Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,3,Mod(65,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 13]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.bc (of order \(18\), degree \(6\), 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: | \(11.7711474204\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 113.1 | ||
Character | \(\chi\) | \(=\) | 432.113 |
Dual form | 432.3.bc.b.65.1 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{18}\right)\) |
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 | ||||||||
\(3\) | −2.99363 | + | 0.195330i | −0.997878 | + | 0.0651100i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.50118 | − | 6.87194i | −0.500236 | − | 1.37439i | −0.891044 | − | 0.453916i | \(-0.850027\pi\) |
0.390808 | − | 0.920472i | \(-0.372196\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.62729 | + | 9.22884i | 0.232470 | + | 1.31841i | 0.847876 | + | 0.530195i | \(0.177881\pi\) |
−0.615405 | + | 0.788211i | \(0.711008\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.92369 | − | 1.16949i | 0.991521 | − | 0.129944i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.02712 | − | 11.0644i | 0.366102 | − | 1.00586i | −0.610728 | − | 0.791840i | \(-0.709123\pi\) |
0.976830 | − | 0.214016i | \(-0.0686545\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.4349 | + | 14.6296i | 1.34115 | + | 1.12536i | 0.981329 | + | 0.192336i | \(0.0616063\pi\) |
0.359820 | + | 0.933022i | \(0.382838\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.82992 | + | 20.0835i | 0.588661 | + | 1.33890i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.5275 | − | 7.81011i | −0.795736 | − | 0.459418i | 0.0462422 | − | 0.998930i | \(-0.485275\pi\) |
−0.841978 | + | 0.539512i | \(0.818609\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.08487 | − | 15.7354i | −0.478151 | − | 0.828182i | 0.521535 | − | 0.853230i | \(-0.325359\pi\) |
−0.999686 | + | 0.0250481i | \(0.992026\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.67419 | − | 27.3099i | −0.317819 | − | 1.30047i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.0574 | − | 4.06564i | −1.00250 | − | 0.176767i | −0.351775 | − | 0.936085i | \(-0.614422\pi\) |
−0.650720 | + | 0.759318i | \(0.725533\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.8166 | + | 18.3063i | −0.872662 | + | 0.732251i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −26.4858 | + | 5.24410i | −0.980957 | + | 0.194226i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −24.8898 | − | 29.6625i | −0.858269 | − | 1.02284i | −0.999460 | − | 0.0328626i | \(-0.989538\pi\) |
0.141191 | − | 0.989982i | \(-0.454907\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.47532 | − | 25.3808i | 0.144365 | − | 0.818735i | −0.823510 | − | 0.567302i | \(-0.807987\pi\) |
0.967875 | − | 0.251433i | \(-0.0809018\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.89451 | + | 33.9094i | −0.299834 | + | 1.02756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 59.3499 | − | 34.2657i | 1.69571 | − | 0.979019i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.45889 | − | 2.52687i | 0.0394294 | − | 0.0682937i | −0.845637 | − | 0.533758i | \(-0.820779\pi\) |
0.885067 | + | 0.465464i | \(0.154113\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −55.0514 | − | 40.3903i | −1.41158 | − | 1.03565i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −26.1577 | + | 31.1736i | −0.637993 | + | 0.760331i | −0.984052 | − | 0.177882i | \(-0.943075\pi\) |
0.346058 | + | 0.938213i | \(0.387520\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −35.7017 | − | 12.9943i | −0.830271 | − | 0.302194i | −0.108301 | − | 0.994118i | \(-0.534541\pi\) |
−0.721970 | + | 0.691924i | \(0.756763\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −30.3565 | − | 58.3980i | −0.674588 | − | 1.29773i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 18.5209 | − | 3.26574i | 0.394063 | − | 0.0694839i | 0.0268941 | − | 0.999638i | \(-0.491438\pi\) |
0.367169 | + | 0.930154i | \(0.380327\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −36.4785 | + | 13.2771i | −0.744458 | + | 0.270961i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 42.0220 | + | 20.7383i | 0.823960 | + | 0.406633i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.3119i | 0.232300i | 0.993232 | + | 0.116150i | \(0.0370554\pi\) | ||||
−0.993232 | + | 0.116150i | \(0.962945\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −86.1066 | −1.56557 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 30.2704 | + | 45.3316i | 0.531059 | + | 0.795292i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.38973 | − | 12.0607i | −0.0744022 | − | 0.204418i | 0.896916 | − | 0.442200i | \(-0.145802\pi\) |
−0.971319 | + | 0.237782i | \(0.923580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.6708 | − | 88.8733i | −0.256898 | − | 1.45694i | −0.791154 | − | 0.611617i | \(-0.790520\pi\) |
0.534257 | − | 0.845322i | \(-0.320592\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 25.3145 | + | 80.4522i | 0.401818 | + | 1.27702i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 56.9261 | − | 156.403i | 0.875787 | − | 2.40620i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.68767 | + | 5.61162i | 0.0998159 | + | 0.0837555i | 0.691330 | − | 0.722539i | \(-0.257025\pi\) |
−0.591514 | + | 0.806295i | \(0.701470\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 69.8195 | + | 7.66724i | 1.01188 | + | 0.111119i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −81.5508 | − | 47.0834i | −1.14860 | − | 0.663146i | −0.200057 | − | 0.979784i | \(-0.564113\pi\) |
−0.948546 | + | 0.316638i | \(0.897446\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −25.3297 | − | 43.8724i | −0.346983 | − | 0.600992i | 0.638729 | − | 0.769432i | \(-0.279460\pi\) |
−0.985712 | + | 0.168440i | \(0.946127\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 61.7350 | − | 59.0637i | 0.823134 | − | 0.787516i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 108.665 | + | 19.1606i | 1.41123 | + | 0.248839i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 78.4939 | − | 65.8642i | 0.993593 | − | 0.833724i | 0.00750946 | − | 0.999972i | \(-0.497610\pi\) |
0.986084 | + | 0.166248i | \(0.0531652\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 78.2646 | − | 20.8724i | 0.966229 | − | 0.257684i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1497 | + | 14.4795i | 0.146382 | + | 0.174451i | 0.834253 | − | 0.551381i | \(-0.185899\pi\) |
−0.687871 | + | 0.725833i | \(0.741455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.8359 | + | 112.495i | −0.233363 | + | 1.32347i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 80.3049 | + | 83.9370i | 0.923045 | + | 0.964793i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −52.8907 | + | 30.5364i | −0.594277 | + | 0.343106i | −0.766787 | − | 0.641902i | \(-0.778146\pi\) |
0.172510 | + | 0.985008i | \(0.444812\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −106.643 | + | 184.711i | −1.17190 | + | 2.02979i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.43984 | + | 76.8550i | −0.0907510 | + | 0.826398i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −85.4102 | + | 101.788i | −0.899055 | + | 1.07145i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −139.585 | − | 50.8047i | −1.43902 | − | 0.523760i | −0.499516 | − | 0.866305i | \(-0.666489\pi\) |
−0.939501 | + | 0.342545i | \(0.888711\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 22.9970 | − | 103.445i | 0.232293 | − | 1.04490i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.22458 | − | 0.568581i | 0.0319266 | − | 0.00562952i | −0.157662 | − | 0.987493i | \(-0.550396\pi\) |
0.189589 | + | 0.981864i | \(0.439285\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.2867 | + | 6.65582i | −0.177541 | + | 0.0646196i | −0.429261 | − | 0.903180i | \(-0.641226\pi\) |
0.251720 | + | 0.967800i | \(0.419004\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −170.979 | + | 114.172i | −1.62837 | + | 1.08735i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 24.7281i | 0.231103i | 0.993301 | + | 0.115552i | \(0.0368636\pi\) | ||||
−0.993301 | + | 0.115552i | \(0.963136\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.01801 | 0.00933957 | 0.00466979 | − | 0.999989i | \(-0.498514\pi\) | ||||
0.00466979 | + | 0.999989i | \(0.498514\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.87380 | + | 7.84947i | −0.0348991 | + | 0.0707160i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 53.0907 | + | 145.865i | 0.469829 | + | 1.29084i | 0.917888 | + | 0.396840i | \(0.129893\pi\) |
−0.448059 | + | 0.894004i | \(0.647884\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 29.7319 | + | 168.618i | 0.258538 | + | 1.46624i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 172.693 | + | 110.160i | 1.47601 | + | 0.941542i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 50.0650 | − | 137.553i | 0.420714 | − | 1.15590i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.5123 | − | 11.3382i | −0.111672 | − | 0.0937041i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 72.2175 | − | 98.4316i | 0.587134 | − | 0.800257i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 22.0364 | + | 12.7227i | 0.176291 | + | 0.101782i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −35.9061 | − | 62.1913i | −0.282726 | − | 0.489695i | 0.689330 | − | 0.724448i | \(-0.257905\pi\) |
−0.972055 | + | 0.234753i | \(0.924572\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 109.416 | + | 31.9267i | 0.848185 | + | 0.247494i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.2894 | + | 3.04859i | 0.131980 | + | 0.0232717i | 0.239248 | − | 0.970958i | \(-0.423099\pi\) |
−0.107268 | + | 0.994230i | \(0.534210\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 130.436 | − | 109.449i | 0.980723 | − | 0.822924i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 102.283 | + | 168.893i | 0.757652 | + | 1.25106i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.3559 | − | 15.9169i | −0.0974881 | − | 0.116182i | 0.715095 | − | 0.699028i | \(-0.246384\pi\) |
−0.812583 | + | 0.582846i | \(0.801939\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.08034 | − | 6.12690i | 0.00777221 | − | 0.0440784i | −0.980675 | − | 0.195644i | \(-0.937320\pi\) |
0.988447 | + | 0.151565i | \(0.0484314\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −54.8070 | + | 13.3941i | −0.388702 | + | 0.0949938i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 232.081 | − | 133.992i | 1.62295 | − | 0.937008i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −141.585 | + | 245.233i | −0.976449 | + | 1.69126i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 106.610 | − | 46.8720i | 0.725236 | − | 0.318857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 144.811 | − | 172.579i | 0.971888 | − | 1.15825i | −0.0154918 | − | 0.999880i | \(-0.504931\pi\) |
0.987380 | − | 0.158371i | \(-0.0506242\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 221.794 | + | 80.7264i | 1.46883 | + | 0.534612i | 0.947784 | − | 0.318914i | \(-0.103318\pi\) |
0.521051 | + | 0.853526i | \(0.325540\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −129.849 | − | 53.8747i | −0.848687 | − | 0.352122i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −185.609 | + | 32.7279i | −1.19748 | + | 0.211148i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −34.1578 | + | 12.4324i | −0.217566 | + | 0.0791874i | −0.448503 | − | 0.893781i | \(-0.648043\pi\) |
0.230938 | + | 0.972969i | \(0.425821\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.40488 | − | 36.8573i | −0.0151251 | − | 0.231807i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 219.409i | − | 1.36279i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 68.8785 | 0.422568 | 0.211284 | − | 0.977425i | \(-0.432236\pi\) | ||||
0.211284 | + | 0.977425i | \(0.432236\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 257.772 | − | 16.8192i | 1.56225 | − | 0.101935i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −38.6584 | − | 106.213i | −0.231488 | − | 0.636007i | 0.768505 | − | 0.639844i | \(-0.221001\pi\) |
−0.999993 | + | 0.00383681i | \(0.998779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 60.6039 | + | 343.702i | 0.358603 | + | 2.03374i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −99.4730 | − | 129.794i | −0.581714 | − | 0.759027i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 46.9901 | − | 129.104i | 0.271619 | − | 0.746267i | −0.726625 | − | 0.687034i | \(-0.758912\pi\) |
0.998244 | − | 0.0592329i | \(-0.0188655\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −204.448 | − | 171.552i | −1.16827 | − | 0.980296i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.4971 | + | 35.2478i | 0.0875540 | + | 0.199140i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −166.758 | − | 96.2777i | −0.931608 | − | 0.537864i | −0.0442884 | − | 0.999019i | \(-0.514102\pi\) |
−0.887320 | + | 0.461155i | \(0.847435\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −38.0528 | − | 65.9094i | −0.210237 | − | 0.364140i | 0.741552 | − | 0.670895i | \(-0.234090\pi\) |
−0.951788 | + | 0.306755i | \(0.900757\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 64.2721 | + | 262.993i | 0.351214 | + | 1.43712i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.0134 | − | 3.70523i | −0.113586 | − | 0.0200283i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −140.891 | + | 118.222i | −0.753429 | + | 0.632202i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −91.4971 | − | 235.900i | −0.484112 | − | 1.24815i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 132.171 | + | 157.515i | 0.691992 | + | 0.824684i | 0.991595 | − | 0.129380i | \(-0.0412986\pi\) |
−0.299603 | + | 0.954064i | \(0.596854\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 50.6060 | − | 287.001i | 0.262207 | − | 1.48705i | −0.514665 | − | 0.857391i | \(-0.672084\pi\) |
0.776872 | − | 0.629659i | \(-0.216805\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −139.866 | + | 479.334i | −0.717261 | + | 2.45812i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −263.147 | + | 151.928i | −1.33577 | + | 0.771209i | −0.986178 | − | 0.165692i | \(-0.947014\pi\) |
−0.349595 | + | 0.936901i | \(0.613681\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −133.234 | + | 230.767i | −0.669515 | + | 1.15963i | 0.308525 | + | 0.951216i | \(0.400165\pi\) |
−0.978040 | + | 0.208418i | \(0.933169\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.1165 | − | 15.4928i | −0.105057 | − | 0.0770788i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 233.247 | − | 277.974i | 1.14900 | − | 1.36933i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 279.648 | + | 101.784i | 1.36414 | + | 0.496505i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −210.512 | − | 9.31507i | −1.01697 | − | 0.0450004i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −210.689 | + | 37.1502i | −1.00808 | + | 0.177752i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 83.5395 | − | 30.4059i | 0.395922 | − | 0.144104i | −0.136384 | − | 0.990656i | \(-0.543548\pi\) |
0.532306 | + | 0.846552i | \(0.321326\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 253.330 | + | 125.021i | 1.18934 | + | 0.586954i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 277.841i | 1.29228i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 241.518 | 1.11299 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 84.3976 | + | 126.390i | 0.385377 | + | 0.577124i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −121.592 | − | 334.071i | −0.550190 | − | 1.51164i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −50.4092 | − | 285.885i | −0.226050 | − | 1.28199i | −0.860667 | − | 0.509168i | \(-0.829953\pi\) |
0.634617 | − | 0.772827i | \(-0.281158\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −173.275 | + | 188.874i | −0.770112 | + | 0.839439i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 63.1774 | − | 173.578i | 0.278315 | − | 0.764663i | −0.719239 | − | 0.694762i | \(-0.755510\pi\) |
0.997554 | − | 0.0699006i | \(-0.0222682\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −261.099 | − | 219.088i | −1.14017 | − | 0.956715i | −0.140724 | − | 0.990049i | \(-0.544943\pi\) |
−0.999444 | + | 0.0333342i | \(0.989387\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −329.046 | − | 36.1342i | −1.42444 | − | 0.156425i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 262.837 | + | 151.749i | 1.12806 | + | 0.651283i | 0.943445 | − | 0.331528i | \(-0.107564\pi\) |
0.184611 | + | 0.982812i | \(0.440898\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −68.7662 | − | 119.107i | −0.292622 | − | 0.506837i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −222.117 | + | 212.505i | −0.937201 | + | 0.896648i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 431.057 | + | 76.0070i | 1.80359 | + | 0.318021i | 0.971574 | − | 0.236735i | \(-0.0760773\pi\) |
0.832013 | + | 0.554756i | \(0.187188\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −124.647 | + | 104.591i | −0.517209 | + | 0.433990i | −0.863657 | − | 0.504079i | \(-0.831832\pi\) |
0.346449 | + | 0.938069i | \(0.387387\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −230.219 | + | 77.7717i | −0.947401 | + | 0.320048i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 182.479 | + | 217.469i | 0.744810 | + | 0.887630i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 71.8100 | − | 407.255i | 0.290729 | − | 1.64881i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −39.2001 | − | 40.9730i | −0.157430 | − | 0.164550i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −394.843 | + | 227.963i | −1.57308 | + | 0.908219i | −0.577292 | + | 0.816538i | \(0.695891\pi\) |
−0.995788 | + | 0.0916811i | \(0.970776\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −137.839 | + | 238.744i | −0.544817 | + | 0.943652i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 37.4077 | − | 340.643i | 0.146697 | − | 1.33585i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −266.990 | + | 318.187i | −1.03887 | + | 1.23808i | −0.0682006 | + | 0.997672i | \(0.521726\pi\) |
−0.970672 | + | 0.240408i | \(0.922719\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.6941 | + | 9.35188i | 0.0992049 | + | 0.0361076i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −256.799 | − | 235.591i | −0.983904 | − | 0.902646i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 420.070 | − | 74.0696i | 1.59722 | − | 0.281633i | 0.697003 | − | 0.717068i | \(-0.254517\pi\) |
0.900220 | + | 0.435435i | \(0.143405\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 84.6067 | − | 30.7943i | 0.319271 | − | 0.116205i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 152.371 | − | 101.746i | 0.570676 | − | 0.381071i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 229.784i | − | 0.854215i | −0.904201 | − | 0.427108i | \(-0.859533\pi\) | ||
0.904201 | − | 0.427108i | \(-0.140467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 247.394 | 0.912892 | 0.456446 | − | 0.889751i | \(-0.349122\pi\) | ||||
0.456446 | + | 0.889751i | \(0.349122\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 283.170 | − | 573.788i | 1.03725 | − | 2.10179i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 114.690 | + | 315.109i | 0.417056 | + | 1.14585i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.5477 | + | 144.888i | 0.0922299 | + | 0.523062i | 0.995561 | + | 0.0941179i | \(0.0300031\pi\) |
−0.903331 | + | 0.428944i | \(0.858886\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.2537 | − | 231.724i | 0.0367517 | − | 0.830553i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.8083 | + | 43.4331i | −0.0562575 | + | 0.154566i | −0.964638 | − | 0.263578i | \(-0.915097\pi\) |
0.908381 | + | 0.418145i | \(0.137319\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −94.8323 | − | 79.5738i | −0.335097 | − | 0.281179i | 0.459676 | − | 0.888087i | \(-0.347966\pi\) |
−0.794773 | + | 0.606907i | \(0.792410\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 235.805 | − | 321.399i | 0.827385 | − | 1.12772i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −330.262 | − | 190.677i | −1.15074 | − | 0.664379i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −22.5044 | − | 38.9787i | −0.0778698 | − | 0.134874i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 427.789 | + | 124.826i | 1.47007 | + | 0.428954i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 134.669 | + | 23.7457i | 0.459621 | + | 0.0810435i | 0.398664 | − | 0.917097i | \(-0.369474\pi\) |
0.0609563 | + | 0.998140i | \(0.480585\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −71.9008 | + | 60.3319i | −0.243731 | + | 0.204515i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −48.6387 | + | 314.169i | −0.163767 | + | 1.05781i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −342.525 | − | 408.206i | −1.14557 | − | 1.36524i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 61.8256 | − | 350.630i | 0.205401 | − | 1.16489i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.54217 | + | 2.33198i | −0.0314923 | + | 0.00769631i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −571.537 | + | 329.977i | −1.87389 | + | 1.08189i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 148.518 | − | 257.240i | 0.483771 | − | 0.837915i | −0.516056 | − | 0.856555i | \(-0.672600\pi\) |
0.999826 | + | 0.0186398i | \(0.00593359\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 53.4436 | − | 23.4970i | 0.172957 | − | 0.0760422i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −237.230 | + | 282.720i | −0.762797 | + | 0.909067i | −0.998021 | − | 0.0628746i | \(-0.979973\pi\) |
0.235224 | + | 0.971941i | \(0.424418\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 322.695 | + | 117.451i | 1.03097 | + | 0.375244i | 0.801452 | − | 0.598059i | \(-0.204061\pi\) |
0.229522 | + | 0.973303i | \(0.426284\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 489.547 | − | 375.186i | 1.55412 | − | 1.19107i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 537.404 | − | 94.7588i | 1.69528 | − | 0.298924i | 0.759239 | − | 0.650812i | \(-0.225572\pi\) |
0.936042 | + | 0.351889i | \(0.114460\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −428.433 | + | 155.937i | −1.34305 | + | 0.488830i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.83013 | − | 74.0268i | −0.0150471 | − | 0.230613i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 283.815i | 0.878685i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −648.185 | −1.99441 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.04756 | + | 0.198848i | −0.00931975 | + | 0.000608099i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 60.2780 | + | 165.612i | 0.183216 | + | 0.503381i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.4888 | + | 178.582i | 0.0951322 | + | 0.539522i | 0.994707 | + | 0.102754i | \(0.0327656\pi\) |
−0.899575 | + | 0.436767i | \(0.856123\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.0635 | − | 24.2551i | 0.0302207 | − | 0.0728382i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.8356 | − | 59.9929i | 0.0651810 | − | 0.179083i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −287.391 | − | 241.149i | −0.852791 | − | 0.715577i | 0.107611 | − | 0.994193i | \(-0.465680\pi\) |
−0.960403 | + | 0.278616i | \(0.910124\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −187.426 | − | 426.298i | −0.552879 | − | 1.25751i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −262.801 | − | 151.728i | −0.770678 | − | 0.444951i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 47.7015 | + | 82.6215i | 0.139072 | + | 0.240879i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −121.943 | − | 498.973i | −0.353457 | − | 1.44630i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −167.538 | − | 29.5415i | −0.482820 | − | 0.0851341i | −0.0730598 | − | 0.997328i | \(-0.523276\pi\) |
−0.409760 | + | 0.912193i | \(0.634387\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 126.546 | − | 106.185i | 0.362596 | − | 0.304254i | −0.443229 | − | 0.896409i | \(-0.646167\pi\) |
0.805824 | + | 0.592155i | \(0.201723\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −538.498 | − | 296.048i | −1.53418 | − | 0.843442i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −54.0593 | − | 64.4254i | −0.153143 | − | 0.182508i | 0.684018 | − | 0.729465i | \(-0.260231\pi\) |
−0.837161 | + | 0.546956i | \(0.815786\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −119.581 | + | 678.177i | −0.336847 | + | 1.91036i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −123.008 | + | 421.561i | −0.344561 | + | 1.18084i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −289.723 | + | 167.271i | −0.807027 | + | 0.465937i | −0.845922 | − | 0.533306i | \(-0.820949\pi\) |
0.0388953 | + | 0.999243i | \(0.487616\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.4304 | − | 26.7263i | 0.0427436 | − | 0.0740340i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 42.6657 | + | 31.3031i | 0.117536 | + | 0.0862343i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −238.134 | + | 283.797i | −0.652423 | + | 0.777527i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −149.979 | − | 54.5880i | −0.408663 | − | 0.148741i | 0.129505 | − | 0.991579i | \(-0.458661\pi\) |
−0.538168 | + | 0.842838i | \(0.680883\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −196.966 | + | 308.775i | −0.533784 | + | 0.836787i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −113.625 | + | 20.0351i | −0.306266 | + | 0.0540029i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 307.437 | − | 111.898i | 0.824227 | − | 0.299994i | 0.104740 | − | 0.994500i | \(-0.466599\pi\) |
0.719487 | + | 0.694506i | \(0.244377\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −68.4541 | − | 33.7828i | −0.182544 | − | 0.0900875i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 881.293i | − | 2.33765i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 244.316 | 0.644634 | 0.322317 | − | 0.946632i | \(-0.395538\pi\) | ||||
0.322317 | + | 0.946632i | \(0.395538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 119.638 | + | 179.164i | 0.314010 | + | 0.470248i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 132.824 | + | 364.931i | 0.346799 | + | 0.952822i | 0.983372 | + | 0.181605i | \(0.0581292\pi\) |
−0.636573 | + | 0.771217i | \(0.719649\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −140.121 | − | 794.664i | −0.363950 | − | 2.06406i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −333.787 | − | 74.2047i | −0.862500 | − | 0.191743i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −183.766 | + | 504.892i | −0.472406 | + | 1.29792i | 0.443408 | + | 0.896320i | \(0.353769\pi\) |
−0.915813 | + | 0.401604i | \(0.868453\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 280.156 | + | 235.079i | 0.716511 | + | 0.601224i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −52.3536 | − | 5.74922i | −0.133215 | − | 0.0146291i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −648.942 | − | 374.667i | −1.64289 | − | 0.948524i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.55286 | − | 14.8140i | −0.0215437 | − | 0.0373148i | 0.855053 | − | 0.518541i | \(-0.173525\pi\) |
−0.876596 | + | 0.481227i | \(0.840191\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −369.100 | + | 353.128i | −0.925062 | + | 0.885033i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 534.855 | + | 94.3095i | 1.33380 | + | 0.235186i | 0.794674 | − | 0.607037i | \(-0.207642\pi\) |
0.539130 | + | 0.842222i | \(0.318753\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 449.339 | − | 377.040i | 1.11499 | − | 0.935584i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −339.188 | − | 485.624i | −0.837501 | − | 1.19907i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.0832 | − | 26.3177i | −0.0542585 | − | 0.0646627i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3282 | − | 81.2594i | 0.0350323 | − | 0.198678i | −0.962269 | − | 0.272102i | \(-0.912281\pi\) |
0.997301 | + | 0.0734234i | \(0.0233924\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 43.0916 | + | 45.0406i | 0.104846 | + | 0.109588i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 104.163 | − | 60.1384i | 0.252210 | − | 0.145613i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 69.1134 | − | 119.708i | 0.166538 | − | 0.288453i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.03737 | + | 18.5527i | −0.00488578 | + | 0.0444909i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −478.636 | + | 570.416i | −1.14233 | + | 1.36137i | −0.219755 | + | 0.975555i | \(0.570526\pi\) |
−0.922574 | + | 0.385819i | \(0.873919\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 670.000 | + | 243.860i | 1.59145 | + | 0.579240i | 0.977653 | − | 0.210225i | \(-0.0674196\pi\) |
0.613796 | + | 0.789465i | \(0.289642\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 161.456 | − | 50.8026i | 0.381693 | − | 0.120101i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 438.098 | − | 77.2484i | 1.03082 | − | 0.181761i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 794.696 | − | 289.246i | 1.86112 | − | 0.677391i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −668.593 | + | 446.456i | −1.55849 | + | 1.04069i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 60.8696i | − | 0.141229i | −0.997504 | − | 0.0706144i | \(-0.977504\pi\) | ||
0.997504 | − | 0.0706144i | \(-0.0224960\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 542.738 | 1.25344 | 0.626718 | − | 0.779246i | \(-0.284398\pi\) | ||||
0.626718 | + | 0.779246i | \(0.284398\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 375.953 | − | 761.792i | 0.864259 | − | 1.75125i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 145.499 | + | 399.754i | 0.332949 | + | 0.914769i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.32635 | + | 35.8785i | 0.0144108 | + | 0.0817278i | 0.991165 | − | 0.132635i | \(-0.0423437\pi\) |
−0.976754 | + | 0.214363i | \(0.931233\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −309.995 | + | 161.142i | −0.702937 | + | 0.365401i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 102.451 | − | 281.481i | 0.231266 | − | 0.635398i | −0.768725 | − | 0.639579i | \(-0.779109\pi\) |
0.999991 | + | 0.00418102i | \(0.00133086\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 342.134 | + | 287.084i | 0.768840 | + | 0.645133i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −399.802 | + | 544.926i | −0.894412 | + | 1.21907i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 569.528 | + | 328.817i | 1.26844 | + | 0.732332i | 0.974692 | − | 0.223551i | \(-0.0717651\pi\) |
0.293745 | + | 0.955884i | \(0.405098\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 239.577 | + | 414.960i | 0.531213 | + | 0.920088i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −679.738 | − | 198.342i | −1.50053 | − | 0.437842i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1536.06 | + | 270.848i | 3.37595 | + | 0.595271i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −191.262 | + | 160.488i | −0.418517 | + | 0.351177i | −0.827598 | − | 0.561321i | \(-0.810293\pi\) |
0.409082 | + | 0.912498i | \(0.365849\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 399.244 | + | 135.918i | 0.869813 | + | 0.296117i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −100.503 | − | 119.775i | −0.218012 | − | 0.259816i | 0.645943 | − | 0.763385i | \(-0.276464\pi\) |
−0.863955 | + | 0.503569i | \(0.832020\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 112.206 | − | 636.349i | 0.242345 | − | 1.37440i | −0.584235 | − | 0.811585i | \(-0.698605\pi\) |
0.826580 | − | 0.562820i | \(-0.190284\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 549.253 | − | 134.230i | 1.18119 | − | 0.288667i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 142.134 | − | 82.0612i | 0.304356 | − | 0.175720i | −0.340042 | − | 0.940410i | \(-0.610441\pi\) |
0.644398 | + | 0.764690i | \(0.277108\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.9059 | + | 70.8512i | −0.0872195 | + | 0.151069i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 99.8275 | − | 43.8902i | 0.211948 | − | 0.0931851i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −287.550 | + | 342.688i | −0.607927 | + | 0.724500i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 486.258 | + | 176.983i | 1.02370 | + | 0.372597i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.3987 | + | 109.868i | 0.0301859 | + | 0.230331i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 192.731 | − | 33.9838i | 0.402362 | − | 0.0709473i | 0.0311949 | − | 0.999513i | \(-0.490069\pi\) |
0.371167 | + | 0.928566i | \(0.378958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 62.4027 | − | 22.7127i | 0.129735 | − | 0.0472198i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 42.8571 | + | 656.830i | 0.0887311 | + | 1.35990i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1086.29i | 2.23977i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −459.602 | −0.943741 | −0.471870 | − | 0.881668i | \(-0.656421\pi\) | ||||
−0.471870 | + | 0.881668i | \(0.656421\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −206.197 | + | 13.4540i | −0.421671 | + | 0.0275134i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −157.868 | − | 433.740i | −0.321524 | − | 0.883381i | −0.990179 | − | 0.139807i | \(-0.955352\pi\) |
0.668654 | − | 0.743573i | \(-0.266871\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 105.029 | + | 595.652i | 0.213042 | + | 1.20822i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −768.389 | + | 100.701i | −1.55230 | + | 0.203436i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 301.818 | − | 829.238i | 0.607279 | − | 1.66849i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 55.9965 | + | 46.9867i | 0.112218 | + | 0.0941617i | 0.697170 | − | 0.716906i | \(-0.254442\pi\) |
−0.584952 | + | 0.811068i | \(0.698887\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 136.476 | + | 310.412i | 0.272407 | + | 0.619585i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 667.951 | + | 385.641i | 1.32793 | + | 0.766683i | 0.984980 | − | 0.172670i | \(-0.0552393\pi\) |
0.342954 | + | 0.939352i | \(0.388573\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.9725 | − | 20.7370i | −0.0237080 | − | 0.0410634i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −248.561 | − | 1017.08i | −0.490258 | − | 2.00607i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −141.711 | − | 24.9874i | −0.278410 | − | 0.0490912i | 0.0326996 | − | 0.999465i | \(-0.489590\pi\) |
−0.311110 | + | 0.950374i | \(0.600701\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 363.672 | − | 305.157i | 0.711687 | − | 0.597177i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 323.138 | + | 369.125i | 0.629900 | + | 0.719541i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 91.4768 | + | 109.018i | 0.177625 | + | 0.211685i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 38.4525 | − | 218.075i | 0.0743762 | − | 0.421809i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −115.453 | + | 395.669i | −0.222453 | + | 0.762369i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.8121 | − | 11.4385i | 0.0380271 | − | 0.0219550i | −0.480866 | − | 0.876794i | \(-0.659678\pi\) |
0.518893 | + | 0.854839i | \(0.326344\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −504.779 | + | 874.303i | −0.965160 | + | 1.67171i | −0.255977 | + | 0.966683i | \(0.582397\pi\) |
−0.709183 | + | 0.705024i | \(0.750936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 645.550 | + | 473.629i | 1.22962 | + | 0.902150i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −258.767 | + | 308.386i | −0.491018 | + | 0.585173i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.0163 | + | 6.55741i | 0.0340574 | + | 0.0123959i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −53.2775 | − | 102.492i | −0.100334 | − | 0.193017i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −912.117 | + | 160.831i | −1.71129 | + | 0.301746i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 169.930 | − | 61.8494i | 0.317626 | − | 0.115606i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 518.018 | + | 255.647i | 0.964652 | + | 0.476066i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 457.081i | 0.848017i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −593.097 | −1.09630 | −0.548149 | − | 0.836381i | \(-0.684667\pi\) | ||||
−0.548149 | + | 0.836381i | \(0.684667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 126.790 | + | 189.876i | 0.233500 | + | 0.349679i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.54624 | − | 6.99573i | −0.00467199 | − | 0.0128362i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.2102 | + | 177.002i | 0.0570570 | + | 0.323586i | 0.999955 | − | 0.00949559i | \(-0.00302259\pi\) |
−0.942898 | + | 0.333082i | \(0.891911\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −243.778 | − | 774.751i | −0.444039 | − | 1.41120i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −240.632 | + | 661.132i | −0.436719 | + | 1.19988i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 735.583 | + | 617.227i | 1.33017 | + | 1.11614i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 63.6302 | + | 6.98756i | 0.114649 | + | 0.0125902i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −312.376 | − | 180.351i | −0.560819 | − | 0.323789i | 0.192655 | − | 0.981267i | \(-0.438290\pi\) |
−0.753474 | + | 0.657477i | \(0.771624\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −432.353 | − | 748.858i | −0.773441 | − | 1.33964i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 398.685 | − | 381.433i | 0.710668 | − | 0.679916i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −571.890 | − | 100.840i | −1.01579 | − | 0.179111i | −0.359122 | − | 0.933291i | \(-0.616924\pi\) |
−0.656669 | + | 0.754179i | \(0.728035\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 869.589 | − | 729.672i | 1.53910 | − | 1.29145i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 319.987 | + | 688.326i | 0.564351 | + | 1.21398i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −356.121 | − | 424.408i | −0.625871 | − | 0.745884i | 0.356197 | − | 0.934411i | \(-0.384073\pi\) |
−0.982068 | + | 0.188527i | \(0.939629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.9016 | − | 237.636i | 0.0733828 | − | 0.416175i | −0.925881 | − | 0.377815i | \(-0.876676\pi\) |
0.999264 | − | 0.0383598i | \(-0.0122133\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −426.438 | − | 445.725i | −0.744219 | − | 0.777879i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 577.460 | − | 333.396i | 1.00428 | − | 0.579820i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.74580 | − | 16.8802i | 0.0168905 | − | 0.0292552i | −0.857457 | − | 0.514556i | \(-0.827957\pi\) |
0.874347 | + | 0.485301i | \(0.161290\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −95.4359 | + | 869.060i | −0.164829 | + | 1.50097i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −113.858 | + | 135.690i | −0.195968 | + | 0.233546i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 136.224 | + | 49.5815i | 0.233661 | + | 0.0850455i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 325.079 | − | 1462.27i | 0.555690 | − | 2.49961i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 489.063 | − | 86.2350i | 0.833156 | − | 0.146908i | 0.259231 | − | 0.965815i | \(-0.416531\pi\) |
0.573926 | + | 0.818907i | \(0.305420\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −440.036 | + | 160.160i | −0.747090 | + | 0.271918i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 758.091 | − | 506.218i | 1.28273 | − | 0.856545i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 629.836i | 1.06212i | 0.847335 | + | 0.531059i | \(0.178206\pi\) | ||||
−0.847335 | + | 0.531059i | \(0.821794\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1070.47 | −1.79912 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 353.777 | − | 716.857i | 0.592591 | − | 1.20077i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −222.199 | − | 610.488i | −0.370951 | − | 1.01918i | −0.974995 | − | 0.222228i | \(-0.928667\pi\) |
0.604044 | − | 0.796951i | \(-0.293555\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 69.7993 | + | 395.852i | 0.116139 | + | 0.658655i | 0.986180 | + | 0.165677i | \(0.0529808\pi\) |
−0.870042 | + | 0.492978i | \(0.835908\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 66.2414 | + | 42.2552i | 0.109853 | + | 0.0700749i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −44.1186 | + | 121.215i | −0.0729233 | + | 0.200355i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 166.213 | + | 139.470i | 0.273828 | + | 0.229769i | 0.769352 | − | 0.638826i | \(-0.220579\pi\) |
−0.495524 | + | 0.868594i | \(0.665024\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −643.961 | + | 877.711i | −1.05741 | + | 1.44123i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 370.688 | + | 214.017i | 0.606691 | + | 0.350273i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 469.156 | + | 812.602i | 0.765344 | + | 1.32562i | 0.940064 | + | 0.340997i | \(0.110765\pi\) |
−0.174720 | + | 0.984618i | \(0.555902\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −857.046 | − | 250.079i | −1.39357 | − | 0.406633i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 474.755 | + | 83.7120i | 0.769456 | + | 0.135676i | 0.544577 | − | 0.838711i | \(-0.316690\pi\) |
0.224879 | + | 0.974387i | \(0.427801\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −71.9917 | + | 60.4082i | −0.116303 | + | 0.0975900i | −0.699084 | − | 0.715039i | \(-0.746409\pi\) |
0.582781 | + | 0.812629i | \(0.301964\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 632.015 | − | 13.2333i | 1.01774 | − | 0.0213097i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −367.885 | − | 438.428i | −0.590505 | − | 0.703736i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −91.3226 | + | 517.916i | −0.146116 | + | 0.828666i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 623.471 | − | 152.368i | 0.994371 | − | 0.243011i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −39.4702 | + | 22.7881i | −0.0627507 | + | 0.0362291i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 266.288 | − | 461.224i | 0.422010 | − | 0.730942i | −0.574126 | − | 0.818767i | \(-0.694658\pi\) |
0.996136 | + | 0.0878246i | \(0.0279915\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −244.148 | + | 107.342i | −0.385699 | + | 0.169576i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −337.567 | + | 402.297i | −0.531601 | + | 0.633538i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −830.238 | − | 302.182i | −1.30336 | − | 0.474383i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −782.798 | − | 324.785i | −1.22504 | − | 0.508270i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 811.167 | − | 143.031i | 1.26547 | − | 0.223137i | 0.499671 | − | 0.866215i | \(-0.333454\pi\) |
0.765800 | + | 0.643079i | \(0.222343\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −875.130 | + | 318.521i | −1.36101 | + | 0.495367i | −0.916367 | − | 0.400340i | \(-0.868892\pi\) |
−0.444644 | + | 0.895707i | \(0.646670\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −54.2706 | − | 831.754i | −0.0841405 | − | 1.28954i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 255.455i | 0.394830i | 0.980320 | + | 0.197415i | \(0.0632546\pi\) | ||||
−0.980320 | + | 0.197415i | \(0.936745\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −151.122 | −0.232854 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −723.016 | + | 47.1757i | −1.11062 | + | 0.0724665i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −277.404 | − | 762.162i | −0.424815 | − | 1.16717i | −0.948920 | − | 0.315516i | \(-0.897822\pi\) |
0.524105 | − | 0.851653i | \(-0.324400\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.2942 | − | 126.437i | −0.0340370 | − | 0.193033i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −277.343 | − | 361.881i | −0.422136 | − | 0.550808i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −118.588 | + | 325.819i | −0.179952 | + | 0.494414i | −0.996569 | − | 0.0827659i | \(-0.973625\pi\) |
0.816617 | + | 0.577180i | \(0.195847\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −639.014 | − | 536.197i | −0.966739 | − | 0.811190i | 0.0152975 | − | 0.999883i | \(-0.495130\pi\) |
−0.982036 | + | 0.188693i | \(0.939575\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 429.256 | + | 976.337i | 0.647445 | + | 1.47261i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1078.37 | − | 622.598i | −1.62161 | − | 0.936238i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 453.297 | + | 785.133i | 0.679605 | + | 1.17711i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 206.749 | + | 845.988i | 0.309041 | + | 1.26456i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1046.44 | − | 184.515i | −1.55952 | − | 0.274986i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 118.178 | − | 99.1631i | 0.175599 | − | 0.147345i | −0.550752 | − | 0.834669i | \(-0.685659\pi\) |
0.726351 | + | 0.687324i | \(0.241215\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 481.830 | − | 599.265i | 0.713822 | − | 0.887800i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −576.975 | − | 687.612i | −0.852252 | − | 1.01567i | −0.999646 | − | 0.0265971i | \(-0.991533\pi\) |
0.147394 | − | 0.989078i | \(-0.452912\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 241.723 | − | 1370.88i | 0.355998 | − | 2.01897i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −155.225 | + | 531.971i | −0.227937 | + | 0.781161i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 666.874 | − | 385.020i | 0.976390 | − | 0.563719i | 0.0752113 | − | 0.997168i | \(-0.476037\pi\) |
0.901178 | + | 0.433449i | \(0.142704\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −75.9746 | + | 131.592i | −0.110912 | + | 0.192105i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 824.428 | + | 604.868i | 1.20004 | + | 0.880448i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −180.119 | + | 214.657i | −0.261421 | + | 0.311549i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 831.656 | + | 302.698i | 1.20355 | + | 0.438058i | 0.864463 | − | 0.502696i | \(-0.167658\pi\) |
0.339091 | + | 0.940754i | \(0.389881\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 992.102 | + | 43.9002i | 1.43160 | + | 0.0633480i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −44.8058 | + | 7.90048i | −0.0644688 | + | 0.0113676i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 597.318 | − | 217.406i | 0.856984 | − | 0.311917i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −816.479 | − | 402.941i | −1.16807 | − | 0.576454i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 924.832i | 1.31930i | 0.751571 | + | 0.659652i | \(0.229296\pi\) | ||||
−0.751571 | + | 0.659652i | \(0.770704\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −53.0151 | −0.0754127 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 229.126 | + | 343.130i | 0.325002 | + | 0.486709i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.4947 | + | 28.8339i | 0.0148440 | + | 0.0407835i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −173.003 | − | 981.150i | −0.244010 | − | 1.38385i | −0.822780 | − | 0.568360i | \(-0.807578\pi\) |
0.578770 | − | 0.815491i | \(-0.303533\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 623.428 | − | 679.550i | 0.876832 | − | 0.955766i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −206.378 | + | 567.020i | −0.289451 | + | 0.795259i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1501.26 | − | 1259.71i | −2.09967 | − | 1.76183i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1305.27 | − | 143.339i | −1.82047 | − | 0.199915i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 103.540 | + | 59.7791i | 0.144006 | + | 0.0831420i | 0.570272 | − | 0.821456i | \(-0.306838\pi\) |
−0.426266 | + | 0.904598i | \(0.640171\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −91.1833 | − | 157.934i | −0.126468 | − | 0.219049i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 352.719 | − | 337.456i | 0.487854 | − | 0.466744i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1086.02 | + | 191.495i | 1.49796 | + | 0.264130i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −391.062 | + | 328.140i | −0.537911 | + | 0.451361i | −0.870823 | − | 0.491597i | \(-0.836413\pi\) |
0.332912 | + | 0.942958i | \(0.391969\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 673.999 | − | 277.789i | 0.924553 | − | 0.381054i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 381.467 | + | 454.615i | 0.521843 | + | 0.621908i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −61.0496 | + | 346.229i | −0.0832872 | + | 0.472345i | 0.914426 | + | 0.404754i | \(0.132643\pi\) |
−0.997713 | + | 0.0675919i | \(0.978468\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −588.752 | − | 615.380i | −0.801023 | − | 0.837252i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 89.0213 | − | 51.3965i | 0.120789 | − | 0.0697374i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.2066 | + | 74.8360i | −0.0584663 | + | 0.101267i | −0.893777 | − | 0.448511i | \(-0.851954\pi\) |
0.835311 | + | 0.549778i | \(0.185288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −135.424 | + | 1233.20i | −0.182758 | + | 1.66424i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 435.424 | − | 518.918i | 0.586035 | − | 0.698409i | −0.388804 | − | 0.921320i | \(-0.627112\pi\) |
0.974839 | + | 0.222912i | \(0.0715562\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1548.15 | − | 563.482i | −2.07806 | − | 0.756352i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 125.354 | + | 115.001i | 0.167810 | + | 0.153951i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −228.211 | + | 40.2398i | −0.304688 | + | 0.0537247i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 378.743 | − | 137.851i | 0.504318 | − | 0.183557i | −0.0773173 | − | 0.997007i | \(-0.524635\pi\) |
0.581635 | + | 0.813450i | \(0.302413\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1137.49 | − | 759.562i | 1.51061 | − | 1.00871i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1726.07i | − | 2.28618i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 463.787 | 0.612665 | 0.306332 | − | 0.951925i | \(-0.400898\pi\) | ||||
0.306332 | + | 0.951925i | \(0.400898\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 366.005 | − | 741.636i | 0.482220 | − | 0.977122i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.5534 | − | 64.7125i | −0.0309506 | − | 0.0850361i | 0.923255 | − | 0.384188i | \(-0.125519\pi\) |
−0.954206 | + | 0.299152i | \(0.903296\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.65661 | + | 9.39508i | 0.00217117 | + | 0.0123133i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −45.4473 | + | 1027.07i | −0.0594083 | + | 1.34257i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 99.9089 | − | 274.497i | 0.130259 | − | 0.357884i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −587.623 | − | 493.074i | −0.764139 | − | 0.641189i | 0.175062 | − | 0.984557i | \(-0.443988\pi\) |
−0.939201 | + | 0.343369i | \(0.888432\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 737.120 | − | 1004.69i | 0.956057 | − | 1.30309i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 215.221 | + | 124.258i | 0.278423 | + | 0.160747i | 0.632709 | − | 0.774390i | \(-0.281943\pi\) |
−0.354286 | + | 0.935137i | \(0.615276\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 366.992 | + | 635.648i | 0.473538 | + | 0.820191i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −78.7454 | − | 22.9773i | −0.101345 | − | 0.0295718i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 728.169 | + | 128.396i | 0.934749 | + | 0.164821i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −849.365 | + | 712.702i | −1.08754 | + | 0.912551i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 814.780 | + | 655.112i | 1.04059 | + | 0.836669i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 170.870 | + | 203.635i | 0.217668 | + | 0.259407i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −226.645 | + | 1285.37i | −0.287986 | + | 1.63325i | 0.406432 | + | 0.913681i | \(0.366773\pi\) |
−0.694419 | + | 0.719571i | \(0.744338\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1243.07 | + | 303.789i | −1.57550 | + | 0.385031i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1259.77 | + | 727.331i | −1.59264 | + | 0.919508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1026.97 | − | 1778.76i | 1.29504 | − | 2.24307i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −247.267 | + | 108.713i | −0.311027 | + | 0.136746i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 385.545 | − | 459.474i | 0.483745 | − | 0.576505i | −0.467870 | − | 0.883797i | \(-0.654979\pi\) |
0.951615 | + | 0.307292i | \(0.0994230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −276.048 | − | 100.473i | −0.345492 | − | 0.125749i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −436.268 | + | 334.353i | −0.544654 | + | 0.417420i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −587.428 | + | 103.579i | −0.731542 | + | 0.128991i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1507.77 | + | 548.782i | −1.87300 | + | 0.681716i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 44.8837 | + | 687.889i | 0.0556179 | + | 0.852402i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 574.876i | − | 0.710601i | −0.934752 | − | 0.355300i | \(-0.884379\pi\) | ||
0.934752 | − | 0.355300i | \(-0.115621\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −942.729 | −1.16243 | −0.581214 | − | 0.813751i | \(-0.697422\pi\) | ||||
−0.581214 | + | 0.813751i | \(0.697422\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −740.607 | + | 48.3234i | −0.910955 | + | 0.0594384i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −172.278 | − | 473.329i | −0.211384 | − | 0.580772i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 119.873 | + | 679.833i | 0.146723 | + | 0.832109i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −735.631 | + | 1773.02i | −0.898206 | + | 2.16486i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 267.373 | − | 734.600i | 0.325667 | − | 0.894763i | −0.663527 | − | 0.748152i | \(-0.730941\pi\) |
0.989194 | − | 0.146611i | \(-0.0468364\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 417.236 | + | 350.103i | 0.506970 | + | 0.425398i | 0.860061 | − | 0.510190i | \(-0.170425\pi\) |
−0.353091 | + | 0.935589i | \(0.614870\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −404.891 | − | 920.919i | −0.490777 | − | 1.11627i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −813.492 | − | 469.670i | −0.983666 | − | 0.567920i | −0.0802912 | − | 0.996771i | \(-0.525585\pi\) |
−0.903375 | + | 0.428851i | \(0.858918\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 340.470 | + | 589.711i | 0.410699 | + | 0.711352i | 0.994966 | − | 0.100209i | \(-0.0319512\pi\) |
−0.584267 | + | 0.811562i | \(0.698618\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −104.781 | − | 428.752i | −0.126091 | − | 0.515947i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 597.158 | + | 105.295i | 0.716876 | + | 0.126405i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −633.199 | + | 531.317i | −0.758322 | + | 0.636308i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.5668 | + | 695.701i | 0.0174036 | + | 0.831183i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.0697 | + | 28.6852i | 0.0286886 | + | 0.0341897i | 0.780198 | − | 0.625533i | \(-0.215118\pi\) |
−0.751509 | + | 0.659722i | \(0.770674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −114.324 | + | 648.364i | −0.135938 | + | 0.770944i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38.8406 | − | 133.111i | 0.0460743 | − | 0.157901i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2210.32 | − | 1276.13i | 2.61576 | − | 1.51021i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 82.6499 | − | 143.154i | 0.0975795 | − | 0.169013i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 299.437 | + | 219.691i | 0.352693 | + | 0.258765i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43.9114 | + | 52.3316i | −0.0515998 | + | 0.0614943i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 593.167 | + | 215.895i | 0.695389 | + | 0.253101i | 0.665441 | − | 0.746450i | \(-0.268244\pi\) |
0.0299483 | + | 0.999551i | \(0.490466\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −643.134 | + | 1008.21i | −0.752204 | + | 1.17919i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1234.24 | − | 217.630i | 1.44019 | − | 0.253944i | 0.601638 | − | 0.798769i | \(-0.294515\pi\) |
0.838550 | + | 0.544825i | \(0.183404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 753.601 | − | 274.288i | 0.877300 | − | 0.319311i | 0.136180 | − | 0.990684i | \(-0.456517\pi\) |
0.741120 | + | 0.671373i | \(0.234295\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1025.93 | + | 506.307i | 1.19155 | + | 0.588045i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1108.04i | − | 1.28394i | −0.766731 | − | 0.641969i | \(-0.778118\pi\) | ||
0.766731 | − | 0.641969i | \(-0.221882\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1004.73 | −1.16153 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 74.9836 | + | 112.292i | 0.0864862 | + | 0.129518i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −412.645 | − | 1133.73i | −0.474850 | − | 1.30464i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.5030 | + | 195.676i | 0.0396131 | + | 0.224657i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1305.03 | − | 290.122i | −1.49488 | − | 0.332328i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −81.5563 | + | 224.074i | −0.0932072 | + | 0.256085i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −521.708 | − | 437.765i | −0.594878 | − | 0.499162i | 0.294917 | − | 0.955523i | \(-0.404708\pi\) |
−0.889795 | + | 0.456361i | \(0.849152\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −407.787 | − | 44.7812i | −0.463922 | − | 0.0509457i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1449.13 | − | 836.658i | −1.64487 | − | 0.949669i | −0.979065 | − | 0.203547i | \(-0.934753\pi\) |
−0.665810 | − | 0.746122i | \(-0.731914\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 155.212 | + | 268.834i | 0.175778 | + | 0.304456i | 0.940430 | − | 0.339987i | \(-0.110423\pi\) |
−0.764653 | + | 0.644443i | \(0.777089\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 203.460 | − | 194.656i | 0.229898 | − | 0.219950i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 160.295 | + | 28.2644i | 0.180716 | + | 0.0318652i | 0.263274 | − | 0.964721i | \(-0.415198\pi\) |
−0.0825576 | + | 0.996586i | \(0.526309\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 515.523 | − | 432.575i | 0.579891 | − | 0.486587i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 84.2400 | − | 950.008i | 0.0945454 | − | 1.06623i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −219.648 | − | 261.767i | −0.245967 | − | 0.293132i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −244.523 | + | 1386.76i | −0.273210 | + | 1.54945i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1105.13 | + | 1155.11i | 1.23203 | + | 1.28775i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −864.248 | + | 498.974i | −0.961343 | + | 0.555032i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 96.1574 | − | 166.549i | 0.106723 | − | 0.184850i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −116.595 | + | 1061.74i | −0.129119 | + | 1.17579i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −357.749 | + | 426.348i | −0.395302 | + | 0.471103i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −797.885 | − | 290.406i | −0.879697 | − | 0.320183i | −0.137609 | − | 0.990487i | \(-0.543942\pi\) |
−0.742087 | + | 0.670303i | \(0.766164\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 28.1103 | − | 8.84497i | 0.0309244 | − | 0.00973044i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.80554 | − | 0.494692i | 0.00307962 | − | 0.000543021i | −0.172108 | − | 0.985078i | \(-0.555058\pi\) |
0.175188 | + | 0.984535i | \(0.443947\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 209.135 | − | 76.1191i | 0.229064 | − | 0.0833725i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1646.52 | − | 1099.47i | 1.79947 | − | 1.20160i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 164.522i | 0.179413i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 188.322 | 0.204920 | 0.102460 | − | 0.994737i | \(-0.467329\pi\) | ||||
0.102460 | + | 0.994737i | \(0.467329\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −394.361 | + | 799.092i | −0.428187 | + | 0.867636i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −733.020 | − | 2013.96i | −0.794171 | − | 2.18197i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.4296 | + | 81.8343i | 0.0155996 | + | 0.0884695i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −155.401 | + | 80.7806i | −0.167639 | + | 0.0871420i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 270.413 | − | 742.955i | 0.291080 | − | 0.799736i | −0.704829 | − | 0.709377i | \(-0.748976\pi\) |
0.995909 | − | 0.0903589i | \(-0.0288014\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 540.322 | + | 453.384i | 0.580368 | + | 0.486986i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 654.956 | − | 892.698i | 0.701990 | − | 0.956803i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1164.81 | + | 672.502i | 1.24578 | + | 0.719254i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −630.512 | − | 1092.08i | −0.672905 | − | 1.16551i | −0.977077 | − | 0.212888i | \(-0.931713\pi\) |
0.304172 | − | 0.952617i | \(-0.401620\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −988.972 | − | 288.574i | −1.05322 | − | 0.307321i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 534.133 | + | 94.1821i | 0.567623 | + | 0.100087i | 0.450092 | − | 0.892982i | \(-0.351391\pi\) |
0.117531 | + | 0.993069i | \(0.462502\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 729.869 | − | 612.433i | 0.773987 | − | 0.649452i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1392.24 | + | 1218.79i | −1.47327 | + | 1.28973i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 104.599 | + | 124.656i | 0.110453 | + | 0.131632i | 0.818438 | − | 0.574595i | \(-0.194840\pi\) |
−0.707985 | + | 0.706227i | \(0.750396\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 200.215 | − | 1135.48i | 0.210975 | − | 1.19650i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1590.28 | + | 388.644i | −1.67222 | + | 0.408669i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1529.94 | + | 883.311i | −1.60539 | + | 0.926874i | −0.615010 | + | 0.788519i | \(0.710848\pi\) |
−0.990383 | + | 0.138354i | \(0.955819\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 751.849 | − | 1302.24i | 0.787277 | − | 1.36360i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1252.11 | − | 550.503i | 1.30837 | − | 0.575238i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 125.161 | − | 149.161i | 0.130512 | − | 0.155538i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 278.888 | + | 101.507i | 0.290206 | + | 0.105626i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 28.9193 | + | 220.666i | 0.0300304 | + | 0.229144i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2098.83 | + | 370.080i | −2.17495 | + | 0.383502i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1526.43 | + | 555.575i | −1.57852 | + | 0.574535i | −0.974882 | − | 0.222722i | \(-0.928506\pi\) |
−0.603640 | + | 0.797257i | \(0.706283\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −55.4376 | − | 849.639i | −0.0572111 | − | 0.876820i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1343.18i | − | 1.38330i | −0.722235 | − | 0.691648i | \(-0.756885\pi\) | ||
0.722235 | − | 0.691648i | \(-0.243115\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 58.3022 | 0.0599200 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1940.43 | − | 126.610i | 1.99018 | − | 0.129856i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −405.483 | − | 1114.06i | −0.415029 | − | 1.14028i | −0.954482 | − | 0.298268i | \(-0.903591\pi\) |
0.539453 | − | 0.842016i | \(-0.318631\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 124.871 | + | 708.178i | 0.127550 | + | 0.723369i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.08444 | − | 1.19056i | 0.00926038 | − | 0.00121362i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −138.272 | + | 379.900i | −0.140664 | + | 0.386470i | −0.989942 | − | 0.141475i | \(-0.954815\pi\) |
0.849278 | + | 0.527946i | \(0.177038\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1702.22 | + | 1428.33i | 1.72814 | + | 1.45008i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −212.799 | − | 484.009i | −0.215602 | − | 0.490384i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 770.357 | + | 444.766i | 0.778925 | + | 0.449712i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −500.942 | − | 867.656i | −0.505491 | − | 0.875536i | −0.999980 | − | 0.00635207i | \(-0.997978\pi\) |
0.494489 | − | 0.869184i | \(-0.335355\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −129.148 | − | 528.458i | −0.130059 | − | 0.532183i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1919.06 | + | 338.382i | 1.92870 | + | 0.340083i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1154.65 | + | 968.864i | −1.15812 | + | 0.971779i | −0.999878 | − | 0.0156209i | \(-0.995027\pi\) |
−0.158243 | + | 0.987400i | \(0.550583\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.3887 | + | 74.5767i | −0.0254141 | + | 0.0746513i |
(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 | 432.3.bc.b.113.1 | 36 | ||
4.3 | odd | 2 | 108.3.k.a.5.6 | ✓ | 36 | ||
12.11 | even | 2 | 324.3.k.a.125.5 | 36 | |||
27.11 | odd | 18 | inner | 432.3.bc.b.65.1 | 36 | ||
108.11 | even | 18 | 108.3.k.a.65.6 | yes | 36 | ||
108.23 | even | 18 | 2916.3.c.b.1457.5 | 36 | |||
108.31 | odd | 18 | 2916.3.c.b.1457.32 | 36 | |||
108.43 | odd | 18 | 324.3.k.a.197.5 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.k.a.5.6 | ✓ | 36 | 4.3 | odd | 2 | ||
108.3.k.a.65.6 | yes | 36 | 108.11 | even | 18 | ||
324.3.k.a.125.5 | 36 | 12.11 | even | 2 | |||
324.3.k.a.197.5 | 36 | 108.43 | odd | 18 | |||
432.3.bc.b.65.1 | 36 | 27.11 | odd | 18 | inner | ||
432.3.bc.b.113.1 | 36 | 1.1 | even | 1 | trivial | ||
2916.3.c.b.1457.5 | 36 | 108.23 | even | 18 | |||
2916.3.c.b.1457.32 | 36 | 108.31 | odd | 18 |