even | 3 | 8036.2.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.a.165.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1148.2.i.a.821.1 | yes | 2 | 7.2 | even | 3 | inner | |
8036.2.a.c.1.1 | 1 | 7.3 | odd | 6 | |||
8036.2.a.d.1.1 | 1 | 7.4 | even | 3 |