Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,3,Mod(5,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.k (of order \(18\), degree \(6\), 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: | \(2.94278685509\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 65.6 | ||
Character | \(\chi\) | \(=\) | 108.65 |
Dual form | 108.3.k.a.5.6 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{13}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.99363 | + | 0.195330i | 0.997878 | + | 0.0651100i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.50118 | + | 6.87194i | −0.500236 | + | 1.37439i | 0.390808 | + | 0.920472i | \(0.372196\pi\) |
−0.891044 | + | 0.453916i | \(0.850027\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.62729 | + | 9.22884i | −0.232470 | + | 1.31841i | 0.615405 | + | 0.788211i | \(0.288992\pi\) |
−0.847876 | + | 0.530195i | \(0.822119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.92369 | + | 1.16949i | 0.991521 | + | 0.129944i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.02712 | − | 11.0644i | −0.366102 | − | 1.00586i | −0.976830 | − | 0.214016i | \(-0.931345\pi\) |
0.610728 | − | 0.791840i | \(-0.290877\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.4349 | − | 14.6296i | 1.34115 | − | 1.12536i | 0.359820 | − | 0.933022i | \(-0.382838\pi\) |
0.981329 | − | 0.192336i | \(-0.0616063\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.82992 | + | 20.0835i | −0.588661 | + | 1.33890i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.5275 | + | 7.81011i | −0.795736 | + | 0.459418i | −0.841978 | − | 0.539512i | \(-0.818609\pi\) |
0.0462422 | + | 0.998930i | \(0.485275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.08487 | − | 15.7354i | 0.478151 | − | 0.828182i | −0.521535 | − | 0.853230i | \(-0.674641\pi\) |
0.999686 | + | 0.0250481i | \(0.00797389\pi\) | |||||||
\(20\) | 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 | \(-0.385578\pi\) |
0.650720 | + | 0.759318i | \(0.274467\pi\) | |||||||
\(24\) | 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 | 0.141191 | + | 0.989982i | \(0.454907\pi\) |
−0.999460 | + | 0.0328626i | \(0.989538\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.47532 | − | 25.3808i | −0.144365 | − | 0.818735i | −0.967875 | − | 0.251433i | \(-0.919098\pi\) |
0.823510 | − | 0.567302i | \(-0.192013\pi\) | |||||||
\(32\) | 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 | 0.885067 | − | 0.465464i | \(-0.154113\pi\) |
−0.845637 | + | 0.533758i | \(0.820779\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 55.0514 | − | 40.3903i | 1.41158 | − | 1.03565i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −26.1577 | − | 31.1736i | −0.637993 | − | 0.760331i | 0.346058 | − | 0.938213i | \(-0.387520\pi\) |
−0.984052 | + | 0.177882i | \(0.943075\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 35.7017 | − | 12.9943i | 0.830271 | − | 0.302194i | 0.108301 | − | 0.994118i | \(-0.465459\pi\) |
0.721970 | + | 0.691924i | \(0.243237\pi\) | |||||||
\(44\) | 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 | \(-0.508562\pi\) |
−0.367169 | + | 0.930154i | \(0.619673\pi\) | |||||||
\(48\) | 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 | \(-0.962945\pi\) | ||
0.993232 | − | 0.116150i | \(-0.0370554\pi\) | |||||||
\(54\) | 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 | \(-0.854198\pi\) |
0.971319 | + | 0.237782i | \(0.0764203\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.6708 | + | 88.8733i | −0.256898 | + | 1.45694i | 0.534257 | + | 0.845322i | \(0.320592\pi\) |
−0.791154 | + | 0.611617i | \(0.790520\pi\) | |||||||
\(62\) | 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 | \(-0.742975\pi\) |
0.591514 | + | 0.806295i | \(0.298530\pi\) | |||||||
\(68\) | 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 | \(-0.435887\pi\) |
0.948546 | + | 0.316638i | \(0.102554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −25.3297 | + | 43.8724i | −0.346983 | + | 0.600992i | −0.985712 | − | 0.168440i | \(-0.946127\pi\) |
0.638729 | + | 0.769432i | \(0.279460\pi\) | |||||||
\(74\) | 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 | \(-0.502390\pi\) |
−0.986084 | + | 0.166248i | \(0.946835\pi\) | |||||||
\(80\) | 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 | \(-0.814101\pi\) |
0.687871 | + | 0.725833i | \(0.258545\pi\) | |||||||
\(84\) | 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 | 0.172510 | − | 0.985008i | \(-0.444812\pi\) |
−0.766787 | + | 0.641902i | \(0.778146\pi\) | |||||||
\(90\) | 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 | −0.939501 | − | 0.342545i | \(-0.888711\pi\) |
−0.499516 | + | 0.866305i | \(0.666489\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.9970 | − | 103.445i | −0.232293 | − | 1.04490i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.22458 | + | 0.568581i | 0.0319266 | + | 0.00562952i | 0.189589 | − | 0.981864i | \(-0.439285\pi\) |
−0.157662 | + | 0.987493i | \(0.550396\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.2867 | + | 6.65582i | 0.177541 | + | 0.0646196i | 0.429261 | − | 0.903180i | \(-0.358774\pi\) |
−0.251720 | + | 0.967800i | \(0.580996\pi\) | |||||||
\(104\) | 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 | −0.448059 | − | 0.894004i | \(-0.647884\pi\) |
0.917888 | − | 0.396840i | \(-0.129893\pi\) | |||||||
\(114\) | 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 | \(-0.742095\pi\) |
0.972055 | + | 0.234753i | \(0.0754281\pi\) | |||||||
\(128\) | 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 | \(-0.576901\pi\) |
0.107268 | + | 0.994230i | \(0.465790\pi\) | |||||||
\(132\) | 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 | −0.812583 | − | 0.582846i | \(-0.801939\pi\) |
0.715095 | + | 0.699028i | \(0.246384\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.08034 | − | 6.12690i | −0.00777221 | − | 0.0440784i | 0.980675 | − | 0.195644i | \(-0.0626797\pi\) |
−0.988447 | + | 0.151565i | \(0.951569\pi\) | |||||||
\(140\) | 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 | 0.987380 | + | 0.158371i | \(0.0506242\pi\) |
−0.0154918 | + | 0.999880i | \(0.504931\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −221.794 | + | 80.7264i | −1.46883 | + | 0.534612i | −0.947784 | − | 0.318914i | \(-0.896682\pi\) |
−0.521051 | + | 0.853526i | \(0.674460\pi\) | |||||||
\(152\) | 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 | 0.230938 | − | 0.972969i | \(-0.425821\pi\) |
−0.448503 | + | 0.893781i | \(0.648043\pi\) | |||||||
\(158\) | 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 | \(-0.567764\pi\) | ||||
−0.211284 | + | 0.977425i | \(0.567764\pi\) | |||||||
\(164\) | 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 | \(-0.778999\pi\) |
0.999993 | + | 0.00383681i | \(0.00122130\pi\) | |||||||
\(168\) | 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 | 0.998244 | + | 0.0592329i | \(0.0188655\pi\) |
−0.726625 | + | 0.687034i | \(0.758912\pi\) | |||||||
\(174\) | 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 | \(-0.485898\pi\) |
0.887320 | + | 0.461155i | \(0.152565\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −38.0528 | + | 65.9094i | −0.210237 | + | 0.364140i | −0.951788 | − | 0.306755i | \(-0.900757\pi\) |
0.741552 | + | 0.670895i | \(0.234090\pi\) | |||||||
\(182\) | 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 | \(-0.958701\pi\) |
0.299603 | + | 0.954064i | \(0.403146\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 50.6060 | + | 287.001i | 0.262207 | + | 1.48705i | 0.776872 | + | 0.629659i | \(0.216805\pi\) |
−0.514665 | + | 0.857391i | \(0.672084\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 139.866 | + | 479.334i | 0.717261 | + | 2.45812i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −263.147 | − | 151.928i | −1.33577 | − | 0.771209i | −0.349595 | − | 0.936901i | \(-0.613681\pi\) |
−0.986178 | + | 0.165692i | \(0.947014\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 133.234 | + | 230.767i | 0.669515 | + | 1.15963i | 0.978040 | + | 0.208418i | \(0.0668314\pi\) |
−0.308525 | + | 0.951216i | \(0.599835\pi\) | |||||||
\(200\) | 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 | \(-0.456452\pi\) |
−0.532306 | + | 0.846552i | \(0.678674\pi\) | |||||||
\(212\) | 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 | −0.634617 | − | 0.772827i | \(-0.718842\pi\) |
0.860667 | − | 0.509168i | \(-0.170047\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −173.275 | − | 188.874i | −0.770112 | − | 0.839439i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −63.1774 | − | 173.578i | −0.278315 | − | 0.764663i | −0.997554 | − | 0.0699006i | \(-0.977732\pi\) |
0.719239 | − | 0.694762i | \(-0.244490\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −261.099 | + | 219.088i | −1.14017 | + | 0.956715i | −0.999444 | − | 0.0333342i | \(-0.989387\pi\) |
−0.140724 | + | 0.990049i | \(0.544943\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 329.046 | − | 36.1342i | 1.42444 | − | 0.156425i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 262.837 | − | 151.749i | 1.12806 | − | 0.651283i | 0.184611 | − | 0.982812i | \(-0.440898\pi\) |
0.943445 | + | 0.331528i | \(0.107564\pi\) | |||||||
\(234\) | 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 | \(-0.923923\pi\) |
−0.832013 | + | 0.554756i | \(0.812812\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −124.647 | − | 104.591i | −0.517209 | − | 0.433990i | 0.346449 | − | 0.938069i | \(-0.387387\pi\) |
−0.863657 | + | 0.504079i | \(0.831832\pi\) | |||||||
\(242\) | 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 | 0.995788 | + | 0.0916811i | \(0.0292240\pi\) |
0.577292 | + | 0.816538i | \(0.304109\pi\) | |||||||
\(252\) | 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 | −0.970672 | − | 0.240408i | \(-0.922719\pi\) |
−0.0682006 | − | 0.997672i | \(-0.521726\pi\) | |||||||
\(258\) | 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 | \(-0.745483\pi\) |
−0.900220 | + | 0.435435i | \(0.856595\pi\) | |||||||
\(264\) | 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 | \(0.140467\pi\) | ||||
−0.904201 | + | 0.427108i | \(0.859533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −247.394 | −0.912892 | −0.456446 | − | 0.889751i | \(-0.650878\pi\) | ||||
−0.456446 | + | 0.889751i | \(0.650878\pi\) | |||||||
\(272\) | 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 | −0.903331 | − | 0.428944i | \(-0.858886\pi\) |
0.995561 | − | 0.0941179i | \(-0.0300031\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.2537 | − | 231.724i | −0.0367517 | − | 0.830553i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.8083 | − | 43.4331i | −0.0562575 | − | 0.154566i | 0.908381 | − | 0.418145i | \(-0.137319\pi\) |
−0.964638 | + | 0.263578i | \(0.915097\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 94.8323 | − | 79.5738i | 0.335097 | − | 0.281179i | −0.459676 | − | 0.888087i | \(-0.652034\pi\) |
0.794773 | + | 0.606907i | \(0.207590\pi\) | |||||||
\(284\) | 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 | 0.0609563 | − | 0.998140i | \(-0.480585\pi\) |
0.398664 | + | 0.917097i | \(0.369474\pi\) | |||||||
\(294\) | 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 | \(-0.327400\pi\) |
−0.999826 | + | 0.0186398i | \(0.994066\pi\) | |||||||
\(308\) | 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 | \(-0.0200268\pi\) |
−0.235224 | + | 0.971941i | \(0.575582\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 322.695 | − | 117.451i | 1.03097 | − | 0.375244i | 0.229522 | − | 0.973303i | \(-0.426284\pi\) |
0.801452 | + | 0.598059i | \(0.204061\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −489.547 | − | 375.186i | −1.55412 | − | 1.19107i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 537.404 | + | 94.7588i | 1.69528 | + | 0.298924i | 0.936042 | − | 0.351889i | \(-0.114460\pi\) |
0.759239 | + | 0.650812i | \(0.225572\pi\) | |||||||
\(318\) | 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 | 0.899575 | + | 0.436767i | \(0.143877\pi\) |
−0.994707 | + | 0.102754i | \(0.967234\pi\) | |||||||
\(332\) | 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 | −0.960403 | − | 0.278616i | \(-0.910124\pi\) |
0.107611 | + | 0.994193i | \(0.465680\pi\) | |||||||
\(338\) | 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 | \(-0.476724\pi\) |
0.409760 | + | 0.912193i | \(0.365613\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 126.546 | + | 106.185i | 0.362596 | + | 0.304254i | 0.805824 | − | 0.592155i | \(-0.201723\pi\) |
−0.443229 | + | 0.896409i | \(0.646167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 538.498 | − | 296.048i | 1.53418 | − | 0.843442i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −54.0593 | + | 64.4254i | −0.153143 | + | 0.182508i | −0.837161 | − | 0.546956i | \(-0.815786\pi\) |
0.684018 | + | 0.729465i | \(0.260231\pi\) | |||||||
\(354\) | 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 | \(-0.179051\pi\) |
−0.0388953 | + | 0.999243i | \(0.512384\pi\) | |||||||
\(360\) | 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 | \(-0.541339\pi\) |
0.538168 | + | 0.842838i | \(0.319117\pi\) | |||||||
\(368\) | 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 | 0.719487 | − | 0.694506i | \(-0.244377\pi\) |
0.104740 | + | 0.994500i | \(0.466599\pi\) | |||||||
\(374\) | 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 | \(-0.604462\pi\) | ||||
−0.322317 | + | 0.946632i | \(0.604462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 119.638 | − | 179.164i | 0.314010 | − | 0.470248i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −132.824 | + | 364.931i | −0.346799 | + | 0.952822i | 0.636573 | + | 0.771217i | \(0.280351\pi\) |
−0.983372 | + | 0.181605i | \(0.941871\pi\) | |||||||
\(384\) | 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 | −0.915813 | − | 0.401604i | \(-0.868453\pi\) |
0.443408 | − | 0.896320i | \(-0.353769\pi\) | |||||||
\(390\) | 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 | −0.876596 | − | 0.481227i | \(-0.840191\pi\) |
0.855053 | + | 0.518541i | \(0.173525\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 369.100 | + | 353.128i | 0.925062 | + | 0.885033i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 534.855 | − | 94.3095i | 1.33380 | − | 0.235186i | 0.539130 | − | 0.842222i | \(-0.318753\pi\) |
0.794674 | + | 0.607037i | \(0.207642\pi\) | |||||||
\(402\) | 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 | 0.997301 | − | 0.0734234i | \(-0.0233924\pi\) |
−0.962269 | + | 0.272102i | \(0.912281\pi\) | |||||||
\(410\) | 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 | 0.922574 | + | 0.385819i | \(0.126081\pi\) |
0.219755 | + | 0.975555i | \(0.429474\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 670.000 | − | 243.860i | 1.59145 | − | 0.579240i | 0.613796 | − | 0.789465i | \(-0.289642\pi\) |
0.977653 | + | 0.210225i | \(0.0674196\pi\) | |||||||
\(422\) | 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 | \(-0.957656\pi\) |
0.976754 | + | 0.214363i | \(0.0687674\pi\) | |||||||
\(440\) | 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 | \(-0.220891\pi\) |
−0.999991 | + | 0.00418102i | \(0.998669\pi\) | |||||||
\(444\) | 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 | 0.293745 | − | 0.955884i | \(-0.405098\pi\) |
0.974692 | + | 0.223551i | \(0.0717651\pi\) | |||||||
\(450\) | 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 | 0.409082 | − | 0.912498i | \(-0.365849\pi\) |
−0.827598 | + | 0.561321i | \(0.810293\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −399.244 | + | 135.918i | −0.869813 | + | 0.296117i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −100.503 | + | 119.775i | −0.218012 | + | 0.259816i | −0.863955 | − | 0.503569i | \(-0.832020\pi\) |
0.645943 | + | 0.763385i | \(0.276464\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −112.206 | − | 636.349i | −0.242345 | − | 1.37440i | −0.826580 | − | 0.562820i | \(-0.809716\pi\) |
0.584235 | − | 0.811585i | \(-0.301395\pi\) | |||||||
\(464\) | 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 | \(-0.389559\pi\) |
−0.644398 | + | 0.764690i | \(0.722892\pi\) | |||||||
\(468\) | 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 | \(-0.509931\pi\) |
−0.371167 | + | 0.928566i | \(0.621042\pi\) | |||||||
\(480\) | 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 | \(-0.343579\pi\) | ||||
0.471870 | + | 0.881668i | \(0.343579\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −206.197 | − | 13.4540i | −0.421671 | − | 0.0275134i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 157.868 | − | 433.740i | 0.321524 | − | 0.883381i | −0.668654 | − | 0.743573i | \(-0.733129\pi\) |
0.990179 | − | 0.139807i | \(-0.0446483\pi\) | |||||||
\(492\) | 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 | \(-0.745558\pi\) |
0.584952 | + | 0.811068i | \(0.301113\pi\) | |||||||
\(500\) | 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 | \(-0.944761\pi\) |
−0.342954 | + | 0.939352i | \(0.611427\pi\) | |||||||
\(504\) | 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 | −0.311110 | − | 0.950374i | \(-0.600701\pi\) |
0.0326996 | + | 0.999465i | \(0.489590\pi\) | |||||||
\(510\) | 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 | 0.518893 | − | 0.854839i | \(-0.326344\pi\) |
−0.480866 | + | 0.876794i | \(0.659678\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 504.779 | + | 874.303i | 0.965160 | + | 1.67171i | 0.709183 | + | 0.705024i | \(0.249064\pi\) |
0.255977 | + | 0.966683i | \(0.417603\pi\) | |||||||
\(524\) | 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 | \(-0.996977\pi\) |
0.942898 | + | 0.333082i | \(0.108089\pi\) | |||||||
\(548\) | 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 | −0.753474 | − | 0.657477i | \(-0.771624\pi\) |
0.192655 | + | 0.981267i | \(0.438290\pi\) | |||||||
\(558\) | 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 | \(-0.383076\pi\) |
0.656669 | + | 0.754179i | \(0.271965\pi\) | |||||||
\(564\) | 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 | −0.982068 | − | 0.188527i | \(-0.939629\pi\) |
0.356197 | + | 0.934411i | \(0.384073\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.9016 | − | 237.636i | −0.0733828 | − | 0.416175i | −0.999264 | − | 0.0383598i | \(-0.987787\pi\) |
0.925881 | − | 0.377815i | \(-0.123324\pi\) | |||||||
\(572\) | 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 | 0.874347 | − | 0.485301i | \(-0.161290\pi\) |
−0.857457 | + | 0.514556i | \(0.827957\pi\) | |||||||
\(578\) | 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 | \(-0.583469\pi\) |
−0.573926 | + | 0.818907i | \(0.694580\pi\) | |||||||
\(588\) | 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 | \(-0.821794\pi\) | ||
0.847335 | − | 0.531059i | \(-0.178206\pi\) | |||||||
\(594\) | 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 | −0.604044 | − | 0.796951i | \(-0.706445\pi\) |
0.974995 | − | 0.222228i | \(-0.0713329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 69.7993 | − | 395.852i | 0.116139 | − | 0.658655i | −0.870042 | − | 0.492978i | \(-0.835908\pi\) |
0.986180 | − | 0.165677i | \(-0.0529808\pi\) | |||||||
\(602\) | 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 | \(-0.779421\pi\) |
0.495524 | + | 0.868594i | \(0.334976\pi\) | |||||||
\(608\) | 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 | −0.174720 | − | 0.984618i | \(-0.555902\pi\) |
0.940064 | − | 0.340997i | \(-0.110765\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 857.046 | − | 250.079i | 1.39357 | − | 0.406633i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 474.755 | − | 83.7120i | 0.769456 | − | 0.135676i | 0.224879 | − | 0.974387i | \(-0.427801\pi\) |
0.544577 | + | 0.838711i | \(0.316690\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 71.9917 | + | 60.4082i | 0.116303 | + | 0.0975900i | 0.699084 | − | 0.715039i | \(-0.253591\pi\) |
−0.582781 | + | 0.812629i | \(0.698036\pi\) | |||||||
\(620\) | 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 | \(-0.305342\pi\) |
−0.996136 | + | 0.0878246i | \(0.972008\pi\) | |||||||
\(632\) | 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 | 0.765800 | − | 0.643079i | \(-0.222343\pi\) |
0.499671 | + | 0.866215i | \(0.333454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 875.130 | + | 318.521i | 1.36101 | + | 0.495367i | 0.916367 | − | 0.400340i | \(-0.131108\pi\) |
0.444644 | + | 0.895707i | \(0.353330\pi\) | |||||||
\(644\) | 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 | 0.524105 | + | 0.851653i | \(0.324400\pi\) |
−0.948920 | + | 0.315516i | \(0.897822\pi\) | |||||||
\(654\) | 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 | \(-0.0263754\pi\) |
−0.816617 | + | 0.577180i | \(0.804153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −639.014 | + | 536.197i | −0.966739 | + | 0.811190i | −0.982036 | − | 0.188693i | \(-0.939575\pi\) |
0.0152975 | + | 0.999883i | \(0.495130\pi\) | |||||||
\(662\) | 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 | 0.726351 | − | 0.687324i | \(-0.241215\pi\) |
−0.550752 | + | 0.834669i | \(0.685659\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −481.830 | − | 599.265i | −0.713822 | − | 0.887800i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −576.975 | + | 687.612i | −0.852252 | + | 1.01567i | 0.147394 | + | 0.989078i | \(0.452912\pi\) |
−0.999646 | + | 0.0265971i | \(0.991533\pi\) | |||||||
\(678\) | 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 | \(-0.523963\pi\) |
−0.901178 | + | 0.433449i | \(0.857296\pi\) | |||||||
\(684\) | 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 | \(-0.832342\pi\) |
−0.339091 | + | 0.940754i | \(0.610119\pi\) | |||||||
\(692\) | 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 | \(-0.770704\pi\) | ||
0.751571 | − | 0.659652i | \(-0.229296\pi\) | |||||||
\(702\) | 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 | 0.578770 | + | 0.815491i | \(0.303533\pi\) |
−0.822780 | + | 0.568360i | \(0.807578\pi\) | |||||||
\(710\) | 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 | \(-0.693162\pi\) |
0.426266 | + | 0.904598i | \(0.359829\pi\) | |||||||
\(720\) | 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 | \(-0.163587\pi\) |
−0.332912 | + | 0.942958i | \(0.608031\pi\) | |||||||
\(728\) | 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 | −0.997713 | − | 0.0675919i | \(-0.978468\pi\) |
0.914426 | − | 0.404754i | \(-0.132643\pi\) | |||||||
\(734\) | 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 | \(-0.148046\pi\) |
−0.835311 | + | 0.549778i | \(0.814712\pi\) | |||||||
\(740\) | 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 | \(-0.372888\pi\) |
−0.974839 | + | 0.222912i | \(0.928444\pi\) | |||||||
\(744\) | 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 | \(-0.475365\pi\) |
−0.581635 | + | 0.813450i | \(0.697587\pi\) | |||||||
\(752\) | 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 | −0.954206 | − | 0.299152i | \(-0.903296\pi\) |
0.923255 | + | 0.384188i | \(0.125519\pi\) | |||||||
\(762\) | 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 | −0.939201 | − | 0.343369i | \(-0.888432\pi\) |
0.175062 | + | 0.984557i | \(0.443988\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −737.120 | − | 1004.69i | −0.956057 | − | 1.30309i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 215.221 | − | 124.258i | 0.278423 | − | 0.160747i | −0.354286 | − | 0.935137i | \(-0.615276\pi\) |
0.632709 | + | 0.774390i | \(0.281943\pi\) | |||||||
\(774\) | 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 | 0.694419 | + | 0.719571i | \(0.255662\pi\) |
−0.406432 | + | 0.913681i | \(0.633227\pi\) | |||||||
\(788\) | 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 | 0.951615 | − | 0.307292i | \(-0.0994230\pi\) |
−0.467870 | + | 0.883797i | \(0.654979\pi\) | |||||||
\(798\) | 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 | \(0.115621\pi\) | ||||
−0.934752 | + | 0.355300i | \(0.884379\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 942.729 | 1.16243 | 0.581214 | − | 0.813751i | \(-0.302578\pi\) | ||||
0.581214 | + | 0.813751i | \(0.302578\pi\) | |||||||
\(812\) | 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 | 0.989194 | + | 0.146611i | \(0.0468364\pi\) |
−0.663527 | + | 0.748152i | \(0.730941\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −417.236 | + | 350.103i | −0.506970 | + | 0.425398i | −0.860061 | − | 0.510190i | \(-0.829575\pi\) |
0.353091 | + | 0.935589i | \(0.385130\pi\) | |||||||
\(824\) | 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 | \(-0.474415\pi\) |
0.903375 | + | 0.428851i | \(0.141082\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 340.470 | − | 589.711i | 0.410699 | − | 0.711352i | −0.584267 | − | 0.811562i | \(-0.698618\pi\) |
0.994966 | + | 0.100209i | \(0.0319512\pi\) | |||||||
\(830\) | 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 | \(-0.784882\pi\) |
0.751509 | + | 0.659722i | \(0.229326\pi\) | |||||||
\(840\) | 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 | 0.0299483 | − | 0.999551i | \(-0.490466\pi\) |
0.665441 | + | 0.746450i | \(0.268244\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 643.134 | + | 1008.21i | 0.752204 | + | 1.17919i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1234.24 | + | 217.630i | 1.44019 | + | 0.253944i | 0.838550 | − | 0.544825i | \(-0.183404\pi\) |
0.601638 | + | 0.798769i | \(0.294515\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −753.601 | − | 274.288i | −0.877300 | − | 0.319311i | −0.136180 | − | 0.990684i | \(-0.543483\pi\) |
−0.741120 | + | 0.671373i | \(0.765705\pi\) | |||||||
\(860\) | 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 | −0.889795 | − | 0.456361i | \(-0.849152\pi\) |
0.294917 | + | 0.955523i | \(0.404708\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 407.787 | − | 44.7812i | 0.463922 | − | 0.0509457i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1449.13 | + | 836.658i | −1.64487 | + | 0.949669i | −0.665810 | + | 0.746122i | \(0.731914\pi\) |
−0.979065 | + | 0.203547i | \(0.934753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −155.212 | + | 268.834i | −0.175778 | + | 0.304456i | −0.940430 | − | 0.339987i | \(-0.889577\pi\) |
0.764653 | + | 0.644443i | \(0.222911\pi\) | |||||||
\(884\) | 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 | \(-0.584802\pi\) |
0.0825576 | + | 0.996586i | \(0.473691\pi\) | |||||||
\(888\) | 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 | \(-0.456058\pi\) |
0.742087 | + | 0.670303i | \(0.233836\pi\) | |||||||
\(908\) | 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 | \(-0.444942\pi\) |
−0.175188 | + | 0.984535i | \(0.556053\pi\) | |||||||
\(912\) | 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 | \(-0.532671\pi\) | ||||
−0.102460 | + | 0.994737i | \(0.532671\pi\) | |||||||
\(920\) | 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 | 0.995909 | + | 0.0903589i | \(0.0288014\pi\) |
−0.704829 | + | 0.709377i | \(0.748976\pi\) | |||||||
\(930\) | 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 | 0.304172 | + | 0.952617i | \(0.401620\pi\) |
−0.977077 | + | 0.212888i | \(0.931713\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 988.972 | − | 288.574i | 1.05322 | − | 0.307321i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 534.133 | − | 94.1821i | 0.567623 | − | 0.100087i | 0.117531 | − | 0.993069i | \(-0.462502\pi\) |
0.450092 | + | 0.892982i | \(0.351391\pi\) | |||||||
\(942\) | 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 | \(-0.805160\pi\) |
0.707985 | + | 0.706227i | \(0.249604\pi\) | |||||||
\(948\) | 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 | −0.990383 | − | 0.138354i | \(-0.955819\pi\) |
−0.615010 | − | 0.788519i | \(-0.710848\pi\) | |||||||
\(954\) | 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 | \(-0.0714943\pi\) |
0.603640 | + | 0.797257i | \(0.293717\pi\) | |||||||
\(968\) | 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 | 0.539453 | + | 0.842016i | \(0.318631\pi\) |
−0.954482 | + | 0.298268i | \(0.903591\pi\) | |||||||
\(978\) | 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 | \(-0.0451846\pi\) |
−0.849278 | + | 0.527946i | \(0.822962\pi\) | |||||||
\(984\) | 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 | −0.494489 | − | 0.869184i | \(-0.664645\pi\) |
0.999980 | − | 0.00635207i | \(-0.00202194\pi\) | |||||||
\(992\) | 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 | −0.158243 | − | 0.987400i | \(-0.550583\pi\) |
−0.999878 | + | 0.0156209i | \(0.995027\pi\) | |||||||
\(998\) | 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 | 108.3.k.a.65.6 | yes | 36 | |
3.2 | odd | 2 | 324.3.k.a.197.5 | 36 | |||
4.3 | odd | 2 | 432.3.bc.b.65.1 | 36 | |||
27.5 | odd | 18 | inner | 108.3.k.a.5.6 | ✓ | 36 | |
27.7 | even | 9 | 2916.3.c.b.1457.5 | 36 | |||
27.20 | odd | 18 | 2916.3.c.b.1457.32 | 36 | |||
27.22 | even | 9 | 324.3.k.a.125.5 | 36 | |||
108.59 | even | 18 | 432.3.bc.b.113.1 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.k.a.5.6 | ✓ | 36 | 27.5 | odd | 18 | inner | |
108.3.k.a.65.6 | yes | 36 | 1.1 | even | 1 | trivial | |
324.3.k.a.125.5 | 36 | 27.22 | even | 9 | |||
324.3.k.a.197.5 | 36 | 3.2 | odd | 2 | |||
432.3.bc.b.65.1 | 36 | 4.3 | odd | 2 | |||
432.3.bc.b.113.1 | 36 | 108.59 | even | 18 | |||
2916.3.c.b.1457.5 | 36 | 27.7 | even | 9 | |||
2916.3.c.b.1457.32 | 36 | 27.20 | odd | 18 |