Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1088,2,Mod(769,1088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1088.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1088 = 2^{6} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1088.o (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.68772373992\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.163368480538624.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 544) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 897.6 | ||
Root | \(-0.204810 + 1.39930i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1088.897 |
Dual form | 1088.2.o.w.769.6 |
$q$-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 \(\left(\mathbb{Z}/1088\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(511\) | \(513\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 2.08397 | + | 2.08397i | 1.20318 | + | 1.20318i | 0.973194 | + | 0.229985i | \(0.0738679\pi\) |
0.229985 | + | 0.973194i | \(0.426132\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.48929 | − | 2.48929i | −1.11324 | − | 1.11324i | −0.992709 | − | 0.120535i | \(-0.961539\pi\) |
−0.120535 | − | 0.992709i | \(-0.538461\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.409620 | − | 0.409620i | 0.154822 | − | 0.154822i | −0.625446 | − | 0.780268i | \(-0.715083\pi\) |
0.780268 | + | 0.625446i | \(0.215083\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.68585i | 1.89528i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.51325 | − | 3.51325i | 1.05928 | − | 1.05928i | 0.0611564 | − | 0.998128i | \(-0.480521\pi\) |
0.998128 | − | 0.0611564i | \(-0.0194789\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.68585 | 1.29962 | 0.649810 | − | 0.760097i | \(-0.274848\pi\) | ||||
0.649810 | + | 0.760097i | \(0.274848\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 10.3752i | − | 2.67886i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.19656 | − | 3.48929i | −0.532743 | − | 0.846277i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.51663i | − | 1.72443i | −0.506539 | − | 0.862217i | \(-0.669075\pi\) | ||
0.506539 | − | 0.862217i | \(-0.330925\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.70727 | 0.372557 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.83890 | + | 1.83890i | −0.383437 | + | 0.383437i | −0.872339 | − | 0.488902i | \(-0.837398\pi\) |
0.488902 | + | 0.872339i | \(0.337398\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.39312i | 1.47862i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.59722 | + | 5.59722i | −1.07719 | + | 1.07719i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.196558 | + | 0.196558i | 0.0364998 | + | 0.0364998i | 0.725121 | − | 0.688621i | \(-0.241784\pi\) |
−0.688621 | + | 0.725121i | \(0.741784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.18760 | + | 5.18760i | 0.931720 | + | 0.931720i | 0.997813 | − | 0.0660933i | \(-0.0210535\pi\) |
−0.0660933 | + | 0.997813i | \(0.521054\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.6430 | 2.54902 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.03932 | −0.344709 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.489289 | + | 0.489289i | 0.0804385 | + | 0.0804385i | 0.746181 | − | 0.665743i | \(-0.231885\pi\) |
−0.665743 | + | 0.746181i | \(0.731885\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.76515 | + | 9.76515i | 1.56368 | + | 1.56368i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | − | 1.00000i | 0.156174 | − | 0.156174i | −0.624695 | − | 0.780869i | \(-0.714777\pi\) |
0.780869 | + | 0.624695i | \(0.214777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.52946i | 0.385739i | 0.981224 | + | 0.192869i | \(0.0617793\pi\) | ||||
−0.981224 | + | 0.192869i | \(0.938221\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.1537 | − | 14.1537i | 2.10991 | − | 2.10991i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.63848 | 0.238997 | 0.119498 | − | 0.992834i | \(-0.461871\pi\) | ||||
0.119498 | + | 0.992834i | \(0.461871\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.66442i | 0.952060i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.69401 | − | 11.8491i | 0.377237 | − | 1.65921i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.97858i | − | 0.409139i | −0.978852 | − | 0.204570i | \(-0.934421\pi\) | ||
0.978852 | − | 0.204570i | \(-0.0655794\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.4910 | −2.35848 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.6644 | − | 15.6644i | 2.07480 | − | 2.07480i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.02650i | 0.914772i | 0.889268 | + | 0.457386i | \(0.151214\pi\) | ||||
−0.889268 | + | 0.457386i | \(0.848786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.48929 | − | 4.48929i | 0.574795 | − | 0.574795i | −0.358670 | − | 0.933464i | \(-0.616770\pi\) |
0.933464 | + | 0.358670i | \(0.116770\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.32903 | + | 2.32903i | 0.293431 | + | 0.293431i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.6644 | − | 11.6644i | −1.44679 | − | 1.44679i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.490134 | −0.0598794 | −0.0299397 | − | 0.999552i | \(-0.509532\pi\) | ||||
−0.0299397 | + | 0.999552i | \(0.509532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.66442 | −0.922688 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.39680 | − | 5.39680i | −0.640482 | − | 0.640482i | 0.310192 | − | 0.950674i | \(-0.399607\pi\) |
−0.950674 | + | 0.310192i | \(0.899607\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.39312 | + | 7.39312i | 0.865299 | + | 0.865299i | 0.991948 | − | 0.126649i | \(-0.0404222\pi\) |
−0.126649 | + | 0.991948i | \(0.540422\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −15.4070 | + | 15.4070i | −1.77905 | + | 1.77905i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.87819i | − | 0.328001i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.35553 | − | 9.35553i | 1.05258 | − | 1.05258i | 0.0540411 | − | 0.998539i | \(-0.482790\pi\) |
0.998539 | − | 0.0540411i | \(-0.0172102\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.27131 | −0.696812 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.30937i | 0.143722i | 0.997415 | + | 0.0718612i | \(0.0228939\pi\) | ||||
−0.997415 | + | 0.0718612i | \(0.977106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.21798 | + | 14.1537i | −0.349039 | + | 1.53519i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.819240i | 0.0878317i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.335577 | −0.0355711 | −0.0177855 | − | 0.999842i | \(-0.505662\pi\) | ||||
−0.0177855 | + | 0.999842i | \(0.505662\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.91942 | − | 1.91942i | 0.201209 | − | 0.201209i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 21.6216i | 2.24205i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.7111 | + | 18.7111i | −1.91972 | + | 1.91972i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.29273 | + | 1.29273i | 0.131257 | + | 0.131257i | 0.769683 | − | 0.638426i | \(-0.220414\pi\) |
−0.638426 | + | 0.769683i | \(0.720414\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.9758 | + | 19.9758i | 2.00764 | + | 2.00764i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.6858 | 1.26229 | 0.631144 | − | 0.775665i | \(-0.282586\pi\) | ||||
0.631144 | + | 0.775665i | \(0.282586\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.8918 | −1.76293 | −0.881467 | − | 0.472245i | \(-0.843444\pi\) | ||||
−0.881467 | + | 0.472245i | \(0.843444\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.24989 | − | 4.24989i | −0.414746 | − | 0.414746i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.25190 | − | 6.25190i | −0.604394 | − | 0.604394i | 0.337081 | − | 0.941476i | \(-0.390560\pi\) |
−0.941476 | + | 0.337081i | \(0.890560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.86098 | + | 7.86098i | −0.752945 | + | 0.752945i | −0.975028 | − | 0.222082i | \(-0.928715\pi\) |
0.222082 | + | 0.975028i | \(0.428715\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.03932i | 0.193564i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.29273 | + | 7.29273i | −0.686042 | + | 0.686042i | −0.961355 | − | 0.275312i | \(-0.911219\pi\) |
0.275312 | + | 0.961355i | \(0.411219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.15511 | 0.853719 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 26.6430i | 2.46315i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.32903 | − | 0.529528i | −0.213502 | − | 0.0485418i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 13.6858i | − | 1.24417i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.16794 | 0.375810 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.95715 | − | 5.95715i | 0.532824 | − | 0.532824i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.9939i | − | 1.15303i | −0.817088 | − | 0.576513i | \(-0.804413\pi\) | ||
0.817088 | − | 0.576513i | \(-0.195587\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.27131 | + | 5.27131i | −0.464113 | + | 0.464113i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4592 | − | 12.4592i | −1.08856 | − | 1.08856i | −0.995677 | − | 0.0928854i | \(-0.970391\pi\) |
−0.0928854 | − | 0.995677i | \(-0.529609\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.07896 | − | 3.07896i | −0.266980 | − | 0.266980i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 27.8662 | 2.39834 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.6430 | −1.25104 | −0.625518 | − | 0.780210i | \(-0.715112\pi\) | ||||
−0.625518 | + | 0.780210i | \(0.715112\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.86195 | − | 6.86195i | −0.582023 | − | 0.582023i | 0.353436 | − | 0.935459i | \(-0.385013\pi\) |
−0.935459 | + | 0.353436i | \(0.885013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.41454 | + | 3.41454i | 0.287556 | + | 0.287556i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.4625 | − | 16.4625i | 1.37667 | − | 1.37667i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.978577i | − | 0.0812664i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.8884 | + | 13.8884i | −1.14550 | + | 1.14550i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.0428457 | −0.00351006 | −0.00175503 | − | 0.999998i | \(-0.500559\pi\) | ||||
−0.00175503 | + | 0.999998i | \(0.500559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.5696i | 1.75531i | 0.479291 | + | 0.877656i | \(0.340894\pi\) | ||||
−0.479291 | + | 0.877656i | \(0.659106\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 19.8396 | − | 12.4893i | 1.60393 | − | 1.00970i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 25.8269i | − | 2.07446i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.628308 | 0.0501444 | 0.0250722 | − | 0.999686i | \(-0.492018\pi\) | ||||
0.0250722 | + | 0.999686i | \(0.492018\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.20726 | − | 6.20726i | 0.492268 | − | 0.492268i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.50650i | 0.118729i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.47393 | + | 1.47393i | −0.115447 | + | 0.115447i | −0.762470 | − | 0.647023i | \(-0.776014\pi\) |
0.647023 | + | 0.762470i | \(0.276014\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −36.4507 | − | 36.4507i | −2.83768 | − | 2.83768i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.26818 | − | 3.26818i | −0.252900 | − | 0.252900i | 0.569259 | − | 0.822158i | \(-0.307230\pi\) |
−0.822158 | + | 0.569259i | \(0.807230\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.95715 | 0.689012 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 42.7384 | 3.26829 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.196558 | + | 0.196558i | 0.0149440 | + | 0.0149440i | 0.714539 | − | 0.699595i | \(-0.246636\pi\) |
−0.699595 | + | 0.714539i | \(0.746636\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.02837 | + | 3.02837i | 0.228923 | + | 0.228923i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.6430 | + | 14.6430i | −1.10064 | + | 1.10064i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.67780i | 0.274892i | 0.990509 | + | 0.137446i | \(0.0438893\pi\) | ||||
−0.990509 | + | 0.137446i | \(0.956111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.88240 | + | 8.88240i | −0.660224 | + | 0.660224i | −0.955433 | − | 0.295209i | \(-0.904611\pi\) |
0.295209 | + | 0.955433i | \(0.404611\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.7111 | 1.38316 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.43596i | − | 0.179095i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.9758 | − | 4.54169i | −1.46077 | − | 0.332121i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.58546i | 0.333543i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8132 | −0.999487 | −0.499743 | − | 0.866174i | \(-0.666572\pi\) | ||||
−0.499743 | + | 0.866174i | \(0.666572\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.58546 | − | 9.58546i | 0.689977 | − | 0.689977i | −0.272250 | − | 0.962227i | \(-0.587768\pi\) |
0.962227 | + | 0.272250i | \(0.0877677\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 48.6166i | − | 3.48151i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.21798 | − | 1.21798i | 0.0867775 | − | 0.0867775i | −0.662386 | − | 0.749163i | \(-0.730456\pi\) |
0.749163 | + | 0.662386i | \(0.230456\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.47738 | + | 3.47738i | 0.246505 | + | 0.246505i | 0.819535 | − | 0.573030i | \(-0.194232\pi\) |
−0.573030 | + | 0.819535i | \(0.694232\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.02142 | − | 1.02142i | −0.0720456 | − | 0.0720456i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.161028 | 0.0113019 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.97858 | −0.347719 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.4557 | − | 10.4557i | −0.726722 | − | 0.726722i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −26.4078 | − | 26.4078i | −1.82667 | − | 1.82667i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.43266 | + | 5.43266i | −0.374000 | + | 0.374000i | −0.868932 | − | 0.494932i | \(-0.835193\pi\) |
0.494932 | + | 0.868932i | \(0.335193\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 22.4935i | − | 1.54123i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.29655 | − | 6.29655i | 0.429421 | − | 0.429421i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.24989 | 0.288501 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 30.8140i | 2.08222i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.2927 | − | 16.3503i | −0.692364 | − | 1.09984i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.2140i | 0.951842i | 0.879488 | + | 0.475921i | \(0.157885\pi\) | ||||
−0.879488 | + | 0.475921i | \(0.842115\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −42.0361 | −2.80241 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.82262 | + | 4.82262i | −0.320089 | + | 0.320089i | −0.848801 | − | 0.528712i | \(-0.822675\pi\) |
0.528712 | + | 0.848801i | \(0.322675\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.2499i | 1.20599i | 0.797746 | + | 0.602993i | \(0.206025\pi\) | ||||
−0.797746 | + | 0.602993i | \(0.793975\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.99806 | − | 5.99806i | 0.394644 | − | 0.394644i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.6858 | + | 11.6858i | 0.765565 | + | 0.765565i | 0.977322 | − | 0.211757i | \(-0.0679186\pi\) |
−0.211757 | + | 0.977322i | \(0.567919\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.07865 | − | 4.07865i | −0.266062 | − | 0.266062i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 38.9933 | 2.53289 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.5303 | 1.26331 | 0.631655 | − | 0.775249i | \(-0.282376\pi\) | ||||
0.631655 | + | 0.775249i | \(0.282376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5640 | + | 16.5640i | 1.06698 | + | 1.06698i | 0.997589 | + | 0.0693942i | \(0.0221066\pi\) |
0.0693942 | + | 0.997589i | \(0.477893\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.72245 | + | 3.72245i | 0.238795 | + | 0.238795i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.5897 | − | 16.5897i | 1.05988 | − | 1.05988i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 35.2218i | − | 2.24111i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.72869 | + | 2.72869i | −0.172924 | + | 0.172924i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.3760 | 1.72796 | 0.863980 | − | 0.503525i | \(-0.167964\pi\) | ||||
0.863980 | + | 0.503525i | \(0.167964\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.9210i | 0.812339i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −36.2021 | + | 22.7897i | −2.26706 | + | 1.42715i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.6002i | 1.40976i | 0.709327 | + | 0.704879i | \(0.248999\pi\) | ||||
−0.709327 | + | 0.704879i | \(0.751001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.400845 | 0.0249073 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.11760 | + | 1.11760i | −0.0691775 | + | 0.0691775i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 29.9055i | − | 1.84405i | −0.387128 | − | 0.922026i | \(-0.626533\pi\) | ||
0.387128 | − | 0.922026i | \(-0.373467\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.41454 | + | 7.41454i | −0.455471 | + | 0.455471i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.699331 | − | 0.699331i | −0.0427984 | − | 0.0427984i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.2541 | + | 20.2541i | 1.23491 | + | 1.23491i | 0.962054 | + | 0.272860i | \(0.0879697\pi\) |
0.272860 | + | 0.962054i | \(0.412030\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.5303 | −1.18638 | −0.593191 | − | 0.805062i | \(-0.702132\pi\) | ||||
−0.593191 | + | 0.805062i | \(0.702132\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.00000 | 0.484182 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 25.9739 | + | 25.9739i | 1.56628 | + | 1.56628i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.5468 | − | 14.5468i | −0.874034 | − | 0.874034i | 0.118875 | − | 0.992909i | \(-0.462071\pi\) |
−0.992909 | + | 0.118875i | \(0.962071\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −29.4959 | + | 29.4959i | −1.76587 | + | 1.76587i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.60688i | 0.334479i | 0.985916 | + | 0.167239i | \(0.0534853\pi\) | ||||
−0.985916 | + | 0.167239i | \(0.946515\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.2106 | − | 10.2106i | 0.606960 | − | 0.606960i | −0.335191 | − | 0.942150i | \(-0.608801\pi\) |
0.942150 | + | 0.335191i | \(0.108801\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −77.9865 | −4.61952 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.819240i | − | 0.0483582i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.35027 | + | 15.3288i | −0.432369 | + | 0.901697i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.38802i | 0.315851i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.3288 | −1.01236 | −0.506181 | − | 0.862427i | \(-0.668943\pi\) | ||||
−0.506181 | + | 0.862427i | \(0.668943\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.4910 | − | 17.4910i | 1.01836 | − | 1.01836i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 39.3288i | 2.28209i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.61681 | + | 8.61681i | −0.498323 | + | 0.498323i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.03612 | + | 1.03612i | 0.0597207 | + | 0.0597207i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 26.4369 | + | 26.4369i | 1.51876 | + | 1.51876i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.3503 | −1.27977 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.5500 | −1.05871 | −0.529353 | − | 0.848401i | \(-0.677565\pi\) | ||||
−0.529353 | + | 0.848401i | \(0.677565\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −37.2860 | − | 37.2860i | −2.12113 | − | 2.12113i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.08742 | + | 4.08742i | 0.231776 | + | 0.231776i | 0.813434 | − | 0.581657i | \(-0.197596\pi\) |
−0.581657 | + | 0.813434i | \(0.697596\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.60688 | − | 6.60688i | 0.373443 | − | 0.373443i | −0.495286 | − | 0.868730i | \(-0.664937\pi\) |
0.868730 | + | 0.495286i | \(0.164937\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 11.5953i | − | 0.653320i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.21798 | − | 5.21798i | 0.293071 | − | 0.293071i | −0.545221 | − | 0.838292i | \(-0.683554\pi\) |
0.838292 | + | 0.545221i | \(0.183554\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.38111 | 0.0773274 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 26.0575i | − | 1.45439i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.2277 | + | 16.5107i | −1.45935 | + | 0.918681i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.6430i | 1.92165i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −32.7641 | −1.81186 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.671153 | − | 0.671153i | 0.0370019 | − | 0.0370019i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.2209i | 1.00151i | 0.865588 | + | 0.500757i | \(0.166945\pi\) | ||||
−0.865588 | + | 0.500757i | \(0.833055\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.78202 | + | 2.78202i | −0.152454 | + | 0.152454i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.22008 | + | 1.22008i | 0.0666603 | + | 0.0666603i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.9357 | + | 13.9357i | 0.759128 | + | 0.759128i | 0.976164 | − | 0.217036i | \(-0.0696389\pi\) |
−0.217036 | + | 0.976164i | \(0.569639\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −30.3956 | −1.65086 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.4507 | 1.97391 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.59722 | + | 5.59722i | 0.302221 | + | 0.302221i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.0790 | + | 19.0790i | 1.02718 | + | 1.02718i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.51325 | − | 3.51325i | 0.188601 | − | 0.188601i | −0.606490 | − | 0.795091i | \(-0.707423\pi\) |
0.795091 | + | 0.606490i | \(0.207423\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.9786i | − | 0.587670i | −0.955856 | − | 0.293835i | \(-0.905068\pi\) | ||
0.955856 | − | 0.293835i | \(-0.0949316\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.2277 | + | 26.2277i | −1.39993 | + | 1.39993i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.9357 | −1.22075 | −0.610373 | − | 0.792114i | \(-0.708980\pi\) | ||||
−0.610373 | + | 0.792114i | \(0.708980\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.8684i | 1.42602i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.75011 | − | 5.95715i | −0.198477 | − | 0.315286i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 0.161028i | − | 0.00849872i | −0.999991 | − | 0.00424936i | \(-0.998647\pi\) | ||
0.999991 | − | 0.00424936i | \(-0.00135262\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −37.4998 | −1.97367 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.5209 | − | 28.5209i | 1.49696 | − | 1.49696i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 36.8072i | − | 1.92658i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.0805139 | + | 0.0805139i | −0.00420279 | + | 0.00420279i | −0.709205 | − | 0.705002i | \(-0.750946\pi\) |
0.705002 | + | 0.709205i | \(0.250946\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.68585 | + | 5.68585i | 0.295993 | + | 0.295993i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.22008 | − | 1.22008i | −0.0633436 | − | 0.0633436i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.8438 | −0.975693 | −0.487847 | − | 0.872929i | \(-0.662217\pi\) | ||||
−0.487847 | + | 0.872929i | \(0.662217\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.8290 | 1.28217 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.921039 | + | 0.921039i | 0.0474359 | + | 0.0474359i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7489 | − | 10.7489i | −0.552136 | − | 0.552136i | 0.374921 | − | 0.927057i | \(-0.377670\pi\) |
−0.927057 | + | 0.374921i | \(0.877670\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.0790 | − | 27.0790i | 1.38730 | − | 1.38730i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.8466i | 1.26960i | 0.772676 | + | 0.634801i | \(0.218918\pi\) | ||||
−0.772676 | + | 0.634801i | \(0.781082\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.16465 | + | 7.16465i | −0.365145 | + | 0.365145i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.3821 | −0.731083 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.2070i | 1.63296i | 0.577372 | + | 0.816481i | \(0.304078\pi\) | ||||
−0.577372 | + | 0.816481i | \(0.695922\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.4557 | + | 2.37720i | 0.528768 | + | 0.120220i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 51.9290i | − | 2.61947i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −46.5772 | −2.34356 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.2541 | + | 14.2541i | −0.715393 | + | 0.715393i | −0.967658 | − | 0.252265i | \(-0.918824\pi\) |
0.252265 | + | 0.967658i | \(0.418824\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 12.8329i | − | 0.642449i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3503 | − | 13.3503i | 0.666681 | − | 0.666681i | −0.290266 | − | 0.956946i | \(-0.593744\pi\) |
0.956946 | + | 0.290266i | \(0.0937436\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.3083 | + | 24.3083i | 1.21088 | + | 1.21088i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.6111 | + | 15.6111i | 0.775722 | + | 0.775722i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.43799 | 0.170415 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.3503 | 1.10515 | 0.552575 | − | 0.833463i | \(-0.313645\pi\) | ||||
0.552575 | + | 0.833463i | \(0.313645\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −30.5155 | − | 30.5155i | −1.50522 | − | 1.50522i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.87819 | + | 2.87819i | 0.141627 | + | 0.141627i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.25941 | − | 3.25941i | 0.159998 | − | 0.159998i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 28.6002i | − | 1.40056i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.9690 | − | 11.9690i | 0.584725 | − | 0.584725i | −0.351473 | − | 0.936198i | \(-0.614319\pi\) |
0.936198 | + | 0.351473i | \(0.114319\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.3864 | 1.04231 | 0.521154 | − | 0.853462i | \(-0.325502\pi\) | ||||
0.521154 | + | 0.853462i | \(0.325502\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.31614i | 0.452966i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.7967 | − | 16.2394i | 1.25132 | − | 0.787727i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.67780i | − | 0.177981i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 68.6148 | 3.31276 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.67773 | + | 5.67773i | −0.273487 | + | 0.273487i | −0.830502 | − | 0.557015i | \(-0.811946\pi\) |
0.557015 | + | 0.830502i | \(0.311946\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.0361i | 1.68373i | 0.539690 | + | 0.841864i | \(0.318542\pi\) | ||||
−0.539690 | + | 0.841864i | \(0.681458\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.03932 | − | 2.03932i | 0.0977781 | − | 0.0977781i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.8223 | + | 13.8223i | 0.661212 | + | 0.661212i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.61688 | − | 6.61688i | −0.315806 | − | 0.315806i | 0.531348 | − | 0.847154i | \(-0.321686\pi\) |
−0.847154 | + | 0.531348i | \(0.821686\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −37.8929 | −1.80442 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.1362 | −1.28928 | −0.644641 | − | 0.764486i | \(-0.722993\pi\) | ||||
−0.644641 | + | 0.764486i | \(0.722993\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.835347 | + | 0.835347i | 0.0395993 | + | 0.0395993i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.0892891 | − | 0.0892891i | −0.00422323 | − | 0.00422323i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.4507 | − | 23.4507i | 1.10670 | − | 1.10670i | 0.113124 | − | 0.993581i | \(-0.463914\pi\) |
0.993581 | − | 0.113124i | \(-0.0360857\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 7.02650i | − | 0.330865i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −44.9504 | + | 44.9504i | −2.11196 | + | 2.11196i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.55596 | −0.447990 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0790i | 0.611808i | 0.952062 | + | 0.305904i | \(0.0989587\pi\) | ||||
−0.952062 | + | 0.305904i | \(0.901041\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 31.8249 | + | 7.23570i | 1.48546 | + | 0.337733i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.80765i | 0.0841908i | 0.999114 | + | 0.0420954i | \(0.0134033\pi\) | ||||
−0.999114 | + | 0.0420954i | \(0.986597\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.4714 | 0.672543 | 0.336271 | − | 0.941765i | \(-0.390834\pi\) | ||||
0.336271 | + | 0.941765i | \(0.390834\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 53.8223 | − | 53.8223i | 2.49595 | − | 2.49595i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 16.2709i | − | 0.752927i | −0.926431 | − | 0.376464i | \(-0.877140\pi\) | ||
0.926431 | − | 0.376464i | \(-0.122860\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.200768 | + | 0.200768i | −0.00927062 | + | 0.00927062i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.30937 | + | 1.30937i | 0.0603327 | + | 0.0603327i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.88661 | + | 8.88661i | 0.408607 | + | 0.408607i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 55.5713 | 2.54979 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.9357 | 0.775434 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.3495 | + | 22.3495i | 1.02117 | + | 1.02117i | 0.999771 | + | 0.0214027i | \(0.00681321\pi\) |
0.0214027 | + | 0.999771i | \(0.493187\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.29273 | + | 2.29273i | 0.104540 | + | 0.104540i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.13950 | + | 3.13950i | −0.142852 | + | 0.142852i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 6.43596i | − | 0.292242i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.1472 | − | 26.1472i | 1.18484 | − | 1.18484i | 0.206368 | − | 0.978475i | \(-0.433836\pi\) |
0.978475 | − | 0.206368i | \(-0.0661643\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.14323 | −0.277806 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.23967i | − | 0.191334i | −0.995413 | − | 0.0956669i | \(-0.969502\pi\) | ||
0.995413 | − | 0.0956669i | \(-0.0304984\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.254096 | − | 1.11760i | 0.0114439 | − | 0.0503340i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 99.4510i | − | 4.46999i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.42127 | −0.198321 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.1635 | − | 23.1635i | 1.03694 | − | 1.03694i | 0.0376481 | − | 0.999291i | \(-0.488013\pi\) |
0.999291 | − | 0.0376481i | \(-0.0119866\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 13.6216i | − | 0.608567i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.6108 | + | 19.6108i | −0.874403 | + | 0.874403i | −0.992949 | − | 0.118545i | \(-0.962177\pi\) |
0.118545 | + | 0.992949i | \(0.462177\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.5787 | − | 31.5787i | −1.40524 | − | 1.40524i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.6664 | + | 18.6664i | 0.829005 | + | 0.829005i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.20077 | −0.0975473 | −0.0487737 | − | 0.998810i | \(-0.515531\pi\) | ||||
−0.0487737 | + | 0.998810i | \(0.515531\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.05673 | 0.267934 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 42.0722 | + | 42.0722i | 1.85753 | + | 1.85753i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 44.5379 | + | 44.5379i | 1.96258 | + | 1.96258i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.75639 | − | 5.75639i | 0.253166 | − | 0.253166i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.819240i | 0.0359606i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.14950 | + | 7.14950i | −0.313225 | + | 0.313225i | −0.846158 | − | 0.532932i | \(-0.821090\pi\) |
0.532932 | + | 0.846158i | \(0.321090\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.7043 | −0.468066 | −0.234033 | − | 0.972229i | \(-0.575192\pi\) | ||||
−0.234033 | + | 0.972229i | \(0.575192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.6220i | 0.550871i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.70617 | − | 29.4959i | 0.292125 | − | 1.28486i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.2369i | 0.705951i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −39.9516 | −1.73375 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.68585 | − | 4.68585i | 0.202967 | − | 0.202967i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.1256i | 1.34568i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.66442 | + | 7.66442i | −0.330744 | + | 0.330744i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 23.4138 | + | 23.4138i | 1.00850 | + | 1.00850i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.53213 | + | 6.53213i | 0.280838 | + | 0.280838i | 0.833443 | − | 0.552605i | \(-0.186366\pi\) |
−0.552605 | + | 0.833443i | \(0.686366\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −37.0213 | −1.58874 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.1365 | 1.67642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.3766 | − | 20.3766i | −0.871242 | − | 0.871242i | 0.121366 | − | 0.992608i | \(-0.461273\pi\) |
−0.992608 | + | 0.121366i | \(0.961273\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25.5254 | + | 25.5254i | 1.08940 | + | 1.08940i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.47745 | − | 1.47745i | 0.0629415 | − | 0.0629415i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 7.66442i | − | 0.325924i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.07646 | − | 5.07646i | 0.215484 | − | 0.215484i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.31415 | −0.140425 | −0.0702126 | − | 0.997532i | \(-0.522368\pi\) | ||||
−0.0702126 | + | 0.997532i | \(0.522368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.8526i | 0.501314i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.1642 | − | 51.0937i | −1.35797 | − | 2.15718i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 13.3055i | − | 0.560760i | −0.959889 | − | 0.280380i | \(-0.909540\pi\) | ||
0.959889 | − | 0.280380i | \(-0.0904605\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.3074 | 1.52746 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.56885 | + | 2.56885i | −0.107882 | + | 0.107882i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.6283i | 0.613251i | 0.951830 | + | 0.306625i | \(0.0991998\pi\) | ||||
−0.951830 | + | 0.306625i | \(0.900800\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.5554 | + | 16.5554i | −0.692820 | + | 0.692820i | −0.962852 | − | 0.270031i | \(-0.912966\pi\) |
0.270031 | + | 0.962852i | \(0.412966\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −28.7862 | − | 28.7862i | −1.20256 | − | 1.20256i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.5952 | − | 13.5952i | −0.566959 | − | 0.566959i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.60015 | −0.191507 | −0.0957535 | − | 0.995405i | \(-0.530526\pi\) | ||||
−0.0957535 | + | 0.995405i | \(0.530526\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39.9516 | 1.66033 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.536345 | + | 0.536345i | 0.0222513 | + | 0.0222513i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.4645 | − | 10.4645i | −0.433395 | − | 0.433395i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 66.3221 | − | 66.3221i | 2.74208 | − | 2.74208i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12.9939i | − | 0.536317i | −0.963375 | − | 0.268159i | \(-0.913585\pi\) | ||
0.963375 | − | 0.268159i | \(-0.0864152\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 38.9933 | − | 38.9933i | 1.60669 | − | 1.60669i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.07646 | 0.208818 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 41.6707i | − | 1.71121i | −0.517629 | − | 0.855605i | \(-0.673185\pi\) | ||
0.517629 | − | 0.855605i | \(-0.326815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.47949 | + | 7.11579i | 0.183641 | + | 0.291719i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.4935i | 0.593179i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.3063 | 1.23828 | 0.619142 | − | 0.785279i | \(-0.287481\pi\) | ||||
0.619142 | + | 0.785279i | \(0.287481\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3503 | + | 11.3503i | −0.462987 | + | 0.462987i | −0.899633 | − | 0.436646i | \(-0.856166\pi\) |
0.436646 | + | 0.899633i | \(0.356166\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.78682i | − | 0.113488i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −34.0680 | + | 34.0680i | −1.38506 | + | 1.38506i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.289711 | − | 0.289711i | −0.0117590 | − | 0.0117590i | 0.701203 | − | 0.712962i | \(-0.252647\pi\) |
−0.712962 | + | 0.701203i | \(0.752647\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.335577 | + | 0.335577i | 0.0135983 | + | 0.0135983i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.67766 | 0.310605 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.5296 | −0.869573 | −0.434786 | − | 0.900534i | \(-0.643176\pi\) | ||||
−0.434786 | + | 0.900534i | \(0.643176\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.3752 | − | 10.3752i | −0.418368 | − | 0.418368i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.6644 | + | 18.6644i | 0.751401 | + | 0.751401i | 0.974741 | − | 0.223339i | \(-0.0716958\pi\) |
−0.223339 | + | 0.974741i | \(0.571696\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.84221 | − | 7.84221i | 0.315205 | − | 0.315205i | −0.531717 | − | 0.846922i | \(-0.678453\pi\) |
0.846922 | + | 0.531717i | \(0.178453\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 20.5855i | − | 0.826066i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.137459 | + | 0.137459i | −0.00550717 | + | 0.00550717i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.30742 | 0.292297 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 110.066i | − | 4.39562i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.632518 | − | 2.78202i | 0.0252202 | − | 0.110926i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.39493i | − | 0.374006i | −0.982359 | − | 0.187003i | \(-0.940123\pi\) | ||
0.982359 | − | 0.187003i | \(-0.0598774\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.6430 | −0.899978 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −32.3457 | + | 32.3457i | −1.28360 | + | 1.28360i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.2285i | 1.23732i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 30.6853 | − | 30.6853i | 1.21389 | − | 1.21389i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.0575 | + | 13.0575i | 0.515742 | + | 0.515742i | 0.916280 | − | 0.400538i | \(-0.131177\pi\) |
−0.400538 | + | 0.916280i | \(0.631177\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.45240 | + | 4.45240i | 0.175585 | + | 0.175585i | 0.789428 | − | 0.613843i | \(-0.210377\pi\) |
−0.613843 | + | 0.789428i | \(0.710377\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 26.2436 | 1.03334 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.5244 | −1.12141 | −0.560705 | − | 0.828016i | \(-0.689470\pi\) | ||||
−0.560705 | + | 0.828016i | \(0.689470\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.6858 | + | 24.6858i | 0.969004 | + | 0.969004i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.85663 | + | 8.85663i | 0.347119 | + | 0.347119i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.867711 | − | 0.867711i | 0.0339562 | − | 0.0339562i | −0.689925 | − | 0.723881i | \(-0.742356\pi\) |
0.723881 | + | 0.689925i | \(0.242356\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 62.0289i | 2.42367i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −42.0361 | + | 42.0361i | −1.63999 | + | 1.63999i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.3102 | −0.713265 | −0.356633 | − | 0.934245i | \(-0.616075\pi\) | ||||
−0.356633 | + | 0.934245i | \(0.616075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 21.5212i | − | 0.837077i | −0.908199 | − | 0.418539i | \(-0.862542\pi\) | ||
0.908199 | − | 0.418539i | \(-0.137458\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.6237 | − | 55.5232i | 0.490265 | − | 2.15634i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.3288i | 0.594427i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.722900 | −0.0279908 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.6216 | + | 29.6216i | −1.14524 | + | 1.14524i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 31.5440i | − | 1.21774i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.0575 | + | 15.0575i | −0.580425 | + | 0.580425i | −0.935020 | − | 0.354595i | \(-0.884619\pi\) |
0.354595 | + | 0.935020i | \(0.384619\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −41.3809 | − | 41.3809i | −1.59275 | − | 1.59275i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.34606 | + | 8.34606i | 0.320765 | + | 0.320765i | 0.849061 | − | 0.528295i | \(-0.177169\pi\) |
−0.528295 | + | 0.849061i | \(0.677169\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.05906 | 0.0406429 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.1004 | −0.770248 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.59383 | + | 1.59383i | 0.0609864 | + | 0.0609864i | 0.736942 | − | 0.675956i | \(-0.236269\pi\) |
−0.675956 | + | 0.736942i | \(0.736269\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.4507 | + | 36.4507i | 1.39271 | + | 1.39271i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −38.0322 | + | 38.0322i | −1.45102 | + | 1.45102i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 13.9572i | − | 0.531725i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.82262 | + | 4.82262i | −0.183461 | + | 0.183461i | −0.792862 | − | 0.609401i | \(-0.791410\pi\) |
0.609401 | + | 0.792862i | \(0.291410\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.3650 | 0.621654 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 34.1627i | 1.29587i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.68585 | − | 1.29273i | −0.215367 | − | 0.0489657i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 48.7059i | 1.84222i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.2285 | −1.17948 | −0.589741 | − | 0.807592i | \(-0.700770\pi\) | ||||
−0.589741 | + | 0.807592i | \(0.700770\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.67780 | − | 3.67780i | 0.138711 | − | 0.138711i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 16.9995i | − | 0.640240i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.19637 | − | 5.19637i | 0.195430 | − | 0.195430i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.7178 | − | 31.7178i | −1.19119 | − | 1.19119i | −0.976735 | − | 0.214450i | \(-0.931204\pi\) |
−0.214450 | − | 0.976735i | \(-0.568796\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 53.1941 | + | 53.1941i | 1.99494 | + | 1.99494i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.0790 | −0.714513 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −81.9601 | −3.06513 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 40.7005 | + | 40.7005i | 1.51999 | + | 1.51999i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.0056 | + | 33.0056i | 1.23090 | + | 1.23090i | 0.963618 | + | 0.267284i | \(0.0861260\pi\) |
0.267284 | + | 0.963618i | \(0.413874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.32885 | + | 7.32885i | −0.272941 | + | 0.272941i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 69.0379i | 2.56755i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.45317 | + | 1.45317i | −0.0539695 | + | 0.0539695i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.5931 | −0.467052 | −0.233526 | − | 0.972351i | \(-0.575026\pi\) | ||||
−0.233526 | + | 0.972351i | \(0.575026\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 34.3288i | 1.27144i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.82601 | − | 5.55610i | 0.326442 | − | 0.205500i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.82065i | 0.178055i | 0.996029 | + | 0.0890275i | \(0.0283759\pi\) | ||||
−0.996029 | + | 0.0890275i | \(0.971624\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 69.1447 | 2.55044 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.72196 | + | 1.72196i | −0.0634293 | + | 0.0634293i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.67780i | 0.135290i | 0.997709 | + | 0.0676451i | \(0.0215486\pi\) | ||||
−0.997709 | + | 0.0676451i | \(0.978451\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 73.4011 | − | 73.4011i | 2.69646 | − | 2.69646i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.6197 | − | 17.6197i | −0.646403 | − | 0.646403i | 0.305719 | − | 0.952122i | \(-0.401103\pi\) |
−0.952122 | + | 0.305719i | \(0.901103\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.106655 | + | 0.106655i | 0.00390755 | + | 0.00390755i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.44489 | −0.272394 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.12181 | −0.187147 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.0942 | − | 12.0942i | −0.441323 | − | 0.441323i | 0.451133 | − | 0.892457i | \(-0.351020\pi\) |
−0.892457 | + | 0.451133i | \(0.851020\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 57.0508 | + | 57.0508i | 2.07905 | + | 2.07905i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 53.6930 | − | 53.6930i | 1.95409 | − | 1.95409i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.5229i | 1.61821i | 0.587663 | + | 0.809106i | \(0.300048\pi\) | ||||
−0.587663 | + | 0.809106i | \(0.699952\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −26.9270 | + | 26.9270i | −0.977389 | + | 0.977389i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.6002 | −1.03675 | −0.518377 | − | 0.855152i | \(-0.673464\pi\) | ||||
−0.518377 | + | 0.855152i | \(0.673464\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.44003i | 0.233145i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −80.4758 | − | 18.2969i | −2.90961 | − | 0.661527i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32.9251i | 1.18886i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.77154 | −0.172066 | −0.0860330 | − | 0.996292i | \(-0.527419\pi\) | ||||
−0.0860330 | + | 0.996292i | \(0.527419\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −47.0980 | + | 47.0980i | −1.69619 | + | 1.69619i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 39.7367i | − | 1.42923i | −0.699519 | − | 0.714614i | \(-0.746602\pi\) | ||
0.699519 | − | 0.714614i | \(-0.253398\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38.3525 | + | 38.3525i | −1.37766 | + | 1.37766i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.835347 | + | 0.835347i | 0.0299679 | + | 0.0299679i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.51663 | − | 7.51663i | −0.269311 | − | 0.269311i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.9206 | −1.35691 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.20035 | −0.0786341 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.56404 | − | 1.56404i | −0.0558229 | − | 0.0558229i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.6691 | + | 33.6691i | 1.20017 | + | 1.20017i | 0.974114 | + | 0.226059i | \(0.0725843\pi\) |
0.226059 | + | 0.974114i | \(0.427416\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 62.3221 | − | 62.3221i | 2.21873 | − | 2.21873i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.97449i | 0.212429i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.0361 | − | 21.0361i | 0.747014 | − | 0.747014i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −30.9033 | −1.09603 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.6497i | 0.412655i | 0.978483 | + | 0.206327i | \(0.0661512\pi\) | ||||
−0.978483 | + | 0.206327i | \(0.933849\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.59901 | − | 5.71713i | −0.127324 | − | 0.202257i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1.90804i | − | 0.0674172i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 51.9477 | 1.83320 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.75011 | − | 3.75011i | 0.132174 | − | 0.132174i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 84.4178i | 2.97165i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.2070 | − | 17.2070i | 0.604967 | − | 0.604967i | −0.336659 | − | 0.941627i | \(-0.609297\pi\) |
0.941627 | + | 0.336659i | \(0.109297\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.7273 | + | 17.7273i | 0.622489 | + | 0.622489i | 0.946167 | − | 0.323678i | \(-0.104920\pi\) |
−0.323678 | + | 0.946167i | \(0.604920\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −40.7005 | − | 40.7005i | −1.42743 | − | 1.42743i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.33805 | 0.257041 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.0130 | 0.665181 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.9135 | + | 10.9135i | 0.381349 | + | 0.381349i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.61110 | − | 5.61110i | −0.195829 | − | 0.195829i | 0.602380 | − | 0.798209i | \(-0.294219\pi\) |
−0.798209 | + | 0.602380i | \(0.794219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.3889 | + | 20.3889i | −0.710714 | + | 0.710714i | −0.966685 | − | 0.255971i | \(-0.917605\pi\) |
0.255971 | + | 0.966685i | \(0.417605\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 108.257i | 3.76904i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.68516 | − | 4.68516i | 0.162919 | − | 0.162919i | −0.620939 | − | 0.783859i | \(-0.713249\pi\) |
0.783859 | + | 0.620939i | \(0.213249\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.1579 | −1.25582 | −0.627908 | − | 0.778287i | \(-0.716089\pi\) | ||||
−0.627908 | + | 0.778287i | \(0.716089\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 60.6302i | − | 2.10324i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.2541 | − | 14.6388i | 0.805707 | − | 0.507204i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.2709i | 0.563078i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −58.0722 | −2.00727 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.26818 | − | 3.26818i | 0.112830 | − | 0.112830i | −0.648438 | − | 0.761268i | \(-0.724577\pi\) |
0.761268 | + | 0.648438i | \(0.224577\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.9227i | − | 0.997336i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.6846 | + | 11.6846i | −0.402438 | + | 0.402438i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.2969 | − | 22.2969i | −0.767038 | − | 0.767038i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.60599 | − | 5.60599i | −0.192624 | − | 0.192624i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 42.5573 | 1.46056 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.79951 | −0.0616863 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.7967 | + | 10.7967i | 0.369672 | + | 0.369672i | 0.867358 | − | 0.497685i | \(-0.165817\pi\) |
−0.497685 | + | 0.867358i | \(0.665817\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −106.388 | − | 106.388i | −3.63840 | − | 3.63840i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.20077 | + | 7.20077i | −0.245974 | + | 0.245974i | −0.819316 | − | 0.573342i | \(-0.805647\pi\) |
0.573342 | + | 0.819316i | \(0.305647\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 56.3835i | − | 1.92378i | −0.273435 | − | 0.961890i | \(-0.588160\pi\) | ||
0.273435 | − | 0.961890i | \(-0.411840\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.70727 | − | 1.70727i | 0.0581836 | − | 0.0581836i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.20035 | −0.0749008 | −0.0374504 | − | 0.999298i | \(-0.511924\pi\) | ||||
−0.0374504 | + | 0.999298i | \(0.511924\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 0.978577i | − | 0.0332726i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −47.2626 | + | 16.6271i | −1.60512 | + | 0.564686i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 65.7367i | − | 2.22996i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.29669 | −0.0778204 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.35027 | + | 7.35027i | −0.248769 | + | 0.248769i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 4.88034i | − | 0.164985i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.7539 | − | 36.7539i | 1.24109 | − | 1.24109i | 0.281541 | − | 0.959549i | \(-0.409155\pi\) |
0.959549 | − | 0.281541i | \(-0.0908454\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −36.1128 | − | 36.1128i | −1.21805 | − | 1.21805i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.2432 | − | 34.2432i | −1.15368 | − | 1.15368i | −0.985809 | − | 0.167872i | \(-0.946310\pi\) |
−0.167872 | − | 0.985809i | \(-0.553690\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.15039 | −0.139672 | −0.0698358 | − | 0.997558i | \(-0.522248\pi\) | ||||
−0.0698358 | + | 0.997558i | \(0.522248\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 72.9013 | 2.45055 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.13545 | − | 8.13545i | −0.273162 | − | 0.273162i | 0.557210 | − | 0.830372i | \(-0.311872\pi\) |
−0.830372 | + | 0.557210i | \(0.811872\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.32258 | − | 5.32258i | −0.178513 | − | 0.178513i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.0327 | + | 22.0327i | −0.738122 | + | 0.738122i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 12.3158i | − | 0.412134i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.15511 | − | 9.15511i | 0.306022 | − | 0.306022i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −35.9143 | −1.19914 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.03932i | 0.0680152i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.3931 | + | 6.54262i | −0.346245 | + | 0.217966i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.31846i | 0.143709i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 44.2217 | 1.46998 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.59190 | − | 7.59190i | 0.252085 | − | 0.252085i | −0.569740 | − | 0.821825i | \(-0.692956\pi\) |
0.821825 | + | 0.569740i | \(0.192956\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 72.1298i | 2.39239i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.3347 | − | 33.3347i | 1.10443 | − | 1.10443i | 0.110559 | − | 0.993870i | \(-0.464736\pi\) |
0.993870 | − | 0.110559i | \(-0.0352640\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.60015 | + | 4.60015i | 0.152243 | + | 0.152243i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −46.5772 | − | 46.5772i | −1.53980 | − | 1.53980i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.2070 | −0.337066 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.4221 | 1.23444 | 0.617221 | − | 0.786790i | \(-0.288258\pi\) | ||||
0.617221 | + | 0.786790i | \(0.288258\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −38.6577 | − | 38.6577i | −1.27381 | − | 1.27381i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.2886 | − | 25.2886i | −0.832383 | − | 0.832383i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.61737 | + | 3.61737i | −0.118938 | + | 0.118938i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 101.730i | − | 3.34126i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.9572 | + | 24.9572i | −0.818818 | + | 0.818818i | −0.985937 | − | 0.167119i | \(-0.946554\pi\) |
0.167119 | + | 0.985937i | \(0.446554\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.0940 | 1.64177 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.0361i | 0.557737i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 38.4200 | + | 61.0311i | 1.25647 | + | 1.99593i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 52.4653i | − | 1.71397i | −0.515343 | − | 0.856984i | \(-0.672335\pi\) | ||
0.515343 | − | 0.856984i | \(-0.327665\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.5371 | 0.898638 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.5897 | − | 22.5897i | 0.736402 | − | 0.736402i | −0.235478 | − | 0.971880i | \(-0.575665\pi\) |
0.971880 | + | 0.235478i | \(0.0756654\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.67780i | 0.119766i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.4145 | − | 11.4145i | 0.371315 | − | 0.371315i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.4316 | + | 28.4316i | 0.923902 | + | 0.923902i | 0.997303 | − | 0.0734004i | \(-0.0233851\pi\) |
−0.0734004 | + | 0.997303i | \(0.523385\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.6430 | + | 34.6430i | 1.12456 | + | 1.12456i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.7482 | 0.705234 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.8652 | −1.03221 | −0.516107 | − | 0.856524i | \(-0.672619\pi\) | ||||
−0.516107 | + | 0.856524i | \(0.672619\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.3850 | + | 34.3850i | 1.11267 | + | 1.11267i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.87819 | + | 2.87819i | 0.0930388 | + | 0.0930388i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.99806 | + | 5.99806i | −0.193688 | + | 0.193688i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.8223i | 0.736205i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35.5474 | − | 35.5474i | 1.14550 | − | 1.14550i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −47.7220 | −1.53622 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.27682i | 0.234007i | 0.993132 | + | 0.117003i | \(0.0373288\pi\) | ||||
−0.993132 | + | 0.117003i | \(0.962671\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −89.0655 | − | 20.2499i | −2.86120 | − | 0.650520i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.7336i | 1.33929i | 0.742680 | + | 0.669647i | \(0.233554\pi\) | ||||
−0.742680 | + | 0.669647i | \(0.766446\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.62158 | −0.180220 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −72.1949 | + | 72.1949i | −2.31209 | + | 2.31209i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.45738i | 0.174597i | 0.996182 | + | 0.0872986i | \(0.0278234\pi\) | ||||
−0.996182 | + | 0.0872986i | \(0.972177\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.17896 | + | 1.17896i | −0.0376799 | + | 0.0376799i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44.6963 | − | 44.6963i | −1.42704 | − | 1.42704i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.5715 | − | 17.5715i | −0.560444 | − | 0.560444i | 0.368990 | − | 0.929433i | \(-0.379704\pi\) |
−0.929433 | + | 0.368990i | \(0.879704\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.06381 | −0.193209 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.79732 | 0.0890398 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.65142 | − | 4.65142i | −0.147907 | − | 0.147907i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.99595 | + | 4.99595i | 0.158702 | + | 0.158702i | 0.781991 | − | 0.623290i | \(-0.214204\pi\) |
−0.623290 | + | 0.781991i | \(0.714204\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −37.9718 | + | 37.9718i | −1.20500 | + | 1.20500i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 17.3124i | − | 0.548840i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.71775 | − | 9.71775i | 0.307764 | − | 0.307764i | −0.536277 | − | 0.844042i | \(-0.680170\pi\) |
0.844042 | + | 0.536277i | \(0.180170\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.47731 | −0.173294 |
(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 | 1088.2.o.w.897.6 | 12 | ||
4.3 | odd | 2 | inner | 1088.2.o.w.897.1 | 12 | ||
8.3 | odd | 2 | 544.2.o.i.353.6 | yes | 12 | ||
8.5 | even | 2 | 544.2.o.i.353.1 | yes | 12 | ||
17.4 | even | 4 | inner | 1088.2.o.w.769.6 | 12 | ||
68.55 | odd | 4 | inner | 1088.2.o.w.769.1 | 12 | ||
136.19 | odd | 8 | 9248.2.a.bv.1.11 | 12 | |||
136.21 | even | 4 | 544.2.o.i.225.1 | ✓ | 12 | ||
136.53 | even | 8 | 9248.2.a.bv.1.1 | 12 | |||
136.83 | odd | 8 | 9248.2.a.bv.1.2 | 12 | |||
136.117 | even | 8 | 9248.2.a.bv.1.12 | 12 | |||
136.123 | odd | 4 | 544.2.o.i.225.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
544.2.o.i.225.1 | ✓ | 12 | 136.21 | even | 4 | ||
544.2.o.i.225.6 | yes | 12 | 136.123 | odd | 4 | ||
544.2.o.i.353.1 | yes | 12 | 8.5 | even | 2 | ||
544.2.o.i.353.6 | yes | 12 | 8.3 | odd | 2 | ||
1088.2.o.w.769.1 | 12 | 68.55 | odd | 4 | inner | ||
1088.2.o.w.769.6 | 12 | 17.4 | even | 4 | inner | ||
1088.2.o.w.897.1 | 12 | 4.3 | odd | 2 | inner | ||
1088.2.o.w.897.6 | 12 | 1.1 | even | 1 | trivial | ||
9248.2.a.bv.1.1 | 12 | 136.53 | even | 8 | |||
9248.2.a.bv.1.2 | 12 | 136.83 | odd | 8 | |||
9248.2.a.bv.1.11 | 12 | 136.19 | odd | 8 | |||
9248.2.a.bv.1.12 | 12 | 136.117 | even | 8 |